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Strength of Materials: Principle Stresses, & Maximum Shear Stress

The principle stresses are the maximum and minimum normal stress that are caused by the applied stresses. On a graph they will represent the maximum points on the x-axis. This will be discussed further when talking about Mohr's circle. To calculate the principle stresses for a 2d problem equation 1 would be used.

Principle Stress Equation for 2d Mohr's Cirlce (1)

σ = Normal Stress

τ = Shear Stress

The part before the plus and minus sign of equation 1 is the average normal stress, equation 2.

Average Stress Equation for 2d Mohr's Cirlce (2)

In addition to calculating the principle stresses, the maximum shear stress can be calculated. To calculate the maximum shear stress you would used the part after the plus and minus sign of equation 1, refer to equation 3.

Maximum Shear Stress Equation for 2d Mohr's Cirlce (3)

To calculate the graphical angle of the shear stress in respect to the normal stress equation 4 would be used.

Graphical angle relationship between shear stress and principle stress 2d Mohr's Cirlce (4)

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