Shear strengthening of deficient RC deep beams using NSM FRP system: Experimental and numerical investigation

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Test results of all tested specimens

Beam description of half span part	Shear strength (kN)	Note
Beam part with no stirrups	67.1 (DB-NS0)	–
Beam part having stirrups in all span	82.5 (DB-S-F)	23% improvement as compared to DB-NS0
RC beam part with no stirrups but strengthened using NSM U-wrap CFRP strips	112 (DB-FRP)	82% improvement as compared to DB-NS0

Constitutive material models parameters of concrete, Sikadur resin, and CFRP

Material	Parameters	Values	Denotation
Concrete	Dilation angle (ψ)	32°	Calibrated value
	Eccentricity (ε)	0.1	ABAQUS (default value)
	Stress ratio (σb0/σc0)	1.16	ABAQUS (default value)
	Shape factor (Kc)	0.667	ABAQUS (default value)
Sikadur mortar	Dilation angle (ψ)	40°	Calibrated value
	Eccentricity (ε)	0.1	ABAQUS (default value)
	Stress ratio (σb0/σc0)	1.16	ABAQUS (default value)
	Shape factor (Kc)	0.667	ABAQUS (default value)
CFRP sheet	Poisson’s ratio (ν)	0.3	Widely used in FE modeling
	Modulus of Elasticity (E)	230000 MPa	Given by the manufacturer
	Tensile strength (longitudinal: σt1)	1122 MPa	Experimental Value
	Compressive strength (longitudinal: σc1)	10 MPa	Al-Mekhlafi, et al. [11]
	Shear strength (longitudinal: τf1)	10 MPa
	Transversal tensile strength (σt2)	10 MPa
	Compressive strength (transversal: σc2)	10 MPa
	Shear strength (transversal: τf2)	10 MPa

Mixture composition of concrete mixture

Material	Weight (kg/m3)
Cement	650
Silica sand	528
Coarse aggregate (Nominal size = 10 mm)	770
Crush sand	264
Water (w/c = 0.25)	162.5
Super-plasticizer(Gli-110)	3 Liters

Overview of test samples

Specimen	Left half span		Right half span
	Shear stirrups	Shear strengthening	Shear stirrups	Shear strengthening
DB-S-F	2L-f6@100	None	2L-f6@100	None
DB-NS0	2L-f6@100	None	None	None
DB-FRP	2L-f6@100	Yes	None	The specimen has two layers of U-wraps of FRP (25 mm wide) spaced at 100 mm intervals, along with a single layer of horizontally bonded FRP strips (50 mm wide) placed at the mid-depth on each face.

Comparison of experimental and FE results

Specimen ID	Exp. flexural strength (kN)	FE flexural strength (kN)	Error %
DB-S-F	165	172	4.07%
DB-NS0	134	137	2.19%
DB-FRP	212	218	2.75%

Mechanical characterization of steel reinforcement

Mechanical Property	Bar diameter		Test Standard
	10 mm	6 mm
Yield strength, (MPa)	525	280	ASTM A370 (2017)
Ultimate strength, (MPa)	578	380
Modulus of elasticity, (GPa)	200	200

Characteristics of the strengthening materials

Item	Value
CFRP composite
Type of FRP	Unidirectional CFRP sheet
Longitudinal elastic modulus of the primary fibers. (GPa)	77.3
Transverse elastic modulus relative to the primary fiber direction. (MPa)	40.6
Strain at fracture along the primary fiber direction (%)	1.1
Maximum tensile strength along the primary fiber direction (MPa)	846
Thickness of each individual layer, tf (mm)	1.0
Epoxy
Density (kg /l)	1.16
Tensile strength of the adhesive (MPa)	> 4.0 (7 days)
Tensile modulus of elasticity (GPa)	3.5 (7 days)
Sikadur_31 Thixotropic epoxy_resin mortar
Tensile strength of the adhesive (MPa)	15
Density (kg /l)	1.65
Modulus of Elasticity (GPa)	4.3

Mesh convergence analysis results

Mesh types	Beam elements size	Experimental flexural strength (kN)	FE flexural strength (kN)	Experimental/FE
Type 1	25	165	185	89.2%
Type 2	15		178	92.7%
Type 3	7		172	95.6%