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.

 

[DeeNos]

Great job on solving the cantilever beam problem! It seems like you have found a solution for the deflection and slope equations, and have also correctly identified the bounding conditions. Regarding your question about which modulus of elasticity to use, it depends on the material you are using for the beam. The modulus of elasticity, or Young's modulus, is a material property that relates stress and strain and is different for different materials. For example, the modulus of elasticity for steel and aluminum are different. So, you will need to choose the appropriate modulus of elasticity for the material you are using in your problem. You can find the modulus of elasticity for different materials in material property tables or online. Good luck with your further analysis!