(a) Explanation Assumption: The sign conventions for the stress components are explained below. The outward normal on the right-hand face of the element is representing as the positive x and x ' axes. The normal stress σ x and σ x ' are positive if it acts along the positive x and x ' axes. The normal stress σ y and σ y ' are positive if it acts along the positive y and y ' axes. The shear stress τ x y and τ x ' y ' are positive if it acts along the positive x and x ' and y and y ' axes. Find the in-plane principal stresses x ' and y using the relation: σ 1 , 2 = σ x + σ y 2 ± ( σ x − σ y 2 ) 2 + τ x y 2 Substitute 45 MPa for σ x , − 60 MPa for σ y , and 30 MPa for τ x y (b) To determine Find the maximum in-plane shear stress. Find the average normal stress. Specify the orientation of the principal stresses. Specify the orientation of the maximum in-plane shear stress.

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 15P

(a)

To determine

Find the principal stresses.

(b)

To determine

Find the maximum in-plane shear stress.

Find the average normal stress.

Specify the orientation of the principal stresses.

Specify the orientation of the maximum in-plane shear stress.

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Chapter 14.3, Problem 14P

Chapter 14.3, Problem 16P

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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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Find the principal stresses.

Solution Summary: The author explains the sign conventions for the stress components.

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Find the principal stresses.

Find the maximum in-plane shear stress. Find the average normal stress. Specify the orientation of the principal stresses. Specify the orientation of the maximum in-plane shear stress.

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Chapter 14 Solutions

Find the maximum in-plane shear stress.

Find the average normal stress.

Specify the orientation of the principal stresses.

Specify the orientation of the maximum in-plane shear stress.