(a) Explanation 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. The procedure to construct Mohr’s circle is shown below. The coordinate systems are the horizontal axis represents the normal stress with positive towards right and the vertical axis represents shear stress with positive downwards. Plot the center of the circle C which is located σ avg = σ x + σ y 2 from the origin. Plot the reference point A having coordinates A ( σ x , τ x y ) . This point represents that the x ′ axis coincides with the x axis. Hence, θ = 0 ° . Connect the point A with the centre C and find CA by trigonometry which represents the radius of the circle R . Sketch the circle. Apply sign conventions to the given Figure (a). The value of normal stresses are σ x = − 8 ksi and σ y = − 2 ksi . The value of shear stress is τ x y = 0 (b) To determine Sketch the Mohr circle for the given states of stress. (c) To determine Sketch the Mohr circle for the given states of stress.

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.4, Problem 60P

(a)

To determine

Sketch the Mohr circle for the given states of stress.

(b)

To determine

Sketch the Mohr circle for the given states of stress.

(c)

To determine

Sketch the Mohr circle for the given states of stress.

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Chapter 14.4, Problem 59P

Chapter 14.4, Problem 61P

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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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Sketch the Mohr circle for the given states of stress.

Solution Summary: The author explains the sign conventions for the stress components and the procedure to construct Mohr's circle.

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Sketch the Mohr circle for the given states of stress.

Sketch the Mohr circle for the given states of stress.

Sketch the Mohr circle for the given states of stress.

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Chapter 14 Solutions