Cantilever BEAM little problem. I have solved almost everything.

[wildleaf]

Cantilever BEAM ! little problem. I have solved almost everything.

Homework Statement

The link below has the problem:
http://i52.tinypic.com/2r3bcdc.jpg

Homework Equations

M = E*I(d^2*w/dx^2)
slope = E*I (dw/dy) = integral of E*I(d^2*w/dx) + c1
deflection = E*I * (w) = double integral of E*I(d^2*w/dx) + c1x + c2

Bounding Condition: when x = 0 --> w = 0 and slope = 0
when x = L --> V = 0 and M = 0
Yb = ΣAY / ΣA
I = Σ(I* + Ad^2)i

The Attempt at a Solution

E*I(d^2*w/dx^2) = (-px^2/2) + (pLx) - (pL^2/2)
E*I (dw/dy) = (-px^3/6) +(pLx^2/2) - (pL^3/6) + c1 (c1 = 0 using when x = 0, slope=0)
w = (- p/(24*E*I)) * [x^4 - 4*L*x^3 + 6*L^2*x^2] + c2 (c2 = 0 using when x=0, w = 0)

I then solved for the I knowing that Yb = 9. I had to transform everything to steel, using n = 30 / 10 = 3. The new dimensions for steel become 4" by 18" (which is the same) and for Al = (4+4)*3 = 24" by 18". Then i calculated the I, and got I = 13608 in^4.

THE PROBLEM I HAVE IS THAT I DONT KNOW WHICH MODULUS OF ELASTIC TO USE FOR

w = (- p/(24*E*I)) * [x^4 - 4*L*x^3 + 6*L^2*x^2]

we know that p = 500, L = x = 20, I = 13609, E = ?

 

[nvn]

wildleaf: You can use E(steel). However, your n value currently looks wrong. Try again.

 

[wildleaf]

Ohhh... n = 1/3 ?? I always mess that up. If n = 1/3, then I = 3240.

Why do you use E(steel) and not E(Al) ??

 

[nvn]

wildleaf: You use E(steel) because you said you transformed everything to steel.

Your n value now looks correct.