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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.
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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:
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.
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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