To determine The principal strains ε 1 , ε 2 , and ε 3 . Explanation Given information: The principal stresses are σ 1 = 8 ksi , σ 2 = 3 ksi, and σ 3 = − 4 ksi . Modulus of elasticity of aluminum is E al = 10 × 10 3 ksi . Poisson’s ratio is ν a l = 0.33 . Calculation: Apply the generalized Hooke’s law as shown below. Apply the normal strain in x direction as shown below. ε 1 = 1 E ( σ 1 − ν ( σ 2 + σ 3 ) ) Here, E is the modulus of elasticity, σ 1 is the normal stress in x direction, ν is the Poisson’s ratio, σ 2 is the normal stress in y direction, and σ 3 is the normal stress in z direction. Substitute 8 ksi for σ 1 , 3 ksi for σ 2 , − 4 ksi for σ 3 , 10 × 10 3 ksi for E , and 0.33 for ν . ε 1 = 1 10 × 10 3 ( 8 − 0.33 × ( 3 + ( − 4 ) ) ) = 8.33 10 × 10 3 = 833 × 10 − 6 Apply the normal strain in y direction as shown below. ε 2 = 1 E ( σ 2 − ν ( σ 1 + σ 3 ) ) Substitute 8 ksi for σ 1 , 3 ksi for σ 2 , − 4 ksi for σ 3 , 10 × 10 3 ksi for E , and 0

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 10.6, Problem 10.47P

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The principal strains ε1, ε2, and ε3 .

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Chapter 10.6, Problem 10.46P

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