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Parallel beams in bending

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

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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 ?

RE: Parallel beams in bending

(OP)
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!

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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.  

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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.  

RE: Parallel beams in bending

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!

RE: Parallel beams in bending

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.  

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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

RE: Parallel beams in bending

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

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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.

RE: Parallel beams in bending

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

RE: Parallel beams in bending

Sorry. I just noticed your picture. It is a Veirendeel truss. Unless there is a design requirement, I recommend diagonal and vertical infill members. Rigid connections will not be required.  Parallel axis theorem does not apply.   

http://www.FerrellEngineering.com

RE: Parallel beams in bending

What you are showing is a Vierendeel truss.  It would be better if you added a vertical member at each end and re-spaced the vertical members so that one occurs at the load point.

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

Jimandrews:

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

so the lower beam distributes the load into the upper beam ... the problem (as draawn) is symmetrical and doubly redundant.  but it might be easier to solve than that ... assume a load distribution applied to the upper beam, say equal loads (P/6) ... so you've got the reactions to the lower beam, and the applied loads to the upper beam.  can you calculate the deflection of a beam in bending ?  calc for the upper and lower beams at each load point.  how much are the connections straining (under tension) ?  are the deflections compatable ? shuffle the connections loads untillthe deflection in the upper beam = the deflction in the lower beam + the extension of the connections.

GL   

RE: Parallel beams in bending

(OP)
dhengr, I think I'm a pretty savvy engineer.  I described the problem in as simple a manner as I thought would be needed to get it across.  I apologize that I did not meet your strict criteria for presenting a question.  I also think you're rude, but you know, I've been a "regular" in enough forums to know that the new guy needs to learn the lay of the land before spouting off, so I'll leave it at that.

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

Hi jimandrews

Have a look at this link and in particular scroll down till you see Vierendeel Steel Girder it shows formula for stresses etc

 http://docs.google.com/viewer?a=v&q=cache:8jSL1Vdd-bQJ
: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

(OP)
desertfox, thank you for that link.  Lots of stuff there.  At a quick glance, it appears the assembly is treated as an equivalent beam, since the shear & bending moment diagrams look much like they would for a simple beam.  (Actually, that's probably true for any beam analysis, right?  The inertia doesn't come into play until we're looking at the resistance to max bending moment?)

RE: Parallel beams in bending

jimandrews,
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

(OP)
Thanks, hokie66.  As I alluded to, the actual problem is larger -- it's a 3D framed "box" with an internal load.  Can you recommend a good code to handle such 3D weldments?

RE: Parallel beams in bending

I think you should use one of the hand calculation methods, that way you will understand the load paths and the behavior of your structure. Right now, you seem to be looking for a black box solution.

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

RE: Parallel beams in bending

I meant to add, "This is a good problem for moment distribution, especially with spreadsheets available."

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

RE: Parallel beams in bending

(OP)
I can dig into one of Dad's texts and probably learn that method, so I can appreciate the suggestion.  I'll try that this weekend.  I still see this coming up more than once in the future, so any software recommendations would be greatly appreciated.

jim

RE: Parallel beams in bending

desertfox,

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

Hi BAretired

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

Hi desertfox,

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

personally, i prefer not to learn "how to analyze a ... structure" but rather how to analyze structures, generally.  this is a pretty simple redundant problem, complicated if the joints carry moment, so i'd solve it as such.  moment distribution is a good way, complicated by the supports being on elastic foundations; i'd assume a load distribution between the two beams and adjust it to fit the displacements.

RE: Parallel beams in bending

You must have a magnificent mind rb1957, to be able to analyze structures without first having to learn, one type of structure at a time, to analyze the many different types of structure that we meet.

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

RE: Parallel beams in bending

jimandrews,

You stated above:

Quote:

As I alluded to, the actual problem is larger -- it's a 3D framed "box" with an internal load.  Can you recommend a good code to handle such 3D weldments?

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

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