Determine the member end moments and reactions for the frames shown in Figure by using t...

Calculate the fixed end moments of the member CB.

Substitute for w and 15 ft for L.

Consider the sign convention as follows.

Counterclockwise fixed end moments are considered as positive and Clockwise fixed end moments are considered as negative.

The generalized slope deflection equations is,

Here, is the slope at near support, is the slope at far support, is the fixed end moment.

Write the slope deflection for member AC.

Substitute 15 ft for L, 0 for , and 0 for .

…… (1)

Write the slope deflection for member CA.

Substitute 15 ft for L, 0 for , and 0 for .

…… (2)

Write the slope deflection for member CD.

Substitute 15 ft for L, 0 for , 0 for , and 0 for .

…… (3)

Write the slope deflection for member BC.

Substitute 15 ft for L, for , and 0 for .

…… (4)

Substitute for L for , and 0 for

……. (5)

Consider the joint C.

Consider sum of moments at a joint C as zero.

Substitute for , for , and for .

Substitute for in equation (1).

Therefore, the fixed end moment of member AC is .

Substitute for in equation (2).

Therefore, the fixed end moment of member CA is .

Substitute for in equation (3).

Therefore, the fixed end moment of member CD is .

Substitute for in equation (4).

Therefore, the fixed end moment of member BC is .

Substitute for in equation (4).

Therefore, the fixed end moment of member CB is .

Compute the reactions of the frame as follows:

Consider the member CD and draw the free body diagram.

Reverse the direction of the moment if the magnitude is negative.

Therefore, the vertical reaction at D is .

Consider the member BC and draw the free body diagram.

Take moments about C.

Therefore, the vertical reaction at B is .

Consider the member AC and draw the free body diagram.

Take moments about C.

Therefore, the horizontal reaction at A is .

Draw the free body diagram of the frame showing all the reactions.

Apply vertical equilibrium to the frame.

Therefore, the vertical reaction at A is .

Apply horizontal equilibrium to the frame.

Therefore, the horizontal reaction at B is .