Parallel beams in bending

[jimandrews]

I have what is surely a simple question for you structural guys, but I am but a mechanical engineer! If I have 2 equal beams in parallel that are interconnected by "rigid" struts periodically spaced down the length of each beam, and I apply a distributed load to one of the beams, how do I calculate the effective resistance to bending for the assembly? Assume that the reaction to ground occurs at the ends of the non-loaded beam.

Perhaps more to the point -- do I use the parallel axis theorem to calculate an equivalent (larger) moment of inertia? It seems that this could produce a VERY stiff result, and one that I doubt. Is the parallel axis theorem applicable to beam assemblies, or is it merely suited to calculating the moment of inertia for a monolithic single beam of arbitrary shape?

Thanks for any help.

jim

 

[paddingtongreen]

Does this assembly look like a ladder? If so, when looked at from the side or when looked at from the top?

It sounds like a Vierendeel truss.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[rb1957]

ok, IMHO, forget "parallel axis theorem" ...

the answer is draw a free body diagram ... if all your load is applied to one beam, then that's where the reaction is going to be; i'd start by considering one beam in isolation. now for those pesky infinitely stiff connectors ... they're going to try to make the 2nd beam conform to the deflection of the 1st, presumably reducing the deflection so there'll be a couple (vertical load and reaction) at the 2 ends of these connectors, and there'll be end moments reacting the couple (and these end moments are torques on the beams) so i expect the 2nd beam to react some of the applied load and end moments (torques) reacting this off-set load (ie whatever load the 2nd beam is reacting)

clear as mud ?

 

[jimandrews]

Yes, that's a good description -- it looks like a ladder. It's a planar problem, so assume the load is parallel to the ladder "bars", and one "siderail" is constrained to ground at each end. I'm trying to assess the manner in which the two "sidebars" combine so I can figure out how much each bends. (If they have the same cross section, I presume they bend the same amount.)

Thanks for your help!

 

[rb1957]

having posted, i should have said that i imagined parallel to mean side-by-side.

if parallel means above one another, i still don't think parallel axis applies, as there isn't a continuous shear connection (do you see the upper beam reacting tension and the lower one reacting compression (bending as a composite beam ?); but the 2nd beam is clearly going to be more effective in this position than in my original side-by-side assumption. what you have in this case is a highly redundant beam; i think a simple result would be to double the I of one beam (each beam reacts 1/2 the applied load) this would be pretty colse to being right if there are connectors between the two beams at each load application on the upper beam (the connectors would share the load between the two beams) ... more or less connectors would change slightly the load distribution, by changing the displacments.

 

[ToadJones]

If it is a Vierendeel Truss as Paddington has surmised, then I don't think simple beam theory will suffice in an analysis. You have to analyze the frame as a Vierendeel truss.

 

[paddingtongreen]

This is a Vierendeel bridge

It sounds as though yours is similar but without the sloped top chords at the ends. If so, it is statically indeterminate and difficult to analyze unless you have program to do it, or you are one of the old dogs.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[ToadJones]

A lot also depends on how your vertical "struts" are connected to the top and bottom chords. If fixed, there will be a rather complicated moment distribution through the frame.

 

[ToadJones]

The analysis will depend on the relative stiffness of the members....change the member sizes and the stress in the members will change....there is no one answer, per se.
So, this is, in my opinion, not a simple question for we structural guys. In fact, as Paddington has suggested, the best way to analyze this is with software.
I myself have just recently designed a Vierendeel truss and I am very thankful that I had software to do it!

 

[ToadJones]

Paddington-
That bridge is a piece of artwork.
I can't imagine the detailing that went into that thing.
The curved plates and rivet work are beautiful and surely done in a time where that the work was much more difficult than now.
Nice.

 

[paddingtongreen]

I have designed them using Moment Distribution, that's why I referred to "old dogs". I had a modified form of moment Distribution that made the sway calculation a lot less arduous.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

jimandrews,

Provide a sketch. We are not mind readers. It makes a huge difference whether the beams are side by side or one above the other.


BA

 

[ToadJones]

Pad-
If you still have the literature to which you are referring, I'd sure like to have a read.

 

[paddingtongreen]

Toad, I gave all my old books to some of the young guys in my group when I retired.

The first part of the design was to do the normal moment distribution. and the second was a modified way that allowed another distribution to handle the sway. I can't bring it to memory.

I just went to look for a copy of the Steel Designer's Manual, it was the steel designer's bible, they used to be black but I know they made them more colorful. They are expensive, but I found one reasonably priced, on Ebay, in the UK. When it arrives, I'll see if the piece I want is still there. I guess I have to give you another forum where IMs are possible.

You can something of one

http://www.amazon.com/Steel-Designers-Manual-Construction-Institute/dp/0632049251

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[dhengr]

Paddington:

Did you do the design on that bridge, it’s very nice? Was it part of a design competition or some such? Otherwise, do you have any idea why they would have selected a Vierendeel truss instead of a more common truss configuration? I never used a Vierendeel truss for a bridge, but did use them in buildings when we wanted clear openings, without diags.

You’re a very kind and giving fellow if you gave all your books away when you retired. What did you get in return, a gardening spade or golf clubs, maybe a fishing pole? We are all better off for the fact that you did get a home computer, and participate here. As long as I really continue to think I can think, I couldn’t part with my engineering books. Like you said, I can’t always remember exactly how we did some things, but I can usually dig it out of some old notes, job files, or text books. And, I still pretend I’m not retire, although I sure ain’t gettin rich off of payin work these days. My books will mostly make a good contribution to a History of Engineering Library, although I don’t have any on the theory of pyramid construction.

 

[paddingtongreen]

dhengr, sorry, I should have worded that better. I have designed Vierendeel trusses, but not that bridge, I found it on Wiki and posted it as an example.

Vierendeel was a Belgian, and that bridge is in Belgium. there is more here in the link:

http://en.wikipedia.org/wiki/Vierendeel_bridge

The ones that I designed required full access through them otherwise I would have used a normal truss.

I gave away the books, perhaps because an old man gave his to me when he retired, soon after I started out on the drawing board.



Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[jimandrews]

Wow . . . went out of town for a few hours, and I see my thread has spurred a lot of discussion! Thank you so much for all the great input.

Someone asked for a picture. Here's my best "ClipArt + MS Paint" rendition of what I'm describing.

 

[jimandrews]

Let's try that again (I must be doing something wrong):

 

[paddingtongreen]

jimandrews, we need to know if the connections of the verticals to the chords are rigid or pinned. Also, if the bottom chord extensions do anything, are they part of the support?



Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[connectegr]

Rigid struts will resist lateral torsional buckling, but will not increase bending capacity. Each beam must be designed for it's tributary loading

As a truss with parallel chords the design is different.

http://www.FerrellEngineering.com