Plastic Behaviour of structures

Most Engineering design is based on the "Elastic Theory of Bending" and the method is to calculate the maximum Stresses which occur, and to then keep them within the working Stresses in both compression and Tension. These working Stresses are calculated from the Yield (or ultimate) Stress and a Factor of Safety. 

This approach is a little unrealistic since Mild Steel Structures do not fail when the edge Stress of any cross section reaches the Yield point, and will continue to withstand the load as long as the central core of the section remains within the Elastic State. 

Through ductility, structure is able to absorb large deformations beyond elastic limit without the danger of fracture. It is this characteristics feature of steel that makes possible the application of plastic analysis to structural design.

Figure 1: Stress strain diagram (for mild steel)

Stress-strain diagram for mild steel in tension is shown in figure-1. Let ‘ab’ represent the elastic range, b - upper yield point and b' is lower yield point. ‘b'c’ the range where strain increases without load (plastic flow or the plastic Strain at yield is nearly 10 to 20 times the Elastic Strain), point ‘d’ represents the ultimate strength and ‘e’ the breaking load.

For Plastic analysis  the actual Stress- Strain diagram as modified and  shown in Figure :2

Figure 2:Modified Plastic strain diagram

Ideal elastic plastic material 

Ideal elastic plastic material is defined as one witch has definite elastic range and after this range material becomes plastic as shown in fig. ab is elastic range and bc is plastic range. Plastic analysis is based on this ideal elastic- plastic stress strain curve.