Parameters
Material
Pipe Size (NPS)
Schedule
Design Temperature T_d
250 °C
Installation Temperature T_i
20 °C
Pipe Length L
10.0 m
End Condition
Elbow SIF Calculation
Elbow Bend Ratio R/D
1.50
—
Expansion ΔL [mm]
—
Force F [kN]
—
Thermal Stress σ [MPa]
—
SIF Value (i)
Temperature Difference vs Thermal Stress
Thermal Force by Pipe Size (Current Conditions)
Theory (Caesar-II Compliant)
Thermal expansion:
$$\Delta L = \alpha \cdot \Delta T \cdot L$$Thermal stress (fully restrained):
$$\sigma_{th} = \alpha \cdot \Delta T \cdot E$$Thermal expansion force (both ends anchored):
$$F = \sigma_{th} \cdot A = \alpha \cdot \Delta T \cdot E \cdot A$$SIF-corrected equivalent stress (ASME B31.3):
$$S_E = i \cdot \frac{M_c}{Z} \leq S_A$$Flexibility characteristic (elbow): $h = \dfrac{t \cdot R}{r^2}$, $\quad i = \dfrac{0.9}{h^{2/3}}$, $\quad k = \dfrac{1.65}{h}$
Caesar-II Integration: The thermal expansion force and stress above are consistent with Caesar-II static analysis results. For detailed piping routing (loops, offsets) and support span optimization, use dedicated software such as Caesar-II or AutoPipe. In high-temperature petrochemical plants and power stations, accurate SIF and flexibility factor evaluation is the cornerstone of engineering design.