Question

Consider the following statements:
Mohr's strain circle can be drawn
1. for plane stress conditions
2. if strains in three directions are known
3. if strains on two mutually perpendicular planes are known
Which of these statements are correct?

• A. 1, 2 and 3
• B. 2 and 3 only
• C. 1 and 2 only
• D. 1 and 3 only

Answer 1

The correct option is A 1, 2 and 3

Mohr's strain circle can be drawn if strains in three directions are know. To define a general two dimensional state of strain, values of ${\epsilon }_x,{\epsilon }_{y}and{\varphi }_{xy}$ are required. Thus the measurements from three strain gauges must be obtained. These three gages must be arranged at different orientations on the surface to from a strain rosette. A group of three gauges arranged in a particular fashion is called a strain rosette.

${\in }_{\theta 1}={\cos }^2{\theta }_1+{\in }_y{\sin }^2{\theta }_1+{\varphi }_{xy}\sin {\theta }_1\cos {\theta }_1$

${\in }_{\theta 2}={\in }_x{\cos }^2{\theta }_2+{\in }_y{\sin }^2{\theta }_2+{\varphi }_{xy}\sin {\theta }_2\cos {\theta }_2$

${\in }_{\theta 3}={\in }_x{\cos }^2{\theta }_3+{\in }_y{\sin }^2{\theta }_3+{\varphi }_{xy}\sin {\theta }_3\cos {\theta }_3$

Knowing the orientation of the three gages forming a rosette, together with the in-plane normal strains they record, the state of strain at the region of the surface concerned can be found.