# Load-Carrying Capacity of Compressed Wall-Like RC Columns Strengthened with FRP

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Analytical Models

#### 3.2. Experimental Results

#### 3.3. Numerical Modeling

## 4. Results and Discussion

#### 4.1. Analytical Results vs. Experimental Data

#### 4.2. Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Performance of the analytical models in assessment of confined concrete compressive strength vs. confinement ratio.

**Figure 8.**Stresses contour plot of columns II4 and S02C at the peak axial force in longitudinal x direction (

**a**,

**b**), in transverse y direction (

**c**,

**d**), and in vertical z direction (

**e**,

**f**).

**Figure 9.**Lateral confining pressure ratio ${f}_{l}^{\prime}/{f}_{co}^{\prime}$: comparison between FEM and analytical models.

${\mathit{k}}_{\mathit{e}}$ | ${\mathit{k}}_{\mathit{s}}$ | $\frac{{\mathit{A}}_{\mathit{e}}}{{\mathit{A}}_{\mathit{c}}}$ | D | |
---|---|---|---|---|

Lam and Teng [10] | $3.3$ | ${\left({\displaystyle \frac{b}{h}}\right)}^{2}\xb7{\displaystyle \frac{{A}_{e}}{{A}_{c}}}$ | $1-{\displaystyle \frac{\left(\right)open="("\; close=")">b/h}{{w}_{x}^{2}}{w}_{y}^{2}}3\left(\right)open="("\; close=")">1-{\rho}_{s}bh$ | $\sqrt{{b}^{2}+{h}^{2}}$ |

Tan [20] | - | $2{\displaystyle \frac{{A}_{e}}{{A}_{c}}}$ | $1-{\displaystyle \frac{\left(\right)open="("\; close=")">n+1}{{w}_{x}^{2}}3\left(\right)open="("\; close=")">1-{\rho}_{s}bh}$ | b |

Maalej et al. [27] | $6.7{f}_{l}^{\prime}{}^{-0.17}$ | $\frac{{A}_{e}}{{A}_{c}}$ | $1-{\displaystyle \frac{\left(\right)open="("\; close=")">2b/{w}_{x}}{{w}_{x}^{2}}3bh}$ | $\sqrt{{b}^{2}+{h}^{2}}$ |

Lignola et al. [30] | − | 1 | − | b |

Triantafillou et al. [31] | $3.3$ | ${\left({\displaystyle \frac{b}{h}}\right)}^{2}\xb7{\displaystyle \frac{{A}_{e}}{{A}_{c}}}$ | $1-{\displaystyle \frac{\left(\right)open="("\; close=")">{w}_{x}+1.5n{s}_{a}}{{w}_{x}}{w}_{y}^{2}}3\left(\right)open="("\; close=")">n+1bh$ | $\frac{2bh}{b+h}$ |

Vuggumudi et al. [32] | $1.78$ | ${\left({\displaystyle \frac{b}{h}}\right)}^{2}\xb7{\displaystyle \frac{{A}_{e}}{{A}_{c}}}$ | $1-{\displaystyle \frac{\left(\right)open="("\; close=")">b/h}{{w}_{x}^{2}}{w}_{y}^{2}}3\left(\right)open="("\; close=")">1-{\rho}_{s}bh$ | $\sqrt{{b}^{2}+{h}^{2}}$ |

B | H | ${\mathit{r}}_{\mathit{c}}$ | ${\mathit{f}}_{\mathbf{co}}^{\prime}$ | ${\mathit{A}}_{\mathit{s}}$ | ${\mathit{f}}_{\mathbf{sy}}$ | FRP | ${\mathit{t}}_{\mathit{f},\mathit{h}}$ | ${\mathit{t}}_{\mathit{f},\mathit{v}}$ | ${\mathit{f}}_{\mathbf{frp},\mathit{u}}$ | ${\mathit{E}}_{\mathbf{frp}}$ | ${\mathit{P}}_{\mathit{u},\mathbf{exp}}$ | $\mathbf{\Delta}{\mathit{P}}_{\mathit{u},\mathbf{exp}}$ | ${\mathit{\epsilon}}_{\mathit{v},\mathit{u}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\left[\mathbf{mm}\right]$ | $\left[\mathbf{mm}\right]$ | $\left[\mathbf{mm}\right]$ | $\left[\mathbf{MPa}\right]$ | $\left[{\mathbf{mm}}^{2}\right]$ | $\left[\mathbf{MPa}\right]$ | Type | $\left[\mathbf{mm}\right]$ | $\left[\mathbf{mm}\right]$ | $\left[\mathbf{MPa}\right]$ | $\left[\mathbf{MPa}\right]$ | $\left[\mathbf{kN}\right]$ | [%] | [%] | |

Tan [20] | ||||||||||||||

P00 * | 115 | 420 | - | 12.0 | 1068 | 500 | - | - | - | - | - | 1069 | - | - |

P02G | 115 | 420 | 30 | 12.0 | 1068 | 500 | GFRP | 0.706 | - | - | 72,400 | 1181 | +10.5 | - |

P04G | 115 | 420 | 30 | 12.0 | 1068 | 500 | GFRP | 1.412 | - | - | 72,400 | 1097 | +2.6 | - |

K00 * | 115 | 420 | - | 20.0 | 1068 | 500 | - | - | - | - | - | 1318 | - | - |

K02G | 115 | 420 | 30 | 20.0 | 1068 | 500 | GFRP | 2.00 | 1.00 | - | 26,100 | 1754 | +33.1 | - |

N00 * | 115 | 420 | - | 20.0 | 1068 | 467 | - | - | - | - | - | 1566 | - | - |

N02G | 115 | 420 | 30 | 20.0 | 1068 | 467 | GFRP | 2.00 | - | - | 26,100 | 1624 | +3.7 | - |

H00 * | 115 | 420 | - | 12.0 | 1068 | 473 | - | - | - | - | - | 1040 | - | - |

H03G | 115 | 420 | 30 | 12.0 | 1068 | 473 | GFRP | 3.00 | - | - | 26,100 | 1237 | +18.9 | - |

M00 * | 115 | 420 | - | 16.0 | 1068 | 495 | - | - | - | - | - | 1430 | - | - |

M01C | 115 | 420 | 30 | 16.0 | 1068 | 495 | CFRP | 0.165 | - | - | 228,000 | 1636 | +14.4 | - |

M11C | 115 | 420 | 30 | 16.0 | 1068 | 495 | CFRP | 0.165 | 0.165 | - | 228,000 | 1450 | +1.4 | - |

S00 * | 115 | 420 | - | 16.0 | 1068 | 495 | - | - | - | - | - | 1222 | - | - |

S02C | 115 | 420 | 30 | 16.0 | 1068 | 495 | CFRP | 0.334 | - | - | 228,000 | 1372 | +12.3 | - |

S12C | 115 | 420 | 30 | 16.0 | 1068 | 495 | CFRP | 0.22 | 0.11 | - | 228,000 | 1579 | +29.2 | - |

S13C | 115 | 420 | 30 | 16.0 | 1068 | 467 | CFRP | 0.33 | 0.11 | - | 230,000 | 1586 | +29.8 | - |

U00 * | 115 | 420 | - | 20.0 | 1068 | 467 | - | - | - | - | - | 1149 | - | - |

U11C | 115 | 420 | 30 | 20.0 | 1068 | 467 | CFRP | 0.165 | 0.165 | - | 228,000 | 1297 | +12.9 | - |

U12C | 115 | 420 | 30 | 20.0 | 1068 | 467 | CFRP | 0.330 | 0.165 | - | 228,000 | 1608 | +39.9 | - |

Maalej et al. [27] | ||||||||||||||

Control * | 115 | 420 | - | 32.4 | 1376 | 461 | - | - | - | - | - | 2067 | - | 0.28 |

2H2V-NL | 115 | 420 | 30 | 32.4 | 1376 | 461 | GFRP | 2.16 | 2.16 | 1860 | 26,130 | 2657 | +28.5 | 0.43 |

Prota et al. [21] | ||||||||||||||

V * | 115 | 420 | - | 15.0 | 1068 | 500 | - | - | - | - | - | 1035 | - | 0.30 |

UN2 | 115 | 420 | 20 | 15.0 | 1068 | 500 | GFRP | 1.062 | 0.354 | - | 72,400 | 1374 | +32.7 | 0.55 |

UN3 | 115 | 420 | 20 | 18.0 | 1068 | 500 | GFRP | 0.708 | 0.354 | - | 72,400 | 1575 | - | 0.44 |

Triantafillou et al. [31] | ||||||||||||||

C3 * | 150 | 450 | - | 18.0 | 679 | 570 | - | - | - | - | - | 1149 | - | 0.30 |

II3 | 150 | 450 | 20 | 18.0 | 679 | 570 | CFRP | 2.00 | - | 1046 | 93,700 | 1601 | +39.3 | 1.53 |

C4 * | 150 | 600 | - | 18.0 | 905 | 570 | - | - | - | - | - | 1509 | - | 0.44 |

II4 | 150 | 600 | 20 | 18.0 | 905 | 570 | CFRP | 2.00 | - | 1046 | 93,700 | 1908 | +26.4 | 1.47 |

Vuggumudi et al. [32] | ||||||||||||||

CCA1 * | 230 | 600 | - | 20.0 | 2945 | 415 | - | - | - | - | - | 3334 | - | 0.65 |

RCA2 | 230 | 600 | - | 20.0 | 2945 | 415 | CFRP | 1.2 | - | 602 | 67,000 | 4609 | +38.2 | 0.79 |

**Table 3.**Performance of the analytical models in axial load capacity: mean value and standard deviation of the percentage error.

Model | Mean (%) | St. Dev. (%) |
---|---|---|

Lam and Teng [10] | $-5.76$ | $9.69$ |

Tan [20] | $-0.59$ | $10.09$ |

Maalej et al. [27] | $-6.43$ | $8.60$ |

Lignola et al. [22] | $-0.35$ | $12.20$ |

Triantafillou et al. [31] | $-3.60$ | $9.90$ |

Vuggumudi et al. [32] | $-5.94$ | $9.67$ |

Column | ${\mathit{P}}_{\mathbf{exp}}$ (kN) | ${\mathit{P}}_{\mathbf{FEM}}$ (kN) | ${\mathit{P}}_{\mathbf{FEM}}\phantom{\rule{0.166667em}{0ex}}/{\mathit{P}}_{\mathbf{exp}}$ | ${\mathit{f}}_{\mathbf{cc}}^{\prime}\phantom{\rule{0.166667em}{0ex}}/{\mathit{f}}_{\mathbf{co}}^{\prime}$ | ${\mathit{f}}_{\mathit{l}}^{\prime}\phantom{\rule{0.166667em}{0ex}}/{\mathit{f}}_{\mathbf{co}}^{\prime}$ | ${\mathit{\epsilon}}_{\mathbf{frp}}$ (%) |
---|---|---|---|---|---|---|

M01C | 1636 | 1329 | $0.811$ | $1.060$ | $0.070$ | $0.085$ |

S02C | 1372 | 1338 | $0.975$ | $1.071$ | $0.085$ | $0.068$ |

P02G | 1181 | 1143 | $0.968$ | $1.084$ | $0.090$ | $0.036$ |

P04G | 1097 | 1147 | $1.046$ | $1.091$ | $0.110$ | $0.025$ |

N02G | 1624 | 1498 | $0.922$ | $1.026$ | $0.065$ | $0.082$ |

H03G | 1237 | 1115 | $0.902$ | $1.035$ | $0.099$ | $0.060$ |

II3 | 1601 | 1604 | $1.001$ | $1.062$ | $0.061$ | $0.055$ |

II4 | 1908 | 2143 | $1.123$ | $1.061$ | $0.060$ | $0.055$ |

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**MDPI and ACS Style**

Avossa, A.M.; Picozzi, V.; Ricciardelli, F.
Load-Carrying Capacity of Compressed Wall-Like RC Columns Strengthened with FRP. *Buildings* **2021**, *11*, 285.
https://doi.org/10.3390/buildings11070285

**AMA Style**

Avossa AM, Picozzi V, Ricciardelli F.
Load-Carrying Capacity of Compressed Wall-Like RC Columns Strengthened with FRP. *Buildings*. 2021; 11(7):285.
https://doi.org/10.3390/buildings11070285

**Chicago/Turabian Style**

Avossa, Alberto Maria, Vincenzo Picozzi, and Francesco Ricciardelli.
2021. "Load-Carrying Capacity of Compressed Wall-Like RC Columns Strengthened with FRP" *Buildings* 11, no. 7: 285.
https://doi.org/10.3390/buildings11070285