Seismosoft | Earthquake Engineering Solutions

I modeled one column and I defined one time the concentrated mass ,another time the dmass I placed the specific weight of element equal zero ,my teacher said me when you divide column into the smaller parts the deference between relative displacement in the specific nod when dmass is define for undivided element and lump mass when is defined for divided element must to be converged but I see now that when I divide the element and define the lump mass the more parts the more differences are seen although the periods converges together in your opinion how can I define the lmass in the divided column that the results would converge to the undivided element with the dmass
tanks

In a lumped mass formulation, 1/2 of the total mass is assigned to each end and the off-diagonal terms of the mass matrix are zero.

In a consistent mass formulation the diagonal terms are each 1/3 of the total mass, but the off diagonals terms of the mass matrix are not zero, they are 1/6 of the total mass.

So one starting point might be to assign (1/3)/(1/2) = 2/3 of the total mass in a lumped mass model to try and mimic a consistent mass model. But the off diagonals must have an effect which I don't believe you will be able to capture in lumped mass models. How much influence those off-diagonal terms will have may depend on the model. I cannot claim any expertise here, but these are just some thoughts.

Tanks a lot dear huffte ,it works well but I have a question why do we divide (1/2) to(1/3)while It seems we must multiply them ?

The total sum of diagonal mass terms is M in a lumped mass formulation and (2/3)M in consistent mass. So, to get the same diagonal sum as consistent mass using lumped mass, you need 2/3 of the total.

Dear seismosoft
Is It possible to have the same relative top displacement of dmass assigned ,undivided element with lmass assigned divided element with the 1/2 total mass assigned in each nod, logically the more divide the more convergence but when I modeled element so that above-mentioned way the convergence is so slow on the other hand when modeled the element with the 2/3 total mass in each nod the initial dmass model with lmass model in every numbers of divide coincided, I want to know your opinion ,

Tanks a lot

Dear khajehdehia,

We are not sure we understood fully your query, but, in any case, would simply note that you seem to have found the response to your query already, by (pertinently) running test/sensitivity studies using different modelling options/assumptions and comparing the results.

Seismosoft Support