×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Three unequal supports, two concentrated loads problem..

Three unequal supports, two concentrated loads problem..

Three unequal supports, two concentrated loads problem..

(OP)
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.

RE: Three unequal supports, two concentrated loads problem..

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

RE: Three unequal supports, two concentrated loads problem..

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

RE: Three unequal supports, two concentrated loads problem..

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

Regards.

RE: Three unequal supports, two concentrated loads problem..

Of course.

RE: Three unequal supports, two concentrated loads problem..

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.

RE: Three unequal supports, two concentrated loads problem..

(OP)
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.

RE: Three unequal supports, two concentrated loads problem..

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

RE: Three unequal supports, two concentrated loads problem..

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.

RE: Three unequal supports, two concentrated loads problem..

(OP)
No probs - shall be back in a day or two smile

RE: Three unequal supports, two concentrated loads problem..

(OP)
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.

RE: Three unequal supports, two concentrated loads problem..

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.

RE: Three unequal supports, two concentrated loads problem..

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.

RE: Three unequal supports, two concentrated loads problem..

(OP)
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 smile


Regards.

RE: Three unequal supports, two concentrated loads problem..

Truckdesigner, Can you do moment distribution?

RE: Three unequal supports, two concentrated loads problem..

(OP)
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...

RE: Three unequal supports, two concentrated loads problem..

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.

RE: Three unequal supports, two concentrated loads problem..

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.

RE: Three unequal supports, two concentrated loads problem..

Hi truckdesigner

I am looking at solving your beam, perhaps tomorrow or saturday i might get to post a solution.

desertfox

RE: Three unequal supports, two concentrated loads problem..

I'm with hokie here, stuff this this is very standard and suits spacegass to a tee. No need to waste your time doing moment distribution etc. If you want verification post your output and I'll quickly run the model myself for a check  

RE: Three unequal supports, two concentrated loads problem..

the on-line calculator will work just as well, it's set up for metric but it'll work just as well with your imperial units.  then run your FE to check.  then try a textbook solution.

i think you may have been looking for precisely this problem but the general problem (an indeterminate beam) is (should be) in just about every textbook.  the 3 moment equation works well (looks a little scary but it is easy to apply), unit force method is an approach i'd use.  google "indeterminate beam", "3 moment equation", "unit force method".

RE: Three unequal supports, two concentrated loads problem..

I believe that (3-Moment equation) method is the fastest and easier for hand calculation.

If you will use plastic analysis there is very simple method related to work or energy (don't remember the exact name). you can solve this problem in a half page or less by that method.

Note (As I understood, the loads are not moving, if they moves you might need to draw the influence line).

Regards

RE: Three unequal supports, two concentrated loads problem..

For plastic analysis
try to get this book:
Plastic methods for steel and concrete structure - by Stuart S.J.Moy.

The method written in my previous post is (virtual work method).

It allows you to find the collapse load, then you can compare it with the applied loads. or If you want the applied loads to be the collapse load you can find the plastic moment then determine the steel section to be used.

regards

RE: Three unequal supports, two concentrated loads problem..

yeah, that's the unit force method

RE: Three unequal supports, two concentrated loads problem..

My fourth edition of Hibbler has chapter 12 titled "Deflections of Beams and Shafts" and 4 of the 9 sub-sections starts with the three words "Statically Indeterminate Beams." Assuming this wasn't removed between the 4th and 6th editions, I don't know how much more attention you could ask for in a textbook that is pretty general mechanics.

-- MechEng2005

RE: Three unequal supports, two concentrated loads problem..

Superposition was mentioned previously, and BA's approach is one application of the principle.  You could also remove the support at point 2, find the deflection at that point and the load required to produce that deflection if applied at point 2, and add the bending and shear diagrams.

RE: Three unequal supports, two concentrated loads problem..

handex has the correct answer.  R3 should be 11.44, not 10.9, but the formula I gave in my last post was okay.

BA

RE: Three unequal supports, two concentrated loads problem..

People are saying its "routine" because they aren't admitting to the fact that they are using software surprise

RE: Three unequal supports, two concentrated loads problem..

R3 has been worrying me. Why is it there. It is a liability in that it places more force on R2.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Three unequal supports, two concentrated loads problem..

paddington,  I agree it doesn't seem to make a lot of sense.  It's only advantage seems to be that it reduces the maximum moment on the beam from 42 T-m to 34.5 T-m.  Maybe truckdesigner can tell us why they are building it that way.

BA

RE: Three unequal supports, two concentrated loads problem..

release the RH support and apply the load ... the RH end of the beam is deflecting upwards ... so the reaction here has to keep the end from deflecting, so you get a -ve reaction (increasing the reactions at the other two points).  the OP gave an explanation for this construction ... but it's not something i completely understand

RE: Three unequal supports, two concentrated loads problem..

Hi truckdesigner

My soluton as promised, my answers are those of handex.
Also if you convert your beam to english units and use the on line calculator I provided you will obtain similar results, I say similar results because you can't place more than one point load per span, just put a resultant force of 80T on span 1.

desertfox

RE: Three unequal supports, two concentrated loads problem..

(OP)

Folks - to say that I am overwhelmed by the responses is an understatement! Thank you all so much for your advice, concern etc.

I got the exact same result as handex with the Space Gass model, so am confident with its accuracy. I am still battling with the hand calculation to be honest, but when I get some time (after hours) I will sit down and nut it out.

I have attached a photo of the frame in question. We are widening the "working area" to four metres so wanted to check for Max. Bending Stress. I have spoken to another Engineer - one with a little more structural experience than I, and he has told me that two "310 UC 118" members welded side by side will be more than enough, so all good. This is a stock Australian Standard beam. "Full penetration weld all around" of course.

Looking forward to my next encounter with this forum.

Regards.  

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources