Stocky thin- or thick-walled beams: Theory and analysis

The nodal-line method (NLM) is proposed for treating the wide-flange stocky thin- or thick-walled beams featured by (1) clear longitudinal axis, (2) low length/width ratio (≤ 3), and (3) three beamlike stress components. The nodal lines parallel to the axis are distributed on all sides (for both thin and thick walls) plus the interior (for thick walls only) of the beam, and used as the reference frame for imposing the 3D displacement field. The axial and transverse displacements of the nodal lines are taken as the unknown functions and used along with interpolation functions to describe the displacement field. By the principle of minimum potential energy, a set of ordinary differential equations (ODE) and boundary conditions are established for the beam, which are solved by existing ODE solvers. The displacements and stresses of the beam so computed can duly account for the shear-lag effect of wide-flange box beams. For long and medium-long beams, the stocky beam reduces to the Bernoulli-Euler or Timoshenko beam, depending on the range of slenderness ratios. Either asymmetric bending, restrained torsion, or cross-sectional warping of box girders can be easily treated. More phenomena will be explored in the exemplar study of various box girders.