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AISC V.13 BEAM DESIGN (LRFD) A.

DESIGN DATA A.1

B.

MATERIAL PROPERTIES Yield strength of structural steel W Shapes, ASTM A572

Fy := 50ksi

Fy = 345 ⋅ MPa

Modulus of Elasticity of Steel

E s := 29000 ksi

E s = 199948 ⋅ MPa

Shear Modulus

G v := 11200 ksi

G v = 77221 ⋅ MPa

BEAM DESIGN B.1

SECTION PROPERTIES

Properties of :

W10X33

W10X33

A=

9.71

in^2

Cross-sectional area of member Depth of member, parallel to Y-axis

d=

9.73

in

tw =

0.29

in

Thickness of web of member

bf =

7.96

in

Width of flange of member, parallel to X-axis

tf =

0.435

in

Thickness of flange of member

k(des) =

0.935

in

Distance from outer face of flange to web toe of fillet

k(det) =

1.125

in

Distance from outer face of flange to web toe of fillet

k1 =

0.75

in

Distance from web centerline to flange toe of fillet

T=

7.5

in

Distance between fillets for wide-flange or channel shape = d(nom)-2*k(det)

wt./ft. =

33

plf.

Beam weight

bf/(2*tf)

9.15

Slenderness parameter for compact flange

h/tw =

27.1

Slenderness parameter for compact web

Ix =

171

in^4

Sx =

35

in^3

Moment of inertia of member taken about X-axis Elastic section modulus of member taken about X-axis

rx =

4.19

in

Radius of gyration of member taken about X-axis = SQRT(Ix/A)

Zx =

38.8

in^3

Plastic section modulus of member taken about X-axis

Iy =

36.6

in^4

Moment of inertia of member taken about Y-axis

Sy =

9.2

in^3

Elastic section modulus of member taken about Y-axis

ry =

1.94

in

Radius of gyration of member taken about Y-axis = SQRT(Iy/A)

Zy =

14

in^3

Plastic section modulus of member taken about Y-axis

rts =

2.2

in

SQRT(SQRT(Iy*Cw)/Sx)

9.3

ho = J=

in

Distance between centroid of flanges, d-tf

0.583

in^4

Torsional moment of inertia of member Warping constant

Cw =

791

in^6

Wno =

18.5

in^2

Normalized warping function at a point at the flange edge

Sw =

16

in^4

Warping statical moment at a point on the cross section

B.2

Qf =

7.75

in^3

Statical moment for a point in the flange directly above the vertical edge of the web

Qw =

18.9

in^3

Statical moment at the mid-depth of the section

BEAM DESIGN FORCES Service Loads: from Analysis Maximum Moment:

Mmax := 50 ft kip

Mmax = 67.791 ⋅ kN m

Maximum Shear:

Vmax := 50kip

Vmax = 222.411 ⋅ kN

AISCV13 (LRFD) Beam Design.xmcd

Page 1 of 4

LNT4: Dec 2010

AISC V.13 BEAM DESIGN (LRFD) Factored Loads: (Use Load Factor, U := 1.5 for simplicity)

B.3

Maximum Moment:

Mr := Mmax ⋅ U

Mr = 101.686 ⋅ kN m

Maximum Shear:

Vr := Vmax ⋅ U

Vr = 333.617 ⋅ kN

Beam Length:

Lbeam := 30ft

Lbeam = 9.144 ⋅ m

Required Shear Strength

Vr = 75 ⋅ kips

Vr = 333.617 ⋅ kN

Web Slenderness ratio

λw =

CHECK SHEAR

h

=

tw

d − 2kdes tw

λw = 27.1

Resistance Fac & Web Shear Coef Web Shear Coefficient

ϕv = 1

Resistance Factor for Shear

Cv = 1

Web area

Aw := d ⋅ tw

Aw = 1820.448 ⋅ mm

Nominal Shear Strength

Vn := 0.6 ⋅ Fy ⋅ Aw ⋅ Cv

Vn = 376.546 ⋅ kN

Available shear strength

ϕVn := ϕv Vn

ϕVn = 376.546 ⋅ kN

Utilization Ratio

URv :=

Vr

2 [AISC Eqn G2-1]

URv = 0.886

ϕVn

(

Check_Shear := if URv ≤ 1.0 , "O.K., SAFE!" , "N.G., REDESIGN"

)

Check_Shear = "O.K., SAFE!" B.4

DETERMINE SHAPE COMPACTNESS UNSTIFFENED ELEMENTS bf

Flanges of W-Shape

λf =

Compact limit

λpf := 0.38

Noncompact limit

λrf := 1.0

Flange :=

λf = 9.15

2tf Es Fy Es Fy

"is compact" if λf ≤ λpf

λpf = 9.152

[AISC Table B4.1]

λrf = 24.083

[AISC Table B4.1]

Flange = "is compact"

"is noncompact" if λpf < λf ≤ λrf "is slender-element" if λf > λrf STIFFENED ELEMENTS h

Web of W-Shape

λw =

Compact limit

λpw := 3.76

Noncompact limit

λrw := 5.70

AISCV13 (LRFD) Beam Design.xmcd

tw

=

d − 2kdes

Page 2 of 4

tw Es Fy Es Fy

λw = 27.1

λpw = 90.553

[AISC Table B4.1]

λrw = 137.274

[AISC Table B4.1]

LNT4: Dec 2010

AISC V.13 BEAM DESIGN (LRFD) Web :=

"is compact" if λw ≤ λpw

Web = "is compact"

"is noncompact" if λpw < λw ≤ λrw "is slender-element" if λw > λrw B.5

CHECK AVAILABLE FLEXURAL STRENGTH Length between points that are either braced against lateral displacement of compression flange or braced against twist of the cross section Lateral-Torsional Buckling Modification Factor, conservatively, take

Cb := 1.0

Shape Factor for doubly symmetric I-shape

c := 1.0

Limiting laterally unbraced length for the limit state of yielding

Brace Points

n := 1

Lbeam Lb := n+1

Lb = 15 ⋅ ft

[AISC Eqn F2-8a] Es

Lp := 1.76 ⋅ r y ⋅

Fy

Lp = 6.85 ⋅ ft

[AISC Eqn F2-5]

Lr = 21.78 ⋅ ft

[AISC Eqn F2-6]

Limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling Lr := 1.95r ts

⎛ Es ⎞ ⎜ ⎟ ⎝ 0.7Fy ⎠

Jc Sx ⋅ ho

⎛ 0.7Fy ⎝ Es

1 + 6.76 ⎜

1+

Plastic Bending Moment

Mp := Fy ⋅ Z x

Resistance Factor for Flexure

ϕb := 0.90

⋅

Sx ⋅ ho⎞ ⎟ Jc ⎠

2

Mp = 219.191 ⋅ kN m [AISC Eqn F2-1]

YIELD LIMIT STATE, AISC SEC F2.1 MY := Mp

[AISC Eqn F2-1]

MY = 219.191 ⋅ kN ⋅ m

LATERAL-TORSIONAL BUCKLING LIMIT STATE, AISC SEC F2.2 & F3.1

(

)

MLTB UbL :=

[AISC Eqn F2-1]

Mp if UbL ≤ Lp

⎡ ⎣

Ub − L ) ⎛⎜ L L− L p ⎟⎞⎥⎤

(

Cb ⋅ ⎢Mp − Mp − 0.7Fy ⋅ S x ⋅

⎝

r

p

⎠⎦

if Lp < UbL ≤ Lr

[AISC Eqn F2-2]

if UbL > Lr Fcr ←

2 Cb ⋅ π ⋅ E s ⋅ 2 ⎛ UbL ⎞

⎜ ⎝

r ts

1 + 0.078

⎟ ⎠

Jc ⋅ Sx ⋅ ho

⎛ UbL ⎞ ⎜ ⎟ ⎝ r ts ⎠

2 [AISC Eqn F2-4]

Fcr ⋅ S x

( )

MLTB Lb = 175.085 ⋅ kN ⋅ m COMPRESSION FLANGE LOCAL BUCKLING LIMIT STATE, AISC SEC F3.2 MFLB :=

[AISC Eqn F2-3]

Mp if λf ≤ λpf

⎡ ⎛ λf − λpf ⎞⎤ ⎢Mp − ( Mp − 0.7Fy ⋅ S x) ⋅ ⎜ ⎟⎥ ⎣ ⎝ λrf − λpf ⎠⎦

if λpf < λf ≤ λrf

[AISC Eqn F2-1]

if λf > λrf kc ← max ⎛⎜0.35 , min⎛⎜

⎝

⎝

4 λw

, 0.76⎞⎟⎞⎟

[AISC Eqn F3-1]

⎠⎠

0.9E s ⋅ kc ⋅ S x λf

2

MFLB = 219.191 ⋅ kN ⋅ m

AISCV13 (LRFD) Beam Design.xmcd

Page 3 of 4

LNT4: Dec 2010

AISC V.13 BEAM DESIGN (LRFD) (

( )

)

NOMINAL FLEXURAL STRENGTH:

Mn := min MY , MLTB Lb , MFLB

Mn = 175.085 ⋅ kN m

Available Flexural Strength:

ϕMn := ϕb Mn

ϕMn = 157.577 ⋅ kN m

Utilization Ratio:

URf :=

Mr

[AISC Eqn F3-2]

URf = 0.645

ϕMn

(

Check_Flexure := if URf ≤ 1.0 , "O.K., SAFE!" , "N.G., REDESIGN"

)

Check_Flexure = "O.K., SAFE!"

Beam Capacity Beam Capacity as Function of Unbraced L Moment Capacity, kN-m

250 200 150 100 50

0

2

4

6

8

10

Unbraced Length, m

B.6

CHECK DEFLECTION

Nominal Moment Strength Moment at Unbraced Length

Maximum Deflection, from Analysis

δmax := 12mm

Allowable Deflection

δallow :=

Utilization Ratio:

URd :=

Lbeam

δmax

(

SUMMARY

URd = 0.315

δallow

Check_Deflection := if δmax ≤ δallow , "O.K., SAFE!" , "N.G., REDESIGN"

C.

δallow = 38.1 ⋅ mm

240

)

Check_Deflection = "O.K., SAFE!"

Beam_Shape = "W10X33"

BEAM CHECKS SHEAR

Utilization Ratio

URv = 0.886

Check_Shear = "O.K., SAFE!"

FLEXURE

Utilization Ratio

URf = 0.645

Check_Flexure = "O.K., SAFE!"

DEFLECTION

Utilization Ratio

URd = 0.315

Check_Deflection = "O.K., SAFE!"

End of Calculation AISCV13 (LRFD) Beam Design.xmcd

Page 4 of 4

LNT4: Dec 2010