Working Stress Design Method

1. Working Stress Method (WSM)

Assumptions:

• Steel is homogeneous, isotropic and obeys Hooke's law (linear elastic).
• Plane sections remain plane after bending.
• Stresses under working loads must not exceed permissible stresses $\sigma_{perm}=f_y/FOS$ (e.g. $0.6f_y$ in tension).
• A single factor of safety covers all uncertainties; stress-strain curve is linear up to $f_y$.

2. Plastic (ultimate load) method

Assumptions:

• Steel is ductile and behaves as elastic-perfectly plastic with a long yield plateau.
• Plane sections remain plane; full plastic moment $M_p=f_yZ_p$ develops in the hinge.
• Local and lateral-torsional buckling are prevented, so the section reaches $M_p$ and has enough rotation capacity.
• Collapse occurs by a mechanism after enough hinges form; loads are factored (load factor, e.g. 1.7).
• Effects of shear and axial force on $M_p$ are small; deflection is neglected.

3. Limit State Method (LSM)

Assumptions:

• Plane sections remain plane; stress-strain curve is idealised as in IS 800 Fig. 2.
• Characteristic loads are multiplied by partial safety factors $\gamma_f$ and material strength divided by $\gamma_m$.
• The structure is checked for the limit state of strength (yield, buckling, rupture) and serviceability (deflection, vibration).
• Local buckling is controlled using section classification (plastic, compact, semi-compact, slender); residual stresses and imperfections are included in buckling curves.
• Design strength $\ge$ factored effect for each member and connection.

The Working Stress Method (IS 800:1984) is based on the theory of elasticity. Basic assumptions:

1. Steel is homogeneous and isotropic.
2. Stress is proportional to strain up to the permissible stress (Hooke's law); $E$ is constant ($2\times10^5$ N/mm²).
3. Plane sections before bending remain plane after bending (linear strain distribution).
4. Loads used are working (service) loads without load factors.
5. Stresses in members and connections under working loads must not exceed the permissible stresses, which are the yield stress divided by a factor of safety (about $0.6f_y$ for tension, $0.66f_y$ for bending).
6. A single overall factor of safety accounts for variations in load, material, workmanship and analysis.
7. Effects such as residual stress, post-yield strength and redistribution are ignored.
8. Deformations are small and the principle of superposition applies.

As per IS 800:1984 (working stress method), with $f_y$ the yield stress of steel (the 2007 code uses limit states instead):

For $f_y=250$ N/mm²: tension 150, bending 165, shear 100, bearing 187.5 N/mm². For bolts and welds, permissible shear in bolts is 80 N/mm² (4.6) and in fillet weld 108 N/mm² (shop), bearing 250 N/mm² (bolt).