Calculation of Pre-Stressed Structures using High-strength reinforcement without concrete-to-steel bond

. The article deals with the method of calculation of a pre-stressed beam for the first group of limit states without adhesion of wire-rope reinforcement with concrete (monostrand) in the curved position. To verify the plausibility of hypothesis, a numerical simulation was done in the software complex ABAQUS for stress-strain state with such beam until the destruction. The analysis of the received results is executed and the conclusion of the performance a structures of their kind.


Introduction
Pre-stressed structures using high-strength reinforcement without concrete-to-steel bond are distinguished from traditional ones in the fact that pre-stressed wire-rope reinforcement is placed in the polymer tube and covered in grease that protects reinforcement against corrosion and allows reinforcement move over tube.
In traditional bending structures after appearance of normal cracked maximum stresses in reinforcement are achieved only in sections with cracks.
In structures without adhesion of wire-rope reinforcement with concrete, the appearance and opening of cracks causes only slight deformation ∑a crc distributed over the entire length of wire-rope and causing a slight increase in stress Δσ s commensurate with stress losses.
ε s -relative deformations of reinforcement a crc -the width of opening of cracks l 0 -estimated span of the beam E s -module of elasticity This effect is taken into account by standards for the design of reinforced concrete structures.
According to the Russian standards СП 63.13330.2018[2] values of ultimate stresses in reinforcement without adhesion with concrete: h 0 -distance to tensile reinforcement x -height of the compressed concrete zone σ sp -tension in tension reinforcement R s -conditional yield strength It follows that stresses in wire-rope reinforcement in the limit state are lesser than the conditional yield strength R_s.Therefore, reinforcement remains in the elastic stage of work.This leads to the conclusion that the effect of prestressing is preserved and can be taken into account at the stage of structural failure

Object of research
The object of research is a reinforced concrete beam with the geometric and strength characteristic that were resulting from the tests of materials and structure real samples from experiments of Kao Oun [3][4][5].
The size of the sample is 180x400x3200 mm.Reinforcing schemes of beam are shown in figures 1.
Strength of concrete and reinforcement in accordance with the tests samples was assumed as Rb=37.93MPa and Rs=563 MPa, respectively.Pre-stressed with a loss was σ sp =944.1 MPa.
The curvilinear arrangement of the prestressed reinforcement corresponds to the lines of action of the main tensile stresses in the bending elements.
With this arrangement of the reinforcement, a reactive moment arises, which can be taken into account when determining the bearing capacity of the element, figure 2. However, in this case, it is necessary to take into account the increase in the friction force between the reinforcement and the polymer tube during tension.Then the equivalent uniformly distributed force bending the beam upwards will be equal to: l -beam length Based on this, the reactive moment will be equal to: The strength condition, taking into account the reactive moment, is as follows: M внеш -moment from external load Using the methodology proposed by the methodological manual «Reinforced concrete monolithic structures with prestressed reinforcement without concrete-to-steel bond.Design rules» [7], with the same parameters, the external moment is equal to 80.079 kNm.

Modeling a Finite Element Object
To confirm the proposed calculation method, the beam model was tested in the software package Abaqus test in a three-dimensional formulation, taking into account the physical and geometric nonlinearity in the operation of materials and structures in general.
For the destruction of the body of concrete, the Drucker-Prager destruction model was used, which takes into account the plasticity of the material When modeling materials according to methodological manuals [8][9], the same characteristics of materials (concrete and reinforcement) were used as in theoretical calculations.This confirms the theory that in the absence of adhesion of reinforcement to concrete, even with the destruction of the structure, high-strength ropes remain in the elastic stage and continue to resist external loading, and the discrepancy between the maximum moment value between the manual calculation using our method (79.58 kNm) and that obtained in the Abaqus SP (80.1 kNm) is 0.65%.

Conclusion
In the application of the system «monostrand» used the standard forms external ankers.Their size don't allow to place prestressing reinforcement on supports below than about 90 mm from the lower edge of concrete.It is advisable to place reinforcement in curvilinear ways and lower it in the mid-span closer to tension edge so increase the lever arm and bearing capacity of beam.
Methods currently available for the calculation of pre-stressed concrete construction using high-strength reinforcement without concrete-to-steel bond underestimate bearing capacity this construction.
In the design incurvated of pre-stressed concrete beams with curvilineal reinforcement cable without concrete-to-steel bond can be taken into account reaction couple precompaction at the stage of destruction, which increases the bearing capacity of beams to 15%.That is a saving high-strength reinforcement by the same amount

Fig. 2 .
Fig. 2. Scheme of distribution of efforts caused by prestressing reinforcement in the curved position.The reactive moment is determined in accordance with Figure 4. α -angle of inclination of the rope to the longitudinal axis on the support.The vertical component of the precompression of the beam is determined by the formula 4:   =  • sin

E3S 8 ( 9 )Fig. 3 .
Fig. 3. Scheme of forces and diagram of stresses in a section normal to the longitudinal axis of a bent reinforced concrete element, when calculating it for strength.a' -protective layer of compressed reinforcement; a -protective layer of tension reinforcement; h -distance from top face to tension reinforcement; h 0 -distance to tensile reinforcement; x -height of the compressed concrete zone; a sp -protective layer of pre-stressed reinforcement; σ s -stresses in pre-stressed reinforcement; A sp -sectional area of pre-stressed reinforcement; R s -conditional yield strength; A s -sectional area of tensile reinforcement; R sc -design compressive strength of reinforcement; A s ' -sectional area of compressed reinforcement; R b -design values of concrete axial compression resistance; If х<2а', then As' is not taken into account.The reactive moment for these parameters is equal to 11.87 kNm, then:

Fig. 4 .
Fig. 4. Computer model of the beam.The maximum stresses in the rope are on average 1600 MPa, which is 0.93 of the tensile strength.