Question

Derive the error in pressure if 1D stress strain relation is considered compared to 2D stress strain relation.

with explanation please

Answer 1

Ans) We know,

P/A = (L/ L ) x E

where, P = applied load

A= cross section area

L/L = strain

E = Modulus of Elasticity

Also, we know generalized Hook's Law,

  L /L = _x/E - _y /E - _z /E

where, _x , _y and _z are stresses in x , y and z direction respectively

   = Poisson ratio

For 2D , _z =0,

Therefore Pressure in 2D is ,

(P/A)_2D = [(_x -  _y) / E ] x E

(P/A)_2D =  _x -  _y

For 1D , _y = _z = 0 ,

(P/A)_1D = (_x/ E) x E

(P/A)_1D = _x   

Hence error in pressure is,

error = (P/A)_2D - (P/A)_1D

= _x - y - _x

= - _y   

Hence absolute error =| _y|