Shear Flow in Beams

In a Nut Shell:  The topic of shear flow frequently occurs when dealing with “built-up”
beams.  These are beams fabricated with several pieces joined by glue, nails, bolts, or
welds.  These fasteners must be sufficiently strong to withstand the lateral (transverse)
or longitudinal shear.  It is common to describe the load by the term, “shear flow” given
by the following relation:

 q  =  VQ/I

where         q is the shear flow   in (lb/in), (lb/ft), (N/mm), (N/m)
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
I  is the moment of inertia of the entire cross-section about the neutral axis

The shear flow may be used to calculate the shear stress (in the case of continuous joints)
by dividing by the width of the beam supporting the stress.

 τ  =  VQ/It

where            t  is the width of the cross-section at the location where the shear stress is
being calculated

If the joints are not continuous such as in nails, screws, and bolts, then it is more convenient

to use   q  as force per unit length along the beam.

In such a case  q (lb/in)  =  F(lb/nail) / s(in/nail)

Here     F  =  s q   and   F  is the force across one nail and   s  is the nail spacing. 