| name | piping-stress |
| description | Piping stress analysis — ASME B31.3 code stresses, thermal expansion, pipe flexibility, sustained/occasional/expansion loads, Caesar II workflow, nozzle loads, pipe support design. |
| metadata | {"priority":7,"promptSignals":{"phrases":["piping stress","ASME B31.3","pipe stress","thermal expansion","Caesar","pipe flexibility","nozzle load","pipe support"],"minScore":4}} |
Piping Stress Analysis — Complete Skill (ASME B31.3)
Code Compliance Overview (ASME B31.3 — Process Piping)
Three primary stress categories, each with allowable limits:
- Sustained loads (SL): gravity, internal pressure — continuous loading
- Occasional loads (OCC): wind, seismic, relief valve — infrequent
- Expansion loads (EXP): thermal, settlement — cyclic
Design Pressure and Wall Thickness
Required Wall Thickness (ASME B31.3 Eq. 3a)
t_m = t + c
t = PD/(2(SEW + PY)) [basic wall, straight pipe]
c = corrosion + erosion allowance + thread depth [mm]
Where:
P = design pressure [MPa]
D = outside diameter [mm]
S = allowable stress at design temperature [MPa] (ASME B31.3 Table A-1)
E = longitudinal weld quality factor (1.0 seamless, 0.85 ERW, 0.7 furnace butt)
W = weld strength reduction factor (1.0 for T ≤ 510°C)
Y = coefficient from Table 304.1.1 (0.4 for most metals)
Mill tolerance: add 12.5% to t_m for standard pipe (or use nominal per pipe schedule)
Pipe Schedule Selection
Nominal pipe size (NPS) + schedule → wall thickness from ASME B36.10 / B36.19
Schedule 40/80/160/XXS for carbon steel; 10S/40S for stainless
Required: t_nominal × (1 - mill_tol%) ≥ t_m
Pipe Material Properties
| Material | Temp | S_h [MPa] | α [10⁻⁶/°C] | E [GPa] |
|---|
| A106 Gr B (CS) | 20°C | 138 | 12.0 | 200 |
| A106 Gr B (CS) | 400°C | 103 | 13.0 | 186 |
| A312 TP316 (SS) | 20°C | 138 | 16.0 | 193 |
| A312 TP316 (SS) | 400°C | 96 | 17.0 | 174 |
Sustained Load Stress (B31.3 Eq. 320.1)
S_L = P×D/(4×t) + 0.75i × M_A/Z ≤ S_h
Where:
P×D/(4t) = pressure hoop contribution (longitudinal component = hoop/2)
M_A = resultant bending moment from sustained loads [N·mm]
Z = section modulus = π/32 × (D⁴ - d⁴)/D [mm³]
i = stress intensification factor (SIF) per Appendix D
S_h = basic allowable stress at operating temp [MPa]
SIF for fittings (ASME B31.3 Appendix D):
Butt weld: i = 1.0
Socket weld: i = 2.1
Weld-o-let: i = 1.5-3.0 (depends on geometry)
Miter bend: i = 1 + 0.9/h^(2/3) (h = flexibility characteristic = t × R/(r²))
Elbow: i = 0.9/h^(2/3) (in-plane), 0.75/h^(2/3) (out-of-plane)
Occasional Load Stress (B31.3 Eq. 320.2)
S_OCC = S_L + M_B/Z ≤ kS_h
k = 1.33 (wind or seismic), 1.2 (snow/ice)
M_B = bending moment from occasional loads
Thermal Expansion Stress (B31.3 Eq. 319.2.3a)
S_E = √(S_b² + 4S_t²) ≤ S_A
S_b = resultant bending stress = i × M_c/Z
S_t = torsional stress = M_t/(2Z)
M_c = resultant range of bending moment from thermal expansion
Allowable expansion stress range:
S_A = f × (1.25S_c + 0.25S_h) [MPa]
f = stress range reduction factor (f=1 for N≤7000 cycles; decreases for more cycles)
S_c = cold (ambient) allowable stress [MPa]
With stress reduction: S_A = f × [1.25(S_c + S_h) - S_L] (per B31.3 Rev 2020)
Thermal Expansion
Pipe expansion: ΔL = α × L × ΔT
ΔT = T_operating - T_installed [°C]
Example: CS pipe, L=50m, ΔT=200°C: ΔL = 12×10⁻⁶ × 50,000 × 200 = 120 mm
This must be absorbed by: expansion loops, bellows, or system flexibility
Expansion Loop
L-loop, U-loop, Z-loop — bend flexibility absorbs expansion
Minimum loop leg: L_min = 3D_pipe × √(Δ/(3 allowable stress))... from Caesar II analysis
Bellows expansion joints: accommodate large displacements in limited space
Require anchor + guide supports; introduce pressure thrust forces
Tie-rod vs. unrestrained bellows — critical distinction for support design
Caesar II Workflow
- Build pipe model: nodes, elements, material, temperature, pressure
- Define supports: restraints (X/Y/Z), anchors, guides, spring hangers
- Assign boundary conditions: equipment nozzle nodes (anchor or flexibility matrix)
- Define operating cases: OPE (operating), SUS (sustained), EXP (expansion), OCC (occasional)
- Run analysis: check each stress category vs. code allowable
- Check support loads: spring load ranges, anchor forces for equipment nozzle review
- Optimize: add expansion loops, relocate supports, change support types to reduce overstress
Pipe Support Types
| Type | Function | Restraints |
|---|
| Resting support (shoe) | Carry weight | Vertical only (Y) |
| Line stop | Prevent axial movement | Axial (Z or X) |
| Guide | Prevent lateral movement | Lateral only |
| Anchor | Fully fixed | All 6 DOF |
| Spring hanger | Variable support | Y load constant, allows movement |
| Constant load hanger | Fixed load spring | Y load constant through displacement |
| Rigid strut | Carries dynamic loads | Axial |
Support spacing (MSS SP-69 / ASME B31.3):
Water service: span L ≈ 2.5-3× √(t/w) [empirical, depends on pipe size]
Quick estimate: NPS 2 → 3m; NPS 6 → 5m; NPS 12 → 6m; NPS 24 → 8m
Nozzle Loads (Equipment Interface)
Excessive pipe loads on equipment nozzles → equipment distortion, misalignment, failure
Limits: API 610 (pumps), API 617 (compressors), NEMA SM-23 (steam turbines), WRC 107/297 (vessel nozzles)
WRC 107 / WRC 297: compute stresses in nozzle-vessel junction from applied forces/moments
Check: σ_combined vs. 3S allowable (per ASME VIII)
Pump nozzle limits (API 610 Table 4):
Allowable moments and forces as function of nozzle size (NPS)
Example NPS 3: F_x,y,z ≤ 1800 N, M_x,y,z ≤ 500 N·m each
Dynamic Analysis (Slug Flow, PSV, Water Hammer)
PSV (pressure relief valve) reaction force:
F = ṁ × v_jet + (P_back - P_atm) × A_exit
F acts on valve body → creates dynamic pipe load → design per ASME B31.1 Appendix II
Water hammer:
ΔP = ρ × c × ΔV where c = √(K/ρ) for rigid pipe, modified for flexible
c_steel ≈ 1300-1480 m/s (full water), c_flexible ≈ 500-800 m/s
Joukowsky equation: ΔP = ρcΔV (instantaneous valve closure)
Slug flow: two-phase intermittent flow → transient force F = ṁ_slug × v²/g... dynamic analysis required
Output
Provide: wall thickness t_m [mm], pipe schedule, S_L/S_h ratio, S_E/S_A ratio, maximum support span [m], critical expansion loop dimension [m], nozzle loads vs. allowable (API/WRC).
