Design methods and basic assumptions

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; the 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; the full plastic moment $M_p=f_yZ_p$ develops at 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; the stress-strain curve is idealised as elastic-perfectly plastic.
• Characteristic loads are multiplied by partial safety factors $\gamma_f$, and material strength is divided by $\gamma_m$.
• The structure is checked for the limit state of strength (yield, buckling, rupture) and of serviceability (deflection, vibration).
• Local buckling is controlled by section classification (plastic, compact, semi-compact, slender); residual stresses and imperfections are included in the buckling curves.
• Design strength $\ge$ factored effect for each member and connection.