Mechanical Engineering - Strength of Materials - Discussion

It's √M if width has been kept constant and depth varies.

Because M/I = stress/y and y is d/2.

Now I= bd^3/12 solving u get d proportional to √M.

But in this question, depth is kept constant and the I will be same as above so b gets proportional to M.

A beam of uniform strength means the load is uniform (depending on the area the load is applied i.e, if the area is minimum the load applied is minimum and if the area is maximum the load applied is maximum)

The main aim of a beam of uniform strength is to reduce cost and make economical beams.

Width varies directly proportional to M.

Uvl width =wx/L.
Udl width=wL.
Point load/concentrated load=w.

M= Ru * bd2.

Therefore,
M is directly proportional to Breadth.

Why not √M?

Explain the answer.

Bending moment M = (B*D^3)/12.

SO depth constant so M is directly proportional to Breadth(B).

M/I = sigma/Y.

I = (bd^3)/12.

Y = d/2.
Where,
b = width.
d = depth.

So b proportional to M.