Dear Sir,
I tried validation of caesar-II results for simple piping configuration such as (1) cantilever beam with a conc. vertical load at free end, (2) Simply supported beam with a conc. vertical load at mid span and (3) Fixed fixed beam with vertical conc. load at mid span for deflection and rotation at the free end for cantilever case , deflection at mid span and rotation at the supports for S-S Beam and deflection at mid span for the Fixed -fixed beam using Timoshanko formula. I used 4 element model for all cases.

However, I found the results differ by quite a few percentage and the difference is about 14 % for the case of central deflection of Fixed Fixed beam.

Any body explains this discrepency in results ?

Regards,

Debasis Pal

Simple - CAESAR II uses the Euler beam equations. You can find them with a google search. They are not the same as the Timoshenko equations.

Actually I used the Euler Beam equation.For the case of Fixed Fixed beam with vertical concentrated load at mid span

Deflection = PL3/(192 EI)

For a beam with L=100, D= 10 & t=0.60198,

the percentage difference in result between CAESAR-II output and hand calculation from the above formula is about 14% .

Please check and explain.

Debasis Pal

DCPL, Kolkata

Debasis,

I have not done or checked your calc. but few things to note: The end condition of the beam is not fixed in the program ( which is the case using simple strength of materials equations). If you know FEM, you must be knowing that one of the way to model restriants in FEM is to use penalty methods and springs of high stiffnesses are used to model the restraints. Also there are truncation and round off errors. Al these factors can change in results with respect to theoretical analysis.Also are the modulus of elasticity and poisson ratio same in both the models?

I don't know about the experience level you have but if you are an young engineer , I certainly appreciate your way of working as many young stress engineers are only bothered to see PASS/FAIL in CAESAR w/o going into the results and their accucary.

Best Regards

Beam Euler :
f = (F*L*L*L) / 3*E*I

f = displacement ==> 1,6156 mm with :

F = Force ==> 2000 N
L = 1000 mm Beam lenght
E = 210 000 N/mm2 elastic module
I = 1964944 mm4
with D = 100 mm ; s = 6 mm D ( Outsidiameter pipe) s (thickness)

Caesar result ( only Load F ,without Weight case):
f = 1,644 mm

Differenz : 1,76 % << your 14 % !!!!

Anindya,

Thanks for giving valueable insight. In SAP -IV etc FEM program, we used to model the built-in condition by locking the particular DOF as boundary condition.

More over, there can be truncation and rounding off error but deviation of 14% is not explained. But what is the roll of poisson's ratio here is not understood.

Also, if Caesar-II uses very high stiffness springs to simulate the anchoring conditon, fine. But this is a typical loading case where classical result which forms the basis of our knowledge is far from CASER-II results and our understanding for stress analysis by reputed software is shaken.

I wish the people who coded CAESAR-II should clarify this for the benefit of all the CAESAR-II users like me and dispel our doubts.

Debasis

Hi Debasis

I think you are calculating vertical deflection only for external force while comparing with beam formulae Deflection = PL3/(192 EI)

By subtracting deflection from Caesar (W+P1+F1) & (W+P1) you will get deflection only for external force.

I cross check with 10" dia, sch 30 length 8000 mm error coming 3%.
When I increase the length % error is decreasing.
As Anindya-da mention earlier restraint stiffness (1.0E12 N/cm),truncation and round off errors could be possible factor for small error.

When I increase the length even error come down below 1%.

Regards

Habib

Your claim is that the program results do not match your (hand) calculations. You then ask that someone take action to either clarify the program results or point out the error of your ways.
I believe you will resolve this issue very quickly if you work up your own calculations and demonstrate your position explicitly. With hard numbers, we can move this forward.

... and if you just want deal with the applied load, setup a load case that contains only "F1".

Debasis,

Poisson ratio has nothing to do with this particular problem but in general , as you know Posson ratio is a part of stiffness matrix and there can be difference between the results of hand calc. and computerized calc. between because of difference in values of this parameter.

Anyway, coming to the problem in hand, I still hold my answer and believe that is the case.

Why don't you do a comparison of the results of this problem using standard FE Programmes like ANSYS, ABAQUS , SAP IV etc and check for the variance? I am sure that it will be an interesting study.

For any problem , between any two FE code variance ( linear elastic analysis only) is 5-10% ( my own experience and some of the papers I read),14% in my opinion is not that much of a big number.

Also, pl. remember that a widely reputed software like CAESAR II has to undergo lot of benchmark tests and QA and only then it is marketted.

Also. pl. work out the way as advised by Shr and Richard and let us know your finding.

Regards

Study of various theories for beam revealed that , for beams of small span/depth ratio, shear stresss are high and resulting deflection due to shear can not be neglected. For high L/h results from Euler beam are close to that using Timoshanko beam since the effect of shear deformation on deflection is negligible.

So, beam deflection from my hand calculated results are differing considerably from that obtained from CAESAR=II analysis since in my case the L/D is 10 (which is very less). When the L/D for the same example is increased to 100 or more the results from hand calculations (using Euler beam formula) seem to come much closer to that obtained by use of CAESAR-II(which possibly uses additional correction factor due to shear deformation into account in its element stiffness matrix formulation) .

Regards,

Debasis Pal

Hi Debasis

Appreciate if you attached result with input in both way calculation.

When both the values are less you should not calculate difference in percentage( approximation error). I suggest check result with standard support span deflection from comparison

Just one reminder Caesar do not address buckling. It is assumed that stress engineer should never put two anchor or two line stop in a line.

In that case caesar will show zero expansion stress but huge axial load.

Regards

Habib

Debasis,

CAESAR II is not based on Timoshenko theory but Euler Bernoulli, so the issue of shear deformation is not the point here.

Have you checked the points I mentioned in my previous post?If you have, pl. share the results with us.

One more example I can give you. Say you have apipe fixed at both ends and subject to temp. rise. The axial force at the two ends will not change irrespective of the length of the pipe. This is as pr strength of materials theory. If however if you model the same in CAESAR II you will find it is not the case depending.The reason is what I have mentioned before.

Modelling of restraints in a FE program ( typical penalty method) has lot to do w.r.t the type of observation that you have mentioned.

Regards

Example:

Assume a cantilever beam, 10ft long, 4 inch std pipe, low carbon steel, with a tip load of 1000 lb down. Then:

L = 120 in
Do = 4.50 in
t = 0.237 in
E = 29.5E6 lb/in^2
Di = 4.026 in
P = -1000 lb


Deflection = PL^3 / (3EI )

I is computed as 7.233 in^4, so

Deflection = (-1000 lb) ( 120 in)^3 / [3 * 29.5E6 lb/in^2 * 7.233 in^4 ]
Deflection = -2.699 in

The resulting tip deflection from the corresponding CAESAR II run yields a value of -2.7063 in.

% error = ( 2.7063/2.699 - 1 ) * 100 = 0.27%

Hi Richard

Will you like to terms as % error ?
I think we should call manual calculation value as theoretical value.
Caesar output value more realistic practical value ?

In lieu of infinite anchor stiffness we are using Caesar anchor stiffness (1.0E12 N/cm), that might cause small changes in this particular example.

Thanks & Regards

Habib

Dear Richard,

We all know that for greater L/D ratio the classical & CAESAR-II results for beam deflection comes closer and will evantually match. All the more is the case for the case of cantilever beam with a tip load.
But I had enquired about the case of F-F beam and for a L/D ratio of 10 or less.
Yesterday I sent a private communication to you also requesting that I should be able to submit to you or to the public the documents showing this discripency of results in form of actual attachments.

I hope you will respond to this so that someone can really find out the real cause of this discripency of results for the case of F-F beam with a central con. load.

Regards,

Debasis

Send your calculations to "techsupport@coade.com".

I have sent my calculations and CAESRAR-II results for Fixed Fixed beam case to "techsupport@coade.com". as suggested by you now.

Hope I get a satisfactory explanation for the discripency in results as observed by me.

Regards,

Debasis

As per my calculations regarding the F-F Beam with Central Load: Case-1D - CONCENTRIC INTERMEDIATE LOAD; LEFT END FIXED; RIGHT END FIXED.

Reference Roark's Formulas for Stress and Strain
Writer: Warren C. Young
6th Edition.

L = 120 in
Do = 4.50 in
t = 0.237 in
E = 29.5E6 lb/in^2
Di = 4.026 in
P = -1000 lb

*** Theoratical Caesar II 5.10 % Error X-software % Error
1-Deflection 0.0042 -0.0024 -42.86 -0.0046 9.52
2-Reaction A -500 -53.9 -89.22 -554 10.80
3-Reaction B -500 -53.9 -89.22 -554 10.80
4-Moment A -1250 -89.83 -92.81 -1340 7.20
5-Moment B 1250 89.83 -92.81 1340 7.20

Units:
Deflection in inches
Reaction in lbs
Moments in lbs-ft

Clearly Caesar II giving very much less reaction loads as any other software or calculation can predict.

I have also attached mathcad calculation file for Roark's Theoretical formulas I used.

Deflection is same i.e -WL3/192EI etc please see attached file.

Please let me know for any corrections or comments.

You have made one or more mistakes with your CAESAR II model.

In the table above, for the "Deflection", you show a theoretical value of "0.0042". This is incorrect, if you look at your attached PDFs the theoretical value is "0.042".

The first clue that your comparison is in error is that the reaction loads are way off - you're comparing 500 to 53.9 ? That 53.9 lb load, and the deflection of -0.0024in are the values from the "W" load case alone - that is the self-weight of the beam, not the concentrated load you're interested in.

If you setup another load case, that contains the single load primative of "F1" (assuming you put -1000lb in F1), then you should obtain DY= -0.0438in and reaction loads of -500lb.

Oops! My apologies for flipping you out.:S

Indeed you are right about self-weight based result I posted. Most softwares automatically consider the W as combined:Gravity + any no. of applied load/s so I missed out "F1" factor in loadcase of Caesar because of being fresh in usage of caesar.

Anyway, so the percentage error boils down to 4.28 % only for deflection and 0 % for Reaction loads & Moments for this particular case.
Exactly same are the results of the X-software mentioned in comp: sheet.

Thanks Richard for your comments and corrections. Now I have a much better understanding.

Regards,
Salz