Question

A circle of diameter 100 mm is inscribed on a thin plate of copper as shown in Fig. 3.33. The stresses on plate are σxx = −60 MPa, σyy = +100 MPa and τxy = 60 MPa which are now applied on the thin plate. If E = 100 GPa and n = 0.35 for copper, determine the dimensions of major and minor axes of the ellipse, in which the circle is transformed.

Answer 1

Let us first determine principal stresses and principal angles.

Major axis = 100 + 1.48 × 10−3 × 100 = 100.148 mm

Major axis = 100 − 1.11 × 10−3 × 100 = 100 − 0.115 = 99.885 mm