Pier rigidity matching determination method for multi-span continuous rigid frame bridge

Abstract

The invention belongs to the technical field of bridge engineering, and particularly relates to a pier rigidity matching determination method for a multi-span continuous rigid frame bridge. For multi-span continuous integral rigid frame bridges with different pier heights and joint lengths, a calculation method for the pier top bending moment under the action of horizontal force and temperature force is established respectively. According to the principle that the bending moment of the pier top of each pier is uniformly distributed and does not exceed the cracking bending moment, the method for rapidly determining the reasonable anti-pushing rigidity of each pier is obtained. According to the method, the difficulty in determining the rigidity of each pier of the multi-span continuous rigid frame bridge under the conditions of different pier heights and joint lengths is solved, and the reasonable matching design of the flexible piers and the rigid piers and the rapid determination of the anti-pushing rigidity of the flexible piers and the rigid piers can be realized.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a method for determining pier stiffness matching of a multi-span continuous rigid frame bridge. Background Art

[0002] Multi-span, long-span, rigid-frame viaducts are a special type of continuous rigid-frame bridge, widely used in the construction of urban highway bridges and rail transit bridges. As a special type of bridge, long-span rigid-frame bridges are subject to complex load conditions, with factors such as pier selection, size, height, and stiffness significantly influencing their internal forces.

[0003] Internationally, the use of integral multi-span continuous rigid frame bridges dates back to the mid-1960s. Tennessee and five other US states adopted integral abutment bridges and bridges without expansion joints as standard structures. Starting in the late 1990s, this type of bridge began to gain momentum in the US. By 2005, according to a survey by the AASHTO Bridge and Structures Section, there were approximately 13,000 integral bridges in use in the US, including approximately 9,000 with integral abutments and 4,000 with semi-integral abutments. Engineers and scholars have accumulated a wealth of experience and expertise in the practical application and construction of integral bridges.

[0004] However, there are currently few systematic studies on the stiffness matching of long-span rigid-frame bridges, and design methods are still lacking. Given the significant impact of pier stiffness matching on structural stress and deformation, it is essential to study the overall mechanical performance of multi-span long-span rigid-frame viaducts. It is also crucial to study the appropriate stiffness matching between piers to guide the rational layout of the upper and lower structures of this system. Summary of the Invention

[0005] In response to the above technical problems, the present invention provides a method for determining the stiffness matching of piers for multi-span continuous rigid frame bridges. Based on the pier height and joint length, and according to the mechanical equilibrium conditions, deformation compatibility conditions, and constitutive relations, the design cracking moment and the maximum bending moment at the top (bottom) of the piers for multi-span continuous rigid frame bridges under horizontal and temperature forces are derived. The stiffness matching design of the piers of the rigid frame bridge is completed using the reference pier stiffness as the initial stiffness and based on the criterion that the maximum bending moment is less than the design cracking moment. The present invention provides a reasonable design process for matching the anti-thrust stiffness of flexible piers and rigid piers in actual engineering, providing theoretical support for the stiffness matching design of piers for multi-span continuous rigid frame bridges.

[0006] To achieve the above technical objectives, the present invention solves the technical problems by adopting the following technical solutions: the method is targeted at multi-span long-jointed rigid frame bridges, uses basic bridge parameters as input, calculates formulas for the design cracking moment and the maximum bending moment at the pier top, and completes the rigid frame bridge pier stiffness matching design based on the criterion that the maximum bending moment is less than the design cracking moment. The specific steps are as follows:

[0007] Step 1: Calculate the cracking stress σ of the concrete section edge under the assumed conditions according to the ultimate tensile strain of the material cr ;

[0008] Step 2: Calculate the cracking moment M cr according to the cracking stress σ of the concrete section edge calculated in Step 1 cr ;

[0009] Step 3: Determine the safety factor λ, and calculate the design cracking moment λ[M cr according to the cracking moment M cr calculated in Step 2; Step 4: Calculate the actual anti-pushing stiffness k' of each pier considering the pile-soil interaction effect;

[0010] Step 5: Combine the calculation results of Step 4 to calculate the maximum moment M i at the top of each pier under braking force and temperature force;

[0011] Step 6: Compare the design cracking moment λ[M cr with the maximum moment M i at the top of each pier to judge whether the moment of the side pier exceeds the design moment value. If it does not exceed the limit, the structural design is reasonable and the pier stiffness remains unchanged; if it exceeds the limit, make the maximum moment M i of the pier equal to the design cracking moment λ[M cr , obtain the adjusted anti-pushing stiffness of the pier and return to Step 5 to calculate the adjusted moment value at the top of the pier. At the same time, perform the discrimination of Step 6 on the moment of the sub-side pier, and so on until the forces of all piers are reasonable.

[0012] Beneficial effects: For multi-span continuous rigid frame bridges, based on basic parameters such as pier height and span length of the bridge, the design cracking moment and the maximum moment formula at the top (bottom) of the pier of the multi-span continuous rigid frame bridge under horizontal force and temperature force are derived according to the mechanical equilibrium condition, deformation compatibility condition, and constitutive relationship. Taking the reference pier stiffness as the initial stiffness, and according to the criterion that the maximum moment is less than the design cracking moment, the stiffness matching design of the piers of the rigid frame bridge is completed, and a reasonable design process for the anti-pushing stiffness of flexible piers and rigid piers under actual engineering conditions is given, and a reasonable design criterion for the pier stiffness of this type of bridge is established from the perspective of optimizing the mechanical performance.

[0013] As a further optimization of the present invention, the calculation formula of the cracking stress σ cr of the concrete section edge in Step 1 is as follows:

[0014]

[0015] In the formula, f t,r is the representative value of the uniaxial tensile strength of concrete, and its value can be taken as f respectively according to the actual structural analysis requirementst , f tk , E c is the elastic modulus of concrete, and ε t,r is the cracking strain at the edge of the concrete cross-section.

[0016] Beneficial effects: It has higher accuracy for calculating the cracking stress at the edge of the pier cross-section of multi-span continuous rigid-frame bridges.

[0017] As a further preference of the present invention, the cracking moment M cr in step 2 is calculated according to the following formula:

[0018]

[0019] Where:

[0020] d s = b - d c - a s (4)

[0021] d′ s = d c - a′ s (5)

[0022]

[0023] In the formula, a is the width of the pier in the transverse direction of the bridge, b is the width of the pier in the longitudinal direction of the bridge, E c is the elastic modulus of concrete, E s is the elastic modulus of steel bars, A s is the area of the tension zone of the cross-section, A s ' is the area of the compression zone of the cross-section, σ s is the tensile stress of the steel bars in the tension zone, σ s ' is the compressive stress of the steel bars in the compression zone, σ c is the compressive stress of the concrete in the compression zone, σ c ' is the tensile stress of the concrete in the tension zone, d c is the height of the compression zone of the cross-section, d s is the distance from the tensile steel bars to the neutral axis of the cross-section, d s ' is the distance from the compressive steel bars to the neutral axis of the cross-section, and N is the axial force of the neutral axis of the cross-section; a s is the thickness of the protective layer of the steel bars in the tension zone, a s ' is the thickness of the protective layer of the steel bars in the compression zone.

[0024] Beneficial effects: In view of the complex and diverse forces of the integral long - span rigid - frame bridge, the present invention conducts a theoretical analysis on the key mechanical properties of the piers of the long - span rigid - frame bridge. Based on the calculated cracking stress of concrete, before cracking, the pier is regarded as a completely elastic member. By establishing a mechanical equilibrium equation through the cracking stress at the edge of the concrete, the cracking moment of the pier is obtained, and a theoretical formula for calculating the cracking moment of the pier is proposed.

[0025] As a further preference of the present invention, the calculation formula for the actual lateral stiffness k' of each pier in step 4 is as follows:

[0026]

[0027] Where:

[0028]

[0029] In the formula, the main beam provides a rotational restraint with stiffness k1 to the pier, the pile - soil interaction provides a rotational restraint with stiffness k2 and a horizontal spring restraint with stiffness k3 to the pier, EI is the flexural stiffness of the pier section, H is the height of the pier, and θ1' and θ2' are the rotations at the top and bottom of the pier without considering the equivalent lateral stiffness of the pile foundation, respectively.

[0030] Beneficial effects: Based on the characteristics of the long - span rigid - frame bridge, the present invention focuses on the influence of pier stiffness on the mechanical properties of this type of bridge. The actual lateral stiffness of the piers under various foundation restraint conditions such as fixed, rigid, and elastic are calculated respectively, and a theoretical calculation model for the lateral stiffness of the piers under various foundation conditions is established. Design calculation criteria for pier stiffness are proposed from multiple dimensions such as crack control, stability, and bearing capacity.

[0031] As a further preference of the present invention, the maximum moment M at the top of each pier in step 5 i The calculation formula is as follows:

[0032]

[0033] Where: P is the magnitude of the braking force, H i is the height of each pier, k i ' is the actual lateral stiffness of each pier, K is the total integrated lateral stiffness of the bridge, Δs i ' is the actual horizontal displacement at the top of the pier, m i is the moment at the top of the pier under unit displacement of each pier;

[0034]

[0035]

[0036] When n is odd, the actual horizontal displacement value Δs at the top of the pier i ' is calculated by the following formula:

[0037]

[0038] When n is an even number, the actual horizontal displacement value Δs at the top of the pier i is calculated by the following formula, where Δs1' = 0:

[0039]

[0040] In the formula, P is the braking force, H i is the height of each pier, k i ' is the actual lateral stiffness of each pier, K is the total integrated lateral stiffness of the bridge, Δs i ' is the actual horizontal displacement at the top of the pier, m i is the moment at the top of the pier under unit displacement of each pier, EA0 is the axial stiffness of the main girder, m t 、m b are the moment at the top of the pier and the moment at the bottom of the pier under unit displacement at the top of the pier respectively, ΔT is the temperature change value, α is the concrete expansion coefficient, and L is the single-span length.

[0041] Beneficial effects: The present invention takes the temperature force and braking force after the bridge is completed as control factors to study the key stress responses of multi-span continuous rigid-frame bridges. Considering the deviation influence of the incomplete restraint effect of the pile foundation on the pier on the calculation, the moments at the top (bottom) of the pier under the action of temperature force and horizontal force are respectively deduced, and the theoretical calculation formula for the maximum moment at the top (bottom) of the pier under the coupling action of the two is given, and the formula is verified by finite element simulation, and it can be popularized and applied to the calculation of long-span rigid-frame bridge systems with different spans and different pier heights.

[0042] In step 2, the safety factor λ is taken as 0.75 or 0.85.

[0043] In summary, the present invention gives a reasonable matching design process for the lateral stiffness of flexible piers and rigid piers in actual engineering, establishes a systematic pier stiffness matching design method from the perspective of optimizing mechanical properties, and provides a theoretical support for the pier stiffness matching design of multi-span continuous rigid-frame bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The present invention will be further described below in conjunction with the drawings and embodiments.

[0045] Figure 1 is the step block diagram of the method in the present invention;

[0046] Figure 2 is the schematic diagram of the cross-section stress and strain of the compression-bending member;

[0047] Figure 3 is the schematic diagram for calculating the cracking moment in step 2;

[0048] Figure 4 It is a diagram of the calculation and analysis model for the anti-pushing stiffness of a pier fixed at both ends in step 4;

[0049] Figure 5 It is a diagram of the calculation of the anti-pushing stiffness of a pier considering the rotational restraint of the main girder on the pier in step 4;

[0050] Figure 6 It is a diagram of the calculation of the anti-pushing stiffness of a pier considering the pile-soil interaction effect in step 4;

[0051] Figure 7 It is the bridge type layout diagram of the 7×30m rigid frame bridge in Verification Example 1 of the present invention;

[0052] Figure 8 It is a verification schematic diagram of the theoretical solution of the maximum moment at the pier top under the action of uniform temperature in Verification Example 1 of the present invention;

[0053] Figure 9 It is a verification schematic diagram of the theoretical solution of the maximum moment at the pier top under the action of uniform temperature for a 6×30m rigid frame bridge (even spans). Detailed implementation manners

[0054] Now, the present invention will be further described in detail with reference to the accompanying drawings. These drawings are all simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, so they only show the components related to the present invention.

[0055] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "left side", "right side", "upper part", "lower part", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. "First", "second", etc. do not represent the importance of components, so they cannot be understood as limitations on the present invention. The specific dimensions adopted in this embodiment are only for illustrating the technical solution by way of example and do not limit the protection scope of the present invention.

[0056] Embodiment 1

[0057] This embodiment provides a preferred implementation manner, a method for determining the stiffness matching of piers of a multi-span continuous rigid frame bridge, as Figures 1 to 9As shown, this design method is for multi-span continuous integral rigid frame bridges. Based on basic parameters such as pier height and span length, the design cracking moment of multi-span continuous rigid frame bridges under horizontal force and temperature force and the formula for the maximum moment at the top (bottom) of the bridge piers are derived according to the mechanical equilibrium condition, deformation compatibility condition, and constitutive relationship. Taking the reference pier stiffness as the initial stiffness, and according to the criterion that the maximum moment is less than the design cracking moment, the stiffness matching design of the rigid frame bridge piers is completed. After determining the span, pier height, and number of spans, the cracking moment of the bridge pier and the maximum moment at the top of the bridge pier can be calculated. By comparing the magnitudes of the cracking moment of the bridge pier and the maximum moment at the top of the bridge pier, it is judged whether to set flexible piers and the recommended ratio of their stiffness to that of rigid piers.

[0058] The above evaluation method specifically includes but is not limited to the following steps, such as Figure 1 shown:

[0059] Step 1: Calculate the cracking stress σ at the edge of the concrete section under the assumed conditions based on the ultimate tensile strain of the material cr :

[0060] The cracking stress σ at the edge of the concrete section cr is calculated as follows:

[0061]

[0062] In the formula, f t,r is the representative value of the uniaxial tensile strength of concrete, and its value can be taken as f t , f tk respectively according to the actual structural analysis needs, E c is the elastic modulus of concrete, and ε t,r is the cracking strain at the edge of the concrete section.

[0063] Step 2: Calculate the cracking moment M cr based on the cracking stress σ at the edge of the concrete section calculated in Step 1 cr :

[0064] The cracking moment M cr is calculated as follows:

[0065]

[0066] Among them:

[0067] d s = b - d c - a s (4)

[0068] d′ s = d c - a′ s (5)

[0069]

[0070] In the formula, a is the width of the pier in the transverse direction of the bridge, b is the width of the pier in the longitudinal direction of the bridge, and E c is the elastic modulus of concrete, and E s is the elastic modulus of steel bars, A s is the area of the tensile zone of the cross-section, and A s ' is the area of the compression zone of the cross-section, and σ s is the tensile stress of the steel bars in the tensile zone, and σ s ' is the compressive stress of the steel bars in the compression zone, and σ c is the compressive stress of the concrete in the compression zone, and σ c ' is the tensile stress of the concrete in the tensile zone, and d c is the height of the compression zone of the cross-section, and d s is the distance from the tensile steel bars to the neutral axis of the cross-section, and d s ' is the distance from the compressive steel bars to the neutral axis of the cross-section, and N is the axial force of the neutral axis of the cross-section; a s is the thickness of the protective layer of the tensile steel bars, and a s ' is the thickness of the protective layer of the compressive steel bars.

[0071] Step 3: Determine the safety factor λ (generally take 0.75 or 0.85), and calculate the design cracking moment λ[M cr , according to the cracking moment M cr calculated in Step 3;

[0072] Step 4: Calculate the actual anti-pushing stiffness k' of each pier considering the pile-soil interaction effect:

[0073] The calculation formula of k' is as follows:

[0074]

[0075] Among them:

[0076]

[0077] In the formula, the main beam provides a rotational restraint with stiffness k1 to the pier, the pile-soil interaction provides a rotational restraint with stiffness k2 and a horizontal spring restraint with stiffness k3 to the pier, EI is the flexural stiffness of the pier cross-section, H is the height of the pier, and θ1' and θ2' are the rotations at the top and bottom of the pier without considering the equivalent anti-pushing stiffness of the pile foundation, respectively.

[0078] Step 5: Combine the calculation results of Step 5 to calculate the maximum moment M i at the top (bottom) of each pier under braking force and temperature force:

[0079] The maximum moment M i at the top (bottom) of each pier is calculated as follows:

[0080]

[0081] Among them:

[0082]

[0083] When n is odd, the actual horizontal displacement value Δs at the top of the pier i is calculated by the following formula:

[0084]

[0085] When n is even, the actual horizontal displacement value Δs at the top of the pier i is calculated by the following formula, where Δs1' = 0:

[0086]

[0087] In the formula, P is the braking force, H i is the height of each pier, k i is the actual lateral stiffness of each pier, K is the total integrated lateral stiffness of the bridge, Δs i is the actual horizontal displacement at the top of the pier, m i is the moment at the top of the pier under unit displacement of each pier, EA0 is the axial stiffness of the main beam, m t 、m b are the moment at the top of the pier and the moment at the bottom of the pier under unit displacement at the top of the pier respectively, ΔT is the temperature change value, α is the concrete expansion coefficient, and L is the single-span span.

[0088] Step 6. Compare the design cracking moment λ[M cr with the maximum moment M i at the top of each pier to judge whether the moment of the side pier exceeds the design moment value. If it does not exceed the limit, the structural design is reasonable and the pier stiffness remains unchanged; if it exceeds the limit, make the maximum moment M i equal to the design cracking moment λ[M cr , obtain the adjusted lateral stiffness of the pier and return to Step 5 to calculate the adjusted moment value at the top of the pier. At the same time, perform the discrimination in Step 6 on the moment of the secondary side pier, and so on until the forces of all piers meet the requirements.

[0089] Verification Example 1

[0090] In order to verify the accuracy of this embodiment, the following verification example was carried out:

[0091] A certain viaduct is a 7×30m continuous rigid frame T-beam bridge. The pier concrete material is C50, and the standard value of the axial tensile strength of the concrete is f tk= 2.64 MPa, the axial stiffness of the main girder EA0 = 663814 kN, the pier height H = 15 m, the pier size parameters are taken as a = 2.2 m, b = 2.2 m, the uniform temperature rise and fall ΔT = 18 °C, and the linear expansion coefficient of concrete α = 1×10 -5 , the braking force is calculated according to one-way five lanes, and the lateral reduction coefficient P = 0.1×(10.5nL + 360)×5×0.6 = 772.65 kN is considered. The flexural stiffness of a single pier EI = 6.73×10 8 kN·m 2 , then the flexural stiffness of the side-by-side piers is 2EI = 1.35×10 9 kN·m 2 . The restricted rotation stiffness k1 of the main girder on the pier = 7.15×10 7 kN·m / rad, the equivalent rotational spring stiffness at the pile top is k2 = 6.04×10 7 kN·m / rad, and the equivalent horizontal thrust stiffness at the pile top is k3 = 1.47×10 6 kN / m.

[0092] The specific verification process is as follows:

[0093] 1) Referring to Step 1, the cracking stress σ at the edge of the concrete section is obtained cr = 3.788 MPa;

[0094] 2) Referring to Step 2, the cracking moment M is obtained cr = 11960.23 kN·m;

[0095] 3) Referring to Step 3, taking the safety factor as 0.85, the design cracking moment λ[M cr = 10166.20 kN·m;

[0096] 4) Referring to Step 4, k1' = k2' = k3' = 2.49×10 5 kN / m is obtained;

[0097] 5) Referring to Step 5, the actual displacement at the top of the pier is obtained according to Equation (16) as follows:

[0098]

[0099] Furthermore, the maximum moment M at the top of each pier is obtained according to Equation (11) and Equation (12) i as shown in the following table:

[0100] Table 1 Moments at the Tops of Each Pier under Different Pier Heights (Unit: kN·m)

[0101]

[0102] 6) Referring to Step 6, M3' = 13587 > λ[M cr = 10166.20. It is thus judged that the moment value of the side pier exceeds the limit, and its anti-pushing stiffness needs to be adjusted. The anti-pushing stiffness is designed according to the moment value of 0.75[M cr . The new anti-pushing stiffness of the side pier is set as k' = 0.65k. After back substitution, the corrected pier top moment is obtained as shown in the following table:

[0103] Table 2 Corrected Pier Top Moments of Piers (Unit: kN·m)

[0104]

[0105] Due to the reduction of the side pier stiffness, the displacement at the pier top increases, and the internal forces of the middle pier and the secondary side pier increase. It can be seen from the above table that the corrected pier top moments of the secondary side pier and the middle pier do not exceed the limit and meet the force requirements, and the stiffness matching calculation is completed.

[0106] 7) According to the above calculation results, for the rigid frame bridge with pier height H = 15m and span length 7×30m in the example, flexible piers should be set for its side piers, and the stiffness can be set as 0.65 times the stiffness of the rigid pier.

[0107] In view of the lack of research on the stiffness matching design of long-span rigid frame bridges in the background technology, the present invention proposes a method for determining the stiffness matching of piers of multi-span continuous rigid frame bridges. The present invention aims at multi-span continuous integral rigid frame bridges. Based on basic parameters such as bridge pier height and span length, according to the mechanical equilibrium condition, deformation compatibility condition, and constitutive relationship, the design cracking moment and the formula for the maximum moment at the pier top (bottom) of multi-span continuous rigid frame bridges under horizontal force and temperature force are derived. Taking the reference pier stiffness as the initial stiffness, and according to the criterion that the maximum moment is less than the design cracking moment, the stiffness matching design of the piers of the rigid frame bridge is completed. The present invention gives a reasonable matching design process for the anti-pushing stiffness of flexible piers and rigid piers under actual engineering conditions, and establishes a systematic pier stiffness matching design method from the perspective of optimizing the mechanical performance, providing a theoretical support for the stiffness matching design of piers of multi-span continuous rigid frame bridges.

[0108] The present invention derives the theoretical calculation formula for the maximum bending moment of bridge piers under the action of horizontal force and temperature force for any joint length and pier height, and gives the reasonable matching design process of the anti-pushing stiffness of flexible piers and rigid piers in practical engineering; affected by the temperature effect, when the pier is relatively short, the bending moment of the side pier is very large, and flexible piers need to be set. As the pier height increases, the structural flexibility increases, which can effectively reduce the bending moment at the top of the pier. Although the bending moment caused by the horizontal force will increase, the proportion is very small. When the pier is relatively high, the lower structure becomes flexible and can no longer effectively hinder the displacement of the top of the pier, so the bending moment at the top of the pier decreases as the pier height increases; for continuous rigid frame bridges with multiple spans of different numbers, when the pier heights of all piers are greater than a certain fixed value, flexible piers do not need to be set. According to the method for determining the stiffness matching of piers of multi-span continuous rigid frame bridges in the invention, Table 3 shows the pier layout and stiffness distribution of a seven-span long-span continuous rigid frame bridge under different pier height settings.

[0109] Table 3 Pier stiffness distribution of a seven-span long-span continuous rigid frame bridge under different pier height conditions

[0110]

[0111] Those skilled in the art of this technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used here have the same meaning as the general understanding of those of ordinary skill in the field to which this application belongs. It should also be understood that terms defined in general dictionaries should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as here.

[0112] The meaning of "and / or" as described in this application refers to the situation where each exists alone or both exist simultaneously.

[0113] The meaning of "connection" as described in this application can be a direct connection between components or an indirect connection between components through other components.

[0114] Taking the above ideal embodiments of the present invention as inspiration, through the above description, relevant staff can completely make various changes and modifications without departing from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for determining the stiffness matching of piers of a multi-span continuous rigid frame bridge, characterized in that: The method is aimed at multi-span long-connected rigid frame bridges. Taking the basic parameters of the bridge as the input, the formulas for calculating the design cracking moment and the maximum moment at the pier top are deduced. According to the criterion that the maximum moment is less than the design cracking moment, the stiffness matching design of the rigid frame bridge piers is completed. The specific steps are as follows: Step 1: Calculate the cracking stress σ of the concrete section edge under the assumed conditions based on the ultimate tensile strain of the material cr ; Step 2: Calculate the cracking moment \(M\) cr according to the cracking stress \(\sigma\) cr of the concrete section edge obtained in Step 1; cr cr ​​ Step 3: Determine the safety factor λ, and calculate the design cracking moment λ[M cr according to the cracking moment M calculated in Step 2; cr ; Step 4: Calculate the actual thrust resistance stiffness k' of each pier considering the pile-soil interaction effect; Step 5: Combine the calculation results of Step 4 to calculate the maximum moment M at the top of each pier under braking force and temperature force i ; Step 6: Compare the designed cracking moment λ[M cr with the maximum moment M i at the top of each pier to determine whether the moment of the side pier exceeds the designed moment value. If it does not exceed the limit, the structural design is reasonable and the stiffness of the pier remains unchanged; If it exceeds the limit, let the maximum moment M of the pier i be equal to the design cracking moment λ[M cr , obtain the adjusted pier thrust stiffness and return to step 5 to calculate the adjusted pier top moment value. At the same time, perform the discrimination in step 6 on the moment of the secondary side piers, and so on until the forces on all piers are reasonable.

2. The method for determining the pier stiffness matching of a multi-span continuous rigid-frame bridge according to claim 1, characterized in that: The cracking stress σ of the concrete section edge in Step 1 cr The calculation formula is as follows: where f t,r is the representative value of the uniaxial tensile strength of concrete, and its value can be taken as f t , f tk respectively according to the actual structural analysis requirements. E c is the elastic modulus of concrete, and ε t,r is the cracking strain at the edge of the concrete section.

3. The method for determining the pier stiffness matching of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The cracking moment M in Step 2 cr The calculation formula is as follows: Wherein, a is the width of the pier in the transverse direction of the bridge, b is the width of the pier in the longitudinal direction of the bridge, A s is the area of the tension zone of the cross-section, A s ' is the area of the compression zone of the cross-section, σ s is the tensile stress of the reinforcement in the tension zone, σ s ' is the compressive stress of the reinforcement in the compression zone, σ c is the compressive stress of the concrete in the compression zone, σ c ' is the tensile stress of the concrete in the tension zone, d c is the height of the compression zone of the cross-section, d s is the distance from the tensile reinforcement to the neutral axis of the cross-section, d s ' is the distance from the compressive reinforcement to the neutral axis of the cross-section, and N is the axial force of the neutral axis of the cross-section.

4. A method for determining the pier stiffness matching of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The calculation formula for the actual thrust resistance stiffness k' of each pier in Step 4 is as follows: Where: In the formula, the main girder provides a rotational constraint with stiffness k1 to the pier, the pile-soil interaction provides a rotational constraint with stiffness k2 and a horizontal spring constraint with stiffness k3 to the pier, EI is the flexural stiffness of the pier cross-section, H is the pier height, and θ1 ' and θ2 ' are respectively the rotations at the top and bottom of the pier when not considering the equivalent lateral stiffness of the pile foundation.

5. The method for determining the pier stiffness matching of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The maximum moment M at the top of each pier in Step 4 i The calculation formula is as follows: Where: P is the braking force magnitude, H i is the height of each pier, k i ' is the actual lateral stiffness of each pier, K is the total integrated lateral stiffness of the bridge, Δs i ' is the actual horizontal displacement at the top of the pier, m i is the bending moment at the top of the pier under unit displacement of each pier; When n is odd, the actual horizontal displacement value Δs at the top of the pier i ' is calculated by the following formula: When n is an even number, the actual horizontal displacement value Δs at the top of the pier i ' is calculated by the following formula, where Δs1 ' = 0: Where P is the braking force magnitude, H i is the height of each pier, k i ' is the actual lateral stiffness of each pier, K is the total integrated lateral stiffness of the bridge, Δs i ' is the actual horizontal displacement at the pier top, m i is the moment at the pier top under unit displacement of each pier, EA0 is the axial stiffness of the main girder, m t 、m b are the moment at the pier top and the moment at the pier bottom under unit displacement at the pier top respectively, ΔT is the temperature change value, α is the concrete expansion coefficient, and L is the single-span length.

6. The method for determining the pier stiffness matching of a multi-span continuous rigid-frame bridge according to claim 1, wherein: In Step 2, the safety factor λ is taken as 0.75 or 0.85.

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