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

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.
REFERENCES
[1] M. Gong, L. Li, Y. H. Chui, K. Li and N. Yuan.:
Modelling of recovery of residual stress in densified
wood. In 10th World Conference on Timber
Engineering, 2008.
[2] R. A. Shenoi and W. Wang. Through-thickness
stresses in curved composite laminates and sandwich
beams. Composites Science and Technology,
61:1501-1512, 2001.
[3] L. De Lorenzis, J. G. Teng and L. Zhang. Interfacial
stresses in curved members bonded with a thin plate.