Solve Problem 15.2 for the loading shown in Fig. P15.2 and a settlement of . at support...

Fixed end moments:

Slope deflection sign convention

Counterclockwise fixed end moments are considered as positive, and

Clockwise fixed end moments are considered as negative.

Chord rotation

Using

Slope deflection equations:

On further calculating:

Equilibrium equation:

Sum of moments at a joint is zero. Thus, we obtain the equilibrium equation

Therefore

Member end moments:

Now substituting the value in equation (1) to (4), to get the member end moments; Thus

Member end shear:

The member end shears, obtained by considering the equilibrium of each member.

By considering the member AB

Sum of moments about A is zero

Algebraic sum of vertical forces is zero

By considering the member BC

Sum of moments about C is zero

Algebraic sum of vertical forces is zero

To determine the vertical reaction at the roller support B, we consider the equilibrium of the joint B in the vertical direction, to obtain

Shear and bending moment diagrams