Parallel beams in bending
Parallel beams in bending
(OP)
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
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






RE: Parallel beams in bending
It sounds like a Vierendeel truss.
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
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 ?
RE: Parallel beams in bending
Thanks for your help!
RE: Parallel beams in bending
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.
RE: Parallel beams in bending
RE: Parallel beams in bending
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.
RE: Parallel beams in bending
RE: Parallel beams in bending
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!
RE: Parallel beams in bending
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.
RE: Parallel beams in bending
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
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
RE: Parallel beams in bending
If you still have the literature to which you are referring, I'd sure like to have a read.
RE: Parallel beams in bending
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 h
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
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.
RE: Parallel beams in bending
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.
RE: Parallel beams in bending
Someone asked for a picture. Here's my best "ClipArt + MS Paint" rendition of what I'm describing.
RE: Parallel beams in bending
RE: Parallel beams in bending
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
As a truss with parallel chords the design is different.
http://www.FerrellEngineering.com
RE: Parallel beams in bending
http://www.FerrellEngineering.com
RE: Parallel beams in bending
The solution to this truss can be easily determined by hand methods or a by using a 2D Frame program.
BA
RE: Parallel beams in bending
I'll bet your trip out of town for a couple hours was to the dentist, because getting information out of you is like pulling teeth, real tough. Even if you are "but a mechanical engineer," you have to have a little mechanical and structural savvy, and you must be able to describe your problem well enough so we can make some meaningful comments. If you want help.
Look at your first post, read it assuming that you know nothing about your own problem, as is the case with all of the rest of us here, and ask yourself if you properly described, in words, the picture you show us now. It appears to me that you didn't say anything misleading, but I wouldn't have gotten 'a ladder on its edge' from your description. Paddington guessed right, but he's clairvoyant, so that's not fair; everyone else was just guessing wildly. Now, as people have asked, we need to know what the t & b chord sections are, what the vert. web members are, how they are connected, and the dimensions. You might have said that the truss was hung from the ends of the top chord, which is not otherwise loaded. That isn't what I got out of your OP. You said the other beam (bot. chord) had a distributed loading, what magnitude, lds./ft., but that's not what you show now. Which is it? Are the vert. web members spaced at about 5' and welded to the t & b chords? Are there actually shear panels (shown in black) in-filling the area between the t & b chords and the vert. web members, I suspect not? I would put vert. web members under the hanger reaction points, and I would ultimately check lateral stability.
BA>> I'll bet you a dollar to a doughnut, that you took a picture like this, that we had to drag out of the OP'er, a month and a half ago; and to fix an end canti. bending problem, you added a cable from the end, sloping up and inward 7' to anchor at the same point as the existing cable support. Look at LTB of a Vierendeel Truss, thread 507-263853.
RE: Parallel beams in bending
GL
RE: Parallel beams in bending
Yes, I did shift from a distributed load to a point load in my crude drawing. Again, my apologies. I did it at home with clip art and MS Paint. I didn't think it mattered in the context of my original question, which was intended to be somewhat general.
Some more information:
1. assume the "ladder" is welded, not pinned.
2. assume the "crossbars" are rigid, as stated before
3. the black areas are empty space, not panels
4. the upper "siderail" is hung from each end
5. the lower "siderail" is loaded in a uniform manner.
I did solve an extension of this problem with a general FEA code, and the answers are quite out of whack with some reported test results (which frankly, I don't believe). If I take the load and apply it to ONE of the two beams in question, using Roark & Young, I get results bounding my FEA answer, depending on whether or not I use simply supported or cantilevered end conditions. I am trying to assess whether or not the addition of the 2nd beam would dramatically stiffen the first beam, perhaps through an "Ad2" type adder (i.e., the parallel axis theorem). If this is true, then I have to question why my FEA results are so incongruous with reality.
As an aside, I'd love to hear some recommendations for a cost-effective Windows code that could handle analysis of 3D welded frames.
Again, my thanks for all the help. I've learned a great deal. My father was a structures prof at Missouri-Rolla, so I'd ask him, but he passed away last spring. I have some textbooks he wrote, but we're talking about a couple of semesters of senior-level structures homework here, and I'd like to solve this problem, say, before Christmas!
RE: Parallel beams in bending
Have a look at this link and in particular scroll down till you see Vierendeel Steel Girder it shows formula for stresses etc
http://d
:www-classes.usc.edu/architecture/structures/Arch213B/lecture-prints/12-vierendeel.pdf+how+to+stress+a+Vierendeel+truss&hl=en&gl
=uk&pid=bl&srcid=ADGEESg3HXu07Oqx1ayXrLW_HaGwizKM2Cdmmp
UR26QhUkElSR2rA1GtLWFcMeTXt4bXwls4qBZiUtnWLLJdwDr6VBm8KPzY1-7BZ-8MZY1oqsCyM3YO4PNbDw3cxnY0opv8nwqtGXPY&sig=AHIEtbQhqt_
MWosYbtfso7MuuttMuxw_lA
desertfox
RE: Parallel beams in bending
RE: Parallel beams in bending
Hi Jimandrews
Here is another reference on analysis download it and go to page 13 on the pdf bar
http://web.njit.edu/civil/fabric/revint/chap7+.pdf
desertfox
RE: Parallel beams in bending
The parallel axis theorem is accurate only for shapes which have solid webs. The behavior of triangulated trusses can be approximated by using a factored moment of inertia, but that doesn't work for Vierendeel frames. As BA said above, you either need to learn to do it by moment distribution or use a plane frame program. You don't need 3D.
RE: Parallel beams in bending
RE: Parallel beams in bending
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
jim
RE: Parallel beams in bending
I was unable to download your first reference. I got the message "Bad Request - Error 400", so I'm not sure what went wrong there as jimandrews apparently was able to download it successfully.
I was able to download your second reference, Chapter 7 which seems to be very good. Do you know the name of the book and the author?
BA
RE: Parallel beams in bending
I tried going back to the original search but sadly couldn't find a title or author for that book but I'll keep searching.
regards
desertfox
RE: Parallel beams in bending
Copy paste the entire link
ht
RE: Parallel beams in bending
Thanks, but don't spend too much time searching. It looks like it may be a good addition to my library.
slickdeals,
You were right. I was able to download the first reference using your link.
BA
RE: Parallel beams in bending
RE: Parallel beams in bending
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Parallel beams in bending
You stated above:
Do you mean it is an orthogonal grid of Vierendeel trusses crossing each other? If so, moment distribution would not be the best way to go.
Maybe it would be best to post a sketch.
BA