Structural behaviour of composite sandwich panels

for applications in the construction industry

Maria Inês Avó de Almeida

M.Sc. Thesis Extended Abstract

October 2009

1

Structural behaviour of composite sandwich panels

for applications in the construction industry

1 Introduction

The recent need for structures with low self-weight, high stiffness and durability has increased the demand for

composite materials, from which sandwich structures are an example [1]. And, in fact, the use of composite

materials in general and glass fiber reinforced polymers (GFRP) in particular has increased significantly in the

past few years due to their low self-weight, high strength, good insulation properties and improved durability

even in harsh environments. However, due to the low Young’s modulus their design is often influenced by

instability phenomena and deformability. In addition, in alkaline environments and when submitted to high

temperatures, an appropriate special design is required [2].

Sandwich panels are applied in situations that require high mechanical strength and low weight and, in

addition, when adequate levels of sound and thermal insulation are needed. Sandwich panels are composite

materials with a three layer structure: two thin, stiff and resistant composite material skins (such as GFRP),

separated by a layer of a low density material that can be much less stiff, resistant and durable than the skins

[3]. The proper combination of different core and skin materials allows merging the most advantageous

properties of each constituent material, and even eliminating some of their negative properties. The

combination of GFRP skins with appropriate cores allows obtaining high stiffness-to-weight and strength-to-

weight ratios.

The durability of GFRP skins allows increasing the service life of built structures with relatively lower life cycle

costs and fewer load restrictions [4]. The development of new production techniques has made sandwich

panels affordable and their pre-fabrication allows an easier mounting, with greatly reduced construction times.

When protected by the skins, the core material may confer excellent thermal insulation properties [5], good

stress dissipative characteristics and energy absorption [6]. However, the low resistance to high temperatures,

the potential excessive deflections for relatively high loads, the poor acoustic insulation (comparing to

structural solutions with higher mass, such as concrete and masonry), a wide variety of failure modes and,

above all, the lack of information for engineers and designers, make the acceptance of sandwich panels by the

construction industry more difficult [7].

Marine and aerospace industries had an important role in the development of composite materials and were

responsible for the first applications of sandwich panels. Subsequently, their field of application was extended

to the automobile and shipbuilding industries and, more recently, to the transportation industry [8], to

geotextil infrastructures, to the stabilization and drainage of soils [4], to offshore oil structures [9], to the wind

industry and sports [7]. In construction, sandwich panels have been applied as structural elements in vehicular

bridges, in footbridges, in the rehabilitation or replacement of concrete bridges, in cladding, roofing and also as

partition wall elements [8], sometimes with translucent properties [10].

In order to improve the performance of sandwich panels with standard geometry, different types of

reinforcements have been studied. Stitches have been one of the most studied ones. Potluri et al. [11]

concluded that the mechanical properties of the skins, including their strength, stiffness and fatigue behaviour

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can vary according to the type of composite material and sewing technique. Lascoup et al. [12] studied the

effect of introducing stitches crossing the two skins and the core and concluded that stitching increases

significantly the stiffness and the ultimate strength, in terms of bending, shear in the core and flatwise

compression. Hassan and Reis [1] studied the effect of introducing fiber elements with a three-dimensional

architecture that join the GFRP skins and the foam core and concluded that this strengthening technique

increases the stiffness of the sandwich panel and that the uncracked foam used as a filling material confines

the fibers and contributes to increase significantly the core shear modulus. Sharaf and Fam [13] studied

different configurations of ribs and their influence on the mechanical properties of panels made of GFRP skins

and polyurethane foam core. They concluded that the ribs significantly increase the strength and stiffness of

the panel.

In this paper the possible use of GFRP sandwich panels as structural elements in construction is investigated. In

particular, their possible use in floors of buildings or decks of pedestrian bridges is envisaged. An experimental

campaign was performed in order to study two types of composite sandwich panels with GFRP skins and a core

made of either (i) rigid polyurethane foam or (ii) honeycomb polypropylene core material. In addition to the

evaluation of the effect of the core material on the service and ultimate behaviour of the GFRP sandwich

panels, the objective of this research project was to investigate the effect of adding GFRP reinforcements to

the longitudinal lateral edges of these two types of panels. Dynamic tests were also performed to determine

and compare the dynamic behaviour of these panels. The study was complemented by the numerical modelling

of rigid polyurethane foam core sandwich panels. The objective was to develop simple numerical models

capable of simulating the mechanical behaviour of sandwich panels at service and ultimate limit states,

calibrated with the experimental results, therefore avoiding the need to carry out further experimental tests on

different geometries.

2 Analytical study of sandwich panels behaviour

In order to predict the service and ultimate behaviour of sandwich panels, a survey of analytical equations that

describe their behaviour was first undertaken. The behaviour of a panel or a sandwich beam can be compared

to an I beam, where the skins act as flanges, supporting the tensile and compressive axial stresses, and the core

functions as the web of the profile, setting the distance between the skins and resisting to shear stresses. The

skins are connected to the core by means of an adhesive material that transfers the stresses between the two

elements. The maximum deflections of sandwich panels are an important design criterion for the service limit

state. The vertical displacement of a sandwich panel is the sum of two parts: (i) the bending deflection and

(ii) the shear deflection. The maximum deflection at mid-span of a sandwich panel (w) subjected to a

concentrated load (P) or a uniformly distributed load (p) along the span (L) may be estimated by equations (2.1)

and (2.2), respectively, where b is the width, ec is the core thickness, eL is the skin thickness, D is the flexural

stiffness and Gc is the core shear modulus. The values of the constants Kg and Ks are presented in table 2.1 for

different supporting and loading conditions [13]. Certain materials, such as some foams and GFRP skins,

present a considerable creep, which should be considered in service limit states design.

3

cGLeceb

PLsK

D

PLgKw

)(

3

(2.1)

cGLeceb

pLsK

D

pLgKw

)(

24

(2.2)

Table 2.1 Values of Kg e Ks for different supporting and loading conditions (adapted from [15]).

Support conditions and load type Kg Ks Support conditions and load type Kg Ks

1/48 1/4

1/8 1/2

1/192 1/4

5/384 1/8

1/3 1

1/384 1/8

A sandwich panel has several different failure modes, which may condition its load-bearing capacity. Such load-

bearing capacity depends on the sandwich materials, the panel dimensions and the structural geometry itself.

Table 2.2 presents the most common failure modes and their corresponding design equations.

Table 2.2 Most frequent failure modes of sandwich panels and corresponding design equations.

Tensile failure of the skins [16] uLbL

eu

P ,2

Co

mp

ress

ive

stre

ss

Buckling failure [16]

dbcG

DL

D

bP2

2

2

Shear crimping failure [16] bcGcecbP ,

Intra-cellular buckling failure [17]

2

)2

1(

2

.,

s

Le

L

LE

celcr

Wrinkling failure [16] 31

50.0, LECGCEwcr

Core shear failure [9] Cvbdu

V

Crushing failure of the skins and the core [9] Cc

sL

uF

d - distance between center-lines of opposite skins; s - cellular core dimension; Ec - core Young’s moduli; EL - skin Young’s moduli;

νL- skin Poisson’s ratio;

Vu - ultimate shear force Pu - ultimate tensile force; Pb - ultimate compressive force (buckling); Pb,c - ultimate compressive force (shear crimping);

σL,u - skin tensile strength; σcr,cel. - intra-cellular buckling compressive strength; σcr,w - wrinkling compressive strength; σCc - compressive strength; τCv - shear strength.

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3 Experimental investigations

3.1 Experimental programme

The objective of the experimental programme was to study and to compare the behaviour of four composite

sandwich panels: (i) two standard sandwich panels with GFRP skins, and different core materials - one of them

with polyurethane (PU) rigid plastic foam core and the other one with polypropylene (PP) honeycomb core

(designated by PU-U and PP-U, respectively); and (ii) two sandwich panels with GFRP skins, comprising GFRP

ribs on the longitudinal edges, each one with the referred core materials (designated by PU-R and PP-R,

respectively). The sandwich panels were produced with the hand lay-up technique (figure 3.1) by the

Portuguese company ALTO, Perfis Pultrudidos, Lda. The GFRP skins were made of three different types of mats

(bride veil mats, chopped strand mats and woven fabric mats), embedded in a polymer matrix of polyester

resin. The lateral reinforcements (ribs) were made by folding the skin mats (the upper one) through the border

of the other skin (the lower one).

Figure 3.1 Hand lay-up technique.

The experimental programme included different types of mechanical tests. Initially, the material of the

sandwich panels was characterized by means of (i) flatwise tensile tests of the GFRP laminates and (ii) edgewise

and (iii) flatwise compressive tests of GFRP sandwich specimens (figure 3.2). Subsequently, the structural

behaviour and some of the most relevant mechanical properties of the sandwich panels, such as their elastic

constants and strength, were evaluated by means of full-scale flexural tests, that included static tests to

determine the service and ultimate behaviour and dynamic tests to investigate the dynamic behaviour.

Figure 3.2 Flatwise tensile test of a GFRP skin (left) and flatwise (centre) and edgewise (right) compressive tests of sandwich specimens.

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3.2 Tests on sandwich panels coupons

3.2.1 Flatwise tensile tests of GFRP laminates

A total of 6 GFRP laminates identical to those used in the skins of the panels were tested with the following

nominal dimensions: height of 300 mm, width of 25 mm, thickness of 6 mm and distance between grips of

150 mm. The tensile force was applied in the laminate longitudinal axis with an Instron universal hydraulic

testing machine (with a load capacity of 250 kN). Load was applied at a speed of 0.18 mm/s with a grip

pressure of 40 bar. The load and displacement of the machine during the tests were registered on a PC using a

HBM data acquisition system with 8 channels, model Spider8. The axial strains were measured in the

longitudinal direction of 3 specimens with TML electrical strain gauges. The GFRP laminates showed a linear

elastic behaviour until failure and a Young's modulus (EGFRP) of 20.5 GPa was measured. A brittle tensile failure

occurred for a maximum average load (Fmax) of 32.6 kN. The average values of the tensile strength (u) and

strain at failure (u) were also experimentally determined (see table 3.1).

Table 3.1 Properties of GFRP laminates.

Test Material Fmax [kN] u [MPa] u [µstrain] EGFRP [GPa]

Flatwise tensile (ISO 527-1,4) [18, 19]

GFRP 32.60 ± 1.98 202.39 ± 15.35 1128 ± 84 20.47 ± 0.916

3.2.2 Flatwise compressive tests

In these tests the flatwise compressive behaviour of the different core materials was evaluated. The tests were

performed on sandwich specimens (6 for the PP core and 5 for the PU core) with 5 mm thick GFRP skins and

90 mm thick core materials, and with a square cross section of 100 × 100 mm2. To ensure a uniform transfer of

loads from the testing machine to the specimen surfaces, a layer of polyester resin was applied in the skins in

order to level out their surface, thereby guaranteeing that the specimen surface was fully in contact with the

plate of the testing machine. The load was applied with the same machine used in tensile tests and the values

of the load and machine displacement were registered on a PC using a HBM data acquisition unit of 8 channels,

model Spider8. Specimens made of both core materials showed an approximately linear initial behaviour up to

the maximum load (Fmax), whose average value was 24.1 kN for the PP honeycomb and 3.01 kN for the rigid PU

foam. After the occurrence of a load reduction (which was less pronounced in the rigid polyurethane foam

specimens), the load-deflection curves of both materials showed a plateau with an increase of the

displacement values for approximately constant loads of about 10-12 kN and 2.75 kN for the PP and PU foam

cores, respectively. High residual deflections were observed after unloading (see figure 3.3). Average

compressive strengths (u) and stiffnesses (K) were estimated, together with the apparent Young’s modulus

(Eapparent) of both materials, which were estimated based on the assumption that the GFRP skins did not deform

(table 3.2). The results obtained allowed concluding that in the flatwise direction the PP honeycombs were

stiffer than the PU foam - the Young’s modulus of the PP honeycomb core (52.9 MPa) were significantly higher

than that of the PU foam core (5.6 MPa) - and, at the same time, they were considerably stronger (2.40 MPa vs.

0.29 MPa).

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Figure 3.3 Load-displacement curve for (i) PP honeycomb core (left) and (ii) PU foam core (right) specimens.

Table 3.2 Flatwise and edgewise compressive properties of PP honeycomb core and PU foam core sandwich specimens.

Test Material Fmax [kN] u [MPa] E [MPa] K [kN/mm]

Flatwise compressive (ASTM C365-03) [20]

PP 24.09 ± 1.41 2.40 ± 0.16 52.90 ± 5.21 10.43 ± 1.54

PU 3.01 ± 0.06 0.29 ± 0.01 5.60 ± 0.45 1.02 ± 0.10

Edgewise compressive (ASTM C364-99) [21]

PP 212.90 ± 28.70 3.31 ± 0.43 - 65.49 ± 10.76

PU 122.28 ± 19.56 2.01 ± 0.29 - 67.95 ± 9.62

3.2.3 Edgewise compressive tests

The egdewise compressive tests allowed evaluating the in-plane behaviour of the sandwich panels specimens.

The specimens used in these tests (6 for each type of core) had a thickness of 101 mm and presented a square

section of 250 × 250 mm2. The surfaces of the specimens in contact with the plates of the testing machine were

also levelled. For the PP specimens, this was accomplished by adding a layer of polyester resin as the surface of

this core is discontinuous due to the geometry of the honeycombs. In about half of the tests (specimens

Ct.PU5, Ct.PU6, Ct.PP4, Ct.PP5 and Ct.PP6) two transducers were placed on each side of the specimens to

measure the horizontal displacements at their centre. The same hydraulic machine used in the tensile tests was

used to apply the load. Both types of specimens showed a non-linear initial behaviour most likely due to the

loading system, namely due to the adjustment of the plates to the specimen. The load increased up to a value

of about 110 kN and, approximately for this load, the load-vertical displacement curves exhibited a small

section with increased displacements for an approximately constant load. After this small section, the load

increased again until failure (see figure 3.4). The average ultimate strength (Fmax) of the PP honeycomb core

specimens (212.9 kN) was approximately twice of that of the PU foam core specimens (122.3 kN) (table 3.2).

Failure of PP honeycomb core specimens occurred (i) by buckling instability of the skins, sometimes followed by

delamination, and (ii) by crushing of the skins near the hydraulic machine’s plates. Failure of PU foam core

specimens occurred (i) by buckling instability of the skins, followed by delamination, or (ii) by shear failure of

the PU foam and/or by crushing of the skins next to the metal plates of the testing machine. The higher

flexibility in the out-of-plane direction of the PU foam (compared to that of the PP honeycombs) allowed it to

follow the skins deformation. The axial stiffness of the two types of sandwich panels is similar as it depends

essentially on the skins. Based on simple calculations, it was concluded that the axial stiffness of the tested

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panels is considerably lower than the axial stiffness of current concrete or timber floors - this is a disadvantage

when the use of sandwich panels in building floors is planned and it may be necessary to adopt thicker skins. In

this case, a similar stiffness to that of timber floors may be obtained by doubling the skins thickness.

Figure 3.4 Load-displacement curves for (i) PP honeycomb core (left) and (ii) PU foam core (right) specimens.

3.2.4 Flexural test of a PP honeycomb core panel

To determine the bending and shear stiffness of the PP honeycomb core, a panel of this material was tested

(without skins) according to ASTM C393-00 standard [22] with the following dimensions: length of 2.50 m,

width of 0.50 m and thickness of 0.09 m. The mid-span point load was applied by successively placing metal

plates, within 1 minute intervals. A TML displacement transducer, model CDP100, with a stroke of 100 mm and

a precision of 0.01 mm, was used to measure deflections at mid-span. The elastic constants were tentatively

estimated by performing a linear regression analysis of the slope values obtained from the load-deflection

curves (δ/PL) concerning panels with different lengths: (i) 1.5 m, (ii) 2.0 m and (iii) 2.4 m. The slope corresponds

to 1/48D and the intercept to 1/4U. This method is only valid for linear elastic behaviour materials and, in this

case, for all spans and load levels, a significant creep was observed. Therefore, it was not possible to estimate

the apparent elastic constants of the core material with this technique.

3.3 Full-scale static flexural tests on sandwich panels

Two types of static flexural tests were performed: tests for the characterization of (i) service and (ii) ultimate

behaviour. In the first type of tests the panels were loaded in a 3 point bending configuration up to a 10 mm

displacement at mid-span. In the second type of tests the panels were loaded in a 4 point bending scheme up

to failure (figure 3.5). The panels, with a length of 2.50 m, a width of 0.50 m and a thickness of 0.10 m (5 mm

skins and 90 mm core) were tested according to ASTM C393 [22] in a 2.3 m span supported by cylindrical

bearings contacting with the lower surface of the panels in an area of 0.06 × 0.5 m2. Load was applied with an

Enerpac hydraulic jack (with a load capacity of 300 kN) and measured with a Novatech load cell (with a load

capacity of 200 kN), placed between the jack and the sandwich panels. In order to guarantee a uniform load

distribution along the width of the panel, in the 3 point bending tests, a metallic tubular spreader plate (with a

0.04 m × 0.08 m section) was placed between the sandwich panel and the hydraulic jack; in the 4 point bending

tests, the loads were applied at a distance of 0.38 m from the mid-span section - two spreader beam plates

(with a width of 0.10 m) were used and a metallic beam was interposed between the hydraulic jack and the

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spreader plates. Three TML, APEK and M = M electrical transducers with a stroke of 100 mm were placed under

the panel at mid-span and at a distance of 0.38 m from the mid-span section, coinciding with the two load

application points in the 4 point bending tests. For the failure tests, 4 strain gauges were placed in the mid-

span section, at a distance of 7.5 cm from the center of the width of the panel, in order to measure the

longitudinal strains in this section.

3.3.1 Tests for the characterization of the sandwich panels service behaviour

Three loading-unloading tests were performed in order to allow characterizing the mechanical behaviour of the

sandwich panels. In the second and third tests, the maximum load was applied for 10 minutes before

unloading. All panels showed a linear elastic behaviour for displacements up to about 10 mm, with the residual

displacements after unloading being lower than 1 mm. The bending and shear stiffness parameters and the

apparent elastic constants of the sandwich panels were determined using the equations that allow obtaining

the mid-span displacement in 3 point and 4 point bending. Knowing the values of the span, the applied load

and the corresponding displacement, the bending, D, and shear, U, stiffness values were determined. Based on

the equations presented in standard C393 [22], the apparent Young’s modulus of the skins, EGFRP, and the

apparent core shear modulus, Gc, were also estimated. The results obtained using this method were not always

congruent, particularly in what concerns the determination of the bending stiffness. Therefore, it was

concluded that somehow the method was not suitable to estimate the elastic constants of sandwich panels –

this issue should be addressed in future investigations.

3.3.2 Tests for the characterization of the sandwich panels ultimate behavior

Before applying the load up to failure, two loading-unloading tests were conducted up to a 10 mm

displacement at mid-span in order to guarantee the necessary adjustment of the test system. The ultimate load

(Fu) was significantly higher in the reinforced sandwich panels than in the panels without reinforcements (with

an increase of 158% and 171% in the panels with PP and PU cores, respectively). All panels presented a linear

behaviour up to failure, with a slight loss of stiffness occurring for loads close to the collapse load (figure 3.6).

The PP-U panel was slightly stiffer (Kp) than the PU-U panel (about 24%), which is in accordance with the

compressive tests that revealed the PP honeycombs to be stiffer than the PU foam. The stiffness of the

reinforced panels was very similar for the two different core materials and significantly higher than that of the

unreinforced panels – this can be easily perceived by the higher slope of the load-deflection curves. This higher

stiffness is provided by the lateral GFRP ribs.

Figure 3.5 4 point bending test setup.

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The failure of PP-U panel occurred due to shear of the core material in a vertical surface of the honeycomb

cells, at about 60 cm from the left extremity of the panel. Delamination between the skins and the core also

occurred but it did not reach the support section of the panel. The failure of PU-U panel occurred also due to

shear of the PU foam, with a 45° angle failure surface at a distance of about 20 cm from the left extremity of

the panel. Delamination between the bottom skin and the core occurred up to the left extremity of the panel.

In the PP-R panel, the compressive force on the upper skin led to a local separation from the core material in

the mid-span section, forming a kind of bubble, and failure occurred by crushing/delamination on the top of

the bubble. The cracks spread through the side ribs, reaching its lower part but without reaching the bottom

skin. The failure of the PU-R panel was similar to that of the PP-R panel, also occurring in the area between the

application of the load but in a section near the left load application point. Unlike the panel PP-R, the cracks

spread through the side ribs and reached one side of the bottom skin.

Figure 3.6 Load-mid-span deflection curves of sandwich panels (left) and failure modes (right) in ultimate behaviour tests.

The load-strain curves of the unreinforced panels presented a linear evolution and the positive (ut) and

negative (uc) strains were similar, in absolute value. The reinforced panels showed a non-linear progress,

influenced by the bubble in the mid-span section which may have caused errors in the readings of the strain

gauges. In fact, in the panels without ribs, the neutral axis was exactly at mid-height of the cross section and

the increase of the strains was directly proportional to the bending moment increase. The PU-R panel axial

strain-section height curves show a significant increase of negative strains on the upper skin. The delamination

caused by the bubble led to a loss in stiffness in the failure section and therefore to an increase of the neutral

axis depth. The readings of the gauges in the PP-R panel were not valid – here, the strains data may contain

some errors due to the possibility of a deficient bonding of the gauges because of the skin surface excessive

irregularity/roughness.

Although no equations are available for the shear stresses of reinforced panels, it is reasonable to note that the

stresses at the core of the reinforced panels shall be lower than those of the unreinforced panels because most

of these stresses are taken by the ribs. Thus, shear stresses shall be approximately uniform across the width of

the core in unreinforced panels and they are expected to vary in reinforced panels (this was confirmed in the

numerical investigations). The properties in failure of each panel are presented on table 3.3.

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Table 3.3 Properties of PP-U, PU-U, PP-R and PU-R sandwich panels.

Fu

[kN] δmax

[mm] Kp

1

[kN/mm] σmax

2

[MPa] τmax

3

[MPa] εu,c

[µstrain] εu,t

[µstrain] Ec

4

[GPa] Et

5

[GPa]

PP-U 28.26 51.57 0.665 43.58 0.30 -2015 2007 21.77 21.81

PU-U 31.74 72.54 0.536 48.94 0.33 -2751 2565 18.06 19.33

PP-R 72.83 72.30 1.084 78.09 - - 3498 - -

PU-R 86.13 89.16 1.246 85.81 - -2509 4572 - -

3.4 Full-scale dynamic flexural static tests on sandwich panels

In these tests centered and eccentric strikes were manually applied approximately at mid-span section of the

panels and their corresponding vertical vibration was measured with two accelerometers, A1 and A2,

symmetrically positioned at midspan at a distance of 5 cm from the lateral border of the panel. The

accelerometers (one from Bruel & Kjaer, model 4379, and the another one, equivalent, from Endevco), with a

precision of 0.01 mm, were connected to amplifiers (also Bruel & Kjaer, model 2635). The signal readings were

performed at a rate of 400 scans per second. The recording of the measuring apparatus was performed in PC

through an acquisition unit with 8 channels from HBM, model Spider8. In these tests, steel weights were placed

over the top skin of the panels in the support area to prevent them from lifting during the application of the strikes.

Although the strikes may have not been applied exactly with the same intensity in the different tests, maximum

values of vertical vibrations showed that the displacements in the unreinforced panels were higher than those

of the reinforced panels. Fast Fourier Transform (FFT) analysis allowed determining the natural frequencies and

their spectral values (see table 3.4). The highest spectral values corresponded to frequencies of about 1.0 to

1.5 Hz. However, they may not correspond to any natural vibration mode of the panels and may be influenced

by any other element of the testing system. For this reason, the scale of spectral values was reduced in order to

obtain the frequencies corresponding to the vibration modes of each panel. The introduction of lateral ribs

increased the flexural frequency and reduced the torsion frequency. Thus, the increase in torsional stiffness

was not sufficient to offset the extra weight of the panel6.

Table 3.4 Flexural and torsional frequencies of the sandwich panels.

Panel type Flexural frequencies [Hz] Torsional frequencies [Hz]

PP-U 1.07 (from 1.07 to 1.17);

29.84 (from 29.79 to 29.88)

0.98 (from 0.88 to 1.07); 14.16

PU-U 1.11 (from 0.88 to 1.27);

24.37 (from 23.93 to 25.39)

1.07 (from 0.93 to 1.27);

13.26 (from 12.99 to 13.38)

PP-R 1.09 (from0.98 to 1.47);

31.54 (from 30.76 to 33.30)

0.88 (from 0.78 to 0.98);

13.20 (from 13.09 to 13.28)

PU-R 11.46 (from 1.95 to 30.18);

31.18 (between 30.18 to 32.71)

1.03 (from 0.88 to 1.17);

12.68 (between 12.40 to 13.09)

1 Stiffness of the panel: determined by the slope of loads and respective displacements. 2 Maximum axial stress: determined by the quotient between the maximum bending moment and the flexural moduli. 3 Maximum shear stress: determined by beam theory (τ=V/bd). 4 Compressive Young’s modulus: determined by the slope of skin compressive tension and respective skin strains. 5 Tensile Young’s modulus: determined by the slope of skin tensile tension and respective skin strains. 6 Concerning the numerical results, as for the flexural frequencies between 1.0 and 1.5 Hz, it is believed that this value may not correspond the first vibration torsional mode being associated to another element of the experimental system.

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4 Numerical investigations

4.1 Description of the finite element models

The three-dimensional finite element models were developed with the commercial software SAP2000 (version

11.07). Due to the higher difficulty in modeling the PP honeycombs (because of both their geometry and

anisotropic behavior) and due to time constraints, only the PU foam core sandwich panels (PU-U and PU-R)

were modeled. In order to reproduce as faithfully as possible the conditions of the experimental tests, the

panels were modeled with the same dimensions of the sandwich panels used in the flexural tests. The skins

were modeled with thin shell finite elements (thickness of 6 mm), the core material with solid finite elements

(4 layers with a thickness of 22.5 mm) and the lateral ribs of the PU-R panel with thin shell finite elements with

the same thickness of the top and bottom skins. The panels supports were modeled with solid finite elements

with the same width and thickness of the metallic plates of the cylindrical bearings in contact with the bottom

skin of the panels and the support restraints were set by the central nodes of the lower surface of those plates.

One support (the left one) was fixed and the other (the right one) also allowed to slide. The total load was

applied with uniform loads on the upper surface area corresponding to the metal plates used in the

experimental tests. For the dynamic analyses, masses were applied in the upper skin nodes at each support

area (4.55 × 10-5

kg per node) – these masses correspond to the weight of the metal plates placed on the

supports to prevent the lifting of the panels. All materials were modeled assuming linear-elastic behaviour

(table 4.1). In the reinforced panel, only the numerical model and experimental values were compared due to

the absence of equations describing the reinforced panels behaviour.

Table 4.1 Properties of modeled materials.

Material Density [kg/m3] Ex; Ey [kN/m

2] Ez [kN/m

2] Gxy; Gxz; Gyz [kN/m

2] νxy νxz = νyz

GFRP 1582 20 × 106 7.5 × 10

6* 3.5 × 10

6* 0.3* 0.1*

PU 69.67 16900 16900 6500 0.3 0.3

*[15]

4.2 Service behaviour

The panels were loaded with a 100 kN/m2 uniformly distributed load, equivalent to a total load of 10 kN, which

falls into the linear section of the load-displacement curve of the panels (see figure 3.6).

The calculated displacements at mid-span of both PU-U and PU-R panels were similar to those obtained

experimentally - the stiffness obtained with the numerical models of both panels (and also that of the

theoretical model stiffness, in PU-U panel) was slightly lower than the experimentally measured stiffness. The

error in the PU-U panel was about 15.5%, and in the PU-R panel it was about 26.2%, which is considered to be

acceptable taking into account the uncertainty on some materials properties, especially the rigid PU foam, and

the thickness of the skins and ribs (which, according to the experimental measurements, presented some

variability). In the PU-U panel, an increase of the Young’s modulus of the PU foam led to a better agreement

between the numerical model and the experimental values of mid-span displacement; the effect of varying the

GFRP skins Young’s modulus on such displacement was significantly lower. In the PU-R panel, the variation of

the Young’s modulus of the PU foam had a little effect, which shows that in those reinforced panels the

deformability is mainly driven by the ribs. The variation of the GFRP skins Young’s modulus reveals an

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important effect on the behaviour of the panel - the variation in the mid-span displacement of panel PU-R was

about twice of that of panel PU-U, as in the former panel such variation affects both the skins and the ribs. The

variation of the shear modulus of the GFRP in the reinforced panel (PU-R) had some effect on the deformability

of the panel (although reduced), in opposition to the PU-U panel, where no influence was perceived (as

expected7). This shows that the lateral ribs contribute considerably to the stiffness of the panel and have an

important role in the serviceability behaviour of the panel. The variation of the thickness of the skins (and the

ribs, in the PU-R panel) has a significant influence in the mid-span displacement. Thus, the uncertainty of such

thickness in the tested panels may be one of the causes for the difference between experimental results and

numerical and theoretical (analytical) calculations.

In the PU-U panel, both calculated tensile (lower skin) and compressive (upper skin) strains8 were relatively

close to the experimental results - the numerical values were lower in absolute value, with errors of 7.7% and

11.1% concerning the negative and positive strains, respectively. The theoretical values were the highest, in

absolute value, with errors of 4.1% and 14.6% concerning the negative and positive strains, respectively. In the

PU-R panel, the numerical strains deviated significantly from those obtained experimentally, which may be due

to the already referred deficient bonding of the gauges on the test that certainly influenced the experimental

readings.

4.3 Ultimate behaviour

The theoretical and numerical stiffness of the PU-U panel were very similar but, as already mentioned, were

both lower than the experimental one for load levels corresponding to the linear-elastic behaviour. Regarding

the mid-span deflection at failure, the difference between numerical and experimental values was only about

6%. This reduction in the difference between calculated and measured deflections is mainly due to the fact that

the PU-U panel had a non-linear behaviour for load values higher than about 20 kN, with a significant increase

in deformability – therefore, measured deflections prior to failure tended to approach the corresponding

numerical values.

In the PU-R panel, the numerical load-deflection curve is below the experimental one in the path

corresponding to the linear behaviour and the deflection corresponding to the experimental failure load is

about 10% higher than the numerical deflection value. In what concerns maximum displacements, the model

reproduces with acceptable accuracy the behaviour in the vicinity of failure. In general, the model reasonably

reproduces the behaviour of the reinforced panel, although it provides higher displacements than those

observed in the experiments.

In the numerical model, the shear stresses on the core of the PU-R panel are approximately uniform along the

height but vary across the width, presenting lower values near the edges (figure 4.1). In fact, the lateral ribs

absorb a significant portion of shear force and, in the PU-U panel, the numerical shear stress determined for

7 Note that the skins were modeled with thin shell finite element-type and, thus, could not present any shear

deformation.

8 Determined by the quotient between the numerical stress value of each skin and the skin Young’s modulus.

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the ultimate load was twice the stress in the PU-R panel, which justifies the non-occurrence of core shear

failure in the reinforced panel.

Figure 4.1 Shear stresses in the PU-U (on the left) and PU-R (on the right) sandwich panels.

4.4 Dynamic behavior

The calculated flexural frequencies are similar to those obtained in the experimental tests with a very low error

of 0.5% in the PU-U panel, and an acceptable error of 17.4% in the PU-R panel (table 4.2). It was not possible to

compare the torsional frequencies because these were not detected in the experimental tests.

Table 4.2 Vibration modes and respective flexural and torsional frequencies.

Vibration mode Flexural mode [Hz] Torsional mode [Hz]

PU-U Numerical 24.20 52.60

Experimental 24.07 (not detected)

PU-R Numerical 35.50 102.56

Experimental 30.18 (not detected)

5 Conclusions

This paper has demonstrated that composite sandwich panels using either PU foam core or PP honeycomb core

between two GFRP skins have a great potential for structural applications, with a considerable strength and

stiffness, particularly when reinforced with lateral GFRP ribs. The following main conclusions can be addressed

based on the analytical, experimental and numerical investigations:

1. Sandwich panels tested in bending showed a linear-elastic behaviour with a slight loss of stiffness for

load levels relatively close to the collapse load;

2. Unreinforced sandwich panels with PP honeycomb core are stiffer than those made with PU foam core;

3. The mid-span deflections of sandwich panels submitted to bending can be estimated with simple

equations that have to take into account the shear contribution to overall deformability;

4. The ultimate strength of unreinforced sandwich panels was governed by the shear strength of the core

material; in opposition, the ultimate strength of the reinforced sandwich panels was governed by the

instability of the top skins under compressive forces;

5. The adding of longitudinal ribs had an important effect on the behaviour of the panel: (i) the stiffness

increased significantly and therefore caused mid-span deflections to decrease; (ii) the ultimate

strength increased considerably, with the ribs absorbing a great part of the shear stresses, originally

taken by the core; (iii) the vibration frequencies were modified;

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6. The numerical models developed, which were calibrated with the experimental results, in general, are

able to simulate the static and dynamic mechanical behaviour of the PU sandwich panels, for both

service and failure conditions.

6 References

[1] Hassan, T., Reis, E., and Rizkalla, S., Innovative 3-D FRP Sandwich Panels for Bridge Decks, Proceedings of the Fifth Alexandria International Conference on Structural and Geotechnical Engineering, Alexandria, Egypt, December 20-22, 2003, CD-ROM.

[2] Correia, J.R., Branco, F.A., Ferreira, J., GFRP - concrete hybrid cross-sections for floors of buildings, Elsevier - Engineering Structures, 2008, Vol. 31, No. 6, 1331-1343.

[3] Allen, H.G., Analysis and design of structural sandwich panels, Pergamon Press, Oxford, 1969, 283 p.

[4] Alampalli, S., Field performance of an FRP slab bridge, Elsevier - Composite Structures, 2005, Vol. 72, No. 4, 494-502.

[5] Hause, T.J., Thermomechanical Postbuckling of Geometrically Imperfect Anisotropic Flat and Doubly Curved Sandwich Panels, PhD Thesis in Engineering Mechanic, Faculty of Virginia Polytechnic Institute and State University, 1998.

[6] Zhou, F., Ultimate Strength of Clamped Steel-Elastomer Sandwich Panels under Combined In-plane Compression and Lateral Pressure, PhD Thesis in Aerospace Engineering, Faculty of the Virginia Polytechnic Institute and State University, 2008.

[7] Leite, M., Freitas, M., Silva, A., Sandwich construction, Apresentação IST , DesignStudio, 2004.

[8] Site of company PortaFab Corporation: http://portafab.com, in 23/08/2009.

[9] Davies, J.M., Lightweight Sandwich Construction, Osney Mead, Oxford OX2 0EL: Blackwell Science Lta, 2001, 370 p.

[10] Site of company Kalwall: www.kalwall.com, in 10/09/2009.

[11] Potluri, P., Kusak, E. e Reddy, T.Y., Novel stitch-bonded sandwich composite structures, Elsevier - Composite Structures, 2003, Vol. 59, No. 2, 251-259.

[12] Lascoup, B., Aboura, Z., Khellil, K., Benzeggagh, M., Maquet, J., On the interest of stitched sandwich panel. Available at http://home.nordnet.fr/~jmaquet/b.lascoup.pdf

[13] Sharaf, T., Fam, A., Flexural load tests on sandwich wall panels with different rib configurations, 4th International Conference on FRP Composites in Civil Engineering (CICE2008), 2008.

[14] Nidaplast, Résistance en flexion, Technical bulletin of company Nidaplast – honeycomb, 2007, 4 p.

[15] Correia, J.R., Glass fibre reinforced polymer (GFRP) pultruded profiles (GFRP). Use of GFRP-concrete hybrid beams in construction, MSc Thesis in Construction, Instituto Superior Técnico, 2004 (in Portuguese).

[16] Hexcel Composites, Honeycomb sandwich design technology, Company brochure, 2000, 28 p.

[17] Kuenzi, E.W., Edgewise Compressive Strength of Panels and Flatwise Flexural Strength of Strips of Sandwich Construction, FPL Report 1827, 1951 (cited by [3]).

[18] ISO 527-1, Determination of Tensile Properties – Part 1: General Principles.

[19] ISO 527-4, Determination of Tensile Properties –

Part 4: Test conditions for isotropic and

orthotropic fibre-reinforced plastic composites.

[20] ASTM C365-03, Standard Test Method for

Flatwise Compressive Properties of Sandwich

Cores.

[21] ASTM C364-99, Standard Test Method for

Edgewise Compressive Strength of Sandwich

Constructions.

[22] ASTM C393-00, Standard Test Method for

Flexural Properties of Sandwich Construction.