## A SIMPLE PROBLEM BUT PUZZLING

## A SIMPLE PROBLEM BUT PUZZLING

(OP)

I had a peculier observation in analysing a simple single bay single storyed symmetrical frame,with fixed supports and with a uniformly distributed load on the beam.

A very simple problem to solve indeed. The moment at the column base shall be 50% of the moment at the top of the column. Since, we deal with only relative stiffnesses between the column and the beam at the junctions, the answer shall be same for the given load,irrespective of the actual stiffness of the members as long as the stiffness ratio between the beam and the column is unchanged.

I observe that the result is not so. For values of lower stiffnesses (lower I/L), the results are accurate. But the support moment at the column base reduces drastically (as low as 10% of the top moment for higher stiffnesses)if the stiffness of the individual members are increased keeping their ratios same. However, the other moments remain unchanged.

I am not able to find any logical reason for this.

I fear that this may give rise to a gross underestimation of column base moments leading to underdesign of foundations, if the results from the output are taken as correct.

Can anyone offer any reason for this?

Has anyone noticed this before?

Can anyone check this in any other proven software and inform the result?

Thanks

A very simple problem to solve indeed. The moment at the column base shall be 50% of the moment at the top of the column. Since, we deal with only relative stiffnesses between the column and the beam at the junctions, the answer shall be same for the given load,irrespective of the actual stiffness of the members as long as the stiffness ratio between the beam and the column is unchanged.

I observe that the result is not so. For values of lower stiffnesses (lower I/L), the results are accurate. But the support moment at the column base reduces drastically (as low as 10% of the top moment for higher stiffnesses)if the stiffness of the individual members are increased keeping their ratios same. However, the other moments remain unchanged.

I am not able to find any logical reason for this.

I fear that this may give rise to a gross underestimation of column base moments leading to underdesign of foundations, if the results from the output are taken as correct.

Can anyone offer any reason for this?

Has anyone noticed this before?

Can anyone check this in any other proven software and inform the result?

Thanks

## RE: A SIMPLE PROBLEM BUT PUZZLING

I try a model in both Staad-pro and Sap2000 and both of them gave approximattly same results.

I have obseved that when I increase columns moment of inertia 10 times beam inertia, then the moment at top and botton of the column became even.

I think there is something wrong in the alogarithm of programming.

## RE: A SIMPLE PROBLEM BUT PUZZLING

Now that it is clear that it is not a bug in the software but could be due to some numerical problem in handling large numbers in the computer.

I am concerned about the reliability on the foundation forces obtained using the software in bigger frames involving members of higher stiffnesses.

I hope someone will give a suggestion to overcome this difficulty.

Thank you once again for your response

Regards

## RE: A SIMPLE PROBLEM BUT PUZZLING

In your example with high Inertia and normal Area there is axial deformation and a redistribution of the force/moment reactions.

[In problems where both ends of the members can displace/ rotate and the member is very stiff and there is large movement of the member, then member force/stress recovery must be in Double Precision to get the difference in end displacements accurately. STAAD does this but some programs may not, since it is rarely necessary.]

## RE: A SIMPLE PROBLEM BUT PUZZLING

Your problem arises from the the softwares' ability to automatically account for SHEAR AND AXIAL deformation in analysis. Whereas the therical result of 2 times ignores these deformations.

Try it out, you will see.