Curvature ductility of RC sections based on eurocode: Analytical procedure

Abstract

Correct estimate of curvature ductility of reinforced concrete members has always been an attractive subject of study as it engenders a reliable estimate of capacity of buildings under seismic loads. The majority of the building stock needs structural assessment to certify their safety under revised seismic loads by new codes. Structural assessment of existing buildings, by employing nonlinear analyses tools like pushover, needs an accurate input of moment-curvature relationship for reliable results. In the present study, nonlinear characteristics of constitutive materials are mathematically modelled according to Eurocode, currently in prevalence and analytical predictions of curvature ductility of reinforced concrete sections are presented. Relationships, in explicit form, to estimate the moment-curvature response are proposed, leading to closed form solutions after their verification with those obtained from numerical procedures. The purpose is to estimate curvature ductility under service loads in a simpler closed form manner. The influence of longitudinal tensile and compression steel reinforcement ratios on curvature ductility is also examined and discussed. The spread sheet program used to estimate the moment-curvature relationship, after simplifying the complexities involved in such estimate, predicts in good agreement with the proposed analytical expressions. Avoiding somewhat tedious hand calculations and approximations required in conventional iterative design procedures, the proposed estimate of curvature ductility avoids errors and potentially unsafe design

An Analytical Step-by-Step Procedure to Derive the Flexural Response of RC Sections in Compression

“…The flexural response of a class of RC sections, characterized by assigned values of the geometrical and mechanical parameters defined above, is obtained by imposing the equilibrium condition expressed by (15) and (16).…”

“…(iii) when the assigned value of is reached with an acceptable tolerance (i.e., (15) is verified with very good approximation), the assigned values of̃and , and the value of that was found, make it possible to calculate the corresponding values of 1 , 2 , and expressed by (24), (36), and (49), and the sum of these contributions of moment is the ordinate of the point having the abscissã, belonging to the -c urve sought;…”

“…An alternative approach was proposed in [14], where, by using a simplified model, complex nonlinear geometric effects were embedded in the nonlinear material behaviour of the cross-section. Chandrasekaran et al [15] proposed an analytical relationship providing in explicit form the moment-curvature response of a section, by considering nonlinear constitutive laws of materials, chosen in accordance with the European technical codes, which can be applied by the use of a spreadsheet.…”

New procedure for determining the moment–curvature relationship of a reinforced concrete section

“…An idealised m-ö relationship is normally used because of the inconvenience of the real relationship (Jirásek and Bažant, 2001), such as a tri-linear model (Löhning et al, 2009). Recently, analytical solutions have been used to calculate the ultimate moment and curvature (Colajanni et al, 2013), as well as the curvature ductility (Chandrasekaran et al, 2011;Guler et al, 2013).…”

Investigation of the influence of design and material parameters in the progressive collapse analysis of RC structures

“…The present description enables a more realistic representation of the crosssectional behaviour of reinforced concrete members where axial load-bending moment interactions are considered in combination with material nonlinearities, potentially including material rate effects. It also avoids the need to postulate closed-form relationships between generalised stresses and strains at the sectional level, preventing the related identification problem whenever the design and/or material parameters need to be modified or when a rate dependent approach is considered [33]. The complexity of quantifying the rotational capacity of RC members has been demonstrated in the literature.…”