ASME B31.3 CODE REQUIREMENTS
Introduction to Pipe Stress Analysis and CAESAR II
SCOPE OF ASME B31.3
• The scope of this code includes all fluids. This scope
specifically excludes the following:
• Piping with an internal design pressure between 0 and 15 psi
(105 kPa)
• Power boilers and BEP which is required to be in accordance
with B31.1
• Tubes inside fired heaters
• Pressure vessels, heat exchangers, pumps, or compressors.
Credits: Piping Systems Manual, Brian Silowash, McGraw-Hill
ASME B31.3 FOR PIPE STRESS ANALYSIS
• CHAPTER II : Design
• All about minimum requirements of piping design philosophy
including flexibility analysis can be found in this chapter
• APPENDIX A : Allowable Stresses and Quality Factors
for Metallic Piping
• Table A-1 Basic Allowable Stresses in Tension for Metals
• Appendix C Physical Properties of Piping Materials
• Appendix D Flexibility and Stress Intensification Factors
• Appendix H Sample Calculations for Branch Reinforcement
• Appendix P Alternative Rules for Evaluating Stress Range
• Appendix S Piping System Stress Analysis Examples
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Pressure
• The design pressure (internal or external) is generally set at the
most severe condition of concurrent pressure and temperature
expected during service [1]
• The most severe condition is that which results in the greatest
required component thickness and the highest component
rating. [2]
• For internal pressure (from most of engineering textbooks):
➢ Longitudinal Pressure Stress :
𝑆𝑙𝑝 =
𝑃𝐷
4𝑡
➢ Circumferential Pressure Stress (Hoop Stress):
𝑆ℎ𝑝 =
𝑃𝐷
2𝑡
▪ 𝑃 = internal pressure
▪ 𝐷 = Pipe outside diameter
▪ 𝑡 = pipe wall thickness
[1] Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
[2] Credits: ASME B31.3 2012 para.301.2.1(b)
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Test pressure generally is not design parameter. It is quality
control measure used to find out the poor quality welding
and flange joints. The test pressure at testing temperature is
calculated as
1.5𝑃𝑆𝑇
𝑃𝑇 =
𝑆
• 𝑆𝑇 is the allowable stress of the pipe material at test temperature
• 𝑆 is the allowable stress of the pipe material at design
temperature
• 𝑃 is the design temperature
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Test pressure (continued)
• The test stress shall not exceed 100% yield strength (some code
uses 90% yield strength)
• When the test hoop stress at test temperature exceeds the above
limit, the test pressure shall be reduced to the maximum pressure
that meets this test stress limit.
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Temperature
• The temperature at the most severe condition of concurrent
temperature and pressure expected during service is generally
selected as the design temperature [1]
•
Ambient temperature is used as referent temperature of pipe
thermal expansion (sometimes called Installation temperature)
• Steam-out temperature is the steam temperature when process
equipment is being cleaned and purged by steam.
[1] Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Temperature
Guided Cantilever method is one of the
approximated approaches for calculating
bending stress from thermal
expansion/contraction.
𝑆𝑏,𝑇 =
•
•
•
•
•
•
•
•
𝑀 6𝐸𝐼
3𝐸𝐷
= 2 ∆= 2 ∆
𝑍 𝑍𝐿
𝐿
𝑆𝑏,𝑇 = bending stress due to thermal expansion
𝑀 = bending moment
𝑍 = pipe section modulus
𝐸 = modulus of elasticity
𝐼 = area moment of inertia
𝐷 = pipe outside diameter
𝐿 = displacement absorb leg
Δ = thermal displacement
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Weight
o All of these weights shall be considered
➢ Pipe and piping components
➢ Working and test fluid
➢ Insulation
➢ Refractory lining
➢ Pipe attachment weight
➢ Etc.
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
Basic Beam Formula for Weight
stress approximation:
𝑆𝑏,𝑊 =
∆𝑚𝑎𝑥 =
𝑤𝐿2
8𝑍
(at center)
5𝑤𝐿4
384𝐸𝐼
(at center)
Simple Beam
𝑆𝑏,𝑊 =
Fixed Beam
∆𝑚𝑎𝑥 =
𝑤𝐿2
12𝑍
𝑤𝐿4
384𝐸𝐼
(at end)
(at center)
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Wind
• Calculate wind force :
𝐹 = 𝑃𝑒𝑞 𝑆A
•
•
•
•
𝐹 = the total wind force on the element
𝑃𝑒𝑞 = the equivalent wind pressure (dynamic pressure)
𝑆 = the pipe element wind shape factor
𝐴 = the pipe element exposed area as shown
• If wind velocity versus elevation is provided, dynamic pressure can be
calculated from
𝑃𝑒𝑞 =
1 2
𝑉
2
• 𝑉 = the wind velocity
•  = the air velocity
Credits: CAESAR II User Guide, Technical Discussion
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Earthquake
• Calculate the static horizontal seismic design force using
equation 13.3-1 from ASCE #7 :
𝐹𝑝 = [(0.4 𝑎𝑝 𝑆𝐷𝑆 𝑊𝑝 ) / (𝑅𝑝/𝐼𝑝 )] (1 + 2 z / h)
since 𝑊𝑝 is "component operating weight“
Define calculated (horizontal) acceleration
𝐹𝑝
𝑎𝐻 = 𝑊
𝑝
Credits: CAESAR II User Guide, Technical Discussion
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Earthquake (continued)
𝑎𝐻 = [(0.4 𝑎𝑝 𝑆𝐷𝑆 ) / (𝑅𝑝 /𝐼𝑝 )] (1 + 2 z / h)
additionally;
𝑎𝐻 ≤ 1.6 𝑆𝐷𝑆 𝐼𝑝
and
𝑎𝐻 ≥ 0.3 𝑆𝐷𝑆 𝐼𝑝
• 𝑎𝑝 = Component amplification factor, from Table 13.6-1
= [2.5 for "Piping"]
• 𝑆𝐷𝑆 = Design elastic response acceleration at short period (0.2 sec),
from Section 11.4.4
• 𝑅𝑝 = Component response modification factor, from Table 13.6-1
= 12.0 for "Piping in accordance with ASME B31... with joints made
by welding or brazing"; v alues range as low as 3.0 for other joints and
for less ductile materials.
• 𝐼𝑝 = Component importance factor, from Section 13.1.3
= 1.5 for life-safety components, components containing hazardous material,
or components that are required for continuous operation; 1.0 for all others
• 𝑧 = Height in structure at point of attachment
• ℎ = Average roof height of structure
Credits: CAESAR II User Guide, Technical Discussion
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
•
PSV Reaction force
(Open system for gas and vapor)
• 𝐹 = reaction force at point of
•
•
•
•
•
•
discharge to atmosphere
𝑊 = flow of any gas
𝑘 = ratio of specific heat
𝑇 = temperature at inlet
𝑀 = molecular weight of process gas
𝐴 = area of the outlet at the point of
discharge
𝑃 = static pressure within the outlet
at the point of discharge
Credits: API RP 520 part 2
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Slug flow
•
•
•
•
2
𝐹𝑥 = 𝜌𝐴𝑉 (1 − 𝑐𝑜𝑠𝜃)
𝐹𝑦 = 𝜌𝐴𝑉 2 𝑠𝑖𝑛𝜃
𝐹𝑦
𝐹𝑥
𝜌 = liquid density
𝐴 = pipe inside projected area
𝑉 = fluid velocity
𝜃 = bending angle
LOADING TO BE CONSIDERED IN PIPE STRESS ANALYSIS
• Other adv ance dynamic loads
• Acoustic Pulsation
• Pressure wav e / Water hammer
/ Steam hammer
• Friction force between pipe or
pipe attachment and support structure
• Harmonic excitation v ibration
induced by support structure
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
Stress Categories
• Primary stresses (Sustained
• Secondary stresses are
stresses) which are developed
by the imposed loading.
• Primary stresses are not selflimiting
• Following lists are the loads
which induced primary stresses:
• Pressure
• Weight
developed by the constraint of
displacements
• These displacements can be
caused either by thermal
expansion or by imposed
restraint and anchor point
movements
• Secondary stresses are selflimiting
Credits: Piping Handbook, Mohinder L. Nayyar, McGraw-Hill
Stress Analysis of Piping System :
Stress Categories
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
ASME B31.3 Basic Allowable Stresses
• Basis for establishing allowable stresses in ASME B31.3 (2012)
can be found in paragraph 302.3
• Appendix A table A-1
• Hot allowable stress, 𝑆ℎ
• Cold allowable stress, 𝑆𝑐
Credits: ASME B31.3 2012 Appendix-A
Stress Analysis of Piping System :
Weld Strength Reduction Factor, W
• The material at weld-effect zone is weaker then the unaffected zone.
• At elevated temperatures, the long-term strength of weld joints may
be lower than the long-term strength of the base material. For
longitudinal or spiral (helical seam) welded piping components, the
product of the allowable stress and the applicable weld quality factor,
SE, shall be multiplied by the weld joint strength reduction factor, W,
when determining the required wall thickness for internal pressure
• The weld joint strength reduction factor, W, is equal to 1.0 when
evaluating occasional loads such as wind and earthquake.
• It is also not required when calculating the allowable stress range for
displacement stresses, SA.
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
Stress Intensification Factor (SIF)
• A piping system consists of many different components.
However, in the analysis we normally idealize these various
components into two types of elements:
➢ the straight pipe beam element
o
When a straight pipe is subject to bending, it behaves like any
straight beam: its cross-section remains circular and the maximum
stress occurs at the extreme outer fiber.
➢ the curved pipe beam element
o When subject to a bending moment, the circular cross-section of
the bend becomes oval.
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
Stress Intensification Factor (SIF)
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
Stress Intensification Factor (SIF)
• The ovalization tendency of the curved pipe has resulted in the
following peculiar phenomena:
o
Increase of flexibility. Ovalization is caused by the relaxation of the
extreme outer fiber of the bend.
o Increase of longitudinal bending stress. The relaxation of the
extreme outer fiber reduced in the moment resisting arm.
o Creation of circumferential shell bending stress. Squeezing the
circular cross-section into an oval shape generates bending on the
pipe wall.
Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
Stress Intensification Factor (SIF)
• Code SIFs
o Stress intensification factors (SIF) in ASME B31.3 Appendix-D
are intended for use only on self-limiting stresses. [1]
o For sustained loads, a separate set of SIFs is required. ASME
B31.3 2012 provides these factor as “Moment Index”.
o The stress intensification and flexibility factors at elbows and
bends are sensitive to flanged ends and internal pressure. [1]
[1] Credits: Pipe Stress Engineering, L.C. Peng, ASME Press
Stress Analysis of Piping System :
Stress Intensification Factor (SIF)
Credits: ASME B31.3 2012 Appendix-D
ASME B31.3 2012 Fig. 319.4.4A and Fig. 319.4.4B
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Sustain Loads, 𝑆𝐿
• Stress Due to Sustained Loads
• See Appendix S, Example 2 for guidance on loading conditions and
support scenarios that result in the greatest 𝑆𝐿 for each operating
condition being considered.
• The loads due to weight should be based on the nominal thickness
• Section moduli used to compute the stresses shall be based on
nominal pipe dimensions less allowances
• Areas used to compute the stresses in this paragraph assume
nominal pipe dimensions less allowances affecting the inside
diameter of the pipe
• the stress due to sustained loads, 𝑆𝐿 such as pressure and weight
𝑆𝐿 =
𝑆𝑎 + 𝑆𝑏
2+
2𝑆𝑡
2
Credits: ASME B31.3 2012 para. 320.2
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Sustain Loads, 𝑆𝐿
• The Stress due to sustained bending moment:
𝑆𝑏 =
𝐼𝑖 𝑀𝑖
2+
𝐼𝑜 𝑀𝑜
2
𝑍
• 𝐼𝑖 = sustained in-plane moment index. In the absence of more applicable
data, 𝐼𝑖 is taken as the greater of 0.75𝑖𝑖 or 1.00.
• 𝐼𝑜 = sustained out-plane moment index. In the absence of more applicable
data, 𝐼𝑜 is taken as the greater of 0.75𝑖𝑜 or 1.00.
• 𝑀𝑖 = in-plane moment due to sustained loads, e.g., pressure and weight
• 𝑀𝑜 = out-plane moment due to sustained load s, e.g., pressure and weight
• 𝑍 = sustained section modulus using nominal pipe dimensions less allowances
Credits: ASME B31.3 2012 para. 320.2
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Sustain Loads, 𝑆𝐿
• The Stress due to sustained torsional moment:
𝐼𝑡 𝑀𝑡
𝑆𝑡 =
2𝑍
• 𝐼𝑡 = sustained torsional moment index. In the absence of more applicable
data, It is taken as 1.00.
• 𝑀𝑡 = torsional moment due to sustained loads, e.g., pressure and weight
Credits: ASME B31.3 2012 para. 320.2
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Sustain Loads, 𝑆𝐿
• The Stress due to sustained longitudinal force:
𝐼𝑎 𝐹𝑎
𝑆𝑎 =
𝐴𝑝
• 𝐴𝑝 = cross-sectional area of the pipe, considering nominal pipe dimensions
less allowances
• 𝐹𝑎 = longitudinal force due to sustained loads, e.g., pressure and weight
• 𝐼𝑎 = sustained longitudinal force index. In the absence of more applicable
data, 𝐼𝑎 is taken as 1.00.
Credits: ASME B31.3 2012 para. 320.2
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Sustain Loads, 𝑆𝐿
Stresses Due to Sustained Loads, 𝑺𝑳 .
“The sum of the longitudinal stresses due to sustained loads, 𝑆𝐿 , such as pressure
and weight in any component in a piping system shall not exceed 𝑆ℎ , where 𝑆ℎ is
taken from ASME B31.3 Table A-1 at the metal temperature of the operating
condition being considered.”
𝑆𝐿 ≤ 𝑆ℎ
• 𝑆ℎ = basic allowable stress at maximum metal temperature expected during the
displacement cycle under analysis
• For castings, the basic allowable stress shall be multiplied by the applicable
casting quality factor, 𝐸𝑐 . For longitudinal welds, the basic allowable stress need
not be multiplied by the weld quality factor, 𝐸𝑗
Credits: ASME B31.3 2012 para. 302.3.5(c)
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
• Flexibility Analysis
• Piping systems shall have sufficient flexibility to prevent thermal expansion or
contraction or movements of piping supports and terminals from causing
[1]
o failure of piping or supports from overstress or fatigue
o leakage at joints
o distortion in piping and valves or in connected equipment (pumps and
turbines, for example), resulting from excessive thrusts and moments in the
piping
• the computed displacement stress range
𝑆𝐸 =
𝑆𝑎 + 𝑆𝑏
[2]
2
+ 2𝑆𝑡
2
[1] Credits: ASME B31.3 2012 para. 319.1.1
[2] Credits: ASME B31.3 2012 para. 319.4.4
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
• 𝑺𝒂 = axial stress range due to displacement strains
•
= 𝑖𝑎 𝐹𝑎/𝐴𝑝
• 𝑖𝑎 = axial stress intensification factor. In the absence of more applicable data
𝑖𝑎 = 1.0 for elbows, pipe bends, and miter bends (single, closely spaced,
and widely spaced), and 𝑖𝑎 = 𝑖0 (or 𝑖 when listed) in Appendix D for other
components
• 𝐹𝑎 = range of axial forces due to displacement strains between any two
conditions being evaluated
• 𝐴𝑝 = cross-sectional area of pipe
Credits: ASME B31.3 2012 para. 319.4.4
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
• The resultant bending stresses, 𝑺𝒃
• for elbows, miter bends, and full size outlet branch connections (Legs 1, 2, and 3)
shall be calculated from following equation:
𝑆𝑏 =
𝑖𝑖 𝑀𝑖
2+
𝑖𝑜 𝑀𝑜
2
𝑍
• for reducing outlet branch connections shall be calculated from following equation:
o For Header (Leg 1 and Leg 2)
𝑆𝑏 =
𝑖𝑖 𝑀𝑖
𝑖𝑜 𝑀𝑜
2
𝑍
o For Branch (Leg 3)
𝑆𝑏 =
2+
𝑖𝑖 𝑀𝑖
2+
𝑖𝑜 𝑀𝑜
2
𝑍𝑒
Credits: ASME B31.3 2012 para. 319.4.4
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
• 𝑖𝑖 = in-plane stress intensification factor (Appendix D)
• 𝑖𝑜 = out-plane stress intensification factor (Appendix D)
• 𝑍𝑒 = effective section modulus for branch
•
•
•
•
•
= 𝜋𝑟22 𝑇𝑠
𝑇𝑠 = effective branch wall thickness, lesser of 𝑇തℎ and 𝑖𝑖 𝑇ത𝑏
𝑟2 = mean branch cross-sectional radius
𝑇തℎ = thickness of pipe matching run of tee or header exclusive of reinforcing
elements
𝑇ത𝑏 = thickness of pipe matching branch
𝑍 = section modulus of pipe
• Torsional stress,
𝑆𝑡 = 𝑖𝑡 𝑀𝑡 /2𝑍
• 𝑖𝑡 = torsional stress intensification factor. In the absence of more applicable
data, 𝑖𝑡 p 1.0
• 𝑀𝑡 = torsional moment
Credits: ASME B31.3 2012 para. 319.4.4
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
Allowable Displacement Stress Range, SA.
“The computed displacement stress range, SE, in a piping system shall
not exceed the allowable displacement stress range, SA”
𝑆𝐸 ≤ 𝑆𝐴
𝑆𝐴 = 𝑓 1.25𝑆𝐶 + 0.25𝑆ℎ
•
(1a)
When 𝑆ℎ is greater than 𝑆𝐿 , the difference between them may be
added to the term 0.25𝑆ℎ in eq. (1a). In that case, the allowable stress
range is calculated by eq. (1b):
𝑆𝐴 = 𝑓 1.25 𝑆𝐶 + 𝑆ℎ + 𝑆𝐿
(1b)
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Displacement Stress Range, 𝑆𝐸
Credits: ASME B31.3 2012 para. 302.3.5
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Occasional Loads
• The sum of the longitudinal stresses, 𝑆𝐿 , due to sustained loads, such as
pressure and weight, and of the stresses produced by occasional
loads, such as wind or earthquake, may be as much as 1.33 times the
basic allowable stress given in Appendix A. Wind and earthquake
forces need not be considered as acting concurrently.
𝑆𝐿
𝑆𝑈𝑆
+ 𝑆𝑂𝐶𝐶 ≤ 1.33𝑆ℎ
• Stresses due to test conditions are not subject to the limitations in para.
302.3. It is not necessary to consider other occasional loads, such as
wind and earthquake, as occurring concurrently with test loads.
Credits: ASME B31.3 2012 para. 302.3.6
Stress Analysis of Piping System :
Limits of Calculated Stresses due to Test Loads
• Refer to ASME B31.3 2012 para 345.4.2(c)
•
𝑆𝑇
Minimum test gage pressure, 𝑃𝑇 = 𝑃
𝑆
• if the test pressure as defined above would produce a nominal
pressure stress or longitudinal stress in excess of the yield strength at test
temperature or a pressure more than 1.5 times the component rating
at test temperature, the test pressure may be reduced to the
maximum pressure that will not exceed the lesser of the yield strength
or 1.5 times the component ratings at test temperature.
•
CAESAR II has implement this paragraph in to their recommended
load case setup as
𝑆𝐻𝑌𝐷 ≤ 𝑆𝑦
References
• ASME B31.3 Process Piping edition 2012
• Pipe Stress Engineering, L.C. Peng, ASME Press
• Piping Systems Manual, Brian Silowash, McGraw-Hill
• Piping Handbook, Mohinder L. Nayyar, McGraw-Hill
• CAESAR II 2013 User Guide, Technical Discussion
• API RP 520 part 2 : Installation