Strengthening of Continuous Reinforced Concrete Deep Beams with Large Openings Using CFRP Strips
<p>Illustration of a reinforced concrete continuous deep beam.</p> "> Figure 2
<p>Typical layouts of the tested specimens (<b>a</b>) RCCDBs without openings; (<b>b</b>) RCCDBs with openings (all dimensions are in mm).</p> "> Figure 3
<p>Details of steel reinforcement for the tested specimens: (<b>a</b>) specimen CDB–Solid; (<b>b</b>) specimens CDB–O–U and CDB–O–S (all dimensions are in mm).</p> "> Figure 4
<p>Illustration of the strengthening scheme with CFRP strips around openings of specimen CDB–O–S (all dimensions are in mm).</p> "> Figure 5
<p>Test setup.</p> "> Figure 6
<p>Modes of failure for the tested specimens. (<b>a</b>) Specimen CDB–Solid; (<b>b</b>) Specimen CDB–O–U; (<b>c</b>) Specimen CDB–O–S.</p> "> Figure 7
<p>Load mid-span deflection curves for the tested specimens.</p> "> Figure 8
<p>Concrete uniaxial compressive and tensile stress–strain curves. (<b>a</b>) In compression; (<b>b</b>) in tension.</p> "> Figure 9
<p>FE mesh and discretization.</p> "> Figure 10
<p>Load mid-span deflection curves for the experimental and FE results. (<b>a</b>) Specimen CDB–Solid; (<b>b</b>) specimen CDB–O–U; (<b>c</b>) specimen CDB–O–S.</p> "> Figure 11
<p>Crack patterns of the tested specimens in experimental setup and ABAQUS. (<b>a</b>) Specimen CDB–Solid; (<b>b</b>) specimen CDB–O–U; (<b>c</b>) specimen CDB–O–S.</p> "> Figure 11 Cont.
<p>Crack patterns of the tested specimens in experimental setup and ABAQUS. (<b>a</b>) Specimen CDB–Solid; (<b>b</b>) specimen CDB–O–U; (<b>c</b>) specimen CDB–O–S.</p> "> Figure 12
<p>Typical layouts of the RCCDBs with different ratios of the opening dimensions (all dimensions are in mm): (<b>a</b>) ratio: 1.5; (<b>b</b>) ratio: 2.0.</p> "> Figure 13
<p>Effect of the ratio of the opening dimensions on the behavior of RCCDBs. (<b>a</b>) Un-strengthened beams; (<b>b</b>) strengthened beams.</p> "> Figure 14
<p>Effectiveness of CFRP strips on strengthening RCCDBs with different ratios of the opening dimensions. (<b>a</b>) Opening ratio of 1.0; (<b>b</b>) opening ratio of 1.5; (<b>c</b>) opening ratio of 2.</p> "> Figure 14 Cont.
<p>Effectiveness of CFRP strips on strengthening RCCDBs with different ratios of the opening dimensions. (<b>a</b>) Opening ratio of 1.0; (<b>b</b>) opening ratio of 1.5; (<b>c</b>) opening ratio of 2.</p> "> Figure 15
<p>Effect of ratios of the opening dimensions on the FE crack patterns for the un-strengthened RCCDBs. (<b>a</b>) CDB–O–U-R1.0; (<b>b</b>) CDB–O–U-R1.5; (<b>c</b>) CDB–O–U-R2.0.</p> "> Figure 16
<p>Effect of ratios of the opening dimensions on the FE crack pattern for the strengthened RCCDBs. (<b>a</b>) CDB–O–S-R1.0; (<b>b</b>) CDB–O–S-R1.5; (<b>c</b>) CDB–O–S-R2.0.</p> "> Figure 17
<p>Typical layout of the RCCDBs with openings to consider the load distribution factor.</p> "> Figure 18
<p>Effect of the load distribution factor on load–mid-span-deflection relationships of RCCDBs without openings (solid).</p> "> Figure 19
<p>Effect of the load distribution factor on load–mid-span-deflection relationships of the un-strengthened RCCDBs with different ratios of the opening dimensions. (<b>a</b>) Opening ratio of 1.0; (<b>b</b>) opening ratio of 1.5; (<b>c</b>) opening ratio of 2.0.</p> "> Figure 20
<p>Effect of the load distribution factor on load–mid-span-deflection relationships of the strengthened RCCDBs with different ratios of the opening dimensions. (<b>a</b>) Opening ratio of 1.0; (<b>b</b>) opening ratio of 1.5; (<b>c</b>) opening ratio of 2.0.</p> "> Figure 20 Cont.
<p>Effect of the load distribution factor on load–mid-span-deflection relationships of the strengthened RCCDBs with different ratios of the opening dimensions. (<b>a</b>) Opening ratio of 1.0; (<b>b</b>) opening ratio of 1.5; (<b>c</b>) opening ratio of 2.0.</p> ">
Abstract
:1. Introduction
2. Experimental Program
2.1. Description and Details of the Tested Specimens
2.2. Material Properties
2.3. Instrumentation and Test Setup
3. Test Results and Discussions
3.1. Initial Cracks and Modes of Failure
3.2. Load Mid-Span Deflection Relationships
4. Finite Element Analysis
4.1. Constitutive Models of Materials
4.2. Element Type and Meshing Scheme
4.3. Boundary Conditions
5. Validation of the FE Model
5.1. Load–Deflection Relationships
5.2. FE Crack Pattern
6. Parametric Study
6.1. Effect of the Ratio of the Opening Dimensions
6.2. Effect of Load Distribution Factor
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- ACI Committee 318. Building Code Requirements for Structural Concrete: (ACI 318-19); American Concrete Institute: Farmington Hills, MI, USA, 2019. [Google Scholar]
- Darwin, D.; Dolan, C.W.; Nilson, A.H. Design of Concrete Structures; McGraw-Hill Education: New York, NY, USA, 2016. [Google Scholar]
- Nie, J.-G.; Pan, W.-H.; Tao, M.-X.; Zhu, Y.-Z. Experimental and Numerical Investigations of Composite Frames with Innovative Composite Transfer Beams. J. Struct. Eng. 2017, 143, 04017041. [Google Scholar] [CrossRef]
- Mansur, M.; Tan, K.-H. Concrete Beams with Openings: Analysis and Design; CRC Press: New York, NY, USA, 1999. [Google Scholar]
- Realfonzo, R. CNR-DT 200 R1/2012: Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures; Consiglio Nazionale delle Ricerche: Roma, Italy, 2012. [Google Scholar]
- Allawi, A.A.; Oukaili, N.K.; Jasim, W.A. Strength compensation of deep beams with large web openings using carbon fiber-reinforced polymer sheets. Adv. Struct. Eng. 2021, 24, 165–182. [Google Scholar] [CrossRef]
- Al-Ahmed, A.H.A.; Al-Jburi, M.H.M. Behavior of Reinforced Concrete Deep Beams Strengthened with Carbon Fiber Reinforced Polymer Strips. J. Eng. 2016, 22, 37–53. [Google Scholar]
- Al-Bayati, N.; Muhammad, B.; Faek, M. Strengthening of self-compacting reinforced concrete deep beams containing circular openings with CFRP. MATE. Web. Conf. EDP Sci. 2018, 162, 04015. [Google Scholar] [CrossRef] [Green Version]
- Almusallam, T.; Al-Salloum, Y.; Elsanadedy, H.; Alshenawy, A.; Iqbal, R. Behavior of FRP-Strengthened RC Beams with Large Rectangular Web Openings in Flexure Zones: Experimental and Numerical Study. Int. J. Concr. Struct. Mater. 2018, 12, 47. [Google Scholar] [CrossRef]
- Fatehi Makki, R.; Jassem, A.T.; Al-Latef Jassem, H.A. Behavior of Reactive-Powder Concrete Deep Beams with CFRP-Strengthened Openings. Pract. Period. Struct. Des. Constr. 2019, 24, 04019016. [Google Scholar] [CrossRef]
- Rahim, N.I.; Mohammed, B.S.; Al-Fakih, A.; Wahab, M.M.A.; Liew, M.S.; Anwar, A.; Amran, Y.H.M. Strengthening the Structural Behavior of Web Openings in RC Deep Beam Using CFRP. Materials 2020, 13, 2804. [Google Scholar] [CrossRef] [PubMed]
- Gergely, V.; Pop, M.; Campian, C.; Chira, N. Finite element modelling of different strengthening strategies for reinforced concrete deep beams. IOP Conf. Ser. Mater. Sci. Eng. 2019. [Google Scholar] [CrossRef]
- Hassan, H.M.; Arab, M.A.E.S.; el-kassas, A.I. Behavior of high strength self-compacted concrete deep beams with web openings. Heliyon 2019, 5, e01524. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Funari, M.F.; Spadea, S.; Fabbrocino, F.; Luciano, R. A Moving Interface Finite Element Formulation to Predict Dynamic Edge Debonding in FRP-Strengthened Concrete Beams in Service Conditions. Fibers 2020, 8, 42. [Google Scholar] [CrossRef]
- Hawileh, R.A.; El-Maaddawy, T.A.; Naser, M.Z. Non-linear FE Analysis of RC Deep Beams with openings Strengthened with CFRP Composites. In Proceedings of the First Middle East Conference on Smart Monitoring, Dubai, United Arab Emirates, 8–10 February 2011. [Google Scholar]
- Ombres, L.; Verre, S. Experimental and Numerical Investigation on the Steel Reinforced Grout (SRG) Composite-to-Concrete Bond. J. Compos. Sci. 2020, 4, 182. [Google Scholar] [CrossRef]
- Loreto, G.; Babaeidarabad, S.; Leardini, L.; Nanni, A. RC beams shear-strengthened with fabric-reinforced-cementitious-matrix (FRCM) composite. Int. J. Adv. Struct. Eng. 2015, 7, 341–352. [Google Scholar] [CrossRef] [Green Version]
- Khalaf, M.R.; Al-Ahmed, A.H.A. Shear strength of reinforced concrete deep beams with large openings strengthened by external prestressed strands. Structures 2020, 28, 1060–1076. [Google Scholar] [CrossRef]
- Abaqus, Abaqus 6.2: Computer Software for Finite Element Analysis; Dassault Systems Simulia: Johnston, RI, USA, 2020.
- Hafezolghorani, M.; Hejazi, F.; Vaghei, R.; Jaafar, M.S.B.; Karimzade, K. Simplified Damage Plasticity Model for Concrete. Struct. Eng. Int. 2018, 27, 68–78. [Google Scholar] [CrossRef]
- Sanez, L.P. Discussion of Equation for the Stress-Strain Curve of Concrete by Desayi and Krishnan. J. Am. Concr. Inst. 1964, 61, 1229–1235. [Google Scholar]
- Belarbi, A.; Hsu, T.T. Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete. Struct. J. 1994, 91, 465–474. [Google Scholar]
Specimen * | Cross-Section (mm2) | Span (mm) | Openings (mm2) | Strengthening |
---|---|---|---|---|
CDB–Solid | 160 × 400 | 1190 | Solid | - |
CDB–O–U | 160 × 400 | 1190 | 160 × 160 | - |
CDB–O–S | 160 × 400 | 1190 | 160 × 160 | CFRP |
CFRP Strips | SikaWrap 231C |
---|---|
Fiber Orientation | 0° |
Areal weight | 450 g/m2 |
Fabric design thickness | 0.255 mm (based on the total area of carbon fibers) |
Tensile strength of fibers | 4800 MPa |
Tensile E—modulus of fibers | 230,000 MPa |
Elongation at break | 2.1% |
Fabric width | 500 mm |
Epoxy | Sikadur-330 |
---|---|
Appearance | Yellow |
Density | 1.1 g/cm3 |
Mixing ratio | 2:1 by weight (at +25 °C) |
Open time | 30 min |
Tensile strength | 25 MPa |
E-modulus (Flexural) | 2700 MPa |
Elongation | 3% |
Specimen | Initial Crack Load (kN) | Ultimate Capacity (kN) | Ultimate Deflection (mm) | Initial Stiffness (kN/mm) | Mode of Failure |
---|---|---|---|---|---|
CDB–Solid | 200 | 730 | 2.4 | 1745 | Shear failure |
CDB–O–U | 140 | 580 | 1.7 | 1142 | Bearing failure |
CDB–O–S | 210 | 680 | 2.4 | 1390 | Bearing failure |
Parameter | Value |
---|---|
φ | 33° |
ε | 0.1 |
29/25 | |
K | 2/3 |
μ | 0.0001 |
Specimen | Ultimate Capacity (kN) | % Change * | Ultimate Deflection (mm) | % Change * | ||
---|---|---|---|---|---|---|
Exp. | FE | Exp. | FE | |||
CDB–Solid | 730 | 770 | + 5.5 | 2.5 | 2.8 | + 12 |
CDB–O–U | 580 | 625 | + 7.7 | 1.7 | 1.6 | − 5.9 |
CDB–O–S | 680 | 735 | + 8.1 | 2.4 | 2.5 | + 4.2 |
Specimen | Ultimate Capacity (kN) | % Change * | Ultimate Deflection (mm) | % Change * |
---|---|---|---|---|
CDB–O–U– R 1.0 | 625 | 18 | 1.6 | 7 |
CDB–O–S– R 1.0 | 735 | 2.5 | ||
CDB–O–U– R 1.5 | 455 | 23 | 1.2 | 23 |
CDB–O–S– R 1.5 | 560 | 1.7 | ||
CDB–O–U– R 2.0 | 337 | 35 | 1.0 | 40 |
CDB–O–S– R 2.0 | 454 | 1.4 |
Specimen | Opening Ratio | Distribution Load Factor (k) | Ultimate Load (kN) | Ultimate Mid-Span Deflection (mm) |
---|---|---|---|---|
CDB–Solid | - | 0.50 | 770 | 2.788 |
CDB–Solid– k 0.40 | 0.40 | 650 | 4.210 | |
CDB–Solid– k 0.30 | 0.30 | 562 | 4.272 | |
CDB–Solid– k 0.25 | 0.25 | 523 | 4.567 | |
CDB–O–U–R1.0 | 1.0 | 0.50 | 625 | 1.569 |
CDB–O–U–R1.0– k 0.40 | 0.40 | 513 | 1.682 | |
CDB–O–U–R1.0– k 0.30 | 0.30 | 435 | 1.704 | |
CDB–O–U–R1.0– k 0.25 | 0.25 | 402 | 1.667 | |
CDB–O–U–R1.5 k 0.50 | 1.5 | 0.50 | 455 | 2.221 |
CDB–O–U–R1.5– k 0.40 | 0.40 | 373 | 1.110 | |
CDB–O–U–R1.5– k 0.30 | 0.30 | 319 | 1.486 | |
CDB–O–U–R1.5– k 0.25 | 0.25 | 297 | 1.141 | |
CDB–O–U–R2.0 | 2.0 | 0.50 | 337 | 1.031 |
CDB–O–U–R2.0– k 0.40 | 0.40 | 281 | 1.089 | |
CDB–O–U–R2.0– k 0.30 | 0.30 | 242 | 1.085 | |
CDB–O–U–R2.0– k 0.25 | 0.25 | 226 | 1.189 | |
CDB–O–S–R1.0 | 1.0 | 0.50 | 735 | 2.541 |
CDB–O–S –R1.0– k 0.40 | 0.40 | 603 | 2.630 | |
CDB–O–S –R1.0– k 0.30 | 0.30 | 501 | 2.510 | |
CDB–O–S –R1.0– k 0.25 | 0.25 | 468 | 2.493 | |
CDB–O–S–R1.5 | 1.5 | 0.50 | 560 | 1.669 |
CDB–O–S–R1.5– k 0.40 | 0.40 | 459 | 1.523 | |
CDB–O–S–R1.5– k 0.30 | 0.30 | 385 | 1.461 | |
CDB–O–S–R1.5– k 0.25 | 0.25 | 360 | 1.500 | |
CDB–O–S–R2.0 | 2.0 | 0.50 | 454 | 1.446 |
CDB–O–S–R2.0– k 0.40 | 0.40 | 366 | 1.294 | |
CDB–O–S–R2.0– k 0.30 | 0.30 | 312 | 1.327 | |
CDB–O–S–R2.0– k 0.25 | 0.25 | 292 | 1.347 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 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 (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Khalaf, M.R.; Al-Ahmed, A.H.A.; Allawi, A.A.; El-Zohairy, A. Strengthening of Continuous Reinforced Concrete Deep Beams with Large Openings Using CFRP Strips. Materials 2021, 14, 3119. https://doi.org/10.3390/ma14113119
Khalaf MR, Al-Ahmed AHA, Allawi AA, El-Zohairy A. Strengthening of Continuous Reinforced Concrete Deep Beams with Large Openings Using CFRP Strips. Materials. 2021; 14(11):3119. https://doi.org/10.3390/ma14113119
Chicago/Turabian StyleKhalaf, Mohammed Riyadh, Ali Hussein Ali Al-Ahmed, Abbas AbdulMajeed Allawi, and Ayman El-Zohairy. 2021. "Strengthening of Continuous Reinforced Concrete Deep Beams with Large Openings Using CFRP Strips" Materials 14, no. 11: 3119. https://doi.org/10.3390/ma14113119