New ground-motion scaling method for asymmetric buildings using modal pushover

When Buildings Twist: New Ground-Motion Scaling Method Gives Asymmetric Towers a Fairer Earthquake Test

When a large earthquake rattles a city, the buildings most likely to surprise their engineers are often not the tallest or the oldest, but the ones whose floor plans refuse to be symmetrical. L-shaped hospitals, T-shaped schools, and residential towers with re-entrant corners carry a structural liability that is easy to draw and notoriously hard to analyze: their centers of mass and centers of stiffness do not coincide, so horizontal shaking is converted partly into rotation, twisting the building about its vertical axis and concentrating damage along the vulnerable edges of the plan. A new study published in February 2026 in the journal Earthquake Engineering and Engineering Vibration takes direct aim at this problem. A team of civil engineers at Islamic Azad University’s Isfahan (Khorasgan) Branch in Iran has developed a ground-motion scaling and record-selection procedure built specifically for such asymmetric-plan buildings, and demonstrated that it outperforms both an established research method and the scaling rules written into current United States design codes.

Behind the new procedure lies a deceptively simple question that stands behind every rigorous seismic simulation: when an engineer runs a nonlinear response-history analysis — the most demanding tool in earthquake engineering, in which a detailed computer model of a structure is marched through a recorded earthquake second by second — which ground-motion records should be used, and by how much should each be amplified or attenuated? Because no two earthquakes are alike, engineers must select a handful of recorded accelerograms and scale them so that each represents the hazard level under study. The problem has spawned an entire research subfield, spanning spectral-matching algorithms, conditional-mean-spectrum methods, and generalized conditional intensity measures, all wrestling with the same challenge. Design codes such as ASCE/SEI 7-16 typically anchor scaling to a single spectral quantity at the building’s fundamental period. For a symmetric building, whose dominant mode of vibration is a simple side-to-side sway, that anchor works reasonably well. For an asymmetric-plan building, whose fundamental mode blends translation with torsion, a single spectral ordinate cannot characterize the incoming motion, and demand estimates drawn from the scaled records can be badly skewed.

The difficulty is rooted in structural dynamics. When a building’s plan is asymmetric along one direction — what the researchers call one-way asymmetry — lateral translation couples with rotation about the vertical center of stiffness. The coupled mode shapes mean the building does not merely lean with the ground; it pivots, and the flexible edge of the plan swings through larger displacements than the motion of the center of mass alone would suggest. Demand parameters such as interstory drift ratios and edge-frame deformations therefore scatter far more widely for irregular structures than for regular ones, and the choice of intensity measure becomes critical. A good intensity measure correlates tightly with the engineering demand parameters — the drifts, displacements, and force demands that designers care about — reducing the dispersion that otherwise forces analysts to run more records to reach the same level of confidence. Researchers have explored richer scalar measures, including spectral-shape indicators such as the parameter epsilon, and, most relevant here, spectra computed for oscillators that are allowed to yield rather than held elastic: the inelastic deformation spectrum.

The new procedure descends from a distinguished lineage. In 2011, researchers Erik Kalkan and Anil Chopra introduced the modal pushover-based scaling procedure, known as MPS, which scales each ground motion so that the inelastic displacement of a single-degree-of-freedom oscillator tuned to the building’s fundamental mode approaches a target derived from the structure’s own nonlinear pushover behavior. Later work extended MPS to multistory unsymmetric-plan buildings. Meanwhile, study co-author Mohammad Sadegh Birzhandi and colleague A. M. Halabian had developed the two-degree-of-freedom modal pushover analysis, or 2DMPA, which represents a plan-asymmetric building with a pair of coupled oscillators — one translational, one torsional — and applied it to fragility analysis of such structures. First author Hamid Hojaji, together with Birzhandi and Mohammad Mahdi Zafarani, fused these two threads into what they call the two-degree-of-freedom modal pushover-based scaling procedure, 2DMPS. In essence, they rebuilt the MPS philosophy on the 2DMPA skeleton, producing a scaling method whose idealized model finally matches the physics of the buildings it is meant to interrogate.

At the heart of 2DMPS lies what the authors call the inelastic 2DOF modal stick: an idealized two-degree-of-freedom system standing in for the building’s fundamental coupled lateral-torsional mode. Instead of scaling records to match an elastic spectral ordinate, the optimized procedure adjusts each candidate ground motion iteratively until the inelastic displacement of this first-mode 2DOF modal stick approaches a target value drawn from an inelastic deformation spectrum computed for the two-degree-of-freedom system. Because that target encapsulates the yielding behavior of the coupled system — its strength, its post-yield characteristics, its deformation capacity — the scaled records arrive at the full structural model already tuned to the nonlinear regime in which a real building must survive a design-level earthquake. For taller structures in which higher modes contribute significantly, the authors extend the procedure to reflect those modes, so the scaling does not blind itself to the higher-mode demands that frequently govern damage in the upper stories of taller moment frames. The payoff sought is twofold: unbiased median demand estimates, and reduced record-to-record dispersion.

To determine whether the added sophistication pays for itself, the researchers mounted a disciplined head-to-head trial. They selected three reinforced-concrete special moment-resisting frame buildings — 4, 6, and 13 stories tall — and subjected detailed nonlinear models of each to ground motions scaled three different ways: by the new 2DMPS procedure, by the original single-degree-of-freedom MPS, and by the scaling provisions of ASCE/SEI 7-16. Special moment-resisting frames are among the most ductile concrete systems in modern practice, and their response under severe shaking is governed by the controlled flexural yielding of beams and columns — precisely the nonlinear behavior that a scaling procedure must respect. A set of 21 unscaled ground-motion records served as the benchmark, providing reference distributions of engineering demand parameters against which every scaled group could be judged. The nonlinear dynamic analyses were carried out on a commercial performance-based design platform, and the team tracked how closely the median demands from each scaled set reproduced the benchmark medians, and how tightly the individual demands clustered around them.

The verdict was unambiguous. Median values of the engineering demand parameters computed from records scaled with 2DMPS closely matched the benchmark results for the buildings studied. More strikingly, the bias in demand estimates within each group of scaled records — the systematic deviation from the group median that scaling can inject — proved lower than the dispersion observed across the 21 unscaled records themselves. In practical terms, scaling the records did not distort the answer; it refined it. That a scaled subset can land within the envelope of variability of the raw records is the central test of any scaling scheme, and the authors report that it held across the buildings studied. The comparison also delivered a conceptual conclusion: the inelastic response spectra of the two-degree-of-freedom modal stick are better suited to calculating seismic demands for one-way asymmetric-plan structures than the single-degree-of-freedom inelastic spectra that underpin the older methods — an advantage that held for the small 4-story frame, the mid-rise 6-story building, and the 13-story tower where higher-mode response intrudes.

Why does this matter beyond the journal’s pages? The earthquake engineering community has long worried about the side effects of record scaling. Amplifying the record of a moderate earthquake to represent a rare, larger event distorts the frequency content and duration that a structure experiences, and studies have shown that such scaling can bias estimates of collapse probability derived from the analyses. Intensity measures that are more sufficient — that carry more of the information a structure actually responds to — shrink both that bias and the record-to-record variability that inflates design uncertainty. The 2DMPS approach attacks the problem at its source. By scaling to a target that already knows the building is asymmetric and nonlinear, it leaves the record’s idiosyncrasies less room to contaminate the demand estimates, delivering what the authors describe as both accuracy and efficiency: medians that land close to the truth, and scatter small enough that fewer analyses are needed for the same confidence.

The implications reach into everyday practice. Fragility curves — the probability statements that tell a hospital operator or a city planner how likely a class of buildings is to exceed a given damage state under shaking of a given intensity — are only as trustworthy as the demand estimates beneath them, and the authors’ earlier work applied the 2DMPA framework precisely to fragility analysis of plan-asymmetric structures. A scaling procedure that reproduces benchmark medians with lower dispersion feeds directly into sharper fragility estimates, and from there into retrofit prioritization for the irregular schools, L-shaped hospitals, and corner towers that populate seismic cities from Tehran to Tokyo to Los Angeles. The study also offers code committees a concrete alternative, having benchmarked its method directly against the ASCE/SEI 7-16 scaling procedures — the kind of head-to-head evidence that eventual revisions of seismic design provisions tend to demand.

None of this makes asymmetric buildings safe by decree; geometry remains unforgiving, and torsional response will always punish careless edge detailing. What the study changes is the fidelity of the microscope. For decades, engineers have viewed plan-asymmetric structures through analytical lenses ground for symmetric ones — single oscillators, elastic anchors, purely translational modes. Hojaji, Birzhandi, and Zafarani have ground a new lens, one that twists when the building twists. The next irregular tower on an engineer’s screen may owe its margin of safety not to extra concrete, but to a two-degree-of-freedom idealization quietly at work inside the scaling factor of every earthquake record on the desk.