3D reaction force calculation 2

[mdc1973]

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

 

[BAretired]

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

 

[haynewp]

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.

 

[paddingtongreen]

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

 

[BAretired]

The sum of your reactions is 1.45kN, Michael.

BA

 

[paddingtongreen]

Oops. B should be 0.95 (0.5_x1.9) 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 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

 

[BAretired]

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 M_y 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

 

[BAretired]

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

 

[haynewp]

OK, I took moments about the wrong axis.

 

[msquared48]

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

 

[BAretired]

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

 

[IDS]

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/

 

[ThomasH]

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

 

[chicopee]

I agree with some of the responders, it can be solved by Statics alone. Please see the attachment.

 

[paddingtongreen]

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

 

[haynewp]

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.

 

[chicopee]

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.

 

[paddingtongreen]

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

 

[haynewp]

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..

 

[rb1957]

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?


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