Special case in rectangular plate bending 1

[greycloud]

Greetings

I'm dealing with a case where a rectangular plate is subjected to a bending moment applied mid span of the plate along the shorter edge. I tried looking for a formula for this case but couldn't find any so hope you can help

 

[graybeach]

I agree with paddington. If the frame reaches the edges, you should assume that all of the moment will be attracted there because theoretically the fixed edges are infinitely stiffer than the middle of the plate. I call this kind of situation trying to load a lasagna noodle.

 

[BAretired]

Assuming that you can apply the line moment as shown in the diagram, it seems to me there will be no deflection on the line where the moment is applied. Plate rotation will vary from zero at each edge to a maximum at b/2.

You should be able to consider half the plate, a/2 * b, clamped on three sides and free on the fourth side with a uniform moment of M/2 applied on the free edge. Because there is no deflection on the fourth edge, it could be taken as a simple support instead of a free edge.

That doesn't solve the problem, but it provides another model to be investigated.

BA

 

[greycloud]

paddington and graybeach: now i get what u both say and it can be correct if we assume no deflections occuring but we are not sure of that. however, thanks to you i believe the loading case is more of moments applied to side only since the winch is fixed on an h beam.

BA: why did u divide M by half when taking half the plate and why do you think it won't solve the problem,I believe timoshinko mentioned such method in his book "theory of plates and shells"

 

[BAretired]

I divided the moment in two because there would be two plates, each having fixity on three sides and free on the fourth, each carrying one half the applied moment due to symmetry. I have not gone through "Plates and Shells" to see if he handles this particular case. If he does, then it should solve the problem.

BA

 

[KootK]

FEM would be the way to go but I can certainly understand why one might not want to head down that path for a one off design with little fee associated with it.

Yield line design would be another attractive option. However, I'm hesitant to go that route unless I feel very confident that I've got the right yield line model. And for me, that usually means that it's a very simple scenario or I've seen the model in print some place before.

For designs where I want reasonable proportions but I don't want to invest the time required to do FEM, I've had some success treating steel plates as assemblages of orthogonal, discrete beam "strips". Essentially a grid analysis yielding a lower bound capacity. This requires some redistribution capacity in the system and, as a result, I tend to be quite conservative with my weld designs.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[rb1957]

we all agree that fixed edges are too stiff, and pinned are maybe too soft. why not solve the plate (as BA suggests, look at a plate fwd of the winch and one aft) with both edge supports, and then combine the results ... semi-fixed ?

instead of a line moment, i'd suggest a line couple (up on one edge, down on the other). maybe model the deckplate from the winch CL (where not much should be happening) so your plate would have two sides "fixed" and two SS (maybe 4 sides fixed ?, but i think the winch CL is SS) and an applied line force somewhere across the panel.

you might find more plate loading solutions in Roark's reference ... google "Moody Rectangular Plates" (seriously!).

FE should be a reasonable solution. how torisionally rigid are the edge frames ?

Quando Omni Flunkus Moritati

 

[dhengr]

Greycloud:
It seems to me that you have been working on this winch supported on a barge deck problem for some time now, and have asked essentially the same question several different ways, hoping to find a grand formula that will answer all. Please reread your earlier threads and answer some of the questions some of us have already asked and you have ignored. Also, provide some meaningful sketches of the actual situation, loads, dimensions, etc., because a winch of any real size should probably not (would likely not) be loading a plate the way you are suggesting. You have not structured the foundation (the barge deck structure) for the winch properly if it is. The base on any meaningful winch will be quite stiff itself. And, it will impart a substantial shear reaction to the deck, along with the reactions to the line pull which is some distance above the deck, imparting a moment which I suppose is what you’ve been talking about. You have to take these reaction loads into some real structural members under the deck plate, I would think.

 

[greycloud]

Wow!! sorry guys i thought no one commented after BA, guess I miss counted the comments. I hope u are still around

KOOTK: u mean to divide the plate into smaller strips and divide my load equally by those strips?

rb: ba's method is sound and mentioned by timoshinko; however through my discussion with the guys above it turns out my loading case is different. I'm upploading some drawings and sketches to clear things up. I now believe my loading is more of a varying line load along the longer edges. so i will need an equation for a varying load and then use ba's method.

dhengr: this is more like an exercise for me by my boss and it goes aside whenever we have some real job so that is why i'm still on it. for now i'm only concerned with bending reactions and i will supply some drawings and sketches hope they can clear things up.

 

[greycloud]

here are some sketches

 

[greycloud]

and an autocad drawing

 

[greycloud]

neglect the winch weight

 

[BAretired]

Based on your latest sketches, I would not attempt a solution using plate theory. I would resolve the forces into reactions on the various beams, then solve them individually. It is probably reasonable to assume that the winch base rotates as a rigid body, i.e. it does not deform.

The drawings are a little puzzling. Why are you adding four new beams instead of just two? Why are you cutting the 635 deeps beams to receive the 150 x 90 angles instead of adding the beam below the angles and if necessary fitting stiffener plates between the angles?

The left ends of the 635 beams seem to be supported on the side shell plate. The right side seems to be unsupported. In short, the framing is not clear and until it is, it is difficult to recommend a design approach.

BA

 

[greycloud]

BA: the whole extra fitting thing was not my idea, it was done by production unit based on experience only;it was a modification job. our shipyard is small and not very profissional and that is in part why i'm facing some difficulties. I'm just asked to calculate the stresses in this current structure. the 635 is supported by the side shell plate and by a big l angle at the right side combined with a bracket. i understand it may not be too clear since its an autocad drawing converted to pdf. finally, why don't u think i should use plate analysis for this case.

i'll upload a better detail of the beam

 

[BAretired]

It doesn't matter whose idea it was. You have asked us to comment on the current structure which is what I am trying to do, but I don't fully understand what the drawing is showing. You can't calculate stresses without knowing how the structure behaves.

The four 635 deep beams are supported by an unyielding support on the left end and by a deflecting "large L angle" of unknown size and unknown span on the right. Is the large angle supported at each bulkhead? The lack of clarity has nothing to do with converting from autocad to PDF.

Plate analysis is used for a plate of uniform thickness. Your plate is reinforced with angle stiffeners in one direction and four hefty beams in the other. It will not behave as a plate. It will behave as a beamed structure.

BA

 

[rb1957]

my strategy would be to take the applied moment and make it into a couple on the fwd and aft edges (the tapering forces on the other sides only react a small portion of the moment, so this assumption in reasonably conservative). i'd then react these loads by the new beams under the deck, which carry the load into some bulkheads/frames. it looks like the applied loading is a UDL along the beams ... directions are hard to see in your sketches ... what's longitudinal, what's transverse, where's the load applied ...



Quando Omni Flunkus Moritati

 

[rb1957]

i'd worry about how the winch structure itself will deflect ? your crude hand sketch shows the winch having side plates, so that most of the moment load would go to the tapering loads on the sides (completely the opposite of what i said above !) unless the winch baseplate is man enough to redistibute load into the fwd and aft edges.

presumably the shear loadpath into the deck plate is plenty strong (it usually is).

is 40 tons the working load, or some ultimate design load ?

Quando Omni Flunkus Moritati

 

[dhengr]

Greycloud:
Come-on, get with it and start thinkin a little bit. Don’t keep showing the same sketches or sections without providing any new or meaningful design info. You showed almost the same damn inadequate sketch of the winch in one of your earlier threads without a bit of meaningful info. on it either. We do understand what a winch is to the extent that your sketches show it. Get the spec. sheets of on the winch, and post them here so we can see it, since you don’t seem able to pick the important info. off of them. How high, above the deck, is the 40T cable force applied? You actually have several darn smart people here trying to help you, but you keep mis-directing the discussion by ignoring their questions. This is not likely a plate bending problem, however much you want to learn about plate theory. What does this winch have to do with the funny shaped cut-out just above it in your plan view? Is that the base for a crane of some sort? What is the 2680x2800mm doubler pl. intended to do? What is its thickness and how is it attached to the deck pl. be specific and complete? How is the winch attached to the barge deck, show this in detail, with dimensions, etc. This attachment had better relate to the new added beams, or you may have to make some adjustments. Show a large section through the added beams, dimensions, welding, etc. The lower added beam will be loaded upward by the winch base, and the upper added beam will be loaded downward by the winch base. Show a large section of the new ‘large L angle’ with all dimensions, welding, reaction points, etc. We are not nit-picking here, we are trying to get a sense of the proportions and details of the problem. We are trying to understand the framing system and how the winch loads will be put into the deck structure, and it better not involve a bunch of pl. bending or pl. action. If you want to put a name on your barge deck system, it is a gridwork of ribs and beams, or an orthotropic deck.

 

[greycloud]

BA: the large L angle penetrates the bulkheads along the length of the barge IE: it extends from one edge of the barge to the other. the winch is resting on an h-beam sitting on a doubler plate fixed to the deck structure; the h beams are rigid and forget about the doubler plate. Don't worry about the size of the large l angle as i don't need u to calculate the stress for me i just need guidance as on what approach to take.

plate analysis is indeed used for stiffened plates and plated structures as u might see in many books and standard so wold u explain why its not applicable here.

RB: the winch is seated on h beams fixed around its four edges. the h beams are then bolted to the deck plate. consider everything above the deck plate as rigid. the 40 tons is ultimate design load. im uploading another sketch of loads causing the bending moment induced by the h beam into the deck structure.

it looks like u both advise neglecting the plate in the analysis. won't that affect the analysis in a big way? its like your saying the plate is taking none of the load.

I should thank you both for your patience with me so far

 

[rb1957]

"it looks like u both advise neglecting the plate in the analysis. won't that affect the analysis in a big way? its like your saying the plate is taking none of the load." what i think we're saying is that this doesn't look to be a classical plate bending problem. i think you'd include some effective plate when calculating the bending properties of the angles.

"the winch is seated on h beams fixed around its four edges. the h beams are then bolted to the deck plate." that maybe so, but your sketch shows the winch having side plates so there's a more direct loadpath into the sides (with the tapering bending field reactions (as opposed to the ends where the applied moment is reacted as a couple). if the base of the winch is fastened around into the H-angles then there's a story there. In the end it's your analysis; remember we could just be a bunch of lunes, drooling and typing in our bath-robes.

btw, what's your level of education, experience ? it seems to me that you're trying to do the "right" thing, or else you've gotten caught in an inspection and someone has said "show me". attaching a 40ton winch is no small matter. it could well be that rules of thumb and general experience can produce an acceptable design ... but they can always overlook things.

a small thing, the bolts attaching to the deck are carrying shear and tension loads.

Quando Omni Flunkus Moritati

 

[greycloud]

"i think you'd include some effective plate when calculating the bending properties of the angles." How should i decide on how much effective plating i should take?

"your sketch shows the winch having side plates so there's a more direct loadpath into the sides" i'm not sure i get what u mean by the side plates,are u talking about the shell side plate? there are no side plates around the winch other wise.

actually, I tried dealing with the problem as a system of beams but my boss,a naval architect, dismmised it as a wrong approach. his method is to get the bending moment for a plate portion between transverse frames and then divide it by the combined section modulous of the plate and longitudinal stiffeners. i have an experience of only 4 months and under grad education in mechanical engineering if ur asking.

dhenger: for some reason your comment didnt show up before, i'm sorry if my supplied details are lacking and if i'm frustrating u all but problem is now the actual vessel is gone and this is the only info i can get.