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Structural Analysis

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

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Section
BuyFindarrow_forward

Structural Analysis

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

Chapter 4, Problem 53P, 4.51 through 4.55 Determine the force in each member of the space truss shown. FIG. P4.53 , example  1

Chapter 4, Problem 53P, 4.51 through 4.55 Determine the force in each member of the space truss shown. FIG. P4.53 , example  2

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.

MemberProjections(ft)Length(ft)
xyz
AB200020
AC1401017.2
BC601011.66
AD1020522.91
BD1020522.91
CD420521

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.

Fx=0(1022.91)FAD+(1022.91)FBD+(421)FCD+25=00.436FAD+0.436FBD+0.190FCD+25=00.436FAD+0.436FBD+0.190FCD=25        (1)

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

Fz=0(2022.91)FAD(2022.91)FBD(2021)FCD30=00.872FAD0.872FBD0.952FCD30=00.872FAD0.872FBD0

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Chapter 4 Solutions

Structural Analysis
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Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - Determine the force in each member of the truss...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - 4.6 through 4.28 Determine the force in each...Ch. 4 - Determine the force in each member of the truss...Ch. 4 - 4.30 and 4.31 Determine the force in each member...Ch. 4 - 4.30 and 4.31 Determine the force in each member...Ch. 4 - Determine the forces in the top chord member GH...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - Determine the forces in the members identified by...Ch. 4 - 4.33 through 4.45 Determine the forces in the...Ch. 4 - 4.46 through 4.50 Determine the force in each...Ch. 4 - 4.46 through 4.50 Determine the force in each...Ch. 4 - 4.46 through 4.50 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...Ch. 4 - 4.51 through 4.55 Determine the force in each...

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