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Bending Moment of 2 parallel beams
4

Bending Moment of 2 parallel beams

Bending Moment of 2 parallel beams

(OP)
Hi,

I am currently designing a machine that has 3 pairs of parallel beams supporting a single central unit.

I am unaware of how to calculate the bending moment when there are two beams in parallel, as a single beam it can be modeled as a cantilever beam, but if the beams are connected at either end (a rectangular construction can be assumed), how does the bending moment change? This construction has been adopted to increase the system stiffness.

Any guidance would be great.

Ollie

RE: Bending Moment of 2 parallel beams

Post a sketch, please.

Two beams have twice the strength, three have tripple. Likewise with stiffness. The devil, however, is in the details. If the beams are not bound composite they will each resist and deflect according to their proportionate loading.

If your unit has its centroid at the centre and a reasonably stiff frame with skid type supports, the centre beam is going to see half of the load and each of the litter beams one quarter. If the unit has legs on the putter corners, the centre beam will never see any load (don't laugh my friend, I has seen this mistake be built!). You also have to watch for an offset centroid (very common) which will change the apportionment of load to the individual beams.

Sketch; Anything else is conjecture and half measure in helping.

RE: Bending Moment of 2 parallel beams

(OP)
The attached image gives a basic example of the configuration. Initial analysis is of the bending of the beams in one orientation, with the final analysis looking at beams mounted in 3 locations equally about the triangular center piece.

thanks,

RE: Bending Moment of 2 parallel beams

What book is this from?

RE: Bending Moment of 2 parallel beams

(OP)
It's not from a book, its a concept I am currently working on. The sketch was a solid edge model annotated as a JPEG.

RE: Bending Moment of 2 parallel beams

What you've attached is an indeterminate beam-couple... This does not readily yield itself to hand solutions.

Quick questions:

- Can the left hand side rotate? I'm betting yes.
- Are the ends of the rods (beams) fixed to the supports (triangle and box)? I'm betting yes.
- Can the beams translate freely up and down? I'm betting yes.

If so, this is going to result in a beam-column for the top beam (ie: flexural and compressive forces) and an uplift condition beam column for the bottom (flexural and tension forces).

I'm betting this isn't going to work. Your top beam-column is going to be too slender to take the imparted compression loads.

In my opinion you need a 2D FE structural analysis software to work this one out.

RE: Bending Moment of 2 parallel beams

(OP)
You are correct in your answers, for the sake of the basic model I'm looking at it in only one plane, i.e a complicated cantilever beam. Is it possible to work out the bending moment simply for the attached image? I have access to Ansys software, I was looking to validate results using hand calcs, and possibly produce a BM diagram.

Cheers,

RE: Bending Moment of 2 parallel beams

You could come up with a rough (possibly unconservative) approximation by figuring out the capacity of one cantilevered beam in your given setup and then doubling the capacity. As CELinOttawa stated this wont be accurate as one beam will be in flexural-compression while one is in flexural-tension. Should work well enough for a hand-calc double check of software though.

Maine EIT, Civil/Structural.

RE: Bending Moment of 2 parallel beams

cannot you make a truss out of your proposed set-up?

RE: Bending Moment of 2 parallel beams

Okay, the biggest problem you have is restraining the motion of the left side so that you actually get flexural-compression and flexural-tension. The beam is going to do everything it can to yield in only flexure, meaning you have a serious torsional problem if you cannot or have not restrained the out of plain motion of the left hand "triangle".

You need to make sure this can work in the real world. As detailed, it will not.

Here is an INACCURATE back-of-the-envelope checking procedure:

0) Solve for the fixed end moment on the Right Hand Side (RHS) as if this was one beam.
1) Split the end reaction into two equal reactions on the RHS's two beams (NB: NOT accurate, but realistic).
2) Solve for all forces in the system as if pinned.
3) Apply fixity to each end of beams on LHS in terms of 20 or 30% of the fixed moment calculated. Deduct same from RHS.
4) Rework with the moments in your sum of forces analysis from (2).
5) Verify you have a possible solution by summing and accounting for all force applied.

Dirty, and not quick, but it should give you results within 20% or so of the "correct" solution.

Your rig must be FORCED to behave this way as well as be constrained in order to be stable.

RE: Bending Moment of 2 parallel beams

(OP)
Thanks :)

RE: Bending Moment of 2 parallel beams

Hey ogg22, One more thing: When you deduct the moment from the RHS and solve for all forces, you should find that there is now a couple (compressive force at top, tension force at bottom) on your RHS supports which compensates for the deducted moment.

You cannot have a valid solution if the tension couple plus the two RHS fixed end moments do not add up to your original input moment of 29.5kN·m. That value is assuming your drawing is to scale, and the load is actually input at the horizontal centre of the triangular LHS. [Thus 590mm from ultimate support to point of load application, making force times distance = 50kN x 590mm]

RE: Bending Moment of 2 parallel beams

i think the structure will work as two independent beams in bending, 1/2 shear on each ...
where you have some uncertainity is does the outbd fttg fix that end of the beam, so you have a "guided" cantilever. then these end moments (at the outbd end) would be balanced by a couple

Quando Omni Flunkus Moritati

RE: Bending Moment of 2 parallel beams

The triangle looks very stiff to me, much stiffer than the beams, so:
Move the force to the end of the beams, calculate the moment of the force multiplied by its distance from the ends of the beam and divide it by the beam spacing. Apply these as tension and compression loads on the beams. Now divide the force by two beams, multiply by the length of the beams, divide by two ends. These are the moments at the ends of the beams, there is zero moment in the center. If the triangle is not comparatively rigid, Cel's solution is better.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

RE: Bending Moment of 2 parallel beams

i think it's important to recognise that the two beams are carrying shear loads (and have increasing moments in them)
and that they are not working like caps of a single beam (which'd have increasing endload).

if the beams weren't parallel it'd behave very differently (the beams would be predominantly axially loaded).

Quando Omni Flunkus Moritati

RE: Bending Moment of 2 parallel beams

Lol... If the sum of forces analysis doesn't show shear in each beam, I'll chew on my own shoe...

RE: Bending Moment of 2 parallel beams

rb1957, The only beam that I know of that has bending without exterior shear is one in circular bending.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

RE: Bending Moment of 2 parallel beams

i was thinking that the OP might be looking at the two bars as caps of a beam.

and yes, i know that doesn't work ('cause there's no web to take the shear, to join the two caps together).

so then the problem is "merely" two cantilever beams, each carrying 1/2 the shear (that is if you assume the loaded end is pinned). if the loaded end is fixed then you have a guided cantilever, the outbd ends of both beams resists some moment, which is reacted as a couple between the beams; could become a large deflection problem (but if it does there are probably other issues with the structure).

Quando Omni Flunkus Moritati

RE: Bending Moment of 2 parallel beams

Assuming:
  • triangular center piece is a rigid body
  • both beams are fixed each end
  • distance from applied load to beam ends is x
  • c/c distance between beam is h


  • F = 50 x/h (compression in top beam, tension in bottom)
    M = 50*500/4 = 6250 N-mm in each beam

    In other words, I agree with PaddingtonGreen.

    BA

    RE: Bending Moment of 2 parallel beams

    Ah, I missed the fact that repeats on the two other sides of the triangle, thus simplifying the problem greatly.

    My analysis applies to the problem as-drawn if the triangle is free to rotate. Go with the simplified assumption and you should be okay in this case as rotation and translation relative to the RHS are fixed in reference by the two other identical "mirrorring" beam sets.

    RE: Bending Moment of 2 parallel beams

    i see both beams reacting 25N shear, peak moment = 25*500 = 62500Nmm
    this assumes pinned at the triangle.

    if you assume the triangle is not free to rotate, then it turns into a guided cantilever; these fixed end moments are reacted as a couple between the beams (to make a FB of the triangle).

    not sure of BA's "F = 50 x/h" ... this looks like you're reacting the load moment (50x) with a couple between the beams ... which wouldn't happen, 'cause the beams are independent (there's no web between them).

    Quando Omni Flunkus Moritati

    RE: Bending Moment of 2 parallel beams

    rb, you are the only one in step!
    The beams are rigidly attached at both ends (stated above).
    BA is transferring the shear in to the end of the beams and needs to account for the moment.
    The triangle is prevented from any but a small rotation by the beams.

    Michael.
    "Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

    RE: Bending Moment of 2 parallel beams

    "The triangle is prevented from any but a small rotation by the beams." ... yes, the triangle will displace but not rotate (=guided support)

    from Roark, the guided end moment = WL/2 (surprisingly big) where W is the load on one beam (= P/2)
    so 1/2 the cantilever moment is reacted at the triangle, which will set up a couple in the two beams = PL/2h
    and the max moment in the beams is PL/4 = 6250 Nmm (as BA had, my number above ... hopelessly wrong !!)

    at the fixed supports, the applied moment is 50*500 = 25000 Nmm,
    1/2 of this is reacted by a couple between the beam, and 1/2 by the fixed end moments of the beams.

    Quando Omni Flunkus Moritati

    RE: Bending Moment of 2 parallel beams

    Not sure of the boundary conditions. If the beams are pinned at the triangle, then each beam carries 25N shear with a max. moment of 25*500 = 12,500N-mm at the right end. Axial force in each beam would be 50x/h, tension in one and compression in the other.

    If the beams are rigidly connected at both ends, each beam carries 25N shear and the maximum moment is half of the above or 6250N-mm. I think the axial force becomes (50x + 12,500)/h, contrary to what I stated in my earlier post.

    Are we all in agreement?

    BA

    RE: Bending Moment of 2 parallel beams

    "Axial force in each beam would be 50x/h, tension in one and compression in the other." ... i don't get this.

    if the beams are pinned at the triangle, then the applied moment (50*500) is reacted by two fixed end moments (25*500), and no couple.

    if the traingle end is considered guided, then the fixed end moments are 1/2d and the remaining 1/2 is carried by a couple between the beam.

    Quando Omni Flunkus Moritati

    RE: Bending Moment of 2 parallel beams

    rb,
    Axial force 50x/h arises from the fact that the 50N force is applied a distance 'x' outside the two hinges. The diagram does not give the x dimension but the force is clearly applied to the left of the two hinges.

    BA

    RE: Bending Moment of 2 parallel beams

    ok, the small offset in the triangle ...

    Quando Omni Flunkus Moritati

    RE: Bending Moment of 2 parallel beams

    BA, If the beams are pinned at the triangle, then there should be no increase in axial force over the transfer from the load point down to the hinges. It becomes two flag poles linked with a hinged member in the direction of the force.

    If the beams are fixed at the triangle, the relative stiffness of the triangle controls the additional axial load. If the triangle is infinitely rigid, the added force is half the total moment divided by the beam spacing, just as you have it.

    Michael.
    "Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

    RE: Bending Moment of 2 parallel beams

    paddington,
    If you draw a free body diagram of the rigid triangle and take moments about the upper hinge, there is a moment of 50x which must be resisted by an axial tension in the lower beam. Similarly, there must be a compression in the upper beam. The magnitude of each of those axial forces is 50x/h.

    Considering the entire assembly as a cantilever, the support moment is 50(x+500). The x dimension has not been provided.

    BA

    RE: Bending Moment of 2 parallel beams

    i think michael is saying that the offset moment is included in the fixed end moments of the beams.

    if the beams are pinned on the triangle, then the offset of the load will be reacted by a couple between the beams.

    if the beams are fixed to the triangle this couple still exists and now the beams are adding significant moment to the triangle, again reacted by a couple between the beams.

    if you assume that the load is inline with the ends of the beams, then the small offset moment (and its reacting couple) doesn't exist.

    each beam reacts 1/2 the applied load (assuming the beams are the same section).

    Quando Omni Flunkus Moritati

    RE: Bending Moment of 2 parallel beams

    Seems like a lot of discussion for a simple statical problem.

    BA

    RE: Bending Moment of 2 parallel beams

    BA:
    I must be reading a different thread than the rest of you. My understanding is that there are two more pairs of two beams each, which radiate out from the other two sides of the triangle on the left of the OP’ers. sketch, identical to the one he shows, and at 120̊ intervals. That will certainly change the whole analysis if true, making the whole problem even more indeterminate. I would then start with compatibility at the center triangle, and assume the left two pairs of beams are much stiffer axially, than the right beam pair (the OP’ers. sketch) is in bending.

    Ogg22:
    Come on, wake up and smell the coffee. If you can’t describe your problem any better than you have, you should probably not be pretending to be an engineer. Is your sketch a plan view or a side view; and is that the true orientation of the load w.r.t. the two beams shown? Do the other two sets of beams radiate from the other two faces/sides of the triangle on the left, in plan; and otherwise look the same as the one you’ve shown? This would drastically change the whole analysis and make everything above a bunch of bad guesswork based on a poor description of the problem. Could you draw some sketches of the whole system, without solid works/edge, several different views (plan, side views, details at connections, etc.) and describe what this thing is and how it works. Dimensions, reasonable proportions, loads, etc. are all important. I don’t really care that you might use solid works/edge to do your sketches, but if you can’t express yourself without solid works/edge, I think you are in big trouble. You have several fairly smart engineers here guessing at what you think you are doing. You’re wasting their time if you can’t respond to their questions or assumptions, in real engineering terminology. What does the triangle really represent? What do the semi-circular thingies at the ends of the beams represent? What are the boxes on the right?

    RE: Bending Moment of 2 parallel beams

    dh,
    You may be correct. Speaking of coffee, I think I'll go and have one.

    BA

    RE: Bending Moment of 2 parallel beams

    Looking at ogg22's 10 Apr 14 7:03 posting, I have to admit that dhengr is correct. I'll join you with the coffee, but I'm going to reinforce mine with something stronger.

    Michael.
    "Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

    RE: Bending Moment of 2 parallel beams

    (OP)
    All, I apologize for the minimal activity, I have been otherwise engaged. The feedback provided has been of great use so and for that I thank you.

    dhengr, Due to developments in the project I can not release further information so as you have clearly pointed out what I have provided isn't substantial enough and would be wasting people's time to further this thread.

    Thanks to everybody for replying and again I apologize for the late feedback.

    RE: Bending Moment of 2 parallel beams

    Maybe it's a top secret component for NASA's apace program...who knows?

    BA

    RE: Bending Moment of 2 parallel beams

    i think most of the replies are spurious since we forgot that you've got 3 pairs of beams.

    in this case the load will be reacted mostly by tension/compression in the beams ... i'd model the FBD of the triangle as the load reacted by three forces (one for each pair of beams). certainly you know the directions of the three forces but not their relative magnitudes. since all the beams are the same size i think it's reasonable to assume that they all have the same magnitude (sounds like the minimum strain energy).

    a confusion might be are the pairs in-plane or out-of-plane ? in the load in-plane (as shown) or out-of-plane ? (this clearly has a very different solution)

    Quando Omni Flunkus Moritati

    RE: Bending Moment of 2 parallel beams

    Ogg22:
    I’m not just picking on you, this is true of half the OP’ers. coming here these days.

    Damn-it, I wasn’t asking for the project name, all the client contact names and phone numbers, your social security number, your boss’s name and number, and your profit on the project. But, if you can’t describe and sketch your problem to fairly truly represent the real world conditions, you are wasting our time, and not even getting reasonably useful answers, although you may not know it. And, doubly so, if you don’t keep up with the thread and correct people when they are not discussing the real problem. And, you have to be smart enough to do that, or maybe you shouldn’t be asking this question and working on this problem, whatever it is. The general discussion was well reasoned and debated btwn. several very smart engineers, but meaningless if it doesn’t even represent the real problem. And, it is your responsibility to keep the discussion on the right track, assuming you are smart enough to do that, and realize (have some understanding) how your problem really works. I’m so damn tired of people coming here with questions which are so vague and poorly defined that you can’t tell if it is a 2nd grader asking the question or just a really dumb person pretending they have some technical knowledge and responsibility. My goodness, if you can’t divulge any meaningful info., how do you expect us to understand what your are dealing with. We can’t see it from here and you won’t inform us. If you can’t properly define your problem and have some vague idea how it works, so you give the needed info., you will probably never solve the problem. Go to your boss with your problems, there should be no embarrassment in that. At least he knows what you are working on, and can look at the same drawings and specs. you are working with. I’m certainly not expecting young engineers to know everything, we all started out with a lot still to learn. But, you must learn how to ask a well formed question, with sufficient engineering detail and good terminology to elicit a meaningful well directed discussion.

    RE: Bending Moment of 2 parallel beams

    +
    I am guessing that the central triangle is supported by three pairs of beams 120o apart and that the triangular center piece is subjected to an applied moment of 150x about a vertical axis where x is the dimension from the centroid of the triangle to any of the sides. In that case, the model shown is not a bad representation of the true situation.

    BA

    RE: Bending Moment of 2 parallel beams

    if the triangle's supported on three sides, why any moment ?

    (before the load was off-set from the 1 pair of beams, now the load is in the middle of 3 sets of bem pairs)

    Quando Omni Flunkus Moritati

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