   # Determine the forces in the members identified by “x” of the truss shown by the method of sections. FIG. P4.36

#### Solutions

Chapter
Section
Chapter 4, Problem 36P
Textbook Problem
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## Determine the forces in the members identified by “x” of the truss shown by the method of sections. FIG. P4.36

To determine

Find the forces in the members BC, CI, and IJ of the truss by the method of sections.

### Explanation of Solution

Sign convention:

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 sections:

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

The Figure of the truss is shown.

The members identified by “x” are BC, CI, and IJ.

Consider the forces in the members BC, CI, and IJ are denoted by FBC, FCI, and FIJ.

Calculation:

Show the free body diagram of the truss as shown in Figure 1.

Refer Figure 1.

The angle made by the bottom chord of the truss with the horizontal is θ=20°.

Consider the horizontal axis is along the bottom chord of the truss.

Find the horizontal and vertical component of the forces at B, C, D, E, and F as follows:

HorizontalComponent=30k×sin(20°)=10.26k

VerticalComponent=30k×cos(20°)28.2k

Find the horizontal and vertical component of the forces at G as follows:

HorizontalComponent=15k×sin(20°)=5.13k

VerticalComponent=15k×cos(20°)14.1k

Consider a vertical section passing through the members BC, CI, and IJ denoted by a-a.

Show the portion of the truss to the right of the section as shown in Figure 2.

Refer Figure 1 and Figure 2.

For Equilibrium of forces,

Take the sum of all vertical forces in y direction as zero.

Fy=0FCI28

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