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An in-depth explanation of shear strain, its definition, and its relationship with shear stress. It covers the concept of couples, the generation of moments, and the calculation of shear strain using the angle of deformation. The document also includes problem-solving examples and homework questions.
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We can start by looking at an element of material undergoing a shear stress (the red arrows)
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directed parallel to it that it equal and opposite to the force that is acting parallel to the top face. This assumes that the area of the top and bottom face are equal.
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magnitude but opposite in direction generate a couple on the element. Since the element is in equilibrium, something must offset the moment produced by this couple.
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when an element in under shear.
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faces of the element cause a deformation of the element. If the lower left corner is considered stationary, we can look at how much the upper left corner of the element moves.
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The sine of this angle is δ
L
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x is very small with respect to L, which is generally the case, then the value of the angle in radians is approximately equal to the sign of the angle. δ
L
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because we are looking at the shear strain in the xy plane I have labeled it with a y subscript because it is the angle made with the y-axis. γ
= δ
L
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difference between the original angle between the side along the y-axis and the side along the x-axis and the angle after loading θ’ γ
= δ
L
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above or below the x-axis, it must also be included to solve for θ’ θ ' = π 2 − γ