Answer Happy

ONLY ANSWERS FOR C) ARE NEEDED!
A timber beam, with rectangular cross section (h × b) will be
reinforced with steel plates of thickness t securely connected on
the top, left and right sides, and thickness 2t on the bottom. This
will ensure composite action in bending. The section is then used
as a simply supported beam of length L (given by the span to depth
ratio L/h below). The beam is oriented such that the minor
principal axis is vertical.
It should be taken that ρsteel = 7850 kg/m3, ρtimber = 1150
kg/m3, Etimber = 10500 MPa and Esteel = 200000 MPa, and that both
materials exhibit linear elastic behaviour.
The design engineer needs to ensure the following:
 Timber bending stress in tension ≤ 7 MPa
 Timber bending stress in compression ≤ 7.5 MPa
 Steel bending stress (tension or compression) ≤ 175 MPa
 Ignore stresses due to shear
a) Consider self weight only. Draw the stress and strain
distributions at midspan.
b) Now ignore self weight. The beam is loaded by two vertical
point loads, each of magnitude P, that act at L/3 and 2L/3 along
the beam. What is the maximum value of P so that the stress
criteria above are satisfied? Draw the stress and strain
distributions (values required) for both the steel and the timber
on the critical cross-section for this value of P.
c) Use your answers to comment on the following (about 150 words
for each item)
(i) The significance of self-weight
(ii) The effectiveness/appropriateness of using 2t on the
bottom, rather than t
Please do not reuse solutions to other questions or give
incorrect/incomplete answers, or I will have to give a thumbs down
and report.