Modal analysis + seismic base shear for a multi-storey shear building.
Modal analysis + seismic base shear for a multi-storey shear building. Model the building as a lumped-mass stick (a mass and an interstorey stiffness per floor) and it solves the real symmetric generalized eigenproblem K.phi = omega^2 M.phi for the natural frequencies, periods and mode shapes (mass-normalized cyclic-Jacobi), then computes the ASCE 7-22 12.8 Equivalent Lateral Force base shear V = Cs.W and its vertical distribution. The eigensolve is cross-checked against the exact uniform-shear-building closed form omega_n = 2.sqrt(k/m).sin((2n-1)pi/(2(2N+1))) and its measured residual sets the trust verdict; modal orthogonality phi_i^T M phi_j = 0 holds. Honest scope: a hand-calc-grade lumped shear model (rigid floors, no flexural/P-delta/torsion/SSI) + the approximate ELF code procedure (Ta and seismic coefficients are confirmed inputs). A design-aid bridge to ETABS/SAP2000, not a replacement. Deterministic, in-browser, no API/key/network/AI.
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