Concept explainers
Using the method of virtual work, determine separately the force and couple representing the reaction at A.
Fig. P10.53 and P10.54
Find the force representing the reaction at A using the virtual work method.
Find the couple representing the reaction at A using the virtual work method.
Answer to Problem 10.53P
The force representing the reaction at A is
The couple representing the reaction at A is
Explanation of Solution
Find the force at A;
Show the free-body diagram of the continuous beam as in Figure 1.
Consider the member AB is horizontal.
The vertical displacement at point A is
Find the vertical displacement
Find the vertical displacement
Find the vertical displacement
Find the vertical displacement
Use the concept of virtual work;
Substitute
Therefore, the force representing the reaction at A is
Find the couple at A;
Show the free-body diagram of the continuous beam as in Figure 2.
Rotate the member AB in the beam through
Find the vertical reaction
Find the vertical displacement
Find the vertical displacement
Find the vertical displacement
Use the concept of virtual work;
Substitute
Therefore, the couple representing the reaction at A is
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Chapter 10 Solutions
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