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

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