Max bending in tapering rod

pongo38

Answer to post #16 is that you can test this proposal for yourself by letting x=0 and x=L to see if you get sensible answers (You don't). But it's nearly right.

pongo38

answer to post #17 is to use differential calculus. If you had numbers instead of symbols, you could plot the graph. The question doesn't ask for the maximum stress- just its location, which would be independent of W and pi.

MMCS

Bearing this is mind, i am still unsure of how to get to an equation that defines the position. Is it a form of the equation i gave in post 15 (ecluding the W and pi values) or is it a different equation. Is it possible to give me further assitance in the last part of this quesiton as i have spent alot of time on this

Thanks for your help

pongo38

Can you interpret stress=My/I where M, y and I are all functions of x? Then d(stress)/dx=0 will give you an equation in x, at least one of whose solutions will be what you are looking for.

MMCS

no i cant interperet it. thats what iv been sayin. i cant write what i know as an equation of x without having other terms which arnt included in the equation i need to prove. i dont understand how to do it. id appreciate it if you could just show me.

pongo38

Let f be the stress at section X
Let e be the diameter at section X
Can you confirm that you agree with M=Wx, and e=d+x*(D-d)/L
Also confirm that you have I=pi*e^4/64 where e is the function of x above.
Putting all that together: f=My/I = (a function of x that you can put together)
Put df/dx=0 and solve for x=