In fatigue life, which coefficient is higher for spans with more deflection prone behavior?

• A. n
• B. ADTT
• C. M prime
• D. K factor

Answer: (A)

The main idea here is how fatigue life responds to the stress range from repetitive loading. In fatigue relationships, the number of cycles to failure is often described by an S-N curve where the fatigue life scales with the stress amplitude raised to a negative exponent, commonly referred to as n. This exponent controls how steeply life decreases as stress increases—the larger the n, the more sensitive the life is to changes in stress range.

Spans that deflect more under live loads experience larger stress ranges and more pronounced bending effects per cycle. That means each cycle does more damage, and the overall life declines more rapidly with increasing loading. To capture that greater sensitivity to stress range, the fatigue life model uses a higher n for these deflection-prone spans.

The other factors listed—traffic volume (ADTT), a moment modification term (M prime), and a dynamic amplification factor (K factor)—influence how loads are applied or amplified, but they do not describe how quickly fatigue damage accumulates with stress range in the same way. So the coefficient that increases for deflection-prone spans is the fatigue exponent.