Damage-Aware Closed-Form Tuning of Rooftop Mass Dampers for Long-Period RC Towers Under Inelastic Period Drift

Seismic design of long-period reinforced concrete tall buildings is drift-dominated, and yet closed-form tuned mass damper (TMD) calibration lacks a rank-oriented robustness framework and a deterministic treatment of inelastic period drift. First, a two-layer closed-form calibration procedure is verified on 30-, 48- and 60-storey RC towers with periods of 3.80 to 8.45 s on a rock-like Istanbul site under eleven spectrum-matched records. The first layer, a Robust Tuning Index built on four design requirements, weighs nominal suppression against detuning robustness through a closed-form dominance condition and a unique crossover at the ±13% band. The second layer, a period-elongation-aware anchor, sets the calibration period to the mean of the elastic and DD-2 secant first-mode periods, capping the worst-case offset at ±9.0% to ±12.1% against +19.7% to +27.6% under elastic anchoring. Response-history analyses give mean peak roof-drift reductions of 2.8% to 4.6% with statistically inseparable formulation means at exact tuning, while the Sadek calibration cuts dispersion by more than a third and stroke by roughly a third, carries 2.3 to 2.5 times less frequency-response loss at the anchor offsets, and ranks first in 122 of 144 envelope scenarios. The framework replaces numerical retuning with a transparent closed-form route within the linear verification tier.