Minimum steel ratios in reinforced concrete beams made of concrete with different strengths—Theoretical approach

Abstract

R SUMMinimum reinforcement is provided in concrete beams in order to improve their behaviour towards cracking and ductility at failure.Generally, codes of practice equations for the minimum steel ratios, longitudinal and transversal, are mainly empirical and do not include all the influential parameters in them. For this reason and due to the fact that they do lack of a theoretical background, different codes can give values for the minimum steel ratios that greatly differs from one another. Also the validity of these equations may be questioned particularly in the case of high strength concrete beams and prestressed concrete beams for which limited test data are available.In this work, a theoretical approach for the minimum steel ratios that are required for the ductile behaviour at failure in bending, shear and torsion, in concrete beams made of concrete with different strengths is presented. Comparisons are also made between the proposed expressions, the codes expressions and available test results. Un renforcement minimum des poutres en b~ton arm~ est pr&u pour am(liorer leur comportement en cas de fissuration et leur ductilit~ dans la rupture. En g&&al les formules des normes techniques pour tes pourcenrages minimum des armatures longitudinales et transversales sont simplement empiriques et ne contiennent pas tous les param~tres influents. Pour cette raison et comme elles ne prennent pas en consid&ation des fondements th&riques, les diff&ents r~glements donnent des valeurs trbs diff&entes pour les pourcentages minimum d'acier. La validit~ de ces formules peut &e raise en doute particuli}rement clans les cas de poutres en b~ton h haute r&istance et des poutres pr~-contraintes pour lesquelles seuIs des r&ultats d' essais tr}s

Minimum reinforcement revisited

“…Minimum reinforcement has been studied in many publications. Some of these publications, however, are focused only on robustness reinforcement to avoid brittle failure from a very practical code‐type formulation, or on how robustness reinforcement can be optimized by consideration of fracture mechanics, and its implications on the size effect, and are mostly centered on bending without axial force . Others are focused on minimum reinforcement required for control of cracking, but these either address cases of pure bending or pure axial forces but not the combination of both or deal only with cracking from imposed strains …”

“…Some of these publications, however, are focused only on robustness reinforcement to avoid brittle failure from a very practical code-type formulation, 1 or on how robustness reinforcement can be optimized by consideration of fracture mechanics, and its implications on the size effect, and are mostly centered on bending without axial force. [2][3][4][5][6] Others are focused on minimum reinforcement required for control of cracking, but these either address cases of pure bending or pure axial forces but not the Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication.…”

Modified Minimum depth-span ratio of beams and slabs

“…Beal and Thomason [3], presented an approximated depth-span ratio for the preliminary design specification in term of rather than to include the effect of steel design stress. Shehata et al [4], presented a theoretical study for the minimum steel ratio is required for bending, shear and torsion for beams with different concrete strengths. ACI code [1], provides the minimum depth of one-way slab and beams shown in Table (1) [1], [5]- [8]…”