Evaluation of Embedment Strength Data to Enable...

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


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

+= + + −

+ +


Determination Embedment strength according to EN383

Determination Embedment strength Determination Embedment strength according to EN383according to EN383


Stress displacement diagramsParallel and Perpendicular

Stress displacement diagramsStress displacement diagramsParallel and Perpendicular Parallel and Perpendicular


Embedment DefinitionEmbedment DefinitionEmbedment Definition


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


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


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


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


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


Data analysesData analysesAssumption:Assumption:--Density and Diameter are Density and Diameter are Independent variablesIndependent variables


Identified combinations Identified combinations for multifor multi--linear regression linear regression analysesanalyseswithwith

NAILS DOWELSConiferous parallel parallel

perpendicular perpendicularDeciduous parallel parallel

perpendicular perpendicular


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= + + +


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


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


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]



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]



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]



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


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


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


Principal of lower 5%Principal of lower 5%--FractileFractile predictionprediction

EC5EC5


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


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


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



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



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



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



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


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

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