CN108416116A - Vault ballast method for determination of amount when arch springing increasing section reinforces parabolic arch - Google Patents
Vault ballast method for determination of amount when arch springing increasing section reinforces parabolic arch Download PDFInfo
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Abstract
Vault ballast method for determination of amount when reinforcing parabolic arch the invention discloses a kind of arch springing increasing section, the method is according to design drawing and arrangement and method for construction, by establishing the one-to-one relationship formula between arch springing concreting amount and vault ballast amount, it can be quick, it is accurate and determining when front abutment concreting amount lower arch top pressure weight in real time, the analytic expression directly reflects the mechanical relationship between vault deflection value and each parameter of structure, assurance conducive to engineer to Design of Reinforcement and arrangement and method for construction, the difference amount of pouring lower arch top pressure weight when determining arch springing casting concrete, ensure the structure safety in Arch Bridges Strengthening construction.Relative to presently the most common FInite Element, the method is easy to operate, is easily achieved, and scientific calculator can be coordinated to use, and one calculation procedure of editor can be generally applicable to similar engineering situation, finite element numerical model need not be all established per bridge block, save a large amount of time and resource.
Description
Technical field
When reinforcing parabolic arch the invention belongs to bridge structure strengthening construction field more particularly to a kind of arch springing increasing section
Vault ballast method for determination of amount.
Background technology
Arch is both structure and building, is liked by people.Foundation comes China and has built large number of arch bridge, however,
With the raising of social industrial level, the increase of traffic loading, and it is low by former design standard and bridge material status is degenerated
Etc. factors influence, many arch bridges built in the past have become four classes or five class bridges, these bridges urgently maintenance and reinforcement or remove weight
It builds.From economic benefit angle analysis, for the bridge that can be transformed, the method using maintenance and reinforcement is more preferably to select.
Using being one of common reinforcement means of arch bridge in arch springing external wrapping concrete increasing section, this method can effectively improve
Anti-bending bearing capacity, shear-carrying capacity and the rigidity of arch rib and its normal section bearing capacity and rigidity.For using Enlargement of Section
It reinforces for arch bridge, operating mode the most unfavorable is in arch springing concreting process, because reinforcing layer has not yet been formed just at this time
Degree, cannot not only participate in stress, but also also add dead load, so need to generally take corresponding measure in the process.And arch springing
When casting concrete vault can on emit be most need pay close attention to and solve, in construction common solution be in vault ballast,
Middle use water tank ballast is most common mode.But with the increase that arch springing concreting side is measured, vault ballast amount also need to be with
Variation, the purpose with water tank ballast is also the convenient size for adjusting ballast amount in real time, i.e., vault ballast amount is that dynamic adjusts
In and there are one and concreting sides to measure the optimal value to match, it is excessive or too small for control arch deformation and entire
It is very unfavorable for structure safety.
Invention content
The technical problem to be solved in the present invention is to provide a kind of arch springing increasing sections easy to operate, being easily achieved to reinforce throwing
Vault ballast method for determination of amount when object line encircles, the difference amount of pouring lower arch top pressure weight when determining arch springing casting concrete,
Ensure the structure safety in Arch Bridges Strengthening construction.
In order to solve the above technical problems, the present invention uses following technical scheme：
Vault ballast method for determination of amount when arch springing increasing section reinforces parabolic arch, according to design drawing and construction organization
Design obtains structure various parameter values, with catenary line approximate substitution parabola, is applied in the reinforcing of arch springing increasing section with vault amount of deflection
It is remained unchanged in work as principle, establishes vault ballast amount GpIncrease the concrete square amount V poured in strengthened section with both sides arch springingc
One-to-one relationship formula, vault ballast amount G when according to the relational expression real-time control arch springing casting concretep；The method is suitable for
Cross-section parabola fixed arch.
Vault ballast method for determination of amount when above-mentioned arch springing increasing section reinforces parabolic arch, includes the following steps：
The first step obtains various parameter values by design drawing and construction scheme, including across footpath l, rise f, arch springing are cut
The level inclination of face tangent lineThe thickness t and width w of arch springing increasing section part, the unit weight γ of arch springing casting concretec, arch cut
Face Anti-pull-press rigidity EA and bending stiffness EI；
Second step, with the arch of catenary line approximate substitution original bridge, the arch that equivalent catenary line is obtained using dichotomy is normal
Number a；
Third walks, and is remained unchanged as principle in arch springing increasing section strengthening construction with vault amount of deflection, establishes vault ballast
Measure GpIncrease the concrete square amount V poured in strengthened section with both sides arch springingcOne-to-one relationship formula, according to the correspondence
Vault ballast amount G when formula real-time control arch springing casting concretep。
Correspondence formula is：
In formula, the amount of deflection of crown section when v (x) is function unit power at the x of parabolic arch section；Using vault as origin
(0,0) is x-axis along span of arch diameter direction, and rise direction is under the coordinate system of y-axis, and calculation formula is
V (x)=f (x)-k1f1(x)-k2f2(x)-k3f3(x)；When v (0) indicates parabolic arch crown section function unit power
The amount of deflection in the section；Each parameter value is calculated by following formula in v (x) calculating formulas：
k1=c1/δ11
k2=c2/δ22
k3=c3/δ33
For existing arch springing increasing section reinforce parabolic arch when vault pressure Weight control there are the problem of, inventor establish
Vault ballast method for determination of amount when a kind of arch springing increasing section reinforces parabolic arch, the method is according to design drawing and construction party
Case can be quick, accurate and real-time by establishing the one-to-one relationship formula between arch springing concreting amount and vault ballast amount
Ground, which determines, works as front abutment concreting amount lower arch top pressure weight, which directly reflects that vault deflection value is respectively joined with structure
Mechanical relationship between number is conducive to assurance of the engineer to Design of Reinforcement and arrangement and method for construction, to determine arch springing casting concrete
The Shi Butong amount of pouring lower arch top pressure weight ensures the structure safety in Arch Bridges Strengthening construction.Relative to presently the most there are commonly
The first method of limit, the method is easy to operate, is easily achieved, and scientific calculator can be coordinated to use, and one calculation procedure of editor can be fitted generally
For similar engineering situation, finite element numerical model need not be all established per bridge block, save a large amount of time and resource.
Description of the drawings
Fig. 1 is the method for the present invention flow chart.
Fig. 2 is the calculation flow chart of the parabolical catenary line arch constant a of equivalent substitution.
The amount of deflection of arch arbitrary section i calculates schematic diagram when Fig. 3 is function unit power at parabola fixed arch section x.
The calculating schematic diagram of vault ballast amount when Fig. 4 is parabola fixed arch arch springing increasing section strengthening construction.
Specific implementation mode
Vault ballast method for determination of amount when arch springing increasing section reinforces parabolic arch, the method are suitable for cross-section parabola
Fixed arch specifically includes following steps：
The first step obtains various parameter values by design drawing and construction scheme, including across footpath l, rise f, arch springing are cut
The level inclination of face tangent lineThe thickness t and width w of arch springing increasing section part, the unit weight γ of arch springing casting concretec, arch cut
Face Anti-pull-press rigidity EA and bending stiffness EI；
Second step obtains equivalent suspension cable with the arch (i.e. parabola) of catenary line approximate substitution original bridge using dichotomy
The arch constant a of line；
Third walks, and is remained unchanged as principle in arch springing increasing section strengthening construction with vault amount of deflection, establishes vault ballast
Measure GpIncrease the concrete square amount V poured in strengthened section with both sides arch springingc(both sides arch springing concrete symmetrically pours, VcFor both sides
Total side of concreting measures) one-to-one relationship formula, when according to the correspondence formula real-time control arch springing casting concrete
Vault ballast amount Gp。
Correspondence formula is：
In formula, the amount of deflection of crown section when v (x) is function unit power at the x of parabolic arch section；Using vault as origin
(0,0), is x-axis (to the left for just) along span of arch diameter direction, and rise direction is to be calculated under the coordinate system of y-axis (downwards for just)
Formula is v (x)=f (x)-k1f1(x)-k2f2(x)-k3f3(x)；V (0) indicates to be somebody's turn to do when parabolic arch crown section function unit power
The amount of deflection in section；Each parameter value is calculated by following formula in v (x) calculating formulas：
k1=c1/δ11
k2=c2/δ22
k3=c3/δ33
The above method is also applicable for variable cross-section parabola fixed 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 and third step.
For parabolic 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 parabola 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；Y ' is the first derivative of parabolic arch axial equation；X is to sit
Mark origin is located at the coordinate along across footpath direction of vault；L is across footpath；F is rise；R is the radius of skene arch；A encircles for catenary line
Shape parameter.
Relative to straight line and circular arc line, catenary line is then closer to parabola, and therefore, the present invention is approximate using catenary line
Substitute parabola.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 parabolic arch axis
Integral can be obtained the higher Approximate Explicit Solution of precision.The solution of parameter a can utilize dichotomy.According to parabolic 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 parabolic arch with catenary line, when deriving function unit power at parabolic 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
It is shown, parabolic equation y=4fx2/l2, arch section Anti-pull-press rigidity be EA, bending stiffness 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.Parabola, the simplification integrated to curve according to formula (4), it can be deduced that redundant force calculation formula solved are substituted with catenary line
Journey 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 Fig. 2, 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 deflection value 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 parabolic 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 cross-section parabola 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 l, the span of arch diameter 117.5m, rise 22.158m, section Anti-pull-press rigidity 2329804.38kN, bending stiffness
9552.1994kNm2, function unit load (1kN) on arch；Example 2, rise 39.5m, other parameters are the same as example l.This hair
Bright 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 0.40%, verification
Formula of the present invention, which calculates cross-section parabola fixed arch vault amount of deflection, has very high engineering precision.On this basis, by
Attached drawing 4 calculates separately vault amount of deflection h in concreting processcLower vault amount of deflection h is acted on vault ballastp, see formula (23) and
Formula (24).To simplify the calculation, vault ballast is reduced to act on the concentrated force of vault.
hp=Gpv(0) (24)
It is remained unchanged as principle in arch springing increasing section strengthening construction with vault amount of deflection, i.e., in arch springing casting concrete mistake
Always there is following formula establishment in journey：
hc=hp (25)
So, vault ballast amount GpIncrease the concrete square amount V poured in strengthened section with both sides arch springingc(both sides arch springing is mixed
Solidifying soil symmetrically pours, VcMeasured for total side of both sides concreting) then there is correspondences below：
In formula, the amount of deflection of crown section when v (x) is function unit power at the x of parabolic arch section.V (0) indicates parabolic arch
The amount of deflection in the section when function unit power of crown section.
Vault ballast amount G according to formula (26)pIncrease the concrete square amount V poured in strengthened section with both sides arch springingcOne
One corresponds to relational expression, then may be implemented in arch springing increasing section casting concrete in the process to the real-time control of vault counterweight.
Claims (3)
- Vault ballast method for determination of amount when 1. a kind of arch springing increasing section reinforces parabolic arch, it is characterised in that according to design drawing Paper and Design of Construction Organization obtain structure various parameter values, with catenary line approximate substitution parabola, are increased in arch springing with vault amount of deflection It is remained unchanged in big strengthened section construction as principle, establishes vault ballast amount GpIncrease in strengthened section with both sides arch springings and pours Concrete square amount VcOne-to-one relationship formula, vault ballast amount G when according to the relational expression real-time control arch springing casting concretep； The method is suitable for cross-section parabola fixed arch.
- 2. vault ballast method for determination of amount when arch springing increasing section according to claim 1 reinforces parabolic arch, special Sign is to include the following steps：The first step obtains various parameter values by design drawing and construction scheme, including across footpath l, rise f, arch springing section are cut The level inclination of lineThe thickness t and width w of arch springing increasing section part, the unit weight γ of arch springing casting concretec, arch section it is anti- Tension and compression rigidity EA and bending stiffness EI；Second step obtains the arch constant a of equivalent catenary line with the arch of catenary line approximate substitution original bridge using dichotomy；Third walks, and is remained unchanged as principle in arch springing increasing section strengthening construction with vault amount of deflection, establishes vault ballast amount GpWith Both sides arch springing increases the concrete square amount V poured in strengthened sectioncOne-to-one relationship formula, it is real-time according to the correspondence formula Vault ballast amount G when controlling arch springing casting concretep。
- 3. vault ballast method for determination of amount when arch springing increasing section according to claim 2 reinforces parabolic arch, special Sign is that the correspondence formula is：In formula, the amount of deflection of crown section when v (x) is function unit power at the x of parabolic arch section；Using vault as origin (0,0), It is x-axis along span of arch diameter direction, rise direction is under the coordinate system of y-axis, and calculation formula is v (x)=f (x)-k1f1(x)- k2f2(x)-k3f3(x)；V (0) indicates the amount of deflection in section when parabolic arch crown section function unit power；In v (x) calculating formulas Each parameter value is calculated by following formula：k1=c1/δ11k2=c2/δ22k3=c3/δ33
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| CN116383942A (en) * | 2023-04-07 | 2023-07-04 | 浙江大学 | Design method and device of main arch structure |
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