Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

Abstract

The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time “t”, two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated.The creep functions is suggested by the model CEB MC90-99 and the “ACI 209R-92 model. The elastic modulus of concrete Ec(t) is assumed to be constant in time ‘t’. The obtained results from the both models are compared.

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

“…To solve this problem, we exploit the compatibility of strains at the steel-concrete interface. This condition has been used by several researchers in the formulation of their model, such as: [12][13][14][15][16][20][21][22][23].…”

“…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],…”

Layered finite elements in the analysis of composite structures exposed to long-term effects

“…where De c (t k ) is the free strain of concrete and is given by: (4) E c(k,k-1) represents the generalized, and E c(k,k-1) the derived deformation modulus of concrete, which depends on the type of numerical integration that is used for the adopted function of the creep of concrete. These modules are related using the following expression: (5) where is: Equation (3) represents a unique generalized form as all known stress-strain ratio forms for concrete can be applied including the Age-adjusted effective modulus method (AAEM method; Bazant, 1972).…”

“…The finite element method (FEM) [3] is the best known and most widely used where, instead of differential equations, simple algebraic equations are established, whose matrix shape is highly suitable for programming and computer use. A comprehensive and broad overview of methods for long-term analysis, including procedures defined in EN 1992, EN 1994-1-1, and EN 1994-2, is presented in [4] and [5]. An overview of the state-of-the-art in the wider area of design and analysis of steel-concrete composite structures, with a specific focus on determination of the effective slab width, is presented in [6].…”

Comparative analysis of the influence of creep of concrete composite beams of steel - concrete model based on Volterra integral equation

“…of normal forces and bending moments, arising due to creep and shrinkage of concrete (Fig.1). For a composite bridge girder with suggestion of(Partov and Kantchev, 2009), the equilibrium conditions in time t are the following:…”