Structural Dynamics and Seismic Design
Domain overview
This section tests dynamic analysis and earthquake-resistant design: natural period, damping, response spectra and code base shear. It also examines regularity, ductility and capacity design, where strength and detailing must work together.
Core rules
- SDOF period T=2π√(m/k); stiffness and mass both matter, so adding stiffness shortens T.
- Response spectrum ordinates depend on period, damping and soil condition; design spectrum is not the elastic spectrum divided arbitrarily.
- Base shear V=AhW, with Ah=(Z/2)(Sa/g)/(R/I) in the IS 1893 format; Z, I, R and soil type must be justified.
- Irregularities, torsional eccentricity, soft storeys and discontinuities require extra analysis or amplification; ductile detailing follows IS 13920.
Worked example
A regular building has W=10,000 kN, Z=0.35, Sa/g=2.5, R=5 and I=1.2. Then Ah=(0.35/2)×2.5/(5/1.2)=0.175×2.5/4.1667=0.105. Base shear V=0.105×10,000=1050 kN. Distribute V over the height according to the code's storey-weight and height formula, then apply torsional design eccentricity. Check that the chosen R is consistent with the actual ductile detailing; otherwise use a lower R or elastic analysis.
Traps
Using R as a load factor in the wrong direction, omitting importance factor, ignoring soil-dependent spectrum, and assuming regularity without checking plan and vertical discontinuities.