{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T04:47:04Z","timestamp":1758862024982,"version":"3.41.2"},"reference-count":7,"publisher":"Emerald","issue":"7","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004,10,1]]},"abstract":"<jats:p>The aim of this paper is to obtain the analytical solution for the optimal design of reinforced concrete sections under ultimate design. The equilibrium equations of the section under bending moment and axial force in rupture are derived. The ultimate conditions are considered either in the steel or in the concrete according to the concrete design codes. The definition of the strains and stresses in the materials is based on the use of Heaviside functions. With this definition the equilibrium equations are described by unique equations. The optimization can then be developed with any design variables in the geometric definition, as area of the reinforcement and location. The optimization is developed with yielding of tensile steel and crushing of concrete. Although this is the current situation in reinforced concrete design, future developments of the model can include other steel and concrete conditions. Cost optimization and variable materials strength ratio are possible applications of the model. The interest of the model is the use of closed form unique equilibrium equations in the optimization of reinforced concrete sections. Numerical examples of the optimization of a rectangular section with minimum reinforcing steel area and economic bending moment are presented. The originality of the paper is the use of Heaviside functions in the definition of the ultimate strains in the reinforced concrete section. Unique equations for the objective function and restrictions are derived. The paper is useful for the design of reinforced concrete. The equations derived can be implemented into computer programs.<\/jats:p>","DOI":"10.1108\/02644400410565298","type":"journal-article","created":{"date-parts":[[2006,7,18]],"date-time":"2006-07-18T06:36:20Z","timestamp":1153204580000},"page":"761-776","source":"Crossref","is-referenced-by-count":13,"title":["Closed form solution of optimal design of rectangular reinforced concrete sections"],"prefix":"10.1108","volume":"21","author":[{"given":"M.H.F.M.","family":"Barros","sequence":"first","affiliation":[]},{"given":"A.F.M.","family":"Barros","sequence":"additional","affiliation":[]},{"given":"C.A.","family":"Ferreira","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022021820472750000_b1","doi-asserted-by":"crossref","unstructured":"Adamu, A. and Karihaloo, B.L. (1994a), \u201cMinimum cost design of reinforced concrete beams using continuum\u2010type optimality criteria structures\u201d, Structural Optimisation, Vol. 7, pp. 91\u2010102.","DOI":"10.1007\/BF01742512"},{"key":"key2022021820472750000_b2","doi-asserted-by":"crossref","unstructured":"Adamu, A. and Karihaloo, B.L. (1994b), \u201cMinimum cost design of RC beams using DCOC\u201d, Advances in Structural Optimisation, pp. 151\u201060.","DOI":"10.4203\/ccp.25.6.1"},{"key":"key2022021820472750000_b3","doi-asserted-by":"crossref","unstructured":"Balling, R.J. and Xiaoping, Y. (1997), \u201cOptimization of reinforced concrete frames\u201d, Journal of Structural Engineering, pp. 193\u2010202.","DOI":"10.1061\/(ASCE)0733-9445(1997)123:2(193)"},{"key":"key2022021820472750000_b4","unstructured":"CEB\u2010FIP (1982), Manual on Bending and Compression, Bulletin no. 141."},{"key":"key2022021820472750000_b5","unstructured":"EC2 (1991), Design of Concrete Structures, ENV 1992\u20101\u20101."},{"key":"key2022021820472750000_b6","doi-asserted-by":"crossref","unstructured":"Kanagasundaram, S. and Karihaloo, B.L. (1990), \u201cMinimum cost design of reinforced concrete structures\u201d, Structural Optimisation, Vol. 2, pp. 173\u201084.","DOI":"10.1007\/BF01836566"},{"key":"key2022021820472750000_frd1","unstructured":"CEB\u2010FIP Model Code 1990, Committee Euro\u2010International du Beton."}],"container-title":["Engineering Computations"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/02644400410565298","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/02644400410565298\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/02644400410565298\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:34:32Z","timestamp":1753403672000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/ec\/article\/21\/7\/761-776\/78437"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,1]]},"references-count":7,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2004,10,1]]}},"alternative-id":["10.1108\/02644400410565298"],"URL":"https:\/\/doi.org\/10.1108\/02644400410565298","relation":{},"ISSN":["0264-4401"],"issn-type":[{"type":"print","value":"0264-4401"}],"subject":[],"published":{"date-parts":[[2004,10,1]]}}}