To determine The stress components acting on the inclined plane AB using the method of equilibrium. Explanation Let the sectioned area be Δ A and the adjacent areas of the segment be Δ A sin θ and Δ A cos θ . Sketch of the arbitrary section of the lower segment of the element is shown in Figure 1. The force acting on each segment can be obtained by multiplying the stress components on each face by the area upon which the stress acts. Let the normal and shear stress components acting on the + x ' face of the element be σ x ' and τ x ' y ' . Let the sectioned force in the y ' face be Δ F y ' and the sectioned force in the x ' face be Δ F x ' . Draw the free body diagram of the segment showing the force that acting on the segment as in Figure 2. Calculation: Apply Equilibrium equations to the free body diagram of the segment. Sum of forces in the y ' face of the element is equal to 0. ∑ F y ' = 0 [ Δ F y ' + ( 45 Δ A sin 45 ° ) cos 45 ° − ( 45 Δ A sin 45 ° ) sin 45 ° − ( 80 Δ A sin 45 ° ) cos 45 ° ] = 0 Δ F y ' = − 22.5 Δ A + 22.5 Δ A + 40 Δ A Δ F y ' = 40 Δ A Sum of forces in the x ' face of the element is equal to 0. ∑ F x ' = 0 [ Δ F x ' + ( 45 Δ A sin 45 ° ) cos 45 ° + ( 45 Δ A cos 45 ° ) sin 45 ° − ( 80 Δ A sin 45 ° ) cos 45 ° ] = 0 Δ F x ' = − 22

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 9.3, Problem 9.6P

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The stress components acting on the inclined plane AB using the method of equilibrium.

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