Modified continuity conditions of plates in beam-column using the Mindlin plate theory

• The first order shear deformation plate theory FSDT.
• Two independent functions of displacements: the total lateral displacement w and the bending deflection φ.
• Hamilton's principle employing the classical Mindlin approach.
• The shear locking is not ignored but the boundary layer effect is neglected.
• A method of the modal solution to the buckling problem within Koiter's asymptotic theory has been used.

In the present paper, two independent functions of displacements along the z axis direction, i.e., the total lateral displacement w and the bending deflection φ, have been introduced within the first order shear deformation plate theory FSDT. The differential equations of motion and boundary conditions have been derived from Hamilton's principle employing the classical Mindlin approach. Modified conditions of two adjacent component plate interactions have been formulated. A plate model of the plate structure has been adopted to describe all possible buckling modes. The obtained equations are approximate since the shear locking is not ignored but the boundary layer effect is neglected. A method of the modal solution to the buckling problem within Koiter's asymptotic theory has been used. The calculations have been conducted for a few beam-columns of various shapes of cross-sections. The obtained results that account for transverse shear deformation have been compared to the results attained for the classical thin plate theory.