RU186427U1 - Reinforced concrete half-sleeper rubber cover for subway - Google Patents

Abstract

The utility model relates to the construction field and is aimed at increasing the efficiency of damping vibrations with a half-sleeper when rolling stock is moving without complicating the design due to the tight fit of the cover to the half-sleeper. The specified technical result is achieved in a rubber rubber half-sleeper case reinforced concrete, consisting of a shell in the form of a hollow, truncated pyramid open on top, at the base of the bottom of which lies a trapezoid.

Description

The utility model relates to the construction field, in particular to the construction of the railway upper structure of the subway track, and is intended for use in LVT systems.

In the prior art, a reinforced concrete half-sleeper cover is known which is used in the unit of the sleeper unit for rail track systems, decreases in length and width from top to bottom, and on the upper edge of which there is a circumferential upward and outward sealing lip that lies on a ledge (US 9752285, 07/05/2017).

The disadvantages of this design are low efficiency and availability.

The technical problem to which the proposed utility model is aimed is to expand the arsenal of technical means and create a reinforced concrete rubber half-sleeper cover for the subway, the parameters of which eliminate the above disadvantages and provide improved operational characteristics.

The technical result achieved by the implementation of this utility model is to increase the damping efficiency of half-sleeper vibrations during rolling stock movement without complicating the design due to the tight fit of the cover onto the half-sleeper. Also, this form of the cover allows you to use a half-sleeper of a trapezoidal shape, which allows you to fix the path for a longer time and during operation leads to less path displacement due to wear of the supporting components.

The specified technical result is achieved in a rubber rubber half-sleeper case reinforced concrete, consisting of a shell in the form of a hollow, truncated pyramid open on top, at the base of the bottom of which lies a trapezoid.

The shell (casing) contains a bottom, sides and end sides, with a trapezoid at the base of each side.

The height H of the sides is 153 ± 1.5 mm, the inner length L of the cover is 650 ± 3 mm, the internal length L1 of the bottom is 640 ± 2.5 mm, the width B1 of one of the end faces of the bottom is 197 ± 1.5 mm, the width is B2 the other end side of the bottom is 178 ± 1.5 mm.

Each side is made with inner ribs.

The reinforced concrete rubber half-sleeper cover is made of transverse styrene-butadiene rubber.

This embodiment of the cover from the shell in the form of a hollow, truncated pyramid open at the top of the base of which is a trapezoid, is a suitable and technically successful solution for repairing and reconstructing existing underground paths that use a wooden half-sleeper (rail support) in the shape of a parallelepiped, because it provides adaptation during installation of the LVT system with the claimed cover in the existing seat (bed), which leads to an increase in the geometric stability of the path (a better way), and also to reduce the cost of reconstruction of the path, because there is no change in the seat after the dismantling of the wooden half-sleeper, and the expansion of the arsenal of technical means and scope, as well as increased operational characteristics by reducing mechanical vibration during the passage of rolling stock, noise level and increasing endurance limit by ensuring the ability to withstand heavy loads condition.

The essence of the utility model is illustrated by drawings, where in FIG. 1 shows a top view of the cover; in FIG. 2 is a section AA in FIG. 1, in FIG. 3 is a section BB of FIG. one; in FIG. 4 - load eccentricity; in FIG. 5 - beam on an elastic base with side supports; in FIG. 6 - Smith chart for concrete in the shear zone, increased to 2 million (load cycles for β _F / β _BZ / = 0.5 (min σ = 0); n = number of load cycles); in FIG. 7 - Veler curve.

The rubber cover is an integral part of the LVT system design and is made of transverse styrene-butadiene rubber with internal ribs longitudinal in length and is a shell consisting of bottom 1, side 2 and end 3 sides. At the base of each side 2, 3 and bottom 1 is a trapezoid.

The list of indicators of the rubber cover is shown in table 1.

The rubber cover is an insulator of the half-sleeper from the ballastless base of the path, as well as a guide that sets the motion vector when the gasket is operating. When mounting the LVT system, a cover with an embedded gasket and an installed half-sleeper is monolithic in a ballastless track base. The LVT system itself consists of reinforced concrete blocks on elastic gaskets, laid in a rubber cover and then monolithic in unreinforced concrete, which reduces noise due to the claimed cover design (a denser fit of the trapezoidal cover prevents half-sleepers from moving inside the seat, and, as a result , reduces mechanical stress and vibrations transmitted to the base of the path, while maintaining isolation between the elements for elastic damping of vertical and horizontal s dynamic loads and contributes to longer life and stability polushpaly its position relative to the web path), and the inner ribs 4 provide additional damping polushpaly horizontal base of ballastless way to preserve the geometry of the seat.

When mounting into the seat of the LVT system installed after the dismantling of the wooden half sleeper installed in the claimed cover design, the difference (the space formed) between the shapes and sizes of the old half sleeper and the LVT system is concreted (volume / space is filled with concrete). This difference is provided by the form of the claimed cover, as well as by the dimensions of the cover, which increases the stability of the geometric parameters of the path.

The dimensions of the rubber cover indicated in Table 1 are optimal for ensuring the claimed technical result and preserving (strength, durability, etc.) of reinforced concrete blocks in the LVT system and increasing track fixation, which is confirmed by the calculations below.

Loads on the LVT system (hereinafter - LVT blocks).

In this section, the determination of the load on the LVT block is indicated, in this case, the loads in the Ultimate Operational State (ORS) and in the Ultimate Deformation State (PSD) are considered separately.

Loads for ORS - cyclically occurring loads. These loads are used to check the restrictions on the thickness of cracks and fatigue of concrete and metal.

The ultimate state - deformation (PSD) is considered to determine the strength of the bearing elements. These regulatory loads are increased by partial safety factors during the strength test.

The calculations and checks for the above two cases were carried out for two different scenarios. A load distribution with a coefficient of 0.34 (Load Scenario 1; CH1) was calculated using the Zimmermann theory (see clause 2.2), a distribution coefficient of 0.5 (Load Scenario 2; CH2) was obtained using a more conservative distribution of 50% of the load on the considered support and 25% of the load on two adjacent supports.

Axle and wheel loads.

The value of the static load from the axis Q _k = 170 kN was chosen according to the design requirements of the Moscow Metro.

The static load from the wheels Q _v , _stat , _k (excluding centrifugal forces and eccentricity) is half the static load from the axis.

Qv, stat, k = Qk / 2 = 85 kN

Load distribution from the axle / wheel pair on the rail.

The load distribution from the axle relative to the wheelset for Load Scenario 1 was calculated using the Zimmermann theory (see also document DCA138.A298 - Design Document DCA 138.A298 for the Moscow Metro Project, Sonneville AG, 2012). Given the total coefficient of elasticity for the supports in the amount of 20 kN / mm, the distance between the blocks is 600 mm and the use of rails of the R50 type, the load distribution is μ = 0.34.

Dynamic coefficient.

The dynamic coefficient can be determined depending on the speed, quality of the tracks and the distance between the supports.

Different sources can be used to estimate the dynamic coefficient.

Due to the fact that the ballastless railway tracks in question are easy to maintain and maintain, the following formula is applied according to Eurocode 1, German technical standard DIN 101 (EN 1991.2: 2003. Eurocode 1: Impacts on structures - Part 2: Transport loads on bridges, 2003; German technical standard DIN 101, impacts on bridges, March 2009 issue) for the Limit state - deformation (PSD).

For the Ultimate Working State (ORS) and endurance limit, the dynamic coefficient is reduced:

, где

where

Thus, according to Eurocode 1, the German technical standard DIN 101, the following dynamic coefficients are applied:

Alternatively, the dynamic coefficient can be calculated after calculating the elements of the upper structure of the path according to the method of prof. Leykaufa (“Railway tracks and components”, brochure, Technical University of Munich, 2001), where the influence of the state of the track and speed can be selected using the following equation:

где

Where

n = influence of the upper structure of the path

F = speed effect

The following table shows the dynamic coefficients for paths of different states and different speeds. Due to the characteristic features of ballastless paths, only very good (n = 0.1) and good (n = 0.15) conditions are taken into account.

Dynamic values taking into account the upper structure of the path. Prof. Leykauf.

The following dynamic factor was chosen for static calculations, similar to “static calculation using standard LVT blocks” (“27-1063 - static calculation of standard LVT blocks”, SSF-Ingenieure, Munich, 07.30.2010. Calculation of standard LVT blocks with different scenarios load):

For Ultimate Performance State (ORS) and endurance limit:

F _PRS = 1.5

For the Ultimate state - deformation (PSD):

F _PSD = 1.8

Redistribution of vertically directed forces.

The eccentricity of the load.

Due to the presence of eccentricity of the application of the load (in the vertical direction) and centrifugal forces, the supports are subjected to unstable loads.

The eccentricity of the load is set in Eurocode and the German technical standard DIN 101 according to FIG. 4, where:

In the regulatory documents governing the arrangement of railway tracks (German Oberbauvorschriften), this case of load is not considered. For the purpose of a higher level of safety, the load distribution coefficient f _EX is used for the calculation of LVT blocks in relation to the ultimate strain state (PSD).

The value of the load redistribution from the wheelset due to the eccentricity is set as follows: f _EX = 1.25

Centrifugal force.

When the train passes the turning section of the tracks, centrifugal forces begin to act, which are compensated to the extent that the track has an internal slope. However, for the path of this design, full compensation is possible only at a certain speed.

In normative legal documents concerning the superstructure of a track (B. Lichtberger: “Railway Track Handbook”, Tetzlaff Verlag, 2nd edition of 2004), the value of load redistribution from a wheel set due to centrifugal forces is usually f _B = 1.1-1.2.

For further calculations, when analyzing the Ultimate operable state and the Ultimate state - deformation, the redistribution coefficient due to centrifugal forces f _B = 1.2 will be used.

Lateral forces.

Lateral guiding forces arise in bends and are taken into account using the coefficient L / V = Н _В / Q _B = 0,5

Block loads.

Taking into account the above factors and loads, the table below shows the values of the load coefficient for the Ultimate operable state (ORS) + endurance limit and the Ultimate state - deformation (PSD):

Unit loads for analysis of Ultimate Performance State (ORS) + endurance limit:

Block loads for analysis of the Limit state - deformation (PSD):

Q _k [kN] Axle load Q _{v, stat, k} [kN] Wheel load rating f _EX [-] Eccentricity coefficient f _B [-] Centrifugal force coefficient Q _{v, dyne, k} [kN] Normative dynamic load of a pair of wheels μ Load sharing coefficient Q _{B, ORS, k} [kN] Standard vertical bearing load for ORS + endurance limit N _{In, ORS, k} [kN] Standard lateral bearing load for ORS + endurance limit Q _{B, PSD, k} [kN] Standard vertical bearing load for PSD N _{in, psd, k} [kN] Standard lateral load on the support for PSD

Settlement for LVT blocks

Material Properties

Concrete: C45 / 55 - compressive strength f _ck = 45 N / mm ² - standard compressive strength (cylinder) f _cd = (η xf _ck ) / γ _c - calculation of compressive strength according to the German standard DIN 1045 - 1 γ _c - partial safety factor for concrete (fatigue) η = (30 / f _ck ) ^1/3 = (30/45) ^1/3 = 0.87 f _cd = (η xf _ck ) / γ _c = 0.87 x 45 / 1.5 = 26.2 N / mm ² - bending strength minimum value according to those. the requirements of STR081.A298 (see Appendix D)
f _ctm = 6.0 N / mm ² (to be verified by actual tests) Steel reinforcement: Brand BSt 500 - tensile strength f _yk = 500 N / mm ²
f _yd = f _yk / γ _s = 500 / 1.15 = 435 N / mm ² Steel corner: S355 JO 65 x 65 x mm

Calculation model

The beam on an elastic base (see Fig. 5).

Base

An elastic beam serves as the basis for calculating internal forces. The elastic coefficient of the beam is obtained based on the stiffness of the shock-absorbing gasket under the block and the rubber cover along the entire length of the block. Separate side supports A and B are located at each end of the unit. beams, the stiffness of these supports is obtained based on the stiffness of the rubber cover. The calculation of internal forces is not linear, it must be borne in mind that the base and two side supports are only active when a pressure reaction occurs.

Transverse stiffness of the base

The upper part is a base that responds only to pressure. The stiffness of the base c _{v is} obtained based on the obtained value of the coefficient of elasticity c _{RES of the} stiffness of the gasket of the block with _BP and the stiffness of the rubber cover c _RB in accordance with the following formula:

c _RES = 1 / (1 / s _BP + 1 / s _RB )

c _RES = 1 / (1/25 + 1/2000) = 24.7 kN / mm = 24700 kN / m

Depending on the length of the block L _Block and the obtained value of the coefficient of elasticity c _{RES, the} stiffness of the base c _{v is} calculated as follows:

c _v = C _RES / L _Block = 24700 kN / m / 0.64 m = 38594 kN / m

Stiffness of individual supports

The side part is a separate side support that responds only to pressure. The stiffness is calculated as follows:

Rigidity of a wall of a rubber cover: C _{B, L} = 2.6 x 10 ^-3 kN / mm ³ Rubber Cover Height: h = 120 mm The width of the rubber cover on the narrow side of the block: b _A = 204 mm The width of the rubber cover on the wide side of the block: b _E = 184 mm

The stiffness of the side support A (narrow side) is calculated as follows:

with _H = 2.6 × 10 ^-3 × 120 × 204 = 63.7 kN / mm = 63648 kN / m

The stiffness of the side support B (wide side) is calculated as follows:

s _N = 2.6 × 10 ^-3 × 120 × 184 = 57.4 kN / mm = 57408 kN / m

Internal load

External load is distributed through the rail - the sole of the rail to the LVT block. In this case, a 1: 1 tilt to the block axis is used (see Appendix A). The point of impact of the load from the wheelset (in the vertical and horizontal direction) is located eccentrically relative to the vertical axis (eccentricity e _z ) and the upper part of the rail (eccentricity e _y ). This creates a moment of force M _{x, k} , which is calculated as follows:

M _x , _k = M _x , _Q , _k , + M _x , _{H, k}

M _{x, Q, k} = Q _B , _k , × e _y

M _{x, H, k} = H _{in, k} , × e _z

The moment M _x , _{k is} used to calculate the linear load with ordinates q _{1, k} and q _{2, k} , which are used to determine the internal forces.

q _{1, k} = Q _{B, k} / b + (6 × M _x , _k / b ² )

q _{2, k} = Q _{B, k} / b - (6 × M _x , _k / b ² )

Ordinates for Ultimate Performance State (ORS) and Endurance Limit for Load Scenario 1:

M _{x, k} = M _{x, Q k} + M _{x, H, k}

M _{x, k} = 53.55 kN × 0.023 m + 26.78 kN × 0.229 m = 7.36 kNm

q _{1, k} = 53.55 kN / 0.309 m - 6 × 7.36 kNm / (0.309 m) ² = -228.40 kNm (upward)

q _{2, k} = 53.55 kN / 0.309 m + 6 × 7.36 kNm / (0.309 m) ² = 636.00 kNm (down)

Ordinates for Ultimate Performance State (ORS) and endurance limit for Load Scenario 2:

M _{x, k} = M _x , _Q , _k + M _x , _{H, k}

M _{x, k} = 76.50 kN × 0.023 m + 45.10 kN × 0.229 m = 12.27 kNm

q _{1, k} = 76.50 kN / 0.309 m - 6 × 12.27 kNm / (0.309 m) ² = -523.51 kNm (upward)

q _{2, k} = 76.50 kN / 0.309 m + 6 × 129.27 kNm / (0.309 m) ² = 1018.65 kNm (down)

The ordinates for the Limit State — Warp (PSD) for Load Scenario 1:

M _{x, k} = M _{x, Q, k} + M _{x, H, k}

M _{x, k} = 80.43 kN × 0.023 m + 48.20 kN × 0.229 m = 12.88 kNm

q _{1, k} = 80.33 kN / 0.309 m - 6 × 12.88 kNm / (0.309 m) ² = -549.68 kNm (upward)

q _{2, k} = 80.33 kN / 0.309 m + 6 × 12.88 kNm / (0.309 m) ² = 1069.59 kNm (downward)

The ordinates for the Ultimate State - Strain (PSD) for Load Scenario 2:

M _{x, k} = M _{x, Q, k} + M _{x, H, k}

M _{x, k} = 114.75 kN × 0.023 m + 68.95 kN × 0.229 m = 18.41 kNm

q _{1, k} = 114.75 kN / 0.309 m - 6 × 18.41 kNm / (0.309 m) ² = -785.26 kNm (upward)

q ₂ , _k = 114.75 kN / 0.309 m + 6 × 18.41 kNm / (0.309 m) ² = 1527.98 kNm (down)

The rail slope is already laid in a concrete block, therefore, the support in the lower part is parallel to the lateral forces and there is no need to modify the supports to create a slope (F _h = F _h ', Fv = Fv').

Internal forces

Bending moments calculated using the FEM AxisVM software application have negative values. These bending moments produce a tensile force acting on the lower part of the block.

Internal forces for Ultimate Performance and Endurance, Load Scenario 1:

Internal forces for Ultimate Performance and Endurance, Load Scenario 2

Internal forces for Ultimate state - deformations, Load scenario 1:

Internal forces for Ultimate state - deformations, Load scenario 2:

Cross Section Values

For a static calculation of the values for the ORS and PSD states specified in paragraph 2, a transverse section is taken at the point where the highest bending moment occurs.

b indicates the width of the block at the location selected for the cross section h block height at the location selected for the cross section steel corner cross-sectional area A _su sectional area of the bottom reinforcement A _so sectional area of the upper reinforcement

I _{y, c} - moment of inertia of the cross section of concrete in the place under consideration;

I _yL - moment of inertia of the steel angle profile;

I _{y_As1} - moment of inertia of the bottom reinforcement;

I _{y_As2} - moment of inertia of the upper reinforcement;

I _{y, id} - The idealized moment of inertia of the cross section of the block;

A _c - Cross section of concrete in the place in question;

W _{u, c} - Moment of resistance of the cross section in the considered place;

A _id - An idealized cross-section in the place in question;

W _{u, id} - The moment of resistance of an idealized transverse cut in the place in question.

Analysis of LVT blocks

In railway and road construction, it is customary to use unreinforced concrete and, thus, take into account the tensile strength of concrete.

For this reason, fatigue analysis is carried out on concrete without cracks according to the work “Concrete ways” prof. Leykaufa (Technical University of Munich) (Eisenman, Leykauf: “Concrete tracks”, 2nd edition, Verlag Ernst & Sohn, 2003).

Ultimate Performance State (ORS) and endurance limit

The following fatigue tests are performed:

a) Fatigue analysis of concrete without cracks in state I (without cracks)

Damage from fatigue leads to the formation of cracks in concrete, this is taken as a transition state to state II.

b) Fatigue analysis of steel reinforcement (state II)

In this case, concrete with cracks is considered.

Damage from fatigue leads to breakage of the reinforcing material.

Fatigue analysis of concrete in state I (concrete without cracks)

In order to analyze the fatigue of concrete in state I, bending strength is analyzed. The fatigue strength of concrete is based on the Smith diagram.

Standard bending strength of concrete: f _{ct (BZ), k} = 6.0 N / mm ²

Fatigue strength of concrete under bending stress: Δσ _{c, R} = 0.5 × f _{ct (BZ), k} = 3.0 N / mm ²

The table below shows the results of the analysis of fatigue strength at bending moment for the ultimate working condition (ORS) and Load Scenario 1 (CH 1).

Δσ _s [N / mm ² ] = M _k / W _u , _id + N _k / A _id

The table below shows the results of the analysis of fatigue strength at bending moment for the ultimate working condition (ORS) and load scenario 2 (CH 2).

Δσ _s [N / mm ² ] = M _k / W _u , _id + N _k / Ai _d

The existing bending moment in the blocks is less than the fatigue strength of concrete.

The endurance limit is not reached, damage to concrete from fatigue in the ultimate working condition does not occur.

Fatigue Analysis of Steel Reinforcement in Condition II (Cracked Concrete)

This analysis is carried out in accordance with Eurocode 2 for building structures; it is fundamentally important that concrete with cracks is always taken (condition II).

The fatigue strength of steel reinforcement is determined on the Weler curve (see Fig. 7), where A is the yield strength of the reinforcement.

Weler curve for steel reinforcement acc. EN 1992-2: Eurocode 2: Design of reinforced and prestressed concrete structures - Part 2: Concrete bridges - design and construction rules, 2007 and German technical standard DIN 1045, “Concrete structures, reinforced and prestressed concrete - Part 1: design and manufacturing. ”, 2008 edition.

The fatigue strength of steel reinforcement is defined as follows: N = 5 × 106 load cycles ("27-1063 - static calculation of standard LVT blocks", SSF-Ingenieure, Munich, July 30, 2010. Calculation of standard LVT blocks with different load scenarios). To calculate the upper structure of the path, it is sufficient to use the standard values of fatigue (quantile value of 95%).

Fatigue strength of steel reinforcement (N = 5 × 10 ⁶ ):

Δσ _{D, mouth} = (N * / N) ^{1 / k2} × Δσ _Rsk = (1 × 10 ^6/5 × ¹⁰ June) ^1/9 × 162,5 = 136 N / mm ²

The table below shows the results of the analysis of the fatigue strength of steel reinforcement at the maximum bending moment for the Limit state - deformation (PSD) in state II (concrete with cracks) and Load Scenario 1 (CH 1).

The table below shows the results of the analysis of fatigue strength at bending moment for the ultimate working condition (ORS) and load scenario 2 (CH 2).

A _Su = existing reinforcement in the stretch zone of the block

d = distance from the top of the block to the reinforcement in the tensile zone

In the trapezoidal block under consideration, the endurance limit of steel reinforcement was not reached, so there are no restrictions on the service life of steel.

Limit state - deformation (PSD), load scenario 1

The calculations for the necessary reinforcement were carried out using bending moments with loads at PSD, load scenario 1, while the following values were obtained:

Payment

The compressive strength of concrete and the bending strength of steel are changed by partial safety factors according to Eurocode 2.

The final results for the Ultimate state - deformation (PSD), load scenario 1:

Limit state - deformation (PSD), load scenario 2

The calculations for the necessary reinforcement were carried out using bending moments with loads during PSD, load scenario 2, while the following values were obtained:

Payment

The compressive strength of concrete and the bending strength of steel are changed by partial safety factors according to the Eurocode.

The final results for the Ultimate state - deformation (PSD), load scenario 2:

Ultimate Performance Bending Moments (ORS) were used to analyze fatigue strength. A comparison of the bending strength of concrete with the existing bending moment of the block showed that the ultimate bending strength is not exceeded. Thus, fatigue failure is not expected in Ultimate Performance and Endurance.

The coefficient of necessary reinforcement was determined on the basis of bending moments in the Ultimate state - deformation for two load scenarios - 1 and 2.

The existing coefficient goes far beyond the coefficient of necessary reinforcement, which guarantees additional safety.

Claims (5)

1. The rubber half-sleeper cover is reinforced concrete, characterized in that it consists of a shell in the form of a hollow, truncated pyramid open at the top, at the base of the bottom of which lies a trapezoid. 2. The rubber half-sleeper cover is reinforced concrete according to claim 1, characterized in that the shell contains a bottom, sides and ends, with a trapezoid at the base of each side. 3. The rubber half-sleeper cover is reinforced concrete according to claim 2, characterized in that the height H of the sides is 153 ± 1.5 mm, the internal length L of the cover is 650 ± 3 mm, the internal length L1 of the bottom is 640 ± 2.5 mm, width B1 one of the end sides of the bottom is 197 ± 1.5 mm, the width B2 of the other end side of the bottom is 178 ± 1.5 mm. 4. The rubber half-sleeper cover is reinforced concrete according to claim 1, characterized in that each side is made with internal ribs. 5. The rubber half-sleeper cover is reinforced concrete according to claim 1, characterized in that it is made of transverse styrene-butadiene rubber.

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