Rapid modeling method and structural design method of truss type arch rib

Abstract

The invention relates to the technical field of civil engineering structure analysis and design, in particular to a rapid modeling method and structure design method for a truss type arch rib, and the rapid modeling method for the truss type arch rib comprises the steps that a plurality of processing modules are established, the arch rib is divided into a plurality of feature areas according to web member distribution features, and a plurality of processing modules are established; modularization and parameterization of the arch rib modeling process are achieved, the arch rib plane geometric model can be rapidly, accurately and efficiently established on the basis of the drafted basic size information of the arch rib in combination with programming software, the modeling time is shortened, the labor cost is reduced, the efficiency of engineering technicians in the truss arch bridge design process is improved, and the construction efficiency is improved. According to the structural design method of the trussed arch rib, on the basis of rapid modeling of the trussed arch rib, an arch rib plane structure diagram can be rapidly obtained, the method can be rapidly applied to arch rib structural design, the efficiency and accuracy of structural design of the trussed arch bridge are improved, and the safety and applicability of design and construction of the arch bridge are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering structure analysis and design, and particularly relates to a rapid modeling method and a structural design method for a truss arch rib. Background Art

[0002] With the continuous improvement of the construction technology of arch bridges, the spanning ability and applicability of arch bridges have been continuously enhanced. Among them, the truss arch rib has become a common arch rib form for large-span and super-large-span arch bridges due to its characteristics of being able to fully utilize the axial mechanical properties of materials and having a light weight. In the construction, design, and construction process of the truss arch rib, structural finite element modeling and analysis are very important. For the modeling of the upper and lower chord members in the existing structural finite element modeling and analysis of the truss arch rib, a continuous function form is mostly used. For the web members of the truss arch rib, the method of manually establishing nodes and connecting elements is often used, which reduces the efficiency of structural analysis to a certain extent, limits the engineer's ability to comprehensively master the overall structure, and also weakens the ability of engineering parametric analysis, resulting in a waste of labor costs. Summary of the Invention

[0003] The purpose of the present invention is to overcome the deficiencies in the prior art that the efficiency of the structural finite element modeling and analysis process of the web members of the truss arch rib is relatively low, which affects the overall modeling time of the structure and causes a waste of labor costs, and to provide a rapid modeling method and a structural design method for a truss arch rib.

[0004] In the first aspect, the present invention provides a rapid modeling method for a truss arch rib, including: S1. According to the determined basic dimensions of the arch rib, establish a first processing module, and the first processing module includes an arch axis, an upper chord tube center line, and a lower chord tube center line; S2. According to the distribution characteristics of the web members, divide a number of characteristic regions in the first processing module; S3. Respectively determine the intersection positions of the web members and the upper chord tube center line and the intersection positions of the web members and the lower chord tube center line in each characteristic region, and sequentially connect the intersection points on the upper chord tube center line and the intersection points on the lower chord tube center line to form a second processing module; S4. According to the determined arch rib segmentation information, replace the web members involved at the segmentation with double web members in the second processing module to obtain an arch rib plane geometric model considering arch rib segmentation.

[0005] The rapid modeling method for a truss arch rib of the present invention realizes the modularization and parameterization of the arch rib modeling process by establishing multiple processing modules and dividing the arch rib into multiple characteristic regions according to the distribution characteristics of the web members. It can quickly, accurately, and efficiently establish the arch rib plane geometric model based on the determined basic dimension information of the arch rib, combined with programming software, shorten the modeling time, reduce labor costs, and improve the efficiency of engineering and technical personnel in the design process of truss arch bridges.

[0006] Preferably, in step S2, the characteristic regions include a first characteristic region, a second characteristic region, a third characteristic region, and a fourth characteristic region; The first characteristic region includes the distribution characteristics of vertical web members and diagonal web members alternately distributed, with vertical web members at both ends in the arch axis direction; The third characteristic region includes the distribution characteristics of radial web members and diagonal web members alternately distributed, with the radial web members perpendicular to the arch axis and radial web members at both ends in the arch axis direction; The fourth characteristic region includes the triangular region of the temporary hinge at the arch foot. The fourth characteristic region includes the distribution characteristics of a single radial web member and two connecting web members, with one end of the connecting web member connected to the end of the radial web member and the other end of the connecting web member connected to the temporary hinge at the arch foot; The second characteristic region includes the distribution characteristics of four web members, forming three intersections on the center line of the upper chord tube and two intersections on the center line of the lower chord tube;

[0007] Preferably, in step S2, the first characteristic region, the second characteristic region, the third characteristic region, and the fourth characteristic region are formed in sequence along the direction from the mid-span to the arch foot, and adjacent characteristic regions share web members at both ends of the arch axis, or, the first characteristic region, the second characteristic region, and the fourth characteristic region are formed in sequence along the direction from the mid-span to the arch foot, and adjacent characteristic regions share web members at both ends of the arch axis.

[0008] Preferably, step S1 includes: According to the curve form of the arch axis, determine the arch axis function and the tangential function of any point on the arch axis; According to the form of the change in the height of the arch rib along the longitudinal bridge direction, determine the truss height function of any point on the arch rib; According to the arch axis function, the tangential function, and the truss height function, determine the center line equation of the upper chord tube and the center line equation of the lower chord tube.

[0009] Preferably, step S1 includes: discretize the center lines of the upper chord tube and the lower chord tube into a number of sequentially numbered nodes, substitute them into the arch axis function, the center line equation of the upper chord tube, and the center line equation of the lower chord tube to obtain the original sequence of node coordinates.

[0010] Preferably, step S3 includes: S3.1. Determine the longitudinal bridge coordinates of the intersections of the web members and the center line of the upper chord tube in each characteristic region by means of equal division and / or the method of specifying the spacing one by one; S3.2. Substitute the longitudinal bridge coordinates of each intersection into the center line equation of the upper chord tube and the center line equation of the lower chord tube for calculation, or, use the method of sequence interpolation to substitute the longitudinal bridge coordinates of each intersection into the original sequence of node coordinates for calculation to determine the vertical coordinates of the intersections of each web member and the center line of the upper chord tube. S3.3. Organize to obtain the abdominal bar information sequence.

[0011] Preferably, the abdominal bar information includes data information such as the coordinates of the two ends of the abdominal bar, the midpoint coordinates, the direction vector, the slope, and the normal slope.

[0012] Preferably, step S4 includes: S4.1. Determine the segment information of the arch rib and the double abdominal bar spacing, and determine the longitudinal coordinate at the segmentation point; S4.2. By means of sequence interpolation, substitute the longitudinal coordinate at the segmentation point into the abdominal bar information sequence for calculation to obtain the abdominal bar information involved at the segmentation point; S4.3. According to the abdominal bar information involved at the segmentation point, determine the intersection coordinates of the two ends of the double abdominal bar; S4.4. After organizing and connecting the lines, obtain the center line of the abdominal bar considering the segment division.

[0013] Preferably, step S4.3 includes: S4.3.1. According to the centroid coordinates and normal slope of the abdominal bar involved at the segmentation point, determine the coordinates of any point on the double abdominal bar; S4.3.2. According to the coordinates and slope of any point on the double abdominal bar, determine the straight line equation where the double abdominal bar is located; S4.3.3. Simultaneously solve the straight line equations where the double abdominal bar is located, the center line equation of the upper chord tube, and the center line equation of the lower chord tube to obtain the intersection coordinates of the two ends of the double abdominal bar, or, use the bisection interpolation method, and simultaneously solve the straight line equation where the double abdominal bar is located and the original sequence of node coordinates to obtain the intersection coordinates of the two ends of the double abdominal bar.

[0014] A structural design method for a truss arch rib, using the above-mentioned fast modeling method for a truss arch rib to obtain a plane structure diagram of the truss arch rib and perform structural design.

[0015] The structural design method for a truss arch rib of the present invention, based on the fast modeling of the truss arch rib, can quickly obtain the plane structure diagram of the arch rib, can be quickly applied to the arch rib structure design, improve the efficiency and accuracy of the truss arch bridge structure design, and improve the safety and applicability of the arch bridge design and construction.

[0016] Compared with the prior art, the beneficial effects of the present invention: 1. The present invention provides a fast modeling method for a truss arch rib. By establishing multiple processing modules and dividing the arch rib into multiple characteristic regions according to the distribution characteristics of the abdominal bars, the modularization and parameterization of the arch rib modeling process are realized. Based on the proposed basic dimension information of the arch rib and combined with programming software, the establishment of the plane geometric model of the arch rib can be quickly, accurately and efficiently realized, shortening the modeling time, reducing the labor cost, and improving the efficiency of engineering and technical personnel in the design process of truss arch bridges; 2. A structural design method for a truss arch rib according to the present invention, based on the rapid modeling of the truss arch rib, can quickly obtain the arch rib plane structure diagram, can be quickly applied to the arch rib structure design, improve the efficiency and accuracy of the truss arch bridge structure design, and improve the safety and applicability of the arch bridge design and construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic flow chart of a rapid modeling method for a truss arch rib according to the present invention.

[0018] Figure 2 It is a modeling result diagram obtained after dividing a certain truss arch rib into 2000 parts in Embodiment 1.

[0019] Figure 3 It is a schematic diagram of dividing the feature area corresponding to step S2 in Embodiment 1.

[0020] Figure 4 It is a schematic diagram of a certain truss arch rib after dividing the feature area in Embodiment 1.

[0021] Figure 5 It is a schematic diagram of determining the web members at the corresponding arch rib segmentation positions of a certain truss arch rib in Embodiment 1.

[0022] Figure 6 It is an arch rib plane geometric model of a certain truss arch rib considering arch rib segmentation obtained by using the modeling method of Embodiment 1.

[0023] Reference signs in the figures: 1 - First feature area, 2 - Second feature area, 3 - Third feature area, 4 - Fourth feature area, 5 - Center line of upper chord tube, 6 - Center line of lower chord tube, 7 - Inclined web member, 8 - Vertical web member, 9 - Radial web member, 10 - Connecting web member. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] The present invention will be further described in detail below with reference to specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments. Any technology implemented based on the content of the present invention belongs to the scope of the present invention.

[0025] Unless otherwise specified, in the description of the specific embodiments of the present invention, the expression terms indicating the orientation or positional relationship such as "upper", "lower", "left", "right", "center", "inner", "outer", etc. are all based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship when the invention product / device / device is commonly used. These terms of orientation or positional relationship are only for the convenience of describing the solution of the present invention or simplifying the description in the specific embodiments, so as to facilitate technicians to quickly understand the solution, rather than indicating or implying that a specific device / component / element must have a specific orientation or be constructed and operated in a specific positional relationship. Therefore, it should not be construed as a limitation to the present invention.

[0026] In addition, if terms such as "horizontal", "vertical", "hanging", "parallel" appear, it does not mean that the corresponding device / component / element is required to be absolutely horizontal or vertical or hanging or parallel, but can be slightly inclined or have a deviation. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined. Or, it can be simply understood that the corresponding device / component / element is arranged in the directions of "horizontal", "vertical", "hanging", "parallel", etc., and can have an error / deviation of ±10% relative to the corresponding direction setting, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still play its role in the solution of the present invention.

[0027] In addition, the expressions "first", "second", "third", etc. that appear in the terms are only used to distinguish the description of the same or similar components, and should not be understood as emphasizing or implying the relative importance of specific components.

[0028] In addition, in the description of the embodiments of the present invention, "several", "multiple", "a plurality of" represent at least 2. It can be any situation such as 2, 3, 4, 5, 6, 7, 8, 9, etc., and even more than 9.

[0029] In addition, in the description of the technical solution of the present invention, unless otherwise clearly specified / defined / limited, where terms such as "set", "installed", "connected", "connected", "provided with", "laid", "arranged" appear, they should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection. It can be connection means commonly used in the art such as welding, riveting, bolting, threaded connection, etc. This connection can be a mechanical connection, an electrical connection or a communication connection; it can be directly connected, or indirectly connected through an intermediate medium, and can be the communication inside two components.

[0030] Embodiment 1 As Figure 1 shown, a rapid modeling method for a truss arch rib includes: S1. Based on the determined basic dimensions of the arch rib, establish a first processing module, which includes the arch axis, the center line of the upper chord tube, and the center line of the lower chord tube; S2. According to the distribution characteristics of the web members, divide and form several characteristic regions within the first processing module; S3. Respectively determine the intersection positions of the web members and the center line of the upper chord tube, and the intersection positions of the web members and the center line of the lower chord tube within each characteristic region, and sequentially connect the intersection points on the center line of the upper chord tube and the intersection points on the center line of the lower chord tube to form a second processing module; S4. According to the determined arch rib segmentation information, replace the web members involved at the segmentation in the second processing module with double web members to obtain the arch rib plane geometric model considering the arch rib segmentation.

[0031] Step S1 is used to establish a first processing model according to the determined basic dimensions of the arch rib, providing a data basis for the subsequent modeling process.

[0032] In one or several embodiments, step S1 may include: S1.1. According to the curve form of the arch axis, determine the arch axis function and the tangential function of any point on the arch axis; S1.2. According to the form of the change of the arch rib height along the longitudinal bridge direction, determine the truss height function of any point on the arch rib; S1.3. According to the arch axis function, the tangential function, and the truss height function, determine the equation of the center line of the upper chord tube and the equation of the center line of the lower chord tube.

[0033] In an optional embodiment, the determined basic dimensions of the arch rib may include parameters such as span, rise, rise-span ratio, arch axis coefficient, chord tube diameter, etc.

[0034] In an optional embodiment, the curve form of the arch axis may be any one of a catenary form, a parabola form, an arc line form, or other continuous smooth curve forms.

[0035] In an optional embodiment, the form of the change of the arch rib height along the longitudinal bridge direction may include any one of the truss height linearly changing with respect to the longitudinal bridge coordinate, the truss height parabolically changing with respect to the longitudinal bridge coordinate, or the moment of inertia formed by the truss height and the chord tube linearly changing with respect to the longitudinal bridge coordinate.

[0036] Taking a rapid modeling method for a certain truss arch rib as an example for illustration: The determined basic dimensions of the arch rib include a span L = 508m, a rise f = 122.25m, a rise-span ratio △ = 1 / 4.155, the curve form of the arch axis is a catenary form, the arch axis coefficient m = 1.9, the coordinate origin is set at the midpoint of the truss height of the mid-span arch rib, and the arch axis function is determined as: —— Equation 1; In the formula: cosh is the symbol of the hyperbolic cosine function.

[0037] The first derivative formula of the arch axis line is: —— Equation 2; The tangential function at any point on the arch axis line is: —— Equation 3; When the change of the arch rib height is taken as the linear change of the truss height with respect to the coordinate along the bridge axis, the truss height function at any point on the arch axis line is: —— Equation 4; In the formula: d1 is the truss height at the crown; d2 is the truss height at the arch foot; When the change of the arch rib height is taken as the parabolic change of the truss height with respect to the coordinate along the bridge axis, the truss height function at any point on the arch axis line is: —— Equation 5; When the change of the arch rib height is taken as the linear change of the moment of inertia formed by the truss height and the chord tube with respect to the coordinate along the bridge axis, the parameter of the chord tube diameter D0 is supplemented and determined, and the truss height function at any point on the arch axis line is: —— Equation 6; Among them: —— Equation 7; ; ; ; In the formula: n is the intermediate variable; I d is the moment of inertia of the crown section; I j is the moment of inertia of the arch foot section; y’ is the first derivative of the arch axis line; d0 is the chord tube diameter; d j is the same as d2 which is the truss height at the arch foot.

[0038] According to the arch axis line function, tangential function and truss height function, the center line equation of the upper chord tube can be determined as: —— Equation 8; The center line equation of the lower chord tube is: —— Equation 9; In the formula: x up is the coordinate of the center line of the upper chord tube along the bridge axis, y up is the vertical coordinate of the center line of the upper chord tube, x down is the coordinate of the center line of the lower chord tube along the bridge axis, y down is the vertical coordinate of the center line of the lower chord tube, is the first derivative of the arch axis line.

[0039] According to step S1, taking the midpoint of the arch rib's mid-span truss height as the origin, a first processing module for the half-span arch rib including the arch axis, the center line of the upper chord tube, and the center line of the lower chord tube can be established.

[0040] In one or several embodiments, step S1 can also take the midpoint of the arch rib's mid-span truss height as the origin, evenly divide the first processing module into several parts, calculate the coordinates of each part as a node, so as to obtain the coordinates and linear shapes of all nodes on the arch axis, the center line of the upper chord tube, and the center line of the lower chord tube. That is, the center lines of the upper chord tube and the lower chord tube are discretized into several sequentially numbered nodes, and the original sequence of node coordinates is obtained by substituting them into the arch axis function, the equation of the center line of the upper chord tube, and the equation of the center line of the lower chord tube.

[0041] In an optional embodiment, the length of each divided part can be less than the panel length, and the number of divided parts can be determined according to the computer performance. The number of divided parts is positively correlated with the calculation result accuracy.

[0042] In an optional embodiment, the length of each divided part can be less than or equal to 1 m.

[0043] Taking the example of dividing the half-span arch rib with the longitudinal bridge coordinate in the range of 0 to L / 2 of the half-span into 2000 parts, the modeling result in the negative X coordinate plane is drawn, as Figure 2 shown; and the original sequence of node coordinates of the half-span arch rib is obtained, as shown in Table 1.

[0044] Table 1

[0045] Step S2 is used to divide the arch rib into multiple characteristic regions with obvious characteristics according to the distribution characteristics of the web members, providing a basis for the subsequent positioning of the web members.

[0046] In one or several embodiments, the half-span arch rib can be divided into a first characteristic region, a second characteristic region, a third characteristic region, and a fourth characteristic region, as Figure 3 shown.

[0047] The first characteristic region includes the distribution characteristics of vertical web members and diagonal web members alternating, and vertical web members at both ends in the arch axis direction.

[0048] Specifically, the first characteristic region only includes vertical web members and diagonal web members. The two ends of the diagonal web members are connected to the intersection points of the vertical web members and the upper and lower chord tubes. Since the vertical web members and the diagonal web members are alternately distributed, and both ends in the arch axis direction of the first characteristic region are vertical web members, therefore, within the first characteristic region, the number of intersection points between the web members and the center line of the upper chord tube is equal to the number of intersection points between the web members and the center line of the lower chord tube, and the intersections are vertically corresponding one by one. The longitudinal bridge coordinates of the vertically corresponding intersections are the same.

[0049] The third characteristic region includes the distribution characteristics of radial web members and diagonal web members that are alternately distributed, with the radial web members perpendicular to the arch axis and both ends in the arch axis direction being radial web members.

[0050] Specifically, the third characteristic region is a region that only includes radial web members and diagonal web members. The radial web members are perpendicular to the arch axis direction. The two ends of the diagonal web members are connected to the intersection points of the radial web members and the upper and lower chord tubes. Since the radial web members and the diagonal web members are alternately distributed, and both ends in the arch axis direction of the third characteristic region are radial web members, therefore, within the third characteristic region, the number of intersection points between the web members and the center line of the upper chord tube is equal to the number of intersection points between the web members and the center line of the lower chord tube, and each intersection point corresponds one by one along the radial direction of the arch axis. The coordinates of the radially corresponding intersection points in the arc length direction are the same and they have the same node numbers in the original node coordinate sequence.

[0051] The fourth characteristic region includes the triangular region of the temporary hinge at the arch foot. The fourth characteristic region includes the distribution characteristics of a single radial web member and two connecting web members, with one end of the connecting web member connected to the end of the radial web member and the other end of the connecting web member connected to the web member of the temporary hinge at the arch foot.

[0052] Specifically, the fourth characteristic region is the triangular region of the temporary hinge at the arch foot, which only has one panel. It is composed of three web members distributed in a triangle. Only the two ends of the radial web member in the fourth characteristic region intersect with the upper and lower chord tubes. Since the two intersection points are at both ends of the same radial web member, therefore, the coordinates of the two intersection points in the arc length direction are the same and they have the same node numbers in the original node coordinate sequence. The second characteristic region includes the distribution characteristics of four web members, forming three intersection points on the center line of the upper chord tube and two intersection points on the center line of the lower chord tube.

[0053] Specifically, the second characteristic region is generally a transition region for connecting adjacent characteristic regions. It only includes four web members, and the web members at both ends of the arch axis are shared with the adjacent characteristic regions. A triangular region can be formed by two web members within the second characteristic region.

[0054] In an alternative implementation, in step S2, the first characteristic region, the second characteristic region, the third characteristic region, and the fourth characteristic region can be divided and formed in sequence along the direction from the mid-span to the arch foot. Adjacent characteristic regions share web members at both ends of the arch axis. The second characteristic region is the transition region between the first characteristic region and the third characteristic region, and this is also the basic division mode in the rapid modeling process of most truss arch ribs.

[0055] As Figure 4 shown, it is an example after the characteristic region division of the above-mentioned truss arch rib in step S2 based on step S1.

[0056] In an alternative embodiment, in step S2, when the length of the third characteristic region is too short to set the corresponding web member, it is also possible to divide and form a first characteristic region, a second characteristic region, and a fourth characteristic region arranged in sequence from the mid-span to the springing of the arch. Adjacent characteristic regions share web members at both ends of the arch axis, and the second characteristic region is a transition region between the first characteristic region and the fourth characteristic region.

[0057] Step S3 is used to determine the longitudinal coordinates of the intersections of the web members with the center line of the upper chord tube in each characteristic region, in combination with the originally determined basic dimensions of the arch rib or the sequence of node coordinates, and then, based on the distribution characteristics of the web members in each characteristic region, quickly obtain the vertical coordinates of the web members with the center line of the lower chord tube, thereby realizing the determination of the center line of the web members. It is possible to obtain the information of the web members of the arch rib without considering the segmentation of the arch rib, and obtain a second processing module for determining the position of the center line of the web members to form double web members without considering the segmentation of the arch rib.

[0058] In one or several embodiments, step S3 may include: S3.1. Determine the longitudinal coordinates of the intersections of the web members with the center line of the upper chord tube in each characteristic region by using an equal division method and / or a method of specifying the spacing one by one.

[0059] Specifically, the equal division method means positioning the coordinates of each intersection in the characteristic region in a state where the difference between the longitudinal coordinates, that is, the X-direction coordinates, of the intersections is the same, that is, the spacing of the intersections in the X direction is equal; the method of specifying the spacing one by one means specifying the longitudinal spacing between adjacent intersections according to the actual situation, which is applicable to characteristic regions with a small number of intersections, such as the second characteristic region.

[0060] In an alternative embodiment, the equal division method and the method of specifying the spacing one by one can be used alternatively, or different methods can be used for different characteristic regions.

[0061] In an alternative embodiment, the intersections of the web members with the center line of the upper chord tube in the fourth characteristic region can be determined by the distance from the mid-span to the intersection, or by the distance from the intersection to the temporary hinge at the springing, or by the maximum longitudinal coordinate of the intersection with the upper chord tube.

[0062] In an alternative embodiment, the longitudinal coordinates of the intersections of the web members with the center line of the upper chord tube in the first characteristic region and the second characteristic region are determined by using the equal division method, and the longitudinal coordinates of the intersections in the fourth characteristic region are determined by the maximum longitudinal coordinate of the intersection with the upper chord tube.

[0063] As shown in Table 2, it is an example of the longitudinal coordinates of the intersections of the web members with the center line of the upper chord tube in four characteristic regions determined based on step S3.1 of the above-mentioned truss arch rib.

[0064] Table 2

[0065] In Table 2, "31@7.5" in the first row means that there are 32 vertical web members in the first characteristic region, the spacing between adjacent vertical web members in the longitudinal direction of the bridge is 7.5 m, from the mid-span to the arch springing direction, the longitudinal coordinate of the first intersection point in the longitudinal direction of the bridge is 0, and the longitudinal coordinate of the last intersection point in the longitudinal direction of the bridge is 31×7.5 = (-)232.5 m.

[0066] In Table 2, "8, 6.5" in the second row means that from the mid-span to the arch springing direction in the second characteristic region, the horizontal spacing between the intersection points of the web members and the upper chord tube is 8 m and 6.5 m. The first intersection point is taken as the intersection point of the last web member and the upper chord tube in the first characteristic region.

[0067] In Table 2, 6.17 in the fourth row means that in the fourth characteristic region, the distance from the point with the maximum longitudinal coordinate of the intersection of the web member and the upper chord tube is 6.17 m. Through the basic dimensions of the arch rib, the maximum longitudinal coordinate of the upper chord tube is determined to be -259.241 m, so the longitudinal coordinate of the intersection point of the web member and the center line of the upper chord tube is -253.071 m.

[0068] In Table 2, "1@" in the third row means that there is only one panel in the third characteristic region, including two web members. From the mid-span to the arch springing direction, the longitudinal coordinate of the intersection point of the web member and the center line of the upper chord tube in the third characteristic region is -247 m, that is, the last intersection point in the second characteristic region, and -253.071 m, that is, the first intersection point in the fourth characteristic region.

[0069] In one or several embodiments, step S3 may include: S3.2. Substitute the longitudinal coordinates of each intersection point into the equations of the center lines of the upper chord tube and the lower chord tube for calculation, or use the method of sequence interpolation to substitute the longitudinal coordinates of each intersection point into the original sequence of node coordinates for calculation to determine the vertical coordinates of the intersection points of each web member and the center line of the upper chord tube.

[0070] Preferably, since the equations of the center lines of the upper chord tube and the lower chord tube are transcendental equations and are not easy to solve, it is preferred to use the method of sequence interpolation to determine the vertical coordinates of the intersection points of each web member and the center line of the upper chord tube.

[0071] Specifically, for the first characteristic region, assuming that the longitudinal coordinate of the web member in the given first characteristic region is x a1 , according to the characteristics of the web member in the first characteristic region, the longitudinal coordinate of the intersection point of the web member and the center line of the chord tube is x a1 = x a1_up = x a1_down . Therefore, in Table 1, taking (x up , y up ) as the original sequence pair, interpolate x a1 to calculate the second coordinate as y a1_up , and then take (xdown , y down ) is the original sequence pair, interpolating x a1 The second coordinate at time is y a1_down , the intersection coordinates of the web member and the center line of the chord tube in the first characteristic region can be obtained as shown in Table 3

[0072] Table 3

[0073] Specifically, for the third characteristic region, assume that the longitudinal coordinate of the web member in the given third characteristic region is x a3 , the longitudinal coordinates of the intersections of the web members and the chord tubes have the same point number nth. In Table 1, taking (x up , nth) as the original sequence pair, interpolating x a3 The second point number is calculated to be nth a3 ; then taking (nth, x up ) as the original sequence pair, interpolating nth a3 The second coordinate is calculated to be x a3_up ; then taking (nth, y up ) as the original sequence pair, interpolating nth a3 The second coordinate is calculated to be y a3_up ; then taking (nth, x down ) as the original sequence pair, interpolating nth a3 The second coordinate is calculated to be x a3_down ; finally taking (nth, y down ) as the original sequence pair, interpolating nth a3 The second coordinate is calculated to be y a3_down , the intersection coordinates of the web member and the center line of the chord tube in the third characteristic region can be obtained as shown in Table 4

[0074] Table 4

[0075] Specifically, for the fourth characteristic region, assume that the longitudinal coordinate of the web member in the given fourth characteristic region is x a4 , according to the characteristics of the web members in the fourth characteristic region, the longitudinal coordinates of the intersections of the web members and the chord tubes have the same point number. In Table 1, taking (x up , nth) as the original sequence pair, interpolating x a4 The second point number is calculated to be nth a4 ; then taking (nth, x up ) as the original sequence pair, interpolating nth a4 The second coordinate is calculated to be x a4_up ; then taking (nth, y up) is the original sequence pair, interpolating the nth a4 The second coordinate is calculated to be y a4_up ; Then, taking (nth, x down ) as the original sequence pair, interpolating the nth a4 The second coordinate is calculated to be x a4_down ; Finally, taking (nth, y down ) as the original sequence pair, interpolating the nth a4 The second coordinate is calculated to be y a4_down , and the intersection coordinates of the web members and the center lines of the chord pipes in the fourth characteristic region can be obtained as shown in Table 5, and the second point among them is the springing end points of the upper and lower chord pipes.

[0076] Table 5

[0077] Specifically, for the second characteristic region, since this region is the transition region between the first characteristic region and the third characteristic region, there are only two intersection points of the web members and the center line of the lower chord pipe in this region, which are the intersection point of the last web member in the first characteristic region and the center line of the lower chord pipe and the intersection point of the first web member in the third characteristic region and the center line of the lower chord pipe respectively. The intersection coordinates of the web members and the center lines of the chord pipes in the second characteristic region can be obtained as shown in Table 6.

[0078] Table 6

[0079] In one or more embodiments, step S3 may include: S3.3. Organize and obtain the sequence of web member information.

[0080] Specifically, classify the intersection coordinates of the web members and the chord pipes in each characteristic region according to the upper and lower chord pipes, remove the duplicate points, and arrange them in order, then the complete intersection coordinates of the web members and the center lines of the upper and lower chord pipes can be obtained. Connect the intersection points on the center lines of the upper and lower chord pipes in order, and the center line of the web member can be obtained.

[0081] As Figure 5 shown, it is the second processing module after determining the center line of the web member based on step 3.3 of the above-mentioned truss arch rib.

[0082] In one or more embodiments, on the basis of the second processing module, further organize and obtain the sequence of web member information including web member information, and the web member information includes data information such as the node coordinates at both ends of the web member, the midpoint coordinates, the direction vector, the slope, and the normal slope.

[0083] Taking the above-mentioned truss arch rib as an example, obtaining the second processing module based on step 3.3 and organizing and obtaining the sequence of web member information for illustration: The coordinates of both ends of the web member obtained by the second processing module are (x web_up , y web_up ), (x web_down ,y web_down ), then the centroid coordinates of the web member are: x web_center =(x web_up + x web_down ) / 2 —— Equation 10; y web_center =(y web_up + y web_down ) / 2 —— Equation 11; The direction vector of the web member is: x ∥ =x web_up - x web_down —— Equation 12; y ∥ =y web_up - y web_down —— Equation 13; The slope of the web member is: k web = y ∥ / x ∥ —— Equation 14; The normal slope of the web member is: k web⊥ =- x ∥ / y ∥ —— Equation 15.

[0084] Arrange in ascending order according to the longitudinal coordinates of the midpoints along the bridge, and obtain the web member information sequence, as shown in Table 7 - Table 8.

[0085] Table 7 Results of Web Member Endpoint and Centroid Coordinates

[0086] Table 8 Results of Web Member Direction Vector, Slope, and Normal Slope

[0087] Step S4 is used to further obtain the arch rib plane geometric model considering the double web member situation with arch rib segmentation based on the second processing module according to the proposed arch rib segmentation information for finite element calculation.

[0088] In one or several embodiments, step S4 may include: S4.1. Determine the arch rib segmentation information and the double web member spacing, and determine the longitudinal coordinates at the segmentation; S4.2. Use the method of sequence interpolation, substitute the longitudinal coordinates at the segmentation into the web member information sequence for calculation, and obtain the web member information involved at the segmentation; S4.3. Determine the intersection coordinates at both ends of the double web members according to the web member information involved at the segmentation point; S4.4. After sorting and connecting the lines, obtain the center line of the web members considering the segment division.

[0089] In one or several embodiments, step S4.3 includes: S4.3.1. Determine the coordinates of any point on the double web members according to the centroid coordinates and normal slope of the web members involved at the segmentation point; S4.3.2. Determine the straight line equation where the double web members are located according to the coordinates and slope of any point on the double web members; S4.3.3. Simultaneously solve the straight line equations where the double web members are located, the center line equations of the upper chord pipe and the lower chord pipe to solve the intersection coordinates at both ends of the double web members, or, use the bisection interpolation method, and simultaneously solve the straight line equation where the double web members are located and the original sequence of node coordinates to solve the intersection coordinates at both ends of the double web members.

[0090] Corresponding to step S4.1, taking a certain truss arch rib as an example, the segment length of the arch rib can be formulated as "8@30", that is, the half-span arch rib is divided into 9 segments. The 8 segments from the mid-span to the arch foot are 30 m in length, and the remaining length is taken as one segment. The segmentation points are x segm =(0, -30, -60, -90, …, -210, -240) m. The normal distance of the double web members at the segmentation position, that is, the normal distance of the web members involved at the segmentation point, is d3 = 1.4 m.

[0091] Corresponding to step S4.2, in Table 7, taking (x web_center , nth web ) as the original sequence pair, interpolate x segm and calculate to obtain the web member serial number as nth segm . Then, the centroid, direction vector, slope, normal slope and other web member information at the segmentation point can be determined. According to this information, it can be displayed in the second processing module. As Figure 5 shown, the dotted line is the schematic of the segmentation line, and the thick solid line is the web member involved in the segment division line.

[0092] Corresponding to step S4.3, according to the web member information involved in the segment division line, the coordinates and slope of any point on the double web members can be determined, and then the intersection coordinates of the double web members with the upper and lower chord pipes can be determined.

[0093] Specifically, corresponding to step S4.3.1, from the centroid (x web_center , y web_center ) and the normal slope k web⊥ of the web members involved in the segment division line, the coordinates of a certain point on the double web members can be calculated as: ——Equation 16 Since the double web is parallel to the web involved in the segment dividing line, its slope is the same as that of the web involved in the segment dividing line.

[0094] Specifically, corresponding to step S4.3.2, from the coordinates and slope of the points on the double-web member, the equation of the straight line where the double-web member is located can be obtained as: y web_s0 =k web (x web_s0 -x web_s )+ y web_s ——Formula 17 Specifically, corresponding to step S4.3.3, equation 17, equation 8 and equation 9 can be combined to solve the intersection point of the double-ribbed member and the chord tube; or equation 17 and Table 1 can be combined to use bisection interpolation to obtain the intersection point of the double-ribbed member and the chord tube.

[0095] Preferably, when the web member involved in the segment dividing line is a vertical web member, the formula 18 can be used. ” Substitute Equation 17 for solution.

[0096] Specifically, corresponding to step S4.4, in the set of the coordinates of the intersections of the web members and the upper and lower chords, the coordinates of the intersections of the web members related to the segment dividing line are removed, and the corresponding intersections of the double web members and the upper and lower chords are added and sorted. The intersections of the center lines of the upper and lower chords are connected in a specific order, and the center lines of the web members after considering the segment division are obtained, and then the plane geometric model of the arch rib considering the arch rib segmentation is obtained, such as Figure 6 shown.

[0097] A rapid modeling method for a trussed arch rib in this embodiment establishes multiple processing modules and divides the arch rib into multiple feature areas according to the distribution characteristics of the web members, thereby realizing modularization and parameterization of the arch rib modeling process. Based on the proposed basic size information of the arch rib and in combination with programming software, the design and modeling workload of the steel tube concrete arch rib, which takes 4 hours, can be reduced to less than 1 second. The arch rib plane geometric model can be established quickly, accurately and efficiently, shortening the modeling time and reducing the labor cost. The work efficiency of engineering and technical personnel in the trussed arch bridge design process can be improved, and the extra time can be used for comparing, adjusting and optimizing the structural parameters, thereby improving the design quality of the trussed arch rib structure.

[0098] Example 2 A structural design method for a trussed arch rib adopts a rapid modeling method for a trussed arch rib in Example 1 to obtain a plane structural drawing of the trussed arch rib and perform structural design.

[0099] A structural design method for a truss arch rib of the present invention, based on the rapid modeling of the truss arch rib, can quickly obtain the plane structure diagram of the arch rib, can be quickly applied to the arch rib structure design, improve the design efficiency and accuracy of the truss arch bridge structure, and improve the safety and applicability of the arch bridge design and construction.

[0100] In one or several embodiments, the plane structure diagram of the truss arch rib obtained through Embodiment 1 can be applied to 3D modeling software such as CAD to quickly establish the 3D model of the truss arch bridge structure for application to the arch rib structure design.

[0101] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A rapid modeling method for trussed arch ribs, characterized in that: include: S1. According to the proposed basic size of the arch rib, establish a first processing module, the first processing module includes the arch axis, the center line of the upper chord tube and the center line of the lower chord tube; S2. According to the distribution characteristics of the webs, a number of characteristic areas are formed in the first processing module; S3, respectively determining the intersection positions of the web member and the centerline of the upper chord tube and the intersection positions of the web member and the centerline of the lower chord tube in each characteristic area, and sequentially connecting the intersection points on the centerline of the upper chord tube and the intersection points on the centerline of the lower chord tube to form a second processing module; S4. According to the proposed arch rib segmentation information, the web members involved in the segmentation are replaced with double web members in the second processing module to obtain the arch rib plane geometric model considering the arch rib segmentation.

2. The rapid modeling method of a trussed arch rib according to claim 1, characterized in that: In step S2, the characteristic regions include a first characteristic region, a second characteristic region, a third characteristic region and a fourth characteristic region; The first characteristic region includes the web member distribution characteristics in which vertical web members and diagonal web members are alternately distributed and both ends of the arch axis direction are vertical web members; The third characteristic region includes radial web members and diagonal web members alternately distributed, radial web members perpendicular to the arch axis, and web member distribution characteristics where both ends of the arch axis are radial web members; The fourth characteristic area includes a triangular area of ​​the temporary hinge of the arch foot, and the fourth characteristic area includes the distribution of a single radial web member and two connecting web members, one end of the connecting web member is connected to the end of the radial web member, and the other end of the connecting web member is connected to the temporary hinge of the arch foot. The second characteristic region includes the distribution of four web members, three intersection points formed on the center line of the upper chord tube, and two intersection points formed on the center line of the lower chord tube.

3. The rapid modeling method of a trussed arch rib according to claim 2, characterized in that: In step S2, the first characteristic area, the second characteristic area, the third characteristic area and the fourth characteristic area are divided and arranged in sequence along the mid-span to the arch foot, and adjacent characteristic areas share a web at both ends of the arch axis. Or, the first characteristic area, the second characteristic area and the fourth characteristic area are divided and arranged in sequence along the mid-span to the arch foot, and adjacent characteristic areas share a web at both ends of the arch axis.

4. The rapid modeling method of a trussed arch rib according to claim 3, characterized in that: Step S1 includes: According to the curve form of the arch axis, determine the arch axis function and the tangent function of any point on the arch axis; According to the form of the arch rib height change along the direction of the bridge, determine the truss height function of any point on the arch rib; According to the arch axis function, tangent function and truss height function, the centerline equations of the upper chord tube and the lower chord tube are determined.

5. The rapid modeling method of a trussed arch rib according to claim 4, characterized in that: Step S1 includes: The center lines of the upper and lower chord tubes are discretized into a number of sequentially numbered nodes, and the arch axis function, the center line equation of the upper and lower chord tubes and the center line equation of the lower chord tube are substituted to obtain the original sequence of node coordinates.

6. The rapid modeling method of a trussed arch rib according to claim 5, characterized in that: Step S3 includes: S3.

1. Determine the coordinates of the intersection of the web member and the centerline of the upper chord tube in each characteristic area along the bridge by means of equal division and / or by means of specifying the spacing one by one; S3.2, substitute the coordinates of each intersection along the bridge into the centerline equation of the upper chord tube and the centerline equation of the lower chord tube for calculation, or substitute the coordinates of each intersection along the bridge into the original series of node coordinates by series interpolation to determine the vertical coordinates of the intersections of each web member and the centerline of the upper chord tube; S3.

3. Arrange and obtain the series of belly bar information.

7. The rapid modeling method of a trussed arch rib according to claim 6, characterized in that: The web member information includes the data information of the node coordinates at both ends of the web member, the midpoint coordinates, the direction vector, the slope, and the normal slope.

8. The rapid modeling method of a trussed arch rib according to claim 7, characterized in that: Step S4 includes: S4.

1. Determine the segmentation information of the arch rib and the spacing between the double web members, and determine the longitudinal coordinates of the segmentation; S4.

2. Using the method of series interpolation, substitute the longitudinal coordinates of the segment into the web member information series to calculate and obtain the web member information involved in the segment; S4.

3. Determine the coordinates of the intersection points of the two ends of the double webs according to the web information involved in the segmentation; S4.

4. Arrange and connect the lines to obtain the center line of the web after considering the segment division.

9. The rapid modeling method of a trussed arch rib according to claim 8, characterized in that: Step S4.3 includes: S4.3.

1. Determine the coordinates of any point on the double web based on the centroid coordinates and normal slope of the web involved in the segmentation; S4.3.

2. Determine the equation of the line on which the double web is located based on the coordinates and slope of any point on the double web; S4.3.

3. Combine the equation of the straight line where the double-web member is located, the equation of the centerline of the upper chord tube, and the equation of the centerline of the lower chord tube to solve the coordinates of the intersection points at both ends of the double-web member. Alternatively, use bisection interpolation to combine the equation of the straight line where the double-web member is located and the original series of node coordinates to solve the coordinates of the intersection points at both ends of the double-web member.

10. A structural design method for a trussed arch rib, characterized in that: A rapid modeling method for a trussed arch rib according to any one of claims 1 to 9 is used to obtain a plan view of the trussed arch rib and perform structural design.

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