   # 4.51 through 4.55 Determine the force in each member of the space truss shown. FIG. P4.53

#### Solutions

Chapter
Section
Chapter 4, Problem 53P
Textbook Problem
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## 4.51 through 4.55 Determine the force in each member of the space truss shown.  FIG. P4.53

To determine

Find the forces in the members of the space truss.

### Explanation of Solution

Given information:

Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below.

• For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
• For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
• For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as negative and the counter clockwise moment as positive.

Method of joints:

The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates Tension (T).

Calculation:

Consider the member AB.

The projections of the member AB in the x direction is 20ft.

The projections of the member AB in the y direction is 0ft.

The projections of the member AB in the z direction is 0ft.

Calculate the length of the member AB as follows:

AB=(20)2+(0)2+(0)2=400=20ft

Similarly, find the length of the members AC, BC, AD, BD, CD, and tabulate the values as in Table 1.

 Member Projections(ft) Length(ft) x y z AB 20 0 0 20 AC 14 0 10 17.2 BC 6 0 10 11.66 AD 10 20 5 22.91 BD 10 20 5 22.91 CD 4 20 5 21

Consider the joint D.

Show the joint D as shown in Figure 1.

Refer Figure 1.

Take the sum of the forces in the x-direction as zero.

Take the sum of the forces in the y-direction as zero.

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