A probabilistic study of brittle failure in dowel-type timber connections with steel plates loaded parallel to the grain

Figures & data

Figure 1. The different types of brittle failure for connections with large diameter fasteners and the definition of the lateral L and the head H failure planes for the row and block shear failure modes.

Figure 2. Analysed connections types, with the definition of the different geometrical parameters. From left to right: front view of the connections; lateral view of the two analysed types WSW and SWS.

Table I. Distribution characteristics according to JCSS (2006) and property values used in the present study.

	Parameter	Unit	Distribution type	Value		CV
				Mean	Char.
1	fm	[mm^2]	Lognormal	37.1	24	0.25
2	ft,0	[mm^2]	Lognormal	32.5	19.2	0.3
3	ft,90	[mm^2]	Weibull	1.1	0.5	0.25
4	fc,0	[mm^2]	Lognormal	33.9	24	0.2
5	fc,90	[mm^2]	Normal	3.0	2.5	0.1
6	fv	[mm^2]	Lognormal	5.5	3.5	0.25
7*	fr	[mm^2]	Lognormal	1.9	1.2	0.25
8	Et,0	[mm^2]	Lognormal	11500	9600	0.13
9	Et,90	[mm^2]	Lognormal	320	250	0.13
10	Gv	[mm^2]	Lognormal	650	540	0.13
11*	Gr	[mm^2]	Lognormal	65	54	0.13
12	ρ	[kg/m^3]	Normal	420	385	0.10
13*	A	[-]	Lognormal	0.097		0.23
14*	B	[-]	Normal	1.07		0.0374
15*	C	[-]	Normal	−0.25		0.048
16*	D	[-]	Lognormal	1		0.11

Note: The characteristic property values 1–7 and the mean property values 8–12 are based on EN 14080. The distribution properties labelled with asterisk are not included in JCSS (2006). The distribution parameters of values 7 and 11 are chosen referring to values 6 and 10, respectively. The values 13–16 are taken from Leijten et al. (2004).

Table II. Correlations of parameters A, B, C and D for the generation of embedment strength.

	A	B	C	D
A	1	−0.99	−0.24	0
B		1	0.11	0
C			1	0
D				1

Table III. Correlation of parameters for strength and stiffness values given Table I.

	fm	ft,0	ft,90	fc,0	fc,90	fv	fr	Et,0	Et,90	Gv	Gr	ρ
fm	1	0.8	0.3	0.8	0.6	0.4	0.3	0.6	0.6	0.4	0.2	0.6
ft,0		1	0.2	0.5	0.5	0.6	0.4	0.8	0.2	0.4	0.2	0.4
ft,90			1	0.2	0.4	0.6	0.4	0.4	0.4	0.4	0.2	0.4
fc,0				1	0.6	0.4	0.2	0.4	0.6	0.4	0.2	0.8
fc,90					1	0.4	0.2	0.4	0.2	0.4	0.2	0.8
fv						1	0.4	0.4	0.6	0.6	0.4	0.6
fr							1	0.2	0.4	0.4	0.2	0.4
Et,0								1	0.4	0.6	0.4	0.6
Et,90									1	0.6	0.4	0.6
Gv										1	0.4	0.6
Gr											1	0.4
ρ												1

Figure 3. Examples of the simulated material properties.

Figure 4. Changing of probability distributions of brittle (red) and ductile (black) failure capacities for WSW connection. Top: the effect of increasing timber thickness (h_w/d) (a₁=5d). Bottom: the effect of increasing parallel spacing (a₁) (h_w=20d).

Figure 5. Effect of changing timber thickness (h_w/d) on characteristic strength (top) and likelihood of brittle failure (bottom) (WSW, a₁=5d). (Legend: B_c – brittle resistance, D_c – characteristic ductile resistance, D_eff,c – reduced characteristic ductile resistance), B₅, D₅ – 5th-percitle values of the simulated brittle and ductile failure capacities, P(B < D) – probability that the brittle capacity is lower than the ductile one, CV(R) – coefficient of variation of connection resistance.

Figure 6. Effect of changing parallel spacing (a₁) on characteristic strength and likelihood of brittle failure (WSW, h_w=20d). (Legend: B_c – brittle resistance, D_c – characteristic ductile resistance, D_eff,c – reduced characteristic ductile resistance), B₅, D₅ – 5th-percitle values of the simulated brittle and ductile failure capacities, P(B < D) – probability that the brittle capacity is lower than the ductile one, CV(R) – coefficient of variation of connection resistance.

Figure 7. Characteristic vs 5th percentile values for ductile (top left) and brittle (top right) failure capacity; characteristic brittle vs ductile failure capacities (bottom left) and probability of brittle failure governing (bottom right) (WSW).

Figure 8. Changing of probability distributions of brittle (red) and ductile (black) failure capacities for SWS connection. Top: the effect of increasing timber thickness (h_w/d) (a₁=5d). Bottom: the effect of increasing parallel spacing (a₁) (h_w=20d).

Figure 9. Effect of changing timber thickness (h_w/d) on characteristic strength and likelihood of brittle failure (SWS, a₁=5d). (Legend: B_c – brittle resistance, D_c – characteristic ductile resistance, D_eff,c – reduced characteristic ductile resistance), B₅, D₅ – 5th-percitle values of the simulated brittle and ductile failure capacities, P(B < D) – probability that the brittle capacity is lower than the ductile one, CV(R) – coefficient of variation of connection resistance.

Figure 10. Effect of changing parallel spacing (a₁) on characteristic strength and likelihood of brittle failure (SWS, h_w=20d). (Legend: B_c – brittle resistance, D_c – characteristic ductile resistance, D_eff,c – reduced characteristic ductile resistance), B₅, D₅ – 5th-percitle values of the simulated brittle and ductile failure capacities, P(B < D) – probability that the brittle capacity is lower than the ductile one, CV(R) – coefficient of variation of connection resistance.

Figure 11. Characteristic vs 5th percentile values for ductile (top left) and brittle (top right) failure capacity; characteristic brittle vs ductile failure capacities (bottom left) and probability of brittle failure governing (bottom right) (SWS).

Joint Committee on Structural Safety (2006) Probabilistic Model Code, JCSS.

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Leijten, A., Köhler, J. and Jorissen, A. (2004) Review of probability data for timber connections with dowel-type fasteners. Proc. of the CIB-W18 meeting 37, Edinburgh, UK. Paper No. CIB-W18/37-7-13.

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