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A COMPARATIVE STUDY OF RCC & STEEL PILE FOUNDATION FOR AN INTEGRAL BRIDGE A Dissertation Work Submitted in Partial Fulfillment for the Requirements for the award of Degree of Master of Engineering in CIVIL - Computer Aided Structural Analysis and Design To Gujarat University
Prepared by: Viral B Panchal Guided by: Prof C S Sanghvi
Applied Mechanics Department L. D. College of Engineering Ahmedabad-380 015 August 2011
GOVERNMENT OF GUJARAT L. D. COLLEGE OF ENGINEERING AHMEDABAD – 380015
CERTIFICATE This is to certify that the work presented in the Dissertation Entitled “A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge” has been carried out by Panchal Viral Bipinchandra Registration No: ME 45 Date: 31/8/06 Seat No: 3006 Year: June 2008 in a manner sufficiently satisfactory to warrant its acceptance as a partial fulfillment of the requirements for the award of the Degree of
“Master of Engineering in CIVIL-CASAD” This is a bonafide work done by the student and has not been submitted to any other University / Institute for the award of any other Degree / Diploma. Prof. C. S. Sanghvi Guide Prof (Dr) H S Patel P.G. In-charge
Prof (Dr) R K Gajjar Prof. & Head of Dept. Prof. M. N. Patel Principal
Applied Mechanics Department L. D. College of Engineering, Ahmedabad – 380015 Gujarat, India August 2011
I
DISSERTATION APPROVAL SHEET Dissertation entitled “A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge” is submitted by Panchal Viral Bipinchandra of L. D. College of Engineering, Ahmedabad is approved for the Award of the Degree of Master of Engineering (Civil) in the field of Computer Aided Structural Analysis and Design by Gujarat University.
INTERNAL EXAMINER (S): (Prof. C. S. SANGHVI)
EXTERNAL EXAMINER (S): (
)
II
INDEX
Chapter
Content
No.
1
Page No.
Abstract
(i)
Acknowledgement
(iii)
Introduction
1
1.1 Introduction To Integral Bridges
1
1.2 Bridge Substructure
10
2
Literature Review
17
3
Project Description
20
4
Analysis
24
5
4.1 Load Description
24
4.2 Load Calculation
43
4.3 Pile Analysis
61
Pile Design
73
5.1 Geotechnical Design Of RCC Piles
73
5.2 Structural Design Of RCC Piles
83
5.3 Geotechnical Design Of Steel Piles
89
5.4 Structural Design Of Steel Piles
97
6
Comparison Of Results
108
7
Conclusion And Future Scope
113
8
References
115
Appendix – A - Wave Force Calculation Charts
117
Appendix – B - Super structure Analysis & Design
129
Appendix – C - General Arrangement Drawing
Appendix – D - Construction Sequence Drawing
Appendix – E - RCC Pile Detail Drawing
Appendix – F - Steel Pile Detail Drawing
Appendix – G - Pile Cap Reinforcement Detail Drawing
Appendix –H - Longitudinal Beam Reinforcement Detail Drawing
Appendix –I - Diaphragm Reinforcement Detail Drawing
Appendix –J - Deck Slab Reinforcement Detail Drawing Papers For Publication 1). A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge 2). Integral Bridges
LIST OF FIGURES Figure No. 1 2 3 4 5 6 7 8 9 10 11 12
Description Sketch Of A Typical 3 Span Integral Bridge Transfer Of Movements In Integral Bridges Different Types Of End Supports For Integral Bridge IRC Class AA Loading IRC Class 70R Loading IRC Class A Loading IRC Class B Loading Curves For Impact Factor Enveloping Cylinders Pressure Distribution Definition Sketch Of Wave Forces On A Vertical Cylinder. Breaking Wave Height & Regions Of Validity Of Various Wave Theories
Page No. 1 3 4 25 26 26 26 28 34 35 36 41
13 14 15 16 17 18 19 20 21 22 23 24 25
Application Of Wave Force – Operating & Extreme Application Of Current Force – Operating Application Of Current Force – Extreme Cross Section Of Staad Model 3D View Of Staad Model RCC Pile Bending Moment Mz Envelop RCC Pile Bending Moment My Envelop RCC Pile Axial Force Envelope RCC Pile Shear Force Envelope Steel Pile Bending Moment Mz Envelope Steel Pile Bending Moment My Envelope Steel Pile Axial Force Envelope Steel Pile Shear Force Envelope
56 57 58 61 62 63 63 64 64 67 68 68 69
26 27 28 29 A.1 A.2 A.3 A.4 A.5
Parabolic variation of subgrade modulus Neutral axis Shear key details Concrete plug neutral axis Values Of Kim Values Of KDm Values Of Sim Values Of SDm Values Of Фm For W=0.05
76 87 101 107 117 118 119 120 121
A.6 A.7 A.8
Values Of Фm For W=0.1 Values Of Фm For W=0.5 Values Of Фm For W=1
122 123 124
A.9 A.10 A.11 A.12 B.1 B.2
Values Of αm For W=0.05 Values Of αm For W=0.1 Values Of αm For W=0.5 Values Of αm For W=0.5 Longitudinal & Pile Cap Beam Arrangement Precast deck plank arrangement
125 126 127 128 129 134
LIST OF TABLES Table No. 1 2 3.1 3.2 4.1 4.2 5 6 7.1
Description Values Of Ce Pressure Distribution Co-efficient Grid A – Design forces Grid A – Service forces Grid B – Design forces Grid B – Service forces Axial Forces Deflection Steel Pile Grid A Forces- Axial compression with bending (operating)
Page No. 34 35 65 65 66 66 67 67 69
7.2
Steel Pile Grid A Forces- Axial compression with bending (extreme)
70
8.1
Steel Pile Grid B Forces- Axial compression with bending (operating)
70
8.2
Steel Pile Grid B Forces- Axial compression with bending (extreme)
71
9 10.1 10.2 11.1
Steel pile – Axial Forces Steel pile grid A -Concrete Plug Design Forces Steel pile grid A -Concrete Plug Service Forces Steel pile grid B -Concrete Plug Design Forces
71 71 72 72
11.2 12 13 14 15.1-15.2 16 17 18.1-18.2 19 20.1-20.2 21
Steel pile grid B -Concrete Plug Service Forces Deflection Range of Modulus of Subgrade Reaction ks Values of Cm Spring Constant Calculation Soil Properties Reinforcement Summary Crack Width Check Summary Rate Of Corrosion For Structural Steel Steel Pile Design Summary Concrete Plug Reinforcement Summary
72 72 75 76 78 80 85 87-88 98 99-100 104
22.1-22.2 B.1.1 B.1.2 B.2.1-B.2.2 B.3.1-B.3.2
Concrete Plug Crack Width Check Summary Pilecap Beam Design Forces Pilecap Beam Service Forces L-beam Design And Service Forces End Diaphragm Forces
107 129 130 131 134
ABSTRACT The twentieth century heralded a new era in bridge building concepts with large improvements in material and methods. Rapid developments in the theory of structures along with the advent of the computer made it possible to pioneer innovative designs. The design of bridge structures has become intricate with the changeover from the conventional simply supported girder slab bridges to complex forms such as bridges without joints, cable stayed and suspension bridges. The analysis of such structures, having different forms and shapes, requires ingenuity of a high order as research may lag behind practical possibilities. Bridge design and construction all over the world has undergone remarkable changes in the past two decades. The increase in demand for complex roadway alignments, advances in construction technology and availability of computing power for bridges design, are some of the factors for these developments. Concept of “Integral Bridges” is one of these developments. Such bridges are the answer for short and medium length bridges where bearings and expansion joints can either be eliminated altogether or reduced to a minimum. By incorporation of intermediate expansion joints the integral bridge concept can be extended to long bridges and viaducts too. This concept is already in practice in countries like US, UK, Australia etc. Due to ease & economy in construction and maintenance, It is also getting popular in India. This concept is widely used in recent projects of Delhi Metro. Integral bridge concept is widely adopted in marine structures. This concept is used as a approach bridge to connect berthing structure to the shore. Their function is to provide supporting structure material handling system like conveyors in addition to providing carriageway for vehicular traffic like in case of road bridges. Main reasons for increasing popularity of integral concept in marine structures are efforts of minimizing use of bearings and to resist large lateral forces. Bearings are difficult to maintain and more difficult to replace. Also it is a vulnerable point in structure at time of extreme events like earthquake and cyclones. Also integral bridge requires flexible foundation to accommodate thermal stresses and stresses produced from lateral forces like waves, current, wind, seismic etc. As pile foundation is a flexible foundation as compared to piers or caissons and because of ease of construction it is generally adopted in marine approach bridges. However there can be variations in pile foundations for integral bridges like bored cast in situ RCC piles, driven precast piles, driven precast prestress piles, driven steel piles etc. This study is based on integral bridge concept with two different pile types. This study deals with the introduction, behavior, analysis, design, conclusion and future scope. The
i
analysis and design of one integral approach bridge which is constructed at Dahej is done using Staad Pro 2007 software. The necessary data related to site conditions and loadings is obtained from PMC Projects (India) Private Limited, Ahmedabad. Analysis and design of two alternatives are carried out here. One alternative is analyzed and designed using RCC bored cast in situ piles. Design of a typical integral piled approach (superstructure and substructure) is presented in this alternative. In second alternative, foundation is changed to driven vertical steel pile keeping superstructure system same as in first alternative. Structural comparison is made between these two alternatives. Assuming all the data regarding length, site conditions and loading to be constant, a comparison between results obtained from analysis and design of two alternatives (bored RCC piles and driven steel piles) of bridge is made.
ii
ACKNOLEDGEMENT I grab this opportunity to express my profound gratitude to all the individuals who helped me and guided me at different stages of my dissertation work. To begin with, I would like to thank my guide Prof. C.S.Sanghvi, Applied Mechanics Dept., L.D.C.E., who has given immense contribution at every stage of this research work. I will remain grateful to Mr. Munish Kotwal (Stup Consultants) for their support and PMC Projects (I) Pvt. Ltd providing me training at design office. I am indebted to Mr. Nirav Shah (PMC Projects (I) Pvt. Ltd) and Mr. Tushar Pandya (Stup Consultants) for providing me all the necessary data for formulating thesis topic and thesis content. I am very much thankful to both of them for their invaluable guidance and support throught the tenure of this dissertation work. I wish to express my sincere thanks to my classmates and friends Dhyan, Rajmayur, Dhruva, Jignesh for their motivation. I am very much thankful to my friends Khyati and Dharmesh for their continuous support during this course work.
iii
CHAPTER 1 INTRODUCTION
Chapter-1
Introduction
1.1 Introduction To Integral Bridges 1.1.1 Integral Bridge Concept: Integral bridges are bridges where the superstructure is continuous and connected monolithically with the substructure with a moment-resisting connection. As an effect we obtain a structure acting as one unit. The terminology varies in different sources, so sometimes the bridges which just do not have dilatations are called jointless bridges. These structures still have bearings, so the structure still can move in the horizontal plane (but these movements are limited).In polish literature, there are many definitions used with regard to discussed structures: bridges with spans connected with supports with no hinged connection (with regard to the way of supporting spans on supports), frame bridges (with regard to static scheme of construction), bridges supported on piles (with regard to the type of foundation), etc. However, there is no definition which describes all the features of integral structures (a material, foundation type, static scheme and cooperation with surrounding soil). Here in this thesis, integral bridge supported on piles is taken for study. Integral bridges accommodate superstructure movements without conventional expansion joints. With the superstructure rigidly connected to the substructure and with flexible substructure piling, the superstructure is permitted to expand and contract. The integral abutment bridge concept is based on the theory that due to the flexibility of the piling, thermal stresses are transferred to the substructure by way of a rigid connection between the superstructure and substructure. Such bridges are the answer for small and medium length bridges where bearings and expansion joints can be either eliminated altogether or reduced to a minimum. By incorporation of intermediate expansion joints, the integral bridge concept can be extended to long bridges and viaducts too. Integral bridges are designed to provide resistance to thermal movements, breaking forces, seismic forces and winds by the stiffness of the soil abutting the end supports and the intermediate supports. A typical three span integral abutment bridge is shown in Fig. 1.
Fig.1 Sketch Of A Typical 3 Span Integral Bridge
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
1
Chapter-1
Introduction
The principle difference between the integral bridge and conventional bridge is in the design of sub structure and end supports. In a conventional bridge, thermal movements, structural flexure, shrinkage etc. are accommodated by a designed and clearly delineated movement joint. In an integral bridge, reliance is placed upon compliance of the soil behind abutment with imposed movements of the bridge structure. Any required provision for movement in the carriageway is then placed outside the structure length where it will cause less deterioration to the structure. Fig. 2 shows three principle methods by which an integral bridge can accommodate movements of the super structure. Fig. 3 shows different types of end supports used for integral bridges. The main types of the end supports can be categorized and described as: a). Frame abutment:- Full height frame abutments are suitable for short single-span bridges. The horizontal movements will only be small, so the earth pressures should not be very high. b). Embedded wall abutment:- Embedded wall abutments are also suitable for short single-span integral bridges. c). Piled abutment with reinforced soil wall :- A piled abutment with reinforced soil abutment wall and wing walls is a form of construction that should have a wide application. d). End screen (semi integral) :- Semi-integral construction with bearings on top of a rigid retaining wall is a design method that can be used for full-height abutments for bridges of any length. Jacking of the deck can result in soil movement under the abutment soffit. This can obstruct the deck from returning to its original level. e). Piled bank seat :- Piled bank seats are recommended for widespread use. The piles prevent settlement while allowing horizontal movement and rotation. f). Piled bank seat with end screen (semi integral):- Bank seats can be designed as semi-integral abutments. The footing is not required to move horizontally and piled or spread footings can be used. g). Bank pad abutment :- Shallow abutments on spread footings are only considered to be suitable for situations where the foundation is very stiff and there can be no settlement problems. A granular fill layer should be placed below the footing to allow sliding.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
2
Chapter-1
Introduction
Fig. 2 Transfer Of Movements In Integral Bridges
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
3
Chapter-1
Introduction
(a)
(c)
(e)
(b)
(d)
(f)
(g) Fig. 3 Different Types Of End Supports For Integral Bridges A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
4
Chapter-1
Introduction
1.1.2 Background: Joints and bearings are expensive to buy, install, maintain and repair and more costly to replace. The most frequently encountered corrosion problem involves leaking expansion joints that permit salt laden runoff water from the roadway surface to attack girder ends, bearings and supporting RCC substructure. Also bridge deck joints are subjected to continual wear and heavy impact from repeated live loads as well as continual stages of movement from expansion and contraction caused by temperature changes, creep and shrinkage or long term movement effects such as settlement and soil pressure. It is necessary to detail these joints so that adequate space is available for maintenance and replacement of bearings. The problems arising from provision of bearings and expansion joints can be summarized as: • Increased incidence of inspection and maintenance required, bridge durability is often impaired. • Necessity of replacement during the service life of the bridge since their design life is lesser than that of the rest of the bridge elements. • Decrease in redundancy and difficulties in providing adequate ductility for resisting earthquake effects, leading to larger earthquake design forces.
Surajbari new bridge superstructure shifted in the transverse direction
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
5
Chapter-1
Introduction
Bridge between Surajbari & Bhachau – Violent shaking has resulted in pier head being damaged due to pounding of deck Possibilities of dislodgement of superstructure during accidental loads, especially those due to earthquakes, is a clear danger requiring expensive and clumsy attachments. The latest amendments to the Indian Road Congress codes require the positive measures such as restrainers be provided so that girders do not get dislodged during earthquake. • Bridges presents soft target for terrorists who could put them out of service with little difficulty. Because of above mentioned problems, use of integral or integral abutment bridge is being increased all over the world. Simply supported bridges are still popular in India. The main reason for their popularity is that these structures are simple to design and execute. The sub-structural design is also greatly simplified because of the determinate nature of the structure. Sometimes there are situations where bearings/simply supported spans/expansion joints can not be altogether avoided because of the length of the bridge. In such cases intermediate joints will be provided with bearings to allow horizontal movements. But these joints will be lesser in numbers as compared to simply supported bridges. On the other hand, monolithic joints and redundancy of the structural system do result in savings in the cost of the construction and maintenance. Elimination of bearings improves the structural performance during earthquakes. Finally, integral form of construction will require lesser inspection and maintenance efforts. Several urban structures in India have been built with this concept. However no national standards or A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
6
Chapter-1
Introduction
uniform policy regarding the permissible bridge length, skews and design procedures have been clearly established, although certain general concepts become common in practice. The advisory note BA 42/96 recommends that all bridges need to be integral if overall length exceeds 60 m and skews less than 30 deg. The longitudinal movement in the bridge abutment is limited to 20mm from the position at time of restraint during construction. Integral bridges are designed for same range of temperatures as other bridges. According to IAJB 2005, the range of design criteria for selection of integral bridge is summarized in Table below. Steel girders
Concrete
Maximum span (ft)
65-300
60-200
Total length (ft)
150-650
150-1175
Maximum skew (degree)
15-70
15-70
Maximum curvature
0-10
0-10
Length of the bridge taken for study in this thesis is more than above mentioned range. However it is still designed with integral concept with provision of intermediate expansion joints to cater for horizontal movements. It is still considered integral because of the monolithic moment connection of the superstructure with foundation (piles). Some of the common features of monolithic bridge construction include: i) Elimination of the pier cap which improves bridge aesthetics. ii) Heavily reinforced slender piers iii) Change in the structural system. 1.1.3 Benefits of Integral Bridges: Some of the advantages of adopting Integral bridges over that of the conventional bridges are summarized below: i.
Simplified Construction- The simple characteristics of integral bridges make for rapid and economical construction. For example, there is no need to construct cofferdams, make footing excavations, place backfill, remove cofferdams, and prepare bridge seats, place bearings, back walls, and deck joints. Instead, integral construction generally results in just four concrete placement days. After the embankments, piles and pile caps have been placed and deck stringers erected, deck slabs, continuity connections, and approach slabs can follow in rapid succession.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
7
Chapter-1 ii.
Introduction
No bearings and Joints- Integral bridges can be built without bearings and deck joints. Not only will this result in savings in initial costs, the absence of joints and bearings will reduce maintenance efforts. This is an important benefit because presently available deck joint sealing devices have such short effective service lives.
iii.
Improved Design efficiency- Tangible efficiencies are achieved in substructure design due to an increase in the number of supports over which longitudinal and transverse superstructure loads may be distributed. Built-in abutments can be designed to accommodate some bending moment capacity, reducing end span bending moments with possible savings in end span girders. Due to rigid connection between superstructure and substructure, bending moments are considerably less thus resulting in smaller sections and economy in reinforcement and concrete.
iv.
Enhanced load distribution- One of the most important attributes of integral bridges is their substantial reserve strength capacity. The integrity of their unified structural system makes them extremely resistant to the potentially damaging effects of illegal super imposed loads, pressures generated by the restrained growth of jointed rigid pavements, earthquakes, and debris laden flood flows. A joint less bridge with integral abutments will have a higher degree or redundancy that may be beneficial in earthquake zones. The problem of retaining the superstructure on its bearing during seismic events is eliminated and the inherent damping of the integral bridge structural system allows it to better absorb energy and limit damage. The reasons for adopting integral bridges in India and elsewhere could be quite
different. When earthquake forces like predominant or when considerations like increased resistance to blast are to be reckoned with or there is a strong need of incorporating reduced cost of inspection & maintenance integral bridge concept is an excellent option. Application of Integral bridge concept is also widely seen in pile supported marine structures. In such water front structures, it is very difficult and costly to replace bearings. Also due to the equipments on the deck level, movement of the deck is limited in horizontal directions. So, less numbers of joints are required to reduce these longitudinal and lateral movements. Also many a times, marine structures are supported on piles or sheet piles which are easier to construct as compared to other deep foundations in ocean water with aggressive environmental conditions. And super structure is rigidly connected to piles. So lateral A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
8
Chapter-1
Introduction
movements induced due to temperature produced stresses and environmental loadings such as waves, current and wind are effectively sustained by piles and transferred to the ground. As piles are slender flexible members, it can sustain more bending and deflections.
1.1.4 Problems and uncertainities:Despite the significant advantages of integral abutment bridges, there are some problems and uncertainties associated with them. Many articles, mentioned that the main problem connected with integral bridges are consequences of temperature variations and traffic loads, which cause horizontal bridge movements. Horizontal movements and rotations of the abutment cause settlement of the approach fill, resulting in a void near abutment if the bridge has approach slabs. Effects of lateral movements of integral abutments under cyclic loadings are obvious problem which demands solving, but positive aspect in this case is that temperature induced displacements in the traditional bridge is over twice bigger than displacement at the end of (considering objects with the same span length) integrated structure because of symmetrical nature of the thermal effects as illustrated in the Figure..
The other uncertainties connected with designing and performance of integral abutment bridges are: The elimination of intermediate joints in multiple spans results in a structural continuity that may induce secondary stresses in the superstructure. These forces due to shrinkage, creep, thermal gradients, differential settlement, differential deflections, and earth pressure can cause cracks in concrete bridge abutments. Wingwalls can crack due to rotation and contraction of the superstructure. Also, differential settlement of the substructure can cause more damage in case of integral bridges as compared to traditional briges. Integral bridges should be provided with approach slabs to prevent vehicular traffic from consolidating backfill adjacent to abutments, to eliminate live load surcharging of backfill, and to minimize the adverse effect of consolidating backfill and approach embankments on movement of vehicular traffic. For bridges with closed decks (curbs, barriers, etc.), approach slabs should be provided with curbs to confine and carry deck
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
9
Chapter-1
Introduction
drainage across backfill to the approaches and prevent erosion, or saturation and freezing of the backfill. The piles that support the abutments may be subjected to high stresses as a result of cyclic elongation and contraction of the bridge structure. These stresses can cause formation of plastic hinges in the piles and may reduce their axial load capacities. The application of integral bridge concept has few other limitations. Integral bridges can not be used with weak embankments or subsoil, and they can only be used for limited lengths, although the maximum length is still somewhat unclear. Integral bridges are suitable if the expected temperature induced moment at each abutment is certain value specified by suitable authorities in every country, and somewhat larger moments can be tolerable.
1.2 Bridge Substructure: Usually substructure of a bridge refers to that part of it which supports the structure that carries the roadway (called superstructure). Thus the substructure covers pier and abutment bodies together with their foundations, and also the arrangements above the piers and abutments through which the superstructure sits, i.e. bears on the substructure. The latter are called the bearings. The more usual types of foundation for substructure are briefly discussed below: Shallow Type:These are foundations generally placed after open excavation, and are called open foundations. Examples of such foundations are isolated footing, combined footing, strip footing, raft etc. Deep Type:These are constructed by various special means. Deep foundations are piles and caissons (or wells). Piles are essentially giant-sized nails (of concrete, steel or timber) that are either driven into the subsoil (in which case they displace the soil in their place) or are placed-in after boring holes in subsoil (in which case they replace the soil in their place). These giant-sized- 'nails' can be square, rectangular, H-shaped or circular in section (20 to 200 cm or more in diameter), and can range in length from about 4 to 40 m or more. A group of piles is capped together at top (usually by a reinforced concrete cap) to support the pier or abutment body above. Caisson is basically constructed at the open surface level in portions and sunk downwards by essentially mechanically excavating soil from within its dredge-hole all the way till its cutting edge reaches the desired founding level, after which the well is effectively sealed (i.e.. plugged) at
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
10
Chapter-1
Introduction
bottom, then filled by sand (at least partly), and then capped at or near the surface level. The pier or abutment body is then constructed on the cap. Pile Foundations:Piles are columnar elements in a foundation which have the function of transferring load from the superstructure through weak compressible strata or through water, onto stiffer or more compact and less compressible soils or onto rock. They may be required to carry uplift loads when used to support tall structures subjected to overturning forces from winds or waves. Piles used in marine structures are subjected to lateral loads from the impact of berthing ships and from waves. Combinations of vertical and horizontal loads are carried where piles are used to support retaining walls, bridge piers and abutments, and machinery foundations. The British Standard Code of Practice for Foundations (BS 8004) places piles in three categories. These are as follows: Large displacement piles comprise solid-section piles or hollow-section piles with a closed end, which are driven or jacked into the ground and thus displace the soil. All types of driven and cast-in-place piles come into this category. Small-displacement piles are also driven or jacked into the ground but have a relatively small cross-sectional area. They include rolled steel H- or I-sections, and pipe or box sections driven with an open end such that the soil enters the hollow section. Where these pile types plug with soil during driving they become large displacement types. Replacement piles are formed by first removing the soil by boring using a wide range of drilling techniques. Concrete may be placed into an unlined or lined hole, or the lining may be withdrawn as the concrete is placed. Preformed elements of timber, concrete, or steel may be placed in drilled holes. Types of piles in each of these categories can be listed as follows. Large displacement piles (driven types) 1. Timber (round or square section, jointed or continuous). 2. Precast concrete (solid or tubular section in continuous or jointed units). 3. Prestressed concrete (solid or tubular section). 4. Steel tube (driven with closed end). 5. Steel box (driven with closed end). 6. Fluted and tapered steel tube. 7. Jacked-down steel tube with closed end. 8. Jacked-down solid concrete cylinder. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
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Chapter-1
Introduction
Large displacement piles (driven and cast-in-place types) 1. Steel tube driven and withdrawn after placing concrete. 2. Precast concrete shell filled with concrete. 3. Thin-walled steel shell driven by withdrawable mandrel and then filled with concrete. Small-displacement piles 1. Precast concrete (tubular section driven with open end). 2. Prestressed concrete (tubular section driven with open end). 3. Steel H-section. 4. Steel tube section (driven with open end and soil removed as required). 5. Steel box section (driven with open end and soil removed as required). Replacement piles 1. Concrete placed in hole drilled by rotary auger, baling, grabbing, airlift or reversecirculation methods (bored and cast in place). 2. Tubes placed in hole drilled as above and filled with concrete as necessary. 3. Precast concrete units placed in drilled hole. 4. Cement mortar or concrete injected into drilled hole. 5. Steel sections placed in drilled hole. 6. Steel tube drilled down. Composite piles Numerous types of piles of composite construction may be formed by combining units in each of the above categories, or by adopting combinations of piles in more than one category. Thus composite piles of a displacement type can be formed by jointing a timber section to a precast concrete section, or a precast concrete pile can have an H-section jointed to its lower extremity. Composite piles consisting of more than one type can be formed by driving a steel or precast concrete unit at the base of a drilled hole, or by driving a tube and then drilling out the soil and extending the drill hole to form a bored and cast in place pile. 1.2.1 Selection of pile type The selection of the appropriate type of pile from any of the above categories depends on the following three principal factors: The location and type of structure The ground conditions Durability Considering the first factor, some form of displacement pile is the first choice for a marine structure. A solid precast or prestressed concrete pile can be used in fairly shallow water, but A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
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Introduction
in deep water a solid pile becomes too heavy to handle and either a steel tubular pile or a circular cast in place RCC pile is used. Steel tubular piles are preferred to H-sections for exposed marine conditions because of the smaller drag forces from waves and currents. Piling for a structure on land is open to a wide choice in any of the three categories. Bored and cast-in-place piles are the cheapest type where unlined or only partly-lined holes can be drilled by rotary auger. These piles can be drilled in very large diameters and provided with enlarged or grout-injected bases, and thus are suitable to withstand high working loads. Augered piles are also suitable where it is desired to avoid ground heave, noise and vibration, i.e. for piling in urban areas, particularly where stringent noise regulations are enforced. Driven and cast-inplace piles are economical for land structures where light or moderate loads are to be carried, but the ground heave, noise and vibration associated with these types may make them unsuitable for some environments. Timber piles are suitable for light to moderate loadings in countries where timber is easily obtainable. Steel or precast concrete driven piles are not as economical as driven or bored and cast-in-place piles for land structures. Jacked-down steel tubes or concrete units are used for underpinning work. The second factor, ground conditions, influences both the material forming the pile and the method of installation. Firm to stiff cohesive soils favour the augered bored pile, but augering without support of the borehole by a bentonite slurry, cannot be performed in very soft clays, or in loose or water-bearing granular soils, for which driven or driven-and-cast-in-place piles would be suitable. Piles with enlarged bases formed by auger drilling can be installed only in firm to stiff or hard cohesive soils or in weak rocks. Driven and driven-and-cast-in-place piles cannot be used in ground containing boulders or other massive obstructions, nor can they be used in soils subject to ground heave, in situations where this phenomenon must be prevented. Driven-and-cast-in-place piles which employ a withdrawable tube cannot be used for very deep penetrations because of the limitations of jointing and pulling out the driving tube. For such conditions either a driven pile or a mandrel-driven thin walled shell pile would be suitable. For hard driving conditions, e.g., boulder clays or gravelly soils, a thick-walled steel tubular pile or a steel H-section can withstand heavier driving than a precast concrete pile of solid or tubular section. Thin steel shell piles are liable to tearing when being driven through soils containing boulders or similar obstructions. Some form of drilled pile, such as a drilledin steel tube, would be used for piles taken down into a rock for the purpose of mobilizing resistance to uplift or lateral loads.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
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Chapter-1
Introduction
The factor of durability affects the choice of material for a pile. Although timber piles are cheap in some countries they are liable to decay above ground-water level, and in marine structures they suffer damage by destructive mollusc-type organisms. Precast concrete piles do not suffer corrosion in saline water below the ‘splash zone’, and rich well-compacted concrete can withstand attack from quite high concentrations of sulphates in soils and ground waters. Cast-in-place concrete piles are not so resistant to aggressive substances because of difficulties in ensuring complete compaction of the concrete, but protection can be provided against attack by placing the concrete in permanent linings of coated light-gauge metal or plastics. Steel piles can have a long life in ordinary soil conditions if they are completely embedded in undisturbed soil but the portions of a pile exposed to sea water or to disturbed soil must be protected against corrosion by suitable means if a long life is required. Bored And Cast In Place Piles: In stable ground an unlined hole can be drilled by hand or mechanical auger. If reinforcement is required, a reinforcement cage is then placed in the hole, followed by the concrete. In loose or water-bearing soils and in broken rocks casing is needed to support the sides of the borehole, this casing may be withdrawn during or after placing the concrete. In stiff to hard clays and in weak rocks an enlarged base can be formed to increase the endbearing resistance of the piles The enlargement is formed by a rotating expanding tool, or by hand excavation in piles having a large shaft diameter. A sufficient cover of stable cohesive soil must be left over the top of the enlargement in order to avoid a ‘run’ of loose or weak soil into the unlined cavity. Bored piles drilled by mechanical spiral-plate or bucket augers or by grabbing rigs can drill piles with a shaft diameter up to 7.3m, but it is usual to limit the maximum size to 2.13m diameter to suit the auger plant generally available. Boreholes up to 120m deep are possible with the larger rotary auger machines. For reasons of economy and the need to develop skin friction on the shaft, it is the normal practice to withdraw the casing during or after placing the concrete. As in the case of drivenand-cast-in-place piles, this procedure requires care and conscientious workmanship by the operatives in order to prevent the concrete being lifted by the casing and thus resulting in voids in the shaft or inclusions of collapsed soil. The shafts or bored-and-cast-in-place piles are liable to ‘necking’ or ‘waisting’ in soft clays or peats. Sometimes a permanent casing of light spirally-welded metal may provided over the portion of the shaft within these soil types.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
14
Chapter-1
Introduction
Steel Piles: Steel piles have the advantages of being robust, light to handle, capable of carrying high compressive loads when driven on to a hard stratum, and capable of being driven hard to a deep penetration to reach a bearing stratum or to develop a high skin frictional resistance, although their cost per metre run is high compared with precast concrete piles. They can be designed as small displacement piles, which is advantageous in situations where ground heave and lateral displacement must be avoided. They can be readily cut down and extended where the level of the bearing stratum varies; also the head of a pile which buckles during driving can be cut down and re-trimmed for further driving. They have a good resilience and high resistance to buckling and bending forces. Types of steel piles include plain tubes, box-sections, H-sections, and tapered and fluted tubes (Monotubes). Hollow-section piles can be driven with open ends. If the base resistance must be eliminated when driving hollow-section piles to a deep penetration, the soil within the pile can be cleaned out by grabbing, by augers, by reverse water-circulation drilling, or by airlift. It is not always necessary to fill hollow-section piles with concrete. In normal undisturbed soil conditions they should have an adequate resistance to corrosion during the working life of a structure, and the portion of the pile above the sea bed in marine structures or in disturbed ground can be protected by cathodic means, supplemented by bituminous or resin coatings or by any other suitable means. Concrete filling may be undesirable in marine structures where resilience, rather than rigidity, is required to deal with bending and impact forces. Piles are driven open ended to increase the ease of penetration, particularly when dense sand layers exist in the soil stratum. This enables the pile to be installed to the full design length and thus the design capacity of the pile to be obtained. This is especially relevant to long piles which are often designed for friction, with the end bearing component making little contribution to the final capacity. In this mode of penetration a plug of soil forms up the middle of the pile. Generally a concrete plug is formed at junction of pile with superstructure for transferring forces to piles. Geotechnical and structural design of bored cast in situ RCC pile as well as driven steel pile is described in proceeding chapters.
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15
CHAPTER 2 LITERATURE REVIEW
Chapter-2
Literature Review
2.1 Literature Review: 1. Tomlinson M.J., “Pile Design And Construction Practice”, E & FN Spon, Fourth Edition This book provides all the basic details about pile foundations. It covers almost every aspects of piling including analysis for vertical as well as lateral loading, design, construction of different types of piles. Also topics covered in the book such as piling for marine and offshore structures helped in carrying out research work. Problems related to lateral loadings have been given detailed treatment in this book. 2. Poulos H.G. and Davis E.H., “Pile Foundation Analysis and Design”, John Willey And Sons Publications. This book provides detail information about various methods for analysis of different types of piles and pile groups for vertical and lateral loadings. Settlement analysis of piles and pile groups is also presented in detail in the book. Special topics such as pile-raft systems, piles in swelling-shrinking soils, piles in soil undergoing lateral movements are also covered in the book. 3. Bowles Joseph E., “Foundation Analysis and Design”, McGraw-Hill Companies, Inc., Fifth Edition. This book provides basic knowledge regarding soil mechanics and foundation analysis in general. Non-linear behavior of piles is explained here with methods like FEM, FDM and closed form solution approach. Use of modulus of subgrade reaction in analyzing pile for lateral loading is also explained in detail. Modelling of “soil-pile interaction” in the form of providing spring stiffness is shown in the book. 4. Raina V.K., “Concrete Bridge Practice”, The McGraw-Hill Publishing Company Limited, Second Edition. This book covers almost all the aspects of concrete bridges. Topics such as structural analysis and design of superstructure and substructure of different types of concrete bridges, distribution of thermal stresses, bearings etc. are covered in book which are partly applicable to marine structures also. 5. Dawson Thomas H., “Offshore Structural Engineering”, United Status Naval Academy Detailed information regarding calculation of environmental loads and effect of these loading on offshore structures is provided in this book. 6. Hambly E.C., “Bridge Deck Behavior”, E & F N Spon Publications, Second Edition
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17
Chapter-2
Literature Review
Different methods of analysis of different types of bridge deck systems are given in the book. 7. O’brien Eugene J. and Keogh Damien L., “Design Details Of Integral Bridges”. Integral bridge concept is discussed in this book in detail. Topics such as modeling of expansion and contraction of integral bridges, connection in integral bridges, time dependent effects in composite integral bridges are covered in this book. 8. Tandon Mahesh, “Recent Integral Bridges” In this paper author has provided conceptual information of integral bridges. Advantages and disadvantages of integral bridges versus conventional bridges are presented in this paper. It also provides details of integral bridges built in India. 9. Roman Eugenia, Khodair Yasser and Sophia Hassiotis, “Design Details Of Integral Bridges” Details of connections of approach slab with bridge deck, abutment with bridge decks for integral bridge systems are studied in this paper. 10. API Recommended Practice 2A-WSD This standard of American Petroleum Institute gives specifications for design of superstructure as well as sub structure of fixed offshore platform. It is also widely used in field for geotechnical and structural design of driven steel piles. In this thesis also , this standard is referred for steel pile design. 11. Coastal Engineering Manual – 2006 - US Army Corps Of Engineers This excellent publication from US Army Corps Of Engineers gives extensively detailed information regarding almost all aspects of coastal structures. Manual is widely used as a standard for assessing the effects of environmental loads such as waves, current etc. Planning, design and re-strengthening of coastal structures, effects of environmental forces on coastal structures, case studies etc. are covered in detail in this manual. Theoretical background of waves and assessment of wave forces are discussed in detail in it. In thesis, this manual has been referred for calculation of wave forces on piles.
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18
CHAPTER 3 PROJECT DESCRIPTION
Chapter-3
Project Description
3.1 Project Description: Piled approach connects offshore berth to the rock bund which is connected to shore. Offshore berth is a free standing structure on piles and connected to shore by 2410 m long approach. The approach has an 1167.9 m bridge portion supported on piles apart from a rubble bund portion of about 1240 m long. The approach bridge and bund will provide access to back up yard. The general arrangement drawings are shown in Appendix C. Approach bridge carries 7.5 m wide carriageway with provision for steel trestle for conveyor galleries. The structure consists of bored cast in situ piles with pilecap beams spanning across pile bents. Entire approach is divided into 7 unit each unit consisting of approximately 125 m length. Each unit consists of approximately 13 pile bents at a spacing of 12m. Each unit is separated from adjacent unit by expansion gaps. Site Information: 1. Wind: Basic wind speed :
19 m/s for operating condition; 44 m/s for storm condition.
2. Tidal Data: Principal levels with reference to chart datum (0.0m ) are given below: HAT
:
10.1
m
MHWS
:
9.1
m
MHWN
:
7.1
m
MSL
:
5.1
m
MLWN
:
3.0
m
MLWS
:
1.0
m
LAT
:
0.0
m
3. Wave Data: Description
Operating Condition
Survival Condition
Wave Height (m)
2.2
6.5
Direction Of Approach
180-270 N
210 N
Time Period (sec)
6.0
10.0
4. Current Data: The design current parameters to be considered are as below: Current velocity at surface
:
3.85 m/s
Current velocity at mid depth :
2.25 m/s
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20
Chapter-3 Current velocity at bottom
Project Description :
1.80 m/s
Direction of current is NNE during flood and SSW during ebb. 5. Levels: Design dredged level for approach varies from (+) 3.15 m to (-) 15.0 m. The deck elevation of the approach shall be (+) 15.0 m for units 1 to 6. Deck level shall be gradually increased from (+)15.0m to (+)17.0 m CD in last unit. 6. Earthquake: Seismic loading will be considered in accordance with IS: 1893 (part 1): 2000. 50 % live load shall be considered during earthquake. 7. Design Life: Design life will be considered as 50 years for approach. 8. Deflection: Horizontal deflection will be checked under serviceability load combinations and will be limited to 50mm at top of deck to suit proper functioning of material handling system installed over deck. 9. Scour: General Scour- A scour of 4m in deep water and 1.0 m in shallow water from sea bed level will be considered in design. Sea bed level upto (+)1.0m CD will be considered as shallow water and greater than that will be considered as deep water. Local Scour – In addition to the general scour, a local scour of 1.0 m around pile will also be considered. 10. Crack width: Crack width will be checked under serviceability load combinations and will be limited to 0.004 times clear cover to main reinforcement. 11. Parameters for materials: Grade of concrete: M40 for piles and M30 for beams and slab of superstructure. Grade of reinforcement: Fe500 conforming to IS 1786 12. Load Combinations: Load combinations for analysis and design are considered in accordance with IS: 4651(part 4) and IS 456:2000. Analysis and Design: The 3-D modeling and analysis of the structure is carried out with Staadpro 2007 package. Structural design of RCC elements is done for Limit state of collapse and checked for limit state of serviceability as per IS:456-2000. The geotechnical design of bored cast in situ RCC A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
21
Chapter-3
Project Description
piles is also carried out as per the IS:2911 (part 1/sec 2)-1979. Structural as well as geotechnical design of steel piles is done in accordance with API RP 2A-WSD. Analysis and design is carried out keeping in view construction stages. Design of superstructure member is checked for each of the following construction stages (refer Appendix D): •
Initially piles will be constructed.
•
Precast pile muffs will be placed over piles and then concreting will be done for pile muff hole.
•
Precast pliecap beams will be placed over precast pilemuff and stage-I concreting will be done over pile muff upto top of precast pilecap beam.
•
As stage-I concrete integrates with the precast pilecap beam, pilecap beam will start behaving as a continuous member. After achieving required strength, precast longitudinal beams will be placed over precast pilecap beams. Precast deck planks will be placed over precast longitudinal beams then and stage-II concreting upto top of deck will be done.
Three types of models are used in analysis. Model-1 is used for analysis of the structure for moving loads. All possible moving load combinations loads in accordance with IRC:62000 are generated to attain any position on the carriageway portion. Different worst possible positions of vehicles were identified from this model for producing maximum stresses in piles and superstructure components like pilecap beams, longitudinal girder and slab. Results of this model are used for generating moving load in main analysis model i.e. model-2. Model-2 is used for analysis of piles and superstructure for all possible loads and load combination. Model-3 is used for analysis of structure for stage-II loads. Stage-II loads are dead loads imposed on pilecap beam after stage-I concreting and remaining live loads as well as environmental loads. Results of this model are used for crack width check. In all staad models, soil is modeled in the form of springs providing stiffness to piles in all the three directions. In model, pilecap beams are modeled as inverted U shape beam and longitudinal T beams are modeled as rectangular beams ignoring haunch portion. Load combinations are in accordance with relevant IS codes. Description of loads and load combinations is presented in proceeding chapters. Structural design of piles is done using spreadsheets “RCC PILE DESIGN”, “STEEL PILE DESIGN”. Geotechnical design of piles is done using spreadsheets “RCC PILE CAPACITY” and “STEEL PILE CAPACITY” Structural design of super-structural elements is done using spreadsheets “BEAM DESIGN” and “BEAM DESIGN”. Soil
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
22
Chapter-3
Project Description
stiffness is calculated using spreadsheet “SPRING CONSTANT”. However sample calculation is presented for each of the above mentioned calculations.
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23
CHAPTER 4 PILE ANALYSIS
Chapter-4
Pile Analysis
4.1 Load Description: Loads are differentiated between static and dynamic. The static loads on the structure come from gravity loads, deck loads, hydrostatic loads and current loads. The dynamic loads originate from the variable wind and waves. Following is the list of main loads whose effects should be analyzed to estimate the forces (shear, moments etc.) at all critical sections of the structure. Only then the structure should be designed for those forces to decide section size, reinforcement, prestress etc., so as to resist these forces at the specified stress levels and serviceability criteria (crack width, deflections etc.) 1.
Dead load of the structure
2.
Construction, erection and handling loads
3.
Vehicular and other possible live load
4.
Impact load of moving live load
5.
Braking force
6.
Wind load
7.
Seismic force
8.
Wave force
9.
Water current force
10.
Buoyancy
11.
Thermal effect
12.
Secondary effects (creep, shrinkage etc.)
All above mentioned loads are briefly discussed here: 1. Dead Load : It includes weight of all permanent portions of the entire structure and includes weights of the anticipated future additions. a). Structural Dead Loads- Structural dead loads are the loads imposed on a member by its own weight and the weight of the other structural elements that it supports including rails, side walks, slabs, beams etc. This dead load may come in stages in case of stage construction b). Super Imposed Dead Loads- In addition to the structural dead loads, member should be designed to support the weight of the super imposed dead loads including footpath, earth fill, wearing course, kerbs , pipes, cables and any other immovable appurtenances installed on the structure. 2. Construction, Erection and Handling Loads: Consideration should be given to the effect of temporary imposed by sequence of construction stages, forming, false work and construction equipment and the stresses created A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
24
Chapter-4
Pile Analysis
by lifting or placing precast members. The stability of the precast members during and after construction should be investigated. 3. Live Load: Bridge design standards specify the design loads, which are meant to reflect the worst loading that can be caused on the bridge by traffic, permitted and expected to pass over it. For the highway bridges, the Indian Road Congress has specified standard design loadings in IRC section II. IRC: 6 - 2000 – section II gives the specifications for the various loads and stresses to be considered in bridge design. There are three types of standard loadings for which the bridges are designed namely, IRC class AA loading, IRC class A loading and IRC class B loading. Within kerb to kerb width of roadway, the standard vehicle or train of standard vehicle shall be assumed to travel parallel to the length of the bridge and shall be assumed to occupy any position which will produce maximum stresses provided that the specified minimum clear distance between a vehicle and the roadway face of the kerb and between two passing or crossing vehicles is not encroached upon. For each of the standard vehicle or train, all axle of a unit of vehicles shall be considered as acting simultaneously in a position causing maximum stresses. Brief description of these standard loadings is given here.
Fig.4 IRC Class AA Loading IRC class AA loading consists of either a tracked vehicle of 70 tonnes or a wheeled vehicle of 40 tonnes with dimensions as shown in Fig. 4. The units in the figure are mm for length and tonnes for load. Normally, bridges on national highways and state highways are designed for A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
25
Chapter-4
Pile Analysis
these loadings. Bridges designed for class AA should be checked for IRC class A loading also, since under certain conditions, larger stresses may be obtained under class A loading. Sometimes class 70 R loading given in the Appendix - I of IRC: 6 - 2000 - Section II can be used for IRC class AA loading. IRC classs 70R loading also consists of either a tracked vehicle of 70 tonnes or a wheeled vehicle of 100 tonnes as shown in Figure 5. Tracked vehicle of class AA and class 70R are same in terms of loading with the difference in their dimension as shown in figures.
Fig.5 IRC Class 70R Loading
Fig.6 IRC Class A Loading
Fig.7 IRC Class B Loading Class A loading consists of a wheel load train composed of a driving vehicle and two trailers of specified axle spacing. This loading is normally adopted on all roads on which permanent bridges are constructed. Class B loading is adopted for temporary structures and for bridges in specified areas. Nominal pedestrian live load is considered on portion adjacent to carriage way A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
26
Chapter-4
Pile Analysis
and conveyor area. Live load due to operation of conveyor which includes belt pull, material live load, belt and idler weight is also considered. 4. Impact Load On Moving Live Load: The dynamic force induced by vehicle-bridge interaction resulting from the passage of vehicles plays a significant role in bridge design. In practice to allow for such a dynamic effect, it is required that static vehicle force be increased by a dynamic allowance factor, called the impact factor in design. However, it has been observed that dynamic vehicle load on bridge depends on dynamic properties of vehicle, dynamic properties of bridge, vehicle speed and bridge surface roughness. This dynamic force is an important parameter in bridge design and evaluation. In addition to the importance in design, dynamic vehicle load causes subtle problems and contributes to fatigue, surface wear and cracking of concrete that leads to corrosion. It continually degrades bridges and increases the necessity of regular maintenance. The need to develop an approach and derive a simple closed form solution to predict the dynamic vehicle load for applications of bridge design is apparent. More detailed analysis is required to reach such a closed form solution which is out of scope of this study. While the actual modeling of this effect can be a complex affair, the impact factor used by IRC allows for a conservative solution of the problem. As per Cl. 211 of IRC:6-2000, impact factor for standard vehicles is given as under: For class A & B loading: a). Impact factor for RCC bridges = 4.5/(6+L) b). Impact factor for steel bridges = 9/(13.5+L), where L is span in meters. For class AA & 70R loading: a). For spans less than 9 m: i). For tracked vehicles- 25% for spans upto 5m linearly reducing to 10% for spans of 9m ii). For wheeled vehicles- 25% b). For spans of 9 m or more: i). RCC bridgesFor tracked vehicles- 10% for spans up to 40 m and in accordance with
the
curve
given in figure 5 for span in excess of 40 m. For wheeled vehicles- 25% for spans up to 12 m and in accordance with the curve given in figure 5 for span in excess of 12 m. ii). Steel bridgesFor tracked vehicles- 10% for all spans
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
27
Chapter-4
Pile Analysis
For wheeled vehicles- 25% for spans up to 23 m and in accordance with the curve given in Figure 8 for span in excess of 23 m.
Fig.8 Curves For Impact Factor As per Cl. 211.7 of IRC:6-2000, for calculating pressure on the bearings and on the top surface of the bed blocks, full value of the appropriate impact factor is allowed. But for the design of piers, abutment and structures, generally below the level of top of bed block, the appropriate impact factor shall be multiplied by factor given by below: a). for calculating pressure at the bottom surface of bed block - 0.5 b). for calculating pressure on top 3m of the structure below the bottom surface of bed block – 0.5 c). for calculating pressure on the portion of the structure more than 3m below the bed block –0 5. Braking Force: Braking force comes under the category of longitudinal forces. These longitudinal forces arise from one or more of the following causes: a).
Tractive effort caused through acceleration of the driving wheels;
b).
Braking effect resulting from the application of the brakes to braked wheels; and
c).
Frictional resistance offered to the movement of free bearings due to change of temperature or any other cause.
However, generally braking effect is invariably greater than the tractive effort.
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Chapter-4
Pile Analysis
As per IRC, the braking effect on a simply supported span or a continuous span or any other type of bridge unit shall be assumed to have the following value: a).
In case of single lane or a two lane bridge: 20% of the first train load plus 10% of load
of succeeding train or part thereof, the train load in one lane only being considered at a time. Where the first train is not entirely covering the full span, the braking force shall be taken as equal to 20% of the loads actually on the span. b).
In case of bridge having more than two lanes: as in a). above for the first two lanes
plus 5% of the loads on the lanes in excess of two. This braking force is assumed to act at a height of 1.2 m above the roadway surface. The distribution of longitudinal horizontal forces among bridge supports is affected by horizontal deformation of bridges, flexing of supports and rotation of foundations. IRC:6 gives procedure for the distribution of horizontal forces for spans resting on stiff and flexible supports. As present case is of flexible supports, only later case is presented here. In simple and continuous decks with flexible supports, distribution of horizontal forces can estimated after taking into account of deformation of bearings, flexing of piers and abutment and rotation of foundation as well as location of Zero Movement Point (Z.M.P.) of the deck. Shear rating of a support is the horizontal force required to move the top of the support through a unit distance taking into account horizontal deformation of the bridge, flexibility of the support and rotation of the foundation. The distribution of the horizontal forces depends solely on shear ratings of the supports and may be estimated in proportion of shear rating of individual support to the sum of shear ratings of all the supports. But here in this study, braking force to be distributed to each support is calculated as total braking forces divided by number of supports because there are other horizontal forces which are large in magnitude (wave, wind,
current, earthquake etc.) which are governing the
design. So distribution of the braking force like above mentioned method gives quite satisfactory results. 6. Wind Load: Wind load on a bridge may act – -
Horizontally, transverse to the direction of span.
-
Horizontally, along the direction of span,
-
Vertically upwards, causing uplifts.
-
Wind load on vehicles.
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29
Chapter-4
Pile Analysis
Wind load may not generally significant in short span bridges. For medium span bridges, the design of substructure is affected by wind loading. The super structure design is affected by wind only in case of long span bridges. The bridge covered in this study project is not of long span but still effect of wind force on the structure is analyzed for because it is situated into the sea and flexibility and slenderness of the piles. Wind force is calculated in accordance with IS:875 part 3 -1987. A brief description of wind load is presented here. Wind means motion of air in atmosphere. The response of structure to wind depends upon characteristics of wind. From point of view of assessing wind load, it is convenient to divide the wind into two categories: rotating and non rotating. Rotating winds are caused by tropical cyclones and tornadoes. The wind speed caused by this may exceed 200 km/h. Non rotating winds are caused by differential pressures and thus move in the preferred direction. These are also called pressure system wind. Their speed can also exceed 200 km/h. A large number of structures those are being constructed at present tend to be wind sensitive because of their shapes, slenderness, flexibility, size and lightness. Tall and slender structures are flexible and exhibit a dynamic response to wind. Tall structure vibrate in the wind due to turbulence inherent in the wind as well as that generated by the structure itself due to separation of the flow. Thus there is a mean and fluctuating response to the wind. Besides this dynamic forces act not only in the direction of the wind flow but also in a direction perpendicular to it so that tall structures exhibit across wind response also. Along wind response has a mean component and fluctuating component. The latter is further expressed as a sum of background and resonant components. If the damping is small, which is usually the case, the bulk of the contribution is due to the resonant portion. Across wind response is on account of flow separation from cross section of the structure which results in vortices being shed at a given frequency. The pattern of this across wind phenomenon is comparatively more regular for circular sections such as those for chimneys and towers which can undergo resonant vibrations when the structural frequency matches with the forcing frequency. The response is affected significantly by the turbulence content of the wind. A theoretical treatment of tall slender structures in the along wind direction is better developed than for across wind direction and for this reason it may be advisable to undertake model studies in a wind tunnel for such structures. Clause 7.1 of IS:875 (part 3)-1987 contains methods of evaluating the dynamic effects of wind on flexible structures that can oscillate in wind. The wind on earth’s surface is turbulent in nature that gives rise to randomly varying wind pressures about a certain value associated A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
30
Chapter-4
Pile Analysis
with the mean wind speed. The dynamic part of the wind pressure would set up oscillations in a flexible structure which may be defined as one having the fundamental time period of vibration more than 1 second. Oscillations will thus be caused in the along wind direction. Flexible structures also respond to across wind direction on account of vortex shedding. In the cross wind direction, a flexible structure would tend to oscillate due to shedding of eddies alternately from either side of the structure at regular intervals, thus imposing a dynamic force that has a major component in a direction normal to that of wind(lift) and only a small component along the wind(drag). The frequency of eddy shedding is dependent on structural size, shape and wind speed, all grouped into a non dimensional parameter called Strouhal Number. The present code does not lay down any specific procedure for determining the design wind force related to the cross wind motion. Code gives for procedure for only determining along wind force using Gust Factor method. This method uses hourly mean wind speed concept instead of 3 second gust wind speed as in static method of calculating wind pressures. The static wind pressure thus obtained is then multiplied by Gust factor G. The structure is considered to vibrate in its fundamental mode of vibration. The gust factor G includes the effect of non correlation of the peak pressures by defining a size reduction factor S. It also accounts for the resonant and the nonresonant effects of the random wind pressures. The equation for G contains two terms one for the low frequency wind speed variations called the non resonant or background effects and other for resonance effects. The first term accounts for the natural frequency of vibration of the structure while the second term depends on the gust energy and aerodynamic admittance at the natural frequency of vibration as well as on damping of the system. The resonant response is insignificant for rigid structures (T>1.0 sec). For flexible structures, the background factor B may be small resulting in reduced wind forces obtained from dynamic analysis as compared to static analysis. The roughness factor r together with the peak factor gf is a measure of the turbulence intensity present in the wind. Thus gf.r is equivalent to twice the turbulence intensity. The integral piled approach which is covered in this study is a flexible structure having natural time period of more than 1.0 second. So wind force is applied to the exposed face of the elements (pile, beams and slab) of the structure as per Gust factor method described in IS:875(part 3)-1987 using force coefficient in both lateral directions (positive and negative). In addition to this, wind load on moving vehicles over bridge as per Cl.212.4 of IRC:6-2000. This clause states that the lateral wind force against any exposed moving live load shall be
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
31
Chapter-4
Pile Analysis
considered as acting at 1.5 m above the roadway and shall be assumed to have the following values: Highway bridges, ordinary
-
300 kg/linear meter.
Highway bridges, carrying tramway
-
450 kg/linear meter.
While calculating the wind force on live load, clear distance between the trailers of train of vehicles shall not be omitted. Wind load is applied both for operating case and extreme (storm wind) case. Wind speed considered in each of these cases is obtained from site investigation report. 7. Seismic Force: In general, structures subjected to earthquake forces are to be designed to survive the strains resulting from the design earthquake motion. Factors that are considered when designing to resist earthquake motions are: 1. The proximity of the site to known active faults. 2. The seismic response of the soil at the site. 3. The dynamic response characteristics of the total structure. Bridge as a whole and every part of it shall be designed and constructed to resist stresses produced by lateral forces produced due to earthquake. The stresses shall be calculated as the effect of a force applied horizontally at the centre of mass of the elements of the structure into which it is conveniently divided for the purpose of design. The forces shall be assumed to come from any horizontal direction. All components of the bridge, that is, superstructure, substructure, bearing, foundation and soil are susceptible to damage in the event of strong ground shaking. The earthquake resistant design should consider the effect of earthquake motions on each component of the bridge. The design should ensure that seismic resistance of the bridge and its components is adequate to meet the general requirement so that emergency communication after the earthquake shall be maintained with appropriate reliability for the design basis earthquake. As per IRC:6-2000, all bridges in seismic zone V shall be designed for seismic forces. Major bridges i.e. with total lengths of more than 60m in zones III and IV shall be designed for seismic forces. Bridges in zones I and II need not be designed for seismic forces. The vertical seismic coefficient shall be considered in case of structures built in zone IV and V in which stability is criterion for design or for overall stability analysis of the structure. Following are the assumptions given in the draft version of IS:1893-1984 “Criteria For Earthquake Resistant Design Of Structures (Part 3) Bridges and Retaining Walls” for the earthquake analysis of bridges:
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Chapter-4
Pile Analysis
a) The seismic forces due to design basis earthquake (DBE) should not be combined with design wind forces, b) The scour to be considered for design shall be based on mean design flood. In the absence of detailed data the scour to be considered for design shall be 0.9 times the maximum design scour depth, c) The earthquake accelerations should be applied to full mass in case of submerged structures and not on buoyant mass, d) The seismic force on live load in bridges should not be considered in longitudinal direction. The seismic force on live load should be considered in transverse direction as, e) The seismic force on flowing mass of water in the longitudinal direction in case of aqueducts should not be considered, however seismic force on this water mass be considered in transverse direction. The hydrodynamic action of water on the walls of water carrying trough be considered on liquid retaining structures, f) The earthquake accelerations on embedded portion of bridges foundation should be reduced as per provisions made in code , g) The value of elastic modulus of material, where required, may be taken as for static analysis unless a more definite value is available for use in seismic condition. As per IS:1893-1984 “Criteria For Earthquake Resistant Design Of Structures”, seismic force due to live load shall be ignored while acting in the direction of traffic but shall be taken into consideration while acting in the direction perpendicular to traffic. Seismic force due to live load shall be calculated for 50% of the design live load excluding impact for railway bridges and 25% of the design live load excluding impact for road bridges. For calculating stresses due to live load during earthquake, 100% design live load for railway bridges and 50% design live load for road bridge is considered. Horizontal as well as vertical seismic coefficient shall be calculated based on specifications given in IS:1893-2002. The super structure of the bridge shall have a minimum factor of safety of 1.5 against overturning in the transverse direction due to simultaneous action of horizontal and vertical accelerations. The seismic forces on the sub structure above the normal scour depth shall be as follows: 1).
Horizontal and vertical forces due to dead, live and seismic loads transferred from
superstructure to the substructure through the bearings. 2).
Horizontal and vertical seismic forces due to self-weight applied at the centre of mass
ignoring reduction due to buoyancy or uplift. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
33
Chapter-4 3).
Pile Analysis
Hydrodynamic force acting on piers and modification in earth pressure due to
earthquake given in acting on abutments. The hydrodynamic force on submerged portion of pier is also assumed to act in a horizontal direction corresponding to that of earthquake motion. The total horizontal force is given by the following formula: F = Ce Ah We
…………………4.1
Where, Ce
=
a coefficient (see Table 1)
Ah
=
design horizontal seismic coefficient
We
=
weight of water in the enveloping cylinder. Table1- Values Of Ce
Height Of Submerged Portion Of Pier (H) / Radius Of Enveloping Cylinder
Ce
1.0
0.390
2.0
0.575
3.0
0.675
4.0
0.730
Some typical cases of submerged portion of piers and enveloping cylinders are illustrated in following Figure 9.
Figure.9 Enveloping Cylinders A typical diagram showing distribution of hydrodynamic pressure is shown in the Figure 10 below. Values of coefficients C1,C2,C3 and C4 for use in figure are shown in Table 2.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
34
Chapter-4
Pile Analysis
Figure.10 Pressure Distribution Table2- Pressure Distribution Co-efficient C1
C2
C3
C4
0.1 0.2 0.3 0.4 0.5 06 0.8 1.0
0.410 0.673 0.832 0.922 0.970 0.990 0.999 1.000
0.026 0.093 0184 0.289 0.403 0.521 0.760 1.000
0.9345 0.8712 0.8103 0.7515 0.6945 0.6390 0.5320 0.4286
When relative movement between two adjacent units of a bridge are designed to occur at a separation/expansion joint, sufficient clearance shall be provided between them, to permit the calculated relative movement under design earthquake conditions to freely occur without inducing damage. Where the two units may be out of phase, the clearance to be provided may be estimated as the square root of the sum of squares of the calculated displacements of the two units under maximum elastic seismic forces. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
35
Chapter-4
Pile Analysis
8. Wave Force: Wave force on vertical cylindrical pile is calculated in accordance with Coastal Engineering Manual (Part 6)-2006. A brief description of the same is given here: Morison et al. (1950) suggested that the horizontal force per unit length of a vertical cylindrical pile subjected to waves is analogous to the mechanism by which fluid forces on bodies occur in unidirectional flow, and this force can be expressed by the formulation,
f = fi + f D = CM ρ
πD 2 du 4
dt
+ CD
1 ρDu u 2
…………………4.2
Where, fi
= inertial force per unit length of pile;
fD
= drag force per unit length of pile;
ρ
= mass density of fluid;
D
= pile diameter;
u
= horizontal water particle velocity at the axis of the pile;
du/dt = horizontal water particle acceleration; CD
= drag hydrodynamic force coefficient;
CM
= inertia or mass hydrodynamic coefficient;
Variables important in determining wave forces on circular pile subjected to wave motion are shown in Figure.11 below.
Figure.11 Definition Sketch Of Wave Forces On A Vertical Cylinder.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
36
Chapter-4
Pile Analysis
The inertia force fi term is of the form obtained from an analysis of the force on a body in an accelerated flow of an ideal non viscous fluid. The drag force term fD is the drag force exerted on a cylinder in a steady flow of a real viscous fluid. Using linear wave theory, MacCamy and Fuchs (1954) analyzed theoretically the problem of waves passing a circular cylinder. Their analysis assumed an ideal non viscous fluid and led to an inertia force having the form given for fi under special conditions. Although their theoretical result is valid for all ratios of pile diameter to wavelength, D/L, the inertia force was found to be nearly proportional to the acceleration du/dt for small values of D/L (where L is wavelength calculated by linear theory). This theoretical result provides an indication of how small the pile should be for above equation to apply, and the restriction is given as:
D < 0.05 L Where L is calculated by linear wave theory. This restriction will seldom be violated for slender pile force calculations; however, the restriction may be important when applying above equation to larger structures such as cylindrical caissons. For application of above equation, it is necessary to choose an appropriate wave theory for estimating particle velocity and acceleration from values of wave height H, wave period T and water depth d and for that particular wave condition, appropriate values of coefficient CD & CM must be selected. Calculation of forces and moments:
For structural design of a single vertical pile, it is often unnecessary to know in detail the distribution of forces over the height of the pile. Instead, the designer needs to know the total maximum force and the total maximum moment about the mud line (z = -d) acting on the pile. The total time-varying force and the time-varying moment acting about the mud line is found by integrating equation 4.2 between the bottom and the free surface, i.e., n
F=
n
∫ f dz + ∫ f i
−d
D
dz = Fi + FD
…………………4.3
−d
n
n
−d
−d
M = ∫ ( z + d ) f i dz + ∫ ( z + d ) f D dz = M i + M D
…………………4.4
In general form these quantities may be written Fi = C M ρg
πD 2 4
HK i
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
…………………4.5
37
Chapter-4 FD = C D
Pile Analysis
1 ρgDH 2 K D 2
…………………4.6
M i = C M ρg
M D = CD
πD 2 4
HK i dS i
…………………4.7
1 ρgDH 2 K D dS D 2
…………………4.8
in which CM and CD may be assumed as constant and factors Ki,KD,Si and SD are dimensionless parameters that depends on the specific wave theory used in integrations. Linear wave theory:
The force on a slender cylindrical pile can be estimated using linear wave theory, but the result is limited to situations where linear wave theory provides a reasonable approximation of the wave kinematics. This implies small amplitude waves and greater depths. With the pile center line located at x = 0, as shown in Figure 8, the equations for surface elevation, horizontal component of local fluid velocity and horizontal component of local fluid acceleration are respectively,
η=
H ⎡ 2πt ⎤ cos ⎢ 2 ⎣ T ⎥⎦
u=
H gT cosh[2π ( z + d ) / L] ⎡ 2πt ⎤ cos ⎢ ⎥ 2 L cosh[2πd / L] ⎣T ⎦
…………………4.9
…………………4.10
Introducing above equations into basic equation of force gives following equations for inertia and drag force. f i = C M ρg
⎡ π cosh[2π ( z + d ) / L]⎤ ⎡ 2πt ⎤ H⎢ ⎥ sin ⎢− ⎥ 4 ⎣ L cosh[2πd / L] ⎦ ⎣ T ⎦
πD 2
⎡ gT 2 ⎡ cosh[2π ( z + d ) / L ]⎤ 1 f D = C D ρgDH 2 ⎢ 2 ⎢ ⎥ 2 ⎢⎣ 4 L ⎣ cosh[2πd / L] ⎦
2
⎤ ⎡ 2πt ⎤ ⎡ 2πt ⎤ cos ⎢ ⎥ cos ⎢ ⎥ ⎣T ⎦ ⎣ T ⎥⎦ ⎥⎦
…………………4.11
…………………4.12
Above equations show that the two force components vary with elevation z on the pile and with time t. The inertia force fi is maximum for sin (-2πt/T) = 1, which corresponds to t = -T/4 for linear wave theory. Thus, the maximum inertia force on the pile occurs T/4 seconds before the passage of the wave crest that occurs at t = 0. The maximum value of the drag force component fD coincides with passage of the wave crest at t = 0.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
38
Chapter-4
Pile Analysis
The magnitude of the maximum inertia force per unit length of pile varies with depth the same as the horizontal acceleration component. The maximum value occurs at the swl (z = 0) and decreases with depth. The same trend is true for the maximum drag force per unit length of pile except the decrease with depth is more rapid because the depth attenuation factor (cosh[2π(z+d)/L}/cosh[2πd/L]) is squared in equation. The total time-varying force and the time-varying moment acting about the mudline is found for linear wave theory by integrating equations 4.11 & 4.12 between the bottom and the swl (z = 0) using the expressions for fi and fD given by equations respectively. The integration results in total force and moment components given by equations with values of the dimensionless parameters Ki , KD , Si , and SD given by,
Ki =
1 ⎡ 2πd ⎤ ⎡ 2πt ⎤ tanh ⎢ sin ⎢− ⎥ 2 ⎣ L ⎥⎦ ⎣ T ⎦
…………………4.13
KD =
⎡ 1 4πd / L ⎤ ⎡ 2πt ⎤ ⎡ 2πt ⎤ tanh ⎢1 + cos ⎢ cos ⎢ ⎥ ⎥ 8 ⎣ T ⎥⎦ ⎣T ⎦ ⎣ sinh[4πd / L]⎦
…………………4.14
=
1 ⎡ 2πt ⎤ ⎡ 2πt ⎤ cos ⎢ n cos ⎢ ⎥ 4 ⎣ T ⎥⎦ ⎣T ⎦
Si = 1 +
SD =
1 − cosh[2πd / L] (2πd / L) sinh[2πd / L]
…………………4.15
1 1 ⎡1 1 − cosh[4πd / L] ⎤ + + ⎢ 2 2n ⎣ 2 (4πd / L) sinh[4πd / L]⎥⎦
…………………4.16
Where, n=
Cg C
=
1⎡ 4πd / L ⎤ 1+ ⎢ 2 ⎣ sinh[4πd / L ]⎥⎦
The maximum values for total inertia force and moment are found by taking t = -T/4 in equations. Likewise, the maximum values for total drag force and moment are found by taking t = 0 in equations. A conservative design approach would be to sum the individual maximum inertia and drag components that occur during a wave cycle to get total maximum force and
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
39
Chapter-4
Pile Analysis
moments. However, the individual maximums do not occur simultaneously, so the real maximum total force and moment will be somewhat less. The correct method is to calculate the time-varying sum of inertia and drag components, and then use the maximum sum that occurs over the wave cycle. The time at which the maximum occurs may vary depending on the selected values for CM and CD. Although linear wave theory provides a nice closed-form solution for forces and moments on slender cylindrical piles, in practice the hydrodynamics associated with the steeper design wave conditions will not be well predicted by linear wave theory. Even more critical is the fact that linear theory provides no estimate of the force caused by that portion of the wave above the swl, an area where the horizontal velocities and accelerations are the greatest. An adhoc adjustment is to assume a linear force distribution having a maximum value of force estimated at the still-water line and a value of zero at the crest location of the linear wave (H/2 above the swl). Most likely, the design wave will be nonlinear with steep wave crests and with much of the wave height above the swl, and it would be well advised to use an appropriate nonlinear wave theory in the force and moment calculation. Non linear wave theory:
Design conditions for vertical cylindrical piles in coastal waters will most likely consist of nonlinear waves characterized by steep crests and shallow troughs. For accurate force and moment estimates, an appropriate nonlinear wave theory should be used to calculate values of u and du/dt corresponding to the design wave height, wave period, and water depth. The variation of fi and fD with time at any vertical location on the pile can be estimated using values of u and du/dt from as Stoke's fifth-order wave theory (Skjelbriea et al. 1960) or stream-function theory (Dean 1974). The separate total maximum inertia force and moment and total drag force and moment on a vertical cylindrical pile subjected to nonlinear waves can be estimated using equations 4.7 to 4.10. Values for Ki , KD , Si , and SD in these equations are given by Kim , KDm , Sim, and SDm , respectively, in the nomograms shown in Figures A.1 through A.4 of Appendix A. These nomograms were constructed using stream-function theory (Dean 1974),
and they provide the maximum total force and total moment for the inertia and drag components considered separately rather than the combined total force and moment. The curves in these figures represent wave height as a fraction of the breaking wave height. Breaking wave height is obtained from Figure 12 for values of d /gT2 using the curve labeled Breaking Limit. Same figure can also be used for selecting appropriate wave theory for design wave. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
40
Chapter-4
Pile Analysis
For linear waves, the maximum inertia force occurs at t = -T/4 and the maximum drag force occurs at t = 0. However, for nonlinear waves the times corresponding to maximum inertia and drag forces are phase dependent and not separated by a constant quarter wavelength as in linear wave theory. The total maximum force Fm, where the sum of the inertia and drag components is maximum can be estimated as,
Fm = φ m C D ρgH 2 D
…………………4.17
Similarly maximum moment Mm can be estimated as,
M m = α m C D ρgH 2 Dd …………………4.18
Values of Фm and αm are estimated from Figure A.5 to A.6 of Appendix A. These figures are also constructed using stream function theory. Selection of figure depends upon non dimensional parameter W given as, W =
CM D CD H
…………………4.19
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
41
Chapter-4
Pile Analysis
Figure.12 Breaking Wave Height & Regions Of Validity Of Various Wave Theories.
Wave force is calculated and applied for both operating and extreme (storm) cases. 9. Water Current Force:
For structures those are located in a place where there are strong currents such as a tidal currents or river flow, it is necessary to carry out investigations on the forces produced by the currents with largest velocity from the most unfavorable direction. Depending upon the type of the structures or members, it may also be necessary to consider vertical distribution of the current velocity. When waves coexist with currents, it is necessary to use the current velocity and direction in the state of coexistence. Type of currents in the sea area include ocean currents, tidal currents and wind driven drift currents along with density currents caused by density differences due to salinity or water temperature. In addition in the coastal area, there are longshore currents and rip currents caused by waves.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
42
Chapter-4
Pile Analysis
Force due to water current is applied as per provisions given in IRC:6. As per Cl. 213 of IRC:6-2000, any part of a bridge which may be submerged in running water shall be designed to sustain safely the horizontal pressure due to the force of current. On piers parallel to the direction of water current, the intensity of pressure shall be calculated from the following equation: P = 52KV2 Where
…………………4.20
P = intensity of pressure in kg/m2; V = velocity of the current at the point where pressure is being calculated; K = a coefficient having following value for different shape of piers; a). square ended pier
=
1.5
b). circular pier
=
0.66
c). piers with triangular cut and ease waters, the angle
=
0.5
=
0.5 to 0.7
=
0.7 to 0.9
included between faces being 30 degrees or less d). piers with triangular cut and ease waters, the angle included between faces being more than 30 degrees but less than 60 degrees e). piers with triangular cut and ease waters, the angle included between faces being more than 60 degrees but less than 90 degrees Current force is applied for operating and extreme cases. In operating case, mean sea level is considered as top water level and in extreme condition HAT level is considered as top water level. 10. Buoyancy:
Effect of buoyancy is considered in calculating the weight of portion of foundation under water. Buoyancy effect is also considered in working out bearing capacity of pile foundation. 11. Thermal Effects:
There are two thermal effects which can induce stresses in bridges. The first is a uniform temperature change which results in an axial expansion or contraction. If restrained, such as in an arch or a frame bridge, this can generate significant axial force, bending moment and shear. The second effect is that due to differential changes in temperature. If the top of a beam heats up relative to the bottom, it tends to bend; if it is restrained from doing so, bending moment and shear force are generated. Integral bridges undergo repeated expansions and contractions due to daily or seasonal temperature fluctuations. For analysis, coefficient of thermal expansion is taken as 11.7x10-6 /degree centigrade for reinforced concrete and steel. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
43
Chapter-4
Pile Analysis
12. Shrinkage And Creep:
These two effects need to be considered together they are interrelated. As concrete ages it shrinks slightly. The rate at which the concrete shrinks decreases approximately exponentially with time, with half of the total shrinkage normally occurring in the first one month and remaining 75% in six months from commencement of drying. Creep in concrete is response to long term stress; the concrete strain gradually increases to two or three times the elastic strain. The creep strain rate decreases with time, similar to the way the shrinkage rate decreases.
2.1.1 Load Combinations:
Load combinations are considered as per IS 456:2006, IS 4651 (Part 4):1989 and IRC 6:2000. Detailed load combinations are given in chapter of load calculations.
4.2 Load Calculation: 1. Dead Load :
kN/m3
Unit weight of concrete
=
25
a). Self weight of pile = π x 1.0 x 1.0 x 25/4
=
19.635 kN/m
b). Self weight of pile muff = ((2.4 x 2.4 x 0.35) + (((2.4 x 2.4) + (1.5 x 1.5) + (sqrt (1.5 x 1.5 x 2.4 x 2.4))) x 0.35/3) – (π x 1.0 x 1.0 x 0.7)) x 25 =
70.52 kN
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
44
Chapter-4
Pile Analysis
c). Self weight of precast pile cap = ((((0.2 + 0.275) x 0.2/2) + (0.4 x 0.9) + ((0.125 + 0.1) x 0.6/2))x2) x 25 =
23.75 kN/m
d). Self weight of precast longitudinal girders L-girder-1 & 8 = ((0.4 x 0.725) + ((0.2 + 0.15) x 0.25/2) + ((0.2 + 0.15) x 0.6 / 2)) x 25
=
10.97 kN/m
=
9.44 kN/m
L-girder-2 to 5 = ((0.4 x 0.725) + ((0.2 + 0.15) x 0.25)) x 25
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
45
Chapter-4
Pile Analysis
L-girder-6 & 7 = ((0.4 x 0.725) + ((0.2 + 0.15) x 0.25/2) + ((0.2 + 0.15) x 0.45/2)) x 25
=
10.34
kN
=
46.01
kN
/m
e). Self weight of insitu concrete over pilecap = ((16.4 x 2 x 1.005 x 25) – (10.97 + (4 x 9.44) + (2 x 10.34))) / 16.4 /m f). Self weight of insitu concrete over pile muff = (2.4 x 1.5 x 0.9 x 25) – (23.75 x 1.5)
=
45.375 kN
g). Self weight of cross diaphragm = 0.8 x 1.005 x 25 =
20.1 kN
h). Self weight of deck slab (precast+insitu) = 0.35 x 25 =
7 kN /m2
i). Self weight of wearing course
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
46
Chapter-4 = 0.112 x 22
Pile Analysis =
2.464 kN /m2
j). Self weight of kerb = 0.25 x 0.25 x 25
=
1.5625 KN/m
k). Dead load due to handrail (approx.)
=
1
kN/m
On left side of carriage way
=
10
kN
On right side of carriage way
=
15
kN
=
4.56
kN/m
Weight of water in pipe = π x 0.6 x 78.5 x 2
=
5.82
kN/m
Total weight including 10% of wt. for pipe staging
=
11.41 kN/m
k). Dead load from conveyor pedestal
=
15
l). Dead load due to light pole
j). Dead load due to pipelines Considering 2 steel pipes of 600mm diameter and 15 mm each. Weight of pipe = π x (0.632-0.62) x 78.5 x 2 2
kN
2. Construction, Erection and Handling Loads:
Following value of load is considered as construction live load in design of precast elements. Precast pile cap beam
=
20
kN
Precast longitudinal girder
=
20
kN
Precast deck plank
=
2
kN/m2
An impact factor of 1.25 is considered for checking design of precast members for handling. 3. Live Load: 3.1 Vehicular Live Load:
Width of carriageway = 7.5 m As per Cl. 207.4 of IRC:6-2000, 2 lanes are considered for design purpose. Following combination of vehicles are considered. 1. One lane of IRC Class 70R tracked vehicle. 2. One lane of IRC Class 70R wheeled vehicle. 3. Two lane of IRC class A. 4. In addition to above stated IRC specified live loads, a 100 T crane is also considered in analysis and design is considered as per user requirement. Configuration of 100T crane is same as that of IRC Class AA tracked with the difference is only that in 100T crane, total load will be 100 T instead of 70T as in case of Class AA tracked vehicle. 3.2 Conveyor Live Load:
Live load due to operation of the conveyor system is taken as 1.8 kN in longitudinal direction as received from material handling department.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
47
Chapter-4
Pile Analysis
In addition to above mentioned live loads, live load of 150 kg/m2 is considered on the deck portion except at carriageway and at conveyor pedestals. 4. Impact Load Of Moving Live Load:
Impact factor are calculated as per Cl. 211 of IRC:6-2000. IRC Class 70R tracked vehicle
=
10 %
IRC Class 70R wheeled vehicle
=
25 %
IRC Class A vehicle
=
25 %
100 T crane
=
10%
Impact factor is considered only for design of super structure elements not for design of piles. 5. Braking Force:
Braking force is calculated as per Cl. 214.2 of IRC:6-2000. IRC Class 70R tracked vehicle:
Nos. of trains of vehicles per unit of bridge Braking force per support
=
=
5
((700x20%) + (4x700x10%)) / 28
=
15
=
4
kN
IRC Class 70R wheeled vehicle:
Nos. of trains of vehicles per unit of bridge Braking force per support
=
((1000x20%) + (3x1000x10%)) / 28 =
17.85 kN
IRC Class A vehicle:
Nos. of trains of vehicles per unit of bridge
=
4
Braking force per support
=
9.892 kN
Nos. of trains of vehicles per unit of bridge
=
2
Braking force per support
=
10.71 kN
=
((554x20%) + (3x554x10%)) / 28
100 T crane:
=
((1000x20%) + (1000x10%)) / 28
6. Wind Load:
Wind load is calculated as per Gust Factor method as per Cl. 8 of IS:875 (part3)-1987. 6.1. Operating Condition:
Basic wind speed
-
19 m/s
Height of structure above mean sea level
-
10 m
Terrain category
-
1
Class of structure
-
C
Probability factor k1 =
1
Terrain factor
k2,
=
0.78
..………Table33 of IS:875(part3)-1987
Topography factor
k3,
=
1
………Cl.5.3.3.1 of IS:875(part3)-1987
…………Table1 of IS:875 (part3)-1987
Design wind speed, Vz = Vbx k1x k2x k3, A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
48
Chapter-4
Pile Analysis
Vz = 14.82m/s
……… Cl.8.2.1 of IS:875 (part3)-1987
Wind Pressure Pz = 0.6 V2z,
…………Cl.8.3 of IS:875 (part3)-1987
Pz = 131.78 N/m2
Along wind load on the structure, Fz = Cf Ae Pz G
…………Cl.8.3 of IS:875 (part3)-1987
Where, Cf
= force coefficient,
Ae
= effective frontal area considered for the structure,
Pz
= design wind pressure,
G
= gust factor and is given by, ⎡ SE ⎤ 2 G = 1 + g f r ⎢ B(1 + φ ) + β ⎥⎦ ⎣
Where, gf
= peak factor defined as the ration of the expected peak value to the root mean value of a fluctuating wind,
r
= roughness factor which is dependent on the size of the structure in relation to the ground roughness,
B
= background factor indicating measure of slowly varying component of fluctuating wind load,
SE/β
= a measure of the resonant component of the fluctuating wind Load.
Now for category 1 and height of 14m, gf.r
=
1.0
……………Figure 8 of IS:875 (part3)-1987
L(h)
=
1000
……………Figure 8 of IS:875 (part3)-1987
Cy
=
10
Cz
=
12
Cz h / L(h)
=
0.17
Width of structure b =
160
λ=
9.52
Cyb/Cyh
=
m
Background factor B =
0.6
Natural frequency f0 =
0.67
Vh
14.82 m/s
=
……………Figure 9 of IS:875 (part3)-1987 Hz
Reduced natural frequency F0 = Cz f0 h / Vh = 7.64
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
49
Chapter-4
Pile Analysis
Size reduction factor S
=
f0 L(h) / Vh
=
45.47
gust energy factor E =
0.041
Gust factor G
1.8
=
0.012
Wind load in transverse direction: Wind load on pile:
Length of member l
=
14.0
m
Width of the member b
=
1.0
m
l/b
=
14.0
m
Force coefficient Cf
=
0.8
…………Figure 5 of IS:875 (part3)-1987 …………Table25 of IS:875 (part3)-1987
(for member of infinite length) Reduction factor k
=
0.845
Force coefficient
=
0.675
(for considering reduction factor k) Wind load F = Cf Ae Pz G Where
Cf =
force coefficient,
Ae =
effective area of the object normal to the wind direction,
Pz =
design wind pressure,
G =
gust factor,
Wind load on pile
=
160.168N/m
Wind load on exposed face of cross beam:
Height of beam
=
0.9
m
Width of beam
=
0.8
m
Exposed area Ae
=
0.72
m2
Force coefficient
=
1
Wind load on cross beam
=
170.845N
Wind load on front longitudinal beam:
Height of beam
=
0.725 m
Exposed area Ae
=
0.725m2/m
Force coefficient
=
1
Wind load on cross beam
=
172N
Wind load on front exposed face of slab:
Height of beam
=
0.280 m
Exposed area Ae
=
0.280 m2/m
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
50
Chapter-4
Pile Analysis
Force coefficient
=
1
Wind load on cross beam
=
66N
Wind load on vehicle:
Wind force on moving vehilce
=
3.0
kN /m
Length
=
160
m
Nos. of piles
=
28
Wind load per pile
=
18
=
0.335 kN
kN
Wind load on conveyor pedestal:
Wind load on conveyor pedestal
Wind load in longitudinal direction: Wind load on pile:
Wind load on pile
=
160.168N/m
Wind load on exposed face of cross beam:
Height of beam
=
0.9
m
Exposed area Ae
=
0.9
m2/m
Force coefficient
=
1
Wind load on cross beam
=
214N
6.2. Extreme Condition:
Basic wind speed
-
44 m/s
Height of structure above mean sea level
-
4.5 m
Terrain category
-
1
Class of structure
-
C
Probability factor
k1
=
1
Terrain factor
k2,
=
0.78
Topography factor
k3 ,
=
1
………… Table1 of IS:875 (part3)-1987 ………… Table33 of IS:875 (part3)-1987 ………… Cl.5.3.3.1 of IS:875 (part3)-1987
Design wind speed, Vz = Vbx k1x k2x k3, ………… Cl.8.2.1 of IS:875 (part3)-1987
Vz = 34.32 m/s
Wind Pressure Pz = 0.6 V2z,
………… Cl.8.3 of IS:875 (part3)-1987
Pz = 706.71 N/m2
Now for category 1 and height of 14m, gf.r
=
1.0
………… Figure 8 of IS:875 (part3)-1987
L(h)
=
1000
………… Figure 8 of IS:875 (part3)-1987
Cy
=
10
Cz
=
12
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
51
Chapter-4
Pile Analysis
Cz h / L(h)
=
0.17
Width of structure b =
160
λ=
9.52
Cyb/Cyh
=
m
Background factor B =
0.6
Natural frequency f0 =
0.67
Vh
14.82 m/s
=
………… Figure 9 of IS:875 (part3)-1987 Hz
Reduced natural frequency F0 = Cz f0 h / Vh = 3.29 Size reduction factor S=
0.05
f0 L(h) / Vh
=
19.63
gust energy factor E =
0.075
Gust factor G
=
1.91
=
14.0
m
Width of the member b=
1.0
m
l/b
=
14.0
m
Force coefficient Cf
=
0.8
Wind load on pile:
Length of member l
………… Figure 5 of IS:875 (part3)-1987
(for member of infinite length) Reduction factor k
=
0.845
Force coefficient
=
0.675
………… Table25 of IS:875 (part3)-1987
(for considering reduction factor k) Wind load F = Cf Ae Pz G Where
Cf =
force coefficient,
Ae =
effective area of the object normal to the wind direction,
Pz =
design wind pressure,
G =
gust factor,
Wind load on pile
=
912.77N/m
Wind load on exposed face of cross beam:
Height of beam
=
0.9
m
Width of beam
=
0.8
m
Exposed area Ae
=
0.72
m2
Force coefficient
=
1
Wind load on cross beam
=
973.629N
Wind load on front longitudinal beam:
Height of beam
=
0.725 m
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
52
Chapter-4
Pile Analysis
Exposed area Ae
=
0.725 m2/m
Force coefficient
=
1
Wind load on cross beam
=
978.75N
Wind load on front exposed face of slab:
Height of beam
=
0.280 m
Exposed area Ae
=
0.280 m2/m
Force coefficient
=
1
Wind load on cross beam
=
378 N
Wind load on conveyor pedestal:
Wind load on conveyor pedestal
=
1.8
kN
Wind load in longitudinal direction: Wind load on pile:
Wind load on pile
=
912.77N/m
Wind load on exposed face of cross beam:
Height of beam
=
0.9
m
Exposed area Ae
=
0.9
m2/m
Force coefficient
=
1
Wind load on cross beam
=
1215 N
7. Earthquake Force: 7.1 Transverse and longitudinal seismic force:
Seismic force is applied on full dead load and 50% of live load including conveyor live load. Seismic force is calculated as per Cl.6.4.2 of IS:1893-2002. The design horizontal seismic co-efficient is given by, Ah = Z I (Sa/g) / 2R Zone factor ‘z’
=
0.16
Importance factor ‘I’
=
1.5
Response reduction factor ‘R’
=
3
Time period ‘T’ (from staad)
=
1.59
sec
Damping percentage
=
5
%
Damping factor
=
1.00
Sa/g
=
0.855
Ah
=
0.034
As per analysis in staad, time period is almost same in both direction. So, same design horizontal seismic coefficient is applied in both directions. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
53
Chapter-4
Pile Analysis
7.2 Hydrodynamic force due to seismic action:
Horizontal force F = Ce Ah We Diameter of pile
=
1.0
m
Marine growth
=
50
mm
Radius of enveloping cylinder ‘R’
=
0.55
m
=
1.95
m
H/R
=
3.54
Ce
=
0.704
Weight of enveloping cylinder ‘We’
=
18.99 kN
Total horizontal force ‘F’
=
0.454 kN
=
0.835 m
=
2000 kN
Nos. of supports over which load is to be distributed
=
28
Seismic co-efficient
=
0.034
=
1.21
Height of submerged portion of pile ‘H’=
5.1-1.15
For C1 = 1 & C4 = 0.4286 CG of this horizontal force above bed level = C4H 7.3 Seismic force on vehicle in transverse direction:
Total vehicular live load on a unit of approach (two train of 100T vehicle)
Seismic force =
0.034 x 2000 x 0.5 / 28
kN
8. Wave Force: 8.1. Operating Condition (longitudinal & transverse direction):
Operating wave is considered in transverse as well as longitudinal direction consecutively in the analysis. Input: Wave height (H)
=
2.2
m
Time period (T)
=
6.0
sec
Bed level
=
(+)3.15 CD
Still water level
=
(+)5.10 CD
Direction of wave
=
180-270N
Density of sea water (γ)
=
10.25 kN /m3
Diameter of pile (D)
=
1.0
m
Marine growth
=
50
mm
Deep water wave length (Lo) =
gT2/2π
=
56.21 m
Still water depth (d)
=
5.1 – 3.15
=
1.95
Dimensionless water depth
=
d/gT2
=
0.01
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
m
54
Chapter-4
Pile Analysis ⎡ 4π 2 ⎤ Lo tanh ⎢ 2 ⎥ ⎣ gT ⎦
=
26.04 m
Max. horizontal wave velocity (Umax) = HgT/2L
=
2.49
Viscosity (ν)
=
9.29X10-7m2/s
=
2.94X106
Drag coefficient (CD)
=
0.7
Inertia coefficient (CM)
=
1.5
=
1.13
>
0.78
Wave length (L)
=
Reynold’s number (Re)
Relative wave height
=
Umax D/v
=
H/d
m/s
Hence it is a breaking wave. Non dimensional parameter (W)
=
CM D/ CD H
=
1.07
>
1.0
=
0.0075.
Breaking wave height (Hb)
=
2.649 m
Ratio H/Hb
=
0.831
Kim
=
0.4
KDm
=
0.6
Sim
=
0.8
SDm
=
0.9
=
11.72 kN
FDm = CD x γ x D x H2 x KDm / 2
=
10.94 kN
Total force F = Fim + FDm
=
22.65 kN
=
18.28 kN.m
=
19.20 kN.m
=
37.47 kN.m
=
1.65
m
=
6.5
m
Dimensionless wave steepness
=
Hb/gT2
Maximum inertial force on pile, Fim = CM x γ x g x π x D x H x Kim / 4 Maximum drag force on pile,
Maximum moment due to inertial force Mim = Fim x d x Sim Maximum moment due to drag force MDm = FDm x d x SDm Total moment M =
Mim + MDm
C.G. of this force about bed level
=
M/F
8.2. Extreme Condition(at angle of 210 deg.): Input:
Wave height (H)
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
55
Chapter-4
Pile Analysis
Time period (T)
=
10.0
sec
Bed level
=
(+)3.15 CD
Still water level
=
(+)10.5 CD
Direction of wave
=
210
Density of sea water (γ)
=
10.25 kN /m3
Diameter of pile (D)
=
1.0
m
Marine growth
=
50
mm
N
Deep water wave length (Lo) =
gT2/2π
=
156.1 m
Still water depth (d)
=
10.5 – 3.15
=
7.35
=
2
=
0.01
=
83.71 m
Max. horizontal water particle velocity (Umax) = HgT/2L
=
3.81
Viscosity (ν)
=
9.29X10-7m2/s
=
4.51X106
Drag coefficient (CD)
=
0.7
Inertia coefficient (CM)
=
1.5
=
0.88
>
0.78
Dimensionless water depth Wave length (L)
=
Reynold’s number (Re)
Relative wave height
d/gT
=
=
⎡ 4π 2 ⎤ Lo tanh ⎢ 2 ⎥ ⎣ gT ⎦
Umax D/v
H/d
m
m/s
Hence it is a breaking wave. Non dimensional parameter (W)
=
CM D/ CD H
=
2
=
0.36
3000 kN.
This value is also useful for finding out value of spring stiffness at the bottom of pile. Assuming 10 mm settlement, Stiffness = Load / settlement = 4134/0.01 =413400 kN/m
5.4 Structural Design Of Steel Piles Design of steel pile section is done with working stress method. Design is done in accordance with API RP-2A WSD. Design is checked for all possible severe combination of resultant forces and design is presented for a typical governing force combination (moment and axial force combination). Design of piles is done using spread sheet “API STEEL PILE DESIGN”. A typical design is presented here. 5.4.1 Typcial Design For Operating Case: Basic Inputs:-
Outside diameter of pile
D’o
Corrosion Allowance
=
1.016
m
=
5
mm
Corroded outside diameter
Do
=
1.011
m
Structural thickness
t
=
17
mm
Inside diameter of pile
Di
=
0.977
m
Unsupported length of pile
L
=
13.0
m
Effective length factor
K
=
1.2
Grade of steel
Fy
=
240
N/mm2
Modulus of elasticity
E
=
200000
N/mm2
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
93
Chapter 5
Pile Design
Loads:-
Axial force
Pu
=
2353
kN
Moment My
Mx
=
1119
kN.m
Moment Mz
Mz
=
388
kN.m
Design resultant moment
Mu
=
1184
kN.m
Effective length of pile
Leff
=
1.2*13
=
15.6
=
∏/4 (Do2–Di2)
=
53086.63
=
P/A
=
44.32
=
2CEt/Do
Considering root mean square value,
m
Compressive stress
Cross sectional area
A
Actual compressive stress Elastic local buckling stress
fa Fxe
mm2 N/mm2 N/mm2
(API RP 2A-WSD Cl.3.2.2.b)
Where C = critical elastic buckling co-efficient Inelastic local buckling stress
=
0.3
Fxe
=
2017
Fxc
= lesser of Fxc1 and Fxc2
N/mm2
(API RP 2A-WSD Cl.3.2.2.b)
Where Fxc1 = Fy x [1.64 – 0.23(Do/t)1/4]≤ Fxe, Fxc2 = Fy
Therefore,
Fxc1
=
240.3
N/mm2
Fxc2
=
240
N/mm2
Fxc
=
240
N/mm2
I
=
∏/64 (Do4–Di4)
=
6558355778 mm4
=
I / (Do/2)
=
12973997.58 mm3
=
M/Z
=
91.259
Bending Stress
Moment of inertia Section Modulus Actual bending stress
Z fb
N/mm2
Since (10340/Fy) < (Do/t) = 67.4 < (20680/Fy), Allowable bending stress
Fb
= [0.84 – 1.74 (FyDo) / (Et)] Fy =
171.80
N/mm2
Check for combined stresses
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
94
Chapter 5
Pile Design
fa f + b ≤ 1.0 0.6 Fxc Fb
fa f + b 0.6 Fxc Fb
(API RP 2A-WSD Cl.3.3.1.b)
= 0.30 + 0.53 = 0.83 ≤ 1.
Therefore OK.
5.4.2 Typcial Design For Extreme Case: Basic Inputs:-
D’o
Outside diameter of pile Corrosion Allowance
=
1.016
m
=
5
mm
Corroded outside diameter
Do
=
1.011
m
Structural thickness
t
=
15
mm
Inside diameter of pile
Di
=
0.981
m
Unsupported length of pile
L
=
13.0
m
Effective length factor
K
=
1.2
Grade of steel
Fy
=
240
N/mm2
Modulus of elasticity
E
=
200000
N/mm2
Axial force
Pu
=
2660
kN
Moment My
Mx
=
333
kN.m
Moment Mz
Mz
=
1347
kN.m
Mu
=
1387
kN.m
A
=
∏/4 (Do2–Di2)
=
46935.39
=
P/A
=
56.67
N/mm2
=
2CEt/Do
N/mm2
Loads:
Considering root mean square value, Design resultant moment Compressive stress
Cross sectional area Actual compressive stress
fa
Elastic local buckling stress
Fxe
mm2
(API RP 2A-WSD Cl.3.2.2.b)
Where C
= critical elastic buckling co-efficient
Inelastic local buckling stress
=
0.3
Fxe
=
1780
Fxc
=
lesser of Fxc1 and Fxc2
N/mm2
(API RP 2A-WSD Cl.3.2.2.b) 1/4
Where Fxc1 = Fy x [1.64 – 0.23(Do/t) ]≤ Fxe, Fxc2 = Fy A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
95
Chapter 5
Pile Design
Therefore,
Fxc1
=
235
N/mm2
Fxc2
=
240
N/mm2
Fxc
=
235
N/mm2
I
=
∏/64 (Do4–Di4)
=
5821402815 mm4
=
I / (Do/2)
=
11516128.22 mm3
=
M/Z
=
120..43
Bending Stress
Moment of inertia Section Modulus Actual bending stress
Z fb
N/mm2
Since (10340/Fy) < (Do/t) = 67.4 < (20680/Fy), Allowable bending stress
Fb
= [0.84 – 1.74 (FyDo) / (Et)] Fy =
167
N/mm2
Check for combined stresses fa f + b ≤ 1.33 0.6 Fxc Fb
fa f + b 0.6 Fxc Fb
(API RP 2A-WSD Cl.3.3.1.b)
= 0.401 + 0.721 = 1.122 ≤ 1.33.
Therefore OK.
Check for shear stress: Basic Inputs:-
Outside diameter of pile
D’o
Corrosion Allowance
=
1.016
m
=
5
mm
Corroded outside diameter
Do
=
1.006
m
Structural thickness
t
=
11
mm
Inside diameter of pile
Di
=
0.984
m
Shear Force
Fx
=
230.17
kN
Shear Force
Fz
=
56.564
kN
Design resultant shear force
Fu
=
237
kN
Area of cross section
A
=
34384.73
mm2
Actual Shear stress
fv
=
Fu / 0.5A
=
13.78
Loads:
Considering root mean square value,
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
N/mm2 96
Chapter 5
Pile Design
Allowable shear stress
=
Fv
0.4 Fy
(API RP 2A-WSD Cl.3.2.4.a)
=
96
N/mm2
>
13.78
N/mm2.
5.4.3 Minimum Wall Thickness:
As per Cl.6.10.6 of API RP 2A-WSD, the D/t ratio of the entire length of a pile should be small enough to preclude local buckling at stresses up to the yield strength of the pile material. Consideration should be given to the different loading situations occurring during the installations and service life of a piling. For piles that are to be installed by driving where sustained hard driving is anticipated, the minimum piling wall thickness used should not be less than t = 6.35 + D/100 where t= thickness (mm) D= diameter (mm) For diameter of 1016 mm, t = 6.35 + 1016/100 = 16.51mm.
2823
kN.
Hence OK.
According to Cl.7.4.4.c of API RP 2A-WSD, following limitations should be observed while designing shear keys: 17.25 MPa ≤ fcu = 40 MPa ≤ 110 MPa Shear key ratio
h/s = 0.1
≤ 0.1
Shear key shape factor
1.5 ≤ w/h=2 ≤ 3
Product of fcu and h/s = 4 ≤ 5.5 MPa. Hence shear key dimension and spacing is satisfying all above stated limitations. Weld Design:
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
102
Chapter 5
Pile Design
Axial force to be transferred through each shear key
=
705750
N
Assumed size of fillet weld
=
6
mm
=
4.24
N/mm2
Permissible shear stress in fillet weld
=
108
N/mm2
Length required for weld
=
1540
mm.
Effective throat thickness
=
0.707 x 6
=705750 / (4.242 x 108)
5.4.8 Design Of Concrete Plug:
Design of plug is done as per IS:456-2000 & SP 16. Design is checked for all possible severe combination of resultant forces and design is presented for a typical governing force combination (moment and axial force combination). Design of insitu concrete plug is done using spread sheet “PILE DESIGN”. A typical design is presented here. Basic Inputs:-
Diameter of pile
D
=
0.966
m
Unsupported length of pile
L
=
13.00
m
=
1.2
Effective length factor Grade of concrete
fck
=
40
N/mm2
Grade of steel
fy
=
500
N/mm2
Dia. of bar assumed
Ф
=
28
mm
Dia. of helicals assumed
Фh
=
12
mm
Clear cover to outermost reinforcement,
d
=
75
mm
Axial force
Pu
=
3013
kN
Moment My
Mx
=
227
kN.m
Moment Mz
Mz
=
2267
kN.m
Design resultant moment
Mu
=
2278
kN.m
Effective length of pile
Leff
=
1.2*13
=
15.6
m
Loads:-
Considering root mean square value,
Effective cover
d'
=
101
mm
Area of pile
Ag
=
0.73289909
m2
Area of pile core
Acr
=
31741.60
m2
e
=
58.2
mm
Me
=
112/26
kN.m
Minimum eccentricity e = (L/500) + (D/30) ≥ 20 mm
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
103
Chapter 5
Pile Design < Mu =
1924
Pu / fck D2
=
0.08
Mux / fck D3
=
0.063
From SP:16 chart 59 to 62,
Pt / fck
=
0.05
Therefore
Pt
=
2.0 %
Ast required
=
14657.98
Minimum reinforcement required
=
0.80%
=
5863.19
mm2
Dia of bars provided
=
32
mm
No. of bars provided
=
19
Ast provided
=
11699.29
=
max. of 6 mm or
Therefore Final actual moments
Me
kN.m
The section is now checked for biaxial bending:-
mm2
mm2
Design of helical reinforcement Dia. of helicals required
Dia. of main bar/4 =
7
mm
Pitch required
=
150
mm
Dia. of helicals provided
=
12
mm
Pitch provided
=
150
mm
=
1.5
N/mm2
Design bond stress
=
2.4
N/mm2
Stress in bar σs = 0.87 fy
=
435
N/mm2
=
46.00 times dia
Development Length
Ld = Ф σs / 4 τbd Bond stress 60% increase for deformed bars
Development Length
Ld
Concrete Plug Design Summary: Table-21 PILE
R/F
Grid A 19-32mmФ Grid B 17-32mmФ
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
104
Chapter 5
Pile Design
5.4.9 Check For Serviceability:
Piles are checked for serviceability under all possible severe combination of working loads. Deflections at top of piles are summarized in table below. Load Combination
Deflection (mm)
Operating
48
Seismic
75.5
Storm
66
As per Cl. 43.2 IS:456-2000, Cracks due to bending in a compression member subjected to a design axial load greater than 0.2fckAc, where fck is the characteristic compressive strength of concrete and Ac is the area of the gross section of the member, need not be checked. Here, maximum axial load on the pile = 4044 kN < 0.2*40*785398.1634 = 6283.185 kN Therefore check for crack width must be done. Crack width is found out as per Annex F IS: 456-2000. Design surface crack width, Wcr =
3acr ε m 2(a cr − C min ) 1+ h−x
Where, acr
= distance from point considered to the surface of the nearest
longitudinal bar. Cmin
= clear cover to main reinforcement
h
= overall depth of the member
x
= depth of neutral axis
εm
= average steel strain given by,
ε m = ε1 −
b(h − x)(a − x) 3E s As (d − x)
Where, As
= area of tension steel
b
= width of the section
a
= distance from the compression face to the point at which
crack width is
being calculated. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
105
Chapter 5 ε1
Pile Design = strain at level considered ignoring the stiffening of the concrete in the tension zone.
Es
= Young’s modulus for steel
Basic Inputs:-
Diameter of pile
h
=
0.966
m
Grade of concrete
fck
=
40
N/mm2
Grade of steel
fy
=
500
N/mm2
Dia. of main reinforcement
Ф
=
28
mm
No. of bars
N
=
19
Dia. of helicals
Фh
=
12
mm
=
75
mm
Cmin
=
87
mm
Axial force
Pu
=
2206
kN
Moment My
Mx
=
1175
kN.m
Moment Mz
Mz
=
94
kN.m
Design resultant moment
Mu
=
1178
kN.m
Effective diameter
d
=
966 – 87 – 87 – 28
=
764
mm
deff
=
865
mm
Depth of neutral axis
x
=
391.334
mm
Stress in reinforcement
fs
=
186.24
MPa
=
πd/N
=
126.32
mm
=
48629
mm2
Clear cover to outermost reinforcement Clear cover to main reinforcement Loads:-
Considering root mean square value,
Effective depth Neutral axis and stress calculations:-
Using spread sheet “PILE CRACK”,
Approx. spacing between bars Area of tension reinforcement
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
106
Chapter 5
Pile Design
Figure.29 Concrete Plug Neutral Axis
C.G. of tension reinforcement
=
686.83
mm
Width of section at C.G. of tension reinforcement
=
875.76
mm
Distance from compression face, a
=
966
mm
Distance to the surface of nearest bar, acr
=
105.12
mm
Strain at level considered, ε1
=
0.00112
Average steel strain, εm
=
0.0009
Design surface crack width, Wcr
=
0.29
Permissible crack width
=
0.004 times clear cover
mm
(As per IS: 4651-1989 part 4 Cl. 8.3.4) =
0.348
mm
Therefore O.K. Crack Width Check Summary: Table-22.1 GRID A Fx
My
Mz
Mu
N.A.
Stress in
Crackwidth
(kN)
(kN.m)
(kN.m)
(kN.m)
(mm)
reft.(N/mm2)
(mm)
220
122
2206
1175
94
391.33
186.24
0.29
4774
133
848
648
295
335.56
154.55
0.22
Beam
Table-22.2 GRID B Fx
My
Mz
Mu
N.A.
Stress in
Crackwidth
(kN)
(kN.m)
(kN.m)
(kN.m)
(mm)
reft.(N/mm2)
(mm)
221
127
2353
1119
388
343.61
159.13
0.23
4775
121
1036
743
252
393.47
191.38
0.30
Beam
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107
CHAPTER 6 COMPARISON OF RESULTS
Chapter 6
Comparison Of Results
6.1 Comparison Between Various Steel Pile Diameters: 6.1.1 Without restricted deflection: Here, comparision of weight between 4 different diameters is done keeping total structural thickness equal to what is required from strength point of view. Table 23 Weight Comparision O.D. (mm)
Spool Details (Length - Thickness)
Total Weight(T)
Spool-1
Spool-2
Spool-3
Spool-4
1016
4m-25mm
11m-20mm
11m-18mm
11m-18mm
17.6
1118
4m-25mm
11m-20mm
11m-18mm
11m-18mm
19.4
914
11m-25mm
4m-20mm
11m-18mm
11m-18mm
16.5
813
11m-25mm
4m-25mm
11m-18mm
11m-18mm
15
Table 24 Deflection Comparision Pile Options
Load Case Operating
Seismic
Storm
1000mm Dia. RCC
46
68
60
1118mm O.D. Steel
46
74
58
1016mm O.D. Steel
49
79
69
914mm O.D. Steel
52
86
84
813mm O.D. Steel
58
100
106
Table 25 Founding Level Comparision Pile Options
Founding Level (m CD)
1000mm Dia. RCC
(-)25.00
1118mm O.D. Steel
(-)25.00
1016mm O.D. Steel
(-)25.00
914mm O.D. Steel
(-)25.00
813mm O.D. Steel
(-)25.00
6.1.2 With Restricted Deflection: As mentioned in Chapter 3 – Project Description, deflection at top of deck in operating condition is to be restricted to 50mm for proper functioning of material handling system installed over deck, plate thickness were revised to suit this limit. Analysis and design with increased structural thickness is done for pile diameters 914mm and 813m as for other two diameters, deflection is well within limit.
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108
Chapter 6
Comparison Of Results Table 26 Weight Comparision
O.D. (mm)
Spool Details (Length - Thickness)
Total Weight(T)
Spool-1
Spool-2
Spool-3
Spool-4
1016
4m-25mm
11m-20mm
11m-18mm
11m-18mm
17.6
914
11m-28mm
4m-25mm
11m-20mm
11m-18mm
18.5
813
11m-34mm
4m-32mm
11m-30mm
11m-30mm
22.39
Table 27 Deflection Comparision Pile Options
Load Case Operating
Seismic
Storm
1016mm O.D. Steel
49
79
69
914mm O.D. Steel
50
83
75
813mm O.D. Steel
50
85
75
6.2 Comparison Of Forces In Pile: MOMENT COMPARISION FOR OPERATING LOADCASES
MOMENT (KN.M)
RCC
Steel
1400 1200 1000 800 600 400 200 0 0
0.083 0.167
0.25 0.333 0.417
0.5
0.583 0.667
0.75
0.833 0.917
1
H/L
MOMENT COMPARISION FOR SEISMIC LOADCASES RCC
STEEL
MOMENT (KN.M)
2500 2000 1500 1000 500 0 0
0.083 0.167
0.25 0.333 0.417
0.5
0.583 0.667
0.75
0.833 0.917
1
H/L
H = length of segment measured from top of pile, L = Total length up to fixity measured from pile top.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
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Chapter 6
Comparison Of Results
MOMENT COMPARISION FOR STORM LOADCASES RCC
STEEL
MOMENT (KN.M)
2000 1500 1000 500 0 0
0.083 0.167
0.25 0.333 0.417
0.5
0.583 0.667
0.75
0.833 0.917
1
H/L
MOMENT (KN.M)
MOMENT COMPARISION RCC OPERATING
RCC SEISMIC
RCC STORM
STEEL OPERATING
STEEL SEISMIC
STEEL STORM
2500 2000 1500 1000 500 0 0
0.083 0.167
0.25 0.333 0.417
0.5
0.583 0.667
0.75
0.833 0.917
1
H/L
SHEAR FORCE COMPARISION FOR OPERATING LOADCASES
SHEAR FORCE (KN)
RCC
STEEL
200 150 100 50 0 0
0.083 0.167
0.25 0.333 0.417
0.5
0.583 0.667
0.75 0.833 0.917
1
H/L
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
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Chapter 6
Comparison Of Results
SHEAR FORCE COMPARISION FOR SEISMIC LOADCASES
SHEAR FORCE (KN)
RCC
STEEL
300 250 200 150 100 50 0 0
0.083 0.167
0.25 0.333 0.417
0.5
0.583 0.667
0.75 0.833 0.917
1
H/L
SHEAR FORCE COMPARISION FOR STORM LOADCASES
SHEAR FORCE (KN)
RCC
STEEL
300 250 200 150 100 50 0 0
0.083 0.167
0.25 0.333 0.417 0.583
0.5
0.667
0.75 0.833 0.917
1
H/L
AXIAL FORCE COMPARISION
AXIAL FORCE (KN)
RCC
STEEL
2800 2750 2700 2650 2600 OPERATING
SEISMIC
STORM
LOADING CONDITION
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
111
Chapter 6
Comparison Of Results
6.3 Comparison Of Deflection In Pile DEFLECTION COMPARISION
DEFLECTION (MM)
RCC
STEEL
100 80 60 40 20 0 OPERATING
SEISMIC
STORM
LOADING CONDITION
6.4 Comparison Of Forces In Beams COMPARISION OF FORCES FOR PILE-CAP BEAM
VALUE
RCC
Steel
4000 3000 2000 1000 0 Hogging at Sagging at Sagging at midsupport (KN.m) support (KN.m) span (KN.m)
Shear at support (KN)
FORCES
COMPARISION OF FORCES FOR LONGITUDINAL BEAMS RCC
STEEL
VALUE
1500 1000 500 0 Hogging at support (KN.m)
Sagging at mid-span (KN.m)
Shear at support (KN.m)
FORCES
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
112
CHAPTER 7 CONCLUSION AND FUTURE SCOPE
Chapter 7
Conclusion & Future Scope
7.1 Conclusion: Following conclusions are derived based on the present work. ¾ For required structural thickness, 914mm O.D. pile and 813mm O.D. pile are weighing 6.25% and 14.77% less than 1016mm O.D. pile respectively. And 1118 mm O.D. pile is weighing 10.22% more than 1016mm O.D. pile. ¾ But deflection is limited to 50mm in operating condition at top of deck for proper functioning of the material handling system installed above deck. Deflection is higher than this limit in 914mm O.D. pile and 813mm O.D. pile. To reduce deflection, thickness needs to be increased. With increased thickness (by providing thickness required to reduce deflection to 50mm), 914mm O.D. pile and 813mm O.D. pile are weighing 5.11% and 27.21% more than 1016mm O.D. pile respectively. Thus it can be concluded that for given deflection limit, 1016mm O.D. pile option is most economical steel pile for the structure studied in this thesis. ¾ Founding level of all the three steel piles are coming same as piles are founded in sand layer to avoid founding into clay layer which is considered as weak for end bearing. All three piles are penetrated into sand layer by 2m as per guidelines given in API RP 2A-WSD. ¾ Founding level of 1.0m dia. bored cast in situ RCC pile and 1.016m outer dia. steel piles is coming same because of avoiding founding into clay. Because static calculation shows formation of soil plug inside steel pile which reduces pile bearing capacity and there is large reduction in the end bearing resistance in clayey soil in case of RCC piles. At same founding, level hollow steel pile gives more bearing capacity than that of solid RCC pile. This is because skin friction is available on outer side as well as on inner side of the steel pile whereas it is available only at outer side of the RCC pile. ¾ In comparison between 1.0m dia. bored cast in situ RCC pile and 1.016m outer dia. steel pile, it can be seen that forces are almost same in both the cases except for seismic load case where slight variation in forces is observed. Moments are approx. 6% higher in steel pile and shear force is approx. 8% higher in steel in seismic load case. ¾ Base shear co-efficient for RCC pile is 0.04 whereas for steel pile is 0.05. Although hollow steel piles are flexible foundation compared to solid RCC pile but
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
113
Chapter 7
Conclusion & Future Scope
multiplication of damping factor of value 1.4 with base shear coefficient increases seismic force in steel piled structures as compared to RCC piles structure. ¾ Moment of inertia (I) of 1.0 m dia. RCC pile is approx. 7.4 times moment of inertia of 1.016m outer dia. steel pile. At the same time, modulus of elasticity (E) of steel material is approx. 6.3 times E of RCC material. But product of EI for RCC pile is only 1.16 times EI of steel pile. Because of this, there is not major variation in RCC pile and steel pile option.
7.2 Future Scope: ¾ In this dissertation work, both steel pile and RCC pile options are analyzed by using soil spring stiffness method. Same can be done by depth of fixity approach. ¾ Bearing capacity of steel piles can be evaluated by dynamic methods. ¾ Further research can be done on using batter driven steel pile for reducing deflection. ¾ Further work can be done on economics of steel pile and RCC pile option. ¾ Further studies can be done on other pile types such as precast RCC piles, precast prestress piles etc. ¾ Dynamic analysis can be carried out for the given structure for dynamic loads such as waves, current, wind, earthquake are acting on the.
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114
CHAPTER 8 REFERENCES
Chapter 8
References
1. Arora K.R., “Soil Mechanics and Foundation Engineering”, Standard Publishers, Third Edition. 2. Aswani M.G. and Vazirani V.N. and Ratwani M.M., “Design Of Concrete Bridges”, Khanna Publishers 3. Babu P.V.Mayur and Bhandari N.M, “A Comparative Study of Integral Bridges versus Simply Supported Bridge” 4. Bowles Joseph E., “Foundation Analysis and Design”, McGraw-Hill Companies, Inc., Fifth Edition. 5. Broms Bengt B., “Design of Laterally Loaded Piles”. 6. Byrne Byron, “Driven Pipe Piles in Dense Sand” 7. Chen Wai Fah and Duan Lian, “Bridge Engineering Handbook”, CRC Press. 8. Connal John, “Integral Abutment Bridges – Australian and US Practice” 9. Dawson Thomas H., “Offshore Structural Engineering”, United Status Naval Academy 10. Duggal S.K., “Design of Steel Structures”, The McGraw-Hill Publishing Company Liminted, Second Edition, 11. Elson W.K., “Design of Laterally Loaded Piles”. 12. Evans Keith Martin, “A Model Study of The End Bearing Capacity of Piles In Layered Calcareous Soils”. 13. Flener Esra Bayoglu, “Soil Structure Interaction in Integral Bridges”. 14. Hambly E.C., “Bridge Deck Behavior”, E & F N Spon Publications, Second Edition. 15. Mistry Vasant C., “Integral Abutment and Jointless Bridges” 16. Mokwa R.L., “Analysis of Laterally Loaded Pile Groups” 17. Murthy V.N.S, “Soil Mechanics and Foundation Engineering”, Sri Kripa Technical Consultants, Third Edition. 18. Nayak Narayan, “Foundation Design Manual”, Dhanpat Rai Publications, Fourth Edition 19. O’brien Eugene J. and Keogh Damien L., “Design Details Of Integral Bridges”. 20. Park R. and Paulay T., “Reinforced Concrete Structure”, John Willey And Sons Publications. 21. Poulos H.G. and Davis E.H., “Pile Foundation Analysis and Design”, John Willey And Sons Publications. 22. Prakash Shamsher and Sharma Hari D., “Pile Foundations in Engineering Practice”, John Willey And Sons Publications. 23. Raina V.K., “Concrete Bridge Practice”, The McGraw-Hill Publishing Company Limited, Second Edition. A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
115
Chapter 8
References
24. Reynolds Charles E. and Steedman James C., “Reinforced Concrete Designer’s Handbook”, E & F N Spon Publications, Tenth Edition. 25. API Recommended Practice 2A-WSD Recommended Practice For Planning, Designing And Constructing Fixed Offshore Platforms – Working Stress Design 26. BS:6349(Part1)-2000 Maritime Structures- Code Of Practice For General Criteria. 27. Coastal Engineering Manual(Part VI)- 2006 Chapter5 – Fundamentals Of Design. 28. IRC:6-2000 Standard Specifications And Code Of Practice For Road Bridges. Section IILoad And Stresses. 29. IRC:22-1986 Standard Specifications And Code Of Practice For Road Bridges. Section VI- Composite Construction. 30. IS:1893(Part 1)-2002 Code Of Practice For Earthquake Resistant Design Of StructuresGeneral Provisions And Buildings. 31. IS:1893-1984 Criteria For Earthquake Resistant Design Of Structures. 32. IS:2062-1999 Steel For General Structural Purpose-Specification 33. IS:2911 (Part 1/Sec 2) – 1979 Code Of Practice For Design And Construction Of Piles, Bored Cast In Situ Piles 34. IS:456-2000 Plain And Reinforced Concrete – Code Of Practice 35. IS:4651 (Part 4) -1989 Code Of Practice For Planning And Design Of Ports And Harbours, General Design Considerations. 36. IS:800-1984 Code Of Practice For General Construction In Steel 37. IS:816-1969 Code Of Practice For Use Of Metal Arc Welding For General Construction In Mild Steel 38. IS:875 (Part 1) – 1987 Code Of Practice For Design Loads (Other Than Earthquake 32. Loads) For Buildings And Structures – Dead Loads 39. IS:875 (Part 2) – 1987 Code Of Practice For Design Loads (Other Than Earthquake Loads) For Buildings And Structures – Imposed Loads 40. IS:875 (Part 3) – 1987 Code Of Practice For Design Loads (Other Than Earthquake Loads) For Buildings And Structures – Wind Loads 41. SP:16-1980 Design Aids To IS:456-1978, 42. SP:34-1987 Handbook On Concrete Reinforcement And Detailing, 43. SP:64-2001 Explanatory Handbook On Code Of Practice For Design Loads (Other Than Earthquake Loads) For Buildings And Structures – Wind Loads
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
116
APPENDIX ‐ A WAVE FORCE CALCULATION CHARTS
Appendix A
Wave Force Calculation Charts
Figure.A.1 Values Of Kim.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
117
Appendix A
Wave Force Calculation Charts
Figure. A.2 Values Of KDm.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
118
Appendix A
Wave Force Calculation Charts
Figure. A.3 Values Of Sim.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
119
Appendix A
Wave Force Calculation Charts
Figure. A.4 Values Of SDm.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
120
Appendix A
Wave Force Calculation Charts
Figure. A.5 Values Of Фm For W=0.05.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
121
Appendix A
Wave Force Calculation Charts
Figure. A.6 Values Of Фm For W=0.1.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
122
Appendix A
Wave Force Calculation Charts
Figure. A.7 Values Of Φm For W=0.5.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
123
Appendix A
Wave Force Calculation Charts
Figure. A.8 Values Of Фm For W=1.0.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
124
Appendix A
Wave Force Calculation Charts
Figure. A.9 Values Of αm For W=0.05.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
125
Appendix A
Wave Force Calculation Charts
Figure. A.10 Values Of αm For W=0.1.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
126
Appendix A
Wave Force Calculation Charts
Figure. A.11 Values Of αm For W=0.5.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
127
Appendix A
Wave Force Calculation Charts
Figure. A.12 Values Of αm For W=1.0.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge -
128
APPENDIX ‐ B SUPER STRUCTURE ANALYSIS & DESIGN
Appendix B
Super-structure Analysis & Design
B.1Super-structure Analysis: B.1.1 Pilecap Beam Analysis:
Figure.B.1 Longitudinal & Pile Cap Beam Arrangement Structural Idealization and Analysis Results: 3D analysis carried out on the same structural model which is used for design of piles. Following set of design forces depict the maximum forces taken at face (1m) of support (for hogging, sagging and shear at support) and sagging at mid span and corresponding torsion is added appropriately as given in IS:456 2000 Cl.41.4.2 (equivalent moment) and 41.3.1 (equivalent shear). Equivalent BM, Me = Mu + Mt ; Mt = Tu * (1+(D/b))/1.7 Equivalent shear, Ve = Vu + (1.6*Tu/b) Forces at a section 2.25m from centre of pile are also shown to see the possibility of curtailment of main reinforcement. Table B.1.1 Limit State Of Collapse Force
V/M
T
Ve/Me
(kN/kN.m)
(kN.m)
(kN/kN.m)
517
3590.00
562.33
4708
4770
671
529.82
207.30
942.113
Beam
L/C
Hogging at face of support
4282
Sagging at face of support Shear at ‘d’ distance from face of
4282
460
2144.115
606.45
3357
support Hogging at 2.25m from support
626
435
66.688
678.848
1416.8
Sagging at 2.25m from support
4280
489
1662.37
135.546
1932
Shear at 2.25m from support
4282
460
1955.03
606.45
3167.93
Sagging at mid span
4281
464
3011.56
665.57
4335.36
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
129
Appendix B
Super-structure Analysis & Design Table B.1.2 Limit State Of Collapse Force
V/M
T
Ve/Me
(kN/kN.m)
(kN.m)
(kN/kN.m)
-
549.847
0
549.847
4281
185
1151.479
171.076
1491.761
-
-
132.356
0
132.356
4282
195
67.375
598.356
1252.00
-
-
1047
0
1047
-
-
564
0
564
Beam
L/C
Sagging at mid span for stage-I
-
Sagging at mid span for stage-II Sagging at 2.25 from support for stage-I Sagging at 2.25 from support for stage-II Shear at ‘d’ distance from face of support for L-shear check Shear at 3m from support for Lshear check
B.1.2 Longitudinal Beam Analysis: 3D analysis carried out on the same structural model which is used for analysis of pile cap beams. Following set of design forces depict the maximum forces taken at face (1m) of support (for hogging, sagging and shear at support) and sagging at mid span and corresponding torsion is added appropriately as given in IS:456 2000 Cl.41.4.2 (equivalent moment) and 41.3.1 (equivalent shear). Equivalent BM, Me = Mu + Mt ; Mt = Tu * (1+(D/b))/1.7 Equivalent shear, Ve = Vu + (1.6*Tu/b) Forces at a section 3m from centre of pile are also shown to see the possibility of curtailment of main reinforcement.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
130
Appendix B
Super-structure Analysis & Design
Girder 2 to 4 Table B.2.1 Limit State Of Collapse Force
Beam L/C SF/BM (KN/KNm)
Hogging at face of support
3554
435
934.119
Hogging at 3m from support
165
517
102.834
Sagging at mid span
4702
547
1531.8
Sagging at 3m from support
4432
513
1344.19
Shear at ‘d’ distance from face of support
4466
519
909
Shear at 3m from support
4651
541
577.5
Table B.2.2 Limit State Of Serviceability Force
Beam L/C SF/BM (KN/KNm)
Sagging at mid span for stage-I
-
-
386.69
Sagging at mid span for stage-II
2244
225
612.55
Sagging at 3m from support for stage-I
-
-
312
Sagging at 3m from support for stage-II
4719
219
603
-
-
451
-
-
305.381
Shear at ‘d’ distance from face of support for L-shear check Shear at 3m from support for L-shear check
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
131
Appendix B
Super-structure Analysis & Design
Girder 1 & 5 Table B.3.1 Limit State Of Collapse Force
Beam L/C SF/BM (KN/KNm)
Hogging at face of support
3086
429
778.867
Hogging at 3m from support
163
517
106.548
Sagging at mid span
3458
432
1050
Sagging at 3m from support
3424
433
923.393
Shear at ‘d’ distance from face of support
3543
433
527.1
Shear at 3m from support
3509
435
344.8
Table B.3.2 Limit State Of Serviceability Force
Beam L/C SF/BM (KN/KNm)
Sagging at mid span for stage-I
-
-
386.69
Sagging at mid span for stage-II
3441
182
360
Sagging at 3m from support for stage-I
-
-
312
Sagging at 3m from support for stage-II
4717
217
282.74
-
-
180
-
-
108
Shear at ‘d’ distance from face of support for L-shear check Shear at 3m from support for L-shear check
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
132
Appendix B
Super-structure Analysis & Design
Girder 6 to 8 Table B.3.3 Limit State Of Collapse Force
Beam L/C SF/BM (KN/KNm)
Hogging at face of support
3091
429
651.667
Hogging at 3m from support
170
519
61.85
Sagging at mid span
4705
461
790.5
Sagging at 3m from support
4654
461
726.41
Shear at ‘d’ distance from face of support
3548
433
403.5
Shear at 3m from support
4350
513
226.4
Table B.3.4 Limit State Of Serviceability Force
Beam L/C SF/BM (KN/KNm)
Sagging at mid span for stage-I
-
-
386.69
Sagging at mid span for stage-II
4688
203
200
Sagging at 3m from support for stage-I
-
-
312
Sagging at 3m from support for stage-II
4722
203
181
-
-
112
-
-
69
Shear at ‘d’ distance from face of support for L-shear check Shear at 3m from support for L-shear check
B.1.3 End Diaphragm Analysis: 3D analysis carried out on the same structural model which is used for analysis of pile cap beams. Following set of design forces depict the maximum forces taken at face (1m) of support (for hogging, sagging and shear at support) and sagging at mid span and
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133
Appendix B
Super-structure Analysis & Design
corresponding torsion is added appropriately as given in IS:456 2000 Cl.41.4.2 (equivalent moment) and 41.3.1 (equivalent shear). Equivalent BM, Me = Mu + Mt ; Mt = Tu * (1+(D/b))/1.7 Equivalent shear, Ve = Vu + (1.6*Tu/b) Table-B.4.1 Limit state of Collapse Force
Beam
L/C
SF/BM
T
Ve/Me
(KNm) 77
(KN/KNm) 1514
Hogging at face of support
4765
545
(KN/KNm) 1411
Sagging at mid span
4762
547
1049
295
1440
Shear at face of support
4765
463
1003
101
1203
Table-B.4.2 Limit state of Serviceability
Force Sagging at mid span
Beam L/C 4762
218
SF/BM
T
Ve/Me
(KN/KNm) (KNm) (KN/KN.m) 907
193
1164
B.1.4 Deck Slab Analysis:
Figure.B.2 Precast Deck Planks Arrangement The deck slab is modeled in the STAAD as a rectangular beam of 1m width and 280 mm depth. Vehicular loads are restricted within the road width of approach and a live load of 1.5 kN/m2 is considered in the rest. The vehicular load is placed at various positions in the transverse direction and results are obtained as below: Deck Plank DP1 Design sagging moment
=
77.09
kNm
Design hogging moment
=
60.6
kNm
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134
Appendix B
Super-structure Analysis & Design
Design shear force
=
250.5
kN
Serviceability shear
=
157
kN
Serviceability moment
=
51.3
kN
Design sagging moment
=
7.05
kNm
Design hogging moment
=
32
kNm
Design shear force
=
30
kN
Serviceability shear
=
30
kN
Serviceability moment
=
4.7
kN
Deck Plank DP2
B.2 Design of Pile Cap Beam: Design of longitudinal beam is done using spread sheet “Pile-Cap”. However, one typical design is presented here. Grade of concrete,
fck
=
30
M
Grade of steel,
fy
=
500
Fe
Dia. of stirrups
=
16
mm
Clear cover
=
50
mm
Width of flange,
bf
=
2000
mm
Width of web,
bw
=
800
mm
Overall depth,
D
=
1905
mm
Depth of flange,
Df
=
1005
mm
B.2.1 Design for sagging moment at mid span: Equivalent BM,
Me
=
4335.36
KNm
Dia. of bar 1
Φ1
=
32
mm
Dia. of bar 2
Φ2
=
20
mm
Number of bars 1
=
6
Number of bars 2
=
4
=
1805.94
=
830.73 mm
Effective depth,
d
Xulim
mm
(IS:456-2000,Cl.38.1.) Ast provided
=
6082.12
Xuactual
=
122.48 mm
=
4641.91
mm2
Xu < Df – Xu. Neutral axis lies within flange. Moment of resistance
MR
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
KNm
135
Appendix B
Super-structure Analysis & Design >
4335.36
KNm
OK Provide 6 bars of 32 mm dia. and 4 bars of 20 mm dia. B.2.2 Design for maximum hogging moment at face of pile: Equivalent BM,
Me
=
4708
KNm
Dia. of bar 1
Φ1
=
32
mm
Dia. of bar 2
Φ2
=
25
mm
Number of bars 1
=
6
Number of bars 2
=
4
=
1802.28
Xulim
=
829.05 mm
Ast provided
=
6788.98
mm2
Xuactual
=
341.8
mm
Effective depth,
d
mm
4708
KNm
Provide 6 bars of 32 mm dia. and 4 bars of 25 mm dia. B.2.3 Shear design: Maximum shear force,
Vu
=
2144.55
KN
Corresponding torsion,
Tu
=
606.5
KN
Design equivalent shear force,
Ve
=
3557.353
KN
Effective depth,
d1
=
1802.28
mm
Width,
b1
=
800
mm
Effective depth,
d2
=
923
mm
Width,
b2
=
1200
mm
=
1.395
MPa
=
0.266
=
0.379
Nominal shear stress,
τ ve =
Ve (b1 × d 1 ) + (b 2 ×d 2 )
Percentage of reinforcement, 100
Pt
Ast (b1 × d1 ) + (b 2 ×d 2 )
Permissible shear stress in concrete,τc
MPa
(IS:456-2000,Cl.40.2.1.)
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
136
Appendix B
Super-structure Analysis & Design τcmax
=
3.5
MPa
(IS:456-2000,Cl.40.2.3.) τc < τve < τcmax, Transverse reinforcement is to be designed as per IS:456 2000, Cl.41.4.3 Yield stress for stirrups
=
415
MPa
Dia. of stirrups
=
16
mm
=
175
mm
C/C dist. Between corner bars in width direction,b*1
=
472
mm
C/C dist. Between corner bars in depth direction,d*1
=
1741
mm
Assume spacing of stirrups
Sv
Area of shear reinforcement required will be taken as maximum of following three values.
Asv =
Tu × S v Vu × S v + * b d 1 (0.87 f y ) 2.5d *1 (0.87 f y )
=
* 1
596.196
mm2
(IS:456-2000,Cl.41.4.3)
Asv =
(τ ve − τ c ) × b × S v 0.87 f y
=
mm2
393.9
(IS:456-2000,Cl.41.4.3)
Minimum area of shear reinforcement required Asv =
0.4 × b × S v 0.87 f y
=
155.103
mm2
(IS:456-2000,Cl.26.5.1.6)
Assume No. of legs,
=
4
Shear reinforcement provided
=
804.1472
mm2
Provide 4 legged 16 mm dia. stirrups @ 175 mm C/C. Summary of reinforcement is given at the end of this chapter and typical R/F detail is given in Appendix G. B.2.4 Check for longitudinal shear:
Neutral axis for composite section from compression face Effective depth,
d
=
1802.28
Modular ratio,
m
=
9.33
Area of tension reinforcement
Ast
=
6788.98
mm mm2
Taking moment about neutral axis,
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
137
Appendix B
Super-structure Analysis & Design
bx 2 = mAst (d − x) 2
Solving this equation, Depth of neutral axis,
x
=
460.95 mm
Area of concrete up to N.A.
=
368763.51
M.I. of concrete area about N.A.
=
26118160988 mm4
Transformed area of steel
=
63363.829
mm2
M.I. of steel area about N.A.
=
114001451969
mm4
Net M.I. about N.A.
=
140119612958
mm4
mm2
As per IRC: 22-1986 Cl.608.2.2, VL =
V . Ac .Y I
= The longitudinal shear per unit length at the interface in the
Where VL
section
under consideration V
= Vertical shear due to dead load and live load including impact acting on the section
Ac
= Transformed compressive are of concrete above N.A.
Y
= Distance from the neutral axis to the centre of area under consideration,
I
= Moment of inertia of whole composite section about N.A.
Vertical shear,
V
=
1047
KN
Longitudinal shear
VL
=
635.07
KN
Dia. of stirrups
=
16
mm
No. of legs
=
4
Spacing
=
175
mm
Area of one stirrup
=
840.247
mm2
Yield stress of steel
=
230
MPa
Shear resistance of one stirrup
=
184.97
KN
No. of stirrups in 1m length
=
5.71
Total shear resistance
=
1057.01
>
635.07 KN
KN
OK. Provide 4 legged 16 mm dia. stirrups @ 175 mm C/C.
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
138
Appendix B
Super-structure Analysis & Design
B.2.5 Check For Precast Beam:
Precast beam is checked for (self weight of beam + load due to in situ concrete + deck slab + load from L-girder) including construction live load of 20 KN at the centre of beam. Self weight of beam
=
23.8
KN/m
Load due to in situ concrete 1.005*25*2
=
50.25
KN/m
Total UDL acting on beam
=
74.05
KN/m
Load from precast longitudinal girder
=
91.25
KN
Load from deck slab over girder 2 to 5
=
0.28*2.275*25*10
=
159.25 KN
=
0.28*1.9375*25*10
=
135.625
=
0.28*1.75*25*10
=
122.5
Total concentrated load from girder 2 to 5
=
253.75 KN
Total concentrated load from girder 1 & 8
=
245.375
KN
Total concentrated load from girder 6 & 7
=
236
KN
Construction live load at the centre of beam
=
20
KN
Max hogging moment
=
1536.2 KNm
=
1843.44
KNm
Dia. of bars provided 1
=
32
mm
No. of bars provided 1
=
8
Clear cover
=
25
mm
Load from deck slab over girder 1 & 8 Load from deck slab over girder 6 & 7
Design hogging moment
Mu
KN KN
Hogging reinforcement:-
Grade of concrete
fck
=
30
M
Grade of steel
fy
=
500
Fe
=
6433.982
mm2
Ast provided Width of section
b
=
800
mm
Depth of section
D
=
900
mm
Effective depth
d
=
843
mm
Xulim
=
387.78
mm
Xuactual
=
323.93
mm
1843.44
KNm
Moment of resistance
MR
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
139
Appendix B
Super-structure Analysis & Design OK.
Provide 8 bars of 32 mm dia.
Max sagging moment
=
549.847
KNm
=
659.164
KNm
Dia. of bars provided
=
32
mm
No.of bars provided
=
6
Design sagging moment
Mu
Grade of concrete
fck
=
30
M
Grade of steel
fy
=
500
Fe
Ast provided
=
4825.486
mm2
Dia. of stirrups
=
16
mm
Width of section
b
=
800
mm
Depth of section
D
=
900
mm
Effective depth
d
=
818
mm
Xulim
=
387.78 mm
Xuactual
=
242.949
>
Xulim – Under reinforced.
=
1555.34
KNm
>
659.164
KNm
Moment of resistance
MR
mm
OK.
Max. shear
=
952.34 KN
Design shear
Vu
=
1142.808
KN
Grade of steel
fy
=
415
MPa
Effective depth
d
=
843
mm
Width of section
B
=
800
mm
Nominal shear stress
τve
=
1.693
MPa
Percentage of reinforcement
Pt
=
0.954
Shear strength of concrete
τc
=
0.644
MPa
Permissible shear stress
τcmax
=
3.5
MPa
=
707.667
KN
Dia. of stirrups
=
16
mm
No. of legs
=
4
Area of stirrups provided
=
804.247
in concrete τc < τve < τcmax, Transverse reinforcement is to be designed. Net shear force
Vus
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
mm2 140
Appendix B Spacing provided
Super-structure Analysis & Design Sv
Area of shear reinforcement required Asv =
175
mm
=
406.885
mm2
=
155.103
mm2
1531.8 KNm
mm2
Xu < Df – Xu. Neutral axis lies within flange.
Moment of resistance
M.R.
KNm
OK. Provide 4 bars of 36 mm dia and 4 bars of 36 mm dia. B.3.2 Design for maximum hogging moment at face of pile:
Equivalent BM,
Me
=
934.12
kNm
Dia. of bar 1
Φ1
=
25
mm
Number of bars 1
=
6
Number of bars 2
=
0
=
927
Xulim
=
426.26 mm
Ast provided
=
2945
Xuactual
=
296.56 mm
934.12 KNm
=
909
Effective depth,
Moment of resistance
d
M.R.
mm mm2
KNm
Provide 6 bars of 25 mm dia. B.3.3 Shear design:
Maximum shear force,
Vu
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
KN 149
Appendix B
Super-structure Analysis & Design
Effective depth,
d
=
927
mm
Width,
b
=
400
mm
=
2.45
MPa
=
0.79
=
0.620
Nominal shear stress,
τ ve =
Ve b×d
Percentage of reinforcement, 100
Pt
Ast b×d
Permissible shear stress in concrete,τc
MPa
(IS:456-2000,Cl.40.2.1.)
τcmax
=
3.5
MPa
(IS:456-2000,Cl.40.2.3.)
τc < τve < τcmax, Transverse reinforcement is to be designed as per IS:456 2000, Cl.41.4.3 Yield stress for stirrups
=
415
MPa
Dia. of stirrups
=
12
mm
No. of legs
=
2
Dia. of stirrups
=
12
No. of legs
=
2
=
200
mm
=
405
mm2
Assume spacing of stirrups
Sv
Area of shear reinforcement required Asv =
(τ ve − τ c ) × b × S v 0.87 f y
(IS:456-2000,Cl.40.4.a)
Minimum area of shear reinforcement required Asv =
mm
=
0.4 × b × S v 0.87 f y
88
mm2
(IS:456-2000,Cl.26.5.1.6)
Shear reinforcement provided
=
452
mm2
Provide 2 legged 12 mm dia. and 2 legged 12 mm dia. stirrups @ 200 mm C/C. Summary of reinforcement is given at the end of this chapter and typical R/F detail is given in Appendix H. B.3.4 Check for longitudinal shear:
Neutral axis for composite section from compression face, Effective depth,
d
=
926.5
Modular ratio,
m
=
9.33
Area of tension reinforcement
Ast
=
2945
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
mm mm2 150
Appendix B
Super-structure Analysis & Design
Taking moment about neutral axis, bx 2 = mAst (d − x) 2 Solving this equation, Depth of neutral axis,
x
=
294.68 mm
Area of concrete up to N.A.
=
117874.19
M.I. of concrete area about N.A.
=
3412047111 mm4
Transformed area of steel
=
27488.93
M.I. of steel area about N.A.
=
10973296365 mm4
Net M.I. about N.A.
=
14385343476 mm4
mm2 mm2
As per IRC: 22-1986 Cl.608.2.2, VL =
V . Ac .Y I
Where VL
= The longitudinal shear per unit length at the interface in the section under consideration
V
= Vertical shear due to dead load and live load including impact acting on the section
Ac
= Transformed compressive are of concrete above N.A.
Y
= Distance from the neutral axis to the centre of area under consideration,
I
= Moment of inertia of whole composite section about N.A.
Vertical shear,
V
=
451
KN
Longitudinal shear
VL
=
544
KN
Dia. of stirrups
=
12
mm
No. of legs
=
2
Dia. of stirrups
=
12
No. of legs
=
2
Spacing
=
200
mm
Area of stirrups
=
452
mm2
Yield stress of steel
=
230
MPa
Shear resistance of a pair of stirrups
=
104
KN
No. of stirrups in 1m length
=
5
Total shear resistance
=
520
KN
549
KN.
B.3.5 Check for handling stresses:
Precast beam is checked for handling stresses during lifting and stacking.
Self weight of section = ((0.4*0.725)+((0.2+0.15)*0.25/2)+ ((0.2+0.15)*0.6/2))*25=
10.97
KN/m
Max. hogging moment = 1.5*10.97*2*2/2
=
32.91
KNm
Grade of concrete
fck
=
15
MPa
Grade of steel
fy
=
500
MPa
Width of section
b
=
400
mm
Depth of section
D
=
725
mm
Effective depth
d
=
667
mm
Dia. of main reinforcement
=
16
mm
No. of main reinforcement
=
2
Ast provided
=
402.12
mm2
Xulim
=
306.82
mm
Xuactual
=
80.98
mm
32.91
KNm
Moment of resistance
MR
A Comparative Study Of RCC & Steel Pile Foundation For An Integral Bridge
152
Appendix B
Super-structure Analysis & Design OK.
B.3.6 Design of lifting hook:
Lifting weight of precast beam
=
109.7
Impact during handling
=
1.25
Total tensile force in hook
=
137.125
KN KN
(Although 2 hooks are provided, it is assumed that total load acts on one hook taking errors possible during handling into consideration.) Grade of steel
=
250
MPa
Permissible direct tension
=
140
MPa
Assume dia. of hook
=
25
mm
No. of hooks
=
2
C/S area of the hook
=
981.75 mm2
Area required
=
979
Xulim – Over reinforced.
=
957.06 KNm
>
579.282
Moment of resistance
MR
KNm
OK.
Max. shear
=
144.475
KN
Design shear
Vu
=
216.7125
KN
Grade of steel
fy
=
415
MPa
Effective depth
d
=
643
mm
Width of section
B
=
400
mm
Nominal shear stress
τve
=
0.8425 MPa
Percentage of reinforcement
Pt
=
1.31
Design shear stress
τc
=
0.72
MPa
τcmax
=
3.5
MPa
=
31.507
KN
Dia. of stirrups
=
16
mm
No. of legs
=
4
Area of stirrups provided
=
804.247
mm2
=
200
mm
=
27.143
mm2
=
88.630
mm2