Optimization of reinforced concrete beams using Solver tool

Due to the development in structural analysis studies, optimization techniques have become part in the design of reinforced concrete structures. Making it possible to design structures with optimized cross-sections. Thus, the present study aims to implement optimization techniques, using the Solver tool, to design procedure of reinforced concrete beams following the precepts of Brazilian Standard ABNT NBR 6118:2014. Focusing to minimize the cost of reinforced concrete beams, where the design variables are the height and width of the beam cross-section and the constraints are imposed by the relevant technical standards and design variables limitations.

Keywords:
structural optimization; beams; reinforced concrete

Authorship

R. S. CORREIA

Federal University of Pernambuco, Post-graduation program of Civil and Environmental Engineering, Caruaru, PE, Brazil. rubenssilvacorreia@gmail.com giuliana.franca@gmail.com bonogustavo@gmail.comFederal University of PernambucoBrazilCaruaru, PE, BrazilFederal University of Pernambuco, Post-graduation program of Civil and Environmental Engineering, Caruaru, PE, Brazil. rubenssilvacorreia@gmail.com giuliana.franca@gmail.com bonogustavo@gmail.com

https://orcid.org/0000-0002-5378-385X

G. F. F. BONO

https://orcid.org/0000-0002-3668-135X

G. BONO

https://orcid.org/0000-0003-4666-8703

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (11)
Tables (4)

Concrete
Source	Type	Price (R$/m³)
94964 - SINAPI 12/2016	C20	258.97
94965 - SINAPI 12/2016	C25	252.39
94966 - SINAPI 12/2016	C30	260.52
MASTERMIX/CARUARU	C35	298.00
94968 - SINAPI 12/2016	C40	299.64
CA-50 steel
Source	Diameter (mm)	Price (R$/kg)
-	5	9.47
92760 - SINAPI 12/2016	6.3	9.47
92761 - SINAPI 12/2016	8	9.14
92762 - SINAPI 12/2016	10	7.43
92763 - SINAPI 12/2016	12.5	6.17
92764 - SINAPI 12/2016	16	4.85
Formworks
Source		Price (R$/m²)
92446 - SINAPI 12/2016		119.03

Span (m)	Loading (kN/m)									Average ratio (%)
Span (m)	10	15	20	25	30	35	40	45	50
2	12.50	12.50	12.50	12.60	12.50	12.50	12.70	14.20	13.40	12.82
2.5	10.00	10.00	10.00	10.08	11.60	10.08	10.56	11.60	12.80	10.75
3	8.40	8.60	9.60	9.20	9.87	10.80	11.73	12.53	12.93	10.41
3.5	7.26	8.23	8.06	9.14	10.29	10.69	11.54	12.00	13.77	10.11
4	7.40	7.45	8.35	9.55	10.00	10.60	11.10	11.55	12.35	9.82
4.5	7.60	7.78	8.89	9.42	9.78	10.71	11.02	12.00	11.73	9.88
5	7.80	7.96	8.76	9.36	10.12	10.20	10.92	10.88	10.92	9.66
5.5	6.84	7.67	8.58	8.95	9.64	9.82	10.04	10.25	10.98	9.20
6	7.07	7.83	8.70	9.20	9.47	9.57	9.97	10.23	11.53	9.29
6.5	7.17	8.06	8.37	8.89	9.14	9.45	10.31	11.17	11.94	9.39
7	6.94	7.97	8.03	8.31	8.54	10.00	10.49	11.31	11.54	9.24

Domain 2		Domain 3
Concrete strains (‰)	% of optimum cross-sections	Steel strains (‰)	% of optimum cross-sections
≤ 1	3.64	≤ 2.5	0.00
1 - 2	18.18	2.5 - 5	52.27
2 - 3	38.18	5 - 7.5	33.86
3 - 3.5	40.00	7.5 - 10	13.87

Savings (%)	% of optimized cross-sections
≤ 5	14.96
5 - 10	27.57
10 - 15	17.60
15 - 20	15.54
20 - 25	10.26
25 - 30	9.09
30 - 35	3.81
35 - 40	1.17