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

 

[connectegr]

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

 

[BAretired]

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

 

[dhengr]

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.

 

[rb1957]

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

 

[jimandrews]

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!

 

[desertfox]

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

:

http://www-classes.usc.edu/architec...pdf+how+to+stress+a+Vierendeel+truss&hl=en&gl

=uk&pid=bl&srcid=ADGEESg3HXu07Oqx1ayXrLW_HaGwizKM2Cdmmp
UR26QhUkElSR2rA1GtLWFcMeTXt4bXwls4qBZiUtnWLLJdwDr6VBm8KPzY1-7BZ-8MZY1oqsCyM3YO4PNbDw3cxnY0opv8nwqtGXPY&sig=AHIEtbQhqt_
MWosYbtfso7MuuttMuxw_lA

desertfox

 

[jimandrews]

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?)

 

[desertfox]

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

 

[hokie66]

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.

 

[jimandrews]

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?

 

[paddingtongreen]

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.

 

[paddingtongreen]

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.

 

[jimandrews]

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

 

[BAretired]

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

 

[desertfox]

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

 

[slickdeals]

@BA:
Copy paste the entire link

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

http://www-classes.usc.edu/architec...qtGXPY&sig=AHIEtbQhqt_MWosYbtfso7MuuttMuxw_lA

 

[BAretired]

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

 

[rb1957]

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.

 

[paddingtongreen]

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.

 

[BAretired]

jimandrews,

You stated above:

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