SHEAR FLOW IN BUILT-UP MEMBERS

Occasionally in engineering practice, members are “built up” from several
composite parts in order to achieve a greater resistance to loads. An
example is shown in Fig. 7–13. If the loads cause the members to bend,
fasteners such as nails, bolts, welding material, or glue will be needed to
keep the component parts from sliding relative to one another, Fig. 7–2.
In order to design these fasteners or determine their spacing, it is necessary
to know the shear force that they must resist. This loading, when measured
as a force per unit length of beam, is referred to as shear flow, q.*
The magnitude of the shear flow is obtained using a procedure similar
to that for finding the shear stress in a beam. To illustrate, consider
finding the shear flow along the juncture where the segment in Fig. 7–14a
is connected to the flange of the beam. Three horizontal forces must act
on this segment, Fig. 7–14b. Two of these forces, F and F + dF, are the
result of the normal stresses caused by the moments M and M + dM,
respectively. The third force, which for equilibrium equals dF, acts at the
juncture. Realizing that dF is the result of dM, then, like Eq. 7–1, we have