SOLUTION: Hi, Stuck here with this particular problem, please can somebody help The equation governing the buckling load P of a strut with one end fixed and the other end simply supporte

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Question 383758: Hi, Stuck here with this particular problem, please can somebody help
The equation governing the buckling load P of a strut with one end fixed and the other end simply supported is given by tan (Mu)L = (Mu)L where (Mu) = Sqrt (P/EI), L the length of the strut and EI the flexural rigidity of the strut.
By writing x = (Mu)L, solve the equation tan x = x using three iterations of the Newton-Raphson method, taking
an initial approximation x0 = 4.5
Thanks very Much
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

First write your equation as a function:

Newton-Raphson says

So take the first derivative of the function:

Then start with

Once you have fat-fingered your calculator (in Degrees mode) to get a nice approximation of , plug that number into:

to calculate , that you then plug into:

Which is your third iteration and the approximation you need. If you don't come up with something very close to , then re-do your calculations.

John

My calculator said it, I believe it, that settles it