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3D reaction force calculation
2

3D reaction force calculation

3D reaction force calculation

(OP)
Hello,
I wish to calculate the reaction force at Cz to keep the structure in equilibrium.

The linked diagram shows a platform that weighs 500kg.
The platform has a point load 1.9KN.
The platform size is 2.8m long x 0.9m wide and it is restrained by two shafts on opposing corners, free to rotate axially.


Link

RE: 3D reaction force calculation

Is this a trick question? Looks like the 500kg platform will be shared equally by supports A and B. Support C will not participate in supporting the platform. Supports A, B and C will each carry 1/3 of the concentrated load. So Cz = 1.9/3 = 0.63kN.

BA

RE: 3D reaction force calculation

Agree. Support C can't react under the self weight or it would spin about the diagonal axis. For the point load; taking moments about the x axis gives 1.9*0.6/(2*0.9)=0.633 for each reaction B and C. So A is 0.633.

RE: 3D reaction force calculation

I disagree, on my recent record I may regret this.
Moments about A<>C, says that the reaction at B must be half the load and the sum of the reactions at A & C, must also be half.

Moments about B<>C say that the reaction at A is one third, therefore the reaction at C must be one sixth.

A =0.633, B = 0.5 and C = 0.317.

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: 3D reaction force calculation

The sum of your reactions is 1.45kN, Michael.

BA

RE: 3D reaction force calculation

Oops. B should be 0.95 (0.5x1.9) I didn't finish the multiplication for B.

Corrected. A =0.633, B = 0.95 and C = 0.317 and a total of 1.9.

I must stop doing these on my way to bednosmiley

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: 3D reaction force calculation

I believe, contrary to my first post, that the structure is indeterminate. The reaction at C cannot be found by statics alone. Paddingtongreen's solution would be correct if supports A, B and C were hinged in all directions. As it is, supports A and B are hinged about the X axis but not about the Y axis. It is not possible to solve for the reaction at C by taking moments about line A-C because we do not know that My is zero at supports A or B. The reaction at C is redundant as the structure is stable without it.

Very strange support conditions.

BA

RE: 3D reaction force calculation

I should have added:

We can say that the reaction at A is P/3 and the sum of the reactions at B and C is 2P/3 but we cannot determine how that is distributed between B and C without more information.

BA

RE: 3D reaction force calculation

OK, I took moments about the wrong axis.

RE: 3D reaction force calculation

1. The platform weight is totally carried by A and B.

2. If we sum moments about the diagonal between A and B, we can determine force C that will resist the OTM due to the 1.9Kn load.

3. Then it is just a matter of statics to distribute the 1.9Kn vertical load between points A, B, and C based on the relative distances between the supports to the load.

I see this as a determinate problem for the vertical forces and moments. Am I missing something here?

Mike McCann
MMC Engineering

RE: 3D reaction force calculation

Yes, Mike. The problem is indeterminate to the second degree. You cannot sum moments about the diagonal A-B to find the reaction at C because the platform is not free to rotate about axis A-B.

BA

RE: 3D reaction force calculation

I agree with BAretired (revised).

Dare I suggest that a simple FE Analysis would be informative?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: 3D reaction force calculation

Hi

Maybe I am missing something but how about this. Three equations and three unknowns.

First the 1.9 kN load.

M_AC: 1.9*1.4-Bz*2.8=0 : Bz=0.95
M_BC: 1.9*0.3-Az*0.9=0 : Az=0.63
Vertical: Cz=1.9-0.95-0.63=0.32
Ay=By=0

The same approach for platform means that Az and Bz share the load 50% each.

If there are no locked rotations at the supports this should work.

So, am I correct or not?

Thomas

RE: 3D reaction force calculation

The simple solution that several of us have proposed, is only valid if the three supports are all pinned in all directions. The pipe extensions imply that rotation about the Y axis may be restrained at A and B, making it a statically indeterminate problem.

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: 3D reaction force calculation

Reaction A in the vertical direction can still be found even with y-moments restrained at A and B by summing moments along the axis that connects B and C in the along x direction. But then it is sill 1 degree indeterminate and that does not include Ay and By.

I don't see any simplifying assumptions to solve it with taking into account deformation compatibility. I am going to make an FE of it out of curiosity.

RE: 3D reaction force calculation

Haynewp, let us know of the results as well as the assumptions that you made.
paddingtongreen, we can approximate pin connections by supporting the pipe extensions A and B solidly imbedded in the slab, and at support C;, otherwise, you are correct being a statically indeterminate problem.

RE: 3D reaction force calculation

chicopee, I already posted the determinate answer, however, as we usually do, one or more of us, in this case, BA, re-looked at the interpretation of the diagrammed supports.

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: 3D reaction force calculation

Here is the file, there's not much to it. Varying the thickness of the plate of course varies the reactions. I used steel for the material and english units because I don't like metric. I used the moment fixed at A and B about the y axis only. Horiz and vert reactions at A and B restrained. Vertical roller at C.

One thing I am not sure of is how RISA treats "RIGID" material in FE. I tried using it instead of steel and I don't get any joint deflections but I get rotations. I have temporarily lost my RISA access..

RE: 3D reaction force calculation

sorry but what am i missing ?

a down load of 1.9kN, causing a moment of 299Nm about the axis 1-2.
C is off-set from 1-2 by 0.857m
reaction at C = 349N
reaction at A and B = 1551/2N + 250kgf

no?

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

my numbers were a little off ...

ptC is off-set 0.857m from the axis 1-2,
but the load point is 1/6 of this (at point C the y-component of the offset is 0.9m, and the loading point it is 0.15m)

so the reaction at C is 1900/6 = 317N

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

and B = 950N (+250kgf)
and A = 633N (+250kgf)

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

rb1957, what you are missing is the fact that the structure is indeterminate so your method is not valid. It would be valid if supports A, B and C were hinge/rollers but they are not. Supports A and B are free to rotate about the X axis but not about the Y axis.

BA

RE: 3D reaction force calculation

If the boundary conditions that I assumed together with several others are correct, than that solution should also be correct. That is the solution that rb1957 has given.

I guess the only one who can clarify is the OP and he seems to be offline. We'll just have to wait and see I guess.

Thomas

RE: 3D reaction force calculation

haynewp, I couldn't make any sense of your link, but it seems to me that if the platform is deemed rigid, there should be no deflections and no rotations, thus the reaction at point C should be zero.

BA

RE: 3D reaction force calculation

Do you have RISA? You need it to open the file.

I agree. I am not sure how RISA treats "rigid" material. It gives a solution to the reactions with rotations and not deflections. I don't really get it. I am temporarily locked out of the program right now due to a VPN issue.

RE: 3D reaction force calculation

@BA ... i guess we're free to read the sketch as we want. for all we know A and B could have spherical bearings, or a hoop of piano wire. the sketch could be a little off, and the dowels and A and B could be along the 1-2 axis

sure, to include the My moments at A and B the load causes a moment about the 1-2 axis, reacted by the vector sum of MyA, MyB and MC

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

Quote:

The platform size is 2.8m long x 0.9m wide and it is restrained by two shafts on opposing corners, free to rotate axially.

Expressio Unius Est Exclusio Alterius : the expression of one thing is the exclusion of the other

In this case the statement that the shafts are free to rotate axially implies that they are not free to rotate about the Y or Z axes.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: 3D reaction force calculation

See attached images from an analysis in Strand7.

Increments are:
1) Self weight
2) Point load
3) 1) + 2)

The plate was assumed to be steel 25 mm thick (with the density adjusted to give a mass of 500 kg).
Nodea A and B were restrained in position and for rotation about the Y axis.
Node C was restrained in the Z direction only.
Tabulated reactions are at point C.
Deflections are scaled by 100

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: 3D reaction force calculation

No. Thhe shafts can still deflection t from gravity loads.

Mike McCann
MMC Engineering

RE: 3D reaction force calculation

Quote:

No. Thhe shafts can still deflection t from gravity loads.


I don't know what that means.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: 3D reaction force calculation

The platform has a mass of 500kg or a weight of about 4.88kN. The reaction at C was 0.1 kN, not very large compared to the total weight, so the bulk of the dead weight is carried by supports A and B.

The reaction of 0.3184kN at C due to the concentrated load is very close to the value found by others assuming completely hinged supports, namely P/6 or 0.3157kN. I would not have expected it to be larger than 0.3167 but smaller as it seems to me that any restraint at supports A and B would tend to reduce the reaction at C, so I am wondering why those restraints actually increased the reaction at C. That is not clear to me at the moment. Perhaps someone can shed some light on that.

BA

RE: 3D reaction force calculation

*** 0.3157kN should read 0.3167kN

BA

RE: 3D reaction force calculation

BA - good question. It does seem anti-intuitive, but I presume it is due to the combination of the reaction due to the moment restraint plus the torsion between point A and point C.

I checked it with pinned supports at A and B, and it does give the correct reaction for that case (see attached image).

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: 3D reaction force calculation

And the real winner in all this is mdc1973!

RE: 3D reaction force calculation

Thanks Doug. Nice presentation.

BA

RE: 3D reaction force calculation

Hi again

I would say that the OP needs to clarify the sketch. On the sketch there are five reactions implied and that's it. For some reason some posters have added some extra constraints. Maybe the rods at A and B is just something to attach a wire hoop.

If the five reactions are all there is then the solution came in one of the early posts. A simple hand calculation.

I'll wait for the OP to clarify.

Regards

Thomas

RE: 3D reaction force calculation

ThomasH, Five reactions are two too many. Nobody has added extra constraints. The structure is indeterminate and cannot be analyzed by statics alone. Why do you persist in arguing?

BA

RE: 3D reaction force calculation

BAretired:

I thought if was a friendly discussion and not an argument. But never mind the semantics smile.

You say five reactions. In the figure there are five: Ay, Az, By, Bz and Cz. Do you have any others?
Some have mentioned constrained rotations but I cant see that in the figure.

If we agree on the five reactions, then i believe there is a solution.

Friendly Regards

Thomas

RE: 3D reaction force calculation

ThomasH:

In that case, each joint has 6 potential constraints, namely Fx, Fy, Fz, φx, φy and φz. Joint A has 5 constraints as φx is zero (free to rotate about the x axis). φz does not enter the picture so it is assumed to be zero also, leaving only 4 constraints for Joint A. Joint B has 3 constraints, Fx, Fz and φy. Joint C has only Fz. So, looking at it that way, the number of constraints is 4 + 3 + 1 = 8.

BA

RE: 3D reaction force calculation

Correction:

Joint B has 3 constraints, Fx, Fz and φy.
should read:
Joint B has 3 constraints, Fy, Fz and φy.

BA

RE: 3D reaction force calculation

BAretired:

Then perhaps you can understand my question. The figure has five stated constraints. You mentioned five constraints, but not those five. Instead you have "added" two based on your interpretation of the figure. And also skipped two that are in the figure smile. Hence, the question.

In your first post I believe you had the same interpretation as I have. Then you changed it for some reason. Maybe your latest interpretation is correct, maybe not. Only the OP can clarify that.

But I disagree on your statement that it can't be analyzed by statics alone. It is a static problem.

Friendly Regards

Thomas

RE: 3D reaction force calculation

This has been an interesting thread, with some of E-Tip’s sharpest members participating, with some slightly different interpretations of what’s really going on. What distresses me lately is that a fairly large percentage of the OP’ers. who come here don’t understand their own problem well enough to explain it in a meaningful way to other smart engineers. They leave us guessing. They’ve got some wild assed Rube Goldberg idea with no idea how it works, and actually think that is good engineering. And yet, they claim/pretend to be engineers or capable technical people. The number of poorly defined problems and questions that are presented here is really scary. Too many of the members seem to be designing and building a bunch of crap for the general public without even being able to define what they are doing, how it really works or why that strange arrangement is needed, and still they are pushing that stuff out the door, and thinking that’s good, and safe design.

RE: 3D reaction force calculation

ThomasH,

In my first post, I recognized that, due to the two hinges about the X axis, it was possible to solve for the reaction at A which I found to be P/3. I could see that the sum of reactions at B and C had to be 2P/3 and because P was halfway between the two, I erroneously jumped to the conclusion the BC reaction was split evenly between B and C.

I then realized that, not only was I wrong but it was not possible to calculate the split between B and C because there were unknown moments acting on A and B which could not be solved by statics alone. IDS came up with a solution by considering some assumed properties of the plate. As you can see, his analysis for the point load is substantially different than his later analysis using your assumptions.

And finally, it may be necessary to ask the OP what he meant to say but it is not necessary to ask him what he did say. His first post left no room for guesswork.

BA

RE: 3D reaction force calculation

BAretired:

Regardless of if my interpretation or your interpretation of the constraints is correct, the problem seems to me to be static. It may be indeterminate but that does not make it less static. I can't see any need to use dynamics.

As for the correct boundary conditions, we may never know since the OP seems to have left the discussion smile.

Regards

Thomas

RE: 3D reaction force calculation

ThomasH,

Nobody is suggesting that dynamics must be used. The problem is statically indeterminate which means compatible deformations must be considered in order to arrive at a solution.

A beam with fixed ends is also statically indeterminate by definition.

BA

RE: 3D reaction force calculation

if there is no My restraint at A and B then it is statically determinate.

if there is (My restraint at A and/or B) then it is statically indeterminate (just as a doubly cantilevered beam is statically indeterminate, or "hyper-static" in today's lingo). it does seem odd (but not wrong) that these fixed end moments are penalising redundancies, as shown by the increase in Cz based on the posted FEA results.

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

BAretired,

I know exactly what it means.

It was not me who stated "could not be solved by statics alone". That was the reason for my comment.

I'll think I will just leave it for now. We'll see if the OP comes back and if he has any comments.

Regards

Thomas

RE: 3D reaction force calculation

rb1957,

Quote (rb1957)

if there is no My restraint at A and B then it is statically determinate.

if there is (My restraint at A and/or B) then it is statically indeterminate (just as a doubly cantilevered beam is statically indeterminate, or "hyper-static" in today's lingo). it does seem odd (but not wrong) that these fixed end moments are penalising redundancies, as shown by the increase in Cz based on the posted FEA results.

I agree with you except for your example (a doubly cantilevered beam is statically determinate), but I get the idea. As for the penalising of Cz, it made only a slight difference, presumably because My at A was greater than My at B. However, it made a huge difference to the magnitude and sign of the moments within the plate itself.

ThomasH,

Are we still having a friendly discussion? Perhaps I should have said "could not be solved by the equations of statics alone". Those equations state that the sum of forces and moments in each principal direction must add up to zero.

BA

RE: 3D reaction force calculation

is that the sound of hairs being split ?

smile, remember the adage about arguing with an engineer and mud wrestling with a pig ...
or was it arguing with a pig and ...

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

BAretired,

We are still friendly (I hope). But I think you perhaps should be open to the possibility for other interpretations than your own. I thing the tread proves that there is more than one possible interpretation for the boundary conditions.

And:

You have six equations for static equilibrium. They may or may not be enough depending on the boundary conditions. If they are not enough you add criteria for deformations, based on (again) static assumptions. They are all static equations, some for equilibrium others for deformations. Correct?

You can add dynamics but in this case if would be very redundant.

And I can agree with rb1957 that it is a bit of splitting hairs. But since the way of communication in this case is written posts I can only comment on your written comments, do I agree or not. And when you say that statics isn't enough, I disagree. But I hope we still can be friends.

rb1957:
I think the line is: Arguing with an engineer is a bit like mud wrestling with a pig. After a while you realize that he likes it smile.

Friendly Regards

Thomas

RE: 3D reaction force calculation

agreed (with the aruging/wrestling line) ... i was trying to have a little fun with it ...

failed again, sigh

Quando Omni Flunkus Moritati

RE: 3D reaction force calculation

rb1957:

I apologize for ruining your joke, I missed that one.

But I agree with the statement. 50+ posts for a fairly simple problem, that is a bit excessive.

Regards

Thomas

RE: 3D reaction force calculation


Quote:

But I agree with the statement. 50+ posts for a fairly simple problem, that is a bit excessive.

As often here, the back-story is more interesting than the original question.

I do think it is interesting (and instructive) that some think the ambiguous diagram in the OP is quite unambiguous, especially since there are (at least) two different versions of what it unambiguously shows. FWIW, I think the most likely interpretation is that rotation about the Y axis is intended to be restrained, since rotation about the X axis is explicitly stated to be released. In any case, in any real structure the % restraint would be something between 0 and 100, so we should look at both cases.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: 3D reaction force calculation

ThomasH, if you really think that repeating that it is a statically determinate problem will make it so, no matter what, you are mistaken.

If those are trunnions at A and B, that is, restrained in all directions and restrained from rotation about the vertical and Y axes, the result is in the platform, unless it is rigid within itself, but we are structural engineers so we know that cannot be.

Dynamics are not involved here, they are not required to make a structure statically indeterminate.

OPs frequently try to simplify a problem and in doing so change it. When the answers do not suit, more info emerges. The fact that the OP in this case had to ask seems to imply that there is more than the simple problem we all answered at the beginning.

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: 3D reaction force calculation

BAretired, IDS, paddingtongreen,

Ok, I will try to explain my reasoning and perhaps also apologize.

First, I completely that repeating a wrong answer does not make it correct. That is obvious.

Now if we look at the structure. It is a rectangular plate supported in three corners. Regardless of the support conditions it is a fairly simple problem. I would give it to any engineer on his/her "first day" at work and expect it to be solved. Either "by hand" or by using a computer.

It does not require any dynamics, on that we agree. And perhaps I was a but to stubborn regarding the statics so I just apologize.

As for the support conditions. Perhaps you are correct, I don't know. But I have seen this type of supports in a figure before (in an old textbook). And this leads to my final observation. This is the OP first post, on his first day of membership. This was one of my first observations since I thought the question was fairly simply. So there is no history. Student posting, perhaps. Again, I have no idea.

Now if I have irritated anybody, I apologize. That was never my intention.

Best Regards

Thomas

RE: 3D reaction force calculation


ThomasH,

There is no need to apologize, so far as I am concerned but if you are apologizing, then apology accepted. It is probably time to put this issue to bed.

Best Regards,

BA

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