Steel Structures by M.Teja, Lecture notes of Civil Engineering

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Design of Steel Structures – Limit State Method

(As Per IS 800: 2007)

By

Vaisakh G.

(Assistant Professor in Civil Engineering, Sree Buddha College of Engineering)

08.601. DESIGN OF STEEL STRUCTURES

Module I

Properties of structural steel, Structural steel sections, Limit state and working stress design concepts, Types of connections - Design of welded and bolted connections, Design of tension members and compression members, Design of laterally supported and unsupported beams - Built up beams, Simple beam to column connections.

Module II

Plate girders- design of section, curtailment of flange plate, bearing and intermediate stiffeners, connections, flange and web splices, Gantry girders (only design concept).

Columns- Design of axially and eccentrically loaded compression members, simple and built up sections, lacing and battening, Column bases- slab bases and gusseted bases.

Module III

Light gauge steel structures – Types of sections, Flat width ratio, buckling of thin elements, Effective design width, Form factor, Design of tension, compression members and beams.

Plastic design- basic assumptions - shape factor, load factor- Redistribution of moments - upper bound, lower bound and uniqueness theorems- analysis of simple and continuous beams, two span continuous beams and simple frames by plastic theory - static and kinematic methods.

References:

1. Subramanian N., Design of steel structures, Oxford University Press
2. Arya A.S. and J. L. Ajmani, Design of Steel Structures, Nemchand & Bros
3. Dayaratnam P., Design of Steel Structures, Wheeler
4. Ramachandra, Design of Steel Structures, Standard books
5. Duggal S.K., Design of Steel Structures, T.M.H. Publications
6. IS. Codes: IS:800-2007, IS:811-1987, IS:801- 1975

Note

Question Paper:

Duration: 3 hours

The question paper consists of Part A and Part B. Part A is for 40 marks. There will be 8 compulsory short answer questions of 5 marks each covering entire syllabus. Part B is for 60 marks. There will be two questions from each module. The candidate has to answer one question of 20 marks from each module.

Use of IS Codes: 800-2007, 811-1987, 801- 1975 and Structural Steel Tables is permitted in the Examination Hall.

No other charts, tables, codes are permitted in the Examination hall .If necessary relevant data shall be given along with the question paper by the question paper setter

1. INTRODUCTION

Ever since steel began to be used in the construction of structures, it has made possible some of the grandest structures both in the past and also in the present day. Steel is by far the most useful material for building structures with strength of approximately ten times that of concrete, steel is the ideal material for modern construction. Due to its large strength to weight ratio, steel structures tend to be more economical than concrete structures for tall buildings and large span buildings and bridges. Steel structures can be constructed very fast and this enables the structure to be used early thereby leading to overall economy. Steel structures are ductile and robust and can withstand severe loadings such as earthquakes. Steel structures can be easily repaired and retrofitted to carry higher loads. Steel is also a very eco-friendly material and steel structures can be easily dismantled and sold as scrap. Thus the lifecycle cost of steel structures, which includes the cost of construction, maintenance, repair and dismantling, can be less than that for concrete structures. Since steel is produced in the factory under better quality control, steel structures have higher reliability and safety. To get the most benefit out of steel, steel structures should be designed and protected to resist corrosion and fire. They should be designed and detailed for easy fabrication and erection. Good quality control is essential to ensure proper fitting of the various structural elements. The effects of temperature should be considered in design. To prevent development of cracks under fatigue and earthquake loads the connections and in particular the welds should be designed and detailed properly. Special steels and protective measures for corrosion and fire are available and the designer should be familiar with the options available.

A steel structure, like any other, is an assemblage of a group of members which contribute to resist the total load and thereby transfer the loads safely to ground. This consist members subjected to various actions like axial forces (Compression & Tension), bending, shear, torsion etc or a combination of these. The elements are connected together by means of rivets, pins or welds. Depending on the fixity of these joints, the connections are classified as rigid, semi rigid and flexible.

1.1. PROPERTIES OF STRUCTURAL STEEL

The properties of structural steel, as per clause 2.2.4 of IS 800:2007, for use in design, may be taken as given in clauses 2.2.4.1 and 2.2.4.2 of the code.

1.1.1. Physical properties

Physical properties of structural steel, as detailed by cl.2.2.4.1 of IS 800:2007, irrespective of its grade may be taken as: a) Unit mass of steel, p = 7850 kg/m^3 b) Modulus of elasticity, E = 2.0x10^5 N/mm^2 (MPa) c) Poisson ratio, p = 0.3 d) Modulus of rigidity, G = 0.769x10 5 N/mm^2 (MPa) e) Coefficient of thermal expansion cx .=12x10 -6^ / 0 C

1.1.2. Mechanical properties

The principal mechanical properties of the structural steel important in design, as detailed by the code IS 800:2007 in cl. 2.2.4.2, are the yield stress, f (^) y; the tensile or ultimate stress, fu ; the maximum percent elongation on a standard gauge length and notch toughness. Except for notch toughness, the other properties are determined by conducting tensile tests on samples cut from the plates, sections, etc, in accordance with IS 1608. Commonly used properties for the common steel products of different specifications are summarized in Table 1 of IS 800:2007. Highlights of the table are reproduced for ready reference as Table 1.

Table 1. Tensile Properties of Structural Steel Products

IS Code Grade Yield stress (Mpa) min (for d or t)

Ultimate tensile stress (MPa) min

Elongation Percent min <20 20 – 40 >

IS 2062

E 165 (Fe 290) 165 165 165 290 23 E250(Fe410W)A 250 240 230 410 23 E250(Fe 410 W)B 250 240 230 410 23 E250(Fe 410 W)C 250 240 230 410 23 E 300 (Fe 440) 300 290 280 440 22 E 350 (Fe 490) 350 330 320 490 22 E 410 (Fe 540) 410 390 380 540 20 E 450 (Fe 570) D 450 430 420 570 20 E 450 (Fe 590) E 450 430 420 590 20 1.1.2.1. Stress – strain behaviour: tensile test

The stress-strain curve for steel is generally obtained from tensile test on standard specimens as given in Figure 1. The details of the specimen and the method of testing is elaborated in IS: 1608 (1995). The important parameters are the gauge length ‘L (^) c’ and the initial cross section area So. The loads are applied through the threaded or shouldered ends. The initial gauge length is taken as 5.65√S (^) o in the case of rectangular specimen and it is five times the diameter in the case of circular specimen. A typical stress-strain curve of the tensile test coupon is shown in Figure 2 in which a sharp change in yield point followed by plastic strain is observed. After a certain amount of the plastic deformation of the material, due to reorientation of the crystal structure an increase in load is observed with increase in strain. This range is called the strain hardening range. After a little increase in load, the specimen eventually fractures. After the failure it is seen that the fractured surface of the two pieces form a cup and cone arrangement. This cup and cone fracture is considered to be an indication of ductile fracture. It is seen from Figure 2 that the elastic strain is up to εy followed by a yield plateau between strains εy and εsh and a strain hardening range start at εsh and the specimen fail at εult where εy, εsh and εult are the strains at onset of yielding, strain hardening and failure respectively.

Depending on the steel used, εsh generally varies between 5 and 15 εy, with an average value of 10 εy typically used in many applications. For all structural steels, the modulus of elasticity can be taken as 205,000 MPa and the tangent modus at the onset of strain hardening is roughly 1/30th of that value or approximately 6700 MPa. High strength steels, due to their specific microstructure, do not show a sharp yield point but rather they yield continuously as shown in Figure 2. For such steels the yield stress is always taken as the stress at which a line at 0.2% strain, parallel to the elastic portion, intercepts the stress strain curve.

Figure 1 Standard specimen for tensile test.

The nominal stress or the engineering stress is given by the load divided by the original area. Similarly, the engineering strain is taken as the ratio of the change in length to original length.

1.2. ROLLED STEEL SECTIONS

Figure 4 Standard Rolled Sections

Hot Rolling is usually used to produce the standard section. In this process, the molten steel is poured in to continuous casting systems where it is passed through a series of rollers which squeeze it to the desired shape before if solidifies completely. It is subsequently cut in to desired standard lengths. Cross section and size of the members are governed by optimum use of material, functional requirement etc. Usually sections with larger modulus of section compared to cross sectional area are preferred. IS Handbook 1 published by BIS provides the dimensions, weights and other sectional

properties of various standard sections. Some of the sections as detailed by Figure 2 of IS 800:2007 is reproduced here in Figure 4.

1.2.1. Conventions for member axes

Unless otherwise specified, x-x axis is considered along the length of the member; y-y axis of the cross section is the axis perpendicular to the flanges in general and the axis perpendicular to the smaller leg in the case of angles; z-z axis of the cross section is the axis parallel to the flanges in general and the axis parallel to the smaller leg in the case of angles; u-u axis is the major axis of the section and v-v axis is the minor axis of the section. This is schematically represented in Figure 5.

Figure 5 Axes of Members

2.2.2. Imposed Loads (Cl. 3.2.1.2 of IS 800:2007)

IS 800:2007 specifies in Cl.3.2.1.2 that imposed loads for different types of occupancy and function of structures shall be taken as recommended in IS 875 (Part 2). Imposed loads arising from equipment, such as cranes and machines should be assumed in design as per manufacturers/suppliers data (Cl. 3.5.4 of IS 800:2007). Snow load shall be taken as per IS 875 (Part 4).

2.2.3. Wind loads (Cl. 3.2.1.3 of IS 800:2007)

Wind loads on structures shall be taken as per the recommendations of IS 875 (Part 3).

2.2.4. Earthquake loads (Cl. 3.2.1.4 of IS 800:2007)

Earthquake loads shall be assumed as per the recommendations of IS 1893 (Part 1).

2.2.5. Erection Loads (Cl. 3.3 of IS 800:2007)

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. The structure as a whole and all parts of the structure in conjunction with the temporary bracings shall be capable of sustaining these loads during erection.

2.2.6. Temperature Effects (Cl. 3.4 of IS 800:2007)

Expansion and contraction due to changes in temperature of the members and elements of a structure shall be considered and adequate provision made for such effect. The co-efficient of thermal expansion for steel is as given in Cl. 2.2.4.l of IS 800:2007.

2.2.7. Load Combinations

Load combinations for design purposes shall be those that produce maximum forces and effects and consequently maximum stresses and deformations. The following combination of loads with appropriate partial safety factors as given in Table 4 of IS 800:2007 may be considered. The table is reproduced here as Table 2 for ready reference. a) Dead load + imposed load, b) Dead load + imposed load + wind or earthquake load, c) Dead load + wind or earthquake load, and d) Dead load+ erection load. The effect of wind load and earthquake loads shall not be considered to act simultaneously. The load combinations are outlined in detail in Cl. 3.5 of IS 800:2007.

Table 2 Partial safety factors for loads for limit states

2.3. GEOMETRICAL PROPERTIES

The geometrical properties, as detailed in Cl. 3.6 of IS 800:2007, of the gross and the effective cross-sections of a member or part thereof, shall be calculated on the following basis: a) the properties of the gross cross-section shall be calculated from the specified size of the member or part thereof or read from appropriate table b) The properties of the effective cross-section shall be calculated by deducting from the area of the gross cross-section, the following:

• The sectional area in excess of effective plate width, in case of slender sections.
• The sectional areas of all holes in the section except for parts in compression. In case of punched holes, hole size 2 mm in excess of the actual diameter may be deducted. 2.4. CLASSIFICATION OF CROSS-SECTIONS

Plate elements of a cross-section may buckle locally due to compressive stresses. The local buckling can be avoided before the limit state is achieved by limiting the width to thickness ratio of each element of a cross-section subjected to compression due to axial force, moment or shear. When plastic analysis is used, the members shall be capable of forming plastic hinges with sufficient rotation capacity (ductility) without local buckling, to enable the redistribution of bending moment required before formation of the failure mechanism. When elastic analysis is used, the member shall be capable of developing the yield stress under compression without local buckling. On basis of the above, Cl. 3.7 of IS 800:200 categorizes the sections in to four classes as follows.

When different elements of a cross-section fall under different classes, the section shall be classified as governed by the most critical element. The maximum value of limiting width to thickness ratios of elements for different classifications of sections are given in Table 2 of IS 800:2007 which is reproduced here as

Table 3.

2.4.1. Class 1 (Plastic)

Cross-sections which can develop plastic hinges and have the rotation capacity required for failure of the structure by formation of plastic mechanism fall under this category. The width to thickness ratio of plate elements shall be less than that specified under Class 1 (Plastic), in Table 2 of IS 800:2007.

2.4.2. Class 2 (Compact)

Cross-sections which can develop plastic moment of resistance, but have inadequate plastic hinge rotation capacity for formation of plastic mechanism, due to local buckling come under this class. The width to thickness ratio of plate elements shall be less than that specified under Class 2 (Compact), but greater than that specified under Class 1 (Plastic), in Table 2 of IS 800:2007.

2.4.3. Class 3 (Semi-compact)

Cross-sections in which the extreme fiber in compression can reach yield stress but cannot develop the plastic moment of resistance, due to local buckling. The width to thickness ratio of plate elements shall be less than that specified under Class 3 (Semi-compact), but greater than that specified under Class 2 (Compact), in Table 2 of IS 800:2007.

2.4.4. Class 4 (Slender)

Cross-sections in which the elements buckle locally even before reaching yield stress. The width to thickness ratio of plate elements shall be greater than that specified under Class 3 (Semi- compact), in Table 2 of IS 800:2007. In such cases, the effective sections for design shall be calculated either by following the provisions of IS 801 to account for the post-local-buckling strength or by deducting width of the compression plate element in excess of the semi-compact section limit.

2.6. MAXIMUM EFFECTIVE SLENDERNESS RATIO

The maximum effective slenderness ratio, as per Cl. 3.8 of IS 800:2007, KL/r values of a beam, strut or tension member shall not exceed those given in Table 3 of IS 800:2007. ‘KL’ is the effective length of the member and ‘r’ is appropriate radius of gyration based on the effective section as defined in Cl. 3.6.1 of IS 800:2007. This data is reproduced here in Table 4.

Table 4 Maximum effective slenderness ratio

Member

Maximum Effective Slenderness Ratio (KL/r) A member carrying compressive loads resulting from dead loads and imposed loads 180 A tension member in which a reversal of direct stress occurs due to loads other than wind or seismic forces 180 A member subjected to compression forces resulting only from combination with wind/earthquake actions, provided the deformation of such member does not adversely affect tbe stress in any part of the structure

Compression flange of a beam against lateral torsional buckling 300 A member normally acting m a tie in a roof truss or a bracing system not considered effective when subject to possible reversal of stress into compression resulting from the action of wind or earthquake forces

Members always under tension (other than pre-tensioned members) 400

3. LIMIT STATE DESIGN

The current revision of the code of practice, IS 800:2000, recommends limit state method for design of structures using hot rolled sections. This method is outlined in section 5 of IS 800:2007. However, it retained working stress method of design which was the design method for decades. But the scope of the working stress method is limited to those situations where limit state method cannot be conveniently employed.

3.1. BASIS FOR DESIGN

In the limit state design method, the structure shall be designed to withstand safely all loads likely to act on it throughout its life. It shall not suffer total collapse under accidental loads such as from explosions or impact or due to consequences of human error to an extent beyond the local damages. The objective of the design is to achieve a structure that will remain fit for use during its life with acceptable target reliability. In other words, the probability of a limit state being reached during its lifetime should be very low. The acceptable limit for the safety and serviceability requirements before failure occurs is called a limit state. In general, the structure shall be designed on the basis of the most critical limit state and shall be checked for other limit states.

Steel structures are to be designed and constructed to satisfy the design requirements with regard to stability, strength, serviceability, brittle fracture, fatigue, fire, and durability such that they meet the following: a) Remain fit with adequate reliability and be able to sustain all actions (loads) and other influences experienced during construction and use; b) Have adequate durability under normal maintenance; c) Do not suffer overall damage or collapse disproportionately under accidental events like explosions, vehicle impact or due to consequences of human error to an extent beyond local damage. The potential for catastrophic damage shall be limited or avoided by appropriate choice of one or more of the following:

• Avoiding, eliminating or reducing exposure to hazards, which the structure is likely to sustain.
• Choosing structural forms, layouts and details and designing such that: i) the structure has low sensitivity to hazardous conditions; and ii) the structure survives with only local damage even after serious damage to any one individual element by the hazard.
• Choosing suitable material, design and detailing procedure, construction specifications, and control procedures for shop fabrication and field construction as relevant to the particular structure. The following conditions may be satisfied to avoid a disproportionate collapse: The building should be effectively tied together at each principal floor level and each column should be effectively held in position by means of continuous ties (beams) nearly orthogonal, except where the steel work supports only cladding weighing not more than 0.7 kN/m^2 along with imposed and wind loads. These ties must be steel members such as beams, which may be designed for other purposes, steel bar reinforcement anchoring the steel frame to concrete floor or steel mesh reinforcement in composite slab with steel profiled sheeting directly connected to beam with shear connectors. These steel ties and their end connections should be capable of resisting factored tensile force not less than the factored dead and imposed loads acting on the floor area tributary to the tie nor less than 75 kN. Such connection of ties to edge column should also be capable of resisting 1 percent of the maximum axial compression in the column at the level due to factored dead and imposed loads. All column splices should be capable of resisting a tensile force equal to the largest of a factored dead and live load reaction from a single floor level located between that column splice and the next column splice below that splice. Lateral load system to resist notional horizontal loads prescribed in Cl. 4.3.6 of IS 800:2007 should be distributed throughout the building in nearly orthogonal directions so that no substantial portion is connected at only one point to such a system. Precast concrete or other heavy

The actions (loads), as detailed in Cl. 5.3 of IS 800:2007, to be considered in design include direct actions (loads) experienced by the structure due to self weight, external actions etc., and imposed deformations such as that due to temperature and settlements.

3.2.3.1. Classification of Actions

Actions are classified by Cl. 5.3.1 of IS 800:2007, by their variation with time as given below:

• Permanent actions (Qp ): Actions due to self weight of structural and non-structural components, fittings, ancillaries, and fixed equipment, etc.
• Variable actions (Qv ): Actions due to construction and service stage loads such as imposed (live) loads (crane loads, snow loads, etc.), wind loads, and earthquake loads, etc.
• Accidental actions (Qa ): Actions expected due to explosions, and impact of vehicles, etc. 3.2.3.2. Characteristic Actions (Loads)

The Characteristic Actions, QC, as defined by the code in Cl.5.3.2, are the values of the different actions that are not expected to be exceeded with more than 5 percent probability, during the life of the structure and they are taken as: a) the self-weight, in most cases calculated on the basis of nominal dimensions and unit weights [see IS 875 (Part 1)], b) the variable loads, values of which are specified in relevant standard [see IS 875 (all Parts) and IS 1893 (Part l)], c) the upper limit with a specified probability (usually 5 percent) not exceeding during some reference period (design life) and d) specified by client, or by designer in consultation with client, provided they satisfy the minimum provisions of the relevant loading standard.

3.2.3.3. Design Actions

The Design Actions, Qd , is expressed as ∑γfk Qck, where γfk = partial safety factor for different loads k, given in Table 4 of IS 800:2007 to account for: a) Possibility of unfavourable deviation of the load from the characteristic value, b) Possibility of inaccurate assessment of the load, c) Uncertainty in the assessment of effects of the load, and d) Uncertainty in the assessment of the limit states being considered. This is detailed in Cl. 5.3.3 of IS 800:2007.

3.2.4. Strength

The ultimate strength calculation as detailed in Cl. 5.4 of IS 800: 2000 require consideration of the following: a) Loss of equilibrium of the structure or any part of it, considered as a rigid body; and b) Failure by excessive deformation, rupture or loss of stability of the structure or any part of it including support and foundation.

3.2.4.1. Design Strength

The Design Strength given in 5.4.1 of IS 800:2007, Sd , is obtained from ultimate strength, S (^) u and partial safety factors for materials, γm given in Table 5 of IS 800:2007 by the relation Sd ≤ S (^) u /γm, where partial safety factor for materials, γm account for: a) Possibility of unfavourable deviation of material strength from the characteristic value, b) Possibility of unfavourable variation of member sizes, c) Possibility of unfavourable reduction in member strength due to fabrication and tolerances, and d) Uncertainty in the calculation

3.2.5. Factors Governing the Ultimate Strength

The following factors are considered by IS 800:2007 as those governing the ultimate strength.

3.2.5.1. Stability

Stability shall be ensured for the structure as a whole and for each of its elements. This should include overall frame stability against overturning and sway, as given in Clause 5.5.1.1 and 5.5.1.2 of IS 800:2007.

3.2.5.2. Stability against overturning

The structure as a whole or any part of it shall be designed to prevent instability due to overturning, uplift or sliding under factored load as given below: a) The Actions shall be divided into components aiding instability and components resisting instability. b) The permanent and variable actions and their effects causing instability shall be combined using appropriate load factors as per the Limit State requirements, to obtain maximum destabilizing effect.

3.2.5.3. Sway stability

The whole structure, including portions between expansion joints, shall 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 loads such as given in Cl. 4.3.6 of IS 800:2007 to evaluate the sway under gravity loads.

3.2.5.4. Fatigue

Generally 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 normally need not be considered. Fatigue design shall be in accordance with Section 13 of IS 800:2007. When designing for fatigue, the partial safety factor for load, γf , equal to unity shall be used for the load causing stress fluctuation and stress range.

3.2.5.5. Plastic Collapse

Plastic analysis and design may be used, if the requirement specified under the plastic method of analysis (Cl. 4.5 of IS 800:2007) are satisfied.

3.2.6. Limit State of Serviceability

Serviceability limit state is related to the criteria governing normal use. Serviceability limit state is limit state beyond which the service criteria specified below, are no longer met: a) Deflection limit, b) Vibration limit, c) Durability consideration, and d) Fire resistance.

3.2.6.1. Deflection

The deflection under serviceability loads of a building or a building component should not impair the strength of the structure or components or cause damage to finishings. Deflections are to be checked for the most adverse but realistic combination of service loads and their arrangement, by elastic analysis, using a load factor of 1.0. Table 6 of IS 800:2007 gives recommended limits of deflections for certain structural members and systems. Circumstances may arise where greater or lesser values would be more appropriate depending upon the nature of material in element to be supported (vulnerable to cracking or not) and intended use of the structure, as required by client.

3.2.6.2. Vibration

Suitable provisions in the design shall be made for the dynamic effects of live loads, impact loads and vibration due to machinery operating loads. In severe cases, possibility of resonance, fatigue or unacceptable vibrations shall be investigated. Unusually flexible structures (generally the height to effective width of lateral load resistance system exceeding 5:1) shall be investigated for lateral