It is important that each of the simplified beam sections (sub-beams) are in
the
appendix
(or handbook). This beam has been split into three sub-beams: 1)
cantilever with a point load, 2) cantilever with a moment load, and 3) cantilever
with a distributed load. (The beam could be split into other sub-beam combinations.)
Notice that the beam loading has also been distributed to the sub-beams. The
equivalent loading for the uniform distributed load on the right sub-beam is
P = [(0.04 N/mm2)(12 mm)] (50
mm)
= (0.048 N/mm)(50 mm) = 24
N
M = F d
= [(0.04 N/mm2)(12
mm)(50 mm)] (25 mm)
= [24 N] (25 mm) = 600
N-mm
These loads are also the internal shear and moment at the joint between the
sub-beams.
Sub-beam 3) is modeled as a cantilever beam since its deflection will
be in additional to the deflection of the right beam section. The total deflection
will be
vtotal =
vP +
vM +
vw + θP L
+ θM L
The δ terms are straight forward and simply added together.
The right beam also rotates (θP + θM)
at its tip due to the point load,P, and moment load, M. These rotations will
cause added deflection for the left sub-beam.
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