To determine To calculate: The resultant internal loadings acting on the cross section of through point B . Explanation Given information: The curved rod AD of radius r has a weight per length of w . Calculation: Sketch the Free Body Diagram of the curved rod as shown in Figure 1. Refer to Figure 1. The distance from the centroid C of segment AB to point O is O C = 2 r sin ( θ 2 ) θ . Sketch the Free Body Diagram of the cross section of the curved rod through point B as shown in Figure 2. Refer to Figure 2. Find the internal loadings as shown below. Apply the Equations of Equilibrium as shown below. Summation of forces along horizontal direction is Equal to zero. ∑ F x = 0 N B + w r θ cos θ = 0 N B = − w r θ cos θ Summation of forces along vertical direction is Equal to zero. ∑ F y = 0 − V B − w r θ sin θ = 0 − V B = w r θ sin θ V B = − w r θ sin θ Take moment about O is Equal to zero. ∑ M O = 0 w r θ ( cos θ 2 ) ( 2 r sin ( θ 2 ) θ ) + ( N B ) r

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 1.2, Problem 1.29P

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To calculate: The resultant internal loadings acting on the cross section of through point B.

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Chapter 1.2, Problem 1.28P

Chapter 1.2, Problem 1.30P

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MECHANICS OF MATERIALS-TEXT

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