This paper combines a hyper‐reduction procedure, the proper orthogonal decomposition unassembled discrete empirical interpolation method, with a non‐iterative α‐operator splitting (α‐OS) time‐integration scheme for accelerating parametric analyses on damageable civil engineering structures subjected to earthquakes. Applications on a two‐story reinforced concrete frame building modeled by multi‐fiber beams provide guidelines to define hyper‐reduced order models (HROMs) for real‐life applications that use seismic databases or variable loading assumptions. The α‐OS HROMs proved their applicability in approximating high‐fidelity dynamic responses with speed‐up factors higher than 60 and errors lower than 0.6% for the present case study.