Mechanical Engineering Technical Note
ASME Sec on VIII – Division 2 – 2023:
ELASTIC STRESS METHOD
Dennis Clyde G. Acantilado, PME, ASEAN Eng., PSM-REE, RMP
Table of Contents
A.
Protec on Against Plas c Collapse ............................................................................................... 2
Elas c Stress Analysis Method ........................................................................................................... 2
Stress Categoriza on (ASME BPVC Sec on VIII Div 2 page 582 (Figure 5.1, Table 5.6).................... 2
Assessment Procedure ....................................................................................................................... 3
B.
Protec on Against Ratche ng ....................................................................................................... 5
Analysis Method ................................................................................................................................. 5
C.
Protec on Against Local Failure .................................................................................................... 6
Elas c Analysis – Triaxial Stress Limit ................................................................................................ 6
D.
Protec on Against Collapse from Buckling ................................................................................... 6
Capacity Reduc on Factors for Buckling Analysis ............................................................................. 7
E.
APPENDICES ................................................................................................................................... 8
Stress Categories and Limits of Equivalent Stress ............................................................................. 8
Load Combina ons Parameters ......................................................................................................... 9
Load Case Combina ons and Allowable Stress for Elas c Analysis ............................................... 10
Load Case Combina ons for Buckling Analysis ............................................................................... 11
From Nozzle Pro................................................................................................................................ 12
CAESAR II Loadings ........................................................................................................................... 13
NOZZLE PRO SET-UP ......................................................................................................................... 14
References ............................................................................................................................................ 17
1|Page
Mechanical Engineering Technical Note
A. Protec on Against Plas c Collapse
There are three analysis methods in evalua ng pressure vessels against plas c collapse. This paper
deals with the elas c stress analysis method.
Plas c collapse is also known as “Duc le Failure”, it refers to the point (load) at which structure losses
overall stability and can no longer sustain the applied loads. In a system, this may manifest itself in a
variety of ways such as burst, collapse, leak and fracture (h ps://fea ps.com/2022/10/17/plas ccollapse-load-vs-limit-load/).
Elas c Stress Analysis Method
Stresses are computed using elas c analysis, classified into categories, and limited to allowable values
that have been conserva vely established such that plas c collapse will not occur.
1. A quan ty known as the equivalent stress is computed at loca ons in the component and
compared to an allowable value of the equivalent stress to determine if the component is
suitable for the intended design condi ons. The equivalent stress is a measure of stress,
calculated from stress components u lizing a yield criterion, which is used for comparison with
the mechanical strength proper es of the material obtained in test under uniaxial load.
2. The maximum distor on energy yield criterion shall be used to establish the equivalent stress.
In this case, the equivalent stress is equal to the von Mises equivalent stress given below.
=
=
√
−
+
−
+
−
Stress Categoriza on (ASME BPVC Sec on VIII Div 2 page 582 (Figure 5.1, Table 5.6)
1. General Primary Membrane Equivalent Stress (Pm) -> is the equivalent stress, derived from
the AVERAGE value across the thickness of a sec on, of the general primary stresses produced
by the design internal pressure and other specified mechanical loads but excluding all
secondary and peak stresses. These stresses are found away from junc on and are compared
directly with allowable limits.
2. Local Primary Membrane Stress (Pl) -> is the equivalent stress, derived from the AVERAGE
value across the thickness of a sec on, of the local primary stresses produced by the design
pressure and specified mechanical loads but excluding all secondary and peak stresses. A
region of stress in a component is considered as local if the distance over which the equivalent
stress exceeds 1.1S does not extend in the meridional direc on more than √ . These stresses
are assumed to be at cri cal loca ons like junc ons, supports, sudden change in cross sec on,
other geometric irregularity, etc. Limits are higher for local membrane due to fact of, addi onal
stresses will come due to irregular sec ons.
3. Primary Membrane (General or Local) Plus Primary Bending Equivalent Stress (Pl + Pb) -> is
the equivalent stress, derived from the HIGHEST value across the thickness of a sec on, of the
linearized general or local primary membrane stresses plus primary bending stresses produced
by design pressure and other specified mechanical loads but excluding all secondary and peak
stresses.
2|Page
Mechanical Engineering Technical Note
Assessment Procedure
Step 1. Determine the types of loads ac ng on the component. In general, separate load cases are
analyzed to evaluate “load-controlled” loads such as pressure and externally applied reac ons due to
weight effects and “strain-controlled” loads resul ng from thermal gradients and imposed
displacements.
Step 2. At the point on the vessel that is being inves gated, calculate the stress tensor (six unique
components of stress) for each type of load.
•
•
•
•
General primary membrane equivalent stress – Pm
Local primary membrane equivalent stress – Pl
Primary bending equivalent stress – Pb
Secondary equivalent stress – Q
Addi onal equivalent stress produced by a stress concentra on or a thermal stress over and above the
nominal (P + Q) stress level – F
Step 3. Sum the stress tensors (stresses are added on a component basis) are assigned to each
equivalent stress category. The result is a stress tensor represen ng the effects of all the loads assigned
to each equivalent stress category.
Note that in applying STEPs in this paragraph, a detailed stress analysis performed using a numerical
method such as finite element analysis typically provides a combina on of Pl + Pb and Pl + Pb + Q + F
directly.
If a load case is analyzed that includes only “load-controlled” loads (e.g., pressure and weight effects),
the computed equivalent stresses shall be used to directly represent the Pm, PL + Pb, or PL + Pb + Q.
For example, for a vessel subject to internal pressure with an ellip cal head; Pm equivalent stresses
occur away from the head to shell junc on, and Pl and Pl + Pb + Q equivalent stresses occur at the
junc on.
If a load case is analyzed that includes only “strain-controlled” loads (e.g., thermal gradients), the
computed equivalent stresses represent Q alone; the combina on PL + P b + Q shall be derived from
load cases developed from both “load-controlled” and “strain-controlled” loads.
If the stress in category F is produced by stress concentra on or thermal stress, the quan ty F is the
addi onal stress produced by the stress concentra on more than the nominal membrane plus bending
3|Page
Mechanical Engineering Technical Note
stress. For example, if a plate has a nominal primary membrane equivalent stress of Se and has a
fa gue strength reduc on characterized by a factor Kf, then: Pm = Se, Pb = 0, Q = 0, and F = Pm (Kf −
1). The total equivalent stress is Pm + F
Step 4. Determine the principal stresses of the sum of the stress tensors assigned to the equivalent
stress categories and compute the equivalent stress using equa on.
Step 5. To evaluate protec on against plas c collapse, compare the computed equivalent stress to
their corresponding allowable values in table 5.3 (see ASME Sec VIII Div 2 sec 5.2.2.2).
The allowable limit on local primary membrane and local primary membrane plus bending, SPL, is
computed as the larger of the quan es shown below.
•
•
1.5 mes the tabulated allowable stress from Annex 3-A.
Sy for the material from Annex 3-A, except that the value from (a) shall be used when the ra o
of the minimum specified yield strength to ul mate tensile strength exceeds 0.70, or the value
of S is governed by me-dependent proper es as indicated in Annex 3-A.
The following are the criteria in evalua ng the protec on against plas c collapse.
 Pm ≤ S
 PL ≤ SPL (SPL is the larger of 1.5S or SY)
 (PL + Pb) ≤ SPL (SPL is the larger of 1.5S or SY)
P
= specified design pressure
Pb
= primary bending equivalent stress (Shell Bending Stress)
PL
= local primary membrane equivalent stress (Equivalent to Sustained Stress in Piping
Stress)
Pm
= general primary membrane equivalent stress
S
= allowable stress based on the material of construc on and design temperature
Sa
= alterna ng stress obtained from a fa gue curve for the specified number of
opera ng cycles
SPL
= allowable limit on the local primary membrane and local primary membrane plus
bending stress categories (see ASME Sec VIII Div 2 sec 5.2.2.4.)
SPS
= allowable limit on the primary plus secondary stress range
SQ
= allowable limit on the secondary stress range
4|Page
Mechanical Engineering Technical Note
B. Protec on Against Ratche ng
Protec on Against Failure from Cyclic Loading: Ratche ng using the elas c stress analysis method.
Contrasted to Protec on Against Plas c Collapse, where you have a wide variety of design loading
combina ons, in Ratche ng you only have opera ng load ranges. To repeat, opera ng load ranges.
Under normal (and planned-for abnormal) opera on, each component will undergo a load range. That
may be from a specified low internal pressure to a high internal pressure, external pressure to internal
pressure, or no pressure to internal pressure. Thermally, you can also have opera ng load ranges.
The focus here is on the load range, and the resul ng stress range. Unlike Protec on Against Plas c
Collapse, which is only interested in total stress values, here we are interested in the stress ranges.
Significantly, we want to make sure that we are on the lookout for stress reversals. So, when we
calculate the stress ranges, we must ensure that we perform the stress difference calcula ons at the
component level, calcula ng the component stress ranges, before rolling the component stress ranges
up into an equivalent (von Mises) stress range. When evalua ng protec on Against Failure from Cyclic
Loading: Ratche ng, we perform stress range calcula ons based on the opera ng load ranges.
(h ps://becht.com/becht-blog/entry/asme-sec on-viii-division-2-elas c-analysis-discussion-collapsevs-ratche ng/).
Analysis Method
1. To evaluate protec on against ratche ng, the following limit shall be sa sfied.
∆
,
≤
2. The primary plus secondary equivalent stress range, ∆ , , is the equivalent range, derived
from the highest value across the thickness of a sec on, of the combina on of linearized
general or local primary membrane stress plus primary bending stresses plus secondary
stresses (PL + Pb + Q). This is produced by specified opera ng pressure and other specified
mechanical loadings and by general thermal effects.
3. The maximum range of this equivalent stress is limited to SPS. The quan ty SPS represents a
limit on the primary plus secondary equivalent stress range. The allowable limit on the primary
plus secondary stress range, SPS, is computed as the larger of the quan es below.
a. Three mes the average of the S values for the material from Annex 3-A at the highest
and lowest temperatures during the opera onal cycle.
b. Two mes the average of the SY values of the material from Annex 3-D at the highest
and lowest temperature during the opera onal cycle, except that the value from (a)
shall be used when the ra o of the minimum specified yield strength to ul mate
strength exceeds 0.70 or the value of S is governed by me dependent proper es as
indicated in Annex 3-A.
 (PL + Pb + Q) ≤ SPS (SPS is the larger of 3S or 2SY)
5|Page
Mechanical Engineering Technical Note
C. Protec on Against Local Failure
In addi on to demonstra ng protec on against plas c collapse, the applicable local failure criteria
below shall be sa sfied or a component.
Elas c Analysis – Triaxial Stress Limit
The algebraic sum of the three linearized primary principal stresses from Design Load Combina on
shall be used for checking this criterion.
+
+
≤
It is not necessary to evaluate protec on against local failure, if the component design is in accordance
with Part4 (e.g., component wall thickness and weld detail per 4.2).
D. Protec on Against Collapse from Buckling
A design factor should also be applied to avoid collapse from buckling components with a compressive
stress field.
•
•
Each load case is evaluated to ensure that the elas c analysis meets required validity criteria.
Then a unique allowable membrane stress is calculated for each load case using an eigenvalue
buckling analysis in combina on with the applicable capacity reduc on factor, βcr.
This method is intended for use on independent individual components (e.g., heads, cylinders, and
cones) assessed in isola on. However, the procedure can be used when assessing two or more
components as an assembly. If at any point in the procedure the requirements are not met, then the
procedure in Method B shall be used.
Step 1. For each load combina on in Table 5.14 [k = (1), (2), … (n)], perform an eigenvalue buckling
analysis using βbcomponent,k = 1.0. Separate eigenvalues shall be extracted for each component in
the assembly, λcomponent,k.
Step2. For each load combina on in Table 5.14, perform a separate elas c stress analysis with the
applicable load mul plied by the corresponding eigenvalue (βbcomponent,k = λcomponent,k). If
assessing mul ple components simultaneously in one assembly, each component’s loads shall be
mul plied by its domina ng eigenvalue, βbcomponent,k =λcomponent,k.
Step 3. At the cri cal buckling loca on (as determined from the eigen mode shape), extract the
equivalent membrane stress at the mid surface for each component.
a. If the cri cal buckling loca on is in a cylinder or cone, then mul ply the equivalent membrane
stress from Step3 by the applicable capacity reduc on factor, βcr (a) & (b).
b. If the cri cal buckling loca on is in a sphere or formed head, then mul ply the equivalent
membrane stress by the capacity reduc on factor, βcr, (c).
If the cri cal buckling loca on is not covered by (a) or (b), then Method B shall be used.
Step 4. The product of the equivalent membrane stress with capacity reduc on factor, as calculated in
Step 3, is σcomponent,crit,k. Compare each of the component’s σcomponent,crit,k to 0.55Sy.
a. If σcomponent,crit,k ≤ 0.55Sy, then divide σcomponent,crit,k by the design margin of 2.0.
Designate this value Sc,k, where k corresponds to the specific load combina on k = (1), (2), …
6|Page
Mechanical Engineering Technical Note
,(n); this is the allowable membrane buckling equivalent stress for the kth load combina on in
Step 5.
b. If σcomponent,crit,k > 0.55Sy, then Sc,k = 0.55Sy/2 or Method B may be used.
Step 5. For each load combina on in Table 5.14 with βb =1 at the cri cal buckling loca on, compare
the computed buckling equivalent membrane stress, Pm,k, to the corresponding allowable value.
,
≤
,
Step 6. Any components that do not sa sfy the equa on above shall be modified un l the component
sa sfy the equa on, and the design criteria are met. Alterna vely, Method B may be used to sa sfy
the design criteria.
Capacity Reduc on Factors for Buckling Analysis
The capacity reduc on factors, βcr, shown below shall be used in the Method A buckling analysis unless
alterna ve factors can be developed from published informa on.
a. reduc on factor for the axial stress component in a cylinder or cone
= 0.207 %&'
=
338
389 +
()
()
%&'
≥ 1247
()
< 1247
b. reduc on factor for the hoop stress component in a cylinder or cone
= 0.80
c. reduc on factor for the hoop and meridional stress components in a sphere, or formed head
= 0.124
7|Page
Mechanical Engineering Technical Note
E. APPENDICES
Stress Categories and Limits of Equivalent Stress
8|Page
Mechanical Engineering Technical Note
Load Combina ons Parameters
Primary Stress
: PL < SPL = 1.5kS
Secondary Stress
: PL + Pb + Q < SPS = 2SY = 3S
Fa gue Stress
: PL + Pb + Q + F < Sa
Sa
= Allowable from the ASME Sec on VIII Division 2, Appendix 5 allowable stress curve.
Note that this value is computed based on an allowed number of opera ng load cycles.
If not given this value defaults to 7000 cycles, a value selected by one of the original
piping code developers, A.R.C. Markl, and used in most piping programs worldwide
today.
S
= Hot Allowable Stress
9|Page
Mechanical Engineering Technical Note
Load Case Combina ons and Allowable Stress for Elas c Analysis
10 | P a g e
Mechanical Engineering Technical Note
Load Case Combina ons for Buckling Analysis
11 | P a g e
Mechanical Engineering Technical Note
From Nozzle Pro
12 | P a g e
Mechanical Engineering Technical Note
CAESAR II Loadings
For insulated line, there are no thermal
difference between inside and outside
surface.
This is used to evaluate the stresses across the
thickness.
13 | P a g e
Mechanical Engineering Technical Note
NOZZLE PRO SET-UP
14 | P a g e
Mechanical Engineering Technical Note
15 | P a g e
Mechanical Engineering Technical Note
16 | P a g e
Mechanical Engineering Technical Note
References
ASME BPVC Sec on VIII Division 2 - 2023
h ps://becht.com/becht-blog/entry/asme-sec on-viii-division-2-elas c-analysis-discussion-collapsevs-ratche ng/. (n.d.).
h ps://fea ps.com/2022/10/17/plas c-collapse-load-vs-limit-load/. (n.d.).
17 | P a g e