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

 

[rb1957]

""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?" ... assuming the decking is in compression, i'd use 30t; if the decking is in tension you can you as much as you want, 1/2 the distance to adjacent beams.

""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." ... like i say, your earlier sketch, the hand drawn one (4:47 on the 24th), shows the winch axle supported by two plates on the sides, so this is where the load will prefer to go (stiffer loadpath). now granted the winch will have a base plate and this will distribute some the load along the ends (the couple reaction to the applied moment) but is it "butch" enough to be considered infinitely rigid ?

we taking about reacting the load as a system of beams. If your boss wants you to do something with plate moments then he's taking a different tack to us. he should help you ...
1) solve this problem his way, and
2) show you why his way is preferred (is it simpler than beams ?). i suspect he's thinking there are simple conservative assumptions that make the job easy to solve with conservative results.


Quando Omni Flunkus Moritati

 

[BAretired]

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.

What transverse frames? You have a rigid plate element on one side and a "large angle" on the other side which spans from bow to stern. If you had a rigid plate element on both sides, the problem would be a little easier, but we have no idea how the large angle is going to deflect under the applied forces.

Where is the large angle supported? Where is the ribbed deck supported? At present, it appears they both span the entire length of the ship. How can you determine the behavior of members without knowing the span?

BA

 

[greycloud]

rb: i got u now, u mean the plates supporting the wire rope drum will transfer the load directly to the h beams under them leaving the other two edges lightly loaded unless the winch is rigid enough to distribute the load. i believe the winch is rigid enough not to behave this way.
as for my boss, i spoke to him today he said that treating the system as beams makes the problem simpler and is not the professional way to do it as the plate is contributing to holding the load. he also said that the plate needs to be taken into consideration if the h beam under the winch is laid on a plate portion that is not supported by a beam since plates won't transfer loads.
is it anyway practical to lay the beams supporting a winch directly over a deck structure without som mounting plate?

ba:both the large angle and ribbed deck span the entire length of the ship. do u think the problem with this large l angle is that it will cause the side fixed to the shell plate to be loaded more than the beams on the side of the large l angle?

 

[rb1957]

the plate is relevent if the H-frame is attached to the plate which has supporting beams attached to it ... ie it is the loadpath from the winch to the beam. clearly the closer these two are together, the better. so this treatment of the plate would consider individual cells with maybe one load from the H-frame being reacted by several bolts into the supporting structure.

the problem becomes very difficult very quickly since you have a continuous plate supported at many places, loaded at a bunch of other ones. i'd suggest FEA is the only reasonable way to analyze this. that said, there are always simplfying assumptions ... you might say that each H-frame load is reacted by a circle of plate, simplify to SS, and you can quickly get a plate bending moment.

Quando Omni Flunkus Moritati

 

[BAretired]

ba:both the large angle and ribbed deck span the entire length of the ship. do u think the problem with this large l angle is that it will cause the side fixed to the shell plate to be loaded more than the beams on the side of the large l angle?

No! That is not my concern. I am still trying to understand your framing plan which is not at all clear. Are the ribs and large angle supported vertically by FR-4, FR-6 etc.? The thing marked 'Bulkhead'...is that FR-5?

If the ribbed deck and large angle are spanning the entire length of the ship, a dimension which you have not provided, I would be concerned that deflections would be excessive. If, on the other hand the ribs and angle are supported by bulkheads at closer centers, that is another matter.

BA

 

[dhengr]

Greycloud:
No one is planning to do your design and analysis for you. But, we can’t even really give you very good direction if you can’t give some more meaningful info. You would be surprised how much an experienced engineer can glean from properly proportioned and dimensions sketches and other significant basic info. What thickness are the doubler pl. and deck pl? It isn’t that the pls. don’t come into play, its just that they probably shouldn’t come into play the way you were going about it earlier. How are all of these various pieces welded together? That will determine how they come into play in your design and analysis.

I’m not a navel architect or engineer, but I’ll bet your boss and the rest of us are talking approx. the same engineering language, some terminology may need to be ironed out. There might be ship hull forces and stresses which must be combined with the new, more concentrated, stresses from this new winch loading. You do have to make some educated/experience based judgements here, which aren’t really covered in any text book or by any magic formula. Please, please, tell us how high the cable (40T tension force) is above the deck so we can get a feel for the magnitude of the moment. Then tell us the size of the winch base and the bolt spacing and locations on the deck. Reread my last post for some of its actual engineering meaning, and answer the questions. These answers are needed to start to formulate an approach to solving this problem. How thick are the doubler pl. and deck pl., and how are the longitudinal angle ribs and the new large L beams welded to the deck, weld sizes, etc. You need this info. to start to make a judgement about how these elements work with the deck pl. as built-up structural members. Where are the winch data sheets, does anyone have any design drawing on the barge, what about your ship yard? You have to locate the winch hold down bolts with respect to the ribs and large L beam to start making sense out of this problem.

Start with what you know, the winch and winch force. What’s the moment caused by the 40T cable force, (40T)(dist. above deck), are there any variations to this? How is the moment taken out and into the deck, how many bolts, spacing, lever arm btwn. bolt rows, front and back? Can the deck pl. take these bolt loads upward and the line of compression downward, or do I need to add some pl. or structure under the deck pl. to help distribute these bolt loads? Can I situate the winch so the loads go directly into the new large L beams? I would guess that’s how and why the shipyard located these new beams, to relate to the winch base. Then what bending loads do these bolt forces induce in the rib/deck pl. or large L beam/deck pl. built-up beams?

 

[greycloud]

clearly the closer these two are together, the better

which two do u mean here?

the problem becomes very difficult very quickly since you have a continuous plate supported at many places, loaded at a bunch of other ones. i'd suggest FEA is the only reasonable way to analyze this. that said, there are always simplfying assumptions ... you might say that each H-frame load is reacted by a circle of plate, simplify to SS, and you can quickly get a plate bending moment.

i just thought of this, can't the transverse beams transfer the h-beam loads to the sorrounding longitudinal beams and thencontinue the problem like the loads are distributed among the longitudinal beams alone? it is a simplifying assumption offcourse i know that.

 

[greycloud]

I am still Are the ribs and large angle supported vertically by FR-4, FR-6 etc.?

if u mean transversly, yes they are

If the ribbed deck and large angle are spanning the entire length of the ship, a dimension which you have not provided, I would be concerned that deflections would be excessive. If, on the other hand the ribs and angle are supported by bulkheads at closer centers, that is another matter.

they are indeed supported by a bulkheads at closer centers

 

[rb1957]

"clearly the closer these two are together, the better" ... "two" refers to 1),the connection from the H-frame to the deck, and 2), the connection from the deck to the beams ... the closer these are together the less work is being done by the plate.



Quando Omni Flunkus Moritati

 

[BAretired]

At last you have provided an answer to my question. Please see the attached sketch.

Assume the force is H and is located a distance h above the deck. Then the moment is H*h. This will be delivered by the two beams shown in green to the ribbed deck. It will result in a couple, i.e. two forces, one up, one down to the green beams. The magnitude of each force will be H*h/d where d is the distance between the two green beams. If I am not mistaken, d = 914 + 216 + 1075 = 2205 mm. By the way, you should dimension to the nearest millimeter, not fractions of millimeters.

Those forces are applied to the continuous beam supported by the bulkheads shown in red. The continuous beam is the ribbed slab. The number of ribs effective in resisting the load is perhaps six (judgment call).

The span is approximately 1830 mm (distance between red lines). In the worst case, the load is approximately at midspan, so simple span M = PL/4 = H.h.L/4 where L = 1830 mm. In the other case, simple span M = Pab/L. From this, knowing the properties of the ribbed deck, you can work out the bending stresses.

You can refine your analysis with a 2D frame program but I would be inclined to accept the above approximation as sufficiently accurate for your purposes.

BA

 

[BAretired]

In addition to the two vertical forces discussed above, there is a horizontal force H. It is carried by the deck plate which must be capable of transferring the force to the hull of the ship by diaphragm action.

BA

 

[BAretired]

In the worst case, the load is approximately at midspan, so simple span M = PL/4 = H.h.L/4 where L = 1830 mm.

Oops...that should be M = PL/4 = H.h.L/4d.

BA

 

[rb1957]

yes, but this a beam approach like i imagine the OP did unitll his boss said "do a plate analysis".

this there a direct connection between the beams under the deck and the H-frame above it ?

Quando Omni Flunkus Moritati

 

[greycloud]

The magnitude of each force will be H*h/d where d is the distance between the two green beams

shouldn't that be .5d?

In addition to the two vertical forces discussed above, there is a horizontal force H. It is carried by the deck plate which must be capable of transferring the force to the hull of the ship by diaphragm action.

here u are talking about the shear force reight?

 

[rb1957]

"shouldn't that be .5d?" ... no the overturning moment H*h is reacted as a couple "d" apart ... P*d = H*h
note, this is taking the overturning moment out at the ends, and neglecting (conservatively) the contribution of the tapering forces along the sides. which is what i'd do for a quick answer, but in this case i see the loadpath to the sides as being more direct than the ends. but it's a matter of judgement.

Quando Omni Flunkus Moritati

 

[dhengr]

Rb1957:
However you cut it, BA has the right idea. You (or the OP’er.) can FEA the hell out of it if you wish, and it’ll still lead essentially to what BA has shown, because that’s how it will act, once we have some meaningful details/facts on the matter. The only thing I would add the BA’s comments is that the OP’er. had better pay some attention to the continuity of the longitudinal angle ribs/deck action over bulkhead ‘FR4 ‘, since both winch reaction forces, fore and aft, will cause increased tension on the bottom leg (horiz. leg) of the angle ribs under the front of the winch. I have some trouble imagining that the boss would have nixed BA’s presentation, if it had actually been offered in the first place. In fact, looking at his post 26AUG,1:01, 3rd para.; what he says the boss told him to do, is essentially BA’s presentation. And, more of the same in his post 26AUG,17:33, 2nd para. Again, this is an orthotropic deck plate or gridwork of beams problem, and only secondarily a plate problem.

 

[BAretired]

rb,

I think this is what the OP's boss meant by plate analysis rather than looking at individual beams. But I don't really know as I am not clairvoyant. I am assuming that the 635 mm deep beams are infinitely rigid over their short length so that deflection of those beams can safely be ignored.

If I had known that the bulkheads were acting as bearing walls, I would have suggested the above analysis much earlier. I thought the span of the ribbed slab and the large angle was the overall length of the ship. As it is, the spans are much shorter, so the above seems like a sensible and simple solution.

BA

 

[BAretired]

shouldn't that be .5d?

No! There is an applied moment of M which resolves into two equal and opposite forces of M/d.

Perhaps you are getting confused with my earlier suggestion of applying M/2 to each half of the plate which we were discussing. That was correct and I will leave you to sort that out in your head.

here u are talking about the shear force reight?

I am talking about the applied force H which your earlier sketch suggested was 40 Tonnes. It is also the value of the shear between the winch base and the deck but inside the deck, it is not a shear force. It may be a combination of shear, tension and compression...whatever is required to get the force into the structure of the ship.


BA

 

[dhengr]

Let’s the three of us watch this thread for the next two minutes and see if there are 3 or 4 more posts, and see if we aren’t just echoing each other, as our posts pass in the ether.

 

[greycloud]

thanks alot for the help poeple.