Shear strength model of the reinforced concrete beams with embedded through-section strengthening bars

doi:10.1007/s11709-022-0834-0

Front. Struct. Civ. Eng.

2022, Vol. 16

Issue (7) : 843-857 https://doi.org/10.1007/s11709-022-0834-0

RESEARCH ARTICLE

Shear strength model of the reinforced concrete beams with embedded through-section strengthening bars

Linh Van Hong BUI, Phuoc Trong NGUYEN(

)

Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City 700000, Vietnam

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Abstract

In this study, finite element (FE) analysis is utilized to investigate the shear capacity of reinforced concrete (RC) beams strengthened with embedded through-section (ETS) bars. Effects of critical variables on the beam shear strength, including the compressive strength of concrete, stiffness ratio between ETS bars and steel stirrups, and use of ETS strengthening system alone, are parametrically investigated. A promising method based on the bond mechanism between ETS strengthening and concrete is then proposed for predicting the shear resistance forces of the strengthened beams. An expression for the maximum bond stress of the ETS bars to concrete is developed. This new expression eliminates the difficulty in the search and selection of appropriate bond parameters from adhesion tests. The results obtained from the FE models and analytical models are validated by comparison with those measured from the experiments. Consequently, the model proposed in this study demonstrates better performance and more accuracy for prediction of the beam shear-carrying capacity than those of existing models. The results obtained from this study can also serve researchers and engineers in selection of the proper shear strength models for design of ETS-strengthened RC beams.

Keywords embedded through-section strengthening fiber-reinforced polymer finite element shear strength model bond mechanism

Corresponding Author(s): Phuoc Trong NGUYEN

Just Accepted Date: 26 July 2022 Online First Date: 11 October 2022 Issue Date: 17 November 2022

Cite this article:

Linh Van Hong BUI,Phuoc Trong NGUYEN. Shear strength model of the reinforced concrete beams with embedded through-section strengthening bars[J]. Front. Struct. Civ. Eng., 2022, 16(7): 843-857.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0834-0
https://academic.hep.com.cn/fsce/EN/Y2022/V16/I7/843

Fig.1 Specifications of the beams tested in previous studies [12,14,16] (dimensions in mm). (Reprinted from Journal of Composites for Construction, 16(5), Mofidi A, Chaallal O, Benmokrane B, Neale K W, Experimental tests and design model for RC beams strengthened in shear using the embedded through-section FRP method, 540–550, Copyright 2012, with permission from American Society of Civil Engineers.) (Reprinted from Composite Structures, 126, Breveglieri M, Aprile A, Barros J A O, Embedded through-section shear strengthening technique using steel and CFRP bars in RC beams of different percentage of existing stirrups, 101–113, Copyright 2015, with permission from Elsevier.)

group	beams	ρ_sw (%)	E_sw (GPa)	d_sw (mm)	d_b (mm)	ρ_f (%)	E_f (GPa)	$f c ′ (M P a)$	f_f (MPa)	E_fρ_f/E_swρ_sw	E_fρ_f + E_swρ_sw (MPa)
Mofidi et al. [12]	S0-12d130s	−			12.7	0.64	148	29.6	1885	-	947.2
	S1-9d260s	0.25	200	8	9.5	0.18	148	29.6	1885	0.533	766.4
	S1-12d260s	0.25	200	8	12.7	0.32	148	29.6	1885	0.947	973.6
	S1-12d130s	0.38	200	8	12.7	0.64	148	29.6	1885	1.246	1707
	S1-9d260p	0.25	200	8	9.5	0.18	155	29.6	2800	0.558	779
	S3-12d130s	0.38	200	8	12.7	0.64	148	29.6	1885	1.246	1707
Breveglieri et al. [14]	2S-C180-90 (C1)	0.10	200	6	8	0.16	160	29.7	1920	1.280	456
	2S-C180-45 (C2)	0.10	200	6	8	0.22	160	29.7	1920	1.760	552
	4S-C180-90 (C3)	0.17	200	6	8	0.16	160	32.3	1920	0.753	596
	4S-C180-45 (C4)	0.17	200	6	8	0.22	160	32.3	1920	1.035	692
Bui et al. [16]	B1	0.11	200	6	10	0.24	50	38	1076	0.551	341.2
	B2	0.11	200	6	10	0.34	50	38	1076	0.779	391.4
	B3	0.24	200	9	10	0.24	50	38	1076	0.253	601.2
	B4	0.24	200	9	10	0.34	50	38	1076	0.357	651.4

Tab.1 Beam configurations for experiments in previous studies

group	beams	ρ_sw (%)	E_sw (GPa)	d_sw (mm)	d_b (mm)	ρ_f (%)	E_f (GPa)	$f c ′ (M P a)$	f_f (MPa)	E_fρ_f/E_swρ_sw	E_fρ_f + E_swρ_sw (MPa)
Group 1 (for $f c ′$ = 20 MPa varying stiffness ratio)	G1_Original	0.24	200	9	10	0.24	50	20	1076	0.257	592.4
	G1_B1	0.14	200	6	10	0.29	40	20	755	0.417	395.6
	G1_B2	0.10	200	6	10	0.15	75	20	1366	0.521	318.5
	G1_B3	0.31	200	9	9.5	0.13	100	20	1500	0.209	759.6
	G1_B4	0.10	200	6	10	0.10	120	20	1700	0.556	325.8
	G1_B5	0.39	200	9	9	0.08	160	20	2400	0.160	911.1
	G1_B6	0.19	200	10	8	0.06	200	20	–	0.320	512.0
Group 2 (for $f c ′$ = 38 MPa varying stiffness ratio)	G2_Original	0.24	200	9	10	0.24	50	38	1076	0.257	592.4
	G2_B1	0.14	200	6	10	0.29	40	38	755	0.417	395.6
	G2_B2	0.10	200	6	10	0.15	75	38	1366	0.521	318.5
	G2_B3	0.31	200	9	9.5	0.13	100	38	1500	0.209	759.6
	G2_B4	0.10	200	6	10	0.10	120	38	1700	0.556	325.8
	G2_B5	0.39	200	9	9	0.08	160	38	2400	0.160	911.1
	G2_B6	0.19	200	10	8	0.06	200	38	–	0.320	512.0
Group 3 (for $f c ′$ = 70 MPa varying stiffness ratio)	G3_Original	0.24	200	9	10	0.24	50	70	1076	0.257	592.4
	G3_B1	0.14	200	6	10	0.29	40	70	755	0.417	395.6
	G3_B2	0.10	200	6	10	0.15	75	70	1366	0.521	318.5
	G3_B3	0.31	200	9	9.5	0.13	100	70	1500	0.209	759.6
	G3_B4	0.10	200	6	10	0.10	120	70	1700	0.556	325.8
	G3_B5	0.39	200	9	9	0.08	160	70	2400	0.160	911.1
	G3_B6	0.19	200	10	8	0.06	200	70	–	0.320	512.0
Group 4 (for ETS only)	G4_Original	–	–	–	10	0.24	50	38	1076	–	121.2
	G4_B1	–	–	–	10	0.29	40	38	755	–	116.4
	G4_B2	–	–	–	9.5	0.13	100	38	1366	–	131.3
	G4_B3	–	–	–	10	0.10	120	38	1500	–	116.4
	G4_B4	–	–	–	9	0.08	160	38	2400	–	125.7
	G4_B5	–	–	–	8	0.06	200	38	–	–	124.1

Tab.2 Beam configurations for parametric studies using FEM

Fig.2 Modelings for FEM simulation: (a) concrete model in compression [25,26]; (b) concrete model in tension [25,26]; (c) steel and FRP material models [25,26]; (d) bond model [25,26]. (Reprinted from Journal of Building Engineering, 29, Bui L V H, Stitmannaithum B, Jongvivatsakul P, Comprehensive investigation on bond mechanism of embedded throughsection fiber-reinforced polymer bars to concrete for structural analysis, 101180, Copyright 2020, with permission from Elsevier.)

Fig.3 A half FE model.

Fig.4 Comparison between experiment and FEM simulation: (a) load?deflection curves for representative specimens B1, B2, C1, and C2; (b) beam shear capacity; (c) ETS shear contribution.

Fig.5 Failure patterns. Note: The gray color displayed in the strain contour demonstrates the exceeding ultimate strain occurred in concrete. (photos of the experimental results of the beams are reproduced from Breveglieri et al. [14] with permission). (Reprinted from Composite Structures, 126, Breveglieri M, Aprile A, Barros J A O, Embedded through-section shear strengthening technique using steel and CFRP bars in RC beams of different percentage of existing stirrups, 101–113, Copyright 2015, with permission from Elsevier.)

Fig.6 Stress in steel reinforcement and ETS-FRP bars in the specimen 2S-C180-45 (C2) (stress unit in MPa).

Fig.7 Scheme to determine equivalent bond mechanism: (a) equivalent bond block [25] (Reprinted from Journal of Building Engineering, 29, Bui L V H, Stitmannaithum B, Jongvivatsakul P, Comprehensive investigation on bond mechanism of embedded throughsection fiber-reinforced polymer bars to concrete for structural analysis, 101180, Copyright 2020, with permission from Elsevier.); (b) example for determination of the critical crack plane and crack angle via smeared cracks from the FEM simulation.

Fig.8 Verification of shear resisting models. Note: τ_m in the model of Mofidi et al. [12] and the proposed model is selected to have best fit with ETS shear contribution.

Tab.3 Accuracy of the models

Fig.9 Relationship between material function and maximum bond stress.

Fig.10 Verification of the shear strength models with proposed expression for maximum bond stress.

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