Probabilistic reliability cost of drift uniformity in optimized strongback steel frames

Abstract The Strongback system effectively mitigates soft-story mechanisms by enforcing uniform inter-story drift. While deterministic optimization utilizing the Drift Uniformity Factor (DUF) achieves this target, it inherently neglects structural uncertainties. This study quantifies the “probabilistic cost” of the DUF constraint through a system reliability assessment of optimized 4- and 6-story Strongback steel frames across three topologies ( $$\alpha$$ = L/4,L/3,5L/12). Utilizing a Stochastic Finite Element Method framework, 12,000 simulations (1000 per scenario) were executed, incorporating four lognormal random variables for material and load uncertainties with a 10% coefficient of variation. The probabilistic results reveal a scale-dependent paradox. In 6-story frames, enforcing DUF systematically degraded system reliability; for the optimal $$\alpha =L/3$$ configuration, the probability of failure ( $${P}_{f}$$ ) surged by 208%, escalating from 14.7% (without DUF) to 45.3% (with DUF). Conversely, in shear-dominant 4-story frames ( $$\alpha =L/3$$ ), the DUF constraint acted as a “redemptive penalty” its deterministically imposed structural overstrength inadvertently enhanced stochastic robustness, reducing $${P}_{f}$$ from $$49.1$$ to 37.7% (a 23.2% reduction). Ultimately, this study demonstrates that imposing rigid kinematic constraints like DUF tightens the feasible design space, often critically compromising probabilistic safety margins. Geometric nonlinearities are approximated through P–Δ effects using leaning columns in OpenSees. These findings are specific to the adopted linear-static equivalent-load framework and should not be interpreted as general nonlinear dynamic seismic performance.