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DESIGN GUIDE for midas Civil

AASHTO LRFD Prestressed Concrete Girder Design Steel Composite Girder Design Steel Composite Bridge Load Rating

The objective of this design guide is to outline the design algorithms which are applied in midas Civil finite element analysis and design system. The guide aims to provide sufficient information for the user to understand the scope, limitations and formulas applied in the design features and to provide relevant references to the clauses in the Design standards. The design guide covers prestressed concrete girder design, steel composite girder design and steel composite girder bridge rating as per AASHTO LRFD. It is recommended that you read this guide and review corresponding tutorials, which are found on our web site, http://www.MidasUser.com, before designing. Additional information can be found in the online help available in the program’s main menu.

DISCLAIMER Developers and distributors assume no responsibility for the use of MIDAS Family Program (midas Civil, midas FEA, midas FX+, midas Gen, midas Drawing, midas SDS, midas GTS, SoilWorks, midas NFX ; hereinafter referred to as “MIDAS package”) or for the accuracy or validity of any results obtained from the MIDAS package. Developers and distributors shall not be liable for loss of profit, loss of business, or financial loss which may be caused directly or indirectly by the MIDAS package, when used for any purpose or use, due to any defect or deficiency therein. Accordingly, the user is encouraged to fully understand the bases of the program and become familiar with the users manuals. The user shall also independently verify the results produced by the program.

Foreword The objective of this design guide is to outline the design algorithms which are applied in midas Civil finite element analysis and design system. The guide aims to provide sufficient information for the user to understand the scope, limitations and formulas applied in the design features and to provide relevant references to the clauses in the Design standards. The design guide covers prestressed concrete girder design, steel composite girder design and steel composite girder bridge rating as per AASHTO LRFD. It is recommended that you read this guide and review corresponding tutorials, which are found on our web site, http://www.MidasUser.com, before designing. Additional information can be found in the online help available in the program’s main menu.

Organization This guide is designed to help you quickly become productive with the design options of AASHTO LRFD.

Chapter 1 provides detailed descriptions of the design parameters, ULS/SLS checks, design outputs used for prestressed concrete girder design to AASHTO LRFD. Chapter 2 provides detailed descriptions of the design parameters, ULS/SLS checks, design outputs used for steel composite girder design to AASHTO LRFD. Chapter 3 provides detailed descriptions of the design parameters, ULS/SLS checks, design outputs used for steel composite bridge load rating to AASHTO LRFR.

Contents Chapter 1. Prestressed Concrete Girder Design (AASHTO LRFD)

01

Strength Limit States 1. Flexural resistance

03

2. Shear resistance

16

3. Torsion resistance

28

Serviceability Limit States 1. Stress for cross section at a construction stage

34

2. Stress for cross section at service loads

40

3. Tensile stress for Prestressing tendons

44

4. Principal stress at a construction stage

47

5. Principal stress at service loads

49

6. Principal stress at service loads

51

7. Check crack

52

Chapter 2. Steel Composite Girder Design

(AASHTO LRFD)

55

Introduction 1. AASHTO LRFD 07 and 12 Steel Composite

57

2. Considerations Steel Composite Design

59

3. Calculation of Plastic Moment and Yield Moment

59

Modeling and Design Variables 1. Modeling Design Variables

67

Application of AASHTO LRFD 12 1. I Girder Section

87

2. Box / Tub Girder Section

111

3. Shear Connector

127

4. Stiffener

131

5. Difference Between AASHTO-LRFD 4th(2007) and 6th(2012)

135

Steel Composite Design Result 1. Strength Limit State Result

138

2. Service Limit State Result

141

3. Constructibility Result

142

4. Fatigue Limit State Result

145

5. Shear Connector Result

146

6. Stiffener Result

147

7. Span Checking

148

8. Total Checking

149

Chapter 3. Steel Composite Bridge Load Rating (AASHTO LRFD)

151

Introduction 1. AASHTO LRFR 2011 Bridge Load Rating

153

2. Load Rating Levels

155

3. Process of Load Rating

157

Modeling and Design Variables 1. Modeling Design Variables

158

Application of AASHTO LRFR 11 1. Rating Factor Calculation

171

2. Strength Limit State

178

3. Service Limit State

180

4. Fatigue Limit State

181

Bridge Load Rating Result 1. Result Tables

186

2. Rating Detail Table

191

3. Load Rating Report

194

Chapter 1.

Prestressed Concrete Girder Design AASHTO LRFD 7th (2014)

Chapter 1.

Prestressed Concrete Girder Design (AASHTO LRFD 14) Prestressed concrete box girders and composite girders need to be designed to satisfy the following limit states.

Ultimate Limit States Flexural Resistance Shear Resistance Torsion Resistance

Serviceability Limit States Stress for cross section at a construction stage Stress for cross section at service loads Tensile stress for Prestressing tendons Principal stress at a construction stage Principal stress at service loads Check crack

Chapter 1. Prestressed Concrete Girder Design: AASHTO-LRFD 7th (2014)

Strength Limit States 1. Flexural resistance The factored flexural resistance shall satisfy the following condition, Mu ≤ΦMn. Where, Mu : Factored moment at the section due to strength load combination ΦMn : Factored flexural resistance

1.1. Resistance Factor

AASHTO LRFD14 (5.5.4.2.1)

Resistance factor Φ shall be taken as follow.

[Fig.1. 1] Resistance Factor

  0.75   0.583  0.25

  1.0

if  t  0.002 dt c

if 0.002   t  0.005

(1.1)

if  t  0.005

Where, dt : Distance from extreme compression fiber to the centroid of the extreme tension steel element c : Distance from the extreme compression fiber to the neutral axis εt : Net tensile Strain

In midas Civil, εt is applied as strain of a reinforcement which is entered at the extreme tensile fiber.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

3

Input reinforcements to be used in the calculation of resistance in the dialog box below. ▶ Model>Properties>Section Manager>Reinforcements

Rebar coordinate at the section

Entered rebar data

[Fig.1. 2] Input Longitudinal reinforcement

Once reinforcement is entered at the PSC section, the rebar which is placed at the closest position to the extreme compression fiber will be used to calculate the strain. In short, the rebar at the bottom most is used under the sagging moment. And the rebar at the top most is used under the hogging moment. Input tendon profile to be used in PSC design in the dialog box below. ▶ Load>Temp./Prestress>Section Manager >Tendon Profile

Tendon position which is placed at the closest position to the extreme tensile fiber will be used to calculate the strain.

[Fig.1.3] Tendon Profile

4

Design Guide for midas Civil

1.2 Calculate neutral axis depth Neutral axis is determined by the iteration approach as shown in the figure below. Assume neutral axis depth, c

Initial c = H/2 (H=Section Height)

Calculate Cc (Concrete)

(1)

Calculate Ts, Cs (Reinforcement)

(2)

Calculate Tps (Tendon)

(3) (4)

Cc+Cs-(Ts+Tps)=0?

NO

YES Get neutral axis depth, c [Fig.1. 4] Flow chart to calculate neutral axis depth, c

(1) Calculate force of concrete, Cc. In midas Civil, the natural relationship between concrete stress and strain is considered as the equivalent rectangular concrete compressive stress block.(Compressive strain limit of concrete, εcu = 0.003)

[Fig.1. 5] Calculate force of concrete, Cc

Cc  0.85 f 'c Ac

(1.2)

Where, f 'c : Specified compressive strength of concrete for design Compressive strength to be used in PSC design is defined in PSC Design Material dialog box.

  0.85  0.85  0.05( f 'c  4.0)  0.65

Ac

if f 'c  4.0ksi

if f 'c  4.0ksi

: Concrete area of compressive zone

 (1c)  width

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

5

▶ PSC>PSC Design Data> PSC Design Material…

Concrete

[Fig.1. 6] PSC Design Material

Enter the concrete and reinforcement grade to be used in PSC design. The strength can be checked for the selected material grade according to the selected material code. When “None” is selected in Code field, the strength of concrete and reinforcement can be directly entered.

AASHTO LRFD14 (5.7.2.2)

Fig.1. 3 PSC Design Material (Composite) For the composite type PSC sections, the Design Material window changes to allow users to define the material properties of the slab. The concrete and rebar material properties entered for slab are used for every calculation such as the neutral axis calculation.

6

Design Guide for midas Civil

(2) Calculate force of reinforcement, Ts, Cs. Tensile resistance due to longitudinal reinforcement (Ts)and compression resistance due to concrete (Cs) is calculated as shown in the following equation.

Ts  As f s , Cs  As ' f s '

(1.3)

Where, As, As’ : the cross sectional area of tensile and compressive reinforcement It is entered in Section Manager>Reinforcements as shown in the Fig1. 2. fs , fs’: the stress of tensile and compressive reinforcement

In order to calculate the tensile stress of reinforcement, midas Civil calculate the corresponding strains as per the strain compatibility condition. And then the related tensile stresses are calculated by the stress-strain relationship. The equation is shown as follows. ▪ Strain

s 

dt  c c  dc  cu ,  s '   cu c c

(1.4)

Where, εs : the strain of tensile reinforcement. εs’ : the strain of compressive reinforcement. εcu : the ultimate compressive strain in the concrete. (εcu = 0.003) c : the neutral axis depth. dt : Distance from the compression fiber of concrete to the extreme tensile fiber of reinforcement dc : Distance from the compression fiber of concrete to the extreme compressive fiber of reinforcement

▪ Stress If the tensile stress of reinforcement reaches its yield stress limit, tensile stress will be applied as yield stress. If not, the tensile stress will be calculated as “εs x Es”.

 s Es fs    fy

( fs  f y ) ( fs  f y )

,

 s ' Es fs '    fy

( fs '  f y ) ( fs '  f y )

(1.5)

Where, Es : Modulus of elasticity in reinforcement Fy : Yield tensile stress in reinforcement

(3) Calculate force of tendon, Tps. Tensile resistance of prestressing steel, Tps, is calculated as shown in the following equation.

Tps   Ap f ps

(1.6)

Where, Ap : the cross sectional area of tendon. fps : the stress of tendon.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

7

▶ PSC> Design Parameter> Parameters…

[Fig.1. 7] PSC Design parameter Dialog - Flexural Strength

Tensile stress of prestressing steel fps can be calculated by code or strain compatibility as specified in PSC design Parameter dialog box. When code is selected in flexural strength option, the tensile stress fps is calculated by the equation as per AASHTO-LRFD for bonded and unbounded tendon respectively. When strain compatibility is used, the tensile stress fps is calculated by the stress-strain relationship. ▶ Load>Temp./Prestress>Section Manager>Tendon Property

Tendon Type Total Tendon Area fpu fpy

Bond Type

[Fig.1. 8] Tendon Property Dialog

▪ Tendon Type Internal(Pre-Tension) Internal(Post-Tension) External ▪ Bond Type Bonded: Section properties reflect the duct area after grouting. When tendon type is specified as Internal (Pre-Tension), bond type will be taken as Bonded Type. Unbonded: Section properties exclude the duct area.

8

Design Guide for midas Civil

When tendon type is specified as external, bond type will be taken as Unbonded Type. [Table1. 1] Applicable Bond Type by Tendon Types

Tendon Type Internal (Pre-tension)

Bond Type Bonded Bonded Unbonded Unbonded

Internal (Post-tension) External ▪ Total Tendon Area

Enter the tendon area (Ap). Click to select the number of strands and diameter in order to calculate the tendon area automatically. ▪ fpu, fpy Enter the ultimate strength fpu and yield strength fpy of prestressing steel. Tensile stress of prestressing steel fps will be calculated as shown in the following table. [Table1. 2] Calculation of tensile stress of prestressing steel

Flexure Strength option Code Strain compatibility

Bond Type Bonded Unbonded Bonded Unbonded*

Tensile Stress fps for Bonded Type fps for Unbonded Type Strain compatibility fps for Unbonded Type

* When flexure strength option is entered as strain compatibility and bond type is entered as unbonded type, tensile stress will be calculated using the code equation of unbonded tendon instead of strain compatibility method. It is because strain compatibility method is valid for fully bonded tendons.

Tensile stress of prestressing steel fps is calculated as follows. ▪Code equation for bonded type tendon

AASHTO LRFD14 (5.7.3.1.1) (Eq. 5.7.3.1.1-1)

 c  f ps  f pu 1  k   d p  

(1.7)

 f py  k  2 1.04    f pu  

(1.8)

AASHTO LRFD14 (5.7.3.1.1) (Eq. 5.7.3.1.1-2)

Where, fpy: Yield strength of prestressing steel fpu: Specified tensile strength of prestressing steel dp: Distance from extreme compression fiber to the centroid of the prestressing tendons c: Distance between the neutral axis and the compressive face

▪ Code equation for unbonded type tendon

 dp  c  f ps  f pe  900    f py  le 

le 

2li 2  Ns

(1.9)

(1.10)

AASHTO LRFD14 (5.7.3.1.2) (Eq. 5.7.3.1.2-1)

AASHTO LRFD14 (5.7.3.1.2) (Eq. 5.7.3.1.2-2)

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

9

Where, li : length of tendon between anchorages Ni : number of support hinges crossed by the tendon between anchorages or discretely bonded point. It is always applied as “0” in midas Civil.

▪ fps by Strain compatibility When flexure resistance is calculated by strain compatibility method, tensile stress of prestressing tendon is calculated by the stress-strain relationship.

[Fig.1. 9] Stress-strain model of prestressing tendon

(4) Determination of neutral axis position In order to find the neutral axis, the iteration analysis will be performed until compressive strength (C=Cc+Cs) becomes equal to the tensile strength (T=Ts+Tps). The convergence criterion is applied as shown in the following equation. • Convergence condition: C  1.0  0.001 (Tolerance) T

(1.11)

1.3 Calculate moment resistance Mn Once the neutral axis is determined, flexural resistance is calculated by multiplying the distance from the neutral axis.

M n  Cc ac  Cs as ' Ts as   Tps a pi  where, ac, as, as’, api : the distance from neutral axis depth, c to concrete, reinforcement rebar, tendon.

10

Design Guide for midas Civil

(1.12)

0.85f’c

a

ac

c as ap

Cc

as'

Cs

As’

Ap

Tps As

Ts

[Fig.1. 10] Forces and distances from neutral axis depth for Mn

If a tendon in tension is located at the upper part from the neutral axis under the sagging moment, the flexural resistance will have (-) sign and it will reduce the total moment resistance.



M n  Cc ac  Cs as ' Ts as   Tps a pi  Tps' a 'pi



(1.13)

1.4 Factored Flexural Resistance

Mr  Mn

(1.14)

AASHTO LRFD14 (5.7.3.2.1) (Eq. 5.7.3.2.1-1)

where, Mn : nominal resistance Φ : resistance factor

1.5 Minimum Reinforcement The moment resistance with considering entered reinforcements or tendons shall satisfy the following condition.

M r  max(1.33M u , M cr )

AASHTO LRFD14 (5.7.3.3.2)

(1.15)

▪ Cracked Moment ( Mcr) For composite sections, the equation 1.16 is used to calculate the cracked moment (Mcr).

  S  M cr   3 ( 1 f r   2 f cpe ) Sc  M dnc  c  1   Snc  

(1.16)

AASHTO LRFD14 (5.7.3.3.2) (Eq. 5.7.3.3.2-1)

The Mdnc is taken from the Muy caused by the dead load of girder section during the construction stage analysis. The Snc value is obtained from the section modulus of the pre-composite section under the tensile stress. The Sc value is taken from the section modulus of the post-composite section

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

11

under the tensile stress. In midas Civil, cracked moment shall be calculated as per the following equation. (For the composite type sections, the equation 1.16 is used; for the non-composite type sections, the equation 1.17 is used.

M cr   3 ( 1 f r   2 fcpe )Sc 

(1.17)

Where,

γ1 :

flexural cracking variability factor 1.2 for precast segmental structures 1.6 for all other concrete structures

γ2 :

prestress variability factor 1.1 for bonded tendons 1.0 for unbounded tendons If both bonded and unbonded type tendons are assigned in a section, which is more conservative value.

γ3 :

 2 will be applied as 1.0

ratio of specified minimum yield strength to ultimate tensile strength of the reinforcement 0.67 for A615 ,Grade 60 reinforcement 0.75 for A706, Grade 60 reinforcement 1.00 for prestressed concrete structures In midas Civil,

 3 wil be applied as 1.0.

fr : modulus of rupture of concrete specified in Article 5.4.2.6 AASHTO LRFD14 (5.4.2.6) (C5.4.2.6)

In midas Civil, fr will be always applied as 0.37 f 'c . Sc : section modulus for the extreme fiber of the composite section where tensile stress is caused by 3 externally applied loads (in ) In midas Civil, section modulus under tension is applied. fcpe : compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads (ksi)

It is obtained in elastic state (uncracked section) and the following equation has been applied in midas Civil.

f cpe 

A

f

ps e

Ag



A

fe

ps e p

S

(1.18)

Where, f e : Effective prestress forces of prestressing tendons

e p : Distance from the neutral axis to the centroid of the prestressing tendons Aps : Area of prestressing tendon

Ag : Gross area of cross-section

S : Sectional modulus in compression

In midas Civil, construction type of PSC section is determined in PSC design parameter dialog box.

12

Design Guide for midas Civil

▶ PSC> Design Parameter> Parameters…

[Fig.1. 4] PSC Design parameter Dialog - Construction Type

Construction type: Segmental, Non-Segmental The selected construction type will affect the calculation of cracked moment, shear and torsional resistance, and tensile stress limit of concrete.

1.6 Check moment resistance In midas Civil, factored moment is obtained from load combinations specified in Load Combinations dialog box. In AASHTO LRFD specification, load combinations need to be generated as shown in the fig 1.12.

AASHTO LRFD14 (3.4.1)

[Fig.1. 5] Load Combinations and Load factors for strength limit state

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

13

▶Results>Load combinations>Concrete Design tab

Active: Strength/Stress

Active: Serviceability

[Fig.1. 6] Load Combinations dialog

In midas Civil, load combinations can be automatically generated by clicking [Auto Generation…] button. The load combinations need to be generated in concrete design tab. The most critical load combination among Strength/Stress type load combinations will be used to obtain factored moment, factored shear force, and factored torsional moment. The Service type load combinations will be used to verify the serviceability limit state. The verification of flexural moment obtained from Strength/Stress type load combination can be divided into two following cases. 1) No need to satisfy minimum reinforcement

M r  Mu

(1.19)

2) Need to satisfy minimum reinforcement

M r  M u and M r  M cr

1.7 Moment resistance verification 1.7.1 by Result Tables The results can be checked as shown in the table below. ▶Design>PSC Design>PSC Design Result Tables>Check Flexural Strength…

[Fig.1. 7] Result table for moment resistance

14

Design Guide for midas Civil

(1.20)

Elem : Element number Part : Check location (I-End, J-End) of each element. Positive/Negative : Positive moment, negative moment. LCom Name : Load combination name. Type : Displays the set of member forces corresponding to moving load case or settlement load case for which the maximum stresses are produced. CHK : Flexural strength check for element Muy : Design moment Mcr : Crack Moment Mny : Nominal moment resistance. PhiMny : Design moment resistance. Ratio : Muy/ PhiMny : Flexural resistance ratio, The verification is satisfied when it is less than 1.0. PhiMny /min(1.33Muy, Mcr) : Verification of minimum reinforcement. The verification is satisfied when it is less than 1.0. If the verification of minimum reinforcement is not required, it will be displayed as 1.0.

1.7.2 by Excel Report Detail verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1. 8] Excel report for moment resistance

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

15

2. Shear resistance Shear resistance without consideration of effects of torsion shall be verified to satisfy the following condition.

M u  Vn

AASHTO LRFD14 (5.5.4.2.1)

(1.21)

Where, strength reduction factor, Φ=0.9.

Refer to the clause 2.3 Torsion Resistance for the verification of shear resistance where the effects of torsion are required to be considered. In AASHTO-LRFD (2012), the design for shear and torsion will be performed for segmental and non-segmental box girders.

2.1 Classification of Segmental Box Girder The program will consider a section is segmental box girder when the following 2 conditions are satisfied. 1. In PSC Design Parameter dialog box, Construction Type is specified as Segment. 2. When a section is defined with PSC box section (ex. PSC-1CELL, 2CELL, 3CELL, nCELL, cCELL2, PLAT, and Value type) ▶ Property > Section Property > Section >PSC

[Fig.1.16] PSC section data dialog

2.2 Parameters for shear 2.2.1 Effective web width (bv) bv : effective web width taken as the minimum web width within the depth dv as determined in Article 5.8.2.9 (in.)

Effective web width (bv) is taken as web thickness. For PSC multi-cell girder, web thickness can be automatically taken as a summation of thickness for all webs. Also this value can be entered by the user directly as shown in the figure below.

16

Design Guide for midas Civil

AASHTO LRFD14 (5.8.3.3.3)

▶ Property > Section Property > Section >PSC

[Fig 1.17] Consideration of effective web width

1) When the user directly enters values for web thickness Apply the minimum value among the entered web thickness values. 2) When “Auto” option is selected Apply the minimum web thickness among t1, t2, and t3. These values are automatically taken as a summation of thickness for both webs at the stress point, Z1, Z2, and Z3.

2.2.2 Effective shear depth (dv) ▪ Non-Segmental Box Girder dv

: effective shear depth takem as the distance , measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure; it need not be taken less than the greater of 0.9de or 0.72h(in.)

In midas Civil, the value of effective shear depth, dv, is calculated as shown in the equation below.

  Mn dv  min  , 0.9de , 0.72h   As f s  Aps f ps   

de 

AASHTO LRFD14 (5.8.2.9)

(1.22)

Aps f ps d p  As f s d s (1.23)

Aps f ps  As f s

Where, dp : Distance from extreme compression fiber to the centroid of the prestressing tendons ds : Distance from extreme fiber to the centroid of nonprestressed tensile reinforcement

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

17

[Fig.1.18] Effective shear depth

▪ Segmental Box Girder dv

: 0.8h or the distance from the extreme compression fiber to the centroid of the prestressing reinforcement , whichever is greater (in.)

In midas Civil, the value of effective shear depth, dv, is calculated as shown in the equation below.

dv  max  0.8h, dt 

AASHTO LRFD14 (5.8.6.5)

(1.24)

Where, h = Total height of a section dt = Distance from extreme compression fiber to the centroid of the prestressing tendons

2.2.3 Net longitudinal tensile strain (εs)

s

is the net longitudinal tensile strain in the section at the centroid of the tension

reinforcement

 Mu  0.5 Nu  Vu  V p  Aps f po  d v s    Es As  E p Aps  

     

AASHTO LRFD14 (5.8.6.5) (Eq. 5.8.3.4.2-4)

(1.25)

Where,

0   s  0.006 f po  0.7 f pu M u  Vu  Vp dv As and Ap are taken as area of nonprestressing and prestressing steel on the flexural tension side of the member respectively. dv

: 0.8h or the distance from the extreme compression fiber to the centroid of the prestressing reinforcement , whichever is greater (in.)

In midas Civil, the value of effective shear depth, dv, is calculated as shown in the equation below.

dv  max  0.8h, dt 

18

Design Guide for midas Civil

(1.26)

Where, h : Total height of a section dt : Distance from extreme compression fiber to the centroid of the prestressing tendons

[Fig 1.19] Net longitudinal tensile strain

2.3 The nominal shear resistance, Vn 2.3.1 Vn (Non-Segmental Box Girder) For non-segmental box girders, the nominal shear resistance, Vn, shall be determined as the lesser of:

Vn  Vc  Vs  Vp

(1.27)

Vn  0.25 fc'bv dv  Vp

(1.28)

AASHTO LRFD14 (5.8.3.3) (Eq. 5.8.3.3-1) (Eq. 5.8.3.3-2)

Where, Vc : shear resistance component that relies on tensile stresses in the concrete Vs : shear resistance component that relies on tensile stresses in the transverse reinforcement Vp : shear resistance component in the direction of the applied shear of the effective prestressing force. In midas Civil, shear resistance due to prestressing force, Vp, includes primary prestress force. The secondary effects from prestressing shall be included in the design shear force obtained from the load combinations. bv: Effective web width taken as the minimum web width within the depth, dv (refer to the clause 1.2.2.1 Effective web width) dv: Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

2.3.2 Vn (Segmental Box Girder) For segmental box girders, the nominal shear resistance, Vn, shall be determined as the lesser of:

Vn  Vc  Vs  Vp

(1.29)

Vn  0.379 f c' bv dv  Vp

(1.30)

AASHTO LRFD14 (5.8.6.5) (Eq. 5.8.6.5-1) (Eq. 5.8.6.5-2)

Where, Vc : shear resistance component that relies on tensile stresses in the concrete Vs : shear resistance component that relies on tensile stresses in the transverse reinforcement Vp : shear resistance component in the direction of the applied shear of the effective prestressing force. In midas Civil, shear resistance due to prestressing force, Vp, includes primary prestress force. The secondary effects from prestressing shall be included in the design shear force obtained from the

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

19

load combinations. bv: Effective web width taken as the minimum web width within the depth, dv (refer to the clause 1.2.2.1 Effective web width) dv: Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

2.4 The nominal shear resistance by concrete, Vc Design for shear may utilize any of the two methods (simplified and general procedure) for prestressed sections identified in AASHTO-LRFD12. In midas Civil, sections can be designed as per the general procedure.

2.4.1 Vc (Non-Segmental Box Girder) Vc  0.0316 

AASHTO LRFD14 (5.8.3.4)

AASHTO LRFD14 (5.8.3.3) (Eq. 5.8.3.3-3)

(1.31)

f c ' bv dv

Where, bv: Effective web width taken as the minimum web width within the depth, dv (refer to the clause 1.2.2.1 Effective web width) dv: Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth) β : Factor indicating ability of diagonally cracked concrete to transmit tension and shear as specified in Article 5.8.3.4

For the sections containing at least the minimum amount of transverse reinforcement :



4.8 (1  750 s )

AASHTO LRFD14 (5.8.3.4.2)

(1.32)

When sections do not contain at least the minimum amount of shear reinforcement:



4.8 51 (1  750 s ) (39  S xe )

S xe  S x

1.38 ag  0.63

12.0(in.)  S x  80.0(in.)

(1.33)

,

Where, Sx: The lesser of either dv or the maximum distance between layers of longitudinal crack control reinforcement, where the area of the reinforcement in each layer is not less than 0.003bvsx, as shown in Figure 5.8.3.4.2-3(in.) . In midas Civil, it is applied as dv. ag : maximum aggregate size(in.)In midas Civil, it is applied as “1in.”. εs: net longitudinal tensile strain in the section at the centroid of the tension reinforcement.Refer to the clause 1.2.2.3 Net longitudinal tensile strain.

2.4.2 Vc (Segmental Box Girder) Vc  0.0632K

f c ' bv dv

(1.34)

Where, bv: Effective web width taken as the minimum web width within the depth, dv (refer to the clause 1.2.2.1 Effective web width) dv: Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

K: Stress variable K shall not be taken greater tham 1.0 for any section where the stress in the extreme tension fiber, calculated on the basis of gross section properties, due to factored load and effective prestress force after losses exceeds 0.19√f’c in tension

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Design Guide for midas Civil

AASHTO LRFD14 (5.8.3.4.2) (Eq. 5.8.6.5-3)

K  1

f pc

(1.35)

0.0632 f c '

AASHTO LRFD14 (5.8.6.3) (Eq. 5.8.6.3-3)

In midas Civil, the value of K is calculated as below. 1) Calculate the tensile stress of tendon, ft, after losses Tendon based on the uncracked section. 2) If ft  0.19

f c ' , K = min(K, 1.0)

If ft  0.19

f c ' , K = min(K, 2.0)

AASHTO LRFD14 (5.8.6.3)

Where, fpc : Unfactored compressive stress in concrete after prestress losses have occured either at the centroid of the cross-section resisting transient loads or at the junction of the web and flange where the centroid lies in the flange (ksi) In midas Civil, fpc is calculated as follows.

When the centroid lies in the flange, verify the stress at a junction of the web and flange.

f pc 

A

ps

fe

Ag



A

ps

Ig

feep

y jo int 

Nu Ag

(1.36)

Where, yjoint is a distance from the centroid to the junction of the web and flange

When the centroid lies in the web, verify the stress at the centroid of the cross-section.

f pc 

A

ps

Ag

fe



Nu Ag

(1.37)

2.5 The nominal shear resistance by shear reinforcement, Vs The nominal shear resistance by shear reinforcement, Vs, is calculated as follows:

2.5.1 Vs (Non-Segmental Box Girder) Vs 

Av f y dv (cot   cot  )sin  s

(1.38)

AASHTO LRFD14 (5.8.3.3.3) (Eq. 5.8.3.3-4)

Where, dv:Refer to 1.2.2.2 Effective shear depth (for Non-Segmental Box Girders) θ: angle of inclination of diagonal compressive stresses as determined in Article 5.8.3.4 (degrees) ; if the procedures of Article 5.8.3.4.3 are used, cotθ is defined therein.

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21

[Fig.1.20] angle of inclination of transverse Compressive stress

The following equation is incorporated in midas Civil:

  29  3500 s

(1.39)

 s :Refer to 1.2.2.3 Net longitudinal tensile strain α: Angle of inclination of transverse reinforcement to longitudinal axis (degrees) Enter the Angle of transverse reinforcement as shown in Fig1.22.

s:

Spacing of transverse reinforcement Enter the Pitch of transverse reinforcement as shown in Fig1.22.

▶Model>Properties>Section Manager>Reinforcements

Transverse Reinforcement

[Fig.1.21] Transverse Reinforcement

The required input data for transverse reinforcement are as follows: - Pitch: Enter the spacing of transverse reinforcement - Angle: Enter the angle of inclination of transverse reinforcement - Aw: Enter the total area of all transverse reinforcements in the web

2.5.2

Vs (Segmental Box Girder)

midas Civil applies the following equation where the angle of inclination (α) of transverse reinforcement is taken into account:

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Design Guide for midas Civil

AASHTO LRFD14 (5.8.3.4.2) (Eq. 5.8.3.4.2-3)

(1.40)

AASHTO LRFD14 (5.8.3.3.3) ((Eq. 5.8.6.5-4)

The maximum spacing of transverse reinforcement can be checked by the following steps:

AASHTO LRFD14 (5.8.2.7)

Vs 

Av f y dv (sin   cot  ) s

Where, dv: refer to 1.1.2.2 Effective shear depth (for Segmental Box Girders)

α: angle of inclination of transverse reinforcement to longitudinal axis (degrees) Enter the Angle of transverse reinforcement as shown in Fig1.22.

2.6 Maximum spacing for transverse reinforcement (smax) 1) Calculate the shear stress (vu) acting on the concrete.

vu 

Vu  V p

(1.41)

 bv dv

AASHTO LRFD14 (5.8.2.7) (Eq. 5.8.2.9-1)

Where,

Φ = Use the shear strength reduction factor of 0.9. bv: refer to 1.1.2.1 Effective web width dv: refer to 1.1.2.2 Effective shear depth (for Non-Segmental Box Girders)

2) Calculate smax differently, depending on whether the section is Segmental Box Girder or not and on the range of vu. 3) Compare the entered spacing of transverse reinforcement with smax.

2.6.1 smax (Non-Segmental Box Girder)  If vu < 0.125f’c AASHTO LRFD14 (5.8.2.7)

smax = 0.8dv ≤ 24.0 in.

 If vu ≥ 0.125f’c smax = 0.4dv ≤ 12.0 in. Where, dv: refer to 2.1.2.2 Effective shear depth (for Non-Segmental Box Girders)

2.6.2 smax (Segmental Box Girder)  If vu < 0.19√f’c

AASHTO LRFD14 (5.8.6.6)

smax = 0.8dv ≤ 36.0 in.

 If vu ≥ 0.19√f’c

AASHTO LRFD14 (5.8.2.7)

smax = 0.4dv ≤ 18.0 in. Where, dv: refer to 1.2.2.2 Effective shear depth (for Segmental Box Girders)

midas Civil calculates vu using Eq. 5.8.2.9-1 for the shear check and using Eq. 5.8.6.5-5 for the torsion check.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

23

2.7 Minimum required transverse reinforcement (Av,min) The minimum required transverse reinforcement can be checked according to the following steps: 1)

Calculate the minimum required reinforcement, Av,min , differently dependng on

whether the section is Segmental Box Girder or not. ▪ For Non-Segmental Box Girders

Av ,min  0.0316 fc'

bv s fy

(1.42)

AASHTO LRFD14 (5.8.2.4) (Eq. 5.8.2.5-1)

(1.43)

(Eq. 5.8.2.5-2)

▪ For Segmental Box Girders

Av ,min  0.05

bw s fy

In midas Civil bw=bv. 2) Calculate the shear strength of the section, and then verify the transverse reinforcement using the following equations: ▪ For Vu < 0.5Φ(Vc+Vp) Skip the transverse reinforcement checks. ▪ For Vu ≥ 0.5Φ(Vc+Vp)

Av ,req1 

V

u

 0.5 (Vc  Vp ) s

 f y dv (sin   cot  )

(1.44)

Av,req 2  Av ,min Av,req  min( Av,req1 , Av,req 2 ) If the area of transverse reinforcement (Av) is greater than or equal to Av,req , it says OK. The area of transverse reinforcement (Av) is Aw which is entered from Fig.1.22.

24

Design Guide for midas Civil

2.8 Interface Shear For the composite sections, the Shear Friction caused during construction sequences needs to be considered. Therefore, the Interface Shear check function is activated for the precomposite section design check.

2.8.1 Calculate Vni

The Vni value is calculated based on the above calculation. The A cv is the Interfacial Shear section area. The Acf value is the cross section of the shear reinforcement of the Interfacial Shear section. The following equation (5.8.4.4-1) needs to be satisfied about the minimum shear reinforcement rea.

The Pc value is the compressive force acting on the interface. In the program, the Pc value is calculated based on the selfweight of slab. The program suggests the factors used in design. In midas Civil, they are applied as shown below: Table. The design factors used in midas Civil

AASHTO-LRFD12 Standard In Acv = bci x Lvi, bci value is taken from the Bvi input by the user and the Lvi value is taken from the girder length of the program model.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

25

The Avf is the cross section of the reinforcement rebars in the interfacial shear plane (Acv). The calculator is activated when the button is clicked. So that the cross section is calculated based on the rebar diameter, number and gap inputted by the user.

The Vri value is calculated based on the above equation (5.8.4.1-1). Also, the Vri value should be equal to or greater than Vui. For PSC design check, the Φ is taken as 1.0.

The Interface Shear calculation can be reviewed in the MS Excel Report.

The Interface Shear check result can be also checked in the Shear Resistance Results table.

2.9 Check shear resistance midas Civil checks the shear strength limit state for the Vmax and Vmin cases among the Active: Strength/Stress load combinations, which are defined in Fig.1.12 Load Combinations dialog.

2.10 Check the shear resistance results 2.10.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design>PSC Design Result Tables>Check Shear Strength…

[Fig.1.22] Result table for shear resistance Elem : Element number Part : Check location (I-End, J-End) of each element Max./Min. : Maximum shear, minimum shear LCom. Name : Load combination name. Type : Displays the set of member forces corresponding to moving load case or settlement load case for which the maximum stresses are produced. CHK : Shear strength check for element Vu : Maximum shear force among Strength/Stress load combinations Mu : Bending moment for the LCom which has Vu Vn : Nominal Shear resistance. Phi : Resistance factor for shear Vc : Shear resistance of concrete.

26

Design Guide for midas Civil

Vs : Shear resistance of shear reinforcement. Vp : Shear force of the effective prestressing force. PhiVn : Design Shear resistance. de : Effective web width dv : Effective depth for shear ex : Longitudinal Strain theta : Angle of inclination of transverse compressive stresses beta : Factor indicating ability of transversely cracked concrete to transmit tension and shear Avs : Area of shear reinforcement Ast : Area of longitudinal reinforcement Al : Area of longitudinal torsional reinforcement bv : Effective width Avs_min : Minimum required transverse reinforcement Avs_req : Required transverse reinforcement Al_min : Minimum longitudinal torsional reinforcement bv_min : Minimum effective web width

Vri : Nominal interface shear resistance Vui : factored interface shear force due to total load based on the applicable strength and extreme event load combinations.

2.10.2 by Excel Report The detailed results, which contain the calculations, are produced in the Excel Report. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1.23] Excel Report for shear resistance

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

27

3. Torsion resistance Check the combined shear and torsional resistance.

3.1 Dimension of section for torsion The dimensions of section that are required for checking torsion are as follows: Ao : Area enclosed by the shear flow path, including any area of holes therein (in2) midas Civil uses the area of the closed section enclosed by the torsion reinforcement, instead of the shear flow path. Ph : Perimeter of the centerline of the closed transverse torsion reinforcement (in) Acp : Total area enclosed by outside Perimeter of the concrete section (in2) P : The length of the outside perimeter of concrete section (in)

Ao(ph Acp(pc )

[Fig.1.24] Dimension of section for torsion **Additional information for the torsional area Ac and circumference Ph calculation of the composite section. In midas Civil, when Ao section is applied for the composite section, the girder and slab sections (section areas with the Torsion Thk Offset applied in the Section Manager) are calculated separately and then added. The Ph circumference is calculated based on the same approach but the value of bw*2 is substracted in order to consider the contact area between the girder and slab. ex)

3.2 Calculate torsional resistance Torsional resistance can be checked according to the following steps: 1) Calculate the torsional cracking moment (Tcr) differently, depending on whether the section is Segmental Box Girder or not. 2) Compare the factored torsional moment (Tu) with the limit, which differs depending on the type of girder (segmental box girder or non-segmental box girder), in order to decide whether the effect of torsion should be considered or not. 3) In case where the torsional effect should be considered, calculate the design torsional strength and compare it with Tu.

28

Design Guide for midas Civil

3.2.1 Torsional cracking moment (Tcr) ▪ For Non-Segmental Box Girders

Tcr  0.125 f c'

Acp2 pc

1

f pc

(1.45)

0.125 f c'

AASHTO LRFD14 (5.8.2.1) (Eq. 5.8.2.1-4)

Where,

fpc: compressive stress in concrete after prestress losses have occurred at either the centroid of the cross-section resisting transient loads or at the junction of the web and flange where the centroid lies in the flange (ksi)

midas Civil calculates fpc as follows: If the centroid lies in the flange: calculate at the junction of the web and flange.

f pc 

A

ps

fe

Ag



A

ps

fee p

Ig

(1.46)

y jo int

Where, yjoint is the distance from the centroid to the junction of the web and flange.

If the centroid lies in the web: calculate at the centroid of the corss-section.

f pc 

Acp2 pc

A

ps

fe

(1.47)

Ag

shall be less than or equal to 2Aobv for a box section.

▪ For Segmental Box Girders

Tcr  0.0632 K fc' Aobe

(1.48)

AASHTO LRFD14 (5.8.6.3) (Eq. 5.8.6.3-2)

Where, K : Refer to the value of K specified in 2.1.4.2. be : effective width of shear flow path, but not exceeding the minimum thickness of the webs or flanges comprising the closed box section (in.). be shall be adjusted to account for presence of ducts as specified in Article 5.8.6.1. midas Civil uses bv.

3.2.2 Condition for torsion check ▪ For Non-Segmental Box Girders

Tu  0.25Tcr

(1.49)

AASHTO LRFD14 (5.8.2.1) (Eq. 5.8.2.1-3)

▪ For Segmental Box Girders

Tu  1/ 3Tcr

(1.50)

AASHTO LRFD14 (5.8.6.3) (Eq. 5.8.6.3-1)

Where, Φ = resistance factor for torsion(=0.9)

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

29

3.2.3 Torsional resistance In accordance with AASHTO-LRFD12, the torsional resistance should meet the condition Tu≤ΦTn for the cases of segmental box girders and non-segmental box girders.

AASHTO LRFD14 (5.5.4.2.1)

▪ For Non-Segmental Box Girders

Tn 

2 Ao At f y cot 

(1.51)

s

AASHTO LRFD14 (5.8.3.6.2) (Eq. 5.8.3.6.2-1)

Where, At: area of one leg of closed transverse torsion reinforcement in solid menbers, or total area of 2 transverse torsion reinforcement in the exterior web of cellular members (in. ). Awt of Torsional Reinforcement entered in Fig.1. 26 will be used. s :Pitch of Torsional Reinforcement entered in Fig.1. 26 will be used. Θ: angle of crack as determined in accordance with provisions of Article 5.8.3.4 with the modifications to the expressions for v and Vu herein (degrees). The same equation, which was used for the shear check, will be used:

  29  3500 s

(1.52)

 s : Refer to 1.2.2.3 Net longitudinal tensile strain.

AASHTO LRFD14 (5.8.3.4.2) (Eq. 5.8.3.4.2-3)

▪ For Segmental Box Girders

Tn 

2 Ao At f y

(1.53)

s

Where, At : Awt of Torsional Reinforcement entered in Fig.1. 26 will be used. s : Pitch of Torsional Reinforcement entered in Fig.1. 26 will be used.

The reinforcement data used for the torsion check are as follows: ▶ Model>Properties>Section Manager>Reinforcements

Torsional Reinforcement

[Fig.1.25] Transverse Reinforcement

- Pitch : spacing of transverse torsional reinforcement - Awt : area of transverse torsional reinforcement

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Design Guide for midas Civil

AASHTO LRFD14 (5.8.6.4) (Eq. 5.8.6.4-2)

(the area of a single stirrup among the outer closed stirrups) - Alt : area of longitudinal torsional reinforcement (the area of all reinforcing steels which are close against the outer closed stirrups)

3.3 Check longitudinal reinforcement Check the longitudinal reinforcement to resist torsion. Check it for box sections and for solid sections, respectively. ▪ For Solid sections Aps is the area of tensile tendon and As is the area of tensile reinforcement.

Aps f ps  As f y 

Mu

 dv



0.5 Nu



2

V   0.45 phTu   cot   u  Vp  0.5Vs         2 Ao 

2

AASHTO LRFD14 (5.8.3.6.3) (Eq. 5.8.3.6.3-1)

(1.54) Where, dv: refer to 2.1.2.2 Effective shear depth (for Non-Segmental Box Girders)

▪ For Box sections The Code suggests that the reinforcement for resisting torsion is limited to the following equation for box sections:

Al 

Tn ph 2 Ao f y

(1.55)

AASHTO LRFD14 (5.8.3.6.3) (Eq. 5.8.3.6.3-2)

midas Civil incorporates the above equation to check the longitudinal torsional reinforcement. The Alt of Torsional Reinforcement entered in Fig.1. 26 will be used. Alt is only for resisting warping torsion and is used only for box sections.

Alt 

(Tu /  ) ph 2 Ao f y

(1.56)

AASHTO LRFD14 (5.8.6.4) (Eq. 5.8.6.4-3)

3.4 Check combined torsional and shear stress For Segmental Box Girders, check the combined shear and torsional stress.

 Vu   bv dv

  Tu    2 Aobe

 '   0.474 f c 

(1.57)

AASHTO LRFD14 (5.8.6.5) (Eq. 5.8.6.5-5)

Where, bv: refer to 1.1.2.1 Effective web width dv: refer to 1.1.2.2 Effective shear depth (for Segmental Box Girders) be : effective thickness of the shear flow path of the elements making up the space truss model resisting torsion calculated in accordance with Article 5.8.6.3 (in). midas Civil uses bv.

midas Civil calculates the maximum combined stress using the equation below.

Vu Tu   0.474 f c' bv dv 2 Aobe

(1.58)

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

31

3.5 Check torsional moment resistance midas Civil checks the combined shear and torsional strength limit state for the Vmax, Vmin and Tmax cases among the Active: Strength/Stress load combinations, which are defined in Fig.1.12 Load Combinations dialog.

3.6 Check the torsional resistance results 3.6.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design>PSC Design Result Tables>Check Combined Shear and Torsion Strength…

[Fig.1.26] Result table for torsional resistance Elem : Element number Part : Check location (I-End, J-End) of each element Max./Min.: Maximum torsion/shear, minimum torsion/shear LCom Name: Load combination name. Type: Displays the set of member forces corresponding to moving load case or settlement load case for which the maximum stresses are produced. CHK: Shear and torsion strength check for element Vu : shear force for the corresponding LCom Mu : bending moment for the corresponding LCom Tu : torsional moment for the corresponding LCom Vn : Nominal Shear resistance. Tn : Nominal Torsional resistance. Phi : strength reduction factor for shear Phi_t : strength reduction factor for torsion Vc : Shear resistance of concrete. Vs : Shear resistance of shear reinforcement. Vp : Shear force of the effective prestressing force. PhiVn : Design Shear resistance. Phi_tTn : Design Torsional resistance. de : Effective web width dv : Effective depth for shear ex : Longitudinal Strain theta : Angle of inclination of transverse compressive stresses beta : Factor indicating ability of transversely cracked concrete to transmit tension and shear Avs : Area of shear reinforcement Ast : Area of longitudinal reinforcement Al : Area of longitudinal torsional reinforcement bv : Effective width Avs_min : Minimum required transverse reinforcement Avs_req : Required transverse reinforcement Al_min : Minimum longitudinal torsional reinforcement bv_min : Minimum effective web width At : Area of transverse torsional reinforcement At_req : Required transverse torsional reinforcement

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Design Guide for midas Civil

3.6.2 by Excel Report Detail verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1.27] Excel report for torsional resistance

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

33

Chapter 1. Prestressed Concrete Girder Design: AASHTO-LRFD 7th (2014)

Serviceabiltiy Limit States 1. Stress for cross section at a construction stage The allowable stress at a construction stage differs depending on the generated stress because the precompressed tensile zone is defined differently depending on the generated stress. Therefore, the generated stress at every stage and step is compared to the corresponding allowable stress, and the most unfavorable ratio of the generated stress to the allowable stress is searched and checked against the criteria. That is to say, calculate the ratio of generated stress to allowable stress for every stage and see if the highest ratio meets the criteria.

1.1 Allowable stress of concrete (1) Allowable compressive stress of concrete σca = 0.60 f’ci

AASHTO LRFD14 (5.9.4.1.1)

(1.59)

Where, the definition of f’ci is stated in 2.1.2.

(2) Allowable tensile stress of concrete AASHTO LRFD14 (5.9.4.1.2)

[Fig.1.28] Allowable tensile stress of concrete

34

Design Guide for midas Civil

Midas Civil calculates the allowable tensile stress of concrete using Table 5.9.4.1.2-1, as stated in the table below: [Table 1.3] Allowable tensile stress of concrete Construction Type

Case Precompressed Tensile Zone

Non-Segment Other Than Precompressed Tensile Zone

Without tendon

bonded

reinforcement

and

With bonded reinforcement or bonded tendon Without tendon

bonded

reinforcement

and

With bonded reinforcement or bonded tendon Precompressed tensile Zone

Joint Other cases Segment Non Joint

With bonded reinforcement or bonded tendon

Allowable stress(ksi) σta = 0.0

bonded If reinforcement stress ≤ min(0.5fy, 30ksi)

σta = 0.24*SQRT(f'ci )

If reinforcement stress > min(0.5fy, 30ksi)

σta = 0.0 σta = 0.0948f'ci ≤ 0.2

bonded If reinforcement stress ≤ min(0.5fy, 30ksi)

σta = 0.24*SQRT(f'ci)

If reinforcement stress

σta = 0.0

> min(0.5fy, 30ksi)

Reinforcement stress≤ 0.5fy σta = 0.0948*SQRT(f'ci) With bonded reinforcement or bonded Reinforcement stress > 0.5fy σta = 0.0 tendon σta = 0.0 If reinforcement stress ≤ min(0.5fy, 30ksi)

σta = 0.19*SQRT(f'ci )

If reinforcement stress

σta = 0.0

> min(0.5fy, 30ksi)

σta = 0.0

Other cases

Description on each item is as follows:

AASHTO LRFD14 (5.2)

Precompressed Tensile Zone: According to the Code, Precompressed Tensile Zone is defined as Any region of a prestressed component in which prestressing causes compressive stresses and service load effects cause tensile stresses. midas Civil calculates the concrete stress in cross-section using the following methods and defines the Precompressed Tensile zone at Before Loss (construction stage). If it is compressive stress for TendonPrimary(CS)+Tendon Secondary(CS), and if it is tensile stress for Summation(CS)-(Tendon primary+Tendon secondary). Joint/non-Joint: In midas Civil, joints can be defined in the dialog below: AASHTO LRFD14 (5.5.4.2.1)

▶PSC> PSC Segment Assignment

[Fig.1.29] PSC Segment Assignment

As shown in Fig.2.2, if elements 1, 2 and 3 are assigned as one segment, i-end of element 1 and j-end of element 3 become the joints and the rest become the non-joints.

AASHTO LRFD14 (C 5.9.1.4)

Bonded reinforcement It is assumed that the tensile reinforcement or the tendon defined as Bond Type in Fig.1. 7 are bonded reinforcement. Based on the aforementioned, if tensile reinforcement or bonded tendon is present in the tension zone, it is assumed that bonded reinforcement exists.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

35

Check the stress in reinforcement The Code states that the bonded reinforcement, which retains a specific stress value (0.5fy or 30ksi), shall resist the tensile force on the tension zone. midas Civil applies the above regulation as follows: Compute the concrete triangular stress block on the tension zone, using the extreme fiber tension stress and the extreme fiber compression stress of concrete. Compute the tension force of concrete by multiplying the compression stress by the area of the concrete triangular stress block. Compute the tension force of reinforcement by multiplying the area of reinforcement and tendon, which are included in the triangular stress block, by the specific stress (0.5fy or 30ksi). If the tension force of reinforcement is larger than that of concrete, it is concluded that the tensile stress of reinforcement satisfies the regulation.

[Fig.1.30] Check the tension force of reinforcement

1.2 Compressive strength of concrete at time of loading, f’ci The Code defines f’ci as: f’ci is specified compressive strength of concrete at time of initial loading or precompressing; nominal concrete strength at time of application of tendon midas Civil computes the compressive strength of concrete (f’ci) during the construction stages according to the construction days defined in Fig.2.4 and the function of concrete strength defined in Fig.2.5. The days for each construction stage can be defined in Fig2.4. ▶Load> Construction Stage> Compose construction Stage…

Additional Steps

Stage

Activation

[Fig.1.31] Compose construction Stage dialog

Stage>Duration: Enter the duration of the construction stage. It is the basic unit where elements become active or inactive, boundary conditions become active or inactive and loads are applied or removed.

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Design Guide for midas Civil

AASHTO LRFD14 (5.3)

Additional Step>age: Define the specific days for the analysis steps within the construction stage. Within a construction stage where the model and boundary conditions remain unchanged, changes in load application timing or additional loads may be incorporated through additional steps. Activation>Group List>age: Select relevant element groups, which are applicable to the current stage, in the Group List and activate the selected groups by moving them to Activation Group List. Specify the Age of the selected element groups. The age entered here will be used to reflect the effects of creep and shrinkage that took place prior to the current construction stage. The age of the element, which is casted at the start of the current construction stage, is zero. The age typically represents the time span from the time of concrete casting to the time of removal of formwork during which the concrete is considered as a structural element, that is to say the curing period of concrete. Based on the inputs shown in Fig.2.4, midas Civil takes the following days for the construction stage analysis: The duration of the construction stage CS1 is 30 days, the duration of the additional step within CS1 is 15 days, and the Activation age is 5 days. The actual duration of CS1 is 35 days (Stage Duration + Activation age). The compressive strength of concrete is computed at 5 days, 20 days and 35 days for CS1. If the next stage CS2 is defined with the duration of 20 days, CS2 starts at 35 days and ends at 55 days. The development of concrete compressive strength with days is defined in the dialog below.

AASHTO LRFD14 (5.7.2.2)

▶ Properties> Time Dependent Materials>Comp. Strength…

[Fig.1.32] Time Dependent Materials dialog

Development of Strength: Define the function to compute the compressive strength of concrete during the construction stages. Define a function by selecting ACI, CEB-FIP or Structural Concrete Design Code, or directly define the values. The compressive strength of concrete is computed by reflecting the variation of the modulus of elasticity with concrete ages. For CS1 the compressive strengths of concrete are computed at 5 days, 20 days and 35 days, and they are compared to the corresponding stresses.

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1.3 Check stress for cross section at a construction stage  c   ca ,  t   ta

(1.60)

1.4 Check the stress results for cross section at a construction stage 1.4.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design >PSC Design Result Tables>Check stress for cross section at a construction stage…

[Fig.1.33] Result table for stress at a construction stage Elem : Element number Part : Check location (I-End, J-End) of each element Comp./Tens.: Compression or Tension Stress Stage : Construction stage at which stresses are maximum at the corresponding section. CHK : Combined stress check for construction stages FT : Combined Stress due to My and axial force at Top fiber FB : Combined Stress due to My and axial force at Bottom fiber FTL : Combined Stress due to My, Mz and axial force at Top Left fiber FBL : Combined Stress due to My, Mz and axial force at Bottom Left fiber FTR : Combined Stress due to My, Mz and axial force at Top Right fiber FBR : Combined Stress due to My, Mz and axial force at Bottom Right fiber FMAX : Maximum combined stress out of the above six components. ALW : Allowable stress of cross section at construction stage.

Girder/Slab : The girder of the composite section is indicated as Girder(composite); the slab of the composite section is indicated as Slab(composite); the non-composite PSC section is indicated as Girder(PSC).

Right click on mouse >> Context Menu >> Activate Records The results can be filtered and selected for the Girder and Slab. The results can be output separately for the Girder(Composite) and Slab(Composite). For the non-composite PSC sections, the results are ouput for the Girder(PSC). For the non-composite PSC sections, even if the Slab part is selected, the results are not output for the Slab(Composite).

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Design Guide for midas Civil

1.4.2 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design >PSC Design Calculation…

[Fig.1.34] Result table for stress at a construction stage

**The stress result is output for the girder and slab separately with the addition of the composite section design check.

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2. Stress for cross section at service loads The element stress at service loads after losses should meet the following conditions: The maximum compressive stress at service loads after losses ≤ allowable compressive stress of concrete: σc ≤ σca The maximum tensile stress at service loads after losses ≤ allowable tensile stress of concrete: σt ≤ σta The Code suggests that the stresses in PSC structures after losses shall be checked for the followings: Check compressive stress: for the load combinations of Service Limit state 1 Check tensile stress: for the load combinations of Service Limit state 3

[Fig.1.35] Load Combination for Service Limit state

In midas Civil, the Load Cases to check compressive stress and tensile stress after losses can be selected via the dialog box shown in Fig.2.9. The Load Cases in Service Limit1 will be used to check compressive stress, and the Load Cases in Service Limit3 will be used to check tensile stress.

[Fig.1.36] Concrete Allowable Stress Load Case dialog

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Design Guide for midas Civil

AASHTO LRFD14 (5.9.4.2.1) (5.9.4.2.2)

2.1 Allowable stress of concrete (1) Allowable compressive stress of concrete

AASHTO LRFD14 (5.9.4.2.1)

[Fig.1.37] Allowable compressive stress of concrete

The following formula is incorporated in midas Civil: σca = 0.45 f’c

(1.61)

(2) Allowable tensile stress of concrete

AASHTO LRFD14 (5.9.4.2.2)

[Fig.1.38] Allowable tensile stress of concrete

midas Civil calculates the allowable tensile stress of concrete using Fig.2.11, as stated in the table below:

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[Table1.4] Allowable tensile stress of concrete Construction Type

Non-Segment

Case Precompressed Tensile Zone

With bonded reinforcement or bonded tendon

Without bonded reinforcement tendon Other Than Precompressed Tensile Zone

Joint

and

Allowable stress(ksi) corrosion condition - not Worse

σ

ta

= 0.19*sqrt(fck)

corrosion condition -severe

σ

ta

= 0.0948*sqrt(fck)

σ

ta

= 0.0

σ

ta

= 0.0

σ

ta

= 0.0948*SQRT(f'c)

σ

ta

= 0.0

σ

ta

= 0.0

If reinforcement stress ≤ min(0.5fy, 30ksi) ,

σ

ta

= 0.19*SQRT(f'c)

If reinforcement stress > min(0.5fy, 30ksi)

σ

ta

= 0.0

σ

ta

= 0.0

bonded

If reinforcement stress≤ 0.5fy, (Precompressed Tensile Zone) and (With bonded reinforcement or bonded ) If reinforcement stress > 0.5fy, tendon Other cases

Segment Non Joint

With bonded reinforcement or bonded tendon Other cases

Description on each item is as follows: Precompressed Tensile Zone According to the Code, Precompressed Tensile Zone is defined as Any region of a prestressed component in which prestressing causes compressive stresses and service load effects cause tensile stresses. midas Civil calculates the concrete stress in cross-section using the following methods and defines the Precompressed Tensile zone at After Loss (construction stage). -If it is compressive stress for TendonPrimary(CS)+Tendon Secondary(CS), and -if it is tensile stress for Service Limit State load combination(SLS)-(Tendon primary+Tendon secondary). Corrosion Condition The data for Corrosion Condition can be entered in the dialog box below: ▶ PSC> Design Parameter> Parameters…

[Fig.1.39] PSC Design parameter Dialog -corrosion condition

The input parameters and the corresponding terms defined in the Code are listed in the table below:

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Design Guide for midas Civil

AASHTO LRFD14 (5.2)

[Table1.5] corrosion condition

Input parameter Severe Moderate/Mild

Term of the Code Severe Not worse

1) Joint/non-Joint Bonded reinforcement Check the stress in reinforcement

: refer to 2.1.1 : refer to 2.1.1 : refer to 2.1.1

2.2 Check stress for cross section at service loads  c   ca ,  t   ta

(1.62)

2.3 Check the stress results for cross section at service loads 2.3.1 by Result Tables The results can be checked as shown in the table below. ▶Design>PSC Design>PSC Design Result Tables>Check stress for cross section at service loads…

[Fig.1.40] Result table for stress at service loads Elem: Element number Part: Check location (I-End, J-End) of each element Comp./Tens.: Compression or Tension Stress LCom Name: Load Combination Name Type: Displays the set of member forces corresponding to moving load case or settlement load case for which the maximum stresses are produced CHK: Combined stress check for Service loads FT: Combined Stress due to My and axial force at Top fiber FB: Combined Stress due to My and axial force at Bottom fiber FTL: Combined Stress due to My, Mz and axial force at Top Left fiber FBL: Combined Stress due to My, Mz and axial force at Bottom Left fiber FTR: Combined Stress due to My, Mz and axial force at Top Right fiber FBR: Combined Stress due to My, Mz and axial force at Bottom Right fiber FMAX: Maximum combined stress out of the above six components. ALW: Allowable stress in concrete at service limit state.

Girder/Slab : The output is presented separately for the Composite Section as the Girder(composite) and Slab(Composite).

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2.3.2 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶Design>PSC Design>PSC Design Calculation…

[Fig.1.41] Excel report for stress at service loads

**The stress result is output separately for the Girder/Slab with the addition of the Composite Section Design.

3. Tensile stress for Prestressing tendons Compare the stress in tendon with the allowable stress for each tendon group. After immediate losses at anchorages, the maximum stress in tendon ≤ allowable stress. Elsewhere away from anchorages, the maximum stress in tendon ≤ allowable stress. After all losses, the maximum stress in tendon ≤ allowable stress.

3.1 Allowable stress of tendon The Code presents the following stress limits for tendons depending on the tendon types:

AASHTO LRFD14 (5.9.3)

[Fig.1.42] Stress Limit for Prestressing Tendons

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Design Guide for midas Civil

Tendon Type can be specified from the Design parameters dialog. ▶ PSC> Design Parameter> Parameters…

[Fig.1.43] PSC Design parameter Dialog – Tendon Type

The input parameters of the dialog and the corresponding terms defined in the Code are listed in the table below: [Table1.6] Tendon Type Input parameter

Low Relaxation Tendons Stress Relieved Tendons Prestressing Bar

Term of the Code

Low Relaxation Strand Stress Relieved Strands and Plane High-strength Bar Deformed Hige-strength Bar

Pre/Post tensioning can be specified as showin in Fig.1. 8 Tendon Property Dialogue. Midas Civil applies the stress limits for tendons differently, depending on the Tendon Type and whether it is Pre/Post tensioning. Allowable stress in tendon immediately after anchor set at anchorages(AFDL1) The maximum allowable stress in tendon at anchorages after immediate losses. The values for “At anchorages and couplers immediately after anchor set” of Table 5.9.3-1 are set as the limits. Allowable Stress in Tendon immediately after anchor set elsewhere(AFDL2) The maximum allowable stress in tendon elsewhere along length of member away from anchorages. The values for “Elsewhere along length of member away from anchorages…” of Table 5.9.3-1 are set as the limits. This is not applicable to Pretension. Allowable stress in tendon at service limit state after losses(AFLL1) The maximum allowable stress in tendon at service limit state after all losses. The values for “At service limit stage after losses” of Table 5.9.3-1 are set as the limits.

3.2 Check the stress in Prestressing tendons 3.2.1 by Result Tables The stress results of tendon can be checked as shown in the table below. ▶Design>PSC Design>PSC Design Result Tables>Check tensile stress for Prestressing tendons …

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[Fig.1.44] Result table for tensile stress for prestressing tendon Tendon: Tendon profile name. For Post-tensioned: FDL1: Stress in tendon at anchorages. The maximum stress in tendon at anchorages after immediate losses FDL2: Maximum stress in tendon along the length of the member away from anchorages, immediately after anchor set. The maximum stress in tendon elsewhere along length of member away from anchorages immediately after anchor set FLL1: Maximum stress in tendon after all losses at the last stage. The maximum stress in tendon at service limit state after all losses AFDL1: Allowable stress in tendon immediately after anchor set at anchorages. The allowable stress for FDL1 AFDL2: Allowable stress in tendon immediately after anchor set elsewhere. The allowable stress for FDL2 AFLL1: Allowable stress in tendon at service limit state after losses. The allowable stress for FLL1 For Pre-tensioned: FDL1: Stress in tendon. FDL2: FLL1: Maximum stress in tendon after all losses at the last stage. AFDL1: Allowable stress in tendon prior to transfer. AFDL2: AFLL1: Allowable stress in tendon at service limit state after losses.

3.2.2 Tendon Time-dependent Loss Graph The stress in each tendon for each construction stage can be checked from the dialog below: ▶ Result > Bridge> Tendon Loss Graph…

[Fig.1.45] Tendon Time-dependent Loss Graph

In the graph above the stress at the beginning represents the stress in tendon at anchorage after immediate losses (FDL1), and the largest stress in the graph represents the maximum stress in tendon elsewhere along length of member away from anchorages immediately after anchor set (FDL2).

3.2.3 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶Design>PSC Design>PSC Design Calculation…

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Design Guide for midas Civil

[Fig.1.46] Excel Report for tensile stress for prestressing tendons

4. Principal stress at a construction stage Find the maximum principal tensile stress among the stress check points 1~10 of the crosssection at a construction stage and compare it to the allowable stress. In other words, maximum principal tensile stress ≤ allowable stress.

4.1 Allowable tensile stress The Code presents the following equation of allowable tensile stress for Segmentally

AASHTO LRFD14 (5.9.4.1.2)

Constructed Bridges:

 ta  0.110 fci'

(1.63)

Where, f’ci is identical to that of 2.1.2.

midas Civil applies the above equation for both Segment and Non-segment.

4.2 Maximum principal stress The maximum principal tensile stress for each point at a constructions stage is computed as follows:  ps 

1  x   z   2 

 x   z 2  4 s   t   p 2 



(1.64)

where, σx : Sum of axial stresses in ECS x-direction σz : Sum of axial stresses in ECS z-direction τs : Shear stress due to shear. τt : Shear stress due to torsion. τp : Shear stress due to shear reinforcement.

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4.2.1 Beam stresses of PSC The stress components to compute the maximum principal tensile stress can be checked from the Result Table below: ▶ Results>Result Tables>Beam>Stress(PSC)…

[Fig.1.47] Beam stresses of PSC Sig-xx (Axial): Axial stress due to the axial force (Fx) in the ECS x-direction Sig-xx (Moment-y): Stress due to My (moment about the ECS y-axis) in ECS x-direction Sig-xx (Moment-z): Stress due to Mz (moment about the ECS z-axis) in ECS x-direction Sig-xx (Bar): Axial stress due to shear steel bars in the ECS x-direction Sig-xx (Summation): Sum of the axial stress in the ECS x-direction and the axial stress due to shear steel bars in the ECS x-direction Sig-zz: Stress in the ECS z-direction Sig-xz (shear): Sum of shear stresses due to shear force and shear steel bars Sig-xz (torsion): Shear stress due to torsion Sig-xz (bar): Shear stress due to shear steel bars Sig-Is (shear): Transverse stress due to shear force Sig-Is (shear+torsion): Transverse stress due to torsion and shear force Sig-Ps1: Maximum principal stress Sig-Ps2: Minimum principal stress

4.3 Check principal stress at a construction stage

 ps   ta

(1.65)

4.4 Check the principal stress results at a construction stage 4.4.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design>PSC Design Result Tables>Principal stress at a construction stage …

[Fig.1.48] Result table for principal stress at a construction stage Elem: Element number. Part: Check location (I-End, J-End) of each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: Principal stress check for construction stages. Sig_P1: Principal Stress at the left top of top flange. Sig_P2: Principal Stress at the right top of top flange. Sig_P3: Principal Stress at the right bottom of bottom flange.

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Design Guide for midas Civil

Sig_P4: Principal Stress at the left bottom of bottom flange. Sig_P5: Principal Stress at the top of left web.(at Z1 Level) Sig_P6: Principal Stress at the top of right web.(at Z1 Level) Sig_P7: Principal Stress at the neutral axis in left web.(at Z2 Level) Sig_P8: Principal Stress at the neutral axis in right web.(at Z2 Level) Sig_P9: Principal Stress at the bottom of left web.(at Z3 Level) Sig_P10: Principal Stress at the bottom of right web.(at Z3 Level) Sig_MAX: The maximum Principal stress among P1-P10. Sig_AP: Allowable principal stress at neutral axis in the web.

4.2.2 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1.49] Excel Report for principal stress at a construction stage

5. Principal stress at service loads (Excluding torsional shear stress) Find the maximum principal tensile stress among the stress check points 1~10 of the crosssection at service loads and compare it to the allowable stress. In other words, maximum principal tensile stress ≤ allowable stress. Here the shear effect due to torsion is excluded.

2.5.1 Allowable tensile stress The Code (Table .9.4.2.2-1) presents the following equation of allowable tensile stress for Segmentally Constructed Bridges:

 ta  0.110 fc'

(1.66)

AASHTO LRFD14 (5.9.4.2.2)

midas Civil applies the above equation for both Segment and Non-segment.

2.5.2 Maximum principal stress The maximum principal tensile stress for each point at a construction stage is computed as follows:  ps 

1  x   z   2 

 x   z 2  4 s   t   p 2  

(1.67)

where, σx : Sum of axial stresses in ECS x-direction σz : Sum of axial stresses in ECS z-direction τs : Shear stress due to shear. τt : Shear stress due to torsion. τp : Shear stress due to shear reinforcement.

5.2.1 Beam stresses of PSC The stress components to compute the maximum principal tensile stress can be checked from the Result Table below:

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Refer to 3.4.2.1 Beam stresses of PSC.

5.3 Check principal stress at service loads

 ps   ta

(1.68)

5.4 Check the principal stress results at service loads 5.4.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design>PSC Design Result Tables > Result table for principal stress at service loads(excluding torsional shear stress)…

[Fig.1.50] Result table for principal stress at service loads (excluding torsional shear stress) Elem: Element number. Part: Check location (I-End, J-End) of each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: Principal stress check for construction stages. Sig_P1: Principal Stress at the left top of top flange. Sig_P2: Principal Stress at the right top of top flange. Sig_P3: Principal Stress at the right bottom of bottom flange. Sig_P4: Principal Stress at the left bottom of bottom flange. Sig_P5: Principal Stress at the top of left web.(at Z1 Level) Sig_P6: Principal Stress at the top of right web.(at Z1 Level) Sig_P7: Principal Stress at the neutral axis in left web.(at Z2 Level) Sig_P8: Principal Stress at the neutral axis in right web.(at Z2 Level) Sig_P9: Principal Stress at the bottom of left web.(at Z3 Level) Sig_P10: Principal Stress at the bottom of right web.(at Z3 Level) Sig_MAX: The maximum Principal stress among P1-P10. Sig_AP: Allowable principal stress at neutral axis in the web.

5.4.2 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1.51] Excel report for principal stress at service loads (excluding torsional shear stress)

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Design Guide for midas Civil

6. Principal stress at service loads Find the maximum principal tensile stress among the stress check points 1~10 of the crosssection at service loads and compare it to the allowable stress. Here both shear and torsion will be reflected in the stress calculation. In other words, maximum principal tensile stress ≤ allowable stress.

6.1 Allowable tensile stress The Code (Table .9.4.2.2-1) presents the following equation of allowable tensile stress for Segmentally Constructed Bridges: AASHTO LRFD14 (5.9.4.2.2)

 ta  0.110 fc'

(1.69)

midas Civil applies the above equation for both Segment and Non-segment.

6.2 Maximum principal stress The maximum principal tensile stress for each point at a construction stage is computed as follows:  ps 

1  x   z   2 

 x   z 2  4 s   t   p 2  

(1.70)

where, σx : Sum of axial stresses in ECS x-direction σz : Sum of axial stresses in ECS z-direction τs : Shear stress due to shear. τt : Shear stress due to torsion. τp : Shear stress due to shear reinforcement.

6.2.1 Beam stresses of PSC The stress components to compute the maximum principal tensile stress can be checked from the Result Table below: Refer to 3.4.2.1 Beam stresses of PSC.

6.3 Check principal stress at service loads

 ps   ta

(1.71)

6.4 Check the principal stress results at service loads 6.4.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design>PSC Design Result Tables>Principal stress at service loads…

[Fig.1.52] Result table for principal stress at service loads

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Elem: Element number. Part: Check location (I-End, J-End) of each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: Principal stress check for construction stages. Sig_P1: Principal Stress at the left top of top flange. Sig_P2: Principal Stress at the right top of top flange. Sig_P3: Principal Stress at the right bottom of bottom flange. Sig_P4: Principal Stress at the left bottom of bottom flange. Sig_P5: Principal Stress at the top of left web.(at Z1 Level) Sig_P6: Principal Stress at the top of right web.(at Z1 Level) Sig_P7: Principal Stress at the neutral axis in left web.(at Z2 Level) Sig_P8: Principal Stress at the neutral axis in right web.(at Z2 Level) Sig_P9: Principal Stress at the bottom of left web.(at Z3 Level) Sig_P10: Principal Stress at the bottom of right web.(at Z3 Level) Sig_MAX: The maximum Principal stress among P1-P10. Sig_AP: Allowable principal stress at neutral axis in the web.

6.4.2 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1.53] Excel report for principal stress at service loads

7. Check crack The limit state for crack can be checked by comparing the applied spacing of tensile reinforcement with the maximum spacing of reinforcement. In accordance with AASHTO-LRFD, the crack limit shall be checked for the “mild steel reinforcement”. The applied spacing of tensile reinforcement shall be compared to the computed maximum spacing of reinforcement. In other words, applied spacing of reinforcement ≤ maximum spacing of reinforcement

7.1 Maximum spacing of reinforcement The maximum spacing of reinforcement is computed as follows:

smax 

700 e  2d c  s f ss

s  1 

dc 0.7(h  dc )

(1.72)

(1.73)

dc: thickness of concrete cover measured from extreme tension fiber to center of the flexural reinforcement located closest thereto (in.) fss: tensile stress in steel reinforcement at service limit state (ksi) fss is computed according to the following steps: 1) Compute the concrete stress (fcs) at the location of tensile reinforcement using

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Design Guide for midas Civil

AASHTO LRFD14 (5.7.3.4) (Eq. 5.7.3.4-1)

the extreme fiber tension stress and the extreme fiber compression stress. 2) Compute the strain of concrete (εcs=fcs/Ec) with regard to fcs. 3) Compute fss (fss = Es εcs). γe :exposure factor 1.00 for Class 1 exposure condition 0.75 for Class 2 exposure condition Exposure condition can be entered in the PSC Design parameters dialog.

▶ PSC> Design Parameter> Parameters…

[Fig.1.54] PSC Design parameter Dialog - Exposure Factor

7.2 Spacing of reinforcement The spacing of Longitudinal reinforcement entered from Section Manager>Reinforcements shall be used as the applied spacing of tensile reinforcement. ▶ Model>Properties>Section Manager>Reinforcements

Spacing of reinforcements

Top and bottom reinforcement data

[Fig.1.55] Input Longitudinal reinforcement

When the positive moment is checked, the spacing of bottom reinforcements will be used. When the negative moment is checked, the spacing of top reinforcements will be used.

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7.3 Check the crack width at service loads 7.3.1 by Result Tables The results can be checked as shown in the table below. ▶ Design>PSC Design>PSC Design Result Tables>Check crack width at service loads…

[Fig.1.56] Result table for crack width at service loads Elem: Element number Part: Check location (I-End, J-End) of each element Top/Bottom: At top of element, at bottom of element LCom. Name: Load combination name. Type: produce maximum and minimum member force components for the load combinations including moving load cases or settlement load cases. Check : OK/NG FT : Stress at the top (+ compression, - tension) FB : Stress at the bottom (+ compression, - tension) s_use : The spacing of tensile reinforcement in use. s_max : The calculated maximum spacing of reinforcement.

If the compressive stress is applied at the design check location, the crack check is omitted. For the Composite Section, the deck crack is ignored. Therefore, the crack check at the slab top of the composite section is not provided in midas Civil. **Degree of Continuity at Various Limit States(5.14.1.4.5)

7.3.2 by Excel Report Verification results can be checked in MS Excel report as shown in the figure below. ▶ Design>PSC Design>PSC Design Calculation…

[Fig.1.57] Excel report for crack width at service loads

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Design Guide for midas Civil

Chapter 2.

Steel Composite Girder Design AASHTO LRFD 6th (2012)

Chapter 2.

Steel Composite Girder Design (AASHTO LRFD 12) Steel composite girders need to be designed to satisfy the following limit states.

Steel Composite I-Girder Bridge Check Strength Limit State Check Service Limit State Check Fatigue Limit State Check Constructability Check Shear Connector Check Longitudinal Stiffener

Chapter 2. Steel Composite Girder Design : AASHTO-LRFD 4thand6th (2007 & 2012)

Introduction 1. AASHTO LRFD 07 and 12 Steel Composite 1.1 Check List of AASHTO LRFD 07 and 12Steel Composite For AASHTO LRFD 07 and 12 Steel Composite Design, Limit State Design is applied. The criteria that Steel Composite Section must follow for Limit State Design is as follows. (1) Cross-Section Proportion Limit State Review on section properties, e.g. width-thickness ratio (2) Strength Limit State Review on flexure strength, shear strength and torsional strength (3) Service Limit State Review on permanent deformation (4) Constructibility Review on shear and flexure occurring from load combinations during construction stages (5) Fatigue Limit State Review on fatigue in steel and concrete materials in Steel Composite girder

1.2 Classification of Steel Composite Steel Composite section can be categorized by the following classification groups. (1) Section Shape Type There are three main section shape types in midas Civil; I, Box and Tub shapes. In the case of box and tub sections, there are two more cases, single or multiple box section. [Table2. 1] Section Shape Type

I

Box

Tub

(2) Moment Type : Positive / Negative For continuous beams, negative moments may occur around interior supports. Design code may apply different formulas for these cases.

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57

(3) Bridge Type : Straight / Curved Based on the horizontal alignment of a bridge, it can be classified as either straight or curved. The program recognizes curved bridges based on the input of the girder radius for each component. (4) Compact Type : Compact / Noncompact / Slender [Table2.2] Steel Section Classification

Type

Compact

Noncompact

Slender

Description A composite section in positive flexure, which satisfies specific steel grade, web slenderness, and ductility requirements, is capable of developing a nominal resistance exceeding the moment at first yield, but not to exceed the plastic moment. A composite section in positive flexure for which the nominal resistance is not permitted to exceed the moment at first yield. Cross-Section of a Compression member composed of plate components of sufficient slenderness such that local buckling in the elastic range will occur.

1.3 Stiffeners of Steel Composite The program considers transverse and longitudinal stiffeners. [Table2 3] Types of Stiffeners

Type

Transverse Stiffeners

Description Transverse stiffeners are usually provided to increase shear resistance by tension field action. These work as anchors for the tension so that post buckling shear resistance can be developed. It should be noted that elastic web shear buckling cannot be prevented by transverse stiffeners.

Longitudinal Stiffeners

Longitudinal stiffeners may be provided to increase flexural resistance by preventing local buckling. These work as restraining boundaries for compression elements so that inelastic flexural buckling stress can be developed in a web. It consists of either a plate welded longitudinally to one side of the web, or a bolted angle.

[Fig.2.1] Longitudinal Stiffener and Transverse Stiffener

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Compact Type AASHTO LRFD 12 (6.2)

2. Considerations Steel Composite Design 2.1 Construction Stage for steel composite During the construction of a steel composite bridge, the steel girder is constructed before the construction of the concrete deck of the upper part of the structure. The steel composite section is divided into three major steps. [Table2.4] Construction Stage for Steel Composite Section

Construction stage for steel composite section

Description

Only Steel Girder (non-composite)

Only the steel girder has been constructed.

Steel girder and concrete deck as load (non-composite)

Although the concrete deck has been constructed, it has not hardened yet. Therefore, the weight of the wet concrete is applied as a load condition.

Steel girder and concrete deck as member (composite)

After concrete is hardened, the strength and stiffness are formed. Hereafter, the steel girder and concrete deck work as a complete composite section.

In order to find and portray the Steel Composite Section Design Process within the program, utilize the Construction Stage function.

2.2 Time Dependent Material ▪ Steel composite section is composed of steel and concrete. Concrete is a time dependent material and transforms due to creep and shrinkage. Also, the restraints imposed by the shear connectors cause additional stresses within the composite section. Therefore, time dependent characteristics (creep and shrinkage) must be taken into consideration. ▪ Modular ratio is the ratio of modulus of elasticity of steel to that of concrete. The short-term modular ratio "n" is used for transient loads in the program. Long-term modular ratio "3n" is used for permanent loads acting after composite action. For normal-weight concrete, AASHTO-LRFD 07 and 12 recommend the values of the short-term modular ratio.

3. Calculation of Plastic Moment and Yield Moment ▪ The plastic moment Mp for a composite section is defined as the moment that causes yielding in steel section and reinforcement and uniform stress distribution of 0.85 in compression concrete slab. In positive flexure regions, the contribution of reinforcement in concrete slab is small and can be neglected. ▪ The yield moment, My, for a composite section is defined as the moment that causes the first yielding in one of the steel flanges or the moment at which an outer fiber first attans the yield stress. My is the sum of the moments applied to the pre-composite steel section, the short-term composite concrete and steel section, and the long-term composite concrete and steel section.

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3.1 Plastic Moment(Mp), Yield Moment( My) in Positive Flexure (1) Cross section proportions I section and Box/Tub steel composite sections must satisfy the following criteria regarding cross section proportions. If the conditions have not been met after the design has been completed, it will be indicated as an “NG” on the design report generated.

1) Web Proportions [Table 2.5] Web Proportions

Case

Condition

Web with longitudinal stiffener

D  150 tw

Web without longitudinal stiffener

D  300 tw

WEB For I section AASHTO LRFD 12 (6.10.2.1.1-1) (6.10.2.1.2-1)

For Box/Tub Section AASHTO LRFD 12 (6.11.2.1.2-1) (6.11.2.1.3-1)

2) Flange Proportions [Table 2.6] Flange Proportions

Section Type I

bf 2t f

Box / Tub

 12.0

bf

D bf  6

2t f

0.1 

I yc I yt

 12.0

bf 

t f  1.1tw

Flange For I section AASHTO LRFD 12 (6.10.2.2-1) (6.10.2.2-2) (6.10.2.2-3) (6.10.2.2-4)

D 6

For Box/Tub Section AASHTO LRFD 12 (6.11.2.2-1) (6.11.2.2-2) (6.11.2.2-3)

t f  1.1tw

 10

Where, Iyc : moment of inertia of the compression flange of the steel section about the vertical axis in the plane of the web Iyt : moment of inertia of the tension flange of the steel section about the vertical axis in the plane of the web

I yc 

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t fc b fc 12

3

,

I yt 

t ft b ft 12

3

(2.1)

(2) Section Classification

Section Classification AASHTO LRFD 12 (6.10.6.2)

Section Classification of Positive Flexure Moment 6.10.6.2

Yes

Straight Bridge?

min( F yc , F yt )  70 . 0 ksi

No :Curved Bridge

d / t w  150 2

D cp tw

 3 . 76

Es F yc

No

Yes

Compact Section

Noncompact Section

End [Fig.2.2] Section Classification of Negative Positive Moment Where, 𝐷𝑐𝑝 : depth of the web in compression at the plastic moment determined as per Article D6.3.2

▪ The Section Classifications of I, Box, Tub are all the same. ▪ In a positive moment, the following ductility conditions must be met at all times. If not, the program will show NG.

Dp  0.42Dt

(2.2)

Ductility AASHTO LRFD 12 (6.10.7.3)

Where, 𝐷𝑝 : Distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment 𝐷𝑡 : Total depth of the composite section

(3) Plastic Moment in Positive Moment (MP) If the positive moment is applied on a compact section, MP should be calculated as shown in Table 2.7.

Plastic Moment AASHTO LRFD 12 (D6.1)

[Fig.2.3] Case of calculation of Mp in positive moment

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̅ and Mp for section in Positive Flexure [Table 2.7] Calculation of 𝐘

Case

Ⅰ

PNA

In Web

̅ and Y

Condition

Pt  Pw  Pc  Ps  Prb  Prt

Mp for section

 D  P  Pc  Ps  Prt  Prb Y   [ t  1] Pw 2

P  2 M   w [Y  (t  Y ) 2 ]  2D   [ Ps d s  Prt d rt  Prb d rb  Pw d w  Pt d t ]

t c Pw + Pt − Ps − Prt − Prb ̅ Y = ( )[ + 1] 2 Pc Ⅱ

In Top flange

Pt  Pw  Pc  Ps  Prb  Prt

P  2 M   c [Y  (t  Y ) 2 ]  2t c   [ Ps d s  Prt d rt  Prb d rb  Pw d w  Pt d t ]

Pt  Pw  Pc

Ⅲ

Concrete Deck, Below Prb

c    rb  Ps  Prb  Prt  ts 

Pc + Pw + Pt − Prt − Prb ̅ Y = (t s ) [ ] Ps Y 2P s M   2t s 

   

 [ Prt d rt  Prb d rb  Pc d c  Pw d w  Pt d t ]

Ⅳ

Ⅴ

Concrete Deck, at Prb

Pt  Pw  Pc  Prb

c    rb  Ps  Prt  ts 

Concrete Pt  Pw  Pc  Prb Deck, c  Above Prb   rt  Ps  Prt t  Below Prt  s 

Y  C rb

 Y 2P s M   2t s 

   [ Prt d rt  Pc d c  Pw d w  Pt d t ]  

 P  Pw  Pt  Prt  Prb  Y  (t s )  c  Ps    Y 2P s M   2t s 

   

 [ Prt d rt  Prb d rb  Pc d c  Pw d w  Pt d t ]

Ⅵ

Ⅶ

Concrete Deck, at Prt

Concrete Deck, Above Prt

Pt  Pw  Pc  Prb  Prt

c   rt  ts

  Ps 

Pt  Pw  Pc  Prb  Prt

c   rt  ts

  Ps 

Y  C rt

 Y 2P s M   2t s 

   [ Prb d rb  Pc d c  Pw d w  Pt dt ]  

P  P  P  P  P  Y  (t s )  rb c w t rt  Ps    Y 2P s M   2t s 

   

 [ Prt drt  Prbdrb  Pc dc  Pwd w  Pt dt ]

Where,

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in Positive Flexure AASHTO LRFD 12 (Table D6.1-1)

Mp

+

𝑑𝑟𝑡 : Distance from the plastic neutral axis to the centerline of the top layer of longitudinal concrete deck. 𝑑𝑟𝑏 : Distance from the plastic neutral axis to the centerline of the bottom layer of longitudinal concrete deck. 𝑑𝑡 : Distance from the plastic neutral axis to the midthickness of the tension flange. 𝑑𝑤 : Distance from the plastic neutral axis to middepth of the web. 𝑑𝑐 : Distance from the plastic neutral axis to midthickness of the compression flange. 𝑑𝑠 : Distance from the plastic neutral axis to midthickness of the concrete deck. 𝑃𝑟𝑡 = 𝐹𝑦𝑟 𝐴𝑟𝑡

(by reinforcement)

𝑃𝑟𝑏 = 𝐹𝑦𝑟 𝐴𝑟𝑏

(by reinforcement)

𝑃𝑡 = 𝑏𝑓𝑡 𝑡𝑓𝑡 𝐹𝑦𝑡 𝑃𝑤 = 𝐷 𝑡𝑤 𝐹𝑦𝑤 𝑃𝑐 = 𝑏𝑓𝑐 𝑡𝑓𝑐 𝐹𝑦𝑐 𝑃𝑠 = 0,85 𝑓𝑐𝑘 𝑏𝑠 𝑡𝑠

(by steel girder) (by steel girder) (by steel girder) (by concrete slab)

(4) Yield Moment in Positive Moment (My) When a positive moment is applied on a compact section, My is calculated as shown in Equation 2.3.

M y  Min(M yTop , M yBot )

(2.3)

My AASHTO LRFD 12 (D6.2.2)

Where, MyTop : Yield Moment of Top Flange MyBot : Yield Moment of Bottom Flange

Fy 

M D1 M D2 M AD   STop STop(3n ) STop( n )

(2.4)

M yTop  M D1  M D 2  M AD Fy 

M D1 M D 2 M   AD S Bot S Bot (3n ) S Bot ( n )

(2.5)

Fy AASHTO LRFD 12 (Eq. D6.2.2-1)

M_ytop AASHTO LRFD 12 (Eq. D6.2.2-2)

M yBot  M D1  M D 2  M AD Where, S: Non-composite section modulus S3n : Long-term composite section modulus Sn : Short-term composite section modulus MD1 : Moment of non-composite section MD2 : Moment of long-term composite section MAD : Additional yield moment of short-term composite section

3.2 Plastic Moment(Mp), Yield Moment(My) in Negative Flexure For I sections in negative flexure, Mp and My are calculated. (1) Cross Section Proportions For negative flexure, cross section proportions must meet the following requirements. If the program does not meet the requirements, NG will be reported after the design.

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63

1) Web Proportions [Table 2.8] Web Proportions

Case

Condition

D  150 tw D  300 tw

Web with longitudinal stiffeners

Web without longitudinal stiffeners

2) Flange proportions [Table 2.9] Flange Proportions

Section Type :

bf 2t f

I / Box / Tub

 12.0

bf 

D 6

t f  1.1t w

0.1 

I yc I yt

 10

(2) Section Classification Section Classification AASHTO LRFD 12 (6.10.6.2.3)

[Fig.2.4] Section Classification of Negative Flexure Moment Where, 𝐷𝑐 : Depth of the web in compression in the elastic range. Iyc : moment of inertia of the compression flange of the steel section about the vertical axis in the plane of the web Iyt : moment of inertia of the tension flange of the steel section about the vertical axis in the plane of the web

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Design Guide for midas Civil

▪ Minimum Negative Flexure Concrete Deck Reinforcement Under negative moment, concrete deck has to meet the minimum rebar ratio requirement. Once the requirements of Equation 2.6 are satisfied, the next design step can be taken.

Ars  0.01Adeck

(2.6)

(3) Plastic Moment in Negative Moment (Mp) Under negative moment, Mp is only calculated when Appendix A6 is used. Mp is calculated by either of the two following methods. Please refer to Table 2.10 for the equations.

Plastic Moment AASHTO LRFD 12 (D6.1)

[Fig.2.5] Case of calculation of Mp in Negative Moment

̅ and Mp for section in Negative Flexure [Table 2.10] Calculation of 𝐘

Case

Ⅰ

Ⅱ

PNA

In Web

In Top flange

Where, 𝑃𝑟𝑡 = 𝐹𝑦𝑟𝑡 𝐴𝑟𝑡 𝑃𝑟𝑏 = 𝐹𝑦𝑟𝑏 𝐴𝑟𝑏 𝑃𝑐 = 𝐹𝑦𝑐 𝑏𝑐 𝑡𝑐 𝑃𝑤 = 𝐹𝑦𝑤 𝐷𝑡𝑤 𝑃𝑡 = 𝐹𝑦𝑡 𝑏𝑡 𝑡𝑡

̅ Y and

Condition

Mp for section in Negative Flexure AASHTO LRFD 12 (Table D6.1-2)

Mp

D Pc − Pt − Prt − Prb ̅ Y = ( )[ + 1] 2 Pw Pc  Pw  Pt  Prb  Prt

Pw 2 ̅ + (D − ̅ [Y Y)2 ] 2D +[Prt drt + Prb drb + Pt dt + Pc dc ] Mp =

t t Pw + Pc − Prt − Prb ̅ Y = ( )[ + 1] 2 Pt Pc  Pw  Pt  Prb  Prt

Pt 2 ̅ + (t t − Y ̅)2 ] [Y 2t +[Prt drt + Prb drb + Pw dw + Pc dc ]

Mp =

(by reinforcement) (by reinforcement) (by steel girder) (by steel girder) (by steel girder)

(4) Yield Moment in Negative Moment (My) When Appendix A6 is used for negative flexure, My is calculated and utilized. My is calculated as shown below in Equation 2.7.

M y  Min(M yTop , M yBot )

My in Negative Moment AASHTO LRFD 12 (D6.2.3)

(2.7)

Where, MyTop : Yield Moment of Top Flange MyBot : Yield Moment of Bottom Flange

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65

M D1 M D 2 M   AD STop STop( R ) STop( R )

(2.8)

M yTop  M D1  M D 2  M AD

(2.9)

M D1 M D 2 M   AD S Bot S Bot ( R ) S Bot ( R )

(2.10)

Fy 

Fy 

M yBot  M D1  M D 2  M AD Where, SR : Long-term composite section modulus with longitudinal reinforcements

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(2.11)

Chapter 2. Steel Composite Girder Design : AASHTO-LRFD 4thand6th (2007/2012)

Modeling and Design Variables 1. Modeling Design Variables In this chapter, the design variable values, the meaning behind the design requirements, and the design process for Steel Composite Design in midas Civil are explained.

1.1. Composite Section Data The steel composite section is mainly composed of steel girder and concrete slab. Stiffeners can be added to steel girder section while longitudinal reinforcement can be added to reinforce concrete slab. In this section, the input methods for these sections and the meaning and application of design variables are explained. Contents

Explanation

1.1.1 Composite Section (1) Composite Section Data

1.1.1 Composite Section (1) Composite Section Data 1) Girder Num ▶ Properties > Section > Section Properties> Add > When the Girder Num is inputted as more than Composite Tab 1, the moment of inertia of area in transverse direction (Izz) is increased assuming that slab behaves in consistence with each girder in analysis. When the number of girder is inputted as more than 1, it is excluded from the consideration of design. For design, Girder Num must be inserted as 1. In such case, cross beams should be modelled to consider the transverse stiffness instead of increasing the girder number. 2) The value of Bc for the slab is used as the effective width of the concrete deck. 3) Multiple Modulus of Elasticity Option To design the steel composite section, the modulus of elasticity for short-term and longterm effect in creep and shrinkage can be input. The modulus of elasticity input here is applied for construction stage analysis of Steel Composite section as shown in [Fig.2.7]. [Fig.2.6] Section Data Dialog Box

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Contents

Explanation

[Fig.2.7] Elastic Modulus ratio for Construction Stage

(2) Section Stiffener ▶ Properties > Section > Section Properties> Add > Composite Tab > Stiffeners Button...

(2) Section Stiffener (Longitudinal) 1) Types of longitudinal stiffeners that are useable are Flat, Tee, and U-Rib. 2) For I sections, stiffeners can be added on either side of the web. For Box/Tub sections, upper and lower flanges can be installed as well as the web panel. 3) When the check box under c column is checked on, the stiffness value of the stiffener is considered in analysis. Otherwise, the value is not considered for analysis. Regardless of whether or not the check box is checked on or off, longitudinal stiffeners are considered in design. Based on the assignment of longitudinal stiffener, Rb, web load shedding factor varies for stiffened web/unstiffened web. It is also required for classifying the interior panels in shear check as stiffener/unstiffened.

[Fig.2.8] Section Stiffener Dialog Box

1.1.2 Longitudinal Reinforcement ▶Design > Composite Design > Longitudinal Reinforcement ...

1.1.2 Longitudinal Reinforcement In a steel composite section, the longitudinal reinforcements are arranged within the concrete deck. The strength is calculated as shown in Table 2.11. [Table 2.11] Applicability of material under the calculation of strength

Positive Flexure

Negative Flexure

Concrete Slab

Applied

None

Reinforce -ment

None

Applied

Case

Figure

[Fig.2.9] Longitudinal Reinforcement Dialog Box

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Design Guide for midas Civil

Contents 1.1.3 Transverse Stiffener (1) Transverse Stiffener ▶ Design > Composite Design > Transverse Stiffener ...

Explanation 1.1.3 Transverse Stiffener Figure 2.10 shows the window in which users can arrange transverse stiffeners in steel composite section. When the transverse stiffeners are installed, the existence and spacing between stiffeners determine whether the web is stiffened or unstiffened under strength limit state. Tension field action in Shear check for Strength Limit State is considered only for stiffened interior panels.

[Fig.2.10] Transverse Stiffener Dialog Box

[Fig.2.11] Transverse Stiffener Parameters

(1) Stiffener Type 1) One / Two Stiffener Option Button Choose between one or two stiffeners. The two stiffener option is available for I/Box/Tub sections.

[Fig.2.12] Stiffener Type Dialog Box

2) Pitch (do) Pitch refers to transverse stiffener spacing. At the strength limit state, this can be used to distinguish between stiffened and unstiffened webs or calculate shear strength of the web.

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1.2. Design Material Data For the design of steel composite section, construction stage and time dependent material properties of concrete must be defined. In this section, the input method for concrete's time dependent properties and steel composite section material information is defined. Contents

Explanation

1.2.1 Time Dependent Material (1) Creep/Shrinkage ▶ Properties > Creep/Shrinkage ...

Time

Dependent

Material

1.2.1 Time Dependent Material (1) Creep/Shrinkage > The time dependent properties of concrete, such as creep and shrinkage, are defined. During construction stage analysis of bridges, these properties are utilized for concrete material. During analysis, they are reflected in the calculation of member forces but not reflected in the design of the steel composite section.

[Fig.2.13] Add/Modify Time Dependent Material Dialog Box (Creep/Shrinkage)

(2) Comp. Strength ▶ Properties > Time Dependent Material > Comp. In order to reflect the change in the modulus of elasticity of the time dependent property of Strength ... concrete, the change in compressive strength or modulus of elasticity is defined. (2) Comp. Strength

Aging effects may vary for each construction stage since concrete is poured at different locations. The varying aging effects are reflected in the calculation of the member force but not in the design of the composite sections.

[Fig.2.14] Add/Modify Time Dependent Material Dialog Box (Compression Strength)

1.2.2 Modify Composite Material (1) Modify Composite Material ▶ Design > Composite Design > Design Material ...

1.2.2 Modify Composite Material The material utilized for steel composite sections are provided in the SRC material properties. The materials should be defined as SRC Type.

(1) Modify Composite Material Figure 2.15 shows the dialog box where users

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Design Guide for midas Civil

Contents

Explanation can type in material characteristics for the steel composite section design. The material property values entered will have a priority over the values entered in Material Data dialog box. 1) Steel Girder Section - Steel □ Hybrid Factor Hybrid factor is considered in the case where flanges and web have different material properties. 2) Concrete of Concrete slab 3) Steel materials of Concrete slab

[Fig.2.15] Modify Composite Material Dialog Box

(2) Hybrid Factor

(2) Hybrid Factor(Rh) When the check box for Hybrid Factor is selected, icon on the right is activated. The different materials for the top and bottom flanges and web of the steel girder can be defined. Hybrid Factor (Rh) is determined based on these material information.

[Fig.2.16] Hybrid Factor Dialog Box

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1.3. Design Parameters for Composite Section Contents 1.3.1 Design Parameter

Explanation 1.3.1 Design Parameter

▶ Design > Composite Design > Design Parameters ... (1) Strength Resistance Factor Strength Resistance Factor is defined. By clicking , the resistance factors are automatically set to the default values defined in AASHTO LRFD 12. The values also may be modified or entered manually. (2) Girder Type for Box/Tub Section □ Consider St.Venant Torsion and Distortion Stress If the Multiple Box Sections option is selected, lateral bending stress is considered in accordance with St.Venant Torsion and Distortion Stress. If the Single Box Sections option is selected, the lateral bending stress is always considered.

[Fig.2.17] Composite Steel Girder Design Parameter Dialog Box

(3) Options For Strength Limit State □ Appendix A6 for Negative Flexure Resistance in Web Compact/Noncompact Sections If this option is checked, Appendix A6 is applied for the flexure strength of straight composite Isections in negative flexure with compact/ noncompact webs. Use of Appendix A6 is optional in accordance with the code as shown below.

[Fig.2.18] Negative Flexure Resistance Compact/Noncompact Sections

in

Web

□ Mn≤1.3RhMy in Positive Flexure and Compact Sections(6.10.7.1.2-3) Before deciding, whether to apply this check or not, following conditions need to be manually verified:

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Contents

Explanation -

-

-

The span under consideration and all adjacent interior pier sections satisfy the requirements of Article B6.2, The appropriate value of θRL from Article B6.6.2 exceeds 0.009 radians at all adjacent interior-pier sections In which case the nominal flexural resistance of the section is not subject to the limitation of Eq. 6.10.7.1.2-3.

If the above three conditions are not satisfied for the compact sections under positive flexure in a continuous span, the Mn value is restricted to 1.3RhMy. □ Post-buckling Tension-field Action for Shear Resistance (6.10.9.3.2) If this option is checked, post buckling resistance due to tension field action is considered in the nominal shear resistance of an interior stiffened web panel. If not, Vn is taken as, CVP. where, C = ratio of shear-buckling resistance to the shear yield strength Vp = plastic shear force.

(4) Design Parameters Design and result outputs are generated for the limit states checked in the Design Parameters.

1.3.2 Unbraced Length ▶ Design > Composite Design > Unbraced Length ...

1.3.2 Unbraced Length Unbraced length factor for steel composite section is considered. The value input here has higher priority than the value calculated from Span Group. (1) Lb Lateral Unbraced Length is used to calculate lateral torsional buckling resistance in compression flange of I Girder or top flange of Tub Girder. If the lateral unbraced length is not added, the program will use span lengths. If span lengths are not defined either, the lateral unbraced length is applied for the corresponding member length.

[Fig.2.19] Unbraced Length Dialog Box

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Contents 1.3.3 Shear Connectors ▶ Design > Composite Design > Shear Connectors ...

Explanation 1.3.3 Shear Connectors In this program, studs are used for shear connectors. The parameters used for calculation are shown below. (1) Category Category defined by 75yr-(ADTT)SL equivalent to Infinite Life (Table 6.6.1.2.3-2) (2) Fu Shear Resistance of Shear Connector (3) Shear Connector Parameters

[Fig.2.21] Shear Connector Parameters

[Fig.2.20] Shear Connector Dialog Box

(4) Length Between Maximum Moment and Zero Moment The Length between Maximum Moment and Zero Moment needs to be inputted by users to verify pitch as per strength limit state. (5) Nominal Shear Force Calculation (6.10.10.4.2) One of the two conditions needs to be selected for the calculation of the nominal shear force, P which is applied for the verification of pitch at the strength limit state.

1.3.4 Fatigue Parameter ▶ Design > Composite Design > Fatigue Parameter ...

1.3.4 Fatigue Parameter (1) Category Category defined by 75ye-(ADTT)SL equivalent to infinite life (Table 6.6.1.2.3-2) (2) (ADTT)SL Number of trucks per day in a single-lane averaged over the design life (3.6.1.4.2) (ADTT)SL can be manually calculated as per 3.6.1.4.2-1. (3) N Number of stress range cycles per truck passage Value can be taken from Table 6.6.1.2.5-2. (4) Longitudinal Warping Stress Range

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Contents

Explanation For the verification of fatigue, flexure stress is calculated as the summation of Longitudinal Bending Stress Range and Longitudinal Warping Stress Range. By choosing the Auto-Calculation option, fatigue vertical bending moment is simply increased by 10% for the longitudinal warping stress. Longitudinal warping stress range can be manually calculated as per BEF (Beam on Elastic Foundation) analogy presented by Wright and Abdel-Samad. The designer guide to Box Girder by Bethlehem Steel Corporation also presents this method. Detailed calculations can be seen in Design Example 5: Three Span Continuous Curved Composite Tub-Girder Bridge (page 85-94).

[Fig.2.22] Fatigue Parameters Dialog Box

Software calculations do not account for Transverse Bending Stress due to Distorsion. Therefore, transverse bending stress range at the top or bottom corners of the tub section need to be manually checked with the nominal fatigue resistance. If the User Input option is selected, longitudinal bending stress range is summated with the inputted value of the Longitudinal Warping Stress Range for top or bottom flange depending upon the flexure condition at the section. These distorsion stresses are considered only for the sections having box flange as those are the section in which the torsion is considered.

1.3.5 Span Information

1.3.5 Span Information ▶ Structure > Wizard > Composite Bridge > Span The elements of composite sections are defined as Information ... one Span Group. The Span Group will serve the following functions. (1) Finding the most critical parts of the group unit and providing the corresponding results in the Span Checking table. Refer to Chapter 7 of "Steel Composite Design Result" for more information. (2) Calculation of Unbraced Length When assigning a span group, support properties are considered for calculating the unbraced length. The unbraced length can also be manually inputted once the corresponding support conditions under the support column are selected. Using the span parameters inputted, the unbraced length can be calculated automatically. However, if the unbraced length is inputted in

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Explanation Section 1.3.2, this value will be applied as the unbraced length first.

(3) End web panels For each element, location of support, if any, can be identified as i or j. The stiffened webs with supports are identified as end panels. Also, the elements that are assigned with i or j for the support are considered as end panels. Tension field action is not considered for the end panel in Shear Check.

[Fig.2.23] Span Information Dialog Box

1.3.6 Curved Bridge Information ▶ Design > Composite Design > Curved Bridge Info ...

1.3.6 Curved Bridge Information Once the girder radius value of the element units in the steel composite section is entered, the corresponding elements are categorized as curved bridges. (1) Radius is used for the review of shear connectors' pitch and the moment of inertia of area for the longitudinal stiffener attached to web. The curve type needs to be determined as convex or concave so the program determines whether the longitudinal stiffener is on the side of the web away or toward from the center of the curvature. Lateral bending stress due to curvature is obtained from the analysis results and not using V-Load equation.

[Fig.2.24] Curved Bridge Information Dialog Box

(2) If convex, left stiffener is on the side of the web away from the center of curvature and right stiffener is on the side of the web toward the center of curvature. If concave, the opposite case of the convex is applied. Please refer to the table below for the equations applied to each case.

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Explanation [Table 2.12] Curvature Correction Factor for Longitudinal Stiffener

Case Left Stiffener

 

Z 1 6

(6.10.11.3.3-3)

Convex Right Stiffener



Z 1 12

(6.10.11.3.3-4) Left Stiffener



Z 1 12

(6.10.11.3.3-4)

Concave Right Stiffener

 

Z 1 6

(6.10.11.3.3-3) where, β : Curvature correction factor for longitudinal stiffener rigidity Z : Curvature Parameter

1.3.7 Deck Overhang Loads

1.3.7 Deck Overhang Loads Design parameters for the Deck Overhang load can be entered. The fl value obtained from F(Distributed force) and P(Concentrated force) is not applied to Box section, but only for I-section and top stiffener of Tub section. The fl value for deck overhang is considered only for the constructibility limit state. Distributed Force, F (1) Distributed Force, F Distributed force values are inputted Fl = F tan α (2) Concentrated Force, P Concentrated force values are inputted Pl = P tan α (3) Eccentricity of Overhang Loads, e Eccentricity of overhang loads are inputted -1 α = tan (e/D)

[Fig.2.25] Deck Overhang Loads Dialog Box

The fl value is generated by combining the values produced from the analysis and the value inputted in this dialog box. If this feature is not used, fl value only from the analysis results will be used. Lateral bending moment due to uniformly distributed lateral bracket force (Fl) is estimated as:

FL Ml  l b 12

[Fig.2.26] Deck Overhand Bracket

2

(c6.10.3.4-2)

where, Ml : flange lateral bending moment due to the eccentric loadings from the forming brackets Fl : uniformly distributed lateral force Lb : unbraced length

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Explanation Lateral bending moment due to concentrated lateral bracket force (Fl) assumed to be placed at the middle of the unbraced length is estimated as:

Ml 

Pl Lb (c6.10.3.4-3) 8

where, Ml : flange lateral bending moment due to the eccentric loadings from the forming brackets Pl : concentrated lateral force Lb : unbraced length

P and F are the dead loads and construction loads such as Deck Overhang Weight, Screed rail load, Railing load, Walkway load, Machine Load, etc. considered for the constructability check only. The load coefficient applied to Erection (DC) Load Case is applied to calculate the load in this case.

1.3.8 Design Force/Moment This feature displays design member forces (strong ▶ Design > Composite Design > Design Tables > Design axis moment, My), weak-axis moment (Mz) and Force/Moment... shear stress (VU) for the local axis of elements under selected load combination of steel composite section for each construction stage. For explanation regarding design member forces under construction stages, please refer to Section 1.5 in this chapter. 1.3.8 Design Force/Moment

[Fig.2.27] Design Force/Moment Dialog Box

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1.4 Load Combination for steel composite section 1.4.1 Application of load combination in midas Civil for AASHTO LRFD 12 (1) Application of load combinations and factors in midas Civil for AASHTO LRFD 12 The load combinations used for the review of each limit state as per Table 3.4.1-1, are shown below.

[Fig.2.28] Load Combinations and Load Factors

Using the Auto Generation feature of the program, the load combinations regulated by the design code can be automatically generated. Load factors are considered for each load combinations in this program. Load factors are considered only within the program, and γp value can be designated by Auto Generation feature.

[Fig.2.29] Load Factors for Permanent Loads, γp

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Contents (1) Auto Generation of Load Combinations ▶ Result > Combination > Load Combination > Composite Steel Girder Design > Auto Generation ...

Explanation (1) Auto Generation of Load Combinations This feature automatically generates load combinations under provision of AASHTO LRFD 12. 1) Design Code When load combinations are generated, they strictly follow the design code selected by the user. 2) Load Modifier (ηi) Load modifier is a factor relating to ductility, redundancy, and operational classification. It is defined by the following equations. For loads for which a maximum value of γ i is appropriate: ηi = ηD ηR ηI ≥ 0.95 For loads for which a minimum value of γ i is appropriate: ηi = 1/(ηD ηR ηI ) ≤ 1.0

Where, ηD: a factor relating to ductility as per 1.3.3 ηR: a factor relating to redundancy as per 1.3.4 ηI: a factor relating to operational classification as per 1.3.5

3) Load Factors for Permanent Loads (γp) Load Factors for Permanent Loads are as per Table 3.4.1-2. Each option button for γp value is activated when the corresponding static load case is defined.

[Fig.2.30] Automatic Generation of Load Combinations Dialog Box

If a user wishes to review limit states based on the load combinations defined manually, it can be done by selecting the load combination of interest in Load Combination Type as in Section 1.4.2.

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1.4.2 Used load combination for steel composite design Load combinations used in the steel composite section design are defined under Load Combination Type. Contents

Explanation

(1) Load Combination Type

(1) Load Combination Type 1) Strength Limit State Choose load combinations for use under review of strength limit state.

▶ Design > Composite Design > Load Combination Type...

2) Service Limit State Choose load combinations for review of usability limit state. 3) Fatigue 1 Limit State Choose load combinations for review in fatigue limit state (Fatigue Ⅰ Load Combination is for infinite life design; (ADTT)SL inputted in the software > (ADTT)SL, equivalent to infinite life as per Table 6.6.1.2.3-2). 4) Fatigue 2 Limit State Similarly, choose load combinations for review in fatigue limit state (Conversely to Fatigue I, Fatigue Ⅱ Load Combination is for finite life design). [Fig.2.31] Load Combination Type Dialog Box

1.5 Modeling Steel Composite Sections for Construction Staged Analysis In this section, methods of construction stage modeling, implementation of concrete's time-dependent material properties in steel composite section and 3 types of design member forces applied to steel composite section design are explained. Construction stages of steel composite section can be implemented differently for case 1 to 3 as in table 2.13. [Table 2.13] Modeling Construction Stage Cases for Steel Composite Design

Case

Construction Stage

Case 1

Time Dependent Material(Creep / Shrinkage) Defined

Defined Case 2 Case 3

Not Defined (Apply modular ratio of 3n) Not Defined

Not Defined (Apply modular ratio of 3n)

1.5.1 Member forces and stresses used in steel composite section design (1) Member forces For design of steel composite section, member forces per construction stage of steel composite section must be calculated. The program considers two main factors for design and review of construction stage of steel composite section. ▪Construction stages of steel composite section ▪Time dependent material properties of Concrete (Creep, Shrinkage and Compression Strength)

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Design member forces used for design of steel composite section are divided into three main categories. [Table 2.14]Design Force and Moment for Steel Composite Design

Design Force/Moment

Description

Dead (Before)

Member forces before the concrete deck is activated. Only steel section properties are used.

Dead (After)

Member forces occurring due to erection load cases defined by user with the time dependent material properties (Creep & Shrinkage) of concrete Long term section properties are used.

Short Term

Member forces from the post-construction state and load cases not included in the above categories. Short term section properties are used.

(2) Stress Bending stress (fbu) used for design of steel composite section is calculated as in equation 2.12.

f bu 

M D1 M D 2 M AD   S NC S LT S ST

(2.12)

Where, Md1 : moment of non-composite section Md2 : moment of long-term composite section MAD : additional yield moment of short-term composite section SNC : non-composite section modulus SLT : long-term section modulus SST : short-term section modulus fbu : largest value of the flexural stress in the flanges at the section under consideration

On the other hand, lateral bending stress (fl) is calculated as in equation 2.13.

fl 

M uz  M lat  0.6 Fyf Sl

(2.13)

Where, fl : flange lateral bending stress Sl: lateral section modulus of the flanges about z-axis Muz : flexural moment about z-axis Mlat : lateral bending moment in the flange calculated from the overhang loads Fyf : specified minimum yield strength of a flange

1.5.2 Case 1 In Case 1, construction stages and time dependent material properties of concrete (Creep/Shrinkage) are defined. Composite sections for Construction Stages function must be defined as well; otherwise, the sections shall be excluded from design. If time dependent material property information is inputted as well as long-term modulus of elasticity, long-term modulus of elasticity has higher priority in consideration of calculation.

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▣ Define Composite Section for Construction Stage Contents Composite Section for Construction Stage ▶ Load >Load Type> Construction Stage > Composite Section for C.S...

Explanation Composite Section for Construction Stage For definition of construction stage, information in this window must be defined. (1) Active Stage Construction stage where steel composite section should be activated is inserted. (2) Construction sequence 1) "Material Type" column □ By choosing Element, material property of the element is used. □ By selecting Material, material information chosen under "Material" Column is applied with higher priority.

[Fig.2.32] Add/Modify Composite Section for Construction Stage Dialog

2) Composite Stage column Construction stages where steel girder and concrete slab should be activated are chosen. 3) Age column Age information when each part is activated is input. Information in this column has higher priority over the age input during definition of construction stage.

(1) Member forces under Dead (Before composite) Member forces before activation of Concrete Deck are applied. (Refer to Table 2.4 in "Introduction") For design purposes, Dead (Before) member forces are applied after multiplying the load factors applied in Dead Load (CS) in Load Combination dialog box. (2) Member forces under Dead (After composite) For the member forces under Dead (After), in post-composite stages, the long-term modulus of elasticity is determined by the time dependent material properties defined by users. Member forces under Dead (After) consist of static load cases and construction stage load cases. If Dead Load of Component and Attachments (DC2), Dead Load of Wearing Surfaces and Utilities (DW), Creep (CH), and Shrinkage (SH) are defined as erection loads, they are accounted for the Dead (After).

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▣Define Erection Load Contents (1) Define Erection Load ▶Analysis > Analysis Control > Construction Stage > Load Cases to be Distinguished from Dead Load for C.S Output >Add (Modify/delete)...

Explanation (1) Define Erection Load Erection Load is defined. 1) Load Type for C.S Determine the Load Type for the construction stages of the composite section. Load types are considered by the software for auto generation of load combinations. 2) Assignment Load Cases Define Erection Load by selecting and moving the Load Cases desired from the List of Load Case panel to the Selected Load Case panel.

[Fig.2.33] Define Erection Load Dialog

(3) Calculation of the short-term member forces Short-term modulus of elasticity of the composite section is calculated based on the DB value inputted. All load cases are considered as the short-term loads except the ones defined as Dead (Before) and Dead (After). 1.5.3 Case 2 In Case 2, construction stages are defined without the time dependent material property (Creep/Shrinkage) information. Long term effects are considered using the long term modular ratio entered in the Section Data dialog box. Sections for different construction stages must be defined and differentiated using the Composite Section for Construction Stage definition. Otherwise, they will not be considered for the design check.

(1) Member forces under Dead (Before) Dead (Before) is applied before the concrete deck is activated. (Refer to Table 2.4 in the "Introduction") For the design, the Dead (CS) multiplied by the load factor is applied as the member force under Dead (Before). (2) Member forces under Dead (After) The effects of Creep/Shrinkage are reflected by applying the ratio of elastic modulus that is inputted in the Section Data (Refer to Section 1.1.1 (1)) for the long-term stage. In other words, the Creep/Shrinkage effects are reflected by using the section information with the ratio of elastic modulus that considers the time dependent material property for the analysis and design. These long term modular ratios defined for considering creep and shrinkage, auto generate Section Stiffness Scale Factors for the sections in which these are inputted. Section Stiffness Scale Factors need to be activated in the construction stages in accordance with the Composite Section for Construction Stage definition, i.e. the section stiffness scale factors are activated when the corresponding section becomes composite as per the definition of composite section for CS. If users compose construction stages and define Dead Load of Component and Attachments (DC2), Dead Load of Wearing Surfaces and Utilities (DW), Creep (CH), and Shrinkage (SH) as Erection Load, the load cases will be included in the Dead (After). (3) Short term member forces The ratio of elastic modulus of the composite section is calculated using the DB value inputted. All the load cases which are not activated in the Construction Stage are considered as the short-term loads.

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1.5.4 Case 3 In case the construction stages are not defined, users can model and define steel composite sections by using the Load Case for Pre-Composite Section function at ▶ Load > Load Type > Settlement/Misc. > Misc. > Pre-composite Section. For this case, short- and long-term ratios of elastic modulus defined in the section data (Refer to Section 1.1.1 (1)) are used. In this case, instead of member forces per construction stages, member forces under Dead (Before) is used to check the constructibility of the model. (1) Member force under Dead (Before) In the Load Cases for Pre-Composite Section dialog box, users can define which load cases to account for the member forces and apply as Dead (Before) in design. Since this is for pre-composite state, the steel only section properties are used (Refer to Section 1.1.1 (1)).

Dead Load (Before) [Fig.2.34] Load Cases for Pre-Composite Section

(2) Member forces under Dead (After) Member forces under Dead (After) use the long term section properties. These loads should be separated from the short term member forces by the use of Analysis > Analysis Control > Boundary Change Assignment. 1) Data Selection Check the box corresponding to Section Stiffness Scale Factor. As explained earlier, Section Stiffness Scale Factors are used for considering the long term section properties. 2) Boundary Group Combination Create a boundary group combination considering the appropriate boundary groups from the boundary group list. The created boundary group combinations need to be selected for the post composite long term load cases. For the static load cases assigned with the section stiffness scale factor boundary groups, long term section property will be used.

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Dead Load (After)

[Fig.2.35] Load Cases for Post-Composite Section

(3) Short-term member forces The ratio of elastic modulus from the database is used for the short-term loads of the composite section. All load cases are considered for the short-term loads except the ones considered for the Dead (Before) and Dead (After).

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Chapter 2. Steel Composite Girder Design : AASHTO-LRFD 4thand6th (2007/2012)

Application of AASHTO LRFD 12 1. I Girder Section 1.1. Introduction The program designs I-girder sections according to the orders in the flow chart below. This chapter demonstrates how the AASHTO LRFD 12 is applied in the program.

[Fig.2.36] Flow chart of Composite I-girder bridge

Typical I-Sections have a cross section as shown below:

[Fig.2.37] I-Section in positive flexure

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1.2 Strength Limit State The program checks the strength limit states for the flexure, shear, and ductility of the composite sections.

Strength Limit States 6.10.6

Check Ductility 6.10.7.3

Check flexural resistance 6.10.7 & 6.10.8

Check shear resistance 6.10.9

[Fig.2.38] Flow chart of Strength Limit States

1.2.1 Ductility Ductility shall be checked to prevent premature crushing of concrete. For the verification of a web section that is under positive flexure, the ductility shall be verified as: (2.14)

D p  0.42 Dt

Ductility AASHTO LRFD 12 Dp :distance from the top of the concrete deck to the neutral axis of the composite section at the plastic (Eq.6.10.7.3-1)

Where,

moment Dt : total depth of the composite section

1.2.2 Flexural Resistance There are four cases for checking flexural resistance of I Sections as shown below. Check flexural resistance 6.10.7 & 6.10.8

Yes

Positive Moment?

Check Ductility f sd ks  D p M0c,.Ed42( zcd,bart / I y ,c,bar )

No Straight Bridge?

No

Yes

:Curved

6.10.7.3

Bridge

Yes

Straight Bridge? No :Curved

Yes

No :Compact or Noncompact

Bridge

Compact Section?

Slender Section?

No

No

Use Optional APPENDIX A6?

Yes

Yes

Case 1 : Check flexural resistance of Positive Flexure Moment in Compact Section

Case 2 : Check flexural resistance of Positive Flexure Moment in Noncompact Section

Case 3 : Check flexural resistance of Negative Flexure Moment

6.10.7.1

Case 4 : Check flexural resistance of Negative Flexure Moment by using APPENDIX A6

6.10.7.2

6.10.8

APPENDIX A6

Positive Flexure Moment

Negative Flexure Moment End

[Fig.2.39] Flow chart of flexural resistance

(1) Case 1: Compact Section in Positive flexural moment

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The flexural resistance shall be checked according to the flow chart below if the section is Case 1 under positive flexural moment, satisfies the ductility requirement and is a compact web. If AASHTO LRFD 12 (6.10.7.1) the ductility requirement is not satisfied, the program will display NG in the design result page.

[Fig.2.40] Case 1 : Flow chart of flexural resistance of Positive Flexure Moment in Compact Section

Flow chart of Case 1 AASHTO LRFD 12 (6.10.7.1)

If a section is compact and under positive flexural moment, flexural resistance shall be checked according to the following equation:

Mu 

1 f l S xt   f M n 3

(2.15)

Where, fl : Flange lateral bending stress Mn : Nominal flexural resistance of the section. Mu : Bending moment about the major-axis of the cross-section. ϕf : Resistance factor for flexure.

Flexural Resistance AASHTO LRFD 12 (Eq. 6.10.7.1.1-1)

1) Nominal Flexural Resistance(Mn) [Table 2.15]Calculation of Nominal Flexural Resistance(Mn)

Case

Dp  0.1Dt Otherwise

Mn Mn  M p D   M n  M p 1.07  0.7 p  Dt  

Mn AASHTO LRFD 12 (Eq. 6.10.7.1.2-1) AASHTO LRFD 12 (Eq. 6.10.7.1.2-2)

Where,

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Mp : Plastic moment of the composite section determined as per Article D6.1. Dp : distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment Dt : total depth of the composite section

2) Strength Resistance Factor for flexure (ϕf ) The design code defines the flexural reduction factor as 1.00. However, the program primarily considers the factor that is inputted by users in the design parameters.

[Fig.2.41] Composite Steel Girder Design Parameter

3) Especially, the following requirement regarding the nominal flexural resistance must be satisfied when " M n  1.3Rh M y in Positive Flexure and Compact Sections" is checked at ▶ Composite Steel Girder Design Parameters>Options for Strength Limit State. (Fig.2.41)

M n  1.3Rh M y

(2) Case 2 : Positive flexural moment in noncompact section

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(2.16)

Nominal flexural resistance AASHTO LRFD 12 (Eq. 6.10.7.1.2-3)

The flexural resistance shall be checked according to the below flow chart if a section is Case 2 under positive flexural moment, satisfies the ductility requirement and is noncompact. AASHTO LRFD 12 (6.10.7.2) Curved bridges are considered as noncompact sections.

Case 2 : Check flexural resistance of Positive Flexure Moment in Noncompact Section 6.10.7.2

Check Compression flange f bu   f F nc

F

nc

 R

6.10.7.2.1-1,

R

b

h

F

yc

6.10.7.2.2-1

Check Tension flange

1 f l   f F nt 3 F nt  R h F yt

f bu 

6.10.7.2.1-2,

6.10.7.2.2-2

End

[Fig.2.42] Case 2 : Flow chart of flexural resistance of Positive Flexure Moment in Noncompact Section

1) Compression flange At the strength limit state, the compression flange shall satisfy the below criteria regarding the flexure:

f bu   f Fnc

(2.17) Compression flange

Fnc  Rb Rh Fyc

(2.18)

AASHTO LRFD 12 (Eq.6.10.7.2.1-1) (Eq.6.10.7.2.2-1)

Where, fbu : Flange stress calculated without consideration of flange lateral bending. Fnc : Nominal flexural resistance of the compression flange.

2) Tension flange The tension flange shall satisfy the below criteria regarding the flexure:

f bu 

1 f l   f Fnt 3

Fnt  Rh Fyt

(2.19) (2.20)

Tension flange AASHTO LRFD 12 (Eq.6.10.7.2.1-2) (Eq.6.10.7.2.2-2)

Where, fl: Flange lateral bending stress, 𝑓𝑙 ≤ 0.6 𝐹𝑤 Fnt : Nominal flexural resistance of the tension flange. Rb : Web load-shedding factor.

(3) Case 3: Negative flexural moment in composite section and noncomposite section

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The flexural resistance shall be checked according to the below flow chart if a section is under negative flexural moment and is one of the following cases: ▪ Curved bridge ▪ Straight Bridge but slender section ▪ Straight Bridge and compact or noncompact, but Appendix A6 is not applied

[Fig.2.43] Case 3 : Flow chart of flexural resistance of Negative Flexure Moment

1) Discretely Braced Compression Flange Compression Flange For a compression flange, the following requirement shall be satisfied at the strength AASHTO LRFD 12 limit state: (6.10.8)

f bu 

1 f l   f Fnc 3

(2.21)

Where,

Fnc  Min( Fnc( FLB ) , Fnc( LTB) )

(2.22)

Where, Fnc(FLB) : Local Buckling Resistance based on Discretely Braced Compression Flange Fnc(LTB) : Lateral Torsional Buckling Resistance based on Discretely Braced Compression Flange

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(Eq.6.10.8.1.1-1)

[Table 2.16] Calculation of Fnc(FLB)

Case

Fnc( FLB )

 f   pf

Fnc( FLB )  Rb Rh Fyc

 f   pf

  F     pf   RRF Fnc( FLB )  1  1  yr  f  R F      b h yc  h yc  rf pf   

Fnc(FLB) AASHTO LRFD 12 (Eq.6.10.8.2.2-1)

AASHTO LRFD 12 (Eq.6.10.8.2.2-2)

in which: 𝜆𝑓 : Slenderness ratio for the compression flange 𝜆𝑟𝑓 : Limiting slenderness ratio for a noncompact flange Rb : web load-shedding factor determined as specified in Article 6.10.1.10.2 Rh : hybrid factor determined as specified in Article 6.10.1.10.1

f 

b fc

(2.23)

2t fc

AASHTO LRFD 12 (Eq.6.10.8.2.2-3)

E Fyc

(2.24)

E rf  0.56 Fyr

(2.25)

 pf  0.38

AASHTO LRFD 12 (Eq.6.10.8.2.2-4)

AASHTO LRFD 12 (Eq.6.10.8.2.2-5)

Fyr : compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not including compression-flange lateral bending, taken as the smaller of 0.7Fyc and Fyw, but not less than 0.5Fyc . [Table 2.17] Calculation of Fnc(LTB)

Fnc(FLB)

Case

Fnc( LTB )

Lb  Lp

Fnc( LTB)  Rb Rh Fyc   Fyr Fnc( LTB )  Cb 1  1   R   h Fyc

Lp  Lb  Lr

AASHTO LRFD 12 (6.10.8.2.2)

 Lb  L p    R R F  Rb Rh Fyc  L  L  b h yc p   r 

AASHTO LRFD 12 (Eq.6.10.8.2.3-2)

Fnc( LTB)  Fcr  Rb Rh Fyc

Lb  Lr

AASHTO LRFD 12 (Eq.6.10.8.2.3-1)

AASHTO LRFD 12 (Eq.6.10.8.2.3-3)

Where, Cb: Moment gradient modified

[Table 2.18] Calculation of Cb

Case

Cb

Unbraced cantilevers and for members where fmid/f2 >1 or f2=0

1.0

For all other cases

 f   f  1.75  1.05 1   0.3 1   2.3  f2   f2 

Calculation of Cb 2

Where,

AASHTO LRFD 12 (Eq.6.10.8.2.3-6)

AASHTO LRFD 12 (Eq.6.10.8.2.3-7)

Lb : Unbraced length.

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Lp : Limiting unbraced length to achieve the nominal flexural resistance of R bRhFyc under uniform bending.

L p  1.0rt Lr  rt Fcr 

E Fyc E Fyr

Cb Rb E ( Lb / rt ) 2 2

1 Dc t w rt  b fc / 12(1  ) 3 b fc t fc

(2.26) AASHTO LRFD 12 (Eq.6.10.8.2.3-4)

(2.27) (2.28)

(2.29)

AASHTO LRFD 12 (Eq.6.10.8.2.3-5)

AASHTO LRFD 12 (Eq.6.10.8.2.3-8) AASHTO LRFD 12 (Eq.6.10.8.2.3-9)

Lr : Limiting unbraced length to achieve the onset of nominal yielding in either flange under uniform bending with consideration of compression flange residual stress effect (in). Fcr : Elastic lateral torsional buckling stress. rt : effective radius of gyration for lateral torsional buckling Fyr : compression-flange stress at the onset of nominal yielding within the cross-section, including Dc : depth of the web in compression in the elastic range determined as per D6.3.1 fmid : Stress without consideration of lateral bending at the middle of the unbraced length of the flange under consideration, calculated from the moment envelope value that produces the largest compression at this point, or the smallest tension if this point is never in compression

2) Continuously braced Tension Flange At the strength limit state, the following requirement shall be satisfied for the continuously braced tension flange:

fbu   f Rh Fyt

(2.30)

(4) Case 4 : Flexural resistance of Negative Flexure Moment by using Appendix A6 The optional provisions of Appendix A6 shall apply to the sections in negative flexural and straight bridges and compact and noncompact web I-sections according to the flow chart below.

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Tension Flange AASHTO LRFD 12 (6.10.8.1.3) (Eq.6.10.8.1.3-1)

Check flexure resistance of Negative Flexure Moment by using Appendix A6 APPENDIX A6

2 D cp

Yes : Compact web

R pc  R pt 

No : Noncompact web

  pw ( D cp )

tw

Calculate Web plastification Factor

  R h M yc   w   pw ( Dc )   M p Mp   R pc  1  1    M p   rw   pw ( Dc )   M yc M yc     R h M yt   w   pw ( Dc )   M p Mp   R pt  1  1       M p   rw   pw ( Dc )   M yt M yc  

Mp M yc Mp M yt

Discretely Braced Compression Flange? No :continuously braced

Yes

 f  Rf

Local Buckling Resistance

No : Noncompact flange

Mu   f RpcM yc No :Rolled section Yes : Compact flange

M nc( FLB)  Rpc M yc

Mu   f RptM yt

Yes

kc  4 / D / tw

kc  0.76

0.35 kc  0.76

  Fyr S xc   f  pf    RpcM yc M nc( FLB)  1  1    RpcM yc  rf   pf 

Lb  L p

Yes

Built-up Section?

No

L p  Lb  L r

No

Yes

M nc( LTB)  Rpc M yc Lateral Torsional Buckling Resistance

  F S  L  L  Mnc( FLB)  Cb 1 1 yr xc  b p  RpcM yc  RpcM yc      RpcM yc  Lr  Lp 

Mnc( LTB)  Fcr Sxc  RpcM yc

M nc  minM nc FLB  , M nc LTB   Check Flexural Resistance 1 Mu  fl Sxc   f M nc 3

f l  0 . 6 F yc

End

[Fig.2.44] Case 4: Flow chart of flexural resistance of Negative Flexure Moment by using Appendix A6.

If Appendix A6 is applied at the strength limit state, the following four requirements regarding flexure shall be satisfied. The design verification is done for the compression and tension flanges.

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[Table 2.19] Limit State defined by Appendix A6

Case Discretely-Braced Flange Section

Continuously-Braced Flange Section

Limit State

1 f l S xc   f M nc 3 1 M u  f l S xt   f M nt 3

Limit State by A6 AASHTO LRFD 12 (A6.1.1-1)

Mu 

Compression Tension Compression

M u   f R pc M yc

Tension

M u   f R pt M yt

AASHTO LRFD 12 (A6.1.2-1) AASHTO LRFD 12 (A6.1.3-1) AASHTO LRFD 12 (A6.1.4-1)

Where, ϕf : Resistance factor for flexure. fl : Flange lateral bending stress, 𝑓𝑙 ≤ 0.6 𝐹𝑦𝑐 Mnc : Nominal flexural resistance based on the compression flange. Mu : Bending moment about the major-axis of the cross-section. Myc : Yield moment with respect to the compression flange. Mnt : Nominal flexural resistance based on the tension flange. Myt : Yield moment with respect to the tension flange. Sxc : Elastic section modulus about the major axis of the section to the compression flange taken as Myc/Fyc Rpc : Web plastification factor for the compression flange. Rpt : Web plastification factor for the tension flange. [Table 2.20] Calculation of Rpc and Rpt

Case 2 Dcp tw

2 Dcp tw

  pw ( Dcp )

Web Plastification Factor Compact web

  pw ( Dcp )

& w < rw

R pc 

Noncompact web

R pt 

Mp

Rpc and Rpt

M yc

AASHTO LRFD 12 (A6.2.1-4)

Mp M yt

  R M     pw( Dc )  M p M  R pc  1  1  h yc  w  p     M p  rw   pw( Dc )  M yc M yc     Rh M yt  w   pw( Dc )  M p M p   R pt  1  1   M p  rw   pw( Dc )  M yt M yt  

AASHTO LRFD 12 (A6.2.1-5) AASHTO LRFD 12 (A6.2.2-4)

AASHTO LRFD 12 (A6.2.2-5)

in which: Mp: Plastic moment Dc : Depth of the web in compression in the elastic range determined as per D6.3.1. Dcp : Depth of the web in compression in the plastic moment. My : Yield moment taken as the smaller of Myc and Myt. 𝜆𝑟𝑤 : Limiting slenderness ratio for a noncompact web

E rw  5.7 Fyc

(2.31)

𝛌𝐫𝐰 AASHTO LRFD 12 (A6.2.2-3)

λw : Slenderness ratio for the web based on the elastic moment.

w 

2 Dc tw

𝜆𝑝𝑤(𝐷𝑐 ) : Limiting slenderness ratio for a compact web corresponding to 2D cp/tw

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Design Guide for midas Civil

(2.32)

AASHTO LRFD 12 (A6.2.2-2)

 pw( D

E Fyc

cp

 Dcp   rw  2    Dc Mp  0.54  0.09    Rh M y  

)

  

𝛌𝐩𝐰 (𝐃𝐜𝐩 ) AASHTO LRFD 12 (A6.2.1-2)

(2.33)

1) Discretely braced Compression Flange For the discretely braced compression flanges, the minimum of the local buckling resistance and lateral torsional buckling resistance is used to perform the design check as: M nc  Min[ M nc( FLB ) , M nc( LTB) ]

(2.34) ① Local buckling Resistance (Mnc(FLB)) The local buckling resistance shall be calculated as shown in the following table:

Compression Flange AASHTO LRFD 12 (A6.3.2)

[Table 2.21] Calculate Mnc(FLB)

Case

M nc( FLB )

kc

 f   pf

Rolled

k c  0.76

 f   pf (Noncompact flange)

M nc( FLB )  R pc M yc

-

(Compact flange)

Built-up

kc  4 /

D tw

M nc( FLB )

  Fyr S xc  1  1     R pc M yc

0.35  k c  0.76 Where, 𝜆𝑓 : Slenderness ratio for the compression flange.

f 

b fc

  f   pf    R M      pc yc rf pf  

(2.35)

2t fc

𝜆𝑝𝑓 : Limiting slenderness ratio for a compact flange.

 pf  0.38

E Fyc

(2.36)

𝜆𝑟𝑓 : Limiting slenderness ratio for a noncompact flange.

rf  0.95

𝑴𝒏𝒄 AASHTO LRFD 12 (A6.3.2-1)

Ek c Fyr

(2.37)

AASHTO LRFD 12 (A6.3.2-2)

𝝀𝒇 AASHTO LRFD 12 (A6.3.2-3) 𝝀𝒑𝒇 AASHTO LRFD 12 (A6.3.2-4) 𝛌𝐫𝐟 AASHTO LRFD 12 (A6.3.2-5)

𝑘𝑐 : Flange local buckling coefficient determined as per A6.3.2-6 for built-up sections and 0.76 for rolled shapes. Fyr : compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not including compression-flange lateral bending, taken as the smaller of 0.7Fyc, RhFyt Sxt/Sxc and Fyw, but not less than 0.5Fyc Sxc : Elastic section modulus about the major axis of the section to the compression flange taken as Myc/Fyc Sxt : Elastic section modulus about the major axis of the section to the tension flange taken as Myt/Fyt

② Lateral Torsional Buckling Resistance (Mnc(LTB)) The lateral torsional buckling resistance is calculated as shown in the following table:

Mnc(LTB) AASHTO LRFD 12 (A6.3.3)

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[Table 2.22] Calculation of Mnc(LTB)

Case

𝐌𝐧𝐜(𝐋𝐓𝐁) AASHTO LRFD 12 (A6.3.3-1)

M nc( LTB )

Lb  L p

M nc( LTB)  R pc M yc

L p  Lb  Lr

M nc( LTB)

  Fyr S xc  Lb  L p    R pc M yc  R pc M yc  C b 1  1    R pc M yc  Lr  L p  M nc( LTB)  Fcr S sc  R pc M yc

Lb  Lr

Where, Lp : Limiting unbraced length to achieve the nominal flexure resistance R pcMyc under uniform bending

(2.38)

E Fyc

L p  1.0rt

AASHTO LRFD 12 (A6.3.3-2) AASHTO LRFD 12 (A6.3.3-3)

Lp AASHTO LRFD 12 (A6.3.3-4)

Lr : Limiting unbraced length to achieve the nominal onset of yielding in either flange under uniform bending with consideration of compression flange residual stress effects

Lr  1.95rt

E Fyr

 Fyr S xc h   1  1  6.76 S xc h  E J  J

2

(2.39)

Lr AASHTO LRFD 12 (A6.3.3-5)

▪ Cb: moment gradient modifier, is divided into two cases and calculated according to either A6.3.3-6 or A6.3.3.3-7 of AASHTO LRFD 12. For the detailed calculations, please refer to the section "3.2 Strength Limit State > (1) Flexural Resistance > Case 3".

▪ Fcr : Fcr 

▪J:

Elastic lateral torsional buckling stress Cb 2 E  Lb   rt

  

2

1  0.078

  

2

(2.40)

Fcr AASHTO LRFD 12 (A6.3.3-8)

St. Venant torsional constant 3

J

J  Lb  S xc h  rt

3

3 b fc t fc t fc b ft t ft t ft Dtw  (1  0.63 ) (1  0.63 ) 3 3 b fc 3 b ft

(2.41)

J AASHTO LRFD 12 (A6.3.3-9)

▪ rt : Effective radius of gyration for lateral torsional buckling  1 Dctw   rt  b fc / 121   3b t  fc fc  

(2.42)

Where, 𝐹𝑦𝑟 : compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not including compression-flange lateral bending, taken as the smaller of 0.7𝐹𝑦𝑐 , 𝑅ℎ 𝐹 𝑦𝑡 , 𝑆𝑥𝑡 /𝑆𝑥𝑐 and 𝐹𝑦𝑤 , but not less than 0.5 𝐹𝑦𝑐 . h : Depth between the centerline of the flanges. 𝑀𝑚𝑖𝑑 : Major-axis bending moment at the middle of the unbraced length, calculated from the moment envelop value that produces the largest compression at this point in the flange under consideration, or the smallest tension if this point is never in compression. 𝑀𝑚𝑖𝑑 shall be due to the factored loads and shall be taken as positive when it causes compression and negative when it causes tension in the flange under consideration. 𝑀0 : moment at the brace point opposite to the one corresponding to 𝑀2 , calculated from the moment envelope value that produces the largest compression at this point in the flange under consideration, or the smallest tension if this point is never in compression(kip-in). M0 shall be due to the factored loads and shall be taken as positive when it causes compression and negative when it cause tension in the flange under consideration.

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rt AASHTO LRFD 12 (A6.3.3-10)

𝑀1 : moment at the brace point opposite to the one corresponding to 𝑀2 , calculated as the intercept of the most critical assumed linear moment variation passing through 𝑀2 and either 𝑀𝑚𝑖𝑑 or 𝑀0 , whichever produces the smaller value of 𝐶𝑏 . 𝑀1 may be calculated as follows - When the variation in the moment along the entire length between the brace points is concave in shape AASHTO LRFD 12

(2.43) (A6.3.3-11)

M1  M 0

- Otherwise

(2.44)

M 1  2M mid  M 2  M 0

AASHTO LRFD 12 (A6.3.3-12)

𝑀2 : Except as noted below, largest major-axis bending moment st either end of the unbraced length causing comrpession int the flange under consideration, calculated from the ciritical moment envelop value. 𝑀2 shall be taken as positive. If the moment is zero or cause tension in the flange under consideration at both ends if the unbraced length, 𝑀2 shall be taken as zero. 𝑀𝑦𝑐 : Yield moment with respect to the compression flange. 𝑀𝑦𝑡 : Yield moment with respect to the tension flange.

1.2.3 Shear resistance Shear resistance of an I-web Steel Composite Section is checked as shown in the flow chart below. Shear resistance AASHTO LRFD 12 (6.10.9)

Check shear resistance 6.10.9

No

Stiffened web?

Yes

Unstiffened webs

Stiffened Web Panels

6.10.9.2

No

Yes :Stiffened Interior Web Panels

:Stiffened End panel

Calculate V n

6.10.9.3

Interior Web Panel?

Calculate V n

2Dtw  2.5  bfttft

b t

V n  V cr  CV p

V n  V cr  CV p

V p  0 . 58 F yw Dt w

V p  0 . 58 F yw Dt w

6.10.9.2-1 6.10.9.2-2

6.10.9.3.3-1 6.10.9.3.3-2

fc fc



Yes

No

Calculate V n

Vn

    V p C   

Calculate V n

  0 . 87 (1  C )   2 d0   d0  1    D   D 

6.10.9.3.2-8

    0 . 87 (1  C )   V n  V p C  2  d   1   0     D   

6.10.9.3.2-2

Check V n

Vu  V V n 6.10.9.1-1

End

[Fig.2.45] Flow chart of shear resistance

The program distinguishes Unstiffened and Stiffened webs according to the following criteria:

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[Table 2.23] Classification of Unstiffened web and Stiffened Web

Case

Classification

Without a longitudinal stiffener and with transverse stiffener spacing not exceeding 3D Stiffened web With one or more longitudinal stiffeners and with a transverse stiffener spacing not exceeding 1.5D Otherwise

Unstiffened web

However, even stiffened webs are classified as unstiffened web if the check box is not checked at ▶Composite Steel Girder Design Parameters >Options for Strength Limit State>Post-buckling Tension-field Action for Shear Resistance. (Fig.2.41) (1) Shear Resistance Check Shear resistance shall be checked as: Vu  vVn (2.45)

Shear resistance AASHTO LRFD 12 (Eq. 6.10.9.1-1)

Where, 𝜙𝑣 : Resistance factor for shear. Vn : Nominal shear resistance. Vu : Shear in the web at the section under consideration due to the factored loads

1) Unstiffened Webs The nominal shear resistance of unstiffened webs shall be taken as: (2.46)

Vn  Vcr  CV p

(2.47)

V p  0.58Fyw Dtw

Where, Vcr : Shear -buckling resistance Vp : plastic shear force C : Ratio of shear-buckling resistance to shear yield strength

Unstiffened Webs AASHTO LRFD 12 (6.10.9.2) AASHTO LRFD 12 (Eq. 6.10.9.2-1) (Eq. 6.10.9.2-2)

[Table2.24] Calculation of Ratio of shear-buckling resistance to shear yield strength, C

C

Case

D Ek  1.12 tw Fyw 1.12

Ek D Ek   1.40 Fyw t w Fyw Ek D 1.40  Fyw t w

C  1.0 C

C

1.12 D tw

C AASHTO LRFD 12 (Eq. 6.10.9.3.2-4)

Ek Fyw

1.57  Ek  2    D   Fyw     tw 

AASHTO LRFD 12 (Eq. 6.10.9.3.2-5)

AASHTO LRFD 12 (Eq. 6.10.9.3.2-6)

Where, k : Shear-buckling coefficient

k 5

(2.48)

5  do    D

2

2) Stiffened Webs The nominal shear resistance is calculated differently for the two types of stiffened webs:

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Design Guide for midas Civil

AASHTO LRFD 12 (Eq. 6.10.9.3.2-7)

interior web panels and end web panels. All webs with a support assigned on its i or j node in the Span Information (Fig.2.22) are considered as end panels and the others are Stiffened Webs AASHTO LRFD 12 considered as interior web panels. (6.10.9.3)

[Fig.2.46] Classification of End Panel and Interior Panel

① End panels The nominal shear resistance, Vn, of a web end panel shall be taken as: (2.49)

Vn  Vcr  CV p

End panels AASHTO LRFD 12 (6.10.9.3.3) AASHTO LRFD 12 (Eq. 6.10.9.3.3-1) (Eq. 6.10.9.3.3-2)

V p  0.58Fyw Dtw

(2.50)

② Interior web panels There are two cases of an interior web panel as shown in the following table:

Interior web panel AASHTO LRFD 12 (6.10.9.3.2)

[Table 2.25] Calculation of Vn and Vp of Interior web panel

Case

Vn , V p

2 Dtw  2.5 (b fct fc  b ft t ft )

    0.87(1  C )   Vn  V p C  2   do    1     D  

AASHTO LRFD 12 (Eq.6.10.9.3.2-2)

V p  0.58Fyw Dtw

Otherwise

  0.87(1  C )  Vn  V p C  2 d d   1  o   o  D D  V p  0.58Fyw Dtw

      

AASHTO LRFD 12 (Eq.6.10.9.3.2-8)

Where, 𝑑0 : Transverse stiffener spacing 𝑉𝑛 : Nominal shear resistance of the panel

③ User's option

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101

Users need to specify that the web is stiffened by checking the check box at:

User's option

▶Composite Steel Girder Design Parameters >Options for Strength Limit State AASHTO LRFD 12 >'Post-buckling Tension - Field Action for Shear Resistance (6.10.9.3.2)'. Depending (Eq.6.10.9.3.2-2) on the user's verification, the calculation will differ as shown in the following table:

[Table 2.26] User's option: Post-buckling Tension-field Action for Shear Resistance Vn , V p

Check

    0.87(1  C )   Vn  V p C  2  d   1  o     D  

2 Dtw  2.5 (b fct fc  b ft t ft ) On

Otherwise

Off

AASHTO LRFD 12 (Eq.6.10.9.3.2-8) 6.10.9.3.2-2

V p  0.58Fyw Dtw

6.10.9.3.2-3

    0.87(1  C )   Vn  V p C  2   do    1     D  

6.10.9.3.2-8

V p  0.58Fyw Dtw

6.10.9.3.2-3

Vn  Vcr  CV p

V p  0.58Fyw Dtw

1.3 Service Limit State Flange stress for permanent deformation and web bend-buckling are verified at the service limit Service Limit State state. AASHTO LRFD 12 (6.10.4.2)

The program does not check elastic deformation. Elastic deformation can be reviewed manually after moving load analysis at: ▶ Results > Deformation At the completion stage of the construction, the program applies Service II load combination, specified in AASHTO LRFD 12 Article 6.10.4.2, and reviews the permanent deformation. Therefore, the permanent deformation is reviewed only for the composite section since the section cannot be non-composite in the completed state. But, the software can assume the concrete deck in the composite section to be ineffective as per 6.10.4.2.1, which states that the concrete deck may be assumed to be ineffective for both positive and negative flexure, provided that the maximum tensile stresses in concrete deck at the section under consideration caused by Service II loads are greater than 2fr. Software performs this check and determines whether to consider the concrete deck to be effective or not.

The service limit state is reviewed as shown in the flow chart follows:

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Design Guide for midas Civil

Service Limit State 6.10.4 Check Flexure Yield in flange 6.10.4.2

Check Top flange of Composite Section

f f  0 .95 R h F yf 6.10.4.2.2-1

Check Bottom flange of Composite Section

f

f



fl  0 . 95 R h F yf 2 6.10.4.2.2-2

Check Nominal Bend-buckling Resistance for web 6.10.4.2

Positive Flexure and

D  150 ? tw

No Check Web Bend-buckling resistance for webs

f c  Fcrw

Yes

6.10.4.2.2-4

End

[Fig.2.47] Flow chart of Service Limit State

1.3.1 Flexure Flange shall satisfy the following requirements at the service limit state for the top and bottom flanges of the composite sections: (1) Top Flange The top steel flange of composite section shall satisfy the following requirement. (2.51)

f f  0.95Rh Fyf

Top Flange AASHTO LRFD 12 (Eq.6.10.4.2.2-1)

(2) Bottom Flange The bottom steel flange of composite section shall satisfy the following requirement.

ff 

fl  0.95Rh Fyf 2

(2.52) Bottom Flange

AASHTO LRFD 12 Where, (Eq.6.10.4.2.2-2) 𝑓𝑓 : Flange stress at the section under consideration due to the Service II loads calculated without consideration of flange lateral bending 𝑓𝑙 : Flange lateral bending stress at the section under consideration due to the Service II loads determined, 𝑓𝑙 ≤ 0.6 𝐹𝑤 𝑓𝑦𝑓 :specified minimum yield strength of a flange

1.3.2 Nominal Bend-buckling Resistance for webs If composite section is in positive flexure and the web section property satisfies D/tw≤ 150,

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use the service limit state shall be verified according to: (2.53)

f c  Fcrw

Nominal Bend-

buckling Resistance Where, 𝑓𝑐 : Compression-flange stress at the section under consideration due to the Service II loads calculated AASHTO LRFD 12 (Eq.6.10.4.2.2-4) without consideration of flange lateral bending Fcrw : Nominal bending-buckling resistance for webs with or without longitudinal stiffeners

Fcrw 

0.9 Ek D    tw 

2

(2.54)

 Min ( Rh Fyc , Fyw / 0.7)

Fcrw AASHTO LRFD 12 (Eq.6.10.1.9.1-1)

Where, k : bend- buckling coefficient

k

9 ( Dc / D) 2

(2.55) k

1.3.3 Concrete Deck The program verifies the stress of the concrete deck for shored construction cases in positive flexure as per Article 6.10.1.7. f deck  f r

(2.56)

Where, fdeck : longitudinal flexure stresses in the concrete deck with short-term modular ratio,n Φfr : Φ shall be taken as 0.9 and fr shall be taken as the modulus of rupture of the concrete, 0.24 √f’c as per Article 6.10.1.7

1.4 Check Constructibility Constructibility shall be verified for the three categories as shown in the following chart:

Check Contructibility 6.10.3

Check flexural resistance 6.10.3.2.1 , 6.10.3.2.2

Check longitudinal stresses In concrete deck 6.10.3.2.4

Check Shear requirement for webs 6.10.3.4

[Fig.2.48] Flow chart of Constructibility limit stage

The constructibility is checked based on the design member forces under Dead (Before).

1.4.1 Flexure The program shall verify lateral bending stress in discretely braced compression and tension flanges during the construction stages, for when slabs are not deflected yet. Therefore, the program considers all flanges as discretely braced flanges for the design check. Constructibility is verified in terms of flexural resistance according to the following flow chart:

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AASHTO LRFD 12 (Eq.6.10.1.9.1-2)

[Fig.2.49] Flow chart of flexural resistance in Constructibility Limit State

(1) Section classification [Table 2.27] Section classification

Case

Section

2 Dc E  5.7 tw Fyc

Compact or non-compact Web

2 Dc E  5.7 tw Fyc

Slender Web

Section classification AASHTO LRFD 12 (6.10.6.2.3-1)

(2) Discretely braced flanges in Compression in compression Discretely braced flanges in compression are verified according to the following three AASHTO LRFD 12 (6.10.3.2.1) equations. 1) Check flange nominal flexure yielding For the critical stages of construction, the following equation shall be satisfied. However, the requirement does not need to be checked if a section has slender web and its f l is equal to 0.

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f f  f l   f Rh Fyc

(2.57)

nominal yielding AASHTO LRFD 12 (Eq.6.10.3.2.1-1)

2)Check local buckling and lateral torsional buckling as per Article 6.10.8.2.2 and Article 6.10.8.2.3 respectively

1 f f  f l   f Fnc 3

(2.58)

flexural resistance AASHTO LRFD 12 (Eq.6.10.3.2.1-2)

(2.59)

web bend buckling AASHTO LRFD 12 (Eq.6.10.3.2.1-3)

3) Check web bend buckling as per Article 6.10.1.9 Only for the sections with slender webs, the following equation shall be checked. f bu   f Fcrw

Where, ϕf: resistance factor for flexure specified in 6.5.4.2 fbu : flange stress calculated without consideration of flange lateral bending. 𝑓𝑙 : flange lateral bending stress, 𝑓𝑙 ≤ 0.6 𝐹𝑤 𝑓𝑐𝑟𝑤 : nominal bending-buckling resistance for webs. 𝐹𝑛𝑐 : nominal flexure resistance of the flange.

(3) Discretely braced flanges in Tension The following equation shall be checked for discretely braced tension flanges.

f f  f l   f Rh Fyt

(2.60)

in Tension AASHTO LRFD 12 (6.10.3.2.2) AASHTO LRFD 12 (Eq.6.10.3.2.2-1)

1.4.2 Concrete Deck Concrete Deck If the longitudinal tensile stress in concrete deck determined as per Article 6.10.1.1.1d, AASHTO LRFD 12 exceeds Φffr then the minimum one percent longitudinal reinforcement determined as per (6.10.3.2.4) Article 6.10.1.7 is required at the section. Code recommends that the minimum reinforcement should be No. 6 bars or smaller spaced at not more than 12 inches. The total tensile force in the concrete deck is transmitted from the deck through the shear connectors to the top flange. Software assumes the shear connectors to be sufficiently present at this location to resist the force and prevent potential crushing of concrete. Software doesn’t calculate the length over which this force must be transmitted. Shear connector pitch calculations are as per Fatigue and Strength Limit State only.

Fdeck  f r

(2.61)

Where, f r  0.24

f 'c

modulus of rupture of the normal-weight concrete

ϕ : 0.9 Fdeck: Longitudinal tensile stress in the concrete deck

Fdeck 

My In

Where, 𝑛 = Es /Ec

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Design Guide for midas Civil

(2.62)

AASHTO LRFD 12 (Eq. 6.10.1.1.1d)

1.4.3 Shear The program shall use the load combinations defined in the Load Combination Type (Refer to Section 1.4.2 in this chapter) for the verification of the shear strength. Webs shall satisfy the following requirement during critical stages of construction. (2.63) AASHTO LRFD 12 Vu  vVcr (Eq. 6.10.3.3-1)

Where, 𝑉𝑢 : shear in the web at the section under consideration due to the factored loads ϕv: resistance factor for shear, ∅𝒗 = 𝟏. 𝟎 (Fig.2.41) 𝑽𝒄𝒓 : shear buckling resistance determined from Eq. 6.10.9.3.3-1

The program checks the nominal resistance for unstiffened webs and stiffened webs with the same formula as the tension field action is not considered for Constructibility check. (1) Unstiffened/Stiffened web 1) The nominal shear resistance of unstiffened/stiffened webs shall be taken as: Unstiffened/ (2.64) Stiffened web Vn  Vcr  CV p (2.65)

Vp  0.58Fyw Dtw

AASHTO LRFD 12 (Eq. 6.10.9.3.3-1) (Eq. 6.10.9.3.3-2)

2) Calculation of Ratio of shear-buckling resistance to shear yield strength, C Please refer to Section 1.2.2 in this chapter for the calculation of C.

1.5

Fatigue Limit State

For horizontally curved I-girder bridges, the range of fatigue stress due to major-axis bending plus lateral bending shall be investigated. Article 6.10.5 also mentions the requirements for Fracture. But Fracture Limit State is not considered in midas Civil. Code specifies the fatigue live load in Article 3.6.1.4 for the Fatigue check. But in the software, fatigue check is performed only for the moving load defined for the analysis.

Fatigue Limit State AASHTO LRFD 12 (6.10.5)

For considering the fatigue live load as specified in code, user will have to define a user defined vehicle and then manually edit the auto generated load combinations, so that the fatigue moving vehicle is the only vehicle considered for fatigue check and is only included in fatigue combination. For fatigue limit state, software assumes the shear connector to be provided along the entire length of the girder, ensuring composite action. Therefore, the concrete deck is assumed to be effective in computing all stresses and stress ranges applied to the composite section in the subsequent fatigue calculations.

1.5.1 Load Combinations Used for Fatigue Limit State Check For this part of design check, AASHTO LRFD 07 and 12 are applied differently in the program. Please refer to Section 5.1 in this chapter for more information. Fatigue limit shall be verified according to the two paths. Fatigue limit shall be verified according to Section 1.5.3(1) for the load combinations that are inputted as Fatigue 1 Limit State Load Combination Type (Section 1.4.2 in Chapter "Modeling and Design Variables"). For the load combinations that are inputted as Fatigue 2 Limit State, Section 1.5.3(2) shall be followed. The program verifies the load combinations defined in the Load Combination Type. If users define '(ADTT)SL ≤ 75 year (ADDTT)SL' Equivalent to Infinite Life, the verification shall consider the Fatigue II Load Combination. Otherwise, this combination of fatigue limit state shall be skipped and Fatigue I Load Combination shall be considered for verification.

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[Fig.2.50] Flow chart of Fatigue Limit Stage

1.5.2 Fatigue Limit State For the compression flange, compressive stress due to unfactored dead load is compared with the tensile stress due to factored live load before performing the fatigue check. If two times the tensile stress due to factored live load is greater than the compressive stress due to unfactored dead load, then only the fatigue check is performed. For the tension flange, fatigue check is always performed.

(1) The fatigue limit state shall be verified according to the following.  (f )  (F )n

(2.68)

Fatigue Limit State AASHTO LRFD 12 (Eq.6.6.1.2.2-1)

Where, 𝜸 : Load factor for the fatigue load combination. (𝚫𝐟) : Force effect, live load stress range due to the passage of the fatigue load. (𝚫𝐅)𝐧 : Nominal fatigue resistance.

(2) The load factor, 𝛄, specified in the table below, shall be applied for the fatigue load combination. These factors are automatically considered by the software, while auto generating the load combinations. [Table 2.28] Load combination and Load Factor

Load Combination Limit State Fatigue I LL, IM &CE only Fatigue II LL, IM &CE only

DC, DD, DW, EH, EV, ES, EL, PS, CR, SH

LL, IM, CE, BR,PL, LS

WA

WS

WL

-

1.50

-

-

-

-

0.75

-

-

-

1.5.3 Nominal Fatigue Resistance The nominal fatigue resistance is calculated differently for the load combinations in the Service 1 Limit State and the Service 2 Limit State.

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Load Factor AASHTO LRFD 12 (Table. 3.4.1-1)

(1) Nominal Fatigue Resistance Due to the Load Combinations for Fatigue I Limit State The program shall calculate the nominal fatigue resistance according to the input categories made in the fatigue dialog box (Fig.2.22). (2.69)

(F ) n  (F )TH

The program shall apply the nominal fatigue resistance according to Categories A, B, B', C, C', D, E, and E', specified in the table below. For all other cases, the nominal fatigue resistance shall be considered as 24.0 ksi (165.0 MPa).

Nominal fatigue resistance AASHTO LRFD 12 (Eq.6.6.1.2.5-1)

[Table 2.29] Constant-Amplitude Fatigue Thresholds, (ΔF)TH

Detail Category

Threshold LL, IM, CE, BR,PL, LS

US Unit(ksi) 24.0 16.0 12.0 10.0 12.0 7.0 4.5 2.6

A B B' C C' D E E'

Fatigue Thresholds For US Unit, AASHTO LRFD 12 (Table. 6.6.1.2.5-3)

SI Unit(MPa) 165.0 110.0 82.7 69.0 82.7 48.3 31.0 17.9

For SI Unit AASHTO LRFD 07 (Table. 6.6.1.2.5-3)

(2) Nominal Fatigue Resistance due to the Load Combinations for Fatigue II Limit State If Fatigue Resistance is verified for Fatigue Load Combination 2, the below equation shall be used. For the verification, the program uses the design parameter values inputted by users in the Fatigue dialog box (Fig.2.22). 1

 A 3 (F )n    N

(2.70)

N  (365)(75)n( ADTT ) SL

Fatigue Ⅱ AASHTO LRFD 12 (Eq.6.6.1.2.5-2) AASHTO LRFD 12 (Eq.6.6.1.2.5-3)

(2.71) Where, A : Constant taken from Table 2.30 n : Number of stress range cycles per truck passage taken from Table 2.31

[Table 2.30]

Detail Category A B B' C C' D E E'

Detail Category Constant, A 8

3

US Unit (x 10 (ksi )) 250.0 120.0 61.0 44.0 44.0 22.0 11.0 3.9

Constant, A ! LL, IM, CE, BR,PL, LS

11

3

SI Unit (x10 (MPa )) 82.0 39.3 20.0 14.4 14.4 7.21 3.61 1.28

A For US Unit, AASHTO LRFD 12 (Table. 6.6.1.2.5-1) For SI Unit AASHTO LRFD 07 (Table. 6.6.1.2.5-1)

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[Table 2.31] Cycles per Truck Passage, n

Longitudinal Members

>40.0 ft

≤40.0 ft

1.0

2.0

Near interior support

1.5

2.0

Elsewhere

1.0

2.0

Simple span Girders Continuous Girders

Span Length

Cantilever Girders Orthotropic Deck plate Connections Subjected to Wheel Load Cycling Trusses

Cycles per Truck Passage AASHTO LRFD 12 (Table. 6.6.1.2.5-2)

5.0 5.0 1.0 Spacing

Transverse Members

> 20.0 ft

≤20.0 ft

1.0

2.0

The n value inputted in the Fatigue Parameter dialog box (Fig.2.22) according to Table 2.31 is used for the calculation. Where, (ADTT)SL : ADTT for single lane for Webs AASHTO LRFD 12 (6.10.5.3)

1.5.4 Special Fatigue Requirement for Webs The fatigue limit state shall be verified in terms of shear buckling resistance as: Vu  Vcr

AASHTO LRFD 12

(2.72) (Eq.6.10.5.3-1)

Where, Vu : shear in the web at the section under consideration due to the unfactored permanent loads plus the factored fatigue load

Vcr  CV p V p  0.58Fyw Dtw

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Design Guide for midas Civil

(2.73) (2.74)

AASHTO LRFD 12 (Eq.6.10.9.3.3-1) AASHTO LRFD 12 (Eq.6.10.9.3.3-2)

2. Box / Tub Girder Section

Box/tub

2.1 Introduction Design of Box/Tub steel composite sections follow the same procedure as for I-Girders.

2.2 Strength Limit State The program checks the strength limit states for the flexure, shear and ductility of the composite sections.

Strength Limit States 6.11.6

Check Ductility 6.10.7.3

Check flexural resistance 6.11.7 & 6.11.8

Check shear resistance 6.10.9 & 6.11.9 [Fig.2.51] Flow Chart of Strength Limit State

2.2.1 Ductility Ductility shall be checked to prevent premature crushing of concrete. If a section is under positive flexure, ductility shall be verified as: (2.75)

DP  0.42 Dt

Ductility AASHTO LRFD 12 (Eq.6.10.7.3-1)

2.2.2 Flexure (1) Classification of Composite Section for Flexure There are four cases for checking flexural resistance of Box/Tub composite sections as shown below. Check flexural resistance 6.11.7 & 6.11.8

Yes

Positive Moment ?

No

Straight Bridge?

Compression flange?

Yes

No :Curved Bridge

No :Tension

Yes Compact Section?

No

flange

Yes

Case 1 : Check flexural resistance of Positive Flexure Moment in Compact Section

Case 2 : Check flexural resistance of Positive Flexure Moment in Noncompact Section

6.11.7.1

Case 3 : Check flexural resistance of Negative Flexure Moment & Compression flange

Case 4 : Check flexural resistance of Negative Flexure Moment & Tension flange

6.11.7.2

6.11.8.2

6.11.8.3

Positive Flexure Moment

Negative Flexure Moment End

[Fig.2.52] Strength Limit State for Flexure

The webs that are under positive flexure and satisfy the following requirements shall be

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111

considered as compact sections. Otherwise, they shall be considered as non-compact sections for the positive flexure design check. Sections of a curved bridge are considered to be noncompact. AASHTO LRFD 12 (6.11.6.2.2)

▪ Flange and web yield strength do not exceed 70 ksi (485 MPa) ▪Web satisfies the requirements in Article 6.11.2.1 as shown below. Webs without longitudinal stiffeners: D/tw ≤ 150 Webs with longitudinal stiffeners: D/tw ≤ 300 ▪ Web slenderness limit satisfies the requirements in Article 6.11.6.2.2-1 2Dcp/tw ≤ 3.76√(E/Fyc) The classification of the section under negative flexure, as compact /noncompact /slender is not required for the design checks. (2) Case 1 : Positive Flexural Moment in Compact Section

Case 1 : Check flexural resistance of Positive Flexure Moment in Compact Section 6.11.7.1

Dp  0.1Dt

Yes

No Calculate Mn

Calculate Mn D  M n  M p 1.07  0.7 p Dt  6.10.7.1.2-2

  

Mn  M p

Case 1 AASHTO LRFD 12 (6.11.7.1)

6.10.7.1.2-1

Check Flexural Resistance

Mu   f M n 6.10.7.1.1-1

End [Fig.2.53] Case 1 : Flow Chart of Flexural resistance for Compact Section in Positive Flexure Moment

For compact sections, flexure at the strength limit state shall be verified as:

Mu   f Mn

(2.76) AASHTO LRFD 12 (Eq.6.11.7.1.1-1)

Where,

1) Bending moment about the major-axis( Mu) Mu is the bending moment about the major axis due to the factored loads. The maximum bending moment from the load combinations, applied to Strength Limit State in the Load Combination Type (Refer to Chapter "Modeling Design Variable" Section 1.4.2) is applied as Mu. 2) Nominal flexure resistance(Mn) [Table 2.32] Calculation of Mn of Compact Section in Positive Flexure

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Case

Mn

D p  0.1Dt

Mn  M p

Mn AASHTO LRFD 12 (Eq.6.11.7.1.2-1)

Dp  M n  M p 1.07  0.7 Dt 

Otherwise

AASHTO LRFD 12 (Eq.6.11.7.1.2-2)

  

If a section is under positive flexure, plastic moment is calculated for the location of the plastic neutral axis. For more information, please refer to Chapter "Introduction" Section 3.2. 3)

f

Flexural resistance factor are taken as 1.00 in AASHTO LRFD 12. However, if the factor is defined by users in the design parameter dialog box, the user defined value is utilized as a priority.

(3) Case 2 : Non-compact Section in Positive Moment For non-compact sections, flexural strength limit state is verified as shown in the flow chart follows. Webs of a curved bridge is considered to be non-compact sections.

Flexural resistance factor AASHTO LRFD 12 (6.5.4.2)

Case 2 AASHTO LRFD 12 (6.11.7.2)

Case2 : Check flexural resistance of Positive Flexure Moment in Noncompact Section 6.11.7.2

Compression flange?

Yes

Tub Section?

Yes

No :Tension flange

No :Box Section

Calculate Fnc

Calculate Fnc

Fnc  Fb Rh Fyc

Fnc  Fb Rh Fyc 

Fnt Fnt  Rh Fyt 

6.11.7.2.2-1

6.11.7.2.2-2

6.11.7.2.1-5

Calculate

Check Flexural Resistance

Check Flexural Resistance

f bu   f Fnc

f bu   f Fnt

6.11.7.2.1-1

6.11.7.2.1-2

End [Fig.2.54] Case 2 : Flow Chart of Flexural Resistance for Non-compact Section in Positive Flexure Moment

1) Compression Flange At the strength limit state, compression flanges shall satisfy the following in terms of Compression Flange AASHTO LRFD 12 flexure.

f bu   f Fnc

(Eq.6.11.7.2.1-1)

(2.77)

The nominal flexural resistance of the compression flange, Fnc, is taken differently for box and tub sections as:

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[Table 2.33] Calculation of Fnc

Fnc AASHTO LRFD 12 (Eq.6.11.7.2.2-2)

Section Type

Fnc

Box

Fnc  Fb Rh Fyc 

Tub

Fnc  Fb Rh Fyc

AASHTO LRFD 12 (Eq.6.11.7.2.2-1)

∆ and fv Where,  f    1  3 v  F   yc 

2

in which :

fv 

T 2 Aot fc

(2.78)

AASHTO LRFD 12 (Eq.6.11.7.2.2-3) (Eq.6.11.7.2.2-4)

Δ : a factor dependent on St. Venant torsional shear stress in the bottom flange od the tub section. Rb : Web load shedding factor

[Table 2.34] Calculation of Rb

Case

Rb

Constructibility Limit State is reviewed Rb AASHTO LRFD 12 (Eq.6.10.1.10.2)

Composite web under positive flexure satisfies Article 6.10.2.1.1&6.11.2.1.2 1.0

One or more longitudinal stiffener &

D Ek  0.95 tw Fyc

2 Dc  rw tw Otherwise,

  2 DC  awc  Rb  1    rw   1.0  1200  300awc  tw 

AASHTO LRFD 12 (Eq.6.10.1.10.2-3)

Rh : Hybrid Factor

[Table 2.35] Calculation of Rh

Case Hybrid Section Non-Hybrid or Web strength > flange strength

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Rh

Rh 

12   (3   3 ) 2D t  nw 12  2 Afn in which: 1.0

Hybrid Factor, Rh AASHTO LRFD 12 (6.10.1.10.1)

2) Tension Flange At the strength limit state, tension flanges shall satisfy:

fbu   f Fnt

(2.79)

Tension Flange AASHTO LRFD 12 (Eq.6.11.7.2.1-2)

For both box and tub type composite sections, the nominal flexure resistance of tension flange, Fnt shall be calculated as:

Fnt  Rh Fyt 

(2.80)

AASHTO LRFD 12 (Eq.6.11.7.2.1-5)

Where,

 f   1  3 v F  yt If 1 − 3 (

𝑓𝑣

𝐹𝑦𝑡

   

2

T fv  2 Ao t ft in which :

(2.81)

AASHTO LRFD 12 (Eq.6.11.7.2.2-6) (Eq.6.11.7.2.2-7)

2

) < 0, consider ∆= 0 so that 𝐹𝑛𝑡 = 0

Case 3 and 4 (4) Case 3&Case 4 : Negative Flexure Flexural resistance of negative flexure moment shall be verified as shown in the flow chart AASHTO LRFD 12 (6.11.7.2) below. (6.11.8.2) (6.11.8.3)

Check flexural resistance of Negative Flexure Moment 6.11.7.2

Compression flange?

Yes

Yes

& 6.11.8.2 & 6.11.8.3

No

No :Unstiffened Web

Stiffened web?

No :Tension flange

Yes

Tub Section?

:Closed-Box Section

Check flexural resistance Of Longitudinal Stiffened Flange

Check flexural resistance of Unsiffened Flange

Check flexural resistance of Tension Flange of Tub Section

Check flexural resistance of Tension Flange Closed-box

6.11.8.2.2-1

6.11.8.2.2-1

6.11.8.3-1

6.11.7.2.2-5

Compression flange

Tension flange End

[Fig.2.55] Case 3 & Case 4 : Flow Chart of Flexural Resistance for Negative Flexural Moment

(5) Case 3 : Compression Flange in Negative Flexural Moment For this part of design check, AASHTO LRFD 07 and 12 are applied differently in the program. Please refer to Section 5.4 in this chapter for more information.

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AASHTO LRFD 12 (Eq.6.11.8.1.1-1)

[Fig.2.56] Case 3 : Flow Chart of Flexural Resistance for Compression Flange in Negative Flexure

The program shall distinguish unstiffened and longitudinally stiffened elements depending on whether the longitudinal stiffener is applied on the compression flanges in the section property dialog box. At the strength limit state, the following requirement shall be satisfied in terms of flexure: Unstiffened Flange

fbu   f Fnc 1) Unstiffened Flange For unstiffened flanges, the following requirement shall be satisfied:

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Design Guide for midas Civil

(2.82)

AASHTO LRFD 12 (Eq.6.11.8.2.2-1)

Fnc  Fcb

 f 1   v  v Fcv

  

2

(2.83)

Fcb AASHTO LRFD 12 (Eq.6.11.8.2.2-2)

[Table 2.36] Calculation of Fcb

Case

Fcb

 f  p

Fcb  Rb Rh Fyc 

p   f  r

    0.3   f   p   Fcb  Rb Rh Fyc       Rh  r   p   

r   f

Fcb 

0.9 ERb k

f 2 AASHTO LRFD 12 (Eq.6.11.8.2.2-4)

Where, λf : slenderness ration for the compression flange

f 

b fc t fc

,  p  0.57

Ek Fyc 

and r  0.95

Ek Fyr

(2.84)

For unstiffened flanges, 𝑘 = 4.0 and 𝑘𝑠 = 5.34.

 f   1  3 v F  yc

   

AASHTO LRFD 12 (Eq.6.11.8.2.2-3)

AASHTO LRFD 12 (Eq.6.11.8.2.2-8) (Eq.6.11.8.2.2-9) (Eq.6.11.8.2.2-10)

2

in which :

fv 

T 2 Ao t fc

AASHTO LRFD 12 (Eq.6.11.8.2.2-11) (Eq.6.11.8.2.2-12)

(2.85) Fyr : smaller of the compression-flange stress at the onset of nominal yielding, with consideration of residual stress effects, or the specified minimum yield strength of the web

(2.86)

Fyr  (  0.3) Fyc  Fyw

AASHTO LRFD 12 (Eq.6.11.8.2.2-13)

[Table 2.37] Calculation of Fcv

Case  f  1.12

1.12

Fcv

Ek s Fyc

Ek s Ek s   f  1.40 Fyc Fyc 1.40

Ek s  f Fyc

Fcv

Fcv  0.85Fyc

Fcv 

AASHTO LRFD 12 (Eq.6.11.8.2.2-5)

0.65 Fyc Ek s

Fcv 

f

AASHTO LRFD 12 (Eq.6.11.8.2.2-6)

0.9 Ek s

f 2

AASHTO LRFD 12 (Eq.6.11.8.2.2-7)

2) Longitudinally Stiffened Flange Also for longitudinally stiffened flanges, the following requirement shall be satisfied as for unstiffened flanges. However, the plate-buckling coefficients, 𝑘 and 𝑘𝑠 , shall no longer be constant but calculated to account for Fnc.

Fnc  Fcb

 f 1   v  v Fcv

  

2

(2.87)

Fnc AASHTO LRFD 12 (Eq.6.11.8.2.2-1)

For longitudinally stiffened compression flanges, 𝑘 and 𝑘𝑠 are determined depending on the number and location of stiffeners applied to the flanges. ①Plate-Buckling Coefficient for Uniform Normal Stress(k) Depending on the number of uniformly spaced stiffeners, 𝑘 shall be taken as:

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117

[Table 2.38] Calculation of k

n2

Case

n 1

k

 8I  3 k   3s   wt fc 

1

K

1

 0.894 I s  3 k   3  wt fc 

AASHTO LRFD 12 (Eq.6.11.8.2.3-1) (Eq.6.11.8.2.3-2)

1.0  k  4.0 ② Plate-Buckling Coefficient for Shear Stress (ks) 1

 I 3 5.34  2.84 s 3   wt   fc   5.34 k s n  12

ks (2.88)

AASHTO LRFD 12 (Eq.6.11.8.2.3-3)

Where, Is : moment of inertia of a single longitudinal flange stiffener about an axis parallel to the flange and taken at the base of the stiffener n : number of equally spaced longitudinal flange stiffeners w : larger of the width of the flange between longitudinal flange stiffeners or the distance from a web to the nearest longitudinal flange stiffener

[Fig.2.57] Definition of w

(6) Case 4 : Tension Flange in Negative Flexural Moment For tension flanges, flexural resistance limit state shall be verified as shown in the flow chart: The flexural resistance of negative flexure moment and tension flange will be checked by the process indicated in the flow chart below. Case 4 : Check flexural resistance of Negative Flexure Moment & Tension flange 6.11.8.3

Tub Section ?

Fnt  Rh Fyt

Fnt  Rh Fyt 

6.11.8.3-1

6.11.7.2.2-5

Check Flexural Resistance

f bu   f Fnt

6.11.8.1.1-1

End

[Fig.2.58] Case 4 : Flow Chart of Flexural Resistance for Tension Flange in Negative Moment

The tension flanges shall be verified according to:

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Design Guide for midas Civil

Tension flanges AASHTO LRFD 12 (Eq.6.11.8.1.2-1)

fbu   f Fnt

(2.89)

Fnt shall be taken as: Fnt

[Table 2.39] Calculation of Fnt

AASHTO LRFD 12 (Eq.6.11.8.3-1

Section Type

Fnt

Tub

Fnt  Rh Fyt Fnt  Rh Fyt 

 f   1  3 v F  yt

Closed-Box

2

 T   in which : f v  2 A t o ft 

AASHTO LRFD 12 (Eq.6.11.7.2.2-5) (Eq.6.11.7.2.2-6) (Eq.6.11.8.2.2-7)

2.2.3 Shear Box and tube type steel composite sections shall be verified for its shear strength as shown in the flow chart:

Check Shear resistance 6.11.9

Yes

Stiffened Web?

Interior Web Panel?

No :Unstiffened Web

No

Yes

:End panel

Case 1 : Check Shear resistance of Stiffened & Interior Web Panel

Case 2 : Check Shear resistance of Stiffened & End Web Panel

Case 3 : Check Shear resistance of Unstiffened Web

6.10.9.3.2

6.10.9.3.3

6.10.9.2

Stiffened Web

Unstiffened Web End

[Fig.2.59] Flow Chart of Shear Resistance

The program classifies stiffened and unstiffened webs as shown in the table below: [Table 2.40] Classification of Stiffened Web and Unstiffened Web

Case

Classification

Without a longitudinal stiffener and with transverse stiffener spacing not exceeding 3D Stiffened web With one or more longitudinal stiffeners and with a transverse stiffener spacing not exceeding 1.5D Otherwise

Unstiffened web

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119

(1) Shear Strength Verification Shear strength shall be verified as shown in the flow chart: Check shear resistance 6.10.9

Stiffened web?

No

Yes

Unstiffened webs

Stiffened Web Panels

6.10.9.2

6.10.9.3

Interior Web Panel?

Yes

No

:Stiffened Interior Web Panels

:Stiffened End panel

Calculate V n

Calculate V n

2Dtw  2.5  bfttft

b t

V n  V cr  CV p

V n  V cr  CV p

V p  0 . 58 F yw Dt w

V p  0 . 58 F yw Dt w

6.10.9.2-1 6.10.9.2-2

6.10.9.3.3-1 6.10.9.3.3-2

Vn

fc fc



No

Yes

Calculate V n

Calculate V n

    V p C   

    d0   D 

0 . 87 (1  C )  d  1  0   D 

2

  0 . 87 (1  C )  V n  V p C  2 d   1  0    D  

6.10.9.3.2-8

      

6.10.9.3.2-2

Check V n

Vu  V V n 6.10.9.1-1

End

[Fig.2.60] Flow Chart of Strength Limit State for Shear

Shear strength shall be verified as: Vu  vVn

(2.90)

Shear strength AASHTO LRFD 12 (Eq.6.10.9.1-1)

Where, ϕv: resistance factor for shear Vu : shear in the web at the section under consideration due to the factored loads

1) Unstiffened web For unstiffened webs, the nominal shear resistance (Vn) shall be taken as:

Vn  Vcr  CVp

Unstiffened web AASHTO LRFD 12 (Eq.6.10.9.2-1)

(2.91)

in which:

Vp  0.58Fyw Dtw

Where, C : ratio of the shear-buckling resistance to the shear yield strength Vp : plastic shear force

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Design Guide for midas Civil

(2.92)

AASHTO LRFD 12 (Eq.6.10.9.2-2)

2) Stiffened Web Shear Strength Program shall determine whether a stiffened web belongs to an end panel or interior panel depending on whether its nodes are supported or not in the span information. The web shall be first identified as an end panel or an interior panel and, then, its shear strength shall be verified. If a web is supported at its nodes, the web belongs to an end panel; if not supported, it belongs to an interior panel.

① End panels For end panel webs, the nominal shear resistance shall be taken as:

End panels AASHTO LRFD 12 (Eq.6.10.9.3.3-1)

Vn  Vcr  CVp

(2.93) AASHTO LRFD 12 (Eq.6.10.9.3.3-2)

in which:

Vp  0.58Fyw Dtw

(2.94)

② Interior panels For interior panels, the nominal shear resistance shall be taken as: [Table 2.41] Calculation of Vn for Interior Panel

Case

Nominal shear resistance (Vn)

2 Dtw  2.5 (b fct fc  b ft t ft )

    0.87(1  C )   Vn  V p C  2  d   1  o     D  

Otherwise,

  0.87(1  C )  Vn  V p C  2 d d   1  o   o  D D 

Interior panels AASHTO LRFD 12 (Eq.6.10.9.3.2-2)

      

AASHTO LRFD 12 (Eq.6.10.9.3.2-8)

Where, [Table 2.42] Calculation of Ratio of the shear buckling resistance to the shear yield strength, C

Case

C

D Ek  1.12 tw Fyw

C  1.0

Ek D Ek 1.12   1.40 Fyw t w Fyw

1.40

Ek D  Fyw t w

Where, k: shear-buckling coefficient

1.12 C D tw

C AASHTO LRFD 12 (Eq.6.10.9.3.2-4)

AASHTO LRFD 12 (Eq.6.10.9.3.2-5)

Ek Fyw

1.57  Ek C 2   D   Fyw    tw 

   

AASHTO LRFD 12 (Eq.6.10.9.3.2-6)

k AASHTO LRFD 12 (Eq.6.10.9.3.2-7)

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121

k 5

(2.95)

5  do    D

2

(2) Check for Inclination For box and tube composite sections, inclination of webs shall be considered. Shear force on each section shall be evenly applied to its two webs after the consideration of the incline angle as:

Vui 

Vu cos 

(2.96)

[Fig.2.61] Inclination of Web Where, Vui : shear on each web due to the factored loads Vu : vertical shear due to the factored loads on one inclined web θ: the angle of inclination of the web plate to the vertical(degrees)

2.3 Service Limit State For box and tub composite sections, flexure and web bend-buckling at the service limit state are verified as shown in the flow chart below. The program shall verify service limit state for the composite sections at the completion stage of construction. Load combinations defined in the Load Combination Type (Please Refer to Chapter "Modeling Design Variable" Section 1.4.2) shall be used for the verification of the service limit state.

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Design Guide for midas Civil

Inclination AASHTO LRFD 12 (Eq.6.11.9-1)

Service Limit State 6.11.4 Check Flexure Yield in flange 6.10.4.2

Check Top flange of Composite Section

f f  0 .95 R h F yf

Top steel flange AASHTO LRFD 12 (Eq.6.10.4.2.2-1)

6.10.1.2.2-1

Check Bottom flange of Composite Section

f

f



fl  0 . 95 R h F yf 2 6.10.4.2.2-2

Check Nominal Bend-buckling Resistance for web 6.10.4.2

Calculate Fcrw 

0.9 Ek D    tw 

2

Fcrw

and

 Min ( Rh Fyc , Fyw / 0.7)

6.10.1.9.1-1

Bottom steel flange AASHTO LRFD 12 (Eq.6.10.4.2.2-2)

k k

9 (Dc / D) 2

6.10.1.9.1-2

Check Web Bend-buckling resistance for webs

f c  Fcrw 6.10.4.2.2-4

Bend-buckling AASHTO LRFD 12 (Eq.6.10.4.2.2-4)

End

[Fig.2.62] Flow Chart of Service Limit State Fcrw AASHTO LRFD 12 (Eq.6.10.1.9.1-1)

2.3.1. Flexure Flexure shall be verified at top and bottom flanges. As per Article C6.11.4, Eq. 6.10.4.2.2-1 and 6.10.4.2.2-2 are checked only for compact sections in positive flexure. Thus in midas Civil, these equations are not checked for negative flexure and noncompact sections in positive flexure. k

AASHTO LRFD 12 (Eq.6.10.1.9.1-2)

(1) Verification of Top steel flange of composite sections for flexure Serviceability of top steel flanges shall be verified by comparing the stress as: (2.97)

f f  0.95Rh Fyf

(2) Verification of Bottom steel flange of composite sections for flexure Serviceability of bottom steel flanges shall be verified by examining flexure as shown in the equation below. If a web is under positive flexure and satisfies the requirements in AASHTO LRFD 12 Article 6.11.2.1.2, its strength shall be determined to be satisfactory and verification shall be skipped. For box and tub composite sections, flange lateral bending stress shall be assumed as 0 for the design check.

ff 

fl  0.95Rh Fyf 2

(where, f l = 0)

(2.98)

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123

2.3.2. Web Bend Buckling Except for sections in positive flexure in which the web satisfies the requirement of Article 6.11.2.1.2, all sections shall satisfy Eq.6.10.4.2.2-4 shown below. Webs shall be verified in terms of bend-buckling as: (2.99)

f c  Fcrw

Where, fc : compression-flange stress Fcrw : nominal bend-buckling resistance for webs

Fcrw 

0.9 Ek 2

(2.100)

 Min ( Rh Fyc , Fyw / 0.7)

D    tw  in which: k : bend-buckling coefficient

k

9 ( Dc / D) 2

(2.101)

Where, Dc : Depth of the web in compression in the elastic range

2.4 Check Constructibility For box and tub composite sections, constructibility shall be verified in terms of flexure and shear. Member force under Dead (Before) shall be used as the design member force for the Tub Section AASHTO LRFD 12 verification of constructibility limit strength. (Eq.6.10.3.2.1-1) (Eq.6.10.3.2.1-2)

AASHTO LRFD 12 2.4.1 Flexure The program shall verify flexural strength by assuming that concrete hardening has not (Eq.6.10.3.2.1-3) occurred yet and all section are discretely braced. The flexural verification shall be done in three cases as shown in the figure follows. Tub Section AASHTO LRFD 12 (Eq.6.10.3.2.2-1) Check Constructibility 6.11.3

Yes

Yes

Compression flange?

No :Tension flange

No

Tub Section?

:Closed-Box Section

Check Flange stress of Tub Section in Compression

Check Flange stress of Closed-Box in Compression

Check Flange stress of Closed-Box in Tension

6.10.3.2.1

6.11.3.2-1~2

6.11.3.2-3~5

Comp. Box Flange AASHTO LRFD 12 (Eq.6.11.3.2-1) (Eq.6.11.3.2-2)

End

[Fig.2.63] Flow Chart of Flexural Resistance for Constructibility Limit State

(1) Open Flange (top flange of tub section) in Compression and Tension 1) Open flange in compression For tub composite sections, compression top flanges shall be verified for yielding, flexure and bend buckling of webs, as shown in the equation below. If 𝑓𝑙 = 0 for slender webs,

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Tension Box Flange AASHTO LRFD 12 (Eq.6.11.3.2-3)

AASHTO LRFD 12 (Eq.6.11.3.2-4) (Eq.6.11.3.2-5)

AASHTO LRFD 12 Eq.6.10.3.2.1-1 shall not be verified. f bu  f l   f Rh Fyc

and

1 f bu  f l   f Fnc 3

(2.102)

For slender webs, bend-buckling shall be verified as: (2.103)

f bu   f Fcrw

2) Open flange in tension

Shear AASHTO LRFD 12 (Eq.6.10.3.3-1) AASHTO LRFD 12

For tub composite sections, tension top flanges shall satisfy the requirement of Eq. (Eq.6.10.9.3.3-1) (Eq.6.10.9.3.3-2) 6.10.3.2.2-1 which is same as that for I girder. (2) Noncomposite box flange (top flange of box section and bottom flange of tub or box section) in Compression and Tension ( for constructability check, the top flange of box section is designed as a noncomposite box flange) 1) Noncomposite box flange in compression For box flanges in compression, constructibility shall be examined based on the compressive stress due to flexure and bend buckling on webs. For sections with compact or noncompact webs, Eq. 6.11.3.2-2 shall not be checked as per Article 6.11.3.2. ▪Verification of compression stress due to flexure : f bu   f Fnc (2.104) ▪ Verification of bend buckling on webs : f bu   f Fcrw

(2.105)

2) Noncomposite box flange in tension and continuously braced box flange in tension or compression shall satisfy the following requirement: (2.106)

f bu   f Rh Fyf 

Where,

 f   1  3 v F  yf

   

2

in which :

fv 

T 2 Ao t f

(2.107)

2.4.2 Shear For the verification of constructibility, shear shall be verified to prevent shear buckling at webs according to the following requirement. The program shall distinguish end panel and interior panel for the verification of shear-buckling resistance. (2.108) Vu  vVcr Where,

Vcr  CVp

in which:

Vp  0.58Fyw Dtw

(2.109)

2.4.3 Concrete Deck Constructibility of concrete deck shall not be verified for the box and tub steel composite sections.

2.5 Fatigue Limit State 2.5.1 Load combinations of Fatigue Limit State In this section, AASHTO LRFD 07 and 12 are applied differently. For more information about the 07 edition, please refer to Section 5.1 in this chapter. For more information on basic considerations and assumptions for Fatigue Limit State, please refer to Section 1.5 in this chapter. Fatigue limit state shall be verified as shown in the flow chart:

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125

Fatigue Limit State AASHTO LRFD 12 (Eq.6.6.1.2.2-1)

[Fig.2.64] Flow Chart of Fatigue Limit State for Flexure

The verification of fatigue resistance shall follow Section 2.5.3(1) for the load combinations of Fatigue 1 Limit State in Load Combination Type (Chapter "Modeling Design Variables" Section 1.4.2) and Section 2.5.3(2) for the load combinations of Fatigue 2 Limit State. However, if '(ADTT)SL≤ 75year (ADTT)SL' is inputted, Fatigue II Load Combination is verified. Otherwise, the verification needs not to be done.

2.5.2 Fatigue Limit State As per Article 6.11.5, one additional requirement specified particularly for tub girders sections is in regard to longitudinal warping and transverse bending stresses. When tub girders are subjected to torsion, their cross-sections become distorted, resulting in secondary bending stresses. Therefore, longitudinal warping stresses and transverse bending stresses due to cross-section distortion shall be considered for:  Single tub girder in straight or horizontally curved bridges  Multiple tub girders in straight bridges that do not satisfy requirements of Article 6.11.2.3  Multiple tub girders in horizontally curved bridges  Any single or multiple tub girder with a tub flange that is not fully effective according to the provisions of Article 6.11.1.1.

Fatigue Ⅰ AASHTO LRFD 12 (Eq.6.6.1.2.5-1) AASHTO LRFD 12 (Table. 6.6.1.2.5-3)

Fatigue Ⅱ AASHTO LRFD 12 (Eq.6.6.1.2.5-2) (Eq.6.6.1.2.5-3)

For consideration of these distorsion stresses in the software, Longitudinal Warping Stress Range input is required in the fatigue parameters dialog box. (Fig.2.21) Fatigue limit state shall be verified per stress unit as:  (f )  (F )n Where, γ : load factor for fatigue load combination (∆f) : force effect, live load stress range due to the passage of the fatigue load (∆F)n : nominal fatigue resistance

2.5.3 Nominal Fatigue Resistance

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Design Guide for midas Civil

(2.110)

AASHTO LRFD 12 (Table. 6.6.1.2.5-1) (Table. 6.6.1.2.5-2)

Special Fatigue Requirement AASHTO LRFD 12

The program’s calculation of Nominal Fatigue Resistance will be different based on whether the (Eq.6.10.5.3-1) load combinations are entered into Fatigue 1 Limit State or Fatigue 2 Limit State. Between the two values, the lower value will be applied and reviewed. ASHTO LRFD 12 (Eq.6.10.5.3.3-1) (Eq.6.10.5.3.3-2) (1) The Nominal Fatigue Resistance of Fatigue I Limit State due to load combinations The program will calculate the Nominal Fatigue Resistance based on the category selected in the Fatigue dialog window.

(2.111)

(F ) n  (F ) TH

Within the program, categories of Nominal Fatigue Resistance, such as A, B, B', C, C', D, E, and E' are applied as shown in [Table2.29]. (2) The Nominal Fatigue Resistance of Fatigue II Limit State due to load combinations If fatigue review is performed with consideration to fatigue load combination 2, the following equation is used to calculate the resistance value of fatigue. 1

 A 3 (F ) n    N

in which: N  (365)(75)n( ADTT ) SL

(2.112)

Where, A : Constant taken from Table 6.6.1.2.5-1 n : Number of stress range cycles per truck passage taken from Table 6.6.1.2.5-2 (ADTT)SL : ADTT for single lane

Section Proportion AASHTO LRFD 12 (6.10.10.1.1)

Pitch AASHTO LRFD 12 (Eq.6.10.10.1.2-1)

The value of the Detail Category Constant (A) and 75-yr (ADTT)SL Equivalent to Infinite Life (n, truck per day) are each respectively applied in [Table2.30] and [Table2.31]. If, the n value is entered into the Fatigue Parameter, this value will be applied first. 2.5.4 Special Fatigue Requirement for Webs The program will perform the review of the fatigue due to the shear buckling of the web. (2.113)

Vu  Vcr

Where, Vcr : shear in the web at the section under consideration due to the unfactored permanent loads plus the factored fatigue load

Vcr  CVp

in which: V p

 0.58Fyw Dtw

Center-to-Center Pitch AASHTO LRFD 12 (6.10.10.1.2)

Vsr AASHTO LRFD 12 (Eq.6.10.10.1.2-2)

(2.114) Vfat

AASHTO LRFD 12 (Eq.6.10.10.1.2-3)

Ffar AASHTO LRFD 12 (Eq.6.10.10.1.2-4) (Eq.6.10.10.1.2-5)

3. Shear Connector When the shear connector is defined in the steel composite sections, the review of the shear connectors is performed. The shear connector performs review of Pitch, Transverse spacing, Cover and Penetration, Fatigue, Special Requirement for point, and strength limit state.

3.1 Section Proportion For the ratio of height to diameter of the stud type shear connector, following equation is used.

h  4.0 d

(2.115)

3.2 Pitch The pitch is reviewed using the below equation.

Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012)

127

p

nZ r Vsr

(2.116)

Where, Zr : shear fatigue resistance of an individual shear connector determined as per Article 6.10.10.2 n : number of shear connector in a cross section Vsr : horizontal fatigue shear range per unit length

Also, the program checks if 𝑝 ≥ 6 × 𝑆𝑡𝑢𝑑 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 and 𝑝 ≤ 24 𝑖𝑛𝑐ℎ𝑒𝑠 are satisfied as well k AASHTO LRFD 12 as Equation 2.116. (Eq.6.11.8.2.3-1) (Eq.6.11.8.2.3-2)

V   F 

Vsr 

2

fat

2

(2.117)

fat

in which : Vfat: longitudinal fatigue shear range per unit length

V fat 

Vf Q

(2.118)

I

Ffat : radial fatigue shear range per unit length taken as the largest of either

F fat1 

Abot f lg l wR

or F fat 2 

Frc w

(2.119) in which : σflg: range of longitudinal fatigue stress in the bottom flange without consideration of flange lateral bending Abot: area of the bottom flange Frc : net range of cross-frame of diaphragm force at the top flange l : distance between brace point R : minimum girder radius within the panel w : effective length of deck (in.) taken as 48.0 in., except at end supports where w may be taken as 24.0 in. effective length of deck distance

▪ If it is straight members, the value of Ffat1 is 0. ▪ If it is a Box/Tub section, regardless of whether it is straight or curved, the value of Ffat1 is 0. Zr ▪ The program will consider the value of Ffat2 as 0. AASHTO LRFD 12 ▪ The center-to-center distance of the shear connectors cannot exceed 24inches and 6 times the (Eq.6.10.10.2-2) diameter of the stud. α AASHTO LRFD 12 (Eq.6.10.10.2-3)

3.3 Transverse spacing

(1) The transverse spacing of the shear connector must be more than 4 times the diameter of the stud. Zr (2)The shear connectors must be located 1 inch inwards from the edge.

AASHTO LRFD 12 (Eq.6.10.10.2-1)

[Table 2.43] Calculation of plate-buckling coefficient for uniform normal stress, k

Case

n=1

n=2

K

 8I  3 k   3s   wt fc 

1

1.0  k  4.0

1

 0.894 I s  3 k   3  wt fc 

minimum number of shear connector AASHTO LRFD 12 (Eq.6.10.10.4.1-2)

3.4 Cover and penetration The following conditions must be met for the cover and penetration of the shear connector. (1)The clear depth of concrete cover over the tops of the shear connector must not be at least Qr 2.0 inches. AASHTO LRFD 12 (2) The shear connector must penetrate at least 2.0 inches into the concrete slab.

(Eq.6.10.10.4.1-1)

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Design Guide for midas Civil

3.5 Fatigue Shear Resistance, Zr This part is applied differently in the AASHTO LRFD 07 and 12. For the 07 conditions, follow Section 5.2 of this chapter. The fatigue shear resistance of the shear connector is calculated as shown in the following table. [Table 2.44] Calculation of Fatigue Shear Resistance , Zr

Shear Connector Type

Case

Fatigue shear resistance ( Z r )

Z r  d 2 75  year ( ADTT ) SL  960 Stud

75  year ( ADTT )SL  960

Where,

Case



N 0

34.5

N 0

34.5  4.28 log N

Calculate P AASHTO LRFD 12 (Eq.6.10.10.4.2-1)

Zr  5.5d 2 P1p , P2p AASHTO LRFD 12 (Eq.6.10.10.4.2-2)

3.6 Strength Limit State

(1) Strength Limit State After the strength limit state is calculated, the minimum number of shear connector (n) Is (Eq.6.10.10.4.2-3) calculated as shown in the equation below. P (2.120) n AASHTO LRFD 12 Qr (Eq.6.10.10.4.2-4)

Where, P : total nominal shear force

(2) Factored shear resistance of a single shear connector The resistance of the shear connector is calculated as shown in the equation below.

Qr  scQn

(2.121)

Calculate P Where, AASHTO LRFD 12 Qn : nominal shear resistance of a single shear connector determined as in Article 6.10.10.4.3 (Eq.6.10.10.4.2-5) ϕsc: resistance factor for shear connectors inputted by the user in Composite Steel Design Parameter (Fig.2.17)

PT

(3) Total Nominal Shear Force, P 1) Calculate the Total Nominal Shear Force, P, for the verification of the shear connectors under positive moment.

P

Pp  Fp 2

2

Where, Pp : total longitudinal force in the concrete deck

Pp  Max( P1 p , P2 p )

AASHTO LRFD 12 (Eq.6.10.10.4.2-6)

(2.122)

P1n , P2n (2.123) AASHTO LRFD 12 (Eq.6.10.10.4.2-7) (Eq.6.10.10.4.2-8)

in which :

P1 p  0.85 f s ' bs t s

(2.124)

P2 p  Fyw Dtw  Fyt b ft t ft  Fyc b fc t fc

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129

Fp : total radial force in the concrete deck I t1  I t 2

(2.125) FT

AASHTO LRFD 12 (Eq.6.10.10.4.2-9)

in which : Lp : arc length between an end of the girder and an adjacent point of maximum positive live load plus impact moment

For straight bridges, the value of Fp is calculated as 0.

2) Calculate P when the shear connector experiences a negative moment.

P

PT  FT 2

2

(2.126)

Where, Pt : total longitudinal force in the concrete deck between the point of maximum positive live load plus Qn impact moment and the centerline of an adjacent interior support AASHTO LRFD 12

PT  Pp  Pn

(2.127)

(Eq.6.10.10.4.3-1)

in which : Pn : total longitudinal force in the concrete deck over an interior support taken as:

Pn  Min( P1n , P2n )

(2.128)

in which :

(2.129)

P1n  Fyw Dtw  Fyt b ft t ft  Fyc b fc t fc

P2n  0.45 fc ' bsts Ft : total radial force in the concrete deck between the point of maximum positive live load plus impact moment and the centerline of an adjacent interior support taken as:

FT  PT

Ln R

(2.130)

in which : Ln : arc length between the point of maximum positive live load plus impact moment and the centerline of an adjacent interior support inputted by the user in shear connector dialog box (Fig.2.19)

For straight bridges, the value of Fp is calculated as 0.

(4) Nominal shear resistance, Qn [Table 2.45] Calculation of Nominal Shear Resistance, Qn

Shear Connector Type

Qn Qn  0.5 Asc fc ' Ec  Asc Fu

Stud

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Design Guide for midas Civil

Where, Asc : cross-sectional area of a stud shear connector Ec : modulus of elasticity of the deck concrete Fu : specified minimum tensile strength of a stud shear connector

Projecting width AASHTO LRFD 12 (Eq.6.10.11.1.2-2) AASHTO LRFD 12 (Eq.6.10.11.1.2-1)

4. Stiffener The Stiffener calculates the transverse/longitudinal stiffener attached to the web and the longitudinal stiffener attached to the compression flange.

Stiffeners 6.10.11

Check Transverse Stiffeners

Check Longitudinal Stiffeners

Check Longitudinal Compression Flange Stiffeners

Only Box Section

[Fig.2.65] Flow Chart of Stiffener

4.1 Web Transverse Stiffener (1) Projecting Width Projecting width of transverse stiffener attached to web panel shall satisfy following two conditions: [Table 2.46] Projecting Width Conditions of Web Transverse Stiffener

Check List

I Section

Condition 1

Tub Section

Closed-Box Section

16t p  bt  b f / 4

Condition 2

16t p  bt

bt  2.0 

AASHTO LRFD 12 (Eq.6.10.11.1.3-1) (Eq.6.10.11.1.302)

D 30

Where, tp : thickness of the projecting stiffener element bf :for I-sections, full width of the widest compression flange. for tub section, full width of the widest top AASHTO LRFD 12 flange. For closed box section, the limit of bf/4 does not apply.

(Eq.6.10.11.1.3-3) (Eq.6.10.11.1.3-4) (Eq.6.10.11.1.3-5)

[Table 2.47] Define bf according to Section Type

Section Type

bf

I

Full width of the widest compression flange with in the field section under consideration

Tub

Full width of the widest top flange within the field section under consideration AASHTO LRFD 12 (6.10.11.1.3)

(2) Moment of Inertia Check AASHTO LRFD 12 This part is applied differently in the AASHTO LRFD 07 and 12. For the 07 conditions, follow the (Eq.6.10.11.1.3-6) section 5.3 of this chapter. The program will perform the calculation of the vertical stiffeners attached to the web. 1) Vu>Vn

I t  Min ( I t1 , I t 2 )

(2.131)

Where,

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131

It : moment of inertia of transverse stiffener [Table 2.48] Calculation of Moment of Inertia of the transverse stiffener for I girder section, It

It

Case

It  t p

Single-sided vertical stiffeners

b 3t 3

AASHTO LRFD 12 (Eq.6.10.11.1.3-9)

 b 3t 2 I t  2 t p  bt t p 0.5bt  0.5tw    12 

Double-sided vertical stiffeners

AASHTO LRFD 12 (Eq.6.10.11.1.3-10)

It1  btw J 3

It 2 

J

D 4 t 40

1.3

1.5

 Fyw     E 

(2.132) AASHTO LRFD 12 (Eq.6.10.11.1.3-11)

2.5  2.0  0.5 ( d o / D) 2

Where, J : stiffener bending rigidity parameter

(2.133)

t  Max( Fyw / Fcrs ,1.0) Fcrs : local buckling stress for the stiffener

Fcrs 

0.31E  bt     tP 

2

 Fys

(2.134) longitudinal stiffener AASHTO LRFD 12 (Eq.6.10.11.3.1-1)

Fys : specified minimum yield strength of the stiffener do : the smaller of the adjacent web panel widths b : the smaller of do and D C : ratio of the shear-buckling resistance

2) Vu≤Vn [Table 2.49] Check for Transverse Stiffener when Vu≤Vn

Case

I t1  I t 2

Verifications

Vn  Vcr

 V  vVvr I t  I t1  ( I t 2  I t1 ) u  vVn  vVcr

  

It  It 2

Otherwise Otherwise

projecting width AASHTO LRFD 12 (Eq.6.10.11.3.2-1)

It  It 2

3) The following is calculated when the transverse and longitudinal stiffeners attach to the web at the same time.

 b  D   I l I t   t   bl  3.0d o  Where, bt : projecting width of the transverse stiffener bl : projecting width of the longitudinal stiffener

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Design Guide for midas Civil

(2.135) AASHTO LRFD 12 (Eq.6.10.11.3.3-1) (Eq.6.10.11.3.3-2)

Il : moment of inertia of the longitudinal stiffener

4.2 Web Longitudinal Stiffener (1) Strength limit state The longitudinal stiffener attached to the web is calculated as shown in the falling equation.

f s   f Rh Fys

(2.136)

Where, fs : the flexural stress in the longitudinal stiffener Fys : specified minimum yield strength of the stiffener β

(2) Projecting width AASHTO LRFD 12 The projecting width of the Longitudinal stiffener is limited as per the following equation. As (Eq.6.10.11.3.3-3) per Article C6.11.11.2, for the structural tees, b l should be taken as one half the width of the flange. AASHTO LRFD 12 (Eq.6.10.11.3.3-4)

bl  0.48ts

E Fys

(2.137) Z AASHTO LRFD 12 (Eq.6.10.11.3.3-5)

Where, ts: thickness of the stiffener

(3) Moment of inertia and radius gyration Moment of inertia and radius of gyration are calculated using the dimensions inputted in the Section Stiffener dialog box (Fig.2.8). The moment of inertia and the radius of gyration of the longitudinal stiffener shall satisfy:

  do 2  3 I l  Dtw 2.4   0.13    D  

and

r

0.16d o 1  0.6

Fys E Fyc

(2.138)

projecting width AASHTO LRFD 12 (Eq.6.10.11.2-1)

Rh Fys

Where, do : transverse stiffener spacing R : minimum girder radius in the panel r : radius of gyration of the longitudinal stiffener including an effective width of the web equal to 18*tw taken about the neutral axis of the combined section Moment of inertia Il : moment of inertia of the longitudinal stiffener including an effective width of the web equal to 18*tw AASHTO LRFD 07&12 (Eq.6.10.11.2-2) taken about the neutral axis of the combined section β :curvature correction factor for longitudinal stiffener rigidity [Table 2.50] Calculation of β



Case For cases where the longitudinal stiffener is on the side of the web away from the center of curvature



Z 1 6

For cases where the longitudinal stiffener is on the side of the web toward the center of curvature



Z 1 12

Where, Z : curvature parameter

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133

2

Z

0.95d o  10 Rt w

(2.139)

4.3 Longitudinal Compression Flange Stiffener (for box compression flange) (1) The strength of the stiffeners must be greater than the yield strength of the compression flanges. (2) Projecting Width The Projecting Width (bl) of the Longitudinal Compression Flange Stiffener is calculated as shown in the following equation.

E Fyc

bl  0.48t s

(2.140)

Where, ts: thickness of the projecting longitudinal stiffener element

(3) Moment of inertia Each Moment of inertia of the Longitudinal Compression Flange Stiffener Is calculated as shown in the following equation.

I l  wt fc

3

(2.141)

Where, w : larger of the width of the flange between longitudinal flange stiffeners or the distance from a web to the nearest longitudinal flange stiffener [Table 2.51] Calculation of ψ

Number of the longitudinal stiffener attached to compression flange(n)



n 1

0.125k 3

n2

1.120k 3

n3

Equally applicable as n=2

Where, k : plate-buckling coefficient for uniform normal stress

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Design Guide for midas Civil

5. Difference Between AASHTO-LRFD 4th(2007) and AASHTOLRFD 6th(2012) This section explains how the functions of midas Civil are applied differently in AASHTO-LRFD 4 th Edition (2007) and AASHTO-LRFD 6 Edition (2012).

th

5.1 Fatigue Limit State In both standards, the fatigue resistance is calculated differently. th

th

AASHTO-LRFD 4 Edition (2007)

AASHTO-LRFD 6 Edition (2012)

The calculation only considers the Fatigue 2 Based on the conditions, the calculation Load Combination out of the user load considers the Fatigue 1 or 2 Load Combination. combinations.

Fatigue Resistance (ΔF)n Calculation Fatigue 1 Load Case Combination Is not used in the calculation.

Fatigue Resistance (ΔF)n Calculation When using the Fatigue 1 Load Case Combination, the value of ΔF)n Is calculated as such:

AASHTO LRFD07&12 (6.6.1.2.3) (6.6.1.2.5)

(F ) n  (F )TH

When using the Fatigue 2 Load Case Combination, the value of ΔF)n Is calculated as such:

When using the Fatigue 2 Load Case Combination, the value of ΔF)n Is calculated as such: 1

1 3

1  A (F ) n     (F )TH 2 N in which: N  (365)(75)n( ADTT ) SL

 A 3 (F )n    N in which: N  (365)(75)n( ADTT ) SL

5.2 Fatigue Limit State for Shear Connector In both standards, Fatigue resistance for Shear Connector (Zr) is calculated differently. th

AASHTO-LRFD 4 Edition (2007)

th

AASHTO-LRFD 6 Edition (2012)

The Fatigue resistance(Zr) of the stud type for The Fatigue resistance(Zr) of the stud type for the Shear Connector is calculated as such: the Shear Connector is calculated as such:

38.0d 2 Z r  d 2  2

(in SI Unit)

  238  29.5 log N ( in SI Unit)

AASHTO LRFD07&12 (6.10.10.2)

Z r  d 2 (in US Unit)   34.5  4.28 log N ( in US Unit)

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135

5.3 Transverse Stiffener In both standards, Transverse Stiffener is calculated differently th

th

AASHTO-LRFD 4 Edition (2007) Calculation of the Stiffener bending rigidity parameter(J)

AASHTO-LRFD 6 Edition (2012) Calculation of the Stiffener bending rigidity parameter(J)

2

 D    2.0  0.5 J  2.5  do / D 

J

2.5  2.0  0.5 ( d o / D) 2 AASHTO LRFD07&12 (6.10.11.1.3)

When the Web post buckling or tension-field When the Web post buckling or tension-field resistance is considered, the following is resistance is considered, the following is calculated. calculated.

It  It 2

I t1  I t 2 1) Vn  Vcr

(1)

 V  vVvr I t  I t1  ( I t 2  I t1 ) u  vVn  vVcr 2) Other conditions

It  It 2 (2)

I t1  I t 2 It  It 2

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Design Guide for midas Civil

  

5.4 Flexure Resistance of Box Flange in compression under Unstiffened condition In both standards, the Flexure Resistance of Box Flange in compression under Unstiffened condition is calculated differently.

th

th

AASHTO-LRFD 4 Edition (2007)

AASHTO-LRFD 6 Edition (2012)

(1) Fnc

(1) Fnc

kE Fyc

1)  f  R1

 f  1   v   v Fcv 

Fnc   f Fcb

Fnc  Rb Rh Fyc 

2

AASHTO LRFD07&12 (6.11.8.2.2)

1) Fcb ①  f  p

kE kE   f  R2 Fyc Fyc

2) R1

Fcb  Rb Rh Fyc 

②  p   f  r

Fcb  Rb Rh Fyc      Fyr      R h F yc    

3)  f  R2

Fnc 

   b F fc    R2  fc   t fc kE 1  sin     2 R 2  R1         

                   

kE Fyc

0.9 ERb k  b fc    t   fc 

2

③ r   f 0.9 ERb k Fcb  f 2 2) Fcv

2



    0.2   f   p    Fcb  Rb Rh Fyc 1  1  Rh  r   p   

Rb f v k 2 0.9 Ek s

 b fc    t   fc 

2

Fcv  0.85Fyc

② 1.12 Ek s    1.40 Ek s f Fyc

Fcv 

Where, R1 : constant which when multiplied by kE / F yields the slenderness ratio equal to 0.6 times the slenderness ration for which Fnc from Eq.3 is equal to Rb Rh Fyc 

Fyc

0.65 Fyc Ek s

f

③ 1.40 Ek s   f Fyc

yc

R1 

Ek s Fyc

①  f  1.12

Fcv 

0.9 Ek

f 2

0.57 2 2   f v   k   1 2        4 F  k   2 yc   s    

R2 : constant which when multiplied by yields the slenderness ratio for kE / F yc

Where,

 p  0.57

Ek Fyc 

r  0.595

Ek Fyr

which Fnc from Eq.3 is equal to Rb Fyc 1.23 R2  2 2 2   Fyr   f v   k   1  Fyr   4      F  F  k   1.2  Fyc  yc   yc   s    Fyr  (  0.3) Fyc  Fyw Fyr  (  0.4) Fyc  Fyw

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Chapter 2. Steel Composite Design : AASHTO-LRFD 4thand6th (2007/2012)

Steel Composite Design Result 1. Strength Limit State Result 1.1 Flexure (1) by Result Table As shown in the table below, the results can be checked in the result table. ▶ Design > Composite Design > Design Result Tables > Strength Limit State (flexure)…

[Fig.2.66] Result Table for Strength Limit State of Flexure Where, My : yield moment Mp : plastic moment Mu : moment due to the factored loads phiMn : nominal flexural resistance of a section multiplied by resistance factor, phi, for flexure fbu : largest value of the compressive stress throughout the unbraced length in the flange under condition, calculated without consideration of flange lateral bending phiFn : nominal flexure resistance of a flange Dp :distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment Dt : total depth of the composite section

Based on the different search conditions, the result values which appear will vary, as shown in the table below. [Table 2.52] Result Case Table for Strength Limit State of Flexure Condition

fle xu re (+)

Output Items

Section

Applied Clause

My

Mp

Mu

phiMn

fbu

phiFn

Dp

Dt

compact

6.10 & 6.11

O

O

O

O

-

-

O

O

noncompact

6.10 & 6.11

-

-

-

-

O

O

O

O

-

6.10 & 6.11

-

-

-

-

O

O

-

-

-

Appendix A6

O

O

O

O

-

-

-

-

(-)

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Design Guide for midas Civil

(2) by Excel Report The results can be viewed in an Excel Report as shown below. 1) Positive Flexure

[Fig.2.67] Excel Report for Strength Limit State of Positive Moment

Chapter 2.Steel Composite Girder Design - AASHTO LRFD4th and6th (2007/2012)

139

2) Negative Flexure

[Fig.2.68] Excel Report for Strength Limit State of Negative Moment

1.2 Shear (1) Result Table As shown in the table below, the results can be checked in the result table. ▶ Design > Composite Design > Design Result Tables > Strength Limit State (shear)…

[Fig.2.69] Result Table for Strength Limit State of Shear Where, Vu : shear due to the factored load phiVn : nominal shear resistance multiplied by resistance factor, phi, for shear bt_lim1 : projecting width limit for transverse stiffener, 2.0+(D/30), as per Eq. 6.10.11.1.2-1 bt_lim2 : projecting width limit for transverse stiffener, 16tp, as per Eq. 6.10.11.1.2-2 bt_lim3 : projecting width limit for transverse stiffener, bf/4, as per Eq. 6.10.11.1.2-2 bt : projected width of transverse stiffener as per Article 6.10.11.1.2 lt_lim : limiting moment of inertia of transverse stiffener as per Eq. 6.10.11.1.3-3&4 lt : Moment of Inertia of transverse stiffener as per Article 6.10.11.1.3

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.70] Excel Report for Strength Limit State of Shear

2. Service Limit State Result (1) by Result Table The results can be viewed in an Excel Report as shown below. ▶ Design > Composite Design > Design Result Tables > Service Limit State…

[Fig.2.71] Result Table for Service Limit State Where, fc : compression-flange stress fcrw: nominal bending buckling resistance for webs as per Eq. 6.10.11.9.1-1 fcf : compression-flange stress fcf_lim : limit of compression-flange stress ftf : tension-flange stress ftf_lim : limit of tension-flange stress

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.72] Excel Report or Strength Limit State of Shear

3. Constructibility Result 3.1 Flexure (1) by Result Table The results can be viewed in a result table as shown below. ▶ Design > Composite Design > Design Result Tables > Constructibility (flexure)...

[Fig.2.73] Result Table for Constructibility Limit State of flexure Where, fbuw : flange stress calculated without consideration of flange lateral bending phifcrw : nominal bend-buckling resistance for webs fbuc : compression-flange stress with consideration of flange lateral stress phifc : limit of compression-flange stress fbut : tension-flange stress with consideration of flange lateral stress phift : limit of tension -flange stress fdeck : longitudinal tensile stress in a composite section deck phifr : limit of concrete deck tensile stress. fr shall be taken as the modulus of rupture as per the Article 6.10.1.7

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.74] Excel Report for Constructibility of Positive Moment

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2) Negative Flexure

[Fig.2.75] Excel Report for Constructibility of Negative Moment

3.2 Shear (1) by Result Table The results can be viewed in a result table as shown below. ▶ Design > Composite Design > Design Result Tables > Constructibility (shear)...

[Fig.2.76] Result Table for Constructibility of Shear Where, Vu : shear in the web due to the factored load phiVcr : shear-buckling resistance multiplied by resistance factor, phi, for shear

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.77] Excel Report for Constructibility of Shear

4. Fatigue Limit State Result (1) by Result Table The results can be viewed in a result table as shown below. ▶ Design > Composite Design > Design Result Tables > Fatigue Limit State...

[Fig.2.78] Result Table for Fatigue Limit State Where, γ(Δf) (ΔF)n Lcom :

: Range of Fatigue Limit State : Nominal Fatigue Resistance Load combinations used in the calculation

Vu : shear in the web due to the unfactored permanent load plus the factored fatigue load Vcr : shear buckling resistance as per Eq. 6.10.9.3.3-1

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.79] Excel Report for Fatigue Limit State

5. Shear Connector Result (1) by Result Table The results can be viewed in a result table as shown below. ▶ Design > Composite Design > Design Result Tables > Shear Connector...

[Fig.2.80] Result Table for Shear Connector Where, H/D : height to diameter ratio (H/D)lim : limit value of height to diameter ratio (=4.0) p : pitch of shear connectors specified by the user p_lim1: pitch limit value, nZI/(Vsr), as per Eq. 6.10.10.1.2-1 p_lim2: pitch limit value, 6d s : transverse spacing of shear connectors spacing (Transverse Cross Section) edge : distance of the top compression flange edge_lim (=1.0 in) Cover : clear depth of concrete cover over the tops of the shear connectors (> 2.0 in) Penetration : depth of penetration of the shear connector(>2.0in) n : number of shear connectors entered in transverse direction n_Req : required number of shear connectors

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.81] Excel Report for Shear Connector

6. Stiffener Result (1) by Result Table The results can be viewed in a result table as shown below. ▶ Design > Composite Design > Design Result Tables > Longitudinal Stiffener...

[Fig.2.82] Result Table for Stiffener Where, bl : projecting width bl_lim : limit of projecting width as per Eq. 6.10.11.3.2-1 I : Moment of inertia of cross-section I_lim : limit of moment of inertia of cross-section as per Eq. 6.10.11.3.3-1 r : radius of gyration r_lim : limit of radius of gyration as per Eq. 6.10.11.3.3-2 fs : flexure stress of longitudinal stiffener phiRhFys : limit of flexure stress as per Eq. 6.10.11.3.1-1

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(2) by Excel Report The results can be viewed in an Excel Report as shown below.

[Fig.2.83] Excel Report for Stiffener

7. Span Checking (1) by Result Table ▶ Design > Composite Design > Design Result Table...

Most critical member results in each span can be viewed in a result table as shown below.

[Fig.2.84] Result Table for Span Group

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(2) by Span Result Graph ▶ Design > Composite Design > Design Result Diagram... The results of the span group defined by the span information can be checked here. The flexure and shear results based on distance or node can be checked here. The current applied member force or elasticity is marked in red while the strength or elasticity is marked in green.

[Fig.2.85] Span Result Graph

8. Total Checking (1) by Result Table ▶ Design > Composite Design > Design Result Table... Summary results for each member can be viewed in a result table as shown below.

[Fig.2.86] Result Table for Toal Checking

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Chapter 3.

Steel Composite Bridge Load Rating AASHTO LRFD 2nd (2011)

Chapter 3.

Steel Composite Bridge Load Rating (AASHTO LRFR 11) Steel composite bridge load rating needs to satisfy the following limit states.

Load Rating of Steel Composite Bridge Strength Limit State Service Limit State Fatigue Limit State

Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2nd (2011)

Introduction 1. AASHTO LRFR 2011 Bridge Load Rating 1.1 Definition of Load Rating The NBIS (National Bridge Inspections Standards Regulation) regulations define load rating as “The determination of the live load carrying capacity of a bridge using as-built bridge plans and supplemented by information gathered from the latest field inspection.” Load ratings are expressed as a rating factor (RF) or as a tonnage for a particular vehicle. Emphasis in load rating is on the live-load capacity and dictates the approach of determining rating factors instead of the design approach of satisfying limit states.

1.2 Purpose of bridge rating Bridge load rating provides a measure of a bridge's ability to carry a given live load in terms of a simple factor, referred to rating factor. These bridge rating factors can be used to aid in decisions about the need for (1) load posting, (2) bridge strengthening, (3) overweight load allowances, (4) and bridge closers. [Table3.1] Purpose of bridge rating

Load Posting

Bridge Strengthening

Bridge Closers

1.3 Difference between Bridge Design and Load Rating Bridge design and rating, though similar in overall approach, differ in important aspect. (1) Philosophy of Bridge Design Bridge Design may adopt a conservative reliability index and impose checks to ensure serviceability and durability without incurring a major cost impact. (2) Philosophy of Bridge Load Rating Bridge ratings generally require the Engineer to consider a wider range of variables than is typical in bridge design. In rating, the added cost of overly conservative evaluation standards

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can be prohibitive as load restrictions, rehabilitation, and replacement become increasingly necessary. The rating procedures presented LRFR recognize a balance between safety and economics. In most cases, a lower target reliability than design has been chosen for load rating at the strength limit states to rating is done on a more selective basis than is prescribed for design in the AASHTO LRFD Bridge Design Specifications.

1.4 Application of Load Rating (1) New Construction When designing a new structure, it is required that RF≥1 for the HL-93 vehicle at the Inventory Level; therefore, a Legal Load Rating will never be required on a newly designed structure. (2) Changes in the below category in the existing building: ▪ Live loads ▪ Dead loads ▪ Physical condition ▪ Specifications, Laws [Table3.2] Different Cases for The Load Rating

New Bridges

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Change in the live loads

Change in the Physical condition

2. Load Rating Levels The LRFR methodology consists of three distinct levels of evaluation: (1) Design load rating (2) Legal load rating (3) Permit load rating The result of each evaluation serve specific purpose and also inform the need for further evaluations. The important factors of each load rating level are summarized as shown below.

[Fig.3.1] Load Rating Levels

Each of these three levels of rating are discussed in detail in immediately following sections.

2.1 Design Load Rating Design load rating is a first level assessment of bridges. It is a measure of the performance of existing bridge to current LRFD bridge design standards. (1) Live Load At Design load rating level, the HL-93 live-load model of the LRFD is applied, using dimensions and properties of the bridge in its present as inspected condition. (2) Limit States Under this check, bridges are screened for the strength limit state at the LRFD design level of reliability. Evaluation at a second lower evaluation level of reliability is also an option. The rating also considers all applicable LRFD serviceability limit states (3) purpose Design load rating can serve as a screening process to identify bridges that should be load rated for legal loads. Bridges the pass the design load check (RF≥1) at the Inventory level will have satisfactory load rating for all legal loads that fall within the LRFD exclusion limits.

(4) Level of Design Load Rating There are two levels of the Design Load Rating: 1) Inventory Rating level The Inventory rating level generally corresponds to the rating at the design level of reliability for new bridges in the AASHTO LRFD Bridge Design Specifications, but reflects the existing bridge and material conditions with regard to deterioration and loss of section. Load ratings based on the Inventory level allow compressions with the capacity for new structures and, therefore, result in a live load, which can safely utilize an existing Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR 2011

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structure for an indefinite period of time. 2) Operation Rating level Load rating based of the Operation rating level generally describe the maximum permissible live load to which the structure may be subjected. Generally corresponds to the rating at the Operating level may shorten the life of the bridge.

2.2 Legal Load Rating This second level rating provides a single safe load capacity (for a given truck configuration) applicable to AASHTO and State legal loads. The Previous distinction of Operating and Inventory level ratings is no longer maintained when load rating for legal loads. Legal load rating provides a level of reliability, corresponding to the operating level reliability for redundant bridges in good condition. (1) Live Load Live load is categorized into the two types according to AASHTO LRFR 2011 as: 1) AASHTO Legal loads, as specified in Article 6A.4.4.2.1a 2) The Notional Rating Load as specified in Article 6A.4.4.2.1b or State legal loads. (2) Limit States Strength is the primary limit state for load rating; service limit states are selectively applied. (3) purpose Bridges that do not have sufficient capacity under the design-load rating shall be load rated for legal loads to establish the need for load posting or strengthening.

2.3 Permit Load Rating This third level of rating should only be applied to bridges having sufficient capacity for legal loads. In other words, Permit load rating should be used only if the bridge has a rating factor greater than 1.0 when evaluated for AASHTO legal loads. (1) Live Load The actual permit vehicle’s gross vehicle weight and axle configuration will be the live load used in the permit-load evaluation. The MBE(Manual for Bridge Evaluation) categorizes permit loads into two classes: 1) Routine/annual permits, and 2) Special permits. (2) Limit States Permits are checked using the Strength II limit-state load combination with the Service II limit-state load combination optional for steel bridges to limit potential permanent deformations. (3) purpose Permit load rating checks the safety and serviceability of bridges in the review of permit application for the passage of vehicles above the legally established weight limitations.

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3. Process of Load Rating

Flow Chart AASHTO LRFR 11 ( APPENDIX A6A)

[Fig.3.2] Flow Chart of Load Rating

The process starts with a bridge first being rated at the Design Inventory level under HL- 93 load model. If the bridge is found to be satisfactory at this level of rating, it’s considered not to require posting for “AASHTO legal loads and state legal loads within the LRFD exclusion limits”, and hence the bridge can be evaluated directly for permit load vehicles. However if the rating factor at the Design Inventory level is found to be less than 1.0, the bridge must be evaluated under either the Design Operating level or the Legal load level. At these levels of rating if the bridge is found to be satisfactory it is considered not to require posting for “AASHTO legal loads and state legal loads having only minor variations form the AASHTO legal loads”, and the bridge can be evaluated for permit load vehicles. If, however, the bridge is found to be not satisfactory, load posting will be required for legal loads and no permit analysis is allowed. There is however the option for higher forms of evaluation, such as load testing of the bridge or the use of finite element modeling, for when a bridge is found to be unsatisfactory at the Legal load level and the engineer feels the bridge may not require posting.

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Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2nd (2011)

Modeling and Design Variables 1. Modeling Design Variables In this chapter, the design variables, the meaning behind the design requirements, and the design process for Steel Composite Load Rating in midas Civil are explained.

1.1 Design Parameters for Steel Composite Load Rating In this section, the application of load rating and input method and meaning of the related variables are explained. Contents

1.1.1 Rating Design Code ▶ Rating > Bridge Rating Design > Steel Design> Rating Design Code ...

Explanation

1.1.1 Rating Design Code The program performs the load rating based on the code selected in this dialog box.

[Fig.3.3] Rating Design code

1.1.2 Steel Bridge Load Rating Parameters ▶ Rating > Bridge Rating Design > Steel Design> Rating Parameters ...

1.1.2 Steel Bridge Load Rating Parameters (1) The system factor is inputted according to the System Factor, 𝜑𝑠 , provided in AASHTO LRFR 2011 (Table 3.6). The system factor is multiplied to the flexural strength (Mn) and shear strength (Vn) and, therefore, applied to all elements. (2) Strength Resistance Factor Strength Resistance Factor is defined. The resistance factors are automatically set to the default values defined in AASHTO LRFR 12. The values also may be modified or entered manually. (3) Girder Type for Box/Tub Section If the Single Box Section option is selected, the

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sections are considered as noncompact section; if the Multiple Box Section option is selected, the sections are considered as compact sections. □ Consider St.Venant Torsion and Distortion Stress If the Multiple Box Section option is selected, lateral bending stress is considered in accordance with St. Venant Torsion and Distortion Stress. If the Single Box Section option is selected, the lateral bending stress is not considered. (4) Options For Strength Limit State □ Appendix A6 for Negative Flexure Resistance in Web Compact/Noncompact Sections If this option is checked, Appendix A6 is applied for the flexural strength of straight composite Isections in negative flexure with compact/noncompact webs. □ Mn≤1.3RhMy in Positive Flexure and Compact Sections(6.10.7.1.2-3) If this option is checked, Mn value is restricted to 1.3RhMy under positive flexure. □ Post-buckling Tension-field Action for Shear Resistance (6.10.9.3.2) If this option is checked, post buckling resistance due to tension field action is considered in the nominal shear resistance of an interior stiffened web panel according to AASHTO LRFD 12. If not, Vn is taken as CVp. (5) Service Limit State □ Service Limit State If this option is checked, the service limit is verified according to AASHTO LRFR 2011 6A.6.4.

[Fig.3.4] Load Rating Parameters Dialog Box

If Auto-Calculation is selected, the RF is calculated automatically according to LRFR standards. For more details, please refer to "Application of AASHTO LRFD 12 in Midas Civil" Section 3.3. If User Input is selected, the capacities, parameters calculated for the verification of the RF, can be manually inputted. The allowed compressive stress and tensile stress of the concrete need to be inputted. The compressive and tensile stresses inputted for Design Load and Legal Load are applied for the verification of the Design Load Rating and Legal Load Rating, respectively. (6) Fatigue Limit State □ Fatigue Limit State Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR 2011

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If this option is checked, the program checks the Fatigue Limit State according to AASHTO LRFR 11 6A.6.4. Also, the Load Test Measurement for the Application of Diagnostic Test Result can be selected between Strain and Displacement.

1.1.3 Unbraced Length 1.1.3 Unbraced Length ▶ Rating > Bridge Rating Design > Steel Design> Unbraced Length ...

The Unbraced Length for steel composite section is considered. The value input here has higher priority than the value calculated from Span Group. (1) Lb The Lateral Unbraced Length is used to calculate the lateral torsional buckling resistance for the compression flange of I-Girders. If the Lateral Unbraced Length is not applied, the span information, if defined, is used for the calculation. If the span information is not defined, element lengths are applied as the lateral unbraced length.

[Fig.3.5] Unbraced Length Dialog Box

1.1.4 Shear Connectors 1.1.4 Shear Connectors ▶ Rating > Bridge Rating Design > Steel Design> Shear Connectors ...

Studs are used as shear connectors and the following parameters are used for the calculation: (1) Category Category defined by 75yr-(ADTT)SL equivalent to Infinite Life. (2) Fu Shear Resistance of Shear Connector (3) Shear Connector Pane meters

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[Fig.3.7] Shear Connector Parameters

(4) Length between Max.Moment and Zero Moment The length of the sections where shear connectors need to be considered is inputted for the calculation of the pitch at the strength limit state.

[Fig.3.6] Shear Connector Dialog Box

1.1.5 Fatigue Parameter ▶ Rating > Bridge Rating Design > Steel Design> Fatigue Parameter ...

(5) Nominal Shear Force Calculation The type of nominal shear force calculation is determined for the calculation of the Nominal Shear Force, P, which his used to calculate the minimum number of shear connector, n, at the strength limit state. Based on the calculation type selected, the equations used to calculate P are differed.

1.1.5 Fatigue Parameter (1) Category Category defined by 75yr-(ADTT)SL equivalent to infinite life (Table 6.6.1.2.3-2). (2) (ADTT)SL Number of trucks per day in a single-lane averaged over the design life (3.6.1.4.2) Value can be manually calculated as per 3.6.1.4.21. (3) n Number of cycles per truck passage Value can be taken from Table 6.6.1.2.5-2. (4) Longitudinal Warping Stress Range For the verification of fatigue, flexure stress is calculated as the summation of Longitudinal

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Bending Stress Range and Longitudinal Warping Stress Range. By choosing the Auto-Calculation option, fatigue vertical bending moment is simply increased by 10% for the longitudinal warping stress. If the User Input option is selected, longitudinal bending stress range is summated with the inputted value of the Longitudinal Warping Stress Range for top or bottom flange depending upon the flexure condition at the section.

[Fig.3.8] Fatigue Parameters Dialog Box

1.1.6 Curved Bridge Information ▶ Rating > Bridge Rating Design > Steel Design> Curved Bridge Info ...

1.1.6 Curved Bridge Information Once the girder radius value of the element units in the steel composite section is entered, the corresponding elements are categorized as curved bridges. The inputted girder radius is used for the following equations.

(1) Radius is used for the review of flange lateral bending moment caused due to the curvature. (N is taken as 10.)

M lat 

Ml 2 NRD

(LRFD 2012 c4.6.1.2.4b-1)

where, Mlat : flange lateral bending moment M : major-axis bending moment l

: unbraced length

R : girder radius D : web depth [Fig.3.9] Curved Bridge Information Dialog Box

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N : a constant taken as 10 or 12 in past practice

[Table3.3] Convex and Concave

Convex

Concave

(2) Radius is used for the review of shear connector's pitch and the moment of inertia of area for the longitudinal stiffener attached to web.

(3) Curve Type - Convex, Concave If Convex is selected, Left Stiffener is on the side of the web away from the center of curvature and Right Stiffener is on the side of the web toward the center of curvature. If Concave is selected, the opposite case of the convex is applied. The Left and Right are determined based on the progressing direction of the cross section. Please refer to the table below for the equations applied to each case. [Table3.4]Curvature Correction Factor for Longitudinal Stiffener

Case

Convex

Concave

Left Stiffener Right Stiffener Left Stiffener Right Stiffener

Equation

Z 1 6 Z   1 12 Z   1 12 Z   1 6



(6.10.11.3.3-3) (6.10.11.3.3-4) (6.10.11.3.3-4) (6.10.11.3.3-3)

Where, 𝛽 : Curvature correction factor for longitudinal stiffener 𝑍 : Curvature Parameter

1.1.7 Diagnostic Test Result ▶ Rating > Bridge Rating Design > Steel Design > Diagnostic Test Result...

1.1.7 Diagnostic Test Result Variables that are used to verify the load carrying capacity for the diagnostic test result are inputted in this dialog box. (1) Auto calculation Deflection and impact factor are inputted for the diagnostic test. (2) User Input The Adjustment Factor, K, is inputted by users. K is used to calculate the load-rating factor for the live-load capacity based on the load test result, RFT.

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K  1  K a K b (8.8.2.3.1-1) where, Ka : accounts for both the benefit derived from the load test, if any, and consideration of the section factor (area, section modulus, ect.) resisting the applied test load Kb: accounts for the understanding of the load test results when with those predicted by theory

[Fig.3.10] Diagnostic Test Result Dialog Box

1.2 Design Material Data In this section, the material property information input method for the Steel Composite Load Rating is explained. Contents

1.2.1 Rating material ▶ Rating > Bridge Rating Design > Steel Design> Rating material... (1) Rating material

Explanation

1.2.1 Rating material In this dialog box, the Material Properties can be modified for the calculation of the structure capacity. The material utilized for composite sections are provided in the SRC material properties. The material should be defined as SRC Type. (1) Modify Composite Material This dialog box is used to input material characteristics for the steel composite section design. The material property values entered will have a priority over the values entered in Material Data dialog box.

1) Steel of the Steel Girder Section □ Hybrid Factor Hybrid Factor is considered in the case where flanges and web have different material properties.

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2) Concrete of the Concrete slab 3) Steel Rebar of the Concrete slab

[Fig.3.11] Rating Material Dialog Box

(2) Hybrid Factor

(2) Hybrid Factor(Rh) When the check box for Hybrid Factor is selected, icon on the right is activated. The different materials for the top and bottom flanges and web of the steel girder can be defined. Hybrid Factor (Rh) is determined based on these material information.

[Fig.3.12] Hybrid Factor Dialog box

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1.3 Settings for Load Rating In this section, how to define which part of the structure the load rating is performed and factors and rating levels for each part are explained.

Contents

Explanation

1.3.1 Rating Group Setting

1.3.1 Rating Group Setting

▶ Rating > Bridge Rating Design > Steel Design> Rating Group Setting...

The Bridge Rating Group Setting Dialog allows users to apply Condition Factors per different groups defined already and i- and j-end check positions.

(1) Inputting different Condition Factors and other design features are faster with the elements defined in Groups. Selected Groups are targeted for the design of the Rating Factor. Structure Group is defined in Define Structure Group at: ▶ Tree Menu > Group> Structure Group>New...

[Fig.3.13] Rating Group Setting Dialog Box

[Fig.3.14] Structure Group Dialog Box

(2) Different values of Condition Factor, 𝝋𝒄 , can be applied to different Structure Groups of elements. In the program, the Condition Factor is internally multiplied to Nominal Flexural Strength, Nominal Flexural Resistance, Nominal Shear Strength and Nominal Fatigue Resistance to calculate the Road Factor. For more details, please refer to [Table 3.7] and [Table 3.8]. (3) The Check Position, i- and/or j- end, is considered and selected for the Groups selected for the design.

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1.3.2 Define Rating Case ▶ Rating > Bridge Rating Design > Steel Design> Define Rating Case...

1.3.2 Define Rating Case In Define Rating Case Dialog, Load Factor is defined for each of the Service Limit State, Strength Limit State and Fatigue Limit State. (1) For the Fatigue Limit State calculation, Unfactored dead load should be selected. (2) Default Load Factors are automatically inputted for each Load Type (DC, DW, ...) as per LRFR 2012 and can be manually modified by users. Maximum and Minimum Load Factors are inputted for DC(Before), DC(After), and DW. The default maximum and minimum values are provided according to LRFR 2011 Table 6A.4.2.2-1 and LRFD 2012 Table 3.4.102. Only one load factor is inputted for the Temperature Load, but the load factor is used as positive and negative (+, -) for the calculation. DC(Before) is for the state before the concrete deck is activated. DC(After) is for the state after the concrete deck is activated. DC(After) considers the Erection load case, if defined by user, and the stress caused by the time dependent material property, Creep & Shrinkage. Per different Load Type, Load Cases can be additionally inputted per different Load Type and reflected in the Load Rating Factor calculation.

[Fig.3.15] Define Rating Case Dialog Box

(3) For different Load Types, different Load Cases are selected. Member forces before the composite state are applied to Dead Load (CS) and member forces after the composite state are applied to Erection Load.

Static Load case is defined at: ▶ Load > Load Type > Create Load Cases > Static Load Cases Information inputted in the Load case internally generates the 12 Types results (Fx-max, ... Mymin) per nodes in the calculation. For each node, Max/Min forces are calculated per total 6 degree of freedom (DOF) for each node.

(4) Live Load and Load Factor are inputted

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separately for the Primary Vehicle and Adjacent Vehicle. When is clicked, the load combinations and corresponding Load Factors are generated. When the load combination is clicked, the load combination and load factors are inputted in the Rating Case Dialog Box. Each Live Load should be inputted prior in Moving Load Cases at: ▶Load > Load Type > Moving Load > Moving Load Analysis Data > Moving Load Cases)

[Fig.3.16] Live Load Factor for Rating Dialog Box

(5) Evaluation Live Load Model Load Rating flow as per LRFR standard is explained in [Fig.3.2]. The program does not automatically follow the flow of [Fig.3.2]. In this Live Load Factors for Rating Dialog, rating level needs to be defined as well as the load cases. In the "Introduction" Chapter, Section 2.2 and Section 2.3, different purposes and applications of performing Legal Load Rating level and Permit Load Rating level are explained. However, in this dialog box, the Legal Level and Permit Level both needs to be selected because the same LRFD Load Factors are used in the two level checks.

1.3.3 Position for Rating Output ▶ Rating > Bridge Rating Design > Steel Design > Position for Rating Output...

1.3.3 Position for Rating Output In this Dialog, the Position for Rating Output is inputted.

(1) Users can select Groups in the Filters for Load Rating Summary and define the Position for Rating Output. (2) When Apply is clicked in this dialog box, the elements to be printed in the output is defined and saved.

[Fig.3.17] Position for Rating output Dialog Box

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1.3.4 Rating Design Tables

1.3.4 Rating Design Force/Moment Tables ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Tables > Design Force/Moment

For the selected load combinations, design member force (longitudinal-direction moment (My), transverse-direction moment (Mz), shear (Vu)) are calculated at different part(s) of the elements per construction stages.

[fig.3.18] Rating Design Force/Moment Tables Dialog Box

1.4 Composite Section Data Steel composite section is composed of steel girder and concrete slab. Additional stiffeners may be arranged in the steel girder; longitudinal and sub reinforcement rebars may be arranged in the concrete slab. In this section, Steel Composite Load Rating features and functions and related section input method and design variables are explained. Explanation

Contents

1.4.1 Longitudinal Reinforcement ▶ Rating > Bridge Rating Design > Steel Design> Longitudinal Reinforcement

1.4.1 Longitudinal Reinforcement In a steel composite section, the longitudinal reinforcements are arranged within the concrete deck. The strength is calculated as shown in the below table. [Table3.5] Material Application for Strength Calculation

Positive Flexure

Negative Flexure

Concrete Slab

Apply

None

Reinforce -ment

None

Applied

Case

Figure

[Fig.3.19] Longitudinal Reinforcement Dialog

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Contents

1.4.2 Transverse Stiffener

Explanation

1.4.2 Transverse Stiffener

Figure 3.20 shows the dialog box in which users can ▶ Rating > Bridge Rating Design > Steel Design> arrange transverse stiffeners in steel composite section. Transverse Stiffener... When the transverse stiffeners are installed, the existence and spacing between stiffeners determine whether the web is stiffened or unstiffened under strength limit state.

[Fig.3.20] Transverse Stiffener Dialog

[Fig.3.21] Transverse Stiffener Parameters

(1) Stiffener Type 1) One / Two Stiffener Option Button Choose between one or two stiffeners. The two stiffener option is available for I/Box/Tub sections. 2) Pitch (do) Pitch refers to the Transverse Stiffener spacing. At the strength limit state, this can be used to distinguish between stiffened and unstiffened webs or calculate shear strength of the web. [Fig.3.22] Stiffener Type Dialog

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Design Guide for Midas Civil

Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2nd (2011)

Application of AASHTO LRFR 11 in midas Civil 1. Rating Factor Calculation The Bridge Load Rating function of midas Civil calculates the Rating Factor (RF) at i/j nodes of elements for the Rating Cases according to AASHTO LRFR 2011 standard and finds the minimum RF. Rating load carrying papa city needs to be done at three different levels - Design Load Rating, Legal Load Rating, and Permit Load Rating - according to the AASHTO LRFR 2011. Midas Civil Bridge Load Rating calculates RF by using the equations (3.3) for Design Load Rating and Legal Load Rating for the load cases defined in Define Load Case [fig.3.15]. The RF calculated in Midas Civil determines whether it is safe to carry the Primary Vehicle. If RF>1 it is safe and the larger RF, the greater the load carrying capacity of the bridge.

1.1 RF Calculation as per AASHTO LRFR The RF value shall be taken as below according to the LRFR standard: RF

C  ( DC )( DC)  ( DW )( DW )  ( P )( P) RF  ( L )( LL  IM )

(3.1)

AASHTO LRFR 11 (Eq. 6A.4.2.1-1)

(1.1 Where, RF : Rating factor C : Capacity Capacity, C, is calculated as shown in [Table 3.6] for the corresponding Limit State. [Table3.6] C (Capacity) in AASHTO LRFR 2011

Case

C

Strength Limit States

C  cs Rn ( cs  0.85 )

Service Limit States

C  fR

C AASHTO LRFR 11 (Eq. 6A.4.2.1-2) (Eq. 6A.4.2.1-3) (Eq. 6A.4.2.1-4)

𝑓𝑅 : Allowable Stress specified in the LRFD code DC : Dead-load effect due to structural components and attachments DW : Dead-load effect due to wearing surfaces and utilities P : Permanent loads other than dead loads LL : Live load effect

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IM : Dynamic load allowance 𝛾𝐷𝐶 : LRFD load factor for structural components and attachments 𝛾𝐷𝑊 : LRFD load factor for wearing surfaces and utilities 𝛾𝑃 : LRFD load factor for permanent loads other than dead loads 𝛾𝐿𝐿 : Evaluation live load factor 𝜑𝑐 : Condition factor 𝜑𝑠 : System factor 𝜑 : LRFD resistance factor Rn : Nominal member resistance

1.2 Load Rating in Midas Civil 1.2.1 Review Items In Midas Civil, load rating is reviewed based on the three different limit states for steel composite bridges. For more information about how to define load cases for each limit state, please refer to "Modeling and Design Variables" Section 1.3.2 and this chapter ("Application of AASHTO LRFR 11 in midas Civil") Section 1.2.3.

Load Rating of Steel Composite Bridge Strength Limit State Service Limit State Fatigue Limit State [Fig.3.23] Flow Chart of Load Rating of Steel Composite Bridge in midas Civil

1.2.2 Calculation of RF Midas Civil's PSC Bridge Load Rating function uses the below equation [3.2] upon the request of the California Department of Transportation (Caltrans). RF 

C  ( DC )( DC )  ( DW )( DW )  ( T )(T )  ( SEC )(SEC )  ( P )( P)  ( USER )(USER)  ( AV )( AV ) ( PV )( PV )

(3.2)

For the Steel Composite Load Rating, the equation [3.2] is modified to reflect the steel composite bridge characteristics. The equation [3.3] reflects the member force for before and after the concrete deck is activated and is used to calculate the RF value. RF 

 

C  ( DCB )( DCB )   DC A DCA    DW DW    T T    SEC SEC    P P    USER USER    AV ( AV )

Where, RF : Rating factor calculated by Midas Civil C : Capacity

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 PV PV 

(3.3)

[Table3.7] C (Capacity) Calculated by Midas Civil

C

Case

C  cs Rn ( cs  0.85 )

Strength Limit States Auto-Calculation

C  fR

User Input

User-defined allowable stress in [Fig.3.4]

Service Limit States

C  cs Rn ( cs  0.85 )

Fatigue Limit State

If user-defined 𝜑𝑐 and 𝜑𝑆 result 𝜑𝑐 𝜑𝑆 < 0.85, the program adjusts 𝜑𝑐 𝜑𝑆 to be equal to 0.85 and calculate C. For calculating C, midas Civil uses different 𝜑𝑅𝑛 depending on the type of limit state.

[Table3.8] φR n Calculated by Midas Civil

𝜑𝑅𝑛 Calculated by Midas Civil

Load Rating State Flexural Strength

Mn or Fn according to AASHTO LRFD 12

Shear Strength

Vn according to AASHTO LRFD 12

Strength Limit State Fatigue Limit State

(ΔF)TH calculated according to AASHTO LRFD 2012

DC : Dead load effect due to structural components and attachments DCB :Dead load effect due to structural components and attachments before the concrete deck is activated DCA :Dead load effect due to structural components and attachments due to the erection load case, defined by users, and time dependent material property of concrete (Creep and Shrinkage) DW : Dead-load effect due to wearing surfaces and utilities T : Temperature and Temperature Gradient SEC : In Define Rating Case Dialog Box, Creep Secondary, Shrinkage Secondary and Tendon Secondary can be selected P : Permanent loads other than dead loads USER : User-defined load AV : Adjacent Vehicle load PV: Primary vehicle load 𝛾𝐷𝐶 : LRFD load factor for Dead load effect due to structural components and attachments 𝛾𝐷𝐶𝐵 : LRFD load factor before the concrete deck is activated 𝛾𝐷𝐶𝐴 : LRFD load factor after the Erection load case defined by user and time dependent material property of concrete are activated 𝛾𝐷𝑊 : LRFD load factor for wearing surfaces and utilities 𝛾𝑇 : LRFD load factor for temperature 𝛾𝑆𝐸𝐶 : LRFD load factor for secondary 𝛾𝑈𝑆𝐸𝑅 : LRFD load factor for user-defined load 𝛾𝑃 : LRFD load factor for permanent loads other than dead loads 𝛾𝐴𝑉 : LRFD load factor for adjacent vehicle load 𝛾𝑃𝑉 : LRFD load factor for primary vehicle load

The above factors may be explained in terms of the Define Rating Case dialog box as follows.

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The values input in the red-colored box are applied as the factors directed with the arrow.

[Fig.3.24] Define Rating Case dialog box where factors are inputted

1.2.3 Load Rating Flow in Midas Civil (1) Load Rating Flow The flow of load rating according to LRFR standard is explained in [Fig. 3.2]. In this section, how load rating is performed in midas Civil is explained. In midas Civil, load rating is performed for the load cases defined in Define Rating Case dialog box [Fig. 3.15]. (2) Setting and Input Methods The two pictures in the below table are parts of Define Rating Case dialog box. Limit State

[Fig.3.25] Limit State in Define Rating Case dialog box

Rating Level

[Fig.3.26] Rating Level in Define Rating Case dialog box

The Load Rating is performed for the Limit State selected by user in the right picture above and the Rating Level selected in the left picture. Therefore, user can create and check load cases for maximum six different cases (3 Limit States x 2 Rating Levels = total 6 Cases).

The below figure presents which choices need to be selected in Define Rating Case dialog box and their order in accordance with LRFR Load Rating flow chart.

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[Fig.3.27] Flow Chart of LRFR 11 and Define Rating Case dialog box

(3) Load Applied The vehicle load applied according to the rating level prescribed in the LRFR 2011 is explained in "Introduction" Section 2. To increase the flexibility of the users, vehicle load needs to be manually defined by users. ▶Vehicle loads can be defined at: Load > Load Type > Moving Load > Moving Load Analysis Data > Vehicles. If AASHTO LRFD Load is selected for the Standard Name, the vehicle loads are automatically inputted in accordance with LRFD. The below figure shows the Define Standard Vehicular Load dialog box and the list of the vehicular load type supported in midas Civil when AASHTO LRFD Load is selected as the Standard.

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[Fig.3.28] Define Standard vehicular load dialog box

1.2.4 Condition Factor, 𝝋𝒄 The Condition Factor provides a reduction to account for the increased uncertainty in the resistance of deteriorated members and the likely increased future deterioration of these members during the period between inspection cycles. The condition factor needs to be inputted in the Rating Group Setting Dialog Box [Fig.3.13] in midas Civil.

[Table3.9] Condition Factor

Structural Condition of Member

c

Good or Satisfactory

1.00

Fair

0.95

Poor

0.85

Condition Factor AASHTO LRFR 11 ( 6A.4.2.3)

Condition Factor AASHTO LRFR 11 (Table. 6A.4.2.3-1)

1.2.5 System Factor, 𝝋𝒔 System factor reflects the level of redundancy of the complete superstructure system. System factors that correspond to the load factor modification in the AASHTO LRFD Bridge Design Specifications should be used. The system factors in [Table3.10] are more conservative than the LRFD. If the simplified system factors presented in [Table3.10] are used, they should be applied only

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System Factor AASHTO LRFR 11 (6A.4.2.4)

when checking flexural and axial effect at the strength limit state of typical spans and geometries. The system factor needs to be inputted in the Steel Bridge Load Rating Parameters dialog box [Fig.3.4] in midas Civil. [Table3.10] System Factor

Structural Type

s

Welded Members in Two-Girder/Truss/Arch Bridges

0.85

Riveted Members in Two-Girder/Truss/Arch Bridges

0.90

Multiple Eyebar Members in Truss Bridges

0.90

Three-Girder Bridges with Girder Spacing 6ft

0.85

Four-Girder Bridges with Girder Spacing ≤ 4ft

0.95

All Other Girder Bridges and Slab Bridges

1.00

Floorbeams with Spacing >12 ft and Noncontinuous Stringers

0.85

Redundant Stringer Subsystems between Floorbeams

1.00

System Factor AASHTO LRFR 11 (Table. 6A.4.2.4-1)

A Constant value of ϕs =1.0 is to be applied when checking shear at the strength limit state.

1.3 Load Combination AASHTO LRFR clarifies the Load Factors for different Limit States and loads as shown in [Table 3.11]. The Load Factors are inputted in the Define Rating Case Dialog (Chapter "Modeling and Design Variables" Article 1.3.2) [Table3.11]

Limit States and Load Factors for Load Rating

Load Combination AASHTO LRFR 11 (Table. 6A.4.2.2-1)

▪ Shaded cells of the table indicate optional checks. ▪ Service I is used to check the 0.9 Fy stress Limit in reinforcing steel. ▪ Load factor for DW at the strength limit stress may be taken as 1.23 where thickness has been field measured. ▪ Fatigue limit state is checked using the LRFE fatigue truck. (see LRFR Article 6A.6.4.1)

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1.4 I and Box Section In Load Rating, certain items need to be checked in accordance with AASHTO LRFD Design Article; while some do not. Please refer to the below table for the applicability of each case. [Table3.12] LRFD Design Articles applied per section type and review criteria

I Section

Box Section

Case Straight Bridge Flexural resistance Shear resistance fl

Curved bridge

Straight Bridge

6.10.6.2

6.11.6.2 and 6.11.1.1

6.10.9 Not considered in midas Civil

constructability

Curved bridge

6.10.9 6.10.1.6

-

and 6.11.9 -

No need to be considered

Fatigue requirements for webs

No need to be considered

Composite sections are considered as unshored construction for the load rating in midas Civil according to LRFR 2011 6A.6.9.2. AASHTO LRFR 11 provides standards for box sections only but not tub sections. Therefore, the load rating for tub sections is done in accordance with the box section standards.

2. Strength Limit State The minimum RF is calculated for the Rating Cases inputted for the Strength Limit State. Please refer to [Table 3.12] for the LRFD Articles applied for different section types.

2.1 General Strength Limit State is reviewed for flexural strength and shear strength.

Strength Limit States LRFR 11 6A.6.4.1 and 6A.4.2.1.

Rating Factor for Flexural Strength Rating Factor for Shear Strength [Fig.3.29] Flow chart of Strength Limit State

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I and Box Section AASHTO LRFR 11 ( 6A.6.9.1~6A.6.9.5)

fl AASHTO LRFR 11 ( 6A.6.4.2.2))

2.2 Load Combination Different load combinations are applied per load rating levels for the strength limit state check. [Table3.13] Load Combination

Load Rating Level

Load Combination

Design load level

Strength Ⅰ load combination

Legal load level

Strength Ⅰ load combination

Permit load level

Strength Ⅱ load combination

Load Combination AASHTO LRFR 11 (6A.6.4.1) (6A.6.4.2.1)

2.3 Rating Factor(RF) Calculation 2.3.1 Rating Factor for Flexural Strength The RF is calculated for each Rating Case according to the equation (3.4). The minimum RF is calculated at the i- and j- ends for the positive and negative moments.

RF 

 

C  ( DCB )( DCB )   DC A DCA    DW DW    T T    SEC SEC    P P    USER USER    AV ( AV )

 PV PV 

(3.4)

Where, C :capacity, [Table3.14] C (Capacity) and 𝜑𝑅𝑛

𝜑𝑅𝑛

C

Mn or Fn calculated according to AASHTO LRFD 2012

𝜑𝑐 𝜑𝑠 𝜑𝑅𝑛

[Table3.15] Cases Mn and Fn are calculated

Mn ▪ Compact Section in Positive flexural moment ▪ Flexural resistance of Negative Flexure Moment by using Appendix A6



Fn ▪ Positive flexural moment in noncompact section ▪Negative flexural moment and one of the following cases: - Curved bridge - Straight Bridge but slender section -Straight Bridge and compact or noncompact, but Appendix A6 is not applied



( DCB )( DCB )   DC A DC A    DW DW    T T    SEC SEC    P P    USER USER   AV ( AV ) :

My from Load Case ( PV )PV  : My from Primary Vehicle(P.V)

2.3.2 Rating Factor for Shear Strength The RF is calculated at i/j nodes for the rating cases inputted for the strength limit state according to the equation (3.5) and the minimum RF is found.

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RF 





C  ( DCB )( DCB )   DC A DCA    DW DW    T T    SEC SEC    P P    USER USER    AV ( AV )

 PV PV 

(3.5)

Where, C : V calculated by MIDAS-CIVIL depending on Code of AASHTO LRFD 2012 n





( DCB )( DCB )   DC A DC A    DW DW    T T    SEC SEC    P P    USER USER   AV ( AV )

: Vz from Load Case ( PV )PV  : Vz from Primary Vehicle(P.V)

3. Service Limit State The minimum RF is calculated according to the equation (3.5) for the Rating Cases inputted for the Service Limit State. Then, the minimum RF is determined.

3.1 General The below LRFD Design Article is applied for the Service Limit State check in Load Rating. [Table3.16] LRFD Articles applied for different section type

Case

LRFD Design Article

I Section

6.10.4.2

Box Section

6.11.4

Service Limit State AASHTO LRFR 11 (6A.6.4.2.2)

3.2 Load Combination For the Service Limit State check, Service II load combination is applied for all Load Rating level. [Table3.17] Load Combination

Load Rating Level

Load Combination

Design load level

Load Combination AASHTO LRFR 11 (6A.6.4.1) (6A.6.4.2.2)

Service Ⅱ load combination

Legal load level Permit load level

3.3 Rating Factor(RF) Calculation The RF is calculated for the compressive and tensile stresses at i/j nodes. RF 





C  ( DCB )( DCB )   DC A DCA    DW DW    T T    SEC SEC    P P    USER USER    AV ( AV )

Where, C : Stress





 PV PV 

(3.6)

( DCB )( DCB )   DC A DC A    DW DW    T T    SEC SEC    P P    USER USER   AV ( AV )

: Stress from Load Cases ( PV )PV  : Stress from Primary Vehicle(P.V)

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The capacity, C, changes depending on whether the value is auto-calculated or user-defined in the Load Rating Parameters dialog box shown in [Fig.3.4]. Please refer to the below table. [Table3. 18] C (Capacity) in Service Limit State

c

Case Auto-Calculation

Composite Section

C  f R  0.95Fyf

Noncomposite Section

C  f R  0.8Rh Fyf

User Input

Capacity AASHTO LRFR 11 (6A.6.4.2.2)

Allowable Stress inputted in [Fig.3.4]

In Which, Fyf : Yield Stress

4. Fatigue Limit State The RF is calculated using the equation (3.6) for the rating cases inputted for the Fatigue Limit State and the minimum RF is determined.

4.1 General The fatigue requirements for webs specified in LRFD Design Article 6.10.5.3 does not need to be considered for the Fatigue Limit State verification of the i- and box- type sections. AASHTO LRFR 2011 does not specify the standards for the tub sections; however, the tub sections are verified according to the box section verification in midas Civil.

Fatigue Limit State AASHTO LRFR 11 (Section 7)

Fatigue Requirements AASHTO LRFR 11 (6A.6.9.1)

4.2 Load Combination (1) The Fatigue load combination is applied for the Fatigue Limit State verification as shown in [Table 3.11]. (2) The Fatigue Limit state is only verified for the Design Load Rating level. Legal Load Rating and Permit Load Rating levels are not verified for the Fatigue Limit State.

4.3 Rating Factor(RF) Calculation RF 





C  ( DCB )( DCB )   DC A DCA    DW DW    T T    SEC SEC    P P    USER USER    AV ( AV )

 PV PV 

(3.7)

Where, C: capacity [Table3.19] C (Capacity) and 𝜑𝑅𝑛

𝜑𝑅𝑛

C 𝜑𝑐 𝜑𝑠 𝜑𝑅𝑛



(ΔF)TH calculated by MIDAS-Civil depending on Code of AASHTO LRFD 2012



( DCB )( DCB )   DC A DC A    DW DW    T T    SEC SEC    P P    USER USER   AV ( AV )

: Stress from Load Case

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( PV )( PV )

:Stress from Primary Vehicle(P.V) (∆𝐹) 𝑇𝐻 is constant-amplitude fatigue threshold.

4.3 Levels of Fatigue Limit State 4.3.1 Category Levels AASHTO LRFR 11 (7.1) (7.2.1)

(1 )The two types of Fatigue damage are: ▪ Load-induced fatigue damage ▪ Distortion-induced Fatigue damage The Load-induced fatigue damage is verified in midas Civil. (2) The two levels of load-induced fatigue damage are: ▪ The infinite-life calculation ▪ The finite-life calculation Please refer to [Table 3.20] for the LRFR Design Articles applied in each case. [Table3.20] LRFR Article applied for Fatigue cases

Levels of Fatigue Evaluation Load-induced Fatigue

LRFR Design Article

Infinite - life

7.2 and 7.2.4

Finite - life

7.2 and 7.2.5

Distortion-induced Fatigue

Application of LRFR AASHTO LRFR 11 (7.2.1)

7.3

4.3.2 Flow of Fatigue Limit State The infinite-life calculation and finite-life calculation are distinguished according to the flow chart shown in [Fig.3.30]. Only bridge details that fail the infinite-life check are subject to the more complex finite-life evaluation.

Fatigue Evaluation of Load-induced Fatigue damage 7.2.4 and 7.2.5

Yes

f max  FTH

No

Finite Fatigue Life

Infinite Fatigue Life

Y 

Y 

7.2.4

RR A



365 n ( ADTT ) SL   f

eff



3

Flow AASHTO LRFR 11 (7.2.4) (Eq.7.2.4-1) (7.2.5)

7.2.5

End

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Infinite Fatigue Life AASHTO LRFR 11

(Eq.7.2.4-2)

[Fig.3.30] Flow Chart of Fatigue Evaluation of Load-induced Fatigue damage Where, Y : total fatigue life of a fatigue-prone detail in years (∆𝑓)𝑚𝑎𝑥 : maximum stress range expected at the fatigue-prone detail (∆𝑓)𝑚𝑎𝑥 = 2.0 (∆𝑓)𝑒𝑓𝑓 (𝐴𝐷𝑇𝑇)𝑆𝐿 : Average member of trucks per day in a single lane averaged over the fatigue life 𝑅𝑅 is resistance factor specified for evaluation, minimum, or mean fatigue life. A is Detail Category Constant. n is the number of stress-range cycles per truck passage estimated according to 𝑅𝑅 (in order of increasing apparent accuracy and complexity)

Finite Fatigue Life AASHTO LRFR 11 (Eq.7.2.5.1-1)

In midas Civil, different (∆F)TH , R R and A values are applied per the Fatigue category such as A, B, B', C, C', D, E, and E' inputted in the Fatigue parameters dialog [Fig.3.8]. (∆F)TH is taken as 24.0 ksi (165.0 MPa) except the other cases defined in [Table 3.21]. For n, the n value user defined in the Fatigue Parameters dialog box shown in [Fig.3.8] is used for the calculation. [Table3.21] Constant-Amplitude Fatigue Thresholds, (ΔF)TH

Detail Category A B B' C C' D E E'

Threshold LL, IM, CE, BR,PL, LS

US Unit (ksi) 24.0 16.0 12.0 10.0 12.0 7.0 4.5 2.6

SI Unit (MPa) 165.0 110.0 82.7 69.0 82.7 48.3 31.0 17.9

Fatigue Threshols AASHTO LRFD 12 (Table 6.6.1.2.5-3)

[Table3.22] Resistance factor specified for evaluation, minimum, or mean fatigue life, R R

Detail Category A B B' C C' D E E'

[Table3.23]

Detail Category A

RR Evaluation Life 1.7 1.4 1.5 1.2 1.2 1.3 1.3 1.6

Minimum Life 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Mean Life 2.8 2.0 2.4 1.3 1.3 1.6 1.6 2.5

Resistnace Factor AASHTO LRFR 11 (Table 7.2.5.2-1)

Detail Category Constant, A 8

3

US Unit (x 10 (ksi )) 250.0

Constant, A ! LL, IM, CE, BR,PL, LS

11

3

SI Unit (x10 (MPa )) 82.0

A AASHTO LRFD 12

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B B' C C' D E E'

120.0 61.0 44.0 44.0 22.0 11.0 3.9

(Table 6.6.1.2.5-1)

39.3 20.0 14.4 14.4 7.21 3.61 1.28

4.3.3 Effective Stress Ranges (1) Calculation of Effective Stress Range The Effective Stress Range, (∆feff ), is taken differently for the two cases: 1) Calculating Estimated Stress Range and 2) Measuring Estimated Stress Range. Please refer to [Table 3.24] for the different calculations. [Table3.24] Effective Stress Range

Case

Effective Stress Range

Calculating Estimated Stress Range

(f ) eff  Rs f



(f ) eff  Rs   i f i

Measuring Estimated Stress Range

Effective Stress Range AASHTO LRFR 11 (Eq.7.2.2-1) (Eq.7.2.2.2-1)



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In midas Civil, the Fatigue Limit State is verified with the Calculating Estimated Stress Range method.

Where 𝑅𝑠 : The stress-range estimate partial load factor. Unless otherwise specified, 𝑅𝑠 = 𝑅𝑠𝑎 𝑅𝑠𝑡 𝑅𝑠𝑎 : analysis partial load factor 𝑅𝑠𝑡 : truck-weight partail load factor ∆𝑓 : Measured effective stress range; or 75% of the calculated stress range due to the passage of the fatigue truck as specified in LRFD Design Article 3.6.1.4, or a fatigue truck determined by a truck survey or weigh-in-motion study. 𝛾𝑖 : Percaentage of cycles at a particular stress range ∆𝑓𝑖 : The particular stress range

Rs AASHTO LRFR 11 (Eq.7.2.2.1.1-1)

(2) stress-range estimate partial load factor For calculating Rs , the R sa and R st values are applied according to [Table 3.25]. Therefore, there is no uncertainty in the verification. [Table3.25] Partial Load Factor, R sa , R st and R s

R sa

Case

R st

Rs

For Evaluation or Minimum Fatigue Life Stress range by simplified analysis, and truck weight per LRFD 3.6.1.4 Stress range by simplified analysis,

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1.0

1.0

1.0

1.0

0.95

0.95

Partial Load Factors AASHTO LRFR 11 (Table 7.2.2.1-1)

and truck weight estimated through weigh-in-motion study Stress range by refined analysis, and truck weight per LRFD 3.6.1.4 Stress range by refined analysis, and truck weight estimated through weigh-in-motion study Stress range by field-measured strains

0.95

1.0

0.95

0.95

0.95

0.90

N/A

N/A

0.85

N/A

1.00

For Mean Fatigue Life All method

N/A

4.4 Determining Fatigue-Prone Details Bridge details are only considered prone to load-induced fatigue damage if they experience a net tensile stress. Therefore, if the below requirement is satisfied, the Fatigue Limit State needs to be verified.

2Rs (f ) tension  f deadloadcompression

(3.8)

Fatigue-Prone Details AASHTO LRFR 11 (7.2.3) (Eq. 7.2.3-1)

Where (∆𝑓)𝑡𝑒𝑛𝑠𝑖𝑜𝑛 : Factored tensile portion of the stress range due to the passage of a fatigue truck 𝑓𝑑𝑒𝑎𝑑−𝑙𝑜𝑎𝑑 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 : Unfactored compressive stress at the detail due to dead load.

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Chapter 3. Steel Composite Bridge Load Rating : AASHTO-LRFR 2nd (2011)

Bridge Load Rating Result 1. Result Tables For the element of the worst case, capacity, demand and basis of demand can be reviewed per different rating cases.

1.1 Service Limit State Summary (1) by Result Table The results may be reviewed with the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Service Limit State Summary…

[Fig.3.31] Result Table for Service Limit State Summary Where, Rating Case: Rating Case combination with the minimum RF Component : Indicates the member type: compression/tension Minimum Rating Factor: The minimum RF Location: The Element number and its i/j nodes where the RF is calculated Relative Location: The relative location from the starting point of the bridge (Refer to Span Information dialog box) Allowable Stress: C or allowable stress inputted by the user Demand: Stress demand Point : Design point at i/j nodes (e.g., Right Top, Right Bottom, Left Top, Left Bottom) DC(Before) – Factor : Load Factor for Load Case-DC(Before) DC(Before) – Stress from DC(Before) DC(After) – Factor : Load Factor for Load Case-DC(After) DC(After) – Stress from DC(After) DW – Factor : Load Factor for Load Case-DW DW – Stress : Stress from DW Temperature – Factor : Load Factor for Load Case-Temperature Temperature – Stress : Stress from Temperature Permanent – Factor : Load Factor for Load Case- Permanent Permanent – Stress :Stress from Permanent Secondary – Factor : Load Factor for Load Case-Secondary Secondary – Stress :Stress from Secondary User Defined – Factor : Load Factor for Load Case-User Defined User Defined – Stress : Stress from User Defined

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Pri. LL – Factor : Load Factor for Load Case-Primary live load Pri. LL – Stress : Stress from Primary live load Adj. LL – Factor : Load Factor from Load Case-Adjacent live load Adj. LL – Stress : Stress from Adjacent live load

(2) by Excel Report The results may be reviewed in the form of MS Excel Report as shown in [Fig.3.32].

[Fig.3.32] Excel Report for Service Limit State Summary

1.2. Strength Limit State Summary (1) by Result Table The results may be reviewed in the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Strength Limit State Summary…

[Fig.3.33] Result Table for Strength Limit State Summary Where, Positive/Negative: Positive/Negative moment LRFD Resistance Factor: Resistance Factor according to the standard selected for the Rating Design Code Demand, Mu: moment due to the factored loads Capacity, phiMn: nominal flexural resistance of a section multiplied by phi of flexure Demand, fbu: largest value of the compressive stress throughout the unbraced length in the flange under condition, calculated without consideration of flange lateral bending Capacity, phiFn: nominal flexure resistance of a flange DC(Before) – Force : My from DC(Before) DC(After) – Force: My from DC(After) DW – Force: My from DW Temperature – Force: My from Temperature T.Gradient – Force: My from T.Gradient Permanent – Force: My from Permanent Secondary – Force: My from Secondary User Defined – Force: My from User Defined Pri. LL – Force: Pri. My from LL Adj. LL – Force: My from Adj.

(2) by Excel Report The results may be reviewed in MS Excel report form as shown in [Fig.3.34]. Chapter 3.Steel Composite Bridge Load Rating - AASHTO LRFR 2011

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[Fig.3.34] Excel Report for Strength Limit State Summary

1.3. Flexure Strength Rating Factor The Rating Factor can be reviewed per rating cases. (1) by Result Table The results may be reviewed in the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Flexure Strength Rating Factor…

[Fig.3.35] Result Table for Flexure Strength Rating Factor Where, Group : Name of Element Group defined by user Elem. : Number of Element for which the Rating Factor is calculated Part : i/j nodes and number of the elements used for design System Factor:  s used to calculate RF of the element Condition Factor:  c used to calculate RF of the element Rating Factor : Rating Factor calculated according to equation (2.1) Check : Whether the result is OK or NG (OK if RF>1)

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown in [Fig.3.36]

[Fig.3.36] Excel Report for Flexure Strength Rating Factor

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1.4. Shear Strength Rating Factor The Rating Factor can be reviewed per rating cases and elements. (1) by Result Table The results may be reviewed in the Results Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Shear Strength Rating Factor…

[Fig.3.37] Result Table for Shear Strength Rating Factor

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown in [Fig.3.38].

[Fig.3.38] Excel Report for Flexure Strength Rating Factor

1.5. Steel Stress Rating Factor The Service Limit State verification result can be viewed for the compressive and tensile stress per elements and rating cases. (1) by Result Table The results may be reviewed in the MS Excel Report form as shown in [Fig.3.39]. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Steel Stress Rating Factor…

[Fig.3.39] Result Table for Steel Stress Rating Factor

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown in [Fig.3.40].

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[Fig.3.40] Excel Report for Steel Stress Rating Factor

1.6. Fatigue Rating Factor (1) by Result Table The results may be reviewed in the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Fatigue Rating Factor…

[Fig.3.41] Result Table for Fatigue Rating Factor

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown in [Fig.3.42].

[Fig.3.42] Excel Report for Fatigue Rating Factor

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2. Rating Detail Table The Rating Detail Table presents the rating factor, capacity, basis of demand calculation, and the amount of steel per load cases, elements and rating cases.

2.1 Flexure Strength Rating Detail The Flexure Strength Rating Detail may be viewed with the program Result Table or MS Excel Report document. (1) by Result Table The results may be reviewed in the MS Excel Report form as shown in [Fig.3.43]. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Flexure Strength Rating Detail …

[Fig.3.43] Result Table > Flexure Strength Rating Detail Where, phiMn: nominal flexural resistance of a section multiplied by phi of flexure phiFn: nominal flexure resistance of a flange Areas–Rebar : Rebar Area Areas–min :Minimum Rebar Area Reinforcement Requirement–max: Maximum reinforcement requirement DC(Before) – Force : My from DC(Before) DC(After) – Force: My from DC(After) DW – Force: My from DW Temperature – Force: My from Temperature T.Gradient – Force: My from T.Gradient Permanent – Force: My from Permanent Secondary – Force: My from Secondary User Defined – Force: My from User Defined Pri. LL – Force: My from Pri. LL Adj. LL – Force: My from Adj. LL

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown in [Fig.3.44].

[Fig.3.44] Excel Report for Flexure Strength Rating Detail

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2.2 Shear Strength Rating Detail (1) by Result Table The results may be reviewed in the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Shear Strength Rating Detail …

[Fig.3.45] Result Table > Shear Strength Rating Detail Where, (delta F)n : Nominal Fatigue Limit State DC(Before) – Force : Vz due to DC(Before) DC(After) – Force: Vz due to DC(After) DW – Force: DW에 대한 Vz Temperature – Force: Vz due to Temperature T.Gradient – Force: Vz due to T.Gradient Permanent – Force: Vz due to Permanent Secondary – Force: Vz due to Secondary User Defined – Force: Vz due to User Defined Pri. LL – Force: Vz due to Pri. LL Adj. LL – Force: Vz due to Adj. LL

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown in [Fig.3.46].

[Fig.3.46] Excel Report for Flexure Strength Rating Detail

2.3 Steel Stress Rating Detail The Steel Stress can be reviewed for all load cases and stress types. (1) by Result Table The results may be reviewed in the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Steel Stress Rating Detail …

[Fig.3.47] Result Table for steel stress Rating Detail

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Where, fc : bending stress on web plate fcrw: bending stress limit on web plate Rating Factor – Comp.: RF for the allowable compressive stress Rating Factor – Tens: RF for the allowable tensile stress Allowable Stress– Comp.: Allowable compressive stress user-defined Allowable Stress– Tens.: Allowable tensile stress user-defined DC(Before) -Left Top Stress : Stress at the Left Top due to the DC(Before) Load Cases DC(Before) -Right Top Stress : Stress at the Right Top due to the DC(Before) Load Cases DC(Before) -Right Bottom Stress: Stress at the Right Bottom due to the DC(Before)Load Case DC(Before) -Left Bottom Stress: Stress at the Left Bottom due to the DC(Before) Load Case ※ DW, Temperature, Permanent, Secondary,…Adj. LL can be explained the same way as the above DCXXXXXX bolded.

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown below.

[Fig.3.48] Excel Report for Steel Stress Rating Detail

2.4 Fatigue Rating Detail The Fatigue Rating may be reviewed for all load cases and stress types. (1) by Result Table The results may be reviewed in the Result Table as shown below. ▶ Rating > Bridge Rating Design > Steel Design > Rating Design Result Tables > Fatigue Rating Detail …

[Fig.3.49] Result Table for Fatigue Rating Detail (delta F)n : Nominal Fatigue Limit State DC(Before) –Stress :Stress due to DC(Before) DC(After) – Stress : Stress due to DC(After) DW – Stress :Stress due to DW Temperature – Stress: Stress due to Temperature T.Gradient – Stress: Stress due to T.Gradient Permanent – Stress: Stress due to Permanent Secondary – Stress: Stress due to Secondary User Defined – Stress: Stress due to User Defined

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Pri. LL – Stress: Stress due to Pri. LL Adj. LL – Stress: Stress due to Adj. LL

(2) by Excel Report The results may be reviewed in the MS Excel Report form as shown below..

[Fig.3.50] Excel Report for Fatigue Rating Detail

3. Load Rating Report 2.1 Load Rating Summary Result Table The below table presents the moment and shear at the Strength Limit State and stress at the Service Limit State. The table indicates the worst cases load combination based on the 1) moment at the Strength Limit State, 2) Stress at the Service Limit State, and 3) Shear at the Strength Limit State.

[Fig.3.51] Excel Report for Load Rating Summary Result Table

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DESIGN GUIDE for midas Civil AASHTO LRFD