Explanation Refer the given Figure. The value of normal stress on plane a - a is σ a = 80 ksi . Find the value of normal stress ( σ x ) : σ x = 60 × sin ( 60 ° ) = 51.962 ksi Find the value of shear stress ( τ x y ) : τ x y = 60 × cos ( 60 ° ) = 30 ksi Sketch the stresses for plane a - a on an element as shown in Figure 1. Calculate the normal stress for plane a - a ( σ a ) using the stress transformation equation: σ a = σ x + σ y 2 + σ x − σ y 2 cos 2 θ + τ x y sin 2 θ Substitute 80 ksi for σ a , 51.962 ksi for σ x , 45 ° for θ , and 30 ksi for τ x y . 80 = 51.962 + σ y 2 + 51.962 − σ y 2 cos 2 ( 45 ° ) + 30 sin 2 ( 45 ° ) 80 = 25.98 + σ y 2 + 0 + 30 σ y = 48.04 ksi Calculate the shear stress for plane a - a ( τ a ) using the stress transformation equation: τ a = − σ x − σ y 2 sin 2 θ + τ x y cos 2 θ Substitute 51.962 ksi for σ x , 48

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

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 21P

To determine

Find the shear stress on plane a-a.

The principal stresses.

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Chapter 14.3, Problem 20P

Chapter 14.3, Problem 22P

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Chapter 14 Solutions

Statics and Mechanics of Materials (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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