CN107700336A - A kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag - Google Patents
A kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag Download PDFInfo
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- CN107700336A CN107700336A CN201710993245.2A CN201710993245A CN107700336A CN 107700336 A CN107700336 A CN 107700336A CN 201710993245 A CN201710993245 A CN 201710993245A CN 107700336 A CN107700336 A CN 107700336A
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
- E01D21/00—Methods or apparatus specially adapted for erecting or assembling bridges
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
- E01D11/00—Suspension or cable-stayed bridges
- E01D11/04—Cable-stayed bridges
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
- E01D21/00—Methods or apparatus specially adapted for erecting or assembling bridges
- E01D21/10—Cantilevered erection
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Abstract
The present invention provides a kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag, is related to technical field of bridge engineering.A kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag, at cantilever end rope point of force application, with the shear lag coefficient λ of axle power effectNReflect the actual loading situation of the point;Beam section between Suo Li, at rope point of force application, reflect the actual loading situation of the point than the shear lag coefficient λ of determination according to moment of flexure axle power;The beam section of span centre between rope point of force application, with the shear lag coefficient λ of MomentMReflect the actual loading situation of the point, the beam section between rope point of force application and span centre, the stagnant coefficient of section shear is tried to achieve using linear interpolation.The determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag provided by the invention, the problem of being difficult to accurate description Cable-Stayed Bridge Structure loading characteristic because of the single effective flange width definition of code requirement is avoided, has further ensured the safety of stayed-cable bridge structure system.
Description
Technical field
The present invention relates to technical field of bridge engineering, more particularly to a kind of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag
Determination method.
Background technology
Main Girder of Concrete Cable-stayed Bridge refers mainly to box section, in bridge structure design, due to the shearing of web plates of box girders
Flange plate transfer lag is flowed to, so that there is shear lageffect for flange plate.Stress inhomogeneous caused by shear lageffect
Design work that can be to box beam brings adverse effect, if not accounting for the effect of Shear Lag, it is possible to it is irretrievable to occur some
Consequence.Especially for this complicated structural system of cable-stayed bridge, with the propulsion of construction stage, structure in work progress
System constantly changes, after the completion of folding structures and suspension cable whole tensioning, the geometry linear of cable-stayed bridge bridge completion state and
Internal force situation is changed.
The structural internal force of cable-stayed bridge is a complicated space problem, in the case of uneven loading, torsion, abnormal be present
The effects such as change so that force analysis is more complicated, and carrying out analysis with general box beam computational theory has certain difficulty.At present
The method of edge of a wing developed width is replaced to consider influence of the Shear Lag to box beam, Bridges in Our Country specification rule using effective width in engineering
Determine the computational methods clause to the specific structure effective width such as simply supported beam, continuous beam and cantilever beam, but not clearly to oblique pull
The regulation of bridge design.It is also no to be applied to cable-stayed bridge although external specification has detailed regulation to Flange Effective Distribution Width
The provision of girder.
The content of the invention
The defects of for prior art, the present invention provide a kind of determination of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag
Method, determine the shear lag coefficient that Main Girder of Concrete Cable-stayed Bridge construction stage diverse location should be taken.
A kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag, comprises the following steps:
Step 1, determine Shear Lag at two cantilever end rope points of force application of cable-stayed bridge;
The shear lag coefficient λ acted at two cantilever end rope points of force application of cable-stayed bridge with axle powerNReflect the reality of the point
Stressing conditions and Shear Lag, the computational methods of Shear Lag as caused by axle power are shown below at this:
Wherein, λNFor shear lag coefficient, σ caused by axle power at stayed-cable bridge cantilever end cable force application pointNFor stayed-cable bridge cantilever end
Actual direct stress caused by axle power at rope point of force application,For name caused by axle power at stayed-cable bridge cantilever end cable force application point just
Stress;
Step 2, the Shear Lag for determining beam section between Suo Li;
Step 2.1:Determine the Shear Lag at the rope point of force application of beam section between Suo Li;
Reflect the reality of the point between Suo Li at the rope point of force application of beam section than the shear lag coefficient λ of determination with moment of flexure and axle power
The Shear Lag of border stressing conditions and the point, the computational methods of Shear Lag are shown below at the point:
Wherein, shear lag coefficients of the λ between Suo Li at the rope point of force application of beam section, the Suo Li of σ beam sections between Suo Li
Actual stress at application point,Nominal stress between Suo Li at the rope point of force application of beam section, actual stress σ should with name
PowerIt is the superposition of corresponding direct stress caused by moment of flexure and axle power, λN′Axle power is produced at beam section rope point of force application between Suo Li
Raw shear lag coefficient, λM′Shear lag coefficient caused by moment of flexure, M, N are respectively beam section at beam section rope point of force application between Suo Li
Moment of flexure and axle power suffered by section,Wherein, y be the girder section centre of form to the distance of upper lower edge, A is girder section face
Product, I is girder section the moment of inertia;
Step 2.2:Determine the Shear Lag of span centre beam section at half between rope point of force application;
The span centre beam section at half between rope point of force application, with the shear lag coefficient λ of MomentMReflect the point
Actual loading situation and Shear Lag, the computational methods of Shear Lag are as follows at the point:
Wherein, λMShear lag coefficient, σ caused by the moment of flexure of span centre beam section at half between rope point of force applicationMFor rope
Actual direct stress caused by the moment of flexure of span centre beam section at half between point of force application,Two points between rope point of force application
One of nominal direct stress caused by the moment of flexure of place's span centre beam section;
Step 2.3:Determine the Shear Lag between rope point of force application and span centre beam section;
Shear Lag between rope point of force application and span centre beam section, by the Shear Lag of the rope point of force application of beam section between Suo Li
Between coefficient lambda and rope point of force application at half span centre beam section shear lag coefficient λMBetween using linear interpolation try to achieve should
The shear lag coefficient reflection in beam section section.
As shown from the above technical solution, the beneficial effects of the present invention are:A kind of concrete deck cable stayed bridge provided by the invention
The determination method of main girder construction stage Shear Lag, in single cable plane P C Cable-Stayed Bridges, difference is taken in different positions
Shear lag coefficient carry out plane finite bar elements analysis, avoid the single effective flange width of code requirement and define Shear Lag
Coefficient, the loading characteristic of Cable-Stayed Bridge Structure is accurately described, make stayed-cable bridge structure system safe.
Brief description of the drawings
Fig. 1 is the elevation of cable-stayed bridge provided in an embodiment of the present invention;
Fig. 2 is the cross-sectional view of cable-stayed bridge main-beam provided in an embodiment of the present invention;
Fig. 3 is stayed-cable bridge cantilever provided in an embodiment of the present invention construction schematic diagram;
Fig. 4 is the bending moment diagram of girder at No. 4 bridge piers of cable-stayed bridge provided in an embodiment of the present invention;
Fig. 5 is the axial force diagram of girder at No. 4 bridge piers of cable-stayed bridge provided in an embodiment of the present invention.
In figure:1st, suspension cable;2nd, bridge king-tower;3rd, girder;4th, No. 4 bridge piers;5th, No. 5 bridge piers;6th, middle room;7th, side room;8th, hang
Arm plate;9th, median ventral plate;10th, side web;11st, middle room upper limb;12nd, middle room lower edge.
Embodiment
With reference to the accompanying drawings and examples, the embodiment of the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
The embodiment of the present invention describes the construction stage by taking certain single plane cable stayed bridge prestressed concrete box shape girder bridge as an example
The determination method of bridge diverse location Shear Lag.The main bridge of certain bridge is single cable plane prestressed concrete oblique pull used by the present embodiment
Bridge, as shown in figure 1, suspension cable 1 uses zinc coated high strength steel silk, 15 pairs are arranged on each king-tower, full-bridge totally 120.Bridge king-tower 2 is adopted
To be poured into a mould with C50 concrete, box section, bridge floor above tower height 67.5m, king-tower knuckle is located at bridge floor above 33.9m, wherein under
Duan Tashen is 75 ° with horizontal plane angle, and epimere tower body and hypomere tower body angle are 7.5 °.The main a length of 420m of bridge, span setting are
89m+242m+89m.Girder 3 is single Room of case three, deck-molding 3.414m.Rope is away from being arranged as mid-span rope away from for 14 × 7.4m on girder 3;
End bay rope away from except pygochord area be 1.5m+1.5m+5.75m+7.0m in addition to, remaining is 10 × 6.3m.At No. 4 bridge piers 4 for tower, beam,
The affixed system of pier, for tower beam is affixed, beam pier separation system at No. 5 bridge piers 5.Mid-span and the structure of end bay as shown in Fig. 2 its
In, mid-span each several part size is:Both sides room 7 upper limb thickness 25cm, the middle upper limb thickness 40cm of room 6, lower edge thickness 30cm, side web 10 are thick
25cm, 9 thick 40cm of median ventral plate, the length of cantilever slab 8 are 5m;End bay each several part size is:The upper limb thickness 40cm of both sides room 7, on middle room 6
Edge thickness 50cm, lower edge thickness 40cm, 9 thick 50cm of median ventral plate, 10 thick 30cm of side web, the length of cantilever slab 8 are 5m.
When the present embodiment uses cantilever construction as shown in Figure 3 under typical condition, girder section upper limb shear lag coefficient edge is vertical
To the distribution situation of total length, carry out the shear lageffect in labor Construction of Cable-Stayed Bridges middle girder section.
A kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag, specifically includes herein below:
Step 1, determine Shear Lag at two cantilever end rope points of force application of cable-stayed bridge;
The shear lag coefficient λ acted at two cantilever end rope points of force application of cable-stayed bridge with axle powerNReflect the reality of the point
Stressing conditions and Shear Lag, the computational methods of Shear Lag as caused by axle power are shown below at this:
Wherein, λNFor shear lag coefficient, σ caused by axle power at stayed-cable bridge cantilever end cable force application pointNFor stayed-cable bridge cantilever end
Actual direct stress caused by axle power at rope point of force application,For name caused by axle power at stayed-cable bridge cantilever end cable force application point just
Stress;
In the present embodiment, according to《Highway reinforced concrete and prestressed concrete bridge contain design specification》4.2.3 take girder
Section top flange top plate effective width is 4.00m, and lower flange bottom plate tunneling boring participates in calculating, and obtains stayed-cable bridge cantilever end cable force work
With at actual direct stress caused by axle powerWith axle at stayed-cable bridge cantilever end cable force application point
Nominal direct stress caused by powerWherein N be Suo Li axial thrust load, AEffectivelyFor cable-stayed bridge main-beam
Effective cross-sectional area, AEntirelyFor cable-stayed bridge main-beam area of section.Two cantilever end rope point of force application C4 of cable-stayed bridge finally are calculated
Shear lag coefficient with C4 ' places is
Step 2, the Shear Lag for determining beam section between Suo Li;
Step 2.1:Determine the Shear Lag at the rope point of force application of beam section between Suo Li;
Reflect the reality of the point between Suo Li at the rope point of force application of beam section than the shear lag coefficient λ of determination with moment of flexure and axle power
The Shear Lag of border stressing conditions and the point, the computational methods of Shear Lag are shown below at the point:
Wherein, shear lag coefficients of the λ between Suo Li at the rope point of force application of beam section, the Suo Li of σ beam sections between Suo Li
Actual stress at application point,Nominal stress between Suo Li at the rope point of force application of beam section, actual stress σ should with name
PowerIt is the superposition of direct stress caused by moment of flexure and axle power;
Shear lag coefficient caused by moment of flexure is λ at beam section rope point of force application between definition Suo LiM′, Shear Lag caused by axle power
Coefficient is λN′, the shear lag coefficient after superposition is λ, then has:
Wherein,WithNominal direct stress, σ caused by axle power and moment of flexure respectively at rope point of force applicationN′And σM′Respectively
For actual direct stress caused by axle power at rope point of force application and moment of flexure, the shear lag coefficient of nominal direct stress corresponding thereto is multiplied
Product be actual direct stress;
Above formula right-hand member molecule denominator simultaneously divided byThen
Wherein,Then:
OrderThen
Wherein, y is the girder section centre of form to the distance of upper lower edge, and A is girder section area, and I is girder section the moment of inertia,
M, N is respectively the moment of flexure and axle power suffered by beam section section.
In the present embodiment, the distance y=1.09 of the girder section centre of form to upper limb, girder section area A=22.9, girder are cut
Face the moment of inertia I=26.5,According to《Highway reinforced concrete and prestressed concrete bridge contain design specification》
4.2.3, calculate at rope point of force application caused by axle power during shear lag coefficient, girder section top flange top plate effective width is
4.00m, lower flange bottom plate tunneling boring participate in calculating, and obtain actual direct stress caused by axle power and name at rope point of force application and just should
Power is respectivelyWherein, N ' is rope point of force application
Locate Suo Li axial thrust load, AEffectivelyFor girder effective cross-sectional area, AEntirelyFor girder section area, axle power at rope point of force application is obtained
Caused shear lag coefficient λN′=2.62.Caused by calculated bending moment during shear lag coefficient, top flange top plate effective width is 24m, is obtained
Actual direct stress caused by moment of flexure and nominal direct stress are respectively at rope point of force application Wherein, M ' be rope point of force application at moment of flexure, WEffectivelyFor the effective bending resistant section mould of girder
Amount, WEntirelyFor girder module of anti-bending section, shear lag coefficient λ caused by moment of flexure at rope point of force application is obtainedM′=1.17.
The present embodiment uses the full-bridge plane bar mechanism model that finite element software is established, the moment of flexure and axle of operating mode lower girder of constructing
The internal force diagram of power, the internal force diagram result difference of 4# bridge piers and 5# bridge pier girders is smaller, only extracts the internal force diagram of girder at 4# bridge piers,
4# bridge pier axial force diagrams shown in the bending moment diagram and Fig. 5 of 4# bridge piers as shown in Figure 4.According to Suo Lisuo points of force application in Fig. 4 and Fig. 5
The axle power and moment of flexure at place obtain, rope point of force application C3 '~C1 ' places girder section moment of flexure axle power ratioRespectively:1.49、1.59、
1.64, substitute into formula
It is respectively 1.77,1.75,1.74 to obtain girder section upper limb shear lag coefficient λ at C3 '~C1 ' Suo Li;
Girder section moment of flexure axle power ratio at rope point of force application C3~C1Respectively:1.47、1.81、2.03;Substitute into formula
It is respectively 1.78,1.71,1.67 to obtain girder section upper limb shear lag coefficient λ at C3~C1 Suo Li.
Step 2.2:Determine the Shear Lag of span centre beam section at half between rope point of force application;
The span centre beam section at half between rope point of force application, with the shear lag coefficient λ of MomentMReflect the point
Actual loading situation and Shear Lag, the computational methods of Shear Lag are as follows at the point:
Wherein,The nominal direct stress caused by the moment of flexure of span centre beam section at half between rope point of force application;σMFor
Actual direct stress, λ caused by the moment of flexure of span centre beam section at half between rope point of force applicationMTwo points between rope point of force application
One of shear lag coefficient caused by the moment of flexure of place's span centre beam section.
In the present embodiment, the shearing of the span centre beam section of rope point of force application C3 '~between C1 ' and C3~C1 at half
It is stagnant, with the shear lag coefficient λ of MomentMReflect the actual loading situation of the point, λ is calculatedM=1.17;
Step 2.3:Determine the Shear Lag between rope point of force application and span centre beam section;
Shear Lag between rope point of force application and span centre beam section, by the Shear Lag of the rope point of force application of beam section between Suo Li
Between coefficient lambda and rope point of force application at half span centre beam section shear lag coefficient λMBetween using linear interpolation try to achieve should
The shear lag coefficient reflection in beam section section.
In the present embodiment, C3 ' arrive C3 '~C2 ' half span centres between beam section Shear Lag, should 1.77 and 1.17 it
Between tried to achieve using linear interpolation;C2 ' arrive C2 '~C1 ' half span centres between beam section Shear Lag, should 1.75 and 1.17 it
Between tried to achieve using linear interpolation;The Shear Lag of beam section between C3 to C3~C2 half span centres, should be between 1.78 and 1.17
Tried to achieve using linear interpolation;The Shear Lag of beam section, should be adopted between 1.71 and 1.17 between C2 to C2~C1 half span centres
Tried to achieve with linear interpolation.As C3 points shear lag coefficient be 1.77, C3~C2 half span centres at Shear Lag 1.17, distance C3 points
The shear lag coefficient linear interpolation of beam section is 1.61 at 1 meter.
Finally it should be noted that:The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations;Although
The present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that:It still may be used
To be modified to the technical scheme described in previous embodiment, either which part or all technical characteristic are equal
Replace;And these modifications or replacement, the essence of appropriate technical solution is departed from the model that the claims in the present invention are limited
Enclose.
Claims (4)
- A kind of 1. determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag, it is characterised in that:Comprise the following steps:Step 1, determine Shear Lag at two cantilever end rope points of force application of cable-stayed bridge;Step 2, the Shear Lag for determining beam section between Suo Li;Step 2.1:Determine the Shear Lag at the rope point of force application of beam section between Suo Li;Step 2.2:Determine the Shear Lag of span centre beam section at half between rope point of force application;Step 2.3:Determine the Shear Lag between rope point of force application and span centre beam section;Shear Lag between rope point of force application and span centre beam section, by the shear lag coefficient of the rope point of force application of beam section between Suo Li Between λ and rope point of force application at half span centre beam section shear lag coefficient λMBetween the beam section tried to achieve using linear interpolation The shear lag coefficient reflection in section.
- 2. a kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag according to claim 1, its feature It is:The Shear Lag that Shear Lag at two cantilever end rope points of force application of cable-stayed bridge described in step 1 is acted on axle power at the point Coefficient lambdaNReflect, the computational methods of Shear Lag as caused by axle power are shown below at this:<mrow> <msub> <mi>&lambda;</mi> <mi>N</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>&sigma;</mi> <mi>N</mi> </msub> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>N</mi> </msub> </mfrac> </mrow>Wherein, λNFor shear lag coefficient, σ caused by axle power at stayed-cable bridge cantilever end cable force application pointNFor stayed-cable bridge cantilever end cable force Actual direct stress caused by axle power at application point,Just should for name caused by axle power at stayed-cable bridge cantilever end cable force application point Power.
- 3. a kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag according to claim 1, its feature It is:Shear Lag between Suo Li described in step 2.1 at the rope point of force application of beam section is with moment of flexure at the point and axle power than determination Shear lag coefficient λ reflects that the computational methods of Shear Lag are shown below at the point:<mrow> <mi>&lambda;</mi> <mo>=</mo> <mfrac> <mi>&sigma;</mi> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&lambda;</mi> <msup> <mi>N</mi> <mo>&prime;</mo> </msup> </msub> <mo>+</mo> <msub> <mi>C&lambda;</mi> <msup> <mi>M</mi> <mo>&prime;</mo> </msup> </msub> <mfrac> <mi>M</mi> <mi>N</mi> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>C</mi> <mfrac> <mi>M</mi> <mi>N</mi> </mfrac> </mrow> </mfrac> </mrow>Wherein, shear lag coefficients of the λ between Suo Li at the rope point of force application of beam section, the Suo Li effects of σ beam sections between Suo Li Actual stress at point,Nominal stress between Suo Li at the rope point of force application of beam section, actual stress σ and nominal stress The even superposition for corresponding direct stress caused by moment of flexure and axle power, λN′Between Suo Li at beam section rope point of force application caused by axle power Shear lag coefficient, λM′Shear lag coefficient caused by moment of flexure at beam section rope point of force application, M, N are respectively beam section section between Suo Li Suffered moment of flexure and axle power,Wherein, y is distance of the girder section centre of form to upper lower edge, and A is girder section area, I For girder section the moment of inertia.
- 4. a kind of determination method of Main Girder of Concrete Cable-stayed Bridge construction stage Shear Lag according to claim 1, its feature It is:The Shear Lag of span centre beam section is cut with Moment at the point at half between rope point of force application described in step 2.2 The stagnant coefficient lambda of powerMReflect, the computational methods of Shear Lag are as follows at the point:<mrow> <msub> <mi>&lambda;</mi> <mi>M</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>&sigma;</mi> <mi>M</mi> </msub> <msub> <mover> <mi>&sigma;</mi> <mo>&OverBar;</mo> </mover> <mi>M</mi> </msub> </mfrac> </mrow>Wherein, λMShear lag coefficient, σ caused by the moment of flexure of span centre beam section at half between rope point of force applicationMFor Suo Lizuo With actual direct stress caused by the moment of flexure of span centre beam section at half between point,The half between rope point of force application Locate nominal direct stress caused by the moment of flexure of span centre beam section.
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