Structural behaviour of composite sandwich panels i n
service and failure conditions
Diogo Marques Ferreira
Extended Abstract
Jury
President: PhD Fernando Manuel Fernandes Simões
Supervisor: PhD João Pedro Ramôa Ribeiro Correia
Co-supervisor: PhD Fernando António Baptista Branco
Opponent: PhD Ricardo José de Figueiredo Mendes Vieira
Opponent: PhD Mário Rui Tiago Arruda
October 2012
1/15
Abstract
The high maintenance costs of structures built with traditional materials such as concrete and steel led
to an increasing interest and search for new materials. The composite materials made of fiber
reinforced polymers present an alternative to these traditional materials with high stiffness/weight and
resistance/weight ratios, and good resistance against deterioration. These materials may present
different structural systems. The sandwich panels are a solution composed by two stiff and resistant
faces connected by a less resistant and stiff core. The present investigation is focused on sandwich
panels composed by glass fiber reinforced polymer (GFRP) faces and two different cores:
polyurethane foam (PU) and polypropylene honeycomb (PP). The panels are analysed with the
incorporation of lateral ribs made of GFRP that improve the stiffness and resistance of the whole
system. Initially, the main components of the panels (faces and core) were studied separately. The
faces were subjected to longitudinal and transversal tension; the PP, PU and foam glass cores were
tested under shear, and the PP and PU cores were tested under compression. Later, the dynamic
behaviour of the panels and static behaviour in tension perpendicular to the faces was tested. The
results showed that the PP honeycomb cores are stiffer and more resistant than the PU foam cores.
The faces present a similar behaviour in both directions. The results of the experimental work were
compared with finite element models of the panels and analytical expressions. Similar results were
obtained. Finally, two different solutions using the sandwich panels were designed for use in building
floor slabs and footbridge decks.
Key words: composite materials, sandwich panels, GFRP, structural behaviour, experimental studies,
finite element model
1 Introduction
Due to the limited durability of the traditional materials (usually related with the need for faster
construction processes), new, lighter and more durable structural materials have been developed [1].
In the 1940’s the fiber reinforced polymers (FRP) were developed by the aerospacial and naval
industries. These materials have been used in the construction industry since the 1980’s [2]. These
composite materials present advantages related to high mechanical resistance, low density, low
thermal conductivity and high durability in corrosive environments. On the other hand, they present
some disadvantages, such as low elasticity modulus (especially on composite materials made of fiber
glass), fragile behaviour and poor performance at high temperatures [1].
A system composed by two stiff and resistant faces and a less stiff and less resistant core creates a
sandwich panel. These panels may be complemented with some elements that enhance their
properties, such as lateral ribs. The sandwich composite panels benefit from the properties of the
sandwich systems and the composite materials. The present work investigates the applicability of the
composite sandwich panels on building floor slabs and footbridge decks. The investigation is focused
on sandwich panels with glass fiber reinforced polymers (GFRP) faces and polyurethane foam (PU)
and polypropylene honeycomb (PP) cores.
2/15
Usually, sandwich panels are used in roofs and external or internal walls of single or multiple-storey
commercial and industrial buildings. The sandwich panels used in structures with low loads usually
present a PU core and steel faces [4], which improves the acoustic and thermal insulation. Sandwich
panels with GFRP faces are used in buildings [5, 6] and rehabilitation of road bridges [7], where the
replacement of the existing concrete deck by a lighter solution prevents the interruption of the use of
the superstructure during the construction works.
The sandwich panels should fulfil the requirements for each application. The use of the panels as
footbridge decks should fulfil the requirements regarding mechanical resistance. The panels used in
floor slabs should also account for thermal and acoustic insulation, and fire resistance. These
requirements are defined in specific standards.
The present investigation is focused on the mechanical behaviour of sandwich panels under bending.
A literature review was performed to provide a better understanding of the behaviour of the sandwich
panels in service and failure. An experimental study was carried out to complement the investigations
of Almeida [8]. The following tests were performed: i) characterization of the behaviour of the PU and
PP cores under compression perpendicular to the faces; ii) characterization of the behaviour of the
PU, PP and glass foam under shear; iii) characterization of the faces under tension; iv) behaviour of
the panel under tension perpendicular to the faces; v) characterization of the dynamic behaviour of the
panels under bending. Finite element (FE) models were developed to compare with the experimental
results. The comparison between the FE models and the experimental results was used to calibrate
the models and the analytical formulas. Finally, two cases of application of composite sandwich panels
were studied: a building floor slab with a 4 m span and a footbridge deck with 1.4 m span and two
cantilevers with 0.3 m span.
2 Characterization of the mechanical behaviour of t he sandwich panels
In the present investigation, the sandwich panels were considered as simply supported beams with
unidirectional behaviour. Since the core presents low stiffness, the deformation should consider its
shear deformability [3]. Figures 1 and 2 and Table 1 present the formulas used to calculate the
distortion and stresses in the sandwich panels.
Figure 1 Beam under uniform loading (adapted from [3]).
Figure 2 Beam with point load (adapted from [3]).
3/15
Table 1 Formulas for analysis of sandwich structures (adapted from [3]). Property Uniform loading Point load
Vertical displacement w = qL�24D ξ1 − ξ 1 + 4k + ξ − ξ� w = PL�
6D ξ1 − ε 2k + 2ε − ε�−ξ� ;ξ ≤ ε w = PL�
6D ε1 − ξ 2k + 2ξ − ε�−ξ� ;ξ > ε Maximum vertical displacement w�á� = 5qL�
384D 1 + 3.2k w = PL�48D 1 + 4k
Axial stress on the faces σ ,�á� = ± qL�8eA σ ,�á� = ± PL4eA
Shear stress in the core τ&.�'� = qL2adc τ&.�'� = Pea
with:
k = �+,-./0012 ,G4 = .-×46- , D = E 60 42� ,A8 = b × e
• G8– distortion modulus of the core; • E – elasticity modulus of the faces; • e– distance between the centre of the
faces;
• d - thickness of the faces; • a - panel’s width; • d8– thickness of the core.
Another important factor when studying the service behaviour of the sandwich panels is the natural
vibration frequency. The following formula is used to calculate the vibration frequency (f), considering
the shear deformability:
:;;<=� = 1 + >G4 ?1 + >G4 ? � + ?
where: ;< = @�A2B� C>DE ; ? = DF @AB �
with: • @–vibration mode under bending; • >– elasticity modulus of the material [kN/m2];
• G– distortion modulus of the material [kN/m2]; • E– weight of the material per length unit [ton/m]; • F– surface area of the beam [m2].
The sandwich panels may present different failure modes, which influence the structural design, such
as: i) failure due to axial forces on the faces; ii) failure under shear; iii) failure in the supports. The
design value of an action effect should not exceed the corresponding design resistance. The
maximum axial and shear stresses were calculated according to the formulas previously presented,
and then compared with the resistance. The compression of the faces may result in failure due to
compression of the faces or buckling. The buckling resistance of the faces is corrected by an empiric
coefficient which considers the initial imperfections and defects in the connection between faces and
[2], as follows:
σ&H = 0.65E1E8G8 <� where:
• σ&H- critical buckling resistance of each face (corrected by an empiric coefficient), for Poisson coefficient of 0.30 for the faces and 0.25 for the core.
4/15
The failure of the supporting systems may be studied, conservatively, considering the pressure of the
support on the panel. This pressure is the quotient between the reaction and the surface area of the
support. The resulting stress shall not exceed the resistance of the different elements of the panel in
the direction of the force.
3 Experimental study
3.1 Experimental programme
The experimental study followed the work carried out by Almeida [8]. The present investigation studied
the same sandwich panels, produced by Alto, Perfis Pultrudidos, Lda [10] by the hand lay-up process.
Four different panels were produced: panels with PU and PP cores, with and without lateral ribs. The
panels are referred as PP or PU, depending on the material of the core, and R or U, if it has lateral
ribs or not, respectively. The panels exhibit a length of 2.5 m and a width of 0.5 m. The faces were
produced with polyester resin and three types of mats: surface veil mats (40 gr/m2); chopped strand
mats (300 gr/m2); and symmetric oven fabric mats 0º/90º (800 gr/m2). The first face to be produced
was the bottom face, moulded on a table. The upper face was moulded over the core. The connection
between the core and the faces is accomplished by the matrix. The lateral ribs were connected to the
panels by gluing a face made of pultruded GFRP.
3.2 Compressive behaviour of the cores perpendicula r to the faces
The first compressive strength test aims at characterizing the compressive resistance of the materials
that form the cores of the panels perpendicularly to the faces, according to NP-EN 826 [11]. The tests
were performed on 5 specimens of each core (PU and PP) with 100×100 mm of area and the original
thickness of the cores. The test was performed under displacement control and load was applied at
2.5 mm/s, using a LLOYD INSTRUMENTS universal instrument. The measurement of the load was
performed with a NOVATECH load cell with maximum capacity of 10 kN, and the deformation was
measured with a transducer. The registration of loads and displacements was made on a computer
using a data acquisition unit from HBM, model Spider 8. The load was applied over a stiff steel plate
with a spherical support that enables a uniform distribution of the load on the specimen. The results
obtained for one of the specimens of the PU core were not considered due to errors in the measurement by
the transducer.
The failure of the specimens occurred differently for the two materials. The failure of the PP specimens was
due to buckling of the honeycombs. The PU specimens failed because of change in the texture of the foam
(Figures 3 and 4).
Both materials exhibit linear behaviour until the maximum load is reached, followed by an almost
horizontal zone until unloading. Both specimens show an elevated residual displacement (Figures 5
and 6). The average results are presented in Table 2. The results show that the PP specimens
present higher mechanical properties.
5/15
Figure 3 Failure of the C-PP3 specimen.
Figure 4 Failure of the C-PU3 specimen.
Figure 5 Load-Displacement curves of the polyurethane specimens.
Figure 6 Load-displacement curves of the polypropylene honeycomb specimens.
Table 2 Average compressive properties.
Material Prop erties Cv %
PU JK [kN] 4.16±0.42 10.1 LK [MPa] 0.42±0.05 11.0 E [MPa] 16.42±1.63 9.9
PP JK [kN] 19.59±1.28 6.5 LK [MPa] 1.98±0.14 6.9 E [MPa] 117.85±2.42 2.1
3.3 Shear behaviour of the cores
The shear deformability and strength is of great importance to the total deformability of the panels.
Therefore, it is of great interest to evaluate the shear stiffness and resistance of the cores of the
sandwich panels. The tests were performed according to the ASTM C273 standard [52]. The tests
were performed on PU, PP and foam glass (Ff) cores. Four specimens of Ff with geometry
600×43×50 mm (length-thickness-width) and 5 specimens of PU and PP with 800×thickness of the
core×50 mm were tested (Figures 7 to 9). The PP and PU cores show an approximate linear
behaviour in the first loading phase, and a non-linear behaviour near failure (Figures 10 and 11). The
Ff presents a non-linear behaviour during the whole test (Figure 12).
0
1
2
3
4
5
0 5 10 15 20
Load
[kN
]
Displacement [mm]
C-PU1 C-PU2 C-PU3 C-PU4
0
5
10
15
20
25
30
35
0 5 10 15
Load
[kN
]
Displacement [mm]
C-PP1 C-PP2 C-PP3C-PP4 C-PP5
6/15
Figure 7 Failure of the Ss-Ff2 specimen.
Figure 8 Failure of the S-PU4 specimen.
Figure 9 Failure of the S-PP4 specimen.
The properties of the cores tested under shear are presented in Table 3.
Figure 10 Load-displacement curves for the S-PU tests.
Figure 11 Load-displacement curves for the S-PP tests.
Figure 12 Load-displacement curves for Ss-Ff specimens.
Table 3 Average shear properties Material Mechanical properties CV%
PU Fm [kN] 8.00±1.24 15.5 MK [MPa] 0.2±0.03 16.6 G [MPa] 4.09±0.22 5.4
PP Fm [kN] 20.01±0.91 4.5 MK [MPa] 0.52±0.03 5.0 G [MPa] 6.92±1.09 15.8
Ff Fm [kN] 3.27±0.22 6.8 MK [MPa] 0.11±0.01 6.7 G [MPa] 12.06±2.59 21.5
3.4 Tension behaviour of the panels perpendicular t o the faces
The tension behaviour of the panels perpendicular to the faces was tested according to an adaptation
of the ASTM C297/C 297M-04 standard [13]. Three specimens of each type of sandwich panel were
tested. The specimens presented a surface area of 100×100 mm and the thickness was the thickness
of the panel. The test was performed with displacement control until failure of the specimens, using an
Instron universal instrument with maximum capacity of 250kN. The data was registered using a HBM
data acquisition unit, model Spider 8. The results show different behaviour for different panels (Figure
13). The PP core panels show a non-linear behaviour until the maximum loading is reached, followed
0
2
4
6
8
10
0 2 4 6 8 10
Load
[kN
]
Displacement [mm]
S-PU1 S-PU2 S-PU3
0
5
10
15
20
25
0 10 20 30 40
Load
[kN
]
Displacement [mm]
S-PP1 S-PP2 S-PP3
0
1
2
3
4
0 0.2 0.4 0.6 0.8 1
Load
[kN
]
Displacement [mm]
Ss-Ff1 Ss-Ff2 Ss-Ff3 Ss-Ff4
7/15
by an unloading phase. The PU core panels exhibit linear behaviour until maximum loading occurs,
which corresponded to failure. The different behaviours are explained by the different failure modes
exhibited by the panels, as shown in Figures 14 and 15. The PU core panels present failure of the
core. On the other hand, the PP core panels show failure in the interface between the core and the
faces.
Figure 13 Load-displacement curves for panels with PP and PU cores under tension.
Figure 14 Failure of the T-PU1 specimen.
Figure 15 Failure of the T-PP1 specimen.
The properties of the panels tested under tension are presented in Table 4. The elasticity modulus
presented is the apparent elasticity modulus of the core, since the total displacement of the specimen
is influenced by the stiffness of the faces. The PP core panel shows higher resistance and stiffness
than the PU core panel.
Table 4 Average properties under tension transversal to the panels. Material Prop erties Cv %
PP JK [kN] 7.58±0.18 2.3 LK [MPa] 0.76±0.02 2.3 E [MPa] 119.66±15.86 13.3
PU JK [kN] 3.49±0.40 11.5 LK [MPa] 0.35±0.04 11.5 E [MPa] 15.03±0.80 5.3
3.5 Tension behaviour of the faces
The tension tests performed on the faces of the panels aimed at characterizing the behaviour of the
GFRP faces in both directions, and assess the influence of the manufacturing process (moulded on
the table or over the core) on their behaviour. Four different types of specimens were tested:
longitudinal (L), transverse (T), lower (I) and upper (S) specimens, seven T and L specimens and two I
e S specimens for each panel. The specimens were prepared according to the ISO 527-1,4 standard
[14,15]: 25 mm of width, and 250 mm or 350 mm of length, for S and I or L and T specimens,
respectively. The test consisted of applying a tensile load under displacement control at 0.033 mm/s
velocity using an Instron universal testing machine with maximum capacity of 250 kN (Figures 17 and
18). The results were registered on a computer using a HBM data acquisition unit, model Spider 8. Strain
gauges from HBM, model 10/120LY11, were placed in the I and S specimens, and three strain gauges
0
2
4
6
8
0 1 2 3 4
Load
[kN
]
Displacement [mm]
T-PP1 T-PP2 T-PP3T-PU1 T-PU2 T-PU3
were placed on L and T specimens
manufacturing process, being its average value 7.25
Figure 16 presents the stress-strain
is similar for all specimens, presenting a linear behaviour until
behaviour until failure.
Figure 16 Stress-strain diagrams due to tension of the faces PP-U/T e PP-U/L.
As shown on Table 5, the properties of the specimens vary significantly for each test. These
differences are due to the variability of the thickness of the specimens. The relation
elasticity modulus and the thickness of the specimens is constant
Figure 19). The structural behaviour of the GFRP
depend upon the manufacturing process.
Table 5 Summary of the properties of the faces under tensionSpecimen LK [MPa]
PP-U/T 153.86±10.53 PP-U/L 126.95±9.52 PU-U/T 115.12±8.66 PU-U/L 112.46±11.09 PU-U/S 186 37 PU-U/I 222.01 PP-U/S 136.03 PP-U/I 187.29
All 137.75±30.23
0
20
40
60
80
100
120
140
160
0 5000 10000
Str
ess
[MP
a]
Strain [µstrain]
1PP-U/T 2PP-U/T1PP-U/L 2PP-U/L
were placed on L and T specimens. The thickness of the specimens is variable, due to the
process, being its average value 7.25 mm, with 1 mm standard deviation.
strain curve of the L and T specimens of the PP core panel; the diagram
is similar for all specimens, presenting a linear behaviour until 5000 µstrain, followed by a non
strain diagrams due to tension
Figure 17 Failure of the specimen near the claw.
Figurespecimen at mid
properties of the specimens vary significantly for each test. These
differences are due to the variability of the thickness of the specimens. The relation
and the thickness of the specimens is constant
The structural behaviour of the GFRP tested is similar for both directions, and does not
process.
Summary of the properties of the faces under tension. Cv % εltu [µstrain] Cv % E [GPa]6.8 15 457±476 3.1 11.79±0.647.5 13 889±604 4.3 11.81±0.467.5 10 789±515 4.8 11.60±0.639.9 12 088±958 7.9 11.33±1.09n.c. 15 632 n.c. n.c. 15 303 n.c. n.c. 14 414 n.c. n.c. 16 673 n.c. 21.9 13649±2854 20.9 12.72±2.01
15000
3PP-U/T3PP-U/T
8/15
The thickness of the specimens is variable, due to the
mm, with 1 mm standard deviation.
specimens of the PP core panel; the diagram
, followed by a non-linear
Figure 18 Failure of the specimen at mid-span.
properties of the specimens vary significantly for each test. These
differences are due to the variability of the thickness of the specimens. The relation between the
is similar for both directions, and does not
[GPa]
Cv % 11.79±0.64 5.5 11.81±0.46 3.9 11.60±0.63 5.4 11.33±1.09 9.6
14.59 n.c. 17.35 n.c. 11.55 n.c. 13.88 n.c.
12.72±2.01 15.8
9/15
Figure 19 Relation between the elasticity modulus and the thickness of the specimen.
3.6 Dynamic analysis of the panels
Dynamic analysis of the panels under bending was performed, in order to analyze the vibration
frequency of the panels in bending for a simply supported configuration. The tests were performed on
panels with and without lateral ribs, for two types of cores and two distances between supports: 1.5 m
and 2.3 m. The test consisted of the application of a point load, with the bare hand, central and
eccentric (Figure 20). The accelerations on the panel was measured with two accelerometers, from
Bruel & Kjaer (model 4379) and Endveco. The signal was amplified using two Bruel & Kjaer amplifiers
(model 2635). The data was registered using one HBM data acquisition unit, model spider 8. The
measurements were performed at 400 measurements per second. Five tests of each type were
performed. Figure 21 shows the measurements performed on the PU core panel without lateral ribs,
for different spans. The relation between acceleration and time was analysed by the FFT (Fast
Fourrier Transform), which transforms the results of the accelerations over time in spectral density
over frequency. The analysis of the spectral density peak helps evaluating the frequency of the
vibration modes. The frequencies for the first vibration mode are presented in Table 6.
Figure 20 Dynamic analysis of the PP-U panel.
y = -1.5425x + 23.47R² = 0.7238
10
11
12
13
14
15
16
17
18
4.5 5.5 6.5 7.5 8.5
Ela
stic
ity m
odul
us [G
Pa]
Thickness of the specimen [mm]
10/15
Figure 21 Acceleration-time relation of the first test central hit of the PU-U panel, with 2.3 m (a) of span and 1.5 m (b) of span.
Table 6 Vibration frequency for the first mode for different tests. Central span Panel Vibration frequency for the 1 st mode [Hz]
2.3 m
PU-U 25.92±0.11 PU-R 32.56±0.17 PP-U 25.96±0.30 PP-R 31.26±0.44
1.5 m
PU-U 41.09±0.47 PU-R 57.06±0.80 PP-U 43.50±0.42 PP-R 59.30±0.41
4 Finite Element Modeling
Finite element models of the panels were developed in the ADINA 8.5 software. The models were
developed with solid finite elements (volume) with 27 nodes. The GFRP and PP were modelled as
anisotropic materials; the PU was modelled as isotropic material. The faces were modelled with
7.9 mm thickness, the core had 91.5 mm thickness and the lateral ribs had 6 mm of thickness. The
properties of the materials considered in the models are presented in Table 7.
Table 7 Properties of the materials considered in the FE model Material Densi ty[kg/m3] Ex, Ey [MPa] Ez [MPa] Gxy [MPa] Gxz;Gyz [MPa] νxy νxz ; νyz PU 70 B 16.42 E 16.42 M 6.5 E 6.5 B 0.3 B 0.3 B PP 80 B 5.89 E 117.85 M 0.65 E 13 B 0.3 B 0.3 B GFRPlâminas 1740.49 M 11284.25 M 5500 B 3500 B 3500 B 0.33 B 0.11 B GFRPreforços 1740.49 M 11284.25 M 5500 B 3500 B 3500 B 0.33 B 0.11 B
Static models with 4 point loading were considered (Figure 22), in accordance with the static tests
performed by Almeida [8]; the total load is 10 kN. The results obtained for the mid-span displacement
are, in all cases, higher than the results obtained experimentally. The deviation for the panels without
lateral ribs is around 10%. The model may, therefore, be used on the design of the building floor slabs.
For the panels with lateral ribs, the deviation is higher. However, the model may still be used, but the
results may lead to more expensive solutions than with a more precise model. The displacements
obtained with the analytical formula are higher than the displacements obtained with the FE model in
all cases.
-30
-20
-10
0
10
20
30
3 4 5 6 7 8
Acc
eler
atio
n [m
m/s
²]
Time [s]
A1 A2
-15
-10
-5
0
5
10
15
4 4.5 5 5.5 6
Acc
eler
atio
n [m
m/s
²]
Time [s]
A1 A2a) b)
11/15
Figure 22 Discretization of finite elements with applied static load
Table 8 Vertical displacements at mid-span, determined using the FE model, analytical formula and obtained experimentally, for the PU-U/R PP-U/R panels.
Mid-span displacement
Model Analytical Experimental
Panel [mm] Deviation
[%] Table 1
[mm] Deviation [%] Almeida [8] [mm]
PU-U 20.53 11.9 23.98 30.7 18.35 PP-U 15.24 7.6 17.27 22.0 14.16 PU-R 10.89 35.1 11.57 43.5 8.06 PP-R 10.66 25.9 11.51 35.9 8.47
Table 9 presents the vibration frequency of the 1st mode of vibration (Figure 23), obtained with the FE
model and the analytical formula presented previously. The model reproduces satisfactory the 1st
vibration mode of the panels, with and without lateral ribs, and for both span lengths.
Figure 23 1st vibration mode of the PU-R panel with span of 2.3 m (upper picture) and span of 1.5 m
(lower picture)
12/15
Table 9 Vibration frequency (in Hz) for the 1st mode of vibration measured experimentally, calculated for the FE model and calculated analytically for the panels with and without ribs, with 1.5 m and 2.3 m of span.
Span Source PU-U Deviation [%] PP-U Deviation [%]
2.3 m Experimental 25.92 - 25.96 -
Analytic 24.28 -6.3 28.89 11.3 Model 24.38 -5.9 28.94 11.5
1.5 m Experimental 41.09 - 43.50 -
Model 42.13 2.5 51.47 18.3
Span Source PU-R Deviation [%] PP-R Deviation [%]
2.3 m Experimental 32.56 - 31.26 -.
Analytic 30.47 -6.4 29.18 -6.7 Model 28.79 -11.6 27.95 -10.6
1.5 m Experimental 57.06 - 59.30 -
Model 51.97 -8.9 52.70 -11.1
5 Design of the solutions using sandwich panels
Two different sandwich panels were design: one for use on building floor slabs, with 4 m span, and
one for use on a footbridge deck, with a central span of 1.4 m and two lateral cantilevers with 0.3m.
The solutions were design following the action loads defined on the structural Eurocodes applicable
for each case. On the building floor slabs the following loading actions were considered: 2.5 kN/m2
[16] for the variable loads, considering the weight of the partition walls; 0.3 kN/m2 for the coatings
(accessory permanent load). The partial coefficients for the combinations in Ultimate Limit State (ULS)
are 1.35 for permanent loads and 1.5 for variable loads; for the Serviceability Limit State
combinations, the quasi-permanent combination (QPC) was used with partial coefficients of 0.3 and
1.0 for the variable and permanent loads, respectively [17]. For the footbridge deck solution an uniform
variable load of 5 kN/m2 [18] on the deck and a vertical load of 1 kN/m applied vertically and
horizontally in the lifeguard 1.1 m high were considered. The accessory permanent load was
considered as 0.1 kN/m2. The partial coefficients used for ULS combinations were the same as for
building floor slabs. On SLS, a coefficient of 0.4 was used for the variable loads in the frequent
combination (FC).
The thickness of the faces ranged from 3 mm and 15 mm for the floor slabs and between 3 mm and 7
mm for the footbridge deck. The thickness of the cores varies from 50 mm and 300 mm for the floor
slabs and between 20 mm and 95 mm for the footbridge decks.
The characteristic stresses were calculated from the results of the tests using a normal distribution,
with 95% probability of no exceedance. A partial coefficient of 1.25 was used for verifying the
resistance of the core and the local buckling of the faces in ULS [3]. A partial coefficient of 1.5 was
used in the verification of the ULS on the GFRP [20]. The resistance in SLS was verified considering
the maximum stresses and displacement for each load combination (QPC and FC). The maximum
axial and shear stresses were considered as a percentage of the stress in ULS: 50% for the
fundamental combination and 30% for the quasi-permanent load combination (Table 10 and 11).
13/15
Table 10 Maximum shear strength (in MPa) in the PU face for each combination.
Combination Polyurethane ULS 0.12
SLSQPC 0.04 SLSFC 0.06
Table 11 Maximum axial and shear stresses (in MPa) on the GFRP.
Axial Shear ULS yelding 58.68 16.67 ULS buckling 58.05 n.c. SLSQPC 17.61 5.00 SLSFC 29.34 8.33
The maximum displacement at mid-span was limited at span/250 and span/100 for the solutions for
the building floor slabs and for the footbridge deck, respectively. The long-term displacement of the
floor slab was calculated using a global creep coefficient of 3.9, determined experimentally by Garrido
et al. [21]; for the panels without lateral ribs reductions of 66% and 209% [20] of the elasticity modulus
and distortion modulus of the GFRP were considered, respectively. An average cost of 5400 €/m3 and
620 €/m3 was considered for the GFRP and PU, respectively.
The design of the solutions is conditioned by the long-term displacement for the building floor slabs
and by the shear stress, in the core or in the lateral ribs for the panels with and without lateral ribs,
respectively, for the footbridge decks (Figure 24).
Figure 24 Design for different thickness of the faces, in m: a) long-term displacement for panels without lateral ribs for use in building floor slabs; b) shear stress on the core for panels without lateral ribs for use in footbridge
decks.
The cheapest and lightest solution is, in both cases, the solution with lateral ribs with 3 mm of
thickness (Tables 14 and 15)
Tabela 12 Optimized solutions for building floor slabs (dimensions in [mm]). Thickness of the
ribs Total
thickness Thickness of the
faces Thickness of the
cores Cost [€/m²]
Weight [kg]
0 242 6 230 207.40 € 73.97 3 166 3 160 136.78 € 44.96
Tabela 13 Optimized solutions for the footbridge decks (dimensions in [mm]). Thickness of the ribs Thickness of the faces Thickness of the core Price [€/m²] Weight [kg]
0 3 55 66.50 € 14.29 3 3 35 56.37 € 13.26
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
δM
AX/δ
QP
C
Core's thickness [m]
0.003 0.006 0.0090.012 0.015
0
0.5
1
1.5
2
0 0.02 0.04 0.06 0.08 0.1
τ RD
,ULS
/τS
D,U
LS
Core's thickness[m]
0.003 0.004 0.0050.006 0.007a) b)
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6 Conclusions
The composite sandwich panels with GFRP faces and PU and PP cores present properties that
enable their application in structural elements for Civil Engineering.
The PP core presents higher resistance and stiffness than the PU core, which makes it a good
solution as a core in the sandwich panel. The GFRP faces produced by the hand lay-up process
exhibit similar properties, independently of the direction of testing and the modelling of the faces (on
table or over the core).
The panels with lateral ribs present higher stiffness and resistance, which makes them economic
solutions that verify the mechanical requirements. The finite element models and the analytical
formulas proved to describe adequately the behaviour observed experimentally.
7 References
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[13] ASTM C297/C 297-04 ; Standard test method for flatwise tensile strength of sandwich
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