# Which stress counts when looking at yield

To makes things simple, consider a simple beam fixed at one end an a load applied at the other. This load will produce shear stress, bending stress, and torsional stress. When looking at yield at the fixed end, do I take the biggest stress of the three or do I add their magnitudes to see if it exceeds the yield stress of the beam? Also what do I do if I have shear and bending in 2 directions?

## Answers and Replies

SteamKing
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To makes things simple, consider a simple beam fixed at one end an a load applied at the other. This load will produce shear stress, bending stress, and torsional stress. When looking at yield at the fixed end, do I take the biggest stress of the three or do I add their magnitudes to see if it exceeds the yield stress of the beam? Also what do I do if I have shear and bending in 2 directions?

If you have multiple stresses to sort out, the best thing to do is use Mohr's circle to combine them. Bending stresses usually act in the axial direction; shear stresses can occur in different planes. In general, you cannot simply add the magnitudes of stresses together unless they act in the same direction.

http://en.wikipedia.org/wiki/Mohr's_circle

I thought I could add them using vector addition. If I remember my Mohr's circle correctly, on the circle the maximum stress occurs when shear is 0 and max shear is when stress is 0. So after drawing the circle and finding the maximum stress and shear I look at them individually to see if either exceeds the yield stress, which I assume is different in normal and shearing conditions. Is my reasoning correct?

I had completely forgotten about that. That should solve my problem, thank you for helping.