Question

A material point in equilibrium has 1 independent component of shear stress in the xz plane. a)True b)- False

Answer 1

Answer:

True

Explanation:

For point in xz plane the stress tensor is given by$\left[\begin{array}{ccc}Dx_{} &txz\\tzx&Dz\\\end{array}\right]$

where Dx is the direct stress along x ; Dz is direct stress along z ;  tzx and txz are the  shear stress components

We know that the stress tensor matrix is symmetrical which means that tzx = txz  ( obtained by moment equlibrium )

thus we require only 1 independent component of shear stress to define the whole stress tensor at a point in 2D plane