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MDOF Modal Analysis + SRSS/CQC

n-story shear frame · Modal participation factors Γr · Peak modal responses · SRSS and CQC combination rules · Chopra §12–13

n-Story Shear Frame

Modal Results

Base shear Vb (SRSS/CQC)—
Combined floor displacements—

Citations

Chopra §12.4Γr=φᵣᵀMι/(φᵣᵀMφᵣ) — modal participation
Eq.(13.7)SRSS: u≈√(Σuᵣ²) — for well-separated modes
Eq.(13.8)CQC: u≈√(ΣΣρrs·ur·us) — for closely-spaced modes
TBDY 2018 Md.4.8Modal combination per Turkish seismic code

← 2DOF

Mode Shapes (normalized to unit roof)

Visual explanation

Multi-storey building: vibration modes and mass participation. Shear-building model; periods and mode shapes from the eigenvalue solution
Figure 25. Multi-storey building: vibration modes and mass participationSource: Chopra (2017), Ch. 10–13; TBDY 2018 modal combination method. Example model.

Preliminary educational tool. Verify results against textbook solutions.