Combining Fb's for different sections of similar materials

[alt227]

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!

 

[jdgengineer]

I would think that you wouldn't combine the Fb. I think you would want to solve for the moment of inertia of your composite section. Then assuming elastic behavior, I would determine the stresses to each material based on f = M*c/I. I'd then check each material independently to make sure that the bending stress does not exceed the allowable stresses.

This obviously assumes that your two materials are attached together sufficiently to act compositely.

Stiffness and Strength are not related...

 

[dcarr82775]

Are you connecting the two shapes so that they act compositely?

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.

 

[alt227]

Thanks for the response,

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.

 

[dhengr]

Obviously, a sketch would help us visualize the section and loads and moments you are dealing with, so do one for us. Also, why start talking about steel or wood, whatever, if what you are dealing with is aluminum? Aluminum is almost as easy to type and say as the word steel is, but it is much less friendly to weld and design around because of this loss of strength; and this reduction in strength is going to be a big part of your problem, so why leave that out at first?

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.

 

[alt227]

dhengr,
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!

 

[RFreund]

I don't think that the insert 'takes the majority' of loading. It is not stiffer than than the outer aluminum (same E values). It will only be stressed based on fb=Mc/I.

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

 

[Lion06]

Why are we talking about composite action? If the neutral axis of the two members are aligned vertically and the load is vertical, then each member is taking load in proportion to its relative stiffness. There is no connecting for composite action. The connection is merely to ensure deflection compatibility to make the load-sharing based on relative stiffness valid.

I don't believe you combine anything here. You look at each separately based on its share of the load and analyze each independently.