# If the principal stresses in a plane stress problem, are σ1 = 100 MPa, σ2 = 40 MPa, the magnitude of the maximum shear stress (in MPa) will be

If the principal stresses in a plane stress problem, are σ1 = 100 MPa, σ2 = 40 MPa, the magnitude of the maximum shear stress (in MPa) will be

#### SOLUTION

In the case of 3-D analysis, maximum shear stress can be calculated as:

maximum of $\left[ {\frac{{{\sigma _1} – {\sigma _2}}}{2},\frac{{{\sigma _2} – {\sigma _3}}}{2},\frac{{{\sigma _1} – {\sigma _3}}}{2}} \right]$

And In the case of plane stress analysismaximum shear stress can be calculated by,

${\tau _{{\bf{max}}}} = \frac{{{\sigma _1} – {\sigma _2}}}{2}$

where

σ1 and σ2 are principal stresses in a plane.

Calculation:

Given:

σ1 = 100 MPa

σ2 = 40 MPa

Now, In-plane stress analysis, we have

$\begin{array}{l} {\tau _{{\bf{max}}}} = \frac{{{\sigma _1} – {\sigma _2}}}{2}\\ \\ {\tau _{{\bf{max}}}} = \frac{{100 – 40}}{2} \end{array}$

= 30 MPa

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