Applying of Integral Equation of Volterra for Determining the Section Forces in Composite Beam, Regarding Shrinkage of Concrete

Abstract

During time, the equilibrium state of a steel-concrete mixed beam progresses under the concrete shrinkage. In this context, a contribution to the search of the time-dependant behaviour of mixed beams, including the shrinkage phenomenon of the concrete slab, is dealt with in this paper. The influence of the concrete shrinkage, taking into account the slab reinforcement contribution, on the strength of the mixed beams is taken into account using the linear concrete viscoelasticity theory. With the help of this theory we obtain an analytic model, based on two linear differential equations that result in the over-time-behaviour of the steel-concrete mixed beams. From this model we can determine, at any time t, the values of the normal force and bending moment due to the concrete shrinkage. So it allows us to give an account of the stress state evolution developed in the cross sections of the steel-concrete mixed beams. The results obtained from the application of the suggested model are completely comparable with the results derived by the method proposed by EUROCODE 4

Simplified formulation to evaluate forces due to shrinkage in composite steel- concrete beams with perfect connection

“…The results obtained by this approach are compared to the existing model formulated by Rahal et al [21] and represented on the diagrams of Figs. 3 to 7.…”

“…Based on the theory of linear viscoelasticity, Rahal et al [21] proposed an analytical model analyzing the behavior, over time, of composite steel-concrete beams subjected to concrete shrinkage. The process consists in combining the static equilibrium equations and the two compatibility relations, in curvature and in deformation, of the composite steel-concrete cross-section with the differential (constitutive) equation resulting from the creep rate theory (RCM).…”

“…7) in the static equilibrium equations (Eqs. 5 and 6) of the model proposed by Rahal et al [21], we will nd:…”

“…In order to validate the present approach, we will use the same composite beam used by rahal et al [21] and Beghdad et al [23] to validate their proposed models. This beam was also analyzed (prediction of time-dependent effects) and dimensioned in accordance with Eurocode…”

“…With the use of the theory of linear viscoelasticity, many works, analyzing the time-dependent effects on the behavior of composite steel-concrete beams, are the subject of many analytical and numerical researches such as: Gilbert (1989) [11] ; Partov et Kantchev (2007) [12], Partov et Kantchev (2009) [13], Partov et Kantchev (2011) [14], Partov et Kantchev (2012) [15], Partov et Kantchev (2014) [16], Tarantino et Dezi (1992) [17], Fragiacomo et al (2004) [18] ; Macorini et al (2006) [19]. Tehami et al (2009) [20], Rahal et al (2012) [21], Souici et al (2015) [22], Beghdad et al (2017) [23], Faella et al (2002) [24], Boerave (1988) [25], Somja et al (2008) [26], Virtuoso et al (2004) [27], Jurkiewiez et al (2005) [28], Quang-Huy Nguyen (2010) [29],…”