Final answer:
The question requires calculating the normal stress in a cylindrical rod at specific points using the force due to the weight of the rod and the cross-sectional area, then using the Soderberg relation to evaluate the potential for material failure.
Step-by-step explanation:
The given question explores the structural integrity of a metallic part under variable tensile forces, using the Soderberg relation to assess failure based on given material properties and a certain safety factor. The task involves an analysis of stress concentration and fatigue limits of a material due to a varying load. The Soderberg criterion integrates the mean stress and alternating stress components, accounting for stress concentrations, to determine if a material will yield or fatigue under certain conditions.
Calculating Normal Stress
To analyze the likelihood of failure, we must determine the normal stress at various points along the material. The formula for normal stress is σ = F/A, where F is the force applied and A is the cross-sectional area. The cross-sectional area at a particular distance from the lower end can be considered uniform as the variation in width is not specified at different heights.
Let us consider the following steps to solve the problem:
- Calculate the weight of the cylindrical rod using density (P) and volume (V).
- Find the cross-sectional area (A) of the rod at various points using the diameter given.
- Determine the normal stress (σ) at the specified cross-sections using the weight and the area.
Applying the Soderberg Relation
Once the normal stress values are acquired, they can be input into the Soderberg equation along with the provided material properties, factors of safety, and the endurance limit to assess if the part will withstand the applied forces without failing.