English
Menu

Mechanical properties and fracture

A round bar 10 mm in diameter carries a tensile load of 10 kN. Which value is closest to the engineering stress?

  1. AAbout 31.8 MPa
  2. BAbout 127 MPa
  3. CAbout 0.127 MPa
Show answer and explanation

Answer: B. About 127 MPa

The cross-sectional area is A = πd²/4 = π × (10 mm)²/4 ≈ 78.5 mm², so the engineering stress is σ = F/A = 10000 N / 78.5 mm² ≈ 127 N/mm² = 127 MPa (1 N/mm² = 1 MPa). About 31.8 MPa comes from mistaking the diameter for the radius and taking A = π × (10 mm)² ≈ 314 mm². About 0.127 MPa results from the wrong area conversion 1 mm² = 10⁻³ m²; the correct one is 1 mm² = 10⁻⁶ m². Engineering stress is based on the original cross-sectional area, so it differs from the actual stress after necking begins.

Report an error

Practice this topic Back to topic

Related calculators

Thermal Expansion and Thermal Stress CalculatorCalculate the elongation from a temperature change and the thermal stress when constrained

More Mechanical properties and fracture questions

  1. A steel rod 2.0 m long with a Young's modulus of 200 GPa is loaded in tension to 100 MPa within its elastic range. Which value is closest to the elongation of the rod?
  2. For materials such as aluminum alloys that show no distinct yield point, which correctly describes how the 0.2% offset yield strength is determined?
  3. In a tensile test, the engineering stress was 400 MPa at an engineering strain of 0.20, before necking began. Assuming constant volume during plastic deformation, which value is closest to the true stress at this point?
  4. Which statement about the Vickers hardness test is correct?
  5. A steel plate with a fracture toughness K_IC = 50 MPa·√m carries a tensile stress of 200 MPa. Using K = Yσ√(πa) with a geometry factor Y = 1.0, which value is closest to the critical crack length a at which fracture occurs?