Intro to Dynamics — Lesson 1

What Is a Response Spectrum in Earthquake Engineering / seismic design? 1) Start with the core equation Every building can be simplified (at first) as a Single Degree of Freedom (SDOF) system: m·u¨(t) c·u˙(t) k·u(t) = – m·u¨g(t) • m = mass • k = stiffness • c = damping • u(t) = displacement • u¨g(t) = ground acceleration Key dynamic properties: ωₙ = sqrt(k / m) T = 2π / ωₙ ζ = c / (2·sqrt(k·m)) The natural period T is the critical variable we change to build the spectrum. ⸻ 2) Apply the same ear