CN111506953A - Optimization design method of triangular hanging basket - Google Patents
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Abstract
The invention discloses an optimal design method of a triangular hanging basket, which comprises the following steps: 1) the manufacturing cost of the triangular hanging basket is measured by steel quantity, and a cost model of the triangular hanging basket is constructed: 2) constructing a safety constraint condition of the triangular cradle under the condition of the structural safety of the triangular cradle; 3) and (3) aiming at the minimum steel consumption of the triangular cradle, optimizing and solving by adopting a genetic algorithm to obtain the design size parameters of the triangular cradle and draw up the sizes of all components. According to the method for optimally designing the triangular cradle, the manufacturing cost of the triangular cradle is measured by the steel amount of the triangular cradle, the safety constraint condition of the structure safety of the triangular cradle is combined, the genetic algorithm is utilized to optimally solve the steel amount of the triangular cradle, and then design size parameters of each component when the economy of the triangular cradle is optimal are obtained, so that the structural safety and the structural economy are met, the method has the advantages of better universality and universality, and the design requirements of the ultra-wide and ultra-large bearing capacity cradle can be met.
Description
Technical Field
The invention belongs to the technical field of bridge construction and construction, and particularly relates to an optimal design method of a triangular hanging basket.
Background
In the construction of a large-span continuous beam of a bridge, a cantilever casting method taking a hanging basket as main construction equipment is an important construction method and is also a construction method which is applied more at present. The hanging basket is one of the important equipment in cantilever construction, and the construction technology is mature at present. However, with the development of the urbanization process in China, the traffic volume of cities is increased rapidly, and the width of newly built bridges in cities is increased more and more. The increase of concrete box girder bridge width must lead to the width and the bearing capacity's of hanging the basket of usefulness of cantilever casting increase, and traditional, ripe design is hung the basket and probably can't satisfy the cast-in-place construction requirement of super wide box girder, and the development of super wide, super large bearing capacity is hung the basket and also becomes one of the key problem that must face and solve in the construction of city beam bridge cantilever casting gradually.
Some theoretical researches and engineering practices have been developed for the basket hanging optimization design of the wide bridge in China. Theoretical research indicates that the strength design of the current hanging basket is slightly conservative, and the optimization space of the hanging basket design is large; engineering practice is mainly to design or optimize the hanging basket used in a specific project, such as: the number and the positions of the anchor rod pieces behind the cradle are optimized, so that the economy of the cradle is better, and the stress of the arch ring sections is more uniform; in order to balance the height difference of the cross slope of the bridge floor, the triangular hanging basket is transformed into a special-shaped hanging basket, and the included angle between the diagonal rods and the horizontal direction and the design of the upper cross beam and the lower cross beam are optimized, so that the problem of overlarge deflection of the lower cross beam of the wide box girder is solved; in order to improve the local stress of the front support point hanging basket, a novel structure of a track type sliding rail, an anchoring type thrust device, an inverted triangle pivoting inverted top wheel and the like in the extension bar body is provided.
The current hanging basket optimization design method has the following defects:
(1) most of the existing hanging basket optimization design methods rely on a certain actual project, a certain parameter of the hanging basket is analyzed independently, or certain parts of the hanging basket are specially designed to achieve the purpose of optimization design, and the individuality and pertinence of research results are strong;
(2) at present, the basket optimization analysis mainly focuses on the safety checking calculation of the basket, the game between the safety and the economy of the basket main truss is not considered, and in addition, the research results about the value and combination problems among the most main design parameters (the height of a stand column and the section form of a member) of the basket main truss are relatively few.
(3) At present, the use of the construction hanging basket in China is basically that a construction party uses one hanging basket according to the requirements of project departments, the hanging basket cannot be reused basically after the completion of the project, and the methods waste materials and prolong the preparation work in the early stage of the construction.
Disclosure of Invention
In view of the above, the invention aims to provide an optimized design method of a triangular cradle, which solves the problem that the existing triangular cradle design is not sufficient in consideration of structural economy, has the advantages of better universality and universality, and can meet the design requirements of ultra-wide and ultra-large bearing capacity cradles.
In order to achieve the purpose, the invention provides the following technical scheme:
an optimal design method of a triangular hanging basket comprises the following steps:
1) the manufacturing cost of the triangular hanging basket is measured by steel quantity, and a cost model of the triangular hanging basket is constructed:
2) constructing a safety constraint condition of the triangular cradle under the condition of the structural safety of the triangular cradle;
3) and (3) aiming at the minimum steel consumption of the triangular cradle, optimizing and solving by adopting a genetic algorithm to obtain the design size parameters of the triangular cradle and draw up the sizes of all components.
Further, the cost model of the triangular hanging basket is as follows:
wherein S iscThe steel consumption of the triangular hanging basket is increased; n is the number of trusses of the main truss of the triangular hanging basket; rho is the density of the steel material; h is the height of the main truss column; a. thecIs the cross-sectional area of the main truss column; l is the distance between the intersection point of the main longitudinal beam and the inclined pulling belt and the intersection point of the main longitudinal beam and the main truss upright post; a. therL is the cross-sectional area of the diagonal draw beltgIs the length of the main stringer; a. thegIs the cross-sectional area of the main longitudinal beam; hsThe length of the front sling; a. thesIs the sum of the cross-sectional areas of all the front straps.
Further, the safety constraint conditions are as follows:
Nc≤Pcr
wherein sigma is the maximum stress of each component of the triangular cradle; sigmacIs the stress value of the main truss column; n is a radical ofcIs the axial force of the main truss column; sigmarThe stress value of the inclined pulling belt is obtained; n is a radical ofrThe axial force of the inclined pull belt; sigmagThe stress value of the main longitudinal beam; n is a radical ofgIs the axial force of the main longitudinal beam; mgBending moment of the main longitudinal beam; wgThe bending-resistant section coefficient of the main longitudinal beam; f is the design value of tensile strength, compression strength and bending strength of the steel; pcrIs the euler critical force of the upright column; sigmasThe stress value of the front sling; n is a radical ofsThe total axial force for all front straps; sigma0The maximum stress value allowed for the front sling; delta is the total deformation of the triangular hanging basket; deltatThe deformation of the main truss; e is the Young modulus of steel used for the triangular hanging basket; delta0The maximum deformation allowed by the triangular hanging basket.
Further, the stress value of the main truss column is as follows:
the stress value of the inclined pull belt is as follows:
the stress value of the main longitudinal beam is as follows:
wherein θ is arctan (l/H); f is the vertical force transmitted to the main truss by the front sling; delta l is the horizontal distance between the front intersection point of the main longitudinal beam and the diagonal draw and the front upper cross beam; wgThe bending-resistant section coefficient of the main longitudinal beam;
the axial force of the inclined pull belt is as follows:
wherein, IgIs the moment of inertia of the main stringer;
further, the self weight of the beam section to be cast is simplified into a concentrated load G acting on the mass center of the beam section, and the total axial force N of all front hanging strips can be calculated according to the lever principlesAnd all the main trusses with the triangular hanging basket equally divide the dead weight of the beam section to be cast, and then the front hanging strip transmits the vertical force to the main trusses as follows:
wherein n is the number of trusses of the main truss of the triangular hanging basket, L is the length of the box girder segment under the worst working condition, and the horizontal distance between the lower supporting point of the triangular hanging basket and the rear end of the box girder is delta L.
Further, euler critical force of the main truss upright post of the axis compression rod piece with hinged two ends is as follows:
therein, ζ1Is the coefficient of moment of inertia.
Further, the total deformation of the triangular hanging basket is composed of the deformation of the front hanging strip and the deformation of the main truss, the deformation of the front hanging strip is obtained by calculating the axial force borne by the front hanging strip, the deformation of the main truss is obtained by calculating according to the virtual displacement principle, namely the total deformation of the triangular hanging basket is:
therein, ζ1Is the coefficient of moment of inertia.
Further, each component of basket is hung to triangle adopts square steel or double pin channel-section steel to make, simplifies the double pin channel-section steel into square steel and establishes the η times of square steel wall thickness for its length of side, then:
the bending-resistant section coefficient of the square steel is as follows:
the moment of inertia of the square steel is as follows:
I＝ζ1A2
in the formula (I), the compound is shown in the specification,
further, in the step 2), for the front sling, there are also size constraints:
wherein n issNumber of front straps, phiminIs the smallest nominal diameter of the front sling.
Further, the front straps also have a maximum size constraint:
wherein phi ismaxIs the maximum nominal diameter of the front sling.
The invention has the beneficial effects that:
according to the method for optimally designing the triangular cradle, the manufacturing cost of the triangular cradle is measured by the steel amount of the triangular cradle, the safety constraint condition of the structure safety of the triangular cradle is combined, the steel amount of the triangular cradle is optimally solved by using a genetic algorithm, and then design size parameters of each component when the economy of the triangular cradle is optimal are obtained.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a schematic structural view of a triangular hanging basket;
FIG. 2 is a schematic diagram of a simplified model of a main truss;
FIG. 3 is a schematic diagram of a simplified model base architecture of a main truss;
fig. 4 is a reference diagram of a use state when a triangular hanging basket is arranged on a high home garden compound line bridge.
Detailed Description
The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.
The optimal design method of the triangular hanging basket comprises the following steps:
1) and measuring the manufacturing cost of the triangular hanging basket by using the steel quantity to construct a cost model of the triangular hanging basket. Specifically, the cost model of the triangular hanging basket of the embodiment is as follows:
in order to reduce the steel consumption as much as possible on the premise of ensuring the structure safety so as to reduce the manufacturing cost of the cradle, the steel consumption S of the cradle is definedcFor the objective function: wherein S iscThe steel consumption of the triangular hanging basket is increased; n is the number of trusses of the main truss of the triangular hanging basket; rho is the density of the steel material; h is the height of the main truss column; a. thecIs the cross-sectional area of the main truss column; is mainlyThe distance between the intersection point of the longitudinal beam and the inclined pull belt and the intersection point of the main longitudinal beam and the main truss upright post; a. therL is the cross-sectional area of the diagonal draw beltgIs the length of the main stringer; a. thegIs the cross-sectional area of the main longitudinal beam; hsThe length of the front sling; a. thesIs the sum of the cross-sectional areas of all the front straps.
2) And constructing the safety constraint condition of the triangular cradle under the condition of the structural safety of the triangular cradle. The safety constraint conditions of this embodiment are:
Nc≤Pcr
specifically, in order to ensure the safety of the cradle structure, the working stress and deformation of the cradle need to be limited, and the main truss maximum stress value sigma is set in the embodimentmaxF is less than or equal to f, and f is the design value of tensile strength, compression strength and bending strength of the steel; the front suspender is made of PSB830 finish-rolled deformed steel bar and has stress value sigmas≤σ0415 MPa; the total deformation delta of the cradle is less than or equal to delta0Three constraints of 20 mm. In addition, in order to ensure the stability of the cradle compression member, the present embodiment sets the axial force value N of the axial compression member columnc≤Pcr. Specifically, the euler critical force of the main truss upright post of the axis compression rod piece with two hinged ends is as follows:
therein, ζ1Is the coefficient of moment of inertia; sigma is the maximum stress of each component of the triangular hanging basket; sigmacIs the stress value of the main truss column; n is a radical ofcIs the axial force of the main truss column; sigmarIs inclined toThe stress value of the drawstring; n is a radical ofrThe axial force of the inclined pull belt; sigmagThe stress value of the main longitudinal beam; n is a radical ofgIs the axial force of the main longitudinal beam; mgBending moment of the main longitudinal beam; wgThe bending-resistant section coefficient of the main longitudinal beam; f is the design value of tensile strength, compression strength and bending strength of the steel; pcrIs the euler critical force of the upright column; sigmasThe stress value of the front sling; n is a radical ofsThe total axial force for all front straps; sigma0The maximum stress value allowed for the front sling; delta is the total deformation of the triangular hanging basket; deltatThe deformation of the main truss; e is the Young modulus of steel used for the triangular hanging basket; delta0The maximum deformation allowed by the triangular hanging basket.
3) And (3) aiming at the minimum steel consumption of the triangular cradle, optimizing and solving by adopting a genetic algorithm to obtain the design size parameters of the triangular cradle and draw up the sizes of all components. Specifically, the components needing sizing comprise a main longitudinal beam, a main truss upright post, a diagonal draw belt and a front hanging belt. The embodiment uses matlab genetic algorithm toolbox to carry out optimization solution on the objective function.
Among the dimensions of each component to be planned, the design parameters include:
girder length L of main girdergDetermined by the longest box girder segment that is cantilever-cast; cross-sectional area A of main stringerg；
Height H of the main truss column; cross-sectional area A of main truss columnc；
Cross-sectional area A of diagonal cabler；
Number n of front bracessDetermined by the width of the box girder; length H of front slingsThe height of the box girder segment under the worst working condition is determined; sum of cross-sectional areas of all front harnesses As。
Wherein, basic parameters in the design of the triangular hanging basket comprise:
the number n of the trusses of the main trusses is determined by the positions and the number of the box girder webs, and the main trusses and the box girder webs are arranged in a one-to-one correspondence mode;
number n of front bracessDetermined by the width of the box girder;
the dead weight G of the box girder segment in the worst working condition;
length H of front slingsThe height of the box girder segment under the worst working condition is determined;
box beam segment length at worst case L;
main rail length LgDetermined by the longest box girder segment that is cantilever-cast;
the distance l between the intersection point of the main longitudinal beam and the diagonal draw belt and the intersection point of the main longitudinal beam and the main truss upright post;
the horizontal distance delta l between the front intersection point of the main longitudinal beam and the diagonal draw and the front upper cross beam;
the horizontal distance delta L between the lower supporting point of the cradle and the rear end of the box girder.
Specifically, the stress value of the main truss column is as follows:
the stress value of the inclined pull belt is as follows:
the stress value of the main longitudinal beam is as follows:
wherein θ is arctan (l/H); f is the vertical force transmitted to the main truss by the front sling; delta l is the horizontal distance between the front intersection point of the main longitudinal beam and the diagonal draw and the front upper cross beam; wgThe bending-resistant section coefficient of the main longitudinal beam;
the dead weight of the beam section to be cast is simplified into a concentrated load G acting on the mass center of the beam section, and the total axial force N of all front hanging strips can be calculated according to the lever principlesAnd all the main trusses with the triangular hanging basket equally divide the dead weight of the beam section to be cast, and then the front hanging strip transmits the vertical force to the main trusses as follows:
wherein n is the number of trusses of the main truss of the triangular hanging basket, L is the length of the box girder segment under the worst working condition, and the horizontal distance between the lower supporting point of the Δ L hanging basket and the rear end of the box girder.
After the vertical force transmitted to the main truss by the front hanging strip is obtained, the stress model of the main truss of the triangular hanging basket is converted into a primary statically indeterminate plane rod system structure shown in figure 2, a basic system shown in figure 3 is used, a mechanical equation of a diagonal draw bar of the main truss is established by using deformation coordination conditions, and the axial force N of the diagonal draw bar ad can be obtained after solutionr. Namely, the axial force of the inclined pull belt is as follows:
wherein, IgIs the moment of inertia of the main stringer;
when N is presentrWhen the vertical component is less than F, the maximum bending moment of the longitudinal beam is located at the junction position of the main longitudinal beam and the upright column, and the size is as follows: f (l + Deltal) -Nrl cos θ; and otherwise, the maximum bending moment value of the main longitudinal beam is positioned at the junction position of the main longitudinal beam and the right inclined pulling belt and is F delta l.
Specifically, the total deformation of basket is hung to triangle comprises the deflection of preceding suspender and the deflection of main truss, and the deflection of preceding suspender is calculated by its axial force that receives and is obtained, and the deflection of main truss adopts the virtual displacement principle to calculate and obtains, and the total deformation of basket is hung to triangle promptly becomes:
therein, ζ1Is the coefficient of moment of inertia.
Furthermore, each component of the triangular hanging basket is made of square steel or double-spliced channel steel, the double-spliced channel steel is simplified into the square steel, the wall thickness of the square steel is η times of the side length of the square steel, and bending-resistant section coefficients W and inertia moments I of the square steel pipe can be expressed as functions of sectional areas A through derivation of section characteristics
The bending-resistant section coefficient of the square steel is as follows:
the moment of inertia of the square steel is as follows:
I＝ζ1A2
in the formula (I), the compound is shown in the specification,
then:
further, in step 2), the present embodiment also has a minimum size constraint condition for the front suspension strap:
wherein n issNumber of front straps, phiminIs the smallest nominal diameter of the front sling.
The front straps also have maximum size constraints:
wherein phi ismaxIs the maximum nominal diameter of the front sling.
If the maximum cross-sectional area of all the front hanging strips is not limited, the economical efficiency of the optimized result can be improved to a greater extent. If the maximum cross-sectional area of all the front suspension straps exceeds the specification, the front suspension straps at the two ends of the cross beam can be made of steel plates to complement the maximum cross-sectional area.
Specifically, the constraint conditions of the cross-sectional areas of all the front straps in this embodiment are as follows:
H＝4.73m
As＝0.0196m2
wherein phi ismin＝0.018m，φmax＝0.050m。
The optimal design method of the triangular hanging basket of the embodiment measures the manufacturing cost of the triangular hanging basket by using the steel amount of the triangular hanging basket, combines the safety constraint condition of the structure safety of the triangular hanging basket, optimizes and solves the steel amount of the triangular hanging basket by using a genetic algorithm, and further obtains the design size parameters of each component when the economical efficiency of the triangular hanging basket is optimal, and the triangular hanging basket designed by adopting the optimal design method of the triangular hanging basket of the embodiment meets the structural safety and the structural economical efficiency, has the advantages of better universality and universality, and can meet the design requirements of ultra-wide and ultra-large bearing capacity hanging baskets.
The following describes an optimal design method of the triangular hanging basket according to the embodiment with reference to a specific engineering example.
The triangular hanging basket in the balanced cantilever construction of the complex bridge of the Chongqing Gao garden bridge is optimally designed by using the optimal design method of the triangular hanging basket.
As shown in figure 4, the high home garden bridge compound line bridge is a three-span prestressed continuous rigid frame bridge with span of 140+240+140m, the main beam adopts a single-box double-chamber section, the top plate width of the box beam is 25m, the bottom width is 16m, the cantilever length of the flange plates at two sides is 4.5m, the end part thickness of the cantilever plate is 20cm, the root part thickness is 70cm, the thickness of the top plate in the box chamber is 0.32m, and the thickness of the bottom plate is changed from 1.5m of the root part of the box beam to 0.32m in the span.
During cantilever casting construction, the single-box double-chamber box girder is integrally cast into a box by using a hanging basket at one time, and as the section width reaches 25m and the weight of a No. 1 block with the length L of 2.5m reaches 484.6 tons, the traditional hanging basket cannot meet the construction requirements easily, a hanging basket main girder structure needs to be designed independently, referring to relevant parameters of the traditional triangular hanging basket, the main girder is preliminarily selected to be composed of 3 main girders, the height of the main girder is 4.4m, and the length of the main girder is Lg12.2m main longitudinal beam selects double-spliced I63b HWord steel (A)g＝0.040m2) The upright post and the inclined pull belt adopt double-spliced C40a channel steel (A)c＝Ar＝0.021m2) The front sling adopts 8 pieces of finish-rolled deformed steel with the diameter of 32mm as a middle sling and a steel plate with the diameter of 120mm × 30mm as two side slings (the total cross-sectional area N of the front slings＝0.0136m2) The total steel consumption of the main truss and the front suspension band is 22.15 t. The arrangement of the triangular hanging basket is shown in figure 4.
After the optimal design method of the triangular hanging basket is adopted for optimal design, the optimal design result is as follows:
the optimum design parameter of the hanging basket is H4.73 m and Ag＝0.0157m2、Ac＝0.0212m2、Ar＝0.0163m2、As＝0.0196m2The size of the component can be determined as follows, the main longitudinal beam is 400m × 400mm × 11mm square steel tube (A)g＝0.0171m2) The main truss column is a square steel pipe (A) with the thickness of 400mm × 400mm × 14mmc＝0.0216m2) The diagonal draw belt is a square steel pipe (A) with the thickness of 400m × 400mm × 11mm (A)r＝0.0171m2) The sling is 10 pieces of finish-rolled deformed steel bar with the diameter of 50mm (total cross-sectional area A)sIs 0.0196m2)。
In order to embody the optimization effect of the invention, the following table shows the stress, the Euler critical force and the integral deformation of each component of the front and rear hanging baskets optimized by using a genetic algorithm.
The mathematical model result before optimization is the structural parameters of the triangular cradle designed by the existing method, the mathematical model result after optimization is the structural parameters of the triangular cradle designed by the optimal design method of the triangular cradle of the embodiment, and the Midas model result after optimization is the calculation result of the Midas finite element model established based on the structural parameters of the triangular cradle obtained by the optimal design method of the embodiment. Through comparison before and after optimization, under the condition that the structural safety can still be guaranteed, the steel consumption of the optimized triangular hanging basket is reduced by 32%, and the optimization effect is obvious; comparing the calculation results of the optimized mathematical model and the Midas model, the calculation result of the structural response in the optimized model of the embodiment is substantially the same as the calculation result of the Midas finite element model, and the correctness of the optimized design method of the triangular cradle of the embodiment is proved.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. An optimal design method of a triangular hanging basket is characterized in that: the method comprises the following steps:
1) the manufacturing cost of the triangular hanging basket is measured by steel quantity, and a cost model of the triangular hanging basket is constructed:
2) constructing a safety constraint condition of the triangular cradle under the condition of the structural safety of the triangular cradle;
3) and (3) aiming at the minimum steel consumption of the triangular cradle, optimizing and solving by adopting a genetic algorithm to obtain the design size parameters of the triangular cradle and draw up the sizes of all components.
2. The optimal design method of the triangular hanging basket according to claim 1, characterized in that: the cost model of the triangular hanging basket is as follows:
wherein S iscThe steel consumption of the triangular hanging basket is increased; n is the number of trusses of the main truss of the triangular hanging basket; rho is the density of the steel material; h is the height of the main truss column; a. thecIs the cross-sectional area of the main truss column; l is the distance between the intersection point of the main longitudinal beam and the inclined pulling belt and the intersection point of the main longitudinal beam and the main truss upright post; a. therL is the cross-sectional area of the diagonal draw beltgIs the length of the main stringer; a. thegIs the cross-sectional area of the main longitudinal beam; hsThe length of the front sling; a. thesIs a stand forThere is a sum of the cross-sectional areas of the front straps.
3. The optimal design method of the triangular hanging basket according to claim 1, characterized in that: the safety constraint conditions are as follows:
Nc≤Pcr
wherein sigma is the maximum stress of each component of the triangular cradle; sigmacIs the stress value of the main truss column; n is a radical ofcIs the axial force of the main truss column; sigmarThe stress value of the inclined pulling belt is obtained; n is a radical ofrThe axial force of the inclined pull belt; sigmagThe stress value of the main longitudinal beam; n is a radical ofgIs the axial force of the main longitudinal beam; mgBending moment of the main longitudinal beam; wgThe bending-resistant section coefficient of the main longitudinal beam; f is the design value of tensile strength, compression strength and bending strength of the steel; pcrIs the euler critical force of the upright column; sigmasThe stress value of the front sling; n is a radical ofsThe total axial force for all front straps; sigma0The maximum stress value allowed for the front sling; delta is the total deformation of the triangular hanging basket; deltatThe deformation of the main truss; e is the Young modulus of steel used for the triangular hanging basket; delta0The maximum deformation allowed by the triangular hanging basket.
4. The optimal design method of the triangular hanging basket according to claim 3, characterized in that:
the stress value of the main truss column is as follows:
the stress value of the inclined pull belt is as follows:
the stress value of the main longitudinal beam is as follows:
wherein θ is arctan (l/H); f is the vertical force transmitted to the main truss by the front sling; delta l is the horizontal distance between the front intersection point of the main longitudinal beam and the diagonal draw and the front upper cross beam; wgThe bending-resistant section coefficient of the main longitudinal beam;
the axial force of the inclined pull belt is as follows:
wherein, IgIs the moment of inertia of the main stringer;
5. the optimal design method of the triangular hanging basket according to claim 4, characterized in that: the dead weight of the beam section to be cast is simplified into a concentrated load G acting on the mass center of the beam section, and the total axial force N of all front hanging strips can be calculated according to the lever principlesAnd all the main trusses with the triangular hanging basket equally divide the dead weight of the beam section to be cast, and then the front hanging strip transmits the vertical force to the main trusses as follows:
wherein n is the number of trusses of the main truss of the triangular hanging basket, L is the length of the box girder segment under the worst working condition, and the horizontal distance between the lower supporting point of the triangular hanging basket and the rear end of the box girder is delta L.
6. The optimal design method of the triangular hanging basket according to claim 3, characterized in that: the euler critical force of the main truss upright post of the axis compression rod piece with two hinged ends is as follows:
therein, ζ1Is the coefficient of moment of inertia.
7. The optimal design method of the triangular hanging basket according to claim 3, characterized in that: the total deformation of basket is hung to triangle comprises the deflection of preceding suspender and the deflection of main truss, and the deflection of preceding suspender is calculated by its axial force that receives and is obtained, and the deflection of main truss adopts the virtual displacement principle to calculate and obtains, and the total deformation of basket is hung to triangle promptly becomes:
therein, ζ1Is the coefficient of moment of inertia.
8. The optimal design method of the triangular hanging basket according to any one of claims 3 to 7, wherein each component of the triangular hanging basket is made of square steel or double-spliced channel steel, the double-spliced channel steel is simplified into the square steel, and the wall thickness of the square steel is η times of the side length of the square steel, then:
the bending-resistant section coefficient of the square steel is as follows:
the moment of inertia of the square steel is as follows:
I＝ζ1A2
in the formula (I), the compound is shown in the specification,
9. the optimal design method of the triangular hanging basket according to claim 1, characterized in that: in the step 2), the front sling is also provided with a size constraint condition:
wherein n issNumber of front straps, phiminIs the smallest nominal diameter of the front sling.
10. The optimal design method of the triangular hanging basket according to claim 9, characterized in that: the front straps also have maximum size constraints:
wherein phi ismaxIs the maximum nominal diameter of the front sling.
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