# Stress analysis -- derive equations: bending & yielding

• Strife_Cloud
In summary, the problem is attempting to derive an equation for a panel that is stiffer than a beam because it cannot contract laterally. The students are following a book on mechanical behavior of materials and are having difficulty with a particular problem. The student has posted an image of the problem online. The student has attempted to go through all of the variables given and is waiting for the equation to click.
Strife_Cloud
Problem attached.

I would appreciate anyone's help. I am an alloy chemist working on an MS degree in materials engineering and have come to the mechanical engineering part of the program and am feeling a bit behind. Deriving an equation for this case is proving to be difficult for me although I believe we are still at the elementary mechanical review period.

The basic situation is that of plane stress with an "important focus" on stiffness. The class is following the mechanical behavior of materials book by Dieter. I have a lot of time putting the pieces together but an now a bit stumped.

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All you appear to have in this problem is a simple beam in bending but I can't make much sense of the actual questions at all .

Strife_Cloud
Nidum said:
All you appear to have in this problem is a simple beam in bending

With the subtlety that this panel will be stiffer than a beam because it cannot contract laterally (because of its large width). I wrote a summary of generalized[/PLAIN] Hooke's Law for solving problems like this. It looks like the questions are essentially aiming at a design optimization problem in which the mass of the panel might be minimized while maintaining a given stiffness (in (b)) and strength (in (c))? But "bending momentum" is not a term I'm familiar with; I suppose it's meant to mean the bending moment.

Strife_Cloud, I'd start with a free body diagram of the panel. Have you covered shear and moment diagrams? If so, draw these too. Then find the stress at the bottom of the panel at the middle.

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Strife_Cloud
Yes, we are going to be using this example to compare different materials and focus on what material we should consider. Then factoring in cost of materials and what processes are involved in production and how that leads to the properties of the final product.

The image is what he posted online to be completed before class. Adding that, we would use the equations we derive evaluating materials for the depicted stress state.

Unfortunately, that is all the information given on the sheet so I have been attempting to go through all of the variables we have been given hoping the combination leading to the equation will click but, it hasn't yet. I look forward to reading the information on the link provided and I will let you know how it helps! Thank you both for responding and for your help!

## 1. What is stress analysis?

Stress analysis is a branch of engineering that involves studying the effects of forces and loads on materials and structures. It is used to determine the strength and safety of a structure under different conditions.

## 2. How do you derive equations for bending in stress analysis?

To derive equations for bending in stress analysis, we use the principles of statics and mechanics of materials. This involves considering the external forces acting on a structure, the material properties, and the geometry of the structure. By applying these principles, we can derive equations that relate the stress and strain in a material to the applied forces and geometry.

## 3. What is the significance of yielding in stress analysis?

Yielding is the point at which a material begins to deform permanently under stress. In stress analysis, this is an important consideration as it determines the maximum load a structure can withstand before it fails. By understanding the yield point of a material, engineers can design structures that can safely support the expected loads.

## 4. What are the different types of bending in stress analysis?

There are two main types of bending in stress analysis: pure bending and asymmetric bending. Pure bending occurs when the applied forces are symmetric about the plane of bending, while asymmetric bending occurs when the forces are not symmetric. These types of bending can have different effects on the stress and strain in a structure.

## 5. How can stress analysis help in the design of structures?

Stress analysis is an essential tool in the design of structures as it allows engineers to predict how a structure will behave under different loads and conditions. By understanding the stress and strain in a structure, engineers can ensure that it is strong enough to support the expected loads and will not fail under normal operating conditions.

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