Which expression correctly defines ultimate tensile strength (UTS) in terms of load and cross-section area?

Which expression correctly defines ultimate tensile strength (UTS) in terms of load and cross-section area?

• A. F / A
• B. Pmax / Ao
• C. Pmax * Ao
• D. F * Ao

Answer: (B)

Ultimate tensile strength is the maximum engineering stress a material can sustain in tension. Stress is defined as force per area, and for UTS we use the maximum load the specimen carries before fracture, divided by the original cross-sectional area. This gives the stress at the point of fracture in terms of the material’s original dimensions, allowing meaningful comparison between different samples. So the correct expression uses the maximum load (Pmax) divided by the original cross-sectional area (Ao), yielding Pmax / Ao. Using the original area keeps the value consistent even as the specimen necks and the actual area changes during loading. The other forms either mix in the current (reduced) area, produce units of force times area (not stress), or refer to true stress rather than the standard engineering UTS.

Ultimate tensile strength is the maximum engineering stress a material can sustain in tension. Stress is defined as force per area, and for UTS we use the maximum load the specimen carries before fracture, divided by the original cross-sectional area. This gives the stress at the point of fracture in terms of the material’s original dimensions, allowing meaningful comparison between different samples.

So the correct expression uses the maximum load (Pmax) divided by the original cross-sectional area (Ao), yielding Pmax / Ao. Using the original area keeps the value consistent even as the specimen necks and the actual area changes during loading. The other forms either mix in the current (reduced) area, produce units of force times area (not stress), or refer to true stress rather than the standard engineering UTS.