Theory of Structures II (ENCE 252): Introduction to Plastic Analysis

An Introduction to Plastic Analysis

This chapter introduces Plastic Analysis, a critical method in structural engineering that examines the behavior of structures beyond their elastic limit. While previous chapters focused on the elastic range where deformations are proportional to loads, plastic analysis investigates the ultimate load-carrying capacity of a structure up to the point of collapse. This approach provides a more realistic assessment of a structure’s true factor of safety.

A central concept is the plastic hinge, a yielded zone in a structural member that allows for large rotations at a constant plastic moment ($M_p$). The formation of sufficient plastic hinges turns a determinate or indeterminate structure into a mechanism, leading to collapse. We will explore key parameters such as the Shape Factor ($S$), which is the ratio of the plastic moment to the yield moment ($M_p/M_y$), and the Load Factor ($\lambda$), defined as the ratio of the ultimate (collapse) load to the working load ($\lambda = P_u / P_w$). Understanding these concepts is fundamental to designing ductile structures that can safely redistribute stress before failure.