CN116561856B - Staggered spliced wide bridge segment model test design method - Google Patents
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- 238000013461 design Methods 0.000 title claims abstract description 30
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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Abstract
The application discloses a staggered spliced wide bridge segment model test design method, which comprises the following steps: step 1, enabling a section test piece a, namely enabling the distance between a left fulcrum of a loading distribution beam and a right fulcrum of the section test piece to be equal to the distance between two points of a staggered widening real bridge A, B; step 2, performing dislocation widening real bridge finite element analysis to obtain a bending moment M of A, B two points A 、M B And deflection delta at point a A The method comprises the steps of carrying out a first treatment on the surface of the Step 3, determining the section height h of the right side beam section of the B point of the section test piece 2 The method comprises the steps of carrying out a first treatment on the surface of the Step 4, determining that the hogging moment at the B point of the segment test piece calculated according to the elasticity theory reaches M B When the actuator applies a control force F A The method comprises the steps of carrying out a first treatment on the surface of the And 5, solving a nonlinear equation set to obtain the design parameters of the segment test piece. The application can reduce the requirement on the test site, improve the test efficiency and reduce the test material consumption.
Description
Technical Field
The application belongs to the field of civil (bridge) engineering, and particularly relates to a staggered width-spliced bridge segment model test design method which can be used for verifying the feasibility of a staggered width-spliced bridge design scheme.
Background
In the reconstruction and expansion engineering of the expressway, the method is limited by navigation and flood control requirements, and has the influence of various factors such as road and embankment limit, engineering cost and the like, and the bridge structure is required to be spliced and widened under the condition that new and old bridges are arranged in a staggered manner. Such as: 1) When the longitudinal axis of the bridge is obliquely crossed with the axis of the spanned river or road, the bridge piers of the new bridge and the old bridge cannot be arranged at the same transverse position, namely, staggered arrangement is formed, as shown in the figure 1; 2) When the channel bridge is expanded, the bridge pier of the new bridge needs to avoid the existing embankment arrangement, and the staggered arrangement is also formed.
Unlike conventional bridge splicing, the staggered splicing is not one-to-one corresponding to the positive and negative bending moment areas of the new and old bridges, and the bridges at two sides of the splicing seam are not in coordination with vertical deformation under the action of external load, so that the transverse stress and boundary conditions of the bridge deck become complex. Such as: 1) When the new bridge side span middle section and the old bridge side pivot section are spliced, the new bridge side beam section can flex downwards vertically under the action of vehicle load, but the beam section at the old bridge pivot is restrained vertically by the support, so that the downwarping can not occur. At this time, the deflection difference of the new bridge and the old bridge can cause the bridge deck plate at the side of the old bridge to bear a larger transverse negative bending moment, which has adverse effect on the transverse stress of the old bridge structure, as shown in figure 2; 2) When the new bridge foundation is subjected to post-construction settlement, the bridge deck of the old bridge can bear a large transverse negative bending moment, as shown in figure 3.
Considering that dismantling an old bridge, readjusting bridge span arrangement and newly constructing a bridge in situ can increase engineering cost, it is necessary to perform experimental verification on the engineering feasibility of the design scheme of the staggered spliced wide bridge; if a full bridge model test is used, namely: and when the loading test is carried out on the whole bridge test model with the same size, material and boundary condition of the real bridge in the test field, the space requirement on the test field is higher, the implementation difficulty is higher, the test period is longer, the material consumption for manufacturing the whole bridge model is large, and the test cost is high.
Disclosure of Invention
In order to solve the technical problems in the prior art, the application aims to provide a staggered spliced wide bridge segment model test design method which can test and verify the stress condition of the least favorable segment of a staggered spliced wide bridge, thereby reducing the requirements on a test site, improving the test efficiency and reducing the test material consumption.
In order to further achieve the above purpose, the present application adopts the following technical scheme:
a staggered spliced wide bridge segment model test design method comprises the following steps:
step 1, enabling a section test piece a, namely enabling the distance between a left fulcrum of a loading distribution beam and a right fulcrum of the section test piece to be equal to the distance between two points of a staggered widening real bridge A, B;
step 2, performing dislocation widening real bridge finite element analysis to obtain a bending moment M of A, B two points A 、M B And deflection delta at point a A ；
Step 3, determining the section height h of the right side beam section of the B point of the section test piece 2 ；
Step 4, determining that the hogging moment at the B point of the segment test piece calculated according to the elasticity theory reaches M B When the actuator applies a control force F A ；
And 5, solving a nonlinear equation set to obtain the design parameters of the segment test piece.
Further, in step 2, a bending moment M at two points A, B A 、M B And point a deflection delta A Deducing by a displacement method, wherein the displacement method equation of the segmental test piece is shown as a formula (3):
wherein:
in the formula (EI) S ) 1 The flexural rigidity of the section of the left side beam section at the E point of the segment test piece (EI) S ) 2 The bending rigidity of the section of the right side beam section at the point C of the section test piece, EI S For the flexural rigidity of the section between two points of the segment test piece E, C, F A Is the acting force of the actuator.
Further, to meet the model similarity requirement, M is controlled A 、M B 、δ A And the calculated value is equal, the following needs to be satisfied:
further, equations (3) and (4) are combined:
wherein M is A 、M B And delta A F is obtained by calculating finite element models of the dislocated spliced bridge A The force is controlled for a predetermined actuator.
Further, (EI S ) 1 And (EI) S ) 2 Can be expressed as:
wherein E is the elastic modulus of the concrete material, kappa is the width of the segment test piece, h 1 And h 2 The section height of the two side beam sections of the segmental test piece is equal to the section height of the two side beam sections of the segmental test piece.
Further, by programming in MATLAB software, solving the nonlinear equation set (5) with the fsolve () function, an unknown vector can be obtained
x＝[b 1 b 2 h 1 ] T 。
Compared with the prior art, the technical scheme provided by the application has the beneficial effects that: the method provides an adaptive local segment test scheme aiming at a special structure such as a staggered widening bridge. The key steps are as follows: 1) The section test piece is designed into a hyperstatic structural form by extending the section test piece rightwards at the maximum hogging moment (point B), so that the section test piece can consider the influence of plastic redistribution of the maximum hogging moment of an actual structure caused by concrete cracking and steel bar yielding; 2) By theoretical derivation, the length and the section height of the beam sections on the left side and the right side of the segment test piece are determined, so that the bending moment M of the segment test piece at the A, B two points A 、M B And vertical displacement delta at point a A Theory of homography and finite element modelThe calculation results are consistent, so that the segment test piece can accurately reflect the stress of the actual structure; 3) And reasonable material selection and connection construction measures are determined according to various design parameters of the segment test piece, so that the force transmission reliability of the segment test piece in the test process is ensured.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a schematic diagram of bridge reconstruction and expansion dislocation widening;
FIG. 2 is a schematic illustration of the adverse effect of vehicle loading on the lateral force of an old bridge deck;
FIG. 3 is a schematic illustration of the adverse effect of new bridge foundation settlement on the lateral force of an old bridge deck;
FIG. 4 is a schematic diagram of a staggered splice segment model test measurement index;
FIG. 5 is a schematic diagram of a three-dimensional finite element model of a staggered widening bridge;
FIG. 6 is a schematic drawing of the extraction of forces within a localized segment of a dislocated, spliced wide bridge;
FIG. 7 is a schematic illustration of a segment test piece design;
FIG. 8 is a schematic diagram of a segment test piece solution displacement method calculation;
FIG. 9 is a segment test piece solution displacement method inner force diagram;
FIG. 10 is a flow chart of segment test piece parameter design;
FIG. 11 is a schematic diagram of a segment test piece finally determined: the left side section of the point A is highly weakened;
FIG. 12 is a three-dimensional schematic of a final determined segment test piece.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be described in further detail with reference to the following specific embodiments and the accompanying drawings.
The technical conception of the application is as follows: first, the measurement index of the staggered spliced wide bridge segment model test is described by the figure 2The most unfavorable section of the staggered spliced wide bridge is taken as an example, and a relation curve between the downwarping delta of the new bridge span and the transverse hogging moment M of the root section of the bridge deck of the old bridge is required to be established in a segment model test, as shown in fig. 4. According to the obtained relation curve, when the hogging moment M reaches the limit flexural bearing capacity M of the section u At this time, the corresponding new bridge span center downwarping delta is the maximum allowable downwarping delta of the new bridge in the staggered spliced wide bridge structure u . Therefore, the method can be used as a basis for judging the safety condition of the dislocated spliced wide bridge. For example: if the calculated new bridge mid-span deflection is smaller than the test value delta u The structural stress safety of the staggered spliced wide bridge structure in the operation stage can be judged;
in order to accurately simulate the delta-M relation curve, the boundary condition and the interaction force between a local segment and the whole bridge should be accurately simulated when the segment test piece is manufactured, which is also a difficulty of segment model test;
for this purpose, in designing the segment test piece parameters, a three-dimensional finite element model of the offset-widening bridge structure should be first constructed, as shown in fig. 5, with the bridge span of the new bridge arranged as (L 3 +L 1 +L 3 ) The application adopts L 3 ＝17.5m，L 1 For example, let us say that 30m, the bridge span of the old bridge is arranged as (L 2 +L 2 ) The application adopts L 2 Let us say by way of example, that is, L 1 +2*L 3 ＝2*L 2 The method comprises the steps of carrying out a first treatment on the surface of the The full-step vehicle load at the side of the new bridge is calculated according to the elasticity theory, and the distribution of the transverse internal force (comprising bending moment and axial force) of the bridge deck plate belt with unit width between two points of the worst section A, B spliced at the middle and old bridge fulcrums of the new bridge is shown in the figure 6;
according to the basic principle of material mechanics, when the axial pressure born by the section is not negligible, the situation before and after instability should be studied according to the flexible line equation of the instability of the compression bar. According to the axle force calculation of fig. 6, the bridge deck transverse compressive stress index is about: 0.7MPa, which means that the axial pressure is small and the influence on the bending line is negligible, whereas a conventional beam is subjected to a bending moment (pure bending or small axial force) and the bending line can be approximately expressed as:
in the method, in the process of the application,is the neutral axis curvature, M is the section bending moment, and EI is the bending stiffness of the beam.
The equation of the deflection line of the constant cross section beam obtained by theoretical derivation of the material mechanics is as follows:
EIδ＝-∫[∫M(x)dx]dx+C 1 x+C 2 (2)
wherein x is the coordinate along the length of the beam, delta is the deflection of the beam, C 1 、C 2 Is an integral constant, determined by the boundary conditions of the beam;
therefore, it can be seen from equation (2): to accurately simulate the deflection delta of the point A in the middle A And bending moment M at point B B Correspondence between them, then must: 1) Accurately simulating bending moment distribution between two points A, B; 2) Accurately simulating the boundary conditions of two points A, B;
in addition, the actual bridge structure is a statically indeterminate structure, wherein the internal force of the bridge segment cannot be linearly increased along with the increase of deformation in the loading process, and plastic redistribution can occur, so that the design of the segment test piece can reflect the plastic redistribution of the actual structure at the point B.
Based on the analysis, the staggered spliced wide bridge segment model test design method provided by the application comprises the following steps:
the designed segment test piece is shown in the figure 7, the point position corresponding relation between the segment test piece and the real bridge structure is shown in the figure 7, the point A vertical displacement and bending moment of the segment test piece correspond to the point A vertical displacement and bending moment of the real bridge structure, and the point B bending moment of the segment test piece corresponds to the point B bending moment of the real bridge structure; the distance between the left side supporting point of the section test piece a, namely the loading distribution beam and the right side supporting point of the section test piece is equal to the distance between two points of the staggered widening real bridge A, B; wherein the location of application of the actuator force is at point a;
performing dislocation widening real bridge finite element analysis to obtain a bending moment M of A, B two points A 、M B And deflection delta at point a A The method comprises the steps of carrying out a first treatment on the surface of the To ensure deflection delta at point A A Bending moment M at point A A Moment of bending M at point B B Consistent with the finite element elastic calculation, the displacement method in structural mechanics is adopted for deduction, so that the size parameters of each beam section of the segment test piece in fig. 7 are determined.
Further, the segment test piece extends out of the outer sides of the two points A, B to facilitate the manufacture and loading of the segment test piece, the length of the extending section on the left side of the point A is determined to be 0.5m, and the length of the extending section on the right side of the point B is determined to be 0.9m.
Further, the derivation process of the displacement method is as follows: 1) First, a displacement method calculation schematic diagram of the segment test piece is established and is shown in fig. 8. Wherein a and b 1 、b 2 And c and e are lengths of each beam section of the segmental test piece, specifically, a: the two-point spacing of the segment test pieces A, B; b 1 : the length of the left side beam section of the E point of the segment test piece; b 2 : the length of the right side beam section of the section test piece C point; c: half of the two-point spacing of the segment test pieces B, C; e: the two-point spacing of the segment test pieces A, E; z is Z 1 ～Z 9 Is the displacement and the rotation angle of each point of the segment test piece; specifically, Z 1 Is the corner at the E point of the segment test piece; z is Z 2 Is the corner at the point A of the segment test piece; z is Z 3 Is the corner at the B point of the segment test piece; z is Z 4 Is the corner of the support between the two points of the segment test piece B, C; z is Z 5 Is the corner at the C point of the segment test piece; z is Z 6 Is the vertical displacement at the E point of the segment test piece; z is Z 7 Is the vertical displacement at the point A of the segment test piece; z is Z 8 Is the vertical displacement at the B point of the segment test piece; z is Z 9 Is the vertical displacement at the C point of the segment test piece; 2) Graph of internal force (bending moment and shearing force) of basic system under action of external load (actuator force) -M p Graph and internal force calculation schematic diagram under the action of each unit displacementThe figure is shown in figure 9.
Further, the basic equation of the displacement method of the segment test piece is shown in the formula (3):
wherein, the liquid crystal display device comprises a liquid crystal display device,
in the formula (EI) S ) 1 、(EI S ) 2 And EI S For the section bending stiffness of each beam section of the segment test piece in FIG. 7, F A Is the force of the actuator, (EI S ) 1 The bending rigidity of the section of the left side beam section at the E point of the segment test piece is shown; (EI) S ) 2 The bending rigidity of the section of the right side beam section at the point C of the section test piece is shown; EI (electronic equipment) S The section bending rigidity between two points of the segment test piece E, C.
Further, to meet the model similarity requirement, M is controlled A 、M B 、δ A And the calculated value (namely A, B two-point bending moment value calculated by the finite element model shown in fig. 5 and vertical displacement at the point a.) are equal, the following needs to be satisfied:
still further, simultaneous equations (3) and (4) can be obtained:
wherein M is A 、M B And delta A F is obtained by calculating finite element models of the dislocated spliced bridge A For controlling force of the actuator, and EI S And parameters a, c, e are also known quantities. Therefore, the unknowns include: the section bending stiffness (EI of the two-sided segment test piece beam section in FIG. 7 S ) 1 And (EI) S ) 2 And length b of the two-sided test piece beam section 1 And b 2 。
Further, (EI) S ) 1 And (EI) S ) 2 Can be expressed as:
wherein E is the elastic modulus of the concrete material, kappa is the width (perpendicular to the length direction) of the segment test piece, h 1 And h 2 The section height of the two side beam sections of the segmental test piece is equal to the section height of the two side beam sections of the segmental test piece.
Further, if the section height g of the right side member section at the point B is predetermined in determining the segment test piece parameters 2 The unknowns in equation (5) include: b 1 、b 2 、g 1 。
Further, by programming in MATLAB software, solving the nonlinear equation set (5) with fsolve () function, the unknown vector x= [ b ] can be obtained 1 b 2 g 1 ] T 。
In addition, the section test piece provided by the patent can simulate plastic redistribution near the point B, and because the point B stretches out to the right side for one span, a statically indeterminate structure is formed, and the degree of freedom is redundant, so that the development of plastic redistribution can be simulated at the point B.
Further, the design of the segment test piece also requires determination of the actuator loading control force F A The value of (2) is calculated according to the elasticity theory, and the hogging moment at the B point of the segment test piece reaches M B The force applied by the actuator at point a. Load control force F A The determination of (a) affects the value of the test piece parameter.
The design flow of the segment test piece parameters is shown in fig. 10.
In order to verify the feasibility of the segment test piece design method for the reconstruction and expansion dislocation widening bridge model test, the following is used for verifying a design example. The new bridge and the old bridge in the staggered spliced wide bridge are prestressed concrete T-beam bridges, and the section arrangement conditions of the new bridge and the old bridge are approximately shown in the figures 2 and 3.
According to the design scheme of the staggered widening solid bridge, the distance a=2550mm between the A, B two points in the segment test piece; the bridge is designed by adopting C50 concrete, and the elastic modulus of the concrete material is as follows: e=3.45×10 4 MPa，
The thickness of the flange plates of the new bridge and the old bridge is 200mm, and the cast-in-place concrete integration layer is 80mm, so that the total thickness of the bridge deck is 280mm, and the section height g=280 mm of the beam section between two points of the segment test piece A, B;
establishing a three-dimensional finite element model, and obtaining A, B two-point bending moment M required by test piece design through calculation A 、M B And downwarping delta at point a A The values of (a) are respectively as follows:
M A ＝27.57 kN·m/m、M B ＝111.4 kN·m/m、δ A ＝8.77 mm (8)
let the section height h of the right side beam section at the point B 2 The height of the beam Duan Jiemian between the two points of 280mm and A, B is consistent, so that the design work of the test piece can be simplified;
determining the load control force F of a segment test piece A 70kN, 75kN and 80kN respectively; solving the nonlinear equation set (5) to obtain the test piece design parameter b 1 、b 2 、h 1 As shown in table 1;
table 1 results of test piece parameter calculations
As can be seen from table 1: with loading control force F A Increase in length B of right side beam section at point B 2 No change, however, the length b of the left side beam section at the point A 1 And a section height h 1 Reduced, so that the control force F can be adjusted A The design parameters of the segment test piece reach proper values.
As can be seen from table 1: and finally, the design parameters of the segment test piece are determined, the section of the left side beam at the point A is required to be weakened, and a schematic diagram of the finally determined segment test piece is shown in figure 11.
Furthermore, if the beam section on the left side of the point A of the segment test piece is designed by adopting a concrete material as the beam section on the right side of the point A, the difficulty of manufacturing the test piece is increased, so that steel can be adopted to replace the concrete beam section to design the section weakening beam section on the left side of the point A, and at the moment, the thickness h 'of the steel plate on the left side of the point A' 1 The conversion can be performed according to the following formula:
wherein E is s Is the elastic modulus of steel;
when the left side of the point A is designed by adopting the steel plate, the steel plate and the right side concrete beam section of the point A can be connected by using the reinforced concrete combined section.
A three-dimensional schematic of the final designed segment test piece is shown in fig. 12.
Table 1 meanings of the parameter symbols
/>
It should be understood that the foregoing description of the preferred embodiments is not intended to limit the scope of the application, but rather to limit the scope of the claims, and that those skilled in the art can make substitutions or modifications without departing from the scope of the application as set forth in the appended claims.
Claims (3)
1. The staggered spliced wide bridge segment model test design method is characterized by comprising the following steps of:
step 1, making a segment test pieceNamely, the distance between the left side fulcrum of the loading distribution beam and the right side fulcrum of the segment test piece is equal to the distance between two points of the staggered spliced wide real bridge A, B;
step 2, performing dislocation widening real bridge finite element analysis to obtain a A, B bending moment at two points、/>And->Deflection at point +.>；
Step 3, determining the section height of the right side beam section of the B point of the section test piece；
Step 4, determining that the hogging moment at the B point of the segment test piece calculated according to the elasticity theory reachesWhen the actuator applies a control force +.>;
Step 5, solving a nonlinear equation set to obtain design parameters of the segment test piece;
in step 2, the bending moment at two points A, B、/>And->Point deflection->Deducing by a displacement method, wherein the displacement method equation of the segment test piece is shown as +.>The following is shown:
wherein:
in the method, in the process of the application,bending rigidity of section of left side beam section at E point of section test piece,>the bending rigidity of the section of the right side beam section at the point C of the section test piece is +.>For the section flexural rigidity between two points of the segment test piece E, C, +.>Acting force of the actuator;
to meet model similarity requirements, control、/>、/>And the calculated value is equal, the following needs to be satisfied:
simultaneous formula +.>And->Obtaining:
in the method, in the process of the application,、/>and->Calculated by finite element model of the dislocation spliced bridge>The force is controlled for a predetermined actuator.
2. The trial design method for the staggered spliced wide bridge segment model according to claim 1, wherein,andcan be expressed as:
in (1) the->Is the elastic modulus of the concrete material +.>For the width of the segment test piece>And->The section height of the two side beam sections of the segmental test piece is equal to the section height of the two side beam sections of the segmental test piece.
3. The method of trial design of a staggered span bridge segment model of claim 2, wherein the system of nonlinear equations is solved by fsolve () function by programming in MATLAB softwareObtaining unknown vector
。
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| CN106844965A (en) * | 2017-01-19 | 2017-06-13 | 山西省交通科学研究院 | A kind of method that continuous bridge practical stiffness is recognized based on static test |
| CN111289382A (en) * | 2020-03-31 | 2020-06-16 | 广西交科集团有限公司 | Single-beam damage identification method based on vertical displacement of static load test |
| CN111337212A (en) * | 2020-03-31 | 2020-06-26 | 广西交科集团有限公司 | Method for measuring maximum deflection of simply supported beam based on corner under unknown state |
| CN111859768A (en) * | 2020-07-30 | 2020-10-30 | 广西交科集团有限公司 | Test method for determining deflection of box girder bridge based on single-girder finite element model |
| CN217781780U (en) * | 2022-03-21 | 2022-11-11 | 广东省高速公路有限公司 | A old bridge load sharing amplitude reduction device for piecing together wide bridge |
| CN115541856A (en) * | 2022-10-19 | 2022-12-30 | 重庆交通大学 | Test device for simulating concrete disturbance of joint of spliced wide bridge |
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