Wrc for Nozzles

AD 2000 CODE FOR PRESSURE VESSELS

VESSELS WITH NOZZLES SUBJECT TO ADDITIONAL LOADINGS - AD 2000 S3/6 (WRC CALCULATIONS)

MANUFACTURER: PROJECT NUMBER:

EQUIPMENT TAG: SERIAL NUMBER:

EQUIPMENT DESCRIPTION: OPENING DESCRIPTION:

MATERIAL DATA - AD 2000 W SERIES

SHELL

MATERIAL SPECIFICATION: MATERIAL GRADE:

APPLICABLE MERKBLATT: MATERIAL NUMBER:

NOZZLE



PAD



ANTICIPATED WORK CONDITIONS - AD 2000 B0

MAXIMUM TEMPERATURE: TS °C MAXIMUM PRESSURE: PS BARG

MINIMUM TEMPERATURE: C.E.T °C STATIC COLUMN HEAD: Pf BARG

DESIGN DATA - AD 2000 B0 & S3/0

DESIGN TEMPERATURE: T °C SHELL DESIGN STRESS: K N/mm²

DESIGN PRESSURE: p BARG SAFETY FACTOR S

SHELL MILL UNDERTOL.: c1 mm NOZZLE MILL UNDERTOL.: c1s mm

CORROSION ALLOWANCE: c2 mm NOZZLE COR. ALLOWANCE: c2s mm

SHELL & NOZZLE DATA - AD 2000 B9

SHELL OUTSIDE DIAMETER: Da mm NOMINAL THICKNESS: se mm

NOZZLE OUTSIDE DIAMETER: da mm NOMINAL THICKNESS: ss mm

PAD OUTSIDE DIAMETER: da,p mm NOMINAL THICKNESS: sp mm

APPLICABLE FORCES & MOMENTS

EXTERNAL RADIAL LOAD Fr N (+) FOR OUTWARD LOAD , (-) FOR INWARD LOAD

EXTERNAL LONGITUDINAL SHEAR LOAD Fl N

EXTERNAL CIRCUMFERENTIAL SHEAR LOAD Fc N

EXTERNAL LONGITUDINAL MOMENT Ml Nmm

EXTERNAL CIRCUMFERENTIAL MOMENT Mc Nmm

EXTERNAL TORTIONAL MOMENT Mt Nmm

DESIGN INTERNAL PRESSURE p

VESSEL GEOMETRY IMPORTANT FACTORS

VESSEL MEAN CORRODED RADIUS Rm = (Da - se + c1 + c2) / 2 = mm FOR NOZZLE TO SHELL EXAMINATION

NOZZLE MEAN CORRODED RADIUS ro = (da - ss + c1s + c2s ) / 2 = mm t = se + sp - c1 - c2 = mm

PAD MEAN CORRODED RADIUS ro,p = da,p / 2 = mm FOR PAD/SHELL t=se-c1-c2 = mm

APPLICABLE FACTORS (WRC DIAGRAMS)

N/mm²






γ = Rm / t = β = 0.875 ro / Rm = STRESS CONC. FACTOR Kb Kn

SHEAR STRESSES

tl = Fl / π ro t = tc = Fc / π ro t = SUM: τ=

RADIAL LOAD - STRESSES

FORCES & MOMENTS STRESSES

MEMBRANE FIG 1A Nφ Rm / t (1) Nφ = (1) Fr / Rm σφ = Κn Nφ / t

MEMBRANE FIG 1B Nx Rm / t (2) Nx = (2) Fr / Rm σx = Κn Nx / t

BENDING FIG 2A Mφ / Pr (3) Mφ = (3) Fr σφ =6ΚbMφ/ t²

BENDING FIG 2B Mx / Pr (4) Mx = (4) Fr σx =6ΚbMx/ t²

LONGITUDINAL MOMENT - STRESSES


MEMBRANE FIG 3A (5) σφ = Κn Nφ / t

MEMBRANE FIG 3B (6) σx = Κn Nx / t

BENDING FIG 4A Mφ Rm β / Μl (7) Mφ = (7) Ml / Rm β σφ =6ΚbMφ/ t²

BENDING FIG 4B Mx Rm β / Μl (8) Mx = (8) Ml / Rm β σx =6ΚbMx/ t²

CIRCUMFERENTIAL MOMENT - STRESSES


MEMBRANE FIG 5A (9) σφ = Κn Nφ / t

MEMBRANE FIG 5B (10) σx = Κn Nx / t

BENDING FIG 6A Mφ Rm β / Μc (11) Mφ = (11) Mc / Rm β σφ =6ΚbMφ/ t²

BENDING FIG 6B Mx Rm β / Μc (12) Mx = (12) Mc / Rm β σx =6ΚbMx/ t²

COMBINATION OF STRESSES

STRESS DUE TO:σx ( Ν/mm²) σφ ( Ν/mm²)

0° 90° 180° 270° 0° 90° 180° 270°

RADIAL LOAD MEMBRANE

RADIAL LOAD MEMBRANE

RADIAL LOAD BENDING

RADIAL LOAD BENDING

LONG. MOM. MEMBRANE + -

LONG. MOM. MEMBRANE + -

LONG. MOM. BENDING + -

LONG. MOM. BENDING + -

CIRC. MOM. MEMBRANE + -

CIRC. MOM. MEMBRANE + -

CIRC. MOM. BENDING + -

tt = Mt/2π ro² t = N/mm² N/mm²

N/mm²

N/mm²

Nφ Rm² β / Ml Nφ = (5) Ml / Rm² β

Nx Rm² β / Ml Nx = (6) Ml / Rm² β

N/mm²

Nφ Rm² β / Mc Nφ = (9) Mc / Rm² β

Nx Rm² β / Mc Nx = (10) Mc / Rm² β






CIRC. MOM. BENDING + -

PRESSURE σφ = p Rm / t + + + +

PRESSURE σx = p Rm / 2t + + + +

f3=√ (σφ-σx)²+4τ² =

σ = max(f1,f2,f3)

\

STRESSES SUM: Σ (N/mm²)

f1 = abs [ σφ + σx + √ ( σφ - σx ) ² + 4τ² ] / 2 = N/mm² N/mm² σ≤2,25K/S = Ν/mm² => STRESSES ARE ACCEPTABLE

f2 =abs [ σφ + σx - √ ( σφ - σx ) ² + 4τ² ] / 2 = N/mm² N/mm²

FIGURES 1A 1B

FIGURES 3A 3B

FIGURES 2A 2B

FIGURES 4A 4B






Note: c1 & c1s can be neglected, since accounting for mill undertolerance could lead to extremely conservative results.

MAXIMUM ALLOWABLE PRESSURES SHALL BE TAKEN FROM NOZZLE CALCULATIONS WITHOUT APPLYING THE EXTERNAL LOADS.

FIGURES 5A 5B

FIGURES 6A 6B

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