Elastic Behavior of Tapered Monosymmetric I-Beams

The simultaneous differential equations for bending out of the plane of symmetry and for torsion of tapered monosymmetric I-beams are derived by considering the flange displacements. It is found that these equations are not independent because the shear center and the longitudinal centroidal axes are not parallel, and it is concluded that torsion is always accompanied by bending out of the plane of symmetry. The bending and torsion equations simplify considerably for the particular case of tapered monosymmetric I-beams of constant depth. The elastic stability of tapered monosymmetric simply supported I-beams of constant depth with central concentrated loads acting in the plane of the webs is also investigated both theoretically and experimentally. The governing differential equations for bending and torsion are solved numerically by the method of finite integrals.