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Construction of physical parities in inkrementalnoj to the form for reinforced-concrete integral designs with cracks in a working area of contact of two concrete at the scheme of crossed cracks

Let's consider a characteristic element in which cracks break off concrete in two directions: to the fixed crack on a seam of contact and a crack developing in a direction of the main stretching stresses.

As a result of formation of such scheme of crossed cracks concrete in a considered element loses ability independently to perceive efforts. Only some concrete communications (toothing communication) between edges of cracks in this case remain and ability of concrete on lots between cracks remains to resist to tangential movings of the reinforcing bars crossing a crack.

Let's designate accordingly-angle of slope cracks along a seam of contact of two bars and a crack from the main stretching stresses to an axis h; a//-thickness of a characteristic element, the armature-area in a direction of an axis at, length of a characteristic element falling to unit taking into account damage by its rust, - a percentage of reinforcement for direction armature).

At formation of the fixed longitudinal crack in a working area of contact of two concrete and cracks from the main stretching stresses all efforts operating in a characteristic element indulge on armature. In it arise normal σsyи tangent lines gh „. Pressure (fig. 2.17).

For definition of these pressure sproetsiruem all forces enclosed to sides of an element on an axis h ’ and at ’:

69

Drawing 2.17 - the Scheme of efforts in armature after a clinking in

Characteristic element

Toothing of coast of cracks through concrete communications.

Representing to toothing communication between edges of cracks in a characteristic element uniformly distributed on length of cracks, it is possible to write down the running forces of toothing arising in cracks under formulas: where width of disclosing of a crack, and and mutual shear J of its coast for a crack in a working area of contact of two bars and cracks from the main stretching stresses, accordingly, we accept the equal:

After transformation we will receive:

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Let's express an elastic modulus using dependences offered in [74] for definition of value of shearing force after a clinking, considering "nagelnyj" effect in a transverse reinforcement and arising on coast of a seam of shear of force of toothing:

Using V.M.Bondarenko's hypothesis [30] about invariancy of functions of damages describing deficiency of the running value of the investigated factor of nonequilibrium power resistance of concrete, under the relation to the physicomechanical characteristics of power resistance of concrete for the resulted module of toothing at a warping of coast of cracks it is possible to write down:

The pressure arising in a reinforcing bar.

Believing, that in a considered characteristic element the angle of slope fixed along a seam of contact of an integral design of a longitudinal crack has constant value α =45o, having substituted in system of the equations (2.80) expression (2.83) and having expressed pressure in armature r5vи σv, we will receive:

Where factors of the equations are defined under formulas

-7 1

Dependence ploskonaprjazhyonnogo ferro-concrete in increments.

At crossed cracks concrete loses ability to characterise element deformation in any direction. Hence, average deformations of armature coincide with the general

' ll deformations of an element with cracks. For a considered characteristic element in l axes ’ and at ’ these deformations will make:

Considering communications axial usyи tangential movings υsy a reinforcing bar and movings in a direction of axes h ’ and at ’ according to [80] it is possible to write down:

Rods to tangential displacement. In concrete at crack border as a first approximation according to [80] it it is possible to accept equal 16.

Substituting in (2.93) values of pressure in armature

We receive following parities:

Following [78] dependences (2.95) for two consistently located steps of loading / +1 and / it is possible to write down in increments of pressure and armature deformations. As a result we will receive:

For reception of full system of the physical equations of a considered reinforced-concrete element with cracks we will define an increment of a corner of shear ziγxv-using formulas of transformation of relative deformations and pressure at return turn of co-ordinate axes:

Having substituted in formulas znachenijaiz the equations (2.96) we will receive

Required value of a corner of shear in a following sort:

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Substituting expressions (2.96), (2.99), in (2.89) we come to the following system of physical parities in increments:

Here, factors of a negative mould of a pliability [Cll] for a characteristic element with crossed cracks: cracks in a working area of contact of two concrete and cracks from the main stretching stresses of a flat intense element on increments of pressure and deformations are defined by expressions:

2.3.4

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A source: Gubanova Maria Sergeevna. LONG WARPING PLOSKONAPRJAZHENNYH KORROZIONNO of the DAMAGED INTEGRAL REINFORCED CONCRETE CONSTRUCTIONS. The dissertation on competition of a scientific degree of a Cand.Tech.Sci. Kursk - 2018. 2018

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