## Applications of the Finite Element Method to Beam-column Problems |

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### Contents

FORMULATION FOR THE STIFFNESS MATRIX OF THE BEAM ELEMENT | 9 |

LINEAR STABILITY ANALYSIS OF BEAMCOLUMNS | 43 |

Columns with Distributed Axial Loads | 65 |

9 other sections not shown

### Common terms and phrases

analytical solutions application approximate axis beam element beam theory beam-column problems bimoment boundary conditions Buckling Loads Buckling Modes centroidal-principal axes coefficients Columns Fig Comparison of Finite computed constitutive equations convergence characteristics coordinates critical loads demonstrate derived determined developed displacement field Distributed Axial Loads eigenvalue elastic stiffness matrix end conditions equilibrium Euler evaluated finite element analysis finite element formulation finite element method finite element model Finite Element Solution flexural geometric nonlinearity geometric stiffness matrix given by Eq Incremental Method inertia iterative kinematical large displacements Lateral Torsional Buckling Lehigh University linear stability load increment load vector nodes notation number of elements numerical obtained parameter Piecewise Prismatic Columns Pin Ends polynomial pretwisted columns principal axes procedure reference axes shafts shear center shear strain shown in Fig solving space frame strain components strain field strain-displacement relationship structural tapered columns thin-walled beams torque torsional displacements transformation matrix twist Two-Component Columns variational principle warping