Stress Classification in Pressure Vessels and Piping As Per ASME B31 and BPVC Codes
Stress Classification in Pressure Vessels and Piping As Per ASME B31 and BPVC Codes
Stress Classification in Pressure Vessels and Piping As Per ASME B31 and BPVC Codes
Baskar Jeyalakshmi
Primary Load
Secondary Load
The pipe will react differently for these loads. Hence, a different mode of failure and
different allowable limits.
Primary Load:
According to ASME primary stress is defined as “A normal or shear stress developed by
the imposed loading which is necessary to satisfy the laws of equilibrium of external and
internal forces and moments”.
This includes Fluid pressure, Pipe weight, Insulation weight, cladding weight, refractory
weight, externally applied forces like Slug, Surge, Reaction forces, and Fluid weight.
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When a primary load is acting on a piping system, stresses will be induced in the system
and these stresses are depending on the Geometric property of pipe (Diameter, and
Thickness). But, Displacement (Strain) is a function of Young’s modulus (E). Let us take
an example situation shown below.
A Bar of hallow circular cross-section with uniform thickness “t” is experiencing an axial
pull of load “P”. From the elemental mechanics,
Stress, σ = P/A
Strain, ɛ = σ/E
Where,
A = Cross-sectional area
E = Young’s modulus
Since the Primary load should satisfy the equations of equilibrium, the applied load will
be equal to loads at restraint in CAESAR II. i.e. Loads in the system = Sum of loads at
restraint. An example is given below.
The below images show the sum of “Vertical Restraints” for the same system for the WNC
case which is equal to dead weight of the system shown above. (a slight error is due to
rounded up values)
∑ Fx = 0,
∑ Fy = 0,
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∑ Fz = Weight of the system,
X, Y – Horizontal direction, Z-Vertical direction
The same is true for Fx and Fy forces as well which can be confirmed from Fig. 4.
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Fig. 4: Satisfying Equilibrium Equation
Secondary load:
A hollow circular bar is fixed on one end and it is heated. Now, the Bar will expand and no
loads will be generated in the fixed end as shown in Fig. 5A.
Now, the same bar is fixed on both ends (Fig. 5B) and the bar is heated. The bar will try to
expand and the fixed ends will restrict. Hence, stress will develop in the system. We will
see Stress and Strain for this heated situation.
Stress, σ = α ΔT E
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Strain, ɛ = α ΔT
Load, P = Stress X Area = α ΔT E A
Where, α – Co-efficient of thermal expansion
From the above example, we can clearly differentiate Primary and Secondary loads.
As per ASME secondary loads are defined by “Loads that are developed by the constraint
of adjacent parts or by self-constraint of a structure”
Since, the loads generated in the system itself, the sum of all restraints will be zero in case
of a secondary load.
No external load = no net force on the system. The below image (Fig. 6) shows the net
forces due to expansion in a piping system.
Self-Limiting Behavior
Stress-Strain curve of a typical ductile material is shown below in Fig. 7.
Point A – Proportionality limit, till this limit only Hooke’s law is applicable. Hence, OA is
a straight line
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Point B – Elastic limit, till this point material will exhibit elastic property, AB is non-
linear. i.e. Young’s modulus depends on strain.
Point C & D – Upper Yield Point and Lower Yield point respectively. Most of the
material don’t exhibit upper yield point C. Point C is depending on loading and unloading
conditions. Hence, Point C can’t be taken as yield point. Point D is the yield point of the
material which is independent of loading and unloading conditions.
Point E – Point E is the ultimate limit of the material. The increase in Stress after point
D is due to the phenomena “Strain Hardening”
Point F – F is the failure point of the material. After Point E, necking formation will
happen and material will break into to two halves.
All the codes of ASME and B31 approximate the material as “Elastic-Perfectly Plastic” by
neglecting Strain hardening and all other irregularities in the curve. The material model
used to derive the allowable limit for ASME and B31 code is shown below in Fig. 8.
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Fig. 8: Elastic-Perfectly Plastic Curve
At the starting Stress and strain will be zero (neglecting residual stresses). When
we apply the external load “P”, stress will increase which depends on the geometric
property (A) and strain also. Now let us take the stress is reached point “A”. After point
“A”, an infinitesimal increase in load will create a gross deformation up to the failure
point “B”. This gross deformation should be avoided. Here, from Point “A” to “B”, no
intermediate strain is possible. After point “A”, point “B” will be reached instantaneously.
This behavior is called “load controlled” behavior. This gross deformation is the failure
mode due to primary loads.
With the understanding of Primary and Secondary load, we will try to answer the
following self-evaluation (We let the readers to discuss the answer in comments section)
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In Stress analysis using CII, I have wrongly entered E= 203200MPa instead of
E=126300MPa
Till now we have seen what is primary and secondary load and the difference between
them. Click here to learn the specific differences between primary and
secondary loads in a tabular format.
Now we will explain the failure modes due to primary and secondary loads in a Pressure
Vessel and Piping system.
Longitudinal stress
Hoop Stress
Radial Stress
In these, radial stress is neglected in thin wall vessels like piping and pressure vessels.
Longitudinal and hoop stresses are acting in each and every part of the system as shown
below in Fig. 9.
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Fig. 10: Longitudinal and Hoof Stresses in Piping
When pressure exceeds allowable limit burst or excessive straining of the component
occurs. Excessive straining implies an unacceptable distortion of the part. Hence,
allowable stress for pressure load = Sy
The stress distribution is uniform across the cross-section. Hence, all fibers will yield at
once.
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Failures where weight type loads are excessive causing collapse or excessive straining of
the component. Since weight load will induce local stresses in the piping system allowable
for weight induced stress can be 1.5 Sy. The stress distribution is varying across the cross-
section and maximum at the outer fiber.
Elastic Shakedown:
Since elastic shakedown failure is related to secondary loads (displacement loads), there
won’t be any gross structural deformation. The below example will explain the allowable
stress for Shakedown.
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At the starting of the system, the material has no thermal stress and strain (Point 0) and
now the material gets heated. Expansion is constrained by supports and the system will
get stressed. Even if the system stressed beyond yield, the thermal load is displacement
controlled, so there won’t be any gross structural deformation like pressure or weight
loads.
Now the material reaches the “Point b” which is in the plastic state. After the sometime
system is cooled down and the stresses are reduced. When stress came to zero “Point c”,
some residual strain will be there. Because of the plastic deformation and when the
system comes to its original position i.e. zero strain (point d), stresses in the system will
get reversed. Now the system again heated and stresses. This time there won’t be any
plastic deformation. The system will operate in the line “bcd”. The system brought back to
elastic condition after some initial plastic deformation. This behavior is called “Elastic
shakedown” or “Shakedown to elastic behavior”. If we notice the diagram clearly, all these
shakedown will happen only if
Repeated secondary stress = Syc + Syh = 1.5Sc + 1.5Sh (as per B31 allowable
criteria)
Where, Syc = Cold yield stress and Syh = Hot yield stress
If the allowable stress exceeds these values, plastic hinges will form and gross structural
deformation will take place
Ratcheting:
The typical ratcheting model involves axial, non-repeating stress (WNC stress), with a
superimposed repeating bending stress (Expansion stress). The combination of a repeated
bending stress and non-repeated axial stress produces a plastic deformation in the outer
fibers that increases with each application of the bending load. Ratcheting type failure was
studied by Bree in a beam subjected to constant axial force and repeated secondary
bending moment. The Bree diagram is shown below in Fig. 12.
ASME B31 codes have an allowable of 2/3 of Sy for primary stress. For 2/3Sy primary
stress, from the bree diagram maximum allowable variable secondary bending stress =
1.33*Sy; i.e. Sum of Primary and secondary stress = 2Sy.
Allowable for ratcheting Sa = Syc + Syh = 1.5Sc + 1.5 Sh = 1.25Sc + 1.25Sh (Taking FOS)
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The simple ratcheting requirement gives
us exactly the same limitations on
repeated bending stresses as the
shakedown requirement, and the same
limitations on the constant axial load as
the collapse requirement.
Fatigue:
Peak stresses are the main reason for fatigue failure. Peak Stresses are those
stresses that exist at notches, welds, and other very local stress Concentrations. Fatigue
failure is characterized by “peak stress” and “No. of cycle”
Sa = f (1.25Sc + 0.25Sh)
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f = fatigue strength reduction factor, which can be taken from curve given in B31 codes. As
per B31 codes up to 7000 cycles system will not fail by fatigue. Hence, f = 1, for cycle less
than 7000.
Classification by Area
Classification by type of load
General
Local
Peak
To answer the above questions with reason we will take an example as shown in Fig. 13.
The above diagram shows the loading and stress distribution of a bar subjected to a load
“P”. All fibers in the bar are experiencing the same stress “σ”. Now the load is increased
till the “σ” value reaches the yield point of the material. Load at which material reaches its
yield point noted as “Py1”. Then a significant deformation that can be seen with the naked
eye will take place. Finally, the material breaks. This type of stress is called “General
Membrane” stresses. i.e. all the fibers in the system will reach the yield point at the same
time e.g. Pressure.
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Now the same bar is fixed at one end and a Load “P” is applied on the other end as shown
in Fig. 14.
Fig. 14: One end Fixed and load applied at the Other
If the load “P” is increased until the outer fiber reaches yield point, then nearby fibers get
overstressed. Once all the fibers till neutral fiber gets yield, gross deformation will take
place. The load at which gross deformation takes place is “Py2”. This “Py2” is 1.5 Py1. This
type of stress is called “Local Stress”. These local stresses will act in areas in the order of
(RT)1/2.
The stresses near the hole will reaches the yield point first. Because the stress acting
region is very small (in part of thickness), failure will not happen. Plastic deformation
around the hole occurs and the loads are distributed to the nearby fibers. Since the hole is
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in part of thickness these type of stresses will not cause any gross structural deformation.
But in fatigue loading, cracks will initiate at these locations first. These type of stress is
called “Peak Stress”
By understanding “General”, “Local”, “Peak” it is clear that not only the magnitude of
stress only defines the failure, but area at which stress is acting is also
important.
Note that if General stress is “σ” then, Local stress at structural discontinuity = σ +
stress rise due to discontinuity
Peak Stress at notch or weld = Local stress + Stress rise due to notch or weld = (Local
primary and secondary Stress) * SCF
Where, SCF = stress concentration factor (to be found based on experiments) ASME
BPVC stress classification and its allowable are given in Fig. 16.
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Difference between ASME B31 and BPVC stress classification and
allowable
There are five conditions in the BPVC Code. These five conditions are simplified into two
conditions in B31 codes.
Since B31 codes never classified stress as General and Local, #1, #2, #3 are
replaced by a single condition; Stress due to primary Loads, SL = Sh
B31 uses peak stress for both ratcheting and fatigue protection. But, BPVC uses different
stress for each kind. Click here to know about Types of Stresses in a Piping System
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