1

Behaviour of beam-to-column GFRP bolted connections:

Experimental and numerical investigations

Miguel Enrech Casaleiro Mascarenhas Proença

Civil Engineering Department, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal

Abstract: This paper presents an experimental and numerical study about the behaviour of beam-to-column bolted

connections between glass fibre reinforced polymer (GFRP) tubular profiles. Small-scale coupon tests were first performed in

order to determine the mechanical properties of the GFRP material. The study of the connections comprised full-scale tests on

connection specimens with the following typologies: W1 – one bolt per web; F2 – two bolts per flange; F2S – two bolts per

flange with increased edge-distance; and F4 – four bolts per flange. Three monotonic tests were performed per connection

typology in order to determine their stiffness, strength and damage progression properties. Three cyclic tests were performed

per connection type in order to assess the dynamic behaviour of the joints, in what respects to their stiffness, strength and

energy absorption properties. These cyclic tests provided a better understanding of the damage progression trough the cycles,

and the way it influences both strength and stiffness properties of the joint. Numerical modelling of the connections was

performed to simulate the monotonic tests. The numerical models provided a good agreement with the experimental data in

terms of initial stiffness, initial non-linear behaviour and maximum strength. No significant differences in strength were found

between connections F2 and F4. Despite having more bolts, this result is explained by the smaller edge distance of the bolts in

F4 typology and the fact that the first row of bolts withstands higher forces than the second. Connection type F2S afforded the

best performance, being able to endure large deformations whilst maintaining structural integrity and resisting to higher

loads. As expected, connection type W1 revealed the worst performance.

Keywords: Beam-to-column connections; GFRP pultruded profiles; Moment rotation characteristics; Damage progression;

Numerical modelling.

1. Introduction

Fibre Reinforced Polymer (FRP) composites are

materials made of oriented fibres embedded in a

polymeric matrix. Since there is an unlimited number of

fibre-matrix combinations, FRPs may present a wide range

of mechanical properties (Hollaway 2010). FRPs are

known for their orthotropic behaviour, presenting higher

resistance and stiffness in the fibre alignment direction.

Glass fibre reinforced polymers (GFRP) are the most

widely used FRP materials due to the reduced cost of the

glass fibres. GFRPs have been recently used as a structural

material in civil engineering due to: (i) high resistance-to-

weight ratio; (ii) high resistance to environmental

aggressions (chemical or physical); and (iii) reduced life-

cycle cost, owing to their excellent durability in the most

varied environments. The brittle nature of GFRP, owing to

the behaviour of the glass fibres, is a relevant factor to take

into account when structural applications are considered.

Pultruded profiles are the most frequent shape of

structural elements used in GFRP structures. Pultrusion

manufacturing process allows delivering high-quality

constant-cross-section FRP profiles with high resistance

properties on the pultrusion direction, while presenting

reduced production costs (Bank 2006). One of the main

disadvantages of these profiles lies in the lower resistance

along the transverse directions (to the pultrusion one).

Therefore, there are a number of failure modes typical of

these materials, such as: (i) shear-out failure; and

(ii) shear failure of the web-flange junction.

For structures made of GFRP composite materials,

unlike other materials, deformability is usually the main

conditioning factor for design. As such, a very important

design aspect for a structure built with GFRP profiles lies

in the behaviour of the connections, especially of beam-to-

column connections (Hizam 2013).

Initially, due to the lack of studies about the behaviour

and performance of bolted connections between GFRP

members, they were assumed to be nominally pinned

(Mottram 1996). Therefore, the only design factor

addressed was the shear resistance of the connections.

However, considering connections as pinned sometimes

proved to be very penalizing to the deformations of the

beams, leading to very inefficient and uncompetitive

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designs (Bank and Mosallam 1990). Indeed, larger cross-

sections frequently had to be selected in order to meet the

deflection limits imposed by Service Limit States (SLS)

requirements, which proved to be the most limitative

factor at the design stage. The former drawback led to the

need to develop connections considered as semi-rigid to

reduce deformations on the structures, and ultimately to

reduce cross-section’s dimensions. Studies were

developed in order to create stiffer and stronger

connectors.

The present study was motivated by the need to

develop and understand the behaviour of a number of

beam-to-column connections between GFRP pultruded

profiles with tubular cross-section. Prior understanding of

the material behaviour was crucial to ensure a good design

approach. Small-scale tests were performed on the GFRP

material, in order to evaluate its mechanical properties

when subjected to different load conditions. These studies

were also important to simulate the material behaviour

with the numerical model tests.

The behaviour of four different types of bolted

connections was analysed through experimental tests and

numerical modelling. Real scale models of the connections

were subjected to two different types of tests:

(i) monotonic tests; and (ii) cyclic tests. The connections

were analysed regarding their stiffness, strength and

absorbed energy, in order to determine the connection

type with the best performance, to be included as the

beam-to-column connection in the CLICKHOUSE project.

This project, which aims at designing a modular house for

emergency scenarios, was performed by ALTO Perfis

Pultrudidos, Lda in partnership with Instituto Superior

Técnico (IST) and Universidade do Minho (UM).

2. Previous studies (experimental &

numerical)

Regarding joint design technology, initial studies

(Rosner and Rizkalla 1995; Hassan et al. 1997a,b; Abd-al-

Naby and Hollaway, 1993a,b; Erki 1995; Turvey and Wang

2003) were conducted in simple in-plane connections

(single-lap or double-lap), subjected to tension only. These

studies, reviewed by Mottram and Turvey (2003), were

performed in order to determine the influence of the

geometrical properties of the connections such as:

(i) number of bolts; (ii) arrangement of the bolts; (iii) plate

thickness-to-hole diameter ratio; (iv) bolt edge distance or

pitch distance; (v) fibre orientation; and (vi) lateral

constraint.

Bank (2006) presented a compilation of the

recommended geometric parameters for lap joint

connections. These studies enabled the identification of a

number of different failure modes typical of this material

and the way they are related to the geometrical

parameters. The failure modes identified, presented in

Figure 1, were: (i) net section failure; (ii) cleavage failure;

(iii) bearing failure; and (iv) shear-out failure.

Figure 1 – GFRP bolted connection failure modes (Bank 2006)

This extensive study allowed the determination of the

most preferable failure mode, which was the bearing one.

This failure mode had been studied extensively by Xiao

and Ishikawa (2005a,b). This was the only mode

presenting some sort of ductility, with damage

accumulation, since all other failure modes were fragile.

The study of the behaviour of GFRP bolted connections

started in 1990s. The connections used were based on a

database of connection types typical of steel structures.

Bank and colleagues (Bank and Mosallam 1990; Bank

et al. 1994; Bank et al. 1996) developed and studied

different connection types, deemed to achieve higher

stiffness and resistance levels. These connections were

made of parts of increasing complexity and resistance.

Some of these parts were excessively complex to be

manufactured at an industrial level, therefore discarding

their use in real life applications. Higher resistances were

achieved by minor connection redesign, provided that the

conditioning failure modes and load paths were fully

understood.

Later on, Smith et al. (1998) studied connections of

closed cross-sections such as the RHS profile studied

herein, and these were compared to I-shape profile

connections. Closed cross-sections generally present an

improved mechanical behaviour when compared to

I-shape profiles in terms of local buckling characteristics,

torsional rigidity and weak axis strength and stiffness. The

same authors came to the conclusion that the use of closed

cross-sections and the corresponding connections ensured

an improved structural system when compared to open

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flange profiles and connections. In an attempt to analyse

stiffer and stronger connections, different types of

connections were studied, ranging from simple web-

cleated or flange cleated connections (using thicker cleats

or seats), to joints attempting to achieve a monolithic

behaviour (boxed connections), with the connection parts

being applied to the outside of the profiles (e.g., gusset

plates). In this case, using a boxed section with simple

connection detailing increased stiffness by 25% and

strength by 280%, when compared to regular I-shape

profiles beam-to-column connections.

The former observations were used to compile a list of

design features to serve as guidelines for structural

designers (Smith et al. 1999). The recommendations,

adopted in the development of the connections studied

herein, are the following: (i) avoid bolts in tension trough

the thickness of the section, that might lead to a failure by

punching of the bolt through the FRP material;

(ii) mobilize the entire cross-section of the column, easily

achieved when using bolts crossing the entire section;

(iii) provide reinforcement for both load path and bolt

restraint; and (iv) approximate the design of the joint to a

monolithic connection element, thus reducing the number

of parts, the complexity, and above all, reducing stress

concentrations.

Mottram and co-workers (Mottram and Zheng 1999a,b;

Qureshi and Mottram 2012, 2013, 2014, 2015) focused on

the existent connections, portrayed in manuals from

pultrusion manufacturing companies, and extensively

studied their behaviour. These connections were designed

as pinned. Mottram determined that using regular web-

cleated connections revealed damage on the parts for

service situations, which is deemed unacceptable in

structural terms. Their solution was to use different

materials for the web-cleats (Qureshi and Mottram 2013,

2014), namely steel cleats, or GFRP cleats with a fibre-

architecture designed for the path loads sustained.

The motivation for the present study is the lack of

knowledge on the behaviour of connections of GFRP

tubular profiles, namely those with connection parts inside

the profiles. There was a need to develop the connection

inside the profile due to architectural and panel fitting

reasons.

3. Experimental study

3.1 Experimental program

Coupon tests were performed in order to determine the

mechanical properties of the GFRP material used. The

small-scale specimens were extracted from a RHS

120×120×10,0 profile, identical to the one used in the real-

scale connection testing. The coupon tests comprised:

(i) compressive tests, on both longitudinal and transverse

directions (relative to pultrusion axis); (ii) tensile tests,

only on the longitudinal direction; (iii) flexural tests;

(iv) interlaminar shear tests; and (v) in-plane shear tests,

off-axis tensile tests and Iosipescu shear tests. These tests

aimed at determining the resistance properties of the

material, as well as of the corresponding elastic constants.

Monotonic and cyclic tests were further performed to

evaluate the performance of different connection

typologies. Three monotonic tests were performed per

type of connection, aiming to determine the maximum

resistance of the connections, as well as the corresponding

stiffness. Three cyclic tests were performed per connection

type, in order to characterize their stiffness, resistance,

and energy absorbed per cycle.

3.2 Material characterization tests

Small-scale coupon tests were performed in order to

determine the mechanical properties of the material used.

The results of the performed tests are presented in

Table 1, where the subscripts c, t, f, ci, xy, 10°, u, T and L

stand for compressive tests, tensile tests, flexural tests,

interlaminar shear tests, in-plane shear tests, off-axis

tensile tests, ultimate value, on the transverse or

longitudinal directions, respectively. The material

presented orthotropic behaviour, presenting higher

stiffness and strength in the longitudinal axis of the profile.

On the other hand, the shear resistance values measured

were higher in the transverse direction. For that direction,

the rupture failure plane crosses glass fibres, thus

increasing shear resistance.

Three different methods were used to determine the

shear resistance of the material, and all these methods

retrieved different values for that variable, most likely due

to different test setups and stress state in the material.

It is worth mentioning that the values obtained by

Iosipescu shear tests were considered abnormally high. On

the other hand, the values obtained from the off-axis

tensile test method were considered an underestimate of

the shear resistance of the material, as the latter values

were abnormally low. The interlaminar shear test led to a

more common value of shear resistance for this type of

material. The elasticity modulus derived from the coupon

compressive tests was considered as an underestimate of

the actual modulus, with the tensile tests providing more

reliable results.

The test specimens after testing are presented in

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Figure 2. The material characterization tests comprised

a total of 60 specimens tested to determine the properties

of the GFRP material used in the profiles studied. Some

(limited) specimens’ tests were not considered due to

invalid failure modes or loss of data during the test.

Table 1 – Average mechanical properties of the material tested

Test Method Property Average Unit

ASTM - D695

σcu,L 435.06 [MPa]

Ec,L 21.20 [GPa]

σcu,T 88.94 [MPa]

Ec,T 4.84 [GPa]

EN ISO 527

σtu,L 293.83 [MPa]

Et,L 32.70 [GPa]

ν 0.324 (-)

EN ISO 14125 σfu,L 415.09 [MPa]

Ef,L 24.93 [GPa]

ASTM - D2344 Fci 30.56 [MPa]

ASTM -D5379 τxy,L 41.37 [MPa]

τxy,T 58.71 [MPa]

Hodgekinson / EN ISO 527

τ10° 19.56 [MPa]

Gxy 7.33 [GPa]

Figure 2 – Material characterization test specimens

3.3 Specimen properties, setup, instrumentation and

procedure of the connection tests

The monotonic and cyclic tests were performed in the

laboratory Laboratório de Estruturas e Resistência de

Materiais (LERM) of IST. The test setup, which comprised a

closed steel frame, is presented in Figure 3.

The load was applied to the GFRP beam at 600 mm

from the column’s facing flange by a pinned loading fixture

connected to a hydraulic jack with maximum load

capacities of 600 kN and 250 kN in compression and

tension, respectively, with a stroke of 250 mm. The load

cell (capacity 300 kN) was also attached to that loading

system, in series with the hydraulic jack and the set of

pins. The boundary conditions of the column (fixed

rotations and translations) were ensured by a set of steel

blocks. The out-of-plane displacements of the beam free

end was restricted by two aluminium bars.

Ten displacement transducers and two rotation

transducers were used in the full-scale experimental tests

in order to determine: (i) the vertical displacements of the

beam; (ii) the rotation of the beam; and (iii) the rotation of

the column. Both rotations were measured by a set of

displacement transducers and a rotation transducer. The

results presented in this study in terms of rotations were

computed based on the values of the rotation transducer

and the results presented in force vs. displacement curves

were retrieved from the load cell and the displacement in

the load application point. Data was recorded at a rate of

5 Hz using HBM, model QuantumX data logger.

Monotonic tests were performed until the collapse of

the connection or the end of the hydraulic jack’s stroke

(± 125 mm), whichever occurred first. Cyclic tests were

conducted based on a history of displacements,

determined from the monotonic tests.

Figure 3 – Test Setup

Figure 4 to Figure 8 present the geometrical details of

the steel plate connection parts (column connection

element and beam connection element). Both steel

connection elements were introduced inside the closed

cross-section of the profile. Connection type W1 was

expected to behave as a pinned joint, with one bolt per

web of the beam and minimal moment transfer.

Connections type F2, F2S, F4 had bolts on the flanges of

the beam, exhibiting a stiffer behaviour and a larger

moment transfer capacity. These three types of

connections were designed to evaluate the influence of

bolt number and location on the connection behaviour.

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Figure 4 – Details for column steel plate connection part (mm)

Figure 5 – Details for beam steel plate connection part (Type W1, mm)

Figure 6 – Details for beam steel plate connection part (Type F2, mm)

Figure 7 – Details for beam steel plate connection part (Type F2S, mm)

Figure 8 – Details for beam steel plate connection part (Type F2, mm)

3.4 Monotonic tests

The monotonic tests aimed at determining the strength

and elastic properties of the connections, as well as the

associated failure modes and how these influenced the

connection behaviour.

Figure 9 presents four representative load vs.

displacement (measured under the applied load) curves

from the connection typologies tested (one specimen per

connection type). All connections seemed to exhibit an

initial linear behaviour, following minor initial

adjustments, for vertical displacements ranging from 10 to

30 mm, until the occurrence of first damage. First damage

was identified by the occurrence of loud audible crack

noises, or by the appearance of visual damage to any of the

elements. After first damage all connections presented a

gradual reduction of stiffness.

Table 2 presents the average values of the relevant

computed properties of the connections (rigidity and

resistance). Connection W1 presented the lowest stiffness

and resistance average values; connection F2S achieved

the highest average resistance; and connection F4

exhibited the highest stiffness. The values of stiffness and

resistance varied slightly for the connections with bolts on

the flanges of the beams, whereas connection W1

exhibited much lower values.

Figure 9 – Comparison of representative force vs. displacement curves for the different connection types

Table 2 – Average and standard deviation values for the stiffness and strength properties for each connection type

Connection type

Kδ Fu

[kN/m] [kN]

W1 139.1±19.84 4.08±0.88 F2 202.8±50.36 6.46±0.18 F2S 182.6±20.01 8.73±0.75 F4 245.3±40.34 7.03±0.87

0

1

2

3

4

5

6

7

8

9

10

0 30 60 90 120 150

Lo

ad

(k

N)

Displacement (mm)

F2-M2F4-M4F2S-M3W1-M5

6

Connection type W1 revealed the worst performance,

having the lowest initial stiffness and the lowest load

capacity. The first failure in this connection occurred in the

lower web-flange junction of the beam (shear), causing a

reduction in stiffness followed by the shear-out failure of

the bolts of the beam. Once the shear-out failure took

place, the specimen lost its ability to sustain subsequent

loads, leading to collapse. The fact of not having any bolts

on the flanges prevented the connection from transferring

significant amounts of bending moments, thus behaving

similarly to a nominally pinned joint. Figure 10 illustrates

the failure mode for connection type W1.

Connection types F2 and F4 exhibited very similar

maximum resistant loads, close to twice the value for

connection W1. The increase in the number of bolts did

not improve the connection strength. The main cause for

this inefficiency lies in the smaller edge distance of the

first row of bolts (F4) and the fact that that same row of

bolts endured a larger force than the others, due to

non-uniform load distribution for connections with more

than one row of bolts. The main failure mode for these

connections, which led to collapse, was the shear-out

failure, as illustrated in Figure 11. On the other hand, the

web-flange junction shear failure, identified prior to shear-

out, seemed to affect only the stiffness of the connections

and did not impair the resistance capacity.

Figure 10 – Collapse of connection type W1

Figure 11 – Shear-out of the bolts (connection F4)

Connection type F2S, derived from F2, but with a

larger bolt edge distance, revealed the best performance.

Not only did it sustain higher loads for larger

deformations, but, in some of the tested specimens, it did

not actually achieve maximum resistance load for the

imposed maximum displacement of 125 mm (stroke of the

jack). This performance was achieved by delaying the

occurrence of the shear-out phenomenon (which did not

happen in F2S specimens for monotonic tests) with a

larger edge distance of the bolts. This led to the occurrence

of additional failure modes such as: (i) bearing of the GFRP

near the bolts; (ii) vertical cracking of the column; and

(iii) weld failure of the steel plate connection part of the

beam. The higher load sustained by this type of connection

shifted the damage from the beam to the column. The

presented case of multiple failures for high level loads

reveals that all connection elements endured maximum

stress prior to failure and were taken to their maximum

capacity. This led to consider F2S to be the most efficient

connection design.

3.5 Cyclic tests

Cyclic tests were performed in accordance with ECCS’

cyclic load test recommendations (ECCS 1986). The same

displacement history was considered for all connections so

that the results could be more easily compared. ECCS’s

displacement history is based in the yielding displacement,

in this case considered as the average value of the yielding

displacements for all the tested connections specimens.

The yielding displacement (ey) used was equal to 19 mm

and the displacement history is presented in Table 3. ECCS

recommends analysing the yielding point on both loading

directions (downwards and upwards). Since the

connections were symmetrical, this was not considered.

For the cycles of displacements larger than the yielding

displacement, the ECCS recommendations propose three

repetitions, whereas in this study only two repetitions

were performed.

Table 3 – Displacements history

Cycle Applied displacements

[-] [mm]

1st [-ey/4; +ey/4] [-4.75; +4.75]

2nd [-ey/2; +ey/2] [-9.5; +9.5]

3rd [-3ey/4; +3ey/4] [-14.25; +14.25]

4th [-ey; +ey] [-19; +19]

5th [-2ey; +2ey] [-38; +38]

6th [-2ey; +2ey] [-38; +38]

7th [-4ey; +4ey] [-76; +76]

8th [-4ey; +4ey] [-76; +76]

9th [-6ey; +6ey] [-114; +114]

10th [-6ey; +6ey] [-114; +114]

The parameters considered in the cyclic tests set forth

by ECCS and used in this study were: (i) rigidity ratio;

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(ii) strength ratio; and (iii) absorbed energy. All these

parameters are described in ECCS standard [14] and are

computed from the moment vs. rotation curves. The

rigidity ratio relates the unloading stiffness of one cycle

with the initial linear stiffness. The strength ratio relates

the strength of the yielding point to the ultimate strength

of the cycle. The absorbed energy of the cycle is computed

through the product of the moment by the rotation and is

evaluated in kN.m.rad, measuring the area under the

moment-rotation curve.

Figure 12 presents, as an example, the moment (M) vs.

rotation (θ) curve for the test of connection specimen F2S-

C1, the test type chosen to be used in the Clickhouse

project. In addition, a representative curve of the

monotonic test behaviour of the same joint type is also

plotted (specimen F2S-M3). It can be seen that the

hysteretic curves of the connection presented similar

behaviour in both loading directions (downwards and

upwards), as expected from their symmetrical geometry.

The maximum load points presented in Figure 12 were

achieved at very similar load level and rotation, therefore

confirming the symmetrical behaviour. The monotonic test

results generally feature the envelope of the cyclic test

results.

Figure 12 –Moment vs. rotation curve for connection type F2S

Table 4 presents the maximum moment values and the

corresponding rotations for all specimens tested; the

average values and the corresponding standard deviations

are also presented.

Connection W1 was the one that exhibited the most

asymmetrical behaviour in terms of the loading direction

(downwards, as positive values, and upwards, as negative

values). The first damage, experienced in the downwards

loading phase, impaired the connection, rendering the

following phase to present lesser resistance. This

phenomenon was only observed in W1 type connections.

The maximum moment experienced in cyclic testing is in

agreement with the resistances presented in the

monotonic tests, for all connections tested.

Table 4 – Maximum load points for the cyclic tests

Type Specimen/ value

Mmax Mmin θmax θmin

(kN.m) (kN.m) (rad) (rad)

W1

W1-C1 2.9 -1.4 0.061 -0.076

W1-C2 2.4 -2.3 0.064 -0.013

W1-C3 3.6 -2.9 0.065 -0.067

Average 3.0 -2.2 0.063 -0.092

StDev 0.6 0.7 0.002 0.035

F2

F2-C1 4.0 -4.6 0.118 -0.101 F2-C2 4.2 -5.2 0.102 -0.131

F2-C3 5.2 -3.6 0.120 -0.128

Average 4.5 -4.4 0.113 -0.120

StDev 0.6 0.8 0.010 0.017

F2S

F2S-C1 5.4 -6.3 0.118 -0.101

F2S-C2 6.4 -6.5 0.102 -0.131

F2S-C3 5.2 -6.7 0.120 -0.128

Average 5.7 -6.5 0.113 -0.12

StDev 0.7 0.2 0.010 0.017

F4

F4-C1 4.8 -4.3 0.101 -0.063

F4-C2 5.4 -6.4 0.121 -0.119

F4-C3 4 -4.8 0.077 -0.12

Average 4.7 -5.2 0.099 -0.101

StDev 0.7 1.1 0.022 0.033

Figure 13 presents the rigidity ratios for all

connections tested. The results of one representative

specimen per connection type are illustrated. The rigidity

ratios exhibit an overall downward trend with the increase

of the cycles, for all connection types. For cycles of

displacement smaller than the yield displacement, the

connections display a rigidity ratio above the unity, due to

the overcoming of the initial friction forces.

Figure 13 – Rigidity ratio

Figure 14 presents the resistance ratios for one

specimen per connection type. The resistance ratio

displays an initial increasing tendency until the yielding

displacement cycle. Subsequently, the cycles for the same

displacements show a decrease in resistance ratio with the

repetition of the cycles.

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Figure 14 – Resistance ratio

Figure 15 presents the absorbed energy ratio of one

specimen per connection type. The absorbed energy ratio

is only calculated for cycles of displacement larger than the

yielding displacement. For the repetition of cycles of the

same displacement, the absorbed energy ratio shows a

significant decrease in value. The tendency presented in

this ratio is similar to all types of connections.

Figure 15 – Absorbed energy ratio

Figure 16 presents the total absorbed energies for the

different connections tested; one specimen per connection

type was chosen to best represent the behaviour of that

typology.

Connection type F2S shows a higher absorbed energy

per cycle than the others, leading to a total absorbed

energy for specimen F2S-C1 of over 3 000 kN.m.rad,

representing an almost 50% increase compared to both

connection types F2 and F4. Type W1 was shown to

present the lowest absorbed energy, with only half of the

values of connection types F2 and F4. Despite the increase

in the number of bolts, connection type F4 presents a very

similar behaviour to connection F2, due to the uneven

force distribution per bolt and to the smaller edge distance

of the first row of bolts in connection type F4

Figure 16 – Total absorbed energy per cycle

The failure modes presented in cyclic testing were very

similar to the ones presented in the monotonic testing,

with the exception of connection type F2S that displayed

an additional failure mode on the cyclic tests of shear-out

on the region of the bolts.

In agreement with the results of the monotonic tests,

connection type F2S revealed the best performance. As

mentioned, this connection was later included in the

Clickhouse project. Connection W1 presented the worst

performance; connections F2 and F4 displayed very

similar behaviour, despite the difference in the number of

bolts.

4. Numerical analysis

4.1 Model description

The numerical analysis presented herein was

developed using the finite element software Abaqus V6.13

(Simulia 2013).

4.1.1 Geometrical properties, mesh and

discretization

Due to the existing symmetry and to reduce

computation time, the numerical models only considered

half of the connection.

Table 5 presents the finite element mesh specifications

for the model of connection F2S, which possessed a total of

9 467 elements, 11 721 nodes and 48 429 degrees of

freedom.

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Table 5 – Properties of the finite element mesh (model F2S)

Part Element

Type Number of elements

Number of Nodes

Beam (GFRP) frame B311 10 11

shell SC8R2 608 1328

Column (GFRP)

frame B311 6 8

shell SC8R2 1153 2474

Connection Part (S235)

(beam) C3D8R3 1069 2268

(column) C3D8R3 1564 3330

Bolts

M8_10 C3D104 413 796

M10_10 C3D45 510 167

M10_20 C3D45 582 184 1 B31 – 2 node frame element; 2 SC8R – Continuum Shell with 8 nodes (5 integration points in thickness); 3 C3D8R – 8 node cubic solid element with reduced integration (1 integration point); 4 C3D10 – 10 node solid element (solid) 10-node tetrahedral (4 integration points); 5 C3D4 – solid element (solid) 4-node tetrahedral (1 integration point);

The GFRP parts (beam and column) were modelled

with two types of finite elements: (i) continuum shell with

8 nodes and reduced integration (SC8R), for the stress

concentration zones, near the connection; and (ii) frame

elements (B31) for the remaining zones. The steel

elements (plates and bolts) were modelled with tri-

dimensional solid elements of various types.

The bolt holes were modelled with no clearance (tight

fit) in order to represent the initial contact between

elements, and reduce convergence problems.

The finite element mesh, illustrated in Figure 17, was

generated to evaluate phenomena such as bearing of the

material, shear-out failure on the region of the bolts and

shear failure at the web-flange junction. Smaller elements

were considered in stress concentration zones. The

maximum dimension of the elements was 10 mm, equal to

the GFRP profile wall thickness.

Figure 17 – Finite elements mesh (F2S)

4.1.2 Mechanical properties (stiffness, resistance

and damage progression)

The steel materials were modelled with elasto-plastic

behaviour with linear hardening and an elasticity modulus

of 210 GPa and a Poisson coefficient of 0.3. The orthotropc

properties of GFRP are presented in Table 6.

Table 6 – Elastic constants for GFRP

E11 [GPa] E22 [GPa] υ12 [-] G12 [GPa]

32.7 4.8 0.3 3.2

The Hashin failure criteria was considered, comprising

a total of six failure modes: (i) matrix tension; (ii) matrix

compression; (ii) fibre tension; (iv) fibre compression; (v)

longitudinal shear; and (vi) transverse shear. The

considered strengths of the above mentioned failure

modes are presented in Table 7.

Table 7 – Material failure mode strengths

f1,T [MPa] f1,C [MPa] f2,T = f2,C [MPa] f1,S [MPa] f2,S [MPa]

326 435 89 41 59

The degradation model applied defines damage

progression through a set of fracture energies associated

with four different types of damage: (i) matrix tensile

damage; (ii) matrix compressive damage; (iii) fibre tensile

damage; and (iv) fibre compressive damage.

The fracture energies presented in Table 8 were based

on the work of Nunes et al. (2015), referring to a similar

type of GFRP material. The fracture energies were

estimated by curve fitting procedures based on the area of

the force-displacement curves for the four simple types of

failure.

Table 8 – Fracture energies for the different types of damage

Gf,Ft [MPa] Gf,Fc [MPa] Gf,Mt [MPa] Gf,Mc [MPa]

2.38 5.28 0.65 1.08

4.1.3 Loading and support conditions

Figure 18 presents the considered loading and support

conditions. The loading was applied by imposing a

displacement in the load application point, at a distance of

60 cm from the column facing flange.

The displacements and rotations were restrained at the

column’s extremities, to simulate the restraint induced by

the steel supports. Symmetrical boundary conditions were

also considered.

10

Figure 18 – Loading and boundary conditions

4.1.4 Contact and friction formulation

A frictionless hard contact was considered in all steel-to-

GFRP contact surfaces. A surface-to-surface, small-sliding

discretization method was chosen. A tie restraint was

applied to all steel-to-steel contact screw areas since the

tangential component of the contact force was significant.

4.1.5 Analysis type

A both physically and geometrically non-linear analysis

with damage progression was performed. As mentioned,

the Hashin failure criterion was used in conjunction with a

continuous degradation model based on fracture energies

of the GFRP material, for the different failure modes. To

analyse damage progression, the parameters DAMAGESHR

(damage occurring by shear, used to identify the shear-out

phenomena) and DAMAGEFT (damage occurring by fibre

tension, to identify the transverse tensile failure of web-

flange junction) were considered in ABAQUS software.

4.2 Results

Figure 19 to Figure 22, present the comparison between

the experimental and numerical results regarding the

monotonic tests on the different connection typologies.

Figure 19 – Force vs. displacement curves, experimental and numerical comparison - connection W1

Figure 20 – Force vs. displacement curves, experimental and numerical comparison - connection F2

Figure 21 – Force vs. displacement curves, experimental and numerical comparison - connection F2S

Figure 22 – Force vs. displacement curves, experimental and numerical comparison - connection F4

The numerical models correctly reproduced the

experimental results in terms of: (i) initial linear elastic

stiffness; (ii) maximum strength; and (iii) initial non-linear

behaviour. However, the non-linear behaviour for large

displacements was not simulated with full accuracy. The

resource to the computation of fracture energies based on

the work of another author (and another GFRP material) is

probably the reason to such differences.

A comparison between the experimental and numerical

data for the strength and stiffness characteristics of the

connections is presented in Table 9. This comparison

11

Table 9 – Experimental vs. numerical comparison of stiffness and resistance properties

Connection type

Experimental Numerical

Kδ Fu Kδ Δ Fu Δ

[kN/m] [kN] [kN/m] [%] [kN] [%]

W1 139.12 4.08 179 28.70% 4.4 7.80%

F2 202.82 6.46 210.7 3.90% 6.34 -1.90%

F2S 182.57 8.73 206 12.80% 6.71 -23.10%

F4 245.27 7.03 249.6 -1.80% 7.51 6.80%

comprises the relative difference between the values

obtained from the experimental tests and the

corresponding numerical results. The relative difference of

the above-mentioned parameters ranges from as low as

1,80%, for F4 strength, to as high as 28,70%, for the

stiffness of connection W1.

In light of such good overall agreement with the

experimental data, the use of numerical models such as

those developed in this study is recommended as an

alternative to relatively expensive and long lasting full-

scale experimental campaigns.

5. Conclusions and future developments

5.1 Conclusions

Among the various connection types investigated in the

present experimental and numerical study, connection F2S

was shown to offer the best performance, being able to

resist to higher levels of load for large deformations.

Hence, this connection type was chosen to integrate the

Clickhouse project for the beam-to-column connections of

the modular house. The main drawback of this connection

type is the fact it did not present the highest stiffness. In

the case of GFRP pultruded structures, deformability is

usually the main conditioning factor for their design.

Therefore, maximizing the stiffness connection is

considered of the upmost importance in order to reduce

deformations, and achieve higher efficiency of the overall

structural system.

The experimental study allowed drawing the following

conclusions on the geometrical parameters of the joint:

(i) The edge distance of the bolt is a very

conditioning parameter in terms of joint

resistance, being related with the shear-out failure

phenomenon that can lead to premature failure of

the joint. Hence, an improvement in resistance

from connection F2 to connection F2S was

observed with the increase of the edge distance of

the bolts (from 40 mm to 55 mm).

(ii) The increase in the number of bolts, from

connection F2 to F4, did not provide any

improvement in terms of strength, due to uneven

force distribution between bolt rows (indeed, the

first row, closer to the joint, carries a larger

fraction of the load) and a smaller edge distance of

the first row. On the other hand, the connection F4

presented the highest stiffness due to a more

efficient restraint (more bolts) of the flanges of

the beam in the connection zone.

(iii) As expected, connection type W1 revealed the

worst performance, with the smallest stiffness,

resistance and absorbed energy values. This

connection presented minor initial free rotations,

rendering it impractical for real life applications.

Despite the fact that GFRP material generally presents

brittle failure, with respect to the design of the joint, it is

possible to achieve pseudo-ductility. Connection types F2,

F2S and F4 were able to resist to relatively high levels of

load, at large deformations, attesting that assumption. The

failure mode of the web-flange junction is not considered

brittle, since specimens were able to resist further loading

after the occurrence of this failure mode. The failure of the

web-flange junction only affected the stiffness of the

connection, presenting a gradual decrease in value. On the

other hand, the shear-out failure is considered to be of

brittle nature, since the specimen experienced an

instantaneous load reduction when this failure occurred

As previously stated, in light of the very good

agreement between the numerical and experimental

results, the use of finite element numerical models to

study different connections types between GFRP

pultruded members seems to be viable, as an alternative to

more expensive and time consuming experimental

campaigns.

5.2 Future developments

The extensive study presented herein justify suggesting

the following developments:

12

(i) Further study of the behaviour of the joints in the

plane transverse to the loading plane. This study

is fundamental to describe the connection

behaviour when subjected to horizontal flexure.

This will allow to integrate/consider the

connection in a 3D model.

(ii) Further study of the behaviour of the joints tested

when exhibiting continuity of the joint. The

influence of the continuity and that of the

transversal beams was not addressed in this

campaign, and can be of great influence to the

joint behaviour.

(iii) Parametric studies about the influence of the edge

distance parameters in joints of one row of two

bolts (like the joints studied herein, F2 and F2S) to

determine the optimum value in terms of

connection resistance.

(iv) Full scale frame dynamic tests to determine the

damping coefficient of this types of structures.

Only then, it is possible to model correctly a 3D

structure and evaluate its behaviour to a dynamic

load, such as a seismic load.

(v) Further studies on the fracture energy of the GFRP

material in order to better develop the finite

elements models of the joints. A more accurate

determination of the fracture energies could lead

to models in closer agreement with the

experimental data in the non-linear phase of the

connections’ response.

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13

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