
Concept explainers
Find the reaction and plot the shear and bending moment diagram.

Explanation of Solution
Fixed end moment:
Formula to calculate the fixed moment for point load with equal length are
Formula to calculate the fixed moment for point load with unequal length are
Formula to calculate the fixed moment for UDL is
Calculation:
Consider flexural rigidity EI of the beam is constant.
Show the free body diagram of the entire beam as in Figure 1.
Refer Figure 1,
Calculate the fixed end moment for AC.
Calculate the fixed end moment for CA.
Calculate the fixed end moment for CE.
Calculate the fixed end moment for EC.
Calculate the slope deflection equation for the member AC.
Here,
Substitute 0 for
Calculate the slope deflection equation for the member CA.
Substitute 0 for
Calculate the slope deflection equation for the member CE.
Substitute 0 for
Calculate the slope deflection equation for the member EC.
Substitute 0 for
Write the equilibrium equation as below.
Substitute equation (2) and equation (3) in above equation.
Calculate the moment about AC.
Substitute
Calculate the moment about CA.
Substitute
Calculate the moment about CE.
Substitute
Calculate the moment about EC.
Substitute
Consider the member AC of the beam:
Show the free body diagram of the member AC as in Figure 2.
Calculate the vertical reaction at the left end of the joint C by taking moment about point A.
Calculate the horizontal reaction at point A by resolving the horizontal equilibrium.
Calculate the vertical reaction at point A by resolving the vertical equilibrium.
Consider the member CE of the beam:
Show the free body diagram of the member CE as in Figure 2.
Calculate the vertical reaction at the right end of the joint C by taking moment about point E.
Calculate the horizontal reaction at point E by resolving the horizontal equilibrium.
Calculate the vertical reaction at point E by resolving the vertical equilibrium.
Calculate the total reaction at point C .
Substitute
Show the reaction of the beam in Figure 4.
Refer Figure 4,
Shear diagram:
Point A:
Point B:
Point C:
Point D:
Point E:
Plot the shear force diagram of the beam as in Figure 5.
Refer Figure 4,
Bending moment diagram:
Point A:
Point B:
Point C:
Point D:
Point E:
Plot the bending moment diagram of the beam as in Figure 6.
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Chapter 15 Solutions
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