CN114880738A - Optimization method for transverse earthquake failure mode of inclined bridge tower - Google Patents
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Abstract
The invention provides an optimization method of a transverse earthquake failure mode of an inclined bridge tower, which adopts a continuous mode pushover method (CMP method) to identify the failure mode of the bridge tower under the transverse earthquake, and solves the technical problem of low efficiency of identification of the failure mode of the existing method; the influence of the tower column inclination angle on the bridge tower failure mode is considered by introducing the inclination angle influence coefficient, and the problem that the existing method is not suitable for inclining the bridge tower is innovatively solved; the method is switched in from the angle of capability and requirement, and the bending resistance bearing capacity of the tower column and the cross beam is used as the only adjustment parameter, so that the technical problem that the performance index is complicated in the optimization process of the existing method is solved.
Description
Technical Field
The invention belongs to the technical fields of building construction, building structure research and the like, and particularly relates to an optimization method for a transverse earthquake failure mode of an inclined bridge tower.
Background
In the development process of the mode optimization research of the structure, the failure mode optimization of the structure is developed from the original static elasticity optimization to the consideration of the nonlinear optimization problem and the multi-objective optimization problem, and gradually develops towards the optimization direction based on the performance and the vulnerability, but the optimization process only optimizes the typical frame structure, and the failure mode optimization research of the inclined frame structure (inclined bridge tower) is very little.
Due to the inclined structural characteristics of the tower columns, the internal force change and the structural deformation of the inclined bridge tower under the action of vertical load and horizontal load are greatly different from those of other bridge towers. The concrete points are as follows: under the action of vertical load, the inclined bridge tower cross beam can bear partial axial force, and the magnitude of the axial force is related to the magnitude of the inclination angle. The existence of the beam section axial force directly influences the bending resistance bearing capacity of the beam section, so that the yield sequence of the beam and the column under the action of lateral load is influenced, and the problem that the failure mode of the inclined bridge tower is more complicated is caused.
The cable-stayed bridge is widely applied to the construction of a large-span bridge due to an excellent structural form, and the tower type of a cable-stayed bridge tower is mainly divided into two types: (1) the vertical bridge tower (2) is an inclined bridge tower. Since the 21 st century, inclined pylons (A-type pylons, inverted Y-type pylons, diamond-type pylons) have been widely used in the construction of cable-stayed bridges due to their characteristics of high lateral stiffness, attractive appearance and the like. However, earthquake disasters seriously threaten the structural safety of the inclined bridge tower. The earthquake disasters all the time show that the damage and collapse of structures such as buildings, bridges and the like are main causes of economic burden. Therefore, the method has important significance for exploring the failure rule of the inclined bridge tower, optimizing the failure mode of the inclined bridge tower under the earthquake action, improving the earthquake-resistant performance of the inclined bridge tower under the condition of not obviously increasing the economic burden, and delaying or avoiding the structural collapse.
The related prior art includes:
zhengshan Lock, Sun Long Fei, Semu, Yangwei, Qinqin, recognition and optimization of structural failure mode of section steel concrete frame [ J ] vibration and impact, 2014,33(04): 167-.
The scheme comprises the following steps:
(1) and establishing a structure finite element model according to the related data.
(2) Structural Analysis was performed using the kinetic Incremental method (IDA). Firstly, selecting n relevant earthquake motion records according to a frequency segment control method of a response spectrum, and using the records as earthquake motion input of IDA analysis. Secondly, the maximum interlayer displacement angle theta is adopted max As a structural reaction parameter, the peak acceleration PGA is used as a seismic intensity parameter, a series of different seismic intensities are obtained through amplitude modulation coefficients, time-course analysis is respectively carried out, and the maximum interlayer displacement angle theta is recorded max Plotting PGA-theta max Performing interpolation on the scatter points, and interpolating all the points by using a third-order spline to obtain PGA-theta max Curve, i.e. single-structure IDA curve. Thirdly, repeating the method to obtain n structural IDA curves.
(3) And identifying a structural failure mode and controlling seismic wave selection. And (3) finding out seismic oscillation with the largest influence on the structure from the n input earthquakes through the structure IDA curve, namely, the earthquake with the worst structure seismic performance and the lowest bearing capacity under the action of the seismic oscillation, so as to determine that the failure mode under the action of the seismic oscillation is the weakest structure failure mode. And selecting corresponding seismic waves as structural control seismic waves.
(4) And optimizing the failure mode. And reinforcing the failure section and the weak layer by adjusting the parameters of the structural section.
(5) And inputting control seismic waves, and performing time-course analysis on the structure.
(6) Judging whether the structural failure mode is a reasonable failure mode, if not, returning to the step (4) to continue optimization; if yes, the optimization is finished.
The structural failure mode optimization flow chart is shown in the specification and attached figure 7.
The failure mode optimization method of the above existing scheme has the following disadvantages:
(1) the influence of the tower inclination angle on the failure mode of the inclined bridge tower cannot be considered. Steps S7, S8 are an optimization process of the prior inventive method, which optimizes the structure by adjusting the cross-sectional dimensions, without considering the influence of the tilt angle factor. Therefore, if the method is used for optimizing the failure mode of the inclined bridge tower, a large error is caused.
(2) Has the defects of single optimization and adjustment measure and low optimization efficiency. "step S8: adjusting the cross-sectional dimension "is a specific measure of the optimal adjustment of the existing method. The purpose of adjusting the cross section size is to adjust the bearing capacity of the cross section of the component, and the bearing capacity can be adjusted in various ways, such as adjusting material characteristics, adjusting the cross section size, adding energy consumption devices, and the like. The range of application of this method is limited only by adjusting the cross-sectional size. In addition, the adjustment process of the existing method lacks an adjustment strategy, and the optimization result is obtained by trial calculation continuously according to experience, so that the optimization process causes the problems that the calculated amount of the optimization process is increased, the optimization model is not optimized enough, and the like.
(3) The failure mode assessment method is inefficient in analysis. In step S2 of the conventional method, the IDA method is used, which selects 10 seismic oscillations, each seismic oscillation is amplitude-modulated 15 times, and 150 time-course analyses are performed in total. Conservative estimation 30min of time course analysis each time, 75h in total. Therefore, the existing failure mode evaluation method has the disadvantages of huge calculation amount, overlong calculation time and low efficiency.
The failure mode evaluation results obtained by the existing methods may not be the weakest failure mode of the structure. In step S5 of the existing method, an IDA curve of the structure needs to be obtained through IDA analysis, and then seismic oscillation having the greatest influence on the structure is found out from the IDA curve, and the structure has the worst seismic performance and the lowest bearing capacity under the seismic oscillation, and further the structural failure mode under the seismic oscillation is considered to be the weakest structural failure mode. Because of the uncertainty of the seismic motion in the actual project, the failure mode evaluated by the existing method is not necessarily the weakest failure mode when the selected seismic motion is not representative.
Disclosure of Invention
The problems that an existing structural failure mode optimization method is complicated in optimization steps, low in failure mode identification efficiency, not considering the influence of inclination angle influence factors on the structural failure mode and the like are solved. According to the optimization method for the transverse earthquake failure mode of the inclined bridge tower, the failure mode under the transverse earthquake of the bridge tower is identified by adopting a continuous mode Pushover method (CMP method), and the technical problem that the identification of the failure mode is low in efficiency in the existing method is solved; the influence of the tower column inclination angle on the bridge tower failure mode is considered by introducing the inclination angle influence coefficient, and the problem that the existing method is not suitable for inclining the bridge tower is innovatively solved; the method is switched in from the angle of capability and requirement, and the bending resistance bearing capacity of the tower column and the cross beam is used as the only adjustment parameter, so that the technical problem that the performance index is complicated in the optimization process of the existing method is solved.
The invention specifically adopts the following technical scheme:
an optimization method for a transverse seismic failure mode of an inclined bridge tower is characterized by comprising the following steps: when the structural failure mode is identified and analyzed, a CMP method is adopted; determining a lateral force distribution mode according to the bridge tower vibration mode, and considering the contribution of a high-order bridge tower vibration mode; optimizing the bending resistance bearing capacity of the cross beam and the tower column of each layer from the 1 st layer of the bridge tower by adopting an integral strategy of optimizing layer by layer, selecting the bending resistance bearing capacity of the cross section as an optimization parameter, and considering the inclination angle alpha of the tower column i The influence on the structural failure mode is quantified as the incidence influence coefficient eta i The method is applied to iterative calculation of bridge tower optimization.
Further, it is implemented by means of computer program modules, comprising: the bridge tower failure mode optimizing system comprises a bridge tower calculation analysis and recognition module and a bridge tower failure mode optimizing module;
the execution of the bridge tower calculation analysis and identification module comprises the following steps:
step S1: extracting relevant analysis parameters of the inclined bridge tower, comprising: height h of inclined bridge tower i Beam width b i Angle of inclination of tower column alpha i Tensile strength f of steel bar y And a yield strain ε;
step S2: determining an expected failure mode of the inclined bridge tower under the action of a fortification earthquake according to the bridge seismic fortification requirement of the position of the inclined bridge tower;
step S3: establishing a numerical analysis model of the inclined bridge tower based on the related analysis parameters of the inclined bridge tower;
step S5: solving the dynamic characteristics of the inclined bridge tower, comprising the following steps: period of natural vibration T n The mode mass participation coefficient of each order vibration mode
And a vibration mode vector phi n And the vibration mode vector phi is measured n Normalization to make the modal vector at the top of the inclined bridge tower
Step S6: solving modal lateral force s of inclined bridge tower n ；
Step S7: calculating target displacement D of the top of the inclined bridge tower under seismic oscillation with corresponding intensity t ；
Step S8: performing side-push analysis on the inclined bridge tower based on the CMP method until the displacement of the top of the inclined bridge tower reaches the target displacement D t ；
Step S9: identifying a failure location of an inclined bridge tower: judging the failure component of the inclined bridge tower according to whether the mechanical index and the deformation index of the component of the inclined bridge tower reach the failure standard; if the performance index of a certain component of the inclined bridge tower at a certain position meets or exceeds the failure standard, identifying the component as failed, and recording the failure position of the component;
step S10: identifying a failure sequence of a component of an inclined pylon: sequencing the recorded failure positions of the components according to failure time to obtain a component failure sequence;
step S11: determine if the tilt-bridge tower failure mode identified at step S10 matches the tilt-bridge tower expected failure mode determined at step S2? If yes, go to step S24; if no, go to step S12;
step S24: outputting relevant parameters of the optimized inclined bridge tower;
the execution of the bridge tower failure mode optimization module comprises the following steps:
step S12: determining optimized parameters of the inclined bridge tower: using flexural capacity as an optimization parameter, including M bi And M ci (ii) a Wherein M is bi The bending resistance bearing capacity of the beam end section of the ith layer node of the inclined bridge tower in the clockwise or anticlockwise direction is shown; m ci The bending resistance bearing capacity of the column end section of the ith layer node of the inclined bridge tower in the clockwise or anticlockwise direction is shown;
step S13: and judging whether the ith layer member of the inclined bridge tower fails according to the identification result of the step S9:
if the judgment result is yes, the step S15, S16 and S18 are carried out to calculate the cross section bearing capacity; otherwise, enabling i to be i +1, and entering the judgment of the next layer of the inclined bridge tower;
steps S15, S16, S18 are: calculating the column end section bending resistance bearing capacity M of the ith layer of the inclined bridge tower ci Beam end section bending resistance bearing capacity M bi And inclination angle influence coefficient eta i ；
Step S17: column end section bending resistance bearing capacity M considering dip angle factor sci Calculating;
step S19: judgment M sci >M bi Is there a If the judgment result is no, the step is transferred to the step S20 to make an optimization strategy; if yes, go to step S23;
step S20: an optimization strategy is formulated, and a column end section bending moment adjustment coefficient a and a beam end section bending moment adjustment coefficient b are calculated; the fox-searching optimization strategy is an optimization iteration method determined according to the stress and deformation characteristics of the inclined bridge tower;
the steps S21 and S22 are: recalculating column end section bending resistance bearing capacity M ci Beam end section bending resistance bearing capacity M bi (ii) a After the calculation of the steps S21 and S22 is completed, the column end section bending resistance bearing capacity M of the steps S16 and S18 is updated ci Beam end section bending resistance bearing capacity M bi ；
Step S23: judging whether the optimized ith layer is the maximum layer number n of the inclined bridge tower; if no, go to step S14; if yes, the numerical model is updated, and the process proceeds to step S3.
Further, step S5 specifically includes the following steps:
step S5.1: calculating the vibration mode vector phi of the inclined bridge tower n ：
The motion equation of the inclined bridge tower is shown as the formula (1):
in the formula (I), the compound is shown in the specification,
is the acceleration;
is the speed; u is a displacement; p (t) is an external force; m is a mass matrix; c is a structural damping coefficient matrix; k is a structural stiffness matrix;
as a multiple degree of freedom system, the free motion of the natural mode of vibration of an inclined bridge tower is described in mathematical form as:
u(t)＝q n (t)φ n (2)
in the formula, the vibration mode phi n Not varying with time, displacement q n (t) time-dependent is described by a simple harmonic function:
q n (t)＝A n cosω n t+B n sinω n t (3)
in the formula, ω n Is the structural natural vibration circular frequency; a. the n And B n Is an integration constant determined from the initial conditions of the motion; combining formula (2) and formula (3) yields:
u(t)＝φ n (A n cosω n t+B n sinω n t) (4)
substituting u (t) into equation of motion (1) yields:
the characteristic equation can thus be obtained:
solving the characteristic equation (6) to obtain the natural vibration frequency omega n Then, the self-oscillation frequency is substituted into formula (5) to obtain the oscillation mode vector phi n (ii) a Step S5.2 calculating the natural vibration period T of the inclined bridge tower n：
Wherein, T n Is the natural vibration period of the inclined bridge tower; omega n The natural vibration circle frequency corresponding to the natural vibration period of the inclined bridge tower.
Further, step S6 specifically includes the following steps:
modal lateral force s n Is expressed by equation (8):
s n ＝mφ n r (8)
in the formula: s n The modal lateral force of the inclined bridge tower loaded for the nth step; m is a mass matrix of the inclined bridge tower; phi is a n r Is the normalized mode vector of the nth step.
Further, step S7 specifically includes the following steps:
step S7.1: determining a lateral distribution force mode of the inclined bridge tower, and performing lateral pushing analysis on the inclined bridge tower to obtain a base shearing force F-top displacement D curve;
in this step, the lateral distribution force mode refers to the type of distribution force when the structure is laterally loaded;
step S7.2: the base shearing force (F) -top displacement (D) curve of the inclined bridge tower is equivalent to the base shearing force (F) -top displacement (D) curve of a single-degree-of-freedom system through the formula (9) and the formula (10), namely F * -D * The curve:
in the formula: q * Q is a certain response index of the equivalent single-degree-of-freedom system and the original structure respectively; the gamma is a conversion coefficient of an original structure conversion single-degree-of-freedom system; m is i Is the ith layer mass; phi i Is a modification of the ith layer.
Step S7.3: equivalent system force (F) of single degree of freedom * ) -displacement (D) * ) The curve is bilinearly, and the bilinear process follows the following principle:
firstly, the post-yield rigidity of the bilinear curve is zero;
the force corresponding to the intersection point of the two curves is equal to the yield strength of 60 percent;
the area enclosed by the two curves and the X axis is equal;
step S7.4: bilinear force (F) by equation (11) * ) -displacement (D) * ) The curve is converted into a power spectrum curve, i.e. acceleration (S) a ) -displacement (S) d ) The curve:
in the formula: f * Is of equal efficacy; m is * Equivalent mass;
step S7.5: selection of the elastic response spectrum, i.e. S, according to the respective parameters a -a T-curve;
step S7.6: the elastic reaction spectrum S is represented by the formula (12) a -T-curve conversion into elastic demand spectrum curve acceleration (S) a e ) -displacement (S) d e ) The curve:
wherein: s d e The corresponding spectrum shift of the elastic reaction spectrum; s a e The spectrum acceleration corresponding to the elastic reaction spectrum;
step S7.7: the power spectrum curve S obtained in the step S7.4 a -S d The curve is compared with the demand spectrum curve S obtained in step S7.6 a -S d Drawing the curves on the same graph, determining the intersection point of the two curves, and obtaining the target displacement D of the equivalent single-degree-of-freedom system t * (ii) a Will D t * Multiplying the equivalent single-degree-of-freedom system conversion coefficient gamma to obtain the target displacement D of the inclined bridge tower under the action of earthquake motion t ；
Further, step S8 specifically includes the following steps based on the CMP method:
step S8.1: determining a cumulative effective modal mass coefficient limit value ζ of a mode shape included in the CMP method:
modal shape contribution coefficient of structure
The sum being 1, i.e.
Step S8.2: determining modal lateral force S of CMP method n The mode shape that needs to be included:
calculating to obtain the accumulated effective modal mass coefficient
Satisfy the requirement of
All the front j-order mode shapes of (a); modal lateral force S of CMP process n Including the first j order mode;
step S8.3: using modal side forces S of various orders n Sequentially carrying out CMP method analysis on the inclined bridge tower until the displacement of the top of the inclined bridge tower reaches the target displacement D t ；
The target displacement loaded in each step in the multi-step analysis is
And, the initial state of each step of analysis is the termination state of the previous step of analysis.
Further, the calculation process of steps S15, S16, and S18 specifically includes the following steps:
cross section bending resistance bearing capacity M ci 、M bi Calculation is carried out according to the section type and corresponding specifications;
calculating the inclination angle influence coefficient eta according to the formula (13) i ；
η i ＝f(α i ) (13)
Wherein alpha is i The inclination angle of the ith layer of tower column of the inclined bridge tower is shown; eta i Is the incidence influence coefficient;
f (-) is α i And η i The specific expression of the functional relationship is shown as formula (14):
η i ＝0.00031α i 2 -0.0471α i +2.7846 (14)。
further, the calculation process of step S17 specifically includes the following steps:
M sci ＝M ci /η i (15)
in the formula, M ci The bending resistance bearing capacity of the section of the ith layer node column end of the inclined bridge tower along the clockwise or anticlockwise direction is provided; eta i Is the tilt angle influence coefficient.
Further, the calculation process of steps S21 and S22 specifically includes the following steps:
the calculation is shown in equation (16) and equation (17):
M ci ＝aM ci (16)
M bi ＝bM bi (17)
wherein a is a bending moment adjustment coefficient of a column end section; b is the beam end section bending moment adjustment coefficient.
Compared with the prior art, the invention and some key designs of the preferred scheme thereof are embodied as follows:
(1) the method of the invention considers the tower inclination angle alpha in the steps S15-S19 i The influence on the structural failure mode is quantified as the incidence influence coefficient eta i The method is applied to iterative calculation of bridge tower optimization, so that the failure mode of the inclined bridge tower can be accurately optimized.
(2) In the method, a continuous mode pushover method (CMP method) is adopted to identify the structural failure mode in the steps S5-S10, so that the computational analysis efficiency of the optimization process of the failure mode of the inclined bridge tower is obviously improved.
(3) In steps S12-S23, the method adopts a strategy of gradual optimization from the bottom layer to the top layer, so that the optimization program is well-arranged, and failure positions needing optimization cannot be missed.
The advantages include:
(1) in the method, the influence of the tower inclination angle on the structural failure mode is calculated into an inclination angle influence coefficient eta in the step S15, and the eta is applied to the iterative calculation of the bridge tower optimization process in the step S17, so that the iterative times of the failure mode optimization process of the inclined bridge tower are reduced, and the optimization result is more accurate.
(2) In the invention, when the structural failure mode is identified and analyzed in the step S8, compared with the IDA method, the adopted CMP method can obviously improve the calculation efficiency. The CMP method only needs 25-40min for analysis, and greatly improves the analysis speed on the premise of ensuring the analysis precision.
(3) The CMP method employed in steps S5-S7 of the method of the present invention. Compared with the time-course analysis that only the response of the bridge tower under certain specific earthquake motion can be considered, the CMP method determines the lateral force distribution mode according to the vibration mode of the bridge tower, considers the contribution of the high-order vibration mode of the bridge tower and can properly simulate the stress and deformation of the inclined bridge tower under the action of various earthquake loads. Therefore, the failure mode of the inclined bridge tower identified by the method is very representative.
(4) In step S12, the cross-section bending resistance is selected as an optimization parameter, and various specific optimization and adjustment measures such as adjusting material characteristics, adjusting cross-section size, adding energy consumption devices, etc. are taken into consideration, so that the method can be better suitable for engineering requirements. In addition, the method requires a specific optimization strategy, such as a fixed point iteration method, a secant iteration method, a steepest descent method and the like, to be used in the optimization process, so that the method has a standard flow and is favorable for realizing the optimization of the failure mode of the inclined bridge tower by using computer programming.
(5) The optimization program of the failure mode of the bridge tower (step S12-step S23) adopts an integral strategy of optimizing layer by layer, and from the 1 st layer of bridge tower, the bending resistance bearing capacity of the cross beam and the tower column of each layer is optimized. The optimization program is well-arranged, failure positions needing to be optimized cannot be missed, and the optimization can be quickly carried out to the expected failure mode.
Drawings
FIG. 1 is a schematic diagram of bridge tower parameters according to an embodiment of the present invention.
FIG. 2 is a flowchart of an optimization method according to an embodiment of the present invention.
Fig. 3 is a schematic structural diagram of an inclined bridge tower according to an embodiment of the invention.
FIG. 4 is a schematic diagram of the loading of the lateral force of the bridge tower structure according to the embodiment of the present invention.
FIG. 5 is a schematic diagram of a CMP method for analyzing a failure mode of a diamond-type bridge tower according to an embodiment of the present invention.
FIG. 6 is a schematic diagram illustrating a comparison of failure modes of an optimized front and rear bridge tower structure according to an embodiment of the present invention.
FIG. 7 is a flow chart of prior art structural failure mode optimization.
Detailed Description
In order to make the features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail as follows:
it should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 2, the optimization method for the failure mode of the transverse seismic structure of the inclined bridge tower provided by this embodiment can be divided into two modules, namely: a bridge tower calculation analysis and identification program module, a second module: and optimizing a program module for the failure mode of the bridge tower. The method specifically comprises the following steps:
a first module: inclined bridge tower calculation analysis and recognition program module
Step S1: extracting relevant analysis parameters of the inclined bridge tower.
For example, an inclined pylon height h i Beam width b i Angle of inclination of tower column alpha i Tensile strength f of steel bar y And yield strain ε
And the like. Some of the analysis parameters are shown in figure 1.
Step S2: determining an expected failure mode of the inclined bridge tower under the action of a fortification earthquake according to the bridge seismic fortification requirement of the position of the inclined bridge tower;
step S3: and establishing a numerical analysis model of the inclined bridge tower based on the related analysis parameters of the inclined bridge tower.
Step S5: and solving the dynamic characteristics of the inclined bridge tower. Including period of natural oscillation T n The mode mass participation coefficient of each order vibration mode
And vibration mode vector phi n And the vibration mode vector phi is measured n Normalization to make the modal vector at the top of the inclined bridge tower
Step S5.1: calculating the vibration mode vector phi of the inclined bridge tower n 。
The motion equation of the inclined bridge tower is shown as the formula (1):
in the formula (I), the compound is shown in the specification,
is the acceleration;
is the speed; u is a displacement; p (t) is an external force. m is a mass matrix; c is a structural damping coefficient matrix; k is the structural stiffness matrix.
As a multiple degree of freedom system, the free motion of the natural mode of vibration of an inclined bridge tower is described in mathematical form as:
u(t)＝q n (t)φ n (2)
in the formula, the vibration mode phi n Does not change with time. Displacement q n (t) time-dependent is described by a simple harmonic function:
q n (t)＝A n cosω n t+B n sinω n t (3)
in the formula, ω n Is the structural natural vibration circular frequency; a. the n And B n Is an integration constant and can be determined based on the initial conditions of the motion.
Combining the formula (2) and the formula (3) to obtain
u(t)＝φ n (A n cosω n t+B n sinω n t) (4)
Substituting u (t) into equation of motion (1) yields
[k-ω n 2 m]φ n ＝0 (5)
The characteristic equation can thus be obtained:
'Jiexi' medicine for treating chronic hepatitisObtaining the natural vibration frequency omega by the equation (6) n Then, the self-oscillation frequency is substituted into formula (5) to obtain the oscillation mode vector phi n Step S5.2 calculating the natural vibration period T of the inclined bridge tower n
Wherein, T n Is the natural vibration period of the inclined bridge tower;
ω n the natural vibration circle frequency corresponding to the natural vibration period of the inclined bridge tower.
Step S6: solving modal lateral force s of inclined bridge tower n 。
Modal lateral force s n Is shown in formula (8)
s n ＝mφ n r (8)
In the formula: s n The modal lateral force of the inclined bridge tower loaded for the nth step;
m is a mass matrix of the inclined bridge tower;
φ n r is the normalized mode vector of the nth step.
Step S7: calculating target displacement D of the top of the inclined bridge tower under seismic oscillation with corresponding intensity t 。
Step S7.1: and determining a lateral distribution force mode of the inclined bridge tower, and performing lateral pushing analysis on the inclined bridge tower to obtain a base shearing force F-top displacement D curve (F-D curve).
In this step, the lateral distribution force mode refers to the type of distribution force when the structure is laterally loaded, and may be an inverted triangular distribution force, a uniform distribution force, an equal distribution mode, or the like.
Step S7.2: the base shearing force (F) -top displacement (D) curve of the inclined bridge tower is equivalent to the base shearing force (F) -top displacement (D) curve (F) of a single-degree-of-freedom system through the formula (9) and the formula (10) * -D * Curve)
In the formula: q * Q is a certain response index of the equivalent single-degree-of-freedom system and the original structure, such as force response and displacement response;
the gamma is a conversion coefficient of an original structure conversion single-degree-of-freedom system;
m i is the ith layer mass;
Φ i is a modification of the ith layer.
Step S7.3: equivalent system force (F) of single degree of freedom * ) -displacement (D) * ) The curve is bilinearly, and the bilinear process follows the following principle:
firstly, the post-yield rigidity of the bilinear curve is zero;
the force corresponding to the intersection point of the two curves is equal to the yield strength of 60 percent;
and the area enclosed by the two curves and the X axis is equal.
Step S7.4: bilinear force (F) by equation (11) * ) -displacement (D) * ) The curve is converted into a power spectrum curve (acceleration (S) a ) -displacement (S) d ) Curve) is shown.
In the formula: f * Is of equal efficacy;
m * equivalent mass;
step S7.5: selecting an elastic response spectrum (S) according to the corresponding parameters a -T curve).
Step S7.6: the elastic reaction spectrum (S) is represented by the formula (12) a -T curve) into an elastic demand spectrum curve (acceleration (S) a e ) -displacement (S) d e ) Curve) is shown.
Wherein: s d e The corresponding spectrum shift of the elastic reaction spectrum;
S a e the spectrum acceleration corresponding to the elastic reaction spectrum.
Step S7.7: the power spectrum curve (S) obtained in step S7.4 a -S d Curve) and the demand spectrum curve (S) determined in step S7.6 a -S d Curve) is drawn on the same graph, and after the intersection point of the two curves is determined, the target displacement D of the equivalent single-degree-of-freedom system can be obtained t * . Will D t * Multiplying the equivalent single-degree-of-freedom system conversion coefficient gamma obtained in the previous step to obtain the target displacement D of the inclined bridge tower under the action of rare earthquake t 。
Step S8: performing side-push analysis on the inclined bridge tower based on a continuous Modal push analysis method (CMP method) until the displacement of the top of the inclined bridge tower reaches a target displacement D t 。
The CMP method is a pushover analysis method for determining a distribution force mode by using a mode shape corresponding to each order mode of a structure in order to consider the contribution of a high-order mode shape of the structure. The CMP method comprises the following specific steps:
step S8.1: and determining a cumulative effective modal mass coefficient limit value zeta of the vibration mode included in the analysis of the CMP method.
Modal shape contribution coefficient of structure
The sum being 1, i.e.
Since the CMP method analysis does not consider the mode shape of all orders, the cumulative effective modal mass coefficient limit ζ is set by the user according to the structural characteristics. It is generally recommended that the cumulative effective modal mass coefficient of the mode shape involved in the analysis by the CMP method be greater than 0.9.
Step S8.2: determining modal lateral force S for CMP method analysis n The mode shape involved is required.
Calculating to obtain the accumulated effective modal mass coefficient
Satisfy the requirement of
All the first j-order mode shapes. Modal lateral force S for CMP method analysis n Including the first j order mode. For example: when ζ is 0.9
The modal lateral force of the CMP process includes the first 5 order mode.
Step S8.3: using modal side forces S of various orders n Sequentially carrying out CMP method analysis on the inclined bridge tower until the displacement of the top of the inclined bridge tower reaches the target displacement D t 。
It should be noted that, the target displacement of each step of loading in the multi-step analysis is
And, the initial state of each step of analysis is the termination state of the previous step of analysis.
Step S9: identifying a failure location of the leaning pylon.
And judging the failure component of the inclined bridge tower according to whether the mechanical indexes (steel bar tensile stress, concrete compressive stress and the like) and the deformation indexes (curvature, interlayer displacement and the like) of the component of the inclined bridge tower meet the failure standard. If the performance index of a certain component of the inclined bridge tower at a certain position meets or exceeds the failure standard, the component is identified to be failed, and the failure position of the component is recorded.
Step S10: a failure sequence of the components of the inclined pylon is identified.
And sequencing the recorded failure positions of the components according to failure time to obtain a component failure sequence. The failure sequence is a failure mode of the sloped turret under CMP process.
Step S11: determine if the tilt-bridge tower failure mode identified at step S10 matches the tilt-bridge tower expected failure mode determined at step S2? If yes, go to step S24; if no, the routine proceeds to step S12.
Step S24: and outputting relevant parameters of the optimized inclined bridge tower.
And a second module: inclined bridge tower failure mode optimization program module
Step S12: and determining the optimized parameters of the inclined bridge tower.
Under seismic loading, the column end of an inclined pylon typically undergoes flexural failure due to insufficient flexural capacity. Based on this, the method proposes to use the "flexural capacity" as an optimization parameter, including M bi And M ci . Wherein M is bi The bending resistance bearing capacity of the beam end section of the ith layer node of the inclined bridge tower in the clockwise (anticlockwise) direction is shown; m ci The bending resistance and the bearing capacity along the clockwise (anticlockwise) direction of the column end section of the ith-layer node of the inclined bridge tower are shown.
Step S13: is it determined whether the i-th layer member of the inclined pylon has failed according to the recognition result of step S9?
If the judgment result is yes, the step S15, S16 and S18 are carried out to calculate the cross section bearing capacity; otherwise, the step i is made to be i +1, and the judgment of the next layer of the inclined bridge tower is carried out.
Steps S15, S16, S18: calculating the column end section bending resistance bearing capacity M of the ith layer of the inclined bridge tower ci Beam end section bending resistance bearing capacity M bi And inclination angle influence coefficient eta i 。
Bending-resistant bearing capacity M of section ci 、M bi It is necessary to perform calculations according to the respective specifications, according to the type of section. For example, the bending resistance bearing capacity of the reinforced concrete section is calculated according to the reinforced concrete structure design specification, and the bending resistance bearing capacity of the section steel is calculated according to the steel structure design specification.
Calculating the inclination angle influence coefficient eta according to the formula (13) i 。
η i ＝f(α i ) (13)
Wherein alpha is i The inclination angle of the ith layer of tower column of the inclined bridge tower is shown;
η i is the incidence influence coefficient;
f (-) is α i And η i The specific expression of the functional relationship is shown as formula (14):
η i ＝0.00031α i 2 -0.0471α i +2.7846 (14)
step S17: column end section bending resistance bearing capacity M considering dip angle factor sci And (4) calculating.
M sci ＝M ci /η i (15)
In the formula, M ci The bending resistance bearing capacity of the section of the ith layer node column end of the inclined bridge tower along the clockwise (anticlockwise) direction is provided;
η i is the tilt angle influence coefficient.
Step S19: judgment M sci >M bi Is there a If the judgment result is no, the step is transferred to the step S20 to make an optimization strategy; if yes, the process proceeds to step S23.
Step S20: and (4) establishing an optimization strategy, and calculating a column end section bending moment adjustment coefficient a and a beam end section bending moment adjustment coefficient b.
The optimization strategy is an optimization iteration method determined according to the stress and deformation characteristics of the inclined bridge tower, and the selected optimization strategy can be any optimization iteration method such as a fixed point iteration method, a tangent line iteration method, a steepest descent method and the like.
Steps S21, S22: recalculating column end section bending resistance bearing capacity M ci Beam end section bending resistance bearing capacity M bi ，。
Specifically, the calculation is shown in formula (16) and formula (17):
M ci ＝aM ci (16)
M bi ＝bM bi (17)
in the formula, a is a bending moment adjustment coefficient of a column end section; b is the beam end section bending moment adjustment coefficient.
After the calculation of the steps S21 and S22, the column end section bending resistance bearing capacity M of the steps S16 and S18 is updated ci Beam end section bending resistance bearing capacity M bi 。
Step S23: and judging whether the optimized ith layer is the maximum layer number n of the inclined bridge tower. If no, go to step S14; if yes, the numerical model is updated, and the process proceeds to step S3.
The following provides an exemplary embodiment of the method of the present invention:
1) step S1: determining bridge tower arithmetic parameters:
the present embodiment uses a diamond-shaped main tower (inclined bridge tower) of a cable-stayed bridge as an example. The diamond type bridge tower has a tower height of 213m, and the tower column comprises an upper tower column, a middle tower column and a lower tower column, and the heights of the tower columns are 66.5m, 97.9m and 48.6m respectively. The tower columns on the two sides are respectively connected by an upper beam, a middle beam and a lower beam, and the lengths of the beams are respectively 8.2m, 19.6m and 36.1 m. The inclination angle of the lower tower column is 100 degrees, and the inclination angles of the middle tower column and the upper tower column are 80 degrees. As shown in fig. 3:
2) step S2: an expected failure mode is determined.
The stress division of the diamond-shaped bridge tower is as follows: the tower column mainly bears the vertical load transmitted by the stay cable; the lower cross beam mainly bears axial tension and a small part of gravity load transmitted by the main beam of the cable-stayed bridge; the middle cross beam mainly bears axial force and bending moment; the upper cross beam mainly bears shearing force and partial axial force. The third-level cross beam is connected with the tower column, and provides lateral stiffness for the bridge tower. It can be seen that of the diamond bridge construction, the tower column is of the highest importance, followed by the lower cross-beam, followed again by the middle cross-beam, and finally by the upper cross-beam. Based on the above analysis, the expected failure mode of the diamond-type bridge tower under the action of the lateral load is determined as follows: the upper, middle and lower beams enter a yielding state in sequence, and finally the tower column enters the yielding state.
3) Steps S5 to S8: determining relevant parameters of the CMP method and analyzing and calculating the CMP method.
The embodiment adopts OpenSees software modeling analysis. Taking zeta equal to 0.9 to obtain the first five-order effective modal quality coefficient
Therefore, determining the modal lateral force of the CMP process involves the diamond bridge tower front 5 order mode. The calculated period and effective modal mass coefficients are shown in table 1.
TABLE 1 dynamic characteristics of bridge tower structure
In the embodiment, the contribution of the front 5-order vibration mode of the diamond-shaped bridge tower is considered, and the modal lateral force S of each step is calculated n Is shown in fig. 5. According to step S7, the target displacement is calculated as: 3.69 m.
The CMP process analyzed the failure mode of the diamond-type bridge tower as shown in figure 6. It can be seen from the figure that before the bridge tower is damaged, all key positions of the middle tower column and the lower tower column with the highest importance degree are in a yield state, the lower cross beam, the middle cross beam and the upper cross beam with the second importance degree are not in the yield state, and the final damage position is generated at the key section of the middle tower column. It can be seen that the actual failure mode of a diamond-type bridge differs significantly from the expected failure mode, and that optimization of the failure mode of a diamond-type bridge is required.
4) Step S15: calculating the inclination angle influence coefficient eta according to the formula (14) i The results are shown in table 2:
TABLE 2 influence coefficient of inclination angle of tower column in bridge tower structure
5) Optimizing the iterative process S16-S22
The column end bending moment adjustment coefficient a is 1 and the beam end bending moment adjustment coefficient b is 0.5 in step S20 calculated by an iterative method. The layer 1 iteration is shown in table 3. After completing the optimization of the 1 st layer of bridge tower through 5 times of cyclic calculation, the bending moment iteration adjustment of the 1 st layer of cross beam (lower cross beam) is shown in table 3. (Table 3 shows that the flexural capacity of the 2 nd and 3 rd layers is not changed when the 1 st layer bridge tower is optimized)
TABLE 3 bridge tower end bending moment iteration data
6) Optimizing results
The bridge tower failure modes before and after optimization are shown in figure 6. As can be seen from the yield sequence of fig. 6(a), the failure mode of the optimized rear pylon is consistent with the expected failure mode, i.e., the upper, middle and lower crossbeams enter the yield state in sequence, and finally the pylon enters the yield state. It can be seen from fig. 6(b) failure location that the ultimate failure of the optimum pylon occurs at the top rail location. The failure mode can furthest exert the anti-seismic performance of the bridge tower under the action of strong shock. The damage mode can cause the main stressed component tower column to be less damaged and the sudden structural collapse can not occur.
It follows that diamond bridge tower optimization can be effectively performed using the method of the present invention.
It will be appreciated by those skilled in the art that the above embodiments of the present invention may be provided as a method, apparatus, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations of methods, apparatus (devices), and computer program products according to embodiments of the invention. It will be understood that each flow of the flowcharts, and combinations of flows in the flowcharts, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
The present invention is not limited to the above preferred embodiments, and any other optimization methods for transverse seismic failure modes of an inclined pylon can be derived from the teaching of the present invention.
Claims (9)
1. An optimization method for a transverse earthquake failure mode of an inclined bridge tower is characterized by comprising the following steps: when the structural failure mode is identified and analyzed, a CMP method is adopted, a lateral force distribution mode is determined according to the bridge tower vibration mode, and the contribution of the high-order bridge tower vibration mode is considered; optimizing the bending resistance bearing capacity of the cross beam and the tower column of each layer from the 1 st layer of the bridge tower by adopting an integral strategy of optimizing layer by layer, selecting the bending resistance bearing capacity of the cross section as an optimization parameter, and considering the inclination angle alpha of the tower column i The influence on the structural failure mode is quantified as the incidence influence coefficient eta i The method is applied to iterative calculation of bridge tower optimization.
2. The method of optimizing a transverse seismic failure mode of a leaning tower according to claim 1, comprising: the bridge tower failure mode optimizing system comprises a bridge tower calculation analysis and recognition module and a bridge tower failure mode optimizing module;
the execution of the bridge tower calculation analysis and identification module comprises the following steps:
step S1: extracting relevant analysis parameters of the inclined bridge tower, comprising: height h of inclined bridge tower i Width of beam b i Angle of inclination of tower column alpha i Tensile strength f of steel bar y And a yield strain ε;
step S2: determining an expected failure mode of the inclined bridge tower under the action of a fortification earthquake according to the bridge seismic fortification requirement of the position of the inclined bridge tower;
step S3: establishing a numerical analysis model of the inclined bridge tower based on the related analysis parameters of the inclined bridge tower;
step S5: solving the dynamic characteristics of the inclined bridge tower, comprising the following steps: period of natural vibration T n The mode mass participation coefficient of each order vibration mode
And a vibration mode vector phi n And the vibration mode vector phi is measured n Normalization to make the modal vector at the top of the inclined bridge tower
Step S6: solving modal lateral force s of inclined bridge tower n ；
Step S7: calculating target displacement D of the top of the inclined bridge tower under seismic oscillation with corresponding intensity t ；
Step S8: performing side-push analysis on the inclined bridge tower based on the CMP method until the displacement of the top of the inclined bridge tower reaches the target displacement D t ；
Step S9: identifying a failure location of an inclined bridge tower: judging the failure component of the inclined bridge tower according to whether the mechanical index and the deformation index of the component of the inclined bridge tower reach the failure standard; if the performance index of a certain component of the inclined bridge tower at a certain position meets or exceeds the failure standard, identifying the component as failed, and recording the failure position of the component;
step S10: identifying a failure sequence of a component of an inclined pylon: sequencing the recorded failure positions of the components according to failure time to obtain a component failure sequence;
step S11: determine if the tilt-bridge tower failure mode identified at step S10 matches the tilt-bridge tower expected failure mode determined at step S2? If yes, go to step S24; if no, go to step S12;
step S24: outputting relevant parameters of the optimized inclined bridge tower;
the execution of the bridge tower failure mode optimization module comprises the following steps:
step S12: determining optimized parameters of the inclined bridge tower: using flexural capacity as an optimization parameter, including M bi And M ci (ii) a Wherein M is bi The bending resistance bearing capacity of the beam end section of the ith layer node of the inclined bridge tower in the clockwise or anticlockwise direction is shown; m ci The bending resistance bearing capacity of the column end section of the ith layer node of the inclined bridge tower in the clockwise or anticlockwise direction is shown;
step S13: and judging whether the ith layer member of the inclined bridge tower fails according to the identification result of the step S9:
if the judgment result is yes, the step S15, S16 and S18 are carried out to calculate the cross section bearing capacity; otherwise, enabling i to be i +1, and entering the judgment of the next layer of the inclined bridge tower;
steps S15, S16, S18 are: calculating the column end section bending resistance bearing capacity M of the ith layer of the inclined bridge tower ci Beam end section bending resistance bearing capacity M bi And inclination angle influence coefficient eta i ；
Step S17: column end section bending resistance bearing capacity M considering dip angle factor sci Calculating;
step S19: judgment M sci >M bi Is there a If the judgment result is no, the step is transferred to the step S20 to make an optimization strategy; if yes, go to step S23;
step S20: an optimization strategy is formulated, and a column end section bending moment adjustment coefficient a and a beam end section bending moment adjustment coefficient b are calculated; the fox-searching optimization strategy is an optimization iteration method determined according to the stress and deformation characteristics of the inclined bridge tower;
the steps S21 and S22 are: recalculating column end section bending resistance bearing capacity M ci Beam end section bending resistance bearing capacity M bi (ii) a After the calculation of the steps S21 and S22 is completed, the column end section bending resistance bearing capacity M of the steps S16 and S18 is updated ci Beam end section bending resistance bearing capacity M bi ；
Step S23: judging whether the optimized ith layer is the maximum layer number n of the inclined bridge tower; if no, go to step S14; if yes, the numerical model is updated, and the process proceeds to step S3.
3. The method of optimizing a transverse seismic failure mode of a leaning tower according to claim 2, wherein: step S5 specifically includes the following steps:
step S5.1: calculating the vibration mode vector phi of the inclined bridge tower n ：
The motion equation of the inclined bridge tower is shown as the formula (1):
in the formula (I), the compound is shown in the specification,
is the acceleration;
is the speed; u is a displacement; p (t) is an external force; m is a mass matrix; c is a structural damping coefficient matrix; k is a structural stiffness matrix;
as a multiple degree of freedom system, the free motion of the natural mode of vibration of an inclined bridge tower is described in mathematical form as:
u(t)＝q n (t)φ n (2)
in the formula, the vibration mode phi n Does not change with timeOf displacement q n (t) time-dependent is described by a simple harmonic function:
q n (t)＝A n cosω n t+B n sinω n t (3)
in the formula, ω n Is the structural natural vibration circular frequency; a. the n And B n Is an integration constant determined from the initial conditions of the motion;
combining formula (2) and formula (3) yields:
u(t)＝φ n (A n cosω n t+B n sinω n t) (4)
substituting u (t) into equation of motion (1) yields:
the characteristic equation can thus be obtained:
solving the characteristic equation (6) to obtain the natural vibration frequency omega n Then, the self-oscillation frequency is substituted into formula (5) to obtain the oscillation mode vector phi n ；
Step S5.2 calculating the natural vibration period T of the inclined bridge tower n ：
Wherein, T n Is the natural vibration period of the inclined bridge tower; omega n The natural vibration circle frequency corresponding to the natural vibration period of the inclined bridge tower.
4. A method of optimizing a transverse seismic failure mode of a leaning tower according to claim 3, wherein: step S6 specifically includes the following steps:
modal lateral force s n Is solved byThe formula is shown as formula (8):
s n ＝mφ n r (8)
in the formula: s n The modal lateral force of the inclined bridge tower loaded for the nth step; m is a mass matrix of the inclined bridge tower; phi is a n r Is the normalized mode vector of the nth step.
5. The method of optimizing a transverse seismic failure mode of a leaning tower according to claim 4, wherein: step S7 specifically includes the following steps:
step S7.1: determining a lateral distribution force mode of the inclined bridge tower, and performing lateral pushing analysis on the inclined bridge tower to obtain a base shearing force F-top displacement D curve;
in this step, the lateral distribution force mode refers to the type of distribution force when the structure is laterally loaded;
step S7.2: the base shearing force (F) -top displacement (D) curve of the inclined bridge tower is equivalent to the base shearing force (F) -top displacement (D) curve of a single-degree-of-freedom system through the formula (9) and the formula (10), namely F * -D * The curve:
in the formula: q * Q is a certain response index of the equivalent single-degree-of-freedom system and the original structure respectively; the gamma is a conversion coefficient of an original structure conversion single-degree-of-freedom system; m is i Is the quality of the ith layer; phi i Is a modification of the ith layer.
Step S7.3: equivalent system force (F) of single degree of freedom * ) -displacement (D) * ) The curve is bilinearly, and the bilinear process follows the following principle:
firstly, the post-yield rigidity of the bilinear curve is zero;
the force corresponding to the intersection point of the two curves is equal to the yield strength of 60 percent;
the area enclosed by the two curves and the X axis is equal;
step S7.4: bilinear force (F) by equation (11) * ) -displacement (D) * ) The curve is converted into a power spectrum curve, i.e. acceleration (S) a ) -displacement (S) d ) The curve:
in the formula: f * Is of equal efficacy; m is * Equivalent mass;
step S7.5: selection of the elastic response spectrum, i.e. S, according to the respective parameters a -a T-curve;
step S7.6: the elastic reaction spectrum S is represented by the formula (12) a -T-curve conversion into elastic demand spectrum curve acceleration (S) a e ) -displacement (S) d e ) The curve:
wherein: s d e The corresponding spectrum shift of the elastic reaction spectrum; s a e The spectrum acceleration corresponding to the elastic reaction spectrum;
step S7.7: the power spectrum curve S obtained in step S7.4 a -S d The curve is compared with the demand spectrum curve S obtained in step S7.6 a -S d Drawing the curves on the same graph, determining the intersection point of the two curves, and obtaining the target displacement D of the equivalent single-degree-of-freedom system t * (ii) a Will D t * Multiplying the equivalent single-degree-of-freedom system conversion coefficient gamma to obtain the target displacement D of the inclined bridge tower under the action of earthquake motion t 。
6. The method of optimizing a transverse seismic failure mode of a leaning tower according to claim 5, wherein: step S8 specifically includes the following steps based on the CMP method:
step S8.1: determining a cumulative effective modal mass coefficient limit value ζ of a mode shape included in the CMP method:
modal shape contribution coefficient of structure
The sum being 1, i.e.
Step S8.2: determining modal lateral force S of CMP method n The mode shape that needs to be included:
calculating to obtain the accumulated effective modal mass coefficient
Satisfy the requirement of
All the front j-order mode shapes of (a); modal lateral force S of CMP method n Including the first j order mode;
step S8.3: using modal side forces S of various orders n Sequentially carrying out CMP method analysis on the inclined bridge tower until the displacement of the top of the inclined bridge tower reaches the target displacement D t ；
The target displacement loaded in each step in the multi-step analysis is
And, the initial state of each step of analysis is the termination state of the previous step of analysis.
7. The method of optimizing a transverse seismic failure mode of a leaning tower according to claim 6, wherein: the calculation process of steps S15, S16, S18 specifically includes the following steps:
cross section bending resistance bearing capacity M ci 、M bi Calculation is carried out according to the section type and corresponding specifications;
calculating the inclination angle influence coefficient eta according to the formula (13) i ；
η i ＝f(α i ) (13)
Wherein alpha is i The inclination angle of the ith layer of tower column of the inclined bridge tower is shown; eta i Is the incidence influence coefficient;
f (-) is α i And η i The specific expression of the functional relationship is shown as formula (14):
η i ＝0.00031α i 2 -0.0471α i +2.7846 (14)。
8. the method of optimizing a transverse seismic failure mode of a leaning tower according to claim 7, wherein: the calculation process of step S17 specifically includes the following steps:
M sci ＝M ci /η i (15)
in the formula, M ci The bending resistance bearing capacity of the section of the ith layer node column end of the inclined bridge tower along the clockwise or anticlockwise direction is provided; eta i Is the tilt angle influence coefficient.
9. The method of optimizing a transverse seismic failure mode of a leaning tower according to claim 8, wherein: the calculation process of steps S21, S22 specifically includes the following steps:
the calculation is shown in equation (16) and equation (17):
M ci ＝aM ci (16)
M bi ＝bM bi (17)
wherein a is a bending moment adjustment coefficient of a column end section; b is the beam end section bending moment adjustment coefficient.
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