ISO 10928:2009
(Main)Plastics piping systems — Glass-reinforced thermosetting plastics (GRP) pipes and fittings — Methods for regression analysis and their use
Plastics piping systems — Glass-reinforced thermosetting plastics (GRP) pipes and fittings — Methods for regression analysis and their use
ISO 10928:2009 specifies procedures suitable for the analysis of data which, when converted into logarithms of the values, have either a normal or a skewed distribution. It is intended for use with the test methods and referring standards for glass-reinforced thermosetting plastics (GRP) pipes or fittings for the analysis of properties as a function of time. However, it can be used for the analysis of other data. Depending upon the nature of the data, two methods are specified. The extrapolation using these techniques typically extends the trend from data gathered over a period of approximately 10 000 h, to a prediction of the property at 50 years, which is the typical maximum extrapolation time.
Systèmes de canalisation en matières plastiques — Tubes et raccords plastiques thermodurcissables renforcés de verre (PRV) — Méthodes pour une analyse de régression et leurs utilisations
General Information
Relations
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 10928
Second edition
2009-09-15
Plastics piping systems — Glass-
reinforced thermosetting plastics (GRP)
pipes and fittings — Methods for
regression analysis and their use
Systèmes de canalisation en matières plastiques — Tubes et raccords
plastiques thermodurcissables renforcés de verre (PRV) — Méthodes
pour une analyse de régression et leurs utilisations
Reference number
ISO 10928:2009(E)
©
ISO 2009
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ISO 10928:2009(E)
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ii © ISO 2009 – All rights reserved
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ISO 10928:2009(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Principle.1
3 Procedures for determining the linear relationships – Methods A and B .1
3.1 Procedures common to methods A and B.1
3.2 Method A – Covariance method.2
3.3 Method B – Regression with time as the independent variable .8
4 Application of methods to product design and testing.11
4.1 General .11
4.2 Product design .12
4.3 Comparison to a specified value .12
4.4 Declaration of a long-term value.12
Annex A (normative) GRP pressure pipe design procedure.13
Annex B (informative) Second-order polynomial relationships.20
Annex C (informative) Non-linear relationships.25
Annex D (informative) Calculation of lower confidence and prediction limits for method A .49
Bibliography.51
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ISO 10928:2009(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 10928 was prepared by Technical Committee ISO/TC 138, Plastics pipes, fittings and valves for the
transport of fluids, Subcommittee SC 6, Reinforced plastics pipes and fittings for all applications.
This second edition cancels and replaces the first edition (ISO 10928:1997), which has been technically
revised.
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ISO 10928:2009(E)
Introduction
This International Standard describes the procedures intended for analysing the regression of test data,
usually with respect to time and the use of the results in design and assessment of conformity with
performance requirements. Its applicability is limited to use with data obtained from tests carried out on
samples. The referring standards require estimates to be made of the long-term properties of the pipe for such
parameters as circumferential tensile strength, long-term ring deflection, strain-corrosion and creep or
relaxation stiffness.
A range of statistical techniques that could be used to analyse the test data produced by destructive tests was
investigated. Many of these simple techniques require the logarithms of the data to
a) be normally distributed,
b) produce a regression line having a negative slope, and
c) have a sufficiently high regression correlation (see Table 1).
Whilst the last two conditions can be satisfied, analysis shows that there is a skew to the distribution and
hence this primary condition is not satisfied. Further investigation into techniques that can handle skewed
distributions resulted in the adoption of the covariance method of analysis of such data for this International
Standard.
However, the results from non-destructive tests, such as long-term creep or relaxation stiffness, often satisfy
all three conditions and hence a simpler procedure, using time as the independent variable, can also be used
in accordance with this International Standard.
These data analysis procedures are limited to analysis methods specified in ISO product standards or test
methods. However, other analysis procedures can be useful for the extrapolation and prediction of long-term
behaviour of some properties of glass-reinforced thermosetting plastics (GRP) piping products. For example,
a second-order polynomial analysis is sometimes useful in the extrapolation of creep and relaxation data. This
is particularly the case for analysing shorter term data, where the shape of the creep or relaxation curve can
deviate considerably from linear. A second-order polynomial analysis is included in Annex B. In Annex C,
there is an alternative non-linear analysis method. These non-linear methods are provided only for information
and the possible use in investigating the behaviour of a particular piping product or material, therefore they
might not be generally applicable to other piping products.
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INTERNATIONAL STANDARD ISO 10928:2009(E)
Plastics piping systems — Glass-reinforced thermosetting
plastics (GRP) pipes and fittings — Methods for regression
analysis and their use
1 Scope
This International Standard specifies procedures suitable for the analysis of data which, when converted into
logarithms of the values, have either a normal or a skewed distribution. It is intended for use with the test
methods and referring standards for glass-reinforced thermosetting plastics (GRP) pipes or fittings for the
analysis of properties as a function of time. However, it can be used for the analysis of other data.
Depending upon the nature of the data, two methods are specified. The extrapolation using these techniques
typically extends the trend from data gathered over a period of approximately 10 000 h, to a prediction of the
property at 50 years, which is the typical maximum extrapolation time.
This International Standard only addresses the analysis of data. The test procedures to collect the data, the
number of samples required and the time period over which data is collected, are covered by the referring
standards and/or test methods. Clause 4 discusses how the data analysis methods are applied to product
testing and design.
2 Principle
Data are analysed for regression using methods based on least squares analysis which can accommodate the
incidence of a skew and/or a normal distribution. The two methods of analysis used are the following:
⎯ method A: covariance using a first-order relationship;
⎯ method B: least squares, with time as the independent variable using a first-order relationship.
The methods include statistical tests for the correlation of the data and the suitability for extrapolation.
3 Procedures for determining the linear relationships – Methods A and B
3.1 Procedures common to methods A and B
Use method A (see 3.2) or method B (see 3.3) to fit a straight line of the form given in Equation (1):
ya=+b×x (1)
where
y is the logarithm, lg, of the property being investigated;
a is the intercept on the Y-axis;
b is the slope;
x is the logarithm, lg, of the time, in hours.
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ISO 10928:2009(E)
3.2 Method A – Covariance method
3.2.1 General
For method A, calculate the following variables in accordance with 3.2.2 to 3.2.5, using Equations (2), (3)
and (4):
2
yY−
()
∑ i
Q = (2)
y
n
2
xX−
()
∑ i
Q = (3)
x
n
⎡⎤
xX−×y−Y
()( )
∑ii
⎣⎦
Q = (4)
xy
n
where
Q is the sum of the squared residuals parallel to the Y-axis, divided by n;
y
Q is the sum of the squared residuals parallel to the X-axis, divided by n;
x
Q is the sum of the squared residuals perpendicular to the line, divided by n;
xy
Y is the arithmetic mean of the y data, i.e. given as Equation (5):
y
∑ i
Y = (5)
n
X is the arithmetic mean of the x data, i.e. given as Equation (6):
x
∑ i
(6)
X =
n
x , y are individual values;
i i
n is the total number of results (pairs of readings for x , y ).
i i
NOTE If the value of Q is greater than zero, the slope of the line is positive and if the value of Q is less than zero,
xy xy
then the slope is negative.
3.2.2 Suitability of data
Calculate the linear coefficient of correlation, r, using Equations (7) and (8):
2
Q
xy
2
r = (7)
QQ×
xy
0,5
2
rr= (8)
()
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ISO 10928:2009(E)
Student'stf( )
If the value of r is less than:
2
⎡⎤
nt−+2 Student'sf
()
⎣⎦
then the data are unsuitable for analysis.
Table 1 gives the minimum acceptable values of the correlation coefficient, r, as a function of the number of
variables, n. The Student's t value is based on a two-sided 0,01 level of significance.
Table 1 — Minimum values of the correlation coefficient, r, for acceptable data from n pairs of data
Number of Degrees of Student's Minimum Number of Degrees of Student's Minimum
variables freedom variables freedom
n n − 2 t(0,01) r n n − 2 t(0,01) r
13 11 3,106 0,683 5 26 24 2,797 0,495 8
14 12 3,055 0,661 4 27 25 2,787 0,486 9
15 13 3,012 0,641 1 32 30 2,750 0,448 7
16 14 2,977 0,622 6 37 35 2,724 0,418 2
17 15 2,947 0,605 5 42 40 2,704 0,393 2
18 16 2,921 0,589 7 47 45 2,690 0,372 1
19 17 2,898 0,575 1 52 50 2,678 0,354 2
20 18 2,878 0,561 4 62 60 2,660 0,324 8
21 19 2,861 0,548 7 72 70 2,648 0,301 7
22 20 2,845 0,536 8 82 80 2,639 0,283 0
23 21 2,831 0,525 6 92 90 2,632 0,267 3
24 22 2,819 0,515 1 102 100 2,626 0,254 0
25 23 2,807 0,505 2
3.2.3 Functional relationships
To find a and b for the functional relationship line:
ya=+b×x (1)
First set Γ as given in Equation (9):
Q
y
Γ = (9)
Q
x
then calculate a and b using Equations (10) and (11):
0,5
b =− Γ (10)
()
aY=−b×X (11)
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ISO 10928:2009(E)
3.2.4 Calculation of variances
If t is the applicable time to failure, then set x as given in Equation (12):
u u
xt= lg (12)
uu
Using Equations (13), (14) and (15) respectively, calculate for i = 1 to n, the following sequence of statistics:
⎯ the best fit x ' for true x ;
i i
⎯ the best fit y ' for true y ;
i i
2
⎯ the error variance, σ for x.
δ
Γ×+xby×()−a
ii
x ' = (13)
i
2 × Γ
ya''=+b×x (14)
ii
22
⎡⎤
yy−+''Γ× x−x
() ( )
∑∑ii i i
⎢⎥
2⎣⎦
σ = (15)
δ
n−×2 Γ
()
Calculate quantities E and D using Equations (16) and (17):
2
b ×σ
δ
E = (16)
2 × Q
xy
2
2××Γσb×
δ
D = (17)
nQ×
xy
Calculate the variance, C, of the slope b, using Equation (18):
CD=×()1+E (18)
3.2.5 Check for the suitability of data for extrapolation
If it is intended to extrapolate the line, calculate T using Equation (19):
bb
T== (19)
0,5 0,5
C
var b
()
If the absolute value, ⎜T⎟ (i.e. ignoring signs), of T is equal to or greater than the applicable value for Student's
t, t , shown in Table 2 for (n − 2) degrees of freedom, then consider the data suitable for extrapolation.
v
NOTE Calculation of confidence limits is not required by the test methods or referring standards, however, the
calculation of lower confidence limit, LCL, and lower prediction limit, LPL, are given in Annex D.
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ISO 10928:2009(E)
Table 2 — Percentage points of Student's t distribution
(upper 2,5 % points; two-sided 5 % level of confidence; t for 97,5 %)
v
Degree of Student's t value Degree of Student's t value Degree of Student's t value
freedom freedom freedom
t t t
v v v
(n − 2) (n − 2) (n − 2)
36 2,028 1 71 1,993 9
1 12,706 2
2 4,302 7 37 2,026 2 72 1,993 5
38 2,024 4 73 1,993 0
3 3,182 4
39 2,022 7 74 1,992 5
4 2,776 4
40 2,021 1 75 1,992 1
5 2,570 6
6 2,446 9 41 2,019 5 76 1,991 7
42 2,018 1 77 1,991 3
7 2,364 6
43 2,016 7 78 1,990 8
8 2,306 0
44 2,015 4 79 1,990 5
9 2,262 2
10 2,228 1 45 2,014 1 80 1,990 1
46 2,012 9 81 1,989 7
11 2,201 0
47 2,011 2 82 1,989 3
12 2,178 8
48 2,010 6 83 1,989 0
13 2,160 4
49 2,009 6 84 1,988 6
14 2,144 8
50 2,008 6 85 1,988 3
15 2,131 5
16 2,119 9 51 2,007 6 86 1,987 9
52 2,006 6 87 1,987 6
17 2,109 8
53 2,005 7 88 1,987 3
18 2,100 9
54 2,004 9 89 1,987 0
19 2,093 0
20 2,086 0 55 2,004 0 90 1,986 7
56 2,003 2 91 1,986 4
21 2,079 6
57 2,002 5 92 1,986 1
22 2,073 9
58 2,001 7 93 1,985 8
23 2,068 7
24 2,063 9 59 2,001 0 94 1,985 5
60 2,000 3 95 1,985 3
25 2,059 5
26 2,055 5 61 1,999 6 96 1,985 0
62 1,999 0 97 1,984 7
27 2,051 8
28 2,048 4 63 1,998 3 98 1,984 5
64 1,997 7 99 1,984 2
29 2,045 2
30 2,042 3 65 1,997 1 100 1,984 0
66 1,996 6
31 2,039 5
32 2,036 9 67 1,996 0
68 1,995 5
33 2,034 5
69 1,994 9
34 2,032 2
70 1,994 4
35 2,030 1
3.2.6 Validation of statistical procedures by an example calculation
The data given in Table 3 are used in the following example to aid in verifying that statistical procedures, as
well as computer programs and spreadsheets adopted by users, will produce results similar to those obtained
from the equations given in this International Standard. For the purposes of the example, the property in
question is represented by V, the values for which are of a typical magnitude and in no particular units.
Because of rounding errors, it is unlikely that the results will agree exactly, so for a calculation procedure to be
2
acceptable, the results obtained for r, r , b, a, and the mean value of V, and V , shall agree to within ± 0,1 %
m
of the values given in this example. The values of other statistics are provided to assist the checking of the
procedure.
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ISO 10928:2009(E)
Sums of squares:
Q = 0,798 12;
x
Q = 0,000 88;
y
Q = −0,024 84.
xy
Coefficient of correlation:
2
r = 0,879 99;
r = 0,938 08.
Functional relationships:
Г = 0,001 10;
b = −0,033 17;
a = 1,627 31.
Table 3 — Basic data for example calculation and statistical analysis validation
n V Y Time X
lg V
h lg h
1 30,8 1,488 6 5 184 3,714 7
2 30,8 1,488 6 2 230 3,348 3
3 31,5 1,498 3 2 220 3,346 4
4 31,5 1,498 3 12 340 4,091 3
5
31,5 1,498 3 10 900 4,037 4
6 31,5 1,498 3 12 340 4,091 3
7 31,5 1,498 3 10 920 4,038 2
8 32,2 1,507 9 8 900 3,949 4
9 32,2 1,507 9 4 173 3,620 4
10 32,2 1,507 9 8 900 3,949 4
11 32,2 1,507 9 878 2,943 5
12 32,9 1,517 2 4 110 3,613 8
13 32,9 1,517 2 1 301 3,114 3
14 32,9 1,517 2 3 816 3,581 6
15 32,9 1,517 2 669 2,825 4
16 33,6 1,526 3 1 430 3,155 3
17
33,6 1,526 3 2 103 3,322 8
18 33,6 1,526 3 589 2,770 1
19 33,6 1,526 3 1 710 3,233 0
20 33,6 1,526 3 1 299 3,113 6
21 35,0 1,544 1 272 2,434 6
22 35,0 1,544 1 446 2,649 3
23 35,0 1,544 1 466 2,668 4
24 35,0 1,544 1 684 2,835 1
25 36,4 1,561 1 104 2,017 0
26 36,4 1,561 1 142 2,152 3
27 36,4 1,561 1 204 2,309 6
28 36,4 1,561 1 209 2,320 1
29
38,5 1,585 5 9 0,954 2
30 38,5 1,585 5 13 1,113 9
31 38,5 1,585 5 17 1,230 4
32 38,5 1,585 5 17 1,230 4
Means: Y = 1,530 1 X = 2, 930 5
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ISO 10928:2009(E)
Calculated variances (see 3.2.4):
−2
E = 3,520 2 × 10 ;
−6
D = 4,842 2 × 10 ;
−6
C = 5,012 7 × 10 (the variance of b);
2 −2
σ = 5,271 1 × 10 (the error variance of x).
δ
Check for the suitability for extrapolation (see 3.2.5):
n = 32;
t = 2,042 3;
v
−6 0,5
T = −0,033 17 / (5,012 7 × 10 ) = −14,816 7;
⎜T⎟ = 14,816 7 > 2,042 3.
The estimated mean values for V at various times are given in Table 4 and shown in Figure 1.
Table 4 — Estimated mean values, V , for V
m
Time
V
m
h
0,1 45,76
1 42,39
10 39,28
100 36,39
1 000 33,71
10 000 31,23
100 000 28,94
438 000 27,55
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ISO 10928:2009(E)
Key
X-axis lg scale of time, in hours
Y-axis lg scale of property
1 438 000 h (50 years)
2 regression line from Table 4
3 data point
Figure 1 — Regression line from the results in Table 4
3.3 Method B – Regression with time as the independent variable
3.3.1 General
For method B, calculate the sum of the squared residuals parallel to the Y-axis, S , using Equation (20):
y
2
Sy=−Y (20)
()
y ∑ i
Calculate the sum of the squared residuals parallel to the X-axis, S , using Equation (21):
x
2
Sx=−X (21)
()
x ∑ i
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ISO 10928:2009(E)
Calculate the sum of the squared residuals perpendicular to the line, S , using Equation (22):
xy
⎡⎤
Sx=−X×y−Y (22)
()( )
xy ∑ii
⎣⎦
where
Y is the arithmetic mean of the y data, i.e.
y
∑ i
Y = ;
n
X is the arithmetic mean of the x data, i.e.
x
∑ i
X = ;
n
x , y are individual values;
i i
n is the total number of results (pairs of readings for x , y ).
i i
NOTE If the value of S is greater than zero, the slope of the line is positive and if the value of S is less than zero,
xy xy
then the slope is negative.
3.3.2 Suitability of data
2
Calculate the squared, r , and the linear coefficient of correlation, r, using Equations (23) and (24):
2
S
xy
2
r = (23)
SS×
xy
0,5
2
rr= (24)
()
2
If the value of r , or r, is less than the applicable minimum value given in Table 1 as a function of n, consider
the data unsuitable for analysis.
3.3.3 Functional relationships
Calculate a and b for the functional relationship line [see Equation (1)], using Equations (25) and (26):
S
xy
b = (25)
S
x
aY=−b×X (26)
3.3.4 Check for the suitability of data for extrapolation
If it is intended to extrapolate the line, calculate M using Equation (27):
22
2 tS××S−S
vx()y xy
S
x
M=− (27)
22
Sn−×2S
()
xy y
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ISO 10928:2009(E)
where
t is the applicable value for Student's t determined from Table 2.
v
If M is equal to or less than zero, consider the data unsuitable for extrapolation.
3.3.5 Validation of statistical procedures by an example calculation
The data given in Table 5 are used in the following example to aid in verifying that statistical procedures, as
well as computer programs and spreadsheets, adopted by users will produce results similar to those obtained
from the equations given in this International Standard. Use the data given in Table 5 for the calculation
procedures described in 3.3.2 to 3.3.4 to ensure that the statistical procedures to be used in conjunction with
2
this method will give results for r, r , a, b and V to within ± 0,1 % of the values given in this example.
m
Table 5 — Basic data for example calculation and statistical validation
n Time X V Y
T in h lg T lg V
1 0,10 −1,000 0 7 114 3,852 1
2 0,27 −0,568 6 6 935 3,841 0
3 0,50 −0,301 0 6 824 3,834 1
4 1,00 0 6 698 3,825 9
5 3,28 0,515 9 6 533 3,815 1
6 7,28 0,862 1 6 453 3,809 8
7 20,0 1,301 0 6 307 3,799 9
8 45,9 1,661 8 6 199 3,792 3
9 72,0 1,857 3 6 133 3,787 7
10 166 2,220 1 5 692 3,755 2
11 219 2,340 4 5 508 3,741 0
12 384 2,584 3 5 393 3,731 8
13 504 2,702 4 5 364 3,729 5
14 3 000 3,477 1 5 200 3,716 0
15 10 520 4,022 0 4 975 3,696 8
Means: X = 1,445 0 Y = 3,781 9
Sums of squares:
S = 31,681 1;
x
S = 0,034 7;
y
S = −1,024 2.
xy
Coefficient of correlation:
2
r = 0,955 6;
r = 0,977 5.
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ISO 10928:2009(E)
Functional relationships (see 3.3.3):
a = 3,828 6;
b = −0,032 3.
Check for the suitability for extrapolation (see 3.3.4):
t = 2,160 4;
v
M = 942,21.
The estimated mean values, V , for V at various times are given in Table 6.
m
Table 6 — Estimated mean values, V , for V
m
Time
V
m
h
0,1 7 259
1 6 739
10 6 256
100 5 808
1 000 5 391
10 000 5 005
100 000 4 646
438 000 4 428
4 Application of methods to product design and testing
4.1 General
The referring standards specify limiting requirements for the long-term properties and performance of a
product. Some of these are based on destructive tests, for example hoop tensile strength, whilst others are
based on actual or derived physical properties, such as creep or relaxation stiffness.
These properties require an extrapolated long-term (e.g. 50 years) value for the establishment of a product
design or comparison with the requirement. This extrapolated value is determined by inserting, as necessary,
the values for a and b determined in accordance with 3.1 or 3.2 as appropriate, into Equation (28).
lgya=+b×t (28)
L
where
t is the logarithm, lg, of the long-term period, in hours, [for 50 years (438 000 h), t = 5,641 47].
L L
Solving Equation (28), for y gives the extrapolated value.
The use of the data, and the specification of requirements in the product standards, is in three distinct
categories.
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ISO 10928:2009(E)
4.2 Product design
In the first category, the data is used for design or calculation of a product line. This is the case for long-term
[1]
circumferential strength testing (ISO 7509) .The long-term destructive test data is analysed using method A.
[2]
Short-term test data (ISO 8521) is also required to carry out the design. Annex A describes the procedure
for establishing the pressure design of a GRP pipe.
4.3 Comparison to a specified value
The second category is where the long-term extrapolated value is compared to a minimum requirement given
[6]
in the product standard. This is the case for long-term ring bending (ISO 10471) and strain corrosion
[8]
(ISO 10952) . The long-term destructive test data are analysed using method A to establish a value to
compare to the product standard requirement.
4.4 Declaration of a long-term value
The third category is when the long-term extrapolated value is used to calculate a long-term property and this
[5]
value is then declared by the manufacturer. This is the case for long-term creep (ISO 10468) or relaxation
[9]
(ISO 14828) stiffness. These long-term non-destructive test data are analysed using method B.
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ISO 10928:2009(E)
Annex A
(normative)
GRP pressure pipe design procedure
A.1 Introduction
The design procedure described in this annex is used to formulate the minimum pressure performance
[7] [4]
requirements of GRP pipes made in accordance with the ISO system standards 10639 and 10467 . The
recommended minimum factors of safety relative to the product's performance are given in these ISO system
standards and are repeated in this annex.
[10]
NOTE The same procedures for pressure pipe design are used in CEN system standards, EN 1796 and
[11]
EN 14364 .
Like all plastics materials, GRP is subject to creep under applied loads. GRP pipe products are tested to
establish the regression characteristics because they are influenced by the manufacturing method and the raw
materials used.
This design procedure is based upon the principle that pipe products manufactured using a particular
manufacturing process, product design and identified materials, when tested in accordance with a specified
[1]
regression test method, e.g. ISO 7509 , will exhibit similar regression characteristics. Test data derived from
this test is analysed using method A of this International Standard. The slope of the mean regression line
derived from this analysis represents the general regression characteristics of products made with similar
materials and processes. For products made with similar materials and processes, the regression behaviour is
essentially not dimension-sensitive, i.e. testing products of different diameters and thicknesses will give similar
results.
The properties of GRP products, like all manufactured materials, are recognized as having an inherent
variability, but it is assumed that the manufacturing facility will be operating a quality control system which will
permit the determination of the coefficient of variation and AQL for the initial circumferential tensile strength.
A.2 Minimum factors of safety for long-term pressure requirements
Most GRP pressure pipes are installed underground and are subjected to stress due not only to internal
pressure, but also to ring bending resulting from soil and traffic loads. Consideration of these combined
loadings and examination of the effects of varying the values for the probability of failure at 50 years has
indicated that the factor of safety for the combined loadings, η , shall be not less than 1,5.
hat
Minimum ring deflection requirements are defined with respect to the pipe stiffness, which in effect defines the
limits of the strain due to bending. Knowing the minimum acceptable value for η and the bending conditions,
hat
the minimum acceptable value for the factor of safety in tension η is calculated. Using these concepts, the η
t t
values relating to the 97,5 % LCL and mean values have been calculated and are shown in Table A.1.
Table A.1 — Minimum long-term factors of safety, (η ) and (η )
t, PN, 97,5%LCL t, PN, mean
Property to which factor of safety is to be applied PN32 PN25 PN16 PN10 PN6 PN4 PN2,5
Minimum factor of safety to be applied to long-term 1,3 1,3 1,45 1,55 1,6 1,65 1,7
97,5 % LCL (η )
t, PN, 97,5%LCL
Minimum factor of safety to be applied to long-term 1,6 1,6 1,8 1,9 2,0 2,05 2,1
mean (η )
t, PN, mean
NOTE η is based on a constant safety factor on combined loading (from pressure and bending) of 1,5. See
t, PN, mean
[3]
ISO/TR 10465-3 for a fuller explanation.
© ISO 2009 – All rights reserved 13
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ISO 10928:2009(E)
The factors of safety given in Table A.1 shall be used when the coefficient of variation, Y, for the initial failure
pressure, P i
...
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