Explanation Given information: Hooke’s law can be written as σ x = E ( 1 − ν 2 ) ( ε x + ν ε y ) and σ y = E ( 1 − ν 2 ) ( ε y + ν ε x ) . Explanation: For the case of plane stress σ z = 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 σ z . ε x = 1 E ( σ x − ν ( σ y + 0 ) ) = 1 E ( σ x − ν σ y ) E ε x = σ x − ν σ y Multiply both sides of the Equation by ν . ν E ε x = ( σ x − ν σ y ) ν = ν σ x − ν 2 σ y (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 σ z . ε y = 1 E ( σ y − ν ( σ x + 0 ) ) = 1 E ( σ y − ν σ x ) E ε y = σ y − ν σ x (2) Add Equation (1) and (2)

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.11, Problem 109P

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Show that the plane stress Hooke’s law can be written as

σx=E(1−ν2)(εx+νεy) and σy=E(1−ν2)(εy+νεx).

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Chapter 14.11, Problem 108P

Chapter 14.11, Problem 110P

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Show that the plane stress Hooke’s law can be written as σ x = E ( 1 − ν 2 ) ( ε x + ν ε y ) and σ y = E ( 1 − ν 2 ) ( ε y + ν ε x ) .

Solution Summary: The author explains that the plane stress Hooke’s law can be written as underset_sigmax=E(1-nu

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Show that the plane stress Hooke’s law can be written as

σx=E(1−ν2)(εx+νεy) and σy=E(1−ν2)(εy+νεx).

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Chapter 14 Solutions

Show that the plane stress Hooke’s law can be written as σ x = E ( 1 − ν 2 ) ( ε x + ν ε y ) and σ y = E ( 1 − ν 2 ) ( ε y + ν ε x ) .

Solution Summary: The author explains that the plane stress Hooke’s law can be written as underset_sigmax=E(1-nu

Concept explainers

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Show that the plane stress Hooke’s law can be written as σx=E(1−ν2)(εx+νεy) and σy=E(1−ν2)(εy+νεx).

Want to see the full answer?

Chapter 14 Solutions

Show that the plane stress Hooke’s law can be written as

σx=E(1−ν2)(εx+νεy) and σy=E(1−ν2)(εy+νεx).