There must be sufficient number of plastic and frictionless hinges for beam/structure to form a mechanism. The ultimate load is reached when a mechanism is formed.

The material obeys Hooke?s law till stress reaches f_y. The yield stress and modulus of elasticity have same value in compression and tension. The material is homogeneous and isotropic in both elastic and plastic states. The material is assumed to be sufficiently ductile to permit large rotations of section to take place.

In a fixed beam having concentrated load at one-third point, final ultimate load will be 33% higher than first hinge load.

Semi-compact or class III sections are cross sections in which elastically calculated stress in extreme compression fibre of steel can reach yield strength.

Load factor, F = (f_y/f_bc)v. F = (1/0.66) x 0.14 = 1.27.

Slender or class IV sections are cross section in which local buckling occurs even before yield stress is attained in one or more parts of cross section.

The principle of virtual work is used to satisfy equilibrium condition of plastic analysis. If work condition is formulated correctly equilibrium condition is automatically satisfied.

When equilibrium and plasticity conditions of plastic analysis are satisfied, an lower bound solution of true ultimate load is obtained.

In torsional buckling, failure occurs by twisting about shear centre in longitudinal axis. It occurs when torsional rigidity of member is appreciably smaller than bending rigidity. It can occur only with doubly symmetric cross section with very slender cross sectional elements. Standard hot rolled shapes are not susceptible to torsional buckling.

i) For simply supported plates, if material ceases to be linearly elastic at yield stress f_y, width-to-thickness ratio b/t is given by (b/t)?(f_y /250) = 53.8
ii) For long plate elements simply supported along both transverse edges and one longitudinal edge and free along or longitudinal edge, elastic buckling stress is equal to yield stress if (b/t)?(f_y/250) = 17.5
iii) The elastic buckling stress is equal to yield stress in shear ?y = f_y/?3 when (d/t)?(f_y/250) = 81.9
iv) For long plates elements simply supported along four edges and loaded by bending stress distribution, limiting ratio d/t may be given as (d/t)?(f_y/250) = 131.4.