Explanation Given information: The state of strain at a point on a wrench has components of ε x = 120 × 10 − 6 , ε y = − 180 × 10 − 6 , and γ x y = 150 × 10 − 6 . Calculation: Apply the procedure for the construction of Mohr’s circle ass shown below. Find the centre of the circle C located ε avg = ε x + ε y 2 from the origin. Plot the reference points A having coordinates A ( ε x , γ x y 2 ) . This point represents the case when the x ′ axis coincides with the x axis. Hence, θ = 0 . Connect the point A with C and from the shaded triangle find the radius R of the circle. Sketch the circle using calculated radius R . Construct the Mohr’s circle as shown below. Find the centre of the circle using average normal strain as shown below. ε avg = ε x + ε y 2 Here, ε x is the normal strain in x direction and ε y is the normal strain in y direction. Substitute 120 × 10 − 6 for ε x and − 180 × 10 − 6 for ε y . ε avg = ( 120 × 10 − 6 ) + ( − 180 × 10 − 6 ) 2 = − 30 × 10 − 6 Hence, the average normal strain is ε avg = − 30 × 10 − 6 _ . The centre of the circle is C = − 30 × 10 − 6 . Coordinates of the reference point A . A = ( ε x , γ x y 2 ) Here, γ x y is the shear strain of the element. Substitute 120 × 10 − 6 for ε x and 150 × 10 − 6 for γ x y . A = ( 120 × 10 − 6 , 150 × 10 − 6 2 ) = ( 120 × 10 − 6 , 75 × 10 − 6 ) Find the radius of the circle as shown below. R = ( ε x − ε a v g ) 2 + ( γ x y 2 ) 2 Substitute − 30 × 10 − 6 for ε avg , 120 × 10 − 6 for ε x , and 150 × 10 − 6 for γ x y

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Chapter 10.3, Problem 10.18P

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The maximum in-plane shear strain and average normal strain on an element using Mohr’s circle.

To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.

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Chapter 10.3, Problem 10.17P

Chapter 10.3, Problem 10.19P

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The maximum in-plane shear strain and average normal strain on an element using Mohr’s circle. To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.

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The maximum in-plane shear strain and average normal strain on an element using Mohr’s circle. To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.

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The maximum in-plane shear strain and average normal strain on an element using Mohr’s circle.

To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.