ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules

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2010 SECTION VIII, DIVISION 2

5-69

Stress Evaluation Line

Weld Toe

Elements should

be orthogonal to

Weld Joint

nozzle

corner joint with fillet

weld

head

butt joint

(a) Component Geometry (b) Finite Element Mesh

Figure 5.A.5

Continuum Finite Element Model Stress Classification Line for the Structural Stress Method

2010 SECTION VIII, DIVISION 2

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Elements Orthogonal to Stress

Evaluation Line

Internal Nodal Forces (NF

)

Transformed to local coordinate system

(Element Width for 3D

continuum)

Figure 5.A.6

Computation of Membrane and Bending Equivalent Stresses by the Structural Stress Method Using

Nodal Force Results from a Finite Element Model with Continuum Elements

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Element Nodal

Internal Forces

See Detail A

i=1

i=2

i=3

EL1

EL2

EL3

EL4

i=1,2,3 following

weld toe

Detail A

i=3 i=2 i=1

EL1

EL2

EL3

EL4

Section A-A

Figure 5.A.7

Processing Nodal Force Results with the Structural Stress Method Using the Results from a Finite

Element Model with Three Dimensional Second Order Continuum Elements

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t/2

Structural Stress Structural Stress Range

t/2

Structural Stress Structural Stress Range

Tension

Bending

(a) Symmetric Structural Stress State (symmetric joint and symmetric loading)

(b) Anti-symmetric Structural Stress State (symmetric joint and anti-symmetric loading)

t/2

SCL at fillet weld toe (extends

across one-half of the thickness)

Figure 5.A.8

Processing Structural Stress Method Results for a Symmetric Structural Stress Range

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Head Thickness

Nozzle Thickness

Weld Leg

Weld Throat Thickness (see Note 1)

Shell Model at Mean

Radius of Nozzle and Shell

Stress Evaluation Point

Note 1: The thickness and material properties of the shell element used to model the fillet weld should be

established based on producing an equivalent stiffness of the actual fillet weld.

Figure 5.A.9

Computation of Membrane and Bending Equivalent Stresses by the Structural Stress Method Using

the Results from a Finite Element Model with Shell Elements

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EL1

i=1 i=2 i=3

NF1

NF2

NF3

NF1-NF3 Transformed to Y

direction

weld toe

See Detail A

Detail A

Figure 5.A.10

Processing Nodal Force Results with the Structural Stress Method Using the Results from a Finite

Element Model With Three Dimensional Second Order Shell Elements

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2010 SECTION VIII, DIVISION 2

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Nozzle Neck

SCL

Shell SCL

Element set

processed for

shell SCL

Element set

processed for

nozzle SCL

Thin

Plate

SCL

Thick

Plate

SCL

Element set

processed for

thick plate SCL

Element set

processed for

thin plate SCL

Figure 5.A.11

Element Sets for Processing Finite Element Nodal Stress Results with the Structural Stress Method

Based on Stress Integration

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ANNEX 5.B

HISTOGRAM DEVELOPMENT AND CYCLE COUNTING FOR

FATIGUE ANALYSIS

(INFORMATIVE)

5.B.1 General

This annex contains cycle counting procedures required to perform a fatigue assessment for irregular stress

or strain versus time histories. These procedures are used to break the loading history down into individual

cycles that can be evaluated using the fatigue assessment rules of Part 5. Two cycle counting methods are

presented in this Appendix. An alternative cycle counting method may be used if agreed to by the Owner-

User.

5.B.2 Definitions

The definitions used in this Annex are shown below.

a) Event – The Users’ Design Specification may include one or more events that produce fatigue damage.

Each event consists of loading components specified at a number of time points over a time period and

is repeated a specified number of times. For example, an event may be the startup, shutdown, upset

condition, or any other cyclic action. The sequence of multiple events may be specified or random.

b) Cycle – A cycle is a relationship between stress and strain that is established by the specified loading at

a location in a vessel or component. More than one stress-strain cycle may be produced at a location,

either within an event or in transition between two events, and the accumulated fatigue damage of the

stress-strain cycles determines the adequacy for the specified operation at that location. This

determination shall be made with respect to the stabilized stress-strain cycle.

c) Proportional Loading – During constant amplitude loading, as the magnitudes of the applied stresses

vary with time, the size of Mohr’s circle of stress also varies with time. In some cases, even though the

size of Mohr’s circle varies during cyclic loading, if the orientation of the principal axes remains fixed, the

loading is called proportional. An example of proportional loading is a shaft subjected to in-phase torsion

and bending, where the ratio of axial and torsional stress remains constant during cycling.

d) Non-Proportional Loading – If the orientation of the principal axes are not fixed, but change orientation

during cyclic loading, the loading is called non-proportional. An example of non-proportional loading is a

shaft subjected to out-of-phase torsion and bending, where the ratio of axial and torsional stress varies

continuously during cycling.

e) Peak – The point at which the first derivative of the loading or stress histogram changes from positive to

negative.

f) Valley – The point at which the first derivative of the loading or stress histogram changes from negative

to positive.

5.B.3 Histogram Development

5.B.3.1 The loading histogram should be determined based on the specified loadings provided in the Users’

Design Specification. The loading histogram should include all significant operating loads and events that are

applied to the component. The following should be considered in developing the loading histogram.

a) The number of repetitions of each event during the operation life.

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b) The sequence of events during the operation life, if applicable.

c) Applicable loadings such as pressure, temperature, supplemental loads such as weight, support

displacements, and nozzle reaction loadings.

d) The relationship between the applied loadings during the time history.

5.B.4 Cycle Counting Using the Rainflow Method

5.B.4.1 The Rainflow Cycle Counting Method (ASTM Standard No. E1049) is recommended to determine the

time points representing individual cycles for the case of situations where the variation in time of loading,

stress, or strain can be represented by a single parameter. This cycle counting method is not applicable for

non-proportional loading. Cycles counted with the Rainflow Method correspond to closed stress-strain

hysteresis loops, with each loop representing a cycle.

5.B.4.2 Recommended Procedure

a) STEP 1 – Determine the sequence of peaks and valleys in the loading histogram. If multiple loadings

are applied, it may be necessary to determine the sequence of peaks and valleys using a stress

histogram. If the sequence of events is unknown, the worst case sequence should be chosen.

b) STEP 2 – Re-order the loading histogram to start and end at either the highest peak or lowest valley, so

that only full cycles are counted. Determine the sequence of peaks and valleys in the loading history. Let

denote the range under consideration, and let Y denote the previous range adjacent to

c) STEP 3 – Read the next peak or valley. If out of data, go to STEP 8.

d) STEP 4 – If there are less than 3 points, go to STEP 3; If not, form ranges X and Y using the three most

recent peaks and valleys that have not been discarded.

e) STEP 5 – Compare the absolute values of ranges X and Y.

1) If

Y< go to STEP 3

2) If

Y≥

go to STEP 6

f) STEP 6 – Count range

Y as one cycle; discard the peak and valley of Y . Record the time points and

loadings or component stresses, as applicable, at the starting and ending time points of the cycle.

g) STEP 7 – Return to STEP 4 and repeat STEPs 4 to 6 until no more time points with stress reversals

remain.

h) STEP 8 – Using the data recorded for the counted cycles perform fatigue assessment in accordance with

Part 5.

5.B.5 Cycle Counting Using Max-Min Cycle Counting Method

5.B.5.1 Overview

The Max-Min Cycle Counting Method is recommended to determine the time points representing individual

cycles for the case of non-proportional loading. The cycle counting is performed by first constructing the

largest possible cycle, using the highest peak and lowest valley, followed by the second largest cycle, etc.,

until all peak counts are used.

5.B.5.2 Recommended Procedure

a) STEP 1 – Determine the sequence of peaks and valleys in the loading history. If some events are

known to follow each other, group them together but otherwise arrange the random events in any order.

2010 SECTION VIII, DIVISION 2

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b) STEP 2 – Calculate the elastic stress components

produced by the applied loading at every point in

time during each event at a selected location of a vessel. All stress components must be referred to the

same global coordinate system. The stress analysis must include peak stresses at local discontinuities.

c) STEP 3 – Scan the interior points of each event and delete the time points at which none of the stress

components indicate reversals (peaks or valleys).

d) STEP 4 – Using the stress histogram from STEP 2, determine the time point with the highest peak or

lowest valley. Designate the time point as

t , and the stress components as

e) STEP 5 – If time point

t is a peak in the stress histogram, determine the component stress range

between time point

t and the next valley in the stress histogram. If time point

t is a valley, determine

the component stress range between time point

and the next peak. Designate the next time point

t , and the stress components as

. Calculate the stress component ranges and the von Mises

equivalent stress range between time points

and

mn m n

ij ij ij

σσ

Δ= −

(5.B.1)

()()

()( )

0.5

11 22 22 33

222

33 11 12 23 31

mn mn mn mn

range

mn mn mn mn mn

σσ σσ

σσ σσσ

⎡⎤

Δ−Δ +Δ−Δ +

⎢⎥

Δ=

⎢⎥

Δ−Δ + Δ+Δ+Δ

⎢⎥

⎣⎦

(5.B.2)

f) STEP 6 – Repeat STEP 5, for the current time point,

and the time point of the next peak or valley in

the sequence of the stress histogram. Repeat this process for every remaining time point in the stress

histogram.

g) STEP 7 – Determine the maximum von Mises equivalent stress range obtained in STEP 5 and record

the time points

t and

t that define the start and end points of the

k cycle.

h) STEP 8 – Determine the event or events to which the time points

t and

t belong and record their

specified number of repetitions as

and

, respectively.

i) STEP 9 – Determine the number of repetitions of the

k cycle.

1) If

NN< : Delete the time point

t from those considered in STEP 4, and reduce the number of

repetitions at time point

t from

N to ()

NN− .

2) If

NN>

: Delete the time point

from those considered in STEP 4, and reduce the number of

repetitions at time point

t from

N to ()

NN− .

3) If

NN= : Delete both time points

t and

t from those considered in STEP 4.

j) STEP 10 – Return to STEP 4 and repeat STEPs 4 to 10 until no more time points with stress reversals

remain.

k) STEP 11 – Using the data recorded for the counted cycles, perform fatigue assessment in accordance

with Part 5. Note that an elastic-plastic fatigue assessment (see Part 5, paragraph 5.5.4) may be applied

range

SΔ exceeds the yield point of the cyclic stress range-strain range curve of the material.

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