Question

Determine the force in each member of the truss supporting a floor deck as shown in Fig. P4.28. The deck is simply supported on floor beams which, in turn, are connected to the joints of the truss. Thus, the uniformly distributed loading on the deck is transmitted by the floor beams as concentrated loads to the top joints of the truss.

Answer 1

Loading on the deck is shown in the following figure.

The load on the floor beam at A is calculated as follows:

Similarly, the load on the floor beam at E is .

The load on the floor beam at B is calculated as follows:

Similarly, the load on the floor beam at C and D are and .

Draw the free body diagram of the truss.

Calculate the reaction at point A. Apply the moment at E from the free body diagram of the truss.

Apply the horizontal equilibrium condition for the free body diagram of the truss.

Calculate the reaction at point E. Apply the vertical equilibrium condition for the free body diagram of the truss.

Consider section 1-1.

Calculate the forces in the members.

Apply the moment at F for the above section1-1.

Apply the vertical equilibrium condition for the above section1-1.

Apply the horizontal equilibrium condition for the above section1-1.

Consider section 2-2.

Calculate the forces in the members.

Apply the moment at G for the above section 2-2.

Apply the vertical equilibrium condition for the above section 2-2.

Apply the horizontal equilibrium condition for the above section 2-2.

Consider section 3-3.

Calculate the forces in the members.

Apply the moment at H for the above section 3-3.

Apply the vertical equilibrium condition for the above section 3-3.

Apply the horizontal equilibrium condition for the above section 3-3.

Consider joint D.

Calculate the reaction at point A.

Apply the vertical equilibrium condition for the joint.

Applying horizontal equilibrium condition for the joint, we obtain

Consider joint A.

Calculate the force in the member AF. Apply the conditions of equilibrium along the x-axis.

Consider joint B.

Calculate the force in the member BG. Apply the conditions of equilibrium along the y-axis.

Consider joint C.

Calculate the force in the member CH. Apply the conditions of equilibrium along the y-axis.

Consider joint E.

Calculate the force in the member EI. Apply the conditions of equilibrium along the x-axis.