Concept explainers
Analyze and find all the reactions of the frame.
Explanation of Solution
Determine the deflection position of AB and BA using the relation;
Determine the deflection position of BC and CB using the relation;
Determine the end moment of each member as shown below;
Apply Equilibrium at joint B;
Apply Equilibrium at joint C;
Solve Equation (1) and (2).
Calculation of end moment of each member as shown below;
Hence, the end moment of member AB is
Hence, the end moment of member BA is
Hence, the end moment of member BC is
Hence, the end moment of member CB is
Hence, the end moment of member BE is
Hence, the end moment of member EB is
Hence, the end moment of member CD is
Hence, the end moment of member DC is
Show the free body diagram of support A, span AB, span BC, span EB, and span DC as in Figure (1).
Consider span AB;
Consider clockwise moment is positive and counterclockwise moment is negative.
Determine the vertical reaction at support B;
Take moment about point A;
Consider upward is positive and downward is negative.
Determine the vertical reaction at A;
Hence, the vertical reaction at A is
Consider span BC;
Determine the vertical reaction at support C;
Take moment about point B;
Determine the vertical reaction at B;
Hence, the total reaction at B is
Consider span BE;
Refer Figure (1),
The vertical reaction of 30.8 kips acts as upward reaction at B.
Determine the vertical reaction at E;
Determine the horizontal reaction E;
Take moment about B;
Determine the horizontal reaction at B;
Consider span CD;
Refer Figure (1),
The vertical reaction 12.2 kips at point C will acts downward reaction at C.
Determine the vertical reaction at E;
Hence, the vertical reaction at D is
Determine the horizontal reaction D;
Take moment about C;
Determine the horizontal reaction at C;
Determine the horizontal force at A and B for span AB;
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