
Find the reactions and moments of the members in the frame.
Find the horizontal displacement of joint B.

Answer to Problem 27P
Therefore, the horizontal displacement at point B is
Explanation of Solution
Given information:
The value of Young’s modulus (E) is
The moment of inertia (I) of the material is
Calculation:
Show the free-body diagram of the sway as in Figure 1.
Find the stiffness of each member connected to joint B as follows;
Find the total stiffness at joint B as follows;
Find the distribution factors at joint B using the relation;
Find the stiffness of each member connected to joint C as follows;
Find the total stiffness at joint C as follows;
Find the distribution factors at joint C using the relation;
Find the stiffness of each member connected to joint D as follows;
Find the total stiffness at joint D as follows;
Find the distribution factors at joint D using the relation;
Find the fixed end moments in the member AB as follows:
Find the fixed end moments in the member DE as follows:
Find the fixed end moments in the member CF as follows:
Show the moment distribution computations as in Figure 2.
Show the free-body diagram of the members split up as in Figure 3.
Due to symmetry the vertical reaction at the joint C will be zero. Therefore consider the member BCD for the calculation purpose.
Consider member BCD:
Take moment about point B.
Resolve the vertical component of forces.
Consider the member AB:
Take moment about point B;
Also,
Consider the member CF:
Take moment about point C;
Consider the member DE:
Take moment about point D;
Also,
Find the value of using the relation:
Find the horizontal displacement at point B using the relation:
Therefore, the horizontal displacement at point B is
Multiply all the values in the Figure 3 by 0.71 in. to get the corrected reaction and moment values.
Show the final reaction and moment values as in Figure 4.
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Chapter 11 Solutions
Fundamentals of Structural Analysis
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