(a) Explanation Given information: The stress component along x direction is σ x = 100 MPa . The stress component along y direction is σ y = 20 MPa . The shear stress component is τ x y = 75 MPa . The yield stress is σ Y = 160 MPa . The principal stress is σ z = + 45 MPa . Calculation: Sketch the state of stress in a machine component as shown in Figure 1. Refer to Figure 1. σ x = 100 MPa σ y = 20 MPa τ x y = 75 MPa Apply the procedure to construct the Mohr’s circle as shown below. Find the centre of the circle C located σ avg = σ x + σ y 2 from the origin. Plot the reference points A having coordinates A ( σ x , τ A ) . Connect the point A with C and from the shaded triangle find the radius R of the circle. Sketch the circle once R has been determined. Construct the Mohr’s circle as shown below. Calculate the centre of the circle ( σ avg ) using average normal stress as shown below. σ avg = σ x + σ y 2 Substitute 100 MPa for σ x and 20 MPa for σ y . σ avg = 100 + 20 2 = 120 2 = 60 MPa The centre of the circle is C = 60 MPa . Coordinates of the reference point x . x = ( σ x , − τ x y ) Substitute 100 MPa for σ x and 75 MPa for τ x y . x = ( 100 MPa, − 75 MPa ) Coordinates of the reference point y as follows: y = ( σ y , τ x y ) Substitute 20 MPa for σ y and 75 MPa for τ x y . y = ( 20 MPa , 75 MPa ) Calculate the radius ( R ) of the circle as shown below. R = ( σ x − σ avg ) 2 + ( τ x y ) 2 Substitute 100 MPa for σ x , 60 MPa for σ avg , and 75 MPa for τ x y (b) To determine Check whether the yield occurs when σ z = − 45 MPa by using the maximum-distortion energy criterion.

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Chapter 11.3, Problem 37P

(a)

To determine

Check whether the yield occurs when σz=+45 MPa by using the maximum-distortion energy criterion.

(b)

To determine

Check whether the yield occurs when σz=−45 MPa by using the maximum-distortion energy criterion.

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Chapter 11.3, Problem 36P

Chapter 11.3, Problem 38P

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Check whether the yield occurs when σ z = + 45 MPa by using the maximum-distortion energy criterion.

Solution Summary: The author analyzes the state of stress in a machine component as shown in Figure 1.

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Check whether the yield occurs when σz=+45 MPa by using the maximum-distortion energy criterion.

Check whether the yield occurs when σz=−45 MPa by using the maximum-distortion energy criterion.

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