# Load, Deflection, rotation, Designing basic beam?

• wildleaf
In summary, the conversation discusses the problem of designing a basic beam and the relevant equations and concepts that need to be considered. The question is asking for a design approach, and it is suggested to use a material, such as steel, and analyze the deflection and rotational displacement characteristics. The conversation also mentions the torsion equation and the need to approach the problem as a designer rather than just an analyst.
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.

#### Attachments

• Problem .jpg
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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.

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?

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.

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.

## 1. What is load and how does it affect a beam?

Load is a force that is applied to a beam. It can come from various sources such as gravity, wind, or a structure or object resting on the beam. Load can cause deflection, rotation, and stress in the beam, which can affect its overall stability and strength.

## 2. What is deflection and how is it calculated?

Deflection is the degree to which a beam bends or sags under a load. It is typically measured in inches or millimeters. The amount of deflection in a beam can be calculated using the beam's material properties, dimensions, and the applied load. There are various mathematical equations and software programs that can be used to calculate deflection.

## 3. How does rotation affect the design of a basic beam?

Rotation is the amount of twisting or turning that a beam experiences under a load. It can affect the stability and strength of a beam, so it must be carefully considered in the design process. The amount of rotation can be calculated using the same methods as deflection and can help determine the appropriate dimensions and materials needed for a beam.

## 4. What factors should be considered when designing a basic beam?

Designing a basic beam involves considering various factors such as the expected load, the material properties of the beam, the dimensions and shape of the beam, and the desired level of deflection and rotation. Other factors such as environmental conditions, safety requirements, and cost may also play a role in the design process.

## 5. How can I ensure the safety and stability of a basic beam design?

To ensure the safety and stability of a basic beam design, it is important to follow engineering principles and standards, accurately calculate the loads and stresses on the beam, and use appropriate materials and dimensions. It is also important to regularly inspect and maintain the beam to ensure it is functioning properly and can withstand any potential changes in load or environmental conditions.

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