system ductility and redundancy of frp beam structures with ductile adhesive joints

System ductility and redundancy of FRP beam structures

with ductile adhesive joints

Thomas Keller*, Julia de Castro

Composite Construction Laboratory CCLab, Swiss Federal Institute of Technology EPFL, BP Ecublens, Station 16, CH-1015 Lausanne, Switzerland

Received 3 December 2004; revised 28 April 2005; accepted 1 May 2005

Available online 24 June 2005

Abstract

This paper reports on a structural concept for engineering structures composed of FRP components to provide system ductility that

compensates for the lack of material ductility inherent to FRP materials. The concept includes the use of redundant structural systems and

ductile or flexible adhesive joints. To demonstrate the feasibility of the proposed concept, quasi-static experiments on pultruded GFRP beams

were performed. The two-span beams were connected with flexible adhesive joints at the middle support. The flexible joints from highly non-

linear adhesives provided a favorable redistribution of the internal and external forces in the statically indeterminate system compared to

single-span and continuous beams, which were also examined. In the case of adhesive joint failure, structural collapse was prevented because

of system redundancy. Due to the stiffness-governed design of the GFRP beams, the stresses in the flexible adhesive joints were small and

creep deformations in the joints could be controlled.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: B. Plastic deformation; E. Pultrusion; E. Joints/joining; Adhesive

1. Introduction

Fiber-reinforced polymer (FRP) composites are being

used increasingly in engineering structures thanks to their

advantageous material properties. Applications for strength-

ening purposes are accepted worldwide. For new

construction, structural FRP components such as profiles

and sandwiches are also starting to be used. The main

applications for these components are pedestrian bridges

and bridge decks where the properties of these materials,

such as high specific strength, insensitivity to frost and

de-icing salts, and rapid installation of components are

advantageous [1].

There are, however, also some material properties that

still hinder the widespread acceptance of new FRP

construction by structural engineers familiar with traditional

construction materials such as steel or reinforced concrete.

One of these disadvantages is the lack of ductility inherent

to FRP materials. Ductile materials allow the redistribution

1359-8368/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesb.2005.05.001

* Corresponding author.

E-mail address: [email protected] (T. Keller).

of internal forces leading to an increase in structural safety,

the dissipation of energy from impact or seismic actions and

give warnings of a possible structural problem due to large

plastic or inelastic deformations before failure.

A second disadvantage of structural FRP components

concerns the difficulty of joining the elements due to the

brittle fibrous and anisotropic character of the materials. The

current practice of bolting is not material-adapted and leads,

in most cases, to an over-sizing of the components [1].

Adhesive bonding is more appropriate for FRP materials.

The relatively high stiffness of the brittle epoxy adhesives

currently used, however, leads to high shear and peeling

stress peaks at the edges of the bonded joints [2].

Furthermore, the surface preparation and process of

applying the adhesives are very demanding, and simple

non-destructive quality control procedures do not yet exist.

Therefore, in an engineering structure composed of FRP

components and adhesive joints, the unexpected failure of a

bonded joint cannot be ruled out and must be considered in

the structural concept.

To overcome the drawbacks of bolted or epoxy-bonded

FRP engineering structures, the authors propose a new

concept for structures composed of brittle FRP components

that includes system ductility through the use of ductile

Composites: Part B 36 (2005) 586–596

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http://www.elsevier.com/locate/compositesb

T. Keller, J. de Castro / Composites: Part B 36 (2005) 586–596 587

adhesive joints and statically indeterminate structural

systems. The proposed concept envisages adhesives with

initial elastic behavior that is sufficiently stiff to meet short-

and long-term serviceability requirements. However, when

the serviceability (SLS) and ultimate (ULS) loads are

exceeded, the behavior of the adhesives should change and

become plastic or at least highly non-linear/inelastic with a

much smaller stiffness. In the highly non-linear/inelastic

case, the behavior is designated in the following as flexible

and not ductile. The ductile or flexible joints can

compensate for the lack of material ductility of FRP

components by providing ductility in the structural system,

called system ductility, which offers the same advantages as

the aforementioned advantages for material ductility. In the

case of unexpected joint failure, the redundant (statically

indeterminate) system provides alternative load paths and

redistribution of the cross-section forces due to the presence

of other ductile or flexible joints. In this way, a structural

collapse can be prevented.

Furthermore, the elasto-plastic or highly non-linear/

inelastic behavior of the adhesives prevents the occurrence

of high stress peaks. Shear and peeling stresses are much

more evenly distributed in the bonded surface, which leads to

less sensitive and more robust joints with regard to premature

and unexpected failure. This concept has already been

introduced in Keller et al. [2] in order to control the stresses in

the flanges of adhesively bonded sandwich girders.

The behavior of bolted joints is often described as ‘semi-

rigid’ [3–5]. This term was intentionally avoided in this

study, because it is too general and does not differentiate

between elastic, flexible or ductile joint behavior. To

demonstrate the feasibility of the proposed concept of

FRP structures with system ductility, experiments were

performed on continuous FRP beams with flexible adhesive

joints. The results of these experiments are presented in this

paper.

2. System ductility in FRP structures

System ductility, as described in the preceding section,

can comprise several distinct ‘sub-concepts’ that were

developed in earlier works by different researchers. Table 1

summarizes and classifies these sub-concepts as follows.

System ductility can include two different sub-concepts:

ductility and pseudo-ductility. Ductile concepts

Table 1

System ductility and redundancy—overview

System ductility System redu

Concepts Description Concepts

Ductility Combinations of brittle/ductile

components or connections

Structural r

indetermina

Pseudo-ductility Combinations of brittle/brittle

components or connections

Cross-sectio

include combinations of ‘brittle’ and ‘ductile’ structural

components or connections at the system level. Examples

are GFRP bridge decks adhesively bonded to steel girders.

Keller and Gurtler [6] reported on ductile failures of hybrid

FRP/steel girders. Brittle GFRP bridge decks failed during

the yielding of the bottom steel flanges. Other examples are

brittle FRP bars in concrete elements where the (small)

plasticity of the compressed concrete is used to provide a

ductile failure [7,8]. Ductile adhesive joints, as described in

this paper, can develop plastic hinges and are also classified

under ductile concepts.

Pseudo-ductility is the term used for the behavior of

combinations of ‘brittle’ and ‘brittle’ structural components

or connections at the system level. Non-linear, inelastic

load–deformation behavior, showing decreasing stiffness

with increasing load similar to the behavior of ductile

structures, can be achieved by progressive failure of brittle

components or connections. To prevent structural collapse,

however, structural redundancy is required. Combinations

of rigid carbon fiber laminates and flexible glass fiber

sections have been proposed by Deskovic et al. [9]. The

carbon fiber laminates are used to increase the stiffness

during the serviceability limit state, while the glass fiber

sections increase the deformations before failure (and ensure

the strength). Based on a similar concept, Razaqpur and Ali

[10] developed concrete beams reinforced externally by

bonded carbon fiber sheets and internally by a low modulus

polypropylene fiber grid.

Comparable non-linear, inelastic load–deformation

behavior can also occur on the component level by means

of a non-linear, inelastic increase in deformation caused by

progressive internal failures. Keller and Gurtler [11]

reported on experiments on bridge deck specimens

subjected to in-plane shear loading. Transverse bending in

the deck webs led to progressive local delamination failures

and non-linear, inelastic behavior, similar to the behavior of

a ductile material. In contrast to ductile structures, however,

pseudo-ductile structures can only dissipate energy within a

limited number of loading cycles, depending on the degree

of static indeterminacy. After a certain number of failures,

pseudo-ductile structures become statically determinate,

whereby a further failure would lead to a brittle collapse.

Analogous to system ductility at the system level, the

term system redundancy is proposed and discussed in the

following as a requirement for pseudo-ductile behavior.

Table 1 also gives an overview of possible sub-concepts of

ndancy

Description

edundancy (statically

te systems)

Systems with alternative load paths,

back-up systems

nal redundancy Multi-component cross-sections

Fig. 2. Bonded joint over middle support of beam PH1 with strain gages and

clinometers.

T. Keller, J. de Castro / Composites: Part B 36 (2005) 586–596588

system redundancy. Concepts of structural redundancy

(statically indeterminate systems) and cross-sectional

redundancy are proposed. Statically indeterminate systems

provide alternative load paths in the case of failure of a

component or a connection. An example is the truss

structure of the Pontresina Pedestrian Bridge with adhe-

sively bonded joints in one span [2]. The crossed diagonals

offer alternative load paths in the case of failure of one or

several of the components or bonded joints. Furthermore,

the addition of bolts in the adhesive joints provides a

mechanical back-up system. The second concept of

redundancy, called cross-sectional redundancy, is provided

in multi-component cross-sections. The sandwich girders

with adhesively bonded flanges or the built-up sections of

the Eyecatcher building, reported in [2], are examples of

cross-sectional redundancy. In both the Pontresina and

Eyecatcher examples, single cross-sectional components or

the adhesive bond between single components can fail

without failure of the whole section.

3. Experiments on bonded pultruded beams

3.1. Beam description

As already introduced, experiments on FRP beams with

flexible adhesive joints were carried out and can be seen in

Fig. 1. Four two-span beams, PH1–PH4, were examined.

The beams were built up from two single span beams. The

spans of the built-up beams were two times 3.60 m.

Pultruded beams with square box cross-sections of 240!240 mm and a 12 mm wall thickness were used. The depth/

span-ratio was 1/15.

The beam flanges were connected at the middle support,

i.e. at the location of the maximum negative bending

moment, with adhesive strap joints, as shown in Fig. 2. The

strap joints had different overlap lengths: 2!100 mm

(PH3), 2!200 mm (PH1 and PH2) and 2!300 mm

(PH4), as listed in Table 2. Due to the size of the support

Fig. 1. Loading test set-up for bonded beam PH2.

surface required at the middle support, the beam with upper

overlaps of 2!100 mm (PH3) had lower overlaps of 2!200 mm. The flanges were connected with cover plates of

the same thickness (12 mm) and width (240 mm), as shown

in Fig. 2. The cover plates were cut from identical beam

sections. The average gap between the connected beams

was between 12 and 16 mm on the centerline. The beam

webs were not connected. The bonded joints, therefore,

were able to transfer bending moments over the middle

support, but no vertical shear forces. The chosen adhesive

thickness was 2 mm due to the tolerances of the sections and

the wires of the strain gages bonded on the flanges in the

joints.

The layout of the bonded beams and the experimental

set-up were primarily chosen from a scientific point of view

to demonstrate the feasibility of the global structural

concept. The practical application of this layout with the

bonded joints over the supports was not the main concern.

For comparison purposes, three single-span beams,

PS1–PS3, with 3.60 m span as well as three continuous

two-span beams, PC1–PC3, without bonded joints over the

middle support were also examined. Table 2 gives details of

the beams and the experimental results at failure.

3.2. Materials

The beams were composed of approximately 45%

E-glass fibers by volume and an isophthalic polyester

resin. The architecture consisted of approximately 67%

UD-rovings and two outer and two inner combined mats

(CSM and 08/908 fabrics stitched together). The overlaps of

the combined mats at the corners of the cross-section were

visible. The wall thickness was slightly increased in the

overlap region on a width of approximately 30 mm on each

side of the corners. On the outside, a polyester surface veil

was added. The stiffness of the beams was determined

experimentally with the single-span beams (PS1–PS3) by

three-point and four-point bending tests and compared to

Table 2

Overview experimental beams and results at failure

Beam Specification Ultimate fail-

ure load (kN)

Maximum

deflection at

failure (mm)

Rotation at

middle sup-

port (8)

Reaction at

middle sup-

port (kN)

Moment at

middle sup-

port (kNm)

Moment at

jack location

(kNm)

Failure

location

PS1–PS3 Single span 155G5 66G3 2.9G0.1 103G3 0 125G4 Loading point

PC1–PC3 Continuous 146G11 32G6 0 242G17 K86G7 60G5 Middle sup-

port

PH1 Adhesive joint

overlap 2!200 mm

180 45 1.6 278 K67 99 Loading point

PH2 Adhesive joint

overlap 2!200 mm

178 50 1.8 267 K53 107 Loading point

PH3 Adhesive joint

2!100 mm

(top) 2!200 mm

(bottom)

(1) 135 (1) 38 (1) 1.5 200 (1) K36 (1) 84 (1) Adhesive

joint

(2) 154 (2) 55 (2) 2.2 206 (2) 0 (2) 122 (2) Loading

point

PH4 Adhesive joint

overlap 2!300 mm

178 47 1.4 274 K66 98 Loading point


the values given in the pultruder’s design manual [12].

Table 3 gives an overview of the results. The full-section

elastic and shear moduli were calculated in different ways

from the measured deflections, rotations and strains. The

shear modulus, determined from the strains, was calculated

from readings of gages in the 458 direction on the centerline

of the webs. The shear coefficient, K (synonymous with the

shear correction factor), was estimated according to Bank

[13] and Omidvar [14]. The properties used to predict the

behavior of the beams were 30.0 GPa for the elastic

modulus and 3.0 GPa for the shear modulus.

The acrylic-based two-component SikaFast 5221 struc-

tural adhesive, based on the ADP (acrylic double

performance) technology developed by Sika [15], was

used in bonding of the specimens. The adhesive choice was

based on previous experiments on bonded GFRP double-lap

joints with epoxy, polyurethane and acrylic adhesives. The

shear stress–strain behavior, t–g, of the ADP adhesive was

determined from napkin-ring tests [16], which are based on

EN 11003-1 specifications [17]. The adhesive behavior was

highly non-linear, as shown in Fig. 3. The stress–strain

curve can be modeled as bi-linear with two different shear

Table 3

Properties of GFRP beams

Data origin Maximum stress (MPa) E

Design Manual [12] 240 (tension and compression

strength)

2

Eurocomp [19] 100 (onset of buckling)

Obtained from beams PS1–PS3 99/153 (onset/post-buckling)

From deflections 3

From rotations (E)

and deflections (G)

2

From strain gages

08 (E) and 458 (G)

3

Used for calculations 3

moduli Ge (elastic) and Gp (plastic), where Gp is

approximately 11 times smaller than Ge. The properties of

the ADP adhesive are listed in Table 4.

3.3. Experimental set-up and instrumentation

The experimental set-ups can be seen in Figs. 1 and 4.

The two-span beams were loaded by a hydraulic jack of

500 kN capacity in each span. The jacks were each located

at a distance of one-third of the span from the middle

support. For the single-span beams, in addition to the three-

point load configuration, a four-point load configuration was

used to determine the beam properties given in Table 3.

Timber plates and 5 mm thick neoprene pads were placed

between the beams and the jacks and supports. The timber

plates at the most critical middle supports were 300 mm

long, 260 mm wide and 27 mm thick. In addition, the edges

of the plates were chamfered to a 10 mm radius to relieve

stress concentrations, as shown in Fig. 2.

Each beam was instrumented with load and displacement

sensors in the jacks, load sensors at each support, vertical

displacement transducers (up to 12), electronic clinometers

lastic modulus, E (GPa) Shear modulus, G (GPa)

3.0 3.0

2.1G1.8 2.1G0.5

9.8G0.2 3.3G0.2

0.3G0.4 4.3G0.1

0.0 3.0

0

2

4

6

8

10

0.0 0.5 1.0 1.5 2.0 2.5

Shear strain [-]

She

ar s

tres

s [M

Pa]

Fig. 3. Shear stress–strain behavior of ADP adhesive.

Fig. 4. Loading positions: (a) single beams PS, (b) continuous beams PC,

(c) bonded beams PH (dimensions in mm).


at the supports (4) and strain gages (up to 20) at different

cross-sections. The strain gages were used to measure the

axial strain distributions through the depth and across the

width of the beams. In addition, strain gages were placed

in the bonded joints of beams PH1–PH4 on the top and

bottom flanges (40 gages in each joint). The strain

gage arrangement in the upper joint of beam PH2 with

2!200 mm overlap length is shown in Fig. 5 (24 gages).

12span 1 (North)span 2 (South)

3.4. Experimental program

In the first phase of the experimental program, each beam

was subjected to several load cycles at different load levels

to observe the behavior of the beams and the instrumenta-

tion. These cycles were carried out under load-control at a

rate of 5 kN/min. In the second phase, the beams were

loaded up to failure under displacement-control at rates of

1.2–2.3 mm/min. The single-span beams were loaded in the

three-point configuration up to failure with the load at the

one-third span position. With regard to the flexible adhesive

used, a creep experiment was performed on the bonded

beam PH2 between the first and second phases of the

experimental program. The beam was subjected to a load of

40 kN per jack for a period of 7 days. The resulting

deflection-to-span ratio of 1/400 was approximately equal to

the admissible deflection ratio at the serviceability limit

state in building construction.

240

108

108

18overlap edge

4. Experimental results

The results of the first phase of the experimental program

showed that the axial strains through the depth of all beams

Table 4

Properties of ADP adhesive (Napkin-ring test)

Shear strength,

tu (MPa)

Shear strain at

failure, gu (%)

Shear modulus

Ge (GPa) Gp (GPa)

8.3 2.3 0.033 0.003

remained linear. The neutral axis was approximately 2 mm

below the centerline in the spans. This small shift was likely

due to the slightly different elastic tensile and compressive

moduli. (The values from 08 strain gages given in Table 3

are average values from the tension and compression

flange.) It was also seen that the compressive strains were

slightly higher than the tensile strains. Furthermore, the

strains across the width of the flanges remained constant. No

reductions in strain due to shear lag were observed. Only the

results of the failure experiments and the creep experiment

on beam PH2 are presented in the following sections.

4.1. Behavior of single-span beams

The load–deflection curves of the three single-span

beams, PS1–PS3, are shown in Fig. 6. The behavior of the

beams was identical and linear-elastic up to a load of

approximately 100 kN per jack (approximately 65% of the

ultimate failure load). At this load level, a slight decrease in

the stiffness was observed. The stiffness decrease coincided

with the onset of buckling of the compression (top) flange of

200

20 20 20 40 40 40 40 20

12

40 40 40 40

200

Fig. 5. Strain gage arrangement in upper adhesive joint with 200 mm

overlap (dimensions in mm).

0

50

100

150

200

0 10 20 30 40 50 60 70Vertical deflection [mm]

Load

per

load

ing

poin

t [kN

]

PS1-3

PC1-3

PH1 PH2

PH3

PH4

PH1

0

25

50

0 5 10

Fig. 6. Load–deflection curves of all beams, deflections at loading section.

Fig. 8. Failure of beam PS1 near patch load.


the beams, which could be traced back with the strain gages

distributed across the width of the top flanges. Fig. 7 shows

the strain measurements across the top and bottom flanges

of beam PS2, 50 mm from the edge of the patch load. The

strains in the tension (bottom) flange increased linearly up to

failure, whereas the strains in the compression (top) flange

began to decrease non-linearly as the load exceeded

approximately 65% of the ultimate failure load.

Subsequent to the onset of buckling, the stiffness of the

beams continued to decrease slightly up to failure

(cf. Fig. 6). The top flange failed in beams PS1 and PS3,

as shown in Fig. 8. At the same time, horizontal cracks

formed in the webs at the locations of the overlap edges of

the combined fiber mats. In beam PS2, only the webs failed

and two horizontal cracks formed on each side, one of them

again at the locations with the overlap edges of the

combined mats. The failure modes of the top flanges and

webs were interconnected and very complex.

Fig. 9 shows the measured load–rotation behavior of the

beams at the support closer to the jack in the three-point

bending tests. The rotation curves showed the same elastic/

non-linear behavior as the deflection curves. The measured

ultimate failure loads, maximum deflections at the load

application points and maximum rotations at the support

Fig. 7. Strain distribution across tension and compression flanges of beam

PS2 (dimensions in mm).

closer to the jack (location of middle support for the

continuous beams) are listed in Table 2 (average values and

standard deviations).

4.2. Behavior of continuous beams

The load–deflection curves of the three continuous

beams, PC1–PC3, are shown in Fig. 6. The average values

of the two jack loads and of the deflections at the load

application points are indicated. In general, the measured

values of the two spans correspond well; the maximum

variations were approximately 2%. The behavior of the

beams was identical and linear-elastic up to a load of

approximately 100 kN per jack (approximately 70% of the

ultimate failure load). As for the single-span beams, the

stiffness began to decrease at this point due to the onset of

buckling of the compression flange and, particularly, of the

webs. In the continuous beam configuration, the most highly

compressed flange and webs were the bottom flange and

webs at the middle support. Ultimate failure occurred in the

webs at the middle support. Horizontal cracks formed

30 mm above the lower corners in the region where the

overlaps of the combined fiber mats ended. The support

plate punched into the beam, as can be seen in Fig. 10 for

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0 2.5 3.0Rotation [˚]

Load

per

load

ing

poin

t [kN

] PH2

PH3

PH4 PH1

PC1-3

Middle support

PS1-3

Fig. 9. Load–rotation curves at middle support.

Fig. 10. Failure of beam PC3 at middle support. Fig. 11. Deformation of bonded beam PH1 at onset of failure.


beam PC3. Furthermore, two longitudinal cracks formed in

the lower flange of all three beams 30 mm from the lower

corners (edges mat overlaps).

No rotations occurred over the middle support. The main

experimental results are listed in Table 2. The ultimate

failure loads were slightly below the values of the single-

span beams. The maximum deflections varied between 27

and 38 mm (approximately span/110) and reached approxi-

mately 50% of the single-span beam values.

0.00

0.02

0.04

0.06

0.08

0.0 0.2 0.4 0.6 0.8 1.0Normalized overlap length [-]

Axi

al s

trai

n [%

]

PH1PH2PH3PH4

Fig. 12. Measured axial strain distributions on upper flanges in adhesive

joints of beams PH1–PH4 at load of 50 kN per jack.

4.3. Behavior of bonded beams with 200 mm overlap (PH1

and PH2)

The load–deflection responses of the bonded beams PH1

and PH2 with 2!200 mm joint overlap are shown in Fig. 6.

The beams exhibited tri-linear behavior. In the first part, up

to approximately 125 kN (70% of the ultimate failure load),

the behavior can be described as bi-linear, as it was for the

ADP adhesive. In the load range up to approximately 20 kN

per jack, the stiffness dropped to a value which,

subsequently, remained constant. In the second part,

above 125 kN, a further stiffness decrease was seen that

coincided with the onset of buckling of the top flanges and

the webs below the patch loads, and the bottom flanges and

the webs at the middle support. Beam PH1 was slightly

stiffer than beam PH2, which may have been due to the

different temperatures in the laboratory during the exper-

iments (PH1 228, PH2 288). The failures in both beams

occurred in the webs below one of the jacks, similar to what

was observed for the single-span beams. Fig. 11 shows the

deformed beam PH1 at the onset of failure. The negative

curvature over the middle support due to the continuity

effect provided by the bonded joint is visible. Below the left

jack, buckling of the web is also visible. The subsequent

failure occurred at this location in the area of the edge of the

mat overlap. No damage or failure was observed in the

bonded joints from visual inspection and strain

measurements.

Fig. 9 shows the measured load–rotation behavior of the

beams at the middle support. The rotation curves showed the

same bi-linear behavior as the deflection curves in the first

phase of the experiments. However, the stiffness decrease in

the second phase due to buckling could not be detected. The

main experimental results are listed in Table 2 for both

beams.

Fig. 12 shows the measured axial strains along the upper

strap joints at a load of 50 kN for both beams PH1 and PH2.

The symbols represent average values from four strain gage

readings from gages at equal positions in the joint. The

strain distribution was nearly linear along the major part of

the overlap. The strains increased non-linearly only in the

first and last 20 mm. A linear least-squares fit is also shown

in Fig. 12.

As mentioned above, beam PH2 was subjected to 7 days

of creep loading. The first hour of the measured deflection–

time curve is shown in Fig. 13. The loading curve up to

9 mm deflection is not entirely linear due to the manually

driven loading system. When subjected to constant loads,

the maximum deflection increased from 9.1 to 11.6 mm

(approximately 27%) during 7 days. Seventy percent of the

increase occurred within the first 5 min.

0

5

10

15

20

0 15 30 45 60

Time [min]

Ver

tical

def

lect

ion

[mm

]

North span

South span

~ 5 min

Fig. 13. Creep deformations of bonded beam PH2 during first hour of

loading.

Fig. 14. First failure of bonded beam PH3 at middle support (strain gages

staggered in 100 mm overlap).


4.4. Behavior of bonded beam with 300 mm overlap (PH4)

The bonded beam with 2!300 mm overlap lengths,

PH4, showed almost the same load–deflection and load–

rotation behavior as the beams PH1 and PH2 with 200 mm

overlaps, as shown in Figs. 6 and 9. In the buckling phase

(above 155 kN per jack), the stiffness loss was less

pronounced than in beams PH1 and PH2. The failure

occurred through buckling of the webs below one of the

jacks and was similar to the failures of beams PH1 and PH2.

The bonded joint remained undamaged.

The main experimental results are listed in Table 2. The

ultimate failure load was 178 kN per jack and the maximum

deflection reached 47 mm. Both the load and deflection

values corresponded well with those of beam PH2. The

maximum rotation at the middle support was 1.48, which is

12% less than that of beam PH1 and 23% less than that of

beam PH2.

The measured axial strain distribution in the joint was

approximated by a linear least-square fit, as was done for the

beams PH1 and PH2. The slope of the straight line fit is

smaller than that of beams PH1 and PH2, as shown in

Fig. 12. The symbols represent average values from four

strain gage readings.

4.5. Behavior of bonded beam with 100 mm overlap (PH3)

The bonded beam with 2!100 mm top overlap lengths,

PH3, showed load–deflection and load–rotation responses

similar to beams PH1, PH2 and PH4 up to approximately

120 kN. The stiffness was slightly lower than that of the

other beams, as shown in Fig. 6. At higher than 120 kN, the

stiffness also began to decrease due to the onset of buckling

in the compression flange and webs below the jacks and at

the middle support. At a load of 135 kN, however, the

behavior of beam PH3 changed distinctly from that of the

others. One part of the adhesive joint in the upper flange

failed, as shown in Fig. 14. Failure occurred partially in the

outer mat of the pultruded beam (interlaminar failure) and

partially in the interface between the beam and the adhesive

(adhesion failure). The load dropped slightly after this first

failure due to the displacement-control being used in the

loading (cf. Fig. 6). Subsequently, however, the load

increased again with increasing deflection. The load–

deflection path progressed then parallel to the single-span

beams up to an ultimate failure load of 154 kN. The ultimate

failure occurred below one of the jacks, as was observed for

the single-span beams and the other bonded beams. The

webs buckled and the same horizontal cracks formed, as

already described.

The load–rotation measurements, illustrated in Fig. 9,

showed an analogous response to Fig. 6. After the first

failure, the slope changed and the curve developed parallel

to the single-span beams. The main experimental results are

listed in Table 2. The measured axial strain distribution in

the joint was approximated by a linear least-squares fit, as

for the other beams. Fig. 12 shows that the slope of the fitted

straight line is higher than that of the other beams.

5. Discussion

5.1. Load–deflection and load–rotation behavior

The full-section elastic and shear moduli calculations

indicated that approximately 83% of the vertical deflections

were due to bending and 17% due to shear. As expected, the

deflections of the bonded beams were between the values of

the single-span beams (28% smaller) and the continuous

beams (49% higher) (refer to Table 5). The bonded beams

showed a tri-linear behavior with a first loss of stiffness due

to the bi-linear behavior of the adhesive and a second loss

due to the onset of buckling in the compression flange.

Beam PH3 showed an additional loss of stiffness due to the

failure of the bonded joint. Therefore, the bonded beams

exhibited system ductility at first (concept of ductility,

according to Table 1), however, the effect was quite

small because the adhesive was initially too flexible.

Table 5

Comparison of beams with adhesive joints and single/continuous beams

Beams Ultimate failure load Maximum deflection at failure

Beams with

adhesive

joints

Single span

(reference

155 kN)

Continuous

beam (refer-

ence 146 kN)

Single span

(reference

66 mm)

Continuous

beam (refer-

ence 32 mm)

PH1

(200 mm)

C16% C23% K32% C42%

PH2

(200 mm)

C15% C22% K24% C58%

PH3

(100 mm)

K1% C5% K17% C74%

PH4

(300 mm)

C15% C22% K29% C48%

Average

(PH3

excluded)

C15.3G0.6% C22.3G0.6% K28.3G4.0% C49.3G8.1%


Ideally, the adhesive should be much stiffer at the beginning

(elastic modulus comparable to an epoxy adhesive) and then

should behave plastically. The loss of stiffness due to local

buckling was small and it was not possible to detect if the

deformations were elastic and reversible or not. According

to [18], losses of stiffness due to local buckling may not be

elastic and reversible in pultruded sections in the post-

buckling range. The additional loss of stiffness due to the

failure of the bonded joint of beam PH3 can be considered

as additional system ductility (concept of pseudo-ductility,

according to Table 1).

The creep experiment showed that, even though a very

flexible adhesive was used, the creep deformation was kept

within admissible values due to the design-governing

deflection limit for the GFRP beams and the associated

low shear stresses of approximately 1.1 MPa in the adhesive

joint. The shear stress was calculated according to Eq. (1)

(see Section 5.2).

5.2. Estimation of the rotation angles and moment

distributions

The measured axial strains of the flanges in the joints of

beams PH1–PH3 showed a linear distribution with a

noticeable slope, with the exception of small regions at

the beginning and at the end (approximately 5% of the joint

length each, cf. Fig. 12). This indicates that the shear

stresses in the adhesive layer were almost constant over the

joint length and the magnitude of constant shear stress was

proportional to the slope of the straight-line fit to the axial

strains. Only beam PH4, which had the longest overlap

Table 6

Estimation of rotation angles and moments at middle support

Beam t (MPa) g (%) qcalc. (8) qmeas. (8)

PH1 5.7 1.0 1.3 1.5

PH2 5.7 1.0 1.3 1.8

PH3 6.2 1.2 1.2 1.5

PH4 4.3 0.5 1.1 1.4

lengths of 2!300 mm, deviated slightly from this con-

clusion. The slope of the straight-line fit for beam PH4 was

quite small and, therefore, a considerable part of the shear

stresses were transmitted towards the edges of the overlaps.

Based on the assumption of a constant shear stress

distribution in the adhesive bond, an estimate of the

resulting angles of rotation at the middle support at failure

can be made. The constant shear stress, t, is calculated from

the axial force, F, in the beam flange while the axial force,

F, can be obtained from the negative bending moment over

the middle support, M, according to Eq. (1)

t ZF

lbZ

M

ðh K tÞlb(1)

Due to the eccentricity of the cover plate, small secondary

moments were produced in the cover plate. These secondary

moments, however, were neglected. In Eq. (1) the maximum

negative bending moment is used and any decrease along

the length of the overlap is neglected. The denominator in

Eq. (1) comprises: the section height, hZ240 mm, the

flange thickness of the beam, tZ12 mm, the section width,

bZ240 mm, and the overlap length, lZ100/200/300 mm.

The elongation of the upper overlap, Dl, is composed of

the shear deformations of the adhesive layer, Dl1, and the

axial elongation of the cover plate and the top flange, Dl2, as

follows

Dl Z Dl1 CDl2 (2)

Dl1 Z agðtÞ (3)

Dl2 ZMl

ðh K tÞtbE(4)

where a is the adhesive layer thickness (2 mm), g(t) is the

shear strain of the adhesive according to Fig. 3, and E is the

full-section elastic modulus (30.0 GPa). From these

elongations, the total rotation angle over the middle support,

qcalc., is calculated as follows:

qcalc: Z arctan2 Dl

h Ca(5)

Now, the bending moment distributions are calculated for a

static system consisting of two single-span beams connected

by a non-linear rotational spring at the middle support (i.e.

the adhesive joints). The stiffness of the spring, kq, is

calculated as follows:

Dq (%) Mcalc. (kNm) Mmeas. (kNm) DM (%)

K13 K62 K67 K5

K28 K62 K53 C15

K20 K34 K36 K6

K21 K71 K66 C8

0.4

0.8

1.2

1.6

2.0

0 50 100 150 200Load per loading point [kN]

Ben

ding

mom

ent r

atio

M- /M

+ [-]

PH3

PH1PH2

PH4

Fig. 16. Redistribution of bending moments from middle support (MK) to

loading point cross-sections (MC).


kq ZM

qcalc:

(6)

For the pultruded beams, the full-section elastic and shear

moduli given in Table 3 were considered. Due to the non-

linear behavior of the adhesive, an iterative calculation

procedure was necessary.

The results calculated for the angles of rotation (qcalc.)

and the negative bending moments at the middle support

(Mcalc.) are shown in Table 6 and are compared to the

measured values (qmeas., Mmeas.). The percentage difference

between measured and calculated values, Dq and DM, are

also indicated. The calculated rotations underestimate the

measured rotations by 13–28%. The variations from the

‘measured’ moments at the middle support (that is,

the moments calculated from the measured support reactions)

are between K5 and C15%. The largest deviations between

measured and calculated values were observed in beam PH2,

which was loaded at a different temperature.

5.3. Moment redistribution and failure behavior

Fig. 15 shows the bending moment diagrams along the

beam length for all beams at 135 kN per jack, which

corresponds to the lowest failure load (beam PC2). The

results for the single-span beams are mirrored. The

moments were calculated from the measured support

reactions. Compared to the single-span and continuous

beams, the flexible adhesive joints led to a more uniform

distribution of moments and support reactions. The

maximum moments and the support reactions at the middle

support were considerably lower as compared with the

continuous beam (PC2), which failed at this location.

Compared to the single-span beams, the cross-sections

below the jacks were more lightly loaded due to the partial

fixity at the middle support. The loads could thus be

increased in the bonded beams beyond the failure loads of

the single-span and continuous beams due to the remaining

flexural capacities in the load and support cross-sections. As

given in Table 5, the ultimate failure loads of the bonded

beams were increased by 15% as compared with the single-

span beams and 22% compared with the continuous beams

-100

-50

0

50

100

150

Ben

ding

mom

ent [

kNm

]

7.2

PC1-3

PS1-3

PH1,4

PH3

1.2 2.4 4.8 6.0PH2

Axis

Fig. 15. Bending moment distributions along beam length (at 135 kN load

per jack).

(average values excluding beam PH3). In this respect,

however, a direct comparison of the failure loads is not

possible, since the bottom cover plate additionally

reinforced the support region of the bonded beams.

Fig. 16 shows that a redistribution of the moments from

the support (MK) to the loading point regions (MC) in the

PH beams occurred. The reason for this redistribution is the

non-linear behavior of the adhesive joint. As expected,

the redistribution effect increased with decreasing overlap

length. However, the effect was again smaller than

expected, because the adhesive was too flexible during the

early load stages. Ideally, the bending moment ratio should

be constant up to the ULS load (approximately 1.5!40 kNZ60 kN, 40 kNZSLS load), and then start to

decrease.

The maximum compressive flange stresses at failure

were approximately 153 MPa (PS beams, post-buckling)

and, therefore, far below the value of 240 MPa given in the

pultruder’s design manual [12]. The short overlap of the

combined fiber mats proved to be a weak area in the beams.

The post-buckling value of 153 MPa was approximately

50% above the compressive flange stress at the onset of

flange buckling of 100 MPa, calculated according to the

Eurocomp Design Code and Handbook ([19], Eq. 4.9, with

ExZ30.0 GPa, EyZ8.5 GPa, GxyZ3.0 GPa, nxyZ0.27,

nyxZ0.09, cf. Table 3). The Eurocomp value, however,

exactly matched the calculated compressive flange stress at

the onset of buckling of the PS beams (99 MPa at a load of

100 kN, cf. Table 3).

6. Conclusions

Quasi-static and creep experiments on brittle GFRP

beams connected with flexible adhesive joints were carried

out and were compared to quasi-static experiments on


single-span and continuous beams. The adhesively con-

nected beams showed the following characteristics:

(1) The flexible joints composed of a highly non-linear

adhesive provided a favorable redistribution of the

internal and external forces in the redundant system.

(2) In the case of adhesive joint failure, structural collapse

was prevented due to structural redundancy of the

statically indeterminate system. After joint failure, the

load was increased by 14% up to the ultimate load.

(3) Due to the almost constant shear stress distribution in

the adhesive joints arising from the low stiffness and

highly non-linear behavior of the adhesive, the rotations

in the joints could be estimated using a simple

analytical model. From these rotations, the internal

forces in the statically indeterminate system were

calculated using beam theory. Results from measure-

ments and calculations showed a good agreement.

(4) Due to the stiffness-governed design of GFRP beams,

the stresses in flexible adhesive joints were small and

creep deformations in the joints could be controlled.

The results of this research confirm the feasibility of the

proposed concept for beam structures composed of brittle

FRP components. The concept combines redundant beam

systems, and ductile or flexible adhesive joints to provide

system ductility that compensates for the lack of material

ductility inherent to FRP beams. Further research will be

carried out to define the adhesive properties required to

enhance the ductile behavior of the joints.

Acknowledgements

The authors wish to acknowledge the support of the

Swiss Innovation Promotion Agency CTI (Contract

No. 4676.1 KTS), Fiberline Composites A/S Denmark

(supplier of the pultruded profiles) and Sika AG Zurich

(supplier of the adhesives).

References

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http://www.fiberline.com/gb/home/index.asp

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