CN110598250B - Method and system for optimizing bending moment distribution of continuous rigid frame bridge - Google Patents
Method and system for optimizing bending moment distribution of continuous rigid frame bridge Download PDFInfo
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Abstract
The invention discloses a method and a system for optimizing bending moment distribution of a continuous rigid frame bridge, wherein the method comprises the following steps: calculating the hogging moment M of the first worst cross-section A-A of the vertical cross-sections of the first beam section 1 (ii) a The side span main beam is provided with a jacking position, and the jacking position is close to the side pier; according to M 1 And a preset target negative bending moment M 1 Difference of DeltaM 1 And the distance L between the first worst cross-section A-A and the jacking position 1 Calculating and obtaining a jacking force F by using a first preset algorithm; pouring a side span main beam, and arranging a jacking device on the beam end; after the full bridge is closed, a jacking device is utilized to apply a vertically upward jacking force F to the beam end, so that the hogging moment of the first beam section is reduced to M 1 '. The hogging moment of the first beam section in the pier top area of the main pier adjacent to the side pier can be reduced without increasing the beam height and the prestress beam, and the anti-cracking performance of the side span main beam is ensured to meet the standard requirement.
Description
Technical Field
The invention relates to the field of design and construction of continuous rigid frame bridges, in particular to a method and a system for optimizing bending moment distribution of a continuous rigid frame bridge.
Background
The continuous rigid frame bridge usually takes a concrete beam as a main part, a midspan can also be provided with a steel beam with a certain length as required to be made into a structural form of a mixed beam, and a main pier can be in a thin-wall pier or V-shaped pier form. The main beam of the bridge structure mainly bends, the beam section in the pier top area of the main pier is subjected to negative bending moment, and the beam section in the midspan and midspan area of the side span is subjected to positive bending moment. For concrete beam sections, after determining a reasonable main beam construction size, prestressing is usually arranged reasonably to resist the action of bending moments according to the stress characteristics.
For a continuous rigid frame bridge with a concrete main girder as a side span, the side span main girder positioned in a pier top area of a main pier adjacent to the side span is defined as a first girder section, the side span main girder positioned in a midspan area of the side span is defined as a second girder section, the negative bending moment borne by the first girder section is much larger than the positive bending moment borne by the second girder section, and in order to enable the first girder section to meet the anti-cracking requirement, the number of prestressed bundles arranged on a top plate of the first girder section is far larger than that of prestressed bundles arranged on a bottom plate of the second girder section.
However, when the beam height of the side span concrete main beam is limited, the bending resistance of the cross section cannot be continuously improved by increasing the beam height, and the first beam section subjected to negative bending moment still cannot meet the requirement of the anti-cracking specification, the number of prestressed tendons on the top plate of the first beam section is increased to meet the requirement of the anti-cracking specification. However, the number of the prestressed tendons that can be arranged on the top plate is limited, and once the prestressed tendons are fully distributed on the top plate, the first beam section still cannot meet the anti-cracking requirement, the first beam section can only return to the initial stage of the bridge design, and the beam height is adjusted and even the vertical plane linearity of the side span main beam is correspondingly increased to meet the requirements of under-bridge clearance and the like, so that the consequences of increased engineering scale, increased cost, adverse influence on the vertical plane linearity of the bridge and the like are caused.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for optimizing the bending moment distribution of a continuous rigid frame bridge, which can reduce the negative bending moment of a first beam section in the pier top area of a main pier adjacent to a side pier without increasing the beam height and a prestress beam, and ensure that the anti-cracking performance of a side span main beam meets the standard requirement.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
a method for optimizing bending moment distribution of a continuous rigid frame bridge comprises the following steps:
calculating the hogging moment M of the first most unfavorable cross-section A-A of the vertical cross-sections of the first beam section 1 ；
The side span main beam is provided with a jacking position, and the jacking position is close to the side pier; according to M 1 With a predetermined target hogging moment M 1 Difference of ` Δ M 1 andbase:Sub>A distance L between the first worst cross-section A-A and the jacking position 1 Calculating and obtaining a jacking force F by using a first preset algorithm;
pouring the side span main beam, and arranging a jacking device at the jacking position;
after the full bridge is closed, applyingbase:Sub>A vertically upward jacking force F to the jacking position by using the jacking device so as to reduce the hogging moment of the first worst cross section A-A to M 1 ＇。
On the basis of the above technical solution, the first preset algorithm is:
F＝ΔM 1 /L 1 。
on the basis of the technical scheme, before the side span main beam is poured, the method further comprises the following steps:
according to the F, calculating and obtaining the vertical jacking displacement delta h of the jacking position by using a second preset algorithm;
when the pouring of the side span girder is completed, the following conditions are met:
the reserved height difference between the top surface of the approach bridge main beam and the top surface of the jacking position is delta h, when the jacking position moves upwards vertically for delta h, the top surface of the jacking position is flush with the top surface of the approach bridge main beam, and the negative bending moment of the first worst cross section A-A is M 1 ＇。
On the basis of the above technical solution, the second preset algorithm is:
Δh＝F/K
and K is the vertical linear rigidity of the side span main beam at the jacking position.
On the basis of the technical scheme, the pier top of the side pier is in an L shape, the L shape comprises a vertical section and a horizontal section which are connected with each other, one end of the approach bridge main beam is arranged at the top end of the vertical section, and the jacking position is arranged on the horizontal section.
On the basis of the technical scheme, the method further comprises the following steps:
calculating the positive bending moment M of the second most unfavorable cross section B-B in the vertical cross section of the second beam section 2 ；
According to F and the distance L between the second worst cross section B-B and the jacking position 2 Calculating and obtaining an adjustment value M of the positive bending moment of the second worst cross section B-B by using a third preset algorithm 2 ＇；
According to M 2 Checking whether the second worst cross section B-B meets the crack resistance requirements.
On the basis of the above technical solution, the third preset algorithm is:
F＝(M＇ 2 -M 2 )/L 2 。
the invention also provides a system for optimizing the bending moment distribution of the continuous rigid frame bridge, which comprises the following components:
base:Sub>A server equipped withbase:Sub>A calculation and analysis module for calculating the hogging moment M of the first worst section A-A of the vertical sections of the first beam section by means of said calculation and analysis module 1 ；
The control device is used for setting a jacking position close to the side pier according to M 1 And a preset target negative bending moment M 1 Difference of ` Δ M 1 andbase:Sub>A distance L between the first worst cross-section A-A and the jacking position 1 Calculating and obtaining a jacking force F by using a first preset algorithm;
the jacking device is arranged at the jacking position and used for applying a vertically upward jacking force F to the jacking position after the full bridge closureSo that the negative bending moment of the first worst cross section A-A is reduced to M 1 ＇。
On the basis of the technical scheme, the calculation analysis module is a finite element analysis module.
On the basis of the technical scheme, the jacking device comprises a plurality of jacks, and the jacks are arranged at intervals along the transverse bridge direction.
Compared with the prior art, the invention has the advantages that:
(1) The method for optimizing the bending moment distribution of the continuous rigid frame bridge is simple, and compared with an internal adjusting method for arranging the prestressed beams to resist the bending moment, the method for jacking the beam ends adopted by the embodiment of the invention belongs to an external adjusting means, and can obviously and effectively reduce the negative bending moment of the first beam section under the condition of not increasing the beam height and the number of the prestressed beams, so that the side span main beam meets the anti-cracking performance requirement, and simultaneously can reduce the engineering number and reduce the engineering cost.
(2) The system for optimizing the bending moment distribution of the continuous rigid frame bridge is simple, the key parameters F and delta h required by design and construction can be determined only by a simple calculation formula and combined with finite element analysis, and the negative bending moment of the first beam section 1 can be obviously and effectively reduced under the condition of not increasing the beam height and the number of prestressed beams, so that the side span main beam 2 meets the anti-cracking performance requirement.
Drawings
FIG. 1 is a schematic structural diagram of a continuous rigid frame bridge according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a poured side span main beam in an embodiment of the invention;
FIG. 3 is a schematic structural diagram of a continuous rigid frame bridge before jacking in the embodiment of the invention;
FIG. 4 is a view taken in the direction C-C of FIG. 3;
FIG. 5 is a schematic structural diagram of a continuous rigid frame bridge after jacking in the embodiment of the invention;
fig. 6 is a view in the direction D-D of fig. 5.
In the figure: 1-a first beam section, 2-a side span main beam, 20-a jacking position, 3-a side pier, 4-a jacking device, 40-a jack, 5-a second beam section and 6-an approach main beam.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Referring to fig. 1 and 2, an embodiment of the present invention provides a method for optimizing bending moment distribution of a continuous rigid frame bridge, including the following steps:
s1, side piers 3, main piers adjacent to the side piers 3, a first beam section 1 and an approach bridge girder 6 are poured in advance;
s2, calculating the hogging moment M ofbase:Sub>A first worst cross section A-A in the vertical cross section of the first beam section 1 in the state that the side span main beam is closed and lifted before jacking 1 Wherein the first worst cross sectionbase:Sub>A-base:Sub>A representsbase:Sub>A cross section of the first beam section 1 having the worst crack resistance among vertical cross sections;
s3, a jacking position 20 is arranged on the side span main beam, and the jacking position 20 is arranged close to the side pier 3; according to M 1 And a preset target negative bending moment M 1 Difference of DeltaM 1 And the distance L between the first worst cross-section A-A and the jacking position 20 1 Calculating and obtaining a jacking force F by using a first preset algorithm; target hogging moment M preset in the embodiment of the invention 1 Meeting the requirement of crack resistance, and reducing the negative bending moment of the cross section with the worst crack resistance to obtain M 1 Decrease to M 1 Effect of meeting the requirement of crack resistance in each vertical section of the first beam section 1, according to a first preset algorithm F = Δ M ″ 1 /L 1 Calculating to obtain the magnitude of the jacking force F applied to the jacking position 20;
s4, using the side span support to cast the side span main beam 2 in situ, and setting reverse pre-arching on the cast-in-situ side span main beam 2 according to the pre-arching value of the side span main beam 2 to ensure the structural line shape of the bridge, wherein the pre-arching value of the side span main beam 2 already contains the influence of the vertical displacement of the jacking position 20;
s5, arranging a jacking device 4 at the bottom of the jacking position 20;
s6, after the full bridge closure, utilizing the jacking device 4 to applybase:Sub>A vertically upward jacking force F to the jacking position 20, wherein the first worst cross section A-A of the first beam section 1 is subjected tobase:Sub>A delta M 1 So that the first beam section is made1 the negative bending moment of the first most unfavorable cross-section A-A is represented by M 1 Decrease to M 1 Let the first beam section 1 meet the requirements for crack resistance.
The method for optimizing the bending moment distribution of the continuous rigid frame bridge in the embodiment of the invention is simple, and compared with an 'internal' adjusting method for arranging the prestressed tendons to resist the bending moment, the method for jacking the jacking position 20 adopted in the embodiment of the invention belongs to an 'external' adjusting means, and can obviously and effectively reduce the negative bending moment of the first beam section 1 under the condition of not increasing the beam height and the number of the prestressed tendons, so that the side span main beam 2 meets the anti-cracking performance requirement, and simultaneously, the engineering number can be reduced, and the engineering cost can be reduced.
Referring to fig. 3 and 4, before pouring the side span main beam 2, the method further comprises the following steps:
according to the F, calculating and obtaining the vertical jacking displacement delta h of the jacking position 20 by using a second preset algorithm; wherein, the second preset algorithm is as follows:
Δh＝F/K
in the formula, K is the vertical linear stiffness of the side span main beam 2 at the jacking position 20.
When accomplishing the pouring of side span girder, satisfy following condition:
the difference between the height of the top surface of the reserved approach main beam and the height of the top surface of the beam end is delta h, as shown in fig. 5 and 6, when the jacking beam end moves up and down delta h, the top surface of the beam end is flush with the top surface of the approach main beam, and the negative bending moment of the first worst cross section A-A is M 1 ". The flatness of the whole bridge deck is maintained while the negative bending moment of the side span main beam 2 is reduced.
Preferably, as shown in fig. 3, the pier top of the side pier 3 is L-shaped, the L-shape includes a vertical section and a horizontal section which are connected with each other, one end of the approach bridge girder 6 is arranged at the top end of the vertical section, and the jacking position 20 is arranged on the horizontal section. The top surface of the approach bridge main beam 6 is higher than the top surface of the jacking position 20, so that a height difference of delta h can be reserved between the two.
The embodiment of the invention also comprises a positive bending moment M of the second worst cross section B-B in the vertical cross section of the second beam section 5 2 The verification process specifically comprises the following steps:
calculating the positive bending moment M of the second most unfavorable cross-section B-B in the vertical cross-section of the second beam section 5 2 Wherein the second worst cross section B-B is a cross section with the worst crack resistance among the vertical cross sections of the second beam section 5, and whether the crack resistance requirement is satisfied after applying a positive bending moment to the cross section is checked, thereby indicating whether the entire second beam section 5 satisfies the crack resistance requirement;
according to F and the distance L between the second worst cross section B-B and the lifting position 20 2 Calculating and obtaining an adjusting value M of the positive bending moment of the second worst cross section B-B by using a third preset algorithm 2 ＇；
Wherein, the third preset algorithm is as follows: f = (M') 2 -M 2 )/L 2 Obtaining M according to a third preset algorithm 2 Value of 2 Value of min to M 2 Large;
according to M 2 Checking whether the second most unfavorable cross-section B-B meets the requirement for crack resistance, if M 2 The value "satisfies the requirement of crack resistance, it means that the second beam section 5 satisfies the requirement of crack resistance, since M 1 To M 2 Is much larger, so as long as M 1 The value of "meets the requirement for crack resistance, so in general M 2 Also meeting the requirement of crack resistance, therefore M 2 The value of' is used only as a reference value for the auxiliary check.
The embodiment of the invention also provides a system for optimizing the bending moment distribution of the continuous rigid frame bridge, which comprises a server provided with a calculation analysis module, a control device and a jacking device 4. The server carries out finite element analysis on the first beam section 1 through the finite element analysis module to findbase:Sub>A first worst cross section A-A and calculate the hogging moment M of the first worst cross section A-A in the vertical cross section of the first beam section 1 1 (ii) a Control means for controlling in accordance with M 1 With a predetermined target hogging moment M 1 Difference of DeltaM 1 And the distance L between the first worst cross-section A-A and the jacking position 20 1 Calculating and obtaining a jacking force F by using a first preset algorithm; the jacking device 4 is arranged at the jacking position 20 and is used for applying a vertically upward jacking force F to the jacking position 20 after the full bridge closure, so thatThe negative moment of the first worst cross-section A-A is reduced to M 1 ". The system for optimizing the bending moment distribution of the continuous rigid frame bridge in the embodiment of the invention is simple, the key parameters F and delta h required by design and construction can be determined only by a simple calculation formula and combined with finite element analysis, and the negative bending moment of the first beam section 1 can be obviously and effectively reduced under the condition of not increasing the beam height and the number of prestressed beams, so that the side span main beam 2 meets the anti-cracking performance requirement, and meanwhile, the number of projects can be reduced, and the construction cost is reduced.
Preferably, the pier top of the side pier 3 is in an L shape, the L shape comprises a vertical section and a horizontal section which are connected with each other, the jacking device 4 comprises a plurality of jacks 40, the jacks 40 are arranged on the horizontal section at intervals along the transverse bridge direction, and after jacking is completed, the jacks 40 are replaced by supports and cushion stones to support the jacking position 20.
The present invention is not limited to the above-described embodiments, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements are also considered to be within the scope of the present invention. Those not described in detail in this specification are well within the skill of the art.
Claims (10)
1. A method for optimizing bending moment distribution of a continuous rigid frame bridge is characterized by comprising the following steps:
calculating the hogging moment M of the first most unfavourable section A-A of the vertical sections of the first beam section (1) 1 ；
A jacking position (20) is arranged on the side span main beam (2), and the jacking position (20) is arranged close to the side pier (3); according to M 1 And a preset target negative bending moment M 1 Difference of ` Δ M 1 andbase:Sub>A distance L between the first worst cross-section A-A and the jacking position (20) 1 Calculating and obtaining a jacking force F by using a first preset algorithm;
pouring the side span main beam (2), and arranging a jacking device (4) at the jacking position (20);
after the full bridge is closed, the jacking device (4) is utilized to apply vertical upward jacking to the jacking position (20)base:Sub>A lift force F to reduce the negative bending moment of the first worst cross section A-A to M 1 ＇。
2. The method for optimizing bending moment distribution of a continuous rigid frame bridge of claim 1, wherein the first predetermined algorithm is:
F＝ΔM 1 /L 1 。
3. the method for optimizing bending moment distribution of continuous rigid frame bridges according to claim 1, wherein before casting the side span main beam (2), further comprising the steps of:
according to the F, calculating and obtaining the vertical jacking displacement delta h of the jacking position (20) by using a second preset algorithm;
when the pouring of the side span main beam (2) is completed, the following conditions are met:
the height difference of the top surface of the approach bridge main beam (6) and the top surface of the jacking position (20) is delta h, when the jacking position (20) vertically moves upwards delta h, the top surface of the jacking position (20) is parallel to the top surface of the approach bridge main beam (6), and the negative bending moment of the first worst cross section A-A is M 1 ＇。
4. The method of optimizing bending moment distribution for a continuous rigid frame bridge of claim 3, wherein the second predetermined algorithm is:
Δh＝F/K
and K is the vertical linear rigidity of the side span main beam (2) at the jacking position (20).
5. The method for optimizing bending moment distribution of a continuous rigid frame bridge according to claim 3, wherein the pier top of the side pier (3) is L-shaped, the L-shaped comprises a vertical section and a horizontal section which are connected with each other, one end of the main approach bridge beam (6) is arranged at the top end of the vertical section, and the jacking position (20) is arranged on the horizontal section.
6. The method of optimizing bending moment distribution for a continuous rigid frame bridge of claim 1, further comprising the steps of:
calculating the positive bending moment M of the second most unfavorable cross section B-B in the vertical cross section of the second beam section (5) 2 ；
According to F and the distance L between the second worst cross section B-B and the lifting position (20) 2 Calculating and obtaining an adjustment value M of the positive bending moment of the second worst cross section B-B by using a third preset algorithm 2 ＇；
According to M 2 Checking whether the second worst cross section B-B meets the crack resistance requirements.
7. The method of optimizing bending moment distribution for a continuous rigid frame bridge of claim 6, wherein the third predetermined algorithm is:
F＝(M＇ 2 -M 2 )/L 2 。
8. a system for optimizing the distribution of bending moments of a continuous rigid frame bridge, comprising:
base:Sub>A server equipped withbase:Sub>A calculation and analysis module for calculating by means of said calculation and analysis module the hogging moment M of the first worst section A-A of the vertical sections of the first beam section (1) 1 ；
A control device, wherein a jacking position (20) is arranged on the side span main beam (2), the jacking position (20) is arranged close to the side pier (3), and the control device is used for controlling the lifting position according to M 1 And a preset target negative bending moment M 1 Difference of ` Δ M 1 andbase:Sub>A distance L between the first worst cross-section A-A and the jacking position (20) 1 Calculating and obtaining a jacking force F by using a first preset algorithm;
base:Sub>A jacking device (4) arranged on the jacking position (20) and used for applyingbase:Sub>A vertically upward jacking force F to the jacking position (20) after full-bridge closure, so that the negative bending moment of the first worst cross section A-A is reduced to M 1 ＇。
9. The system for optimizing bending moment distribution for a continuous rigid frame bridge of claim 8, wherein the computational analysis module is a finite element analysis module.
10. System for optimizing bending moment distribution for continuous rigid-frame bridges according to claim 8, wherein said jacking device (4) comprises a plurality of jacks (40), said jacks (40) being arranged at intervals along the transverse bridge.
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