Explanation Given information: The normal strain along the x and y axes are ε x = − 800 μ and ε y = + 450 μ . The shearing strain along x y is γ x y = + 200 μ . The value of angle θ is 25 ° (clockwise). Calculation: Consider the coordinates of the point X and Y are ( ε x , − 1 2 γ x y ) and ( ε y , 1 2 γ x y ) . Then, The points X and Y are X ( − 800 μ , − 100 μ ) and Y ( 450 μ , 100 μ ) . Consider the coordinates of the centre point C is ( ε x + ε y 2 , 0 ) and ( ε y , 1 2 γ x y ) . Then, The centre of the Mohr circle is C ( − 175 μ , 0 ) . Then, Consider C as the centre and XY as the diameter of the Mohr circle, draw the Mohr circle as shown in Figure 1. Refer to Figure 1. The point O is the origin with coordinate as O ( 0 , 0 ) . Calculate the value of α as follows: tan α = 100 625 α = tan − 1 ( 0.16 ) α = 9.09 ° Calculate the radius R of the Mohr circle using the relation: R = ( ε x − ε y 2 ) 2 + ( γ x y 2 ) 2 (1) Substitute − 800 μ for ε x , + 450 μ for ε y , and + 200 μ for γ x y in Equation (1). R = ( − 800 − 450 2 ) 2 + ( 200 2 ) 2 = 625 2 + 100 2 = 400 , 625 = 632.94 μ Calculate the average strain using the relation: ε ave = ( ε x + ε y 2 ) (2) Substitute − 800 μ for ε x and + 450 μ for ε y in Equation (2). ε ave = ( − 800 + 450 2 ) = − 350 2 = − 175 μ Calculate the value of the angle β using the relation: β = 2 θ − α (3) Substitute 9

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Chapter 7.9, Problem 132P

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Find the state of plane strain with the axes x′ and y′ rotated through an angle θ.

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Find the state of plane strain with the axes x ′ and y ′ rotated through an angle θ .

Solution Summary: The author calculates the state of plane strain associated with the axes xprime 'x' and 'y'' rotated through an angle.

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