SDOF MODEL 1

[euranian]

How do you find distribution of column shears and moments over the height of bldg in SDOF model?

 

[ishvaaag]

Strictly, a SDOF model is just for only 1 story able to displace laterally. If you refer to multiple SDOFs lumped at center of gravity of every floor, the method should (better!) be restricted to regular buildings. First you determine the modes of vibration and then you find the participation of the modes to give projections of what the expected response will be. If the input is a purported true motion record you can follow the motion of the nodes in one sense or the other, i.e., get "true" expected signs of the movements -essentially you are using a look-up table of what the movement will be when the input motion record is at specific values-, but if your input is just a cover-all one, as in the response spectrum method, you just predict the amount of movement in any DOF without sign, i.e., you can't know the "true" shape under the "excitation" (because there is not "one" excitation, but a coverall of many) and so the predicted amounts of movement must be signed in whatever the selected way ("modes of signage") to get deformed shapes useful (or used!) for design.

The process of getting moments and shears is just establishing them from the surmised deformed shapes through slope deflection or akin matricial relationships.

In all, the many uncertainties of the response spectrum method bring to at least a major structural software provider to warn that the actual response of the structure might be much different from what ascertained from the calculations, i.e., they are very well aware that when using these procedures even being standardized after about 60 years of development, things can go badly when one starts to make imaginative suppositions, much statistical that they be.

Practical application to regular buildings of the method you can find in PCA's book

Earthquake and Wind Forces
Ghosh, Domel