
Concept explainers
Find the reactions and sketch the shear and moment diagram.
Locate the point of maximum deflection for the beam.

Answer to Problem 1P
The reaction at A and C are
The bending moment at A is
Explanation of Solution
Given information:
EI is constant.
Calculation:
Consider the vertical reaction at C is denoted by
Sketch the beam as shown in Figure 1.
Refer Figure 1.
The horizontal reaction at A is
The vertical reaction at C is the constraint in the structure.
Select the vertical reaction at C as the redundant.
Remove the redundant from the beam to get the released structure.
Calculate the gap
Calculate the gap
The deflection
Refer Figure 1.
Take the upward deflection as positive and downward deflection as negative.
Apply the compatibility Equation as follows:
Thus, the reaction at C is
Find the reaction
Thus, the reaction at A is
Find the moment at A as follows:
Thus, the bending moment at A is
Find the moment at B as follows:
The bending moment
Consider the point of contra flexure is at a distance x from the fixed support A as follows:
The bending moment
Find the shear-force at A, B, and C as follows:
Show the shear force, bending moment diagram as shown in Figure 2.
Refer Figure 2.
The point of maximum deflection occurs at 9 ft from the left support.
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