Stresses under Combined Loadings

When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.

The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from the neutral axis to the outer edges.

Shearing stresses, which act tangentially to the section, arise from shear forces and torsional or twisting moments. These stresses provide insights into the overall stress state within the tube. In addition, the calculated stresses are combined to identify the principal stresses at specific points, which are the maximum and minimum normal stresses without shear components.

From these, the maximum shearing stress is determined, a crucial factor in assessing the potential for failure.

Saint-Venant's principle allows for the assumption that stresses become uniformly distributed in sections far from the points of load application. This principle allows the use of superposition to combine effects from different loads, provided the stresses remain within the material's proportional limits. This method ensures accurate predictions of how structural components behave under real-world conditions.