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CWR Rail Thermal Buckling Calculator engineering
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CWR Rail Thermal Buckling Calculator

Railway civil engineering: Model Continuous Welded Rail (CWR) longitudinal thermal expansion force ($P_{therm}$), lateral ballast resistance, critical buckling load ($P_{cr}$), and allowable rail temperature rise.

Rail & Temperature Specifications

Thermal Force & Buckling Safety

Thermal Compressive Force $P_{therm}$
--
kN (total across both rails)
Critical Buckling Load $P_{cr}$
--
kN (limit equilibrium threshold)
Allowable Temp Rise $\Delta T_{allow}$
--
°C above neutral temperature
Rail Compressive Stress $\sigma_{therm}$
--
MPa ($E \alpha \Delta T$)
Track Buckling Safety Margin
--
$P_{cr} / P_{therm}$ factor
Breathing Zone Length $L_{br}$
--
meters (longitudinal expansion)

Track Lateral Resistance vs Buckling Curve

Rail Temperature Rise $\Delta T = T - T_N$ (°C) Compressive Force $P$ (kN) P_cr Limit Thermal Force $P_{therm}(\Delta T)$ Critical Resistance Limit $P_{cr}$
Thermal compressive load increases linearly with temperature rise above the Neutral Temperature ($T_N$). Buckling occurs if $P_{therm}$ exceeds lateral ballast restraint.

CWR Buckling & Neutral Temperature Mechanics

Continuous Welded Rail eliminates mechanical fishplate joints by welding rail sections into continuous strings thousands of meters long. Thermal restraint develops massive compressive forces:

$$P_{\text{therm}} = 2 \, E \, A \, \alpha \, (T_{\max} - T_N)$$ $$P_{cr} \approx 2 \sqrt{2 \, E \, I_y \, F_{\text{lat}}} \left( 1 - 0.25 \frac{w_0}{w_{cr}} \right)$$

Where $\alpha = 1.15 \times 10^{-5} \, \text{K}^{-1}$ is the thermal expansion coefficient of rail steel. Installing rails at an optimal Stress-Free Temperature (SFT / $T_N \approx 28 - 35^\circ\text{C}$) ensures a balanced risk profile between summer sun-kinks (buckling) and winter tensile rail pull-aparts.

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