Homogenized model of a common vierendeel member being equivalent to a solid web member under uniformly distributed transverse loading

The current analytical approach for modeling RC Vierendeel girders, RC trusses, and RC perforated beams with regular rectangular openings (collectively referred to as Vierendeel members) as equivalent solid web members exhibits a significant deflection error of 28.79% in shear deformation calculations. This discrepancy poses safety risks in structural modeling involving Vierendeel members. To address this issue, this study proposes a new homogenization method using distribution coefficients. The distribution coefficients for shear, bending, and axial stiffness of the shear key were analytically derived based on the forces acting on typical Vierendeel members. The total deflection, comprising bending and shear components, was calculated using the linear elastic equilibrium differential equation and validated through finite element method (FEM). The proposed method achieves higher accuracy for deflection calculations under both small and large shear deformations. A theoretical equation was then developed to model Vierendeel sandwich slabs, Vierendeel space trusses, and perforated beams as equivalent solid web members. For practical engineering applications, the formula was further simplified through regression analysis. This study provides valuable insights into shear deformation and offers a more accurate method for modeling Vierendeel members.