Bending Moment of 2 parallel beams 4

[ogg22]

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

 

[rb1957]

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

 

[paddingtongreen]

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

 

[rb1957]

"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

 

[BAretired]

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

 

[rb1957]

"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

 

[BAretired]

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

 

[rb1957]

ok, the small offset in the triangle ...

Quando Omni Flunkus Moritati

 

[paddingtongreen]

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

 

[BAretired]

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

 

[rb1957]

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

 

[BAretired]

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

BA

 

[dhengr]

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?

 

[BAretired]

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

BA

 

[paddingtongreen]

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

 

[ogg22]

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.

 

[BAretired]

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

BA

 

[rb1957]

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

 

[dhengr]

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.

 

[BAretired]

+
I am guessing that the central triangle is supported by three pairs of beams 120^o 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

 

[rb1957]

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