Question

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

Answer 1

True

Step-by-step 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