Establishment of a Mounting Offset Index and Its Application to Dynamic-Response Evaluation of Long-Span Steel Structures

Discrete ancillary equipment and local added masses are common in long-span steel structures, yet equal total mass can produce different dynamic responses because existing quantity-based descriptions do not encode spatial redistribution. This study establishes a mounting offset index (MODI) from mass intensity MI, eccentricity EI, dispersion DI, and central–subcentral synergy CI. Shaking-table tests on a 1:40 single-layer cylindrical reticulated-shell model examined one unloaded baseline and 44 mounted-mass layouts in the X, Y, and 45° structural orientations, yielding 135 orientation-specific cases. Same-orientation normalization produced four response ratios. All the responses differed significantly among the orientations (p<0.001), while the equal-mass layouts exhibited distinct MODI values and responses. In 100 repeated five-fold analyses, the four-component model achieved Q2=0.554±0.039 for the X-orientation time-domain peak ratio and 0.364±0.052 for its frequency-domain peak ratio; the composite MODI had no stable predictive capability. These results establish a hierarchical evaluation framework: the MODI supplies a pre-test spatial coordinate for layout comparison, the components support selected within-orientation interpretations, and the directional sensitivity index with the three-orientation envelope identifies direction-sensitive and relatively unfavorable measured-node responses. The MODI is therefore an engineering screening descriptor rather than a universal response-prediction formula.