This presentation file is provided by Mr. Ghanbari and published under permission. The presentation gives an introduction and general guideline for pressure vessel design by analysis. The “design by analysis” procedures are intended to guard against eight possible pressure vessel failure modes by performing a detailed stress analysis of the vessel with the sufficient design factors. The failure modes are: 1.excessive elastic deformation, including elastic instability, 2.excessive plastic deformation, 3.brittle fracture, 4.stress rupture/creep deformation (inelastic), 5.plastic instability - incremental collapse, 6.high strain - low cycle fatigue, 7.stress corrosion, and 8.corrosion fatigue Most of the “design by analysis” procedures that are given in ASME BPVC relate to designs based on “elastic analysis.” The design-by-analysis requirements are organized based on protection against the failure modes listed below. The component shall be evaluated for each applicable failure mode. If multiple assessment procedures are provided for a failure mode, only one of these procedures must be satisfied to qualify the design of a component. a)All pressure vessels within the scope of this Division, irrespective of size or pressure, shall be provided with protection against overpressure in accordance with the requirements of this Part. b)Protection Against Plastic Collapse – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules. c)Protection Against Local Failure – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules. It is not necessary to evaluate the local strain limit criterion if the component design is in accordance with Part 4 (i.e. component wall thickness and weld detail per paragraph 4.2). d)Protection Against Collapse From Buckling – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules and the applied loads result in a compressive stress field. e)Protection Against Failure From Cyclic Loading – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules and the applied loads are cyclic. In addition, these requirements can also be used to qualify a component for cyclic loading where the thickness and size of the component are established using the design-by-rule requirements of Part 4.

1. DESIGN BY ANALYSIS
HEDCO
Spring 2009
G. Ghanbari
A GENERAL GUIDELINE

2. Overall Design Procedure of Pressure Vessel
ASME Sec VIII Div. 1
Input Data
(Mechanical and Process
Data Sheets)
Shell Design (Thickness of Shell) under
External Pressure (UG-16, 28, 31)
Material Selection for Vessel Components
1. Service
2. Design Temperature (UG-23 and ASME Sec. II Tables)
3. MDMT and Impact Test (UCS-66, 67, UHA-51, UG-20 (f), UG-84)
Shell Design (Thickness of Shell) under
Internal Pressure (UG-16, 27, 31)
Calculation of Stiffening Rings
(UG-29, 30)
Head Design (Thickness of Formed Head)
under Internal Pressure
(UG-16,32, 34)
Head Design (Thickness of Formed Head)
under External Pressure (UG-33, 34)
Nozzle / Opening and Reinforcement Design
(UG-36, 37, 38, 39, 40, 41, 42, 43, 44, 45,
UW-15, 16)
Calculation of Nozzle Load and
Strength (WRC-107, 297)
Welding Design (UW-9, 12, 13)
Definition of PWHT (UW-40, UCS-56, UHA-32)
Requirement for Examinations (UG-99, UW-11, 52)
Support Design Skirt, Leg, etc.
(Standard Drawings)
Wind and Seismic Calculations for
Vessel and Anchoring Design
(Appendix L, UBC, ASCI-112)
Design of External Attachments and Transportation
Components lifting lug, Tailing lug, Piping clip (Standard
Drawings)
Tolerances (specification,
UG-80,81)
Vortex shedding, vibration analysis
(Specification)
Is External
pressure applied
YES
Is External pressure
applied
YES
NO
Weight Calculations
Design Review (QA procedure,
Relevant Paragraphs)
Cylindrical Shell
YES
NO
NO

3. 0.00E+00 2.00E+07 4.00E+07 6.00E+07 8.00E+07 1.00E+08 1.20E+08 1.40E+08 1.60E+08
Div. 1
Div. 2
Div. 3
Pressure Scope
Not Recommended Recommended Allowed
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00E+00 2.00E+07 4.00E+07 6.00E+07 8.00E+07 1.00E+08 1.20E+08 1.40E+08 1.60E+08
Thickness/InnerRadius
Pressure, Pa
t/Ri Div 1
t/Ri Div 2
t/Ri Div 3
t/Ri Div 1 considering allowable stress of Div 2
PSE
P
R
t
i 6.0−
=
1exp −





=
SE
P
R
t
i
1
2
3
exp −








=
yi S
P
R
t

4. Introduction to DBA
The “design by analysis” procedures are intended to guard against eight possible pressure
vessel failure modes by performing a detailed stress analysis of the vessel with the sufficient
design factors.The failure modes are:
1. excessive elastic deformation, including elastic instability,
2. excessive plastic deformation,
3. brittle fracture,
4. stress rupture/creep deformation (inelastic),
5. plastic instability - incremental collapse,
6. high strain - low cycle fatigue,
7. stress corrosion, and
8. corrosion fatigue
Most of the “design by analysis” procedures that are given in ASME BPVC relate to designs
based on “elastic analysis.”

5. Introduction to DBA
The design-by-analysis requirements are organized based on protection against the failure modes listed
below.The component shall be evaluated for each applicable failure mode. If multiple assessment
procedures are provided for a failure mode, only one of these procedures must be satisfied to qualify the
design of a component.
a) All pressure vessels within the scope of this Division, irrespective of size or pressure, shall be provided
with protection against overpressure in accordance with the requirements of this Part.
b) Protection Against Plastic Collapse – these requirements apply to all components where the thickness
and configuration of the component is established using design-by-analysis rules.
c) Protection Against Local Failure – these requirements apply to all components where the thickness
and configuration of the component is established using design-by-analysis rules. It is not necessary
to evaluate the local strain limit criterion if the component design is in accordance with Part 4 (i.e.
component wall thickness and weld detail per paragraph 4.2).
d) Protection Against Collapse From Buckling – these requirements apply to all components where the
thickness and configuration of the component is established using design-by-analysis rules and the
applied loads result in a compressive stress field.
e) Protection Against Failure From Cyclic Loading – these requirements apply to all components where
the thickness and configuration of the component is established using design-by-analysis rules and
the applied loads are cyclic. In addition, these requirements can also be used to qualify a component
for cyclic loading where the thickness and size of the component are established using the design-by-
rule requirements of Part 4.

6. Overall Design Procedure of Pressure Vessel
ASME Sec VIII Div. 2 Vessel Design Data
(Generally extracted from UDS)
P>3000 psi
1-Engineering judgment
2-Client’s Specification
3-Economics
YES
NODiv 1
Div 2
Design By Rule
Is the DBR enough?
(1-Engineering judgment
2-Client’s Specification)
Material Properties: E, ν, App. 3.D
Material Model: Actual, Associated
Plasticity, von Misses
Formulation: Large Displacement
Updated Lagrangian
Material Properties: E, ν, Sy
Material Model: Elastic perfectly Plastic
Formulation: Small Displacement
Total Lagrangian
Material Properties: E, ν
Material Model: Linear Elastic
Formulation: Small
Displacement
Limit Load
YES
Vessel Design
calculation
Report
Tentative
Geometry for
Analysis
NO
Stress
Analysis Method
(R/t)>4 ElasticElastic Plastic
YES
1-Modify the configurations
2-Reduce applied Loads
Limit Check
Fig 5.1
Does the problem
converge?
Does the problem
converge?
NO
NONO
Specifying
Vessel Areas to
be Locally
Evaluated
YES
YES
Load-Control Loads
Displacement-Control Loads
Establishing Design Load
Combinations Table 5.3
Determine of
Load Parameters
Table 5.2
Definition of Loading
Conditions Table 5.1
Post-processing and
Classification of Stresses Table
5.6 Appendix 5.A
Establishing Design Load
Combinations and Load Factors
Table 5.4
Establishing Design Load
Combinations and Load Factors
Table 5.5

7. Overall Design Procedure of Pressure Vessel
ASME Sec VIII Div. 2 (Con.)
Fabrication
Detail
Non-Standard Standard Elastic Analysis
Elastic-Plastic
Analysis
σ1+σ2+σ3≤4Sεpeq+εcf≤εL
1-Modify the configurations
2-Reduce applied Loads
NO NO
Buckling Analysis YESYES
Analysis Type Bifercation
Determination of Capacity
Reduction Factor, βcr
Determination of Minimum
Design Factor, ФB
Load Factors of Table 5.5
Explicit
1-Modify the configurations
2-Reduce applied Loads
Probable Buckling Modes occur at loads
greater than design Loads multiplied by ФB
NO
Does the problem
converge?
NO
Cyclic Analysis
Requirement Check
YESYES

8. Table 5.1 – Loads and Load Cases To Be Considered in a Design
Loading Condition Design Loads
PressureTesting 1. Dead load of component plus insulation, fireproofing, installed internals, platforms and other
equipment supported from the component in the installed position.
2. Piping loads including pressure thrust
3. Applicable live loads excluding vibration and maintenance live loads.
4. Pressure and fluid loads (water) for testing and flushing equipment and piping unless a pneumatic test
is specified. 5.Wind loads
NormalOperation 1. Dead load of component plus insulation, refractory, fireproofing, installed internals, catalyst, packing,
platforms and other equipment supported from the component in the installed position.
2. Piping loads including pressure thrust
3. Applicable live loads.
4. Pressure and fluid loading during normal operation. 5.Thermal loads.
NormalOperation plus
Occasional (note: occasional
loads are usually governed by
wind and earthquake;
however, other load types
such as snow and ice loads
may govern, see ASCE-7)
1. Dead load of component plus insulation, refractory, fireproofing, installed internals, catalyst, packing,
platforms and other equipment supported from the component in the installed position.
2. Piping loads including pressure thrust
3. Applicable live loads.
4. Pressure and fluid loading during normal operation.
5. Thermal loads.
6. Wind, earthquake or other occasional loads, whichever is greater.
7. Loads due to wave action
Abnormal or Start-up
Operation plus Occasional
(see note above)
1. Dead load of component plus insulation, refractory, fireproofing, installed internals, catalyst, packing,
platforms and other equipment supported from the component in the installed position.
2. Piping loads including pressure thrust
3. Applicable live loads.
4. Pressure and fluid loading associated with the abnormal or start-up conditions.
5. Thermal loads.
6. Wind loads.

9. Table 5.2 – Load Descriptions
Design Load
Parameter
Description
P Internal and external maximum allowable working pressure
Ps Static head from liquid or bulk materials (e.g. catalyst)
D Dead weight of the vessel, contents, and appurtenances at the location of interest, including
the following:
• Weight of vessel including internals, supports (e.g. skirts, lugs, saddles, and legs), and
appurtenances (e.g. platforms, ladders, etc.)
• Weight of vessel contents under operating and test conditions
• Refractory linings, insulation
• Static reactions from the weight of attached equipment, such as motors, machinery, other
vessels, and piping
L • Appurtenance Live loading
• Effects of fluid momentum, steady state and transient
E Earthquake loads (see ASCE 7 for the specific definition of the earthquake
load, as applicable)
W Wind Loads
Wpt
Is the pressure test wind load case.The design wind speed for this case shall be specified by
the Owner-User.
Ss Snow Loads
T Is the self-restraining load case (i.e. thermal loads, applied displacements). This load case
does not typically affect the collapse load, but should be considered in cases where elastic
follow-up causes stresses that do not relax sufficiently to redistribute the load without
excessive deformation.

10. Table 5.3 – Load Case Combinations and Allowable Membrane Stresses for an
Elastic Analysis
Design Load Combination Allowable General Primary
Membrane Stress (1),(2),(3)
1) P +Ps +D S
2) P + Ps + D + L S
3) P + Ps+ D + Ss S
4) 0.6D + (W or 0.7E) (4) S
5) 0.9P + Ps + D+ (W or 0.7E ) S
6) 0.9P + Ps + D + 0.75L + 0.75 Ss S
7) 0.9P + Ps + D + 0.75(W or 0.7E) + 0.75L + 0.75Ss S
Notes
1) The parameters used in the Design Load Combination column are defined inTable 5.2.
2) The term 0.9P is considered an operating pressure.
3) S is the allowable stress for the load case combination.This value represents the general primary
membrane stress limit for “load-controlled” loads. Stress limits for local membrane and
bending stresses from “load-controlled” or “strain-controlled” loads are provided in paragraph
5.2.2.4.
4) This load combination addresses an overturning condition. If anchorage is included in the
design, consideration of this load combination is not required.

11. Design Conditions
Criteria Required Factored Load Combinations
Global Criteria
1) 1.5 (P+ Ps+ D)
2) 1.3 (P+ Ps+ D+T ) + 1.7L + 0.54 Ss
3) 1.3 (P+ D) + 1.7Ss + max[1.1L , 0.86W]
4) 1.3 (P + D) + 1.7W + 1.1L + 0.54Ss
5) 1.3 (P + D) + 1.1E + 1.1L + 0.21Ss
Local Criteria PerTable 5.5
Serviceability Criteria Per User’s Design Specification, if applicable, seeTable 5.5
Hydrostatic Test Conditions
Global Criteria {max[1.43, 1.25 (ST/S)]}.(P + Ps + D) + 2.6 Wpt
Serviceability Criteria Per User’s Design Specification, if applicable.
Pneumatic Test Conditions
Global Criteria 1.15 (ST/S).(P + Ps + D) + 2.6 Wpt
Serviceability Criteria Per User’s Design Specification, if applicable.
Notes:
1) The parameters used in the Design Load Combination column are defined inTable 5.2.
2) See paragraph 5.2.3.4 for descriptions of global and serviceability criteria.
3) S is the allowable membrane stress at the design temperature.
4) ST is the allowable membrane stress at the pressure test temperature.
Table 5.4 – Load Case Combinations and Load Factors for a Limit Load Analysis

12. Design Conditions
Criteria Required Factored Load Combinations
Global Criteria
1) 2.4 (P+ Ps+ D)
2) 2.1 (P+ Ps+ D+T ) + 2.6L + 0.86 Ss
3) 2.1 (P+ D) + 2.6Ss + max[1.7L , 1.4W]
4) 2.4 (P + D) + 2.6W + 1.7L + 0.86Ss
5) 2.4 (P + D) + 1.7E + 1.7L + 0.34Ss
Local Criteria 1.7 (P+ Ps+ D)
Serviceability Criteria Per User’s Design Specification, if applicable, see paragraph 5.2.4.3.b.
Hydrostatic Test Conditions
Global Criteria {max[2.3, 2.0 (ST/S)]}.(P + Ps + D) +Wpt
Serviceability Criteria Per User’s Design Specification, if applicable.
Pneumatic Test Conditions
Global Criteria 1.8 (ST/S).(P + Ps + D) +Wpt
Serviceability Criteria Per User’s Design Specification, if applicable.
Notes:
1) The parameters used in the Design Load Combination column are defined inTable 5.2.
2) See paragraph 5.2.4.3 for descriptions of global and serviceability criteria.
3) S is the allowable membrane stress at the design temperature.
4) ST is the allowable membrane stress at the pressure test temperature.
Table 5.5 – Load Case Combinations and Load Factors for an Elastic-Plastic
Analysis

13. Table 5.6 – Examples Of Stress Classification
Vessel
Component
Location Origin of Stress Type of Stress Classification
Any shell
including
cylinders,
cones,
spheres and
formed
heads
Shell plate remote
from
discontinuities
Internal pressure
General membrane
Gradient through plate thickness
Pm
Q
Axial thermal gradient
Membrane
Bending
Q
Q
Near nozzle or
other opening
Net-section axial force and/or bending
moment applied to the nozzle, and/or
internal pressure
Local membrane
Bending
Peak (fillet or corner)
PL
Q
F
Any location
Temperature difference between shell
and head
Membrane
Bending
Q
Q
Shell distortions
such as out-of-
roundness and
dents
Internal pressure
Membrane
Bending
Pm
Q
Cylindrical or
conical shell
Any section across
entire vessel
Net-section axial force, bending
moment applied to the cylinder or
cone, and/or internal pressure
Membrane stress averaged through the
thickness, remote from discontinuities; stress
component perpendicular to cross section
Pm
Bending stress through the thickness; stress
component perpendicular to cross section
P b
Junction with head
or flange
Internal pressure
Membrane
Bending
PL
Q
Dished head
or conical
head
Crown Internal pressure
Membrane
Bending
Pm
P b
Knuckle or
junction to shell
Internal pressure
Membrane
Bending
PL [note (1)]
Q
Flat head
Center region Internal pressure
Membrane
Bending
Pm
P b
Junction to shell Internal pressure
Membrane PL

14. Table 5.6 – Examples Of Stress Classification (Con.)
Vessel
Component
Location Origin of Stress Type of Stress Classification
Perforated
head or shell
Typical ligament in
a uniform pattern
Pressure
Membrane (averaged through cross section)
Bending (averaged through width of ligament., but
gradient through plate)
Peak
Pm
P b
F
Isolated or atypical
ligament
Pressure
Membrane
Bending
Peak
Q
F
F
Nozzle (see
paragraph
5.6)
Within the limits of
reinforcement
given by paragraph
4.5
Pressure and external loads and
moments including those attributable to
restrained free end displacements of
attached piping
General membrane
Bending (other than gross structural discontinuity
stresses) averaged through nozzle thickness
Pm
Pm
Outside the limits
of reinforcement
given by paragraph
4.5
Pressure and external axial, shear, and
torsional loads including those
attributable to restrained free end
displacements of attached piping
General Membrane Pm
Pressure and external loads and
moments, excluding those attributable
to restrained free end displacements of
attached piping
Membrane
Bending
PL
P b
Pressure and all external loads and
moments
Membrane
Bending
Peak
PL
Q
F
Nozzle wall Gross structural discontinuities
Membrane
Bending
Peak
PL
Q
F
Differential expansion
Membrane
Bending
Peak
Q
Q
F

15. Table 5.6 – Examples Of Stress Classification (Con.)
Vessel
Component
Location Origin of Stress Type of Stress Classification
Cladding Any Differential expansion
Membrane
Bending
F
F
Any Any
Radial temperature distribution [note
(3)]
Equivalent linear stress [note (4)]
Nonlinear portion of stress distribution
Q
F
Any Any Any Stress concentration (notch effect) F
Notes:
1. Consideration shall be given to the possibility of wrinkling and excessive deformation in vessels with large diameter-to-thickness ratio.
2. If the bending moment at the edge is required to maintain the bending stress in the center region within acceptable limits, the edge bending is
classified as Pb ; otherwise, it is classified as Q .
3. Consider possibility of thermal stress ratchet.
4. Equivalent linear stress is defined as the linear stress distribution that has the same net bending moment as the actual stress distribution.

16. Figure 5.1 – Stress Categories and Limits of Equivalent Stress
Stress
Category
Primary Secondary Membrane plus
Bending
Peak
General Membrane Local Membrane Bending
Description
(For
examples,
seeTable
5.6)
Average primary
equivalent stress
across solid section.
Excludes
discontinuities and
concentrations.
Produced only by
mechanical loads.
Average equivalent
stress across any solid
section.
Considers
discontinuities but not
concentrations.
Produced only by
mechanical loads.
Component of
primary equivalent
stress proportional to
distance from
centroid of solid
section. Excludes
discontinuities and
concentrations.
Produced only by
mechanical loads.
Self-equilibrating equivalent
stress necessary
to satisfy continuity of structure.
Occurs at structural
discontinuities.
Can be caused by mechanical load
or by differential thermal
expansion.
Excludes local stress
concentrations.
1.Increment added
to primary or
secondary
equivalent stress
by a concentration
(notch).
2.Certain thermal
stresses which may
cause fatigue but
not distortion of
vessel shape.
Symbol Pm PL Pb Q F
Pm S SPS
1.5S
PL
PL+Pb 1.5S
PL+Pb+Q
Δ(PL+Pb+Q+F) 2Sa
Design Load
Operating Load
SPS=max[3S, 2SY]

17. 0.E+00
1.E+08
2.E+08
3.E+08
4.E+08
5.E+08
6.E+08
0 0.02 0.04 0.06 0.08 0.1 0.12
Stress,Pa
Strain
Stress
Linear Elastic
Primary plus Secondary Stress Limit
Primary Stress Limit
100% Primary
100% Secondary
Mixed Responce
Load-Control OriginalDisplacement-Control Mixed Loading
δ
σ=Kδ/A σ=W/(2A)σ=W/(2A)
+Kδ/A

18. Stress Classification

19. THANKS FOR YOUR ATTENTION