To determine The principal stresses. The absolute maximum shear stress. Explanation For the y - z plane: Apply sign conventions to the given Figure. The value of normal stresses are σ y = 60 MPa and σ z = 90 MPa . The value of shear stress is τ y z = − 20 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 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 y + σ z 2 (1) Substitute 60 MPa for σ y and 90 MPa for σ z in Equation (1). σ avg = 60 + 90 2 = 75 MPa Therefore, the coordinates of the reference point C is ( 75 , 0 ) . The coordinates of the reference point A ( σ y , τ y z ) = ( 60 , − 20 ) . Find the radius of the circle using the relation: R = ( σ y − σ avg ) 2 + ( τ y z ) 2 (2) Substitute 75 MPa for σ avg , 60 MPa for σ y , and − 20 MPa for τ y z in Equation (2). R = ( 60 − 75 ) 2 + ( − 20 ) 2 = 25 MPa Sketch the Mohr’s circle as shown in Figure 1

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Chapter 9.5, Problem 9.79P

To determine

The principal stresses.

The absolute maximum shear stress.

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Chapter 9.5, Problem 9.78P

Chapter 9.5, Problem 9.80P

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Chapter 9 Solutions

MECHANICS OF MATERIALS-TEXT

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