Calculation method for factory-made pre-camber of long-span N-shaped steel truss bridge

Abstract

The present invention discloses a calculation method for the factory - made camber of a long - span N - type steel truss bridge. The existing calculation methods for factory - made camber will generate camber stress and require repeated trial calculations. The present invention calculates the coordinates of each node of the 1# and 2# segments after considering the theoretical camber at the lower chord node; calculates the accurate length of the 2# upper chord, rounds it off, and then calculates the factory - made camber of the 2# lower chord node according to the geometric relationship between the lower chord, vertical web members, and diagonal web members; rounds off the accurate length between the upper chord nodes of the segments on both sides of the mid - span to obtain Lz. If it is an even number, the designed length of the upper chord on both sides of the mid - span is Lz / 2. If it is an odd number, the designed length of the upper chord on one side of the mid - span is (Lz + 1) / 2, and the other side is (Lz - 1) / 2; calculates the coordinates of the upper chord node at the mid - span position and the factory - made camber of the lower chord node on the right side of the mid - span. The present invention is concise, fast, and accurate in results, obtaining an ideal linear shape of the steel truss bridge.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge engineering, and particularly relates to a calculation method for the factory - made camber of a long - span N - type steel truss bridge. Background Technique

[0002] The setting of the bridge camber is to offset the deflection generated by the bridge span structure under the action of loads, and it is a correction amount reserved in the opposite direction of the displacement during construction or manufacturing, which is crucial for ensuring the smoothness of the line and improving the operation quality of the line. Both the "Code for Design of Steel Structures of Railway Bridges" and the "Code for Design of Steel Highway Bridges" stipulate that steel bridges should be provided with cambers, and the camber curve should preferably have the same shape as the deflection curve generated by the dead load and half of the static live load, but in the opposite direction.

[0003] The theoretical camber of a long - span steel truss bridge can be obtained by establishing a finite - element analysis model, calculating according to the specification method and then considering the bridge longitudinal slope. The factory - made camber refers to the camber set during the actual manufacturing process of the steel truss beam. Due to the manufacturing accuracy of the factory, the theoretical camber and the factory - made camber are not exactly the same.

[0004] The setting of the factory - made camber of the steel truss beam is generally achieved by telescopic members. For a through - type steel truss beam, considering that the setting of the camber does not affect the deck system, the lengths of the lower chord and the web are usually kept unchanged, and only the length of the upper chord is extended or shortened.

[0005] Currently, the commonly used camber design methods mainly include the temperature - rise - and - fall method, the displacement - load camber method, and the geometric method.

[0006] The temperature - rise - and - fall method adjusts the member length by raising or lowering the temperature to make the displacement of the truss control point approach the theoretical camber. A long - span steel truss beam is generally a multi - redundant statically indeterminate structure. Using the temperature - rise - and - fall method will cause the secondary internal force of the arching and the arching support reaction of the structure, resulting in redundant constraint equations and difficult solution.

[0007] The displacement - load camber method takes the theoretical camber as the input load to solve the telescopic amount of the member. In principle, this method is feasible, but it may generate a large camber stress.

[0008] The geometric method calculates the relationship between the theoretical camber and the telescopic amount of the upper chord according to the geometric relationship between the upper and lower chords and the web of the steel truss beam. Usually, it is necessary to repeatedly trial - calculate to obtain a factory - made camber that is in good agreement with the theoretical camber. This method is only applicable to steel truss bridges with simple structural forms. Summary of the Invention

[0009] In order to make up for the deficiencies of the prior art, the present invention provides a calculation method for the factory - made camber of a long - span N - type steel truss bridge, which can quickly and accurately obtain a factory - made camber that is relatively consistent with the theoretical camber.

[0010] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0011] A calculation method for the factory - made pre - camber of a long - span N - shaped steel truss bridge, characterized by comprising the following steps:

[0012] Step 1: Determine the theoretical pre - camber of each lower chord node of the steel truss beam;

[0013] Step 2: Calculate the coordinates of each node of the 1# segment after considering the theoretical pre - camber at the lower chord nodes;

[0014] Step 3: Calculate the coordinates of each node of the 2# segment after considering the theoretical pre - camber at the lower chord nodes, and calculate the exact length of the upper chord of the 2# segment according to the coordinates;

[0015] Step 4: Round off the exact length of the upper chord of the 2# segment according to the factory manufacturing accuracy to obtain the designed length of the upper chord of the 2# segment, and then calculate the factory - made pre - camber of the lower chord nodes of the 2# segment according to the geometric relationship between the lower chord, vertical web members, and diagonal web members;

[0016] Step 5: Repeat Steps 3 - 4 to calculate the designed length of the upper chord and the factory - made pre - camber of the lower chord nodes of the same type or similar steel truss beam segments;

[0017] Step 6: Calculate the coordinates of each node of the segment on the right side of the mid - span after considering the theoretical pre - camber at the lower chord nodes, and calculate the exact length between the upper chord nodes of the segments on both sides of the main - span mid - span according to the coordinates;

[0018] Step 7: Based on the factory manufacturing accuracy, round off the exact length between the upper chord nodes of the segments on both sides of the mid - span to obtain the length Lz. If Lz is an even number, the designed lengths of the upper chords on both sides of the mid - span are both Lz / 2; if Lz is an odd number, the designed length of the upper chord on one side of the mid - span is (Lz + 1) / 2, and the designed length of the upper chord on the other side is (Lz - 1) / 2;

[0019] Step 8: Calculate the coordinates of the upper chord node at the mid - span position according to the designed length of the upper chord on the left side of the mid - span;

[0020] Step 9: Calculate the factory - made pre - camber of the lower chord node on the right side of the mid - span according to the designed length of the upper chord on the right side of the mid - span;

[0021] Step 10: Adopt the calculation methods in Steps 3 - 9 to calculate the designed lengths of the upper chords and the factory - made pre - cambers of the lower chord nodes of the remaining steel truss beam segments.

[0022] Further, the specific content of Step 1 is: Establish a finite - element analysis model of the steel truss beam, calculate the pre - camber of each lower chord node according to the standard method, and then consider the bridge longitudinal slope to obtain the theoretical pre - camber of each lower chord node.

[0023] The beneficial effects of the present invention:

[0024] 1) The calculation method of the present invention is a derivation of geometric relationships. The internal forces of the members are not involved in the calculation process, which can effectively avoid the generation of arching stresses after the structure is provided with a camber. The calculation is simple and can provide favorable technical support for the design and manufacture of long-span steel truss girders;

[0025] 2) By adopting the calculation method of the present invention, the shop-fabricated camber of the lower chord node of the segment is only related to the factory manufacturing accuracy of the upper chord of this segment and the theoretical camber at this point. There is no cumulative error in the calculation of the shop-fabricated camber, which is beneficial to obtaining an ideal alignment of the steel truss girder, effectively ensuring the smoothness of the line and improving the operation quality of the line;

[0026] 3) The camber calculation method of the present invention is based on the theoretical camber of the lower chord node of the segment, ensuring that the right triangle formed by the lower chord, vertical web member, and diagonal web member of the steel truss girder has a constant shape. By calculating the node coordinates, the design length of the upper chord and the shop-fabricated camber that fits well with the theoretical camber are obtained. The calculation is simple, fast, and the results are accurate and reliable, which is worthy of further promotion. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is the overall working flow chart of the present invention;

[0028] Figure 2 is the elevation layout schematic diagram of the steel truss girder without considering the camber in the embodiment;

[0029] Figure 3 is the schematic diagram of Step 2 in the embodiment;

[0030] Figure 4 is the schematic diagram of Step 3 in the embodiment;

[0031] Figure 5 is the schematic diagram of Step 4 in the embodiment;

[0032] Figure 6 is the schematic diagram of Step 5 in the embodiment;

[0033] Figure 7 is the schematic diagram of Step 6 in the embodiment;

[0034] Figure 8 is the schematic diagram of Step 7 in the embodiment;

[0035] Figure 9 is the schematic diagram of Step 8 in the embodiment;

[0036] Figure 10 is the schematic diagram of Step 9 in the embodiment;

[0037] Figure 11 is the schematic diagram of Step 10 in the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0038] The present invention will be described in detail below in conjunction with specific embodiments.

[0039] Aiming at the drawbacks of the arch stress generated after setting the camber by the temperature rise and fall method and the displacement load camber method in the prior art, and the deficiency of repeated trial calculations required when setting the camber by the geometric method, the present invention proposes a calculation method for the factory-made camber of a long-span N-shaped steel truss girder bridge, which can quickly and accurately obtain a factory-made camber that is relatively consistent with the theoretical camber.

[0040] This embodiment is applied to a certain special highway-railway bridge. The bridge is a four-tower three-main-span low-tower steel truss girder cable-stayed bridge with a span of (84 + 144 + 228 + 240 + 300 + 120 + 60) m, a truss height of 15 m, a panel length of 12 m, and an N-shaped truss; as Figure 2 shown, this figure only shows the mid-span positions of the 84 m side span and the 228 m main span of the bridge, including the lower chord nodes E0~E7, E26~E30, and the upper chord nodes A1~A7, A26~A30.

[0041] As Figure 1 shown, the present invention includes the following steps:

[0042] Step 1: Establish a finite element analysis model of the steel truss girder, calculate the camber of each lower chord node according to the standard method, and then consider the bridge longitudinal slope to obtain the theoretical camber of each lower chord node;

[0043] Step 2: As Figure 3 shown, based on the theoretical camber of the lower chord node of the 1# segment, ensure that the right triangle shape formed by the lower chord, vertical web member, and diagonal web member of the steel truss girder remains constant, where the length of the lower chord is equal to the panel length and the length of the vertical web member is equal to the truss height, and calculate the coordinates of each node of the 1# segment considering the theoretical camber of the lower chord node, specifically as follows:

[0044] 1) Select the fulcrum of the lower chord of the 1# segment of the steel truss girder as the reference point, with coordinates E0(0,0). E0 is located at the fulcrum, and its theoretical camber h0 = 0;

[0045] 2) Calculate the horizontal and vertical coordinates of the lower chord node E1 adjacent to the reference point E0. The vertical coordinate of E1 is the vertical coordinate of E0 plus the theoretical camber h1 = 85.8 mm at E1. Then, from the distance between E1 and E0 being the panel length L1 = 12 m, E1(11.9997, 0.0858) can be obtained;

[0046] 3) Calculate the upper chord node A1 adjacent to E1. The distance between A1 and E1 is the truss height H = 15 m, and the distance between A1 and E0 is the length of the diagonal web member L = 19.2094 m. Thus, A1(11.8924, 15.0854) is obtained;

[0047] Step 3: As shown in Figure 4 , calculate the coordinates of each node of the 2# segment considering the theoretical camber for the lower chord nodes using the method in Step 2, and calculate the exact length of the upper chord of the 2# segment based on the coordinates, as follows:

[0048] 1) Using the method in 2) of Step 2, where the theoretical camber h2 at E2 is 165.2 mm, the coordinates of E2(23.9994, 0.1652) can be obtained;

[0049] 2) Using the method in 3) of Step 2, the coordinates of A2(23.9002, 15.1649) can be obtained;

[0050] 3) Based on the coordinates of points A1 and A2, the exact length of the upper chord A1A2 of the 2# segment is 12.0081 m;

[0051] Step 4: As shown in Figure 5 , round off the exact length of the upper chord of the 2# segment according to the factory manufacturing accuracy to obtain the designed length of the upper chord, and then calculate the factory-made camber of the lower chord nodes of the 2# segment based on the geometric relationship between the lower chord, vertical web members, and diagonal web members;

[0052] The exact length of the upper chord corresponds to the theoretical camber of the lower chord nodes. Due to the manufacturing accuracy of the members, the factory cannot manufacture exactly according to the exact length of the upper chord. At this time, the upper chord needs to be stretched or contracted to obtain the designed length of the upper chord. After the upper chord is stretched or contracted, the shape of the right triangle formed by the lower chord, vertical web members, and diagonal web members remains constant, only a rigid body rotation occurs, and the position of the lower chord nodes of the segment changes accordingly. At this time, the vertical coordinate at the node is the factory-made camber of the lower chord nodes, as follows:

[0053] 1) Taking the factory manufacturing accuracy as mm level, after rounding off the exact length of the upper chord, the designed length of the upper chord of the 2# segment is 12.008 m;

[0054] 2) After the 2# segment upper chord adopts the designed length, A2 becomes A2'. The distance between A2' and A1 is the designed length of 12.008 m, and the distance between A2' and E1 is the length of the diagonal web member L = 19.2094 m. Thus, A2'(23.9002, 15.1649) is obtained.

[0055] 3) After the 2# segment upper chord adopts the designed length, E2 becomes E2'. The distance between E2' and A2' is the truss height H = 15 m, and the distance between E2' and E1 is the panel length L2 = 12 m. Thus, E2'(23.9994, 0.1652) is obtained. Therefore, the factory-made camber h2' of E2' is 165.2 mm;

[0056] Step 5: Repeat Step 3 to Step 4 to calculate the design length of the upper chord and the pre-camber at the factory for the lower chord nodes of the same type or similar steel truss girder segments, as Figure 6 shown;

[0057] Step 6: As Figure 7 shown, the form of the N-type truss changes at the mid-span of the main span. Use the method in Step 2 to calculate the coordinates of each node in the segment on the right side of the mid-span of the lower chord nodes considering the theoretical pre-camber. Calculate the exact length between the upper chord nodes of the segments on both sides of the mid-span of the main span according to the coordinates, specifically as follows:

[0058] 1) The theoretical pre-camber h 29 at point E 29 = 1868.5 mm, and the coordinates of E 29 (347.9948, 1.8685) can be obtained;

[0059] 2) The coordinates of A 29 (347.9183, 16.8683) are obtained;

[0060] 3) According to the coordinates of points A 29 and A 27 ’, the exact length between the upper chord nodes of the segments on both sides of the mid-span of the main span is 24.0067 m;

[0061] Step 7: As Figure 8 shown, based on the factory manufacturing accuracy, round the exact length between the upper chord nodes of the segments on both sides of the mid-span to obtain the length Lz (mm). If Lz is an even number, the design lengths of the upper chords on both sides of the mid-span are both Lz / 2. If Lz is an odd number, the design length of the upper chord on one side of the mid-span is (Lz + 1) / 2, and the design length of the upper chord on the other side is (Lz - 1) / 2;

[0062] After rounding the exact length of 24.0067 m between the upper chord nodes of the segments on both sides of the mid-span, the length 24007 mm is obtained. Since 24007 is an odd number, the design length of the upper chord on the left side of the mid-span is 12.004 m, and the design length of the upper chord on the right side of the mid-span is 12.003 m;

[0063] Step 8: As Figure 9 shown, calculate the coordinates of the upper chord nodes at the mid-span according to the design length of the upper chord on the left side of the mid-span, specifically as follows:

[0064] The distance between A 28 and A 27 ’ is the design length of the upper chord on the left side of the mid-span, which is 12.004 m. The distance between A 28 and E 28 ’ is the truss height H = 15 m. Thus, the coordinates of A 28 (335.9157, 16.8070) are obtained;

[0065] Step Nine: As Figure 10 shown, according to the designed length of the upper chord rod on the right side of the mid-span, calculate the shop-made pre-camber of the lower chord rod node on the right side of the mid-span, specifically:

[0066] 1) Adopt the method in Step Four 2) to obtain A 29 ’(347.9186, 16.8681);

[0067] 2) Adopt the method in Step Four 3) to obtain E 29 ’(347.9948, 1.8682), so the shop-made pre-camber h 29 ’ of E 29 ’ is 1868.2 mm;

[0068] Step Ten: As Figure 11 shown, adopt the calculation methods in Steps Three to Nine to calculate the designed length of the upper chord rod and the shop-made pre-camber of the lower chord rod node of the remaining steel truss beam segments.

[0069] Step Eleven: Compare the calculated shop-made pre-camber with the theoretical pre-camber to verify the correctness of the calculation method. The comparison between the shop-made pre-camber and the theoretical pre-camber of some lower chord rod nodes is shown in Table 1; it can be seen that the maximum difference between the shop-made pre-camber and the theoretical pre-camber is only 0.4 mm, verifying the accuracy of the calculation method proposed by the present invention.

[0070] Table 1 Comparison between Shop-made Pre-camber and Theoretical Pre-camber

[0071]

[0072] The content of the present invention is not limited to the examples listed. Any equivalent transformation of the technical solution of the present invention adopted by those of ordinary skill in the art through reading the specification of the present invention is covered by the claims of the present invention.

Claims

1. A calculation method for the factory - made pre - camber of a long - span N - shaped steel truss bridge, characterized in that: It includes the following steps: Step 1: Determine the theoretical camber of each lower chord node of the steel truss girder; Step 2: Calculate the coordinates of each node of Section 1# of the lower chord nodes considering the theoretical camber; Step 3: Calculate the coordinates of each node of Section 2# of the lower chord nodes considering the theoretical camber, and calculate the exact length of the upper chord of Section 2# according to the coordinates; Step 4: Round off the exact length of the upper chord of Section 2# according to the factory manufacturing accuracy to obtain the designed length of the upper chord of Section 2#, and then calculate the factory-made camber of the lower chord nodes of Section 2# according to the geometric relationship between the lower chord, vertical web members and diagonal web members; Step 5: Repeat Steps 3 to 4 to calculate the designed length of the upper chord and the factory-made camber of the lower chord nodes of steel truss girder segments of the same type; Step 6: Calculate the coordinates of each node of the segment on the right side of the mid-span of the lower chord nodes considering the theoretical camber, and calculate the exact length between the upper chord nodes of the segments on both sides of the main span mid-span according to the coordinates; Step 7: Based on the factory manufacturing accuracy, round off the exact length between the upper chord nodes of the segments on both sides of the mid-span to obtain the length Lz. If Lz is an even number, the designed lengths of the upper chords on both sides of the mid-span are both Lz / 2. If Lz is an odd number, the designed length of the upper chord on one side of the mid-span is (Lz + 1) / 2, and the designed length of the upper chord on the other side is (Lz - 1) / 2; Step 8: Calculate the coordinates of the upper chord node at the mid-span position according to the designed length of the upper chord on the left side of the mid-span; Step 9: Calculate the factory-made camber of the lower chord node on the right side of the mid-span according to the designed length of the upper chord on the right side of the mid-span; Step 10: Use the calculation methods in Steps 3 to 9 to calculate the designed length of the upper chord and the factory-made camber of the lower chord nodes of the remaining steel truss girder segments.

2. The calculation method of the factory - made pre - camber of a long - span N - shaped steel truss bridge according to claim 1, characterized in that: Specifically, Step 1 is as follows: Establish a finite element analysis model of the steel truss girder, calculate the camber of each lower chord node according to the standard method, and then the theoretical camber of each lower chord node is obtained after considering the bridge longitudinal slope.

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