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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’ y_bar

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

stress is zero

y_bar 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.

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