| name | piping-flexibility |
| description | Piping flexibility analysis — thermal expansion, stress intensification factors (SIF), sustained/thermal/occasional loads, ASME B31.3 stress limits, Caesar II analysis, pipe support design. |
| metadata | {"priority":7,"promptSignals":{"phrases":["piping flexibility","thermal expansion pipe","pipe stress analysis","stress intensification factor","ASME B31.3 stress","Caesar II","pipe support"],"minScore":3}} |
Piping Flexibility Analysis — Complete Skill
Thermal Expansion
Linear thermal expansion:
ΔL = α × L × ΔT
α = thermal expansion coefficient [mm/m·°C]:
Carbon steel: 0.012; 300-series SS: 0.016; Aluminum: 0.023; Ti: 0.0086
ΔT = T_operating - T_installed (usually T_ambient = 20°C)
Expansion per 100m (carbon steel, ΔT = 200°C):
ΔL = 0.012 × 100 × 200 = 240 mm
Reaction force (fully restrained):
F = E × α × ΔT × A_pipe_wall [N]
For fully restrained pipe: σ_thermal = E × α × ΔT [no stress from DT if free to expand]
Load Categories (ASME B31.3)
Sustained Loads (Primary)
Dead weight (gravity) + internal pressure
Allowable sustained stress:
S_h = allowable stress at hot temperature [from ASME B31.3 Table A-1]
S_L (longitudinal) from pressure + weight: S_L ≤ S_h
- Hoop stress from pressure (pressure governs wall thickness)
- Longitudinal stress: σ_L = P × D / (4t) + M_b / Z
Thermal / Displacement Loads (Secondary — Self-Limiting)
Stresses from thermal expansion; pipe bends/loops absorb expansion
Allowable expansion stress range:
S_A = f × (1.25 S_c + 0.25 S_h)
S_c = allowable stress at cold/ambient temperature
S_h = allowable stress at hot temperature
f = cyclic reduction factor:
f = 1.0 for N ≤ 7,000 cycles; f = 6000 × N^(-0.2) for N > 7,000
Expansion stress range:
S_E = √(S_b² + 4S_t²) [resultant of bending and torsion expansion stresses]
S_b = bending stress from expansion = i × M_expansion / Z_pipe
S_t = torsional stress = M_torsion / (2Z)
Requirement: S_E ≤ S_A
Occasional Loads
Wind, seismic, water hammer; short duration
Occasional stress limit:
S_L + S_OCC ≤ 1.33 S_h
Operating Case (Pressure + Weight + Thermal)
Combined check; ASME B31.3 App. S (more rigorous) or simplified above
Stress Intensification Factor (SIF)
Elbows, bends, tees amplify stress vs. straight pipe:
Effective bending moment:
M_eff = i × M_actual where i = SIF ≥ 1.0
SIF for elbows/bends (ASME B31.3 Appendix D):
i = 0.9 / h^(2/3) ≥ 1.0 [in-plane and out-of-plane]
h = t × R_bend / r² = pipe bend flexibility characteristic
t = wall thickness; R_bend = bend radius; r = pipe mean radius
Typical SIF values:
Long radius elbow (R/D = 1.5): i ≈ 1.5–2.0
Short radius (R/D = 1.0): i ≈ 2.0–3.0
Tee (reinforced, r/D = 0.5): i ≈ 2.5–3.5
Tee (unreinforced): i ≈ 4.0–6.0
Reducer: i ≈ 1.5–2.5 depending on taper
Flexibility factor k: elbow deflects more than equivalent straight pipe
k = 1.65/h [for in-plane bending; same formula structure]
Expansion Loops and Expansion Joints
L-shaped and Z-shaped arrangements
L-shape: single bend; limited flexibility — calculate leg length for ΔL:
L_2 = √(3 × E × D × ΔL / S_A) [required flexibility leg]
Expansion loop:
U-loop provides much greater flexibility than L-bend
Length of loop L_loop: 2 × L_2 from above formula
Expansion Joints (Bellow)
Axial bellows: absorbs axial movement; no rotation
Lateral bellows: absorbs lateral offset; generates forces at anchors
Hinged/gimbal: absorbs angular rotation; no forces (only moments)
Key parameters:
Spring rate (axial): K_ax [N/mm]
Effective pressure area: A_eff → anchor forces from pressure: F_p = P × A_eff
Design life: 10,000–100,000 cycles (EJMA specification)
Disadvantage: failure point; not used in high-reliability or corrosive service without sleeve
Caesar II (Hexagon PPM) Analysis
Load cases (required minimum):
W = weight
T = thermal
P = pressure
OCC = wind/seismic/water hammer
Code compliance check cases:
Sustained (W + P): compare to S_h
Expansion (T only): compare to S_A
Operating (W + T + P): for support loading and nozzle loads
Occasional (W + P + OCC): compare to 1.33 × S_h
Output review:
Code stress ratios > 1.0 → over-stressed; add flexibility (loop, bend, reduce support restrain)
Support loads → size supports (anchors, guides, resting)
Equipment nozzle loads → compare to API 610 (pumps), API 661 (air-coolers), NEMA SM23 (turbines)
Pipe Support Design
Support Types
Rest/Hanger: vertical support; weight load only; allow thermal movement
Guide: lateral restraint; vertical free; horizontal perpendicular to pipe axis restrained
Anchor: all 6 DOF restrained; absorbs all thermal loads from pipe
Spring hanger (variable/constant): accounts for thermal vertical movement; maintains support load
Spring Hanger Selection
Variable spring: support load changes with position; use if load change < 25%
Constant support: maintains constant load regardless of movement; for sensitive equipment
Variability: Var = (F_hot - F_cold) / F_cold × 100% [%]
< 25%: variable spring acceptable; > 25%: use constant support hanger
Support Span for Natural Frequency
Minimum span (sag limit = 13mm):
L_span = 128 × √(Z × S / (w × D)) [Crane rule; various forms]
Simply supported beam natural frequency:
f_n = (π²/L²) × √(EI/ρA) [Hz]
Target: f_n > 4 × pipe excitation frequency (pump BPF or pulsation frequency)
Water Hammer / Surge Analysis
Joukowski pressure rise:
ΔP = ρ × a × ΔV [Pa]
a = wave speed = 1/√(ρ(1/K + D/(E×t))) [m/s; K = bulk modulus liquid]
For water in steel pipe: a ≈ 1200–1400 m/s
Design check: P_operating + ΔP_surge ≤ 1.33 × P_design (occasional load)
Output
Provide: maximum sustained stress S_L vs. allowable S_h [MPa], maximum expansion stress S_E vs. allowable S_A [MPa], governing SIF at critical fitting, thermal expansion ΔL [mm] in each direction, support loads (vertical + horizontal) at each support, equipment nozzle load comparison vs. allowable, expansion loop or expansion joint specification, applicable code (ASME B31.3 for process; B31.1 for power piping; B31.4/B31.8 for pipeline).
