Load, Deflection, rotation, Designing basic beam?

[wildleaf]

Homework Statement

The problem is in attached.
Desgining basic beam

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

ΣM*= 0
ΣFx = 0
ΣFy = 0

Yb = ΣAY / ΣA
I = Σ(I* + Ad^2)i
bending stress = MC / I

The Attempt at a Solution

I don't understand the question. If someone can clear it up for me that would be nice. If someone can tell me what the question asks for, and how I would attack this problem by telling me the first few steps.

 

[pongo38]

The question is asking you to do a design. That means: making some initial choices of material, cross-sectional shape and dimensions, possibly elevational shape, and end conditions; then, analyse the proposed structure for its deflection and rotational displacement characteristics; then revisit your initial assumptions and adjust as necessary to comply with the limits given. You will need at least an hour, possibly three, to do this properly. I notice that your section on 'relevant equations' doesn't include anything on torsion yet.

 

[wildleaf]

You would just take a material, say steel for example, and try and find the deflection function for it, see if the max deflection of the beam is 1" and max rotation is 1" ?

Which torque equation would help me?

 

[pongo38]

You have probably heard of the engineers bending equation f/y=M/I=E/R. Well. there is a similar equation for torsion t/r=T/J=GA/L where A is the angle of rotation. You can look it up in books, where the notation may be different, but the idea is the same. Your question suggests that you are approaching this from the point of view of an analyst, but what is needed is the hat of a designer - trying things to see if they work (using analysis to evaluate). With such a long span, I would expect self-weight deflection to be just as important as that due to the camera.