CN108411797A - Vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction - Google Patents
Vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction Download PDFInfo
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- E—FIXED CONSTRUCTIONS
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Abstract
The invention discloses vault amount of deflection control methods in a kind of Catenary arch arch springing increasing section strengthening construction, structure basic parameter value is obtained according to design drawing, with catenary line approximate substitution catenary, the amount of deflection of crown section when calculating function unit power at Catenary arch arbitrary section, the reinforcing segment length that is determined by arrangement and method for construction and the side's amount for needing casting concrete calculate vault amount of deflection at this time, and field measurement vault amount of deflection is compared with the amount of deflection for calculating determination；The method is used for constant section catenary fixed arch.Relative to presently the most common FInite Element, the present invention can coordinate scientific calculator real-time control at the construction field (site), has the advantages that the defects of easy to operate and be easily achieved, to overcome that calculate the time caused by the FInite Element generally used now long, parameter affecting laws can not be directly acquired.Meanwhile analytic expression directly reflects the mechanical relationship between vault deflection value and each parameter of structure in the present invention, is conducive to assurance of the engineer to Design of Reinforcement and arrangement and method for construction.
Description
Technical field
The invention belongs to bridge structure strengthening construction process control fields more particularly to a kind of increase of Catenary arch arch springing to cut
Vault amount of deflection control method in the strengthening construction of face.
Background technology
Arch bridge has a long history in China, embodies the standard of construction of Bridges in Our Country.Arch is both structure and building,
It is favored by people.China has built large number of arch bridge since the establishment of the nation, however, with the raising of social industrial level, hands over
The increase of logical load, and influenced by factors such as the low degenerations with bridge material status of former design standard, that built in the past is very much
Arch bridge has become four classes or five class bridges, these bridges urgently rebuild by maintenance and reinforcement or dismounting.From economic benefit angle analysis, for
The bridge that can be transformed, the method using maintenance and reinforcement are more preferably to select.
According to《Highway bridge and culvert construction technique normalizing》(JTG/T F50-2011) the 15.13rd trifle content：" Arch Bridge Construction mistake
Cheng Shiying carries out process control to it, should ensure that stability, deformation and internal force of the arch structure in construction work are in peace always
In gamut.For large span arch bridge, construction process control should be carried out by the regulation of specification；For Medium and small span arch bridge, can adopt
The method for taking relative ease easy carries out Construction control ".The maintenance and reinforcement of arch bridge need to equally meet the code requirement, especially
Medium and small span arch bridge researches and develops a kind of easy-to-use construction safety control method right and wrong often with there is engineering practical value.
Invention content
The technical problem to be solved in the present invention is to provide a kind of Catenary arch arch springing increases easy to operate, being easily achieved to cut
Vault amount of deflection control method in the strengthening construction of face, to ensure arch bridge in carrying out arch springing increasing section construction structure safety with
And determine rational strengthening construction scheme.
In order to solve the above technical problems, the present invention uses following technical scheme：
Vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction obtains structure base according to design drawing
This parameter value, with catenary line approximate substitution catenary, the amount of deflection of crown section when calculating function unit power at Catenary arch section x
V (x), the reinforcing segment length n determined by arrangement and method for construction and the side amount V of casting concrete is needed to calculate vault amount of deflection at this time, will showed
Field actual measurement vault amount of deflection is compared with determining amount of deflection is calculated；The method is used for constant section catenary fixed arch.
Vault amount of deflection control method in above-mentioned Catenary arch arch springing increasing section strengthening construction, includes the following steps：
The first step obtains structure basic parameter value, including across footpath l, rise f, arch axis coefficient m, catenary by design drawing
Equation variable k, arch elastic modulus E and arch section bending resistance the moment of inertia I；
Second step obtains the arch constant a of equivalent catenary line with catenary line approximate substitution catenary using dichotomy；
Third walks, and is x-axis along span of arch diameter direction using vault as origin (0,0), and rise direction is that v axis establishes coordinate system,
Obtain under this coordinate system at the x of Catenary arch section vault amount of deflection v (x) when function unit power；
4th step is determined by arrangement and method for construction when arch springing uses Enlargement of Section strengthening construction and reinforces segment length n and need to pour
The side amount V for building concrete determines that the amount of deflection h, V of vault at this time are that total side of both sides concreting measures, i.e., in [- l/2 ,-l/2+
N] and [l/2-n, l/2] range in effect vertical uniform load γ V/2n, γ be the unit weight of concrete；
5th step shows through field measurement vault amount of deflection if actual measurement amount of deflection, which is less than in the 4th step, calculates determining amount of deflection
Arch deformation is in the controllable state of safety always during arch springing casting concrete, otherwise, is in uncontrollable state.
Vault amount of deflection v (x) is calculated as follows：
V (x)=f (x)-k1f1(x)-k2f2(x)-k3f3(x)
In formula：
k1=c1/δ11
k2=c2/δ22
k3=c3/δ33
The amount of deflection h of vault is calculated as follows：
For in existing Catenary arch arch springing increasing section strengthening construction vault amount of deflection control there are the problem of, inventor builds
Vault amount of deflection control method in a kind of Catenary arch arch springing increasing section strengthening construction has been found, structure base is obtained according to design drawing
This parameter value, with catenary line approximate substitution catenary, the amount of deflection of crown section when calculating function unit power at Catenary arch section x
V (x), the reinforcing segment length n determined by arrangement and method for construction and the side amount V of casting concrete is needed to calculate vault amount of deflection at this time, will showed
Field actual measurement vault amount of deflection is compared with determining amount of deflection is calculated；The method is used for constant section catenary fixed arch.Relative to current
The most commonly used FInite Element, the present invention have the advantages that it is easy to operate and be easily achieved, can be by means of scientific calculator
Scene obtains the size of the vault amount of deflection under different concreting side's amounts, and obtains influence of the structural parameters to vault amount of deflection
Rule, whether quickly and accurately assess arch deformation in arch springing increase strengthened section construction can really realize reality in safe range
When control on the spot avoid causing permanent damage to structure convenient for pinpointing the problems and solving the problems, such as in time at the scene.It overcomes
It is long to calculate the time caused by the FInite Element that generally uses now, the defects of can not directly acquiring parameter affecting laws.Meanwhile
Analytic expression directly reflects the mechanical relationship between vault deflection value and each parameter of structure in the present invention, is conducive to engineer to reinforcing
The assurance of design and construction scheme.
Description of the drawings
Fig. 1 is the method for the present invention flow chart.
Fig. 2 is the calculation flow chart of the catenary line arch constant a of equivalent substitution catenary.
The calculating schematic diagram of vault amount of deflection when Fig. 3 is function unit power at the x of catenary ream less arch section.
The calculating schematic diagram of vault amount of deflection when Fig. 4 is catenary ream less arch arch springing increasing section strengthening construction.
Specific implementation mode
Vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction, the method for constant section catenary without
Hinged arch specifically includes following steps：
The first step obtains structure basic parameter value, including across footpath l, rise f, arch axis coefficient m, catenary by design drawing
Equation variable k, arch elastic modulus E and arch section bending resistance the moment of inertia I；
Second step obtains the arch constant a of equivalent catenary line with catenary line approximate substitution catenary using dichotomy；
Third walks, and is x-axis (to the left for just) along span of arch diameter direction using vault as origin (0,0), rise direction is v axis
(downwards for just) establishes coordinate system, obtains under this coordinate system at the x of Catenary arch section vault amount of deflection v (x) when function unit power；
Vault amount of deflection v (x) is calculated as follows：
V (x)=f (x)-k1f1(x)-k2f2(x)-k3f3(x)
In formula：
k1=c1/δ11
k2=c2/δ22
k3=c3/δ33
4th step is determined by arrangement and method for construction when arch springing uses Enlargement of Section strengthening construction and reinforces segment length n (in x-axis
Projected length) and need casting concrete side amount V (both sides arch springing concrete symmetrically pours, V be both sides concreting it is total
Side's amount), i.e., (γ is concrete to effect vertical uniform load γ V/2n in [- l/2 ,-l/2+n] and [l/2-n, l/2] range
Unit weight), and determine the amount of deflection h of vault at this time；
The amount of deflection h of vault is calculated as follows：
5th step shows through field measurement vault amount of deflection if actual measurement amount of deflection, which is less than in the 4th step, calculates determining amount of deflection
Arch deformation is in the controllable state of safety always during arch springing casting concrete, otherwise, is in uncontrollable state, need to stop
It only constructs, analyzes and find out reason, should take safety measures or adjust when necessary concreting process.
The above method is also applicable for variable cross-section catenary ream less arch, and only cross sectional moment of inertia I is the function of x.
For ease of understanding, it is elaborated below for crucial second step, third step and the 4th step.
For Catenary arch, because the integral along its arch does not have explicit expression, see formula (1), thus in deformation or
Generally use straight line, circular arc line or catenary line carry out approximate substitution catenary when the calculating such as internal force, and the integral of these curve of approximation is equal
With compact expression, formula (2)~formula (4) is seen respectively
∫sDs=x (2)
∫sDs=sinh (x/a)/a (4)
In formula (1)~formula (4), s is arch path of integration；F (x) is integrand；X is that coordinate origin is located at vault
Coordinate along across footpath direction；L is across footpath；F is rise；M is the arch axis coefficient of Catenary arch；K is catenary equation variable,R is the radius of skene arch；A is catenary line arch parameter.
Relative to straight line and circular arc line, catenary line is then closer to catenary, and therefore, the present invention is approximate using catenary line
Substitute catenary.Using vault as under the coordinate system of origin, catenary line equation is：
As long as adjusting parameter a so that the curve newly built and former arch axis curve are close as possible, then along Catenary arch axis
Integral can be obtained the higher Approximate Explicit Solution of precision.The solution of parameter a can utilize dichotomy.According to Catenary arch perimeter strip
Part has been apparent from following formula establishment：
Equation can be obtained as a result,
The value that parameter a can be obtained in formula (7) is solved using dichotomy, flow chart is shown in attached drawing 2.For convenience, unit across footpath is listed
Under the corresponding a values of common ratio of rise to span, refer to table 1.
The value of the corresponding parameter a of common ratio of rise to span under 1 unit across footpath of table
| Ratio of rise to span | 1/3 | 1/4 | 1/5 | 1/6 | 1/7 | 1/8 | 1/9 | 1/10 |
| a | 0.421166 | 0.537160 | 0.655863 | 0.776289 | 0.897848 | 1.020178 | 1.143053 | 1.266324 |
On the basis of encircleing equivalent substitution Catenary arch with catenary line, when deriving function unit power at Catenary arch section x
The Deflection Formula of crown section：
(1) thinking is calculated
Deflection line is solved using static(al) method, unit force P is acted at arbitrary section b, crown section is solved and scratches
Degree influences line.According to elastic center method, fixed arch under unit force effect is converted to the statically determinate structure of redundant force, such as attached drawing 3
Shown, catenary equation y=f [cosh (2xk/l) -1]/(m-1), arch section bending stiffness is EI,For arch axis tangent line and level
Wire clamp angle, redundant force include moment of flexure x1, axle power x2, shear x3, elastic center is y away from vault distances.To seek crown section amount of deflection,
Illusory load need to be acted in the position, and internal force of the basic structure under all load actions is listed in table 2.
Basic structure internal force under 2 all load actions of table
(2) redundant force calculates
By basic mechanical principle, finds out basic structure (attached drawing 3) redundant force under unit force effect and be to solve for before encircleing amount of deflection
It carries.Catenary, the simplification integrated to curve according to formula (4) are substituted with catenary line, it can be deduced that redundant force influences line computation formula,
Solution procedure and formula are listed in table 3.
3 redundant force of table calculates
Note：Δ1p、Δ2p、Δ3pTo act on left half across pushing away card by unit force, when unit force act on right half across when,
Δ1pAnd Δ2pStill take left half across respective value, Δ3pIt takes corresponding left partly across -1 times of value.
(3) solution of vault deflection value
Such as attached drawing 3, the amount of deflection Δ of O points when basic structure B point function unit power and redundant forceOFor：
ΔO=ΔOp+x1ΔO1+x2ΔO2+x3ΔO3 (8)
Each meaning of parameters and calculation formula are listed in table 4 in formula (8).
The calculating of 4 vault amount of deflection of table
By formula (8), table 3 and table 4, the amount of deflection v (x) of crown section is when obtaining function unit power at the x of Catenary arch section：
V (x)=f (x)-k1f1(x)-k2f2(x)-k3f3(x) (9)
In formula：
k1=c1/δ11 (14)
k2=c2/δ22 (15)
k3=c3/δ33 (16)
Wherein, coefficient k1、k2And k3Each parameter value in calculating formula is calculated by following formula：
(4) Example Verification
Divide by taking 2 constant section catenary fixed arch as an example for the vault amount of deflection calculating formula accuracy that the verification present invention derives
Not Cai Yong FInite Element and the method for the present invention calculate, and judge that formula of the present invention calculates mistake on the basis of Finite element analysis results
Difference.
Example 1, span of arch diameter 117.5m, rise 22.158m, arch axis coefficient 1.347, section bending stiffness
9552.1994kNm2, function unit concentrated force (1kN) on arch；Example 2, arch axis coefficient 2.240, other parameters are the same as example 1.This
Invention formula calculates and FEM calculation crown section deflection value comparative situation is listed in table 5.
52 example exemplary value contrast tables of table
Note：Amount of deflection is upwards for just, downward is negative in table.
As can be seen from Table 5, formula calculating of the present invention is differed with Finite element analysis results maximum is no more than 3.60%, verification
Formula of the present invention calculates the accuracy of constant section catenary fixed arch crown section amount of deflection.On this basis, by attached drawing 4, root
According to arrangement and method for construction, casting concrete side's amount is V in [- l/2 ,-l/2+n] and [l/2-n, l/2] range, that is, applies evenly load
When γ V/2n, the amount of deflection h of vault is：
Claims (4)
1. vault amount of deflection control method in a kind of Catenary arch arch springing increasing section strengthening construction, it is characterised in that according to design drawing
Paper obtains structure basic parameter value, with catenary line approximate substitution catenary, encircles when calculating function unit power at Catenary arch section x
The amount of deflection v (x) of top section, the reinforcing segment length n determined by arrangement and method for construction and the side amount V of casting concrete is needed to calculate arch at this time
Amount of deflection is pushed up, field measurement vault amount of deflection is compared with determining amount of deflection is calculated；The method is used for constant section catenary fixed arch.
2. vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction according to claim 1, special
Sign is to include the following steps：
The first step obtains structure basic parameter value, including across footpath l, rise f, arch axis coefficient m, catenary equation by design drawing
Variable k, arch elastic modulus E and arch section bending resistance the moment of inertia I；
Second step obtains the arch constant a of equivalent catenary line with catenary line approximate substitution catenary using dichotomy；
Third walks, and is x-axis along span of arch diameter direction using vault as origin (0,0), rise direction is that v axis establishes coordinate system, is obtained
Vault amount of deflection v (x) when function unit power at the x of Catenary arch section under this coordinate system；
4th step is determined by arrangement and method for construction when arch springing uses Enlargement of Section strengthening construction and reinforces segment length n and need to pour mixed
The side amount V of solidifying soil determines that the amount of deflection h, V of vault at this time are that total side of both sides concreting measures, i.e., at [- l/2 ,-l/2+n] and
Effect vertical uniform load γ V/2n in [l/2-n, l/2] range, γ are the unit weight of concrete；
5th step shows encircleing through field measurement vault amount of deflection if actual measurement amount of deflection, which is less than in the 4th step, calculates determining amount of deflection
Arch deformation is in the controllable state of safety always during foot casting concrete, otherwise, is in uncontrollable state.
3. vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction according to claim 2, special
Sign is that vault amount of deflection v (x) is calculated as follows：
V (x)=f (x)-k1f1(x)-k2f2(x)-k3f3(x)
In formula：
k1=c1/δ11
k2=c2/δ22
k3=c3/δ33
4. vault amount of deflection control method in Catenary arch arch springing increasing section strengthening construction according to claim 2, special
Sign is that the amount of deflection h of vault is calculated as follows：
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| CN110387806A (en) * | 2019-07-31 | 2019-10-29 | 中交路桥北方工程有限公司 | A kind of restressed beam slab deflection deformation control method |
| CN111041969A (en) * | 2019-12-31 | 2020-04-21 | 深圳市桥博设计研究院有限公司 | Large-span combined arch bridge based on bending design theory and design and construction method |
| CN112560321A (en) * | 2020-12-29 | 2021-03-26 | 重庆交通大学 | Calculation method for ring-divided segmented pouring length of concrete wrapped outside arch ring of stiffened framework concrete arch bridge |
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| CN110387806A (en) * | 2019-07-31 | 2019-10-29 | 中交路桥北方工程有限公司 | A kind of restressed beam slab deflection deformation control method |
| CN111041969A (en) * | 2019-12-31 | 2020-04-21 | 深圳市桥博设计研究院有限公司 | Large-span combined arch bridge based on bending design theory and design and construction method |
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| CN108411797B (en) | 2020-07-31 |
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