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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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 invention relates to the technical field of bridge engineering, in particular to a method for determining shear force stagnation of a main beam of a concrete cable-stayed bridge in a construction stage.
Background
The main beam of the concrete cable-stayed bridge mainly refers to a box-shaped section, and in the design of a bridge structure, the shear force of a box-shaped beam web plate is transferred to a flange plate to delay, so that the flange plate has a shear force delay effect. The non-uniformity of stress due to shear hysteresis can adversely affect the design of the box beam, and irreparable consequences can occur if the shear hysteresis effect is not taken into account. Particularly, for a complex structural system of the cable-stayed bridge, the structural system is continuously changed along with the propulsion of a construction stage in the construction process, and after the structure is folded and the stay cables are completely tensioned, the geometric linear shape and the internal force condition of the cable-stayed bridge in a bridge state are changed.
The structural internal force of the cable-stayed bridge is a complex space problem, under the condition of uneven loading, torsion, distortion and other effects exist, so that the stress analysis is more complex, and certain difficulty exists in analysis by using a general box girder calculation theory. The influence of shear hysteresis on box girders is considered by adopting a method of replacing the actual width of flanges with an effective width in the prior engineering, and the national bridge specification stipulates a calculation method term for the effective width of specific structures such as simply supported girders, continuous girders and cantilever girders, but does not clearly stipulate the design of cable-stayed bridges. Although the foreign specifications have detailed regulations on the effective distribution width of the flanges, the foreign specifications also have no provisions suitable for the main beam of the cable-stayed bridge.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for determining shear hysteresis of a concrete cable-stayed bridge girder in a construction stage, which is used for determining shear hysteresis coefficients to be adopted at different positions of the concrete cable-stayed bridge girder in the construction stage.
A method for determining shear hysteresis of a main beam of a concrete cable-stayed bridge in a construction stage comprises the following steps:
step 1, determining shear hysteresis at the action points of cable forces of two cantilever ends of a cable-stayed bridge;
shear hysteresis coefficient lambda of cable-stayed bridge with axial force acting at two cantilever end cable force acting pointsNThe actual stress condition and the shear hysteresis of the point are reflected, and the calculation method of the shear hysteresis generated by the axial force at the point is shown as the following formula:
wherein λ isNShear hysteresis coefficient, sigma, generated by the axial force at the action point of the cantilever end cable force of the cable-stayed bridgeNThe actual normal stress generated by the axial force at the action point of the cable force of the cantilever end of the cable-stayed bridge,the nominal normal stress is generated by the axial force at the action point of the cable force of the cantilever end of the cable-stayed bridge;
step 2, determining the shear hysteresis of the beam section between the cable forces;
step 2.1: determining the shear hysteresis at the cable force action point of the beam section between the cable forces;
the shear hysteresis coefficient lambda determined by the bending moment and the axial force ratio at the cable force action point of the beam section between the cable forces reflects the actual stress condition of the point and the shear hysteresis of the point, and the calculation method of the shear hysteresis of the point is shown as the following formula:
wherein, lambda is the shearing hysteresis coefficient of the cable force action point of the beam section between the cable forces, sigma is the actual stress of the cable force action point of the beam section between the cable forces,the nominal stress at the cable force action point of the beam section between the cable forces, the actual stress sigma and the nominal stressBoth of which are the superposition of the corresponding normal stresses, lambda, produced by bending moments and axial forcesN′Is the shear hysteresis coefficient, lambda, generated by the axial force at the action point of the cable force of the beam section between the cable forcesM′M, N are respectively bending moment and axial force applied to the section of the beam section,wherein y is the distance from the centroid of the section of the main beam to the upper edge and the lower edge, A is the area of the section of the main beam, and I is the inertia moment of the section of the main beam;
step 2.2: determining the shear hysteresis of a midspan beam section at one half position between the cable force action points;
spanning the middle beam section at one half position between the cable force action points, and using the shear hysteresis coefficient lambda of bending moment actionMReflecting the actual stress condition and shear hysteresis of the point, wherein the shear hysteresis calculation method at the point is as follows:
wherein λ isMShear hysteresis coefficient, sigma, generated by bending moment of the span-middle beam section at one half position between the acting points of cable forceMIs the actual normal stress generated by the bending moment of the span-middle beam section at the half part between the acting points of the cable force,nominal normal stress generated by bending moment of a span middle beam section at one half position between cable force action points;
step 2.3: determining shear hysteresis between a cable force action point and a midspan beam section;
shear hysteresis between the cable force action point and the span-middle beam section is determined by the shear hysteresis coefficient lambda of the cable force action point of the beam section between the cable forces and the shear hysteresis coefficient lambda of the span-middle beam section at the half part between the cable force action pointsMBetweenAnd the shear hysteresis coefficient of the section of the beam section obtained by linear interpolation is used for reflecting.
According to the technical scheme, the invention has the beneficial effects that: according to the method for determining the shear hysteresis of the main girder of the concrete cable-stayed bridge, provided by the invention, in the construction stage of the single-cable-plane P C cable-stayed bridge, different shear hysteresis coefficients are adopted at different positions for carrying out plane rod finite element analysis, so that the condition that the shear hysteresis coefficients are defined by adopting a standard single effective flange width is avoided, the stress characteristics of a cable-stayed bridge structure are accurately described, and the cable-stayed bridge structure system is safe.
Drawings
Fig. 1 is an elevation view of a cable-stayed bridge according to an embodiment of the present invention;
fig. 2 is a cross-sectional view of a main beam of a cable-stayed bridge according to an embodiment of the present invention;
fig. 3 is a schematic view of the construction of a cable-stayed bridge cantilever according to an embodiment of the present invention;
fig. 4 is a bending moment diagram of a main beam at pier No. 4 of the cable-stayed bridge according to the embodiment of the invention;
fig. 5 is an axial diagram of a main beam at a pier of a cable-stayed bridge No. 4 according to an embodiment of the invention.
In the figure: 1. a stay cable; 2. a bridge main tower; 3. a main beam; 4. no. 4 bridge pier; 5. no. 5 bridge pier; 6. a middle chamber; 7. a side chamber; 8. a cantilever plate; 9. a middle web plate; 10. a side web; 11. the upper edge of the middle chamber; 12. the lower edge of the middle chamber.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The embodiment of the invention describes a method for determining the shear hysteresis of different positions of a bridge in a construction stage by taking a prestressed concrete box-shaped main beam bridge of a single-cable-plane cable-stayed bridge as an example. A bridge main bridge adopted in this embodiment is a single-cable-plane prestressed concrete cable-stayed bridge, and as shown in fig. 1, a galvanized high-strength steel wire is adopted as a cable-stayed bridge 1, 15 pairs of full bridges are arranged on each main tower, and the total number of the full bridges is 120. The main tower 2 of the bridge is cast by C50 concrete, the section of the box is a section, the height of the tower above the bridge floor is 67.5m, the break angle of the main tower is 33.9m above the bridge floor, the included angle between the lower tower body and the horizontal plane is 75 degrees, and the included angle between the upper tower body and the lower tower body is 7.5 degrees. The main bridge length is 420m, and the span is arranged to be 89m +242m +89 m. The main beam 3 is a single-box three-chamber beam with the height of 3.414 m. The cable distance on the girder 3 is arranged to be 14 multiplied by 7.4 m; the side span cable distance is 10 multiplied by 6.3m except for the tail cable area of 1.5m +1.5m +5.75m +7.0 m. No. 4 bridge piers are provided with tower, beam and pier fixing systems, and No. 5 bridge piers are provided with tower beam fixing systems and beam-pier separating systems. The structure of the mid-span and the side-span is shown in fig. 2, wherein the sizes of the parts of the mid-span are as follows: the thickness of the upper edges of the two side chambers 7 is 25cm, the thickness of the upper edges of the middle chambers 6 is 40cm, the thickness of the lower edges is 30cm, the thickness of the side web plates 10 is 25cm, the thickness of the middle web plate 9 is 40cm, and the length of the cantilever plate 8 is 5 m; the dimensions of each part of the side span are as follows: the thickness of the upper edges of the two side chambers 7 is 40cm, the thickness of the upper edges of the middle chambers 6 is 50cm, the thickness of the lower edges is 40cm, the thickness of the middle web plate 9 is 50cm, the thickness of the side web plate 10 is 30cm, and the length of the cantilever plate 8 is 5 m.
In this embodiment, the distribution of the shear hysteresis coefficients of the upper edge of the main beam section along the longitudinal full length is used to analyze the shear hysteresis effect of the main beam section in the cable-stayed bridge construction process in detail under the typical working condition of cantilever construction as shown in fig. 3.
A method for determining shear hysteresis of a concrete cable-stayed bridge girder in a construction stage specifically comprises the following steps:
step 1, determining shear hysteresis at the action points of cable forces of two cantilever ends of a cable-stayed bridge;
shear hysteresis coefficient lambda of cable-stayed bridge with axial force acting at two cantilever end cable force acting pointsNThe actual stress condition and the shear hysteresis of the point are reflected, and the calculation method of the shear hysteresis generated by the axial force at the point is shown as the following formula:
wherein λ isNShear hysteresis coefficient, sigma, generated by the axial force at the action point of the cantilever end cable force of the cable-stayed bridgeNThe actual normal stress generated by the axial force at the action point of the cable force of the cantilever end of the cable-stayed bridge,the nominal normal stress is generated by the axial force at the action point of the cable force of the cantilever end of the cable-stayed bridge;
in this embodiment, according to "design criteria for reinforced concrete and prestressed concrete bridges and culverts" 4.2.3, the actual normal stress generated by the axial force at the action point of the cantilever end cable force of the cable-stayed bridge is obtained by taking the effective width of the top plate of the upper flange of the section of the main beam as 4.00m and taking the full-section calculation of the bottom plate of the lower flange of the section of the main beamAnd nominal normal stress generated by axial force at the action point of cable-stayed bridge cantilever end cable forceWherein N is the axial component of the cable force, AIs effectiveIs the effective cross-sectional area of the main beam of the cable-stayed bridge AAll-purposeIs the cross section area of the main girder of the cable-stayed bridge. Finally, the shear hysteresis coefficients at the cable force action points C4 and C4' of the two cantilever ends of the cable-stayed bridge are obtained through calculation
Step 2, determining the shear hysteresis of the beam section between the cable forces;
step 2.1: determining the shear hysteresis at the cable force action point of the beam section between the cable forces;
the shear hysteresis coefficient lambda determined by the bending moment and the axial force ratio at the cable force action point of the beam section between the cable forces reflects the actual stress condition of the point and the shear hysteresis of the point, and the calculation method of the shear hysteresis of the point is shown as the following formula:
wherein, lambda is the shearing hysteresis coefficient of the cable force action point of the beam section between the cable forces, sigma is the actual stress of the cable force action point of the beam section between the cable forces,the nominal stress at the cable force action point of the beam section between the cable forces, the actual stress sigma and the nominal stressThe normal stress generated by bending moment and axial force are superposed;
defining the shear hysteresis coefficient generated by the bending moment at the cable force action point of the beam section between cable forces as lambdaM′The shear hysteresis coefficient generated by the axial force is lambdaN′And the superimposed shear hysteresis coefficient is lambda, then:
wherein,andnominal positive stress, sigma, produced by axial force and bending moment at the point of application of cable forceN′And σM′Actual normal stress generated by axial force and bending moment at the action point of the cable force is respectively, and the product of the nominal normal stress multiplied by the corresponding shear hysteresis coefficient is the actual normal stress;
the numerator and denominator at the right end of the above formula are simultaneously divided byThen
Wherein,then:
order toThen
Wherein y is the distance from the centroid of the section of the main beam to the upper and lower edges, A is the area of the section of the main beam, I is the moment of inertia of the section of the main beam, and M, N is the bending moment and the axial force applied to the section of the beam section respectively.
In the embodiment, the distance y from the centroid of the main beam section to the upper edge is 1.09, the area a of the main beam section is 22.9, the moment of inertia I of the main beam section is 26.5,according to the design specification of highway reinforced concrete and prestressed concrete bridges and culverts 4.2.3, when the shear hysteresis coefficient generated by the axial force at the cable force action point is calculated, the effective width of the top plate of the upper flange of the section of the main beam is 4.00m, and the full section of the bottom plate of the lower flange participates in the calculation, so that the actual normal stress and the nominal normal stress generated by the axial force at the cable force action point are respectively obtainedWherein N' is the axial component of the cable force at the cable force action point, AIs effectiveIs the effective cross-sectional area of the main beam, AAll-purposeThe section area of the main beam is obtained to obtain the shear hysteresis coefficient lambda generated by the axial force at the action point of the cable forceN′2.62. When the shear hysteresis coefficient generated by bending moment is calculated, the effective width of the top plate of the upper flange is 24m, and the actual normal stress and the nominal normal stress generated by the bending moment at the action point of the cable force are respectively obtained Wherein M' is a bending moment at a cable force action point, WIs effectiveIs the effective bending section modulus of the main beam, WAll-purposeObtaining the shear hysteresis coefficient lambda generated by the bending moment at the action point of the cable force for the bending section modulus of the main beamM′＝1.17。
In the embodiment, a full-bridge plane bar system model established by finite element software is used, the internal force diagrams of the bending moment and the axial force of the main beam under the construction condition are smaller in difference between the internal force diagram results of the main beam of the 4# pier and the main beam of the 5# pier, and only the internal force diagram of the main beam at the 4# pier is extracted, such as the bending moment diagram of the 4# pier shown in fig. 4 and the axial force diagram of the 4# pier shown in fig. 5. The axial force and the bending moment at the cable force action point are obtained according to the axial force and the bending moment at the cable force action point in the figures 4 and 5, and the axial force ratio of the bending moment of the section of the main beam at the cable force action point C3 'to C1' is obtainedRespectively as follows: 1.49, 1.59, 1.64, substituting into the formula
Obtaining shear hysteresis coefficients lambda of the upper edge of the main beam section at the cable force positions of C3 '-C1' to be 1.77, 1.75 and 1.74 respectively;
the axial force ratio of the bending moment of the main beam section at the cable force action point C3-C1Respectively as follows: 1.47, 1.81, 2.03; substitution formula
The shear hysteresis coefficients lambda of the upper edges of the sections of the main beams at the cable force positions of C3-C1 are respectively 1.78, 1.71 and 1.67.
Step 2.2: determining the shear hysteresis of a midspan beam section at one half position between the cable force action points;
spanning the middle beam section at one half position between the cable force action points, and using the shear hysteresis coefficient lambda of bending moment actionMReflecting the actual stress condition and shear hysteresis of the point, wherein the shear hysteresis calculation method at the point is as follows:
wherein,nominal normal stress generated by bending moment of a span middle beam section at one half position between cable force action points; sigmaMThe actual positive stress generated by the bending moment of the span-middle beam section at the half part between the acting points of the cable force, lambdaMThe shear hysteresis coefficient is generated by the bending moment of the span-middle beam section at the half position between the acting points of the cable force.
In the embodiment, the shear hysteresis of the midspan beam section at the half position between the cable force action points C3 'to C1' and C3 to C1 and the shear hysteresis coefficient lambda of the action of bending momentMReflecting the actual stress condition of the point, and calculating to obtain lambdaM＝1.17；
Step 2.3: determining shear hysteresis between a cable force action point and a midspan beam section;
the shear hysteresis between the cable force acting point and the span-middle beam section is determined by the shear hysteresis coefficient lambda of the cable force acting point of the beam section between cable forces and one half of the cable force acting pointShear hysteresis coefficient lambda of midspan beam sectionMThe shear hysteresis coefficient of the section of the beam section obtained by linear interpolation is reflected.
In the embodiment, the shear hysteresis of the beam section between the half spans from C3 ' to C3 ' to C2 ' is obtained by linear interpolation between 1.77 and 1.17; the shear hysteresis of the beam section between one half span of C2 ' to C2 ' to C1 ' is obtained by linear interpolation between 1.75 and 1.17; the shear hysteresis of the beam section between C3 and C3-C2 half span is obtained by linear interpolation between 1.78 and 1.17; the shear hysteresis of the beam section between C2 and C2-C1 half span is obtained by linear interpolation between 1.71 and 1.17. For example, the shear hysteresis coefficient of a point C3 is 1.77, the shear hysteresis of a half-span part between C3 and C2 is 1.17, and the linear interpolation of the shear hysteresis coefficient of a beam section 1 meter away from the point C3 is 1.61.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (4)
1. A method for determining shear force stagnation of a main beam of a concrete cable-stayed bridge in a construction stage is characterized by comprising the following steps: the method comprises the following steps:
step 1, determining shear hysteresis at the action points of cable forces of two cantilever ends of a cable-stayed bridge;
step 2, determining the shear hysteresis of the beam section between the cable forces;
step 2.1: determining the shear hysteresis at the cable force action point of the beam section between the cable forces;
step 2.2: determining the shear hysteresis of a midspan beam section at one half position between the cable force action points;
step 2.3: determining shear hysteresis between a cable force action point and a midspan beam section;
shear hysteresis between the cable force action point and the span-middle beam section is determined by the shear hysteresis coefficient lambda of the cable force action point of the beam section between the cable forces and the shear hysteresis coefficient lambda of the span-middle beam section at the half part between the cable force action pointsMThe shear hysteresis coefficient of the section of the beam section obtained by linear interpolation is reflected.
2. The method for determining shear hysteresis of the main beam of the concrete cable-stayed bridge in the construction stage according to claim 1, which is characterized in that: step 1. the shear hysteresis at the action point of the cable force of the two cantilever ends of the cable-stayed bridge is the shear hysteresis coefficient lambda of the axial force action at the pointNReflecting that the shear hysteresis generated by the axial force at this point is calculated as follows:
<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 λ isNShear hysteresis coefficient, sigma, generated by the axial force at the action point of the cantilever end cable force of the cable-stayed bridgeNThe actual normal stress generated by the axial force at the action point of the cable force of the cantilever end of the cable-stayed bridge,the nominal normal stress is generated by the axial force at the action point of the cable-stayed bridge cantilever end cable force.
3. The method for determining shear hysteresis of the main beam of the concrete cable-stayed bridge in the construction stage according to claim 1, which is characterized in that: 2.1, the shear hysteresis at the cable force action point of the beam section between the cable forces is reflected by a shear hysteresis coefficient lambda determined by the ratio of the bending moment and the axial force at the point, and the calculation method of the shear hysteresis at the point is shown as the following formula:
<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, lambda is the shearing hysteresis coefficient of the cable force action point of the beam section between the cable forces, sigma is the actual stress of the cable force action point of the beam section between the cable forces,the nominal stress at the cable force action point of the beam section between the cable forces, the actual stress sigma and the nominal stressIs a superposition of the corresponding normal stresses generated by bending moment and axial force, lambdaN′Is the shear hysteresis coefficient, lambda, generated by the axial force at the action point of the cable force of the beam section between the cable forcesM′M, N are respectively bending moment and axial force applied to the section of the beam section,wherein y is the distance from the centroid of the section of the main beam to the upper edge and the lower edge, A is the section area of the main beam, and I is the section inertia moment of the main beam.
4. The method for determining shear hysteresis of the main beam of the concrete cable-stayed bridge in the construction stage according to claim 1, which is characterized in that: step 2.2 shear hysteresis of the midspan beam section at one half position between the cable force action points uses the shear hysteresis coefficient lambda of the action of the bending moment at the pointMReflecting, the shear hysteresis at this point is calculated as follows:
<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 λ isMShear hysteresis coefficient, sigma, generated by bending moment of the span-middle beam section at one half position between the acting points of cable forceMIs the actual normal stress generated by the bending moment of the span-middle beam section at the half part between the acting points of the cable force,is the nominal positive stress generated by the bending moment across the middle beam section half way between the cable force action points.
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Cited By (2)
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| CN111881613A (en) * | 2020-08-05 | 2020-11-03 | 武汉市政工程设计研究院有限责任公司 | Inversion method and system for three-dimensional stress field with different weights of normal stress and shear stress |
| CN112832114A (en) * | 2020-12-10 | 2021-05-25 | 中铁第四勘察设计院集团有限公司 | Stay cable bridge and anchoring optimization method thereof |
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