   # Determine the forces in the members identified by “x” of the truss shown by the method of sections. FIG. P4.34

#### Solutions

Chapter
Section
Chapter 4, Problem 34P
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. P4.34

To determine

Find the forces in the members FG, FC, and BC of the truss by the method of sections.

### 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 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 FG, FC, and BC.

Calculation:

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

Refer Figure 1.

Consider the horizontal and vertical reaction at A are denoted by Ax and Ay.

Consider the vertical reaction at D is denoted by  Dy.

Take the sum of the moment about A and Equate to zero.

MA=0Dy×24(100×8)(100×12)(50×16)(60×6)=0Dy×243160=0Dy=316024Dy=131.67kN

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

Dy+Ay=100+100+50Dy+Ay=250131.67+Ay=250Ay=250131.67Ay=118.33kN

Find the angle (θ) made by the member CF with the horizontal as follows:

tanθ=64θ=tan1(64)θ=56.30°

Consider a vertical section a-a passing through the members FG, FC, and BC.

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

Refer Figure 1 and Figure 2.

Consider the forces in the members FG, CF, and BC as FFG,FCF,FBC

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