S-BT Threaded Fastener Specification

page 72 Specifications
Test results and evaluation procedure
Thestatisticalevaluationofthetestresultsandthenalset-upofafatiguereference
classandS-Ncurveweredoneinthreesteps.
1.Determinationoflinearregressionline(meanS-Ncurve)offatiguetestseries
2.DeterminationofacharacteristicdesignS-Ncurvewithacertainprobability
offailurebasedontherequirementswithregardstothestatisticalintervals
(condencelevel,probabilityofsurvival)asgiveninthespeciccodesand
standards.
3.RecommendationofanaldesignS-Ncurveandfatiguereferenceclassbased
ontheaforementionedstatisticalevaluationandengineeringjudgmenttaking
intoaccountthespecicS-Ncurvetypesandclassesasgivenintherelevant
codes and standards.
Table2summarizestheresultsofastatisticalevaluationacc.toEN1993-1-9
combiningalltestresultswithregardstothebasematerialthickness,stress
rationR,installationconditionandfastenermaterial.
page 44
Test results and evaluation procedure
The statistical evaluation of the test results and the final set-up of a fatigue
reference class and S-N curve were done in three steps.
1. Determination of linear regression line (mean S-N curve) of fatigue test
series
2. Determination of a characteristic design S-N curve with a certain probability
of failure based on the requirements with regards to the statistical intervals
(confidence level, probability of survival) as given in the specific codes and
standards.
3. Recommendation of a final design S-N curve and fatigue reference class
based on the afore mentioned statistical evaluation and engineering
judgment taking into account the specific S-N curve types and classes as
given in the relevant codes and standards.
Table 2 summarizes the results of a statistical evaluation acc. to EN 1993-1-9
combining all test results with regards to the base material thickness, stress
ration R, installation condition and fastener material.
Table 2: Statistical evaluation combining all test results
In Figure 1, all test data and the statistically evaluated design S-N curve are
plotted in comparison to the detail category 100 (m
1
= 5) as given in EN 1993-
1-9 [5] and the IIW-Recommendations [11]. Both curves fit very well, which
means that the fatigue strength of Hilti S-BT fastening system can be well
described by the detail category 100 (m = 5).
Figure 1: Statistical evaluation of all test results
Test facility for fatigue tests
Specimen for fatigue tests
Fracture surface
Statistical evaluation acc. to
EN 1993-1-9 (EC 3)
Table2:Statisticalevaluationcombingalltestresults
InFigure1,alltestdataandthestatisticallyevaluateddesignS-Ncurveareplotted
incomparisontothedetailcategory100(m
1
=5)asgiveninEN1993-1-9[5]andthe
IIW-Recommendations[11].Bothcurvestverywell,whichmeansthatthefatigue
strengthofHiltiS-BTfasteningsystemcanbewelldescribedbythedetailcategory
100(m=5).
Universität Stuttgart
Institut für Konstruktion und Entwurf
Schwerpunkte: Stahlbau, Holzbau und Verbundbau
Prof. Dr.-Ing. Ulrike Kuhlmann
2017-06-30 S-BT Fatigue Page 42
10.2 Recommended design S-N curve and fatigue class
10.2.1 General
On the basis of the existing test results outlined in this document and a statistical evaluation of
these test data according to the provisions given in EN 1993-1-9:2005 (Eurocode 3) it is recom-
mended to use following general design S-N curve for the Hilti S-BT fastening system, see
Fig-
ure 36
:
log N = log a – m
∙ log S (9)
with
log N logarithm to base 10 of corresponding number of cycles to failure N
log a = 16.300 intercept on the log N axis
m = 5.0 negative slope of S-N-curve being linear on a log-log basis
log S logarithm to base 10 of stress range 
This recommended design S-N curve corresponds e.g. to detail category 100 according to EN
1993-1-9 having a slope of m = 5. Regarding a possible slope intersection of the S-N curve and
a constant amplitude fatigue limit (CALF) it is referred to the relevant codes and standards.
In the following sections this recommended S-N curve is presented according to the relevant
codes and standards.
50
500
1,0E+04 1,0E+05 1,0E+06 1,0E+07 1,0E+08
Number of cycles N [-]
Nominal stress range  [N/mm
2
]
300
200
100
S235
t = 3 - 20mm
R = 0.1 - 0.3
test results
stat. evaluated S-N curve
recommended S-N curve
400
50
500



t
Hilti S-BT
m=5
1

C
= 100 MPa
P
Ü
= 50%
P
Ü
 97,7%
log a = 16.300

 = 72.4 MPa
Figure 36. Recommended basis design S-N curve for Hilti S-BT fastening system
Figure1:Statisticalevaluationofalltestresults
Testfacilityforfatiguetest
Specimenforfatiguetest
Fracturesurface
Universität Stuttgart
Institut für Konstruktion und Entwurf
Schwerpunkte: Stahlbau, Holzbau und Verbundbau
Prof. Dr.-Ing. Ulrike Kuhlmann
2017-06-30 S-BT Fatigue Page 21
7.3 Statistical evaluation procedure
7.3.1 General
Statistical evaluation procedure of fatigue test data are given e.g. in [9] - [12] and ISO
14345:2012.
When applying the classification method using the S-N curve concept it is assumed, that the
number of cycles N, that a constructional details can withstand until failure is considered as a
function of the applied stress range S (=
). Consequently, the stress range S is referred as
being the independent variable while the number of cycles N (fatigue life) represents the de-
pendent variable. The regression analysis is a statistical technique for estimation the relation-
ship between the fatigue life N and the stress range S.
Traditionally in fatigue design it is assumed that that there is a linear relationship between S
and N on a double–logarithmic scale as follows, see Figure 21:
log N = log a – m ∙ log S (2)
with
log N logarithm to base 10 of corresponding number of cycles to failure N
log a intercept on the log N axis
m negative slope of S-N curve being linear on a log-log basis
log S logarithm to base 10 of stress range
log S = log 
log N
2·10
6
1
m
 97.7% probability
of survival


m

C
statistical distribution of test
results with standard deviation s
s
test results
log a
regression line: log N = log a + m · log S
log N
C
log a
C
Figure 21. Statistical evaluation of the test results according to EN 1993-1-9:2005
In general the statistical evaluation and the final set-up of a fatigue reference class and
S-N curve are realized in 3 steps:
1. Determination of linear regression line (mean S-N curve) of fatigue test series
2. Determination of a characteristic design S-N curve with a certain probability of failure based
on the requirements with regard to the statistical intervals (confidence level, probability of
survival) as given in the relevant code and standard.
Statisticalevaluationacc.to
EN1993-1-9(EC3)