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Calculation of timber connections

What are timber connections ?

The timber connections ensure the link between several parts in a traditional way (usually by contact like oblique thrust, dovetailed scarf or Mortise and Tenon), or through fasteners (bolts, pins, tips, screws, etc.) or metal connectors.

How to calculate a bolted connection ?

Watch the Timber Connections video

Spacings between the bolts and distances to the edges (EN 1995-1-1 table 8.2 + table 8.4)

a3 a1 a1 a4 a4 a2 a2
Spacing and end/edge distances Angle α Minimum spacing or distance
Spacing a1 (parallel to grain) 0° ≤ α ≤ 360° (4 + |cos α|) ⋅ d
Spacing a2 (perpendicular to grain) 0° ≤ α ≤ 360° 4 ⋅ d
Distance a3,t (loaded end) -90° ≤ α ≤ 90° max(7 ⋅ d; 80mm)
Distance a3,c (unloaded end) 90° ≤ α ≤ 270° (1 + 6 ⋅ sin α) ⋅ d
4 ⋅ d
(1 + 6 ⋅ |sin α|) ⋅ d
Distance a4,t (loaded edge) 0° ≤ α ≤ 180° max[(2 + 2 ⋅ sin α) ⋅ d; 3 ⋅ d]
Distance a4,c (unloaded edge) 180° ≤ α ≤ 360° 3 ⋅ d

Failure modes for timber and panel connections

with :

Single shear
  1. crushing wood in element 1
  2. crushing wood in element 2
  3. crushing wood in both elements
  4. crushing wood in element 1 and plastic hinge in the fastener
  5. crushing wood in element 2 and plastic hinge in the fastener
  6. crushing wood in both elements and plastic hinges in the fastener
Double shear
  1. crushing wood in the external elements 1
  2. crushing wood in the internal element 2
  1. crushing wood in the external elements 1 and plastic hinge in the fastener
  2. crushing wood in all elements and plastic hinges in the fastener

Failure modes for steel-to-timber connections

The characteristic load-carrying capacity of a steel-to-timber connection depends on the thickness of the steel plates. Steel plates of thickness less than or equal to 0,5d are classified as thin plates and steel plates of thickness greater than or equal to d with the tolerance on hole diameters being less than 0,1d are classified as thick plates. The characteristic load-carrying capacity of connections with steel plate thickness between a thin and a thick plate should be calculated by linear interpolation between the limiting thin and thick plate values.
Thin steel plate in single shear
  1. crushing wood in element 1
  2. plastic hinge in the fastener
Thick steel plate in single shear
  1. crushing wood in element 1
  2. crushing wood in element 1 and plastic hinge in the fastener
  3. plastic hinges in the fastener
Steel plate between thin and thick in single shear
Steel plate of any thickness as the central member of a double shear connection
  1. crushing wood in element 1
  2. crushing wood in element 1 and plastic hinge in the fastener
  3. plastic hinges in the fastener
Thin steel plates as the outer members of a double shear connection
  1. crushing wood in the internal element 2
  2. plastic hinges in the fastener
Thick steel plates as the outer members of a double shear connection
  1. crushing wood in the internal element 2
  2. plastic hinges in the fastener

Rope effect

The rope effect increases the resistance to lateral effort with more or less importance depending on the type of organ and its ability to withstand axial stress.
The contribution to the load-carrying capacity due to the rope effect in equal to 25% of the characteristic axial withdrawal capacity of the fastener. For bolts, it should also be limited to 25% of the part of the equation from Johansen theory.

Effective number of bolts nef

For one row of n bolts parallel to the grain direction, the load-carrying capacity parallel to grain should be calculated using the effective number of bolts nef where:

where :

For loads perpendicular to grain, the effective number of fasteners should be taken as nef=n.

For angles 0°<α<90° between load and grain direction, nef may be determined by linear interpolation.

Other failure modes

Example of results given by the software

See the features of Timber Connections
Available in English/French, otherwise «Google Translate»!
B1 - Joint parameters
truss - intersection - timber to timber
2
h1 a1,1 a1,2 a4top,1 a4bottom,1 a2,1 a4top,2 a4bottom,2 a2,2 h2 a3,2
Elements Fasteners
Height h1 225mm Bolts M16 4.8
Thickness t1 50mm a1,1 111.7 mm
a1,2 162.6 mm
Height h2 175mm a2,1 115 mm
a2,2 79 mm
Thickness t2 75mm
a3,2 112 mm
Timber class C24 a4,sup,1 55 mm
a4,sup,2 48 mm
Angle 45.0° a4,bas,1 55 mm
a4,bas,2 48 mm
The timber element 1 is double (external elements arranged on each side of the element 2)
B11 - Characteristics of the elements
Dimensions Mechanical characteristics
Net cross-sectional area for tensile resistance Anet External ones - Characteristic tensile strength along the grain for block shear ft,0,k 14.5MPa
Internal one 105.75cm2
Net cross-sectional area perpendicular to the grain for block shear resistance Anet,T Externes - Characteristic shear strength fv,k 4.0MPa
Internal one 46.5cm2
Net shear area in the parallel to grain direction for block shear resistance Anet,V External ones - Characteristic density ρk 350.0kg/m3
Internal one 373.702cm2
B2 - Loadings
Simple cases Axial force in the internal element
Nx
Maximum shear force for both sides of the joint in the external elements
Vz
Permanent 1500daN 1000daN
Imposed - category A 0daN 0daN
Snow - elevation=0m 2000daN 500daN
Wind (up) -1200daN -500daN
Wind (down) 800daN 200daN
Seism 0daN 0daN
B3 - Combinations
Number Description Category kmod γM
1 1.35G ULS-STR 0.6 1.3
2 G + 1.5S ULS-STR 0.9 1.3
3 1.35G + 1.5S ULS-STR 0.9 1.3
4 G + 1.5S + 0.9W ULS-STR 1.1 1.3
5 1.35G + 1.5S + 0.9W ULS-STR 1.1 1.3
6 G + 1.5S + 0.9W ULS-STR 1.1 1.3
7 1.35G + 1.5S + 0.9W ULS-STR 1.1 1.3
8 G + 1.5W1 ULS-STR 1.1 1.3
9 1.35G + 1.5W1 ULS-STR 1.1 1.3
10 G + 1.5W1 + 0.75S ULS-STR 1.1 1.3
11 1.35G + 1.5W1 + 0.75S ULS-STR 1.1 1.3
12 G + 1.5W2 ULS-STR 1.1 1.3
13 1.35G + 1.5W2 ULS-STR 1.1 1.3
14 G + 1.5W2 + 0.75S ULS-STR 1.1 1.3
15 1.35G + 1.5W2 + 0.75S ULS-STR 1.1 1.3
C1 - Bolt strength C11 - Forces in the connection for the design combination
1.35G + 1.5S + 0.9W
Total VEd Bolts Shear planes Force per bolt and per plane Fv,Ed angle α
5745.0daN 4 2 718.1daN 45.0°
C12 - Checking the shear strength
Standard αv fub Gross area A γM2 Fv,Rd Ratio
EN 1993-1-8 table 3.4 0.6 400MPa 201.1mm2 1.25 =3860.4daN 0.186
C2 - Geometry checks
Element 1
EN 1995-1-1 table 8.4 Current Minimum Checking
Spacing parallel to grain a1 111.7 mm 75.3mm
Spacing perpendicular to grain a2 115 mm 64mm
Distance to the end a3 112 mm 112.0mm
Distance to the top edge a4,top 55 mm 54.6mm
Distance to the bottom edge a4,bottom 55 mm 54.6mm
Total height h 225 mm 225mm
Element 2
EN 1995-1-1 table 8.4 Current Minimum Checking
Spacing parallel to grain a1 162.6 mm 80.0mm
Spacing perpendicular to grain a2 79 mm 64mm
Distance to the end a3 112 mm 112.0mm
Distance to the top edge a4,top 48 mm 48.0mm
Distance to the bottom edge a4,bottom 48 mm 48.0mm
Total height h 175 mm 175mm
C3 - Load-carrying capacity of the connection C31 - Forces in the connection for the design combination
1.35G + 1.5S
Total VEd Bolts Shear planes Force per bolt and per plane Fv,Ed angle α
5025.0daN 4 2 628.1daN 45.0°
C32 - Characteristic load-carrying capacity for a fastener
Characteristic embedment strength Ratio between the embedment strength β Characteristic yield moment My,Rk
External elements fh,1,k Internal element fh,2,k
18.616MPa (α=45.0°) 24.108MPa (α=0°) 1.295 162141.1mm.N
Standard Failure modes Load-carrying capacity Contribution from the rope effect Fv,Rk
25% of the Johansen part Fax,Rk / 4
EN 1995-1-1 §8.2.2 Timber crush in external elements (g) = 1489.3daN - - 1489.3daN
Timber crush in internal element (h) = 1446.5daN - - 1446.5daN
Timber crush in external elements and plastic hinge in the fastener (j) = 860.5daN 215.1daN 320.4daN 1075.6daN
Timber crush in all of the elements and plastic hinge in the fastener (k) = 1200.7daN 300.2daN 320.4daN 1500.8daN
C33 - Effective number of fasteners
Element 1
Rows from top to bottom n a1,1 angle α
1 2 111.7 mm 1.598 2 45.0° 1.765
2 2 111.7 mm 1.598 2 1.765
Element 2
Rows from top to bottom n a1,2 angle α
1 2 162.6 mm 1.755 2 0° 1.755
2 2 162.6 mm 1.755 2 1.755
C34 - Checking the load-carrying capacity
Standard Fv,Rk n nef Fv,ef,Rd Ratio
EN 1995-1-1 §8.5.1.1 1075.6daN 4 3.509 = 653.3daN 0.961

C4 - Block shear failure

1.35G + 1.5S
Standard Elements Force component parallel to grain Fbs,Ed Ratio
EN 1995-1-1 Annex A
Internal one 10463.7daN 7244.1daN 5025.0daN 0.694

C5 - Net cross section tensile failure

1.35G + 1.5S
Standard Elements Tensile force NEd Ratio
EN 1995-1-1 §6.1.2
Internal one 15333.8daN 10615.7daN 5025.0daN 0.473

C6 - Splitting failure

1.35G + 1.5S
Standard Elements he Shear force Vz,Ed Ratio
EN 1995-1-1 §8.1.4 External ones 170.0mm 3692.0daN 2556.0daN 2100.0daN 0.822
C7 - Conclusion
Maximum work rate: 96.1%, the joint is correct.