P M  R A B C Problem Collar B can slide along rod AC and is attached by a pin to a block that can slide in the vertical slot shown. Derive an expression for the magnitude of the couple M required to maintain equilibrium.

P M  R A B C 1. Apply the principle of virtual work. If a system of connected rigid bodies is in equilibrium, the total virtual work of the external forces applied to the system is zero for any virtual displacement of the system. 1a. Define a virtual displacement. By using a single variable, define a virtual displacement of all the forces that do work. Solving Problems on Your Own Collar B can slide along rod AC and is attached by a pin to a block that can slide in the vertical slot shown. Derive an expression for the magnitude of the couple M required to maintain equilibrium. Problem

P M  R A B C 1b. Express the total virtual work done by the forces and couples during the virtual displacement.  U = F.  r and  U = M  where  U is the virtual work, F is a force undergoing a virtual displacement  r, and M is a couple undergoing a virtual rotation . 1c. Set the virtual work to zero and solve for the variable. Solving Problems on Your Own Collar B can slide along rod AC and is attached by a pin to a block that can slide in the vertical slot shown. Derive an expression for the magnitude of the couple M required to maintain equilibrium. Problem

Problem Solution Define a virtual displacement. P M  R A B C y B =  y B = R tan  _ R sec 2   tan 2  _ R  sin 2  P M  R A B C yByB Datum

Express the total virtual work done by the forces. Set the virtual work to zero and solve for the variable. P M  R A B C yByB Datum Virtual work:  U = 0  U = _ M  _ P  y B _ M  + P R  = 0 M = M = P R csc 2  sin 2  1 P R Problem Solution