Ultimate flexural strength of prestressed concrete beams: validation and model error evaluation

In this work a computational model is presented to evaluate the ultimate bending moment capacity of the cross section of reinforced and prestressed concrete beams. The computational routines follow the requirements of NBR 6118: 2014. This model is validated by comparing the results obtained with forty-one experimental tests found in the international bibliography. It is shown that the model is very simple, fast and reaches results very close to the experimental ones, with percentage difference of the order of 5%. This tool proved to be a great ally in the structural analysis of reinforced and prestressed concrete elements, besides it is a simplified alternative to obtain the cross section ultimate bending moment.

Keywords:
reinforced concrete; prestressed concrete; ultimate bending moment; beams

Authorship

M. W. MOURA

Escola de Engenharia, Universidade Federal do Rio Grande, Rio Grande, RS, Brasil; mwmoura@gmail.com mvrealgm@gmail.com Universidade Federal do Rio GrandeBrazilRio Grande, RS, Brazil Escola de Engenharia, Universidade Federal do Rio Grande, Rio Grande, RS, Brasil; mwmoura@gmail.com mvrealgm@gmail.com

M. V. REAL

D. D. LORIGGIO

Departamento de Engenharia Civil, Universidade Federal de Santa Catarina, Florianópolis, SC, Brasil. d.loriggio@gmail.comUniversidade Federal de Santa CatarinaBrazilFlorianópolis, SC, Brazil Departamento de Engenharia Civil, Universidade Federal de Santa Catarina, Florianópolis, SC, Brasil. d.loriggio@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (17)
Tables (9)

Beam	b cm	h cm	d_p cm	A_p cm²	f_c kN/cm²	f_pt kN/cm²	f_py kN/cm²	f_se kN/cm²	M_u,exp kN · m
B1	15.24	30.48	23.14	1.497	3.79	169.34	142.03	74.33	49.975
B2	15.62	30.86	24.21	0.748	3.74	169.27	142.03	80.53	29.679
B3	15.24	30.78	24.43	0.374	2.59	169.34	142.03	82.74	15.361
B4	15.49	30.71	23.34	1.497	2.37	169.34	142.03	78.53	45.162
B5	15.49	30.63	23.70	1.606	3.90	171.68	151.55	78.67	55.602
B6	15.39	30.63	20.62	2.206	2.03	171.68	151.55	79.98	50.938
B7	15.57	30.81	20.55	3.013	4.07	171.68	151.55	77.77	72.943
B8	15.57	30.63	20.29	3.013	2.26	171.68	151.55	77.84	67.167
B9	15.39	30.63	23.44	1.510	4.36	165.47	142.51	13.72	47.725
B10	15.39	30.56	22.89	0.381	2.43	165.47	142.65	13.10	13.314
B11	15.39	30.63	23.39	1.510	2.70	165.47	142.51	14.07	47.223
B12	15.39	30.81	21.16	2.832	3.83	165.47	142.65	14.07	62.029
B13	15.29	30.73	20.70	2.077	2.59	165.47	142.51	14.62	48.023
B14	15.24	30.68	20.29	2.832	2.59	165.47	142.51	13.93	53.094
B15	15.32	30.71	23.60	1.510	3.94	165.47	142.65	103.42	48.308
B16	15.27	30.51	22.86	0.381	2.30	165.47	142.65	103.63	14.141
B17	15.24	30.51	23.09	1.510	3.16	165.47	142.65	104.11	45.894
B18	15.24	30.38	21.06	2.077	2.83	165.47	142.51	102.59	52.172
B19	15.44	30.66	21.01	2.832	4.29	165.47	142.65	104.32	71.560
B20	15.37	30.81	23.55	1.006	2.63	171.68	151.55	81.77	31.753
B21	15.44	30.66	22.99	1.006	4.52	171.68	151.55	81.36	34.397
B22	15.42	30.66	23.19	2.006	5.26	171.68	151.55	79.43	66.937
B23	15.34	30.56	20.83	3.013	5.65	171.68	151.55	80.88	79.980
B24	15.42	30.58	20.93	2.406	4.22	171.68	151.55	80.25	66.964
B25	15.39	30.58	20.35	2.006	2.25	171.68	151.55	78.94	50.165
B26	15.49	30.40	23.55	1.606	0.88	171.68	151.55	80.32	38.993
B27	15.42	30.66	21.23	3.013	3.16	171.68	151.55	81.36	70.136

Beam	E_p kN/cm²
F28	20477.43
F29	20477.43
F30	19925.85
F31	19925.85
F32	20408.48
F33	20408.48

Beam	E_p kN/cm²	E_s kN/cm²	f_y kN/cm²	A_s cm²	d_s cm²
TD37	20000.00	20000.00	26.70	1.57	25.00
TD38	20000.00	20000.00	26.70	2.36	25.00
TD39	20000.00	20000.00	26.70	1.00	25.00

Beam	M_u,exp [kN · m]	M_u,calc [kN · m]	M_u,exp M_u,calc	Beam	M_u,exp [kN · m]	M_u,calc [kN · m]	M_u,exp M_u,calc
B1	49.975	46.049	1.085	B22	66.937	65.933	1.015
B2	29.679	25.226	1.177	B23	79.980	83.915	0.953
B3	15.361	12.872	1.193	B24	66.964	66.650	1.005
B4	45.162	43.951	1.028	B25	50.165	47.249	1.062
B5	55.602	53.684	1.036	B26	38.993	30.326	1.286
B6	50.938	47.026	1.083	B27	70.136	73.456	0.955
B7	72.943	77.557	0.941	F28	30.70	26.056	1.178
B8	67.167	54.800	1.226	F29	50.63	46.377	1.092
B9	47.725	47.467	1.005	F30	17.64	15.678	1.125
B10	13.314	12.157	1.095	F31	44.93	45.150	0.995
B11	47.223	45.071	1.048	F32	65.31	69.177	0.944
B12	62.029	67.702	0.916	F33	43.36	41.489	1.045
B13	48.023	45.198	1.063	W34	40.79	44.74	0.912
B14	53.094	48.060	1.105	W35	22.37	21.060	1.062
B15	48.308	47.966	1.007	W36	64.29	71.916	0.894
B16	14.141	12.260	1.153	TD37	35.00	27.744	1.262
B17	45.894	45.833	1.001	TD38	61.60	58.039	1.061
B18	52.172	52.538	0.993	TD39	71.40	60.004	1.190
B19	71.560	73.274	0.977	M40	93.44	94.840	0.985
B20	31.753	33.621	0.944	M41	109.93	105.484	1.042
B21	34.397	34.005	1.012	-	-	-	-

Beam	b cm	h cm	d_p cm	A_p cm²	f_c kN/cm²	f_pt kN/cm²	f_py kN/cm²	f_se kN/cm²	M_u,exp kN · m
F28	15.62	30.56	20.14	1.494	1.72	128.24	97.91	63.78	30.70
F29	15.65	30.58	20.50	2.615	2.95	128.24	97.91	63.91	50.63
F30	15.47	30.73	20.52	0.561	1.99	170.99	137.90	69.71	17.64
F31	15.44	32.26	20.90	1.868	2.38	170.99	137.90	64.88	44.93
F32	15.24	30.81	23.67	1.839	4.95	176.51	169.61	79.50	65.31
F33	15.32	30.66	23.06	1.103	5.74	176.85	163.41	80.60	43.36

Beam	b cm	h cm	d_p cm	A_p cm²	f_c kN/cm²	f_pt kN/cm²	f_py kN/cm²	f_se kN/cm²	M_u,exp kN · m
TD37	16.00	28.00	22.00	0.588	3.56	166.00	136.00	92.40	35.00
TD38	16.00	28.00	22.00	1.568	3.56	166.00	136.00	87.90	61.60
TD39	16.00	28.00	22.00	1.960	3.56	166.00	136.00	82.50	71.40

Beam	E_p kN/cm²	E_s kN/cm²	f_y kN/cm²	A_s cm²	d_s cm	b_f cm	h_f cm
M40	19500.00	21000.00	37.71	Sup. 0.62	1.91	-	-
				Inf. 0.62	28.58
M41	19500.00	21000.00	37.71	Sup. 0.62	1.91	96.52	5.08
				Inf. 0.62	28.58