Modified eccentric compression method considering torsional restraint stiffness of end diaphragms

Abstract

The application discloses a modified eccentric compression method considering torsional constraint stiffness of end cross beams. The steps are as follows: (1) obtaining relevant parameters of the beam bridge according to engineering data; (2) calculating the torsional constraint stiffness of the end cross beams to the main beam; (3) calculating the load transverse distribution coefficient at the fulcrum point through the lever principle method, and the single-web section main beam and double main beam bridge are calculated by using a single beam model, and the double-web three main beam and more main beam bridges with multiple pieces are calculated by using a double beam model; (4) calculating the load transverse distribution coefficient of the main beam in the longitudinal bridge direction at any position by the modified eccentric compression method considering the torsional constraint of the beam end; (5) considering the change of the load transverse distribution along the longitudinal bridge direction for the concentrated load, taking the load transverse distribution coefficient at the midspan position for the uniformly distributed load, and then calculating the load effect. The method considers the elastic support of the stiffness of the end cross beam to the torsional deformation of the main beam, and provides a new high-precision method for the load transverse distribution calculation of the box section beam bridge.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of engineering technology and relates to a bridge engineering structure internal force calculation method, in particular to a modified eccentric pressure method considering torsional constraint stiffness of end cross beams. BACKGROUND

[0002] The calculation method of load transverse distribution coefficient is obtained by changing the parameters of the bridge to obtain the influencing parameters and then regressing to obtain the calculation formula abroad, and the transverse distribution coefficient of each main beam is obtained by calculating the transverse distribution influence line of each main beam through the lever principle method, the eccentric pressure method, the modified eccentric pressure method, the rigidly connected (hinged) beam (plate) method, the analogous orthotropic plate method and the like at home. The rigidly connected beam method has higher precision than the precision of the AASHTO specification formula of the United States and has a wider application range.

[0003] The research work of the load transverse distribution coefficient calculation method has been carried out very early. For example, Li Guohao and Shi Dong published a monograph Highway Bridge Load Transverse Distribution Calculation in 1987. A large number of tables are given in the monograph according to the characteristics of the method, which facilitates the calculation of various transverse distribution methods. Hu Zhaozhi published a monograph Bridge Span Structure Simplified Analysis-Load Transverse Distribution in 1996. The theory of transverse distribution, especially the modified eccentric pressure method, is described in detail. The early literatures mostly adopt T-beam bridges for testing. With the application of box girder, hollow slab and composite structure girder bridges (such as channel steel box composite girder, narrow steel box composite girder and the like), it is found in some literatures that the theoretical load transverse distribution coefficient calculated by the existing method is about 7% smaller than the test value. The biggest difference between the box section and the T-section is that the box section has large torsional stiffness. It is possible that the existing theory overestimates the influence of the torsional stiffness of the box girder. Therefore, for the box girder bridge, how to improve the calculation method of the load transverse distribution coefficient and improve the calculation precision has important engineering research value. SUMMARY

[0004] In view of the problem that the theoretical calculation value of the load transverse distribution coefficient of the box girder bridge is small, the application provides a modified eccentric pressure method considering torsional constraint stiffness of end cross beams.

[0005] The modified eccentric pressure method considering torsional constraint stiffness of end cross beams provided by the application has the steps as follows:

[0006] (1) According to the engineering data, the relevant parameters of the simply supported girder bridge are obtained, including the bridge span L, the cross section arrangement, the sectional bending inertia moment and the sectional torsional inertia moment of each piece of main girder, the sectional size of the end cross beam, the material elastic modulus E, the shear modulus G and the Poisson's ratio v;

[0007] (2) The torsional constraint stiffness of the end cross beam to the main girder is calculated;

[0008] (3) The load transverse distribution coefficient at the fulcrum is calculated through the lever principle method:

[0009] a) for T-shaped, I-shaped single-web section girder, single beam model is used for calculation;

[0010] b) for small box girder, hollow slab double-web section girder, single beam model is used for calculation for double main girder bridge, and double beam model is used for calculation for three main girder and above number of main girder multi-main girder bridge;

[0011] The load transverse distribution coefficient calculated by single beam model is denoted as m 01 , and the load transverse distribution coefficient calculated by double beam model is denoted as m 02 ;

[0012] (4) The load transverse distribution coefficient at any position in the longitudinal direction of the main girder is calculated by the modified eccentric compression method considering the torsional constraint of the beam end;

[0013] (5) The change of load transverse distribution along the longitudinal direction of the concentrated load is considered, the load transverse distribution coefficient at the mid-span position is taken for the uniformly distributed load, the load is reduced through the load transverse distribution coefficient, and then the load effect is calculated;

[0014] In step (2), according to the lever principle method, the end diaphragm is simplified as a simply supported beam, and the torsional elastic support stiffness k of the main girder on the adjacent side is:

[0015] ;

[0016] Wherein: EI h is the bending stiffness of the end diaphragm, l h is the span of the end diaphragm, G is the shear modulus of the material, A sz is the effective shear area of the end diaphragm, κ is the shear coefficient of the beam section, and k R is the elastic support stiffness of the support;

[0017] For the side main girder, only one end diaphragm is connected, the torsional constraint stiffness of the beam end is k, and for the middle main girder, two end diaphragms are connected, the torsional constraint stiffness of the beam end is 2k, that is:

[0018] ;

[0019] Wherein: i is the main girder number, n is the number of main girders, k i is the torsional constraint stiffness of the beam end of the i-th main girder, the 1st and n-th main girders are side main girders, and the other numbered main girders are middle main girders;

[0020] In step (4), the steps for calculating the load transverse distribution coefficient at any position in the longitudinal direction of the main girder by the modified eccentric compression method considering the torsional constraint of the beam end are:

[0021] a) Calculate the load transverse distribution influence line η i

[0022] ;

[0023] ;

[0024] wherein: η ie is the load transverse distribution influence line value of the i-th main beam when eccentric load acts on the transverse bridge direction position e, e is the load acting transverse bridge direction position, taking negative number on the left side of the section centroid and positive number on the right side, I i is the section bending moment of inertia of the i-th main beam, n is the number of main beams, a i is the distance from the i-th main beam to the section centroid, taking negative number on the left side of the main beam and positive number on the right side, E is the elastic modulus of the material, L is the span of the main beam, x is the eccentric load acting on the longitudinal bridge direction position, taking the left end support point of the beam as the coordinate origin and the right end as the positive direction, k i is the i-th main beam beam end torsional restraint stiffness, GJ i is the torsional stiffness of the i-th main beam;

[0025] By the load transverse distribution influence line value of the i-th main beam when load acts on multiple positions in the transverse bridge direction is obtained, such as , , connecting in a straight line, the load transverse distribution influence line η i of the i-th main beam is obtained;

[0026] ;

[0027] ;

[0028] ;

[0029] wherein: y is the transverse bridge direction position, the coordinate axis origin is the section centroid position, taking negative number on the left side of the section centroid and positive number on the right side;

[0030] b) calculating the load transverse distribution coefficient

[0031] After obtaining the load transverse distribution influence line η i of the i-th main beam, the vehicle load is laid according to the most unfavorable load position, and the load transverse distribution coefficient of the automobile load is calculated:

[0032] ;

[0033] wherein: m iqki is the load transverse distribution coefficient of the automobile load of the i-th main beam, ξ is the automobile load transverse lane distribution coefficient, i.e. the transverse multi-lane reduction coefficient, N is the number of loaded vehicles, η ijThe load transverse distribution influence line value of the i-th main beam when the vehicle tire acts on the j-th position in the transverse direction of the bridge;

[0034] The load transverse distribution coefficient m of the i-th main beam for the crowd load irki The calculation is as follows:

[0035] ;

[0036] η ir is the load transverse distribution influence line value of the i-th main beam when the crowd load acts on the center of gravity position of the sidewalk;

[0037] In step (5), for the concentrated load, when it is a double main beam bridge, the value of is directly taken, and for a multi-main beam bridge with three main beams or more, the change scheme of the load transverse distribution along the longitudinal direction of the bridge is as follows:

[0038] a) Calculate the transition zone length x t

[0039] The length of the transition zone is calculated by the following formula:

[0040] ;

[0041] wherein L is the span of the main beam, x is the longitudinal position, is the load transverse distribution coefficient value of the automobile load at the x position, , are the load transverse distribution coefficient values of the automobile load at the support point and the mid-span position, respectively;

[0042] b) Adjust the load transverse distribution coefficient value in the transition zone length x t range

[0043] ;

[0044] wherein: is the adjusted load transverse distribution coefficient of the automobile load in the transition zone, m 02 is the load transverse distribution coefficient calculated by the double beam model.

[0045] Specifically, in step (1), the bending and torsional inertia moments of the main beam section are calculated by finite element software such as midas civil, bridge doctor, ansys, or by AutoCAD software, or by theoretical mechanics method.

[0046] Specifically, in step (1), the shear modulus G is calculated by the following formula:

[0047] .

[0048] Specifically, in step (1), if the beam bridge is a continuous beam bridge or a continuous rigid frame bridge, the equivalent simply supported beam method is used to correct the bending stiffness and torsional stiffness of the main beam section.

[0049] Specifically, in step (2), the shear coefficient κ of the beam section is calculated as follows:

[0050] ;

[0051] Where: A h is the cross-sectional area of the end cross beam, A sz is the effective shear area of the end cross beam.

[0052] Specifically, in step (2), when the span-depth ratio of the end cross beam is greater than 10, take , i.e. without considering the influence of shear deformation.

[0053] Specifically, in step (2), for steel bearings, take , i.e. without considering the deformation of the bearing, for plate rubber bearings and pot rubber bearings, calculated as follows:

[0054] ;

[0055] Where: E e is the compressive elastic modulus of the rubber bearing, A e is the area of the rubber bearing, h e is the total thickness of the rubber layer of the rubber bearing.

[0056] Specifically, in step (2), it is for the conventional beam bridge with one bearing arranged under each piece of main beam. If other bearing arrangement forms are used, the torsional restraint stiffness k i of the main beam end is derived according to the principle of mechanics.

[0057] Specifically, in step (3), the single-beam model refers to the bridge deck being disconnected at the centroidal line of the main beam section, and the double-beam model refers to the bridge deck being disconnected at the intersection of the two webs of the box section main beam and the bridge deck. The bridge deck is calculated as a multi-span simply supported beam.

[0058] Specifically, in step (5), the calculation method of load effect is as follows:

[0059] The general calculation formula for the effect of vehicle load on the i-th main beam is:

[0060] ;

[0061] Where: S q is the effect of vehicle load, μ is the impact coefficient of vehicle load, P k is the concentrated load value in the vehicle load, is the coordinate value of the longitudinal bridge action effect influence line, q k is the uniform load value in the automobile load, Ω is the area of the action effect influence line, and x is the longitudinal bridge position;

[0062] The general calculation formula of the crowd load action effect of the i-th main beam is:

[0063] ;

[0064] Wherein, S r is the crowd load action effect, q r is the crowd load value, and Ω is the area of the action effect influence line.

[0065] The method has the beneficial effects that the method considers the elastic support of the end cross beam stiffness on the torsional deformation of the main beam, instead of rigid support, so that the main beam at the support point can produce a limited torsional angle, the correction coefficient value of the correction eccentric pressure method is increased, the calculation value of the load transverse distribution coefficient is slightly larger than that of the ordinary correction eccentric pressure method, and the actual situation of the bridge is more consistent, the effect of the method is verified through three narrow steel box composite beam bridges, and the method provides a new high-precision method for the load transverse distribution calculation of the box section beam bridge. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 is the load transverse distribution calculation flowchart of the method.

[0067] Figure 2 is the torsional torque action deformation schematic diagram of the elastic support simply supported beam at both ends.

[0068] Figure 3 is the bridge deformation schematic diagram under the action of the eccentric pressure method load.

[0069] Figure 4 is the unit eccentric load force decomposition schematic diagram of the method.

[0070] Figure 5 is the unit central load action deformation schematic diagram of the method.

[0071] Figure 6 is the unit eccentric torque action deformation schematic diagram of the method.

[0072] Figure 7 is the bending moment diagram of the unit end bending moment of the simply supported beam.

[0073] Figure 8 is the shear force diagram of the unit end bending moment of the simply supported beam.

[0074] Figure 9 is the deformation diagram of the elastic support simply supported beam under the action of the unit end bending moment.

[0075] Figure 10 is the torsional restraint stiffness of the beam end of each piece of the main girder of the present application.

[0076] Figure 11 is the cross-sectional view of the three main girders of the first embodiment of the present application (unit: cm).

[0077] Figure 12 is the finite element model of the bridge grid of the three main girders of the first embodiment of the present application.

[0078] Figure 13 is the lateral movement load loading position of the first embodiment of the present application (unit: cm).

[0079] Figure 14 is the calculation schematic diagram of the lateral distribution coefficient of the reaction force load of the No. 1 side main girder support of the first embodiment of the present application.

[0080] Figure 15 is the movement load and measurement arrangement diagram of the first embodiment of the present application (unit: m).

[0081] Figure 16 is the cross-sectional characteristic value of the No. 1 side main girder of the first embodiment of the present application.

[0082] Figure 17 is the cross-sectional size data of the end cross beam of the first embodiment of the present application.

[0083] Figure 18 is the cross-sectional characteristic value of the end cross beam of the first embodiment of the present application.

[0084] Figure 19 is the two load lateral distribution coefficient values calculated by the lever principle method of the No. 1 side main girder of the first embodiment of the present application.

[0085] Figure 20 is the comparison of the lateral distribution coefficient values of the reaction force load of the No. 1 side main girder support of the first embodiment of the present application.

[0086] Figure 21 is the calculation schematic diagram of the load lateral distribution coefficient of the No. 1 side main girder of the first embodiment of the present application.

[0087] Figure 22 is the calculation value of the load lateral distribution coefficient considering and not considering the stiffness of the end cross beam of the first embodiment of the present application.

[0088] Figure 23 is the adjustment schematic diagram of the load lateral distribution coefficient of the first embodiment of the present application.

[0089] Figure 24 is the comparison of the load lateral distribution coefficient values of the No. 1 side main girder of the first embodiment of the present application.

[0090] Figure 25is the effect error of the embodiment one of the present application considering and not considering the effect of the end cross beam stiffness.

[0091] Figure 26 is the analysis condition of the embodiment one of the present application with and without cross beam (unit: m).

[0092] Figure 27 is the cross section characteristic value of the end cross beam of the embodiment two of the present application.

[0093] Figure 28 is the value comparison of the load transverse distribution coefficient of the support reaction of the No. 1 side main beam of the embodiment two of the present application.

[0094] Figure 29 is the calculated value of the load transverse distribution coefficient of the embodiment two of the present application considering and not considering the stiffness of the end cross beam.

[0095] Figure 30 is the value comparison of the load transverse distribution coefficient of the No. 1 side main beam of the embodiment two of the present application.

[0096] Figure 31 is the effect error of the embodiment two of the present application considering and not considering the stiffness of the end cross beam.

[0097] Figure 32 is the arrangement drawing of the B ramp bridge of the embodiment three of the present application (unit: m).

[0098] Figure 33 is the cross section drawing of the double main beam of the embodiment three of the present application (unit: cm).

[0099] Figure 34 is the value comparison of the load transverse distribution coefficient of the support reaction of the No. 1 side main beam of the embodiment three of the present application.

[0100] Figure 35 is the calculated value of the load transverse distribution coefficient of the embodiment three of the present application considering and not considering the stiffness of the end cross beam.

[0101] Figure 36 is the value comparison of the load transverse distribution coefficient of the No. 1 side main beam of the embodiment three of the present application.

[0102] Figure 37 is the effect error of the embodiment three of the present application considering and not considering the stiffness of the end cross beam. DETAILED DESCRIPTION

[0103] The present application is further described below in conjunction with the drawings and embodiments, and the following description refers to the accompanying drawings, in which the same numbers represent the same elements or the similar elements unless otherwise indicated.

[0104] Figure 1 is the flow chart of the eccentric compression method of the present application considering the torsional constraint stiffness of the end cross beam.

[0105] I. Analysis of the stress of a simply supported beam with torsionally restrained supports at both ends under the action of torque

[0106] According to the mechanics of materials, we have:

[0107] (1)

[0108] where: φ AB is the torsion angle between the left end point A and the right end point B of the component, l AB is the length of the component, T is the torque at both ends of the component, G is the shear modulus of the material of the component, and J is the torsional moment of inertia of the cross-section of the component.

[0109] The deformation diagram of a simply supported beam with torsionally restrained supports at both ends under the action of torque is shown in Figure 2 , where the beam cross-section is shown as a circular cross-section. It is assumed that the torsional elastic support stiffness at both ends of the beam is k, and a torque T is applied at a position x distance from the left end. The span of the beam is L. According to the balance of displacement and force, the following equation group can be listed:

[0110] (2)

[0111] where: φ, φ1, φ2 are the torsion angles at the x cross-section position of the beam and at both ends of the beam, respectively, and T1, T2 are the torques distributed by the left and right isolators at the x cross-section position of the beam. These 5 quantities are unknowns to be solved.

[0112] Simplify equation (2) to:

[0113] (3)

[0114] Simplify equation (3) by eliminating φ:

[0115] (4)

[0116] (5)

[0117] The torsion angle at the end of the beam is:

[0118] (6)

[0119] Substitute equation (6) into the first equation of equation (3) to obtain the torsion angle at the position of the torque T:

[0120] (7)

[0121] In summary, the solutions of all 5 unknown variables are:

[0122] (8)

[0123] II. Load transverse distribution influence line calculation of modified eccentric compression method for torsionally restrained support at beam end

[0124] The basic assumption of eccentric compression method is that the middle cross beam can be approximately regarded as a rigid beam with infinite stiffness under the action of automobile load, and the cross beam only has rigid body displacement; for example Figure 3 , a schematic diagram of a 5-piece T-shaped cross-section beam bridge is shown, where B is the bridge width, L is the bridge span, and the load P acts on the bridge at a certain transverse position. Because the middle cross beam has infinite stiffness, the cross beam has rigid body displacement, and the deflection curve c'd' after deformation is a straight line.

[0125] When the unit load P=1 acts at any position (eccentricity e) on the bridge deck, the force R1 borne by No. 1 main beam is analyzed. The cross section is taken at a distance x from the left end support of the bridge. The eccentric load P=1 can be replaced by the central load P=1 acting on the bridge axis and the eccentric moment M=1*e, as shown in Figure 4 , where a i is the distance of i-th main beam from the centroid of the cross section, and I i is the cross-sectional bending moment of inertia of i-th main beam. The forces borne by No. 1 main beam under the two conditions are calculated respectively, and then superimposed.

[0126] (1) Action of central load P=1

[0127] As shown in Figure 5 , under the action of the central load, the rigid middle cross beam translates downward as a whole, so each main beam produces the same deflection, i.e.

[0128] (9)

[0129] In the formula: is the deflection of i-th main beam, n is the number of main beams, is the average deflection.

[0130] According to material mechanics, the load acting on the longitudinal bridge of a simply supported beam at position x and the deflection relationship is:

[0131] (10)

[0132] In the formula: E is the elastic modulus of the material, I i is the cross-sectional bending moment of inertia of i-th main beam, L is the span of the main beam, is the reaction force of i-th main beam.

[0133] From formula (10), we can solve:

[0134] (11)

[0135] (12)

[0136] From the static equilibrium condition, we get:

[0137] (13)

[0138] Find:

[0139] (14)

[0140] Substituting equation (14) into equation (11), we obtain the load distribution of the central load P=1 between the main beams as follows:

[0141] (15)

[0142] If all main beams have the same cross-section, then:

[0143] (16)

[0144] (2) The effect of eccentric moment M=1*e

[0145] like Figure 6 M in the figure Ti Let the resisting torque of the i-th main beam be obtained from equation (8):

[0146] (17)

[0147] In the formula: k i Let GJ be the torsional restraint stiffness at the end of main beam i. i Let be the torsional stiffness of main beam i.

[0148] Under the action of the eccentric moment M, the cross section of the bridge will rotate around the center point by an angle φ. Therefore, the deflection of each main beam is:

[0149] (18)

[0150] Based on geometric relations:

[0151] (19)

[0152] Based on the load-deflection relationship of the main beam:

[0153] (20)

[0154] Substituting equation (20) into equation (19), we get:

[0155] (twenty one)

[0156] Substituting equation (21) into equation (17) yields:

[0157] (twenty two)

[0158] From equation (21) we have:

[0159] (23)

[0160] That is:

[0161] (24)

[0162] According to the moment equilibrium condition we have:

[0163] (25)

[0164] Substitute equation (24) and (22) into equation (25) we have:

[0165] (26)

[0166] Simplify we have:

[0167] (27)

[0168] From equation (27) we have:

[0169] (28)

[0170] In which, the correction coefficient is:

[0171] (29)

[0172] If the influence of end cross beam is not considered, the stiffness is infinite, then , equation (29) degenerates into:

[0173] (30)

[0174] When analyzing the mid-span section, that is, x = L / 2, equation (30) degenerates into the coefficient of the ordinary modified eccentric compression force method:

[0175] (31)

[0176] The relationship between the elastic modulus E and the shear modulus G is:

[0177] (32)

[0178] In which, v is the Poisson's ratio.

[0179] (3) The action of eccentric load P = 1

[0180] The reaction force of eccentric load P = 1 is the superposition of the reaction forces obtained from the central load P = 1 and the eccentric moment M = 1 * e, as shown in equation (33).

[0181] (33)

[0182] In the formula: η ie is the load transverse distribution influence line value of the i-th main beam when the eccentric load P acts at the position e in the transverse direction of the bridge, e is the position of the load in the transverse direction of the bridge, and a i is the distance from the i-th main beam to the centroid of the section, and the main beam on the left side of the centroid of the section takes a negative sign, and the main beam on the right side takes a positive sign.

[0183] The load transverse distribution influence line value of the i-th main beam when the load acts at multiple positions in the transverse direction of the bridge is obtained by equation (33), as shown in 、 , and a straight line is formed, and the load transverse distribution influence line η i of the i-th main beam is obtained.

[0184] (34)

[0185] (35)

[0186] (36)

[0187] In the formula: y is the position in the transverse direction of the bridge, and the origin of the coordinate axis is the position of the centroid of the section, and the left side of the centroid of the section takes a negative sign, and the right side takes a positive sign.

[0188] The above analysis is for simply supported beam bridges, and if it is a continuous beam bridge, the equivalent simply supported beam method can be used to modify the bending stiffness and torsional stiffness.

[0189] III. Calculation of torsional restraint stiffness of end cross beam

[0190] According to the lever principle method, the end cross beam is simplified as a simply supported beam, Figure 7 is the bending moment diagram of the simply supported beam under unit end bending moment, and the rotation angle generated by the end bending moment can be obtained is:

[0191] (37)

[0192] In the formula: EI h is the bending stiffness of the end cross beam, is the bending moment generated by the unit bending moment and the load bending moment, respectively, and l h is the span of the end cross beam.

[0193] Figure 8To obtain the shear force diagram of a simply supported beam under unit end bending moment, the rotation angle caused by the shear force under the beam end bending moment can be calculated. for:

[0194] (38)

[0195] In the formula: A sz The effective shear area of ​​the end diaphragm. These are the shear forces generated by the unit bending moment and the load bending moment, respectively, and κ is the shear coefficient of the beam section.

[0196] (39)

[0197] In the formula: A h The cross-sectional area of ​​the end diaphragm beam is given.

[0198] If elastic supports such as plate rubber bearings are used, under vertical loads, the supports will undergo compressive deformation, causing the end transverse diaphragm beam to rotate. Figure 9 The elastic support rotation angle generated when the beam end bending moment is applied can be obtained. for:

[0199] (40)

[0200] In the formula: k R The elastic support stiffness of the support.

[0201] For steel supports, the following can be adopted: For plate rubber bearings and pot rubber bearings, Calculate using the following formula:

[0202] (41)

[0203] In the formula: E e Let A be the compressive elastic modulus of the rubber bearing. e h is the area of ​​the rubber bearing. e This refers to the total thickness of the rubber layer in the rubber bearing.

[0204] Therefore, the total rotation angle θ generated under the action of the bending moment is:

[0205] (42)

[0206] The stiffness k of the torsional elastic support is:

[0207] (43)

[0208] For the edge main beam, it is connected to only one end transverse diaphragm, and the torsional restraint stiffness at the beam end is taken as k. For the middle main beam, it is connected to two end transverse diaphragms, and the torsional restraint stiffness at the beam end is taken as 2k. Figure 10i.e.

[0209] (44)

[0210] where i is the main girder number, n is the number of main girders, k i is the torsional restraint stiffness of the i-th main girder, the 1st and n-th main girders are side main girders, and the other numbered main girders are middle main girders.

[0211] The above is for the conventional girder bridge with one support arranged under each piece of main girder, if other support arrangement forms are used, the torsional restraint stiffness k i of the main girder end needs to be derived according to the mechanical principle.

[0212] Four, load transverse distribution coefficient calculation

[0213] After the load transverse distribution influence line of the i-th main girder is obtained, the vehicle load is distributed according to the most unfavorable load position, and then the load transverse distribution coefficient of the vehicle load is calculated, as formula (45).

[0214] (45)

[0215] where m iqki is the load transverse distribution coefficient of the vehicle load of the i-th main girder, ξ is the vehicle load transverse lane distribution coefficient, i.e. the transverse multi-lane reduction coefficient, N is the number of loaded vehicles, and η ij is the load transverse distribution influence line value of the i-th main girder when the vehicle tire acts on the transverse bridge direction j position.

[0216] The load transverse distribution coefficient m irki of the i-th main girder pedestrian load is calculated, as formula (46).

[0217] (46)

[0218] where η ir is the load transverse distribution influence line value of the i-th main girder when the pedestrian load acts on the center of gravity of the sidewalk.

[0219] Five, action effect calculation

[0220] The general calculation formula of the vehicle load action effect of the i-th main girder is:

[0221] (47)

[0222] where S q is the vehicle load action effect, μ is the impact coefficient of the vehicle load, P k is the concentrated load value in the vehicle load, is the longitudinal bridge direction action effect influence line coordinate value, and q kis the value of the uniform load in the vehicle load, Ω is the area of the action effect influence line, and x is the longitudinal bridge position.

[0223] The general calculation formula of the i-th main beam crowd load action effect is:

[0224] (48)

[0225] Example 1: 75m span three main beam narrow steel box composite beam bridge

[0226] The civil engineering 10 bid section of Yangxin to Xinyi highway has a starting and ending mileage of K102+874~K141+767.643, a total length of 38.894km, and a main line adopting six-lane highway standard with a design speed of 120km / h. Shuikou south hub is a hub interchange of Yangxin highway and Baomao highway. The present status of Baomao highway is a four-lane highway in both directions with a design speed of 100km / h.

[0227] The Shuikou south hub interchange Baomao highway overline bridge, A, B, E, and F ramp bridges adopt the composite beam bridge of "narrow steel box beam + SC composite bridge deck", the ramp bridges are double main beam structures, the A and E ramp bridges have a span of 70m, the B and F ramp bridges have a span of 75m, the overline bridge is a double-width three main beam structure, and a steel support is arranged under each piece of narrow steel box beam at the beam end. Yangxin highway and Baomao highway are oblique, the three main beam bridge cross section is as shown in Figure 11 , the distance between the narrow steel box beams is 5.7m, the box height is 3m, the width is 1.6m, the upper flange thickness is 20mm, the lower flange thickness is 56mm, the web thickness is 14mm, the overall thickness of the steel-concrete (SC) composite bridge deck is 260mm, the steel bottom plate thickness is 8mm, and the beam spacing is 5m. The steel main beam of the composite beam bridge adopts Q420, the steel cross beam adopts Q355, and the concrete adopts C50.

[0228] To analyze the precision of the method in this paper, the finite element simulation analysis is used to simulate the stress of the actual bridge structure. The specific operation of the finite element method is as follows:

[0229] 1) Finite element model establishment

[0230] The finite element software midas civil is used to establish the spatial beam finite element model of the composite beam bridge, 1m is divided into a unit in the longitudinal bridge direction, and the finite element model is as shown in Figure 12 .

[0231] 2) Load transverse distribution coefficient m calculation principle

[0232] The transverse moving load is loaded, the unit concentrated load P=1 is respectively applied to the 37 positions as shown in Figure 13 (For example, j=1, 2...37 in the figure), and the load effect transverse influence line of the structure is calculated in sequence, and the figure B iFor the position number of the i-th main beam (i=1, 2, 3), the load transverse distribution influence line vertical index value of each piece of main beam is calculated according to formula (49).

[0233] (49)

[0234] In the formula: The load effect of the i-th main beam when the moving load acts on the transverse bridge j position, such as support reaction force (S=R), bending moment (S=M), deflection (S=w), etc., n is the number of main beams, The load effect of the i-th main beam when the moving load acts on the transverse bridge k position, The influence line vertical index value of the i-th main beam when the moving load acts on the transverse bridge j position.

[0235] The influence line vertical index value of the i-th main beam when the moving load acts on the transverse bridge j position. The load transverse distribution influence line of the main beam is obtained by connecting the influence line vertical index values of the loads acting on each position. The load transverse distribution coefficient of the main beam is calculated according to formula (50) through the most unfavorable distribution of the transverse vehicle load.

[0236] (50)

[0237] In the formula: The load transverse distribution coefficient of the i-th main beam c measuring point S effect when the transverse moving load P acts on the longitudinal bridge z position, ξ is the vehicle load transverse lane distribution coefficient, N is the number of loaded vehicles, The influence line vertical index value of the i-th main beam when the vehicle load acts on the transverse bridge k position, which is calculated by linear interpolation of the adjacent points of the influence line.

[0238] The maximum value is taken as the final load transverse distribution coefficient, the support point position is distributed with 2 vehicles, the support reaction force transverse distribution coefficient of the No. 1 beam is the maximum, the calculation process is as follows . Figure 14 .

[0239] 3) Moving load and measurement arrangement

[0240] As shown in Figure 15 , the support reaction force influence line measuring point is arranged at the left support point, i.e. c=0m position, the bending moment and deflection influence line measuring point is arranged at the midspan (c=37m), L / 4 (c=19m), L / 8 (c=10m), L / 16 (c=5m) position, the longitudinal bridge position interval of the transverse moving load is 5m, the midspan 37m position is also loaded once, a total of 16 loading sections, as shown in Figure 15 z position.

[0241] The operation steps of the method are as follows:

[0242] Step (1): According to the engineering data, the relevant parameters of the simply supported beam bridge are obtained: the bridge span L = 75 m, the cross section arrangement is as Figure 11 , the elastic modulus E of steel and concrete material is 2.06 x 10 5 MPa and 3.45 x 10 4 MPa respectively, the Poisson's ratio v is 0.31 and 0.2 respectively, the shear modulus G of steel and concrete material is 0.382 and 0.417 times of E respectively, the G of the combined section is 0.4 times of E, the bending and torsional inertia moments of each piece of the main beam section are taken as an example, the edge main beam is calculated by midas civil to calculate the conversion section characteristics of the combined section (the concrete is converted into steel), such as Figure 16 , the bending and torsional inertia moments are 0.882 m 4 and 0.180 m 4 respectively, the cross section size of the end diaphragm is as Figure 17 , and the cross section characteristics are as Figure 18 .

[0243] Step (2): The torsional restraint stiffness of the end diaphragm to the main beam is calculated

[0244] According to formula (39), the shear coefficient K of the beam section is calculated by the following formula:

[0245] (51)

[0246] In the formula: A h is the cross section area of the end diaphragm, and A sz is the effective shear area of the end diaphragm.

[0247] For the steel support, take , that is, the deformation of the support is not considered, and the torsional elastic support stiffness k is calculated by formula (43) as follows (for convenience of writing, E = 1 is taken in the calculation, because as long as the value of G / E is unchanged, it will not affect the calculation result):

[0248] (52)

[0249] The span-depth ratio of the end diaphragm is 5.7 / 2.6 = 2.19, which is very small, and according to formula (52), the influence of shear deformation is greater than that of bending deformation, so the influence of shear deformation needs to be considered for the end diaphragm with small span-depth ratio.

[0250] Further, the torsional restraint stiffness of the end diaphragm to the main beam is:

[0251] (53)

[0252] Step (3): The load transverse distribution coefficient at the support point is calculated by the lever principle method:

[0253] Single beam model refers to the bridge deck is cut off at the centroidal line of the main beam cross section, double beam model refers to the bridge deck is cut off at the intersection of the two webs of the box main beam and the bridge deck, and the bridge deck is calculated as a multi-span simply supported beam, such as Figure 19 , the m 01 =1.632 calculated by single beam model, and the m 02 =1.561 calculated by double beam model, such as Figure 20 , through comparison with the results of finite element method, it can be seen that for three main beam bridges, the m 02 =1.561 calculated by double beam model is more appropriate.

[0254] Step (4): the steps for calculating the load transverse distribution coefficient of the main beam in the longitudinal bridge direction at any position by the modified eccentric pressure method considering the torsional constraint of the beam end are as follows:

[0255] a) Calculate the load transverse distribution influence line η i , the load transverse distribution influence line values of the load acting on multiple positions of the No. 1 side main beam are obtained according to formula (33), and a straight line is formed, thereby obtaining the load transverse distribution influence line η i of the No. 1 side main beam, such as Figure 21 , the two load transverse distribution influence lines in the figure are the influence lines calculated by formula (29) and (31) with the modified coefficient, wherein 、 It can be seen that the modified coefficient increases and the value of the influence line is also larger after considering the torsional constraint stiffness of the end cross beam.

[0256] b) Calculate the load transverse distribution coefficient

[0257] The vehicle load is arranged according to the most unfavorable load position, such as Figure 21 , the automobile load is arranged close to the left side of the cross section, the number of arranged vehicles is 1-4, and the maximum value calculated in the four cases is taken as the load transverse distribution coefficient of the automobile load, such as Figure 22 , except for the support position, the value of the load transverse distribution coefficient considering the torsional constraint stiffness of the end cross beam is greater than that without considering the torsional constraint stiffness of the end cross beam (the modified coefficient is calculated by formula (30)), and at the support position, both are 1.4825, which is smaller than the m 02 =1.561 of the double beam model, and thus adjustment is needed.

[0258] Step (5): the change of the load transverse distribution along the longitudinal bridge direction is considered for the concentrated load, the load transverse distribution coefficient at the mid-span position is taken for the uniformly distributed load, the load is reduced through the load transverse distribution coefficient, and then the load effect is calculated;

[0259] For three main beam bridges, the change scheme of the load transverse distribution along the longitudinal bridge direction is as follows:

[0260] a) Calculate the transition zone length xt

[0261] like Figure 23 Considering the transition region length x t The lateral load distribution coefficient changes linearly within the range, while the mid-span region remains unchanged. The length of the transition zone is calculated using the following formula, based on the principle that the area before and after the transformation is equal:

[0262] (54)

[0263] In the formula: L is the span of the main girder, and x is the longitudinal position of the bridge. Let x be the lateral load distribution factor of the vehicle load at position x. , These are the lateral load distribution coefficients for vehicle loads at the fulcrum and mid-span positions, respectively.

[0264] In practical calculations, discrete summation can be used instead of integration. Figure 23 There are a total of 38 points, with an actual area of ​​43.3480. , Transition region length x t The value is 18.1643m obtained from equation (55).

[0265] (55)

[0266] b) Regarding the transition region length x t Adjust the lateral load distribution coefficient value within the range.

[0267] (56)

[0268] in: The lateral load distribution factor of the vehicle load after adjustment in the transition zone is m. 02 The lateral load distribution factor is calculated for the double-beam model. The adjusted curve is shown below. Figure 23 The adjusted lateral load distribution coefficient at the support point is m. 02 . Figure 24 It is the lateral load distribution coefficient calculated considering the torsional constraint stiffness at the beam ends. A comparison with the lateral load distribution coefficient calculated by finite element software shows that the two are in good agreement.

[0269] In step (5), when calculating the vehicle load effect, the influence of the impact coefficient μ is temporarily ignored, and the method for calculating the support reaction force is as follows:

[0270] (57)

[0271] In the formula: R1 is the most unfavorable support reaction force of the side main beam, P k qk are the concentrated load and the uniform load value of the highway I-class load respectively, 1.2 is an increase coefficient when calculating the shear force, and L is the span.

[0272] The calculation value of the finite element model of the No. 1 side main beam is 1271.5 kN, and the error is 1.38%, which is good.

[0273] The calculation of the maximum bending moment M1 of each measuring point c of the side main beam is as formula (58).

[0274] (58)

[0275] The bending moment effect error considering and not considering the stiffness of the end cross beam is as Figure 25 (a), the bending moment error considering the torsional constraint stiffness of the end cross beam is basically less than 2%, which is obviously better than that without considering.

[0276] The calculation of the maximum deflection w1 of each measuring point c of the side main beam is as formula (59):

[0277] (59)

[0278] The deflection effect error considering and not considering the stiffness of the end cross beam is as Figure 25 (b), although the deflection error without considering the torsional constraint stiffness of the end cross beam is smaller, the error considering the stiffness is also less than 2%, and the error is also small.

[0279] In addition, the cases with and without cross beams are analyzed, when there is no cross beam, the end cross beam is calculated as a 0.3 m thick concrete slab, and the torsional elastic support stiffness k is: Figure 26

[0280] (60)

[0281] The span-depth ratio of the end cross beam is 5.7 / 0.3=19, which is large, and it can be known from formula (60) that the shear deformation has little effect and can be ignored.

[0282] The theoretical value of the load transverse distribution coefficient of the No. 1 side main beam cross-section is 1.1388, and the finite element value is 1.1498, which is relatively close, and the values with cross beams are 1.0334 and 1.0414 respectively. It is shown that after considering the torsional constraint of the end cross beam on the main beam, the calculated load transverse distribution coefficient value is more consistent with the actual situation.

[0283] Example Two: 35m-span three-main-beam narrow-width steel box composite beam bridge

[0284] On the basis of example one, the span of the bridge is changed to 35m, and the height-span ratio of the beam is kept unchanged, and the influence of the span change on the precision of the method is analyzed.

[0285] ​The operation steps of the method are as follows:

[0286] Step (1): according to the engineering data, the bridge span L=35m, taking the side main beam as an example, the conversion section characteristics of the combined section are calculated by midas civil, the bending inertia moment and the torsional inertia moment are 0.1824m 4 , 0.06636m 4 , the end cross beam section characteristics are as Figure 27 , and the other parameters are the same as those in example one.

[0287] Step (2): calculate the torsional constraint stiffness of the end cross beam to the main beam

[0288] According to formula (39), the shear coefficient κ of the beam section is calculated by the following formula:

[0289] (61)

[0290] The elastic support stiffness k of the torsion is calculated by formula (43):

[0291] (62)

[0292] The span-depth ratio of the end cross beam is 5.7 / 1.3=4.38, which is less than the limit value 5 of the deep beam, and according to formula (62), the influence of shear deformation is slightly greater than that of bending deformation, so for the end cross beam with small span-depth ratio, the influence of shear deformation needs to be considered.

[0293] Further, the torsional constraint stiffness of the end cross beam to the main beam is:

[0294] (63)

[0295] Step (3): calculate the load transverse distribution coefficient at the support point by the lever principle method:

[0296] As Figure 19 , the m 01 =1.632 calculated by the single beam model, and the m 02 =1.561 calculated by the double beam model, as Figure 28 , through comparison with the results of the finite element method, for the three main beam bridge, the m 02 =1.561 calculated by the double beam model is more appropriate.

[0297] Step (4): the load transverse distribution coefficient at any position of the main beam in the longitudinal direction is calculated by the modified eccentric pressure method considering the torsional constraint of the beam end, as Figure 29 , except for the support point position, the load transverse distribution coefficient value considering the torsional constraint stiffness of the end cross beam is greater than that without considering (the modification coefficient is calculated by formula (30)), and at the support point position, both are 1.4825, which is greater than the m02 =1.561 small, thus need to be adjusted.

[0298] Step (5): considering the change of load transverse distribution along the longitudinal bridge, the load transverse distribution coefficient of the mid-span position of the uniformly distributed load is taken, the load is reduced through the load transverse distribution coefficient, and then the load effect is calculated;

[0299] For the three main girder bridge, the adjusted curve is as Figure 30 (a), the load transverse distribution coefficient of the fulcrum after adjustment is m 02 It can be seen that the load transverse distribution coefficient calculated by considering the torsional restraint stiffness of the beam end is in good agreement with the bending moment load transverse distribution coefficient calculated by the finite element software, and the load transverse distribution coefficient calculated without considering the torsional restraint stiffness of the beam end is obviously smaller. From Figure 30 (b), the deflection load transverse distribution coefficient calculated by the finite element software is more close to .

[0300] In step (5), the impact of the impact coefficient μ is not considered when calculating the vehicle load effect, and the calculation method of the support reaction force is:

[0301] (64)

[0302] The finite element model calculation value of the No. 1 side main girder is 901.6 kN, and the error is only 0.38%, which has good precision.

[0303] The bending moment effect error considering and not considering the end cross beam stiffness is as Figure 31 (a), the bending moment error considering the torsional restraint stiffness of the end cross beam is less than 1%, and more than 5% when not considering.

[0304] The deflection effect error considering and not considering the end cross beam stiffness is as Figure 31 (b), the deflection error considering the torsional restraint stiffness of the end cross beam is less than 2%, and the error is basically more than 3% when not considering.

[0305] In addition, in the case of with cross beam and without cross beam, the load transverse distribution coefficient theoretical value of the No. 1 side main girder mid-span section when without cross beam is 1.2759, and the finite element value is 1.2734, which is almost the same, and the values with cross beam are 1.2095 and 1.2373 respectively. It is shown that after considering the torsional restraint of the end cross beam to the main girder, the calculated load transverse distribution coefficient value is more consistent with the actual situation.

[0306] Example three: 75m span double main girder narrow steel box composite girder bridge

[0307] Yangxin highway B ramp bridge arrangement is as Figure 32, the main beam cross section is as shown in Figure 33 , other parameters are same as example one.

[0308] The operation steps of the method are as follows:

[0309] Step (1): parameters are same as example one.

[0310] Step (2): calculate the torsional restraint stiffness of the end cross beam to the main beam

[0311] Referring to example one, the torsional restraint stiffness of the end cross beam to the main beam is obtained as:

[0312] (65)

[0313] Step (3): calculate the load transverse distribution coefficient at the support point by the lever principle method:

[0314] As shown in Figure 19 , the m 01 calculated by the single beam model is 1.632, and the m 02 calculated by the double beam model is 1.561, as shown in Figure 34 , by comparison with the results of the finite element method, for the double main beam bridge, the m 01 calculated by the single beam model is 1.632, which is more appropriate.

[0315] Step (4): calculate the load transverse distribution coefficient at any position of the main beam in the longitudinal direction of the bridge by the modified eccentric pressure method considering the torsional restraint of the beam end, as shown in Figure 35 , except for the support point position, the load transverse distribution coefficient value considering the torsional restraint stiffness of the end cross beam is greater than that without considering (the correction coefficient is calculated by formula (30)), at the support point position, both are 1.632, which is the same as the m 01 calculated by the single beam model is 1.632, so adjustment is not needed.

[0316] Step (5): calculate the load effect:

[0317] For the double main beam bridge, as shown in Figure 36 (a), it can be seen that the load transverse distribution coefficient calculated by considering the torsional restraint stiffness of the beam end is more consistent with the bending moment load transverse distribution coefficient calculated by the finite element software. From Figure 36 (b), the deflection load transverse distribution coefficient calculated by the finite element software is more close to .

[0318] In step (5), when calculating the vehicle load effect, the impact coefficient μ is not considered, and the calculation method of the support reaction force is:

[0319] (66)

[0320] The calculated value of the finite element model of the No. 1 side main beam is 1345.7 kN, and the error is only 0.14%, and the precision is very good.

[0321] The bending moment effect error with and without considering the stiffness of the end cross beam is as shown in Figure 37 (a), the bending moment error considering the torsional constraint stiffness of the end cross beam is basically less than 2%, and when not considering it, part of the error is more than 5%.

[0322] The deflection effect error with and without considering the stiffness of the end cross beam is as shown in Figure 37 (b), the deflection error considering the torsional constraint stiffness of the end cross beam is also slightly less than when not considering it, and the error of the two cases is less than 1.5%.

[0323] In addition, in the case of with and without cross beams, the load transverse distribution coefficient theoretical value of the No. 1 side main beam cross section is 1.2260, and the finite element value is 1.22577, which is in good agreement. The values with cross beams are 1.1880 and 1.19468 respectively. It is shown that after considering the torsional constraint of the end cross beam on the main beam, the calculated load transverse distribution coefficient value is more consistent with the actual situation.

[0324] The above only describes three embodiments of the present application, and any changes and modifications made within the scope of the patent application of the present application are all within the scope of the present application.

Claims

1. A modified eccentric pressure method considering the torsional constraint stiffness of the end transverse diaphragm, characterized in that, Includes the following steps: (1) Based on the engineering data, obtain the relevant parameters of the simply supported beam bridge: bridge span L, cross-sectional layout, bending moment of inertia and torsional moment of inertia of each main beam section, cross-sectional dimensions of the end diaphragm, material elastic modulus E, shear modulus G, Poisson's ratio ν; (2) Calculate the torsional stiffness of the end diaphragm beam on the main beam; (3) Calculate the lateral load distribution coefficient at the fulcrum using the lever principle method: a) For T-shaped and I-shaped single-web section main beams, a single-beam model is used for calculation; b) For small box girders, hollow slab type double web section main girders, and double main girder bridges, a single girder model is used for calculation; for multi-main girder bridges with three or more main girders, a double girder model is used for calculation. The lateral load distribution factor calculated using the single beam model is denoted as m. 01 The lateral load distribution coefficient calculated using the double-beam model is denoted as m. 02 ; (4) The load distribution coefficient at any position in the longitudinal direction of the main beam is calculated by the modified eccentric pressure method considering the torsional constraint at the beam end. (5) For concentrated loads, consider the variation of the lateral distribution of the load along the longitudinal direction of the bridge. For uniformly distributed loads, take the lateral distribution coefficient of the load at the mid-span position. Reduce the load by the lateral distribution coefficient of the load and then calculate the load effect. In step (2), according to the lever principle, the end diaphragm beam is simplified to a simply supported beam. For the main beam on the adjacent side, its torsional elastic support stiffness k is: ； Among them: EI h For the bending stiffness of the end diaphragm, l h Let G be the span of the end diaphragm, G be the shear modulus of the material, and A be the length of the end diaphragm. sz κ is the effective shear area of ​​the end diaphragm, and k is the shear coefficient of the beam section. R The elastic support stiffness of the support; For the edge main beam, it is connected to only one end transverse diaphragm, and the torsional restraint stiffness at the beam end is taken as k. For the middle main beam, it is connected to two end transverse diaphragms, and the torsional restraint stiffness at the beam end is taken as 2k, that is: ； Where: i is the main beam number, n is the number of main beams, and k is the main beam number. i The torsional constraint stiffness at the end of main beam i is given. Main beams 1 and n are side main beams, and the other numbered main beams are middle main beams. In step (4), the steps for calculating the transverse load distribution coefficient at any position in the longitudinal direction of the main girder using the modified eccentric pressure method considering torsional constraints at the beam ends are as follows: a) Calculate the influence line η of the lateral load distribution i ； ； Where: η ie This is the influence line value of the lateral load distribution of the main girder i when an eccentric load is applied at position e in the transverse direction of the bridge. e represents the transverse position of the load application, with a negative sign to the left of the centroid of the section and a positive sign to the right. i Let be the moment of inertia of the section of main beam i, n be the number of main beams, and a be the moment of inertia of the section of main beam i. i Let be the distance from the i-th main beam to the centroid of the cross-section. The main beam to the left of the centroid is considered negative, and the main beam to the right is considered positive. E is the elastic modulus of the material, L is the span of the main beam, x is the position of the eccentric load acting in the longitudinal direction of the bridge, with the left end support of the beam as the origin and the right end as the positive direction. k i Let GJ be the torsional restraint stiffness at the end of main beam i. i Let i be the torsional stiffness of the main beam. pass The influence line values ​​of the lateral load distribution at multiple locations along the transverse direction of the main girder i were obtained, such as... , Connecting these lines with a straight line yields the influence line η of the lateral load distribution of the main beam i. i ; ； ； ； Where: y represents the transverse bridge position, the origin of the coordinate axis is the centroid of the cross section, and negative signs are taken to the left of the centroid of the cross section and positive signs are taken to the right; b) Calculate the lateral load distribution factor The influence line η of the lateral load distribution of the main beam i is obtained. i Then, the vehicle load is distributed according to the most unfavorable load position, and the lateral load distribution coefficient of the vehicle load is calculated: ； Where: m iqki Let ξ be the lateral load distribution coefficient of the vehicle load on main beam i, ξ be the lateral lane distribution coefficient of the vehicle load (i.e., the lateral multi-lane reduction coefficient), N be the number of vehicles loaded, and η be the lateral load distribution coefficient of the vehicle load on main beam i. ij The value of the lateral load distribution influence line of main beam i when the vehicle tires act on position j in the transverse direction of the bridge. For the lateral load distribution coefficient m of the crowd load on main beam i... irki The calculation is as follows: ； Where: η ir The influence line value of the lateral distribution of the load on the main beam i when the crowd load acts on the center point of the resultant force of the sidewalk; In step (5), for concentrated loads, when it is a double main girder bridge, the value is directly taken as... For multi-main-girder bridges with three or more main girders, the load lateral distribution along the longitudinal direction varies as follows: a) Calculate the transition zone length x t The length of the transition zone is calculated using the following formula: ； Where: L is the span of the main girder, and x is the longitudinal position of the bridge. Let x be the lateral load distribution factor of the vehicle load at position x. , These are the lateral load distribution coefficients for vehicle loads at the fulcrum and mid-span positions, respectively. b) Regarding the transition region length x t Adjust the lateral load distribution coefficient value within the range ； in: The lateral load distribution factor of the vehicle load after adjustment in the transition zone is m. 02 The lateral load distribution coefficient is calculated for the double-beam model.

2. The modified eccentric pressure method considering the torsional constraint stiffness of the end transverse diaphragm as described in claim 1, characterized in that: In step (1), the bending moment of inertia and torsional moment of inertia of the main beam section are calculated by finite element software, such as Midas Civil, Bridge Doctor, and ANSYS, or by AutoCAD software, or by theoretical mechanics methods.

3. The modified eccentric pressure method considering the torsional constraint stiffness of the end diaphragm beam according to claim 1, characterized in that: In step (1), the shear modulus G is calculated by the following formula: 。 4. The modified eccentric pressure method considering the torsional constraint stiffness of the end transverse diaphragm as described in claim 1, characterized in that: In step (1), if the beam bridge is a continuous beam bridge or a continuous rigid frame bridge, the equivalent simply supported beam method is used to correct the bending stiffness and torsional stiffness of the main beam section.

5. The modified eccentric pressure method considering the torsional constraint stiffness of the end diaphragm beam according to claim 1, characterized in that: In step (2), the beam section shear coefficient κ is calculated using the following formula: ； Among them: A h Let A be the cross-sectional area of ​​the end diaphragm. sz This represents the effective shear area of ​​the end crossbeam.

6. The modified eccentric pressure method considering the torsional constraint stiffness of the end transverse diaphragm as described in claim 1, characterized in that: In step (2), when the span-to-depth ratio of the end transverse diaphragm is greater than 10, take... That is, the effect of shear deformation is not considered.

7. The modified eccentric pressure method considering the torsional constraint stiffness of the end transverse diaphragm as described in claim 1, characterized in that: In step (2), for the steel support, take That is, without considering the deformation of the support, for plate rubber bearings and pot rubber bearings, Calculate using the following formula: ； Among them: E e Let A be the compressive elastic modulus of the rubber bearing. e h is the area of ​​the rubber bearing. e This refers to the total thickness of the rubber layer in the rubber bearing.

8. The modified eccentric pressure method considering the torsional constraint stiffness of the end diaphragm beam according to claim 1, characterized in that: Step (2) is for a conventional beam bridge with one support under each main girder. If other support arrangements are used, the torsional stiffness k at the beam end of the main girder is derived based on mechanical principles. i .

9. The modified eccentric pressure method considering the torsional constraint stiffness of the end diaphragm beam according to claim 1, characterized in that: In step (3), the single beam model refers to the bridge deck being broken at the centroid line of the main beam section, and the double beam model refers to the bridge deck being broken at the junction of the two webs of the box-section main beam and the bridge deck. The bridge deck is calculated as a multi-span simply supported beam.

10. The modified eccentric pressure method considering the torsional constraint stiffness of the end diaphragm beam according to claim 1, characterized in that: In step (5), the calculation method for the load effect is as follows: The general formula for calculating the effect of vehicle load on main beam i is: ； Wherein: S q The effect of vehicle load is represented by μ, where μ is the impact coefficient of the vehicle load, and P is the effect of vehicle load. k This represents the concentrated load value in the vehicle load. q represents the coordinate value of the influence line of the longitudinal bridge action effect. k Ω represents the uniformly distributed load value in the vehicle load, x represents the area of ​​the influence line of the effect, and x represents the longitudinal bridge position. The general formula for calculating the effect of crowd load on main beam i is: ； Wherein: S r For the effect of crowd load, q r Ω represents the population load value, and Ω represents the area of ​​the influence line of the effect.

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