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Assuming the thickness of the bracket as t
Area of cross section A= b*t = 0.04*t
Direct stress Sd= P/A
Bending stress Sb=(M*c)/I
where c=w+ t/2 i.e., 0.05+ t/2
M=P*t/2
I=(b*(t^3))/12
Maximum tensile stress:
S=Sb+Sd
S=(P/A)+((M*c)/I)
On simplifying above equation,
we get
(S*b)t^2 - (4P)t - 6Pw = 0
30=(500/t)+(155*(100+t) / t^2
Standardizing the dimension, we get t=111.5 mm
The corresponding stress induced is 30.00 MN/m^2
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