huangyhg

moment distribution discrepancy
i have been running continuous beam models in sap2000 and trying to verify those results using hand calculations. the models consist of twenty equal spans with cantilever end spans and a uniform load across the entire beam. the hand method i am most familiar with is moment distribution and the results are not matching within a reasonable percentage for the spans closest to the cantilevered ends. i have had three other fellow engineers check the hand calcs to see if any errors were made in calculating k's, df's, the use of the cof's and for random sign errors, no errors were found. at first i thought i was making an error in the inputs for sap so i checked moment distribution examples from my text book versus results produced by sap. the examples were all two or three span continuous and the results matched fine. it seems the more spans the further off the results get for the spans adjacent to the cantilevers. the moments calculated using the moment distribution method for the first interior support are significantly lower than the sap results. i am puzzled, any helpful tips?
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i don't know how far off you are and i have never used sap but first check to make sure shear deformation is not included and also make sure that you don't have a support fixed for lateral translation which would cause axial load in the beams.
how far are the results off?
when i have compared moment distribution with the stiffness matrix method, i have experienced some cases off by as much as 10%. the differences between the methods have to do with axial or shear deformations which are not taken into account with the moment distribution method.
what you might want to do with your sap model is to input very large cross sectional areas, so that those deformations do not have any influence and your sap results should approach the results obtained by moment distribution.
see if your software allows you to turn off shear deformations. risa allows this, so sap may as well. you could have your hand calc include shear deformation by adjusting your moment of inertia. try reducing your moment of inertia by dividing it by: 1+(36i/a*l^2), where a is your shear area.
are you sure you handled the end conditions of your twenty span continuous beam with cantilever ends properly? the moment at the first support is statically determinant and will be exact in both methods if handled properly. do you have a worked example of a moment distribution problem with a pin supported end? that is the approach you should use. after doing the pin supported end model (both ends, mind you), superimpose the static end moments onto those results and you have the solution. good luck.
thank you very much for all your comments. it was the shear deformations that were causing such dramatic changes in the results. i have a matrix analysis book by kassimali and throughtout the book shear deformations are ignored in the calculation of the stiffness matrices. hidden at the very back of the text was one page which states that whenever your span to section depth ratio exceeds 10 the effects of shear deformation are negligible and when that ratio is below 10 then the effects become considerable. my model involved 24in spans with the default w18x35 section. as you can see the ration of span to depth is well below 10 and the moments were alot bigger than the moment distribution results. i then used a general section i created with most properties set equal to 1 including the depth and the results matched the md results. in addition i also used a bigger section than the default w18x35 and the moments were amplified. thanks again to all who responded
this whole discussion smells fishy. particularly the parts about shear deformation. the matrix analysis and moment distribution i use are based on plane sections remaining plane (basic beam theory). are you sure your software analysis as well as moment distribution are appropriate?
it doesn't sound like you know what your doing, particularly since the extent of your library is an introductory structural analysis book.

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