simulation of residual stress in curved glulam beams - Engineered ...

SIMULATION OF RESIDUAL STRESS IN CURVED GLULAM
BEAMS DURING MANUFACTURING
Enchun Zhu 1 , Huazhang Zhou 2
ABSTRACT: A curved Glulam beam is manufactured by forcing the laminas with an adhesive into the designed curve,
bending stress is thus formed in each lamina. When the adhesive is solidified and the forces are removed, there are
bending stress, shear stress and stress perpendicular to grain remaining in the beam. The residual stresses will affect the
load-carrying capability of the beam. It is, therefore, useful to investigate the residual stresses from production. In this
study, the process of forming the laminas into curved Glulam beams was simulated by FE method incorporating
ABAQUS. The residual stresses, longitudinal and perpendicular to grain in curved Glulam beams during and after
manufacturing were studied. The effect of various parameters, such as the solidification time of adhesive, the thickness
of lamina, the radius of curvature of the Glulam beams and the magnitude of external pressure, on the residual stresses
was discussed. Based on the investigation, a formula for evaluating the longitudinal residual stress in a curved beam
was proposed.
KEYWORDS: Residual stress, Stress perpendicular to grain, Curved Glulam beam, Finite element
1 INTRODUCTION 1iii
A curved Glulam beam is manufactured by forcing the
laminas with an adhesive into the designed curve,
bending stress is thus formed in each lamina. When the
adhesive is solidified and the applied forces are removed,
there are bending stress, shear stress and stress
perpendicular to grain remaining in the beam. The
residual stresses will affect the load-carrying capability
of the beam. A curved Glulam beam is a kind of
prestressed members with both longitudinal stress and
stress perpendicular to grain from manufacturing. In
engineering practice, some curved Glulam beams failed
due to tension of perpendicular to grain. It is, therefore,
useful to investigate the residual stresses from
production for proper design of curved Glulam beams.
Literature on the residual stresses in Glulam is very little.
Gong et al. [1] measured and modelled the recovery of
residual stress in densified wood. He found that the
residual stress increases with the compression in
manufacturing. Shenoi and Wang [2] investigated the
through-thickness and longitudinal stresses in curved
laminated beams and sandwich beam. The stacking
sequence of laminates and the radius of curvature affect
the through-thickness stress. The peak through-thickness
1 Enchun Zhu, Professor, School of Civil Engineering, Harbin
Institute of Technology, P.O. Box 2453, 73 Huanghe Road,
Harbin 150090, China. Email: e.c.zhu@hit.edu.cn
2 Huazhang Zhou, Lecturer, School of Civil Engineering,
Harbin Institute of Technology, P.O. Box 2453, 73 Huanghe
Road, Harbin 150090, China. Email:
huazhang.zhou@hit.edu.cn
stress occurs at the interface between the neutral layer
and the core of sandwich beam, or in the core but very
close to the interface. Lorenzis, Teng and Zhang [3] and
Lorenzis and Zavarise [4] investigated the interfacial
stress in curved members bond with thin plate in the
soffit. The interfacial normal stress is related by
equilibrium to the interfacial shear stress, and the normal
stress is tensile at the concave side of the member and
compression at the convex side of the member. The
stress perpendicular to grain induced by load and the
varying relative humidity (RH) was investigated [5],
while the residual stress induced during the manufacture
was not covered. The residual stress from the
manufacturing is important to understanding of the
performance of curved Glulam beams.
In this paper, a two-dimensional FE model incorporating
ABAQUS was developed to simulate the residual stress
in curved Glulam beams during manufacturing. The
distribution of residual stress in the Glulam was
disclosed. The effect of various parameters, such as the
solidification time of adhesive, the thickness of lamina,
the radius of curvature, the magnitude of external
pressure, on the residual stress was discussed. Based on
the investigation, a formula for predicting the residual
stress in curved beam was proposed.
2 CONSTITUTIVE MODEL OF WOOD
To develop a FE model simulating the process of
manufacturing of curved Glulam beams, some
simplifications are necessary and some principles are to
follow.

The thickness of glueline is neglected due to the fact that
glueline is only a tiny part of Glulam, and the typical
thickness is only 0.076-0.152mm [6]. The thickness of
glueline is very minor compared with the dimensions of
Glulam members. Thus, the thickness of glueline is
neglected in the FE modelling. But the bond
performance of adhesive in glueline is still considered.
The bond performance is different in different stages of
manufacturing. In the stage of forcing the laminas into
the curved shape, the glue is still a liquid. It has no bond
effect and can also reduce the friction between laminas.
While when the adhesive is solidified, the bond effect is
acquired. Laminas can neither slip relatively nor separate
even when the pressure is removed. The deformation is
so restrained that a curved Glulam beam is completed.
Thus remains the residual stress. Because of the tiny
thickness of glueline, the dimension of glueline is
neglected in FE model. The bond performance of
adhesive is considered through the frictional behaviour
and separating behaviour in FE modelling-when the
adhesive is liquid, the coefficient of friction is chosen as
a small value and separating between laminas is allowed;
when the adhesive is solidified, the coefficient of friction
is chosen as a large value (rough friction) and separating
between laminas is prevented.
The material of Glulam is considered as an orthotropic
material. For a two-dimensional problem, the plane
stress relationship is
⎡ 1 υ12
⎤
⎢ − 0 ⎥
E1 E1
⎧ε1 ⎫ ⎢ ⎥⎧σ11⎫
⎪ ⎪ ⎢ υ12
1 ⎥⎪
⎪
⎨ε2 ⎬= ⎢− 0 ⎥⎨σ22⎬
(1)
⎪ E1 E2
γ ⎪ ⎢ ⎥⎪
12 τ ⎪
⎩ ⎭ ⎢ 12
1 ⎥⎩
⎭
⎢ 0 0 ⎥
⎢⎣ G12
⎥⎦
where 1 E , 2
wood; 12 G is the modulus of shear; υ 12 is Poisson’s ratio;
E are the moduli of elasticity (MOE) of
σ 11 , σ 22 and τ 12 are the stress components; ε 11 , ε 22 and
γ are the strain components.
12
3 NUMERICAL SIMULATION OF
STRESSES INDUCED FROM
MANUFACTURING
3.1 MANUFACTURING PROCEDURE
The process of manufacturing curved Glulam beams is
as follows. The laminas sprayed with an adhesive are
pressed on a rigid mould with designed curvature, and
the pressure by applying external forces is kept until the
designed strength of adhesive is reached. Then the
external forces are removed, the curved shape can be
retained due to the effect of bond. The procedure can be
divided into two stages in FE modelling. Stage 1, to
press the stacked laminas into the designed curve; Stage
2, to release the pressure after solidification of the
adhesive between laminas. In stage 1, the coefficient of
friction between laminas is reduced by the liquid
adhesive. However, there is still some friction that
depends on the craftsmanship like adhesive applying
(spraying/brushing) and the type of the adhesive.
Because of the different solidification times of adhesive,
different coefficients of friction occurs in Stage 1. The
coefficient of friction is thus taken as an important factor.
In Stage 2, the curved beam is released from pressure
after the adhesive is entirely solidified, and the strength
of adhesive reaches such an extent that relative slippage
between laminas is prevented, unless failure of glueline
happens. Therefore, the rough friction between laminas
is considered in the Stage 2, i.e. neither relative slippage
nor separation between laminas takes place.
3.2 DETAILS OF THE CURVED BEAMS AND
THE FE MESH
Figure 1 shows a sketch for manufacturing a curved
Glulam beam, which is made of 15 laminas. The crosssection
of the curved Glulam beam is 90mm×180mm,
and the cross-section of each lamina is 90mm×15mm
with a length of L=3.2m. The species of wood is Chinese
larch, the density is 580kg/m 3 , the MOE is 12000N/mm 2 ,
the modulus of shear is 400 N/mm 2 , the Poisson’s ratio
is 0.42. The designed radius of curvature of the neutral
axis is 5.0m. Therefore, the radius of curvature of the
rigid mould is R=4.91m. The magnitude of pressure is
p=0.5MPa. Making use of the symmetry, a half of the
beam is modelled in the FE analysis. On the symmetrical
face, there is no horizontal displacement and rotation.
Each lamina is meshed with 5mm×5mm CPS4R element
[7]. The coefficient of friction between wood is 0.3-0.5
[6]. In Stage 1, the coefficient is set as 0.1 due to the fact
that the liquid adhesive decreases the friction. The rigid
mould is considered as smooth, because the mould is
actually discrete in practice. The residual stress
distribution and the rebounding deformation during
manufacturing of the curved Glulam beams are
discussed as follows.
Symmetry
R
p
L/2
Rigid mould
Figure 1: Sketch of manufacturing a curved Glulam
beam
P
h
Figure 2 shows the longitudinal stress distribution in the
mid-length of a curved Glulam beam after the pressure is
removed. In Stage 1, when the adhesive is liquid, the
laminas can slip relatively. There is no composite action
between laminas. Thus all laminas bend alike. When the
adhesive is solidified, there is no relative slippage
between laminas even when the pressure is removed.
Therefore the entire composite action comes into being.
In general, the longitudinal residual stress in the middle
part of beam is larger than that around the free end. The
stress in the top and the bottom of each lamina is the

largest due to the bending, with a representative value of
about 13.1MPa for tension at the top and 12.9MPa for
compression at the bottom. Thus, the distribution of
longitudinal residual stress exhibits a saw-toothed shape.
In the process of manufacturing, the largest longitudinal
stress is about 13.1MPa, which occurs in bottom lamina
due to most severe bending.
Depth (mm)
90
0
-15 0 15
-90
Longitudinal residual
stress (MPa)
Figure 2: Longitudinal residual stress distribution at the
mid-length of the curved Glulam beam
Also in Stage 1, when the laminas are bent into a curve,
there is compression between them. The compressive
stress perpendicular to grain remains when the pressure
is removed in Stage 2. The stress is all compressive
except for where in the vicinity of glueline at the end of
the beam, as indicated in Figure 3, which shows the local
distribution of stress perpendicular to grain at the end of
the beam. When the glue is hardened and the applied
pressure is removed, the laminas in the upper part of the
beam tend to rebound and are restrained by the
neighbouring laminas below, thus giving rise to tensile
stress between laminas at the end of the beam. The
largest tensile stress perpendicular to grain at the end
cross-section is about 0.16Mpa, while the largest
compressive stress perpendicular to grain is 0.085MPa.
In the mid-length the compression is about 0.04MPa.
Figure 3: Residual stress perpendicular to grain at the
free end of the curved Glulam beam
The rebounding of a curved Glulam beam is also of
concern. Figure 4 shows the deflection of Point P versus
the pressure applied in the process of manufacturing.
The maximum deflection, 248.6mm, occurs when the
pressure reaches the maximum. When the pressure is
removed completely, the amount of rebounding
deformation is 4.9mmm, leaving a deflection of
243.7mm remained. The rebounding is only 1/635 of the
length of beam, a very small portion of the dimension of
the curved Glulam beam. The rebounding deformation,
which reflects the difference between the designed curve
and the curve in manufacturing, is an important factor to
guide the setting up of the mould.
Pressure (MPa)
0.5
0.4
0.3
0.2
0.1
0.0
0 50 100 150 200 250
Deflection of point P (mm)
Figure 4: Rebounding of the beam
4 FACTORS AFFECTING THE
RESIDUAL STRESS
The residual stress in a curved Gulam beam is affected
by factors such as the magnitude of pressure, radius of
curvature of the neutral axis of beam, thickness of
lamina and the time between applying the adhesive and
applying the pressure to force the beam into the curved
shape, as reflected by the coefficient of friction in Stage
1. The effect of these factors will be discussed through
an example of simulating the manufacturing of a curved
Glulam beam with a cross-section of 90mm×180mm. In
order to investigate the effect, some parameters are
prescribed in Table 1.
Table 1: Parameters for manufacturing the curved
Glulam beam
Parameter Unit Value
Radius of curvature R m 3.0 4.0 5.0
Pressure p MPa 0.5 0.75 1.0
Thickness of lamina t mm 15 20 30 45
Coefficient of friction µ 0.05 0.1 0.3 0.5
Figure 5 shows the effect of different parameters on the
residual stress perpendicular to grain in the curved
Glulam beams. As a general trend, the residual stress
perpendicular to grain increases with the coefficient of
friction that increases with the time interval between
adhesive applying and pressure applying. This indicates
that the sooner the process of Stage 1 in the manufacture,
the less the stress in a curved Glulam beam. It can also

e found that larger the pressure and smaller radius of
curvature of the neutral axis give rise larger residual
stress perpendicular to grain. The effect of radius of
curvature is more significant than that of pressure on the
stress perpendicular to grain. For example, under the
condition of µ=0.1, when p=0.5MPa, R=5.0m, the stress
is 0.16MPa; while when p=0.5MPa, R=4.0m, the stress
is 0.18MPa and when p=0.75MPa, R=5.0m, stress is
0.19MPa.
Residual stress perpendicular to grain (MPa)
0.4
0.3
0.2
0.1
p=0.5MPa, R=3.0m
p=1.0MPa, R=3.0m
p=0.75MPa, R=3.0m
p=0.5MPa, R=4.0m
p=0.75MPa, R=4.0m p=1.0MPa, R=4.0m
0.0
p=0.5MPa, R=5.0m
p=1.0MPa, R=5.0m
p=0.75MPa, R=5.0m
0.0 0.1 0.2 0.3 0.4 0.5
Coefficient of friction
Figure 5: Residual stress perpendicular to grain of beam
(cross-section: 90mm×180mm; lamina: 90mm×15mm)
Figure 6 shows the effect of different parameters on the
longitudinal residual stress in curved Glulam beams.
Only the radius of curvature affects the longitudinal
residual stress in a curved beam. The smaller the radius
of curvature of the neutral axis, the more severe the
bending of the laminas and the larger the longitudinal
stress in a lamina. While the coefficient of friction and
the pressure pose little effect on the longitudinal stress.
When radius of curvature R=5.0m, the longitudinal stress
is about 13.2MPa; while when R=4.0m and 3.0m, the
stress are about 16.5MPa and 22.2MPa, respectively.
Longitudinal residual stress (MPa)
21
18
15
p=0.5MPa, R=3.0m p=0.75MPa, R=3.0m
p=1.0MPa, R=3.0m p=0.5MPa, R=4.0m
p=0.75MPa, R=4.0m p=1.0MPa, R=4.0m
p=0.5MPa, R=5.0m p=0.75MPa, R=5.0m
p=1.0MPa, R=5.0m
12
0.0 0.1 0.2 0.3 0.4 0.5
Coefficient of friction
Figure 6: Longitudinal residual stress (cross-section:
90mm×180mm; lamina: 90mm×15mm)
The effect of the parameters on the rebounding
deformation of curved Glulam beams is shown in Figure
7. Parameters listed in Table 1 all affect the rebounding
deformation. The smaller the coefficient of friction in
Stage 1, the more the slippage and the less the composite
action, thus the rebounding deformation is smaller. A
smaller radius of curvature and the larger pressure mean
more severe bending of lamina, resulting in larger
rebounding deformation.
Rebounding deflection (mm)
18
15
12
9
6
3
p=0.5MPa, R=3.0m p=0.75MPa, R=3.0m
p=1.0MPa, R=3.0m p=0.5MPa, R=4.0m
p=0.75MPa, R=4.0m p=1.0MPa, R=4.0m
p=0.5MPa, R=5.0m p=0.75MPa, R=5.0m
p=1.0MPa, R=5.0m
0
0.0 0.1 0.2 0.3 0.4 0.5
Coefficient of friction
Figure 7: Rebounding deflection of curved Glulam beam
(cross-section: 90mm×180mm; lamina: 90mm×15mm)
The effect of thickness of lamina on the residual stress of
curved Glulam beams is shown in Figure 8. Figure 8(a)
shows the residual stress perpendicular to grain versus
the thickness of lamina and Figure 8(b) shows the
longitudinal residual stress versus the thickness of
lamina. The residual stress during manufacturing is
affected by the thickness of lamina. Larger stress either
perpendicular to grain or longitudinal is formed in
thicker laminas. It can be found that thick laminas are
actually not suitable for manufacturing curved beam due
to the large residual stress that could exceed the strength
of wood.
Residual stress perpendicular to grain (MPa)
1.0
0.8
0.6
0.4
0.2
R=5.0m
R=4.0m
R=3.0m
10 20 30 40 50
Thickness of lamina (mm)
(a) The effect of thickness of lamina on the residual
stress perpendicular to grain

Longitudinal residual stress (MPa)
80
60
40
20
R=5.0m
R=4.0m
R=3.0m
0
10 20 30 40 50
Thickness of lamina (mm)
(b) The effect of thickness of lamina on the longitudinal
residual stress
Figure 8: The effect of thickness of lamina on the
residual stress (p=0.5MPa, µ=0.1)
5 THE FORMULA FOR
LONGITUDINAL RESIDUAL STRESS
For a lamina in a curved member under pure bending,
the maximum bending stress is
Et
σ =
h−t 2( R − )
2
(2)
where, E is the MOE of the lamina; R is the radius of
curvature of the neutral axis of beam; h is the depth of
beam; t is the thickness of lamina.
In a curved Glulam beam, the action of glueline, the
normal stress and shear stress, induce bending of the
lamina, which is different from pure bending. The
bending stress can be expressed by Eq. (3) by
introducing an adjustment factor K .
Et
σ max = K
h−t 2( R − )
2
(3)
Through the parametric study, the adjustment factor is
obtained as K =0.76, by regression of the maximum
residual longitudinal stress with different radii of
curvature and thicknesses of lamina. For different
thicknesses of lamina commonly used in curved Glulam
and different radii of curvature, the longitudinal residual
stress from the FE modelling and Eq. (3) are given in
Figure 9, which shows good correlation of the Equation
and the numerical method. The longitudinal residual
stress can thus be evaluated by Eq. (3).
Longitudinal residual stress (MPa)
50
40
30
20
(R=5.0m) FE results Eq.(3) results
(R=4.0m) FE results Eq.(3) results
(R=3.0m) FE results Eq.(3) results
10
10 15 20 25 30 35
Thickness of lamina (mm)
Figure 9: The longitudinal residual stress regressed by
Eq. (3)
6 CONCLUSIONS
A two-dimensional FE model was developed to simulate
the residual stress and rebounding deformation of curved
Glulam beams during manufacture. The residual stress
perpendicular to grain is generally compressive except
for some tension in the laminas around the end of curved
beams. Quite significant longitudinal residual stress
exists in the beam, and the longitudinal residual stress in
the mid-length is larger than that at the end of the length.
Each lamina has the similar stress distribution due to
bending. The longitudinal residual stress can be
evaluated by Eq. (3). The most important influencing
factors on the longitudinal residual stress are the radius
of curvature of the neutral axis and the thickness of
lamina. As for the residual stress perpendicular to grain
and the rebounding deformation, both are closely related
to the radius of curvature, pressure, the time interval
between adhesive applying and pressure applying and
the thickness of lamina. In manufacturing the curved
beams, smaller pressure, smaller thickness of lamina and
quicker manufacturing lead to smaller residual stresses
and rebounding deformation.
Due to the behaviour of creep and relaxation of wood
and adhesive, the residual stress from manufacturing will
decrease. This is worth investigating in future study.
ACKNOWLEDGEMENTS
The writers acknowledge with gratitude the financial
support of this study from the National Natural Science
Foundation of China designated 50878067.
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