15. Draw a 2 x 2-inch square OABC on the engineering paper. The coordinates of O are (0, 0) and of B are (2, 2). Using the displacement field in Problem 13, determine the u and v displacements of the corners of the square. Let the deformed square be denoted as O'A'B'C.

(a) Determine the change in lengths of OA and OC. Relate the changes to the strain components.

(b) Determine the change in ZAOC. Relate the change to the shear strain.

(c) Determine the change in length in the diagonal OB. How is it related to the strain(s)?

(d) Show that the relative change in the area of the square (change in area/original area) is given by AA/A = + sw, = E\ + sj.

Hint: You can use the old-fashioned method of using set-squares (triangles) and protractor or use spreadsheet to do the calculations. Place the origin somewhere in the bottom middle of the paper so that you have enough room to the left of the origin.