Explanation Given information: A soft material is placed within the confines of a rigid cylinder which rests on a rigid support. Poisson’s ration is ν = 0.3 . Calculation: Assuming that ε x = 0 and ε y = 0 . Apply the normal strain in x direction as shown below. ε x = 1 E ( σ x − ν ( σ y + σ z ) ) Here, E is the modulus of elasticity, σ x is the normal stress in x direction, ν is the Poisson’s ratio, σ y is the normal stress in y direction, and σ z is the normal stress in z direction. Substitute 0 for ε x . 0 = 1 E ( σ x − ν ( σ y + σ z ) ) σ x − ν ( σ y + σ z ) = 0 (1) Apply the normal strain in y direction as shown below. ε y = 1 E ( σ y − ν ( σ x + σ z ) ) Substitute 0 for ε y . 0 = 1 E ( σ y − ν ( σ x + σ z ) ) σ y − ν ( σ x + σ z ) = 0 (2) Equating Equations (1) and (2). σ x − σ y = ν ( σ y + σ z ) − ν ( ) σ x − σ y = ν ( σ y + σ z − σ x − σ z ) σ x − σ y = − ν ( σ x − σ y ) ( σ x − σ y ) + ν ( σ x − σ y ) = 0 ( 1 + ν ) ( σ x − σ y ) = 0 σ x − σ y = 0 σ x = σ y Substitute σ x for σ y in Equation (1). σ x − ν ( σ x + σ z ) = 0 ( 1 − ν ) σ x − ν σ z = 0 ( 1 − ν ) σ x = ν σ z σ x = ν ( 1 − ν ) σ z Hence, σ y = ν ( 1 − ν ) σ z . Apply the normal strain in z direction as shown below. ε z = 1 E ( σ z − ν ( σ x + σ y ) ) Substitute ν ( 1 − ν ) σ z for σ x and ν ( 1 − ν ) σ z for σ y

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 10.6, Problem 10.58P

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The increase factor by which the stiffness of the material, or the apparent modulus of elasticity.

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Chapter 10.6, Problem 10.57P

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The increase factor by which the stiffness of the material, or the apparent modulus of elasticity.

Solution Summary: The author explains the increase factor by which the stiffness of the material, or the apparent modulus of elasticity, is 1.35.

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