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
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
BA
RE: 3D reaction force calculation
RE: 3D reaction force calculation
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
BA
RE: 3D reaction force calculation
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 bed
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
Very strange support conditions.
BA
RE: 3D reaction force calculation
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
RE: 3D reaction force calculation
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
BA
RE: 3D reaction force calculation
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
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
RE: 3D reaction force calculation
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 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
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
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
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
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
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 A = 633N (+250kgf)
Quando Omni Flunkus Moritati
RE: 3D reaction force calculation
BA
RE: 3D reaction force calculation
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
BA
RE: 3D reaction force calculation
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
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
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
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
Mike McCann
MMC Engineering
RE: 3D reaction force calculation
I don't know what that means.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: 3D reaction force calculation
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
BA
RE: 3D reaction force calculation
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
RE: 3D reaction force calculation
BA
RE: 3D reaction force calculation
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
BA
RE: 3D reaction force calculation
I thought if was a friendly discussion and not an argument. But never mind the semantics
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
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
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
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
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
RE: 3D reaction force calculation
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
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
Regards
Thomas
RE: 3D reaction force calculation
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 (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
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
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
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
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
Friendly Regards
Thomas
RE: 3D reaction force calculation
failed again, sigh
Quando Omni Flunkus Moritati
RE: 3D reaction force calculation
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
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
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
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