To determine The principal stresses. The absolute maximum shear stress. Explanation Sketch the stresses on the differential element in the x - z plane as shown in Figure 1. Apply sign conventions to Figure 1. The value of normal stresses are σ x = − 1 ksi and σ z = − 6 ksi . The value of shear stress is τ x z = 1 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 ° . 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 (1) Substitute − 1 ksi for σ x and − 6 ksi for σ z in Equation (1). σ avg = − 1 − 6 2 = − 3.5 ksi Therefore, the coordinates of the reference point C is ( − 3.5 , 0 ) . The coordinates of the reference point A ( σ x , τ x z ) = ( − 1 , 1 ) . Find the radius of the circle using the relation: R = ( σ x − σ avg ) 2 + ( τ x z ) 2 (2) Substitute − 3.5 ksi for σ avg , − 1 ksi for σ x , and 1 ksi for τ x z in Equation (2). R = ( − 1 + 3.5 ) 2 + ( 1 ) 2 = 2

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 9.5, Problem 9.81P

To determine

The principal stresses.

The absolute maximum shear stress.

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Chapter 9.5, Problem 9.80P

Chapter 9.5, Problem 9.82P

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Mechanics of Materials

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