PSI - Issue 44

A. Floridia et al. / Procedia Structural Integrity 44 (2023) 504–511

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A. Floridia et al./ Structural Integrity Procedia 00 (2022) 000–000

sides of either 4.62, 7.84 or 12.50 cm². The hoops consist of 8 mm diameter bars with spacing equal to either 5, 10, 15 or 25 cm. The normalised axial force N /( A c f c ) is equal to either 0, 0.1, 0.3 and 0.5 (see Figure 4). 4. Comparison with results of laboratory tests The method has been validated against results of 73 laboratory tests on members tested by other researchers in either single or double bending under a constant value of the axial force (Rossi, 2021). The columns considered are characterized by shear span ratio 2.54≤ a / d ≤6.60, concrete strength 19.6≤ f c ≤48.3 MPa, reinforcement nomina l yield stress 348.3≤ f y ≤586.1 MPa, total longitudinal reinforcement ratio 0.0125≤ ρ l,tot ≤ 0.0328 and transverse reinforcement ratio 0.0024 ≤ ρ sw ≤ 0.0176. Further, the normalised axial force N / A c f c varies from 0 to 0.46, i.e. the columns under examination are subjected to null to moderate axial forces. The parameter adopted for comparison of theoretical and experimental results is V exp num R V V = , where V num is the ultimate shear force obtained by means of the proposed method and V exp is the maximum shear force recorded during the laboratory test. The values of R V vary from 0.83 to 1.41, with a mean value of 1.11, a standard deviation of 0.139 and a coefficient of variation equal to 0.125. The results show no particular trend with the transverse reinforcement ratio, at least for the ranges of values considered in the present validation. On the contrary, the values of R V show a trend with the shear span ratio a / d and with the normalised axial force. In particular, these values of R V decrease with the increase of a / d or N / A c f c and scatter to a higher extent in columns with lower values of a / d . This latter finding is in line with expectations because the resisting mechanism of members with low shear span ratios is mainly characterized by arch action. The results of the validation show that there is also no appreciable trend with the compressive strength of concrete f c and the longitudinal reinforcement ratios ρ l,tot . In view of these results, the application of the proposed method is suggested for normalised axial force not higher than 0.45 and for shear span ratios not lower than 2.5. 5. Conclusion The paper proposes a simple procedure for the calculation of the shear strength resulting from the only truss action in reinforced concrete rectangular members with shear reinforcement and subjected to axial force, bending moment and shear force. The main conclusions of the study are: - the proposed procedure provides the N-M-V ultimate interaction domain of the cross-section by means of simple equations or procedures and is easy to implement within structural programs to perform safety checks of members. - the proposed procedure identifies points of the N-M-V ultimate interaction domain characteristic of limits of behaviour of steel and concrete. - the comparison between the results of the proposed method and those of a more refined non-linear programming problem highlights that the differences between the results of the two methods are negligible. - the comparison between the results of the proposed method and those of laboratory tests highlights that the proposed method can be reliably applied to predict the shear strength of members characterized by normalised axial force not higher than 0.45 and by shear span ratios not lower than 2.5. References Rossi, P.P., Recupero, A., 2013. Ultimate strength of reinforced concrete circular members subjected to axial force, bending moment and shear force, Journal of Structural Engineering 139(6), 915-928. Rossi, P.P., 2013. Evaluation of the ultimate strength of R.C. rectangular columns subjected to axial force, bending moment and shear force. Engineering Structures 57, 339-355. Rossi, P.P., 2021. Simplified evaluation of the N-M-V ultimate domain of R.C. rectangular members with shear reinforcement. Structures 34, 4758 4773. Walther, R., Miehlbradt, M., 1990. Dimensionnement des structures en béton: Bases et technologie. Traité de Génie Civil de l'Ecole Polytechnique Fédérale de Lausanne, vol. 7. Presses Polytechniques et Universitaires Romandes (PPUR). Eurocode 2. Design of concrete structures – Part 1-1: general rules and rules for buildings. European Committee for Standardization, 2004.