# Experimental Investigation of the Shear Strength of RC Beams Extracted from an Old Structure and Strengthened by Carbon FRP U-Strips

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## Abstract

**:**

## Featured Application

**This study presents the experimental results of the shear strength of reinforced concrete (RC) “real” beams extracted from an old RC building in Rome, built in 1929. The concrete strength is very small as in the case of many existing old RC structures. These results about “real” beams are innovative in the literature because the beams are usually built purposely to be retrofitted and tested. The data presented in this paper improve the literature database giving original data about the measured concrete strength variation along the beams, the stiffness, the deflections, and the strengths of the beams before and after retrofitting, and the Carbon FRP U-Strips strains. The shear strengths of these “real” beams, together with the ones obtained in other experimental studies, are in good agreement with the predicted strengths by design code equations.**

## Abstract

## 1. Introduction

## 2. Extracted Beams

^{2}plan dimension) and many columns and beams (Figure 1a–c). The two extracted secondary beams were located very close to each other on the basement floor (Figure 1c) and were probably built by the same concrete cast. The beams were labeled as DB1 and DB2, were cut by means of a diamond wire at two sections very close to the ends and were brought to the Proof testing and Research in Structures and Materials Laboratory (PRiSMa) of the Roma Tre University (Rome, Italy).

#### 2.1. Concrete Geometries and Steel Reinforcement Configuration

#### 2.2. Mechanical Characteristics of the Beam Materials

#### 2.2.1. Compressive Strength of Concrete

_{c}) values obtained by the DTs on the concrete cores were converted in the cubic compressive strength values (R) in Figure 3b and Table 1 by means of Equation (2). This conversion permits comparison of the DT compressive strength values directly with the ones obtained by NDTs using Equation (1) which gives the cubic compressive strength values.

_{m}) are 14.7 MPa and 10.9 MPa for the beam DB1 and DB2 whereas the coefficient of variation (CoV) values are 0.28 and 0.12 for the beam DB1 and DB2. The concretes show a wide scatter of the compressive strength values especially along the beam DB1.

#### 2.2.2. Test on Steel Rebar

_{0.2%}) obtained by these tests are shown in Table 1. The existing rebar extracted by the beams were carefully chosen to be without any sign of yielding, after the beam failure tests. This was confirmed by tensile tests during which no plastic deformation seemed to preexist.

_{0.2%}) and the maximum stresses (f

_{su}) are given considering groups of rebars with the same diameter. The results obtained for the ribbed rebars used for retrofitting, showed very small values for the CoV whereas the results of the smooth rebars were wide scattered, especially in the case of the ϕ6 mm rebars.

## 3. Beams Retrofitting

_{m}= 35 MPa); 5. the construction of a concrete groove with transverse section 20 mm × 20 mm along the entire beam length to anchor the CFRP strips; and 6. the application of epoxy mortar on beam surface to fix the CFRP strips.

^{2}, tensile modulus of 240 GPa, tensile strength of 3500 MPa, thickness of 0.167 mm and width of 100 mm. Each U-strip end was anchored to the beam surface by an improved anchorage system. This anchorage system was realized for the following steps: 1. bending the CFRP fabric in the groove realized the beam web; 2. inserting a 150 mm long composite bar in the groove on the bended fabric; and 3. fixing the bar in the groove by an epoxy mortar that fills the groove (Figure 4d).

## 4. Test on Beams

- The material mechanical characteristics showed variability along the beams (§2);
- The preexisting concrete cracking may be different for the two beams.

#### 4.1. Test Apparatus

#### 4.2. Elastic Tests on the Extracted Beams

_{cm}is the mean compressive cylindrical strength of concrete. The values of f

_{cm}can be obtained by means of the mean compressive cubic strength given in §2.2.1 for each beam. The Young’s modulus values are 23.3 GPa and 21.3 GPa for the beam DB1 and DB2. The elastic beam deflections at midspan for a given applied load can be calculated by the elastic curve equation considering the concrete gross section (pre-cracking stage) properties, the beam length, and the calculated Young’s moduli of concrete. Based on these results, the beam stiffness values before cracking at midspan are 500.0 kN/mm and 349.7 kN/mm for the beams DB1 and DB2. From the beginning of the elastic tests, the experimental stiffness values are smaller than the ones calculated considering the gross section and therefore the beam sections were already cracked before these tests. This is expected because the beams were extracted from a building subjected to loads.

_{c}I

^{exp}) can be evaluated by Equation (4) based on the elastic curve equation.

_{emax}and δ

_{emax}are the maximum load and the corresponding beam deflection at midspan during the elastic test.

- The lower limit equal to the fully cracked flexural rigidity (E
_{c}I^{II}) calculated by Equation (5);$${\mathrm{E}}_{\mathrm{c}}\xb7{\mathrm{I}}^{\mathrm{II}}={\mathrm{E}}_{\mathrm{c}}\xb7\left(\frac{1}{3}\xb7\mathrm{b}\xb7{\mathrm{y}}_{\mathrm{c}}{}^{3}+{\mathrm{E}}_{\mathrm{s}}/{\mathrm{E}}_{\mathrm{c}}\xb7{\mathrm{A}}_{\mathrm{s}}\xb7{\left(\mathrm{d}-{\mathrm{y}}_{\mathrm{c}}\right)}^{2}\right)$$ - The upper lit equal to the uncracked flexural rigidity (E
_{c}I^{0}) calculated by Equation (6)$${\mathrm{E}}_{\mathrm{c}}\xb7{\mathrm{I}}^{0}={\mathrm{E}}_{\mathrm{c}}\xb7\left(1/12\xb7\mathrm{b}\xb7{\mathrm{h}}^{3}\right)$$^{0}is the area moment inertia of the uncracked section, I^{II}the area moment of inertia of the full cracked section, b is the section width, h is the section height, y_{c}is the compression zone height, E_{s}is the steel elastic modulus (200,000 MPa), A_{s}is the tension reinforcement area and d is the distance between the reinforcement and the top of the cross-section.

_{c}I

^{exp}), uncraked (E

_{c}I

^{0}), and fully cracked (E

_{c}I

^{II}) flexural rigidity values are given for each beam in Table 3. The effective depth for flexure (d) was about 72 mm for each beam.

_{c}I

^{exp}/E

_{c}I

^{0}and E

_{c}I

^{II}/E

_{c}I

^{0}shows that the beams DB1 and DB2 presented a significant cracking of the section before the elastic test.

#### 4.3. Failure Tests on the Retrofitted Beams

#### 4.3.1. Beam Deflections

#### 4.3.2. Retrofitted Beam Failure Mechanism and Damage

#### 4.3.3. Experimental Strains of the CFRP Reinforcement

_{max}) applied on the beam and are: F = 0.25F

_{max}(107 kN), the load that produced the beam flexural cracking (F =0.24F

_{max}, on average from the literature); F = 0.50F

_{max}(212 kN); F = 2/3F

_{max}(285 kN), that usually corresponds to the onset of strips debonding [53,54]; F = 0.85F

_{max}(360 kN) and F = 0.95F

_{max}(400 kN). The strains measured at F

_{max}(425 kN) are not included in Figure 9 because the strips detached from the beam surface and so the strain gauge measurement is not interesting at complete debonding of strips. The strains measured before complete debonding for F = 0.95F

_{max}were about equal to 0.3% (Figure 9b–d).

_{f}= 240 GPa). The stress value corresponding to the maximum strain is 720 MPa. The CFRP effective strength (f

_{fed}) that produces debonding of the CFRP reinforcement is 695 MPa by Equation (18) in CNR-DT 200 R1/2013 [66]. This stress is function of the debonding strength (f

_{fdd}) calculated by Equation (23) in CNR-DT 200 R1/2013 [66] that is equal to 715 MPa assuming the tensile strength of the CFRP fabric equal to 2400 MPa, the mean cubic compressive strength of the restored concrete cover equal to 35 MPa and the unit value for the partial safety coefficients in [66]. The experimental CFRP stress at the strips debonding is very similar to the predicted value by the code equations [66].

_{max}were about equal to 0.2–0.3%, except for one U-strip close to the midspan that showed locally strain values of 0.3–0.4%. A modest strain of about 0.1% was measured on the CFRP fabric region close to the beam extrados at top and middle positions along the U-strips, where strips debonding due to concrete cracking started to propagate. The applied load was about 2/3 of F

_{max}and this behavior was already observed by Carolin et al. 2005 [53,54].

#### 4.3.4. Experimental Contributions to the Beam Shear Resistance

_{sw}is the number of the stirrups crossing the shear crack, A

_{sw}is the cross-section area of the stirrups and f

_{0.2%,m}is the mean value of the yield stress of the stirrups from the data in Table 1.

_{sw}was calculated by the ratio between the length of the beam part crossed by the shear crack (800 mm) and the mean spacing of the stirrups. The values of n

_{sw}were 3.5 and 3.4 for the beam DB1-R and DB2-R.

_{f,strips}is the number of the CFRP strips crossing the shear crack, t

_{f}is the CFRP fabric thickness, b

_{f}is the CFRP strip width, E

_{f}is the CFRP fabric Young’s modulus and ${\mathsf{\epsilon}}_{\mathrm{f}\mathrm{exp}}$ is the strain measured on the CFRP U-strips at beam failure (§4.3.3). The CFRP fabric characteristics and the strip geometries are given in §3. The evaluation of the number of the U-strips, which gave a contribution to the shear resistance, is not simple because debonding of the strips was evident and the brittle failure of the CFRP reinforcement did not permitted plastic force distribution. However, n

_{f,strips}equal to 3 is used to evaluate the CFRP contribution in Table 4 because this is the number of the strips crossing the shear crack in Figure 8a,b for each beam. The value of the experimental CFRP strain ${\mathsf{\epsilon}}_{\mathrm{f}\mathrm{exp}}$ was about equal to 0.3% for the beam DB1-R (Figure 9) and 0.25% for the beam DB2-R.

_{l}(the reinforcement ratio for the longitudinal reinforcement) in Equation (12) is evaluated, did not give a contribution to the shear resistance. In fact, the concrete contribution calculated for each beam considering also the contribution of the new bottom rebar (§3) is 111.7 kN for the beam DB1-R and 105.0 kN for the beam DB2-R; values greater than the experimental ones in Table 4.

## 5. Design Equations for the Shear Strength of RC Beams

#### 5.1. Strength of RC Beams before and after Retrofitting

_{Rd}) can be evaluated by the two methods proposed in Eurocode 2 [70]:

- The Standard Method (Equation (9)) that considers the steel (V
_{Rd,s}) and the concrete contribution (V_{Rd,c}); The truss model has the compressive strut inclination angle (ϴ) equal to 45°. - The Variable Inclination Method (Equation (10)) not containing the concrete contribution; The truss model has a variable compressive strut inclination angle (ϴ) lower than 45°$${\mathrm{V}}_{\mathrm{Rd}}=\mathrm{min}\left\{{\mathrm{V}}_{\mathrm{Rd},\mathrm{s}}+{\mathrm{V}}_{\mathrm{Rd},\mathrm{c}};{\mathrm{V}}_{\mathrm{Rd},\mathrm{max}}\right\}$$$${\mathrm{V}}_{\mathrm{Rd}}=\mathrm{min}\left\{{\mathrm{V}}_{\mathrm{Rd},\mathrm{s}};{\mathrm{V}}_{\mathrm{Rd},\mathrm{max}}\right\}$$

_{Rd,s}), can be calculated by Equation (11).

_{ywd}, A

_{sw}and s are the design yield stress, the cross-sectional area and the spacing of the shear steel reinforcement.

_{Rd,c}) can be calculated by Equation (12) assuming member axial load equal to zero.

_{l}is the reinforcement ratio for the longitudinal reinforcement, b

_{w}is the smallest width of the cross-section in the tensile area, f

_{ck}is the characteristic compressive cylinder strength of concrete at 28 days and the parameter ${\mathrm{v}}_{\mathrm{min}}$ may be found in Country National Annex.

_{Rd,max}is the maximum shear capacity of the section calculated by Equation (13) that depends on the compressive strength of the concrete strut (Mörsch’s truss analogy model).

_{cw}and υ

_{1}for use in a Country may be found in its National Annex, f

_{cd}is the design value of concrete compressive strength and α is the angle between shear reinforcement and the beam axis perpendicular to the shear force.

_{Rd,r}) can be predicted by Equation (15) in fib Bulletin 14 [67] or by Equation (16) in CNR-DT 200 R1/2013 [66].

_{Rd,f}is the CFRP U-jacket contribution to shear resistance given in §5.2.

_{Rd,c}. The angle ϴ should be assumed equal to 45° in each equation to limit the value of the V

_{Rd,s}(cot ϴ = 1). In fact, the plastic redistribution of the force in the transverse steel reinforcement could be limited by the CFRP reinforcement.

#### 5.2. CFRP U-Jacket Contribution to Shear Resistance

_{Rd,f}) is calculated by Equation (17) in CNR-DT 200 R1/2013 [66] based on the Mörsch’s truss analogy model. This is the same equation used to evaluate the steel shear contribution (V

_{Rd,s}) in Eurocode 2 [70] considering the cross-section area (A

_{f}= b

_{f}∙t

_{f}where b

_{f}and t

_{f}are the width and the thickness of CFRP strips), the spacing (p

_{f}) and the effective strength of CFRP strips (f

_{fed}) instead of the steel cross-section area (A

_{sw}), the spacing (s) and the yield stress of the steel rebar (f

_{y}).

_{Rd}= 1.2 is the partial factory.

_{fed}) is usually governed by debonding according Equation (18):

_{fdd}is the design debonding strength of FRP, h

_{w}the web depth completely impregnated with U-wrap and l

_{ed}the design effective bond length.

_{fdd}at failure is evaluated from the maximum transmissible force by the anchorage (P

_{max}) given by Equation (19).

_{max}can be measured by tests or alternatively obtained according to Wu et al. 2002 [71] using the following interface law (Equation (20)):

_{f}is the Young’s modulus of elasticity of FRP reinforcement and Γ

_{fd}is the fracture energy that characterizes the bond interface between the FRP sheet and concrete calculated by Equation (21) considering wet lay-up FRP.

_{cm}is the mean value of concrete compressive strength, f

_{ctm}is the mean value of concrete tensile strength, FC is the factor of confidence and k

_{b}is the scale coefficient defined by Equation (22)

_{fdd}).

_{fd}is the partial safety factor depending on the application of the FRP sheet. The design optimal bond length can be calculated by Equation (24) in fib Bulletin 14 [67].

## 6. Shear Strength of the Beams Tested in Lab

#### 6.1. Shear Strength of the Beams before Retrofitting

- A fixed value of ϴ equal to 45°
- A variable value of ϴ smaller than 45° calculated by the variable inclination angle method in §5.1.

_{Rd,s}) in Equation (10). In fact, if the inclination angle of the cracks (ϴ) is smaller than 45°, the number of internal stirrups crossing the crack and the resulting shear carried by the stirrups may be higher, up to the maximum value defined by cotϴ = 2.5.

_{Rd,exp}) of the selected beams is given by the authors (§6) that tested these beams.

_{Rd,exp}/V

_{Rd}for each beam in Figure 10a,b, are given in Table 5.

#### 6.2. Shear Strength of the Beams after Retrofitting by CFRP Reinforcement

_{Rd,r exp}) of the selected beams is given by the authors (§6) that tested these beams.

_{Rd,r exp}/V

_{Rd,r}calculated by Equation (15) or Equation (16) for each beam, are given in Table 6.

#### 6.3. Experimental FRP Reinforcement Contribution to the Shear Resistance

_{rd,f}values for the tested beams selected in §6 and for the beams DB1-R and DB2-R. The line “m” indicates the perfect correspondence between the predicted and the measured shear strength values. One should note that the strength predicted by Equation (17) may be quite unsafe because many points are above the line “m”.

## 7. Conclusions and Discussion

- The stirrup spacing was irregular;
- The plastic force distribution was reduced by the CFRP reinforcement and so some stirrups could give a smaller contribution;
- The CFRP reinforcement limited the crack width and so the stress in the stirrups could be smaller than the yield stress depending on the actual steel strain;
- The scatter of the steel yield and of the maximum steel stresses were wide (§2.2).

- The number of the strips, that gave a contribution at the same time, is uncertain;
- The actual strain of the CFRP fabric could be greater than the one measured locally where strain gauges were placed (Figure 9).

- Before retrofitting, the Variable Angle Method [70] gives values of the shear strength that result in good agreement with the experimental results. The shear carried by the stirrups, considering the real shear crack angle, may be 2.12 times greater than the one estimated considering an inclination angle of 45°.
- After CFRP retrofitting, the experimental beam shear strength is, on average, 1.21 times greater than the predicted one assuming a crack inclination angle of 45° without considering the concrete contribution (CNR-DT 200/2013 [66]). The predictive model capacity should be improved considering the uncertainties about each shear strength contribution.
- The concrete contribution predicted by code equation [70] is similar to the experimental one for the tested beam DB1-R and DB2-R. Further research efforts should be undertaken because the steel and CFRP reinforcement contributions are uncertain.
- The CFRP reinforcement contribution to the shear resistance could be overestimated by the design model [66]. This resisting model seems improper for evaluating the FRP contribution because: i. The brittle failure of the CFRP shear reinforcement does not permit plastic force redistribution; ii. The number of CFRP strips that contribute efficiently to the shear resistance is uncertain; iii. The maximum FRP fabric deformation is still uncertain.
- The experimental CFRP strain can be modest and comparable to the yield strain of the steel reinforcement. In this case, the transverse steel contribution to the shear resistance can be smaller than the one predicted by code equation [70].

- The effect of the material property variability on the capacity of “real” beams
- The strength of the “real” beam retrofitted with proper new rebar anchorages
- The resisting mechanism of the retrofitted beams based on physical assumptions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{sw}/s is the ratio area steel stirrups/spacing; f

_{c}is the compressive strength of concrete; f

_{y}is the yield stress of stirrups; b

_{f}/p

_{f}is the FRP ratio width/spacing; thick is the thickness of the FRP fabric; angle is the inclination angle of FRP strips; E

_{f}is the Young’s modulus of the FRP.

Ref. | Specimens | Base (mm) | Depth (mm) | Span (m) | Geom Ratio | A_{sw}/s | f_{c} Mean (MPa) | f_{y} Mean (MPa) | b_{f}/p_{f} | Thick (mm) | Angle | E_{f} (GPa) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

DB1 | 285 | 750 | 3.47 | 0.006 | 0.26 | 12.2 | 497 | 0.25 | 0.165 | 45° | 240 | |

DB2 | 290 | 750 | 3.89 | 0.006 | 0.22 | 9.0 | 497 | 0.25 | 0.165 | 45° | 240 | |

Bouss 2009 | ED1-S1-0L (ref) | 152 | 350 | 4.52 | 0.037 | 0.57 | 25.0 | 538 | ||||

ED1-S1-1L | 152 | 350 | 4.52 | 0.037 | 0.57 | 25.0 | 538 | 1.00 | 0.107 | 90° | 231 | |

ED1-S1-2L | 152 | 350 | 4.52 | 0.037 | 0.57 | 25.0 | 538 | 1.00 | 0.214 | 90° | 231 | |

ED1-S2-0L (ref) | 152 | 350 | 4.52 | 0.037 | 1.15 | 25.0 | 538 | |||||

ED1-S2-1L | 152 | 350 | 4.52 | 0.037 | 1.15 | 25.0 | 538 | 1.00 | 0.107 | 90° | 231 | |

ED1-S2-2L | 152 | 350 | 4.52 | 0.037 | 1.15 | 25.0 | 538 | 1.00 | 0.214 | 90° | 231 | |

ED2-S1-0L (ref) | 95 | 175 | 3 | 0.036 | 0.39 | 25.0 | 538 | |||||

ED2-S1-1L | 95 | 175 | 3 | 0.036 | 0.36 | 25.0 | 538 | 1.00 | 0.066 | 90° | 231 | |

ED2-S1-2L | 95 | 175 | 3 | 0.036 | 0.36 | 25.0 | 538 | 1.00 | 0.132 | 90° | 231 | |

Garcez 2008 | CB (ref) | 150 | 300 | 3 | 0.005 | 0.89 | 41.4 | 578 | ||||

CFB_01 | 150 | 300 | 3 | 0.005 | 0.89 | 41.4 | 578 | 0.22 | 0.165 | 90° | 227 | |

CFB_02 | 150 | 300 | 3 | 0.005 | 0.89 | 41.4 | 578 | 0.22 | 0.23 | 90° | 227 | |

Monti 2007 | REF (ref) | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | ||||

US90 | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 90° | 390 | |

US60 | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 60° | 390 | |

USVA | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 45° | 390 | |

USVA+ | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 45° | 390 | |

US45+ | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 45° | 390 | |

US90(2) | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 90° | 390 | |

US45++ | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.50 | 0.22 | 45° | 390 | |

US45++D | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.67 | 0.22 | 45° | 390 | |

US45++E | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.67 | 0.22 | 45° | 390 | |

US45++F | 250 | 450 | 2.8 | 0.011 | 0.25 | 11.0 | 500 | 0.67 | 0.22 | 45° | 390 | |

Barros 2006 | A10_C (ref) | 150 | 300 | 1.5 | 0.007 | 37.6 | 549 | |||||

A10_S (steel) | 150 | 300 | 1.5 | 0.007 | 0.19 | 37.6 | 549 | |||||

A10_M (cfrp) | 150 | 300 | 1.5 | 0.007 | 37.6 | 549 | 0.13 | 0.334 | 90° | 390 | ||

A12_C (ref) | 150 | 300 | 1.5 | 0.010 | 37.6 | 549 | ||||||

A12_S (steel) | 150 | 300 | 1.5 | 0.010 | 0.38 | 37.6 | 549 | |||||

A12_M (cfrp) | 150 | 300 | 1.5 | 0.010 | 37.6 | 549 | 0.26 | 0.334 | 90° | 390 | ||

B10_C (ref) | 150 | 150 | 0.9 | 0.014 | 49.5 | 549 | ||||||

B10_S (steel) | 150 | 150 | 0.9 | 0.014 | 0.38 | 49.5 | 549 | |||||

B10_M (cfrp) | 150 | 150 | 0.9 | 0.014 | 49.5 | 549 | 0.31 | 0.334 | 90° | 390 | ||

B12_C (ref) | 150 | 150 | 0.9 | 0.020 | 49.5 | 549 | ||||||

B12_S (steel) | 150 | 150 | 0.9 | 0.020 | 0.75 | 49.5 | 549 | |||||

B12_M (cfrp) | 150 | 150 | 0.9 | 0.020 | 49.5 | 549 | 0.63 | 0.334 | 90° | 390 |

Ref. | Specimens | Base (mm) | Depth (mm) | Span (m) | Geom Ratio | A_{sw}/s | f_{c} Mean (MPa) | f_{y} Mean (MPa) | b_{f}/p_{f} | Thick (mm) | Angle | E_{f} (GPa) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Guadagn 2006 | SB40 (ref) | 150 | 250 | 2.3 | 0.012 | 0.00 | 42.8 | 500 | 90° | |||

SB40R (glass) | 150 | 250 | 2.3 | 0.012 | 0.00 | 42.8 | 500 | 0.25 | 0.11 | 90° | 65 | |

SB41 (ref) | 150 | 250 | 1.8 | 0.012 | 0.00 | 42.8 | 500 | 90° | ||||

SB41R (glass) | 150 | 250 | 1.8 | 0.012 | 0.00 | 42.8 | 500 | 0.25 | 0.11 | 90° | 65 | |

SB42 (ref) | 150 | 250 | 1 | 0.012 | 0.00 | 42.8 | 500 | 90° | ||||

SB42R (glass) | 150 | 250 | 1 | 0.012 | 0.00 | 42.8 | 500 | 0.50 | 0.206 | 90° | 65 | |

Carolin 2005 | Type B R (ref) | 180 | 400 | 3.5 | 0.033 | 0.28 | 45.6 | 515 | ||||

Type B 290 | 180 | 400 | 3.5 | 0.033 | 0.28 | 45.6 | 515 | 1.00 | 0.11 | 90° | 210 | |

Type B 390 | 180 | 400 | 3.5 | 0.033 | 0.28 | 45.6 | 515 | 1.00 | 0.17 | 90° | 210 | |

Zhang 2005 | ZC4 (ref) | 152.4 | 228.6 | 1.22 | 0.012 | 0.28 | 43.8 | 400 | ||||

Z4-90 (cfrp) | 152.4 | 228.6 | 1.22 | 0.012 | 0.28 | 43.8 | 400 | 0.39 | 1 | 90° | 165 | |

Z4-45 (cfrp) | 152.4 | 228.6 | 1.22 | 0.012 | 0.28 | 43.8 | 400 | 0.39 | 1 | 45° | 165 | |

ZC6 (ref) | 152.4 | 228.6 | 1.83 | 0.012 | 0.28 | 43.8 | 400 | |||||

ZC6(2) (ref) | 152.4 | 228.6 | 1.83 | 0.012 | 0.28 | 43.8 | 400 | |||||

Z6-90 (cfrp) | 152.4 | 228.6 | 1.83 | 0.012 | 0.28 | 43.8 | 400 | 0.39 | 1 | 90° | 165 | |

Z6-45 (cfrp) | 152.4 | 228.6 | 1.83 | 0.012 | 0.28 | 43.8 | 400 | 0.39 | 1 | 45° | 165 | |

Adhikary 2004 | B-1 (ref) | 150 | 200 | 2.6 | 0.010 | 0.00 | 34.0 | 389 | ||||

B-8 | 150 | 200 | 2.6 | 0.010 | 34.0 | 389 | 1.00 | 0.167 | 90° | 226 | ||

Pellegr 2002 | TR30D1 (ref) | 150 | 300 | 2.7 | 0.010 | 0.50 | 31.4 | 548 | ||||

TR30D2 (3- plies) | 150 | 300 | 2.7 | 0.010 | 0.50 | 31.4 | 548 | 1.00 | 0.495 | 90° | 236 | |

TR30D3 (1 ply) | 150 | 300 | 2.7 | 0.010 | 0.50 | 31.4 | 548 | 1.00 | 0.165 | 90° | 236 | |

TR30D4 (2 plies) | 150 | 300 | 2.7 | 0.010 | 0.50 | 31.4 | 548 | 1.00 | 0.33 | 90° | 236 | |

Khalifa 2000 | BT1 (ref) | 150 | 405 | 3.05 | 0.011 | 0.00 | 35.0 | 410 | ||||

BT2 (1-ply) | 150 | 405 | 3.05 | 0.011 | 35.0 | 410 | 1.00 | 0.165 | 90° | 228 | ||

BT3 (2-plies) | 150 | 405 | 3.05 | 0.011 | 35.0 | 410 | 1.00 | 0.33 | 90° | 228 | ||

BT4 (90 strip) | 150 | 405 | 3.05 | 0.011 | 35.0 | 410 | 0.25 | 0.165 | 90° | 228 | ||

BT5 (90 strip) | 150 | 405 | 3.05 | 0.011 | 35.0 | 410 | 0.25 | 0.165 | 90° | 228 | ||

BT6 (sheet) | 150 | 405 | 3.05 | 0.011 | 35.0 | 410 | 1.00 | 0.165 | 90° | 228 |

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**Figure 2.**Beams DB1 (

**a**) and DB2 (

**b**); concrete geometries and steel reinforcement configuration for the sections at the beam ends (S1, S2) and at the beam midspan (SM); rebar diameter [mm]; concrete geometries [cm].

**Figure 3.**Beams DB1 and DB2: cubic concrete compressive strength values (R) along the beams obtained by (

**a**) the corrected non-destructive tests at U test stations or (

**b**) by destructive tests on concrete cores (ST).

**Figure 4.**Beam retrofitting: (

**a**) rebars cleaning and protection, addition of new bottom rebars for beam flexural strengthening; (

**b**) concrete cover restoration; (

**c**) CFRP U-jacketing application for beam shear strengthening; (

**d**) Details of U-jacketing anchorage by pultruded composite bar.

**Figure 5.**Three-points loading test apparatus: (

**a**) photo and (

**b**) scheme of the system to apply the loads and to measure deformation of the beam and strain of the CFRP U-strips (frontal view).

**Figure 6.**Extracted beam DB1 and DB2: (

**a**) load-deflection curves and (

**b**) maximum beam deflections during the elastic tests (L is the beam length).

**Figure 9.**Retrofitted beam DB1-R: strips locations on the beam side (

**a**); strains distribution along the diagonal CFRP U-strips FRP-U1 (

**b**), FRP-U2 (

**c**) and FRP-U3 (

**d**).

**Figure 10.**Beam before retrofitting: experimental and predicted shear strength values considering (

**a**) the fixed or (

**b**) the variable inclination angle of the concrete compressive strut.

**Figure 11.**Beam after retrofitting: experimental and predicted shear strength values including (

**a**) or not including (

**b**) the concrete contribution (V

_{Rd,c}).

**Figure 12.**Experimental and predicted values for the CFRP reinforcement contribution to the shear resistance.

**Table 1.**Cubic concrete compressive strength (R) by compressive tests on cores (ST) and steel yield stress (f

_{0.2%}) by tensile tests on steel rebar pieces (RT); [MPa].

DB1 | DB2 | ||||
---|---|---|---|---|---|

Concrete core | R | Steel rebar f_{0.2%} | Concrete core | R | Steel rebar f_{0.2%} |

ST7 | 16.25 | RT1-1 (ϕ6) 384.55 | ST2 | 10.72 | RT2-1 (ϕ6) 344.36 |

ST8 | 9.77 | RT1-2 (ϕ6) 393.54 | ST3 | 10.73 | RT2-2 (ϕ6) 636.51 |

ST10 | 16.51 | RT1-3 (ϕ6) 439.33 | ST8 | 10.08 | RT2-3 (ϕ6) 322.77 |

ST11 | 20.53 | RT1-4 (ϕ10) 537.25 | ST10 | 12.27 | RT2-4 (ϕ6) 304.93 |

ST11inf-1 | 13.94 | RT1-5 (ϕ10) 374.91 | ST11 | 10.65 | RT2-5 (ϕ6) 313.44 |

ST11inf-2 | 7.68 | RT1-6 (ϕ10) 435.53 | ST13 | 8.86 | RT2-6 (ϕ10) 418.32 |

ST14 | 16.02 | ST22 | 12.91 | RT2-7 (ϕ10) 415.38 | |

ST16 | 16.93 | RT2-8 (ϕ10) 367.71 |

**Table 2.**Beams DB1 and DB2: existing and new strengthening bars diameter (ϕ), yield stress at strain of 0.2% (f

_{0.2%}); maximum stress (f

_{su}) [mm, MPa].

Number of Specimens | ϕ | f_{0.2%}(Mean) | f_{0.2%}(CoV) | f_{su}(Mean) | f_{su}(CoV) |
---|---|---|---|---|---|

8 | 6 | 392.43 | 0.28 | 627.25 | 0.32 |

6 | 10 | 424.85 | 0.14 | 675.93 | 0.05 |

4 | 20 | 496.67 | 0.02 | 607.22 | 0.00 |

**Table 3.**Extracted beams DB1 and DB2: experimental (E

_{c}I

^{exp}), fully cracked (E

_{c}I

^{II}) and uncraked (E

_{c}I

^{0}) flexural rigidity [kNm

^{2}].

E_{c}I^{exp} | E_{c}I^{II} | E_{c}I^{0} | E_{c}I^{exp}/E_{c}I^{0} | E_{c}I^{II}/E_{c}I^{0} | |
---|---|---|---|---|---|

DB1 | 56,858 | 31,148 | 224,240 | 0.25 | 0.14 |

DB2 | 42,968 | 37,302 | 217,160 | 0.20 | 0.17 |

**Table 4.**Experimental contribution to the shear resistance of the transverse steel reinforcement (${\mathrm{V}}_{\mathrm{Rd},\mathrm{s}\mathrm{exp}}$ ), the CFRP reinforcement (${\mathrm{V}}_{\mathrm{Rd},\mathrm{f}\mathrm{exp}}$ ) and the concrete (${\mathrm{V}}_{\mathrm{Rd},\mathrm{c}\mathrm{exp}}$ ) [kN].

${V}_{\mathrm{Rd},s\mathrm{exp}}$ | ${V}_{\mathrm{Rd},f\mathrm{exp}}$ | ${V}_{\mathrm{Rd},c\mathrm{exp}}$ | |
---|---|---|---|

DB1-R | 81.55 | 72.14 | 60.06 |

DB2-R | 73.96 | 60.12 | 78.67 |

**Table 5.**Statistical values of the predictions: mean, Standard deviation, Coefficient of Variation, max, min, 5% and 95% percentile of the ratio V

_{Rd},

_{exp}/V

_{Rd}.

Mean | St. Deviation | CoV | max | min | 5% Percentile | 95% Percentile | ||
---|---|---|---|---|---|---|---|---|

V_{Rd,exp}/V_{Rd} | Fixed angle ϴ | 2.12 | 0.48 | 0.23 | 3.04 | 1.43 | 1.48 | 2.91 |

Variable angle ϴ | 0.88 | 0.18 | 0.21 | 1.22 | 0.57 | 0.67 | 1.19 |

**Table 6.**Statistical values of the predictions: mean, Standard deviation, Coefficient of Variation, max, min, 5% and 95% percentile of the ratio V

_{Rd},

_{r exp}/V

_{Rd,r}.

Model | Mean | St. Deviation | CoV | max | min | 5% Percentile | 95% Percentile | |
---|---|---|---|---|---|---|---|---|

V_{Rd,r exp}/V_{Rd,r} | V_{Rd,s}+V_{Rd,f} | 1.21 | 0.27 | 0.23 | 1.93 | 0.67 | 0.97 | 1.82 |

V_{Rd,s}+V_{Rd,f}+V_{Rd,c} | 0.78 | 0.22 | 0.28 | 1.25 | 0.43 | 0.53 | 1.21 |

**Table 7.**Statistical values of the predictions: mean, Standard deviation, Coefficient of Variation, max, min, 5% and 95% percentile of the ratio V

_{Rd},

_{f exp}/V

_{Rd,f}.

Mean | St. Deviation | CoV | max | min | 5% Percentile | 95% Percentile | |
---|---|---|---|---|---|---|---|

V_{Rd,f exp}/V_{Rd,f} | 0.68 | 0.35 | 0.52 | 1.21 | 0.01 | 0.05 | 1.14 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Lavorato, D.; Nuti, C.; Santini, S.
Experimental Investigation of the Shear Strength of RC Beams Extracted from an Old Structure and Strengthened by Carbon FRP U-Strips. *Appl. Sci.* **2018**, *8*, 1182.
https://doi.org/10.3390/app8071182

**AMA Style**

Lavorato D, Nuti C, Santini S.
Experimental Investigation of the Shear Strength of RC Beams Extracted from an Old Structure and Strengthened by Carbon FRP U-Strips. *Applied Sciences*. 2018; 8(7):1182.
https://doi.org/10.3390/app8071182

**Chicago/Turabian Style**

Lavorato, Davide, Camillo Nuti, and Silvia Santini.
2018. "Experimental Investigation of the Shear Strength of RC Beams Extracted from an Old Structure and Strengthened by Carbon FRP U-Strips" *Applied Sciences* 8, no. 7: 1182.
https://doi.org/10.3390/app8071182