Seismic Base Shear Calculator

The equivalent lateral force method treats the earthquake as a set of horizontal forces whose total is the base shear, V = Cs W. The core coefficient is not one expression but three: below the plateau corner TS = SD1/SDS it is SDS/(R/I); between TS and the long-period transition TL it becomes SD1/(T R/I) and decays with period; beyond TL it falls as SD1 TL/(T² R/I). SDS and SD1 are the short-period and 1 s design spectral accelerations from the hazard map and site class, R is the ductility of the system (a well-detailed frame gets a high R and therefore a lower shear because it dissipates energy by yielding), and I is importance, 1.25 to 1.5 for hospitals and schools. A high R means a cheaper structure but larger drift and more damage to non-structural elements; a low R is safe but expensive. That trade-off is the heart of seismic design and it is not a free choice — use the R your code assigns to the system. The period from Ct hn^x is a preliminary estimate only; measured periods are usually 20 to 40% longer because infill walls stiffen the frame. And a coefficient of 0.1 is not small: on a ten-storey building it means tens of tonnes of horizontal force per ground floor column, reversing direction many times, which is why seismic resistance comes from ductile detailing such as closed hoops at closer spacing rather than from bigger sections.