Shear Flow in Thin-walled Members



Key Concepts:  Transverse loads (shear forces) produce shear stresses in thin-walled

members such as box sections and annular sections.   The force per unit length along

the member is termed the shear flow, q.  The same relations to calculate shear stress in

beams applies to the calculation of shear flow.


In a Nut Shell: 
Accurate display of the distribution shear stress is key in the analysis of
shear flow and shear stress in thin-walled closed sections.  Recall that the first moment of area,

Q, used in the calculation of shear flow or shear stress is calculated from the point where the shear stress is zero to the point where it is desired.  The equation for shear flow, q, is:


      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
                      the neutral (centroidal) axis;        Click here for discussion of Q.
                   I  is the moment of inertia of the entire cross-section about the neutral axis

The shear stress is simply the shear flow divided by the wall thickness, t.


      τ  =  VQ/It



The following figure below displays the distribution of shear stress for a thin-walled, closed
box section on the left and a thin-walled, closed round section on the right.  Note that the shear
stress is symmetrical about a vertical axis,  z, starts out at zero on the top, increases to a

maximum at the neutral axis (y), and returns (decreasing) to zero on the bottom for both

sections.  Here  V  denotes the shear force at the section resulting from external loads.


Click here for an example.


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