# Determine the forces in the top chord member GH and the bottom chord member BC of the truss, if h = 3 ft. How would the forces in these members change if the height h of the truss was doubled to 6 ft? FIG. P4.32

### Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

Chapter
Section

### Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 4, Problem 32P
Textbook Problem
99 views

## Determine the forces in the top chord member GH and the bottom chord member BC of the truss, if h = 3 ft. How would the forces in these members change if the height h of the truss was doubled to 6 ft?FIG. P4.32

To determine

Find the forces in the bottom chord member BC and top chord member GH of the truss, when h=3ft.

Find the forces in the bottom chord member BC and top chord member GH of the truss, when h=6ft.

### Explanation of Solution

Given information:

The height of the truss is h.

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).

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 E are denoted by Ey.

For Equilibrium of forces,

Take the sum of all horizontal forces in x direction as zero.

Fx=0Ax=0

Take sum of moments about the support A as zero.

MA=0(Ey×24)(2×24)(4×18)(4×12)(4×6)=0Ey×24=192Ey=19224Ey=8k

Calculate the value of Ay as follows:

Ey+Ay=2k+4k+4k+4k+2kEy+Ay=16k

Substitute 8k for Ey.

8k+Ay=16kAy=8k

Consider a vertical section passes through the members GH and BC.

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

Refer Figure 2.

Consider the forces in the members GH and BC as FGH,FBC.

Take sum of moments about B as zero.

MB=0(8×6)+(2×6)FGH×h=0FGH×h=36FGH=36h (1)

Take sum of moments about H as zero

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