Three unequal supports, two concentrated loads problem..

[truckdesigner]

Attached is a loading diagram that I have come across for a test gantry we are building.

I have not come across such an abnormal loading set-up before, and cannot find any literature that addresses my problem ie. shear and bending moment diagrams and Max shear and bending moment.

Can somebody please help me?

Regards.

 

[desertfox]

Hi truckdesigner

Your beams statically indeterminate, have a look at this site and scroll down to the "three moment equation" "under continous beams"
thats a theory you could use.

http://www.roymech.co.uk/Useful_Tables/Beams/Continuous_Beams.html

desertfox

 

[weab]

No literature addresses this loading? Try a structures textbook. Or try superposition of beam formulas from the steel manual.

 

[hokie66]

Moment distribution, three moment method, superposition, maybe even a simple plane frame program...not abnormal, this is routine.

 

[truckdesigner]

Can I use Space Gass to analyse this - given that it is statically indeterminate?

Regards.

 

[hokie66]

Of course.

 

[Ron]

Since this is a gantry, I would assume the loads will move. If so, are you sure this is your worst loading case? Check it...considering moment, shear and column interaction.

As hokie66 noted...routine analysis.

 

[desertfox]

Hi truckdesigner

Try this free online calculator for continous beams:-

http://www.epcserver.com/Structural/analysis/beams/continous1.asp

but remember to check it against a hand calc.

desertfox

 

[truckdesigner]

Thank you all for your replies. Abnormal to me is this particular scenario - it has been a while since I have to do anything out of the ordinary with regards to beam bending etc.

Anyone care to donate an example of a hand calculation of this?

Regards.

 

[Ron]

TD...take a shot at it..post your calcs...someone will check and comment.

 

[dhengr]

Truckdesigner:
Is your structure a trailer with an 80 ton load on it, composed of the two 40 ton line loads across the trailer? Are reactions R2 & R3 actually axle sets supported by springs or air suspension? The trailer is a beam with some elastic stiffness, and R2 & R3 are reactions with some spring stiffness. And, there should be compatibility btwn. the beam and those two reactions as they deflect under the load.

 

[truckdesigner]

No probs - shall be back in a day or two

 

[truckdesigner]

It is the top of a test frame/gantry we use to load test various lifting equipment. The 40 tonne loads are from an 80 tonne hydraulic ram that push up on the 6500 mm beam.

There is only a 4000 mm working span of which we can place the item to be tested.

 

[gobsmacked]

I find it easier to approach this using plastic theory, assuming collapse in the left hand span. Ignoring beam self weight put the left hand load at 1525 from the left support. An elastic analysis wouldn't be exactly the same but would be fairly close. For what its worth I made the plastic moment 1070 kNm, but no safety factor was applied to get this result.

 

[rb1957]

if you use the online calculator desertfox posted above, you can apply only one load per span. this is fine, use superposition ... apply one load, get the reactions and maybe the moment curve. then apply the second load and add onto the first ... add the reactions (load1+load2), add the moment curves ... do not add the maximum moment from load1 to th emaximum moment from load2 unless you're sure they occur at the same place in the beam. then you can check your results with your FEA.

 

[truckdesigner]

Among currently doing many other things I am still battling with this one. I must say I can't see how this is "routine analysis" when I consider the fact that my sixth edition of Hibbeler Mechanics of Materials and my third edition of Beer and Johnson barely touch on it.

If it were routine there would be tables set up as there is for simply supported beams...

Anyhow - I'll stay in touch


Regards.

 

[gobsmacked]

Truckdesigner, Can you do moment distribution?

 

[truckdesigner]

I can and have before but as I have said - it's been a a while. I am still going back over old jobs etc to jog my memory...

 

[hokie66]

Why didn't you just use SpaceGass? It is easy to use and well verified. For such a simple problem, should take about two minutes. I don't usually recommend using programs unless you can do it by hand, but in this case just making sure the reactions add up and the moments look right should suffice.

 

[dhengr]

Truckdesigner:
One might ask how you get two 40ton downward loads from an 80ton hydraulic ram pushing up on your beam? Then, one might ask, if you are designing and going to build this testing structure (gantry) why are you going out of your way to make it more complex by making it indeterminate? Finally you might want to consider getting an engineer involved in this design and analysis if the good suggestions above are meaningless to you. Most engineers, during their careers, run across several problems which aren’t exactly covered by an example problem in a text book or covered by a tabulation which fits every possible problem and condition. Real engineering involves engineering experience and judgement, which is gained by practicing real engineering, and during the early stages of this development a local mentor is really beneficial. You can both be looking at the same specs. and drawings, do some quick sketches on the spot, and he/she can direct you where to look and how tackle exactly this kind of problem.