CN114969921B - Design method for structural dimension of railway frame bridge - Google Patents
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Abstract
The invention provides a design method of railway frame bridge structure size, firstly determining the frame aperture of a railway frame bridge, the filling height above a top plate, the intersection angle of the frame axial direction and the line normal, the railway live load and the initial roof thickness, then taking the determined data into a roof thickness numerical calculation model, calculating to obtain the roof thickness, and then calculating the bottom thickness and the side wall thickness according to the roof thickness to obtain the railway frame bridge structure size; the design method of the railway frame bridge structure size ensures that the design of the structure size is attributed to quantification, can meet safety requirements, can ensure rationality of economic cost, has high accuracy and is convenient to popularize.
Description
Technical Field
The invention relates to the technical field of railway frame bridge structure design, in particular to a method for designing the structural dimension of a railway frame bridge.
Background
With the development of national road and railway traffic, the phenomenon of road and railway crossing is increasing. The new regulations of railways require that passenger special lines and high-speed railways strictly forbidden to be provided with a level crossing, and the crossing problem of the passenger special lines and the high-speed railways must be solved by adopting an overpass mode. In order to ensure the safety of high-speed rails, the mode of crossing railways by the highways is not suitable any more, and in order to reduce the influence of the highways on railway operation, local roads mostly adopt a scheme of crossing railways under a frame structure.
For the frame bridge with the aperture of 7-16 m, the structure size is not unified at present, and the structure size of the designed frame bridge is quite different for different railway design houses and even different designers. If the design size is smaller, the railway frame bridge structure may crack during later operation, and if the design size is larger, the usage amount of the reinforcing steel bars is larger, so that the cost is increased, and the economic value is low.
The quantitative design scheme for researching the structural size of the railway frame bridge can meet the safety requirement and ensure the rationality of the economic cost, and has very important significance.
Disclosure of Invention
The invention aims at: aiming at the problems of lack of quantitative design method and larger structural design dimension error in the prior art of the design of the structural dimension of the frame bridge, the design method of the structural dimension of the railway frame bridge is provided, so that the design of the structural dimension is attributed to quantification, the safety requirement can be met, and the rationality of the economic cost can be ensured.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a design method of railway frame bridge structure size comprises the following steps:
step 1, determining the frame aperture of a railway frame bridge, the filling height above a top plate, the intersection angle of the axis direction of the frame and the line normal, the railway live load and the initial thickness of the top plate;
wherein, the initial thickness of the top plate is calculated by the formula one: h 0 ＝L 0 In the formula I, H is shown as (20+0.3) 0 Is the initial thickness of the top plate, the unit is m, L 0 The unit is m for the frame aperture of the railway frame bridge;
step 2, the data determined in the step 1 are carried into a top plate thickness numerical calculation model to obtain the top plate thickness;
wherein, roof thickness numerical calculation model is:in which A 1 The thickness of the top plate is m; l (L) 0 The unit is m for the frame aperture of the railway frame bridge; h is the height of the soil filled above the top plate, and the unit is m; h 0 The unit is m, which is the initial thickness of the top plate; f is railway live load, and the unit is kN; alpha is the intersection angle of the frame axis direction and the line normal, and the unit is degree; ζ is a coefficient;
wherein, the value of xi is 0.0062-0.007;
and 3, calculating the bottom thickness and the side wall thickness by using the top thickness obtained in the step 2.
According to the design method for the structural dimension of the railway frame bridge, firstly, the frame aperture of the railway frame bridge, the land filling height above the top plate, the intersection angle of the frame axis direction and the line normal, the railway live load and the initial roof thickness are determined, then the determined data are brought into a numerical calculation model of the roof thickness, the roof thickness is calculated and obtained, then the bottom thickness and the side wall thickness are calculated according to the roof thickness, namely the structural dimension of the railway frame bridge is obtained, the numerical calculation model of the roof thickness is obtained by correcting based on big data and combining classical mechanics and probability theory science, the coefficient is designed in 0.0062-0.007, the safety of running the railway frame bridge is difficult to guarantee when the coefficient is lower than 0.0062, but the use amount of reinforcing steel bars of the railway frame bridge is large when the coefficient is higher than 0.007, and the economic cost is wasted. The design method of the railway frame bridge structure size ensures that the design of the structure size is attributed to quantification, can meet safety requirements, can ensure rationality of economic cost, has high accuracy and is convenient to popularize.
Further, the value of the coefficient ζ is 0.0064-0.0068. When F is higher than 0.0068, the usage amount of the railway frame bridge steel bars is large, waste in economic cost is formed, and when the value of the coefficient xi is 0.0064-0.0068, the economy is more reasonable. Preferably, the value of the coefficient ζ is 0.0064. Not only can the safety be ensured, but also the economic cost is the lowest.
Further, the railway live load is calculated by the following method: when the railway is designed to be ZK single line, the railway live load F=157/(2.6+H); when the railway is designed to be ZKH single lines, the railway live load F=179/(2.6+H); when the railway is designed as a ZC single line, the railway live load F=136/(2.6+H); when the railway is designed to be ZKH double lines, the railway live load F=358/(6.6+H); when the railway is designed to be ZK double-line, the railway live load F=314/(7.2+H); when the railway is designed as ZC double line, the railway live load F=272/(6.6+H); wherein H is the height of the filling soil above the top plate, and the unit is m.
Further, in the step 3, the bottom thickness is calculated by a formula two, formula two: a is that 2 ＝A 1 +0.05+L 0 *0.003, wherein A 2 The thickness of the bottom plate is m; a is that 1 The thickness of the top plate is m; l (L) 0 The frame aperture is the railway frame bridge in m.
Further, in the step 3, the sidewall thickness is calculated by a formula three: a is that 3 ＝A 1 -0.05+(A 2 -A 1 +0.05) a/45, wherein A 3 The unit is m, which is the thickness of the side wall; a is that 2 The thickness of the bottom plate is m; alpha is the intersection angle of the frame axis direction and the line normal, and the unit is DEG.
Further, the railway frame bridge structure comprises 1-4 holes.
Further, the railway frame bridge structure package2-4 holes are included, and the thickness of the middle wall is calculated by using the thickness of the top obtained in the step 2; the thickness of the middle wall is calculated by a formula IV: a is that 4 ＝A 3 -0.1, wherein A 4 The unit is m, which is the thickness of the middle wall; a is that 3 The unit is m, which is the thickness of the side wall.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
according to the design method for the structural dimension of the railway frame bridge, firstly, the frame aperture of the railway frame bridge, the land filling height above the top plate, the intersection angle of the frame axis direction and the line normal, the railway live load and the initial roof thickness are determined, then the determined data are brought into a numerical calculation model of the roof thickness, the roof thickness is calculated and obtained, then the bottom thickness and the side wall thickness are calculated according to the roof thickness, namely the structural dimension of the railway frame bridge is obtained, the numerical calculation model of the roof thickness is obtained by correcting based on big data and combining classical mechanics and probability theory science, the coefficient is designed in 0.0062-0.007, the safety of running the railway frame bridge is difficult to guarantee when the coefficient is lower than 0.0062, but the use amount of reinforcing steel bars of the railway frame bridge is large when the coefficient is higher than 0.007, and the economic cost is wasted. The design method of the railway frame bridge structure size ensures that the design of the structure size is attributed to quantification, can meet safety requirements, can ensure rationality of economic cost, has high accuracy and is convenient to popularize.
Drawings
Fig. 1 is a schematic view of a railway frame bridge structure.
Fig. 2 is a schematic view of a railway frame bridge environment configuration.
Fig. 3 is a schematic top view of a railway frame bridge structure.
Fig. 4 is a graph showing the distribution of ζ values obtained by randomly calculating 100 frame work points.
Fig. 5 is a graph showing the distribution of ζ values obtained by randomly calculating 100 frame work points.
Fig. 6 is a graph showing a ratio of the zeta value distribution intervals.
Fig. 7 is a graph of the normal distribution of the value of ζ.
Fig. 8 is a statistical diagram of the content of the reinforcing steel bars.
Fig. 9 is a graph showing a distribution interval of the content of the reinforcing steel bars.
Icon: 1-a top plate; 2-a bottom plate; 3-side walls; 4-middle wall; 5-rail; 6-filling soil layers; 7-highway pavement.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
The railway frame bridge structure comprises 1-4 holes, and as shown in fig. 1, a structural schematic diagram of a railway frame bridge with two holes mainly comprises a top plate 1; a base plate 2; a side wall 3; a middle wall 4.
1. Traditional experience of frame bridge dimensions
In the prior art, the frame bridge structure designed by different persons is different in size.
The traditional experience of the frame bridge size is rough, and the approximate value range is specifically as follows:
1. top plate thickness
When the span is 5-6 m, the thickness of the top plate is 0.5-0.6 m; when the span is 7-10 m, the thickness of the top plate is 0.6-0.85 m; when the span is 11-16 m, the thickness of the top plate is 0.85-1.2 m.
2. Thickness of the base plate
The thickness of the bottom plate is about 0.1m greater than that of the top plate.
3. Thickness of side and middle wall
The thickness of the side middle wall can be the same, and is generally 0.8-1 time of the thickness of the top plate.
From conventional experience we can generally generalize the formula (unit: m) for the thickness of the top plate: a1 =l 0 /20+0.3
Wherein: l (L) 0 -a frame aperture; a1-top plate thickness.
Along with the continuous progress of railway technology, the railway load form is changed, and meanwhile, due to the improvement of the performances of the basic material concrete and the high-strength steel bars, the structural dimension of the frame bridge, which is drawn by traditional experience, is far from the requirements of the development of the existing railway technology, whether the precision and the application range are the same.
The influence of the load on the structure size is neglected by the traditional formula, and the precision and the application range are not high.
2 solving the frame bridge size formula by classical mechanics
2.1 principal parameters affecting frame bridge size
1. Taking a frame top plate as an example, we are told by classical mechanics, and the aperture L of the frame 0 The larger the top plate mid-span bending moment M is, the larger the bending moment M is, and the bending moment is proportional to the square of the aperture.
2. The larger the load q on the top plate is, the larger the bending moment M in the middle of the top plate is, and the bending moment is in direct proportion to the load. The load q on the top plate consists of three parts, namely the dead weight of the top plate, the constant load in the second period and the live load.
(1) Top plate dead weight:
the dead weight of the top plate is relatively smaller than the dead weight of the whole load q, and can be calculated according to an empirical formula.
(2) Second-stage constant load: the second-stage constant load mainly comprises the weight of line equipment, roadbed filling and railway ballast.
The volume weight of the frame plate top in terms of filling soil can be taken as a value of 20.5kN/m < 3 >, and the secondary constant load (unit: kN) =H is 20.5, wherein H is the filling soil height, namely the distance from the rail bottom to the top plate top, and the unit is m.
(3) Live load
Common railways live with ZKH single lines, ZK single lines, ZC single lines, ZKH double lines, ZK double lines, ZC double lines. The force of the live load acting on the top of the frame is distributed on the bottom surface of the rail bottom according to a special wheel weight, and is downwards diffused in a slope line of 2:1, and when double lines are formed, the live load action between the lines is overlapped and reaches the maximum. The design specification of railway bridge and culvert (TB 10002-2017) gives a calculation formula of the load of the passenger and cargo collinear railway, and according to the formula, we can easily deduce the calculation formulas (unit: KN) of the loads of ZK and ZC.
F-ZKH single line=179/(2.6+h)
F-ZK single line=157/(2.6+h)
F-ZC single line = 136/(2.6+h)
F-ZKH double-line=358/(6.6+h)
F-ZK double line=314/(7.2+h)
F-ZC double line=272/(6.6+h)
4. When the skew angle alpha is 0, the frame is orthogonal to the line, and the larger the skew angle is, the larger the structural dimension is. The roof mid-span bending moment M is inversely proportional to Cos alpha.
5. Rectangular cross-section moment of resistance w=b×h 2 /6. For a frame top plate, b is the length of the frame segment, h is the thickness of the frame top plate, the bending moment and the resisting moment are balanced, and the square of the thickness of the top plate is proportional to the bending moment.
FIG. 2 is an environmental view of a designed railway frame bridge; fig. 3 is a top view of a railway frame bridge structure.
The direction N in fig. 2 and 3 is a method of railway operation. In fig. 2, 5 is a rail, 6 is a filler layer, and 7 is a highway surface; alpha in fig. 3 is the intersection angle of the frame axis direction and the line normal.
2.2 classical mechanical solving the Top plate sizing formula
Because the frame structure is a hyperstatic structure, the structural rigidity and the unbalanced bending moment are distributed, and a standard formula is difficult to directly obtain. The parameters affecting the frame bridge size are combed, the frame structure size and all affecting parameters are correlated, and the coefficient ζ is assumed. Solving xi by using the collected working points, researching the distribution rule according to the solving condition of the xi value, and further obtaining whether the research has guiding significance value; according to the influence parameters, a formula (unit: m) of the frame bridge roof size is preliminarily summarized:
wherein: l (L) 0 -a frame aperture.
A 1 -roof thickness.
H-the height of filling soil, the distance from the rail bottom to the top of the frame top plate.
H 0 The initial dimensions of the top plate, this value being known from experienceThe formula: l (L) 0 /20+0.3
The intersection angle (unit: °) of the alpha-skew angle frame axis direction and the line normal.
F-railway live load
The derivation process of the above formula is as follows:
for ease of calculation, the frame section length is taken to be 1 meter.
(1) Bending moment M and L in roof span 0 ×L 0 Proportional to the ratio. We have been told by classical mechanics, framework pore size L 0 The larger the top plate mid-span bending moment M is, the larger the bending moment M is, and the bending moment is proportional to the square of the aperture.
(2) The larger the load on the top plate, the larger the mid-span bending moment M of the top plate, and the bending moment is in direct proportion to the load. It consists of three parts of forces: (1) dead weight of frame bridge roof + (2) second-stage constant load (filler weight on roof) + (3) train live load
(1) Roof weight = H0 x 26.5 (H0 is roof initial thickness, unit: m;26.5 is volume weight of reinforced concrete, unit: KN/m 3.) roof weight is relatively small in weight of whole load, and can be calculated according to empirical formula.
(2) The second-stage constant load mainly consists of the weight of line equipment, roadbed filling and railway ballast. The converted volume weight of the frame plate top filler can be taken as 20.5kN/m < 3 >, and the secondary constant load is H multiplied by 20.5 (H is the height of the filling soil, the unit is m, and 20.5 is the volume weight of the filling soil, the unit is KN/m < 3 >
(3) Train live load: f (units KN) are of the following types according to railway specifications F.
F-ZKH single line=179/(2.6+h)
F-ZK single line=157/(2.6+h)
F-ZC single line = 136/(2.6+h)
F-ZKH double-line=358/(6.6+h)
F-ZK double line=314/(7.2+h)
F-ZC double line=272/(6.6+h)
(1) The bending moment in the middle of the roof is proportional to (H multiplied by 20.5+H0 multiplied by 26.5+F) = > 2 and 3
(3) The mid-span bending moment M of the roof is inversely proportional to cosa, i.e. 1/Cos 2 Alpha, is proportional to
Because: m is respectively with L 0 ×L 0 、(H×20.5+H0×26.5+F)、1/Cos 2 Alpha is proportional to
So that: m and L 0 ×L 0 ×(H×20.5+H0×26.5+F)/Cos 2 Alpha proportional … … (4)
According to structural mechanics and material mechanics, the resistance w=bh 2/6, for the frame bridge roof structure, b is the frame section length, 1m is uniformly taken for convenient calculation, and h is the thickness A1 of the frame roof. So the formula can be rewritten as w=a 1 ×A 1 /6……(5)
Because the mid-span bending moment M of the top plate is balanced with the resisting moment W, the proportional relation is given by K as a proportional relation coefficient, and the formula (4) =k multiplied by the formula (5) obtains K multiplied by W=M, namely K multiplied by A 1 ×A 1 /6＝L 0 ×L 0 ×(H×20.5+H 0 ×26.5+F)/Cos 2 α
The formula continues to be deformed as:
is provided with
100 framework work points are randomly extracted by using big data, and substituted into the formula to obtain the zeta value, as shown in fig. 4, the zeta value is found to be between 0.0062 and 0.0101 by research, the distribution interval is too large, and the zeta value has no guiding value for actual engineering.
3 correcting the top plate size formula by utilizing big data theory
A large number of engineering cases are batched by software, and a database is established. These cases are reliable structures which have been put into operation for many years in reality, the too discrete points are filtered and removed, and then through big data fitting, deepening research is carried out on the basis of the above formula, and the following hidden relations are found:
the bending moment is mainly borne by the steel bars, the reinforcement diameter is not constant along with the change of the structure height, and the reinforcement diameter is increased along with the change of the structure height, so that the factor must be considered in the formula. Because the diameter value of the reinforcing steel bars on the market is not continuous (the diameters of the reinforcing steel bars on the market are 12, 14, 16, 18, 20, 22, 25 and 28 mm), the value cannot be clearly determined in a formula, and the fact that the diameter value is approximately consistent with the thickness change trend of the structure is considered. Therefore use H 0 (initial dimensions of the top plate) this parameter modifies the formula:100 frame work points extracted randomly are substituted into the formula, and the value of xi obtained is between 0.0056 and 0.0069 as shown in figure 5. The value interval of ζ is defined to be 0.0056-0.0069, and the value of ζ is obtained by dividing the value into 7 intervals according to 0.0002 degree, and the ratio of ζ in each interval is shown in fig. 6. As can be seen from FIG. 6, the average value of the zeta value is 0.061, and the interval is 0.0058 to 0.0064, which is 75%.
The values of ζ were fitted with a normal distribution curve, as shown in fig. 7: the peak value of the curve is 0.0061098, the standard deviation is 0.0002538. Zeta.value, 0.0064 is recommended, and when zeta=0.0064 can be calculated by utilizing a normal distribution curve according to the theory of probability theory, the shadow area occupies 91.3% of the total area, which shows that the value of the parameter is more reasonable, and the design requirement is met.
And (3) combining big data and probability theory related theory, and finishing and summarizing a formula (unit: m) of the thickness of the top plate of the frame bridge:after the size of the top plate is clear, the bottom plate and the side walls can be easily arranged and summarized into an empirical formula (unit: m) related with the size of the top plate.
The thickness of the bottom plate is A 2 ＝A 1 +0.05+L 0 *0.003。
Wall thickness A 3 ＝A 1 -0.05+(A 2 -A 1 +0.05)*a/45。
Wall thickness in porous frame bridge a4=a3-0.1.
Verification of 4 frame bridge size formula
The height of the filling soil of the conventional railway frame bridge is generally 0.8-3 m, and the aperture is 7-16 m. Taking ZK double-line load as an example, the height of filled soil is 1.5m and 3m, the structural size of a frame bridge with the aperture of 7-16 m and the skew angle of 0 degree, 5 degree, 15 degree, 25 degree, 35 degree and 45 degree is calculated by adopting a formula, modeling calculation is performed by adopting large-scale finite element computing software MIDAS, corresponding reinforcing bar diagrams are drawn according to internal force results, and the content of reinforcing bars of each frame is counted as shown in figure 8. The minimum steel bar content of the frame is 140kg/m3, and the maximum steel bar content is 174kg/m 3 . The distribution interval of the steel bar content is shown in fig. 9. As shown in FIG. 9, the content of the reinforcing steel bars is mainly concentrated at 145-160 kg/m 3 The ratio is about 75%, and the frame steel bar content is basically controlled in the most economical area of the frame by adopting the size formulated by the formula, so that the rationality of the formula is further demonstrated.
Example 2
Example 2 numerical calculation model of roof thickness obtained in example 1
And verifying the coefficient xi in the formula (I).
Classical cases were selected and zeta different values were taken for comparison of the frame structure and the results are shown in table 1.
TABLE 1
Through the data analysis of fig. 7 and table 1, the safety of running the railway frame bridge is difficult to ensure when the coefficient is lower than 0.0062, but the usage amount of the railway frame bridge steel bars is large when the coefficient is higher than 0.007, resulting in waste in economic cost; when the value of the coefficient xi is 0.0064-0.0068, the economy is more reasonable. Preferably, the value of the coefficient ζ is 0.0064. When the value of the coefficient xi is 0.0064, the safety can be ensured, and the economic cost is the lowest.
The design method of the railway frame bridge structure size ensures that the design of the structure size is attributed to quantification, can meet safety requirements, can ensure rationality of economic cost, has high accuracy and is convenient to popularize.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (5)
1. The design method of the railway frame bridge structure size is characterized by comprising the following steps of:
step 1, determining the frame aperture of a railway frame bridge, the filling height above a top plate, the intersection angle of the axis direction of the frame and the line normal, the railway live load and the initial thickness of the top plate;
wherein, the initial thickness of the top plate is calculated by the formula one: h 0 ＝L 0 In the formula I, H is shown as (20+0.3) 0 Is the initial thickness of the top plate, the unit is m, L 0 The unit is m for the frame aperture of the railway frame bridge;
the railway live load is calculated by the following method: when the railway is designed to be ZK single line, the railway live load F=157/(2.6+H); when the railway is designed to be ZKH single lines, the railway live load F=179/(2.6+H); when the railway is designed as a ZC single line, the railway live load F=136/(2.6+H); when the railway is designed to be ZKH double lines, the railway live load F=358/(6.6+H); when the railway is designed to be ZK double-line, the railway live load F=314/(7.2+H); when the railway is designed as ZC double line, the railway live load F=272/(6.6+H); wherein H is the height of the soil filled above the top plate, and the unit is m;
step 2, the data determined in the step 1 are carried into a top plate thickness numerical calculation model to obtain the top plate thickness;
wherein, roof thickness numerical calculation model is:in which A 1 The thickness of the top plate is m; l (L) 0 The unit is m for the frame aperture of the railway frame bridge; h is the height of the soil filled above the top plate, and the unit is m; h 0 The unit is m, which is the initial thickness of the top plate; f is railway live load, and the unit is kN; alpha is the intersection angle of the frame axis direction and the line normal, and the unit is degree; ζ is a coefficient;
wherein, the value of xi is 0.0062-0.007;
step 3, calculating the bottom thickness and the side wall thickness by using the top thickness obtained in the step 2;
wherein, the bottom thickness is calculated by formula two: a is that 2 ＝A 1 +0.05+L 0 *0.003, wherein A 2 The thickness of the bottom plate is m; a is that 1 The thickness of the top plate is m; l (L) 0 The unit is m for the frame aperture of the railway frame bridge;
the sidewall thickness is calculated by equation three: a is that 3 ＝A 1 -0.05+(A 2 -A 1 +0.05) a/45, wherein A 3 The unit is m, which is the thickness of the side wall; a is that 2 The thickness of the bottom plate is m; alpha is the intersection angle of the frame axis direction and the line normal, and the unit is DEG.
2. A method of dimensioning a railway frame bridge construction according to claim 1, wherein the value of the coefficient ζ is 0.0064-0.0068.
3. A method of dimensioning a railway frame bridge structure according to claim 2, characterized in that the value of the coefficient ζ is 0.0064.
4. A method of dimensioning a railway frame bridge construction according to any one of claims 1-3, wherein the railway frame bridge construction comprises 1-4 holes.
5. The method for designing a size of a railway frame bridge structure according to claim 4, wherein the railway frame bridge structure comprises 2-4 holes, and the thickness of the middle wall is further calculated by using the top thickness obtained in the step 2; the thickness of the middle wall is calculated by a formula IV: a is that 4 ＝A 3 -0.1, wherein A 4 The unit is m, which is the thickness of the middle wall; a is that 3 The unit is m, which is the thickness of the side wall.
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