BIM Modal / Seismic Response (eigenmodes + ASCE 7 ELF)

What it is

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.

Honest scope

Authorities cited

• A. K. Chopra, Dynamics of Structures, 4th/5th ed. - classical modal analysis of the lumped-mass shear building (K.phi = omega^2 M.phi), mass-normalization, and the uniform-chain closed-form eigenfrequencies.
• ASCE/SEI 7-22, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, section 12.8 (Equivalent Lateral Force): Cs (12.8-2..6), approximate period Ta = Ct hn^x (12.8-7..8), vertical distribution Fx = Cvx V (12.8-11..12).
• G. H. Golub & C. F. Van Loan, Matrix Computations - the cyclic Jacobi method for the symmetric eigenproblem used here.