Notched Beams
Image: Robert Butler
Robert Widmann
EMPA, Swiss Federal Laboratories for Materials Science and Technology
With strong contributions from:
Robert Jockwer
ETHZ, Swiss Federal Institute of Technology, Zurich
EMPA, Swiss Federal Laboratories for Materials Science and Technology
COST FP1101 Training School – University of Mons B – December 2013
Outline

Introduction

Principals
 Types of notches

Design of notches

Shear design
 Reinforcement perpendicular to grain
 SIA 265 and EN 1995-1-1:2004 (German Version)

Example

Research


Inclined reinforcements
Conclusions
COST FP1101 Training School – University of Mons B – December 2013
2
Introduction

Notches at the support of beams

Reduced depth of the beams at the support

Connection of members
Jockwer 2012
COST FP1101 Training School – University of Mons B – December 2013
3
Introduction - Principals

Notches at the support of beams

Reduced depth of the beams
 Connection of members

High stresses perpendicular to the grain

Stress concentrations at notch edge

Notches should be avoided or strengthened !
Vd
Tension perpendicular to the grain:
high
low
Scholten, American Lumberman, 1935
COST FP1101 Training School – University of Mons B – December 2013
4
Introduction - Types of Notches
Rectangular
Rounded / Tapered
Drawings from:
www.harzerstatik.de
COST FP1101 Training School – University of Mons B – December 2013
5
Introduction - Types of Reinforcements
Bonded Straps
Fully threaded screws
Glued-in profiled rods
Drawings from:
www.harzerstatik.de
COST FP1101 Training School – University of Mons B – December 2013
6
Outline

Introduction

Principals
 Types of notches

Design of notches

Shear design
 Reinforcement perpendicular to grain
 SIA 265 and EN 1995-1-1:2004 (German Version)

Example

Research


Inclined reinforcements
Conclusions
COST FP1101 Training School – University of Mons B – December 2013
7
Design of Notches (SIA 265:2012)
VEd h

Calculation of shear stresses
 d  1.5
VEd
 kred fv ,d
b hef
hef
i1
Δ hef
c
b
A)
A)
A)
B)

Reduction of shear strength
B)

General conditions: (c ≤ 0.4 h und hef ≥ 0.5 h )

Δh0

For rounded / inclined notches with inclinations ≤ 1:10 the influence of
stress concentrations can be neglected (kred = 1,0).
25mm for solid timber from softwood
45mm for glulam from softwood
COST FP1101 Training School – University of Mons B – December 2013
8
Design of Notches (SIA 265:2012)

1.2
Calculation of shear stresses
VEd
 kred fv ,d
1 b hef

Reduction factor kred
Abminderungsfaktor
kred [-]
 d  1.5
0.8
VEd h
SIA 265:2012
hef
EN 1995-1-1:2004
Δ hef
DIN 1052:1988
b
Scholten
i1
c
A)
0.6
A)
A)
0.4
B)
Reduction
of shear strength
0.2

General conditions: (c ≤ 0.4 h und hef ≥ 0.5 h )

Δh0
0
B)
25mm for solid timber from softwood
45mm for glulam from softwood
1
0.9
0.8
0.7
0.6
0.5
Notchwith
ratioinclinations
hef / h hef≤ /1:10
h [-]
 For rounded / Ausklinkungsverhältnis
inclined notches
the influence of
stress concentrations can be neglected (kred = 1,0).
COST FP1101 Training School – University of Mons B – December 2013
9
Flowchart for notch design - DIN EN 1995-1-1:2010
Notched bending member
Notch in tension zone
Notch in compression zone
Inclination i < 10
Inclination i ≥ 10
Notch same side as support
Notch opposite side to support
x ≥ hef
x < hef
for LVL
for solid timber
for glulam
COST FP101 Training School – University of Mons B – December 2013
10
Notch design - DIN EN 1995-1-1:2010
Shear capacity
as function of inclination i, a= 0.8, h = 600mm, x = 100mm
Glulam
Solid
Shear capacity
as function of notch ratio a, i = 0, h = 600mm, x = 100mm
LVL
80
60
40
20
0
Glulam
100
Shear Capacity [%]
Shear Capacity [%]
100
[%]kv
Capacity
Shear
Factor
Reduction
for LVL
for structural timber
for glulam
kv as function of notch ratio
Shear
a, capacity
i = 0, h = 600mm, x = 100mm
as function of distance x, i = 0, a= 0.8, h = 600mm
Glulam
Solid
LVL
1
Glulam
Solid
LVL
100
0.8
80
0.6
60
0.4
40
0.2
20
0
0 0.4
0.5
0.6
0.7
0.8
0.9
1
0
50
100
150
200
250
300
notch ratio a = hef/h
Distance x
Solid
LVL
80
60
40
20
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Inclination i
COST FP101 Training School – University of Mons B – December 2013
0.4
0.5
0.6
0.7
0.8
0.9
1
Notch ratio a = hef/h
11
Flowchart for notch design - DIN EN 1995-1-1:2010
kv as function of notch ratio a, i = 0, h = 600mm, x = 100mm
Reduction Factor kv
2.5
2
1.5
1
0.5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Notch ratio a = hef/h
Shear capacity
as function of notch ratio a, i = 0, h = 600mm, x = 100mm
Shear Capacity [%]
100
80
60
40
20
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Notch ratio a = hef/h
COST FP101 Training School – University of Mons B – December 2013
12
Variation of strength values

F
Nordtest method to determine mode 1 fracture
energy on 3-point bending SENB-specimens
 Parameters that influence fracture energy Gf,I
hc



Force [N]

Knots
Angle of grain
Annual ring structure
Cracks
180
160
140
120
100
80
60
40
20
0
G f ,I 
W
1
W  mgu0
hc b
u0
2
3
4
5
Displacement [mm]
6
7
Nordtest Method, NT Build 422, Wood: Fracture energy in tension perpendicular to the grain, 1993
COST FP101 Training School – University of Mons B – December 2013
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Variation of strength values
High variation of fracture energy Gf,I
0.12
Probability Density [-]
0.1
Test results
Lognormal
Probability Density [-]

0.08
0.06
0.04
0.02
0
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Test results
Normal
Lognormal
2p-Weibull
0
Fracture energy Gf,I [N/m]
4 8 12 16 20 24 28 32 36 40 44 48
Notch Strength A' [Nmm-3/2]
Consequence: high variation in notch strength
Gustafsson, P.J., A study of strength of notched beams, 1988
Larsen, H.J. and P.J. Gustafsson, The fracture energy of wood in tension perpendicular to the grain, 1990
Riberholt, H., et al., Timber beams notched at the support, 1991
COST FP101 Training School – University of Mons B – December 2013
14
Reinforcement of Notches

Unreinforced Notches:

Low strength
 Big variations of strength values
Notches have to be reinforced!

Types of reinforcements

Embedded reinforcements


Glued-in rods
 Fully threaded screws
COST FP101 Training School – University of Mons B – December 2013
External reinforcements



Bonded wood based panels
GFRP and / or CFRP
Nail Plates
15
Design of Notches
F
Ft,90,d
F
Ft,90,d / VEd [-]
1.2
1
0.8
0.6
0.4
0.2
0
1
αh
Ft,90,d
Δhef
τ
h VEd
0.9

0.8
0.7
0.6
Notch ratio a = hef/h [-]
0.5
0.4

Ft ,90,d  1.3 31  a   21  a  VEd
2
3
VEd
COST FP101 Training School – University of Mons B – December 2013
16
Introduction - Types of Reinforcements
Bonded Straps
Fully threaded screws
Glued-in profiled rods
Drawings from:
www.harzerstatik.de
COST FP1101 Training School – University of Mons B – December 2013
17
Design of reinforced notch
1 Fully threaded screws
Glued-in rods with dr
2
Bonded wood based panels
Bond line
Bond line for glued-in rods
Wood based panel
COST FP101 Training School – University of Mons B – December 2013
18
Outline

Introduction

Principals
 Types of notches

Design of notches

Shear design
 Reinforcement perpendicular to grain
 SIA 265 and EN 1995-1-1:2004 (German Version)

Example

Research


Inclined reinforcements
Conclusions
COST FP1101 Training School – University of Mons B – December 2013
19
Example for design of reinforced notch
Vd = 78kN, fv,g,k = 3.5MPa, kmod = 0.9, gM = 1.3
 h = 600mm, hef = 450mm, b = 140mm, c = x = 100mm

VEd h
hef
i1
Δ hef
c
b
COST FP101 Training School – University of Mons B – December 2013
20
Example for design of reinforced notch
Vd = 78kN, fv,g,k = 3.5MPa, r,k = 385kg/m3, kmod = 0.9, gM = 1.3
 h = 600mm, hef = 450mm, b = 140mm, c = x = 100mm
GL24h

VEd h
hef
i1
Δ hef
c
b
Reinforcement with fully threaded screws
Pull-out
strength
R1,k [kN]
Pull-out
strength
R1,k [kN]
COST FP101 Training School – University of Mons B – December 2013
21
Example for design of screw reinforced notch
COST FP101 Training School – University of Mons B – December 2013
22
Example for design of reinforced notch
Vd = 78kN, fv,g,k = 3.5MPa, r,k = 385kg/m3, kmod = 0.9, gM = 1.3
 h = 600mm, hef = 450mm, b = 140mm, c = x = 100mm
GL24h

hef
i1
Δ hef
c
Reinforcement with wood based panel
𝜏𝑒𝑓 ,𝑑 ≤ 0.52 MPa = 0.75 MPa ∙
𝑙𝑟 ≥
𝐹𝑡,90,𝑑
2 ∙ h-∙ℎ𝑒𝑓 ∙ 0.52
𝑙𝑟 ≥
VEd h
b
0.9
𝑘𝑚𝑜𝑑
= 𝑓𝑘2,𝑘 ∙
1.3
𝛾𝑀
15.8 ∙ 103
= 101𝑚𝑚
2 ∙ 600-∙450 ∙ 0.52
38mm ≤ 𝑙𝑟 ≤ 75mm
38mm ≤ 101mm ≤ 75mm
Requirement not fulfilled, notch can’t be strengthened with wood based panels
COST FP101 Training School – University of Mons B – December 2013
23
Outline

Introduction

Principals
 Types of notches

Design of notches

Shear design
 Reinforcement perpendicular to grain
 SIA 265 and EN 1995-1-1:2004 (German Version)

Example

Research


Inclined reinforcements
Conclusions
COST FP1101 Training School – University of Mons B – December 2013
24
Reinforcement of Notches

Shear deformations of reinforcement
F
Jockwer, R. 2012
COST FP101 Training School – University of Mons B – December 2013
25
Reinforcement of Notches
Image correlation measurements
ARAMIS

V
Unreinforced notch

Strain perpendicular to grain
y

Shear strain
y
x
x
Jockwer, R. 2012
COST FP101 Training School – University of Mons B – December 2013
26
Reinforcement of Notches
Image correlation measurements
ARAMIS

V
Reinforced notch: Fully threaded screw 90°

Strain perpendicular to grain
y

Shear strain
y
x
x
Jockwer, R. 2012
COST FP101 Training School – University of Mons B – December 2013
27
Reinforcement of Notches
Image correlation measurements
ARAMIS

V
Reinforced notch: Fully threaded screw 45°

Strain perpendicular to grain
y

Shear strain
y
x
x
Jockwer, R. 2012
COST FP101 Training School – University of Mons B – December 2013
28
Tests on reinforced notches



Aim: Determination of influence of inclined reinforcement
Glulam Gl28h, 10 beams b/h 90/315 mm
Reinforcement:
 Fully threaded screws: SFS WRT-13
 CFRP sheets:
SikaWrap
d= 13mm
t= 1mm
l= 400mm
b= 50mm
45° and 90°
45° and 90°
Shear Stress at failure
Residual Cross Section [N/mm2]
3.5
3
2.5
2
1.5
1
0.5
0
unverstärkt Schraube
90°Schraube
45° CFRP
CFR 90°
Unreinforced
Screw 90°
Screw 45°
90°
CFR 45°45°
CFRP
Jockwer, R. 2012
COST FP101 Training School – University of Mons B – December 2013
29
Outline

Introduction

Principals
 Types of notches

Design of notches

Shear design
 Reinforcement perpendicular to grain
 SIA 265 and EN 1995-1-1:2004 (German Version)

Example

Research


Inclined reinforcements
Conclusions
COST FP1101 Training School – University of Mons B – December 2013
30
Conclusions








Notched members to decrease depth at supports
Shear capacity significantly decreases
Tension stresses perpendicular to grain are present
From mechanical point of view notches should be avoided
Rounded / inclined notches have a better performance
Notches need to be strengthened / reinforced
Most used techniques: bonded wood based panels, fully threaded
screws, nail plates and glued-in rods
Research shows that strengthening should also be applied for shear
Thank you for your attention !
COST FP1101 Training School – University of Mons B – December 2013
31