Stress-Strain State of the Fragments of Armored Monolithic Floors with Tubular Inserts
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STRESS-STRAIN STATE OF THE FRAGMENTS OF ARMORED MONOLITHIC FLOORS WITH TUBULAR INSERTS I. V. Mel’nyk
UDC 624.012
The stress-strain state of fragments of an armored floor with tubular inserts is determined with regard for the nonlinearity of deformation of concrete according to SBN V.2.6-98:2009. The applied technique allows us to compute the deflections of the floor depending on the nature of loading and deformation. The comparison of the theoretical and experimental values of the deflections of fragments cut out from the armored floor with unidirectional arrangement of polystyrene inserts with rectangular cross sections reveals their close proximity. Keywords: monolithic armored floors, optimization, tubular inserts, stiffness, stress-strain state.
Monolithic plane reinforced concrete floors are widely used in buildings of various purposes. For large spans, the dead weight of monolithic floors becomes a serious problem. In order to decrease it, the so-called hollow-forming inserts are applied more and more extensively [1–3]. Despite the wide use of plane monolithic floors with inserts, their stress-strain states in cross sections are studied quite poorly. Statement of the Problem For the reliable determination of load-bearing ability, curvature, and displacements of armored floors in strength tests, it is necessary to start from the stress-strain state of the corresponding structure obtained on the basis of the nonlinear stress-strain diagram of concrete. The schematic diagram of the dependence of compressive stresses σ c1 (tensile stresses σ c2 ) on the corresponding strains ε c1 ( ε c2 ) for concrete [4] is shown in Fig. 1. According to [5], the nonlinear relationship between the compressive stresses and strains acting in concrete under short-term loading (Fig. 1) is given by the formula
σ c1 k1η1 − η12 , = fcd1 1 + (k1 − 2)η1
(1)
where
η1 = ε c1 /ε c1,cd1,
and
k1 = Eb ε c1,cd1 / fcd1.
Here, ε c1,cd1 is the strain formed under the maximum compressive stresses, Eb is the computed value of the modulus of elasticity of concrete, and fcd1 is the computed value of the strength of concrete in compression. “L’vivs’ka Politekhnika” National University, Lviv, Ukraine; e-mail: [email protected]. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 52, No. 2, pp. 111–118, March–April, 2016. Original article submitted October 6, 2015. 1068-820X/16/5202–0269
© 2016
Springer Science+Business Media New York
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I. V. MEL’NYK
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Fig. 1. Schematic stress-strain diagram of concrete: (1) compression, (2) tension.
Fig. 2. Design of fragments of the plates: (1) PF-1 (longitudinal direction), (2) PF-2 (transverse direction), (3) unidirectional foamy polystyrene inserts.
We use a similar dependence between tensile stresses and strains but with the parameters corresponding to the case of tension of concrete [4]:
σ c2 k2 η2 − η22 . = fcd 2 1 + (k2 − 2)η2
(2)
Here, η1 = ε c2 /ε c2,cd 2 , k2 = Eb ε c2,cd 2 / fcd 2 , ε c2,cd 2 is the strain under the maximal tensile stresses, and fcd 2
is the computed value of the st
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