Open AccessThe aim of this work is to determine load-carrying capability of the multiply cross-section rod. This calculation is based on the model of the ideal plasticity of the material, so that the desired ultimate torque is a torque at which the entire cross section goes into a plastic state.
The article discusses the cylindrical multiply cross-section rod. To satisfy the equilibrium equation and the condition of plasticity simultaneously, two stress function Ф and φ are introduced. By mathematical transformations it has been proved that Ф is constant along the path, and a formula to find its values on the contours has been obtained. The paper also presents the rationale of the line of stress discontinuity and obtained relationships, which allow us to derive the equations break lines for simple interaction of neighboring circuits, such as two lines, straight lines and circles, circles and a different sign of the curvature.
After substitution into the boundary condition at the end of the stress function Ф and mathematical transformations a formula is obtained to determine the ultimate torque for the multiply cross-section rod.
Using the doubly connected cross-section and three-connected cross-section rods as an example the application of the formula of ultimate torque is studied.
For doubly connected cross-section rod, the paper offers a formula of the torque versus the radius of the rod, the aperture radius and the distance between their centers. It also clearly demonstrates the torque dependence both on the ratio of the radii and on the displacement of hole. It is shown that the value of the torque is more influenced by the displacement of hole, rather than by the ratio of the radii.
For the three-connected cross-section rod the paper shows the integration feature that consists in selection of a coordinate system. As an example, the ultimate torque is found by two methods: analytical one and 3D modeling. The method of 3D modeling is based on the Nadai’s sand analogy, complements and develops it.
The presented technique not only enables us to make calculations of the load-carrying capacity based on the ideal plasticity, but also allows us to investigate complex multiply crosssection rods in the creep.