evaluation of embedment strength data to enable...
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Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Evaluation of Embedment Strength Data to Enable Reliability Analyses of Connections
with dowel type fasteners
Evaluation of Embedment Strength Data to Evaluation of Embedment Strength Data to Enable Reliability Analyses of Connections Enable Reliability Analyses of Connections
with dowel type fastenerswith dowel type fasteners
Ad Leijten TU-DelftJochen Köhler ETH-Zürich
Results of a STSM
Ad Ad Leijten Leijten TUTU--DelftDelftJochen Köhler Jochen Köhler ETHETH--ZürichZürich
Results of a STSMResults of a STSM
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
EC5 Deterministic model EC5 Deterministic model EC5 Deterministic model
− Double shear fasteners−− Double shear fastenersDouble shear fasteners
h,1,k 1
h,2,k 2
y,Rkh,1,k 1v,Rk 2
h,1,k 1
y,Rk h,1,k
(g)0,5 (h)
4 (2 )min 1,05 2 (1 ) (j)
2
21,15 2 (k)1
f t df t d
Mf t dF
f d t
M f d
β ββ β β
β
ββ
+= + + −
+ +
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Determination Embedment strength according to EN383
Determination Embedment strength Determination Embedment strength according to EN383according to EN383
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Stress displacement diagramsParallel and Perpendicular
Stress displacement diagramsStress displacement diagramsParallel and Perpendicular Parallel and Perpendicular
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Embedment DefinitionEmbedment DefinitionEmbedment Definition
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Data basesData basesData basesSource Parallel to grain Perp. To Total
grainNAILS (not-drilled) tension compr. compr.Whale and Smith (1985a,b) 400 120 400 920
DOWELSWhale and Smith (1985a,b) 360 120 360 840Ehlbeck and Werner (1992) 79 45 30 154Sawata and Yasumura (2003) 503 506 1009Mischler (not published) 80 50 130Vreeswijk (2003) 62 62Total Dowels 1249 946 2195Total Nails + Dowels 1769 1346 3115
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
mean st.d COVSitka Spruce 357 393 39,1 10Scots Pine 119 458 59 13European Redwood 358 460 46,6 10European Whitewood 119 390 41,6 11Spruce Pine Fir 119 411 36,8 9Picea jezoerisis (Jap) 1009 398 44,2 11Spruce 151 446 51,7 12
Coniferous ndensity
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
mean st.d COVKeruing 200 707 60,9 9Greenhart 120 905 35,9 4Beech 56 717 33,1 5Teak 5 652 9,7 1Oak 30 718 36,7 5Merbau 19 802 36,5 5Afzelia 20 714 24 3Bongossi 35 1086 56,3 5Massaranduba 10 972 27,3 3Angelim Vermelho 11 1104 40 4Azobe 10 1072 11,2 1Cumaru 10 1142 18,7 2
ndensity
Deciduous
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Correlations Coniferous wood speciesCorrelations Coniferous wood speciesSitka Spruce n=357 Diameter Emb Euro Whitew n=119 Diameter EmbDiameter 1 Diameter 1Embedment 0,16 1 Embedment 0,57 1Density -0,25 0,49 Density 0,36 0,61Scots Pine n=119 Spr. Pine Fir n=119Diameter 1 Diameter 1Embedment 0,07 1 Embedment 0,32 1Density 0,17 0,76 Density -0,09 0,41Euro Redw. n=358 Jap. Pine n=1009Diameter 1 Diameter 1Embedment 0,23 1 Embedment -0,13 1Density 0,03 0,5 Density 0,11 0,28
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Oak n=30 Diameter Emb Beech n=56 Diameter EmbDiameter 1 Diameter 1Embedment -0,24 1 Embedment -0,65 1Density -0,01 0,57 Density 0,18 0,17Bongossi n=35 Merbau n=19Diameter 1 Diameter 1Embedment -0,85 1 Embedment -0,79 1Density 0,85 -0,7 Density 0,5 -0,13
Correlations Deciduous wood speciesCorrelations Deciduous wood species
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Data analysesData analysesAssumption:Assumption:--Density and Diameter are Density and Diameter are Independent variablesIndependent variables
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Identified combinations Identified combinations for multifor multi--linear regression linear regression analysesanalyseswithwith
NAILS DOWELSConiferous parallel parallel
perpendicular perpendicularDeciduous parallel parallel
perpendicular perpendicular
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
for multifor multi--linear regression analyseslinear regression analyses
With:With:ffembemb is the embedment strengthis the embedment strengthA,B and CA,B and C model parametersmodel parameters
is the densityis the densitydd is the fastener diameteris the fastener diameter
B Chf A dρ=
ρρ
* * * *hf A B Cdρ ε= + + +
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Nails Nailsn=397 n=319 n=120 n=80Parallel Perpend Parallel PerpendConiferous Coniferous Deciduous Deciduous
µa0 -4,562785 -3,085869 -5,533446 -7,904825
σa0 0,439676 0,390547 0,513015 0,533076
µa1 1,345241 1,148261 1,506924 1,886664σa1 0,071756 0,064172 0,076790 0,079256
µa2 -0,272704 -0,419665 -0,181376 -0,418183
σa2 0,029885 0,026845 0,037282 0,038645
µsigeps 0,174512 0,140670 0,119008 0,100721
σsigeps 0,004379 0,003938 0,005432 0,005630
cov(a0;a1) -0,995002 -0,994941 -0,993812 -0,993843cov(a2;a1) 0,084639 0,039359 0,005608 0,004097
cov(a2;a0) -0,181708 -0,137500 -0,114606 -0,112836
cov(a2;sigeps) 0,000030 -0,000033 0,000034 0,000258cov(a0;sigeps) 0,000047 0,000580 0,000823 0,000177cov(sigeps;a1) -0,000054 -0,000584 -0,000833 -0,000208
Regression parameters Regression parameters
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsNails Parallel All Coniferous Species
10,015,020,025,030,035,040,045,050,0
300 400 500 600
Density [kg/m3]
Embe
dmen
t [N
/mm
2]
2,65mm top6mm bottom2.65mm data6mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsNails Parallel All Coniferous Species
10,015,020,025,030,035,040,045,050,0
300 400 500 600
Density [kg/m3]
Embe
dmen
t [N
/mm
2]
3,35mm top5mm bottom3.35mm data5mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsNails Perpendicular All Coniferous Species
10,015,020,025,030,035,040,045,050,0
300 400 500 600
Density [kg/m3]
Embe
dmen
t [N
/mm
2]
2,65mm top6mm bottom2.65mm data6mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsNails Perpendicular All Deciduous
0,0
20,0
40,0
60,0
80,0
100,0
120,0
500 600 700 800 900 1000 1100
Density [kg/m3]
Embe
dmen
t [N
/mm
2]
3,35mm top6mm bottom3.35mm data6mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsDowels Parallel Japanese Pine
10,0
15,0
20,0
25,0
30,0
35,0
40,0
45,0
50,0
300 350 400 450 500 550 600
density
embe
dmen
t
8mm top
12mm
16mm
20mm bottom
8mm data
12mm data
16mm data
20mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsDowels Perpendicular Japanese Pine
10,0
15,0
20,0
25,0
30,0
35,0
40,0
45,0
50,0
300 350 400 450 500 550 600
density
embe
dmen
t
8mm top12mm16mm20mm bottom8 mm data12 mm data16 mm data20 mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Regression resultsRegression resultsDowels Parallel Coniferous excl. Japanese data
10,015,020,025,030,035,040,045,050,055,060,0
300 350 400 450 500 550 600
density
embe
dmen
t
5mm top8mm12mm16mm20mm bottom5mm data7mm data8mm data12mm data16mm data20mm data
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Principal of lower 5%Principal of lower 5%--FractileFractile predictionprediction
EC5EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Nailsfor NailsNails d = 3.35 mm (n=140) Parallel All Coniferous Species
0
510
15
20
2530
35
4045
50
300 350 400 450 500 550 600
Density [kg/m^3]
embe
ding
str
engt
h [M
Pa]
5%-Frac
Mean regression
3.5mm data
EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Nailsfor Nails
Nails Perpendicular (n=100) All Coniferous Species
0
10
20
30
40
50
60
300 350 400 450 500 550 600
Density [kg/m^3] (5%-Frac)
embe
ding
str
engt
h [M
Pa] (
5%-
Frac
)
5%-FracMean3.35mm dataEC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Dowelsfor Dowels
Dowels Parallel (n=140) Coniferous excl. Japanese Pine
0
10
20
30
40
50
60
300 350 400 450 500 550 600
Density [kg/m^3]
Embe
ding
str
engt
h [M
Pa]
5%-FracMean 12 mm
12 mm Data
EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Dowelsfor Dowels
Dowels (n = 116) Parallel Japanese Pine
0
10
20
30
40
50
60
300 350 400 450 500 550 600
Density [kg/m^3]
Embe
ding
str
engt
h [M
Pa]
5%-Frac
Mean
20 mm Data
20 mm EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Dowelsfor Dowels
Dowels Perpendicular (n=118) Japanese Pine
0
5
10
15
20
25
30
300 350 400 450 500 550 600
Density [kg/m^3]
embe
ding
str
engt
h [M
Pa]
5%-Frac
20mm Mean
20 mm Data
20mm EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Dowelsfor Dowels
Dowels Parallel (n=65) Deciduous Species
0
20
40
60
80
100
120
140
500 600 700 800 900 1000 1100 1200
Density [kg/m^3]
embe
ding
str
engt
h [M
Pa]
5%-Frac
8 mm Mean
8 mm Data
8 mm EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Prediction of 5%Prediction of 5%--FractileFractile for Dowelsfor Dowels
Dowels Parallel (n=91) Deciduous Species
0
20
40
60
80
100
120
500 600 700 800 900 1000 1100 1200
Density [kg/m^3]
embe
ding
str
engt
h [M
Pa]
5%-Frac
16 mm Mean
16 mm Data
16 mm EC5
Steel&Timber StructuresSteel&Timber StructuresSteel&Timber Structures
Conclusions:Conclusions:
-- Reliability evaluation results in Reliability evaluation results in considerable lower 5% embedment considerable lower 5% embedment strength compared to strength compared to Eurocode Eurocode 5.5.
--Assumed Assumed cov cov of density (10%) and of density (10%) and embedment strength (20%) does not embedment strength (20%) does not affect 5% embedment as much as affect 5% embedment as much as uncertainty in regressionuncertainty in regression