Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 2, Problem 2.7.7P

-7 The truss A BC Shawn in the figure supports a horizontal load P1= 300 lb and a vertical load P2= 9001b. Both bars have a cross-sectional area A = 2.4 in2 and are made of steel with E = 30 X 106 psi.

(a) Determine the strain energy U1of the truss when the load P1acts alone (P2= 0).

(b) Determine the strain energy U2when the load P2acts alone (P1= 0).

(c) Determine the strain energy U3when both loads act simultaneously.

  Chapter 2, Problem 2.7.7P, -7 The truss A BC Shawn in the figure supports a horizontal load P1= 300 lb and a vertical load P2=

(a)

Expert Solution
Check Mark
To determine

The strain energy of the truss when load P1act alone.

Answer to Problem 2.7.7P

The strain energy of the truss when load P1act alone.

Explanation of Solution

Given Information:

The length of the link BC is 60in, area of the cross-section of the link is 2.4in2, and the young’s modulus of elasticity is 30×106psi.

The following figure shows the forces acting at joint B:

  Mechanics of Materials (MindTap Course List), Chapter 2, Problem 2.7.7P

       Figure-(1)

Write the expression for the length of the link AB.

  LAB=LBCcos30°....... (I)

Here, the length of the link BC is LBC.

Write the equilibrium equation for the horizontal forces.

  FABcos30°FBC+P1=0....... (II)

Here, the force applied on the link ABis FAB, the force applied on the link BCis FBC, and horizontal force acting at Bis P1.

Write the equilibrium equation for the vertical forces.

  FABsin30°P2=0....... (III)

Here, vertical force acting at Bis P2.

Write the expression for the strain energy of the truss.

  U=FAB2LAB2AE+FBC2LBC2AE....... (IV)

Here, area of the cross-section of the link is A, and the young’s modulus of elasticity is E.

Calculation:

Substitute 60infor LBCin Equation (I).

  LAB=60incos30°=69.28in

Substitute 0lbfor P2in Equation (III).

  FABsin30°0lb=0FAB=0lb

Substitute 0lbfor FAB, and 300lbfor P1in Equation (II).

  (0lb)cos30°FBC+(300lb)=0FBC=300lb

Substitute 300lbfor FBC, 0lbfor FAB, 69.28infor LAB, 30×106psifor E, and 2.4in2for A, and 60infor LBCin Equation (IV).

  U=(0lb)(69.28in)2(2.4in2)(30×106psi)+(300lb)2(60in)2(2.4in2)(30×106psi)=(300lb)2(60in)2(2.4in2)(30×106psi)=0.0375lbin

Conclusion:

The strain energy of the truss when load P1act alone is 0.0375lbin.

(b)

Expert Solution
Check Mark
To determine

The strain energy of the truss when load P2act alone.

Answer to Problem 2.7.7P

The strain energy of the truss when load P2act alone is= 2.57lbin.

Explanation of Solution

Calculation:

Substitute 900lbfor P2in Equation (III).

  FABsin30°900lb=0FAB=900lbsin30°FAB=1800lb

Substitute 1800lbfor FAB, and 0lbfor P1in Equation (II).

  (1800lb)cos30°FBC+(0lb)=0(1800lb)cos30°FBC=0FBC=1558.84lb

Substitute 1558.84lbfor FBC, 1800lbfor FAB, 69.28infor LAB, 30×106psifor E, and 2.4in2for A, and 60infor LBCin Equation (IV).

  U=(1800lb)2(69.28in)2(2.4in2)(30×106psi)+(1558.84lb)2(60in)2(2.4in2)(30×106psi)=(1800lb)2(69.28in)+(1558.84lb)2(60in)(4.8in2)(30×106psi)=2.57lbin

Conclusion:

The strain energy of the truss when load P2act alone is = 2.57lbin.

(c)

Expert Solution
Check Mark
To determine

The strain energy of the truss when both load acts simultaneously.

Answer to Problem 2.7.7P

The strain energy of the truss when both load acts simultaneously is 2.22lbin.

Explanation of Solution

Calculation:

Substitute 900lbfor P2in Equation (III).

  FABsin30°900lb=0FAB=900lbsin30°FAB=1800lb

Substitute 1800lbfor FAB, and 300lbfor P1in Equation (II).

  (1800lb)cos30°FBC+(300lb)=0(1800lb)cos30°FBC=300lbFBC=1558.84lb+300lbFBC=1258.84lb

Substitute 1258.84lbfor FBC, 1800lbfor FAB, 69.28infor LAB, 30×106psifor E, and 2.4in2for A, and 60infor LBCin Equation (IV).

  U=(1800lb)2(69.28in)2(2.4in2)(30×106psi)+(1258.84lb)2(60in)2(2.4in2)(30×106psi)=(1800lb)2(69.28in)+(1258.84lb)2(60in)(4.8in2)(30×106psi)2.22lbin

Conclusion:

The strain energy of the truss when both load acts simultaneously is = 2.22lbin.

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Chapter 2 Solutions

Mechanics of Materials (MindTap Course List)

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