Question

Consider the following statements :
1. In the infinitesimal strain theory, dilatation is taken as an invariant.
2. Dilatation is not proportional to the algebraic sum of all normal stresses.
3. The shearing modulus is always less than the elastic modulus.
Which of the above statements is/are correct?

• A. $1$ Only
• B. $1$ and $2$ Only
• C. $2$ Only
• D. $1,2$ and $3$

Answer 1

The correct option is A $1$ Only

Dilatation (Volumetric change)
${ϵ}_V=\frac{{\sigma }_x+{\sigma }_y+{\sigma }_z}{E}(1-2\mu )$
Hence directly proportional to sum of all normal stress.
Shearing modulus
$G<E$ if $\mu >-0.5$
$G>E$ if $\mu <-0.5$