Which theory states that failure or yielding occurs at a specific location within a member when the maximum primary or normal stress in a biaxial stress system reaches the material's limiting strength as determined in a simple tension test?

Correct option is C

The theory that states failure or yielding occurs when the maximum normal (primary) stress in a biaxial stress system reaches the material's limiting strength in simple tension is Rankine's Theory. Also known as the maximum normal stress theory, it assumes that failure initiates at the point where the largest normal stress equals the tensile strength of the material. This theory is particularly used for brittle materials, which are more sensitive to normal stress than shear stress.