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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 6P
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.

Chapter 4, Problem 6P, 4.6 through 4.28 Determine the force in each member of the truss shown by the method of joints. FIG

FIG P4.6

To determine

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

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).

Consider the horizontal and vertical reactions at D are Dx and Dy.

Consider the horizontal reaction at A are Ax.

Calculation:

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

Refer Figure 1.

For Equilibrium of forces,

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

Fx=0Dx+Ax=0Dx=Ax (1)

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

Fy=0Dy51010=0Dy=25k

Take sum of moments about the support A as zero.

MA=0Dx×1010×1210×24=010Dx=360Dx=36k

Substitute 36k for Dx in Equation (1).

Ax=36k

Consider the triangle DCA.

Consider the angle DCA is θ. Then,

tanθ=1024θ=tan1(1024)θ=22.61°

Show the joint C as shown in Figure 2.

Refer Figure 2.

Take the sum of the forces acting in the vertical direction as zero. Then,

FECsinθ=10FECsin(22.61°)=10FEC=10sin(22.61°)FEC=26k(T)

Take the sum of the forces acting in the horizontal direction as zero. Then,

FBCFECcosθ=0FBC=FECcos(22.61°)FBC=26cos(22.61°)FBC=24kFBC=24k(C)

Show the joint B as shown in Figure 3.

Refer Figure 3.

Take the sum of the forces acting in the vertical direction as zero. Then,

FBE=10k(T)

Take the sum of the forces acting in the horizontal 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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