A Beam of rectangular cross section 200mm deep and 100mm wide

[forexpipz]

Homework Statement

Please visit my flickr link for a scanned image of the problem statement.

http://www.flickr.com/photos/93763273@N05/8815418518/lightbox/

Homework Equations

M/I = σ/y = E/R This is the flexure or bending formula.

The Attempt at a Solution

a) = 8.333 kN
b) = 12.5 kN
c) = I can do this one

d)

This one is giving me some difficulty. If I increase the 200mm dimension by 20% the stress value goes down 8680 Newtons. I have played around with the other dimension but this could be a laborious process. Could someone please explain to me how I would go about this. Is there some sort of optimal ratio here. Can I use calculus and if so just how do i go about it? Much appreciated.

 

[haruspex]

Can I use calculus and if so just how do i go about it?

Yes, you'll need calculus. It seems intuitive to use as much cross-sectional area as allowed, but we need not assume that. I would approach it as supposing the area is fixed as A and optimising the ratio for that area. Having found that relationship, you can go about optimising the area.