Shear Stress in Beams (continued)  Calculation of   Q

In a Nut Shell:  Q is the first moment of the area between the location where the shear
stress  is being calculated and the location where the shear stress is zero about the
neutral (centroidal) axis.  See the figure below.

 Q  =  A’ ybar

where  A’  is the area between where the shear stress is being calculated to where the shear

stress is zero

ybar  is the distance from the neutral axis of the entire x-section to the centroidal

axis  of A’

The transverse shear stress is then:

 τ  =  VQ/It

where

τ  is the (transverse) shear stress acting at a distance, y, from the neutral axis
V is the value of the shear force at the section
Q is the first moment of the area between the location where the shear stress
is being calculated and the location where the shear stress is zero about
the neutral (centroidal) axis
I  is the moment of inertia of the entire cross-section about the neutral axis
t  is the width of the cross-section at the location where the shear stress is
being calculated

Click here to return to discussion of shear flow in thin-walled members.

Copyright © 2019 Richard C. Coddington
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