IN-PLANE BEHAVIOR OF TUFF MASONRY PANELS STRENGTHENED

WITH FRP DIAGONAL LAYOUT

Giancarlo Marcari1, Daniel Oliveira2, Giovanni Fabbrocino3 and Paulo B. Lourenço4

Abstract
The present paper deals with a quantitative analysis of the shear strength behavior of
masonry panels strengthened with diagonal layout. The objective of the study is to progress
towards understanding the shear strength contributions from masonry and FRP to the lateral
resistance of strengthened panels. To this aim, the experimental data set from 7 masonry
panels subjected to shear-compression loading obtained by [Marcari 2007] have been used.
Additional information includes the local behavior of the shear reinforcement and its effects
on the global response of the panels. In particular, FRP strain profiles along the plies (i.e. the
transferrable tension force within FRP), the lateral drifts and lateral load achieved by the
panels at the occurrence of the debonding of the plies or at the peak strains are discussed.
The role of the anchorage systems used for the diagonal plies (namely full wrapping and
partial-wrapping) on the macro-response of the panels is also examined. The experimental
results show the effectiveness of the anchorage system in restraining the FRP at the
anchored edges, avoiding premature failure due to FRP debonding. As a result, the
specimens were allowed to develop their full lateral resistance. Quantitative evaluation of the
contributions from masonry and FRP is performed by using a truss model approach,
combined with a suitable diagonal shear strength criterion for masonry. Accuracy of the
procedure is assessed through comparison with the experimental data.

Keywords: masonry, shear, composite materials, FRP strains, FRP diagonal layout

1
Assistant Professor, ISISE, University of Minho, Dept. of Civil Eng., 4800-058, Guimarães, Portugal,
marcarigiao@civil.uminho.pt
2
Assistant Professor, ISISE, University of Minho, Dept. of Civil Eng., 4800-058, Guimarães, Portugal,
danvco@civil.uminho.pt
3
Associate Professor, Strega Lab., University of Molise, 86039, Temoli, Italy, giovanni.fabbrocino@unimol.it
4
Full Professor, University of Minho, ISISE, University of Minho, Dept. of Civil Eng., 4800-058, Guimarães,
Portugal, pbl@civil.uminho.pt
 Introduction
In the past two decades, the use of externally bonded fiber reinforced polymer (FRP)
composites has steadily increased as an efficient technique for structural retrofitting and
seismic reinforcement of masonry components. The response of FRP-strengthened masonry
has extensively been studied both experimentally and numerically with an emphasis on
overall shear capacity, ductility, and failure modes [Manfredi 2008]. A recent comprehensive
literature survey on experimental works can be found in the ACI 440.7R-10 guide.
Although significant progress has been made, there is a critical need for the development of
design provisions for FRP diagonal layouts. In this regard it is noted that the recent guidelines
ACI 440.7R-10 and CNR 200/2004 still do not enclose design expressions for FRP diagonal
configurations. Substantial knowledge gaps that still need to be filled for diagonal FRP
layouts include: (i) a link between local (FRP–masonry interfacial) behavior and global
response of the panels, (ii) a quantitative analysis of shear contributions from both masonry
and FRP reinforcement and (iii) development of suitable bond strength models for different
types of masonry substrate.
The present paper focuses on the experimental behavior of masonry panels strengthened
with FRP diagonal configuration. To this aim, the experimental test results of tuff masonry
panels with FRP layout obtained by [Marcari 2007] have been selected. The objective is to
provide additional experimental data with reference to the local strain behavior of the
diagonal reinforcement, and the quantitative evaluation of the weight given to masonry and
FRP shear strength contribution to lateral resistance of the strengthened panels. The local
FRP strain readings allowed to investigate the debonding process of both compressed and
tensioned plies, and its effects on the shear response and lateral deformation of the panels.
The role of the anchorage system on the experimental local and global behavior of the panels
is also investigated. An analytical study on the strength contributions from masonry and FRP
is carried out using a truss model approach, combined with a proper shear strength model for
masonry. From comparisons between computed and experimental data, relevant results are
presented and discussed.

Experimental campaign: brief review of the shear-compression tests

The experimental campaign was carried out since 2005 [Marcari, 2005, Marcari 2007] at
CESI Laboratory in Seriate, Italy.
For the purpose of subsequent analysis, a brief review of the test program is performed.
Information is also given herewith about the system used to anchor the edges of the shear
reinforcement, and the instrumentation setup of the plies. Moreover, the experimental shear-
horizontal displacement curves are presented for all the tested panels.
The tests were performed on multiple leaf tuff masonry panels having dimensions of 1570 x
1480 x 530 mm, characterized by transversal connection between the external leaves.
Through the test equipment it was possible to control the vertical load (No) applied on the top
of the panel. The vertical load was applied first, followed by shear loading. The tests were
displacement controlled.
The reinforcement consisted of diagonal 200 mm wide FRP plies bonded on the two sides of
the panel as shown in Figure 1a. Two composite materials were used, namely CFRP and
GFRP. Moreover, the test variables included the FRP amount, i.e. one layer and two layers
for each diagonal ply. The specimens with one layer are denoted by LD and those with two
layers are denoted by HD. The test program included 7 strengthened panels under shear-
compression loading as follows: panels C1a and C1b with LD CFRP; panels C2a and C2b
with HD CFRP; panel G1a with LD GFRP; panels G2a and G2b with HD GFRP.
The diagonal plies were anchored at the edges thorough horizontal FRP plies either wrapped
around the panel section, or partially-wrapped (called herewith U-wrap), as schematically
illustrated in Figure 1b. The latter system was used for specimens C2a and C2b. The FRP
material properties are given in [Marcari 2007].
The specimens were extensively instrumented. The FRP reinforcement strains were
measured using 5 mm gauge-length strain gauges (SGs), with a measurement range limited
to ±5000 µε. The measurement points are shown in Figure 1a. Symmetry of the gauge points
was ensured on the two sides of the panel. Typically, only one side of the panels was gauged
completely (i.e. side A). Panels C2a and G2a were instrumented with SGs on both sides.
It is worth noting that the experimental program included also tests on 4 plain panels under
vertical compression, and 4 plain panels under shear-compression. The plain panels showed
an average compressive strength calculated over the gross section of 1.1 MPa (CoV=27%),
with an average elastic modulus of 635 MPa (CoV=8%).
FRP plies

V V
δ δ

1 2 9 10
45

45

FULL WRAPPING
0

FULL WRAPPING
3 4 11 12
35

35
0

Strain gauges
5 6 13 14
Bonded zone
7 8 15 16
FRP ply

A side B side U-WRAPPING

(a) (b)
Figure 1. (a) FRP shear strengthening; (b) anchorage system of the diagonal plies

The response of plain panels tested under shear was governed by the formation and
development of inclined diagonal cracks, which propagated through mortar joints and stones.
The average maximum lateral resistance (Vmax) approached 132 kN with CoV equal to 26 %.
All strengthened panels failed in shear, characterized by the formation of diagonal cracks,
with vertical cracks occurring on the lateral compressed side, accompanied normally by
spalling of the external stones. The rupture of the FRP diagonal plies in tension was
observed in the case of panels G1a and G2b.
The shear force vs. horizontal displacement curves (V-δ) are reported in Figure 2. This figure
illustrates also two of the V-δ curves obtained for the plain panels, which are respectively
representative of the lower and upper curve in the behavior of the plain panels. The shear
strength and displacement capacity of the panels are described in detail in [Marcari 2007].
 240 240
V (kN) V (kN)
200 200

160 160

120 120

80 80

40 40
C1a C1b C2a C2b Plain δ (mm) G1a G2a G2b Plain δ (mm)
0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

(a) (b)
Figure 2. Comparisons of experimental shear force-horizontal displacement curves: (a)
CFRP and (b) GFRP

Behavior of FRP strains

The experimental strain vs. horizontal displacement curves (strain profiles) monitored along
the diagonal plies are used to investigate the effect of the local (interfacial) behavior of the
FRP on the global response of the panels, focusing on debonding of the FRP from the
substrate, as well as on the average peak strains within FRP. It is noted that debonding of
FRP from the substrate is intended not as peeling failure (which involves direct tensile
stress), but as shear delamination failure. The results are presented for panels C2a and C2b
which were gauged on the two sides.

Panel C2a
The strain profiles from side A of the panel are illustrated in Figure 3a. It can be observed that
the strain profiles on the opposite sides of the wall followed a similar trend.
The readings on side A started with an average strain level of -315 µε, while those on B side
started with an average of -375 µε, due to the pre-compression load applied to the panel.
The local debonding of the compressed ply on side A and B initiated above the central zone
of the wall at a δ = 5.0 mm (drift=0.35%), as it was detected by the strain readings of SG #1
and #3 on side A (Figure 3a), and SGs #10 and #13 on side B. The average debonding strain
ranged between -700 µε and -1100 µε. At this point, the lateral shear force was approaching
130 kN on the ascending branch, about 70% of the wall peak load. The part of the
compressed plies below the central zone of the panel locally debonded at δ = 9.5 mm
(drift=0.6%), for an average strain of about -1100 µε, as shown by SG #6 and #8 on A side.
At this point the lateral resistance of the wall was close to its peak value. After this
displacement the compressed plies started to buckle locally (Figure 3a).
The tensioned plies, the pairs SG #5 and #14, and SG #7 and #16, placed at the same
location on opposite sides of the walls showed higher strain values since the onset of the test
(Figure 3b). This behavior can be explained by the change in direction of that part of the
plies, caused by the lateral deformation of the panel. The drops of strain occurred at a δ =
16.2 mm (drift =1.0%) on side A, and at δ = 13.5 mm (drift=0.86%) on side B were due to a
sudden debonding of the tensile plies from the substrate (see Figure 3b). The debonding
occurred for a lateral resistance decay of 8% or lesser (Figure 3c). The maximum tensile
strains occurred at δ = 21.1 mm (drift=1.3%), with a lateral load decay of about 18%. The
values approached +2630 µε and +2995 µε on side A and B, respectively. The maximum
tensile strain value, averaged from both sides of the panel was 2810 µε.

Panel G2a
The strain-lateral displacement curves on side B of the panel are illustrated in Figure 4. Once
again it was found that the strain profiles from both sides behaved in a similar manner. The
strain readings started with negative values due to the initial pre-compression loading. The
average compressive deformation approached -228 µε on A side, and -180 µε on B side.
Cracks in the masonry initiated at about δ = 5 mm (drift=0.3%), and about 70% of the peak
load. This led to a reduction of stiffness in the global behavior, as can be seen in Figure 4c.
At this point, the strain profiles showed a change in slope, with an increase of stiffness. The
compressed plies initiated to debond below the central zone of the panel at about 8.0 mm
(drift=0.6%), when the lateral peak force was attained. This behavior can be detected from
the strain readings of SG #6 and #8 on side A, and from SG #13 and #15 on side B (Figure
4a). The compressed plies resulted fully debonded at around δ =13 mm (drift=0.86%) when
the V- δ curve was approaching the softening branch (see Figure 4a and Figure 4c). After
that displacement, the plies buckled locally.
The debonding strains of the compressed plies ranged between -810 µε and -950 µε. Once
again, the strains measured below the centre line of the wall stayed relatively high, as shown
by SG #5 and #14, as well as by SG #7 and #16. In correspondence of this peak lateral
strength, the readings of SGs #7 and #16 exceeded the limit of +5000 µε (Figure 4b).
However, no fracture of the FRP reinforcement was observed.
The experimental curves of SG #2, #4, #5 on side A, and SG #9, #11, #14 on side B indicate
that the maximum tensile strains have been attained when the lateral load resistance
dropped by about 25%-30%, with δ = 20-25 mm (drift=1.3%-1.6%). At that displacement, the
panel was characterized by vertical cracks that developed across stones and mortar joints at
the compressive side of the panel, which caused spalling of the stones.

Discussion of the experimental results

Behavior of the tested panels
Based on the test results, the load transfer mechanisms for the FRP strengthening upon
increasing displacement can be understood. The strengthened panels were initially in an
uncraked state, and the FRP was fully bonded and acted compositely with the masonry. The
initial lateral stiffness of the strengthened panels was not significantly influenced by the FRP.
In fact, no relevant differences have been found between the stiffness of the unstrengthened
and strengthened panels before cracks in the strengthened masonry caused the change of
slope of the V-δ curve (Figure 2). Upon increasing lateral displacement, local debonding of
FRP from the masonry substrate occurred. The FRP-masonry bond was lost typically starting
at the central zone of the panels, and progressing towards the anchored edges.
 0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40
δ (mm) δ (mm)
-600
-600

-1200
-1200

1 -1800
10
-1800 3
12
6 -2400
13
µε 8
-2400 µε 15
-3000
(a) Strain profiles along the compressed ply – A side (a) Strain profiles along the compressed ply – B side
4200 5400
µε 2 µε 9
3600 4 4800 11
3000 5 4200 14
7 3600 16
2400
3000
1800
2400
1200 1800
600 1200
δ (mm) 600
0 δ (mm)
0 5 10 15 20 25 30 35 40 0
-600
-600 0 5 10 15 20 25 30 35 40
(b) Strain profiles along the tensile ply – A side (b) Strain profiles along the tensile ply – B side
240 240
V (kN) V (kN)
200 200

160 160

120 120

80 80

40 40
δ (mm) δ (mm)
0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

(c) Shear force vs. horizontal displacement curve (c) Shear shear vs. horizontal displacement curve

Figure 3. Panel C2a: FRP strain profiles Figure 4. Panel C2b: FRP strain profiles (a,b)
(a,b) and shear force vs. horizontal and shear force vs. horizontal displacement
displacement curve (c) curve (c)

Debonding of the compressed plies developed in the pre-peak regime of the panels. Let
ξdeb=Vdeb/Vmax,exp be the ratio between the lateral force at the debonding of the compressed
plies (Vdeb), and the peak load (Vmax,exp). The wall lateral drifts and the ξdeb ratios experienced
by the panels at debonding of the compressed plies are summarized in Table 1. From this
table it can be seen that the compressed plies debonded when the lateral force was on the
ascending branch of the V-δ curve, ranging between levels of 70% and 100% of the peak
load. However, the lateral drift at which debonding of compressed plies occurred seems not
to be correlated with the FRP type or FRP amount (values ranged between 0.25% and
0.90%).
As for the tensile plies, it is noted that the strains in the FRP showed a non linear behavior,
characterized by an irregular path around the peak lateral force, when major cracks were
developing across masonry.
It is of interest to observe that the tensile strains curves along each ply were similar in shape,
even differences were found in the thickness of the adhesive and in the local material
properties related to resin-rich zones between FRP layers and substrate surface
irregularities. Moreover, a comparison between the strain profiles of the panels instrumented
on both sides (i.e. panels C2a and G2a in Figure 3) indicates that a substantially symmetric
behavior is found in terms of compression and tensile strains profiles, debonding strain and
peak tensile strains. Also, it is noted that the peak of the tensile strains was attained when the
panels were experiencing softening behavior. At this stage, the walls were severely cracked,
and the diagonal tensile plies debonded from the substrate. However, the diagonal tension
action through the FRP was still reacted by a vertical compression in the masonry until the
anchorage system peeled off from the support, or the panel spalled on its compressive side.
The lateral drifts attained in correspondence of the maximum tensile strains (εmax) in the FRP
have been summarized in Table 1. This table shows also the shear strength degradation ratio
Sr calculated as V/Vmax,exp, with V the actual force that corresponds to εmax. The drops of the
strains profiles corresponded with drops in slope of the load-displacement response of the
panels, mainly due to relevant cracks occurring in the masonry or FRP fracture of a tensile
ply.

Table 1. Experimental drifts and lateral force at the debonding of the compressed plies for
the maximum tensile strains
At debonding of the At the maximum tensile strain
compressed plies
Panel FRP FRP
Panel lateral Panel lateral
label type amount ξdeb Sr
drift drift
(%) (%) (%) (%)
C1a 0.50 ÷ 0.65 70 ÷ 85 1.40 15
LD
C1b 0.75 ÷ 0.80 85 ÷ 90 1.30 10
CFRP
C2a 0.35 ÷ 0.60 70 ÷ 100 1.30 20
HD
C2b 0.75 ÷ 0.80 70 ÷ 75 1.90 10
G1a LD 0.45 ÷ 0.50 80 ÷ 100 1.00 ÷ 1.15 20 ÷ 25
G2a GFRP 0.80 ÷ 0.90 95 ÷ 100 1.30 ÷ 1.60 25 ÷ 30
HD
G2b 0.25 ÷ 0.45 75 ÷ 100 0.90 11

It was observed that the lateral displacement of the panel caused direction changes in the
diagonal tensile plies (see Figure 5a and Figure 5c). Consequently, the tensile force was not
perfectly centered along the ply length, and introduced locally a bending moment which lead,
in the case of the lower strength FRP type (i.e. GFRP), to the rupture of the ply (Figure 5c).
Moreover, FRP rupture generally occurred below the horizontal centre line of the wall,
between SG #5 and SG #7. It was also observed that the FRP rupture occurred when the
panel behavior was on its softening branch, with a strength reduction between 20% and 25%.

Peeling failure
Large crack

Buckling

Debonding FRP
Buckling rupture
Fibers not perfectly aligned

(a) Panel G2a: damage at (b) Panel C2b: damage at (c) Panel G1a: damage at
1.4% drift on side A 1.90% drift on side B 1.2% drift on side A
Figure 5. Damage of selected strengthened panels: (a) G2a; (b) C2b; (c) G1a.

Role of the anchorage system

From the experimental tests it emerges that the two anchorage systems envisaged in the
study resulted effective in preventing the debonding of the FRP shear strengthening at the
anchored zones. As a result, the full shear capacity of the masonry panels was developed.
The full wrapping system improved the inelastic behavior of the panels better than the U-wrap
system. In fact, panels C2a and G2a were able to attain relevant drifts without significant
strength degradation in comparison with the specimens C2b and G2b of the same FRP type
and amount, but with U-wrap anchorage (Figure 2).
The anchorage system also affected the failure mode of the panels. It has been observed
that large vertical cracks in the lateral compressive side of the masonry were likely to be
triggered by the U-wrap system (Figure 5b). As a consequence, splitting along the lateral side
of the walls occurred in combination with spalling of lateral stones, which in turn led to a rapid
loss of strength and stiffness. In several cases it was also observed that the U-wrap system
suffered detachment (or peeling failure) from the lateral side of the wall, under the action of
the diagonal reinforcement. In this situation, the diagonal reinforcement was no longer
properly fixed at the top extremity, and therefore it was no longer able to transfer any load to
the masonry in a controlled manner.
However, the experimental results indicate that cracking on the compressed side of the panel
due to the behavior of the U-wrap anchorage, had a decisive effect normally on the post peak
branch of the specimen, when the lateral resistance was reduced by 10%-15%.
 Analytical investigation

Analysis of shear strength contribution from FRP

In order to investigate the FRP contribution to the lateral strength capacity of the
strengthened panels, the truss model shown in Figure 6 is used. The model is characterized
by the diagonal FRP in tension, and the vertical strut of masonry in compression. According
to the experimental results, it is assumed also that the compressed plies do not contribute to
the strength and stiffness of the panels. Notwithstanding some differences in the strain
readings along the tensile plies, it is useful to compute the tensile force developed by the
diagonal reinforcement on the base of average strain profiles. Therefore, the tensile force
developed in the diagonal plies is compute as:

Ffrp = n × (E frp × w frp × t frp ) × ε frp [1]

with n = FRP ply number; εfrp = measured FRP strain, function of the lateral displacement δ;
Efrp = elastic modulus of the FRP; wfrp and tfrp = the width and the thickness of the diagonal
ply, respectively.
For the purposes of this investigation the tensile force developed in panels C2a and G2a is
calculated from the average strain profile from both sides of the specimens. For the rest of
panels the tension force is calculated from the average strain profile on side A.
The contribution from the FRP to the shear strength is computed by considering the
equilibrium of horizontal forces:

Vfrp = Ffrp × cos θ [2]

where θ = the diagonal angle of the masonry wall. The vertical component of Ffrp represents
the increased vertical load carried through the masonry by truss mechanisms:

N m ,frp = Ffrp × senθ [3]

δ
Vfrp
Diagonal tie
FRP ply Nm,frp
Vertical strut
Ffrp

Figure 6. Adopted truss model

Figure 7 presents the values of Vfrp as a function of the displacement δ for all tested panels,
together with the V-δ curves of the plain and the strengthened panels.
The graphs show that the shear contribution of FRP is characterized by an initial
approximately linear behavior until the strengthened panels reach their peak lateral load. On
the other hand, the masonry behavior is typically characterized first by stable microcracks
that propagate in an unstable fashion at around the peak load. This uncontrolled cracking
growth is effectively restrained by the bridging effect of the FRP. In fact, it is observed that
the curves Vfrp(δ) start to increase in slope at around peak load in the V-δ curves of the
strengthened panels. Moreover, as with the trend for the strain profiles, the Vfrp curves show a
non linear and instable behavior. Consequently, the panels are allowed to sustain further load
by truss mechanism, with the diagonal action through the FRP that is reacted by a vertical
compression in the masonry. The peak of Vfrp is seen after the attainment of the peak
strength of the strengthened panels. At this point, the increased vertical load on the
compressed side of the panel (due to truss mechanism) causes the formation of large vertical
cracks across masonry. Therefore, the panels suffer heavy damage with strength and
stiffness degradation until the end of the tests. It is noteworthy that the peak of Vfrp and the
peak shear load of the plain panels occur under different lateral displacements. From the
analysis of the results illustrated in Figure 7 it was observed that panel C2b showed the lower
Vfrp strength but the higher lateral strength capacity. In this case, high shear resistance of
masonry is considered responsible for the high shear resistance attained by panel C2b.

Analysis of shear strength contribution from masonry

Test results are used to compare shear strength equations proposed in the new Italian
NTC08 code, respectively associated to diagonal tension shear failure and rocking failure
mechanism. The shear strength associated to sliding mechanism is dismissed because no
experimental evidence of sliding failure was detected. The diagonal tension shear strength
can be computed with a shear strength formulation originally derived by [Turnšek 1971], and
proposed in the Design Guidelines [2009] to the new Italian NTC 08 [2008] code in the form
[Magenes 1997]:

1.5τ od σo H
Vm ,diag .shear = B ⋅ t ⋅
1+ b = ; 1 ≤ b ≤ 1 .5 [4]
b 1.5τ od B
where B is the base, H the height and t the thickness of the panel; σ0 = N/A is the average
stress on the gross section area A; τod the diagonal shear strength of masonry.
The maximum shear associated to flexural mechanism is calculated according to NTC 08:

B2 ⋅ t σo  σo 
Vm ,flexural = ψ ⋅ 1 −  [5]
H 2  0.85f m 

where H is the wall height, fm is the compressive strength of masonry, and ψ is a parameter
which describes the boundary conditions, taking a value of 2 for fixed-ended wall.
In absence of experimental values of τod, recommended values by building codes can be
taken into consideration. In this regard, the Design Guidelines [2009] provide in Table
C8A.2.1 reference values of mechanical parameters (maxima and minima) for tuff masonry to
be used for safety assessment of existing structures in absence of direct tests. The values
are given for masonry characterized by poor quality, absence of regular courses, wall leaves
merely placed together or badly connected, or with an inner core thinner than the outer leaf.
In accordance with the Guidelines, the expected strength value for τod shall be determined by
multiplying the reference values by appropriate factors given in Table C8A.2.2 of NTC08 that,
in the cases of fairly good transversal connection and poor and/or wide inner core, are equal
to 1.5 and 0.9 respectively.
It is worth noting that the mortar used to build the panels is characterized by poor quality in
accordance with technical literature.

240 240
V (kN) V (kN)
200 200

160 160
C1a
120 C1b 120
C2a
Plain Vfrp - C2a C2b
80 80 Vfrp - C2b
Vfrp - C1b Plain
Vfrp - C1a
40 40
δ (mm) δ (mm)
0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

Panels C1 Panels C2

240 240
V (kN) V (kN)
200 200

160 160
G1a G2a
120 Plain 120 G2b
Plain
80 80

40 Vfrp - G1a 40 Vfrp - G2b Vfrp - G2a

δ (mm) δ (mm)
0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

Panel G1a Panels G2

Figure 7. Experimental V-δ curves and computed shear strength contribution from FRP

The determination of τod from Table C8A.2.1 is based on the value of the compressive
strength obtained in the experimental tests on the plain panels. The obtained shear strength
τod = 0.028 MPa was corrected through the factors 0.9 and 1.5. Therefore, τod = 0.038 MPa.
By assuming the vertical load N equal to the average precompression load (No) in the wall
during the tests, the calculated shear resistance associated to diagonal tension shear failure
(Equation 4) is of 130 kN, and in the case of flexural failure (Equation 5) is equal to 172 kN.
Therefore, good agreement between the result of Equation 4 and the average experimental
strength of the plain panels (Vmax=130 kN) is found.
Based on this result, and considering that the strengthened masonry walls failed typically in
diagonal shear, Equation 4 will be used to predict the masonry contribution to shear
resistance of the reinforced panels. The validity of this assumption will be discussed in the
next section.

Analytical results and discussion

The experimental shear strength of the strengthened panels is computed with Equation 6:

VSM = V'm +Vfrp [6]

where V’m is the masonry shear strength under the increased vertical load No+Nm,frp due to
truss mechanism. For the purposes of the analysis, the maximum values of the functions Vfrp
and Nm,frp have been considered. It is worth noting that these maxima correspond to the
attainment of the maximum tension force Ffrp. Accordingly, the shear strength V’m in Equation
6 has been estimated with Equation 4, assuming N=max(No+ Nm,frp). The experimental and
calculated strengths are reported in Table 2. The calculated strengths (Vfrp, V’m and the sum
VSM) have been then compared to the strengths (Vmax,exp) determined from tests of all seven
specimens. To this aim, the ratios VSM/Vmax,exp have been computed. The results indicated
that Equation 6 seems to provide a good (and slightly conservative) estimate of the capacity
of the FRP-strengthened panels. Therefore, the adoption of Equation 4 in predicting masonry
shear strength of the strengthened specimens is possible.

Table 2. Results and comparisons between experimental and calculated shear strength
contributions
Exp.data Computed values Comparative analysis

Nm,frp Vm,No Vfrp V'm VSM VSM V 'm Vfrp

Specimens No Vmax,exp
(Eq. 3) (Eq. 4) (Eq. 2) (Eq.4) (Eq. 6) Vmax, exp Vmax, exp Vmax, exp
(kN) (kN) (kN) (kN) (kN) (kN) (kN) (-) (%) (%)
C1a 379 156.7 30.7 129.2 28.0 133.8 161.8
0.96 79 17
C1b 391 188.9 33.9 131.2 31.0 136.2 167.2
C2a 384 180.6 61.0 130.1 58.0 139.1 197.1
0.94 69 25
C2b 387 227.0 46.0 129.8 43.0 136.6 179.7
G1a 391 155.8 9.3 131.1 8.7 132.6 141.3 0.91 85 6
G2a 384 179.5 18.3 129.6 17.2 132.4 149.6
0.92 82 10
G2b 386 147.4 15.8 130.4 14.9 132.8 147.7

The weight of the contributions from masonry and FRP to the lateral shear resistance of the
strengthened panels has been evaluated by calculating the ratios Vfrp/Vmax,exp, and V’m/
Vmax,exp. The results are reported as a percentage of Vmax,exp in Table 2.
It was found that the FRP contribution is larger in the case of panels strengthened with CFRP
(25% for panels C2) and lower in the case of panels with GFRP (6% for panel G1a).
Moreover, the contribution of FRP increased about 50% from panels C1 to panels C2, and
about 65% from G1 to G2. Also, the contribution of the reinforcement in the case of C1
panels is about 180% greater than that of G1, while the contribution in the case of C2 was
about 160% greater than that of G2.

Conclusions
In this article a quantitative analysis of the contributions of masonry and FRP to the
experimental lateral resistance of seven strengthened wall panels with FRP diagonal
configuration has been presented. The use of a truss model combined with a proper diagonal
shear strength model for masonry allowed to a simultaneous evaluation of the weight of the
contributions from masonry and FRP to the experimental lateral resistance of the
strengthened panels. A refined numerical analysis would still be advantageous to provide
further insight into the synergistic interactions of FRP and masonry when proper anchorage
of the shear reinforcement is ensured.

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