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DESIGN OF REINFORCEMENT AROUND HOLES IN
LAMINATED VENEER LUMBER (LVL) BEAMS
Manoochehr Ardalany1, Massimo Fragiacomo2, Bruce Deam3, Andrew Buchanan4
ABSTRACT: Many practical situations require holes in timber beams. When the hole is large
relative to the depth, the failure of the beam is governed by crack initiation and propagation around
the hole. Cracking of a timber beam decreases the capacity of the beam considerably. This paper
presents a method for designing the reinforcement around holes in Laminate Veneer Lumber (LVL)
beams so as to recover their full flexural capacity. The design procedure is complemented by a
worked example where all verifications are discussed with great detail.
KEYWORDS: LVL, Screw, Plywood, hole, reinforcement, tensile stresses
1 INTRODUCTION123
Many practical situations like building services,
architectural considerations, etc. require the introduction
of holes in timber beams. Cutting hole into the timber
beam causes concentration of tensile and compressive
stresses around the hole. The inherent low tensile
strength of wood material perpendicular to grain makes
the beam susceptible to crack initiation and propagation
at rather low load levels [1]. Figure 1 presents a photo of
a Laminated Veneer Lumber (LVL) beam with a hole
that has cracked at the perimeter.
Around the hole, the tensile stresses will most likely
exceed the material low tensile strength perpendicular to
grain, in this way causing crack initiation. Subsequently,
the crack propagation due to the coupled shear and
moment in the beam section reduces significantly the
1 Manoochehr Ardalany, Department of Civil and Natural
Resources Engineering, University of Canterbury,
Christchurch, New Zealand.
Email: Manoochehr.ardalany@pg.canterbury.ac.nz
2Massimo Fragiacomo, Department of Architecture, Design
and Urban Planning, University of Sassari, Italy.
Email: fragiacomo@uniss.it
3Bruce Deam, , Department of Civil and Natural resources
Engineering, University of Canterbury, New Zealand.
Email: Bruce.deam@canterbury.ac.nz
4Andy Buchanan, Department of Civil and Natural resources
Engineering, University of Canterbury, New Zealand.
Email: Andy.buchanan@canterbury.ac.nz
strength and stiffness of the beam. Reinforcement around
the hole is an effective option for improving the
behaviour of the timber beam. Different options for
reinforcement could be regarded. A good reinforcement
should recover the load carrying capacity of the beam
completely.
Plywood and screws are two alternatives shown to be
appropriate to control crack propagation. The choice of
the reinforcement type is much dependent on the stresses
in the section, architectural requirements, ease of the
installation, and other factors.
The mechanisms developed by plywood and screws to
control the stresses around the holes are different.
Screws develop stress concentration around the threaded
part, whereas plywood uniformly controls the stresses
around the hole due to its large contact area with LVL.
For thick members where plywood is not so effective,
screws can provide a better means to reduce the stress
concentration around the hole.
Figure 1. Crack propagation around the hole
1.1 Screw reinforcing
Self tapping screws are drilled into the beam to block the
path of the crack propagation, in this way increasing the
load-carrying capacity of the beam (Figure 2). Although
the screws can handle the tensile stresses and control
those stresses very well, it may not possibly stop
propagation of the shear stresses in the section of the
beam effectively. The shear stresses in the section of the
beam will hence increase significantly.
Figure 2 . Reinforcing with screws
The design of the screws is somehow challenging
because the screws should meet a number of design
criteria. The main criteria for the design of the screws
are that the screws should carry tensile forces in the
section without yielding, and without exceeding the
withdrawal capacity. Besides, the screw has to be
inserted at a distance from the opening to prevent wood
splitting. Finally, stress concentration close to the screw
should not cause the edge failure of the beam. A photo of
the edge failure in a LVL beam is presented in Figure 3.
Figure 3. Edge failure in LVL beam reinforced with
screw
1.2 Plywood reinforcing
Another reinforcement option is the use of plywood
sheet glued to the outer edges of the beam. The plywood
and the beam form a unique entity, in this way
decreasing the tensile stresses in the wood. Although
plywood works very well for thin members, it is not of
much use in thick beams as plywood cannot reduce the
stresses at a far distance from its surface. Figure 4 shows
an example of reinforcement using plywood in LVL
beam.
Figure 4 . Reinforcing with plywood
Design of the plywood also needs to be addressed
carefully. Plywood should be designed for the tensile
forces produced in the section of the beam. The plywood
dimensions should be large enough to cover the stressed
area.
1.3 Finite element modelling
There are few finite element models that can handle well
the crack initiation and propagation, particularly for
wood structures. One of the possibilities is the use of the
cohesive elements. The idea of the cohesive element in
crack propagation is to diminish gradually the stiffness
of the elements that have reached the maximum tensile
strength of the material. In this way, numerical problems
are reduced, and crack propagation can be effectively
modelled. Figure 5 shows an example of stress
distribution perpendicular to the grain in a beam at crack
surface, which is located at the level of the most likely
crack plane, namely at the point along the perimeter of
the hole where the maximum tensile stress perpendicular
to the grain is attained in an elastic analysis.
Figure 5. U
modelling
In this paper
screws and
examples are
hole are ca
derived for
ensures that t
section is ob
reinforcemen
2 BEAM
REINF
Design of LV
comprehensi
experimental
mm, 300 mm
depth ratio s
not cause a
However, wi
recommenda
proposed for
than 10. Bas
diameter hol
ratios smalle
load-carrying
3 TENSI
Figure 6(a) a
with a hole w
Use of the
r, the design o
plywood, is
e presented.
alculated usin
LVL beams.
the load-carry
btained by u
nt calculated.
M WITH HO
FORCEME
VL beams wi
ive experim
l programme
m and 400 m
smaller than 1
any reductio
ith the aim to
ation, the lim
r beams with
sed on APA r
le may be use
er than 10 w
g capacity to a
ILE LOAD
and Figure 6(b
with notations
cohesive ele
of both reinfor
s discussed a
The tensile f
ng an analyt
The propose
ying capacity o
sing the min
OLES AND
ENT
th holes was
mental pro
indicated th
mm deep wit
10, a 50 mm h
n in load-ca
o provide a co
mitation to 50
length to dep
ecommendati
ed for beam o
without the ne
allow for the h
D
b) shows a dr
of geometrica
ements for c
rcement meth
and two wor
forces due to
tical formula
ed design met
of the entire b
imum amoun
D NO-
studied throu
ogramme.
hat for beam
th span lengt
hole diameter
arrying capa
onservative de
mm diamete
pth ratios of m
ons [2], a 25
of length to d
eed to reduce
hole.
rawing of a b
al parameters.
crack
hods,
rked
o the
ation
thod
beam
nt of
gh a
The
200
th to
r did
acity.
esign
er is
more
mm
depth
e the
beam
.
Fig
rect
The
mom
the
mom
sect
thro
Equ
with
F୲,ୢ
In E
she
diam
the
con
and
For
term
bec
the
tens
of a
Fin
form
Equ
rect
gure 6. Draw
tangular holes
e tensile load
ment in each
so-called Tru
ment and she
tion of the b
ough truss act
uation (1) for
h circular hole
ൌ √2Vhୢሺ3h
8 h
Equation (1)
ar force in th
meter as show
section of
ntributions: (i)
d (ii) the secon
r the square h
m of the mo
cause the prop
tensile load
sile load due
a beam for a sq
F୲,ୢ ൌ √2V
ally, rectangu
mulations we
uation (3) pro
tangular hole
F୲,ୢ ൌሺ β
4hଷሻV
wing of a
s
d due to the
section of a b
uss model. Th
ear that could
beam due to
tion around th
tensile load p
es:
hଶ െhୢଶ ሻ
hଷ 3
4
F୲,ୢ is the de
he section of
wn in Figure 6
the beam.
) the first con
nd contribution
holes the form
oment (secon
posed formul
considerably.
to the shear a
quare hole.
hୢ ሺ3hଶ െhୢଶ
8hଷ
ular holes we
re derived fo
ovides the ten
in a section of
V hୢ ሺ3hଶ െ h
beam with
shear force
beam was cal
his model assu
d not be trans
o the hole ar
he hole. The m
predictions of
4
M hୢଷ ሺhୢ
hଷ ሺh .hୢ h
esign tensile l
f a beam, dh
6, and M is th
Equation (
ntribution due
n due to the m
mulation was r
nd term in E
lation was ov
Equation (2)
and moment i
ሻ 0.7Mhୢଶ
hଷ
ere investigate
or tensile load
nsile load pro
f beam.
hୢଶ ሻ 0.7M
hୢଶ
hଷ
circular and
and bending
lculated using
umes that the
sferred in the
re transferred
model yielded
f LVL beams
hሻ
hଶ hୢଶሻ (1
oad, V is the
d is the hole
he moment in
(1) has two
to the shear;
moment.
revised in the
Equation (1))
ver-estimating
) presents the
in the section
(2)
ed, and some
d predictions.
oduced due a
ୢଶ
ଷ
(3)
d
g
g
e
e
d
d
s
1)
e
e
n
o
;
e
)
g
e
n
e
.
a
where β sig
βൌMa
It should be
derived from
(3), and (4) w
LVL beams w
The aforeme
up to 400 mm
on beams wi
tensile load
tensile load
400 mm. A
account size
applied to
equation (1)
depth.
Also, for sm
depth (10%
showed that
increases c
showed that
applied to inc
4 LIMIT
Experimenta
yielded the
with the Swe
reinforced w
In the case o
the limit in
plywood incr
in the section
Limitation fr
rectangular
reinforcemen
Limitation fr
plywood rein
Finally, for
suggested by
[4].
gnifies a param
ax ሺ b୦
ඥhୢଶ b୦ଶ
e pointed ou
m the Truss m
were obtained
with holes.
entioned form
m depth. A se
ith circular ho
through Equ
in the reinfor
correction f
e effect. A m
the final ten
is proposed t
mall eccentrici
of beam de
t the tensile
considerably.
a magnifying
crease the fina
TATION O
al tests on rein
following lim
edish glulam h
with fully threa
.0hd≤
of plywood re
n Equation (
reases the she
n:
.0hd≤
rom Equation
holes due
nt as below:
.0hd≤
rom Equation
nforcement:
0hd≤
rectangular h
y the Swedish
meter defined a
and hୢ
ඥhୢଶ b
ut that only e
model, where
through num
mulations were
eries of finite
oles showed t
uation (1) un
rcement for d
factor is requ
modification fa
nsile load p
to take into a
ity of the hole
epth), the nu
e load in th
Again num
g factor of (
al tensile load
OF HOLE S
nforced LVL
mitations, in
handbook [3],
aded screw:
h4.
einforcement f
(5) can be
ear capacity of
h45
(5) was decr
to the cor
h35
(7) can be rel
h4.
holes, the dim
glulam handb
as below:
b୦ଶሻ (
equation (1)
as Equations
merical analyse
e used for be
element anal
that the predi
nderestimates
depth greater
uired to take
factor of ඥh/
predicted thro
account the la
e along the b
umerical anal
he reinforcem
merical anal
/h)h1 d+can
d in the screw.
SIZES
beams with h
good agreem
for circular h
(
for circular ho
released bec
f the beam loc
(
reased slightly
rners for sc
(
leased when u
(
mension limita
book was ado
(4)
was
(2),
es on
eams
lyses
icted
the
than
into
/400
ough
arger
beam
lyses
ment
lyses
n be
holes
ment
holes
(5)
oles,
ause
cally
(6)
y for
crew
(7)
using
(8)
ation
opted
5
5.1
Des
crit
sho
sho
(iii)
5.1.
Figu
with
2,a
lim
DIN
the
LV
Fig
whe
REINFOR
SCREW RE
sign of fully th
eria, viz.: (i)
ould be enoug
ould not yield
) screw should
.1 MINIMU
EDGES O
ure 7 shows a
h two vertica
c and a mu
itations were
N 1052 for th
beam. The d
L beam can o
gure 7 Reinfor
5.2
ere rd is the o
dhh3b<
RCEMENT
EINFORCEM
hreaded SPAX
Distance of s
gh to avoid sp
d due to the te
d not withdraw
UM DISTANC
OF BEAM
a drawing of a
al screws with
utual distance
adopted from
he distances o
distances ensu
ccur.
rcement of scr
c1,r ad5 ≤≤
r2d3a≥
rc2,d5.2a≥
outer diameter
T
MENT DESI
X screw shou
screw from ed
plitting of woo
ensile stresse
w due to the te
CE OF SCRE
a beam with ho
h edge distan
e of .a 2 Th
m the German
of the screw f
ure that no sp
rew
rd4
r
r of the screw.
(9)
IGN
uld meet some
dges of beam
od, (ii) screw
s, and finally
ensile forces.
EW FROM
ole reinforced
nces of c1,a ,
he following
n design code
from edges of
plitting in the
(10)
(11)
(12)
e
m
w
y
d
,
g
e
f
e
5.1.2 YIELDING OF SCREW
Tensile stresses due to holes should not cause yielding in
the screw reinforcement. Controlling of reinforcement
could be ensuring according to:
screw d,y,2
r
dt,90,f
)4
d(
F <π (13)
where screw d,y,f is the design yielding strength of screw
defined as:
m
k,y
modscrew d,y,
fkfγ=
(14)
Note: k,yf is the characteristic yielding strength of
screw,mγ is a partial safety factor for screw of 1.3
according to Eurocode 5 [5].modk signifies the partial
modification factor for load duration and moisture. Such
a parameter should be assumed equal to 1 because screw
design is not affected by the change of the moisture
content in the wood nor by the load duration.
5.1.3 SCREW WITHDRAWAL
The screw should not withdraw. Screw withdrawal could
be prevented by using enough embedment length at both
sides of the crack surface.
d,axdt,90,RF≤
(15)
mmodk,axdax,/kRR γ×≤
(16)
Note: d,axR signifies the design tensile strength of
screw reinforcement, k,axR the characteristic tensile
strength of the screw, mγ partial safety factor that for
LVL is assumed equal to 1.2 and finally modk is a
modification factor for LVL taking into account load
duration and moisture content that for permanent loading
is equal to 0.6. According to Aicher et al [6] d,axR could
be calculated as :
)dLf,Rmin(R rbdk,1k,u,tk,ax =
(17)
Note: k,u,tR signifies the characteristic tensile strength
of screw, k,1f the withdrawal strength of LVL, and bdL
the embedment length of screw. According to the
experiments on LVL specimens, the characteristic
withdrawal strength for screw with outer diameter of 8
mm could be obtained through the Equation (18).
26
k,1 1081f ρ×=−
(18)
where ρ is the density of LVL in 3m/kg . For 550
3m/kg density of LVL, f1,k is 24.5 MPa.
Controlling of bdL is necessary to avoid screw
withdrawal.
)L,d12max(L adrbd≥
(19)
adL and bdL are presented in Figure 8.
Figure 8. Withdrawal length
5.2 PLYWOOD DESIGN
Design of plywood should meet the following criteria,
viz.: (i) plywood should carry the tensile load due to the
hole; and (ii) plywood should cover the portion of beam
where tensile stresses exceed the tensile strength of
LVL.
5.2.1 CONTROL OF DIMENSIONS
Plywood as reinforcement should be glued and
nailed/screwed to both sides of the holes.
Nailing/screwing with gluing of plywood to both sides of
the hole provides full bond between LVL and plywood.
Figure 9 provides a drawing of a hole reinforced with
two plywood sheets with dimension shown in the Figure.
Figure 9. Plywood on both sides of a hole
The limitation below may be used for beams with holes.
)hh(3.0ah25.0 drd+≤≤
5.2.2 TENS
The plywood
stresses due
stresses can
equations:
Note: 90,tσ
plywood per
tensile streng
and K is a fa
distribution a
design tensi
according to
rt are param
According t
strength of
could be obta
Table 1. C
perpendicula
Class of
F
F
F
F
F
5.2.3 ROLL
Rolling she
considered b
recommenda
is presented
glued and n
direction is
beam.
1 2.0h≥
SILE STRES
d should be
e to the hole
n be perform
d,90,t ≤σ
moply,d kf=
d,90,t 2
K=σ
d, signifies
rpendicular to
gth of plywoo
actor taking in
around the hol
le force in p
Aicher et al
eters introduc
to New Zeal
plywood for
ained from Ta
haracteristic
ar to face grain
f plywood
F22
F17
F14
F11
F8
LING SHEA
ear between
but it did not
ation for mitig
in Figure 10.
nailed to the
perpendicular
dh25
SS CONTROL
controlled fo
e. Controllin
med through
ply,df
m
k,90,t
d
f
γ
rr
d,90,t
t.a.2
F.K
the tensile
o face grain,
od perpendicu
nto account n
les in LVL be
plywood due
[6] may be ta
ced in Figure 9
and standard
different cla
able 1.
tensile stren
n [7]
Charac
streng
AR
n plywood
seem to be a
gating the effe
The first ven
LVL beam
r to the grain
(2
(2
L
or the increas
ng of the ten
h the follow
(2
(2
(2
design stress
ply,df the de
ular to face gr
non-uniform st
eams. d,90,tF is
e to the hole
aken as 2. ra
9.
d [7], the ten
asses of plyw
ngth of plyw
cteristics tensil
gth of plywood
34.6
30
22
17.3
133.5
and LVL
a critical issue
ct of rolling s
neer of plywoo
so that its g
n direction of
20)
21)
se in
nsile
wing
22)
23)
24)
s of
esign
rain,
tress
s the
e. K
r and
nsile
wood
wood
le
d
was
e. A
shear
od is
grain
f the
Fig
5.3
Inst
wei
edg
obta
with
load
Figu
and
Fig
Avo
requ
of t
crac
Fig
from
gure 10. Grain
INSTALLA
tallation of pi
ight of the pip
ge of the beam
ained from f
h holes. The b
ded at mid-sp
ure shows tha
d two other sid
gure 11. Stress
oiding extra
uires that the p
the beam to h
ck) as display
gure 12 Detail
m the top part
n direction lay
ATION OF P
pes is an imp
pes should no
m. Figure 11
finite element
beam dimensi
pan by 50 kN
at two opposit
des are in com
s field around
tensile stres
pipe weight b
have a positiv
ed in Figure 1
l of beam pen
t of the beam
yout
PIPES
portant issue in
ot be applied
shows tensil
t analysis of
ion was 2800
kN concentrat
te right sides
mpression.
holes
ss perpendicu
be applied to th
ve effect on c
12.
netration with
n design. The
to the tensile
le stress field
f LVL beams
×400×45 mm
ted load. The
are in tension
ular to grain
he upper edge
crack (closing
pipe hanging
e
e
d
s
m
e
n
n
e
g
g
5.4 STRESS CONCENTRATION
At square/rectangular hole corners stress concentrations
occur and shear stresses rise considerably. According to
Bejtka et al [8], for rectangular holes with sharp edges
the maximum shear stress to average shear stress ratios
vary significantly with increasing hole diameter to beam
depth ratios, as presented in Figure 13 for square holes.
Figure 13. Ratio of the maximum shear to average shear
for different hole sizes to beam depths
Figure 13 shows that for ݄ௗ /݄ ൌ 0.2 the maximum shear
stress produced is 3.3 times the average value and for
݄ௗ /݄ ൌ 0.5 the ratio is 6.4.
Controlling of the shear stresses at the edges of the
rectangle is necessary. Following formulations may be
used for calculation of the maximum shear stress [9]
τଶ ൌκଶ ൈ1.5 Vୢ
bሺh െ hୢ ሻ (25)
κଶ ൌ1.84൬1b୦
h ൰ൈሺhୢ
h ሻ.ଶ (26)
where τଶ is maximum shear produced due to the hole.
The above limitation apply for 0.1 b୦ /h 1 and
0.1 hୢ /h 0.4.
τଶ f୴,ୢ
(27)
f୴,ୢ is design shear stress capacity of the LVL defined as:
f୴,ୢ ൌk୫୭ୢ
f୴,୩
γ୫
(28)
f୴,୩ is characteristic shear force capacity of LVL.
Controlling of the shear capacity for screw
reinforcement in rectangular holes is necessary.
5.5 INTERACTION OF THE HOLES
Interaction of two or more holes (Figure 14)
considerably decreases the capacity of the beam with
holes. Cracks around the holes joining each other can
govern the failure mechanism. Interaction of the holes
was investigated for a set of numerical analyses on
reinforced beams.
Figure 14 Interaction of the holes
Numerical analyses showed that for distances between
screws greater than 1.5h the screws have no interaction
to each other. This distance is recommended as a
minimum clear distance between the screws that should
always be ensured.
WORKED EXAMPLE OF SCREW
REINFORCEMENT DESIGN
A beam of dimensions 3000 ൈ 300 ൈ 45 ݉݉ has been
loaded at mid-span. A hole of diameter 90 mm is
introduced into the beam at a distance of 600 mm from
the end section. The beam is used within a roof of a
house subjected to permanent loads. The design of the
reinforcement using fully threaded SPAX screws of 6
mm core diameter with the thread of 2 mm (see Figure
15) is required.
Figure 15. Beam with hole reinforced with screws
Controlling hole diameter:
The ratio of the hole diameter (hୢ ) to beam dept (h) is
0.3, which is smaller than the limitation for fully
threaded SPAX screw of 0.4. The reinforcement by
screw needs therefore to be designed.
Tensile load perpendicular to grain in screw:
The design here is being performed for maximum shear
force in the section of the beam.
The characteristics shear capacity of LVL in the grain
direction is [10]:
f୴,୩ ൌ6.0MPa
2
4
6
8
0.2 0.3 0.4 0.5Ratio of maximim shear to average shearRatio of hole size to beam depth
The maximum shear force capacity of the beam section
according to Eurocode 5 could be calculated as below:
Vୢ ൌ ଶ
ଷ f୴,୩ bd ൌ
ଶ
ଷ ൈ 6.0 ൈ 45 ൈ 300 ൌ 54 kN
Mୢ ൌVୢ ൈLୡ ൌ 54000 ൈ 600 ൌ 32.4 kNm
So the tensile force in the screw can be evaluated as:
F୲,ଽ,ୢ ൌ F୲,V,ୢ F୲,M,ୢ = √ଶ
଼୦య Vୢ hୢ ൫3hଶ െhୢଶ ൯
ଷ
ସ
M୦ౚయ ሺ୦ା୦ౚሻ
୦యሺ୦.୦ౚ ା୦మା୦ౚమ ሻ
F୲,ଽ,ୢ ൌ √2
8 ൈ 300
ଷ ൈ 54000 ൈ 90
ൈ ሺ3 ൈ 300
ଶ െ90ଶ ሻ 3
4
ൈ 32400,000 ൈ 90
ଷ ൈ ሺ300 90ሻ
300ଷ ሺ300 ൈ 90 300
ଶ 90ଶ ሻ
ൌ10.4 kN
Design of screw reinforcement:
With the assumption of using fully threaded SPAX
screws for the reinforcement, the withdrawal strength
could be calculated as below:
fଵ,୩ ൌ81ൈ10ି ൈ ρଶ ൌ25ൈ10ି ൈ 550
ଶ
ൌ 24.5 N/mm
ଶ
The embedment length of the screw could be calculated
as below:
Lୟୢ ൌ 0.5h െ 0.354hୢ ൌ 0.5 ൈ 300 െ 0.354 ൈ 90
ൌ 118 mm
The aforementioned embedment length can carry the
following load:
Rୟ୶,୩ ൌ 118 ൈ
ሺ81 ൈ 10
ି ሻ ൈ 550
ଶ ൈ 8 ൌ 23.2 kN
Rୟ୶,ୢ ൌ R ୟ୶,୩ K ୫୭ୢ
γ୫
ൌ 23208 ൈ 0.6
1.2 ൌ 11.6 kN
The embedment length of 118 mm provides 11.6 kN
resistance to withdrawal. The above force is higher than
the design force of 10.4 kN in the screw. So that
embedment length will be sufficient.
The screw also should not yield. Since the yielding
strength of the SPAX screw is about 800 MPa, the
yielding force of the screw is:
f ൌ 800 ൈ π ൈ 6
ଶ
4 ൌ 22.0 kN
Since the force of 22 kN is greater than the design axial
force of 10.7 kN in the screw, the design is satisfactory.
Controlling of distance of screw from edges:
Distance of screw from the edges of the beam
2.5d୰ aଵ,ୡ 4d୰
The outer diameter of the screw is 8 mm, therefore we
have:
aଵ,ୡ ൌ3ൈ8ൌ 20 mm
The distance of the screw from the other surface of the
beam is:
aଶ,ୡ 2.5d୰
The distance of the screw from the edge of the beam is:
aଶ,ୡ 2.5d୰ ൌ2.5ൈ8ൌ20 mm
The distance of the hole from the support is controlled
through the following equation:
sൌ൬Lୡ െcെhୢ
2 ൰h
s ൌ ൬600 െ 100 െ
60
2 ൰ ൌ 470 300 mm
The design is now complete for reinforcement with self
tapping screws. Controlling of critical sections also
should be performed that is not included in the worked
example.
WORKED EXAMPLE OF PLYWOOD
REINFORCEMENT DESIGN
A beam of dimension 3000 ൈ 300 ൈ 45 ݉݉ has been
loaded at mid-span. A 90 mm diameter hole of
dimension is introduced into the beam at a distance of
600 mm from the end section. The beam has been used
in the roof of a house and is subjected to permanent
loads (see Figure 16).
Figure 16. Beam with hole reinforced with plywood
Controlling hole diameter:
The ratio of the hole diameter to beam depth is 0.3,
which is smaller than the limitation of 0.45 for plywood
reinforcement. Reinforcing by plywood needs therefore
to be used.
Tensile load perpendicular to grain in plywood:
The maximum shear force capacity of the section
according to Eurocode 5 is:
Vୢ ൌ ଶ
ଷ f୴,୩ bd ൌ
ଶ
ଷ ൈ 6.0 ൈ 45 ൈ 300 ൌ 54 kN
Mୢ ൌVୢ ൈLୡ ൌ 54000 ൈ 600 ൌ 32.4 kNm
The tensile force due to the hole is calculated as:
F୲,ଽ,ୢ ൌ F୲,V,ୢ F୲,M.ୢ
ൌ √2
8hଷ Vୢ hୢ ሺ3hଶ െhୢଶ ሻ
3
4
Mୢ hୢଷ ሺh hୢሻ
ሺh.hୢ hୢଶ hଶ ሻ
F୲,ଽ,ୢ ൌ √2
8 ൈ 300
ଷ ൈ 54000 ൈ 90 ൈ
ሺ3 ൈ 300
ଶ െ90ଶ ሻ
3
4 ൈ 32400000 ൈ 90
ଷሺ300 90ሻ
300ଷ ሺ300 ൈ 90 300
ଶ 90ଶ ሻ
ൌ 10.4 kN
Plywood Dimensions:
The horizontal dimension of the plywood should be
limited with the following equations:
0.25hୢ a୰ 0.3ሺhhୢ ሻ
22.5 a୰ 117
The plywood should carry tensile forces due to the hole
in the section of the beam.
σ୲,ଽ,ୢ R ୢ
fୢ,୮୪୷ ൌk୫୭ୢ ൈ f୲,୩
γ୫
ൌ0.6ൈ 15
1.2 ൌ7.5 MPa
Assuming the use of 15 mm thick plywood, the length of
the coverage area is defined as below:
σ୲,ଽ,ୢ ൌ KൈF୲,ଽ,ୢ
2ൈa୰ ൈt ൌ 2 ൈ 10051
2ൈܽ ൈ15 ൌ 670
ܽ
ܽ 89.3 mm then the value
ܽ ൌ 100 mm is chosen
݄ଵ should be:
hଵ 0.25hୢ ൌ 0.25 ൈ 90 ൌ 22.5 mm, then the
value hଵ ൌ30 mm is chosen.
The actual dimension of the plywood sheet will
be 290 ൈ 150 ൈ 15 mm. Controlling of the other critical
sections should be performed that is not included.
6 CONCLUSIONS
Experiments on LVL beams show that screws and
plywood can be used for reinforcement around holes.
The paper includes a design method for LVL beams with
holes based on controlling tensile stresses at the edges of
the hole. Worked examples are presented for designing
of screws and plywood reinforcement.
Acknowledgements
The authors would like to extend their gratitude to the
University of Canterbury and Structural Timber
Innovation Company (STIC) for funding this research
project.
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