Roark's Beam Formula Superposition Question
Roark's Beam Formula Superposition Question
(OP)
Hello Everyone.
I have a beam bending problem that I am currently working on (please see the attached .pdf).
I am looking for the max deflection of the beam.
A colleague gave me the direct formula from Constrado, "STEEL DESIGNERS' MANUAL," Fourth Edition, pg. 43.
However, I am a Roark's fan and I would like to know how to solve the problem using Roark's bending tables. Roark's doesn't give the direct formula, but I can't help but think that you can solve this using superposition or some other neat manipulation.
You can see my attempt on the attached .pdf, but it doesn't work out (I came out too low). I checked the solution using FEA and confirmed the direct formula result.
Does anyone know how to manipulate Roark's formulas to get the correct result?
I am going nuts trying to figure it out.
Thank you!
I have a beam bending problem that I am currently working on (please see the attached .pdf).
I am looking for the max deflection of the beam.
A colleague gave me the direct formula from Constrado, "STEEL DESIGNERS' MANUAL," Fourth Edition, pg. 43.
However, I am a Roark's fan and I would like to know how to solve the problem using Roark's bending tables. Roark's doesn't give the direct formula, but I can't help but think that you can solve this using superposition or some other neat manipulation.
You can see my attempt on the attached .pdf, but it doesn't work out (I came out too low). I checked the solution using FEA and confirmed the direct formula result.
Does anyone know how to manipulate Roark's formulas to get the correct result?
I am going nuts trying to figure it out.
Thank you!






RE: Roark's Beam Formula Superposition Question
I think you should be using 2d on page 100, for beams.
The one on page 157 also has the axial "P" load added, which is not your case.
Try page 100.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Roark's Beam Formula Superposition Question
Have a look at the first site below under Beams -> Single beam -> Fixed-fixed -> Distr.load : you'll be able to cross check your formulae.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Roark's Beam Formula Superposition Question
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Roark's Beam Formula Superposition Question
msquared48
I am using Roark's, 7th ed. and I am using case 2b on pg.192. Which edition are you using? I don't see any other bending tables 50 or so pages earlier. I will try to hunt down your edition around the office.
prex
You are correct. In the direct formula W is total load (i.e. 6,750lb). In Roark's w is unit load (i.e. 121 lb/in). I will look at your recommended websites when I get home.
IDS
The load you are using is correct, but I am not getting the same result. I just checked and doubled checked and I am still getting 0.0722 in max deflection in the middle. The beam is a W8 x 18 and I modeled it and checked it with CosmosWorks and got 0.07... as well.
Am I still missing something?
RE: Roark's Beam Formula Superposition Question
take the example of a UDL y = wL^4/(384*EI) ... you combined the distributed load (lb/in) with L^4. since the bracket has only L^3 the load is in lbs (not lb/in)
your superposition is fine (seems to give the right answer !)
RE: Roark's Beam Formula Superposition Question
Are you certain that you used the correct values of a in the Roark formulas, during superposition? These definitions change in the various configurations, and a spreadsheet approach (like several of my incorrect ones) could result in this error.
tg
RE: Roark's Beam Formula Superposition Question
Please disregard my last post, now that I have done the calc myself.
I get the same results as you - I am stumped as well...
tg
RE: Roark's Beam Formula Superposition Question
I am using the fifth edition...
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Roark's Beam Formula Superposition Question
My results are attached, (0.0604, the same as Rourke).
(EVAL() is a UDF by the way, but entering an Excel formula in the usual way gioves the same result).
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Roark's Beam Formula Superposition Question
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Roark's Beam Formula Superposition Question
Thank you for your support on this one.
IDS/rb1957
I just put the direct formula in MathCAD and got the 0.0604.
trainguy
Just in case you made the same mistake, I was adding that last term instead of subtracting it.
It hurts to discover that this was the problem all along. I am truly sorry for wasting your time.
Here's how it came to this:
I solved the direct formula (incorrectly) and then confirmed this incorrect result using FEA. Then I tried to use Roark's and couldn't get it to agree with the incorrect answer. It never occurred to me that the initial solution was incorrect because it had the support of the FEA solution (what a sick coincidence). IDS thank you for mentioning the shear deflections because I would still be wondering what was up with that FEA solution.
Well I learned a valuable lesson today.
Thanks guys!
RE: Roark's Beam Formula Superposition Question
Then our time wasn't wasted.
Just a tip on using a FEA program to verify beam or frame calculations: - if you switch off shear deflections in the FEA analysis it should give exactly the same results as a formula based on slope deflection theory, as long as the input values are exactly the same. Even a small difference indicates that there is something not quite right somewhere.
(This only applies to beam elements. Plate and brick elements inherently have some degree of approximation compared with beam theory).
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Roark's Beam Formula Superposition Question
Thank you for your help and the tip!
RE: Roark's Beam Formula Superposition Question