Three-dimensional nonlinear finite element analysis of concrete deep beam reinforced with GFRP bars

Peer review under responsibility of Housing and Building National Research Center.

Figures & data

Fig. 1 Test setup and specimen geometry.

Table 1 Characteristics of GFRP-Reinforced Concrete Deep Beams.

Specimen	ρ, %	Height (h), mm	Width (bw), mm	Shear span (a), mm	a/d	Overhang length, mm^∗	fc′, MPa
A1N	1.49	306	310	276	1.07	874	40.2
A2N	1.47	310	310	376	1.44	874	45.4
A3N	1.47	310	310	527	2.02	874	41.3
A4H	1.47	310	310	527	2.02	623	64.6
B1N	1.70	608	300	545	1.08	605	40.5
B2N	1.71	606	300	743	1.48	605	39.9
B3N	1.71	607	300	1040	2.07	605	41.2
B4N	2.13	606	300	736	1.48	814	40.7
B5H	2.12	607	300	736	1.48	614	66.4
B6H	1.70	610	300	1040	2.06	460	68.5
C1N	1.58	1003	301	974	1.10	826	51.6
C2N	1.56	1005	304	1329	1.49	821	50.7

Table 2 Experimentally Measured Concrete Properties.

Beam code	Ultimate compressive strength, MPa	Young^’s modulus, MPa	Strain at ultimate strength	Strain at end of softening curve	Ultimate tensile strength, MPa	Poisson’s ratio
A1N	40.2	23,020	0.0027	0.0039	2.10	0.2
A2N	45.4	22,850	0.0028	0.0040	2.22	0.2
A3N	41.3	24,150	0.0026	0.0040	2.12	0.2
A4H	64.6	22,450	0.0032	0.0040	2.65	0.2
B1N	40.5	23,320	0.0024	0.0038	2.10	0.2
B2N	39.9	23,210	0.0025	0.0031	2.08	0.2
B3N	41.2	23,680	0.0027	0.0030	2.12	0.2
B4N	40.7	24,290	0.0025	0.003096	2.10	0.2
B5H	66.4	24,140	0.0034	0.0042	2.70	0.2
B6H	68.5	24,010	0.0033	0.0036	2.73	0.2
C1N	51.6	26,870	0.0026	0.0040	2.37	0.2
C2N	50.7	25,260	0.0027	0.0040	2.35	0.2

Table 3 Experimental tension test results of the used GFRP bars.

Bar no.	Bar diameter, mm	Area, mm^2	Failure stress, (ffu), MPa	Modulus of elasticity, (Ef), MPa	Rupture strain, %	Poisson’s ratio (υ)
#6	19	322	765	37,900	1.8	0.26
#7	22	396	709	41,100	1.7	0.26
#8	25	528	938	42,300	2	0.26

Fig. 2 3-D meshing of concrete deep beam model in ABAQUS.

Table 4 Experimental and predicted ultimate load capacity (Pu), deflection at P_u, diagonal cracking load (Pc), and reserve capacity of GFRP-reinforced concrete deep beams.

Specimen	Experimental				Exp/FEA(ABAQUS)				Failure mode^⁎
	Pu, kN	Δu, mm	Pc, kN	Reserve capacity (Pc/Pu)	Pu	Δu	Pc	Reserve capacity
A1N	814	12.4	312	0.38	0.97	1.17	0.99	1.02	FC
A2N	471	11.3	187	0.40	1.02	0.93	0.96	0.96	SC
A3N	243	10.9	143	0.59	1.03	0.97	0.92	0.90	SC
A4H	192	9.5	163	0.85	0.93	0.99	1.05	1.13	DT
B1N	1273	9.1	387	0.30	1.04	0.93	0.94	0.89	FC
B2N	799	13.1	287	0.36	1.04	0.95	1.02	0.98	SC
B3N	431	15.3	237	0.55	0.98	0.98	1.05	1.07	SC
B4N	830	11.5	412	0.50	1.05	0.97	1.1	1.05	SC
B5H	1062	14.2	387	0.36	1.09	0.99	0.94	0.85	S
B6H	376	12.9	212	0.56	0.92	1.06	0.94	1.02	DT
C1N	2269	15.9	613	0.27	1.03	0.88	0.99	0.96	SC
C2N	1324	18.3	413	0.31	1.02	0.99	1.01	0.98	S
Mean	1.01	0.98	0.99	0.98
Standard deviation	0.05	0.07	0.05	0.08

* DT – diagonal concrete tension failure, FC – flexural compression failure, SC – shear compression failure, and S – compression strut failure.

Fig. 4 Experimental and finite element pattern of diagonal concrete tension failure (DT) for specimen B6H.

Fig. 5 Experimental and finite element pattern of flexural compression failure (FC) for specimen A1N.

Fig. 6 Experimental and finite element pattern of shear compression failure (SC) for specimen A2N.

Fig. 7 Experimental and finite element pattern of compression strut failure (S) for specimen B5H.

Fig. 8 Experimental reinforcement strain distribution along the bottom layer of reinforcement as the load increased for beam B1N [1].

Fig. 9 Predicted reinforcement strain distribution along the bottom layer of reinforcement as the load increased for beam B1N by ABAQUS.

Fig. 10 Predicted reinforcement strain distribution along the top layer of reinforcement as the load increased for beam B1N by ABAQUS.

Fig. 11 Simulated locations of strain gauges along the height of deep beam and compression strut by finite element.

Table 5 Maximum compressive strain along mid-span locations and compression strut line.

Specimen	εcu at mid-span	εcu along the strut line
A1N	0.00346	0.000713
A2N	0.00273	0.000794
A3N	0.00180	0.000642
A4H	0.00115	0.000546
B1N	0.00185	0.000574
B2N	0.00133	0.000606
B3N	0.001275	0.000532
B4N	0.00111	0.000632
B5H	0.00138	0.000591
B6H	0.005195	0.000509
C1N	0.00197	0.000669
C2N	0.00335	0.000645

ε_cu: concrete compressive strain at ultimate load.

Fig. 13 Effect of FRP bar type on load–deflection response of deep beams.