A modified Vlasov theory for dynamic analysis of thin-walled and variable open section beams

The equations of motion of thin-walled beams with open cross-section considering the effects of shear flexibility, rotatory inertia in the stress resultants and variable cross-sectional properties are presented. These equations are based on Vlasovʹs theory of thin-walled beams, which is modified to include the effects indicated above. The formulation is also applicable to solid beams, constituting therefore a general theory of coupled flexure and torsion of straight beams. The differential equations are shown to be particularly suitable for analysis in the frequency domain using a state variables approach. The resulting equations are used in the determination of the natural frequencies and the seismic response of a building provided with a thin-walled reinforced concrete core to resist lateral loads. Finally, an example of a variable section channel beam is presented, which provides additional evidence on the generality of the formulation.