Explanation Given information: The state of strain at a point on the bracket due to the load P has components of ε x = 500 × 10 − 6 , ε y = 350 × 10 − 6 , and γ x y = − 430 × 10 − 6 . The element oriented at an angle of 30 ° clockwise from the original position. Calculation: Apply the strain transformation Equations as shown below. Find the normal strain component in x ′ direction as shown below. ε x ′ = ε x + ε y 2 + ε x − ε y 2 cos 2 θ + γ x y 2 sin 2 θ Here, ε x is the normal strain in x direction, ε y is the normal strain in y direction, and γ x y is the shear strain of the element. Substitute 500 × 10 − 6 for ε x , 350 × 10 − 6 for ε y , − 430 × 10 − 6 for γ x y , and − 30 ° for θ . ε x ′ = [ ( 500 × 10 − 6 ) + ( 350 × 10 − 6 ) 2 + ( 500 × 10 − 6 ) − ( 350 × 10 − 6 ) 2 cos 2 ( − 30 ° ) + ( − 430 × 10 − 6 ) 2 sin 2 ( − 30 ° ) ] = ( 425 × 10 − 6 ) + ( 75 × 10 − 6 × 0.5 ) − ( 215 × 10 − 6 × ( − 0.866 ) ) = 649 × 10 − 6 Hence, the normal strain component in x ′ direction is 649 × 10 − 6 _ . Find the normal strain component in y ′ direction as shown below. ε y ′ = ε x + ε y 2 − ε x − ε y 2 cos 2 θ − γ x y 2 sin 2 θ Substitute 500 × 10 − 6 for ε x , 350 × 10 − 6 for ε y , − 430 × 10 − 6 for γ x y , and − 30 ° for θ . ε y ′ = [ ( 500 × 10 − 6 ) + ( 350 × 10 − 6 ) 2 − ( 500 × 10 − 6 ) − ( 350 × 10 − 6 ) 2 cos 2 ( − 30 ° ) − ( − 430 × 10 − 6 ) 2 sin 2 ( − 30 ° ) ] = ( 425 × 10 − 6 ) − ( 75 × 10 − 6 × 0

Statics and Mechanics of Materials - Modified Access

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ISBN: 9780134392363

Author: HIBBELER

Publisher: PEARSON

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Chapter 14.8, Problem 94P

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Find the equivalent in-plane strains on an element.

Sketch the deformed element due to the equivalent in-plane strains within the x-y plane.

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Chapter 14.8, Problem 93P

Chapter 14.8, Problem 95P

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Find the equivalent in-plane strains on an element. Sketch the deformed element due to the equivalent in-plane strains within the x-y plane.

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Find the equivalent in-plane strains on an element. Sketch the deformed element due to the equivalent in-plane strains within the x-y plane.

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Chapter 14 Solutions

Find the equivalent in-plane strains on an element.

Sketch the deformed element due to the equivalent in-plane strains within the x-y plane.