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:
\ =\ \tan(x)\ -\ x)
Newton-Raphson says
}{f'(x_n)})
So take the first derivative of the function:
\ =\ \sec^2(x)\ -\ 1)
Then start with 
\ -\ x_0}{\sec^2(x_0)\ -\ 1}\ =\ 4.5\ -\ \frac{\tan(4.5)\ -\ 4.5}{\sec^2(4.5)\ -\ 1)
Once you have fat-fingered your calculator (in Degrees mode) to get a nice approximation of 
, plug that number into:
\ -\ x_1}{\sec^2(x_1)\ -\ 1})
to calculate 
, that you then plug into:
\ -\ x_2}{\sec^2(x_2)\ -\ 1})
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
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