Carpentry Joints - Thierry Descamps

Carpentry connections
Training school on assessment and reinforcement of timber elements
Thierry DESCAMPS
University of Mons - Belgium
Faculty of engineering - Department of Structural Mechanics
Université de Mons
1
What is it ?
What about strength ?
Design and reinforcement
What about stiffness?
Structural assessment of old timber structures
Université de Mons
Timber frameworks…
Widespread
Natural material (timber):
Variability
Decay and MC
Structural complexity:
Complex geometry and joints (more complex than
masonries ?)
⇒ A simplified analysis considering only plane parts of
the system, is often hard to realize or completely
impossible.
Geometry and joints are characteristic of
An area and a period of time
Carpenters and engineers knowledge: daring
engineering !
Mind blowing timbre structures are not always
new !
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Carpentry joints…
Carpentry joints connect timber elements, often without any dowel type fasteners.
Forces are transferred within the joints via contact pressure and friction. The “smart”
cutting of the joint by the carpenter create notches and contact surfaces between the
connected members.
Within the connections, there is an interaction in terms of stiffness and strength between
the different pathways in which the forces are transferred.
Eccentricities are inherent in this kind of connections ⇒ to be considered.
Carpentry connections can be classified in « families » but there is a huge amount of
carpentry joints… probably as much as major timber buildings and carpenters.
Let’s have a look at some carpentry joints (non exhaustive)…
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Pinned Tenon and
mortise (wooden pegs)
Pin number and placement varied
with the size of the member
and the preferences of carpenter
Drawings: Sobon J. A
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If one piece (here the post) is wider than the the
other, the tenon can be housed into it.
The tenon can be centered or be flush with the
layout face of the post.
Through tenon with outside wedges
(flatwise bending of the tenon)
Drawings: Sobon J. A
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From tenon and mortise joints to dovetails joints
Wedged Dovetail Through Mortise and Tenon
Partially housed wedged dovetail
through mortise and tenon
Drawings: Sobon J. A
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Through Mortise and Tenon with Dovetailed Shoulder
Drawings: Sobon J. A
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Inverted lapped dovetail
Lapped half-dovetail girder joint
Drawings: Sobon J. A
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Notched beams (the simplest joint to craft and insert, and
consequently the most common)
Drawings: Sobon J. A
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Halved scarf with four pins (simplest to fashion).
Halved and undersquinted scarf
(to improve bending strength and resistance
to seasoning twist)
Drawings: Sobon J. A
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Halved and bladed scarf
with pinned tenons
Halved, bladed and cogged scarf
(helps align the scarf and increases its bending
strength against horizontal loads)
Drawings: Sobon J. A
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Splayed scarf joint (the lapped surfaces are sloping).
• The sloped, lapped portion is
stopped before it feathers out to
nothing.
• Compared with the half-lap,
shear strength is vastly improved
by the sloped surface.
Drawings: Sobon J. A
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Splayed, undersquinted and cogged scarf joint
Drawings: Sobon J. A
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Splayed, Undersquinted and Wedges
P. Lemlyn
• Wedges act as a reinforcement.
• The tensile capacity, torsion, and
bending strength in both directions are
greatly increased (cog).
• The pins (and their position) increase the
joint’s overall performance.
• The butts need not be undersquinted.
Drawings: Sobon J. A
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The conscientious builder locates the scarf where bending forces are low...
Splayed with Wedges and Multiple lapped surfaces
Drawings: Sobon J. A
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What is it ?
What about strength ?
Design and reinforcement
What about stiffness?
Structural assessment of old timber structures
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Step joints (rafter and tie-beam
joints or purlin plate)
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Step joints
the slope of the notch must minimize the angle between the stresses and the grain direction
for both connected elements (bisector)
the depth of the notch (tv) should not exceed h/4 for skew angles α ≤ 50º and h/6 for skew
angles α > 60º (Götz et al (1993), DIN 1052:2004 and CTE (2006)).
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Precompression of horizontal beam due to N !
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Support reaction
N tie beam
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The rear face under compression (F2) is generally neglected !
However, Parisi and Piazza (2000) suggest to consider a reduced length d
(possible concentration of high stresses in a limited length)
∙
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,
1
≡
5
1
3
Single posterior step
3 points to check
Crack ?
Gap
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Reinforcement of step joints
(a) binding strip; (b) internal bolt; (c) stirrup; (d) tension ties - Branco (2011).
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15
c
d
10
-
d
+
= 1.4 MPa
F F
+
-
Force (kN)
5
Unstrengthened +
0
Unstrengthened Binding strip +
-5
Binding strip Stirrup +
-10
Stirrup Bolt +
-15
Bolt Tension ties +
-20
Tension ties -
-25
-50
-40
-30
-20
-10
0
10
20
30
40
50
Displacement (mm)
Force-displacement curves for unstrengthened and strengthened connections
with a 30º skew angle under monotonic loading. Branco et al (2011)
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10
8
6
Force (kN)
4
c
d
-
d
+
= 1.4 MPa
F F
+
-
2
Unstrengthend +
0
Unstrengthend Tension ties +
-2
Tension ties -
-4
Stirrup +
Stirrup -
-6
Bolt +
-8
Bolt -
-10
-50
-40
-30
-20
-10
0
10
20
30
40
50
Displacement (mm)
Force-displacement curves for unstrengthened and strengthened connections
with a 60º skew angle under monotonic loading. Branco et al (2011)
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Dovetail joints
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Rounded Dovetail joint
Development thanks to CNC wood-processing machinery
Esthetic
Easy to use on site (plug and play joint)
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From experimental researches, Werner proposed a design guideline (Werner, 2002).
⇒ Since rounded dovetail joints can fail either by breaking of the joist or main beam, the
two members are designed separately:
,
,
!*+,
!"#
2
. '( .
3
0,09. /
),
!*
/( 0
(
2
(Vallée et al, 2010).
Where A1 is the effective dovetail area.
hmain, h1 and b1 are in mm and F is in kN, and:
'(
4
0
tan
. /(
(
2
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(
2
. /(
(
2
0 5.
(²
8
Tannert proposed later on a design guideline that takes into account the size effect
for timber strength in brittle failure (Tannert, 2008).
As rounded dovetails joints are very similar to end notched beam supports, he
proposed a modified design formula based on Eurocode 5 formula for notched
beams with the definition of a specific reduction factor kv (EN 1995:2005).
1,5. 8
'(
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),
3,6::²
.
'(
,
Reinforcement of rounded dovetails
The failure is typically brittle, and occurs in the elastic range ⇒ reinforcements needed:
tuning the geometry (to reduce stress concentrations)
using additional reinforcements
Reinforcement with self-tapping screws at an angle of 45° (left);
reinforcement with an adhesive layer between joist and beam (middle);
combination of self-tapping screws and adhesive layer (right). (Tannert 2012).
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Reinforcement with self tapping screws is very efficient (increase stiffness, capacity of
connections perpendicular to the grain and produce a more ductile failure mode)
In that case, when the performance is governed by the joist member, capacity can be
estimated similar to the capacity of end notched beam supports (see Blass et al 2001).
Consequently, screw withdrawal capacity Rax,k and tensile strength Ru,k dictate the
capacity Vk of a beam support according to (DIN-1052 2004):
8;
. min >
1,3. 3. 1
?,; , >@,;
/, // ²
2. 1
/,
³ /
Where h is the beam height, he is the beam height minus the notch height
and n is the number of screws.
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Tenon and
mortise joints
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Tenon and mortise joint
The bearing capacity of tapered tenon joints is a function of the angle
of the connection, and length of the toe and mortise depth (Aman et
al, 2008, Judd et al, 2012, Litos et al, 2012).
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If F is the normal force in the strut
• the compressive force at the bottom surface is
8
sin D
∙
1
EF ∙ cos D
EF ∙ EI
cos D 0 EF ∙
D ∙:∙
1 EF ∙ EI
• the compressive force at the front side is:
J
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∙ KL D 0
∙:∙
D
EI ∙ 8
m is the ratio of Q to F
Additionally, μH is the coefficient of friction at the front side, μV the coefficient of
friction at the bottom face, γ the connection angle, hs the height of the strut, ls the
length of the strut and tx the distance between the bottom surface and the loading
point of H.
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What is it ?
What about strength ?
Design and reinforcement
What about stiffness?
Structural assessment of old timber structures
Université de Mons
Old timber frameworks…
Widespread
Natural material (timber):
Variability (in the same frame)
Decay
Structural complexity:
Complexity of the global geometry and the connections.
(more complex than masonries ?)
Lack of technical data's :
Sections (+ variations)
Strength classes (visual on site strength grading)
Joints (contact areas, nodes, cracks…)
⇒ Structural assessment and morpho-chronology:
A good understanding of the history of the structure is
necessary .
+ dendochronology
Drawings P. Lemlyn
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Component method
Prediction of the stiffness of the joint. For M, N and V :
Definition of a model statically equivalent.
Each component is an area where contact appears .
A stiffness is associated to each component.
Equivalent spring model !
Three areas of contact appear when the
connection is bend (M+) !
The component 11’ is the pair of surfaces 1 and 1’,
respectively belonging to timber elements A and B.
ICR = peg
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This component is composed of two stiffnesses as 1
correspond to a compression parallel to grain for the
element A and 1’ is perpendicular to the grain?
It is now possible to compute the global stiffness:
Stiffness of two surfaces in contact. If k refers to the component i,j :
Fj
F F
δ k = δ j + δi =
+ i = k
k j ki k k
kk =
1
1
∑
i , j ki
Springs acting in series for any component (pair of
surfaces in contact)!
How to get this stiffness ?
It is not directly E !
The stiffness is obtained by means of the theoretical
deformation of an elastic half.
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Total rotational stiffness :
Under the assumption of small rotations :
ktot =
M
θ
=
∑F z
k
k
θ
k
=
∑k δ
k
k
θ
k
zk
=
∑k (z θ ) z
k
k
k
θ
k
= ∑ kk zk2
k
The global rotational stiffness can easily be estimated
from the geometry and the stiffness of all pairs of
surfaces in contact….
Limitations of the method (strictly analytical) :
The deformation of contact surface can not be estimated
as it is an infinite half space of wood !
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First enhancement of the method: Assumption of an infinite half space ?
First method: FEM
A cut factor Cm,E is defined with the help of elastic finite
element models (FEM) using an orthotropic material,
contact and different slenderness of contact areas
Second method: additional length effect
Komatsu (2009) proposed a pure analytical
correction in his study on traditional Japanese
mud shear wall.
“Nuki” joint ⇒ “Nuki effect”
⇒ modified analytical model
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Equilibrium of forces and a additional length effect – Komatsu 2009
Moreover, Komatsu proposed a post yielding behaviour which allows the definition of a poly-linear
M−θ relationship.
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Comparison of initial stiffness obtained from analytical and experimental results
(Chang 2007)
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The comparison between this first enhanced
model and experimentations is disappointing :
M+
Stiffness
[N.m/mr
ad]
M-
FEM
Component
method
Experime
ntation
FEM
Component
method
Experimen
tation
13.95
66.38
12.08
4.32
18.66
5.43
FEM and experimentation on real size
connections give good results.
Component method largely overestimate the
stiffness
Once again, observations made on real size tests
(broken peg) suggest that the peg is not the center of
rotation of the connection
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Second enhancement of the method:
A geometrical research field is defined and an iterative process is implemented. Let’s call u, v and θ the
displacements and rotation of any point into this field.
For each supposed position of ICR, displacements of contact area are computed.
From their stiffness it is possible to computed the contact forces :
Fi =
y2
∫
y1
ki
× δ i × dl = f ( u , v, θ )
li
Resulting forces at the tenon is :
 V   k11
  
 N  =  k21
M  k
   31
k12
k22
k32
k13   u 
  
k23  ×  v 
k33   θ 
We finally solve this system and the ICR is then supposed to be the point for which the computed
displacement is minimum.
u ² + v²
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Why this focus on stiffness ?
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1. Influence on the design of the joint
Equivalent model
The joint is statically indeterminate !
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2. Influence on the design of the whole structure
Most of the time, connections are supposed to be
moment free (hinges). This assumption :
Simplifies the computations
Is safe as it overestimate the bending moments and the
deflections
What is true only if we also assume that all connections have a sufficient
capacity of deformation in rotation (without any major cracks)
Most of the carpentry connections are not hinges !
Do we have to take care of that ?
Statically indeterminate structure:
the elements will carry loads in
proportion to their relative stiffness
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⇒ reduction of 50 % !
7,6 m
7,96 m
fortified castle of Ecaussinnes-Lalaing
5,6 m
All are statically indeterminate
frames: 7x
13,33 m
Cathedral O-L of Tournai
6,35 m
8,9 m
Abbatiale de la Paix-Dieu
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Château d’Ecaussinnes-Lalaing
Borne inférieure
Borne supérieure
Hinge
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Carpent.
Dowels
Stiff.
Bending
stiffness
Variations de contraintes en fonction de la rigidité de l’assemblage
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K. CANT et F. MIGNONE |
Service de génie civil et mécanique des structures
59
Abbatiale de la Paix-Dieu
Hinge
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Carpent.
Dowels
Stiff.
Bending
stiffness
Cathedrale O-L of Tournai
Hinge
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Carpent.
Dowels
Stiff.
Bending
stiffness
In restoration; keeping the same stiffness should be a
goal too…
Is it always necessary ?
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Thank you for your
attention
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