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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 10P
Textbook Problem
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4.6 through 4.28 Determine the force in each member of the truss shown by the method of joints.

FIG. P4.10

Chapter 4, Problem 10P, 4.6 through 4.28 Determine the force in each member of the truss shown by the method of joints. FIG.

To determine

Find the forces in the members of the truss by the method of joints.

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 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 forces in the member AE, DG, EF, GF, BE, CG, BF, CF, AB, CD, and BC are FAE,FDG,FEF,FGF,FBE,FCG,FBF,FCF,FAB,FCD,FBC.

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

Refer Figure 1.

Consider the horizontal and vertical reactions at A are Ax and Ay.

Consider the vertical reaction at D is Dy.

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

Fy=0Ay+Dy=30+60+30Ay+Dy=120        (1)

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

Fx=0Ax=0

Take the sum of the moments at A is zero.

MA=0(30×4)(60×8)(30×12)+Dy×16=0Dy×16=120+480+360Dy=120+480+36016Dy=60kN

Substitute 60kN for Dy in Equation (1).

Ay+60=120Ay=60kN

Show the joint A as shown in Figure 2.

Refer Figure 2.

Consider the angle made by the the member AE with the horizontal as θ.

Calculate the angle made by the member AE with the horizontal as follows:

tanθ=34θ=tan1(34)θ=36.86°

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

Fy=0Ay+FAEsin(36.86°)=060+0.6FAE=0FAE=600.6

FAE=100kNFAE=100kN(C)

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

Fx=0FAB+FAEcos(36.86°)=0FAB+0.8FAE=0FAB=0.8FAE

Substitute 100kN for FAE.

FAB=0.8×(100)kN=80kN(T)

Show the joint E as shown in Figure 3.

Refer Figure 3.

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

Fx=0FAEcosθ+FEFcosθ=0

Substitute 100kN for FAE and 36.86° for θ.

100cos(36.86°)+FEFcos(36.86°)=080+0.8FEF=00.8FEF=80FEF=800.8FEF=100kN(C)

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

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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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