Endurance strength is nearly proportional to ultimate strength but not with which of the following?

Endurance strength, which refers to the maximum stress a material can withstand for an infinite number of cycles without failing (often referred to as fatigue limit), is indeed closely related to the ultimate tensile strength of a material. However, this relationship does not hold when it comes to yield strength.

Yield strength is the stress level at which a material begins to deform plastically, meaning that after this point, the material will not return to its original shape. In contrast, endurance strength emphasizes the material's behavior under repeated loading conditions. While both yield strength and ultimate strength are measures of a material's response to load, they represent different failure mechanisms: yield strength is concerned with permanent deformation, while endurance strength focuses on fatigue failure, which occurs after many cycles of loading below the ultimate strength.

When considering design stress and shear stress, while they are important factors in the design process, they do not specifically correlate with the endurance strength in the same way yield strength does. Therefore, the relationship of endurance strength is particularly distinct with yield strength due to their inherent definitions and applications, making yield strength the exception in this context.