Lateral Stability of Imperfect Discretely Braced Steel Beams

The lateral stability of imperfect discretely braced steel beams is analyzed using Rayleigh-Ritz approximations for the lateral deflection and the angle of twist. Initially, it is assumed that these degrees of freedom can be represented by functions comprising only single harmonics; this is then compared with the more accurate representation of the displacement functions by full Fourier series. It is confirmed by linear eigenvalue analysis that the beam can realistically buckle into two separate classes of modes: a finite number of node-displacing modes, equal to the number of restraints provided, and an infinite number of single harmonic buckling modes, where the restraint nodes remain undeflected. Closed-form analytical relations are derived for the elastic critical moment of the beam, the forces induced in the restraints, and the minimum stiffness required to enforce the first internodal buckling mode. The position of the restraint above or below the shear center is shown to influence the overall buckling behavior of the beam. The analytical results for the critical moment of the beam are validated by the finite-element program LTBeam, whereas the results for the deflected shape of the beam are validated by the numerical continuation software AUTO-07p, with very close agreement between the analytical and the numerical results.