Draw the Mohr,s cilcle for the stress element shown in figure. Determine the principal stress and maximum shear stress and also draw respective stress elements

 Q# Draw the Mohr,s cilcle for the stress element shown in figure. Determine the principal stress and maximum shear stress and also draw respective stress elements.                                             

 

solution

 

Here

σx = -80Mpa

σy = 50 Mpa

τxy = -25Mpa

 

Principle stress

In mohr's circle  OD = σ1

                             OC= σ2

 

`From measurent           σ1 =        55Mpa

                                      σ2 = -85Mpa

To verify it

σ1, σ2 =  σx + σy /2 ± √(σx - σy / 2)² + τxy²

 

            =  -80+50/2   ± √(-80-50/2)² +  25²

σ1= 54̥◦641941 Mpa

σ2= 84◦641941 Mpa

 

Max shear stress

 In mohr's circle τmax = O'G

from measurement;         τmax= 70Mpa 

From equation

τmax =  √(σx–σy/2)² + τxy²

√(-80-50 / 2)² + 25²

τmax = 69◦641941Mpa

 

σavg = σx + σy/2

           = -80+50/2       = -15 Mpa

 

Principal stress element

Maximum shear  stress element