Handbook of Civil Engineering Calculations

(b) Bending-moment diogrom

at ultimate load

FIGURE 22

elastic design. For example, assume that the support at C does not completely in-

hibit rotation at that end. This departure from design conditions will invalidate the

elastic analysis but will in no way affect the plastic analysis.

DETERMINING THE ULTIMATE LOAD

BY THE MECHANISM METHOD

Use the mechanism method to solve the problem given in the previous calculation proce-
dure.

Calculation Procedure:

1. Indicate, in hyperbolic manner, the virtual displacement
   of the member from its initial to a subsequent position
   To the two phases of beam behavior previously considered, it is possible to add a third.
   Consider that when the ultimate load is reached, the member is subjected to an incremen-
   tal deflection. This will result in collapse, but the behavior of the member can be analyzed
   during an infinitesimally small deflection from its stable position. This is termed a virtual
   deflection, or displacement.
   Since the member is incapable of supporting any load beyond that existing at comple-
   tion of phase 2, this virtual deflection is not characterized by any change in bending
   stress. Rotation therefore occurs solely at the real and plastic hinges. Thus, during phase

(a) Force diagram at

ultimate load