Combining Fb's for different sections of similar materials
Combining Fb's for different sections of similar materials
(OP)
Hello all,
Quick question for anyone who can help clarify something for me. What is your approach for combining the Fb & Fac of a composite section that utilizes the same material (same modulus of elasticity). I am familiar with the transformation of (2) materials to a single material, but that isn't the case in my situation.
Example:
Consider a hollow steel section with a calculated Fb. Now consider an steel insert, whether it be a hollow tube or solid piece, with a different Fb (same Modulus). Assuming the NA of each section is aligned, I can calculate and combine my section properties or determine them from a shape building program. What's the method for combining the Fb1 & Fb2 in relation to the section modulus to determine my allowable bending moment (M=Fb*S). I have not listed actual stress values because I don't want to complicate or deviate from the principle of this question.
Thanks!
Quick question for anyone who can help clarify something for me. What is your approach for combining the Fb & Fac of a composite section that utilizes the same material (same modulus of elasticity). I am familiar with the transformation of (2) materials to a single material, but that isn't the case in my situation.
Example:
Consider a hollow steel section with a calculated Fb. Now consider an steel insert, whether it be a hollow tube or solid piece, with a different Fb (same Modulus). Assuming the NA of each section is aligned, I can calculate and combine my section properties or determine them from a shape building program. What's the method for combining the Fb1 & Fb2 in relation to the section modulus to determine my allowable bending moment (M=Fb*S). I have not listed actual stress values because I don't want to complicate or deviate from the principle of this question.
Thanks!






RE: Combining Fb's for different sections of similar materials
This obviously assumes that your two materials are attached together sufficiently to act compositely.
Stiffness and Strength are not related...
RE: Combining Fb's for different sections of similar materials
If they are not composite, and assuming the load can get to both members, the load is assigned proportional to each members stiffness. Whichever hits Fb 1st is the controlling strength.
If composite, you would have to carry two different Fb's around and whichever max stress gets reached first is your limit.
I always use ultimate strength for this situation. Under ultimate conditions you assume everything goes plastic to Fy. Makes the calcs a lot easier.
RE: Combining Fb's for different sections of similar materials
Yes, I am connecting the two shapes to act together as a composite. I understand both of your approaches regarding the individual fb's in relation to the distance from the centriod (equation as noted above).
I had mentioned steel before, but my question is actually in regards to aluminum. My problem involves a welded aluminum hollow section. As you know, welding aluminum causes local annealing and thus a reduction in the allowable Fb for that section.I planned to reinforce this weakened section with an aluminum insert with more desirable alloy & temper. How do I show that the weaker outer sleeve will benefit from the insert, without limiting myself to the Fb of the welded section? Based on what you said, I will reach my critical welded Fb. Does this mean that I used my section properties of the composite and just limit the allowable Fb to the weaker of the two (similar to checking individual steel elements of a section and using the limiting Fb)? In my mind, the inert has to be taking a majority of the loading. Sorry if this question seems redundant, but I haven't been able to find a solid reference.
Thanks.
RE: Combining Fb's for different sections of similar materials
You must connect the various parts so the shear flows btwn. them are satisfied and they will act as one member. You would improve the situation if you put the stronger material at the extreme fibers which will see the max. stress first. Once the area of material around the weld reaches some reduced stress, due to the welding annealing, it won't take much more load, in effect it has gone plastic (or is approaching this) and will continue to strain, but not take much more load. Now you have a new cross section and new section props. Ix and Sx, maybe think Zx, the start of the plastic section modulus. But, before you really get to Zx as a section property you might consider this as some sort of a transformed section; but the transformation is not really just by a ratio of E1/E2. I have to think about this for a few minutes. Otherwise, the other elements of the built-up member will continue to strain, increase their stress level, take more load, until they start to turn plastic too. Isn't this the basis of plastic design or ultimate strength design? If you are putting your added material on the interior, maybe even as a back-up bar for your welds, there may not be much advantage in it being a stronger material. It won't start to reach yield until the material nearer the outer fiber has pretty much gone beyond yield. Then, maybe more by geometry (width or thickness, but not stronger) the insert will pick up the rest of the load before it goes plastic.
RE: Combining Fb's for different sections of similar materials
Thanks for your input. Sorry, I don't have the ability to scan in a sketch at this moment. Also, I didn't not want to start my problem off with the topic of welded aluminum. Obviously, the bare-bones of this question is the combination of (1) section with allowable stresses & (1) insert with allowable stress acting as a composite beam (Same materials). Sometimes if you want the most straight forward answer, you have to give the most cut and dry questions ;)
Moving forward, I agree with your statement about the outer section reaching it's plastic state and thus not contributing to any additional load support. I did consider a transformed section but wasn't sure how the ratio of E1/E2 would help, considering they are the same. Do you know how the plastic section and the elastic insert (assuming I have not yet reached a plastic state on my insert) work together?
Thanks, I appreciate the input!
RE: Combining Fb's for different sections of similar materials
So the outer aluminum will yield at a certain point before the insert yields. At this point you have an elastic stress distribution. Past this point you start to fall somewhere between a fully plastic section and an elastic section. I'm thinking something along the lines of strain compatibility maybe? I think I'm arriving at the same point as dhenger...
EIT
RE: Combining Fb's for different sections of similar materials
I don't believe you combine anything here. You look at each separately based on its share of the load and analyze each independently.