Steel Structures and their Analysis and Design

Design process

Structural design is an iterative process that goes from the client's need to a safe, serviceable and economical structure.

1. Planning / functional requirements: use of the building, spans, heights, architectural layout, site conditions.
2. Structural system selection: choose framing (portal frame, truss, braced or moment frame), material (steel grade) and joint types (bolted/welded).
3. Estimation of loads: dead load (IS 875 Part 1), imposed load (Part 2), wind (Part 3), earthquake (IS 1893 / NBC 105), and other loads (snow, crane, temperature).
4. Structural analysis: find axial force, shear force and bending moment in every member for the governing load combinations (IS 800:2007 Table 4).
5. Member design: select sections, check strength (tension, compression, flexure, combined), slenderness and deflection.
6. Connection design: design bolted/welded joints, splices, bases and gussets.
7. Check and revise: if a check fails, change the section or system and repeat.
8. Detailing and drawings: fabrication and erection drawings, bill of materials, specifications.

Basis of design (IS 800:2007)

• Limit state design: the structure must not reach any limit state during its design life. Limit state of strength (yielding, buckling, rupture, fatigue, overturning) and limit state of serviceability (deflection, vibration, durability, fire).
• Partial safety factors: on loads $\gamma_f$ (e.g. 1.5 for DL+LL, 1.2 for DL+LL+WL) and on material $\gamma_{m0}=1.10$ (yielding), $\gamma_{m1}=1.25$ (rupture), $\gamma_{mb}=1.25$ (bolts), $\gamma_{mw}=1.25$ (shop weld), 1.50 (field weld).
• Design strength $=$ characteristic strength $/\gamma_m$ and must be $\ge$ the factored action effect $\gamma_f \times$ characteristic load.
• Material: structural steel to IS 2062 (E250, E350 etc.), with $E=2\times10^5$ N/mm², $G=0.769\times10^5$ N/mm², $\mu=0.3$.
• Load combinations: DL+LL, DL+LL+WL/EL, DL+WL/EL, with the load factors of Table 4.
• Serviceability limits: deflection limits of Table 6 (e.g. span/300 for floor beams, span/150 for purlins with elastic cladding), slenderness limits of Table 3.
• Other requirements: stability against overturning and sliding, ductility, robustness, fire resistance and durability.

IS 800:2007 (cl. 3.7, Table 2) classifies cross-sections by how the plate elements (flanges, web) behave under local buckling, using the width-to-thickness ratio $b/t_f$, $d/t_w$ and $\varepsilon=\sqrt{250/f_y}$.

Typical limits (rolled I-section, outstand flange $b/t_f$): Class 1 $\le 9.4\varepsilon$, Class 2 $\le 10.5\varepsilon$, Class 3 $\le 15.7\varepsilon$. For web of I-section in bending (neutral axis at mid-depth): $d/t_w \le 84\varepsilon$ (plastic), $105\varepsilon$ (compact), $126\varepsilon$ (semi-compact).

Design use: Class 1 and 2 sections use plastic section modulus $Z_p$ (with $\beta_b=1.0$); Class 3 uses elastic modulus $Z_e$; Class 4 uses effective properties after deducting the buckled width.

Three philosophies have been used for steel design.

1. Working Stress Method (WSM / Elastic design): stresses under working loads are kept below permissible stresses ($\approx 0.6f_y$ in tension). Behaviour is assumed linearly elastic; one single factor of safety is used. Adopted in IS 800:1984.
2. Ultimate load / Plastic design: the structure is analysed up to the collapse load (formation of plastic hinges and a mechanism). Working loads are multiplied by a load factor (e.g. 1.7 for DL+LL) and the section is designed for the collapse moment $M_p$. Economical for continuous beams and portal frames.
3. Limit State Method (LSM): the structure is designed so that it does not reach any limit state of strength or serviceability, using separate partial safety factors on loads and on material strength. Adopted in IS 800:2007 and is the present standard.

LSM is preferred because it is more rational, takes the probabilistic nature of loads and strengths into account, and gives more uniform safety.

Structural steel as per IS 2062 / IS 800:2007

Structural steel is carbon or low-alloy steel (mainly iron with 0.15-0.25% carbon and manganese) rolled into plates, angles, channels and I-sections for use in construction. IS 800:2007 refers to IS 2062:2011 for hot-rolled steel.

Grade

Grade is expressed by the yield stress. In IS 2062:2011 steel is designated E (Engineering) followed by minimum yield stress in N/mm², e.g. E250, E275, E300, E350, E410, E450, E550, E600. Earlier it was designated Fe410 etc. by ultimate stress.

Yield strength reduces for thicker plates (20-40 mm, >40 mm).

Quality classification

Each grade is supplied in Quality A (no impact test), BR (semi-killed or killed, impact test at room temperature), BO (basic-oxygen steel, impact test at 0 °C) and C (killed, impact tested at a specified low temperature), depending on deoxidation and notch toughness. Example: E250 A (no impact test), E250 BR, E250 C.

Other IS classifications

• By deoxidation: killed, semi-killed, rimmed.
• By strength: mild steel (E250), high-tensile (E350-E450), and low-alloy steels.
• By product: plates, bars, flats, angles (IS 808), channels, I-sections (ISMB, ISLB, ISWB, ISHB).

Structural steel is steel (an alloy of iron with 0.15-0.25% carbon, plus manganese, silicon etc.) that is rolled into standard shapes and used to carry loads in buildings, bridges, towers and trusses. It has high strength, ductility and uniform quality, and is covered by IS 2062.

Classification of structural steel sections

A. Hot-rolled sections (IS 808)

• I-sections: ISLB (light beam), ISMB (medium beam), ISWB (wide flange beam), ISHB (heavy column section).
• Channels: ISLC, ISMC (light and medium channels), ISJC (junior).
• Angles: ISA equal and unequal legs.
• Tees: ISNT, ISHT, ISLT (from cutting I sections).
• Flats, plates, bars, tubes: ISF, plates, round and square bars, circular/rectangular/square hollow sections (IS 1161, 4923).

B. Built-up sections: plate girders, box sections, compound beams (I with cover plates), laced or battened columns, and lattice girders - used when rolled sections are insufficient.

C. Cold-formed (light gauge) sections: formed from thin sheets (1-6 mm) as C, Z, hat and tubular shapes; used for purlins, sheeting rails and light structures (IS 801).

D. By local-buckling behaviour (IS 800:2007): plastic, compact, semi-compact and slender sections.

E. By grade: E250, E350, E410 etc. as per IS 2062.

Structural steel

Structural steel is rolled steel (iron + 0.15-0.25% carbon and alloying elements such as Mn) of grades covered by IS 2062 that is used as the load-carrying material in buildings, bridges and towers.

Factor of safety

It is the ratio of the failure (or yield) stress of the material to the permissible (working) stress, $FOS = f_y/\sigma_{perm}$. In working stress design a single factor (about 1.67 on yield, i.e. $\sigma_{perm}=0.6f_y$) covers all uncertainties in loads and material.

Partial safety factor

In limit state design separate factors are used: $\gamma_f$ multiplies characteristic loads (e.g. 1.5 for DL and LL) and $\gamma_m$ divides characteristic material strength (e.g. $\gamma_{m0}=1.10$ for yielding, $\gamma_{m1}=1.25$ for ultimate strength, 1.25 for bolts, 1.25/1.5 for shop/field welds). Each factor reflects the uncertainty of one particular quantity.

Resistance after local yielding

Mild steel is ductile, with a long yield plateau (strain about 10-15 times the yield strain) and then strain-hardening up to $f_u$.

• At stress concentrations (holes, notches, welds) the local stress may reach $f_y$ and the fibre yields, but it keeps carrying the stress $f_y$ while the strain increases.
• The extra load is transferred to the adjoining elastic fibres, so stresses redistribute and the stress concentration is relieved.
• Residual stresses and bending stresses at connections also redistribute in this way, and a section can go on to form a plastic hinge and resist moment up to $M_p$.
• Hence local yielding does not lead to failure; the structure gives large deformation as warning before collapse.

Advantages of steel: high strength, long spans, ductility, speed of construction, reuse and scrap value, uniform quality. Disadvantages of steel: corrosion, fire protection cost, buckling of slender members, higher cost and fatigue/brittle fracture at low temperature.

Horizontal loads on steel buildings (wind and earthquake) are carried to the foundation by a lateral load resisting system. Floors and roofs act as diaphragms that distribute the lateral force to vertical resisting frames.

Main systems

1. Braced frames (concentric / eccentric): diagonal, X, K or V bracings between columns carry the lateral load by axial force in members. Stiff and economical for low and medium rise buildings.
2. Moment-resisting (rigid) frames: beam-to-column joints are rigid and resist the lateral load by bending of beams and columns. Gives open bays but larger sections and costly joints.
3. Shear walls / core: RC or steel plate shear walls in lift and stair cores resist storey shear.
4. Dual systems: moment frame combined with bracing or shear wall; share the load by relative stiffness.
5. Tube systems: closely spaced perimeter columns and deep spandrels form a stiff tube for tall buildings.
6. Roof/floor bracing and diaphragms: horizontal bracing in plan and rigid slabs transmit forces to the vertical frames.

  Braced frame        Moment frame
  |\  /|              |==|==|
  | \/ |              |  |  |
  | /\ |              |==|==|
  |/  \|              |  |  |

Choice depends on height, drift limit, architectural openness and cost. IS 800 and IS 1893 / NBC 105 control the load and detailing.

The real curve is idealised for design (IS 800:2007 cl. 2.2.4, Fig. 2).

Mild steel (E250)

 stress
  fu |            ___------.
     |         _-/          \
  fy |-------+==============+   <- yield plateau
     |      /|
     |     / |
     |    /  |  E = 2x10^5
     |   /   |
     |__/____|______________|____ strain
        0.00125   ~0.014    ~0.2

• Elastic line up to $f_y$ with slope $E=2\times10^5$ N/mm², yield strain $\varepsilon_y=f_y/E=0.00125$ for $f_y=250$.
• Constant stress $f_y$ (yield plateau) up to roughly 10-15 times $\varepsilon_y$ (strain-hardening starts at about 0.014).
• Strain-hardening to ultimate stress $f_u$ ($\approx410$ N/mm²) at strain about 0.2, then necking and fracture.
• For design the idealised curve is elastic-perfectly plastic (bilinear): $\sigma = E\varepsilon$ up to $f_y$, then $\sigma=f_y$.

High tensile steel (E350-E450, cold-worked)

 stress
  fu |           ___---
     |        _-/
 0.2%|------_/
 proof      /
     |     /
     |    /
     |___/____|__________ strain
       0.002 offset

• No definite yield point or plateau; stress rises smoothly.
• Yield stress is taken as the 0.2% proof stress (line parallel to the elastic part, drawn from 0.002 strain).
• Idealised as elastic up to the proof stress and then flat (or rising slightly). Ductility is lower than mild steel.