Flexural behavior of high strength concrete shallow wide beams reinforced by hybrid longitudinal reinforcement

Figures & data

Table 1. Concrete mix proportions.

Material	Dolomite(kg)	Sand(kg)	Cement(kg)	Water (Liter)	Superplasticizers (Liter)
Mix Proportion (Kg/m^3)	1150	600	425	170	2.6

Figure 1. The grading curve for crushed dolomite.

Figure 2. The grading curve for fine sand.

Table 2. The chemical composites of ordinary Portland cement.

Component	SiO2	AL2O3	Fe2O3	Cao	MgO	SO3	K2O	Na2O	CL^−
Portland cement	20.6	4.5	3.6	62.5	2.6	2.7	0.5	0.2	0.01

Figure 3. Mode of failure for standard A) compressive strength of cubes, B) tensile strength of cylinders.

Figure 4. Tensile strength test for A) steel B) BFRP, and C) GFRP.

Figure 5. Ultimate tensile strength versus corresponding strains for examined BFRP and GFRP.

Table 3. The yield strength, ultimate strength and elongation.

Material	Nominal Diameter (mm)	Yield strength (N/mm^2)	Yield strain	Ultimate strength (N/mm^2)	Modulus of Elasticity (N/mm^2)
Steel (B500DWR)	10	490	0.0022	624	222727
Steel (B500DWR)	12	500	0.0025	640	200000

Table 4. Ultimate tensile strength versus corresponding strains and modulus of elasticity of GFRP and BFRP.

Advanced composite materials	Ultimate tensile strength (N/mm^2)	Corresponding strain	Modulus of Elasticity (N/mm2)
GFRP	1061	0.022	47480
BFRP	1470	0.026	59700

Figure 6. Geometrical dimensions and reinforcement details of experimental specimen’s

Figure 7. Specimens with different flexural reinforcement technique.

Figure 8. Test setup of all shallow wide beams (SWB) specimens.

Table 5. General description for longitudinal tensile reinforcement of all the tested SWB specimens.

Group	Specimen. model	Longitudinal Tensile RFT %
		Steel %	GFRP %	BFRP %
Group (A)	HBC	100	0	0
	HBGF	0	100	0
	HBBF	0	0	100
Group (B)	HBSGF	60	40	0
	HBSBF	60	0	40
	HBSGBF	20	40	40

Figure 9. Installation of strain gauges for steel, GFRP and BFRP bars.

Figure 10. The crack pattern and mode of failure for all specimens.

Figure 11. The schematic diagrams for crack pattern and mode of failure for all specimens.

Figure 12. Deflection profile for all tested specimens.

Figure 13. The load deflection curves for all tested specimens.

Figure 14. Recorded peak load for all specimens.

Figure 15. Recorded maximum deflection for all specimens.

Figure 16. Recorded maximum strain in resisting tensile element for all specimens.

Table 6. Presentation of first cracking load, initial crack displacement, maximum load, maximum deflection, ductility index and energy absorption for tested beams.

Specimen Code	First Cracking Load (kN)	Initial crack displacement (mm)	Maximum Load (kN)	Maximum Deflection (mm)	Ductility Index	Energy Absorption
HBC	65	1.51	239.8	51.7	5.20	4549.70
HBBF	76	5.60	343.2	67.7	1.54	5079.94
HBSBF	69	2.30	313.5	67.9	1.80	12290.27
HBGF	65	2.82	338.4	55.1	1.45	3482.25
HBSGF	71	2.39	302.7	51.9	1.92	9568.11
HBSBGF	49	1.53	339.4	55.5	1.60	6404.15

Figure 17. Concrete compressive stress - inelastic strain.

Table 7. FEM material properties for concrete.

Material	Element	Material Properties
HSC	Solid 65	Elastic modulus of elasticity (Ec=27.828 GPa) Poisson’s ratio (PRXY) (ν = 0.2) Compressive strength (fcu = 40 MPa) Tensile strength (ft =6 MPa) Open shear transfer crack coefficient ${\beta }_t=0.2$ Closed shear transfer crack coefficient ${\beta }_c=0.8$

Figure 18. Stress-strain relationship for steel and FRP reinforcement [25].

Table 8. FEM material properties for reinforcing steel bars.

Material	Element	Material Properties
Reinforcing steel bars	Link180	Elastic Modulus of elasticity of T10 (Es = 222,727 MPa) Poisson’s ratio (PRXY) (ν = 0.3) Yield stress for deformed steel bars T10 (fy = 490 MPa) Area of steel of T10 (As = 78.5 mm2) Elastic Modulus of elasticity of T12 (Es = 200,000 MPa) Poisson’s ratio (PRXY) (ν = 0.3) Yield stress for deformed steel bars T12 (fy = 500 MPa) Area of steel of T12 (As = 113 mm2)

Table 9. FEM material properties for BFRP bars.

Material	Element	Material Properties
BFRP bars	Link180	Elastic Modulus of elasticity (Ef = 59.7 GPa) Tensile strength of T12 (ft = 1470 MPa) Poisson’s ratio (PRXY) (ν = 0.24) Area of steel of T12 (As = 113 mm2)

Table 10. FEM material properties for GFRP bars.

Material	Element	Material Properties
GFRP bars	Link180	Elastic Modulus of elasticity (Ef = 47.48 GPa) Tensile strength of T12 (ft = 1061 MPa) Poisson’s ratio (PRXY) (ν = 0.24) Area of steel of T12 (As = 113 mm2)

Figure 19. Details of FE model for shallow wide beams.

Figure 20. Load-deflection relationship of both experimental and FEA model for control beam HBC.

Figure 21. The crack pattern and mode of failure for both types of failure (FEA).

Table 11. Experimental results versus FE model results.

	Ultimate load, Pu (kN)		Deflection, Δu (mm)
Specimen Model	Experimental results	FE model results	Experimental results	FE model results	Mode of failure
HBC	239.80	249.90	51.70	48.20	Concrete crushing
HBBF	343.20	350.48	67.70	63.11	FRP- Rupture
HBSBF	313.50	324.80	67.90	63.42	Concrete crushing with FRP- Rupture
HBGF	338.40	352.59	55.10	51.48	FRP- Rupture
HBSGF	302.70	313.83	51.90	48.47	Concrete crushing with FRP- Rupture
HBSBGF	339.40	351.87	55.50	51.83	FRP- Rupture

Figure 22. Stresses characteristics at cracking initiation stage for all specimens.

Figure 23. Stresses characteristics at ultimate stage for control specimen HBC.

Table 12. Comparison between experimental results versus theoretical expectations.

Cracking load, Pcr (kN)	Specimen Model
	HBC	HBBF	HBSBF	HBGF	HBSGF	HBSBGF
Experimental	65.00	76.00	69.00	65.00	71.00	49.00
Theoretical	33.82	33.82	33.82	33.82	33.82	33.82
(Theoretical/Experimental)	0.52	0.44	0.49	0.52	0.47	0.69

Table 13. Comparison between experimental results versus theoretical expectations.

Ultimate load, Pu (kN)	Specimen Model
	HBC	HBBF	HBSBF	HBGF	HBSGF	HBSBGF
Experimental	239.80	343.20	313.50	338.40	302.70	339.40
Theoretical	182.10	247.30	232.20	246.67	233.10	247.76
(Theoretical/Experimental)	0.76	0.72	0.74	0.73	0.77	0.73

Kachlakev DI, McCurry D Jr. Simulated full scale testing of reinforced concrete beams strengthened with FRP composites: experimental results and design model verification. Salem, Oregon: Oregon Department of Transportation; 2000.

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