A timber beam, with rectangular cross section (h × b) will be reinforced with steel plates of thickness t securely conne

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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) 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?
b) 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.
Please give exact solutions for this problem. If you reuse
solutions from a different question or give an incorrect/incomplete
solution I will give a thumbs down and report.