A Three‐Parameter Continuum Timoshenko Beam Framework for Evaluating Higher‐Mode Effects in High‐Rise Buildings With Rotational and Translational Base Flexibility

Higher‐mode effects can significantly amplify seismic demands in high‐rise buildings, causing unintended damage over the building height. Engineered mechanisms are introduced at the base of these structures to mitigate higher‐mode effects. Existing continuum formulations for base‐flexible buildings commonly idealize the superstructure as a Euler–Bernoulli beam, neglecting shear deformation and rotational inertia. This assumption can be restrictive for shear‐flexible high‐rise systems, including stocky reinforced concrete wall structures and emerging tall mass‐timber wall buildings. This study extends the two‐parameter Euler–Bernoulli cantilever analogy to a three‐parameter continuum Timoshenko framework by introducing the dimensionless shear stiffness, , alongside the base rotational and translational stiffness parameters, and . The framework is intended as an equivalent‐linear mechanics model that isolates how engineered base mechanisms or soil‐structure interaction‐induced foundation flexibility influences modal properties and response. The analysis shows that shear flexibility has limited influence on the fundamental mode of slender systems but can strongly modify higher‐mode eigenvalues, spatial mode shapes, and modal mass participation. The Timoshenko model identifies second‐spectrum behavior, restraint‐dependent non‐monotonic convergence to the Euler–Bernoulli limit, and local inter‐story drift changes caused by independent shear‐strain fields. Across inter‐story drift, shear, and overturning moment responses, translational base flexibility is the most robust mechanism for suppressing higher‐mode demands, whereas rotational flexibility mainly reduces first‐mode flexural response and does not reliably eliminate higher‐mode contributions when translational restraint remains effective. The resulting framework clarifies when shear deformation and base flexibility must be considered explicitly in mechanics‐based seismic assessment of high‐rise buildings.