piping-stress

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:

1. Sustained loads (SL): gravity, internal pressure — continuous loading
2. Occasional loads (OCC): wind, seismic, relief valve — infrequent
3. 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

1. Build pipe model: nodes, elements, material, temperature, pressure
2. Define supports: restraints (X/Y/Z), anchors, guides, spring hangers
3. Assign boundary conditions: equipment nozzle nodes (anchor or flexibility matrix)
4. Define operating cases: OPE (operating), SUS (sustained), EXP (expansion), OCC (occasional)
5. Run analysis: check each stress category vs. code allowable
6. Check support loads: spring load ranges, anchor forces for equipment nozzle review
7. 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).