Explanation Apply sign conventions to the given Figure. For x - z plane, The value of normal stresses are σ x = 120 MPa and σ z = 0 . The value of shear stress is τ x z = 150 MPa . 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 z 2 from the origin. Plot the reference point A having coordinates A ( σ x , τ x z ) . This point represents that the x ′ axis coincides with the x axis. Hence, θ = 0 ° . Plot the reference point B having coordinates B ( σ z , − τ x z ) . Connect the point A with the centre C and find CA by trigonometry which represents the radius of the circle R . Sketch the circle. Find the average normal stress ( σ avg ) using the relation: σ avg = σ x + σ z 2 Substitute 120 MPa for σ x and 0 for σ z . σ avg = 120 + 0 2 = 60 MPa Therefore, the coordinates of the reference point C is ( 60 , 0 ) . The coordinates of the reference point A ( σ x , τ x z ) = ( 120 , 150 ) . The coordinates of the reference point B ( σ z , − τ x z ) = ( 0 , − 150 ) . Find the radius of the circle using the relation: R = ( σ x − σ avg ) 2 + ( τ x z ) 2 Substitute 60 MPa for σ avg , 120 MPa for σ x , and 150 MPa for τ x z

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 14.5, Problem 81P

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Find the principal stresses.

Find the absolute maximum shear stress.

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Chapter 14.5, Problem 80P

Chapter 14.5, Problem 82P

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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. Find the absolute maximum shear stress.

Solution Summary: The author explains the procedure to construct Mohr's circle. The coordinate systems are the horizontal axis represents the normal stress with positive towards right and the vertical