Assume the steel has a Young's modulus of 193 GPa and a thermal expansion coefficient of 17.3E-6.
Assuming a welded rail line, 1 km long, that is unconstrained except at the ends. The rail has a cross-sectional profile as given. If the rail was installed at a temperature of 20°C, at what temperature would the rail buckle? How much pre-stress would need to be applied to the rail in order to prevent buckling up to a maximum operating temperature of 40°C?
Rail profile
Equivalent profile name: SBB1
Section weight: 46.17 kg/m
Rail height (H): 145.00 mm
Head width (C): 65.00 mm
Web thickness (A): 14.00 mm
Foot width (P): 125.00 mm
Moment of inertia, Ixx cm^4: 1641.10
Moment of inertia, Iyy cm^4: 298.20
46E1