What is the maximum shear stress in the stress element shown?
The stress state shows the normal stresses, σx and σy, to be positive (tension) but the shear stress arrows are in the negative direction. Thus, the stress state is
σx = 10.1 ksi
σy = 6.2 ksi
τxy = -3.7 ksi
Rotated Stress Element
The maximum shear stress is,
This could be either positive or negative due to the square root. Angle that the max shear stress acts at is,
2θτ-max = 27.79o (or -152.21 )
θp = 13.90o
τmax = 4.182 ksi @ 13.90o
It is interesting to note, the new normal stresses are,
σx' = σy' = (σx+ σy)/2 = 8.15 ksi
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