Solve for your reactions and draw shear an moment diagrams to get your max shear and moments in the beam. You can use those with the equations for shear and bending stress to solve for the beam thickness:
Now solve for the minimum thickness required for the max shear allowed:
τ = F / A
τ = 825 kPa = 825 kN/m2
A = b*h = (b)(.15m)
F = max allowable shear = 7.2 kN
So...
825 kN/m2 = (7.2kN) / [(b)(.15m)]
b = .058m = 58mm
Now solve for the minimum thickness required for the max bending allowed:
σ = Mc / Ix
σ = 12 MPa = 12000 kPa = 12000 kN/m
2
M = 3.6 kN*m
c = h/2 = .075m
Ix = (1/12)(b)(h3) = (1/12)(b)(.15m)3 = .000281 b
So...
12000 kN/m2 = (3.6 kN*m)(.075m) / (.000281)(b)
b = .08m = 80mm
So the minimum thickness required to satisfy both conditions would be 80mm.
Hope this helps...
PLEASE RATE!!!!!