Explanation Sketch the stresses for plane b - b on an element as shown in Figure 1. The value of shear stress ( τ x y ) is 45 MPa and the value of normal stress ( σ y ) is 0. The value of angle ( θ ) is − 150 ° . Refer to given Figure. The value of shear stress on plane b - b is τ b = − 25 MPa . Calculate the shear stress for plane b - b ( τ b ) using the stress transformation equation: τ b = − σ x − σ y 2 sin 2 θ + τ x y cos 2 θ Substitute − 25 MPa for τ b , 0 for σ y , − 150 ° for θ , and 45 MPa for τ x y . − 25 = − σ x − 0 2 sin 2 ( − 150 ° ) + 45 cos 2 ( − 150 ° ) − 25 = − 0.433 σ x + 22.5 σ x = 109.7 MPa Calculate the normal stress for plane b - b ( σ b ) using the stress transformation equation: σ b = σ x + σ y 2 + σ x − σ y 2 cos 2 θ + τ x y sin 2 θ Substitute 109.7 MPa for σ x , 0 for σ y , − 150 ° for θ , and 45 MPa for τ x y

Statics and Mechanics of Materials, Student Value Edition (5th Edition)

5th Edition

ISBN: 9780134382890

Author: Russell C. Hibbeler

Publisher: PEARSON

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Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain b…

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Chapter 14.3, Problem 20P

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Find the normal stress on plane b-b.

The principal stresses.

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Chapter 14.3, Problem 19P

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Chapter 14 Solutions

Statics and Mechanics of Materials, Student Value Edition (5th Edition)

Ch. 14.3 - In each ease, the state of stress x, y, xy...Ch. 14.3 - Given the state of stress shown on the element,...Ch. 14.3 - Determine the normal stress and shear stress...Ch. 14.3 - Prob. 2FP Ch. 14.3 - Determine the equivalent state of stress on an...Ch. 14.3 - Prob. 4FP Ch. 14.3 - The beam is subjected to the load at its end....Ch. 14.3 - Prob. 6FP Ch. 14.3 - Prove that the sum of the normal stresses x+y=x+y...Ch. 14.3 - Determine the stress components acting on the...

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