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Do these mean shear and stress in the respective directions? 1

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drennon236

Civil/Environmental
Mar 27, 2020
102
The first three mean stress in the first, second and third direction, for example in the x, y and z direction:

1_puuy5u.png


What would the last three numbers mean -(23,32) , (13,31) , (12,21)? I understand that they represent shear, but how does it work with directions? Are there any good illustrations of this?
 
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If X = 1, Y = 2, and Z = 3 (in your typical coordinate triad), then:
σ11 is the (normal) stress on the X face in the X-direction
σ22 is the (normal) stress on the Y face in the Y-direction
σ33 is the (normal) stress on the Z face in the Z-direction
σ12 is the (shear) stress on the X face in the Y-direction, while σ21 is the (shear) stress on the Y face in the X-direction
σ23 is the (shear) stress on the Y face in the Z-direction, while σ32 is the (shear) stress on the Z face in the Y-direction
σ13 is the (shear) stress on the X face in the Z-direction, while σ31 is the (shear) stress on the Z face in the X-direction
 
The stress tensor is a 3 X 3 matrix, with the normal stresses on the diagonal. The tensor is symmetric, so σ12 = σ21, and so on.
 
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