Explanation Apply sign conventions to the given Figure. The value of normal stresses are σ y = 5 ksi and σ z = − 2.5 ksi . The value of shear stress is τ y z = − 4 ksi . 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 y + σ z 2 from the origin. Plot the reference point A having coordinates A ( σ y , τ y 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 y 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 y + σ z 2 Substitute 5 ksi for σ y and − 2.5 ksi for σ z . σ avg = 5 − 2.5 2 = 1.25 ksi Therefore, the coordinates of the reference point C is ( 1.25 , 0 ) . The coordinates of the reference point A ( σ y , τ y z ) = ( 5 , − 4 ) . The coordinates of the reference point B ( σ z , − τ y z ) = ( − 2.5 , 4 ) . Find the radius of the circle using the relation: R = ( σ y − σ avg ) 2 + ( τ y z ) 2 Substitute 1.25 ksi for σ avg , 5 ksi for σ y , and − 4 ksi for τ y z

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.5, Problem 82P

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Find the principal stresses.

Find the absolute maximum shear stress.

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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