Analysis of the Stiffnesses of Reinforced-Concrete Plane Monolithic Floors with Tubular Inserts
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ANALYSIS OF THE STIFFNESSES OF REINFORCED-CONCRETE PLANE MONOLITHIC FLOORS WITH TUBULAR INSERTS I. V. Mel’nyk
UDC 624.012
To establish the mean stiffnesses of reinforced-concrete beams with effective tubular inserts in bending, we used the finite-element method and the theory of shells. According to the results of theoretical analysis, it is shown that the cylindrical stiffnesses of reinforced-concrete floors with tubular inserts are different in mutually perpendicular directions. Based on the results of numerical simulations, we obtain the comparable values of cylindrical stiffnesses for monolithic reinforced-concrete floors of identical mass with tubular inserts of square, rectangular, and circular shapes. Keywords: monolithic reinforced-concrete floors, tubular inserts, stiffness, stress-strain state.
In recent years, the monolithic plane reinforced-concrete floors are more and more extensively used in various types of buildings (houses, offices, trade and exhibition complexes, etc.). In order to decrease their weight, it is reasonable to apply effective inserts (as separate units made of relatively light and low-cost materials) placed in the bulk of cross section and left in the floor after concrete casting [1, 2]. In order to use reinforced-concrete floors with tubular inserts in a more efficient and, at the same time, reliable way, it is necessary to analyze their stress-strain and limiting states. This would enable us to estimate the strength of monolithic reinforced-concrete floors with effective tubular inserts and choose their optimal shape depending on the general structural scheme of the floors. In this case, it is necessary first to determine the cylindrical stiffnesses of the analyzed reinforced concrete floor with hollows of various geometries. Theoretical Foundations The linear sizes of monolithic reinforced-concrete floors with hollow-forming inserts in two mutually perpendicular directions (width B and length A ) are larger than their thickness h by an order of magnitude. Hence, in order to determine the stress-strain state, we can use the theory of bending of plates [3]. In this case, it is assumed that the reinforced-concrete structure of the floor operates within the limits of linearly elastic deformation. We model its operation by a plate (Fig. 1d), which is regarded as structurally orthotropic [4]. This means that the anisotropic properties are reflected by the hollow structure of the analyzed structure. The plate is considered in a coordinate system xOy (Fig. 1). It is assumed that the principal directions of elasticity at any point of the structurally orthotropic plate coincide with the directions of the coordinate axes: Ox , Oy , and Oz . According to [3], we can write the equilibrium equations in the form
∂M xy ∂M y − + Qy = 0 , ∂x ∂y
−
∂M yx ∂M x − + Qx = 0 , ∂y ∂x
∂Qx ∂Qy + + q = 0, ∂x ∂y
(1)
“L’vivs’ka Politekhnika” National University, Lviv, Ukraine; e-mail: [email protected]. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 50, No. 4, pp. 75–80, July–August, 2014. Ori
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