## Tapered cantilever beam with varying depth structural mechanics question help pleas??

[b]1.
A tapered cantilevered beam of length 1000mm is fixed at the left end and carries both an
upward load 400N and a positive moment (M) at the free right end. The out of plane
thickness of the beam is 10.5mm, and its depth varies from 50mm at the left end to 40mm at the
right end. The yield strength of the beam is 300Gpa. Assume elastic-perfectly plastic
material behaviour.

2.a) For constant F = 400 N, as M is increased from 0, what value of M will cause first
yielding anywhere on the beam, and where will yielding first occur?
b) For all values except 50 and 40 fixed and the value of M determined in part (a),
what values of 50 and 40 should be used to minimize the mass of the beam?
c) For the parameters and value of M determined in part (a) but F increased to 440 N,
what is the maximum depth of yielding anywhere on the beam?
d) After loading as described in part (c) followed by removal of all loads, where
would tensile residual stresses remain?
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