Modified Stiffness in Moment Distr

[dpa]

I have a three span beam with two-three foot overhangs. I treated the ends with the overhangs as pinned and did one moment distribution using modified stiffness (0.75*stiffenss) at the pinned ends and one without modified stiffness. They both converge to within two decimal places (using Excel) but they got different answers at the interior supports. Is it proper to consider a continuous beam with an overhang to be a pinned end? Is modified stiffness mandatory for a pinned end? I thought it was just to speed up convergence which is not a problem with Excel anyway. Everything about the two spreadsheets is identical except the two stiffnesses.

Thanks,
DPA

 

[MotorCity]

If I understand your model correctly, the pinned end is actually a pinned supported cantilever on each end. I am not familiar with the modified stiffness method you describe but you may want to take a closer look at your calculations. The pin does not resist moment, only translation. That does not mean that you cannot have a pin support in a continous beam when applying moment distribution but simply that the moment at a pin support should be zero.
Good luck.

 

[haynewp]

The modified version is just a simplification that should give the same result when done properly, it is not mandatory. You can still apply the modification to a pinned support when there is a cantilever present off of this support.

 

[dpa]

I am not restraining the end of the cantilever. I am simply treating the connection at the supports as pinned. Like I think I said before it is a continuous beam with three spans and two overhangs. The modified stiffness is from Elementary Theory of Structures" by Yuan-Yu Hsieh. It was used at the University of Washington. Modified stiffness is also discussed in "Civil Engineering Reference Manual" by Michael R. Lindeburg P.E. This is the book endorsed by NSPE for taking the PE. I kept mine because it is loaded with all kinds of good information. Both authors state that the modified stiffness is simply for the purpose of speeding up convergence.

apsix,

Thank you for your comments.


Motorcity,

You are right about the moment being zero at a pinned end but not if there is an overhang. When you get to the bottom of the moment distribution the moment on both sides of the pin should be equal to the original moment calculated for a cantilever. In both my spreadsheets the moments at the supports next to the cantilevers do converge to the proper values. It is only the internal supports where there is a difference between the two spreadsheets.


haynewp,

I agree with your answer but I just can't seem to figure out what the problem is. I suspect that the modified stiffness value in Hsieh's book may only apply to a simple pinned end with no overhang. Can't figure out why that should be just yet.

Thanks guys for all the quick responses.
DPA

 

[aggman]

When I have worked problems like yours I have only used the modified stiffness for the propped cantilever. If you have a cantilever then I have always worked it the old way. I hope I am seeing your problem correctly...



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^ ^ ^ ^ ^


My version of the propped cantilever

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^ ^

 

[mrMikee]

I agree with haynewp in that the modified stiffness is a simplification that is not required. In fact I seldom used it because it was more I had to remember and without it just required a few more iterations. Now however, I don't remember much of it at all. Sorry that this doesn't really add anything to the discussion.

-Mike

 

[dpa]

Thanks aggman and Mr Mikee. I like your answer. I don't think I will mess with modified stiffness again. With a spreadsheet a few more iterations amounts to nothing anyway you can copy and paste to get them.

DPA

 

[rb1957]

i think bruhn's example problem A11.5a agrees that there is nothing special about an overhang (and so no 0.75 factor).