Accounting for tension in transverse bending of statically indeterminate elastic rods

Abstract

For statically indeterminate rod structures with excess constraints in the horizontal direction, tension forces arise under transverse loading, significantly affecting the stress-strain state of the rods compared to similar rods caused by bending alone (in the absence of excess longitudinal constraints). This fact requires computational analysis, and in this work, analytical dependencies of the deflection of the rod and the magnitude of tension due to transverse loading were obtained for cases with clamped-clamped and two hinged supports for the ends of the rod based on the derived Lagrangian principles of mechanics. Based on analytical dependencies, a graphical method was developed to determine the axial force under given stiffness and transverse loading for the considered computational cases. These results can be applied to the study of the stress-strain state of rod structures with excess constraints in the horizontal direction under transverse loading.