Compound Sections 1

[LSPSCAT]

I am looking for information on analyzing compound sections that are not connected; simply stacked. Examples are stacked plates for load distribution or vertically stacked wide flange sections in bending. It is in the area of construction and these items are frequently used based on availability.

 

[hokie66]

If the sections are not connected, they are not compound sections. Just sections one above the other. The properties would be for one section, multiplied by the number of sections.

 

[corus]

I thought hokie66 was wrong but I ran a quick FE analysis with 2 cantilever beams in contact, but not connected, with a load applied to the end of the top beam, and indeed the beams act separately for frictionless surfaces, though both bend under the load. I presume that the reason for this is that the beams cannot transmit the shear loads as one slides over the other. If on the other hand friction is present then the beams are effectively connected. For 'rough' friction they will act as one, whereas for some intermediate value you'll get an answer inbetween the two. For your worst case I'd assume you have frictionless surfaces and apply half the load to one beam.

corus

 

[Lion06]

Of course they will act as individual member if there is no connection between the two.
You are better off having them side by side to save some headroom (in the case of W shapes anyway). You will get the same result as long as the load is evenly distributed to both (they deflect together).

 

[renko]

I'd have to agree with hokie66 that unless they are connected you cannot assume compound action.

If you are stacking wide flange sections, why not use a single deep section with a similar flange width?

 

[JLNJ]

The load is distributed by stiffness. You can add the moments of inertia together but you can't just add the section moduli.

 

[nutte]

This is a fundamental concept. Why would someone run a finite element analysis to confirm this? The only reason I can figure is that he didn't have an understanding of these fundamental concepts, in which case the FE software is in dangerous hands.

 

[csd72]

nutte,

it scares me too, but corus is a mech eng, so you cant expect too much from him

 

[DWHA]

If the sections are different, but stacked. One can determine the force in each member by solving for deflection. If the members are stacked, they will have the same deflection. So I set up an excel file and use the solver function to determine the load applied to each, in which the deflections come out to be the same.

 

[hokie66]

JLNJ,

There is no reason you cannot add the section moduli. For a given bending moment, the stress with 2 sections resisting will be half the stress with 1 section. And I agree, corus has no business using a FE program until he understands something of how beams work. The OP was a silly question, but I guess they all deserve an answer.

 

[apsix]

"There is no reason you cannot add the section moduli."
True, but only if the sections are identical.

 

[hokie66]

I know that. My post and the one by DWHA crossed in the mail. I just assumed the sections were identical, which I now agree is an assumption too far.

 

[LSPSCAT]

I am asking because unfortunately I have seen the calculations run a number of different ways from different engineers in the past few months. If I understand here basically generate the load to each beam from the stiffness of the two beams. If both sections are the same each would take 1/2 of the load. If sections have a different moment of inertia it would be based on this ratio. Still consider the neutral axis in bending about each invidual section. How would you consider shear?

 

[hokie66]

The shear is generated by the loading, so must be taken in the same ratio as the moments of inertia also.

 

[DRC1]

Each beam is essentially independent, so each beam will cary its own vertical shear. upper beam may spread the load for the lower beam, so it may be more unifomly loaded. Also, I would think the lower beam would carry slightly more load than the upper beam. The lower beam is fre to deflect, but would inhibit the deflection of the upper beam, as both can not deflect to the same shape, thus slightly more load would be carried by the lower beam. I think it is a minor difference and the only practical use is to win a beer bet at a stuructures conference.

 

[miecz]

So far the discussion has followed ASD design. I'm new to LRFD and a little foggy on the concepts, so please help me out with this. If, at the strength limit, two different size beams would have a combined strength Z_x1+Z_x2, then, at the limit, assuming LTB does not come into play, does each beam carry a load proportional to the Zs, instead of the Is?

 

[Lion06]

Possibly (depending on the sections chosen), but just distribute according to Ix. You can't go wrong there.
This has nothing to do with ASD vs. LRFD, this is a fundamental engineering mechanics concept. The method by which we design for it has nothing to do with it.

 

[miecz]

But, at the limit, things no longer behave elastically. Why distribute the load according to the elastic stiffness?

 

[Grizzman]

DWHA's deflection distribution will dictate how the beams distribute the load. The same way we determine a internal reaction of a 3 bearing point indeterminite beam. That's why you base it on the sections stiffness and not platic or section modulus.

 

[Lion06]

This is similar to distributing loads to shearwalls under seismic loads. We don't expect a structure to behave elastically during a design earthquake, but we distribute the loading based on elastic stiffness (assuming a rigid deaphragm, or course).
If you have 2 simply supported beams on top of each other (not connected) and apply a point load at midspan they will deflect together. I suppose you could do an analysis to see which one will cause firt yield (then first plastic hinge) and do a sort of plastic analysis based on the redundancy, but that really seems unwarrented.
Either way, I would not recommend just distributing based on Z.