CN112906093A - Method for calculating variable cross-section height of arch ring of large-span arch bridge - Google Patents

Method for calculating variable cross-section height of arch ring of large-span arch bridge Download PDF

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CN112906093A
CN112906093A CN202011174909.0A CN202011174909A CN112906093A CN 112906093 A CN112906093 A CN 112906093A CN 202011174909 A CN202011174909 A CN 202011174909A CN 112906093 A CN112906093 A CN 112906093A
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周水兴
张敏
宋功谭
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Chongqing Jiaotong University
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Abstract

The invention provides a method for calculating the variable cross-section height of an arch ring of a large-span arch bridge, which defines the cross-section height of the arch ring at any position of the arch ring of the large-span arch bridge to be calculated as follows: the ratio of the height of the arch crown section to the power of the cosine of the horizontal inclination angle of the arch axis of the section; the power coefficient can be uniquely determined according to the vault section height and the arch foot section height which are planned in advance; compared with the Litter formula, the calculation method is simpler, and the subsequent process of calculating the bridge parameters is simplified; and the height of the section of the arch ring at any position is calculated by using the formula provided by the invention, except that the heights of the sections of the arch foot and the arch crown are equal, the heights of the sections of the arch ring at other arbitrary positions calculated by the calculation method provided by the invention are all smaller than the height calculated by the Litter formula, so that the construction materials can be effectively reduced in the actual engineering, the budget can be reduced, and the economic benefit can be improved.

Description

Method for calculating variable cross-section height of arch ring of large-span arch bridge
Technical Field
The invention relates to the technical field of bridge construction, in particular to a method for calculating the height of a variable cross section of an arch ring of a large-span arch bridge.
Background
The large-span arch bridge is a bridge structure commonly used for spanning rivers and valleys, and hundreds of large-span reinforced concrete arch bridges, steel arch bridges and steel pipe concrete arch bridges are continuously built at home and abroad from the last 40 th century to the present. In order to make the distribution of the internal force of the arch ring section uniform, the arch ring section with the height varying along the span direction is often adopted, and the height of the variable section of the arch ring is often calculated by adopting a Litter formula (Ritter formula) in the engineering design.
The Lit formula assumes that the inertia moment of the arch crown and any section and the arch thickness coefficient are linearly changed, which causes the height of the section of the arch ring near the quarter span to be higher and the bending moment of the section of the arch foot to be larger. However, the quarter span is just positioned in the section positive and negative bending moment alternating region to mainly bear axial force, and the overlarge section not only increases the material consumption, but also increases the bending moment of the section of the arch springing.
The arch axis horizontal dip angle is related to the arch bridge sagittal cross ratio (f/L) and an arch axis coefficient m or an arch axis equation, and under the condition that the arch axis coefficient m or the arch axis equation is selected reasonably, the relationship between the height of any section of the arch ring and the horizontal dip angle can be directly established, so that the formula is simple, and the problems of the Litter formula can be avoided.
Disclosure of Invention
Aiming at the defects in the prior art, according to the embodiment of the invention, the calculation method for the variable cross-section height of the arch ring of the large-span arch bridge is provided, the calculation process for calculating the variable cross-section height of the arch ring at any position of the large-span arch bridge in the prior art is simplified, and the results of the embodiment prove that when the calculation method provided by the invention is compared with the calculation method of the Litter formula, the numerical values of the cross-section heights of the arch ring at other positions are small except that the heights of the arch foot and the arch crown are equal, so that the construction material and engineering investment are saved, and the construction requirements and the technical standards are met.
According to the embodiment of the invention, the method for calculating the variable section height of the arch ring of the large-span arch bridge comprises the following steps:
the arch ring section height h of the large-span arch bridge arch ring at any position needing to be calculated is defined as: height h of vault sectiondWith arch axis of the cross-sectionHorizontal inclination angle
Figure BDA0002748426880000011
The power of the cosine of (a); according to the pre-established height h of the cross section of the vaultdHeight h of arch foot sectionaDetermining a unique power coefficient d; drawing a formula:
Figure BDA0002748426880000012
drawing up the height h of the arch crown section of the large-span arch bridge to be calculateddArch foot section height ha；
Selecting the corresponding arch axis type of the large-span arch bridge to be calculated, and calculating the horizontal inclination angle of the arch axis of the section according to the arch axis equation corresponding to the selected arch axis type
Figure BDA00027484268800000215
And horizontal inclination of arch axis of arch foot section
Figure BDA00027484268800000216
The arch shaft horizontal inclination angle of the arch springing section obtained by calculation
Figure BDA00027484268800000217
And dome cross-sectional height hdArch foot section height haSubstitution formula:
Figure BDA0002748426880000021
calculating to obtain a power coefficient d;
finally, the height h of the section of the vault is determineddHorizontal inclination angle of arch axis of cross section
Figure BDA00027484268800000218
Substituting the power coefficient d into the formula (1) to calculate to obtain the arch ring at any positionThe cross-sectional height h.
Preferably, when the arch axis is catenary, the horizontal inclination angle of the arch axis of the section is
Figure BDA00027484268800000219
The calculation formula of (2) is as follows:
Figure BDA0002748426880000022
when xi takes 1, the horizontal inclination angle of the arch axis of the arch springing section is calculated
Figure BDA0002748426880000023
Wherein: f is the calculated rise; m is the arch axis coefficient; k is a coefficient of the number of the elements,
Figure BDA0002748426880000024
xi is a coefficient of the number of the magnetic poles,
Figure BDA0002748426880000025
and L is the calculation span.
Preferably, when the arch axis type is a secondary or higher parabola, the arch foot is taken as the origin to establish a corresponding coordinate system, and the horizontal inclination angle of the arch axis of the section where the corresponding coordinate system is located is
Figure BDA0002748426880000026
The calculation formula of (2) is as follows:
Figure BDA0002748426880000027
in formula (4): n is more than or equal to 2; a is a coefficient related to f, L and n; f is the calculated rise; and L is the calculation span.
Selecting the specific value of n to obtain the horizontal inclination angle of the arch axis of the section where the corresponding parabola is located
Figure BDA0002748426880000028
For the arch foot section: taking x as 0, and then taking the x as 0,then
Figure BDA0002748426880000029
According to the corresponding coordinate system and the corresponding f and L values in the coordinate system, the arch axis horizontal inclination angle of the arch springing section is calculated
Figure BDA00027484268800000210
Preferably, when xi is 1, the compound is obtained by substituting formula (3) into formula (1);
Figure BDA00027484268800000211
to be provided with
Figure BDA00027484268800000212
Taking logarithms of two sides of the formula (5) as a base to obtain a calculation expression of a power coefficient d:
Figure BDA00027484268800000213
wherein:
Figure BDA00027484268800000214
the horizontal inclination angle of an arch shaft of the arch springing section is shown; h isdIs the height of the section of the vault; h isaIs the height of the arch springing section.
Preferably, when x is 0, i.e., ξ is 1, the horizontal inclination of the arch axis of the arch springing section is obtained by simplifying formula (4) in accordance with the specific value of n selected
Figure BDA0002748426880000031
The formula (2) is obtained by substituting the formula (1) into the formula (1);
Figure BDA0002748426880000032
to be provided with
Figure BDA0002748426880000033
Taking logarithms of two sides of the formula (4) as a base to obtain a calculation expression of a power coefficient d:
Figure BDA0002748426880000034
wherein:
Figure BDA0002748426880000035
the horizontal inclination angle of an arch shaft of the arch springing section is shown; h isdIs the height of the section of the vault; h isaIs the height of the arch springing section.
Preferably, the type of arch ring variable cross-section comprises: rectangular solid sections, hollow box sections or truss-like sections.
The invention also discloses application of the method for calculating the variable cross-section height of the arch ring of the large-span arch bridge, and the method can be used for calculating the concrete-filled steel tube arch bridge, the stone arch bridge, the concrete arch bridge and the steel arch bridge according to the method for calculating the variable cross-section height of the arch ring of the large-span arch bridge.
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a method for calculating the height of an arch ring variable cross section at any position of a large-span arch bridge, which defines the height h of the arch ring cross section at any position of the arch ring of the large-span arch bridge to be calculated as follows: height h of vault sectiondHorizontal inclination angle of arch axis with section
Figure BDA0002748426880000037
The power of the cosine of (a); drawing up a formula to establish the height h of the variable section of the arch ring at any position and the horizontal inclination angle of the arch shaft of the section
Figure BDA0002748426880000036
Height h of vault sectiondCompared with a Lett formula, the calculation method is simpler, and the subsequent process of calculating the bridge parameters is simplified; and calculating arbitrary positions using the formula provided by the inventionThe height h of the section of the arch ring is equal to the height of the section of the arch foot and the arch crown, and the heights of the sections of the arch ring at any positions are calculated according to the calculation method provided by the invention and are all smaller than the height calculated by the Lit formula, so that the construction materials can be effectively saved in the actual engineering, the engineering budget is reduced, the economic benefit is improved, the actual bridge forming parameters calculated by the calculation formula provided by the invention meet the construction and safety standards of the large-span arch bridge through calculation and demonstration, and the authenticity and the feasibility of the invention are further proved.
Drawings
FIG. 1 is a schematic diagram of a computational model of formula (1) of the present invention;
FIG. 2 is a horizontal inclination angle of the arch axis of the cross section of the present invention
Figure BDA0002748426880000038
The computational model map of (1);
FIG. 3 is a schematic diagram of a coordinate system model of quadratic and higher-order parabolas in the present invention;
FIG. 4 is a line drawing of the height values of each section calculated by the actual design drawing of the ebony river bridge, the Litter formula and the calculation formula provided by the invention;
fig. 5 is a line graph of the difference between the height of the variable cross section of the smoked plum river bridge calculated by the calculation formula provided by the present invention and the litter formula and the actual design drawing;
FIG. 6 is an arch ring elevation of the actual design drawing of the ebony river bridge;
FIG. 7 is a line drawing of the upper and lower chord axial forces of the arch rib under the action of the dead weight of the finished bridge, according to the actual design drawing of the dark plum river bridge, the Litter formula and the calculation formula provided by the invention;
fig. 8 is a comparison graph of the absolute value difference of the axial force of the ebony river bridge under the action of self weight after the bridge is formed by the actual design drawing, the litter formula and the calculation formula provided by the invention.
Detailed Description
In order to further clarify the objects, technical solutions and advantages of the present invention, the present invention will be described in further detail below with reference to the accompanying drawings and examples.
The invention aims to provide a novel method for calculating the variable cross-section height of an arch ring of a large-span arch bridge, which is used for replacing the traditional method for calculating the variable cross-section height of the arch ring of the large-span arch bridge by using a Litter formula (Ritter formula) or a fitting method.
The internal force of the section of the arch ring of the large-span arch bridge is mainly controlled by the self weight, usually, the arch crown bears positive bending moment, the arch foot bears negative bending moment, the positive bending moment and the negative bending moment alternately appear in a quarter-span section, and the absolute value of the bending moment in the section is relatively small. The cross section height is drawn up by adopting the Litter formula, and the cross section height of the quarter-span section is usually larger.
Therefore, the invention provides a novel method for calculating the variable section height of the arch ring of the large-span arch bridge, and the height of any section is defined as the ratio of the height of the arch section to the power of the cosine of the horizontal inclination angle of the arch axis of the section. According to the heights of the sections of the arch crown and the arch foot, a unique power coefficient can be determined, so that the height of the variable section of the arch ring at the corresponding position can be calculated, the height of the section of the quarter-span section calculated by the method is smaller than the calculation result of the Lett formula, the building materials can be saved, and the calculation process can be simplified.
In the invention, the most common large-span variable-height truss type concrete-filled steel tube arch bridge is taken as a calculation description;
the large-span concrete-filled steel tube arch bridge adopts a variable cross-section form, and the cross-section height is also determined by a Litter formula. When designing the steel pipe arch, the height h of the arch crown and arch foot section is determineddAnd haThe arch crown section inertia moment I under the condition of neglecting the influence of the web rod on the rigidity of the arch rib sectiondAnd arch foot section moment of inertia IaComprises the following steps:
Figure BDA0002748426880000041
Figure BDA0002748426880000042
in the formula: i isDIs the moment of inertia of the upper/lower chord tube to the self-form axis, ASThe upper/lower chord tube cross-sectional area.
Compared with the moment of inertia generated by the area distance of the chord tube to the whole section, the moment of inertia value of the chord tube per se is much smaller, and the arch thickness coefficient n and the center height h of any section can be determined by substituting the moment of inertia into the Litter formula under the condition of neglecting the influence:
in the litter formula, the arch thickness coefficient n is calculated as:
Figure BDA0002748426880000051
wherein:
Figure BDA0002748426880000052
the horizontal inclination angle of the arch axis of the arch springing section is shown.
Substituting the formulas (6) and (7) into the formula (8) to obtain an expression of the arch thickness coefficient n of the large-span concrete-filled steel tube arch bridge:
Figure BDA0002748426880000053
in the Lit formula, the calculation formula of the arch ring variable section height h of the large-span concrete-filled steel tube arch bridge is as follows:
Figure BDA0002748426880000054
wherein:
Figure BDA0002748426880000055
the horizontal inclination angle of the arch axis of any section is shown.
In formula (10):
Figure BDA0002748426880000056
K1defined as the section height coefficient of the litter equation.
Due to the arch shaft with any sectionHorizontal inclination angle
Figure RE-GDA0002801660630000057
Has a cosine value of less than 1.0 (except for the dome cross-section), and thus has
Figure RE-GDA0002801660630000058
For bridges with small and medium spans, even if a section with a high height is adopted, the height change is not too large, so that the bridge can be determined by the formula (10).
The cross-sectional height of the large-span arch bridge is determined by the Lit formula, although
Figure BDA0002748426880000059
The cosine value of (A) is compared with the value after being squared
Figure BDA00027484268800000510
The cosine value of (a) is large, but the requirement of the height change of the cross section cannot be met in some cases, and the cosine value needs to be determined by using the arch thickness coefficient n. As can be seen from the formulas (9) and (10), the smaller n is, the larger the change of the section height is, and the method is suitable for the requirement of the change of the section height of the steel pipe concrete arch bridge.
Further analysis shows that the height of the cross section obtained by the Litter formula changes more gradually in the whole bridge span range, and the height of the arch foot section changes more sharply due to the combined action of the position of the cross section and the horizontal inclination angle.
For a steel pipe concrete arch bridge with a truss type section, the chord pipe mainly bears axial force, the horizontal thrust is gradually increased from the arch top to the arch springing, and the section height obtained according to the Lit formula is usually larger.
In the litter formula, the calculation formula of the section moment of inertia is as follows:
Figure BDA00027484268800000511
wherein:
Figure BDA00027484268800000512
the horizontal inclination angle of the arch axis of any section is shown.
As can be seen from the formulas (10) and (12), the calculation formulas of the section inertia moment I and the variable section height h both comprise the horizontal inclination angle of the arch axis of any section of the arch
Figure BDA0002748426880000061
The inclination angle is related to the vector-span ratio and the arch axis coefficient, and also implies the relation between the arch ring axial force and the bending moment, so that the arch ring section height h at any position can be represented by the following formula under the condition that the arch axis coefficient is reasonably selected:
Figure BDA0002748426880000062
wherein: h isdIs the height of the section of the vault;
Figure BDA0002748426880000063
the horizontal inclination angle of the arch axis with any section is shown; d is a power coefficient.
The specific position relationship of each parameter in the real bridge in the formula (1) is shown in fig. 1: wherein 1, the section of the arch ring at any position; 2. A dome cross section; 3. a spur section; 4. the horizontal inclination angle of the arch axis of the section is; 5. an arch axis;
selecting the corresponding arch axis type of the large-span arch bridge to be calculated, and calculating the horizontal inclination angle of the arch axis of the section to be calculated according to the corresponding arch axis equation of the selected arch axis type
Figure BDA00027484268800000610
And horizontal inclination of arch axis of arch foot section
Figure BDA00027484268800000611
When the arch axis is catenary, the horizontal inclination angle of the arch axis of the section is
Figure BDA00027484268800000612
The calculation formula of (2) is as follows:
Figure BDA0002748426880000064
when xi takes 1, the horizontal inclination angle of the arch axis of the arch springing section is calculated
Figure BDA00027484268800000613
When xi is 1, the formula (2) is substituted into the formula (1);
Figure BDA0002748426880000065
to be provided with
Figure BDA0002748426880000066
Taking logarithms at two ends of the formula (4) as a base to obtain an expression of a power coefficient d:
Figure BDA0002748426880000067
the arch shaft horizontal inclination angle of the arch springing section obtained by calculation
Figure BDA0002748426880000068
And dome cross-sectional height hdArch foot section height haSubstituting in an expression (2), and calculating to obtain a power coefficient d;
finally, the height h of the section of the vault is determineddHorizontal inclination angle of arch axis of cross section
Figure BDA0002748426880000069
The power coefficient d is substituted into the formula (1) to calculate, and the cross-sectional height h of an arbitrary position is obtained.
When the arch axis type is a quadratic or high-order parabola, the arch springing is taken as the origin, and a corresponding coordinate system is established, wherein the corresponding coordinate system is shown in fig. 3: its parabolic equation f (x) can be expressed by the following equation:
f(x)＝anxn+an-1xn-1+...+a1x1 (13)
wherein: in the formula (13), n is more than or equal to 2;
then the horizontal inclination angle of the arch axis of the cross section
Figure BDA0002748426880000071
The calculation formula of (2) is as follows:
Figure BDA0002748426880000072
in formula (4): n is more than or equal to 2; a is a coefficient related to f, L and n; f is the calculated rise; and L is the calculation span.
Selecting a specific value of n to obtain a specific power number of a parabola, and calculating by taking a quadratic parabola as an example;
taking n as 2, substituting in formula (13), the expression of the quadratic parabolic equation is obtained as follows:
Figure BDA0002748426880000073
then the horizontal inclination angle of the arch axis of the cross section
Figure BDA0002748426880000074
The calculation formula of (2) is as follows:
Figure BDA0002748426880000075
for a pair-arch foot section: substituting x ═ 0, i.e., ξ ═ 1, into formula (15) yields:
Figure BDA0002748426880000076
namely, the horizontal inclination angle of the arch axis of the arch springing section can be calculated
Figure BDA0002748426880000077
Then, formula (16) is substituted into formula (1) to obtain:
Figure BDA0002748426880000078
to be provided with
Figure BDA0002748426880000079
Taking logarithms of two sides of the formula (4) as a base to obtain a calculation expression of a power coefficient d:
Figure BDA00027484268800000710
wherein:
Figure BDA00027484268800000711
the horizontal inclination angle of an arch shaft of the arch springing section is shown; h isdIs the height of the section of the vault; h isaIs the height of the arch springing section.
The above calculation is exemplified by using the arch axis as a quadratic parabola, and when the arch axis type is a high-order parabola of which the parabola coefficient is greater than that of the quadratic parabola, the calculation can also be deduced according to the above calculation process.
When the variable cross-section height at any position is determined by adopting a Lit formula, the same design method is adopted, namely, the formula (10) is replaced by the condition that the arch springsection height and the arch springsection arch axis horizontal inclination angle are known to determine the arch thickness coefficient n, so that the method is obtained:
Figure BDA00027484268800000712
or:
Figure BDA00027484268800000713
note that the terms on the right of (5) and equation (18) are the same, then the reduction is:
Figure BDA0002748426880000081
the arch thickness coefficient n obtained by continuing the simplified expression (12) is as follows:
Figure BDA0002748426880000082
the formula (20) establishes the relationship between the formula and the Litter formula in the invention; it should be noted that, although the relationship between the two is established, the height of the arch ring section h at any position is smaller than the height calculated by the litter formula except that the heights of the arch springing and the arch crown section are equal.
The authenticity and feasibility of the calculation method for the variable cross-section height of the arch ring of the large-span arch bridge provided by the invention are proved by carrying out real bridge substitution calculation.
Selecting a solid bridge: dark plum river bridge
Introduction to real bridge: the dark plum river bridge is a steel tube concrete overhead arch bridge which spans canyons and is marked by TJ12 from Guiyang to Huangping expressway, the calculated span L is 300m, the calculated rise f is 60m, the rise ratio f/L is 1/5, and the arch axis coefficient m is 1.55. The arch axis adopts a catenary, the half main arch ring adopts a 3-truss space truss structure, the cross section adopts a constant width and variable height, the height is changed from 5m of an arch crown to 9m of arch feet (from middle to middle), the transverse distance between each arch rib of the half main arch ring is 5m, the distance between two arch ribs is 7m, a cross beam is arranged between the arch ribs of the half main arch ring, and a K-shaped support is arranged between the two bridges. The upper and lower chord tubes of the arch rib adopt two steel tubes (arranged according to the stress requirement) of phi 1200 multiplied by 24mm and phi 1200 multiplied by 35mm, which are both made of Q345D material, and C55 self-compacting compensation shrinkage concrete is poured into the tubes.
Calculating parameters: h isd/ha5/9; calculated by using an arch shaft horizontal inclination angle formula
Figure BDA0002748426880000083
Substituted type
Figure BDA0002748426880000084
Substituting d into 2.09951004
Figure BDA0002748426880000085
And n is 0.40835859. The design drawing adopts a fitting method to determine the height of the arch ring, and the data in the table 1 are the height of each section of the arch ring calculated by an actual design drawing, a Lit formula and a calculation formula provided by the invention (abbreviated as the invention formula in the table 1); FIG. 4 is a line graph of the height values of each section calculated from the actual design drawing, the Litter equation and the calculation equation provided by the present invention; fig. 5 is a line graph of the difference between the height of the variable cross section of the smoked plum river bridge calculated by the calculation formula provided by the present invention and the litter formula and the actual design drawing; as is clear from fig. 4 and 5, the arch heights (except for the arch crown and the arch foot) of the cross sections calculated by the calculation formula provided by the invention are smaller than those calculated by the design drawing and the litter formula, and are particularly obvious in the l/4 section.
Figure BDA0002748426880000086
Figure BDA0002748426880000091
TABLE 1 calculation of arch height (unit: m) by means of three arch height calculation modes of ebony river bridge
A full-bridge model is established by using Midas/Civil, and the construction stage of concrete pouring in a pipe is considered, so that the internal force of the chord pipe under the action of self weight of the finished bridge and the internal force difference between different design methods are obtained by using three arch height calculation methods as shown in the figures 7 and 8: as can be seen from fig. 7 and 8, the single tube axial forces calculated by the three methods have little difference; in the arch foot area with the largest eccentricity, the upper chord tube axial force obtained by the calculation method of the invention formula is increased, the lower chord tube axial force is reduced, the upper chord axial force obtained by the calculation of the arch height by the Lett formula is increased by 7.00 percent, and the lower chord is reduced by 1.71 percent; due to the change of the chord tube axial force obtained by the formula, the upper chord tube axial force and the lower chord tube axial force in the arch springing area are more uniform, the eccentricity of the section near the arch springing is smaller, and the mechanical property of the concrete filled steel tube is favorably exerted.
The table shows the maximum and minimum web member stresses of the dark plum river bridge, and the results obtained by comparing the three calculation modes are not very different and are far smaller than the designed strength value of Q345D steel. In the table, "-" represents compressive stress, and positive values represent tensile stress.
Stress Design paper Lie formula Invention formula
Maximum of 73.9 72.3 70.6
Minimum size -92.4 -90.5 -92.6
TABLE 2 stress values of web members of large bridge of dark plum river
By
The method has the advantages that the arch height is drawn by the calculation formula provided by the invention, and the dynamic characteristic difference of the full bridge calculated by the design drawing and the drawing drawn by the Litter formula is small. By
TABLE 3 comparison of the dynamic characteristics of the ebony river bridge (unit: Hz)
It can be seen that the stability coefficients are not very different, and are all larger than 7.8, which meets the requirement that the specification is larger than 4.0.
Figure BDA0002748426880000101
TABLE 3 comparison of the dynamic characteristics of the ebony river bridge (unit: Hz)
Instability mode Design paper Lie formula Invention formula
Out-of-first-order instability 7.882917 7.888777 7.913372
First order in-plane instability 20.158485 20.599416 19.60792
TABLE 4 dark plum river bridge flexion analysis
By
As can be seen from the table, the material consumption of the arch height arch ring material determined by the calculation formula provided by the invention is obviously less, the steel materials are reduced by 65.2t and 61.2t respectively compared with the design drawing and the Litter formula, and the economic benefit is obvious.
Weight (D) Design paper Lie formula Invention formula
t 7135.3 7131.3 7070.1
TABLE 5 dosage of steel material for arch ring of Meihe bridge (unit: t)
Finally, the above embodiments are only used for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (7)

1. A method for calculating the variable cross-section height of an arch ring of a large-span arch bridge is characterized by comprising the following steps:
the arch ring section height h of the large-span arch bridge arch ring at any position needing to be calculated is defined as: height h of vault sectiondHorizontal inclination angle of arch axis with cross section
Figure FDA0002748426870000011
The power of the cosine of (a); according to the pre-established height h of the cross section of the vaultdHeight h of arch foot sectionaDetermining a unique power coefficient d; drawing a formula:
Figure FDA0002748426870000012
drawing up the height h of the arch crown section of the large-span arch bridge to be calculateddArch foot section height ha；
Selecting the corresponding arch axis type of the large-span arch bridge to be calculated, and calculating the horizontal inclination angle of the arch axis of the section according to the arch axis equation corresponding to the selected arch axis type
Figure FDA0002748426870000013
And horizontal inclination of arch axis of arch foot section
Figure FDA0002748426870000014
The arch shaft horizontal inclination angle of the arch springing section obtained by calculation
Figure FDA0002748426870000015
And dome cross-sectional height hdArch foot section height haSubstituting into a formula:
Figure FDA0002748426870000016
calculating to obtain a power coefficient d;
finally, the height h of the section of the vault is determineddHorizontal inclination angle of arch axis of cross section
Figure FDA0002748426870000017
And substituting the power coefficient d into the formula (1) to calculate to obtain the section height h of the arch ring at any position.
2. The method for calculating the variable cross-section height of the arch ring of the large-span arch bridge as claimed in claim 1, wherein: when the arch axis is catenary, the horizontal inclination angle of the arch axis of the section is
Figure FDA0002748426870000018
The calculation formula of (2) is as follows:
Figure FDA0002748426870000019
when xi takes 1, the horizontal inclination angle of the arch axis of the arch springing section is calculated
Figure FDA00027484268700000110
Wherein: f is the calculated rise; m is the arch axis coefficient; k is a coefficient of the number of the elements,
Figure FDA00027484268700000111
xi is a coefficient of the number of the magnetic poles,
Figure FDA00027484268700000112
x is the distance from the section to be calculated to the section of the vault; and L is the calculation span.
3. The method for calculating the variable cross-section height of the arch ring of the large-span arch bridge as claimed in claim 1, wherein: when the arch axis type is a secondary or higher parabola, the arch foot is taken as the origin to establish a corresponding coordinate system, and the horizontal inclination angle of the arch axis of the section where the corresponding coordinate system is located
Figure FDA00027484268700000113
The calculation formula of (2) is as follows:
Figure FDA00027484268700000114
in formula (4): n is more than or equal to 2; a is a coefficient related to f, L and n; f is the calculated rise; and L is the calculation span.
Selecting the specific value of n to obtain the horizontal inclination angle of the arch axis of the section where the corresponding parabola is located
Figure FDA00027484268700000115
For the arch foot section: if x is 0, then
Figure FDA0002748426870000021
According to the corresponding coordinate system and the corresponding f and L values in the coordinate system, the arch axis horizontal inclination angle of the arch springing section is calculated
Figure FDA0002748426870000022
4. The method for calculating the variable cross-section height of the arch ring of the large-span arch bridge as claimed in claim 2, wherein: when xi takes 1, substituting formula (3) into formula (1) to obtain;
Figure FDA0002748426870000023
to be provided with
Figure FDA0002748426870000024
Taking logarithms of two sides of the formula (5) as a base to obtain a calculation expression of a power coefficient d:
Figure FDA0002748426870000025
wherein:
Figure FDA0002748426870000026
the horizontal inclination angle of an arch shaft of the arch springing section is shown; h isdIs the height of the section of the vault; h isaIs the height of the arch springing section.
5. A method for calculating the variable cross-sectional height of the arch ring of the large-span arch bridge as claimed in claim 3, wherein: when x is equal to 0, according to the specific value of the selected n, the arch shaft horizontal inclination angle of the arch springing section is obtained by substituting formula (4) for simplification
Figure FDA0002748426870000027
The formula (2) is obtained by substituting the formula (1) into the formula (1);
Figure FDA0002748426870000028
to be provided with
Figure FDA0002748426870000029
Taking logarithms of two sides of the formula (4) as a base to obtain a calculation expression of a power coefficient d:
Figure FDA00027484268700000210
wherein:
Figure FDA00027484268700000211
the horizontal inclination angle of an arch shaft of the arch springing section is shown; h isdIs the height of the section of the vault; h isaIs the height of the arch springing section.
6. The method for calculating the variable cross-section height of the arch ring of the large-span arch bridge as claimed in claim 1, wherein: the type of the arch ring variable cross section comprises: rectangular solid sections, hollow box sections or truss-like lattice sections.
7. Use of a method according to claim 1 for calculating the variable section height of an arch ring of a long-span arch bridge in the construction of concrete-filled steel tube arch bridges, stone arch bridges, concrete arch bridges or steel arch bridges.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116383942A (en) * 2023-04-07 2023-07-04 浙江大学 Design method and device of main arch structure

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004270382A (en) * 2003-03-11 2004-09-30 Ps Mitsubishi Construction Co Ltd Bridge having low girder height
WO2004097335A1 (en) * 2003-04-25 2004-11-11 Ecole Polytechnique Federale De Lausanne (Epfl) Shape and deformation measurements of large objects by fringe projection
CN108416116A (en) * 2018-02-09 2018-08-17 广西交通科学研究院有限公司 Vault ballast method for determination of amount when arch springing increasing section reinforces parabolic arch
US20180314770A1 (en) * 2016-04-29 2018-11-01 China University Of Mining And Technology Method for designing supporting parameters of transition support for mixed mining face of filling and fully-mechanized mining

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004270382A (en) * 2003-03-11 2004-09-30 Ps Mitsubishi Construction Co Ltd Bridge having low girder height
WO2004097335A1 (en) * 2003-04-25 2004-11-11 Ecole Polytechnique Federale De Lausanne (Epfl) Shape and deformation measurements of large objects by fringe projection
US20180314770A1 (en) * 2016-04-29 2018-11-01 China University Of Mining And Technology Method for designing supporting parameters of transition support for mixed mining face of filling and fully-mechanized mining
CN108416116A (en) * 2018-02-09 2018-08-17 广西交通科学研究院有限公司 Vault ballast method for determination of amount when arch springing increasing section reinforces parabolic arch

Non-Patent Citations (9)

* Cited by examiner, † Cited by third party
Title
SHUIXING ZHOU ET AL: "Determination of Cast-in-situ Section Lengths of Reinforced Concrete Arch Bridge in Arch Centering Method", 《ADVANCED MATERIALS RESEARCH》 *
YANYAN SHA ET AL: "Numerical investigations of the dynamic response of a floating bridge under environmental loadings", 《SHIPS AND OFFSHORE STRUCTURES》 *
周倩等: "新型钢-混组合拱桥拱厚系数和分界点位置研究", 《中外公路》 *
周潇等: "拱桥内力计算分析程序开发研究", 《重庆交通大学学报(自然科学版)》 *
张广欣: "基于二分法求解钢管混凝土桁架拱桥主拱肋节点坐标", 《价值工程》 *
张玥: "采用数值方法解算悬链线无铰拱桥", 《包头钢铁学院学报》 *
施智: "一种求解变截面钢管混凝土拱桥计算跨径的方法", 《西部交通科技》 *
杨勇: "重载铁路大跨度上承式钢管混凝土拱桥设计研究", 《铁道标准设计》 *
耿文宾等: "考虑剪力滞效应的变截面箱梁桥固有频率及其影响研究", 《天津建设科技》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116383942A (en) * 2023-04-07 2023-07-04 浙江大学 Design method and device of main arch structure
CN116383942B (en) * 2023-04-07 2023-11-14 浙江大学 Design method and device of main arch structure

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