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.

 

[DeeNos]

I can provide some clarification on the concepts mentioned in the content. Load, deflection, and rotation are all related to the behavior of a beam subjected to external forces. Load refers to the amount of force applied to the beam, while deflection is the amount of bending or displacement of the beam due to the applied load. Rotation refers to the change in angle or slope of the beam as it bends.

Designing a basic beam involves determining the appropriate size and shape of the beam to withstand the expected loads and minimize deflection and rotation. This typically involves using equations such as the ones listed in the content, which relate the applied load, beam properties (such as Young's modulus and moment of inertia), and the resulting deflection and rotation.

To approach this problem, you would first need to determine the type and magnitude of the load that will be applied to the beam. Then, you can use equations such as the bending stress equation and the equations for deflection and rotation to calculate the required properties of the beam. This may involve using the equations multiple times with different assumptions and iterations to arrive at a suitable design.

In summary, designing a basic beam requires a good understanding of the concepts of load, deflection, and rotation, as well as the ability to use equations to determine the appropriate beam properties for a given set of loading conditions.