Attachment M - John Fowler - AnnexXRevB (1)

7/30/2019 Attachment M - John Fowler - AnnexXRevB (1)

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Annex X (Informative)

ASME Design Calculations

X.1 GeneralThis annex describes the design analysis methodology used in the ASME Boiler and

Pressure Vessel Code, Section VIII, Pressure Vessels, Division 2, Alternative Methods,

Appendix 4, up to and including the 2004 version, as well as the ASME Code Section III,

Nuclear Power Components.

Methods are included for both elastic and elastic-plastic analysis, and for closed-form as

well as finite-element analysis methods of calculation, in accordance with the rules ofAppendix 4 of the 2004 Code, Section VIII Division 2.

API has adopted slightly different stress limits from the 2004 ASME Code. For the

purpose of this international standard, the basic stress limits are based on Sm and St,

which are defined as follows:

X.1.1 Sm, the design stress intensity

For standard materials (36K, 45K, 60K, and 75K), the design stress intensity is 2/3 of the

minimum specified yield strength Sy. For non-standard materials, the design stress

intensity is the lower of 2/3 of Sy or of the ultimate tensile strength Su.

X.1.2 St, the maximum allowable general primary

membrane stress intensity at test pressureAPI limits this stress to 90% of the yield strength for all materials.

X.2 Elastic Analysis

For elastic analysis stress components are calculated, combined, and compared to limits

for each category of stress based on multiples of the Design Stress Intensity, Sm, for the

material in use and for the category of stress.

Stress components are combined to find the stress intensity, which is defined as twice

the maximum shear stress. This can be calculated as the difference between the largest

and smallest of the three principal stresses.

X.2.1 Stress Categories

The following categories are used to classify stresses based on the consequences of

exceeding the yield strength in various manners:


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X.2.1.1 Primary Stress

Primary stress is stress distributed in such a way that stresses cannot redistribute The

basic characteristic of primary stress is that it is not self-limiting, and failure, or at least

gross distortion, can occur from one application of the loading. Primary stress is stress

caused by the application of mechanical pressure, forces and moments. Thermal stresses

are not primary stresses.

Primary stress includes both membrane and bending stress and is linearly distributed

across the wall section.

X.2.1.1a. Primary Membrane Stress Intensity

Primary membrane stress intensity is calculated from the average values of the stress

components through the wall of the vessel. Depending on the extent of the stress, is can

be classified as either General or Local.

General Primary Membrane Stress Intensity, Pm: Membrane stress distributed in away such that load redistribution cannot occur, and loading beyond the yieldstrength can proceed to failure. Pm is limited to Sm.

Local primary Membrane Stress Intensity, P l: The following is a direct quote fromASME Section VIII Division 2 Appendix 4:

Cases arise in which a membrane stress produced by pressure or othermechanical loading and associated with a primary and/or a discontinuity effect

would, if not limited, produce excessive distortion in the transfer of load to other

portions of the structure. Conservatism requires that such a stress be classified as

a local primary membrane stress even though it has some characteristics of a

secondary stress. A stressed region may be considered as local if the distance over

which the stress intensity exceeds 1.1 Sm does not extend in the meridional

direction more than 1.0(Rt)1/2

, where R is the midsurface radius of curvature

measured normal to the surface from the axis of rotation and t is the minimum

thickness in the region considered. Regions of local primary membrane stresswhich exceed 1.1 Sm shall not be closer in the meridional direction than 2.5(Rt)

1/2where R is defined as (R1 + R2)/2, and t is defined as (t1+ t2)/2, where t1 and

t2 are the minimum thicknesses at each of the regions considered, and R1 and R2

are the midsurface radii of curvature measured normal to the surface from the axis

of rotation at these regions where the membrane stress exceeds 1.1 Sm. Discrete

regions of local primary membrane stress, such as those resulting from

concentrated loads acting on brackets, where the membrane stress exceeds I. I Sm

shall be spaced so that there is no overlapping of the areas in which the membrane

stress exceeds I. I Sm.An example of a local primary membrane stress is the

membrane stress in a shell produced by external load and moment at a permanentsupport or at a nozzle connection.

Local primary stress intensity is limited to 1.5 Sm.X.2.1.1b. Primary Bending Stress Intensity

The components of primary bending stress intensity Pb are calculated from the linear

primary stress component distributions that have the same net bending moment as the


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actual stress component distribution. Bending stress components are defined as being

proportional to the distance from the centroid of a solid section.

When the bending stress components are combined with the membrane stresscomponents at each surface, the resulting stress intensities Pm+Pb are limited to 1.5 Sm.

X.2.1.2 Secondary Stress

Secondary stress Q is caused by the constraint of adjacent parts or by self-constraint of

the structure, and yielding can cause the source of the stress to be eliminated. One load

cycle can cause local yielding and stress redistribution but cannot result in failure or gross

distortion.

Secondary stresses are membrane plus bending stresses that can occur at gross structural

discontinuities, from general thermal stress, from mechanical preload conditions, or from

combinations of these sources.

The secondary stress variation, for any sequence of test or operating conditions, is limited

to3 Sm.

X.2.1.3 Peak Stress

Peak stress is the increment of stress added by a stress concentration or other source that

does not cause noticeable distortion. Such sources include thermal stress in a cladding

material with a different coefficient of expansion from the base material; by transient

thermal stress, or by the non-linear portion of a thermal stress distribution. The only

concern with peak stress is that it may cause the initiation of a fatigue crack or brittle

fracture.

The total stress, including peak stress, may be used in fatigue analysis, which is beyond

the scope of this annex.

X.3 Special stress limits

X.3.1 Bearing Stress

The average Bbearing stress from primary and secondary loads is limited to Sy. In the

cases where the distance to a free edge is greater than the distance over which the bearing

load is applied, the bearing allowable stress may be increased by a factor of 1.5. allowed

to exceed the yield strength of the material provided that the other stresses in the vicinity

of the bearing load are within acceptable limits. When bearing loads are applied to parts

having free edges, the possibility of a shear failure shall be considered. In the case of load

stress plus secondary stress, the average shear stress shall not exceed 0.5 Sy at all

temperatures.

X.3.2 Pure Shear Stress

The average primary shear stress across a section loaded under design conditions in pure

shear (for example, keys, shear rings, screw threads) shall be limited to 0.6 Sm. Themaximum primary shear under design conditions, exclusive of stress concentration at the

periphery of a solid section in torsion, shall be limited to 0.8 Sm. [Higher limits on shear

allowable stress need to be justified].

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X.3.3 Progressive distortion of nonintegral connections

Screwed-on caps, screwed-in plugs, shear ring closures, breech lock closures, clamps andunions are examples of nonintegral connections which are subject to failure by bell-

mouthing or other types of progressive deformation.

If any combination of loading produces yielding, such joints are subject to ratcheting

because the mating members may slip at the end of each complete cycle, and start the

next cycle in a new relationship with one another. Additional distortion may occur at

each subsequent cycle so that interlocking parts like threads may lose engagement.

Therefore, primary plus secondary stress intensities which could produce slippage shall

be limited to Sy.

X.34 Non-linear analysis

X.34.1 General

Finite-element methods may be used that consider the yielding of the material. The first

of these is called limit analysis, and the second, elastic-plastic analysis.

X.34.2 Limit analysis

Limit analysis assumes elastic-perfectly plastic material properties, and may be based on

small-displacement analysis. As a practical matter, the stress-strain curve that is used is

actually a bi-linear representation. This curve, for stress less than the yield strength has a

slope equal to the elastic modulus of the material and above that point, a slope as near

zero as practical, since a zero slope would force the finite-element program to divide by

zero and immediately stop as soon as the first element reached yield strength.

The yield strength to be used is 1.5 Sm, which for non-standard materials may be less than

the actual specified minimum yield strength. Loading is incrementally increased until the

model diverges, which is the collapse load. Actual rated load capacity can be no more

than 2/3 of the limit analysis collapse loading.

Limit analysis may be used to justify high primary stresses but not secondary stresses. In

addition, limit analysis cannot be used to justify a wall thickness thinner than that

calculated on an elastic basis.

X.34.3 Elastic-Plastic Analysis

Plastic analysis is a method of structural analysis by which the structural behavior under

given loads is computed by considering the actual material stress-strain relationship and

and stress redistribution, and it may include either strain hardening, and large-

displacement change in geometry, or both.

Elastic-Pplastic analysis can be used to justify high primary and secondary stresses.

However, limits for bearing stress, triaxial stress, and buckling shall be calculatedelastically.

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The design is acceptable if shakedown occurs. That is, after successive applications of the

design loading, there is no progressive distortion or stress ratcheting. In addition the

deformations which occur prior to shakedown shall not exceed specified limits.

[I think that a better approach is to consider 2/3 of the ultimate capacity, where the

ultimate capacity is set by a limit on strain (ISO 13628-7 Annex D) or last converged

load].

X.5 Triaxial Stresses

The algebraic sum of the three prmary principal stresses (1+2+3) shall not exceed

four times the design stress intensity Sm.

Attachment M - John Fowler - AnnexXRevB (1)

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