Problem # p015

Thermal Stress

Steel railroad rails are laid in sections, each L = 10 m long. Assume that they are laid at a temperature of 20°C with a gap between adjacent sections of g = 3 mm.
  1. By how many millimeters can each section get longer before adjacent sections (excluding the two end sections) touch ?

  2. At what temperature would adjacent sections touch ?

  3. By how many degrees could the temperature increase further before the thermal stress in the rails reaches 200 MPa (=stress limit for steel) ?

Assume : Coefficient of thermal expansion α=12.0*10-6 m/(m °C) and Young's modulus E = 200 GPa