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September 14, 2026International Journal of Structural Stability and Dynamics

Unified Energy Analysis and K-Factor for Columns with Elastic Rotational End Restraints

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Authors

LHLi HuCYCaiyun YangHZHengming Zhang

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Overview

Variational analysis establishes a unified buckling formulation for columns with rotational restraints, highlighting accurate effective length prediction for structural stability design.

Key Points

  • To develop an energy-based variational reformulation for buckling in columns with elastic rotational end restraints and derive simplified analytical tools for stability design.
  • Formulated a total potential energy functional incorporating column bending strain energy, rotational end spring energy, and external load work under stationary equilibrium conditions.
  • Derived a unified stability characteristic equation, an energy participation coefficient, and an approximate geometric-mean relationship for effective length factor K under asymmetric restraints.
  • Validated the formulation by comparing analytical predictions against beam–spring finite element simulations under equivalent ideal elastic assumptions.
  • The unified characteristic equation consistently degenerated to standard analytical solutions for ideal pinned, fixed, and propped cantilever boundary limits.
  • Cross-validation against finite element beam–spring models revealed an average critical load error of 1.66%.
  • Generated design contour maps to enable direct determination of effective length factors across arbitrary asymmetric rotational stiffness values.

Cite This Study

Hu et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b3440926e14a848b212dhttps://doi.org/10.1142/s021945542850023x
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Also Consider

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  5. 5Multi-Linear and Bi-Linear Stress–Strain Approximations for Finite Element Modelling of Extended End-Plate Moment Connections2026 · 1 citations