
Control of Cracking in Reinforced Concrete Structures
Beschreibung
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Personen
Francis Barre, Géodynamique et Structure.
Philippe Bisch, Egis Industries.
Danièle Chauvel, EDF SEPTEN.
Jacques Cortade, Consultant.
Jean-François Coste, IESF.
Jean-Philippe Dubois, Consultant.
Silvano Erlicher, Egis.
Etienne Gallitre, EDF SEPTEN.
Pierre Labbé, EDF.
Jacky Mazars, University of Grenoble.
Claude Rospars, IFSTTAR - EDF SEPTEN.
Alain Sellier, LMDC, University of Toulouse.
Jean-Michel Torrenti, IFSTTAR.
Inhalt
Notations
Symbols are mentioned only when they are specific and not used currently by Eurocode 2 (EC2) [NF 04, NF 06a, NF 06b] and fib model code 2010 (MC2010) [CEB 12]. However some symbols used less in these codes are also quoted. The units refer to the International System (IS).
Chapter Symbol Description Unit Chapter 2 Tmax-
Tini Temperature differential at a given point between the maximum temperature reached by concrete during its setting and its initial temperature °C Tadiab Adiabatic temperature °C ? Thermal conductivity W-1.m-1.K-1 Q8 Hydration heat per weight unit of cement kJ.kg-1 ?C Heat capacity per weight unit of concrete kJ.kg-1.°C-1 a Diffusivity m2.s-1 ßT Reduction coefficient of temperature rise calculated in accordance with adiabatic conditions:
(-) scm Mean value of concrete compressive strength MPa fctm,scale Mean value of concrete axial tensile strength taking account of scale effect MPa Mean value of concrete axial strength taking account of scale effect, calculated according to Weibull approach MPa Vref Volume loaded by a direct tensile test that characterizes the ultimate tensile strength m3 Veq Maximum volume under direct tensile strength whose failure probability is equal to the failure probability of the full scale volume m3 k Weibull exponent - 5% fractile of the tensile strength including scale effect according to Weibull approach MPa 95% fractile of the tensile strength with scale effect according to Weibull approach MPa ? Reduction coefficient taking into account the non-uniformity of the stress field prior to the first crack (-) hceff Effective height of the considered cross section m Chapter 3 ? Ratio between the effective area and the total section area reflecting the non-uniform stresses across the section: (-) a Exponent of the bond-slip relationship given by Equation 6.1-1 of MC2010 (-) ae Modular ratio Es/Ecm (see EC2 and MC2010) (-) Chapter 4 ? Parameter reflecting the crack width, depending on ssr/ss (seeEC2 and MC2010) (-) eI The relative strain in the section considered un-cracked (-) eII The relative strain in the cracked section. (-) Chapter 5 Stress tensor (Nxx, Nxy = Nyx, Nyy) derived from structural design MPa Nr Membrane force normal to the crack kN/m Tr Membrane force tangential to the crack kN/m N// Membrane force normal to a plan which is perpendicular to the crack kN/m Fsx Effort component on reinforcing bars along Ox kN Fsy Effort component on reinforcing bars along Oy kN heff Effective depth evaluated for the total shear wall thickness, depending on concrete cover to reinforcement m ?° Angle between the reinforcement in the y-direction and the direction of the principal tensile stress (see MC2010) (°) ssx Mean steel bar stress along the x-direction MPa ssy Mean steel bar stress along the y-direction MPa esx Mean steel bar strain along the x-direction (-) esy Mean steel bar strain along the y-direction (-) ?sx,eff Percentage of steel reinforcement in the x-direction % ?sy,eff Percentage of steel reinforcement in the y-direction % a Local distortion rad ? As/Ac, percentage of steel reinforcement As based on the area Ac of concrete in tension % Chapter 6 Asmin Minimum cross sectional area of reinforcement m2 ht Thickness of the concrete layer submitted in high tension to heating or cooling phase or daily temperature cycle m ec (t) Total strain of a concrete element at time t (-) Fct,scale Concrete tensile stress at a given point along the reinforcing bar MPa Chapter 8 See Chapter 2 °C Tmin Minimum temperature up to time t °C a Free coefficient of thermal expansion of concrete K-1 eca(t) Basic creep at time t (-) R Elastic restraint factor on an infinite rigid span (CIRIA C660 guide) (-) H, L Height and length of a wall m h Distance from the given point to the base m Reduction coefficient of restraint factor R (-) Rbridage Restraint factor including reduction (-) Mth,el Elastic bending moment induced by a restrained deformation gradient (e.g. thermal gradient) N.m k Reduction coefficient related to the elastic bending moment (-) Chapter 10 ? Temperature in Kelvin °K ? Hydration degree of cement (-) w(t) Water content at time t Kg.m-3 w??8 Water quantity for cement hydration Kg/m-3 Dw Global coefficient of water diffusion m2.s-1 Sr Degree of concrete water saturation (-) HR8 Relative humidity of environment (-) Mw Molar mass of water g.mol-1 ?w Water density g.m-3 Q8 Hydration heat per volume unit of concrete J.m-3 ?c Thermal capacity of concrete per volume unit J.m-3 w/c Water-cement ratio (-) F Concrete porosity (ratio of voids to the total volume) (-) ?0 Threshold of mechanical percolation (concrete change from liquid state to solid state) (-) S(?) Rigidity matrix (Hook's law) MPa tS Bond stress MPa tM Time constant of permanent creep s trbc Time constant of reversible basic creep s tpbd Characteristic time of creep at temperature ?ref s Fpbc Coefficient of basic permanent creep of...
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