Calculation of a stepped rod under longitudinal-transverse bending with discrete axis loading

Abstract

This paper aims at obtaining formulas for bending moments and shear forces in a rectilinear elastic stepped rod under plane longitudinal-transverse bending. Each step of the rod (segment) can consist of different materials and have its own shape and cross- sectional dimensions. The rod can be loaded by an axial longitudinal force at the beginning of each step. The eccentricity of longitudinal forces at the beginning of each step (segment) is taken into account, which occurs due to the mismatch of longitudinal axes at the current and previous steps. Each segment of the rod can be exposed to a transverse action represented as concentrated bending moments, concentrated forces, and uniformly distributed loading. The resulting algebraic equations of the bending moments and shear forces are obtained for the stepped rod under longitudinal-transverse bending. The numerical model has been considered. The study results show that allowance for longitudinal action on the stepped rod bending with discrete axial loading leads to an increase in the ordinates of epures and bending moments, as well as in shear forces as compared to transverse bending caused by transverse loading only. Moreover, the internal transverse forces do not remain constant on the rod segments which are free from uniformly-distributed transverse loading. The obtained formulas for bending moments and transverse forces can be applied in calculations of elastic stepped rods under longitudinal-transverse bending.