Question

A rectangular region in a solid is in a state of plane strain. The (x, y) coordinates of the corners of the under-deformed rectangle are given by P(0,0), Q(4,0), S(0,3). The rectangle is subjected to uniform strains.

a) The rectangle will deform into a parallelogram.
b) The rectangle will deform into a square.
c) The rectangle will deform into a rhombus.
d) The rectangle will remain a rectangle.

Answer 1

The rectangle will deform into a parallelogram due to the uniform strains.

a)The rectangle will deform into a parallelogram.

Step-by-step explanation:

The rectangle will deform into a parallelogram.

In plane strain, the ratio of the deformed length of a line segment to its original length is equal in all directions. Since the rectangle is subjected to uniform strains, the length of each side will change proportionally, resulting in a parallelogram.

For example, the original length of segment PQ is 4 units, and the original length of segment PS is 3 units. If the uniform strain is 20%, then the deformed length of segment PQ will be: 4 units + 20% = 4.8 units. The deformed length of segment PS will be: 3 units + 20% = 3.6 units. Therefore, the rectangle will deform into a parallelogram.