Solutions For Fundamentals of Structural Analysis Chapter 10 Problem 7P

Consider the equilibrium condition.

As there are no vertical forces the vertical reaction at the support will be zero.

...... (1)

Take the moment about A.

Substitute the obtained values in equation (1).

Consider the joint A of the truss.

Calculate the angle from the figure.

Consider the equilibrium condition.

Thus, our assumption is wrong the force in the member AE is compressive.

Consider the equilibrium condition.

Consider the joint B of the truss.

Consider the equilibrium condition.

Consider the equilibrium condition.

Consider the joint C.

Consider the equilibrium condition.

Consider the equilibrium condition.

Consider the joint D of the truss.

Due to no vertical forces on the member DE, it is take as zero.

Draw the diagram with an assumption of vertical load of 1 kips at joint D for the calculation of vertical components of displacement.

Consider the equilibrium condition.

Take moment about A.

Consider the equilibrium condition.

Consider the joint A of the truss.

Consider the equilibrium condition.

Consider the equilibrium condition.

Consider joint B of the truss.

Consider the equilibrium condition

Consider the equilibrium condition

As there is no force in the member BC, thus the force in the members CD and CE are zero.

Consider joint D of the truss.

Consider the equilibrium condition.

Tabulate the forces of the members of truss.

(a)

Calculate the vertical displacement due to load and unit load by using the formula.

Here, is the vertical displacement, is the tension force due to loads, is the tension force due to horizontal unit load, Q is the unit load, L length of segment, and A area of cross section, E is the modulus of elasticity.

Therefore, the vertical displacement at joint D is .

(b)

Calculate the horizontal displacement of the roller at B.

Here, is the horizontal displacement, is the tension force due to horizontal unit load, Q is the unit load, and L length of segment.

Therefore, the horizontal displacement at joint B is .