3D Statics problem 1

[Heckler]

I need a little help on this 3D statics problem. Any takers?

Heckler
Sr. Mechanical Engineer
o
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This post contains no political overtones or undertones for that matter and in no way represents the poster's political agenda.

 

[corus]

Resolve the forces and moments in all 3 directions to calculate whatever it is you need. Otherwise use a finite element program.

Tara

http://tinyurl.com/4ydjg7m

 

[prex]

In a 3D statics problem you have 6 equilibrium equations, so you cannot resolve a set of forces/moments into more than 6 components (but usually less, as some of the equations may be trivial or unrelevant).
You can go farther only by introducing a structural link between the loads and the reactions.

prex

http://www.xcalcs.com

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[rb1957]

this is a highly redundant problem ... 4 fully fixed attachments, 24 reactions, 6 equations of equilibrium ... 18 redundancies.

one solution would be FE, determining the reactions from the stiffness of the internal structure.

another solution would be to assume effectively an equal stiffness for all the reactions, and mathematically solve the overdefined matrix (google "least squares solution for overdefined set of equations").

another approach, assume your 4 reaction points are pinned (rather than fixed), though that still leaves 6 redundancies. a solution is to solve for each pair of reaction points (6 reactions = 6 equations of equilibrium). this'll give 6 different sets of reactions, assume the average is a reasonable solution.

 

[rb1957]

a simple answer ...

react the applied load so that A and B react 31.46/45.25*1175 = 817 lbf and C and D react 358 lbs. Then A reacts 20.25/17.12 = 990 lbs and B reacts -173 lbs; C reacts 13.25/11.25*358 = 422 lbs and D reacts -64 lbs. check ... 990-173+422-64 = 1175 lbs.

another approach ... each reaction point reacts load along a vector between the point and the load ... now only 4 unknowns ...

 

[msquared48]

I agree with RB. Otherwise, crank it into RISA 3D.

Mike McCann
MMC Engineering

 

[Heckler]

I am running this model in a FEA program but want to see if I could solve the problem by hand.

RB can you expand on your method. I'm having trouble following your path. Thanks

Heckler
Sr. Mechanical Engineer
o
_`\(,_
(_)/ (_)

This post contains no political overtones or undertones for that matter and in no way represents the poster's political agenda.

 

[rb1957]

i gave you several alternatives ... different ways to skin the cat, depending on how accurate you want to be.

if your 4 pts are truly fixed then the problem is quite intractable for a hand calc.

if you run your FE with pinned pts then you'll get something to compare with hand calc and something to show you how critical are the reaction moments.

for a hand calc to compare with this, try ...
1) assume the reaction at each point is along a vector between the point and the load, so the three compenents at each point are direction cosines of the resultant reaction ... 4 unknowns reasonable to solve; or
2) assume only two reaction points are effective (say A and B). solve the equations of equilibrium. again for a different pair (A and C) and so on ... 6 combinations, 6 different results, the average is probably a reasonable compromise.

 

[rb1957]

btw, if you'd said in your initial post "i'm looking to do a hand calc to verify my FE ..." you would have saved us the suggestion of using FE to solve this !?

 

[rb1957]

a thought, you could extend solution 2) to include fixed reaction points ... assume a single fixed point is effective, four solutions, the average should be a reasonable guess to compare with fixed FE results.