Strain and stress tensors Principal stresses and strains A

A strain gauge rosette is glued to the surface of the component at a point that is suspected to have high stresses. Two of the gauges are along the xcy direction, and the third one had to be placed at 70 from the x-axis due to space constraints (see figure). 70° a. The component is made out of steel, with E-200 GPa and v-0.28. In this particular application gauge \"a\" measures a normal strain of 1.17x10, gauge \"b\" reads 7.97x10 and gauge \"c\" 5.05x10 a) Find the strain and stress tensors in the xyz coordinate system. 10 points. b) Find the corresponding principal stresses and strains. 10 points. c) You are told that the component will fail if the maximum shear stress reaches more than 180 MPa. The component is supposed to be designed with a safety factor of 2. How much is the safety factor? Is the component close to or far from failure? 5 points.

Solution

Strain 102

Streess460n/mm2

. .

Principles stress 420n/mm2

Safety factor 3