CN114741648A - Cable force analysis method and device for cable-stayed bridge, electronic device and storage medium - Google Patents
Cable force analysis method and device for cable-stayed bridge, electronic device and storage medium Download PDFInfo
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Abstract
The application discloses a cable force analysis method and device for a cable-stayed bridge, electronic equipment and a storage medium. The cable force analysis method of the cable-stayed bridge can comprise the following steps: determining an attribute value of a cable force value required by a target part of a cable-stayed bridge to influence the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge, and determining an influence matrix of the target part under a unit cable force according to the type of the cable-stayed bridge; establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix; and determining the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
Description
Technical Field
The present invention relates to the field of bridge engineering technologies, and in particular, to a cable force analysis method and apparatus for a cable-stayed bridge, an electronic device, and a storage medium.
Background
The cable-stayed bridge is a bridge deck system, and a support system mainly takes tension of a stay cable and compression of a main tower as a bridge. The stay cable is used as a connecting component of the main beam and the cable tower, the load of the main beam is transmitted to the cable tower through the tension of the stay cable, the external prestress can be applied to the main beam through the tension of the stay cable, and the joint of the stay cable and the main beam can be regarded as a plurality of elastic supporting points in the span of the main beam, so that the bending moment of the main beam is obviously reduced, the size and the weight of the main beam are correspondingly reduced, the stress performance of the main beam is greatly improved, and the spanning capability of the bridge is improved.
In the field of bridge engineering, the stress of a main beam and a main tower of a cable-stayed bridge is very sensitive to the magnitude of cable force, and the constant load state of the cable-stayed bridge can be optimized by adjusting the cable force based on the characteristic that the cable force of the cable-stayed bridge can be adjusted. According to different definitions of reasonable states of the structure, the existing optimization method of the bridge forming force of the cable-stayed bridge can be divided into a rigid support continuous beam method, a zero displacement method, a bending energy minimum method, an influence matrix method and the like.
The existing cable force analysis method has the main problems that:
1. the cable force obtained by optimization has large fluctuation and can not be directly used.
2. The applicability is poor, and the optimization results of different types of main beams, even different side-to-side span ratios of the same main beam type are different.
3. The obtained cable force has large change, can not be directly used and needs manual adjustment
4. The existing built-in cable adjusting tool for commercial software is based on n multiplied by n matrix solving, n cables aim at n target objects, the number of the target objects is limited, and the cable adjusting tool has limitation.
Disclosure of Invention
The embodiment of the invention provides a cable force analysis method and device of a cable-stayed bridge, electronic equipment and a storage medium.
A first aspect of the embodiments of the present disclosure provides a cable force analysis method, including:
determining an attribute value of a cable force value required by a target part of the cable-stayed bridge to influence the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge,
determining an influence matrix of the target part under a unit cable force according to the type of the cable-stayed bridge;
establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix;
and determining the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
Based on the scheme, the type of the cable-stayed bridge is a suspension-cast concrete cable-stayed bridge, and the target part is the bending moment of a beam and a tower of the concrete cable-stayed bridge;
the cable-stayed bridge type refers to a steel box girder, a composite girder and a mixed girder cable-stayed bridge, and the target part refers to the displacement of the girder and the tower of the steel box girder, the composite girder and the mixed girder cable-stayed bridge.
Determining an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge, wherein the method comprises the following steps:
if the target part is the bending moment of the beam and the tower of the concrete cable-stayed bridge, extracting the value ranges of the longitudinal bridge bending moment value and the longitudinal bridge bending moment value of the beam and the tower;
and if the target part is the displacement of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge, extracting the value ranges of the displacement values of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge.
Determining an influence matrix of the target part under a unit cable force according to the type of the cable-stayed bridge, and further comprising:
if the cable-stayed bridge is the finger-suspended concrete cable-stayed bridge, determining an influence matrix of the longitudinal bending moment of the key point of the beam and an influence matrix of the longitudinal bending moment of the key point of the tower;
and if the cable-stayed bridge is the steel box girder, the combined girder and the mixed girder cable-stayed bridge, extracting a vertical displacement influence matrix of the key point of the girder main span and an influence matrix of the forward displacement of the key point of the tower.
Based on the above scheme, the establishing of the equation for solving the cable force value required by the cable-stayed bridge according to the influence matrix further comprises:
and establishing an equation for solving each attribute value according to the cable force value required by the cable-stayed bridge influenced by the target part of the cable-stayed bridge and the influence matrix.
A second aspect of the embodiments of the present disclosure provides a cable force analysis device for a cable-stayed bridge, the device including:
the acquisition module is used for determining an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge;
the determining module is used for determining an influence matrix of the target part under the unit cable force according to the type of the cable-stayed bridge;
the establishing module is used for establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix;
and the calculation module is used for determining the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
Based on the above scheme, still include:
the type of the cable-stayed bridge is a suspension-cast concrete cable-stayed bridge, and the target part is the bending moment of a beam and a tower of the concrete cable-stayed bridge;
the cable-stayed bridge type refers to a steel box girder, a combined girder and a mixed girder cable-stayed bridge, and the target part refers to the displacement of the girder and the tower of the steel box girder, the combined girder and the mixed girder cable-stayed bridge.
The acquisition module is specifically used for extracting the value ranges of the beam-tower longitudinal bending moment value and the longitudinal bending moment value if the target part is the bending moment of the beam and the tower of the concrete cable-stayed bridge;
and if the target part is the displacement of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge, extracting the value range of the displacement values of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge.
The determining module is specifically configured to determine an influence matrix of the longitudinal bending moment at the key point of the beam and an influence matrix of the longitudinal bending moment at the key point of the tower if the cable-stayed bridge is the finger-suspended concrete cable-stayed bridge;
and if the cable-stayed bridge is the steel box girder, the combined girder and the mixed girder cable-stayed bridge, extracting a vertical displacement influence matrix of the key point of the girder main span and an influence matrix of the forward displacement of the key point of the tower.
Based on the above scheme, the establishing module is further configured to establish an equation for solving each of the attribute values according to the cable force value required by the cable-stayed bridge and the influence matrix, where the cable force value is influenced by the target portion of the cable-stayed bridge.
A third aspect of embodiments of the present disclosure provides an electronic device, including:
a memory;
a processor coupled to the memory for executing computer-executable instructions stored on the memory and capable of implementing the method provided by any one of the claims of the first or second aspect.
A fourth aspect of the disclosed embodiments provides a computer storage medium having computer-executable instructions stored thereon; the computer-executable instructions, when executed, enable the method provided by any one of the first or second aspects.
The cable-stayed bridge cable force analysis method provided by the embodiment of the invention comprises the following steps: determining an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge; determining an influence matrix of the target part under a unit cable force according to the type of the cable-stayed bridge; establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix; determining a cable force value required by the cable-stayed bridge by taking the value range of the attribute value as a constraint condition of the solving equation; the method sets different optimization targets according to different cable-stayed bridge types, planning and solving are carried out by combining the influence matrix and the least square method, ideal cable force can be conveniently and quickly obtained, the applicability is wide, the implementation is simple, the obtained cable force value result can be directly used, and manual adjustment is not needed.
Drawings
FIG. 1 is a cable force analysis method for a cable-stayed bridge according to the present invention;
fig. 2 is a schematic view of a unit cable force loading of a cable-stayed bridge according to an embodiment of the present invention;
fig. 3 is a schematic view of a flow chart of a cable force analysis method for a cable-stayed bridge according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a cable force analysis device of a cable-stayed bridge according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of an electronic device provided in an embodiment of the present disclosure.
Detailed Description
So that the manner in which the features and aspects of the present application can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings.
As shown in fig. 1, an embodiment of the present disclosure provides a cable force analysis method for a cable-stayed bridge, where the analysis method includes:
s110: determining an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge;
s120: determining an influence matrix of the target part under a unit cable force according to the type of the cable-stayed bridge;
s130: establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix;
s140: and determining the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
The cable-stayed bridge is a bridge with a main beam directly falling on a bridge tower through a plurality of guys, and is a structural system formed by combining a pressure-bearing tower, a pulled stay cable and a bending-bearing beam body.
According to the functional classification, can divide into highway cable-stay bridge and railway cable-stay bridge at least, this application is mainly applied to railway cable-stay bridge.
In some embodiments of the present invention, the,
and establishing a finite element model of the cable-stayed bridge according to the construction stage, and adding all loads, wherein the loads can comprise dead load and/or live load and the like. The dead load can be the load which is applied to the engineering structure and is not changed, such as dead weight, prestress, initial tension of the stay cable or temporary load in the construction stage.
The type of the cable-stayed bridge is determined by establishing a finite element model of the cable-stayed bridge, the stress condition of the cable-stayed bridge under the actual condition is simulated, and analysis of different target parts of cable force values under different types of cable-stayed bridges is facilitated.
The property values may refer to bending moments and/or displacements of the cable-stayed bridge.
The influence matrix is a cable force nth order matrix [ C ] n multiplied by n of the stay cable, wherein elements { Cij } are the cable force change value of the jth stay cable when the ith stay cable applies unit cable force, and the cable force change value is used as a matrix for solving the influence cable force value.
In some embodiments, the S140 may include: and taking the value range of the attribute value as a constraint condition of the solving equation, and planning and solving the solving equation through an influence matrix and a least square method.
In some embodiments, the S110 may include:
and determining the target part of the cable-stayed bridge according to the type of the cable-stayed bridge. The types of the cable-stayed bridge are classified according to the materials of the beam body, and can be divided into a concrete beam cable-stayed bridge, a mixed beam cable-stayed bridge, a steel box beam, a combined beam cable-stayed bridge and the like according to the materials of the beam.
For example, when the cable-stayed bridge is a concrete beam cable-stayed bridge, the type of the cable-stayed bridge is mainly controlled by bending moment of a beam and a tower, the line shape of the bridge can be adjusted by adjusting elevation of a vertical formwork, the target part is mainly the bending moment of the beam and the tower, and the optimization target is the minimum value of the bending moment of the beam and the tower under the action of constant load and live load.
Further exemplarily, when the cable-stayed bridge is a hybrid beam or steel box girder cable-stayed bridge, the optimization goal is that the bridge formation is a beam arch tower deflection, namely, the main span beam upwarp can be 25% -30% live load deflection, and the tower is laterally displaced towards the side span by 25% -30% live load longitudinal bridge.
When the cable-stayed bridge is a combined beam cable-stayed bridge, the upper layer of the cable-stayed bridge is a concrete bridge deck, the upper layer of the beam is arched to cause the tensile stress of the bridge deck, the optimization aims are that a beam flat tower is straight, or the beam flat tower slightly deviates towards the side span side, the vertical displacement of each control point of a main span beam is close to 0, and the longitudinal displacement of the tower is 0-10% of the live-load longitudinal displacement.
When the cable-stayed bridge is a hybrid beam, a steel box beam or a combined beam cable-stayed bridge, the internal force and the linear shape of the beam and the tower are hooked, and no matter the internal force or the linear shape is taken as a target part, the other condition is naturally achieved, and the target part is mainly the vertical displacement of the beam or the longitudinal displacement of the tower.
In some embodiments, an attribute value of a cable force value required by a target portion of a cable-stayed bridge to affect the cable-stayed bridge and a value range of the attribute value are determined.
When the target part is the bending moments of the beam and the tower, extracting attribute values of longitudinal-bridge bending moments of the beam and the tower under the constant load action respectively, wherein the attribute value of the longitudinal-bridge bending moments of the beam under the constant load action can be { Mbd }, and the attribute value of the longitudinal-bridge bending moments of the tower under the constant load action can be expressed as { Mtd };
the value range of the attribute value is an interval between the minimum value and the maximum value of the longitudinal bridge direction bending moment of the beam and the tower under the live load action, wherein the minimum value of the longitudinal bridge direction bending moment of the beam under the live load action can be expressed as { Mt lmin }, the maximum value of the longitudinal bridge direction bending moment of the beam under the live load action can be expressed as { Mtlmax }, the minimum value of the longitudinal bridge direction bending moment of the tower under the live load action can be expressed as { Mblmin }, and the maximum value of the longitudinal bridge direction bending moment of the tower under the live load action can be expressed as { Mblmax }.
When the target part is the displacement of the beam and the tower, respectively extracting a vertical displacement attribute value of the beam under the dead load effect and a longitudinal bridge displacement attribute value of the tower under the dead load effect, wherein the vertical displacement attribute value can be expressed as { Tbd }, and the longitudinal bridge displacement attribute value can be expressed as { Ttd };
the value range of the attribute value is an interval in which the vertical displacement attribute value of the beam or the vertical displacement attribute value of the tower is larger than a minimum value under the live load effect, wherein the minimum value of the vertical displacement can be expressed as { tblmmin }, and the result of the minimum value of the longitudinal bridge displacement can be expressed as { Ttlmin }.
In some embodiments, the S120 may include:
and applying a unit cable force to each stay cable based on the model. Wherein the unit cord force application may comprise applying a unit of in vivo force, or pull out.
And determining the relative influence matrix of the cable-stayed bridge type through the applied unit cable force.
When the type of the cable-stayed bridge is a concrete beam cable-stayed bridge, determining an influence matrix of the key point longitudinal-bridge directional bending moment of the beam and an influence matrix of the key point longitudinal-bridge directional bending moment of the tower, wherein the influence matrix of the key point longitudinal-bridge directional bending moment of the beam can be expressed as [ Mb ] n multiplied by m, the influence matrix of the key point longitudinal-bridge directional bending moment of the tower can be expressed as [ Mt ] n multiplied by k, n is the number of the stay cables, m is the number of the control nodes on the beam, and k is the number of the control nodes on the tower;
for example, the influence matrix of the longitudinal bending moment at the critical point of the beam can be represented as [ Mb ]]n × m, where the element { MbijThe attribute value of the longitudinal bridge bending moment of the jth point on the beam is obtained when the ith stay cable applies unit cable force;
the effect matrix of bending moments at the critical points of the tower may be [ Mt [ ]]n × k, where the element { MtijAnd expressing the attribute value of the longitudinal bridge bending moment of the jth point on the tower when the ith stay cable applies unit cable force.
When the cable-stayed bridge is a hybrid beam, a steel box beam or a combined beam cable-stayed bridge, determining a vertical displacement influence matrix of a key point of a main beam span and an influence matrix of forward-to-bridge displacement of a key point of a tower, wherein the vertical displacement influence matrix of the key point of the main beam span can be [ delta b ] n x m and the influence matrix of forward-to-bridge displacement of the key point of the tower can be represented as [ delta t ] n x m, wherein n is the number of stay cables and m is the number of control nodes on the beam;
for example, the influence matrix of vertical displacement at a key point of the beam is [ Δ b ]]n × m, where the element { Δ b }ijThe variation value of the vertical displacement of the jth point on the beam when the ith stay cable applies unit cable force is obtained;
the influence matrix of vertical and forward bridge displacement at key points of the tower can be [ delta t ]]n × k, where the element { Δ TijAnd the displacement value of the ith point on the tower in the longitudinal bridge direction is the change value of the displacement of the ith stay cable in the longitudinal bridge direction when the unit cable force is applied to the ith stay cable.
In some embodiments, the S130 may include:
and establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix, wherein the solving equation can be a linear equation.
The linear equation is also established according to the attribute value of the cable force value required by the cable-stayed bridge and the value range of the attribute value:
when the influence matrix is an influence matrix of the longitudinal bending moment of the key point of the beam and an influence matrix of the longitudinal bending moment of the key point of the tower, the established solving equation is as follows:
{ΔC}[Mb]+{Mblmax}+{Mblmin}+2{Mbd}＝{Sb}＝{Sb1,Sb2,…,Sbm}T
wherein, { Δ C } is a cable force adjustment amount to be solved, [ Mb ] is a bending moment matrix of the beam, { Mblmax } is a maximum value of a longitudinal bridge directional bending moment of the beam under live load, { Mblmin } is a minimum value of the longitudinal bridge directional bending moment of the beam under live load, { Mbd } is a longitudinal bridge directional bending moment of the beam under dead load, and { Sb } is a final cable force value for optimizing the rear beam.
{ΔC}[Mt]+{Mtlmax}+{Mtlmin}+2{Mtd}＝{St}＝{St1,St2,…,Stk}T
Wherein, { Δ C } is a cable force adjustment amount to be solved, [ Mt ] is a bending moment matrix of the tower, { Mtlmax } is a maximum value of a longitudinal bridge direction bending moment of the tower under live load, { Mtlmin } is a minimum value of the longitudinal bridge direction bending moment of the tower under live load, { Mtd } is a longitudinal bridge direction bending moment of the tower under constant load, and { St } is a final cable force value of the optimized tower.
The solution condition of the equation is
And the minimum value is that lambda is the bending moment adjustment coefficient of the tower beam, and the initial value can be 0.2 by trial calculation.
When the influence matrix is a vertical displacement influence matrix of a key point of the main span of the beam and an influence matrix of the forward bridge displacement of the key point of the tower;
if the cable-stayed bridge is a hybrid beam or steel box girder cable-stayed bridge, the solving equation is as follows:
{ΔC}[Δb]+{Tbd}+0.25{Tblmin}＝{Sb}＝{Sb1,Sb2,…,Sbm}T
wherein, { Δ C } is a cable force adjustment amount to be solved, [ Δ b ] is a displacement matrix of the beam, { Tbd } is a vertical displacement change value of the beam under live load, { Tblmin } is a vertical direction minimum displacement value of the beam under live load, and { Sb } is a final cable force value of the optimized rear beam.
{ΔC}[Δt]+{Ttd}+0.25{Ttlmin}＝{St}＝{St1,St2,…,Stk}T
Wherein, { Δ C } is a cable force adjustment amount to be solved, [ Δ t ] is a displacement matrix of the tower, { Ttd } is a longitudinal bridge displacement change value of the tower under live load, { Ttlmin } is a longitudinal bridge minimum displacement value of the tower under live load, and { St } is a final cable force value of the optimized tower.
The solution condition of the equation is
And the minimum displacement is K, wherein K is a displacement adjustment coefficient of the tower beam, and can be taken as the ratio of the minimum vertical displacement of the beam to the minimum longitudinal bridge displacement of the tower under the action of live load.
If the cable-stayed bridge is a composite beam cable-stayed bridge, the solving equation is as follows:
{ΔC}[Δb]+{Tbd}＝{Sb}＝{Sb1,Sb2,…,Sbm}T
wherein, { Δ C } is a cable force adjustment amount to be solved, [ Δ b ] is a displacement matrix of the beam, { Tbd } is a vertical displacement change value of the beam under live load, and { Sb } is a final cable force value of the optimized rear beam.
{ΔC}[Δt]+{Ttd}+0.1{Ttlmin}＝{St}＝{St1,St2,…,Stk}T
Wherein, { Δ C } is a cable force adjustment amount to be solved, [ Δ t ] is a displacement matrix of the tower, { Ttd } is a longitudinal bridge displacement change value of the tower under live load, { Ttlmin } is a longitudinal bridge minimum displacement value of the tower under live load, and { St } is a final cable force value of the optimized tower.
The solution condition of the equation is
And the minimum value K is a displacement adjustment coefficient of the tower beam, and can be the ratio of the minimum vertical displacement of the beam to the minimum longitudinal bridge displacement of the tower under the action of live load.
In some embodiments, the S140 may include:
and obtaining the required cable force value through an equation obtained by the cable force influence matrix.
{ΔC}[C]+{Cs}＝{Sc}＝{Sc1,Sc2,…,Scn}T
Wherein { Cs } is a cable force value under the action of constant load, and { Sc } is an optimized final cable force value.
And dividing the result of the { Sc } into an edge-span inhaul cable force and a mid-span inhaul cable force, setting the edge-span inhaul cable force to be gradually reduced from a long cable to a short cable, and setting the mid-span inhaul cable force to be gradually reduced from the long cable to the short cable.
{ Sc } the maximum value of the element does not exceed a first threshold, wherein the first threshold is in the range of 6000kN to 10000kN,
for example, the first threshold may be a predetermined empirical or experimental value such as 7000kN or 8000 kN.
And/or the presence of a gas in the gas,
{ Sc } minimum value of the elements is not less than a second threshold value, wherein the second threshold value is in the range of 1000kN to 40000kN,
for example, the second threshold may be a predetermined empirical or experimental value such as 2000kN or 3000 kN.
And/or the presence of a gas in the gas,
{ Sc } the maximum and minimum values of the element do not differ by more than a third threshold, wherein the third threshold is 3000kN to 7000kN,
for example, the third threshold may be a predetermined empirical value or experimental value such as 4000kN or 5000 kN.
Under the above constraint, the linear equation is solved by planning, wherein the solving method may be a least square method.
The function can be realized by the current common software such as EXCEL, matlab and the like, and can also be programmed. The solution result is the cable force value { delta C } which needs to be adjusted.
Referring to fig. 2, a unit cable force loading of a cable-stayed bridge according to an embodiment of the present invention includes:
and establishing a finite element model according to a construction stage, and adding all loads including dead load, live load and the like, so that the cable force is conveniently analyzed.
At each cable applied unit cable force T1 ═ 1, an influence matrix can be obtained: and the cable force n order matrix [ C ] n multiplied by n of the stay cable, wherein the element { Cij } is the change of the cable force of the jth stay cable when the unit cable force is applied to the ith stay cable. And (3) a displacement matrix [ delta b ] n multiplied by m of the beam, wherein the element { delta bij } is the vertical displacement change of the jth point on the beam when the ith stay cable applies unit cable force. And (3) a displacement matrix [ delta t ] n multiplied by k of the tower, wherein the element { delta Tij } is the change of the longitudinal bridge displacement of the jth point on the tower when the ith stay cable applies unit cable force. A bending moment matrix [ Mb ] nxm of the beam, wherein the element { Mbij } is the change of the longitudinal bridge bending moment of the jth point on the beam when the ith stay cable applies unit cable force; a bending moment matrix [ Mt ] nxk of the tower, wherein an element { Mtij } is the change of a longitudinal bridge bending moment of a jth point on the tower when a unit cable force is applied to an ith stay cable;
vertical displacement of the beam under the constant load { Tbd } - { Tbd1, Tbd2, Tbd3, … and Tbdm } T, and longitudinal bridge bending moment { Mbd } - { Mbd1, Mbd2, Mbd3, … and Mbdm } T; the vertical bridge displacement of the tower { Ttd } - { Ttd1, Ttd2, Ttd3, …, Ttdk } T;
a longitudinal bending moment { Mtd } - { Mtd1, Mtd2, Mtd3, …, Mtdk } T; the vertical minimum displacement (downward is negative) of the beam under live load { tblmn } - { Tbl1min, Tbl2min, Tbl3min, …, Tblmmin } T, and the maximum longitudinal bridge bending moment { Mblmax } - { Mbl1max, Mbl2max, Mbl3max, …, mblmmmax } T; the minimum value of the longitudinal bending moment { Mblmin } - { Mbl1min, Mbl2min, Mbl3min, …, Mblmin } T; minimum displacement of the longitudinal bridge of the tower (negative to main lateral position) { Ttlmin } - { Ttl1min, Ttl2min, Ttl3min, …, Ttlkmin } T; the maximum value of the longitudinal-bridge bending moment { Mtlmax } - { Mtd1max, Mtd2max, Mtd3max, …, Mtdkmax } T; and the minimum value of the longitudinal bending moment { Mtlmin } - { Mtd1min, Mtd2min, Mtd3min, … and Mtdkmin } T. Wherein n is the number of stay cables, m is the number of control nodes on the beam, and k is the number of control nodes on the tower.
Taking the displacement control conditions on the beam as an example (the control conditions of different types of cable-stayed bridges are different), a linear equation is established according to the matrix:
{ΔC}[Δb]where { Δ C } is the amount of cable force adjustment to be required, and { S } is the final result of the optimization, the optimization objective may be displacement or internal force. The solution condition of the equation is
And minimum.
Referring to fig. 3, in some embodiments, a finite element model of a cable-stayed bridge is established and a dead load (including dead weight, prestress, shrinkage creep, initial tension of a stay cable, temporary load during construction, etc.) and a live load are applied. The initial tension of the stay cable can be set up arbitrarily or can be unit force.
And dividing construction stages according to requirements.
Determining an attribute value and a value range of the attribute value, which influence the cable-stayed bridge by a target part of the cable-stayed bridge, according to different types of cable-stayed bridges. The method comprises the following specific steps:
when the type of the cable-stayed bridge is a suspension-cast concrete cable-stayed bridge, the target part is the longitudinal bridge bending moment of the beam and the tower, and the attribute values of the longitudinal bridge bending moment of the beam and the tower under the constant load { Mbd } and { Mtd } need to be extracted; the maximum value and the minimum value of longitudinal bridge bending moment of the beam and the tower under the live load action { Mlmax }, { Mlmin }, { Mtlmax }, and { Mtlmin }.
When the cable-stayed bridge is a steel box girder, a mixed girder or a combined girder cable-stayed bridge, the target part is the vertical displacement of the girder and the longitudinal bridge displacement of the tower, a vertical displacement result { Tbd } of the main span girder under the constant load action needs to be extracted, and a longitudinal bridge displacement attribute value { Ttd } of the tower under the constant load action; the main span beam has a minimum vertical displacement result { Tblmin } under the live load effect, and the tower has a minimum vertical bridge displacement result { Tt lmin } under the live load effect;
determining an influence matrix of the target part under the unit cable force according to different types of cable-stayed bridges, wherein the influence matrix is as follows:
applying a unit cable force T1 to each stay cable as 1, and extracting an influence matrix of an optimized object: the cable force n-order matrix [ C ] n multiplied by n of the stay cable; for the concrete cable-stayed bridge, an influence matrix [ Mb ] nxm of a longitudinal bridge bending moment of a key point of a beam and an influence matrix [ Mt ] nxk of a longitudinal bridge bending moment of a key point of a tower are extracted. For a mixed beam, a steel box beam and a combined beam cable-stayed bridge, extracting a vertical displacement influence matrix [ delta b ] nxm of a key point of a main span of the beam and an influence matrix [ delta t ] nxm of a key point of a tower along the bridge direction.
Establishing a linear equation of the cable force value required by the cable-stayed bridge according to the influence matrix, the attribute value of the cable force value required by the cable-stayed bridge and the value range of the attribute value:
{ΔC}[Mb]+{Mblmax}+{Mblmin}+2{Mbd}＝{Sb}＝{Sb1,Sb2,…,Sbm}T
{ΔC}[Mt]+{Mtlmax}+{Mtlmin}+2{Mtd}＝{St}＝{St1,St2,…,Stk}T
the solution condition of the equation is
And the minimum value is that lambda is the bending moment adjustment coefficient of the tower beam, and the initial value can be 0.2 by trial calculation.
For a hybrid beam and steel box girder cable-stayed bridge, the linear equation is as follows:
{ΔC}[Δb]+{Tbd}+0.25{Tblmin}＝{Sb}＝{Sb1,Sb2,…,Sbm}T
{ΔC}[Δt]+{Ttd}+0.25{Ttlmin}＝{St}＝{St1,St2,…,Stk}T
the solution condition of the equation is
And the minimum value K is a displacement adjustment coefficient of the tower beam, and can be the ratio of the minimum vertical displacement of the beam to the minimum longitudinal bridge displacement of the tower under the action of live load.
For a composite beam cable-stayed bridge, the linear equation is:
{ΔC}[Δb]+{Tbd}＝{Sb}＝{Sb1,Sb2,…,Sbm}T
{ΔC}[Δt]+{Ttd}+0.1{Ttlmin}＝{St}＝{St1,St2,…,Stk}T
the solution condition of the equation is
And the minimum displacement is K, wherein K is a displacement adjustment coefficient of the tower beam, and can be taken as the ratio of the minimum vertical displacement of the beam to the minimum longitudinal bridge displacement of the tower under the action of live load.
Adding constraint conditions to the established linear equation:
for cable-stayed bridges, uniform cable forces are required: the long cable force is large, the short cable force is small, and the difference between the maximum value and the minimum value of the cable force is not too large. And obtaining an optimized cable force value through the cable force influence matrix.
{ΔC}[C]+{Cs}＝{Sc}＝{Sc1,Sc2,…,Scn}T
Wherein { Cs } is a cable force value under the action of constant load, and { Sc } is an optimized final cable force value. And dividing the result of the { Sc } into an edge-span inhaul cable force and a mid-span inhaul cable force, setting the edge-span inhaul cable force to be gradually reduced from a long cable to a short cable, and setting the mid-span inhaul cable force to be gradually reduced from the long cable to the short cable. And the maximum value of the elements in the { Sc } can not exceed 8000 kN; the minimum value is not less than 2000kN, and the difference does not exceed 5000 kN. The maximum value, the minimum value and the difference value can be adjusted according to the calculation result until the force distribution of the stay cable is uniform.
Under the constraint condition, the linear equation is solved through planning, and the function can be realized through the current common software such as EXCEL, matlab and the like and can also be programmed. The solving result is the cable force value (delta C) needing to be adjusted.
The method comprises the steps of acting on a constructed finite element model according to a calculated cable force value to be adjusted to obtain an ideal bridging state and a cable force value, setting different optimization targets according to different cable-stayed bridge types, and planning and solving by combining an influence matrix and a least square method, so that the obtained cable force value can be directly used, the ideal bridging state and cable force can be obtained more conveniently and rapidly, and the complicated process of manual adjustment is avoided.
Referring to fig. 4, an embodiment of the present invention provides a cable-stayed bridge cable force analysis device, where the cable-stayed bridge cable force analysis device includes:
the acquisition module 110 determines an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge;
a determining module 120, configured to determine an influence matrix of the target portion under a unit cable force according to the type of the cable-stayed bridge;
the establishing module 130 is used for establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix;
and the calculation module 140 determines the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
In some embodiments, the obtaining module 110, the determining module 120, the establishing module 130, and the calculating module 140 may be program modules; the program modules may be executed by a processor to perform the operations of the various modules described above.
In another embodiment, the obtaining module 110, the determining module 120, the establishing module 130, and the calculating module 140; the soft and hard combining module includes but is not limited to: various programmable arrays; such programmable arrays include, but are not limited to: field programmable arrays and/or complex programmable arrays.
In yet another embodiment, the obtaining module 110, the determining module 120, the establishing module 130, and the calculating module 140; the pure hardware modules include, but are not limited to: an application specific integrated circuit.
In some embodiments, the obtaining module 110 includes:
the first submodule is used for constructing a cable-stayed bridge model and determining the type of the cable-stayed bridge;
the second submodule is used for determining a target part of the cable-stayed bridge according to the type of the cable-stayed bridge;
the third submodule is used for determining an attribute value of a cable force value required by the cable-stayed bridge and a value range of the attribute value according to the target part;
in some embodiments, the obtaining module 110 is specifically configured to extract a value range of a beam-tower longitudinal bending moment value and a longitudinal-bridge bending moment value if the target portion is the beam-tower bending moment of the concrete cable-stayed bridge;
if the target part is the displacement of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge, extracting the value range of the displacement values of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge
In some embodiments, the cable-stayed bridge model comprises:
and establishing a finite element model of the cable-stayed bridge according to the construction stage, and adding all loads including dead load, live load and the like, wherein the dead load can be the load which is applied to the engineering structure and is unchanged, such as dead weight, prestress, initial tension of a stay cable or temporary load in the construction stage, and the type of the cable-stayed bridge is determined.
In some embodiments, the target portion of the cable-stayed bridge is determined according to the type of cable-stayed bridge. The types of the cable-stayed bridge are classified according to the materials of the beam body, and can be divided into a concrete beam cable-stayed bridge, a mixed beam cable-stayed bridge, a steel box beam, a combined beam cable-stayed bridge and the like according to the materials of the beam.
Illustratively, when the cable-stayed bridge is a concrete beam cable-stayed bridge, the type of the cable-stayed bridge is mainly controlled by the bending moment of the beam and the tower, the line shape of the bridge can be adjusted by adjusting the elevation of the vertical mold, the target part is mainly the internal force of the beam and the tower, and the optimization target is the minimum value of the bending moment of the beam and the tower under the action of constant load and live load.
Further exemplarily, when the cable-stayed bridge is a hybrid beam or steel box girder cable-stayed bridge, the optimization goal is that the bridge forming line is a beam arch tower deflection, namely, the main span beam upwarp can be 25% -30% of live load deflection, and the tower is laterally displaced towards the side span by 25% -30% of live load longitudinal bridge.
When the cable-stayed bridge is a combined beam cable-stayed bridge, the upper layer of the cable-stayed bridge is a concrete bridge deck, the upper arch of the beam causes the tensile stress of the bridge deck, the optimization aims at straightening a beam flat tower or slightly deviating the beam flat tower towards the side span side, the vertical displacement of each control point of a main span beam is close to 0, and the longitudinal displacement of the tower is 0-10% of the live-load longitudinal displacement.
When the cable-stayed bridge is a hybrid beam, a steel box beam or a combined beam cable-stayed bridge, the internal force and the linear shape of the beam and the tower are hooked, the internal force or the linear shape is taken as an optimized object, the other condition is naturally achieved, and the target part is mainly the vertical displacement of the beam or the longitudinal displacement of the tower.
In some embodiments, the determining module 120 is specifically configured to determine an influence matrix of the critical point longitudinal-bridge bending moment of the beam and an influence matrix of the critical point longitudinal-bridge bending moment of the tower if the cable-stayed bridge is the finger-cast concrete cable-stayed bridge;
and if the cable-stayed bridge is the steel box girder, the combined girder and the mixed girder cable-stayed bridge, extracting a vertical displacement influence matrix of the key point of the girder main span and an influence matrix of the forward displacement of the key point of the tower.
In some embodiments, the establishing module 130 is further configured to establish an equation for solving each of the attribute values according to the cable force value required by the target portion of the cable-stayed bridge to affect the cable-stayed bridge and the influence matrix.
As shown in fig. 5, an embodiment of the present disclosure provides an electronic device, including:
a memory;
and the processor is connected with the memory and used for realizing the cable-stayed bridge cable force analysis method provided by any embodiment, such as the cable-stayed bridge cable force analysis method shown in any of the figures 1 to 3, by executing the computer-executable instructions stored in the memory.
The electronic device may be a terminal device and/or a server in a service platform.
As shown in fig. 5, the electronic device may further include a network interface, which may be used for interacting with a peer device through a network.
The disclosed embodiments provide a computer storage medium having stored thereon computer-executable instructions; the computer-executable instructions, when executed by the processor, enable the method of cable-stayed bridge cable force analysis according to any of the embodiments described above, for example, the method of cable-stayed bridge cable force analysis according to any of fig. 1 to 3.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described device embodiments are merely illustrative, for example, the division of the unit is only a logical functional division, and there may be other division ways in actual implementation, such as: multiple units or components may be combined, or may be integrated into another system, or some features may be omitted, or not implemented. In addition, the coupling, direct coupling or communication connection between the components shown or discussed may be through some interfaces, and the indirect coupling or communication connection between the devices or units may be electrical, mechanical or other forms.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present invention, and shall cover the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (12)
1. A cable force analysis method for a cable-stayed bridge is characterized by comprising the following steps:
determining an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge;
determining an influence matrix of the target part under a unit cable force according to the type of the cable-stayed bridge;
establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix;
and determining the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
2. The method of claim 1,
the type of the cable-stayed bridge is a suspension-cast concrete cable-stayed bridge, and the target part is the bending moment of a beam and a tower of the concrete cable-stayed bridge;
the cable-stayed bridge type refers to a steel box girder, a combined girder and a mixed girder cable-stayed bridge, and the target part refers to the displacement of the girder and the tower of the steel box girder, the combined girder and the mixed girder cable-stayed bridge.
3. The method of claim 2, wherein determining the attribute value of the cable force value required by the target portion of the cable-stayed bridge to affect the cable-stayed bridge and the value range of the attribute value according to the type of the cable-stayed bridge comprises:
if the target part is the bending moment of the beam and the tower of the concrete cable-stayed bridge, extracting the value ranges of a longitudinal bending moment value of the beam and the tower and a longitudinal bending moment value of the longitudinal bridge;
and if the target part is the displacement of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge, extracting the value ranges of the displacement values of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge.
4. The method of claim 3, wherein determining an influence matrix of the target portion under a unit cable force based on the cable-stayed bridge type further comprises:
if the cable-stayed bridge is the finger-cast concrete cable-stayed bridge, determining an influence matrix of the key point longitudinal-bridge bending moment of the beam and an influence matrix of the key point longitudinal-bridge bending moment of the tower;
and if the cable-stayed bridge is the steel box girder, the combined girder and the mixed girder cable-stayed bridge, extracting a vertical displacement influence matrix of the key point of the girder main span and an influence matrix of the forward displacement of the key point of the tower.
5. The method of claim 1, wherein the establishing an equation for solving for the cable force values required for the cable-stayed bridge according to the influence matrix further comprises:
and establishing an equation for solving each attribute value according to the cable force value required by the cable-stayed bridge influenced by the target part of the cable-stayed bridge and the influence matrix.
6. A cable force analysis device for a cable-stayed bridge, the device comprising:
the acquisition module is used for determining an attribute value of a cable force value required by a cable-stayed bridge influenced by a target part of the cable-stayed bridge and a value range of the attribute value according to the type of the cable-stayed bridge;
the determining module is used for determining an influence matrix of the target part under the unit cable force according to the type of the cable-stayed bridge;
the establishing module is used for establishing a solving equation of the cable force value required by the cable-stayed bridge according to the influence matrix;
and the calculation module is used for determining the cable force value required by the cable-stayed bridge by taking the value range of the attribute value as the constraint condition of the solving equation.
7. The apparatus of claim 6,
the type of the cable-stayed bridge is a suspension-cast concrete cable-stayed bridge, and the target part is the bending moment of a beam and a tower of the concrete cable-stayed bridge;
the cable-stayed bridge type refers to a steel box girder, a composite girder and a mixed girder cable-stayed bridge, and the target part refers to the displacement of the girder and the tower of the steel box girder, the composite girder and the mixed girder cable-stayed bridge.
8. The device according to claim 7, wherein the obtaining module is specifically configured to extract a value range of a beam-tower longitudinal bending moment value and a longitudinal bending moment value if the target portion is the bending moment of the beam and the tower of the concrete cable-stayed bridge;
and if the target part is the displacement of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge, extracting the value ranges of the displacement values of the beams and towers of the steel box girder, the combination girder and the mixed girder cable-stayed bridge.
9. The apparatus of claim 8, wherein said determining module is configured to determine an influence matrix of a longitudinal bending moment at a key point of said beam and an influence matrix of a longitudinal bending moment at a key point of said tower, if said cable-stayed bridge is of said finger-cast concrete cable-stayed bridge type;
and if the cable-stayed bridge is the steel box girder, the combined girder and the mixed girder cable-stayed bridge, extracting a vertical displacement influence matrix of the key point of the girder main span and an influence matrix of the forward displacement of the key point of the tower.
10. The apparatus of claim 6, wherein the establishing module is further configured to establish an equation for each of the attribute values according to the cable force values required by the target portion of the cable-stayed bridge to affect the cable-stayed bridge and the influence matrix.
11. An electronic device, comprising:
a memory;
a processor coupled to the memory for executing computer-executable instructions stored on the memory and capable of implementing the method provided by any one of claims 1 to 5.
12. A computer storage medium having stored thereon computer-executable instructions; the computer-executable instructions, when executed, enable the method provided by any of claims 1 to 5 to be carried out.
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