Concept explainers
Find the member end moments and reaction for the frames.

Answer to Problem 30P
The end moments at the member AC
Explanation of Solution
Fixed end moment:
Formula to calculate the fixed moment for UDL is
Calculation:
Consider the flexural rigidity EI of the frame is constant.
Show the free body diagram of the entire frame 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 CD.
Calculate the fixed end moment for DC.
Calculate the fixed end moment for DB.
Calculate the fixed end moment for BD.
Chord rotations:
Show the free body diagram of the chord rotation of the frame as in Figure 2.
Calculate the length of AC by using Pythagoras theorem.
Calculate the length of BD by using Pythagoras theorem.
Calculate the chord rotation of the frame AC.
Calculate the chord rotation of the frame BD.
Calculate the chord rotation of the frame CD.
Calculate the slope deflection equation for the member AC.
Substitute 16.49 ft for L, 0 for
Calculate the slope deflection equation for the member CA.
Substitute 16.49 ft for L, 0 for
Calculate the slope deflection equation for the member CD.
Substitute 16 ft for L,
Calculate the slope deflection equation for the member DC.
Substitute 16 ft for L,
Calculate the slope deflection equation for the member DB.
Substitute 16.49 ft for L, 0 for
Calculate the slope deflection equation for the member BD.
Substitute 16.49 ft for L, 0 for
Write the equilibrium equation as below.
Substitute equation (2) and equation (3) in above equation.
Write the equilibrium equation as below.
Substitute equation (4) and equation (5) in above equation.
Show the free body diagram of the entire frame due to sway force as in Figure 3.
Show the free body diagram of the frame due to sway force as in Figure 4.
Calculate the horizontal reaction at the member AC due to sway force by taking moment about point A.
Calculate the horizontal reaction at the member BD due to sway force by taking moment about point B.
Calculate the reaction of the support C and support D due to sway force by taking the moment about O.
Substitute equation (1), equation (2), equation (5), and equation (6) in above equation.
Solve the equation (7), equation (8), and equation (9).
Calculate the moment about AC.
Substitute
Calculate the moment about CA.
Substitute
Calculate the moment about CD.
Substitute
Calculate the moment about DC.
Substitute
Calculate the moment about DB.
Substitute
Calculate the moment about BD.
Substitute
Show the section free body diagram of the member AC, CD and DB as in Figure 5.
Consider the member CD.
Calculate the vertical reaction at the joint D by taking moment about point C.
Calculate the vertical reaction at joint C by resolving the vertical equilibrium.
Consider the member AC.
Calculate the vertical reaction at joint A by resolving the vertical equilibrium.
Calculate the horizontal reaction at the joint A by taking moment about point C.
Consider the member BD.
Calculate the vertical reaction at joint B by resolving the vertical equilibrium.
Consider the entire frame.
Calculate the horizontal reaction at the joint B by considering the horizontal equilibrium.
Show the reactions of the frame as in Figure 6.
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Chapter 15 Solutions
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