CN113536527A - Algorithm considering influence of live load of multi-line travelling crane on external force of pier section - Google Patents
Algorithm considering influence of live load of multi-line travelling crane on external force of pier section Download PDFInfo
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Abstract
The invention discloses an algorithm for considering influence of live load of a multi-line travelling crane on external force of a pier section, which comprises the following steps of: respectively determining the number of lines and the offset distance of a double-line running train unit and a single-line running train unit by taking a bridge pier as a center; analyzing the longitudinal train load of the bridge pier to obtain the worst live load arrangement diagram, and recording the corresponding support reaction force; the two groups of transverse driving modes and the four longitudinal live load arrangement drawings are combined into eight kinds of live load control working conditions; solving the vertical force and the longitudinal bending moment of the pier section under each live load working condition; solving the transverse bending moment of the pier section under each live load working condition; and (3) synthesizing the vertical force, the longitudinal bending moment and the transverse bending moment of the cross section of the pier, and finally calculating the influence of the live load of the multi-line travelling crane on the external force of the cross section of the pier. Aiming at the influence of live load of a multi-line travelling crane on external force of the section of the pier, the method is popularized to the longitudinal direction and the transverse direction on the basis of the support counterforce calculated by a live load diagram of a single-line longitudinal train, and the external force of the section of the pier is accurately calculated.
Description
Technical Field
The invention belongs to the technical field of bridge engineering in the traffic transportation industry, and particularly relates to an algorithm considering influence of live load of a multi-line traveling vehicle on external force of a pier section.
Background
With the continuous improvement of bridge design and construction level, bridges often appear at stations or turnouts, so that the calculation of multi-line bridges is more and more. Usually, the beam and the pier are designed separately, the personnel designing the beam can provide the maximum and minimum live loads of each support to the personnel designing the pier, and the personnel designing the pier can combine the worst live load working condition by using the reaction force of the supports, but the maximum live load reaction force of each support is not generated simultaneously, so that a greater safety degree exists in the design. In order to accurately calculate the influence of multi-line live load on the external force of the section of the pier and match with the existing single-double line pier design program, an algorithm with clear thought and simple and convenient operation needs to be matched with the previous single-double line pier design program to solve the calculation problem of the live load on the external force of the section of the pier.
Disclosure of Invention
The invention is provided for solving the problems in the prior art, and aims to provide an algorithm for considering the influence of live load of a multi-line travelling crane on the external force of the section of a pier.
The technical scheme of the invention is as follows: an algorithm for considering influence of live load of a multi-line travelling crane on external force of a section of a pier comprises the following steps:
A. analyzing the position relation of the transverse direction of the bridge pier and multiple lines by taking the bridge pier as a center, and respectively determining the line number and the offset distance of the double-line traveling crane group and the single-line traveling crane group
The bridge pier is transversely vertical to train running, and the offset distance is the distance between the vertical resultant force acting point of the running set and the center of the bridge pier, wherein the double-line running set comprises n2 lines, the offset distance is E2, the single-line running set comprises n1 lines, and the offset distance is E1;
B. analyzing the longitudinal train load of the pier to obtain the worst live load arrangement diagram, namely a double-hole heavy load, a double-hole light load, a single-hole heavy load and a single-hole light load, and recording the corresponding counter force of the support
The longitudinal direction of the pier is the train running direction, the pier is provided with two supports longitudinally, the counterforce of the left support is R2, the counterforce of the right support is R3, and the sizes of R2 and R3 are solved according to a live load arrangement diagram;
C. the transverse two groups of driving modes and the longitudinal four live load arrangement diagrams can be combined into eight kinds of live load control working conditions, and calculation is required to be carried out according to the eight kinds of live load working conditions
Two groups of driving modes are obtained in the step A, and four live load layout drawings are obtained in the step B;
D. according to the position of the longitudinal support and the counter force of the support, the vertical force and the longitudinal bending moment of the pier section under each live load working condition are obtained
In the longitudinal direction of the bridge pier, the distance from the left support to the center of the bridge pier is a2, the distance from the right support to the center of the bridge pier is a3, the vertical force of the cross section of the bridge pier is N, and the longitudinal bending moment is M1;
E. calculating the transverse bending moment of the pier section under each live load working condition by the transverse traveling block set and the support counterforce
The transverse bending moment of the cross section of the pier is M2;
F. and (3) synthesizing the vertical force, the longitudinal bending moment and the transverse bending moment of the section of the pier, and finally calculating the influence of the live load of the multi-line traveling crane on the external force of the section of the pier.
Furthermore, in the step C, the influence of live load on the section of the pier is considered from the longitudinal direction and the transverse direction respectively under eight live load working conditions, and the worst load under the conditions of large eccentric stress and small eccentric stress is enveloped according to the principles of maximum vertical force, maximum bending moment, minimum vertical force and maximum bending moment.
Furthermore, in the step a, the double-line traveling set is used for obtaining the maximum vertical force of the section of the pier under the live load working condition, so that n2 is the total number of multiple lines, and the single-line traveling set is used for obtaining the maximum transverse bending moment of the section of the pier under the live load working condition, the magnitude of n 1. E1 of the two transverse sides of the pier is compared, and the railway line on the side of the maximum value is taken as the single-line traveling set.
Furthermore, in step B, four live load layout diagrams are shown, which include the following details:
the live load layout diagram of the double-hole heavy load is used for solving the maximum value of R2+ R3;
the live load arrangement diagram of the double-hole light load aims to solve the problem that R2+ R3 are the minimum when the left and right hole beams at the top of the pier bear the maximum vertical force;
the live load layout diagram of the single-hole heavy load is used for solving the maximum value of R2;
r2 of the single-hole light load is the counter force of the support at the other end of the beam when the load is distributed according to the single-hole heavy load;
furthermore, the eight load conditions in step C are as follows: the double-line traveling crane group + double-hole heavy load, the double-line traveling crane group + double-hole light load, the double-line traveling crane group + single-hole heavy load, the double-line traveling crane group + single-hole light load, the single-line traveling crane group + double-hole heavy load, the single-line traveling crane group + double-hole light load, the single-line traveling crane group + single-hole heavy load, and the single-line traveling crane group + single-hole light load.
Furthermore, the vertical force and the longitudinal bending moment of the section of the pier in the step D are calculated respectively according to eight load working conditions.
Furthermore, the transverse bending moment of the pier section in the step E is calculated respectively according to eight load working conditions.
The invention has the following beneficial effects:
aiming at the influence of live load of the multi-line travelling crane on the external force of the section of the pier, the method is popularized to the longitudinal direction and the transverse direction on the basis of the support counterforce calculated by the live load diagram of the single-line longitudinal train, the external force of the section of the pier generated by the live load of the multi-line travelling crane is accurately calculated, the method is more economical compared with the traditional design method, the algorithm is transplanted to the original single-double-line pier calculation program, and the problem of quick and accurate calculation of the multi-line pier is solved.
The method can be used for calculating the sections of different types of piers in the field of transportation, such as railways, highways, municipal works, light rails and the like, and can correctly consider the contribution value of live load of multi-line traveling to the external force of the pier sections.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a transverse front view of a bridge pier according to the present invention;
FIG. 3 is a transverse plan view of a bridge pier according to the present invention;
fig. 4 is a longitudinal parameter diagram of a pier in the present invention.
Detailed Description
The present invention is described in detail below with reference to the accompanying drawings and examples:
as shown in fig. 1 to 4, a calculation method for considering influence of live load of multi-line traveling crane on external force of a pier section comprises the following steps:
A. analyzing the position relation of the transverse direction of the bridge pier and multiple lines by taking the bridge pier as a center, and respectively determining the line number and the offset distance of the double-line traveling crane group and the single-line traveling crane group
The bridge pier is transversely vertical to train running, and the offset distance is the distance between the vertical resultant force acting point of the running set and the center of the bridge pier, wherein the double-line running set comprises n2 lines, the offset distance is E2, the single-line running set comprises n1 lines, and the offset distance is E1;
B. analyzing the longitudinal train load of the pier to obtain the worst live load arrangement diagram, namely a double-hole heavy load, a double-hole light load, a single-hole heavy load and a single-hole light load, and recording the corresponding counter force of the support
The longitudinal direction of the pier is the train running direction, the pier is provided with two supports longitudinally, the counterforce of the left support is R2, the counterforce of the right support is R3, and the sizes of R2 and R3 are solved according to a live load arrangement diagram;
C. the transverse two groups of driving modes and the longitudinal four live load arrangement diagrams can be combined into eight kinds of live load control working conditions, and calculation is required to be carried out according to the eight kinds of live load working conditions
Two groups of driving modes are obtained in the step A, and four live load layout drawings are obtained in the step B;
D. according to the position of the longitudinal support and the counter force of the support, the vertical force and the longitudinal bending moment of the pier section under each live load working condition are obtained
In the longitudinal direction of the bridge pier, the distance from the left support to the center of the bridge pier is a2, the distance from the right support to the center of the bridge pier is a3, the vertical force of the cross section of the bridge pier is N, and the longitudinal bending moment is M1;
E. calculating the transverse bending moment of the pier section under each live load working condition by the transverse traveling block set and the support counterforce
The transverse bending moment of the cross section of the pier is M2;
F. and (3) synthesizing the vertical force, the longitudinal bending moment and the transverse bending moment of the section of the pier, and finally calculating the influence of the live load of the multi-line traveling crane on the external force of the section of the pier.
And C, considering the influence of live load on the section of the pier respectively in the longitudinal direction and the transverse direction under the eight live load working conditions in the step C, and enveloping the worst load under the conditions of large eccentric stress and small eccentric stress according to the principles of maximum vertical force, maximum bending moment, minimum vertical force and maximum bending moment.
In the step A, the double-line travelling crane group is used for obtaining the maximum vertical force of the section of the pier under the live load working condition, so n2 is the total number of multiple lines, the single-line travelling crane group is used for obtaining the maximum transverse bending moment of the section of the pier under the live load working condition, the magnitude of n 1. E1 of the two transverse sides of the pier is compared, and the railway line on the side with the maximum value is taken as the single-line travelling crane group.
In the step B, four live load layout drawings are shown, and the specific contents are as follows:
the live load layout diagram of the double-hole heavy load is used for solving the maximum value of R2+ R3;
the live load arrangement diagram of the double-hole light load aims to solve the problem that R2+ R3 are the minimum when the left and right hole beams at the top of the pier bear the maximum vertical force;
the live load layout diagram of the single-hole heavy load is used for solving the maximum value of R2;
r2 of the single-hole light load is the counter force of the support at the other end of the beam when the load is distributed according to the single-hole heavy load;
the eight load conditions in the step C are respectively as follows: the device comprises a double-line traveling vehicle group and a double-hole heavy load, a double-line traveling vehicle group and a double-hole light load, a double-line traveling vehicle group and a single-hole heavy load, a double-line traveling vehicle group and a single-hole light load, a single-line traveling vehicle group and a double-hole heavy load, a single-line traveling vehicle group and a double-hole light load, a single-line traveling vehicle group and a single-hole heavy load, and a single-line traveling vehicle group and a single-hole light load.
And D, respectively calculating the vertical force and the longitudinal bending moment of the section of the pier in the step D aiming at eight load working conditions.
The calculation formulas of the vertical force N and the longitudinal bending moment M1 in the step D are as follows:
the calculation formula of the double-line running set + double-hole heavy load and the double-line running set + double-hole light load is as follows:
N＝n2(R2+R3)，M1＝n2(R2·a2-R3·a3)
the double-line running set + single-hole heavy load and the double-line running set + single-hole light load are calculated according to the following formula:
N＝n2·R2，M1＝n2·R2·a2
the single-line running set + double-hole heavy load and the single-line running set + double-hole light load are calculated according to the following formula:
N＝n1(R2+R3)，M1＝n1(R2·a2-R3·a3)
the single-line running set + single-hole heavy load, the single-line running set + single-hole light load are calculated according to the following formula:
N＝n1·R2，M1＝n1·R2·a2。
and E, respectively calculating the transverse bending moment of the pier section in the step E aiming at eight load working conditions.
In step E, the calculation formula of M2 is specifically as follows:
the calculation formula of the double-line running set + double-hole heavy load and the double-line running set + double-hole light load is as follows:
M2＝n2·E2(R2+R3)
the double-line running set + single-hole heavy load and the double-line running set + single-hole light load are calculated according to the following formula:
M2＝n2·E2·R2
the single-line running set + double-hole heavy load and the single-line running set + double-hole light load are calculated according to the following formula:
M2＝n1·E1(R2+R3)
the single-line running set + single-hole heavy load, the single-line running set + single-hole light load are calculated according to the following formula:
M2＝n1·E1·R2。
example one
A turnout beam pier is provided with 5 lines, namely 1 line, 2 lines, 3 lines, 4 lines and 5 lines, wherein the distances from the lines to the center line of the pier are respectively 10.6m, 5.3m, 0.7m, 4.5m and 10.2m as shown in figure 2. The calculation result of the longitudinal single-line live load arrangement diagram is shown in table 1, the distance a2 between the center of the longitudinal support and the center of the pier is 0.35 m-0. 3m, and the external force generated by the live load on the section of the pier is calculated.
TABLE 1 counter-force of vertical single line live bearing (unit: kN)
According to the step A, in the two-wire locomotive group, n2 is 5 lines, and the offset E2 is as follows:
in the single-line train group, since 10.6+5.3+0.7>4.5+10.2, considering the left-hand train, n1 is 3 lines, and the offset distance E1 is:
according to the steps D and E, the external force generated by the live load on the section of the pier can be obtained, and the external force is shown in a table 2.
TABLE 2 external force generated by live load on pier section
Comprehensively, the algorithm can accurately calculate the external force of the section of the pier generated by live load of the multi-line travelling crane, and can be transplanted into the original single-double-line pier calculation program.
Aiming at the influence of live load of the multi-line travelling crane on the external force of the section of the pier, the method is popularized to the longitudinal direction and the transverse direction on the basis of the support counterforce calculated by the live load diagram of the single-line longitudinal train, the external force of the section of the pier generated by the live load of the multi-line travelling crane is accurately calculated, the method is more economical compared with the traditional design method, the algorithm is transplanted to the original single-double-line pier calculation program, and the problem of quick and accurate calculation of the multi-line pier is solved.
The method can be used for calculating the sections of different types of piers in the field of transportation, such as railways, highways, municipal works, light rails and the like, and can correctly consider the contribution value of live load of multi-line traveling to the external force of the pier sections.
Claims (7)
1. The utility model provides an algorithm of considering multi-thread driving live load to pier cross section external force influence which characterized in that: the method comprises the following steps:
(A) analyzing the position relation between the transverse direction of the pier and the multiple lines by taking the pier as the center, and respectively determining the line number and the offset distance of the double-line running gear set and the single-line running gear set
The bridge pier is transversely vertical to the trainThe offset distance is the distance between the vertical resultant force action point of the traveling crane group and the center of the bridge pier, wherein the two traveling crane groups share the samen2 lines with an offset ofE2, common to single-line travelling crane groupn1 line with an offset ofE1；
(B) Analyzing the longitudinal train load of the pier to obtain the worst live load arrangement diagram, namely a double-hole heavy load, a double-hole light load, a single-hole heavy load and a single-hole light load, and recording the corresponding counter force of the support
The longitudinal direction of the pier is the running direction of the train, the pier is provided with two supports longitudinally, and the counterforce of the support on the left side isR2, the counter-force of the right support isR3，R2 andR3, solving the size according to the live load layout diagram;
(C) the transverse two groups of driving modes and the longitudinal four live load arrangement diagrams can be combined into eight kinds of live load control working conditions, and calculation is required to be carried out according to the eight kinds of live load working conditions
Two groups of driving modes are obtained in the step (A), and four live load layout drawings are obtained in the step (B);
(D) according to the position of the longitudinal support and the counter force of the support, the vertical force and the longitudinal bending moment of the pier section under each live load working condition are obtained
In the longitudinal direction of the bridge pier, the distance between the left support and the center of the pier isa2, the distance between the right support and the center of the pier isa3, the vertical force of the cross section of the pier isNA longitudinal bending moment ofM1；
(E) The transverse bending moment of the pier section under each live load working condition is calculated by the transverse traveling block set and the support counterforce
The transverse bending moment of the cross section of the pier isM2；
(F) And (3) synthesizing the vertical force, the longitudinal bending moment and the transverse bending moment of the cross section of the pier, and finally calculating the influence of the live load of the multi-line travelling crane on the external force of the cross section of the pier.
2. The algorithm considering influence of live load of multi-line travelling crane on external force of pier section according to claim 1, wherein the algorithm comprises: and (C) respectively considering the influence of live load on the section of the pier in the longitudinal direction and the transverse direction under the eight live load working conditions in the step (C), and enveloping the worst load under the conditions of large eccentric stress and small eccentric stress according to the principles of maximum vertical force, maximum bending moment, minimum vertical force and maximum bending moment.
3. The algorithm considering influence of live load of multi-line travelling crane on external force of pier section according to claim 1, wherein the algorithm comprises: the double-line traveling crane group in the step (A) is used for obtaining the maximum vertical force of the section of the pier under the live load working condition, so thatn2 is the total number of multiple lines, and the single-line traveling set is used for comparing the transverse maximum bending moment of the cross section of the pier under the live load working conditionn1·E1, taking the railway line on the side of the maximum value as a single-line locomotive group.
4. The algorithm considering influence of live load of multi-line travelling crane on external force of pier section according to claim 1, wherein the algorithm comprises: in the step (B), four live load layout drawings are shown, and the specific contents are as follows:
the live load layout of double-hole heavy load is to obtainR2+R3 is a maximum value;
the movable load layout diagram of the double-hole light load aims to solve the problem that the left and right hole beams at the top of the pier bear the maximum vertical forceR2+R3 is minimum;
the live load layout of single-hole heavy load is to obtainR2 is the maximum value;
with a single aperture lightly loadedRAnd 2 is the counter force of the support at the other end of the beam when the load is distributed according to the single-hole load.
5. The algorithm for considering influence of live load of multi-line travelling crane on external force of pier section according to claim 2, wherein the algorithm comprises the following steps: the eight load conditions in the step (C) are respectively as follows: the double-line traveling crane group + double-hole heavy load, the double-line traveling crane group + double-hole light load, the double-line traveling crane group + single-hole heavy load, the double-line traveling crane group + single-hole light load, the single-line traveling crane group + double-hole heavy load, the single-line traveling crane group + double-hole light load, the single-line traveling crane group + single-hole heavy load, and the single-line traveling crane group + single-hole light load.
6. The algorithm considering influence of live load of multi-line travelling crane on external force of pier section according to claim 1, wherein the algorithm comprises: and (D) respectively calculating the vertical force and the longitudinal bending moment of the section of the pier in the step (D) according to eight load working conditions.
7. The algorithm considering influence of live load of multi-line travelling crane on external force of pier section according to claim 1, wherein the algorithm comprises: and (E) respectively calculating the transverse bending moment of the pier section in the step (E) aiming at eight load working conditions.
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| CN109344552A (en) * | 2018-11-29 | 2019-02-15 | 中铁二院工程集团有限责任公司 | Suspension type monorail bridge pier and its design method |
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