Stress analysis -- derive equations: bending & yielding

[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.

 

[Nidum]

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 .

Have you any more information ?

 

[Mapes]

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.

 

[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!