CN112560321A - Calculation method for ring-divided segmented pouring length of concrete wrapped outside arch ring of stiffened framework concrete arch bridge - Google Patents

Calculation method for ring-divided segmented pouring length of concrete wrapped outside arch ring of stiffened framework concrete arch bridge Download PDF

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CN112560321A
CN112560321A CN202011590496.4A CN202011590496A CN112560321A CN 112560321 A CN112560321 A CN 112560321A CN 202011590496 A CN202011590496 A CN 202011590496A CN 112560321 A CN112560321 A CN 112560321A
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周水兴
刘增武
蔡同方
龙俊宇
张笑语
张敏
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Chongqing Jiaotong University
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Abstract

The invention relates to the technical field of bridge engineering construction, in particular to a calculation method for the segmental casting length of concrete wrapped outside an arch ring of a stiff skeleton concrete arch bridge, which comprises the following steps: s1: fitting a bending stiffness framework vault section deflection influence line into a polynomial f (x); s2: obtaining a deformation curve F (x) of the arch crown section of the stiff skeleton arch at a concrete pouring stage of a certain ring through integration; s3: establishing three coordinate systems of f (x), F (x) and the height y of the concrete coated outside a certain ring; s4: according to the number N of the working faces, obtaining a plurality of segmentation points in a F (x) deformation curve coordinate system; the difference between the abscissas of two adjacent segmentation points is the horizontal segmentation length L of each working facei(ii) a S5: according toThe number M of the working sections, and then the corresponding deformation curve F (x) of each working surface respectively obtain the segmentation point of each working section; the difference between the abscissa of the segment point of the adjacent working surface and the abscissa of the segment point of the working segment is the horizontal segment length L of each working segment in the corresponding working surfacei,j。

Description

Calculation method for ring-divided segmented pouring length of concrete wrapped outside arch ring of stiffened framework concrete arch bridge
Technical Field
The invention relates to the technical field of bridge engineering construction, in particular to a calculation method for the length of concrete wrapped outside an arch ring of a stiffened framework concrete arch bridge by adopting ring-dividing segmented pouring.
Background
The reinforced framework concrete arch bridge is an arch bridge structure formed by annularly and sectionally pouring arch ring outer-coated concrete on a reinforced framework erected into an arch, and is suitable for an extra-large span reinforced concrete arch bridge with the span of more than 300 m. In order to control the deformation and stress of the stiff skeleton arch during the pouring process of the outer concrete, a multi-working-surface pouring method is generally adopted. However, how to determine the concrete section position and the pouring length enables the stress of the stiff framework to be uniformly distributed, and prevents the stiff framework arch from repeatedly deforming up and down is the key of the construction of the stiff framework arch bridge. At present, a method for determining a working face is to adopt a trial algorithm, however, the trial algorithm has a large workload, the obtained segmentation position and the obtained pouring length often cannot enable the arch crown section to be uniformly warped downwards when all working faces are synchronously poured, and even the arch crown section is warped upwards, and meanwhile, the stress of the upper chord, the lower chord and the outer concrete possibly does not meet the standard requirement, so how to scientifically determine the segmentation position and the pouring length of the working face of the stiff framework concrete arch bridge is a problem to be solved urgently in the construction of the stiff framework method.
Disclosure of Invention
Aiming at the defects in the existing method, the invention provides a method for calculating the length of concrete sections wrapped outside an arch ring of a stiff skeleton concrete arch bridge, which can thoroughly solve the problems in the existing method, effectively control the deformation of the stiff skeleton arch and improve the stress state of the stiff skeleton arch.
A calculation method for the segmental casting length of concrete wrapped outside an arch ring of a stiff skeleton concrete arch bridge comprises the following steps:
extracting a deflection influence line of the section of the arch crown of the stiff skeleton arch by using a finite element program, fitting the deflection influence line into a polynomial, and recording the polynomial as a deflection influence line f (x);
calculating by the formula (1) to obtain a deformation curve of the vault section of the stiff skeleton arch at a concrete pouring stage of a certain ring, recording the deformation curve as a deformation curve F (x), and obtaining the maximum value F of vault deformation in the whole process of concrete pouring of the ringmaxAnd final deformation value FminPoints B and G in the deformation curve F (x) respectively correspond to points B and G of the inflection point in the deflection influence line f (x);
Figure RE-GDA0002944087940000011
in formula (1): x-the position of the section from the arch springing; a-the cross-sectional area of a certain ring of concrete; rho-reinforced concrete volume weight;
Figure RE-GDA0002944087940000021
-horizontal inclination of the arch axis; f (x)i)-xiThe deflection of the cross section of the arch top influences the line value;
establishing a deflection influence line f (X) coordinate system by taking the arch springing as a coordinate origin, taking an X axis as a horizontal distance from the arch springing, and taking a Y axis as f (X); taking the arch springing as the origin of coordinates, the X axis as the horizontal distance from the arch springing, the Y axis as F (X), and establishing a deformation curve F (X) coordinate system; establishing a certain ring of concrete-coated height Y coordinate system by taking the arch springing as a coordinate origin, an X axis as a horizontal distance from the arch springing and a Y axis as an arch ring height Y below a deformation curve F (X) coordinate system;
according to the number N of the predetermined half-span concrete pouring working faces, making a horizontal lines parallel to an x axis in a positive value range of a deformation curve F (x) coordinate system, making B horizontal lines parallel to the x axis in a negative value range of the deformation curve F (x) coordinate system, meeting the condition that N is 2a + B +2, intersecting the deformation curve F (x) to obtain a plurality of intersection points, wherein projection points of the intersection points, a point B and a point G on the x axis are segmentation points of each working face; the difference between the abscissas of two adjacent segmentation points is the horizontal segmentation length L of each working facei；
According to the predetermined number M of the working sections, respectively making c horizontal lines on the F (x) deformation curve corresponding to each working surface, meeting the condition that M is c +1, intersecting the deformation curves F (x) to obtain a plurality of intersection points, wherein projection points of the intersection points on the x axis are segmentation points of each working section; the difference between the abscissa of the adjacent working surface segment point and the abscissa of the working segment point or the difference between the abscissas of the adjacent working segment point is the horizontal segment length L of each working segment in the corresponding working surfacei,j。
Further, the horizontal segment length L of each work surfaceiUsing the maximum value F of the deformation curve F (x)maxAnd a minimum value FminAnd the intersection of the deformation curve f (x) with the horizontal line; when the number of the half-span working surfaces is N, the number of the segmentation points is N + 1; at this time, the half span is divided into 5 working surfaces, which are respectively recorded as: I. II, III, IV and V, 6 segmentation points need to be determined; in the F (x) deformation curve coordinate system, 3 segmentation points are determined by using the arch foot O point, the B point and the G point, and are marked as x0、x2，x5(ii) a The remaining segmentation points are determined by the intersection of the horizontal line with the deformation curve f (x); two horizontal lines intersecting the deformation curve F (x) are set, and are respectively marked as F1、F2(ii) a The specific determination steps comprise:
(1) make F1In the positive range of the deformation curve F (x), F2Lies within the negative range of the deformation curve f (x); the intersection of the two horizontal lines with the deformation curve f (x) is noted: A. c, E, the projected points corresponding to the x-axis are noted as: x is the number of1，x3，x4(ii) a From x0、x1，x2、x3、x4、x5Vertically projecting the arc length of five working faces on the stiff skeleton arch, and recording the arc length as SI、 SII、SIII、SIV、SVWith F1、F2Moving upwards or downwards, and changing the arc length;
(2) for a certain ring of concrete to be poured, the arc length S is a fixed value, so that the average length of the arc length
Figure RE-GDA0002944087940000031
Also constant, the standard deviation S of the arc length is madeσAt a minimum, it is required to
Figure RE-GDA0002944087940000032
Minimum;
the method comprises the following steps: within OB segment F1Equal arc length of division, make SI＝SIITo obtain F1Position F in the deformation curve1 1While observing the coordinate system, SIIIIs also determined accordingly; by F1、F2Trisecting arc length in BG segment to make SIII＝SIV＝SVThereby obtaining F1、F2In two other positions F in the deformation curve1 2And F2 2Thereby obtaining F1Is divided into zones of F1 1～F1 2；
Secondly, the step of: determine F1After the interval, selecting proper step length by adopting a cyclic calculation method, and selecting the step length from F1 1Is calculated to F1 2While using the arc length SIVAnd SVAliquoting to determine F2At the end of the cycle can be obtained
Figure RE-GDA0002944087940000034
Minimum F1、F2；
(4) Find F1∈(0,Fmax) And F2∈(Fmin0) two horizontal lines, the position x of the segmentation point of five working faces is obtained0、x1、x2、x3、x4、x5These points are the segmentation points of the working surface; the horizontal segment lengths for the five faces are then:
horizontal segment length for working face I: l is1＝x1-x0 (2)；
Horizontal segment length for working face II: l is2＝x2-x1 (3)；
Working surface III correspondsHorizontal segment length of (d): l is3＝x3-x2 (4)；
Horizontal segment length for working face IV: l is4＝x4-x3 (5)；
Horizontal segment length for working plane V: l is5＝x5-x4 (6)。
Furthermore, when five working surfaces I, II, III, IV and V are poured simultaneously, the deformation value generated at the vault of each working surface is calculated according to the following formula:
ΔF1＝F(x1)-F(x0)＝F1-0＝F1 (7)；
ΔF2＝F(x2)-F(x1)＝Fmax-F1 (8)；
ΔF3＝F(x3)-F(x2)＝F1-Fmax＝-ΔF2 (9)；
ΔF4＝F(x4)-F(x3)＝F2-F1 (10)；
ΔF5＝F(x5)-F(x4)＝Fmin-F2 (11)。
further, after calculating the segmentation points of the working surface, the horizontal segmentation length calculation is performed on a single working surface, and it is assumed that each working surface is divided into 2 working segments, and the calculation step includes:
(3) on the deformation curve F (x) corresponding to the working surfaces I, II, III, IV and V, a contour horizontal line is made along the direction of an F axis, namely
Figure RE-GDA0002944087940000041
Four horizontal lines (F)1,1，F1,2The coincidence is regarded as one), and the intersection points of the four horizontal lines and the deformation curve f (x) are recorded as: a. b, c, d, e; the intersection points are projected to the x-axis, and the corresponding coordinates are x1,1、x2,1、x3,1、x4,1、x5,1The coordinates are the position of the segmentation point of the working segment;
(4) two adjacent segmentation pointsIs the horizontal segment length L of each working segment in each working planei,jThen, we can get:
the horizontal segment length L of each working section of the working surface I is as follows: l is1，1＝x1,1-x0、L1,2＝x1-x1,1 (12)；
The horizontal segment length L of each working section of the working surface II is as follows: l is2，1＝x2,1-x1、L2,2＝x2-x2,1 (13)；
The horizontal segment length L of each working segment of the working face III is: l is3，1＝x3,1-x2、L3,2＝x3-x3,1 (14)；
The horizontal segment length L of each working section of the working surface IV is as follows: l is4，1＝x4,1-x3、L4,2＝x4-x4,1 (15)；
The horizontal segment length L of each working section of the working surface V is as follows: l is5，1＝x5,1-x4、L5,2＝x5-x5,1 (16)。
The method comprises the steps of firstly, calculating a deformation curve of a vault section in a certain ring concrete pouring process, namely a deformation curve F (x), according to a deflection influence line of the vault section of a stiff skeleton vault obtained based on a finite element program; obtaining the maximum deformation value F of the stiff skeleton arch in the ring concrete pouring process through the deformation curve F (x)maxAnd the final deformation value F after the pouring is finishedmin(ii) a Secondly, dividing a key position of the annular concrete pouring working surface by using the maximum deformation value, namely the position of a B point; thirdly, drawing a plurality of horizontal lines in the positive value (+) area of the deformation curve F (x), dividing the working surface by using double intersection points of the horizontal lines and the deformation curve F (x), drawing a plurality of horizontal lines in the negative value (-) area of the deformation curve F (x), and dividing the working surface by using single intersection points of the horizontal lines and the deformation curve F (x); fourthly, calculating the specific position of a horizontal line according to the principle of minimum standard deviation of the length of the working surface, and dividing the length and the position of the working surface by using the intersection point of the horizontal line and a deformation curve F (x); finally, the process is carried out in a batch,and drawing a plurality of horizontal lines with the same height on the deformation curve F (x) corresponding to each working surface, and dividing the length and the position of the working section by using the intersection points of the horizontal lines and the deformation curve F (x).
Compared with the prior art, the invention has the following beneficial effects:
according to the calculation method, a deformation curve F (x) of the arch crown section of a concrete pouring stage of a certain ring of the stiff skeleton arch is deduced in an integral mode; and then, respectively establishing a deflection influence line f (x) coordinate system, a deformation curve F (x) coordinate system and a certain ring outsourcing concrete height y coordinate system by using a mode of establishing a coordinate system, wherein the abscissa of the coordinate system is the horizontal distance from the arch springing, so that a mapping method is used for searching a projection point of a corresponding position on an x axis through the intersection point of a horizontal line on the deformation curve F (x), and calculating the horizontal segment length L of each working surface through the difference value between adjacent projection pointsiCorresponding to the horizontal segment length L of each working segment in the working surfacei,jThe method has clear calculation thought and simple and accurate steps, and is suitable for division calculation of six, eight, ten or even more working faces of the full bridge; after the working surface is determined, the segmentation position of each working section can be determined through a drawing method according to the number of the working sections; the vault of the stiff framework can be ensured to be uniformly and downwards flexed all the time when multiple working faces are synchronously poured, and upward deformation cannot occur; the stress of the upper chord member, the lower chord member and the outer concrete of the stiff framework in the construction process of the outer concrete can be ensured to meet the standard requirement, and the arch frame is prevented from generating large deformation, so that the concrete is prevented from cracking; in the calculation process, the position of a most critical segmentation point in the division of the working face of the stiff skeleton arch bridge, namely the position of a B point, is also obtained; in engineering practice, the length of each working section can be finely adjusted according to the actual requirement according to the position of the point, but the deformation value corresponding to the working section positioned to the left of the point is smaller than or equal to the deformation value corresponding to the working section positioned to the right of the point when the pouring is carried out synchronously each time, so that the deformation of the arch ring is ensured to be downward all the time after the pouring is finished each time.
Drawings
FIG. 1 is a schematic illustration of the division of the working surface of the present invention;
FIG. 2 is a schematic view of the present invention illustrating the ring segment of the arch ring;
FIG. 3 is a diagram F of the present invention when calculating the segmentation points of the working surface1、F2A value range schematic diagram;
FIG. 4 is a schematic diagram of the present invention for calculating the horizontal segment length of each working segment in each working plane to divide the working segments;
FIG. 5 is a diagram of a master arch layout according to an embodiment of the present invention;
FIG. 6 is a diagram of a finite element model according to an embodiment of the present invention;
FIG. 7 is a graph of deflection influence lines f (x) and a deformation curve F (x) for an embodiment of the present invention;
FIG. 8 is a comparison graph of the working face and the working segment division of the calculation method provided in the present invention with the working face and the working segment division of the Zhahua Jialing river grand bridge;
FIG. 9 is a diagram showing the comparison of the cumulative displacement of the arch crown at each construction stage after pouring the concrete of the arch bridge bottom plate according to the calculation method of the present invention and the design drawing of the Zhahua Jialing river grand bridge;
FIG. 10 is a graph comparing the stress of the upper chord closed steel tube after pouring the arch bridge bottom plate concrete according to the calculation method of the present invention and the design drawing of the Zhahua Jialing river grand bridge;
FIG. 11 is a graph comparing the stress of the lower chord Syngnathus steel tube after pouring the arch bridge floor concrete according to the calculation method of the present invention and the design drawing of the Zhahua Jialing river grand bridge;
FIG. 12 is a graph comparing the stresses of pouring arch bridge bottom plate concrete according to the calculation method of the present invention and the design drawing of Zhahua Jialing river grand bridge.
In fig. 1: 1. vault section deflection influence line; 2. a vault section deformation curve; 3. a certain ring is wrapped with a concrete height line;
in fig. 2: 4. pouring a ring for the concrete arch ring; 5. a stiff skeleton; 6. a working surface; 7. a working section;
Detailed Description
The technical solution of the present invention is further explained in the following by combining experimental examples and necessary explanations.
First, the definition of the working plane is introduced: the working face is that concrete arch rings are divided into a plurality of rings along the height direction in the concrete arch bridge with the stiff skeleton, as shown in figure 2: in fig. 2, the arch ring is divided into three rings (or more rings according to design requirements) along the height direction, each ring is divided into a plurality of large sections along the span direction, the large sections are called working faces, the sum of the number of the large sections of the half span is the number N of the working faces, each working face is divided into a plurality of small sections along the span direction, the small sections are called working sections, and the sum of the number of the small sections in the same working face is the number M of the working sections.
A calculation method for the segmental casting length of concrete wrapped outside an arch ring of a stiff skeleton concrete arch bridge comprises the following steps:
s1: extracting a deflection influence line of the section of the vault of the stiff skeleton by using a finite element program, fitting the deflection influence line into a polynomial, and marking the polynomial as a deflection influence line f (x);
s2: calculating by the formula (1) to obtain a deformation curve of the vault section of the stiff skeleton arch at a concrete pouring stage of a certain ring, recording as a deformation curve F (x), and obtaining the maximum value F of the vault deformation in the whole concrete pouring process of the ring as shown in the figure 1(b)maxAnd final deformation value FminPoints B and G in the deformation curve of F (x) respectively correspond to the point B of the inflection point and the point G of the span in the deflection influence line f (x);
Figure RE-GDA0002944087940000061
in formula (1): x-the position of the section from the arch springing; a-the cross-sectional area of a certain ring of concrete; rho-reinforced concrete volume weight;
Figure RE-GDA0002944087940000062
-horizontal inclination of the arch axis; f (x)i)-xiThe deflection of the cross section of the arch top influences the line value;
s3: the horizontal segment length L of the work surface to be calculatediUsing the maximum value F of the deformation curve F (x)maxAnd a minimum value FminAnd the intersection point where the deformation curve f (x) intersects the horizontal line; byAs can be seen in fig. 1: pouring concrete in a positive (+) area of a deflection influence line F (x), wherein the section of the arch top deforms upwards, and when the concrete is poured to a point B with the deflection influence line F (x) being zero, the arch top reaches a maximum deformation value F in the whole-ring concrete pouring processmax(ii) a Then, as the concrete is continuously poured, the vault begins to deform downwards, the deformation value is zero when the vault reaches the point D, the pouring is continuously carried out until the vault reaches the final deformation value F when the pouring of the whole ring concrete is finishedmin(ii) a Therefore, the point B is a maximum peak point of the deformation of a certain annular concrete pouring vault, is also an important demarcation point for dividing a working surface, and is an important characteristic point for distinguishing the existing working surface; according to the predetermined number N of the half-span concrete pouring working faces, making a plurality of horizontal lines parallel to the x axis on an F (x) deformation curve, and intersecting the deformation curve F (x) to obtain a plurality of intersection points A, C, E,. the. The projection points of the intersection point, the point B and the point G on the x axis are respectively expressed as: x is the number of1、x2、x3......xi(ii) a The projection points are the segmentation points of each working surface; the difference between the abscissas of two adjacent segmentation points is the horizontal segmentation length L of each working facei(ii) a Take half span divided into 5 working faces as an example: when the number of the working surfaces is N, the number of the segmentation points is N + 1; respectively recording as: I. II, III, IV and V, 5+ 1-6 segmentation points need to be determined; in the coordinate system of the deformation curve F (x), 3 segmentation points are determined by using the arch foot O point, the B point and the G point, and are marked as x0、x2，x5(ii) a The remaining segmentation points are determined by the intersection of the horizontal line with the deformation curve f (x); two horizontal lines intersecting the deformation curve F (x) are set, and are respectively marked as F1、F2(ii) a As shown in fig. 1: the deformation curve F (x) has a deformation rising section OB and a deformation falling section BD in the range of positive values (+), for example, a horizontal line F is drawn in the range of positive values (+)1There are two points of intersection A and C, the corresponding dome deformation values being FAAnd FCAnd has FA＝-FCIt shows that when concrete is poured in the working surfaces AB and BC simultaneously, the vault generates positive deformation and negative deformation, and the positive deformation and the negative deformation are equal in numerical value and opposite in direction and just offset, so that the vault does not generate upward deformation,the problem of the strength nature skeleton upper and lower repeated deformation that causes in the concrete segmental casting in current strength nature skeleton concrete arch bridge is solved. Therefore, AB, BC should be defined as two working planes, e.g. II, III working planes in fig. 1. OA is the I working face, IV and V are the F working faces2Determining; the specific determination step comprises:
(1) make F1In the positive range of the deformation curve F (x), F2Lies within the negative range of the deformation curve f (x); the intersection of the two horizontal lines with the deformation curve f (x) is noted: at A, C, E, the projected points corresponding to the x-axis are noted as: x is the number of1，x3，x4(ii) a From x0、x1，x2、x3、x4、x5(ii) a Vertically projecting the arc length of five working faces on the stiff skeleton arch, and recording the arc length as SI、 SII、SIII、SIV、SVWith F1、F2Moving upwards or downwards, and changing the arc length;
(2) for a certain ring of concrete to be poured, the arc length S is a fixed value, so that the average length of the arc length
Figure RE-GDA0002944087940000071
And is also a constant value, and the value of,
average length of five working faces
Figure RE-GDA0002944087940000072
Calculating according to the formula (2):
Figure RE-GDA0002944087940000073
standard deviation S of five face lengthsσComprises the following steps:
Figure RE-GDA0002944087940000074
unfolding the formula (18) and obtaining after finishing:
Figure RE-GDA0002944087940000075
as can be seen from FIG. 1, the deformation maximum segmentation point B has divided the half span into two major segments OB and BG, and the standard deviation S of the arc length is determinedσAt a minimum, it is required to
Figure RE-GDA0002944087940000081
The minimum, the concrete method is;
the method comprises the following steps: within OB segment F1Equal arc length of division, make SI＝SIITo obtain F1Position F in the deformation curve F (x)1 1While observing the coordinate system, SIIIIs also determined accordingly; by F1、F2Trisecting arc length in BG segment to make SIII＝SIV＝SVThereby obtaining F1、F2Two further positions F in the deformation curve F (x)1 2And F2 2Thereby obtaining F1Is divided into zones of F1 1～F1 2；
Secondly, the step of: determine F1After the interval, selecting proper step length by adopting a cyclic calculation method, and selecting the step length from F1 1Is calculated to F1 2While using the arc length SIVAnd SVAliquoting to determine F2At the end of the cycle can be obtained
Figure RE-GDA0002944087940000083
Minimum F1、F2；
(3) Find F1∈(0,Fmax) And F2∈(Fmin0) two horizontal lines, the position x of the segmentation point of five working faces is obtained0、x1、x2、x3、x4、x5These points are the segmentation points of the working surface; the horizontal segment lengths for the five faces are then:
horizontal segment length for working face I: l is1＝x1-x0 (2)；
Horizontal segment length for working face II: l is2＝x2-x1 (3)；
Horizontal segment length for working face III: l is3＝x3-x2 (4)；
Horizontal segment length for working face IV: l is4＝x4-x3 (5)；
Horizontal segment length for working plane V: l is5＝x5-x4 (6)。
When five working faces I, II, III, IV and V are poured simultaneously, the calculation formula of the deformation value of each working face at the vault is as follows:
ΔF1＝F(x1)-F(x0)＝F1-0＝F1 (7)；
ΔF2＝F(x2)-F(x1)＝Fmax-F1 (8)；
ΔF3＝F(x3)-F(x2)＝F1-Fmax＝-ΔF2 (9)；
ΔF4＝F(x4)-F(x3)＝F2-F1 (10)；
ΔF5＝F(x5)-F(x4)＝Fmin-F2 (11)。
the following equations (7) to (11) show that:
II. III cumulative distortion of the dome by the working face is: Δ F2+ΔF3And (0) showing that concrete pouring of the two working surfaces II and III does not generate displacement to the vault.
I. The cumulative distortion of the IV face to the dome is: Δ F1+ΔF4＝F2I.e. the IV working surface counteracts the upward deformation of the I working surface and only F is generated on the vault2Is deformed downwards.
V working surface generates downward deformation delta F to vault5Adding I, IV displacement F generated by working surface2Final displacement value of Fmin，FminNamely a certain ring of concreteAnd (4) vault deformation value after pouring.
(4) Respectively making equal-height horizontal lines on the deformation curves F (x) corresponding to each working surface according to the predetermined number M of the working sections to obtain intersection points of the deformation curves F (x) and the horizontal lines; the projection point of each intersection point on the x axis is the segmentation point of each working segment; in this case, each working plane is assumed to be divided into 2 working segments, and the calculation steps include:
the method comprises the following steps: making contour horizontal lines along the direction of the F axis on the deformation curves corresponding to the working surfaces I, II, III, IV and V, namely
Figure RE-GDA0002944087940000091
Figure RE-GDA0002944087940000092
Four horizontal lines (F)1,1，F1,2The coincidence is regarded as one), and the intersection points of the four horizontal lines and the deformation curve f (x) are recorded as: a. b, c, d, e; the intersection points are projected to the x-axis, and the corresponding coordinates are x1,1、x2,1、x3,1、x4,1、x5,1The coordinates are the position of the segmentation point of the working segment;
secondly, the step of: the difference between the abscissa of the segmentation point of the two adjacent working surfaces and the abscissa of the segmentation point of the working section is the horizontal segmentation length L of each working section in each working surfacei,j(ii) a Then one can get:
the horizontal segment length L of each working section of the working surface I is as follows: l is1，1＝x1,1-x0、L1,2＝x1-x1,1 (12)；
The horizontal segment length L of each working section of the working surface II is as follows: l is2，1＝x2,1-x1、L2,2＝x2-x2,1 (13)；
The horizontal segment length L of each working segment of the working face III is: l is3，1＝x3,1-x2、L3,2＝x3-x3,1 (14)；
The horizontal segment length L of each working section of the working surface IV is as follows: l is4，1＝x4,1-x3、L4,2＝x4-x4,1 (15)；
The horizontal segment length L of each working section of the working surface V is as follows: l is5，1＝x5,1-x4、L5,2＝x5-x5,1 (16)。
The calculation process in the present invention is further explained below based on actual calculations:
1. calculation procedure of scheme of the invention
(1) An arch ring finite element model is established by adopting MIDAS/Civil, a stiff framework is simulated by adopting a beam unit, concrete filled steel tube is simulated by adopting a combined section, and a concrete arch is simulated by adopting a combined section at a construction stage. The first ring (floor) concrete placement is analyzed below as an example.
(2) Calculating and extracting a stiffness framework arch crown section deflection influence line f (x), and fitting the stiffness framework arch crown section deflection influence line f (x) by adopting a polynomial as follows:
f(x)＝1.22775E-04x+2.61360E-05x2-8.67082E-07x3+1.75327E-08x4-2.62985E-10x5 +2.54546E-12x6-1.47752E-14x7+4.68914E-17x8-6.24576E-20x9+6.54680E-05
(3) calculating a vault section deformation curve F (x) according to a formula (1), wherein due to symmetrical pouring of concrete on two sides, only L/2 deformation needs to be calculated, and the deformation is also fitted into a polynomial:
Figure RE-GDA0002944087940000101
(x∈[0,177.1])
plotting deflection influence lines f (x) and deformation curves f (x) see fig. 7;
(4) working surface segmentation computation
Shown in FIG. 7: known zero point x in the deformation curve F (x)0Maximum deformation value FmaxCorresponding to the abscissa x2And final deformation value FminCorresponding to the abscissa x4。
The bridge is divided into four working faces in half span, and only one working face is determined in the positive value range of a deformation curve F (x)Horizontal line F1The length of the face segmentation can be determined and, in order to reduce the number of calculations, two auxiliary horizontal lines F are used1 1And F1 2Determination of F1As shown in fig. 8: pouring length record S corresponding to four working surfacesi(i＝I,II,III,IV)。
Thirdly, the arc length of the I, II working surface is equally divided to obtain F1 19.5248; the arc lengths of the working surfaces III and IV are equally divided by the same principle to obtain F1 214.4558, whereby F1The interval of (a) is 9.5248 to 14.4558.
From F1 1Calculating S in turn from 9.5248I、SII、SIII、SIVAnd SσUntil the end of the interval F1 2Minimum output of SσAnd corresponding F1And calculating to obtain:
Figure RE-GDA0002944087940000102
F1＝10.2348。
from F1Horizontal coordinate x corresponding to horizontal line1＝50.17m，x3146.02m, the horizontal coordinates of the segmentation points of the four working surfaces are obtained, x0＝0、x1＝50.17m、x2＝105.38m、x3＝146.02m、x4177.51m, the horizontal projection length corresponding to the working planes I, II, III and IV is L1＝x1-x0＝50.17m、L2＝x2-x1＝55.21m、 L3＝x3-x2＝40.64m、L4＝x4-x3＝31.49m。
(5) Calculating the deformation value of each working surface at the vault
Working surface I producing deformation value DeltaF1＝F(x1)-F(x0)＝F1-0＝F1＝10.2348
Working surface II producing deformation value Δ F2＝F(x2)-F(x1)＝Fmax-F1＝17.2089
Working face III Generation of the deformation value Δ F3＝F(x3)-F(x2)＝F1-Fmax＝-17.2089
Working surface IV generating deformation value delta F4＝F(x4)-F(x3)＝Fmin-F1＝-36.0499
II. III cumulative distortion of the dome by the working face is: Δ F2+ΔF3And (0) showing that concrete pouring of the two working surfaces II and III does not generate displacement to the vault.
I. The cumulative distortion of the IV face to the dome is: Δ F1+ΔF4＝FminThat is, the IV working surface counteracts the upward deformation generated by the I working surface and deforms downwards to a final deformation value FminAnd the value is the vault deformation value after the first ring of concrete is poured.
(6) Calculating the coordinates of each segmental casting point in the working surface
Each working face is cast in 10 sections, so that 9 horizontal lines are equally divided along an F axis on a deformation curve F (x) corresponding to each working face, for example, a horizontal line is formed on a first working face
Figure RE-GDA0002944087940000111
Thus obtaining x1,1＝17.08m、x1,2＝23.58m、……、x1,9＝47.98m；
The horizontal projection lengths of the working sections are respectively as follows:
L1，1＝x1，1-x0＝17.08m、L1,2＝x1，2-x1,1＝6.50m、……、L1,10＝x2-x1,9＝2.58m。
and the other working surfaces are the same as the calculation method of the first working surface.
2. And (3) real bridge comparison and checking calculation:
real bridge parameter introduction: a reinforced concrete rigid framework arch bridge with the net span of 350m is designed for the Zhahuajialing river grand bridge, and the net rise is 83.33 m. The main arch ring adopts a constant-section catenary hingeless arch, and the width and the height of the appearance of the arch ring are both 8 m; the thickness of the top plate and the bottom plate of the standard section is 0.4m, and the thickness of the web plate is 0.3 m. Arch foot to second rootThe transition section is arranged between the upright columns, the thickness of the top plate concrete and the bottom plate concrete is linearly changed from 0.8m to 0.4m, and the thickness of the side web plate is linearly changed from 0.55m to 0.3 m. C80 concrete is adopted in the steel pipe of the stiff skeleton, C55 concrete is adopted in the concrete arch ring, construction is carried out in three rings along the height direction of the arch ring, construction is carried out according to eight working faces along the span direction, and all the working faces are equally divided according to the span; except that the first working surface is 9 working sections, the other working surfaces are divided into 10 working sections. The horizontal lengths of the projections of the working surfaces along the x-axis being substantially equal (L)1＝44.13m，L2＝44.59m， L3＝44.49m，L444.58m), the horizontal projection length of the division working section is between 4m and 6 m.
3. Conclusion comparison
Data obtained by calculating the Zhahua Jialing river grand bridge by using the method and the lengths of the working face and the working segment which are designed and divided by the Zhahua Jialing river grand bridge are respectively input into the model to obtain vault displacement curves of two schemes, as shown in figure 10, wherein "+" represents upward deformation and "-" represents downward deformation. In the figure: the first scheme is a design scheme; the second scheme is the scheme provided by the invention. The construction method comprises the steps of synchronously pouring the same working sections for all working surfaces, wherein each working section is divided into 10 construction stages in total. It should be noted that, in the design, the first working surface is only divided into 9 working sections, so that when the 10 th working section is calculated, the working surface is free of concrete pouring.
As can be seen from fig. 9, in the case of the floor concrete, although the arch is deformed downward overall, the upward deformation occurs in the process; and pouring the bottom plate concrete according to the second scheme, wherein the vault is always deformed downwards, upward deformation does not occur in the process, and the accumulated deformation is similar to a straight line, namely the downward deformation of the vault is close to a constant value when each working section is synchronously poured on each working surface, thereby proving the conclusion that the vault can be uniformly and downwards warped all the time and cannot be deformed upwards. After the pouring of the concrete of the bottom plate is completed, the stress of the upper chord and the lower chord of the semi-span stiff skeleton arch is shown in fig. 11, wherein the "-" indicates that the chords are pressed.
As can be seen from fig. 10 and 11, in both of the two schemes, the upper chord member and the lower chord member of the stiff skeleton arch are compressed, but the positions where the maximum stress occurs are different. In the first scheme, the maximum compressive stress of an upper chord appears at an arch springing and is-136.7 MPa; the maximum compressive stress of the lower chord appears on the L/8 section and is-164.5 MPa. In the second scheme, the distance between the maximum compressive stress position of the upper chord and the vault in the horizontal direction is 18.6m and is-122.4 MPa; the maximum stress of the lower chord appears on the L/6 section and is-157.2 MPa. The maximum compressive stress of the upper chord and the lower chord in the two schemes is smaller than the design value 305MPa, but the maximum stress of the stiff framework in the second scheme is smaller than that in the first scheme. Fig. 12 shows the stress distribution of the floor concrete along the span direction, wherein "+" indicates that the concrete is pulled and "-" indicates that the concrete is compressed.
As can be seen from FIG. 12, in the first embodiment, the maximum tensile stress of the concrete is 3.6MPa, which exceeds the design value of 1.89MPa, and the maximum compressive stress is-3.07 MPa. In the second scheme, the maximum tensile stress of the concrete is 1.83MPa, is only 1/2 of the first scheme, is smaller than the design value specified by the specification, and the maximum compressive stress is-3.96 MPa.
In conclusion, compared with the design scheme, the calculation method for the length of the concrete sections wrapped outside the arch ring of the rigid framework concrete arch bridge and the position of the section points can enable the arch top section to be uniformly deformed downwards all the time when all working surfaces are synchronously poured, and the stress of the upper chord member, the lower chord member and the concrete of the rigid framework can be better controlled.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (4)

1. A calculation method for the segmental casting length of concrete wrapped outside an arch ring of a stiff skeleton concrete arch bridge is characterized by comprising the following steps:
s1: extracting a deflection influence line of the section of the arch crown of the stiff skeleton arch by using a finite element program, fitting the deflection influence line into a polynomial, and recording the polynomial as a deflection influence line f (x);
s2: calculating by the formula (1) to obtain a deformation curve of the vault section of the stiff skeleton arch at a concrete pouring stage of a certain ring, recording the deformation curve as a deformation curve F (x), and obtaining the maximum value F of vault deformation in the whole process of concrete pouring of the ringmaxAnd final deformation value FminPoints B and G in the deformation curve F (x) respectively correspond to points B and G of the inflection point in the deflection influence line f (x);
Figure FDA0002866878530000011
in formula (1): x-the position of the section from the arch springing; a-the cross-sectional area of a certain ring of concrete; rho-reinforced concrete volume weight;
Figure FDA0002866878530000012
-horizontal inclination of the arch axis; f (x)i)-xiThe deflection of the cross section of the arch top influences the line value;
s3: establishing a deflection influence line f (X) coordinate system by taking the arch springing as a coordinate origin, taking an X axis as a horizontal distance from the arch springing, and taking a Y axis as f (X); taking the arch springing as the origin of coordinates, the X axis as the horizontal distance from the arch springing, the Y axis as F (X), and establishing a deformation curve F (X) coordinate system; establishing a certain ring of concrete-coated height Y coordinate system by taking the arch springing as a coordinate origin, an X axis as a horizontal distance from the arch springing and a Y axis as an arch ring height Y below a deformation curve F (X) coordinate system;
s4: according to the number N of the predetermined half-span concrete pouring working faces, making a horizontal lines parallel to an x axis in a positive value range of a deformation curve F (x) coordinate system, making B horizontal lines parallel to the x axis in a negative value range of the deformation curve F (x) coordinate system, meeting the condition that N is 2a + B +2, intersecting the deformation curve F (x) to obtain a plurality of intersection points, wherein projection points of the intersection points, a point B and a point G on the x axis are segmentation points of each working face; the difference between the abscissas of two adjacent segmentation points is the horizontal segmentation length L of each working facei；
S5: according to the predetermined number M of working sections, respectively corresponding F (x) deformation on each working faceC horizontal lines are made on the curve, M is equal to c +1, the curve is intersected with a deformation curve F (x) to obtain a plurality of intersection points, and projection points of the intersection points on an x axis are segmentation points of each working section; the difference between the abscissa of the adjacent working surface segment point and the abscissa of the working segment point or the difference between the abscissas of the adjacent working segment point is the horizontal segment length L of each working segment in the corresponding working surfacei,j。
2. The method for calculating the segmental casting length of the concrete wrapped outside the arch ring of the stiff skeleton concrete arch bridge according to the claim 1, wherein the horizontal segmental length L of each working faceiUsing the maximum value F of the deformation curve F (x)maxAnd a minimum value FminAnd the intersection of the deformation curve f (x) with the horizontal line; when the number of the half-span working surfaces is N, the number of the segmentation points is N + 1; at this time, the half span is divided into 5 working surfaces, which are respectively recorded as: I. II, III, IV and V, 6 segmentation points need to be determined; in the F (x) deformation curve coordinate system, 3 segmentation points are determined by using the arch foot O point, the B point and the G point, and are marked as x0、x2，x5(ii) a The remaining segmentation points are determined by the intersection of the horizontal line with the deformation curve f (x); two horizontal lines intersecting the deformation curve F (x) are set, and are respectively marked as F1、F2(ii) a The specific determination steps comprise:
(1) make F1In the positive range of the deformation curve F (x), F2Lies within the negative range of the deformation curve f (x); the intersection of the two horizontal lines with the deformation curve f (x) is noted: A. c, E, the projected points corresponding to the x-axis are noted as: x is the number of1，x3，x4(ii) a From x0、x1，x2、x3、x4、x5Vertically projecting the arc length of five working faces on the stiff skeleton arch, and recording the arc length as SI、SII、SIII、SIV、SVWith F1、F2Moving upwards or downwards, and changing the arc length;
(2) for a certain ring of concrete to be poured, the arc length S is a fixed value, so that the average length of the arc length
Figure FDA0002866878530000024
Also constant, the standard deviation S of the arc length is madeσAt a minimum, it is required to
Figure FDA0002866878530000021
Minimum;
the method comprises the following steps: within OB segment F1Equal arc length of division, make SI＝SIITo obtain F1Position F in the deformation curve1 1While observing the coordinate system, SIIIIs also determined accordingly; by F1、F2Trisecting arc length in BG segment to make SIII＝SIV＝SVThereby obtaining F1、F2In two other positions F in the deformation curve1 2And
Figure FDA0002866878530000023
thereby obtaining F1Is divided into zones of F1 1～F1 2；
Secondly, the step of: determine F1After the interval, selecting proper step length by adopting a cyclic calculation method, and selecting the step length from F1 1Is calculated to F1 2While using the arc length SIVAnd SVAliquoting to determine F2At the end of the cycle can be obtained
Figure FDA0002866878530000022
Minimum F1、F2；
(3) Find F1∈(0,Fmax) And F2∈(Fmin0) two horizontal lines, the position x of the segmentation point of five working faces is obtained0、x1、x2、x3、x4、x5These points are the segmentation points of the working surface; the horizontal segment lengths for the five faces are then:
horizontal segment length for working face I: l is1＝x1-x0 (2)；
Horizontal segment length for working face II: l is2＝x2-x1 (3)；
Horizontal segment length for working face III: l is3＝x3-x2 (4)；
Horizontal segment length for working face IV: l is4＝x4-x3 (5)；
Horizontal segment length for working plane V: l is5＝x5-x4 (6)。
3. The method for calculating the segmental casting length of the concrete wrapped outside the arch ring of the stiff skeleton concrete arch bridge according to claim 2, wherein when five working surfaces I, II, III, IV and V are cast simultaneously, the deformation value of each working surface at the arch crown is calculated by the following formula:
ΔF1＝F(x1)-F(x0)＝F1-0＝F1 (7)；
ΔF2＝F(x2)-F(x1)＝Fmax-F1 (8)；
ΔF3＝F(x3)-F(x2)＝F1-Fmax＝-ΔF2 (9)；
ΔF4＝F(x4)-F(x3)＝F2-F1 (10)；
ΔF5＝F(x5)-F(x4)＝Fmin-F2 (11)。
4. the method for calculating the segmental casting length of the concrete wrapped outside the arch ring of the stiff skeleton concrete arch bridge according to the claim 2, wherein after segmental points of a working surface are calculated, horizontal segmental length calculation is carried out on a single working surface, and at the moment, each working surface is assumed to be divided into 2 working sections, and the calculation step comprises the following steps:
(1) on the deformation curve F (x) corresponding to the working surfaces I, II, III, IV and V, a contour horizontal line is made along the direction of an F axis, namely
Figure FDA0002866878530000031
Four horizontal lines (F)1,1，F1,2The coincidence is regarded as one), and the intersection points of the four horizontal lines and the deformation curve f (x) are recorded as: a. b, c, d, e; the intersection points are projected to the x-axis, and the corresponding coordinates are x1,1、x2,1、x3,1、x4,1、x5,1The coordinates are the position of the segmentation point of the working segment;
(2) the difference between the abscissas of two adjacent segmentation points is the horizontal segmentation length L of each working segment in each working planei,jThen, we can get:
the horizontal segment length L of each working section of the working surface I is as follows: l is1，1＝x1,1-x0、L1,2＝x1-x1,1 (12)；
The horizontal segment length L of each working section of the working surface II is as follows: l is2，1＝x2,1-x1、L2,2＝x2-x2,1 (13)；
The horizontal segment length L of each working segment of the working face III is: l is3，1＝x3,1-x2、L3,2＝x3-x3,1 (14)；
The horizontal segment length L of each working section of the working surface IV is as follows: l is4，1＝x4,1-x3、L4,2＝x4-x4,1 (15)；
The horizontal segment length L of each working section of the working surface V is as follows: l is5，1＝x5,1-x4、L5,2＝x5-x5,1 (16)。
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