Plastic Analysis of Floating Beams

Exact solutions are presented for the load‐deflection behavior of a free‐free beam on an elastic (Winkler type) foundation, which is subjected to a concentrated load at midlength. Two constitutive models are considered: Rigid‐perfectly‐plastic and elastic‐perfectly‐plastic (ideal section), and in each case the problem is reduced to the solution of a nonlinear ordinary differential equation with associated initial conditions. The initial value problems are solved numerically using the fourth order Runge‐Kutta method. For loads greater than the threshold value at which the three‐hinge mechanism forms, both exact solutions produce practically identical results for long beams. This leads to the conclusion that elastic effects are insignificant in a long elastic plastic floating beam, after the three‐hinge mechanism is formed. The second iteration solution of an approximate method of analysis for the rigid‐plastic beam is also presented. Good agreement is found between the approximate and the exact rigid‐plastic results.