International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
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Chapter 10, Problem 10.21P
To determine

The couple Co required to hold the mechanism in the position shown.

Expert Solution & Answer
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Answer to Problem 10.21P

The couple Co required to hold the mechanism in the position shown is 103Nm.

Explanation of Solution

Given:

The mass of each uniform bar is 18 kg/m.

Concept used:

Apply the Principle of virtual work by providing a small angular virtual displacement of δθ to bar AB.

By applying the virtual angular displacement to bar AB then bar AB will rotate, Bar BC will translate and bar CD will rotate

The virtual kinematic diagram after the angular displacement of δθ is shown below:

International Edition---engineering Mechanics: Statics, 4th Edition, Chapter 10, Problem 10.21P

Write the expression to calculate linear displacement of bar AB.

  δyAB=lABδθ ...... (1)

Here, δyAB is the linear displacement of end of bar AB, lAB is the length of bar AB and δθ is the virtual angular displacement.

Write the expression to calculate linear displacement of bar CD.

  δyCD=lCDδθ ...... (2)

Here, δyCD is the linear displacement of end of bar CD, lCD is the length of bar CD and δθ is the virtual angular displacement.

The weight force is the only force applied on the system thus, but similar triangle the displacement of center of bars AB and CD is 0.5δyAB and 0.5δyCD.

Write the expression for the weight of bar.

  W=m˙gl ...... (3)

Here, W is the weight of bar, m˙ is the mass per unit length, g is acceleration due to gravity and l is the length of bar.

Write the expression for virtual work done on system.

  δU=C0δθWAB(0.5δyAB)WBCδyBCWCD(0.5δyCD) ...... (4)

Here, δU is the total virtual work done on system, C0 is the initial couple, WAB is the weight of bar AB, WBC is the weight of bar BC, WCD is the weight of bar CD and δyBC is the displacement of bar BC.

Calculation:

Substitute 480mm for lAB in equation (1).

  δyAB=(480 mm( 1m 1000mm ))δθ=0.48δθ

Displacement of bar BC will be equal to displacement of end B as there is no constraint therefore, δyBC is 0.48δθ.

Substitute 480mm for lCD in equation (2).

  δyCD=(480 mm( 1m 1000mm ))δθ=0.48δθ

Substitute WAB for W, 18 kg/m for m˙, 9.81 m/s2 for g and 480 mm for l in equation (3).

  WAB=18(9.81)(480 mm( 1 m 1000mm ))=84.76N

Substitute WBC for W, 18 kg/m for m˙, 9.81 m/s2 for g and 600 mm for l in equation (3).

  WBC=18(9.81)(600 mm( 1 m 1000mm ))=105.95N

Substitute WCD for W, 18 kg/m for m˙, 9.81 m/s2 for g and 750 mm for l in equation (3).

  WCD=18(9.81)(750 mm( 1 m 1000mm ))=132.44N

Substitute 0 for δU, 84.76 N for WAB, 105.95N for WBC, 132.44N for WCD, 0.48δθ for δyAB, 0.48δθ for δyBC and 0.48δθ for δyCD in equation (4).

  0=C0δθ84.76(0.5)(0.48)δθ105.95(0.48)δθ132.44(0.5)(0.48)δθ0=(C0102.98)δθC0103 Nm

The couple Co required to hold the mechanism in the position shown is 103Nm.

Conclusion:

Thus, the couple Co required to hold the mechanism in the position shown is 103Nm.

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Chapter 10 Solutions

International Edition---engineering Mechanics: Statics, 4th Edition

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