Chapter 1. Introduction – Design of Steel Structures

1

Introduction

1.1 What are Steel Structures?

Structures are earmarks of our civilization. The various structures which come under the realm of civil engineering are buildings, bridges, dams, towers, roads and railway lines and to name a few. The buildings may be for residential, office, commercial or industrial purposes. The bridges may be for highways (roads) and railway lines. Dams and other hydraulic structures are to manage water and its flow. Towers are used for various purposes such as power transmission, radar and TV broadcast, telephone relay towers and nodal towers for cell network. The various structures mentioned here and some more are constructed with a variety of materials such as concrete, steel, masonry, timber, cast iron and plastics to name a few. This textbook mainly deals with the structures constructed using structural steel such as steel buildings, steel bridges and steel towers.

In India, most of the residential and office/commercial buildings are constructed using reinforced concrete. Only industrial buildings, some commercial buildings like godowns and some public buildings like stadiums, transport terminals are constructed with steel. Most of the bridges for railway lines are made of steel. In addition, various towers are also constructed using steel. Unlike in developed countries, fewer structures are constructed with steel in India, probably due to the lack of skilled work force and machinery needed for steel construction.

Nowadays, pre-engineered steel buildings which are popular in other countries are also being increasingly constructed in India. In a pre-engineered building, various components are manufactured in a factory and are erected at the site of construction by which the buildings can be completed very quickly. These buildings are a combination of built-up sections, hot-rolled sections and cold-formed elements which provide the basic steel framework with a choice of single skin sheeting with added insulation or insulated sandwich panels for roofing and wall cladding. This concept provides a complete building-envelope system which is air tight, energy efficient and optimum in weight and cost. These can be used for various purposes such as factories, warehouses, supermarkets and offices.

1.2 What does a Steel Structure Consist of?

One-storey steel buildings are constructed with planar frames shown in Figures 1.1(a)(d) as principal frame elements known as bents. The spacing between bents is known as bay. The details of a typical one-storey steel building are shown in Figure 1.2. Multi-storey steel buildings may be constructed with the plane frames shown in Figures 1.3(a)(b) in which the frames may be unbraced or braced. In an unbraced frame, the joints transfer both the shear and the bending moment, whereas in a braced frame, the joints transfer only the shear. Some steel structures may be really three-dimensional frames, such as circular shaped stadium in-plan.

 

 

Figure 1.1 One-storey plane frames

 

 

Figure 1.2 Typical one-storey steel building

 

 

Figure 1.3 Multi-storey plane frames

 

Steel bridges may be constructed in a variety of ways using structural steel. They are plate girder bridges, truss girder bridges, suspension bridges, cable stayed bridges etc. (Figure 1.4). In plate girder bridges, the main load-carrying members are plate girders, whereas in truss girder bridges, they are the vertical truss girders. In suspension bridges and cable-stayed bridges, the main load-carrying elements are cables.

 

 

Figure 1.4 Types of steel bridges

 

Towers consist of usually plane trusses in three or four vertical planes. Such plane trusses are shown in Figure 1.5.

 

 

Figure 1.5 Types of steel towers

 

Therefore, from Figures 1.1 to 1.5, it is seen that a steel structure consists of structural members connected together so as to form a rigid framework. The connections among structural members may be moment resistant or non-moment resistant. Nowadays, the connections are made using welding/bolting. The various structural elements in a steel structure may be classified as:

  • Tension members
  • Compression members
  • Beams/Girders
  • Beam-columns
  • Column bases and caps
  • Brackets
  • Connections

If the steel structure is a multi-storey building, the floor systems may be reinforced concrete slabs supported monolithically on steel beams/girders with a shear connection between the two so as to take advantage of the composite action. The steel beams/girders together with the reinforced concrete slab act as composite beams.

1.3 Structural Steel

Wrought iron had been produced from the middle ages, if not before, through the firing of iron ore and charcoal in a bloomery. This method was replaced by blast furnaces from 1490 onwards. A century later, the rolling mill was introduced for enhanced output. The melting of iron with coke was discovered in 1709 which lead to the development of workable wrought iron. The method of rolling wrought iron into standard shapes was started in the 18th century. In 1855, Sir Henry Bessemer of England invented the process of making steel. Steel is obtained by adding small quantities of carbon during the manufacturing process of iron. Today, there is a variety of steel produced by adding appropriate quantities of alloying elements such as carbon, manganese, silicon, chromium, nickel and molybdenum to suit the needs of a wide range of applications. In India, J. N. Tata set up the first steel manufacturing plant at Jamshedpur. Later, major steel plants were set up at Bhillai, Rourkela, Bhadravti and Visakhapatnam. Today, there are a number of steel plants in the private sector too.

The Bureau of Indian Standards (BIS) standardized structural steel to be used in steel structures. The latest Indian Standard in this regard is IS 2062:2006 Hot-rolled low, medium and high tensile structural steel. It covers the requirements of steel including micro-alloyed steel plates, strips, shapes and sections (angles, tees, beams, and channels), flats and bars for structural work. The steels are suitable for welded, bolted and riveted structures and for general engineering purposes. Where welding is employed for fabrication and guaranteed weldability is required, the welding procedure should be as specified in IS 9595:1996 Metal-arc welding of carbon and manganese steels – recommendations.

IS 2062:2006 recommends 9 grades of steel designated as E165, E250(A), E250(B), E250(C), E300, E350, E410, E450(D), E450(E) where the numerical value in the designations indicates the yield strength in MPa. The chemical composition of these grades of steel is given in Table 1.1. The mechanical properties of these grades of steel are shown in Table 1.2.

 

Table 1.1 Chemical composition of structural steel

 

Note Steels of qualities A, B and C are generally suitable for welding processes. Weldability increases from quality A to C.

 

Table 1.2 Mechanical properties of structural steel

 

Note t = thickness of steel element

 

The stress-strain diagrams for these grades of steel may be as shown in Figure 1.6. For sharp yielding structural steel, yield strength fy is the stress corresponding to position AB of the stress-strain curve (Figure 1.6(a)). In continuously yielding structural steel, yield strength fy is the stress corresponding to 0.2% strain obtained by drawing a line parallel to OA of the stress-strain curve (Figure 1.6(b)). The stress corresponding to top-most point C on the stress-strain curve is the ultimate strength fu of the steel. The ductility of the steel, i.e., the ability to deform without fracture, is measured in terms of % of elongation which is given by where S0 is the original (initial) cross-sectional area of the test specimen. Irrespective of the grades of steel, the following mechanical properties of steel are assumed.

 

 

Figure 1.6 Stress-strain curves for structural steel

 

The modulus of elasticity (Young's modulus), E = 2 × 105 MPa

Poisson's ratio, ν = 0.3

The modulus of rigidity, G = 0.769 × 105 MPa

1.4 Products of Structural Steel

A variety of structural steel products are manufactured by steel plants for the construction of steel structures. The products are available in different shapes and sizes so as to enable the structural engineer to select suitable sections to suit the requirements of the design. Depending on the manufacturing process, these sections are classified as hot-rolled sections and cold-rolled or cold-formed sections.

1.4.1 Hot-Rolled/Formed Sections

Hot-rolled sections are produced in steel plants from steel billets by passing them through a series of rollers. The various products made using this process are plates, strips, shapes and sections (angles, tees, beams, channels), flats and bars. They are classified by the Bureau of Indian Standards as follows.

1.4.1.1 Beams (as per IS 808:1989, Figure 1.7(a))

 

 

Figure 1.7 Hot rolled or formed sections

 

  1. Indian Standard Junior Beams (ISJB) abbreviated as JB
  2. Indian Standard Light weight Beams (ISLB) abbreviated as LB
  3. Indian Standard Medium weight Beams (ISMB) abbreviated as MB
  4. Indian Standard Wide flange Beams (ISWB) abbreviated as WB

These are designated as, for example, JB150, LB150, MB150, WB150 where 150 is the depth of the section in mm. The properties of these sections are given in Appendix A.

1.4.1.2 Columns/Heavy-Weight Beams (as per IS 808:1989, Figure 1.7(b))

  1. Indian Standard Column Sections (ISSC) abbreviated as SC
  2. Indian Standard Heavy weight Beam (ISHB) abbreviated as HB

These are designated as, for example, SC 200, HB 200 where 200 is the depth of the section in mm. The properties of these sections are given in Appendix A.

1.4.1.3 Parallel Flange Beam and Column Sections (as per IS 12778:2004, Figure 1.7(c))

  1. Indian Standard Narrow Parallel flange Beams(ISNPB) abbreviated as NPB
  2. Indian Standard Wide Parallel flange Beams (ISWPB) abbreviated as WPB

Generally, NPBs are used for beams whereas WPBs are used for beams/columns. They are designated as NPB 200 × 100 × 18.42 where 200 is the depth in mm, 100 is the nominal flange width in mm and 18.42 is the mass in kg/m or WPB 500 × 300 × 107.45 where 500 is the depth in mm, 300 is the nominal flange width in mm and 107.45 is the mass in kg/m. The properties of these sections are given in Appendix B.

1.4.1.4 Channels (as per IS 808:1989, Figure 1.7(d))

  1. Indian Standard Junior Channels (ISJC) abbreviated as JC
  2. Indian Standard Light weight Channels (ISLC) abbreviated as LC
  3. Indian Standard Medium weight Channels (ISMC) abbreviated as MC
  4. Indian Standard Medium weight Parallel flange Channels (ISMCP) abbreviated as MCP

These are designated as, for example, JC150, LC150, MC150, MCP150 where 150 is the depth of the section in mm. The properties of these sections are given in Appendix A.

1.4.1.5 Angles (as per IS 808:1989, Figure 1.7(e))

  1. Indian Standard equal/unequal angle (ISA) abbreviated as ∠

These are designated as, for example, ∠ 200 100 × 10 where 200 and 100 are the lengths of the legs in mm and 10 is the thickness in mm. The properties of these sections are given in Appendix A.

1.4.1.6 T-Sections (as per IS 1173:1978, Figure 1.7(f))

  1. Indian Standard rolled Normal Tee bars (ISNT) abbreviated as NT
  2. Indian Standard rolled Deep legged Tee bars (ISDT) abbreviated as DT
  3. Indian Standard slit Light weight Tee bars (ISLT) abbreviated as LT
  4. Indian Standard slit Medium weight Tee bars (ISMT) abbreviated as MT
  5. Indian Standard slit Tee bars from H sections (ISHT) abbreviated as HT

These are designated as, for example, NT50, DT100, LT200, MT100 and HT100 where the numerical value indicates the depth of the section in mm. Sections (c) to (e) are slit from I sections. The properties of these sections are given in Appendix C.

1.4.1.7 Tubular Sections (as per IS 1161:1998, Figure 1.7(g))

These are designated by their nominal bore and classified as light, medium and heavy depending on the wall thickness. They are further graded as YSt 210, YSt 240 and YSt 310 depending on the yield stress of the material. 210, 240 and 310 are yield strengths in MPa. The properties of these sections are given in Appendix D.

1.4.1.8 Rectangular/Square Hollow Sections (as per IS 4923:1997, Figure 1.7(h))

These are designated by their outside dimensions and thickness. For example, 60 × 40 × 2.9 HF RHS means 60 mm is the depth, 40 mm is the breadth and 2.9 mm is the thickness. HF stands for Hot Formed and RHS for Rectangular Hollow Section. Similarly, 72 × 72 × 3.2 HF SHS means Hot Formed Square Hollow Section with a depth or a breadth of 72 mm and a thickness of 3.2 mm. The material of hot-formed sections is graded as YSt 210, YSt 240 and YSt 310 depending on the yield stress. 210, 240 and 310 are yield strengths in MPa. The properties of these sections are given in Appendix E.

1.4.1.9 Plates, Sheets, Strips and Flats (as per IS 1730:1989)

  1. Plates are designated as ISPL followed by figures denoting length × width × thickness in mm
  2. Sheets are designated as IISH followed by figures denoting length × width × thickness
  3. Strips are designated as ISST followed by figures denoting width × thickness in mm
  4. Flats are designated by the width followed by letters ISF and the thickness in mm

The properties of flats are given in Appendix F.

1.4.2 Cold-Formed Light-gauge Sections (as per IS 811:1987, IS 4923:1997)

Cold-formed light-gauge sections are used where thicker hot-rolled sections become uneconomical especially in small buildings subjected to lighter loads. These are produced from steel strips generally not thicker than 8 mm. For mass production, they are produced by cold-rolling whereas smaller number of special shapes are produced on press brakes. They are available in the form of equal angles, unequal angles, channels, hat sections and Z sections. They are designated by numbers denoting depth (mm) × width (mm) × thickness (mm).

Rectangular/Square hollow cold-formed sections are also available (IS 4923:1997). These are designated in the same way as hot-formed sections like 60 × 40 × 2.9 CF SHS, where CF stands for cold formed.

The properties of cold formed sections are given in Appendix G.

1.5 Standards, Codes and Specifications

Unlike concrete structures which are generally casted at site to any required shape and size, the construction of steel structures involves the assembly of various members which are readily available or fabricated in a workshop. As various members, listed in Sec. 1.4, are manufactured in steel plants, the material used and the shape/size of these members are standardized by the Bureau of Indian Standards (BIS), New Delhi. To assist structural engineers, BIS also standardized loads, specifications, design procedures, testing and inspection. These standards are updated periodically so as to incorporate the latest developments and current practices. For convenience, these standards are designated by a number followed by the year of first publication or revision. For example, IS 800:2007 Code of practice for general construction in steel is the basic code of practice for design of steel structures. The various standards that are commonly used in the design of steel structures and referred to in this book are given in REFERENCES.

1.6 Loads

A structure is designed to carry certain loads so as to serve the intended purpose. A steel structure may have to be designed primarily to dead load, imposed (live) load, wind load, seismic (earthquake) load, snow load, erection load, and effects such as the rise in temperature.

1.6.1 Dead Load

Dead load means the self weight of the structure or its components. This depends on the unit weight of materials used in the structure and the dimensions of the structure or its components. This is obtained by multiplying the volume of structure or its component with the unit weight. IS 875 (Part 1):1987 gives the unit weights of various materials used in construction.

1.6.2 Imposed Load

This is the load due to intended use or occupancy which may be stationary or moving. It includes the load due to impact or vibration. In buildings, it includes the weight of the occupants, the various things and materials kept on the floors. In bridges, it includes vehicular loads on the road or rail. IS 875 (Part 2):1987 gives imposed loads on buildings. The Indian Road Congress (IRC) and the Indian Railways specify the loads to be considered on road bridges and rail bridges, respectively.

1.6.3 Wind Load

Since a structure obstructs the flow of air, a load acts normal to the exposed surface of the structure which is known as wind load. This is an important load on light weight structures, high rise buildings and towers and bridges. IS 875 (Part 3):1987 specifies the wind load to be considered for buildings and structures.

1.6.4 Seismic (Earthquake) Load

When an earthquake occurs, inertia forces mainly in the horizontal direction act on structures. These are calculated as per IS 1893:2002.

1.6.5 Snow Load

In India, this load is to be considered in the Himalayan region where snow fall occurs. This is calculated as per IS 875 (Part 4):1987.

1.6.6 Erection Load

All loads required to be carried by the structure or its components during the positioning of the construction material and the erection equipment including all loads due to operation of such equipment should be considered as erection loads.

1.7 Fatigue

Fatigue is a type of failure that occur in members subjected pulsating or repetitive or cyclic loads. Civil engineering structures such as bridges and gantry girders which are acted upon by moving loads are subjected to fatigue. Fatigue failure is due to the presence of inherent flaws in the material or due to holes, notches and sudden discontinuities in a member (Figure 1.8). At the location of inherent flaw or holes, notches and sudden discontinuities, stress is very high, which is known as stress concentration. This stress concentration is not so serious when the member is subjected to static load if the material is sufficiently ductile. But when the member is subjected to cyclic load, inherent flaws propagate and minute cracks are formed near holes, notches and sudden discontinuities and propagate as shown in Figure 1.8. Finally, the member fails as the cracks extend to the surrounding region since the static strength of the member gets reduced. This process of the formation and the propagation of cracks in the materials of the structures under cyclic stress is called fatigue. Thus, the factors affecting fatigue failure may be summarized as:

 

 

Figure 1.8 Crack formation and growth

 

  1. a large number of loading cycles,
  2. a wide range in stress variation,
  3. a high stress in the member with a small range of stress,
  4. local stress concentrations due to design and fabrication details.

Cyclic loads are of two types. In the first type, the direction of stresses is not reversed during the cycle (Figure 1.9) whereas in the second type, the direction stresses is reversed, i.e., tension to compression or vice-versa. If the maximum and minimum stresses of reversed loading are equal in magnitude but opposite in direction, it is known as complete stress reversal (Smin = −Smax). For a given stress range (SmaxSmin), it is possible to determine the number of cycles at which failure occurs in a member. The maximum stress which the material is able to resist for an extremely large number of cycles is known as endurance limit or fatigue limit, whereas, fatigue strength is defined as the maximum stress which the member can sustain without fracture for a stated number of cycles. To determine the fatigue strength of a material, an endurance test is usually conducted. A typical S-N (Stress-Number of cycles) curve for mild steel for complete stress reversal case is shown in Figure 1.10. To know exactly where the curve becomes flat, generally, Smax is plotted against Log N.

It is observed that most fatigue failures are due to improper detailing rather than the inadequate design of the member for strength. It is very important to avoid any local structural discontinuities and notches by good design and is the effective means of increasing fatigue life. Where a structure is subjected to fatigue, welded joints should be designed and detailed properly. Poor weld details and weld defects are the major reasons of failure of welded connections. The fatigue performance of a welded joint can be enhanced by the use of techniques such as weld geometry, improvements in welding methods and better quality control using non-destructive testing methods. That is, the use of butt welds instead of fillet welds, double-sided fillet welds instead of single-sided fillet welds and proper detailing which does not cause stress concentration are important considerations in the design of a structure with welding subjected to fatigue. Structures subjected to fatigue may be designed as per IS 800:2007 as is explained in Chapter 6.

 

 

Figure 1.9 Fatigue terminology

 

 

Figure 1.10 S-N curve for mild steel specimen

1.8 Brittle Fracture

Brittle fracture is characterised by the sudden failure of the material at stress well below its yield strength. Even though steel is ductile at room temperature, it becomes brittle at temperatures below a certain temperature known as the transition temperature (Figure 1.11). The transition temperature depends on material composition, strain rate, thickness, residual stresses, fabrication flaws and high triaxial stresses which reduces the ductility locally. This type of failure may be avoided by selecting structural steel such that the low service temperature of the structure is more than the transition temperature of the steel.

 

 

Figure 1.11 Transition temperature

 

A quantitative measure of the ability of steel to sustain adverse temperature is the Charphy V-Notch test. In this test, a small simply supported rectangular bar with a specified V-shaped notch at the centre is fractured by a pendulum swung from a fixed height. The amount of energy required to fracture the specimen is calculated from the height to which the pendulum rises after breaking the specimen. The amount of energy required to break the specimen for a range of temperatures is determined and plotted. From this curve, the transition temperature of the steel is obtained. IS 2062:2006 specifies the minimum Charphy V-notch impact energy for the different grades of steel used in steel structures. Though steel is selected for its good Charphy V-notch impact energy rating, it is also important that the design details and the fabrication workmanship do not produce notches which could start cracks.

1.9 Corrosion Protection of Steel Structures

Corrosion is the deterioration or loss of material of steel due to a chemical or electrochemical reaction with the environment. Chemical corrosion makes the surface of the steel oxidize in dry air resulting in thin layers of oxides. On the other-hand, electro chemical corrosion is the dissolution of the steel material due to local electrolysis when the surface is wet.

The effective means of preventing corrosion is the alloying of steel with elements such as chromium or the application of copper or the application of aluminum or zinc coatings. Hot dip zinc coatings, known as galvanisng, involves the dipping of the steel work into a bath of molten zinc at a temperature of about 450°C. A metal coating can also be applied using spraying. Nowadays, epoxy paints are also available which last for very long periods. The corrosion protection guide for steel structures is available in IS 800:2007.

1.10 Design Philosophies

1.10.1 Working Stress Method

Basically, there are two design philosophies in structural design. They are working stress method and limit state method. The working stress method is the more conventional and age-old approach which is based on allowable stress and elastic behaviour. The magnitude of allowable stress is a fraction of the yield strength which is obtained by dividing the yield strength with a factor of safety. This concept of safety is based on the assumption that the first yielding is the useful limit of the structure. The maximum stress in a structural member is calculated due to the maximum probable load and it is ensured that this stress is less than or equal to the allowable stress. This method of design based on service loads, elastic behaviour and allowable stress is widely accepted and has been in practice. The principal disadvantage of this method is that it fails to provide a uniform overload capacity for all the parts and types of structures. It does not take into account the non-linear relationship between stress and strain and the ability of structural members to resist loads even after local yielding. It also does not consider the redistribution of forces and moments in statically indeterminate structures.

1.10.2 Limit State Design

An improved design philosophy to overcome the drawbacks of the working stress method is the limit state method. The limit states are the various requirements that a structure is expected to fulfill so that the performance of the structure satisfies the intended purpose for which it is built. The two limit states that are commonly considered in the design of the steel structure are explained below.

1.10.2.1 Limit State of Strength/Collapse (Ultimate Limit State)

This limit state is associated with failure (or imminent failure) under the action of the probable and the most unfavourable combination of loads on a structure which may endanger the safety of life and property. This limit state includes the loss of stability of a structure or its components considering them as rigid bodies as well as considering their flexibility; the failure by excessive deformation and rupture of the structure or any of its components; fracture due to fatigue; and brittle fracture.

To achieve the design objectives, the design is based on characteristic values for material strengths and applied loads which take into account the probability of variations in the material strengths and in the loads acting on a structure. The characteristic values are based on statistical data, if available; otherwise, they are based on experience. The design values are derived from the characteristic values through the use of partial safety factors, both for material strengths and for loads. The reliability of design is ensured by satisfying the requirement:

Design action ≤ Design strength

1.10.2.1.1 Design Actions

The design actions,

 

 

where

Qck = characteristic actions that are not expected to be exceeded with 5% probability during the life of the structure which include self-weight, live load or imposed load, crane load, wind load, earthquake load

γfk = partial safety factor for different loads k, given in Table 1.3, to account for the possibility of the unfavourable deviation of the load from the characteristic value; the possibility of inaccurate assessment of the load; and the uncertainty in the assessment of effects of the load and the uncertainty in the assessment of the limit states being considered.

 

Table 1.3 Partial safety factors for loads for limit state of strength/collapse

 

Note DL: Dead load; LL: Live or imposed load; CL: Crane load; WL: Wind load; EL: Earthquake load; ER: Erection load

Values in ( ) should be considered when the dead load contribution to stability against overturning is critical or the dead load causes the reduction in stress due to other loads.

 

For three types of loads (k = 1, 2, 3), viz., dead load, live load/crane load and wind load/earthquake load, Qd may be written as:

 

Qd = γf1 Qc1 + γf2 Qc2 + γf3 Qc3     (1.2)

 

where

γf 1 = partial safety factor for dead load

γf 2 = partial safety factor for live load/crane load/erection load

γf 3 = partial safety factor for wind load/earthquake load

Qc1 = characteristic action for dead load

Qc2 = characteristic action live load/crane load/erection load

Qc3 = characteristic action for wind load/earthquake load

1.10.2.1.2 Design Strength

The design strength Sd is given by

 

Sd = Su /γm     (1.3)

 

where

Su = ultimate strength

γm = partial safety factor for materials, given in Table 1.4, to account for the possible unfavourable deviation of the material strength from the characteristic value; the possible unfavourable variation of the member sizes; the possible unfavourable reduction of the member strength due to fabrication and tolerances; and the uncertainty in the calculation of the strength of the members.

 

Table 1.4 Partial safety factors for materials/fasteners, γm

Type of failure of member Partial safety factor
Yielding 1.10
Buckling 1.10
Rupture at ultimate stress 1.25
Type of fastener
Bolts 1.25
Welds 1.25 for shop welding
1.5 for site welding

1.10.2.2 Limit State of Serviceability

This limit state is associated with the functioning of structure or its components under service or working loads. It causes discomfort to the occupants or affects the appearance of a structure and, on the whole, may reduce the functional effectiveness of the structure. It includes deformation/deflection; vibration; repairable damage or crack due to fatigue, corrosion/durability; and fire. It is the limit state beyond which the following service criteria are no longer met.

  1. Deflection limit
  2. Vibration limit
  3. Durability consideration
  4. Fire resistance

The deflection or vibration characteristic of a structure or its components may be calculated using the working stress method outlined in Sec.1.10.1 with partial safety factors for loads given in Table 1.5 for the limit state of serviceability. The limits on deflection are given in Table 1.6.

 

Table 1.5 Partial safety factors for loads for limit state of serviceability

 

Note DL: Dead load; LL: Live or imposed load; CL: Crane load; WL: Wind load; EL: Earthquake load

 

Table 1.6 Limits on deflection

1.11 Methods of Structural Analysis

Any of the following methods of structural analysis may be used to determine the design forces and moments in a member or a connection complying with the requirements of limit states of stability, strength and serviceability as described in Section 4 of IS 800:2007.

  1. Elastic analysis
  2. Plastic analysis
  3. Advanced analysis
  4. Dynamic analysis as per IS 1893 (Part 1):2002 for seismic design

1.12 Plate (Local) Buckling

The various sections used in steel structures consist of relatively thin elements. The thin elements are subjected to compressive stresses when the sections are used as the compression members or the flexural members. The thin elements act as plates and are susceptible to buckling known as local or plate buckling. This type of buckling may be prevented by providing a minimum thickness to the elements of the section. It should be ensured that no local buckling should develop before the member buckles as a whole. Local buckling, if not prevented, may significantly reduce the load-carrying capacity of the member.

A long rectangular plate (Figure 1.12) supported on the four edges subjected to compression buckles into a number of waves so that the length of each wave approximately equals the width of the plate ‘b’. In this case, this critical buckling stress may be expressed as

 

 

 

Figure 1.12 Buckling of a long rectangular plate

 

where k depends on the edge conditions of the plate and aspect ratio the variation of k with is insignificant and k depends mostly on the edge conditions.

To ensure that the yielding of the plate occurs before local buckling, crfy

i.e.,

 

 

or

 

 

Codes prescribe different limiting values for b/t considering factors such as initial imperfections, residual stresses, post-buckling strength.

1.13 Classification of Sections

In the last article, it is seen that plate elements of a section buckle locally due to compressive stresses. It is also seen that the local buckling can be avoided by limiting the width to thickness ratio (b/t) of an element of a section. For using plastic analysis, members should be capable of forming plastic hinges with sufficient rotation capacity, i.e., ductility, without local buckling to enable the redistribution of the bending moment required for the formation of failure mechanism. Similarly, for using elastic analysis, a member should be capable of developing the yield stress under compression without local buckling. Therefore, the sections are classified as plastic, compact, semi-compact and slender depending on their moment-rotation capacity as shown in Figures 1.13 and 1.14.

 

 

Figure 1.13 Stress distribution in cross section

 

 

Figure 1.14 Moment-rotation characteristics of sections

1.13.1 Plastic (Class 1) Sections

These sections can develop plastic hinges and have the sufficient rotation capacity required for the failure of the structure by the formation of plastic mechanism. The width-to-thickness and depth-to-thickness ratios of the plate elements should be as specified under Class 1 in Table 1.7.

 

Table 1.7 Limiting width-to-thickness ratios for section classification

 

Note r1 is the ratio of the actual average axial stress (negative if tensile) to design the compressive stress of the web alone and r2 is the ratio of actual average axial stress (negative if tensile) to design the compressive stress of the overall section

ε = yeild stress ratio = in which fy is the yield strength of steel in MPa.

 

 

Figure 1.15 Width/depth/thickness of plate elements of sections

1.13.2 Compact (Class 2) Sections

These sections can develop plastic moment of resistance (Mp), but have inadequate plastic hinge rotation capacity for the formation of plastic mechanism due to local buckling. The width-to-thickness and depth-to-thickness ratios of the plate elements should be as specified under Class 2 in Table 1.7.

1.13.3 Semi-compact (Class 3) Sections

These are the sections in which extreme fibre compressive stress can reach yield stress but cannot develop the plastic moment of resistance due to local buckling. The width-to-thickness and depth-to-thickness ratios of the plate elements should be as specified under Class 3 in Table 1.7.

1.13.4 Slender (Class 4) Sections

These are the sections in which plate elements buckle locally before extreme fibre compressive stress reaches yield stress. The width-to-thickness and depth-to-thickness ratios of the plate elements are greater than the limits specified under Class 3 in Table 1.7. In these types of sections, the effective area should be calculated by deducting the width of the compression plate element in excess of the width permissible for the semi-compact section. Alternatively, the post-buckling strength of these sections may be considered as per IS 801:1975.

When the different elements of a section fall under different classes, the section should be classified as that governed by the most critical element.