INSDAG GUIDE FOR
THE STRUCTURAL USE OF STEELWORK IN BUILDINGS
Compiled by:
Dr. Rangachari Narayanan Dr. V. Kalyanraman
Published by:
Institute for Steel Development And Growth Ispat Niketan', First Floor 52/1A Ballygunge Circular Road Kolkata 700 019 Phone: (033) 2461 4045/47/66/76, Fax: (033) 2461 4048 Email:
[email protected];
[email protected]^nLneLui March 2003
INSDAG REVISED
Copyright reserved
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PRICE
1 0 0 0 / 52/1 A , Bally gunge CUcuUi Road Kolkata700019
Although care has been taken to ensure, to the best of our knowledge that all the data and information contained herein are correct to the extent that they relate to either matters of fact or accepted practice or matters of opinion at the time of publication, Institute for Steel Development And Growth (INSDAG) assumes no responsibility for any errors in or misinterpretations of such data and/or information or any loss or damage arising from or related to their use. __________________________________ US E M O R E S T E EL  T H E P R EF E RR E D M AT ER I A L O F TH E N E W M IL L EN IUM
FOREWARD INSDAG has played a pivotal role over the last few years in propagating the awareness amongst students, faculties of various engineering institutes and experts and professionals from various industries, about the advantages and benefits of usage of steel in the construction sector. It is now being accepted by most engineering professionals both academic and industrial, that the main stumbling block in the development of the steel construction industry in India is the primitiveness of the methods of design adopted by the Indian codes as against the international codes which allow higher flexibility in design approach. The relevant Indian codes of practice (IS: 8001984 and IS: 8011975) applicable for hotrolled and coldformed steel are based on the "Allowable Stress Design" approach as against the more internationally popular "Limit State Method" approach which has been proved to be technically sound and its use results in optimum economy of the structure.
With the technical contributions from leading academics and professionals, INSDAG has already brought out various publications on the design methodology of steel structures using the Limit State Method of Design (LSM), which have been beneficial to the engineering fraternity in learning the most intricate facets in LSM design.
On request from INSDAG, this publication in the form of a Guide book has been written and compiled by Dr. Rangachari Narayanan and Dr. V. Kalyanraman for the benefit of not only the student community both undergraduate and post graduate level, but also other engineering professionals across the country, since most of the engineering institutions have started including the LSM design in their curriculum and also the engineering professionals need to update themselves with the latest technological advancements. The publication is very timely as it coincides with the revision of IS: 800 1984, which is at its advanced stage.
The entire book has been reviewed by^Dr. T. K. Bandyopadhyay, Deputy Director General and Mr. Arijit Guha, Manager (Civil & Structural). Comments and suggestions received from a large number of faculty member*, have been incorporated. INSDAG expresses its indebtedness to Dr. R. Narayanan and Dr. V. Kalyanraman, academics and researchers of international experience for agreeing to bring'out this publication. Kolkata: February 2003
Special Note The entire document has been written considering Limit State Method of design following stipulations laid down in the relevant British code, BS: 5950 Part 1, 3 & 5 and Eurocode  3 & 4. Since IS: 800 (Code of Practice for General Construction in Steel) is presently being revised to Limit State version, this guide book may undergo certain modifications in some chapters after the publication of revised IS: 800 (LSM version) to accommodate the possible variation in stipulations that are likely to be considered in the revised code. However, this document will be extremely useful to the students of Civil I Structural Engineering to understand the theoretical background associated with advancement in structural steel design based on Limit State Method. ______________________________
CONTENTS Pages 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
General Material General Design Requirements Tension Members Classification of Cross Sections Axially Loaded Columns Design of Members Subjected to Bending Elements Subjected to Axial force and Bending Beams of Hot Rolled Sections Subjectedto 65  65 Portal Frames Multi  Storey Buildings Connection Design Cold Formed Steel Sections Basic Concepts of Composite Construction Composite Beams and Slabs Steel  Concrete Composite Columns
Torsion
23 44 515 16  18 19  21 2231 32  58 59  64 and 66  72 7388 89  109 110  130 131  139 140  153 154  167
LIST OF APPENDICES A. B. C. D. E.
Appendix  A: Terminology Appendix B : Symbols Appendix  C: Relevant Indian Standards Appendix  D: An Approximate Method of Torsion Analysis Appendix  E: Location of Neutral Axis
168  169 170172 173  174 175  180 181  182
PREFACE The low usage of structural steel in India is attributable in part to the prevailing outofdate design practices, which result in uneconomic designs. The relevant Indian Codes of Practice (IS: 800  1984, IS: 801  1975) applicable to the structural use of hotrolled and coldrolled steel are largely based on "Working Stress Method". The more modern "Limit State Design Approach" developed in the 1970's in the West, is technologically sound and results in significant economies in completed structures. This is of particular advantage, as steel is reusable and environment friendly. Compared with competing materials of construction, steel framed buildings have significantly better blast and earthquake resistance and take less than half the time to build. In passing, it may be noted that the Indian Codes of Practice applicable to concrete structures have been revised to conform to Limit State Methodology. This makes the choice of steel in construction an uneconomic proposition. It is also noted that the Code of Practice for steelconcretecomposite buildings (IS: 11384  1985) is based on the Limit State approach but is very limited in its coverage, besides being inconsistent with IS: 800 and IS: 801 written in Working Stress format. This situation posed a challenge, when the Government of India, Ministry of Steel initiated steps to rectify the skills shortage in Steel Construction in 1998. The newly started Institute for Steel Development and Growth (INSDAG) was entrusted with the tasks of (a) improving the teaching standards of Structural Steel Design in Indian Universities, (b) organising incareer courses for enhancing the level of competence of practising engineers (c) publishing design guidance documents for disseminating latest Steel Design Technology (d) organising design competitions for encouraging stateofthe art Structural Steel Designs. As a part of that initiative, an uptodate Resource Material for disseminating the latest Steel Design Technology has been compiled and published in the web site of INSDAG (www.steelinsdag.org). This Design Guide has been complied, as a complementary document and has been drafted after studying the background research work carried out largely in the Western World, which led to the latest British, American, Canadian, Australian and European Codes. Many of the design specifications contained herein have been adopted from these Western Codes and will hopefully serve as a Draft document, when the Bureau of Indian Standards eventually decides to revise the Steel Codes, relevant to Construction. The technical support provided by two young engineers, Mr. S. Sambasiva Rao and Miss P. Usha in compiling this document is gratefully acknowledged. Dr. T.K. Bandhyopadhyay of INSDAG and Professor A. R. Santhakumar of Anna University had reviewed the document before its publication as a draft. Suggestions and comments aimed at improving this document are welcome. We are also grateful to the many engineers  too numerous to mention who suggested improvements in the drafting stage. Rangachari Narayanan V. Kalyanaraman
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SECTION 1: GENERAL 1.1
Scope This Guide provides general recommendations for the design of structural steel work in buildings and allied structures. In the absence of an Indian Standard written in the modern Limit State Format for steel construction, this guide generally follows the provisions contained in British Standard, BS: 5950 (various parts). INSDAG has a Memorandum of Understanding with the British Steel Construction Institute and several supporting documents are available from INSDAG at largely discounted prices for the use of steel designers in India. It will not apply to bridges, chimneys, cranes, tanks, transmission line towers, storage structures, tubular structures, however, general .principles discussed in this guide could be adopted in the design of such structures appropriately.. This guide is in three parts and covers the design of building structures using (i) Hot Rolled Steel section (ii) Cold Rolled Steel sections and (iii) Steel Concrete Composite sections. The guide provides only general advice regarding the various loads to be considered in design. For actual loads to be used reference may be made to IS: 8751987. This document is NOT a statutory document and intended as a guide for students and practicing engineers. It is not intended to replace Codes of Practice.
1.2
Terminology  For the purpose of this Guide, the definitions of various terms are given in Appendix A.
1.3
Symbols  Symbols used in this Guide are defined in Appendix B.
1.4
Reference to other Standards  All the standards referred to in this Guide are listed in Appendix C and their latest version shall be applicable:
1.5
Units and Conversion Factors  The SI system of units is applicable to this Guide. For conversion of system of units to another system, IS: 7861967 (supplement) may be referred.
1.6
Standard Dimensions, Form and Weight The dimensions, form, weight, tolerances of all rolled shapes and other members used in any steel structure shall, wherever available, conform to the appropriate Indian Standards. The dimensions, form, weight, tolerances of all rivets, bolts, nuts, studs, etc. shall conform to the requirements of appropriate Indian Standards, wherever available.
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1.7
Plans and Drawings Plans, drawings and stress sheet shall be prepared according to IS: 6961972 and IS: 9621967. Plans  The plans (design drawings) shall show the complete design with sizes, sections, and the relative locations of the various members. Floor levels, column centres, and offsets shall be dimensioned. Plans shall be drawn to a scale large enough to convey the information adequately. Plans shall indicate the type of construction to be employed; and shall be supplemented by such data on the assumed loads, shears, moments and axial forces to be resisted by all members and their connections, as may be required for the proper preparation of shop drawings. Any special precaution to be taken in the erection of structure from the design consideration shall also be indicated in the drawing. Shop drawings  Shop drawings, giving complete information necessary for the fabrication of the component parts of the structure including the location, type, size, length and detail of all welds, shall be prepared in advance of the actual fabrication. They shall clearly distinguish between shop and field rivets, bolts and welds. For additional information to be included on drawings for designs based on the use of welding, reference shall be made to appropriate Indian Standards. Shop drawings shall be made in conformity with IS: 6961972 and IS: 9621967. A marking diagram allotting distinct identification marks to each separate part of steelwork shall be prepared. The diagram shall be sufficient to ensure convenient assembly and erection at site. It is essential that Steel Designers familiarize themselves with protection methods for structural steelwork, with regard to fire and corrosion. For a great majority of steel buildings which are not subject to alternate wetting and drying, corrosion is NOT a problem. Authentic guidance on protection methods is available from INSDAG. Symbols for welding used on plans and shop drawings shall be according to IS: 8131961
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SECTION 2: MATERIALS
Structural Steel  Ail structural steels used in general construction coming under the purview of this Guide shall, before fabrication conform to IS: 20621984, IS: 85001977 and IS: 19771975, as appropriate. Any structural steel other than that specified in 2.1 may also be used provided that the characteristic yield stresses and other design provisions are suitably modified and the steel is also suitable for the type of fabrication adopted. Other Material  All other materials including manufactured products, welding consumables, steel castings, bolts and nuts and cement concrete shall confirm to the requirements of the appropriate Indian Standards.*
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SECTION 3: GENERAL DESIGN REQUIREMENTS 3.1
Aims of Structural Design The aim of structural design is to provide, with due regard to economy, a structure which is fit for its intended purpose, i.e., it should be capable of fulfilling its intended function and sustaining the design loads for its intended life. The design should facilitate fabrication, erection and future maintenance. The structure should behave as a threedimensional entity. The layout of its constituent parts, such as foundations, steelwork, connections and other structural components should constitute a robust and stable structure under normal loading to ensure that in the event of misuse or accident, damage will not be disproportionate to the cause. To achieve this, it is necessary to define clearly the basic structural anatomy by which the loads are transmitted to the foundations. Any features of the structure, which have a critical influence on its overall stability, can then be identified and taken account of in design. Each part of the structure should be sufficiently robust and insensitive to the effects of minor incidental loads applied during service that the safety of other parts is not prejudiced.
3.2
Overall Stability The designer responsible for the overall stability of the structure should ensure the compatibility of design and details of parts and components. There should be no doubt of this responsibility for overall stability when some or all of the design and details are not made by the same designer.
3.3
General Principles of Limit State Design Structure should be designed considering the Limit States at which they would become unfit for their intended purpose. For verifying the adequacy of the structure, appropriate partial safety factors, based on semiprobabilistic methods described below shall be used. Two partial safety factors, one applied to forces due to loading and another to the material strength shall be employed. allows for; (a) the possible deviation of the actual behaviour of the structure from that of the analysis and design model, (b) the deviation of loads from their specified values and (c) the reduced probability that the various loads acting together will simultaneously reach the characteristic value.
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(e) (f) (g) (h) 3.3.1
the possible deviation of the material in the structure from that assumed in design the possible reduction in the strength of the material from its characteristic value and manufacturing tolerances. Mode of failure (ductile/brittle).
Partial safety factors
In general, calculations take the form of verifying that
where is the calculated factored load effect on the element (like bending moment, shear force etc) and is the calculated factored resistance of the element being checked, and is a function of the nominal value of the material yield strength. is a function of the combined effects of factored dead, live and wind loads. (Other loads  if applicable, are also considered) In accordance with the above concepts, the safety format used in this guide is based on probable maximum load and probable minimum strengths, so that a consistent level of safety is achieved. Thus, the design requirements are expressed as follows:
where
= Design value of internal forces and moments caused by the design Loads, Characteristic Loads. (From IS: 875  1987) a load factor which is determined on probabilistic basis
where
= a material factor, which is also determined on a 'probabilistic basis' when considering yield stress and 1.25 when considering fracture ultimate stress).
It should be noted that IS: 11384  1985 (Code of Practice for Composite Construction) has prescribed for Structural Steel when considering yield stress. The value suggested is therefore consistent with that. 3.3.2
Limit states
(1) A limit state is a state beyond which the structure no longer satisfies the design requirements.
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(2)
(3)
Ultimate limit states are limit states of collapse or other structural failure, which might endanger the safety of people, including: • Excessive deformation / formation of mechanism. • Rupture • Loss of stability • Loss of equilibrium Serviceability limit states are limit states beyond which specified service criteria are no longer met, including those for: • Deflection • Durability • Ponding • Vibration
Thus the following limit states may be identified for design purposes and are provided for in terms of partial factors reflecting the severity of the risks. • Ultimate Limit State is related to the maximum design load capacity under extreme conditions. The partial load factors are chosen to reflect the probability of extreme conditions, when loads act alone or in combination. • Serviceability Limit State is related to the criteria governing normal use. Unfactored loads are used to check the adequacy of the structure. • Fatigue Limit State is important where distress to the structure by repeated loading is a possibility. An illustration of partial safety factors suggested for ultimate load conditions is given in Table 3.1. These values are based on recommendations adopted by Eurocodes. (The Committee formed to review BIS standards have adopted these values). Reference to the Code of Practice for Earthquake Resistant Design should be made, where appropriate. (At the present time, this Code is being revised).
Table 3.1: Recommended Partial safety factors Loading
Yf
Dead Load (unfavourable effects) Dead load restraining uplift or overturning Dead Load + Imposed Load Dead Load + Wind Load Dead Load + Imposed Load + wind Load (Major Load)* Dead Load + Imposed Load (Major Load) + wind Load* Crane Load effects (from BS 5950, Parti) Vertical load Horizontal load Vertical load acting with horizontal load (Crabbing or Surge) Crane load acting with Wind load *If in doubt, calculations for both conditions are needed
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DL 1.35 1.0 1.35 1.35 1.35 1.35
LL
WL


1.05 1.5
1.5 1.5 1.05
1.2
1.6 1.6 1.4 1.2
1.2
1.5


3.4
Loading
3.4.1 Types of loads  For the purpose of computing the maximum stresses in any structure or member of a structure, the following loads and secondary effects shall be taken into account, where applicable: a) b) c) d)
Dead Loads, Imposed loads and Wind loads (as per IS: 875  1987) Earthquake loads (as per IS: 1893  1991) Erection loads; and Secondary effects due to contraction or expansion resulting from temperature changes, creep in steel, shrinkage and creep in contiguous concrete members, differential settlements of the structure as a whole and its components. e) For fire resistant design and fire rating, reference may be made to appropriate specialist publications [For example, Design guide on Structural Fire Safety C1BW14) 3.4.2 Erection loads  All loads required to be carried by the structure or any part of it due to storage or positioning of construction material and erection equipment including all loads due to operation of such equipment shall be considered as 'erection loads'. Proper provision shall be made, including temporary bracings to take care of all stresses due to erection loads. The structure as a whole and all parts of the structure in conjunction with the temporary bracings shall be capable of sustaining these erection loads. Dead load, wind load and also such parts of the live load as would be imposed on the structure during the period of erection shall be taken as acting together with the erection loads. 3.4.3
Temperature effects (a) Expansion and contraction due to changes in temperature of the materials of a structure shall be considered and adequate provision made for the effects produced. (b) The temperature range varies for different localities and under different diurnal and seasonal conditions. Published data should be consulted in assessing the maximum variations of temperature for which provision for expansion and contraction has to be allowed in the structure. (c) The coefficient of expansion for steel shall be taken as 0.000012 per degree centigrade per unit length.
3.5
Robustness Requirements
The requirements for all buildings to maintain Structural integrity (as prescribed by BS: 5950, Part 1 following the Ronan Point Collapse) are given below: Structures should remain as complete integral units even when (due to an accident such as explosion) one of the members fail or become inoperative. This requirement provides a
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significant measure of safety for the occupants and is termed "Structural integrity requirement" or "Robustness requirement". All building frames should be effectively tied together at each principal floor and roof level, in both directions. Either the beams or tie members should be designed so that they provide for the anchorage. Ties may be steel members or steel reinforcement, which are properly anchored to the steel frame work. Each section between expansion joints should be treated as a separate building. These requirements are aimed at ensuring that the collapse of one element of a structure does not trigger the failure of the structure as a whole. By tying the structure together, it is possible to ensure that there is an alternative load path that would help to avoid progressive collapse. Suggested requirements for integrity of buildings of five storeys or more are given below: • •
For sway resistance, no portion of structures should be dependent on only one bracing system. The minimum tie strengths (in respect of the ties referred above) should be internally and externally (but not less than 75 kN for floors and 40 kN at roof level), where  total factored load /. unit area  tie spacing  distance between columns in the direction
• • • • • •
•
At the edge of the structure, columns should be restrained by horizontal ties resisting 1% of column load. Columns should be continuous vertically through the floors, as far as possible. Column splices should be capable of resisting a tensile force of two  thirds of the factored vertical compressive load on the column below the splice. Collapse must not be disproportionate and the role of key elements should be identified. Precast floors must be anchored at both ends against sliding of supporting members. At each storey in turn any single column or beam carrying a column should be capable of being removed without causing collapse beyond a limited portion of the building in the vicinity of the member; in this event substantial permanent deformation may be accepted. This is termed as " Localisation of damage". If the removal of one of these members would cause substantial damage, the member should be designed as a "key element" so that it has a very low probability of failure. Any member or other structural component, which provides lateral restraint vital to the "key element", as well as the "key elements" themselves should be checked for safety and stability, (using appropriate load factors and including the likely accidental loads) in the appropriate directions.
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3.6
General Principles and Design Methods
3.6.1 Methods of design  The design of any structure or its parts may be carried out by one of the methods given in (a) to (d). In all cases, the details of members and connections should be such as to realise the assumptions made in design without adversely affecting any other parts of the structure. (a)
Simple design  The connections between members are assumed moments adversely affecting either the members or the structure as a whole.
not
to
develop
The distribution of forces may be determined assuming that members intersecting at a joint are pin connected. The necessary flexibility in connections may result in some nonelastic deformation of the materials, other than the fasteners. It is necessary to maintain stability against sway and this is ensured complying with provisions of 3.6.2.2 (c). (b)
(c)
Rigid design  The connections are assumed to be capable to developing the strength and / or stiffness required by an analysis assuming full continuity. Such analysis may be made using either elastic or plastic methods. Semirigid design  Some degree of connection stiffness is assumed, but it would be insufficient to develop full continuity. (i)
(ii)
(d)
The moment and rotation capacity of the joints should be based on experimental evidence, which may permit some limited plasticity. On this basis, the design should satisfy the strength, stability and stiffness requirement of all parts of the structure when partial continuity at the joints is to be taken into account in assessing moments and forces in the members. As an alternative, in simple beam and column structures an allowance may be made for the interrestraint of the connections between a beam and a column by an end restraint moment not exceeding 10% of the free moment applied to the beam, assuming this to be simply supported, provided that the frame is braced against side sway in both directions.
Design based on experiments  Where structure is of nonconventional or complex in nature, the design may be based on full scale or model tests subject to the following conditions: (i)
A fullscale test of prototype structure may be done. The prototype shall be accurately measured before testing to determine the dimensional tolerance in all relevant parts of the structure; the tolerances then specified on the drawing shall be such that all successive structures shall be in practical conformity with the prototype. Where the design is based on failure loads, a load factor of not less than 1.5 on the loads or load
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combinations given in Table 3.1 should be used. Loading devices shall be previously calibrated and care shall be exercised to ensure that no artificial restraints are applied to the prototype by the loading systems. The distribution and duration of forces applied in the test shall be representative of those to which the structure is deemed to be subjected. (ii) In the case where design is based on the testing of a smallscale model structure, the model shall be constructed with due regard for the principles of dimensional similarity. The thrusts, moments and deformations under working loads shall be determined by physical measurements made when the loadings are applied to simulate the conditions assumed in the deign of the actual structure. 3.6.2
Ultimate Limit States
3.6.2.1 Limit state of strength (a) General  In checking the strength and stability of the structure the loads should be multiplied by the relevant ^factors given in table 3.1. The factored loads should be applied in the most unfavorable realistic combination for the part or effect under consideration. The load capacity of each member and its connections, as determined by the relevant provisions of this Guide, should be such that the factored loads would not cause failure. 3.6.2.2 Stability limit state (a) General  In considering the overall stability of any structure or part, the loads should be increased by the relevant factors given in table 3.1. The designer should consider overall frame stability, which embraces stability against overturning, and sway stability as given below. (b) Stability against overturning  The factored loads should not cause the structure or any part of the structure (including the foundations) to overturn or lift off its seating. The combination of imposed and dead loads should be such as to have the most severe effect on overall stability. Account should be taken of probable variations in dead load during construction or other temporary conditions. (c) Sway stability  All structures, including portions between expansion joints, should be adequately stiff against sway. To ensure this, in addition to designing for applied horizontal loads, a separate check should be carried out for notional horizontal forces.
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These notional forces may arise from practical imperfections such as lack of vertically and should be taken as the greater of: 1% of factored dead load from that level, applied horizontally; 0.5% of factored total gravity load (dead plus vertical imposed) from that level, applied horizontally. The notional forces should be assumed to act on all structures in any one orthogonal direction at a time and should be applied at each roof and floor level or their equivalent. They should be taken as acting simultaneously with vertical loads. The notional force should not be: • • • •
applied when considering overturning; combined with horizontal loads; combined with temperature effects; taken to contribute to net shear on the foundations.
Sway stability may be provided for example by braced frames, joint rigidity or by utilising staircase, lift cores and shear walls. Whatever system is used, reversal of loading should be accommodated. The cladding, floors and roof should have adequate strength and be so secured to the structural framework as to transmit all horizontal forces to the points of sway resistance. Where such sway stability is provided by construction other than the steel framework, the steelwork designer should state clearly the need for such construction and the forces acting upon it. 3.6.2.3 Foundation design  The design of foundations should accommodate all the forces imposed on them. The stiffness (deformation) of the foundation should reflect the boundary condition assumed in the analysis model of the structural system. Attention should be given to the method of connecting the steel superstructure to the foundations and the anchorage of any holding down bolts. Where it is necessary to quote the foundationreactions it should be clearly stated whether the forces and moments result from factored or unfactored loads. Where they result from factored loads the relevant factors for each load in each combination should be stated. 3.6.2.4 Fatigue  Fatigue need not be considered unless a structure or element is subjected to numerous significant fluctuations of stress. Stress changes due to fluctuations in wind loading need not be considered but account should be taken of windinduced oscillations. 3.6.2.5 Earthquake Resistant Design  The standards appropriate for earthquake resistance of buildings in various parts of the country should be carefully considered and suitable provisions should be made taking into account the Capacity design and requisite ductility.
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3.6.3
Serviceability Limit State
3.6.3.1 Deflection  The deflection under serviceability loads of a building or building component should not impair the strength of the structure/components or cause damage to the finishing. When checking for deflections the most adverse and realistic combination of service loads and their arrangement should be checked by elastic analysis. Table 3.2 gives recommended limitations for certain structural members. Circumstances may arise where greater or lesser values would be more appropriate. (Where the deflection due to Dead + Live load combination is likely to be excessive, consideration should be given to precamber the beams)
Table 3.2: Deflection limits other than for pitched roof portal frame ( a ) Deflection on beams due to unfactored imposed loads Cantilevers Length / 180 Beams carrying plaster or other brittle Span / 325 finish All other beams Span / 325 ( b ) Horizontal deflection of columns other than portal frames due to unfactored imposed and wind loads Tops of columns in singlestorey Height / 325 buildings In each storey of a building with more Height of storey under consideration / 325 than one storey ( c ) Crane gantry girders Refer to IS: 800  1984 NOTE 1. On lowpitched and flat roofs the possibility of ponding needs consideration for Composite Construction using metal decking.
3.6.3.2 Durability  Several factors affecting the durability of the buildings under conditions relevant to their intended life, are listed below: (a) (b) (c) (d) (e)
the environment; the degree of exposure; the shape of the members and the structural detailing the protective measure if any; whether maintenance is possible.
Detailed advice on protection of steel for various environmental/exposure conditions is contained in an INSDAG publication titled "Corrosion Protection for Structural Steel". 3.6.3.3 Ponding a) All roofs with a slope of less than 5% must be checked to ensure that rainwater cannot collect in pools. Allowance must be made for possible construction inaccuracies, settlements of foundations, deflections of roofing
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materials and structural members and the effects of precamber. This also applies to floors of car parks and other opensided structures. b) Precambering of beams can be used to reduce the likelihood of rainwater collecting in pools, provided that rainwater outlets are appropriately located. c) Where the roof slope is less than 3%, it must be checked that collapse cannot occur due to the weight of water (or snow if applicable) collected in pools, which might be formed due to the deflection of structural members or roofing material. 3.6.3.4 Dynamic effects a) The design must make suitable provision for the effects of imposed loads, which can induce impact, vibration, etc. b) Vibration caused by machines and oscillation caused by harmonic resonance must be considered, and provided for. c) To avoid resonance, the natural frequencies of structures or parts of structures must be sufficiently different from those of the excitation source. d) Table 3.3 gives limiting values for the natural frequency or the alternative total deflection to avoid resonance.
Fig 3.1 Vertical deflections to be considered
sagging in the final state relative to the straight line joining the supports, precamber (hogging) of the beam in the unloaded state, (state 0) variation of the deflection of the beam due to permanent loads immediately afterloading, (state 1) variation of the deflection of the beam due to the variable loading plus any time dependant deformations due to the permanent load, (state 2)
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15
SECTION 4: TENSION MEMBERS 4.1 Limiting Load on Plates in Tension In the design of tension members, the loadcausing yield across the section is taken as one of the limiting loads. The corresponding design strength for the member under axial tension is given by
where, is the yield stress of the material (in MP a), is the gross area of cross section in the partial safety factor for failure in tension by yielding. (The suggested value of The design strength in tension as governed by net crosssection at the hole,
and Ym is
is given by
where, is the ultimate stress of the material, is the net area of the cross section after deductions for the hole and is the partial safety factor against ultimate tension failure by rupture (The suggested value of . Similarly threaded rods subjected to tension could fail by rupture at the root of the threaded region and hence net area, is the root area of the threaded section. The lower value of the design tension capacities, as calculated by Eqn. 4.1 and 4.2, will govern the tensile design strength of a plate with holes.
Fig. 4.1 Plates with Bolt Holes under Tension 16
When multiple holes are arranged in a staggered fashion in a plate (Fig 4.1), the net area corresponding to the staggered section will be given by
(4.3) where, n is the number of bolt holes in the staggered section and the summation over is carried over all inclined legs of the section. The design strength in tension will be obtained by substituting the value of in Eqn. 4.2 4.2
Limiting Load on Angles under Tension
When a connection is made through one leg of an angle, the stress in the outstanding leg at the ultimate stage will be closer to the yield stress (due to shear lag) while the net section of the connected leg will often reach the ultimate stress The tensile strength of angles connected by one leg, is evaluated accounting for this phenomenon by 1. 2.
limiting the stress in the outstanding leg to (the yield stress) and the connected leg having holes to (the ultimate stress).
In addition, the potential for "block shear failure" should also be assessed. The design tensile strength, will be the minimum value obtained from (4.4), (4.5), and (4.6) below: (i) Strenfith as governed by the yielding of gross section:
where,
is the gross area of the angle section.
(ii) Strength as governed by tearing at net section:
where, and are the yield and ultimate stress of the material, respectively. and are the net area of the connected leg and the gross area of the outstanding leg, respectively, accounts for the end fastener restraint effect. when the number of fasteners when the number of fasteners is 3 the number of fasteners is 1 or 2 and if the connection is adequately welded
17
if
(iii) Strength as governed by block shear failure: A tension member may fail along end connection due to block shear as shown in Fig. 4.2. If the centroid of bolt pattern is not located between the heel of the angle and the centerline of the connected leg, the connection shall be checked for block shear strength. The corresponding design strength in tension shall be evaluated as the lower of the value obtained from the following equations.
Fig. 4.2 Block Shear Failure
where, and = minimum gross and net area in shear along a line of transmitted force, respectively, and = minimum gross and net area in tension from the hole to the toe of the angle, perpendicular to the line of force, respectively. 4.3
Maximum Slenderness Ratio
The maximum slenderness ratio (length/least radius of gyration of the cross section) of a tension member is limited to 400 (This will provide a margin of safety for members normally acting as ties but subject to reversal of stresses due to wind and earthquake. It will also provide a margin for avoiding excessive selfweight deflection).
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SECTION 5: CLASSIFICATION OF CROSS SECTIONS 5.1
Basis
The proposed classification of cross sections is illustrated by considering the idealised momentrotation characteristics of a symmetrical beam subjected to incremental flexural loading continued till its collapse. A beam capable of developing full plasticity would exhibit an idealised elastic/plastic momentrotation curve as shown in Fig. 5.1. At failure, the stress distribution across the section will consist of two rectangles and a significant rotation will take place. Such a stocky section is termed as a 'plastic' section, and it exhibits considerable "ductility" is the rotation at the onset of plasticity; is the lower limit of rotation for treatment as a plastic section)
Fig. 5.1 Elastic/plastic momentrotation curve. On the other hand, a cross section may develop fully plastic stress distribution across the entire cross section but may not have adequate ductility The horizontal part of the momentrotation diagram will be limited. Such a crosssection is termed 'compact' section. If the section were to be even more slender (higher ratios of it may only be able to sustain an elastic moment up to the attainment of yield strength in the extreme fibres, with a triangular stress distribution. This section is termed as 'semicompact'. If the section were to be further more slender still (i.e. yet higher values of local buckling would occur before the attainment of yield stress in the extreme fibres, i.e. before attaining the theoretical elastic moment capacity. Such a section is termed as 'slender'. Assuming that the flange plate or the web does not buckle locally, these four different modes of behaviour can be expressed graphically on a plot of stress against strain at the
19
extreme fibres (Fig. 5.2). These different modes of behaviour can also be shown by the stress patterns, as in Fig. 5.3.
Fig. 5.2 Stress/strain relation of extreme fibres for different classes of sections
Fig. 5.3 Bending stress distribution for different classes of sections
The class of a section is determined by the lowest class of all its constituent elements, i.e. flange plates and web plate. The class of section determines its resistance (e.g. Moment resistance, shear resistance etc.).
Only plastic sections can be used in forming plastic collapse mechanisms. Compact sections can generally be used in simply supported beams failing soon after reaching at one section. In elastic design, semicompact sections are to be used with the understanding that they will fail at The slender section design is discussed in the section on ColdForm Steel member design.
20
Table 5.1. Limits on Width to Thickness Ratio of Plate Elements*
Type of Element
Type of Section
Outstand element of Welded compression flange Rolled Internal element of Welded compression flange Rolled Web with neutral axis at mid depth Web under uniform compression Single/double angle Tstems Circular tube with outer diameter D
All Welded Rolled Rolled
where are the limits for b/t width of the flange overhang depth of the web outer diameter of the circular tubular section thickness of the plate
* This table is derived from BS 5950: Part 1.
21
SECTION 6: AXIALLY LOADED COLUMNS
6.1
Axial Compression Resistance of Columns
The axial load resistance of steel columns is governed by the type of cross section and the axis of buckling. Axially loaded columns having a slenderness ratio values below are "stocky" and will fail by yielding across the entire cross section. For columns having values in excess of
the following
computations are necessary. The choice of axis of buckling to obtain the design strength is not always clear, so calculations have to be canned out in respect of both principal axes and the lower value of load resistance chosen.
The design axial load resistance for a member subjected to axial compression is given
(Note that no calculations for is needed when as the column would fail by squashing at The compressive strength curves obtained for the various types of sections are shown in Fig 6.1.
22
Fig. 6.1 Compressive strength curves for struts for different values'of 250 Mpa; Based on BS 5950: Part 1J
[For
=
Table 6.1: Choice of appropriate values of
Welded Sections: for cross sections fabricated by welding of plates 20 N/mm2 should reduce the value of Table 6.2 gives the ultimate compressive stress values in compression members corresponding to various values of and for Graphs (similar to Fig. 6.1) and Table 6.2 may be constructed for different values of using equations 6.1 to 6.6. 23
Table 6.2: Ultimate Compressive stress
6.2
i
Effective Length of Columns
Designs of columns have to be checked using the appropriate effective length for buckling about both the strong and weak axes. Effective length, may be regarded as the equivalent length of a pinended column having the same cross section, which would be expected to have the same strength and stiffness as the column being designed. The recommended effective lengths for design purposes are given below
24
6.3 Cross Sectional Shapes for Compression Members and Built  Up Columns When compression members are required for large structures like bridges, builtup sections will be used. Cross section shapes of rolled steel compression members and builtup or fabricated compression members are shown in Fig. 6.2 and Fig. 6.3. For preliminary calculations, approximate values of radii of gyration given in Fig. 6.4 for various builtup sections may be employed.
Fig 6.2: Cross Section Shapes for Rolled Steel Compression Members
( d ) Plated I Section
(e) Built  up I Section
Fig 6.3: Cross Section Shapes for Built  up or fabricated Compression Members
25
Fig 6.4: Approximate radii of gyration (Continued in next page) 26
Fig 6.4: Approximate radii of gyration 6.4
General Guidance for Connection Requirements
When compression members consist of different components, which are in contact with each other and are bearing on base plates or milled surfaces, they should be connected at their ends with welds or bolts. When welds are used, the weld length must be not less than the maximum width of the member. If bolts are used they should be spaced longitudinally at less than 4 times the bolt diameter and the connection should extend to at least times the width of the member. When single angle discontinuous struts connected by a single bolt are employed, it may be designed for 1.25 times the factored axial load and the effective length taken as the centretocentre distance of the intersection at each end. Single angle discontinuous struts connected by two or more bolts in line along the member at each end may be designed for the factored axial load, assuming the effective length to be 0.85 times the centre to centre distance of the intersection at each end.
27
For double angle discontinuous struts connected back to back to both sides of a gusset or section by not less than two bolts or by welding, the factored axial load is used in design,with an effective length conservatively chosen. (A value between is chosen depending upon the degree of restraint provided at the ends). All double angle struts must be tack bolted or welded. The spacing'of connectors must be such that the largest slenderness ratio of each component member is neither greater than 60 nor less than 40. Spacing of tack bolts or welds should be less than 600 mm. A minimum of two bolts at each end and a minimum of two additional connectors spaced equidistant in between will be required. Solid washers or packing plates should be used inbetween. For member thickness up to 10 mm, M16 bolts may be used unless otherwise noted. For members of large thickness M20 bolts may be used. The following guide values are suggested for initial choice of members: (i)
Single angle size: 1/30 of the length of the strut
(ii)
Double angle size: 1/35 of the length of strut
(iii)
Circular hollow sections diameter = 1/40 length
6.5
Design Considerations for Laced and Battened Columns
The two channel constituents of a laced column, shown in Fig. 6.5(a) and 6.5 ( b ) have a tendency to buckle independently. The load that these tying forces cause may be assumed to cause a shearing force equal to 2.5% of axial load on the column. (Additionally if the columns are subjected to moments or lateral loading the lacing should be designed for the additional bending moment and shear). To prevent local buckling of unsupported lengths between the two constituent lattice points (or between two battens), the slenderness ratio of individual components should be less than 50 or 70% of the slenderness ratio of the built up column (whichever is less). In laced columns, the lacing should be symmetrical in any two opposing faces to avoid torsion. Lacings and battens are not combined in the same column. The inclination of lacing bars from the axis of the column should not be less than 40° nor more than 70°. The slenderness ratio of the lacing bars should not exceed 145. The effective length of lacing bars is the length between bolts for single lacing and 0.7 of this length for double lacing. The width of the lacing bar should be at least 3 times the diameter of the bolt. Thickness of lacing bars should be at least l/40th of the length between bolts for single lacing and 1/60 of this length for double lacing (both for welded and bolted connections). The slenderness ratio formula:
of battened columns shall be calculated using the following (6.7)
28
where, is lower value of slenderness of the individual vertical members between centre to centre of batten intervals and is slenderness of the overall column, using the radius of gyration of the whole built up section. The imperfection factor
is calculated from (6.8)
The strength of the battened column is evaluated from = effective slenderness with computed as given in Eqn. (6.8) = calculated using values given in Eqn. (6.7)
Fig. 6.5 Builtup column members
29
6.6
Base Plates for Concentrically Loaded Columns
For a purely axial load, a plain square steel plate or a slab attached to the column is adequate. If uplift or overturning forces are present, a more positive attachment is necessary. These base plates can be welded directly to the columns or they can be fastened by means of bolted or welded lug angles. These connection methods are illustrated in Fig. 6.6.
Fig. 6.6 Column base plates A base plate welded directly to the columns is shown in Fig. 6.6 ( a ) . For small columns these plates will be shopwelded to the columns, but for larger columns, it may be necessary to ship the plates separately and set them to the correct elevations. For this second case the columns are connected to the footing with anchor bolts that pass through the lug angles, which have been shopwelded to the columns. This type of arrangement is shown in Fig. 6.6 When there is a large moment in relation to the vertically applied load a gusseted base may be used. If column base plates are insufficient to develop the applied bending moment or if thinner plates are used, some form of stiffening must be provided. Concrete support area should be significantly larger than the base plate area so that the applied load can disperse satisfactorily on to the foundation. To spread the column loads uniformly over the base plates, and to ensure there is good contact between the two, it is customary not to grind or machine the underside of the base plate, but grout it in place.
Columns supporting predominantly axial loads are designed as being pinended at the base. The design steps for a base plate attached to an axially loaded column with pinned base are explained below. Procedure for empirical design of a slab base plate for axial load only (pinned connection) 1. Determine the factored axial load and shear at the column base. 2. Decide on the number and type of holding down bolts to resist shear and tension. The chosen number of bolts is to be arranged symmetrically near corners of base plate or next to column web, similar to the arrangement sketched in Fig. 6.6. 3. Maximum allowable bearing strength = 0.4 (where = cube strength ofconcrete) Actual bearing pressure to be less than or equal to 0.4 4. Determine base plate thickness For
channel, box or
columns but not less than the thickness of the flange of the
supported column. = pressure in on underside of plate, assuming a uniform distribution. = larger plate projection from column [See Fig. 6.7] = smaller plate projection from column = design strength of mild steel plate, but not greater than divided by
Fig. 6.7 Base plates subjected to concentric force 5. Check for adequacy of weld. Calculate the total length of weld to resist axial load. 6. Select weld size. 7. Check shear stress on weld. 8. Vector sum of all the stresses carried by the weld must not exceed the design strength, of the weld. 9. Check for bolt. Check maximum coexistent factored shear and tension, if any, on the holding down bolts. 10. Check the bolts for adequacy.
SECTION 7: DESIGN OF MEMBERS SUBJECTED TO BENDING 7.1
General
The main failure modes of hot rolled beams of compact or plastic cross section are as follows: •
If the beam is prevented from buckling laterally, and the component elements are compact or plastic, then the failure will be triggered by excessive flexure and the collapse will follow the formation of plastic hinges. Such a beam is termed restrained beam".
•
"Long beams" which are not suitably braced in the lateral direction will fail by a combination of lateral deflection and twist. These are termed "unrestrained beams".
•
Fabricated plate girders may fail by web shear buckling or local buckling of a flange. This type of failure is unlikely to be encountered in hot rolled sections.
•
Local failure by (a) shear yield of the web. (b) local crushing of the web or (c) buckling of thin flanges may sometimes be encountered. These are to be eliminated by provision of web stiffeners for (a) and (b) and the welding of additional flange plates to reduce the plate ratio, in the case of (c).
7.1.1 Laterally restrained beams "Laterally Restrained Beams" are those, which will not fail by lateral instability. Lateral Instability or Lateral Torsional Buckling of beams can be prevented by providing full restraint to the compression flange of member. Adequate restraint may be regarded as being available if there is a positive connection of a floor or other construction fixed to the compression flange capable of resisting a lateral force of not less than 2.5% of the maximum factored force in the compression flange of the member. The design adequacy of a laterally restrained beam is verified using the following criteria: • • • •
lateral restraint force bending resistance of the cross section shear resistance of the cross section combined bending and shear at locations where there are (a) combinations of maximum factored bending moment and coexistent shear and (b) combinations of maximum factored shear force and the coexistent bending moment.
7.1.2. The influence of local buckling of flanges and webs In section 5, all rolled steel sections used as beams are classified in four ways in order to reflect the effect of local buckling of the beam elements.
• Slender  the elastic moment capacity of the cross section can NOT be attained • Semicompact  The elastic moment capacity of the cross section can be attained, but NOT the plastic moment capacity • Compact  The plastic moment capacity can be attained, but the cross section has little rotation capacity. • Plastic  as for compact, but there is sufficient rotation capacity in the cross section, so that the frame can be designed by plastic methods. Hot rolled sections used as beams are generally of the "plastic" or "compact" cross sections. For the plastic or compact sections, the design bending resistance of the cross section is given by
Slender cross sections will not be able to resist a moment equal to the elastic moment resistance, as the maximum fibre stress at failure will be less than The design bending resistance in these sections is given by 7.1.3 Span of beams: The span of a beam should be taken between the effective points of support. 7.1.4 Length of cantilevers: The length of a cantilever should be taken as the distance from the effective point of the support to the tip of the cantilever. 7.1.5 General conditions: All members in bending should meet the following conditions.
(a) At critical points the combination of maximum moment and coexistent shear,and the combination of maximum shear and coexistent moment should be checked at the ultimate limit state (b) The deflection limits prescribed under "serviceability Limits" (Table 3.2) should be adhered to. (c) Unless the compression flange has full lateral restraint, the resistance of the member to lateral torsional buckling should be checked in accordance with specifications detailed in 7.3 section (d) Local buckling should be considered as given in Table 5.1. (e) When loads or reactions are applied through the flange to the web, the conditions of 7.2.5 and 7.2.6 for web buckling and web bearing should be met. 7.2
Shear
7.2.1 Plastic and compact sections The design shear resistance,
Where
of a plastic or compact cross section is taken as
= shear area given by the following for the three cases:
(a) Rolled and channel sections, load parallel to web (b) Builtup sections and boxes, load parallel to webs (c) Solid bars and plates Where = thickness of the web = Total depth of the section = depth of the web = area of the plate or bar. 7.2.2 Elastic shear stress In sections where webs vary in thickness or have holes significantly larger than those required for fasteners, the shear stress should be calculated from first principles assuming elastic behaviour. 7.2.3 Moment resistance with low shear load Where the design shear force of the cross section as the value obtained from • •
is less than 0.6 times the design shear resistance the design moment resistance,should be taken
Equation (7.1) for plastic and compact sections Equation (7.2) for semicompact sections and
34
• Equation (7.3) for slender sections When the depth to thickness ratio,
of a web exceeds
where
then it
should be checked for shear buckling in accordance with the requirements set out under Section 7.4. 7.2.4 Moment resistance with high shear load Where the design shear force exceeds 0.6 times the design shear resistance, (defined in equation 7.4) the moment resistance, should be taken as follows. (a) For plastic or compact sections:
and
is taken as follows:
For sections with equal flanges: the plastic modulus of the shear area, For sections with unequal flanges: the plastic modulus of the gross section less the plastic modulus of that part of the section remaining after deduction of the shear area. 7.2.5 Web buckling To prevent the web buckling under point loads or reactions (applied through the compression flange) the following check is required to be carried out on all beams The buckling resistance,
is given by
Fig. 7.1 Effective width for web buckling If the applied load or reaction (as the case may be) exceeds should be provided.
suitable stiffness
7.2.6 Web Bearing For all beams, the web crippling resistance should also be checked at its junction with the flange to the flangetoweb connection at a slope of 1:2.5 of the plane of the flange. The buckling resistance in crippling, is given by
where
= crippling resistance of the webin buckling =design yield stress of the web = length obtained by dispersion through the flangetoweb connection at a slope of 1:2.5 to the plane of the flange.
Fig. 7.2 Effective width of web bearing If the applied load or the reaction exceeds the crippling resistance of the web, suitably designed bearing stiffeners should be provided.
7.2.7 Plastic and compact beams with web openings Beams with web openings are frequently required for passing service ducts. Beams having (a) an isolated hole (b) a series of web openings at regular intervals are included in this guide. When designing holes in webs, the following aspects should be kept in view: • • • •
The effect of bending The possible need to provide stiffening around the hole The effect of openings on slender webs (covered in the section 7.4) The effect of opening on the stiffness of the section and deflections.
Unreinforced circular openings having a diameter not exceeding 10% of the web depth may be located within the web of compact beams without considering the net section properties, provided that • •
the holes are located within the middle third of the depth and middle half of the span of the member. the load on the member is substantially uniform and no point loads are situated within a distance from the edges of the hole, equal to the depth of the girder.
•
the spacing between the centres of any two adjacent openings measured parallel to the axis of the member is at least 2.5 times the diameter of the larger opening.
•
the factored maximum shear at the support does not exceed 60% of the shear resistance of the section.
When the hole diameter exceeds 10% of the depth of the girder, or if any of the above conditions are not satisfied, the net section properties should be computed and the adequacy of the design should be verified. If web reinforcement is provided, it may be either around the hole or as a flat reinforcement carried past the opening for such a distance that the local shear stress due to the load being transferred from the reinforcement does not exceed 7.3
Laterally Unrestrained Beams of Plastic and Compact Sections 7.3.1
Lateral torsional buckling of symmetric sections The elastic critical moment resistance of a symmetrical I beam subjected to equal end moments undergoing lateral torsional buckling between points of lateral support is obtained as
Comparing the two cases covered by Eqns. (7.6) and (7.7) the ratio of the tw constants is often termed "the equivalent uniform moment factor"
Its value is a
direct measure of the severity of a particular pattern of moments relative to the basic case. This is clear from Fig.7.3. Several factors affect the lateral stability of beams and these are outlined below: (a)
Support conditions
Lateral buckling involves three kinds of deformations, namely lateral bending, twisting and warping. Various types of end conditions are consequently possible but the supports should either completely prevent or offer no resistance to each type of deformation (Solutions for partial restraint conditions are complicated). The effect of various support conditions is taken into account by way of a parameter called effective length. For a beam with simply supported end conditions and no intermediate lateral restraint, the effective length is equal to the actual length between the supports. The effective length factor would indirectly account for the increased lateral and torsional rigidities provided by the restraints. As an illustration, the effective lengths appropriate for different end restraints according to BS 5950 are given in Tables 7.1 and 7.2. (b)
Level of application of transverse loads (Stabilising and destabilising loads)
The lateral stability of a transversely loaded beam is dependent on the arrangement of theloads as well as the position of application of the loads with respect to the centroid of thecross section. A load applied above the centroid of the cross section causes an additional overturning moment and becomes more destabilising than when the same load is applied at the centroid. On the other hand, if the load is applied below the centroid, it produces astabilising effect.
Table 7.1 Effective length of beams of Compact Plastic Cross section between supports
Table 7.2. Effective length,
for cantilever of length
(c)
Influence of the type of loading
So far, only the basic case of beams loaded with equal and opposite end moments has been considered. But, in reality, loading patterns would vary widely from the basic case. Cases of moment gradient, where the end moments are unequal, are less prone to insiability and this beneficial effect is taken into account by the use of "equivalent uniform moments". In this case, the basic design procedure is modified by comparing the elastic critical moment for the actual case with the elastic critical moment for the basic case. The equivalent uniform moment
is defined as
where m = equivalent uniform moment factor and
Fig. 7.3 Equivalent uniform moment
40
bending moment.
(d)
Slenderness correction factor ( n )
For situations, where the maximum moment occurs away from a braced point, e.g. when the beam is uniformly loaded in the span, a modification to the slenderness, may be used. The allowable critical stress is determined for an effective slenderness, where n is the slenderness correction factor, as illustrated in Fig.7.4 for a few cases of loading.
Fig 7.4 Slenderness Correction Factor
41
7.3.2 Limitations of the elastic buckling theory for beams Direct use of the theory described in the foregoing pages for design purposes is in appropriate because •
Formulae (such as Eqns. 7.6 and 7.7) are too complex for routine use.
•
In any case, these are derived on the basis of elastic behaviour and cannot be extrapolated to check the ultimate bending resistance. Significant differences exist between the assumptions forming the basis of the theory and the observed behaviour of beams under ultimate load tests.
The beam slenderness
can be expressed in a nondimensional form using
Fig.7.5 Comparison of test data (mostly I sections) with theoretical elastic critical moments
Fig 7.5 compares a typical set of lateral torsional buckling test data using actual hot rolled sections with theoretical elastic critical moments given by Eqn 7.6, using the nondimensional slenderness so that the results from many test series (using different 42
In region I, lateral instability does not influence the design as these beams will collapse by developing full plasticity.
Region II covers much of the practical range of beams without lateral restraint. The designs must be based on inelastic buckling, with suitable modifications to account for residual stresses and geometric imperfections. The design method will consequently involve some degree of empiricism.
Region III covers beams, which largely fail by elastic instability. The formulae derived so far will provide an upper bound.
7.3.3
Design method
As discussed previously the basic theory of elastic lateral stability cannot be directly used for design purposes because of limitations and its extension to the ultimate range. A simple method of computing the buckling resistance of compact and plastic beams is given below and is analogous to the PerryRobertson approach for columns. (See Fig 7.6) The three categories of beams are listed under section 7.3.2. The buckling resistance moment, is obtained as the smaller root of the equation
43
where = bending strength allowing for susceptibility to lateral torsional buckling and are supplied in Tabulated form by steel makers. For more slender beams,
is a function of
given by, (7.16)
= a buckling parameter, which may be conservatively taken as 0.9 for rolled steel I sections and channels and 1.0 for all other sections.
44
7.4
Plate Girders
7.4.1
General
A fabricated plate girder is employed for supporting heavy loads over long spans. Stiffeners are provided at a spacing of as shown in Fig. 7.7. In these girders, the bending moments are assumed to be carried by the flanges by developing compressive and tensile forces and shear is carried by the web. To effect economy, the web depth is chosen to be large enough to result in low flange forces for the design bending moment.
45
7.4.1.1 Recommended Proportions (Indicative values) Span to Depth Ratios: The recommended span / depth ratios for initial choice of crosssection in a plate girder used in a building are given below as indicative values: i. ii. iii.
Constant depth beams used in simplysupported composite and noncomposite girders with concrete decking Constant depth beams in continuous composite and noncomposite girders Simplysupported crane girders
Web proportions: When the web plate will not buckle. The design, in such cases, is similar to rolled steel beams. In the design of thin webs with shear buckling should be considered. In general we may have an unstiffened web, a web stiffened by transverse stiffeners (Fig. 7.7) or a web stiffened by both transverse and longitudinal stiffeners (Fig. 7.8). By choosing a minimum web thickness the selfweight is reduced, but the webs vulnerable to buckling may have to be stiffened if necessary. The recommended web thickness are (Fig. 7.7): i. For unstiffened web ii. For stiffened web
In practice, however, is rarely used  if at all  in plate girders used in buildings and bridges. Similarly, d/t exceeding 250 is rarely used. To avoid flange buckling into web, i. For unstiffened web where
is the design stress of flange material.
ii. For stiffened web
Flange proportions: Generally the thickness of flange plates is not varied along the spans for plate girders used in buildings. For noncomposite plate girder the width of flange plate is chosen to be about 0.3 times the depth of the section as a thumb rule. It is also necessary to choose the breadth to thickness ratio of the flange such that the section classification is generally limited to plastic or compact sections only This is 46
to avoid local buckling before reaching the yield stress. For preliminary sizing, the overall flange widthtothickness ratio may be limited to 24. For the tension flanges (i.e. bottom flange of a simply supported girder) the width can be increased by 30% if needed.
Fig. 7.8 End panel strengthened by longitudinal stiffener
Stiffener spacing: Vertical stiffeners are provided close to supports to increase the bearing resistance and to improve shear capacity. Horizontal stiffeners are generally not provided in plate girders used in buildings. Intermediate stiffeners also may not be required in the midspan region. When vertical stiffeners are provided, the panel aspect ratio a/d (see Fig.7.7) is chosen in the range of 1.2 to 1.6. The web is able to sustain shear in excess of shear force corresponding to because of vertical stiffeners. Vertical stiffeners help to support the tension field action of the web panel between them. Where the end panel near support is designed without using the tension field action a smaller spacing of is adopted. Sometimes double stiffeners are adopted near the bearing (see Fig. 7.9) and in such cases the overhangs beyond the supports are limited to 1/8 of the depth of the girder.
7.4.2
Design methodology
7.4.2.1 Moment Resistance  Moment resistance resistance of the flanges. Thus,
where,
is computed from the plastic moment
The design stress of the flange steel = Plastic section modulus of flanges about the transverse axis of the section. = Material safety factor for steel (= 1.15)
47
7.4.2.2
Shear Resistance
Thin webs are designed either with or without stiffeners. These two cases are described individually below. Webs without intermediate stiffeners: The shear resistance of unstiffened webs is limited to its elastic shear buckling resistance, given by
The values for for webs, which are not too slender (see Table 7.4) depend on the slenderness parameter defined as
where,
= Elastic critical shear strength values to be used in design for different values of a/d and d/t are tabulated in Table  7.3. Design strength of web = = Material safety factor for steel (= 1.15)
The elastic critical stress has been simplified and given based on a/d and t/d Table as given in Table 7.3 7.3: Elastic critical stress related to aspect ratio
48
Table 7.4 gives the values of
for design purposes.
Note that for very slender webs is limited to elastic critical shear stress. In other cases the value of is a function of design stress of web steel, Webs with intermediate stiffeners: The shear resistance of the plate girders with intermediate stiffeners may be improved by the following two ways. i)
Increase in buckling resistance due to reduced a/d ratio.
ii)
The web develops tension field action and thus resists considerably larger stress than the elastic critical strength of web in shear.
Fig.7.9 shows the diagonal tension fields anchored between top and bottom flanges and against transverse stiffeners on either side of the panel. The full shear buckling resistance is calculated as,
The first term co mprises of critical elastic stress an d the tension field strength of the panel i.e., The term represents the contribution of the flanges to the post buckling strength and depends on plastic moment capacity of the flanges The flanges support the pull exerted by the tension field. When the flanges reach their ultimate capacity they form hinges. is a parameter that relates to the plastic moment capacity of the flange and the web described later. 49
The flangedependent shear strength is simplified and given as
where, When the girder is to resist pure shear, then
However in presence of overall bending moment, the contribution of flange to shear resistance will be reduced by the longitudinal stress induced because of overall bending moment, by the factor When approaches at maximum moment region, the factor nearly becomes zero and hence the contribution of flanges to shear resistance will become negligible. The plastic moment capacity of the web,
7.4.3
is given by
End panels
For tension field action to develop in the end panels, adequate anchorage should be provided all around the end panel. The anchor force required to anchor the tension field force is
The end panel, when designed for tension field will impose additional loads on end post and hence it will become stout [Fig. 7.10(a)]. For a simple design it may be assumed that the capacity of the end panel is restricted to so that no tension field develops in it [Fig. 7.10 (c)]. In this case, end panel acts as a beam spanning between the flanges to resist shear and moment caused by and produced by tension field of penultimate panel. This approach is conservative, as it does not utilise the postbuckling strength of end panel especially where the shear is maximum. This will result in the a/d value of end panel spacing to be less than that of other panels. The end stiffener should be designed for compressive forces due to bearing and the moment, due to tension field in the penultimate panel.
50
In order to be economical the end panel also may be designed using tension field action. In this case the bearing stiffener and end post are designed for a combination of stresses resulting from compression due to bearing and a moment equal to 2/3 caused due to tension in the flanges, The stiffener will be stout. Instead of one stout stiffener we can use a double stiffener as shown in Fig. 7.10(d). Here the end post is designed for horizontal shear and the moment 7.4.4
Stiffeners
Stiffeners are provided to transfer transverse concentrated compressive force on the flange into the web and are essential for desired performance of web panels. These are referred to as bearing stiffeners. Intermediate web stiffeners are provided to improve web shear capacity. Design of these stiffeners is discussed below. Load bearing stiffeners: Whenever there is a risk of the buckling resistance of the web being exceeded, especially owing to concentrated loads, loadbearing stiffeners are provided. Normally a web width of 20 t on both sides as shown in Fig. 7.10 (b) is assumed to act along with the stiffener provided to resist the compression as an equivalent cruciform shaped strut of effective length 0.7 times its actual length between the top and bottom flanges. The bearing stress in the stiffener is checked using the area of that portion of the stiffener in contact with the flange through which compressive force is transmitted. Intermediate stiffeners: The intermediate stiffeners are provided to prevent out of plane buckling of web at the location of stiffeners. The buckling resistance of the stiffeneracting as a strut (with a cruciform section as described earlier) should be not less than where is the maximum shear force in the panel and is the buckling resistance of web without considering tension field action. In its limit will be equal to of the web without stiffeners. Sometimes the stiffeners are provided for more than one of the above purposes. In such cases stiffeners are considered for their satisfactory resistance under combined load effects. Such combined loads are common.
Longitudinal stiffeners: Longitudinal stiffeners are hardly used in building plate girders, but sometimes they are used in highway bridge girders for aesthetic reasons. They are not as effective as transverse stiffeners. Nowadays, the use of longitudinal stiffeners is rare due to higher welding costs.
In order to obtain greater economy and efficiency in the design of plate girders, slender webs are sometimes reinforced both longitudinally and transversely. The longitudinal stiffeners are generally located in the compression zones of the girder. The main function of the longitudinal stiffeners is to increase the buckling resistance of web by subdividing the web and limiting the web buckling to smaller web panels. The additional cost of welding the longitudinal stiffeners invariably offsets any economy resulting in their use.
51
(a) End panel designed using tension field action and end post designed for both bearing and to resist tension field
(d) End panel designed using tension field strengthened by additional stiffener (Double stiffener)
Fig. 7.10 Various treatments for end panel
3
7.4.5
Curtailment of flange plates
For a plate girder subjected to external loading, the maximum bending moment occurs at one section usually, e.g. when the plate girder is simply supported at the ends, and subjected to the uniformly distributed load, then, maximum bending moment occurs at the centre. Since the values of bending moment decreases towards the end, the flange area designed to resist the maximum bending moment is not required at other sections. Therefore the flange plates may be curtailed at a distance from the centre of span greater than the distance where the plate is no longer required as the bending moment decreases towards the ends. It gives economy as regards to the material and cost. At least one flange plate should be run for the entire length of the girder. 7.4.6
Splices
Web splices: A joint in the web plate provided to increase its length is known as web splice. The plates are manufactured up to a limited length. When the maximum manufactured length of the plate is insufficient for full length of the plate girder, web splice becomes essential. It also becomes essential when the length of plate girder is too long to handle conveniently during transportation and erection. Generally, web splices are mainly used in bridges and not buildings. Splices in the web of the plate girder are designed to resist the shear and moment at the spliced section. The splice plates are provided on each side of the web or direct butt welding. Flange splices: A joint in the flange element provided to increase the length of flange plate is known as flange splice. The flange splices should be avoided as far as possible. Generally, the flange plates can be obtained for full length of the plate girder. In spite of the availability of full length of flange plates, sometimes it becomes necessary to make flange splices. Flange joints should preferably be located at the points away from section of maximum bending moment. 7.5
Webs Subjected to Coexistent Bending and Shear
When a girder is subjected to predominant bending moments and low shear, its ultimate capacity is conditioned by the interaction between the effects of the bending moment and shear force. The interaction diagram is generally expressed in the form seen in Fig. 7.11, where the shear capacity is plotted in the axis and the bending capacity in the axis. Any point in the interaction diagram shows the coexistent values of shear and bending moment that the girder can sustain. The vertical ordinates are nondimensionalised using (Yield shear of the web) and the horizontal ordinates by (the fully plastic moment resistance of the cross section). The portion of the curve between points A and C is the region in which the girder will fail by predominant shear, i.e. shear mechanism of the type represented in Fig. 7.12 will develop at collapse. The vertical ordinate at A presents the shear capacity
53
given by Eqn.7.28.
Fig. 7.11 Interaction between bending and shear effects
54
Fig. 7.12 Collapse of the panel This shear capacity will reduce gradually due to the presence of coexistent bending moment. Beyond point in Fig. 7.11 when the applied moment is high, the failure will be triggered by the collapse of flanges by one of the following: (i) by yielding of flange material or (ii) by inward buckling of the compression flange or (iii) by lateral buckling of the flange. Thus there is a distinct change in failure criterion represented by line in Fig. 7.11(a); the left of represents shear failure and the right of flexural failure. Generally the flange failure mode will be triggered, when the applied bending moment is approximately equal to the plastic moment resistance provided by the flange plates only, neglecting the contribution from the web.
This value represents the horizontal coordinate of the point C, i.e. the point F. In zone ABC, the presence of additional bending moment requires the following three factors to be considered. • • •
The reduction in the web buckling stress due to the presence of bending stresses. The influence of bending stresses on the value of membrane stress required causing yield in the web. The reduction of plastic moment capacity of flanges due to the presence of axial flange stresses caused by bending moment.
7.5.1
Reduction of plastic moment capacity of flanges
When high axial forces are developed in the flanges due to bending moments, their effects in reducing plastic moment capacity of flange plates must be taken into account. From plasticity theory, the reduced capacity is given by
55
where, 7.5.2
is the average axial stress for the portion of the flange between hinges. Design procedure
The simplified design procedure due to Rockey et. al (1978) and validated by them by experiments is summarised below: The shear load capacity at point C of the interaction diagram may be obtained approximately from an empirical relationship given below.
This equation gives the vertical ordinate of the point C in the interaction diagram [Fig. 7.11(a)]. The horizontal ordinate as stated previously is given by the value of (See Eqn 7.29). The interaction diagram is constructed in stages as follows [See Fig. 7.11(6)]: (i)
(ii)
(iii)
Between A and B, the curve is horizontal. The horizontal ordinate B is given by maximum bending moment in the end panel given by but limited to a value of Between B and C, the curve may be straight (for simplicity). The moment corresponding to C is given by The point D represents nearly the ultimate capacity of the flanges and the shear values when high bending is present. This is discussed in the next section.
Webs subjected to pure bending: The region beyond C of the interaction diagram represents a high bending moment, so the failure is by bending moment. In a thin walled girder, the web subjected to compressive bending stress will buckle, thereby losing its capacity to carry further compressive stresses. The compression flange will therefore carry practically all the compressive stresses, as the web is unable to be fully effective. Consequently the girder is unable to develop full plastic moment of resistance of the cross section.
If no lateral buckling occurs (e.g. by provision of adequate lateral supports), the girder will fail by inward collapse of compression flange at an applied moment which is approximately equal to the moment required to produce first yield in the extreme fibres of compression flange. This moment is  of course  reduced because of the effects of web buckling. Though the concept is simple, the resulting calculations are complex. The 56
ultimate moment capacity to be determined by a simple formula due to Cooper (1971) is given below:
= Bending moment required to produce yield in the extreme fibre of flange assuming fully effective web (i.e. neglecting web buckling) This value of is the moment required to produce yield in the extreme fibres of the flange. The corresponding stresses in the web will be below yield. (Point D in the interaction diagrams). The ordinate of D can be calculated approximately from
The complete interaction diagram can now be drawn. 7.6 Plate Girders with Web Openings The following general guidance is given for plate girders with web openings. • • • • • • • •
•
• •
The hole should be centrally placed in the web and eccentricity of the opening is avoided as far as possible. Unstiffened openings are not always appropriate, unless they are located in low shear and low bending moment regions. Web opening should be away from the support by at least twice the beam depth, D or 10% of the span whichever is greater The best location for the opening is within the middle third of the span. Clear Spacing between the openings should not be less than beam depth, D. The best location for opening is where the shear force is the lowest. The diameter of circular openings is generally restricted to 0.5D. Depth of rectangular openings should not be greater than 0.5D and the length not greater than 1.5D for unstiffened openings. The clear spacing between such opening should be at least equal the longer dimension of the opening. The depth of the rectangular openings should not be greater than 0.6D and the length not greater than 2D for stiffened openings. The above rule regarding spacing applies. Corners of rectangular openings should be rounded Point loads should not be applied at less than D from side of the adjacent opening.
57
•
If stiffeners are provided at the openings, the length of the welds should be sufficient to develop the full strength of the stiffener.
When a circular web opening of depth is provided, the shear resistance is reduced by If a rectangular opening of is provided, the reduction in shear resistance may be approximately evaluated as Suitable reinforcement to recover this loss of shear resistance may be designed, where necessary.
58
SECTION 8: ELEMENTS SUBJECTED TO AXIAL FORCE AND BENDING 8.1
Basic Behaviour of Beam Columns
Columns subjected to a combined axial force and bending moments are referred to as BeamColumns. In practice, all columns experience bending about one or both axis in addition to axial compression, due to one or more of the following reasons. •
The compressive force may be eccentrically transferred to the column [Fig.
•
In braced rigid portal frames, when the beam is subjected to gravity loads, it will transfer the bending moments to the column in addition to axial loads
•
When a multistorey multibay unbraced frame is subjected to gravity loads as well as lateral loads due to wind or earthquake, the columns are subjected to sway deflection and bending, thereby subjecting the columns to axial compression as well as bending moments
•
Beams from orthogonal directions in corner columns in buildings may be subjected to bending about both principal axes in addition to axial compression
A beamcolumn may be subjected to single curvature bending over its length or reverse curvature bending as shown in causing variation of the nature (positive or negative) of the bending moment and curvature over the length of the column. An overestimate of the vertical loading may inadvertently make the design unsafe by reducing the moment resistance capacity of the column. Hence, the realistic assessment of the vertical load of the column is necessary. The presence of bending moments in the beamcolumns reduces the axial force at which they fail. In "short" columns, the failure is triggered by the material reaching its ultimate capacity. In "long" columns, the failure is normajly due to overall instability of the column, and in some cases due to the material strength having been reached at the ends of the column.
59
Fig.8.1 BeamColumns in Frames 8.2 Short Beam  Columns made of Plastic and Compact Cross sections A short member (stub column), made of nonslender (plastic / compact) section under axial compression, fails by yielding, at the squas load, by
60
give
Where,
is the yield strength of the material, and
is the gross area of the cross section.
If the stub column is made of slender cross section, the plate elements of the cross section undergo local buckling before reaching the yield stress. This causes reduction in the effective area of the cross section to a value below the gross area, and the member fails at a load below given by Eqn.8.1. Similarly a short member made of plastic or compact section and subjected to only bending moment fails at the plastic moment capacity, given by [Fig. 8.2(6)]
where, S = plastic section modulus of the cross section, in the case of plastic and compact sections.
Fig. 8.2 Stresses in Short BeamColumns 8.3
Long BeamColumns
Typically steel columns in practice are long and slender: Such slender columns when axially compressed tend to fail by buckling rather than yielding. The additional deflection and bending moment are due to the axial load acting on the deformed column as given below. • •
in a column within a floor between the ends of the columns (sway) at adjacent floors
The consequent magnified deflection and bending moments are approximately allowed for in the design method described in section 8.5.
61
{a) Single curvature
( b ) Double curvature
( c ) Swav Deformation
Fig. 8.3 Deflection and Moment Magnification 8.3.1 Effects of slenderness ratio and axial force on modes of failure Beamcolumns may fail by flexural yielding or torsional flexural buckling. The actual mode of failure will depend upon the magnitude of the axial load and eccentricity as well as the slenderness ratio. For design purposes, simplified equations are available; using which it is possible to obtain the resistance of members, conservatively. These are discussed below. 8.4
Modes of Failure
The following are the possible modes of failure of beamcolumns 8.4.1 Local section failure This is usually encountered in the columns with relatively small axial compression ratio reverse curvature.
62
case
of
short,
stocky
beam
and beamcolumns bent in
• •
The resistance of the end section (reached under combined axial force and bending moment) governs the failure. The resistance of the section may be governed by plastic buckling of plate elements in the case of plastic, compact sections and semicompact or by elastic local buckling in the case of slender sections.
8.4.2 Overall instability failure under flexural yielding This type of failure is encountered in the case of all members subjected to larger compression and single curvature bending about the minor axis as well as not very slender members subjected to axial compression and single curvature bending about the major axis. •
The member fails by reaching the ultimate resistance of the member at a section over the length of the member, under the combined axial compression and magnified bending moment.
•
In the case of weak axis bending of slender members the failure may be by weak axis buckling, or failure of the maximum moment section under the combined effect of axial force and magnified moment.
• The section failure may be due to elastic or plastic buckling of plate elements depending on the slenderness ratio (b/t) of the plate. 8.4.3 Overall instability by torsional flexural buckling This is common in slender members subjected to large ompression and uniaxial bending about the major axis or biaxial bending. •
At the ultimate stage the member undergoes biaxial bending and torsional instability mode of failure.
8.5 Design Equations The design rules are given below in the form of linear interaction equations to verify resistance of the section against local section failure as well as member failure by flexural yielding and torsional flexural buckling. These are conservative implifications of the complex nonlinear failure envelopes. 8.5.1 Local section failure The interaction equation is given by:
63
where and are the actual compressive force and bending moments about the major axis and minor axis of the cross section, respectively. is the gross area of cross section in the case of plastic / compact cross sections. and are the plastic section moduli of the cross section about the major and minor axis, respectively. The is the design yield strength given by Normally, the moments obtained from the linearelastic analysis would suffice for normal buildings with only a few storeys and low axial compression. In very tall buildings with a large axial compression and large lateral sway, the end moments after accounting for the effects have to be considered. 8.5.2 Overall member failure The interaction equation to check the member capacity as governed by overall member buckling is given by
where, are the actual axial compression, and actual bending moments about the major and minor axes, respectively. are the design compressive strength, and the bending strength about the and axis, respectively, when only the corresponding axial force/bending moment is acting. These are calculated considering minor buckling in the case of compression and lateral torsional buckling in the case of bending about major axis. These design strengths have to be calculated considering the type of section (plastic / compact). are the moment amplification factors which account for the effect of moment gradient over the member length, instead of uniform moment over the entire length, and magnification of moments due to the axial force acting on the deformed column The values of corresponding to the appropriate axis are evaluated from:
= 1.3 (For inplane lateral UDL over the member) = 1.4 (For inplane lateral concentrated load over the member) = Axial compressive strength about the respective axis = Plastic and elastic section moduli, respectively and should be substituted for the corresponding x or yaxis. The effect is accounted for by taking effective length to be greater than one in sway frames. More accurate evaluation of beamcolumn strength is possible by resorting to nonlinear analysis. When a designer feels that a detailed and rigorous analysis is warranted, he is free to do so, not withstanding the approximate analysis procedure detailed in this chapter. 64
SECTION 9: BEAMS OF HOT ROLLED SECTIONS, SUBJECTED TO TORSION AND BENDING 9.1
Introduction
Torsional moments are invariably introduced in beams when the line of action of the resultant transverse force does not pass through the shear centre of the cross section. Beams circular in plan and supported on a few columns, interconnected bridge girders, beams carrying loads predominantly on one side are all examples of structures where torsional moments are important. 9.2
Practical Advice
Designing for torsion is complex and it is wise not to transfer loads by Torsional mode. It is well to remember that torsion will not occur if the section is loaded such that the resultant force passes through the shear centre of the cross section. When possible, the framing should be arranged so as to minimise any torsion. Careful detailing, particularly when considering the load path, and the way loads are transferred to members of the frame will generally help to minimise or eliminate many potential difficulties associated with torsional effects. When significant torsion is unavoidable, the designer should consider using box girders or hollow rolled or plated sections. When torsion is unavoidable due to detailing difficulties, the designer should ensure the following conditions: •
• •
• •
Beams subjected to torsion should have sufficient stiffness and strength to resist the torsional moment and forces in addition to other moments and forces. The connections and bracing of such members should be carefully designed to ensure that the reactions are transferred to the supports. Factored resistance of I  beams subjected to combined flexure and torsion should be determined from Moment  Torque interaction diagrams. Members subjected to compatibility torsion deformations need not be designed to resist the associated torsional moments provided that structure satisfies equilibrium. For fuller description of "equilibrium torsion" and compatibility torsion, reference may be made to IS: 456  2000. Stresses and deflections due to combined effects should be within the specified limits. When necessary, the designer may incorporate more accurate methods of combined torsion and bending from the relevant literature.
6
SECTION 10: PORTAL FRAMES 10.1 General Design Consideration Portal frames are the most commonly used structural forms for singlestorey industrial structures. The slopes of rafters in the gable portal frames (Fig. 10.1) vary in the range of 1 in 10 to 7 in 3 depending upon the type of sheeting and its seam impermeability. With the advent of new cladding systems, it is possible to achieve roof slopes as low as 1°. But in such cases, frame deflections must be carefully controlled and the large horizontal thrusts that occur at the base should be accounted for. Generally, the centretocentre distance between frames is of the order 6 to 7.5 m, with eaves height ranging from 6 15 m . Normally, larger spacing of frames is used in the case of taller buildings, from the point of economy. Momentresisting connections should be provided at the eaves and crown to resist moments under lateral and gravity loadings. The stanchion bases behave as either pinned or fixed, depending upon rotational restraint provided by the foundation and the connection detail between the stanchion and foundations. For the design of portal frames, plastic methods of analysis are mainly used, to obtain economical designs. The most common form of portal frame used in the construction industry is the pinnedbase frame with different rafter and column member size and with haunches at both the eaves and apex connections (Fig. 10.1). Due to transportation requirements, field joints are introduced at suitable positions. As a result, connections are usually located at positions of high moment, i.e. at the interface of the column and rafter members (at the eaves) and also between the rafter members at the apex (ridge) (See Fig. 10.1). It is very difficult to develop sufficient moment resistance at these connections by providing 'tension' bolts located solely within the small depth of the rafter section. Therefore the lever arm of the bolt group is usually increased by haunching the rafter members at the joints. This in addition increases the section strength. Although a short length of the haunch is enough to produce an adequate lever arm for the bolt group, haunch is usually extended along the rafter and column adequately to reduce the maximum moments in the uniform portion of the rafter and columns and hence reduce the size of these members. Due to this, there will be a corresponding increase in the moment in the column and at the columnhaunchrafter interface. This allows the use of smaller rafter member compared to column member. The resulting solution usually proves to be economical, because the total length of the rafter is usually greater than the total length of the column members. The saving in weight is usually sufficient to offset the additional cost of haunch. The effect of introducing the haunches is to ensure that the hinges, which were assumed to be at nodes, are forced away from the actual column rafter junction to the ends of the haunches. Provided the haunch regions remain elastic, hinges can develop at their ends. The haunch must be capable of resisting the bending moment, axial thrust and shear force transferred by the joining members. The common practice is to make the haunch at the connection interface approximately twice the depth of the basic rafter section, so that the haunch could be fabricated from the same basic section.
7
(a) Haunched portal frame
Fig. 10.1 Typical gable frame 10.2 General Design Procedure Detailed steps in the plastic design of portals are prescribed in SP 6(6): 1972 "Handbook for Structural Engineers  Application of Plastic Theory in the Design of Steel Structures". These are summarized below: a) Determine possible loading conditions. b) Compute the factored design load combination(s). c) Estimate the plastic moment ratios of frame members. d) Analyse the frame for each loading condition and calculate the maximum required plastic moment resistance, of the column and rafter. e) Select the section, and f) Check the design for other secondary modes of failure The design commences with determination of possible loading conditions, in which decisions such as, whether to treat the distributed loads as such or to consider them as
67
equivalent concentrated loads, are to be made. It is often convenient to deal with equivalent concentrated loads in computer aided and plastic analysis methods. In step (b), the loads determined in (a) are multiplied by the appropriate load factors to assure the needed margin of safety. The step (c) is to make an assumption regarding the ratio of the plastic moment capacities of the column and rafter, the frame members. The following simple procedure may be adopted for arriving at the ratio. (i)
Determine the absolute plastic moment value for separate loading conditions.
(Assume that all joints are fixed against rotation, but the frame is free to sway). For beams, solve the beam mechanism equation and for columns, solve the panel (sway) mechanism equation. These are done for all loading combinations. The moments thus obtained are the absolute minimum plastic moment values. The actual section moment will be greater than or at least equal to these values. (ii)
Now select plastic moment ratios using the following guidelines. • • •
At joints establish equilibrium. For beams use the ratio determined in step (i) For columns use the corner connection moments
In the step (d) each loading condition is analysed by a plastic analysis method for arriving at the minimum required Based on this moment, select the appropriate sections in step (e). The step (f) is to check the design according to secondary design considerations discussed in the following sections.
10.3 Secondary Design Considerations The 'simple plastic theory' neglects the effects of axial force, shear and buckling on the member resistance. So checks must be carried out for the following factors as recommended by "The Hand book for Structural Engineers" referred above. a) Reductions in the plastic moment resistance due to the effect of axial force and shear force. b) Instability due to local buckling, lateral buckling and column buckling. c) Brittle fracture. d) Deflection at service loads. In addition, connections must be designed carefully to ensure that the plastic moments can be developed at the hinge locations. 10.3.1 Influence of axial force on plastic moment Even though the presence of axial force tends to reduce the magnitude of the plastic moment resistance of the section, the design procedure may be modified to account for its
68
influence, retaining the 'plastic hinge' characteristic. The following recommendations account for effect of axial compression on • Neglect the effect of axial force on the plastic moment resistance unless where P is the actual axial force and is the axial force that could cause yielding of the full cross section. •
If P is greater than 15 percent of is given by
the modified plastic moment resistance,
where, is the plastic moment resistance of the section when the axial force is absent, is the actual axial force; is the axial force corresponding to yielding. The required design value of plastic section modulus of the member (Z) under combined compression and bending, is given by:
10.3.2 The influence of shear force The effect of shear force is also to reduce the plastic moment resistance. Due to the presence of shear, two types of 'premature failure' can occur. (a) General shear yield of the web may occur in the presence of high sheartomoment ratios. (b) After the beam has become partially plastic at a critical section due to flexural yielding, the intensity of shear stress at the centre line may reach the yield condition. (c) The maximum shear resistance of a beam under combined shear and moment should be calculated as
Where, = effective cross sectional area resisting shear after deducting the area that has yielded under flexure. Usually it is found that the reduction in moment resistance due to shear is more than compensated by the strain hardening of extreme fibre under flexure and consequently effect of shear on plastic moment resistance may be neglected in most cases.
69
10.3.3 Local buckling of flanges and webs
If the plates, of which the cross section is made, are not stocky enough, they may be subject to local buckling either before or soon after the first plastic moment is reached. Due to this, the moment resistance of the section would drop off and the rotation resistance would be inadequate to ensure formation of complete failure mechanism. Therefore, in order to ensure adequate rotation at values and to avoid premature plastic buckling, the compression elements should have restriction on the widththickness ratios as given in section 5, corresponding to plastic sections. 10.3.4 Lateral buckling of flexural members To avoid lateral buckling and torsional displacements, bracings should be provided to compression flanges at points as given below (Fig. 10.2). (a) Lateral support to the compression flange should be provided at the location of plastic hinges. (b) The ratio of laterally unsupported length of the compression flange to the radius of gyration of the member about weak axis, should not exceed where v is defined below in Eqn. 10.4.
(c) The slenderness ratio of compression flange, unsupported length where the moment exceeds
of the length, adjacent to the should not be greater
than
(d) The slenderness ratio, of the rest of the elastic portion of the member should be such that the lateral buckling strength of that portion is greater than actual maximum elastic moment in the region. where, = yield stress of the material in Mpa and may be taken conservatively as 1.0 or may be calculated using the following equation.
where is the ratio of the plastic rotation at the hinge point just as the mechanism is formed to the relative elastic rotation of the far ends of the beam segment containing the plastic hinge.
70
10.3.5 Column buckling In the plane of bending of columns which would develop a plastic hinge at ultimate loading, the slenderness ratio should not exceed 120, where is the centretocentre distance of bracing members connecting and providing restraint against weak axis buckling of the column or the distance from such a member to the base of the column. Further, columns in moment resisting frames, where side sway is not prevented, should be so proportioned such that
The slenderness ratio, of the frame in the plane normal to the plane of frame action under consideration should be such that the following condition is satisfied.
the ratio of applied end moment to the plastic moment resistance of columns and other axially loaded members, should not exceed unity or the value given by the following formula.
Case I  For columns bent in double curvature by applied moments producing plastic hinges at both ends of the columns:
Case II  For slender struts, where
in addition to exceeding 0.75 also exceeds
should not contain plastic hinges. However, it is permissible to design the
71
member as an elastic part of a plastically designed structure. Such a member should be designed according to the maximum permissible stress requirements satisfying:
where,
= axial force, compressive or tensile in a member; = maximum plastic moment resistance in the beam  column; = plastic moment resistance of the section when no axial force is acting. = lateral buckling resistance in the absence of axial load = if the beam column is adequately braced against lateral buckling = buckling resistance in the plane of bending if only axially loaded (without any bending moment) and if the beam  column is laterally braced. If the column is not adequately laterally braced, is the weak axis buckling strength under only axial compression. = Euler load =
in the plane of bending;
= yield strength of axially loaded section = effective crosssection area of the member; = a coefficient whose value should be taken as follows: a) For member in frames where side sway is not prevented, b) For members in frames where side sway is prevented and not subject to transverse loading between their supports in the plane of bending:
c) For members in frames where side sway is prevented in the plane of loading and subjected to transverse loading between their supports; the value of is given by, For members whose ends are restrained against rotation, For members whose ends are unrestrained against rotation, = radius of gyration about the same axis as the applied moment; = non dimensional slenderness ratio = the ratio of end moment; 10.4
= actual strut length.
Connections
In a portal frame, points of maximum moments usually occur at connections. Further, at corners the connections must accomplish the direction of forces change. Therefore, the design of connections must assure that they are capable of developing and maintaining the required moment until the frame fails by forming a mechanism. 72
SECTION 11: MULTI  STOREY BUILDINGS 11.1
Introduction
Recent innovations in lateral load resisting systems (e.g. framewall, framed tube, belt truss with outrigger, tube in tube and bundled tube systems) have enabled construction of very tall buildings elsewhere in the world using steel frames. When we build such tall structures it becomes necessary to consider some of the effects such as the effect of lateral deflection, on gravity loading, P which are normally ignored in the design of building frames of three or four storeys. A building frame deflects under lateral load. The columns of tall buildings carry large axial loads. A building frame, which deflects under lateral load, is further forced to undergo additional deflection because of the eccentricity of gravity load from the centre of gravity of the column due to the deflected shape. These two effects of large axial loads P in the columns combined with significant lateral deflection need careful consideration in the design of tall multistorey buildings. The combined effect of the large axial loads P and lateral deflection give rise to the destabilising effect.However, in frames that are only a few storeys high, this effect is negligible and hence ignored in the analysis. It is therefore necessary to classify frames based on the relative importance of effects for the purpose of evaluating design forces. 11.2
Classification of Frames
A frame in which sway is prevented is called a "nonsway" frame. However, there are some frames, which may sway only by a small amount since the magnitude of sway in such frame is small it will have only a negligible effect. Such frames are also classified as "nonsway" frames. Therefore, to define the nonsway frame precisely, its lateral stiffness is used as the criteria irrespective of whether it is braced or not. For such frames lateral stiffness is provided by one of the following: (i) (ii) (iii)
rigidity of the joints. provision of bracing system. connecting the frame to a braced frame, shear core, shear wall or a lift well.
The inter storey deflection (i.e. the difference in deflection of top and bottom end of a column in that storey) is used to quantify the lateral stiffness of the frame. The meaning of inter storey deflection is shown in Fig. 11.1(c). Fig. 11.1 ( a ) shows a typical multi storey frame subjected to factored (dead + live) load. To ascertain the stiffness of the frame, it is analysed when subjected to assumed forces of magnitude 0.5% of factored (dead + live) load applied laterally on the frame at each floor level as shown in Fig. 11.1 ( b ) for getting the inter storey deflection for the storey. Note that the lateral loads are applied without the presence of dead and live loads. The maximum for any storey is taken as a measure of the frame stiffness.
73
Fig. 11.1 Approximate calculation offrame stiffness for classification of frames (according to Home's method)
74
For a frame to be of the nonsway" type the maximum inter storey deflection permitted in any storey is generally taken as follows:
where hi is the height of the i'h storey (
Tablel5.5: Bending moment coefficients according to IS: 4562000 TYPE OF LOAD
SPAN
[OMENTS
SUPPORT] MOMENTS
IVI
Near middle At middle of At support next to the end of end span interior span support + 1/12 + 1/16  1/10
At other interior supports  1/12
Dead load + Imposed load (fixed) Imposed load (not + 1/10 + 1/12  1/9  1/9 fixed) For obtaining the bending moment, the coefficient shall be multiplied by the total design load and effective span. Table 15.6: Shear force coefficients TYPE OF LOAD
At end support
At support n sup Outer side 0.60
ext to the end port Inner side 0.55
At all other interior supports 0.50
Dead load + 0.40 Imposed load (fixed) Imposed load 0.45 0.60 0.60 0.60 (not fixed) For obtaining the shear force, the coefficient shall be multiplied by the total design load 15.9.2 Lateral torsional buckling of continuous beams The concrete slab prevents the top flange of the steel section (connected to concrete slab) from moving laterally. In negative moment regions of continuous composite beams the lower flange is subjected to compression. Hence, the stability of bottom flange should be checked at that region. The tendency of the lower flange to buckle laterally is restrained by the distortional stiffness of the cross section. The tendency for the bottom flange to displace laterally causes bending of the steel web, and twisting at top flange level, which is resisted by bending of the slab as shown in Fig. 22.6.
Fig 15.6 Inverted  U frame Action Lateral Torsional Buckling of Continuous Beams can be neglected if following conditions are satisfied. 1. Adjacent spans do not differ in length by more than 20% of the shorter span or where there is a cantilever, its length does not exceed 15% of the adjacent span. i 148 3
2. The loading on each span is uniformly distributed and the design permanent load exceeds 40% of the total load. 3. The shear connection in the steelconcrete interface satisfies the requirements of section
15.10 Serviceability Composite beams must also be checked for adequacy in the Serviceability Limit State. It is not desirable that steel yields under service load. To check the composite beams serviceability criteria, elastic section properties are used. IS: 113841985 limits the maximum deflection of the composite beam to The total elastic stress in concrete is limited to while for steel, considering different stages of construction, the elastic stress is limited to Unfortunately this is an error made in the Code as the same limits are applied for steel in determining the ultimate resistance of the cross section. Since EC4 gives explicit guidance for checking serviceability Limit State, therefore the method described below follows EC 4. 15.10.1 Deflection The elastic properties relevant to deflection are section modulus and moment of inertia of the section. Applying appropriate modular ratio m the composite section is transformed into an equivalent steel section. The moment of inertia of uncracked section is used for calculating deflection. Normally unfactored loads are used for for serviceability checks. No stress limitations are made in EC 4. Under positive moment the concrete is assumed uncracked, and the moment of inertia is calculated as:
Where is the ratio of the elastic moduli of steel to concrete taking into account creep.
is the moment of inertia of steel section. Simply supported Beams: The midspan deflection of simply supported composite beam under distributed load w is given by
4149
Where, is the modulus of elasticity of steel and is the gross uncracked moment of inertia of composite section. Influence of partial shear connection: Deflections increase due to the effects of slip in the shear connectors. These effects are ignored in composite beams designed for full shear connection. To take care of the increase in deflection due to partial shear connection, the following expression is used.
Where are deflection of steel beam and composite beam respectively with proper serviceability load.
Note: For
this additional simplification can usually beignored
Shrinkage induced deflections: For simply supported beams, when the span to depth ratio of beam exceeds 20, or when the free shrinkage strain of the concrete exceeds shrinkage, deflections should be checked. In practice, these deflections will only be significant for spans greater than 12 m in exceptionally warm dry atmospheres. The shrinkageinduced deflection is calculated using the following formula:
is the effective span of the beam and strain, given by
is the curvature due to the free shrinkage
modular ratio appropriate for shrinkage calculations Note: This formula ignores continuity effects at the supports.
150 5
Continuous Beams: In the case of continuous beam, the deflection is modified by the influence of cracking in the hogging moment regions (at or near the supports). This may be taken into account by calculating the second moment of area of the cracked section under negative moment (ignoring concrete). In addition to this there is a possibility of yielding in the negative moment region. To take account of this the negative moments may be further reduced. As an approximation, a deflection coefficient of 3/384 is usually appropriate for determining the deflection of a continuous composite beam subject to uniform loading on equal adjacent spans. This may be increased to 4/384 for end spans. The second moment of area of the section is based on the uncracked value. Crack Control: Cracking of concrete should be controlled in cases where the functioning of the structure or its appearance would be affected. In order to avoid the presence of large cracks in the hogging moment regions, the amount of reinforcement should not exceed a minimum value given by,
Where is the percentage of steel is a coefficient due to the bending stress distribution in the section is a coefficient accounting for the decrease in the tensile strength of concrete is the effective tensile strength of concrete. A value of 3 adopted. is the maximum permissible stress in concrete
is the minimum
Generally the span/depth ratios specified by codes take care of the shrinkage deflection. However, a check on shrinkage deflection should be done in case of thick slabs resting on small steel beams, electrically heated floors and concrete mixes with high "free shrinkage". Eurocode 4 recommends that the effect of shrinkage should be considered when the span/depth ratio exceeds 20 and the free shrinkage strain exceeds 0.04%. For dry environments, the limit on free shrinkage for normal weight concrete is 0.0325% and for lightweight concrete 0.05%. 15.10.2 Vibration Generally, human response to vibration is taken as the yardstick to limit the amplitude and frequency of a vibrating floor. The present discussion is mainly aimed at design of an office floor against vibration. To design a floor structure, only the source of vibration near or on the floor need be considered. Other sources such, as machines, lift or cranes should be isolated from the building. In most buildings following two cases are considered
6151
i) ii)
People walking across a floor with a pace frequency between 1.4 Hz and 2.5Hz. An impulse such as the effect of the fall of a heavy object.
Fig. 15.7. Curves of constant human response to vibration, and Fourier component factor The root mean square acceleration of the floor is plotted against its natural frequency for acceptable level R based on human response for different situations such as, hospitals, offices etc. The human response Rl corresponds to a "minimal level of adverse comments from occupants" of sensitive locations such as hospital, operating theatre and precision laboratories. Curves of higher response (R) values are also shown in the Fig. 15.7. The recommended values of R for other situations are R = 4 for offices R = 8 for workshops These values correspond to continuous vibration and some relaxation is allowed in case the vibration is intermittent (see BS6472 for further information). Natural frequency of beam and slab: The most important parameter associated with vibration is the natural frequency of floor. For free elastic vibration of a beam or one way slab of uniform section the fundamental natural frequency is,
Where, for simple support; and for both ends fixed. = Flexural rigidity (per unit width for slabs) = span = vibrating mass per unit length (beam) or unit area (slab).
152 7
The effect of damping (being negligible) has been ignored. Uncracked concrete section and dynamic modulus of elasticity should be used for concrete. Generally these effects are taken into account by increasing the value of by 10% for variable loading. In absence of an accurate estimate of mass (m), it is taken as the mass of the characteristic permanent load plus 10% of characteristic variable load. The frequencies for slab and beam (each considered alone)
Where,
and
are given by
is the spacing of the beams.
The natural frequency is given by
Where is the Fourier component factor. It takes into account the differences between the frequency of the pedestrians' paces and the natural frequency of the floor. This is given in the form of a function of in Fig. (15.7): = magnification factor at resonance
=0.03 for open plan offices with composite floor To check the susceptibility of the floor to vibration after finding from Eqn.15.22 and the value of R from Eqn. 15.23 compare the result with the target response curve as in Fig. (15.7).
153 8
16.1
General
A steelconcrete composite column is a compression member, comprising either a concrete encased hotrolled steel section or a concrete filled tubular section of hotrolled steel. Typical crosssections of composite columns with fully and partially concrete encased steel sections are illustrated in Fig. 16.1. Fig. 16.2 shows three typical crosssections of concrete filled tubular sections. Supplementary reinforcement in the concrete encasement prevents excessive spalling of concrete both under normal load and fire conditions.
16.2
Members under Axial Compression
The design method described below is formulated for prismatic composite columns with doubly symmetrical crosssections, and generally follows the guidelines prescribed in EC4.
16.2.1 Resistance of crosssection to compression Encased steel sections and concrete filled rectangular/square tubular sections: The plastic resistance of an encased steel section or concrete filled rectangular or square section (i.e. the socalled "squash load") is given by
Where,
9 154
are the areas of the steel section, the concrete and the reinforcing steel respectively are the yield strength of the steel section, the characteristic compressive strength (cylinder) of the concrete, and the yield strength of the reinforcing steel respectively. is the characteristic compressive strength (cube) of the concrete is strength coefficient for concrete, which is 1.0 for concrete filled tubular sections, and 0.85 for fully or partially concrete encased steel sections.
Fig. 16.3 Stress distribution of the plastic resistance to compression of an encased I section
Concrete filled circular tubular sections: The ductility performance of this type of columns is significantly better than rectangular types. Also, there is an increased resistance of concrete due to the confining effect of the circular tubular section. However, this effect is significant only in stocky columns. For composite columns with a non dimensional slenderness of (where is defined in Eqn.16.5, in section 16.2.2J, or where the eccentricity, of the applied load does not exceed the value d/10, (where d is the outer dimension of the circular tubular section) this effect has to be considered. The plastic compression resistance of concrete filled circular tubular sections is calculated by using two coefficients and as given below.
where t is the thickness of the circular tubular section, and
155 10
and
two coefficients given by
In general, the resistance of a concrete filled circular tubular section to compression may increase by 15% under axial load only when the effect of triaxial confinement is considered. Linear interpolation is permitted for various load eccentricities of The basic values and depend on the nondimensional slenderness which can be read off from Table 16.1.
If the eccentricity e exceeds the value d/10, or if the nondimensional slenderness exceeds the value 0.5 then Table 16.1: Basic value to allow for the effect of triaxial confinement in concrete filled circular tubular sections, as provided in EC 4 applicable for concrete grades
16.2.2 Nondimensional slenderness For convenience, column strength curves are plotted in a nondimensionalised form as shown in Fig. 16.4. The buckling resistance of a column is expressed as a proportion of the plastic resistance to compression, where is called the reduction factor. The horizontal axis is nondimensionalised similarly by
Fig.16.4 Nondimensionalised column buckling curve The European buckling curves have been drawn after incorporating the effects of both residual stresses and geometric imperfections. They form the basis of column buckling design for both steel and composite columns in EC 3 and EC4. For using the European 11 156
buckling curves, the nondimensional slenderness of the column is first evaluated as follows:
Where plastic resistance of the crosssection to compression, according to Eqn (16.1) or Eqn. (23.2) with 1.0; and is the elastic buckling load of the column. 16.2.3 Local buckling of steel sections Both Eqns. (16.1) and (16.2) are valid provided that local buckling in the steel sections does not occur. To prevent premature local buckling, the width to thickness ratio of the steel sections in compression must satisfy the following limits: for concrete filled circular tubular sections
for concrete filled rectangular tubular sections
is the yield strength of the steel section in For fully encased steel sections, no verification for local buckling is necessary as the concrete surrounding it effectively prevents local buckling. However, the concrete cover to the flange of a fully encased steel section should not be less than 40 mm, nor less than onesixth of the breadth, of the flange for it to be effective in preventing local buckling. Local buckling may be critical in some concrete filled rectangular tubular sections with large h/t ratios. Designs using sections, which exceed the local buckling limits for semicompact sections, should be verified by tests.
157
16.2.4 Effective elastic flexural stiffness The value of the flexural stiffness may decrease with time due to creep and shrinkage of concrete. Two design rules for the evaluation of the effective elastic flexural stiffness of composite columns are given below. Short term loading: The effective elastic flexural stiffness, is obtained by adding up the flexural stiffness of the individual components of the crosssection:
Where are the second moments of area of the steel section, the concrete(assumed uncracked) and the reinforcement about the axis of bending considered respectively are the moduli of elasticity of the steel section and the reinforcement is the effective stiffness of the concrete; the factor 0.8 is an empirical multiplier (determined by a calibration exercise to give good agreement with test results). Note is the moment of inertia about the centroid of the uncracked column section.
is the secant modulus of the concrete is reduced to 7.55 for the determination of the effective stiffness of concrete Note: Dividing the Modulus of Elasticity by is unusual and is included here to obtain the effective stiffness, which conforms to test data. Long term loading: For slender columns under longterm loading, the creep and shrinkage of concrete will cause a reduction in the effective elastic flexural stiffness of the composite column, thereby reducing the buckling resistance. However, this effect is significant only for slender columns. As a simple rule, the effect of long term loading should be considered if the buckling length to depth ratio of a composite column exceeds 15. If the eccentricity of loading is more than twice the crosssection dimension, the effect on the bending moment distribution caused by increased deflections due to creep and shrinkage of concrete will be very small. Consequently, it may be neglected and no provision for longterm loading is necessary. Moreover, no provision is also necessary if
158
the nondimensional slenderness, of the composite column is less than the limiting values given in Table 16.2 Table 16.2: Limiting values of for long term loading
Note:
is the steel contribution ratio defined as
However, when exceeds the limits given by Table 16.2 and e/d is less than 2, the effect of creep and shrinkage of concrete should be allowed for by employing the modulus of elasticity of the concrete instead of in Eqn. 16.8, which is defined as follows:
Where P is the applied design load; and permanently acting on the column.
the part of the applied design load
The effect of longterm loading may be ignored for concrete filled tubular sections with provided that is greater than 0.6 for braced (or nonsway) columns, and 0.75 for unbraced (and/or sway) columns.
16.2.5 Elastic buckling load Composite columns may fail in buckling. The elastic critical buckling load (Euler Load), is defined as follows:
Where ( E I ) e is the effective elastic flexural stiffness of the composite column. is the effective length of the column, which may be conservatively taken as system length L for an isolated nonsway composite column.
159
16.2.6 Resistance of members to axial compression For each of the principal axes of the column, the designer should check that Where is the plastic resistance to compression of the crosssection, from Eqn. (16.1) or Eqn. (16.2) and is the reduction factor due to column buckling The European buckling curves illustrated in Fig. 16.5 arc proposed to be used for composite columns. They are selected according to the types of the steel sections and the axis of bending: Curve a
for concrete filled tubular sections
Curve b
for fully or partially concrete encased Isections buckling about the strong axis of the steel sections
Curve c
for fully and partially concrete encased Isections buckling about the weak axis of the steel sections (yy axis)
These curves can also be described mathematically as follows:
1
The factor allows for different levels of imperfections and residual stresses in the columns corresponding to curves a, b, and c. Table 16.3 gives the value of for each buckling curve. Note that the second order moment due to imperfection, has been incorporated in the method by using multiple buckling curves; no additional considerations are necessary. Table 16.3: Imperfection factor a for the buckling curves
The isolated nonsway composite columns need not be checked for buckling, if anyone of the following conditions is satisfied: (a) The axial force in the column is less than buckling load of the column (b) 16.3
The nondimensional slenderness,
where
is the elastic
less than
Combined Compression and UniAxial Bending
16.3.1 Interaction curve for compression and uniaxial bending The resistance of the composite column to combined compression and bending is determined using an interaction curve. Fig. 16.6 represents the nondimensional interaction curve for compression and uniaxial bending for a composite crosssection. Fig. 16.7 shows an interaction curve drawn using simplified design method suggested in the UK National Application Document for This neglects the increase in moment capacity beyond discussed above, (under relatively low axial compressive loads). The method of locating neutral axis for rectangular and circular filled tubular sections is given in Appendix E. Fig. 16.8 shows the stress distributions in the crosssection of a concrete filled rectangular tubular section at each point, A, B and C of the interaction curve given in Fig. 16.7. • Point A marks the plastic resistance of the crosssection to compression (at this point the blending point is is zero).
•
Point B corresponds to the plastic moment resistance of the crosssection (the axial compression is zero).
2
Where are plastic section moduli of the reinforcement, steel section,and concrete about their own centroids respectively and are plastic section moduli of the reinforcement, steel section, and concrete about neutral axis respectively. •
At point follows;
the compressive and the moment resistances of the column are given as
Fig. 16.7 Interaction curve for compression and uniaxial bending using the simplified method
3
Fig. 16.8 Stress distributions for the points of the interaction curve for concrete filled rectangular tubular sections
Fig. 16.9 Variation in the neutral axis positions
4
16.3.2 Analysis of bending moments due to second order effects The second order moment, or 'imperfection moment', does not need to be considered separately, as its effect on the buckling resistance of the composite column is already accounted for in the European buckling curves. For slender columns, the 'first order' displacements may be significant and additional or 'second order' bending moments may be induced under the actions of applied loads. As a simple rule, the second order effects should be considered if the buckling length to depth ratio of a composite column exceeds 15. The second order effects on bending moments for isolated nonsway columns should be considered if both of the following conditions are satisfied: Where is the design applied load, and column.
is the elastic critical load of the composite
(2) Elastic slenderness conforms to:
Where
is the nondimensional slenderness of the composite column
In case the above two conditions are met, the second order effects may be allowed for by modifying the maximum first order bending moment (moment obtained initially),
with a correction factor
which
is defined as follows:
Where is the applied design load and column.
is the elastic critical load of the composite
16.3.3 Resistance of members under combined compression and uniaxial bending The design checks are carried out in the following stages: (1) Check the resistance of the section under axial compression for both (2) Check the resistance of the composite column under combined axial compression and uniaxial bending The design is adequate when the following condition is satisfied: 5
Where is the design bending moment, which may be factored to allow for second order effects, if necessary is the moment resistance ratio obtained from the interaction curve and is the plastic moment resistance of the composite crosssection.
Fig. 16.10 Interaction curve for compression and uniaxial bending using the simplified method Moment resistance ratio evaluated
can be obtained from the interaction curve (Figl6.10) or may be
In accordance with the UK NAD, the moment resistance ratio for a composite column under combined compression and uniaxial bending is evaluated as follows:
is axial resistance ratio due to the concrete,
;
is the design axial resistance
ratio,
16.4
Combined Compression and Biaxial Bending
The design checks are carried out in the following stages: (1) Check the resistance of the section under axial compression for both
and
6
(2) Check the resistance of the composite column under combined axial compressionand biaxial bending The three conditions to be satisfied are:
The interaction of the moments must also be checked using moment interaction curve as shown in Fig. 16.11
Fig. 16.11 Moment interaction curve for biaxial bending The moment resistance ratios
and
for both the axes are evaluated as given below:
7
Where and
are the reduction factors for buckling in the and directions respectively.
When the effect of geometric imperfections is not considered the moment resistance ratio is evaluated as given below:
8
APPENDIX A: Terminology Buckling Load  The load at which a member or a structure as whole collapses in service or buckles in a load test. Characteristic load is that value of the load, which has an accepted probability of not being exceeded during the life span of the structure. Characteristic load is therefore that load which will not be exceeded 95% of the time. Characteristic resistance of a material (such as Concrete or Steel) is defined as that value of resistance below which not more than a prescribed percentage of test results may be expected to fall. (For example the characteristic yield stress of steel is usually defined as that value of yield stress below, which not more than 5% of the test values may be, expected to fall). In other words, this strength is expected to be exceeded by 95% of the cases. Compact Section  A cross section capable of developing full plastic distribution across it, without local buckling in any of the component members but not capable of developing ductility. Dead Loads  The self weights of all permanent constructions and installations including the self weights of all walls, partitions, floors and roofs. Effective Lateral Restraint  Restraint, which produces sufficient resistance in a plane perpendicular to the plane of bending to restrain the compression flange of a loaded strut, beam or girder from buckling to either side at the point of application of the restraint. Elastic Critical Moment  The elastic moment which will initiate yielding or cause buckling. Factor of Safety  The factor by which the yield stress of the material of a member is divided to arrive at the permissible stress in the material.
Gauge  The transverse spacing between parallel adjacent lines of fasteners. Imposed (Live) Load  The load assumed to be produced by the intended use of occupancy including distributed, concentrated, impact and vibration and snow loads but excluding, wind and earthquake loads. Limit States Limit States are states beyond which the structure no longer satisfies the design performance requirements and fulfils the purpose for which it is built. Load Factor  The numerical factor by which the working load is to be multiplied to obtain an appropriate design ultimate load.
9
Main Member  A structural member that is primarily responsible for carrying and distributing the applied load. Pitch  The centretocentre distance between individual fasteners in a line of fastener. Plastic Section  A cross section capable of developing full plasticity across it and exhibit considerable ductility. (Plastic crosssections when used as beams, will fail by formation of plastic hinges) Secondary Member  Secondary member is that which is provided for stability and or restraining the main members from buckling or similar modes of failure. SemiCompact Section  A cross section capable of developing yield stress at the extreme fibres, without buckling of any of the component elements (e.g. with a triangular stress distribution in a beam) but not capable of developing redistribution of stresses. Serviceability Limit States  Serviceability Limit States correspond to states beyond which the criteria for service are no longer met and include deformations and deflections, which adversely affect the appearance or its proper functioning and include vibration that causes discomfort to people or damage to the building Slender Section  In a slender section, local buckling of one of the components will occur before the attainment of yield stress in extreme fibre. Welding Terms  Unless otherwise defined in this standard the welding terms used shall have the meaning given in IS: 8121957. Ultimate Limit States  Ultimate Limit States are those associated with collapse or other forms of structural failure, which may endanger the safety of people. This includes the loss of equilibrium of the structure (or any part of it), failure by excessive deformation, rupture etc. Yield Stress  The minimum yield stress of the material in tension as specified in relevant Indian Standards.
10
APPENDIX B: Symbols Crosssectional area ( used with subscripts has been defined at appropriate place) Respectively the greater and lesser projection of the plate beyond column Length of side of cap or base Width of steel flange in encased member Coefficient The distance centre to centre of battens Distance between vertical stiffeners Respectively the lesser and greater distances from the sections neutral axis to the extreme fibres Overall depth of beam Depth of girder  to be taken as the clear distance between the flange angles or where there are no flange angles the clear distance between flanges ignoring fillets Diameter of the reduced end of the column i) For the web of a beam without horizontal stiffeners  the clear distance between the flanges, neglecting fillets or the clear distance between the inner toes of the flange angles as appropriate. ii) For the web of a beam with horizontal stiffeners  the clear distance between the horizontal stiffener and the tension flange, neglecting fillets or the inner toes of the tension flange angles as appropriate. Twice the clear distance from the neutral axis of a beam to the compression flange, neglecting fillets or the inner toes of the flange angles as appropriate. The modulus of elasticity for steel, taken as Mpa in this Guide. Yield stress Elastic critical stress in bending Elastic critical stress in compression, also known as Euler critical stress. Gauge Outstand of the stiffener Moment of inertia Flexural stiffness Coefficients Distance from outer face of flange to web toe of fillet of member to be stiffened Span/length of the member Effective length of the member Bending moment Maximum moment (plastic) capacity of a section Maximum moment (plastic) capacity of a section subjected to bending and axial loads. Lateral buckling strength in the absence of axial load Number of parallel planes of battens
11
Coefficient in the Merchant Rankine formula, assumed as 1.4 Axial force, compressive or tensile Calculated maximum load capacity of a strut Calculated maximum load capacity as a tension member Euler load Yield strength of axially loaded section The reaction of the beam at the support Radius of gyration of the section Transverse distance between centroids of rivets groups or welding Staggered pitch Mean thickness of compression flange used with subscripts has been defined at appropriate place) Thickness of web Transverse shear Longitudinal shear Calculated maximum shear capacity of a section Total load Pressure or loading on the underside of the base Plastic modulus of the section Ratio of smaller to larger moment Stiffness ratio Slenderness ratio of the member; ratio of the effective length to the appropriate radius of gyration
Characteristic slenderness ratio = Maximum permissible compressive stress in an axially loaded strut not subjected to bending Maximum permissible tensile stress in an axially loaded tension member not subjected to bending Maximum permissible compressive stress in slab base Maximum permissible compressive stress due to bending in a member not subjected to axial force. Maximum permissible tensile stress due to bending in a member not subjected to axial force Maximum permissible stress in concrete in compression Maximum permissible equivalent stress Maximum permissible bearing stress in a member Maximum permissible bearing stress in a fastener Maximum permissible stress in steel in compression Maximum permissible stress in axial tension in fastener Calculated average axial compressive stress Calculated average stress in a member due to an axial tensile force Calculated compressive stress in a member due to bending about a principal axis
12
Calculated compressive stress in a member due to bending about a principal axis Calculated tensile stress in a member due to bending about both principal axes Maximum permissible average shear stress in a member Maximum permissible shear stress in a member Maximum permissible shear stress in fastener Ratio of the rotation at the hinge point to the relative elastic rotation of the far end of the beam segment containing plastic hinge angle of twist (in a beam subjected to torsion) Coefficient Ratio of total area of both the flanges at the point of least bending moment to the corresponding area at the point of greatest bending moment Ratio of moment of inertia of the compression flange alone to that of the sum of the moments of inertia of the flanges each calculated about its own axis parallel to the yy axis of the girder, at the point of maximum bending moment. NOTE  The subscript x, y denote the xx and yy axes of the section respectively. For symmetrical sections, xx denotes the major principal axis whilst yy denotes the minor principal axis.
13
APPENDIX C: Relevant Indian Standards IS: 2261975 Structural steel (standard quality) (fifth revision) 4562000 Code of practice for plain and reinforced concrete (third revision) 6961972 Code of practice for general engineering drawings (second revision) 7861967 (Supplement) SI supplement to Indian Standard conversion factors and conversion tables (first revision) 8001984 Code of Practice for General Construction in Steel 8011975 Code of Practice for the use of coldformed light gauge steel structural members in general building construction 8121957 Glossary of terms relating to welding and cutting of metals 8131961 Scheme of symbols for welding 814 Covered electrodes for metal arc welding of structural steels: (Part 1)  1991 Part 1 for welding products other than sheets (Part 2)  1991 Part 2 for welding sheets 8161969 Code of practice for use of metal arc welding for general construction in mild steel (first revision) 8171966 Code of practice for training and testing of metal arc welders (revised) 8191957 Code of practice for resistance spot welding for light assemblies in mild steel 8751987 Code of practice for structural safety of buildings: Loading standards 9191963 Recommendations for limits and fits for engineering (revised) 9611975 Structural steel (high tensile) (Second revision) 9621967 Code of practice for architectural and building drawings (first revision) 10241992 Code of practice for use of welding in bridges and structures subject to dynamic loading 10301982 Carbon steel castings for general engineering purposes (second revision) 11481973 Hotrolled steel rivet bars (up to 40mm diameter) for structural purposes (second revision) 11491982 High tensile steel rivet bars for structural purposes 12611959 Code of practice for seam welding in mild steel 12781972 Filler rods and wires for gas welding (second revision) 13231962 Code of practice for oxyacetylene welding for structural work in mild steel (revised) 13631967 Black hexagon bolts, nuts and lock nuts (diameter 6 to 39mm) and black hexagon screws (diameter 6 to 24 mm) (first revision) 13641967 Precision and semiprecision hexagon bolts, screws, nuts and lock nuts (diameter range 6 to 39 mm) (first revision) 13671967 Technical supply conditions for threaded fasteners (first revision) 13931961 Code of practice for training and testing of oxyacetylene welders 13951982 Molybdenum and chromium molybdenum vanadium low alloy steel electrodes for metal arc welding (third revision) 1477 Code of practice for painting of ferrous metals in buildings: (Part 1)  1995 Part 1 Pretreatment
173
(Part 2)  1995 Part 2 Painting 18931991 Criteria for earthquake resistant design of structures (third revision) 19291961 Rivets for general purposes (12 to 48 mm diameter) 19771975 Structural steel (ordinary quality) (second revision) 20621992 Weldable structural steel (third revision) 21551982 Rivets for general purposes (below 12 mm diameter) 36131974 Acceptance tests for wireflux combinations for submergedarc welding of structural steels (first revision) 36401967 Hexagon fit bolts 37571972 Hightensile friction grip bolts (first revision) 40001967 Code of practice for assembly of structural joints using high tensile friction grip fasteners 53691975 General requirements for plain washers and lock washers (first revision) 53701969 Plain washers with outside diameter 3 times inside diameter 53721975 Taper washers for channels (ISMC) (first revision) 53741975 Taper washers for Ibeams (ISMB) (first revision) 64191971 Welding rods and bare electrodes for gas shielded arc welding of structural steel 65601972 Molybdenum and chromiummolybdenum low alloy steel welding rods and base electrodes for gas shielded arc welding 66101972 Heavy washers for steel structures 66231972 High tensile friction grip nuts 66391972 Hexagon bolts for steel structures 66491972 High tensile friction grip washers. 72051973 Safety code for erection of structural steel work 72151974 Tolerances for fabrication of steel structures 72801974 Bare wire electrodes for submerged arc welding of structural steels 7307 (Part 1) 1974 Approval tests for welding procedures: Part I Fusion welding of steel 7310 (Part 1) 1974 Approval tests for welders working to approved welding procedures: Part 1 Fusion welding of steel 7318 (Part 1) 1974 Approval tests for welders when welding procedure is not required: Part 1 Fusion welding of steel 85001977 Weldable structural steel (medium and high strength qualities) 95951980 Recommendations for metal arc welding of carbon and carbon manganese steels. SP6  1972 Handbook for Structural Engineers  Application of Plastic theory in the Design of Steel Structures
174
APPENDIX D: An Approximate Method of Torsion Analysis 1.0
An
Approximate Method of Torsion Analysis Due to the complexity of the Torsion analysis, a simple approach often adopted by structural designers for rapid design of steel structures is known as the bimoment method and is sufficiently accurate for practical purposes. The applied torque is replaced by a couple of horizontal forces acting in the plane of the top and bottom flanges as shown in Fig. 1 and Fig. 2. When a uniform torque is applied to an open section restrained against warping, the member itself will be in nonuniform torsion. The angle of twist, therefore, varies along the member length. The rotation of the section will be accompanied by bending of flanges in their own plane. The direct and shear stresses caused are shown in Fig. 3. For an section, the warping resistance can be interpreted in a simple way. The applied torque is resisted by a couple comprising the two forces equal to the shear forces in each flange. These forces act at a distance equal to the depth between the centroids of each flange. Each of these flanges can be visualised as a separate beam subjected to bending moments produced by the forces This leads to bending stresses in the flanges. These are termed Warping Normal Stresses. The magnitude of the warping normal stress at any particular point given by
Where
in the cross section is
= normalized warping function at a particular point in the cross section
16
176
An approximate method of calculating the normalised warping function for any section is described in by Nethercot etal. The inplane shear stresses are called Warping shear stresses. They are constant across the thickness of the element. Their magnitude varies along the length of the element. The magnitude of the warping shear stress at any given point is given by
where = Warping statical moment of area at a particular point Values of warping normal stress and inplane shear stress are tabulated in standard steel tables produced by steel makers. 1.1
The effect of Torsional Rigidity (GJ) and Warping Rigidity (ET) on the Design of Sections
The warping deflections due to the displacement of the flanges vary along the length of the member. Both direct and shear stresses are generated in addition to those due to bending and pure torsion. The stiffness of the member associated with the former stresses is directly proportional to the warping rigidity, When the torsional rigidity is very large compared to the warping rigidity, then the section will effectively be in "uniform torsion". Closed sections (e.g. rectangular or square hollow sections) angles and Tees behave this way, as do most flat plates and all circular sections. Conversely if is very small compared with the member will effectively be subjected to warping torsion. Most thin walled open sections fall under this category. Hot rolled sections as well as channel sections exhibit a torsional behaviour in between these two extremes. In other words, the members will be in a state of nonuniform torsion and the loading will be resisted by a combination of uniform (St.Venant's) and warping torsion. 1.2
End Conditions
The end support conditions of the member influence the torsional behaviour significantly; three ideal situations are described below. (It must be noted that torsional fixity is essential at least in one location to prevent the structural element twisting bodily). Warping fixity cannot be provided without also ensuring torsional fixity. The following end conditions are, therefore, relevant for torsion calculations •
Torsion fixed, Warping fixed: This means that the twisting along the longitudinal (Z) axis and also the warping of cross section at the end of the member are prevented. =0 at the end). This is also called "fixed" end condition.
177
• Torsion fixed, Warping free: This means that the cross section at the end of the member cannot twist, but is allowed to warp. This is also called "pinned" end condition. • Torsion free, Warping free: This means that the end is free to twist and warp. The unsupported end of cantilever illustrates this condition. (This is also called "free" end condition). Effective warping fixity is difficult to provide. It is not enough to provide a connection, which provides fixity for bending about both axes. It is also necessary to restrain the flanges by additional suitable reinforcements. It may be more practical to assume "warping free" condition even when the structural element is treated as "fixed" for bending. 2.0
Pure Torsion and Warping
When a torque is applied only at the ends of a member such that the ends are free to warp, then the member would develop only pure torsion. The total angle of twist
Where
over a length of is given by
= applied torque = Torsional Rigidity
When a member is in nonuniform torsion, the rate of change of angle of twist will vary along the length of the member. The warping shear stress at a point is given by
Where
= Modulus of elasticity = Warping statical moment at a particular point S chosen.
The warping normal stress given by
where 3.0
due to bending moment inplane of flanges (bimoment) is
= Normalised warping function at the chosen point S. Combined Bending and Torsion
There will be an interaction between the torsional and flexural effects, when a load produces both bending and torsion. The angle of twist caused by torsion would be amplified by bending moment, inducing additional warping moments and torsional
178
shears. This is analogous to the checks for buckling effects in columns due to effects.The following design checks are suggested in the SCI publication "Design of members subject to combined Bending and Torsion' by Nethercot, Salter and Malik.
3.1
Maximum Stress Check or "Capacity check"
The maximum stress at the most highly stressed cross section is limited to the design strength Assuming elastic behaviour and assuming that the loads produce bending about the major axis in addition to torsion, the longitudinal direct stresses will be due to three causes.
is dependent on
which itself is dependent on the major axis moment
and the
twist
Methods of evaluating for various conditions of loading and boundary conditions are given in the SCI publication referred above. 3.2
Buckling Check
Whenever lateral torsional buckling governs the design (i.e. when is less than the values of and will be amplified. The SCI publication has suggested a simple "buckling check" along lines similar to BS 5950, part 1
179
3.3
Applied Loading having both Major axis and Minor Axis Moments
When the applied loading produces both major axis and minor axis moments, the "capacity checks" and the "buckling checks" are modified as follows: Capacity check:
3.4 Torsional Shear Stress check Torsional shear stresses and warping shear stresses should also be amplified in a similar manner:
This shear stress should be added to the shear stresses due to bending in checking the adequacy of the section.
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APPENDIX E: Location of Neutral Axis
(1) For concrete encased steel sections: Major axis bendins
181
Note:
is the sum of the
reinforcement area within the region of
(2) For concrete filled tubular
sections Major axis bending
Note: •
For circular tubular section substitute
For minor axis bending the same equations interchanging and as well as the subscripts and
182
can
be
used
by
INSDAG'S ACTIVITIES AND PUBLICATIONS During the past three and half years, INSDAG has undertaken some important projects and already published some valuable documents. Some of the projects are currently on going and the publications will be available in appropriate times. Following are a brief glimpse on some of the activities of INSDAG: A. Publications Avalable For Sale
1.
Directory of Steel Supply Chain The Institute compiled and printed 'Directory of Steel Supply Chain' for improving interaction among professionals engaged directly or indirectly in the business of steel. It contains contact details of more than 5000 architects, builders, designers, consultants, fabricators, steel producers, rerollers, importers etc. The directory fulfills longstanding need of professionals in the country. Publication No INS/PUB/001
2.
Price Rs
685/
Buyer's Manual (including CD ROM) The professionals in the steel supply chain have also been in need of a source book for obtaining ready reference for their steel product needs. The 'Buyer's Manual' brought out by the Institute is a very useful document, which has a listing of about 220 steel companies/traders/importers etc. The manual contains details of products, grades of steel and marketing procedure including lead time, minimum order quantity etc. The manual is also available in the form of userfriendly CD version. Publication No INS/PUB/ 002 Price Rs 350/ for hardcopy and CD ROM version separately, and Rs 550/ for a complete set of hardcopy and CD ROM together.
3.
Reference Manual for Structural Engineers Since the existing BIS Structural Engineers Handbook (last revised in 1964) does not contain information about sectional properties of all the presently available sections from the producers and import as required by designers, INSDAG has prepared and published uptodate "Reference Manual for Structural Engineers". In addition to sectional properties, the Manual also contains brief extract from important codes, details of producers etc. Publication No INS/PUB/003
4.
Price Rs 450/
Handbook on Composite Construction: Bridges and Flyover Steelconcrete Composite Construction is widely used in the advanced countries. Their popularity is largely due to the speed with which bridges / flyovers can be constructed in busy metros. In
8
order to provide guidance to the professionals to use this technology for design of bridges and flyovers, one handbook, based on Indian codes, has been prepared, printed and widely circulated. This handbook is user friendly and contains 4 sample calculations for 16 metre and 24 metre spans along with properties of Composite Sections to help in designing similar problems quickly and accurately. Publication No INS/PUB/ 004
5.
Price Rs 525/
Corrosion Protection of Structural Steel in Buildings and Bridges Corrosion has been told to be the major problem for application of steel in construction sector. In order to provide the engineers proper technical writeup about occurrence of corrosion and ways to overcome it as being done in the developed countries, a comprehensive corrosion protection guide publication has been published. Publication No INS/PUB/ 005
6.
Price Rs 85/
Case Studies on PreEngineered Buildings and Space Frame Preengineered buildings and space frames are widely employed in the advanced countries in view of their multifarious benefits such as: significant saving in time of designing, construction, erection and cost apart from being aesthetically elegant. With a view to popularize their use in India, nine case studies of such constructions recently executed in the country have been prepared and published. Publication No INS/PUB/ 016
7.
Price Rs 285/
Life Cycle Cost Study on Bangalore Mass Rapid Transit System INSDAG has carried out a technoeconomic study on life cycle cost assessment of elevated viaducts for the proposed Bangalore Mass Rapid Transit System Limited with the steel intensive construction route. It has been observed that though the initial cost of the concrete intensive option was 10 percent lower than the steel intensive option, the life cycle cost of the steel option is economical to the owner by 49 percent as well as the BOOT partner by 28 percent. Further detailed analysis has also been made. The study was made in April 2000. Base paper
8.
Price Rs 200/
Life Cycle Cost Assessment of a Typical Urban Flyover Though presently steel intensive construction is not able to compete with concrete construction on the initial cost basis, life cycle cost (LCC) is generally favourable. In the advanced countries, LCC is often used an important tool for decision making. Keeping this in view, an interesting life cycle cost assessment study has been made fore a typical urban flyover for two city locations. The work has been done in association with two leading consultants: M/s STUP Consultants Ltd and M/s CES (I) Pvt. Ltd. Publication No INS/PUB/017
Price Rs
600/
9.
Welding Guide for Structural Steel Various steel products—sections in the form of joists, channels, angles, SHS/RHS and plates of different thicknesses are now available in the domestic market. Though different steel companies and welding suppliers have published some information on welding aspects of their specific products using proprietary consumables, this welding guide will provide consolidated information covering structural steel grades, which could serve a useful reference for the Supervisors/Practicing Engineers engaged in steelwork. The guide is broadly divided into seven chapters namely: Structural steel and welding; Welding process and joints; Electrodes and Equipment; Welding defects, controls and care; Weld economics and cost calculations; Inspection and acceptance criteria; and other useful information. Publication No INS/PUB/ 018
Price Rs 250/
10. Handbooks on Composite Construction : Multilevel Carparks With the same objective of Composite Construction: Bridge and Flyover handbook, design guidebooks are also being prepared on Car Parks (Part 2) and Buildings (Part 3) under the steel intensive composite construction route. The outcome of this study indicates that initial direct cost of 5 level & 7 level steel intensive Carpark is lower than that of RCC option. Publication No INS/PUB/ 019 on Car Park
Price Rs 625/
11. Survey of Important Rail Bridges It had been planned to conduct survey of about 100 important rail bridges to ascertain the performance of steel bridges visavis RCC and prestressed concrete bridges. With the help and support from ED (B&S), RDSO and railway officials in different zones, about 50 rail bridges were visited for data collection, and relevant data for another about 50 bridges have been collected. It has been observed that bridges with steel superstructure constructed even more than 100 years ago are still functioning well. Publication No: INS/PUB/020
Price Rs 350/
12. Handbook on Structural Steel Detailing To simplify the fabrication process by bringing about uniformity in detailing as also to reduce the risk of corrosion and to provide technical aid to small fabricators and designers, a Handbook on Steel Detailing is have been prepared. It is spread over 12 chapters and 6 Appendices namely: Joining; Splices; Trusses; Beam to Beam Connection; and Ladders, Stairs and Hand Railings etc. The book is comprised of about 230 pages including 180 figures and 37 tables. Publication No.: INS/PUB/021
Price Rs 825/
13. Handbook on Composite Construction: MultiStorey Buildings INSDAG brought out this publication to promote steelconcrete composite construction in MultiStorey Building. Writeup on design aspects of composite beams, columns & composite
10
slabs using profiled deck. This design handbook also covers the complete detail design of a typical G+3 & B+G+9 storeyed Residential & Commercial Buildings. Publication No.: INS/PUB/022
Price Rs 625/
14. Economics of Two Steel Framed Commercial Buildings: Under Initial Cost and Life Cycle Cost Assessment Route Steel intensive construction for buildings is gradually becoming a subject of interest in India, though its cost effectiveness is often questioned. The sustainability of construction is also another important modern concept for buildings. Keeping this in view, a study on the construction cost, total initial cost and life cycle cost assessment of two typical urban commercial buildings has been done in association with leading consultants like M N Dastur & Co Private Ltd. and Development Consultants Private Ltd. Publication No.: INS/PUB/023
Price Rs 600/
15. Design of Composit Truss for Building Rolled/fabricated beams are commonly being used as the structural members of medium span structures.Moreover for longer spans, use of steel truss as the structural member of composite section is most desired. Use of steelconcrete composite truss is ideally suited for applications in community halls, industrial buildings, office buildings, conference halls etc. where large column free spans are a necessity. The publication mainly covers framing, analysis and connection details followed in advanced countries. It also contains a detailed example covering all important aspects of design by limit state method. Publication No.: INS/PUB/034
Price Rs. 475/
16. Life Cycle Cost Analysis and TechnoEconomic Study for the Use of Reinforced Cement Concrete Roads in National Highways and Expressways Rigid pavement is widely used in the developed countries. Some beginning has been made in our country also. On life cycle cost basis rigid pavements are very cost effective due much lower vehicle operating cost & maintenance cost. In order to assess the most cost effective pavement solution for National Highways & Expressways INSDAG carried out a study on CRCP and published a document entitled "Life Cycle Cost Analysis and TechnoEconomic Study for the Use of Reinforced Cement Concrete Roads in National Highways and Expressways". The outcome of the study reveals that the LCC cost of CRCP is much lower than flexible pavement. An analysis, based on the applicable Indian, AASHTO and British Standards as well as based on the published literature, shows that LCC cost of CRCP is lower than jointed plain concrete pavement (JPCP). Accordingly CRCP is the best longterm pavement solution both on cost as well as maintenance point of view for National highways & expressways. Publication No INS/PUB/ 035
Price: Rs. 325/
17. Guidebook on Steel Doors and Windows for Domestic Use Traditionally wooden doors and windows have been used in places like homes, offices, hotels, flats, factories and hospitals. With the developments taken place in advanced countries, steel doors and windows are now being preferred for various applications. This publication provides general and technical information concerning steel doors & windows. Users of windows, doors and related accessories will find it very useful in terms of design, manufacturing process, sourcing and application of these products. This guidebook is broadly divided into seven chapters namely: Introduction; Steel windows; Steel Doors; Standards for Manufacturing; Corrosion Protection & Maintenance; Cost Index & Practices and Bibliography. The beneficiaries of this publication are buyers, specifiers / procurement officers, manufacturers, distributors/ retailers, architects, designers, builders and suppliers, policyworkers and government officials. Publication No INS/PUB/ 036
Price: Rs. 300/
18.(B+G+20) Storied Residential Building with SteelConcrete Composite Option In India residential buildings are coming up in numbers with a height of 20 storied and above to accommodate the influx of population to Metros which are facing severe space constraint. This publication covers a study on the cost effectiveness of the fasttrack Steel Concrete Composite construction in comparison with the RCC option based on the same type plan of a (B+G+20) storied residential building which has been collected from a live example. The Composite options have been considered with conventional brick cladding and with lighter cladding material like M2 Panel/Aerocon Blocks/Gypcrete etc., which has indicated substantial savings over its RCC option. The design of the structural elements have been carried out following relevant Indian/foreign standards in Limit State Method of Design both for RCC and Composite construction, this book helps the builders, designers, Architects to selects an econoimic and safe Technical option for their projects. Publication No.: INS/PUB/047
Price Rs 650/
19. (G+3) & (G+6) Storied Residential Buildings with Steel Concrete Composite Option In the publication the modern trend of SteelConcrete Composite construction has been considered. It also includes a study of the cost effectiveness of the steelConcrete Composite options visavis RCC option based on the type plan of (G+3) & (G+6) storied residential buildings collected from a live example. The Composite options have been considered with conventional brick cladding and with lighter cladding material like M2 Panel/Aerocon Blocks/Gypcrete etc., which has indicated substantial savings over its RCC option. The design of the Structural elements has been carried out in Limit State Method of Design following Indian/foreign standards both for RCC & Composite options. Publication No.: INS/PUB/048
Price Rs 650/
20. Typical Design of Costeffective Rural Housing Housing is considered as one of the major problems in the world. The habitation conditions of the Indian villagers particularly need to be improved. This publication includes a Housing scheme with Steel in frame having colums, beams & trusses with SHS sections and FerroCement
12
panels used for roofing and cladding. The housing scheme has been developed with doubledlayered FerroCement cladding having an airgap in between and with sufficient openings for ventilation, which makes habitation comfortable for the villagers, and it is designed to take care of the effects of Earthquake & Wind. Elevated units also take care of water clogging during monsoon. Publication No.: INS/PUB/049
Price Rs 3007
B. Projects Under Progress 1.
Design of a Typical cyclone / Flood relief Center at Paradip At the instance of JPC  one of the major stakeholders, INSDAG had prepared a steel intensive design for a raised twostorey school building (15 m X 15 m X 8 m) with required wind loading to be used as a cyclone/flood relief center in Paradeep, Orissa.
2.
Road Island Project INSDAG has prepared a design of an exquisite inverted pyramid (top: 16 m X 16 m; height: 8 m) of tubular structure displaying steel application in a typical road island.
3.
Earthquake Resistant Design of Structures Steel is globally used for earthquake resistant structures. In view of the need for speedy rehabilitation and reconstruction of earthquake affected areas in Gujarat and based on interaction made with various agencies, the Institute had prepared general arrangement drawings of 7 variants (260 sq. ft. for rural areas; 435 sq. ft., 640 sq.ft. and 840 sq.ft. in G+1 and G+3 modules) with the help of a leading consultant and submitted to concerned authorities in Gujarat. Later on, the Institute has also developed detailengineering drawings for the singlestoreyed building and the G+3 building (640 sqft appartments) and submitted to the concerned authorities in Gujarat. These drawings are available for sale.
4.
Teaching Resource for Structural Steel Design for Faculty of Civil/Structural Engg. The project on Teaching Resource for Structrual Steel Design for the Faculty of Civil/Structural Engineering has been pursued by the Expert Team (Dr V Kalyanraman, Dr A R Santhakumar, DrS.R. Satish Kumar, DrS. Seetharaman, Mr A. Jayachandran and others) under the leadership of Dr. R. Narayanan, expert from Steel Construction Institute, UK. Preparation of all the 45 chapters for one semester course had been completed after expert reviews. Six Workshops for the university faculty have been organized at six different places namely IITChennai, IITMumbai, BE College(DU)Howrah, Delhi College of EngineeringDelhi, Malviya National Institute of TechnologyJaipur and IITRoorkee with total involvement of the expert team to train approximately 220 teachers from 173 engineering colleges using the stateofart teaching material. All the 45 chapters are available in the INSDAG website www.steelinsdag.org.
Technical volumes are available for sale. Price Rs 2500/ for full set (Rs 3000/ with CD). Only CD ROM is available at Rs 800/ only. 5. Refresher Courses on Composite Construction Improving knowledge and skill of professionals in design using composite construction has been identified as an important area of activity. Twelve refresher courses had been conducted till December 2002. These consist of two at Calcutta, two at Chennai, one each at Delhi, Bhubaneswar, Ahmedabad, Hyderabad, Ranchi and IITGuwahati. About 250 professionals and 50 faculties have been exposed to composite construction technology. Considering the importance of ductile design of steel structures, concept of earthquake resistant design had also been included in the lecture material of some refresher courses. The technical volumes are available for sale.
Price Rs 800/ (for each course)
C. Steel Promotional Brochures The Institute has published five attractive promotional/ awareness brochures for free distribution to target customers such as designers, consultants, architects, builders at various conferences and other forums: •
Preengineered Buildings
•
Steel —The Right Choice for Building Construction
•
Steel — The Trusted Material for Bridges and Flyovers
•
Corrosion Protection of Structural Steel in Buildings and Bridges
•
Steel Car Parks  A Worldwide Choice
D. Regular Publications of Insdag 1.
Insdag's Steel in Construction  a half yearly technical journal
Price Rs 90/
2.
INSDAG News  a quarterly news bulletin
Price Rs 20/
3.
Insdag ENews Letter  Monthly
Free
E. Other Activities 1. Student Award Scheme for Best Innovative Use of Steel inArchitecture In the fourth year (2002  03) for the "Student Award Scheme for the Innovative Use of Steel in Architecture", an exciting brief entitled "World Class Shopping Plaza" had been prepared and circulated to more than 100 Schools of Architecture / Engineering Colleges. The last date of recipt of entries is 30th January 2003 The entries will be evaluated by Zonal Committees in the month of April 2003. The final selection will be done in June 2003.
14
2.
Award Scheme for Civil and Structural Engineering Students for Best Innovative Structural Steel Design In the third year (2002  2003) for the "Award Scheme for Civil and Structural Engineering Students for Best Innovative Structural Steel Design", an exciting brief on the theme of "Elevated Light Rail Transit System" has been prepared and circulated to more than 240 Engineering Institutions. The last date of receipt of entries is 31 st March 2003. The entries will be evaluated by Zonal Committees in the month of AprilMay 2003. The final selection will be done in July 2003.
3.
Interfacing with the MOS The Institute has prepared technical documents/Vision Paper for consideration/perusal by concerned authorities: o Use of steel crash barriers on bridges and highways o
Input paper on National Steel Policy with particular focus on construction sector
o Justification for adoption of steel scaffolding in place of bamboo/wood based on life cycle costing and safety requirement 4.
Review of Relevant Documents for Modification of IRC 22, IRC 24 and some IS codes. Advances on knowledge of structural behaviour resulting from research need to be adopted in design practice for innovative / efficient design techniques. This necessitated modification of Codes of Practices (BIS/IRC Codes which have not kept pace with the technological improvements in latest design methodologies), pertaining to construction in steel as well as steelconcrete composite. INSDAG has been involved in IRC B7 Committee engaged in revision of IRC 22, 24 pertaining to construction of composite, steel bridges respectively, and a Committee on IS 800 engaged in modifying the Code of Practice for use of structural steel in general building construction to limit state method. Also, INSDAG has been included in a subcommittee entrusted to preparation of "Guidelines for design of Composite / Steel Box Girder bridges" considered to be cost effective for relatively higher spans where composite bridges using steel plate girders are not economical compared to other competitive options. To make the design of steel bridges as well as steelconcrete composite bridges economical and rational based on the stateoftheart methodologies, modifications have been suggested to clauses pertaining of deflection stipulation, modular ratio and shear connector capacity in the present design environment (working stress method). It has been estimated that amended clause on deflection stipulation itself will reduce the weight of bridge girder to the tune of 13 percent.
F. Copyright Publications From SCI, UK In addition to the above, INSDAG has published 20 important documents under copyright from the steel Construction Institute, UK on steel intensive design of structures. A list of such publications is provided below: