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Whether plate stresses SQX,SQY are One Way stresses or Two Stresses?

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I am no STAAD expert or user. In fact, I'm much more knowledgeable on RISA and SAP2000. So, if STAAD uses some different terminology (I don't think they do) then my response may not be accurate.

SQX and SQY are out of plane shear stresses on the plane perpendicular to the local X or local Y axis. They are not inherently two way or one way bending. It could be either. You have to look at the behavior of the slab as a whole to understand for certain. However, I would say that in cases where one of them is high and the other is low, then that is probably one way bending. In cases where they are both high, then it is probably two way bending.

Personally, I tend to do my punching shear calculations by hand based on the axial force and moments in the column supporting the slab. That tends to be how design examples are done. That being said, the SQX and SQY values should bear some correlation to punching stresses that are in your calculation.
 
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