To determine The displacement ( δ ) of end A . Explanation Given information: The modulus of elasticity of the material is E . The variable radius of the circular bar ( r ) is r = r 0 e a x The axial force acting in the circular bar is P . The length of the circular bar is L Calculation: Calculate the cross-sectional area of the bar A ( x ) as a function of x : A ( x ) = π r 2 (1) Substitute r 0 e a x for r in Equation (1). A ( x ) = π × ( r 0 e a x ) 2 = π r 0 2 e 2 a x Calculate the displacement ( δ ) of end A : δ = ∫ 0 L P ( x ) d x A ( x ) E (2) Substitute P for P ( x ) and π r 0 2 e 2 a x for A in Equation (2). δ = ∫ 0 L P d x π r 0 2 e 2 a x E = P π r 0 2 E ∫ 0 L d x e 2 a x (3) Integrate Equation (3)

9th Edition

ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 4.2, Problem 4.27P

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The displacement (δ) of end A.

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