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The use of mechanicallyfastened fiberreinforced polymer (MFFRP) systems has recently emerged as a competitive solution for the flexural strengthening of reinforced concrete (RC) beams and slabs. An overview of the experimental research has proven the effectiveness and the potentiality of the MFFRP technique which is particularly suitable for emergency repairs or when the speed of installation and immediacy of use are imperative. A finiteelement (FE) model has been recently developed by the authors with the aim to simulate the behavior of RC beams strengthened in bending by MFFRP laminates; such a model has also been validated by using a wide experimental database collected from the literature. By following the previous study, the FE model and the assembled database are considered herein with the aim of better exploring the influence of some specific aspects on the structural response of MFFRP strengthened members, such as the bearing stressslip relationship assumed for the FRPconcrete interface, the stressstrain law considered for reinforcing steel rebars and the cracking process in RC members resulting in the wellknown tension stiffening effect. The considerations drawn from this study will be useful to researchers for the calibration of criteria and design rules for strengthening RC beams through MFFRP laminates.
The use of mechanicallyfastened (MF) fiberreinforced polymer (FRP) systems has recently emerged as an effective solution for the flexural strengthening of reinforced concrete (RC) beams. The technique consists of precured FRP laminates with enhanced bearing strength, which can be fastened to the external surface of concrete members through a variety of steel anchors,
Components of the mechanicallyfastened fiberreinforced polymer (MFFRP) system: (
Wedge bolts are singlepiece, heavy duty anchors that are driven into predrilled holes. Driving of the wedge bolt can be performed with a common rotary drill or impact wrench. As for the PAFs, the efficiency of wedge bolts is dependent on the presence of hard aggregates. Preliminary studies [
In spite of longer installation times, wedge anchors can be used for any type of concrete; they are driven through the laminate into predrilled holes until the nut and washer are firmly secured against the laminate. The anchors are typically tightened by turning the nut with an electrical drill with torque control, according to the specifications of fastener manufactures.
A recently published stateoftheart review of the experimental research has provided compelling evidence of the effectiveness and viability of using MFFRP laminates to rehabilitate RC beams and slabs [
Several analytical and numerical studies have been carried out throughoutyears with the aim of predicting the behavior of RC members strengthened in bending with MFFRP systems: a stateoftheart review on this topic has been recently published by Napoli
Finiteelement (FE) models were also developed to simulate the behavior of MFFRPstrengthened RC beams and slabs. To this aim, the first work Napoli
The numerical simulations discussed herein were mainly aimed at investigating the influence of some specific aspects on the structural response of MFFRPstrengthened members, such as the bearing stressslip relationship assumed for the FRPconcrete interface, the stressstrain law considered for reinforcing steel rebars and the cracking process in RC members, which is often disregarded in modeling methods. The considerations drawn from this study will be useful to researchers for the calibration of criteria and design rules for the strengthening RC beams through MFFRP laminates.
This section presents the key features of the novel 1D finiteelement model formulated for simulating the flexural behavior of RC beams strengthened by MFFRP. Such a model, deeply described in [
The proposed finite element is obtained by assembling the following three components (see
a 1D element that represents the behavior of Euler–Bernoulli’s RC beam;
a rod element that simulates the mechanical behavior of an FRP laminate;
two springs that simulate the behavior of the fasteners and are only translational in the direction of the beam axis.
Key components of the proposed 1D finiteelement.
The relevant displacement and force components of the finite element “
By introducing the stiffness matrix,
The matrix,
Force and displacement components for the proposed finite element.
RC beams with MFFRP plates can be discretized through the
the flexural stiffness of the FRP laminate is neglected, and only the axial one is considered;
equal vertical displacements occur in the connected RC slab and FRP laminate elements;
shear deformations of the RC slab are neglected.
The generic finite element is then used for nonlinear analyses through a fiber discretization of the beam crosssection and by implementing an iterative convergence procedure based on the “tangent” value approach to account for material nonlinearity, including concrete, steel and the concrete–FRP interface, as already demonstrated for the case of EBFRPstrengthened RC members [
Stressstrain law for concrete.
Alternative stressstrain laws for steel reinforcing bars: “accurate” (
As shown in
Bearing stressslip relationship describing the FRP stripconcrete interaction.
It is highlighted that although three of the four
A nonlinear solution procedure can be implemented to determine the response of the structural system under selfweight and other external loads. First of all, the distributed loads corresponding to the beam selfweight are applied in force control, and then, the procedure works in the displacement control for simulating the effect of the imposed external loads. The analysis foresees several steps of imposed displacement increments and, in each step, an iterative search of the forces corresponding to the imposed displacement. In particular, at the
Equation (3) can be solved through classical numerical procedures of the finite element modeling (FEM) based on imposing that one of the
For each element, the local displacement increment
Then, the “plastic correction” can be performed by evaluating the stress increments,
At the end of this substep and after having assembled the new local stiffness matrices,
Then, the (
At the end of the
A wide database was assembled from the literature, which collects a total of 93 four pointbending tests performed on RC beams/slabs externally strengthened with MFFRP laminates.
The configuration of four pointbending tests collected from the literature.
In addition to the symbols clarified in
The fasteners were arranged on single or multiple rows (N = 1, 2, 4) according to aligned (“a”) or staggered (“s”) configurations or combinations thereof (“as”).
As observed from the tables, test specimens have different sizes of crosssection, with values of the heighttowidth (
The geometry and mechanical properties of considered test specimens and main results.
Source  Test 





Steel type 




(mm)  (mm)  (mm^{2})  (mm^{2})  (mm^{2})  (mm)  (MPa)  KN  KN  
Borowicz (2002) [ 
UW2  3505  1372  305 × 305  143  1013  51  44.7  Grade 60 


UW4  2134  686  377 


UW5  2642  940  268 


UW6  3353  1295 



UW7  3454  1346 



UW8  3505  1372 



UW9  3505  1372 



Ebead (2011) [ 
MFD101  2250  850  150 × 250  101  157  25  41  540  51 

MFD102  157  25  38  540  70 


MFD121  226  26  38  550  79 


MFD122  226  26  39  550  75 


MFD161  402  28  40  530  106 


MFD162  402  28  39  530  110 


MPD101  157  25  37  540  44 


MPD102  157  25  38  540  39 


MPD121  226  26  36  550  68 


MPD122  226  26  39  550  68 


MPD161  402  28  36  530  101 


MPD162  402  28  41  530   


Ekenel 
S4F  1829  304  254 × 165  143  214  45  27.6  414  57 

ElMaaddawy (2013) [ 
C0PAF32  2800  1200  250 × 275  339  100  34  30.5  500 


C0PAF52 



C0EAB 



C0TAB 



C1PAF32 



C1PAF52 



C1EAB 



C1TAB 



C2PAF32 



C2PAF52 



C2EAB 



C2TAB 



ElMaaddawy 
C0F5032  1250  550  150 × 210  226  100  30  32  538 


C0F10032 



C0F100322 



C0F5052 



C0F10052 



C1F5032 



C1F10032 



C1F100322 



C1F5052 



C1F10052 



C2F5032 



C2F10032 



C2F100322 



C2F5052 



C2F10052 



C3F5052 



C3F10052 



Galati 
MFP2  2200  600  200 × 250  226  226  29  31.5  462  87 

Lamanna (2002) [ 
D1  1168  483  153 × 153  143  254  50  42  Grade 60 


D2  1168  483  42 



E1  1168  483  42 



E2  1168  483  42 



J1  1168  483  42 



L1  1067  432  42 



T1  1067  432  42 



T2  1067  432  42 



T3  1067  432  42 



F1  1168  483  21 



G1  1168  483  21 



K1  1168  483  21 



M1  1067  432  21 



N1  1067  432  21 



P1  1067  432  21 



Q1  1067  432  21 



R1  1067  432  21 



R2  1067  432  21 



U1  1067  432  21 



Lamanna 
F42S1021R  1067  432  153 × 153  143  254  39  42  Grade 60 


F21S1022R  21 



Bank 
S4YAL32  3353  1118  305 × 305  143  1013  51  35.3  Grade 60 


I4NAL32 



I4YAL32 



I4YAL32R 



I8YAL32 



H1.54YAL32 



H1.54YAL42D 



H1.54YAL47D 



H1.54YAL47D3 



H1.54YAL47D3R 



H1.58YAL32 



H1.04YAL47D5 



Lee 
1  1370  610  200 × 150  157  226  40  34.5  Grade 60  79  84 
2  1370  610  200 × 150  157  226  40  34.5  Grade 60  78  92  
Martin and Lamanna (2008) [ 
6L  3353  1219  305 × 305  143  1013  51  48  Grade 60 


6S 



10L 



12L 



Napoli 
MF1L  3048  1219  305 × 152    380  25  26.7  Grade 60  42 

MF1S  41 


MF2L  36 


MF2S  35 

Note: ^{1} The experimental values indicated in the published papers are reported in italics, whereas the remaining results have been approximately found by the authors.
Details on the strengthening layouts. Na, aligned; s, staggered.
Source  Test 





Fastener type 


Washer  # rows 

(mm)  (mm)  (mm)  (GPa)  (MPa)  (mm)  (mm)  
Borowicz (2002) [ 
UW2  102  3.2  3404  56.5  494  PAF  4.5  47  YES  2a 
UW4  2134  494  2a  
UW5  2642  494  2a  
UW6  3251  743  2a  
UW7  3048  743  2a  
UW8  2997  743  2a  
UW9  6.4  3404  743  2a  
Ebead (2011) [ 
MFD101  102  3.2  2200  72  1003  Screw  4.76  37  YES  2a 
MFD102  2200  1a/2a  
MFD121  2200  2a  
MFD122  2200  1a/2a  
MFD161  2200  2a  
MFD162  2200  1a/2a  
MPD101  1350  2a  
MPD102  1350  1a/2a  
MPD121  1350  2a  
MPD122  1350  1a/2a  
MPD161  1350  2a  
MPD162  1350  1a/2a  
Ekenel 
S4F  102  3.2  1778  62  531  Wedge anchor  9.5  40.3  YES  1s 
ElMaaddawy (2013) [ 
C0PAF32  102  3.2  2600  62  852  PAF  4  32  NO  2a 
C0PAF52  PAF  4  52  NO  2a  
C0EAB  Wedge  8  55  YES  1s  
C0TAB  Screw  8  55  NO  1s  
C1PAF32  PAF  4  32  NO  2a  
C1PAF52  PAF  4  52  NO  2a  
C1EAB  Wedge  8  55  YES  1s  
C1TAB  Screw  8  55  NO  1s  
C1PAF32  PAF  4  32  NO  2a  
C1PAF52  PAF  4  52  NO  2a  
C1EAB  Wedge  8  55  YES  1s  
C1TAB  Screw  8  55  NO  1s  
ElMaaddawy 
C0F5032  51  3.2  1050  62  852  PAF  4  32  NO  1a 
C0F10032  102  32  1a  
C0F100322  102  32  2a  
C0F5052  51  52  1a  
C0F10052  102  52  1a  
C1F5032  51  32  1a  
C1F10032  102  32  1a  
C1F100322  102  32  2a  
C1F5052  51  52  1a  
C1F10052  102  52  1a  
C2F5032  51  32  1a  
C2F10032  102  32  1a  
C2F100322  102  32  2a  
C2F5052  51  52  1a  
C2F10052  102  52  1a  
C3F5052  51  52  1a  
C3F10052  102  52  1a  
Galati 
MFP2  102  3.2  2100  62  835  Wedge anchor  12  100  YES  1s/2a 
Lamanna (2002) [ 
D1  102  3.2  1117  13.8  232  PAF  4  22  YES  2a 
D2  1117  13.8  232  4  22  2a  
E1  1117  13.8  232  4  22  2a  
E2  1117  13.8  232  4  22  2a  
J1  1117  13.8  232  3.7  27  1a  
L1  1016  13.8  232  4.5  32  1a  
T1  1016  13.8  232  3.7  32  1a  
T2  1016  13.8  232  3.7  32  1a  
T3  1016  13.8  232  3.7  32  1a  
F1  1117  13.8  232  3.7  27  1a  
G1  1117  13.8  232  3.7  27  2a  
K1  1117  13.8  232  3.7  32  1a  
M1  1016  13.8  232  3.7  32  1a  
N1  1016  17.0  351  3.7  32  1a  
P1  6.4  1016  15.5  204  3.7  27  1a  
Q1  3.2  1016  27.3  561  3.7  32  1a  
R1  1016  13.8  232  3.5  27  2a  
R2  1016  13.8  232  3.5  27  2a  
U1  51  1016  13.8  232  3.7  32  1a  
Lamanna 
F42S1021R  102  3.2  1016  13.8  232  PAF  3.5  27  YES  2a 
F21S1022R  3.7  32  1a  
Bank 
S4YAL32  102  3.2  3048  15.2  325  PAF  4.5  32  YES  2a 
I4NAL32  102  26.3  695  32  2a  
I4YAL32  102  26.3  695  32  2a  
I4YAL32R  102  26.3  695  32  2a  
I8YAL32  204  26.3  695  32  4a  
H1.54YAL32  102  57.2  828  32  2a  
H1.54YAL42D  102  57.2  828  42  2a  
H1.54YAL47D  102  57.2  828  47  2a  
H1.54YAL47D3  102  57.2  828  47  2a  
H1.54YAL47D3R  102  57.2  828  47  2a  
H1.58YAL32  102  57.2  828  32  4a  
H1.04YAL47D5  102  56.9  916  47  2a  
Lee 
1  102  3.2  1370  68.3  848  PAF  3.5  25  YES  2a 
2  102  3.2  1370  68.3  848  PAF  3.5  32  YES  2a  
Martin and Lamanna (2008) [ 
6L  102  3.2  3251  57.7  805  Screw  12.7  50.8  YES  1a 
6S  1s  
10L  1a  
12L  1a  
Napoli 
MF1L  102  3.2  2718  62  852  Screw  9.5  44.5  NO  1s 
MF1S  2108  1s  
MF2L  2718  1s  
MF2S  2413  1s 
The concretes used for producing members are characterized by mediumhigh values of the compressive strength,
The laminates employed for the MFFRP system have different mechanical properties, determined by mainly varying the combinations of carbon/glass fibers and the amount of embedded fiberglass mats adopted for their manufacturing.
As observed, the mechanical fastening mostly consists of shot fasteners (namely “PAF”), with diameters ranging from 3.5 to 4.5 mm and lengths from 22 to 52 mm.
Screw anchors were also frequently used, for which the diameters span from 4.76 to 12.7 mm and the lengths from 37 to 55 mm. Only in a few cases, instead, the mechanically fastening was performed by using wedge anchors [
The FE model has been used for performing numerical simulations of experimental tests collected in the database of
uncertainty on the actual mechanical properties of steel rebars and mainly on the
selection of the bearing stressslip interface law to model the effect of the partial interaction between concrete and FRP laminate; and
the cracking process in RC members, related to the different tensile response of concrete, which is generally neglected in modeling methods.
The authors highlight that the numerical analyses have been carried out for all beams listed in
As shown in
Influence of the mechanical properties (
The comparisons of
A further aspect of interest in the modeling of the steel rebars’ behavior deals with the approximation level achieved when the elastic plastic stressstrain law (
The low influence of mechanical properties and the stressstrain behavior of steel rebars can be finally verified by observing the experimentalnumerical comparisons in
As mentioned earlier, Elsayed
In particular, among the proposals by Elsayed
The trilinear models proposed by Realfonzo
Comparisons between experimental and numerical forcedeflection curves are shown in
Influence of the bearing stressslip interface law: numerical simulations of tests by Ebead [
In the plots of
In
In the case of tests MF1S and MF1L, the plots show a very good agreement between experimental results and numerical predictions, which are rather accurate in simulating the cracking onset in concrete and yielding in steel rebars. In the cases of tests MF2L and MF2S, the numerical responses before steel yielding are characterized by a slightly greater stiffness with respect to the experimental ones. In all cases, since small values of interfacial slips are activated for these members, the numerical simulations do not significantly change with the use of the two
The simulation of the cracking processes of RC members is a challenging issue, especially in the case of 1D numerical models. Such processes are characterized by the onset of cracking in concrete subjected to tensile stresses: since the actual tensile strength of concrete is generally affected by significant levels of randomness, the prediction of the cracking onset is often a critical issue. Furthermore, the wellknown tensionstiffening effect significantly influences the flexural response of RC members in the postcracking stage.
As mentioned earlier, since the present proposal is based on a continuous (smeared) crack FE model, the tension stiffening effect has been simulated by a conventional softening branch in the tensile stressstrain law of concrete, which is expressed by the following equation [
It is worth highlighting that the shape of the postpeak tensile branch strongly depends on the values of the
Influence of the tensionstiffening effect: numerical simulations of tests by Borowicz [
Observing these plots, it is noted that the effect of a different tensile response of concrete is particularly relevant in terms of flexural stiffness in the postcracking regime. However, a lower tensionstiffness effect (simulated by assuming
A finite element model was developed and used by the authors to simulate the flexural behavior of RC beams externally strengthened by mechanically fastened FRP laminates.
Several numerical analyses were carried out by using experimental results collected in a wide database assembled from the literature. Such analyses were aimed at investigating the influence of some specific aspects on the structural response of MFFRP strengthened members, such as stressstrain laws implemented for steel rebars, bearing stressslip laws assumed for the FRPconcrete interface and the cracking process, with emphasis on the tension stiffening effect developing in RC members.
From the experimentalnumerical comparisons, the following considerations were drawn and can be generalized in the modelling of MFFRPstrengthened members:
as expected, a rather slight dependence of the performed analyses on the stressstrain model used for steel rebars is observed; thus, a simplified elasticplastic law can be successfully chosen in the simulation of tests;
since small values of interfacial slips are activated in the case of MFFRPstrengthened beams, the numerical simulations do not significantly change with the use of two different bearing stressslip relationships, thus implying that both of them are suitable in the modeling of these members;
the use of a lower tensionstiffening effect has an influence on the bending moment of the beam at yielding and provides the most accurate simulations in terms of initial stiffness when shot fasteners are used. In fact, the installation of such a connector type generally induces significant precracking in the concrete, which is well reproduced by a lower contribution of the tensionstiffening effect. For the case of fastening with concrete screws or wedge anchors, instead, the implementation of the tensionstiffening effect with the
The authors declare no conflict of interest.