Question

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
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• A. 0
• B. 0.002
• C. 0.004
• D. -0.004

Hint:

In deformation problems, shear strain arises from relative displacement between points. In this case, the changes in diagonal lengths are symmetrical, leading to zero shear strain.

Answer 1

The Correct Option is A

In this problem, we are asked to calculate the engineering shear strain \( \gamma_{xy} \). Shear strain is typically given by the relative displacement of two points along a line divided by the distance between those points in the undeformed configuration. The engineering shear strain is typically calculated based on changes in the shape of the object. However, in this case, we are given information about the changes in diagonal lengths, but the deformation is symmetric and does not cause any relative displacement of the points along the diagonals, implying no shear deformation. The change in the diagonal lengths is symmetrical, with one diagonal decreasing and the other increasing by equal amounts.
The shear strain is zero since there is no relative displacement of points along the x and y directions, and the shape of the object does not deform in a way that would create a shear strain. Thus, the engineering shear strain \( \gamma_{xy} \) is zero.