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three point reaction loads

three point reaction loads

three point reaction loads

(OP)
Sorry seem to have forgot how to calculate the reaction upon a three point beam, could someone point me in the right direction please... im am on the right path of quadratic equation given you have two unkowns?

please see attached.

thanks

RE: three point reaction loads

(OP)
thanks ill take a look.

RE: three point reaction loads

(OP)

desertfox ; after looking at this example which is almost perfect im not 100% on the workings ; never seen it done that way and confuses me, do you know of a more traditional method?

many thanks.

RE: three point reaction loads

try "three moment equation".

there are many graphical methods for solving singly redundant beams ... "moment area method"

if you're comfortable with calcs, try "unit force method" ...
(1) delete one support, solve the statically determinant beam, calculate the deflection at the deleted support,
(2) apply a unit load (opposite to the deflection) at the deleted support, solve reactions and calc the deflection at the deleted support,
(3) the true reaction at the deleted support is [the deflection from (1)]/[the deflection from (2)] * 1 lb

RE: three point reaction loads

RE: three point reaction loads

Hi Bert2

Just looking at your diagram again and I see that there is no load on the first span, only a load on the second span.
If your beam weight is very small compared with the external load on span2 which is implied by your diagram, I believe you can calculate this as a single span beam using the load and dimensions of span2 and ignore span1 completely because the reaction at the lefthand side of span1 will be very small compared to the reactions on the middle support and far righthand side of the beam.

desertfox

RE: three point reaction loads

The AISC Steel Construction Manual and many structural reference books have formulas for this condition, and you just have to plug in the loads and spans.

RE: three point reaction loads

Bert2:
As Desertfox and I suggested six or seven months ago on your 'maximum stability angle' thread #404-265967, you would benefit yourself greatly by finding yourself a local mentor or advisor.  This is not a difficult problem if you are an engineer, and it would help you if someone right there could draw sketches for you and direct you where to look, as Hokie has.  I'm not suggesting don't ask here and I'm not suggesting you should be embarrassed about not knowing things you haven't seen before, but if someone who you could interact directly with would take you under his wing you might discover a rewarding and enriching relationship and experience.

RE: three point reaction loads

if you neglect the unloaded span and solve the simply supported beam you should get a conservative answer (well conservative for bending of the beam, unconservative to the LH reaction)

RE: three point reaction loads

Classic use of FEM's and Moment Distribution.   

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: three point reaction loads

IMHO, classic misuse of FEM ... unless as a test case to compare with readily hand calc'd solutions

RE: three point reaction loads

rb1957:
I scratched my head for five minutes too, Mike couldn't really mean Finite Element Methods, could he?  Maybe, just maybe he meant fixed end moments.  But maybe he was having a moment and it got redistributed; and classics, I haven't read the classics in years and don't remember moment distribution being covered in any of them.  

RE: three point reaction loads

I'm too old for Finite Elemments, or am I?  Well that's another subject.

I was referring to Fixed End Moments, commonly used with Moment Distribution, but you were just yanking my chain, right?

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: three point reaction loads

Mike:
I was yanking your chain and rb's too, but I did scratch my head for a minute; wondering what the hell, why is Mike using Finite Element Methods and moment distribution in the same sentence here, then the light went on, you weren't pulling our chain.  You couldn't have used two such diametrically different methods for such a simple problem.   But then, only you and I and a few others on this forum even know what moment distribution is, let alone have ever used it in our daily work.
 

RE: three point reaction loads

bigsmile

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: three point reaction loads

(OP)
desertfox;

i cant upload at the moment ....?

ill keep trying to upload a more detailed drawing

i have a programme to for the loading etc, but just want to understand it better of my own back.


thanks

RE: three point reaction loads

How does the truck relate to your original problem?

RE: three point reaction loads

(OP)

i just simplified it into a basic beam with reaction calc.

which is all im after. obviously assume the body of the trailer and chassis of the cab are static with zero deflection.

RE: three point reaction loads

I see.  The problem now is that your beam is not supported as shown in your original sketch, as it is on pneumatic tyres and, I imagine, a suspension system.

RE: three point reaction loads

(OP)
im not considering the suspension or tyres, like i said before just assume there solids with zero deflection

RE: three point reaction loads

If you are only interested in that degree of accuracy, I would just consider that all the load goes directly onto the middle axle.  Then when those tires deflect, the load sheds to the outside.  I'm not a truck designer, but the appropriate bending moment might be something like P/3 x axle spacing.

RE: three point reaction loads

isn't the linkage between the cab and trailer a hinge ? ie you're not looking at the entire vehicle, so what are you looking at, i ask myself ?

it looks to me as though there's an extension on the back of the cab, which sort of looks like your original question, except of course the extension is simply supported so that isn't it.  maybe it's the cab itself, and you're considering the load from the trailer being reacted by all the wheels.

if this is it, you need to consider the flexibility of the tires if you want to get the right answer.

again, another thread unravels as the OP eventually describes the problem as nothing like the original question.  maybe if you'd posted "this is the problem i have" and "this is how i'm modelling it" and "this is the bit i need help with".

sigh

RE: three point reaction loads

(OP)

prize of $1000 for someone to point in the direction of answering my question instead of commenting on how the question was posted.

PS; rb1957 has the prize money.  

RE: three point reaction loads

we're answered, several times, the original question.

it's "just" that the pic doesn't match the original question.

you've posted that you are in fact interested in the reactions of the cab and trailer ... but isn't the linkage between them a hinge ?  

the trailer solves reasonably as a simply supported beam.  there seems to be something between the cab and the trailer, again simply supported.  the cab, again looks simply supported.

no ??

RE: three point reaction loads

(OP)
neglect the hinge and the rear axles on the trailer,

yes my original post was of the three axles on the rear of the tractor unit as i assume as a beam.

the dolly trailer i also took as simply supported.
 

RE: three point reaction loads

"neglect the hinge and the rear axles on the trailer" = neglect the trailer (no?, 'cause you're interested in the tractor unit)

the tractor has a point load from the dolly.

you can model the three rear tires as rigid supports, and we've posted how to solve this.  IMHO, neglecting the tire flexibility introduces significant error into the results.  neglecting the weight of the tractor and the neglecting trailer weight reacted by the fwd tractor tires is probably reasonable (unless you're particularly interested in these tires).

part of your problem is going to be that solving the rear tractor 3 tires as a beam will produce an up load on one of the outer tires, which is obviously unreasonable, hence you need to consider tire flexibility.

all this being said, there probably is a shortcut that has been developed for distributing a load on a rigid beam over flexible supports, with the same stiffness.

RE: three point reaction loads

Bert2:
Your problem is a classic beam on elastic springs problem.  The front axle, and the three tandem axles, and their tires and suspension are spring reactions for your beam, with some spring constants; there may be a walking beam someplace in the rear three tandem arrangement; your beam (the tractor chassis frame) has a stiffness "EI"; and when you achieve compatibility between the beam deflection and the spring deflections, you will have solved your problem.  You must consider these relative stiffness and flexibility issues to even start to get near a meaningful answer to your problem. And, that's true however you want to simplify or screw up your presentation of the real question.  Although, as in our previous meeting, your impressive picture may bear no relation to your actual question.

Your post of 13Aug10, 7:58, is really out of line; your original question or OP bears very little resemblance to the truck picture you have posted.  You got good answers to your original question.  Now, you show a very impressive picture of a truck which does not relate to your original question, and blame us for not being mind readers.  The fact is, you asked the question wrong, but these guys, for the most part, answered your question correctly and with good advice.  This is the very same thing we went around about on your post #404-265967 in FEB10.  If you don't really understand your problem, and then post a question which doesn't relate properly to the real problem, and then post a picture, to impress, which may or may not have prompted your question; you can not be mad at us for not guessing what you want.

Again, you need a local, friendly mentor of your very own, who can help you through these problems, with sketches and text books and the like.  This kind of instruction, guidance and advice is very difficult to give in words alone, when you don't understand the problem well enough to ask the question correctly.  Many of the people here are smart enough and experienced enough to be led immediately to give the correct answer for the question you asked.  However, they can't be blamed if you asked the wrong question, in the wrong way, or you are ignoring important fact of the matter and don't even know it.
 

RE: three point reaction loads

I agree fully with dhengr here.  Classic beam on elastic foundation analysis is needed.  And the the model you choose DOES affect the results.  hammer

Garbage in, garbage out.  flush

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: three point reaction loads

depending on the accuracy required, you could assume ...
1) that the wheels are equally spaced,L,
2) that each wheel unit has the same stiffness, # of tires, tire pressure, etc
3) that the "beam"/chasis/bogie stiffness is much greater than the tire stiffness

then you could apply the direct load equally to the three wheel units ... P/2/3 (/2 for both sides of the chasis)
and account for the offset between the load and the central tire, d, as a couple on the extreme tires ... P/2*d/(2L)

so the maximum load on a wheel unit is P/2*(1/3+d/2L)

but that is pretty rough ...

RE: three point reaction loads

Bert2...still good for $US1000.00? LOL!  I see nobody posted the answer.

Here's the tip, five equations in five unknowns; a guy needs to make an assumption about the stress of the beam.

This is an indeterminate, nonsymmetrical loading case so you cannot approach it in the classical sense.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

RE: three point reaction loads

I've chosen to solve the problem using Singularity Functions, noting the Boundary Conditions as the supports are immovable, fixed.

Integration of the loaded beam starting from the Intensity Function introduces two system constants, one of which becomes zero noting the extreme left hand reaction does not deflect, consistent with the above boundary conditions.

This therefore reduces the five equations in five unknowns to four equations in four unknowns.  I note three boundary conditions at the support have no deflection, plus sum of the forces in the vertical and sum of moments of the beam each equal zero.  I now have the necessary system of similtaneous equations required to draw upon the closed form solution set.

I have used a matrix to manipulate and solve for the reaction supports.  I find the extreme LHS is -1.201, the middle is 26.659, and the RHS as 1.772 units each.

Looking at the shear and bending moment diagram, I note the extreme points of bending provides a zero rotation just to the right of the middle support.  This is the point of maximum rotation.  Further analysis would reveal the maximum point of deflection, which is of particular interest to the problem in your case.

I would design the beam to resist maximum deflection at the point in question and ensure shear above the supports is acceptable.

This problem is a typical static indeterminate form since you have more supports than required.  A guy could of also tried this by Virtual Work, I seem to have remembered the Singularity Functions better from the college days, and thanks for the memories!

Fun little question.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

RE: three point reaction loads

(OP)
many thanks cockroach !!

thought it would lead that way but was un certain with that many unknowns.

 

RE: three point reaction loads

ok, how does a tire react -ve load ?

cockroach has solved (i believe) a beam on many rigid supports.

but it is on several elastic supports that can only react +ve load, no?

RE: three point reaction loads

Doesn't matter, are you suggesting that the tires significantly alter the reaction loads?  Hardly.  Besides, this would be the "steady state solution", transient effects would have dampened out to give you the static load conditions I have noted.  You need to remember that adding elastic supports greatly increases the complexity of the model, we're not looking for six decimal significant digit solutions here.

In keeping it in the general case the reactions show that the middle one takes most of the load and actually acts as a fulcrum point for the bed.  The front tires actually lift up slightly and the rear tires take a little bit better load downwards.

So the shape of the beam is like an "S" as drawn in the diagram, top left hand side.

What I would suggest is now do a second solution in the transverse direction right at the middle support.  You know that the tires on the left and right support half the computed middle load, you can now solve for deflection directly and get the overall solution for the plate at the point underneath the load.

But what is interesting is the rotation maximizing just right of the middle support.

I note that the solution is consistent with everyday observations.  If you have ever been on a loading dock, you will notice the immediate and first response of the truck once the load is placed on the bed is to have the front bumper slightly rise.  Clearly the best place for the heavy load is over the axial, is it not?  I would therefore move the load 155mm to the left of the indicated spot at present, noting the upward reaction of the LHS support is an influence on steering!

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

RE: three point reaction loads

(OP)
cockroach; the 155mm offset is the position of the "fifth wheel"

but i understand what your point is with the front axle and steering.

RE: three point reaction loads

"are you suggesting that the tires significantly alter the reaction loads" ... you better believe it ...

you solved the problem with rigid supports, right ?

how does a tire react -ve load ?? ... it can't

you Have to consider the flexibility of the supports.  you can simplify the problem by assuming equal stiffness and that the beam stiffness is much greater than the tire (ie the beam is rigid).  

talking about the front (steering) wheel confuses the problem ... i thought it was load dstribution about the three sets of tires at the back of the tractor.  if it does involve the front tires, as the previous post suggests, then the attachment of the bogie (carrying the 3 sets of tires) to the tractor chasis comes into the problem ... can't the bogie pivot on the chasis (in the vertical plane) ??

RE: three point reaction loads

RB1957, I would suggest you are greatly over thinking the problem.

As posted, Bert2 admitted simplifying the problem to get the quick and dirty answer.  Looks like most of the conversation centered about the wording of the problem, which correctly raised in later discussions, bought up the relevance of answering the question.  Typically I like to cut to the chase and answer the question, let the politicians make the federal case as life moves on.

Of course Bert2, the fifth wheel.  Didn't think of that at the time.  Pretty hard to move!  Interesting how that location induces a turning moment to the right about the axial.  I'm sure there is a reason behind the original design, I'm oilfield and not automotives so hard to say.

Anyway, cute little problem.  Hope it works out for you.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

RE: three point reaction loads

kenneth, how does a tire react a -ve load ?

RE: three point reaction loads

My basis was downwards as positive, the front end lifts up so the negative implies opposite sense or upwards.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

RE: three point reaction loads

again, how does a tire react -ve load ? ...

it can't ... the three tires will compress under the load with a small change to react the moment, but all tires Must have +ve (= compression) reactions.

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