Method and system for determining arch bridge bending moment increasing coefficient

Abstract

The invention discloses an arch bridge bending moment increasing coefficient determination method and system, and relates to the technical field of arch bridge structure design. Obtaining design parameters of the arch bridge; discretizing a reasonable arch axis of the arch bridge into a series form, and establishing a geometric nonlinear structure response analysis model by combining boundary conditions based on a principle that elastic compression and compression strain are equal along an arc length integral; respectively calculating the total bending moment and the linear bending moment of the arch bridge under the symmetric dead load action through a geometric nonlinear structure response analysis model; calculating an initial bending moment increasing coefficient based on the total bending moment and the linear bending moment; based on the section position distribution of the arch bridge arch rib, determining the applicable values of the bending moment increasing coefficients of different areas, and completing the determination of the arch bridge bending moment increasing coefficient. According to the method, the reasonable arch axis is discretized, the geometric nonlinear analysis model is established, the secondary influence of the axial force on the bending moment is fully considered, the actual bending moment value under the geometric nonlinear effect can be accurately reflected, and the method is suitable for symmetric dead load arch bridges with different spans and different rise span ratios.

Description

Technical Field

[0001] This invention relates to the field of arch bridge structural design technology, and more specifically to a method and system for determining the bending moment amplification factor of an arch bridge. Background Technology

[0002] As bridge spans continue to increase, the ultimate bearing capacity of arch ribs has become increasingly prominent. More and more engineers are finding that the simplified "equivalent beam-column" method used in current bridge codes calculates a significant difference between the cross-sectional bearing capacity of reinforced concrete arch ribs and the actual ultimate bearing capacity. Because the actual stress patterns of arch bridges are not considered, the bending moment amplification factor is overestimated, severely underestimating the true bearing capacity of large-span arch bridges. This leads to an increase in the design size of arch bridges and hinders the further development of arch bridge spans.

[0003] Therefore, how to propose an accurate and efficient method for determining the moment amplification factor based on the actual bearing mechanism of long-span arch bridges is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for determining the moment amplification factor of an arch bridge. Based on the geometric nonlinear analytical theory and bearing mechanism of arch bridges, the moment amplification factor is accurately determined in different regions, taking into account both design accuracy and efficiency.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for determining the bending moment amplification factor of an arch bridge, comprising: Obtain the design parameters of the arch bridge; The reasonable arch axis of the arch bridge is discretized into a series form. Based on the principle that the integral of elastic compression and compressive strain along the arc length is equal, and combined with the boundary conditions, an analytical model of the geometric nonlinear structural response is established. The total bending moment and linear bending moment of the arch bridge under symmetrical dead load were calculated using the analytical model of the geometric nonlinear structural response. The initial bending moment amplification factor is calculated based on the total bending moment and the linear bending moment. Based on the cross-sectional distribution of the arch ribs of the arch bridge, the applicable values ​​of the moment amplification factor in different regions are determined, thus completing the determination of the moment amplification factor of the arch bridge.

[0006] Preferably, the design parameters include span, sag, material elastic modulus, unit weight, design axial compressive stress, linear elastic stability coefficient, and sag-to-span ratio.

[0007] Preferably, discretizing the reasonable arch axis of the arch bridge into a series form includes: discretizing the reasonable arch axis using a cosine series or a polynomial series.

[0008] Preferably, the initial bending moment amplification factor is the ratio of the total bending moment to the linear bending moment, and the linear bending moment under the reasonable arch axis is... The nonlinear bending moment is The initial bending moment increase factor Represented as: ; Where E represents the elastic modulus of the material. represents the horizontal reaction force, This represents the moment of inertia of the arch crown section.

[0009] Preferably, by analyzing the nonlinear bending moment, the control section of the arch crown under symmetrical dead load is obtained, when... When the arch width increases, the expression for the crown moment amplification factor is obtained is: .

[0010] Preferably, the correction formula for the increase factor of the crown bending moment of a variable-height arch under the same parameters is as follows: ; in, , These represent the coefficients for increasing the crown bending moment of arches with varying heights and widths, respectively. , , Let represent the antisymmetric first-order stability coefficient of the arch rib, the axial compressive stress under dead load, and the span, respectively. This is a correction factor.

[0011] The preferred expression for the correction coefficient is as follows: .

[0012] Preferably, a system for determining the bending moment amplification factor of an arch bridge includes: The parameter acquisition module is used to acquire the design parameters of the arch bridge; The model building module is used to discretize the reasonable arch axis of the arch bridge into a series form. Based on the principle that elastic compression and compressive strain are equal along the arc length integral, a geometric nonlinear structural response analytical model is established in combination with boundary conditions. The first calculation module is used to calculate the total bending moment and linear bending moment of the arch bridge under symmetrical dead load using the analytical model of the geometric nonlinear structural response. The second calculation module is used to calculate the initial bending moment amplification factor based on the total bending moment and the linear bending moment. The module for determining the bending moment amplification factor of an arch bridge is used to determine the applicable values ​​of the bending moment amplification factor for different regions based on the cross-sectional location distribution of the arch ribs of the arch bridge, thereby completing the determination of the bending moment amplification factor of the arch bridge.

[0013] As can be seen from the above technical solution, compared with the prior art, this invention discloses a method and system for determining the bending moment amplification factor of an arch bridge. By discretizing a reasonable arch axis and establishing a geometrically nonlinear analytical model, it fully considers the secondary influence of axial force on bending moment, and can accurately reflect the actual bending moment value under geometrically nonlinear effects. It is applicable to symmetrical dead-load arch bridges with different spans and different rise-to-span ratios, providing direct guidance for engineering design. By determining the bending moment amplification factor by region, it avoids the material waste caused by using a uniform extreme value factor for the entire bridge, and effectively reduces the project cost while ensuring structural safety. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0015] Figure 1 The 600m arch rib provided in the embodiments of the present invention ( A schematic diagram showing the distribution and variation of the total bending moment across half the span when the bending moment is at that time. Figure 2 The 600m arch rib provided in the embodiments of the present invention ( A schematic diagram showing the distribution and variation of the total bending moment across half the span when the bending moment is at that time. Figure 3 This is a schematic diagram of the bending moment calculation results under various load levels provided in the embodiments of the present invention; Figure 4 This is a comparative diagram of nonlinear bending moment calculation results provided in an embodiment of the present invention; Figure 5 This is a schematic diagram comparing the differences in the bending moment amplification coefficients of variable-height and variable-width arches provided in an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the distribution and variation law of the bending moment amplification factor provided in an embodiment of the present invention; Figure 7 A schematic diagram of the moment amplification factor of the arch crown section provided in an embodiment of the present invention; Figure 8 This is a schematic flowchart of a method for determining the bending moment amplification factor of an arch bridge, provided by the present invention.

[0016] Figure 9 This invention provides a schematic diagram of a system for determining the bending moment amplification factor of an arch bridge. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] This invention discloses a method for determining the bending moment amplification factor of an arch bridge, such as... Figure 8 As shown, it includes: Obtain the design parameters of the arch bridge; The reasonable arch axis of the arch bridge is discretized into a series form that is easy to solve. Based on the principle that the integral of elastic compression and compressive strain along the arc length is equal, and combined with the boundary conditions (the relative rotation angle between the arch crown and the arch foot is 0), a geometric nonlinear structural response analytical model is established. The total bending moment and linear bending moment of the arch bridge under symmetrical dead load were calculated using the analytical model of the geometric nonlinear structural response. The initial bending moment amplification factor is calculated based on the total bending moment and the linear bending moment. Based on the cross-sectional distribution of the arch ribs of the arch bridge, the applicable values ​​of the moment amplification factor in different regions are determined, thus completing the determination of the moment amplification factor of the arch bridge.

[0019] Specifically, the design parameters include span L, sag f, material elastic modulus E, unit weight γ, and design axial compressive stress σ. m Linear elastic stability coefficient η, rise-to-span ratio S (S=f / L). Span L=400~1000m, rise-to-span ratio f / L=0.17~0.23, design axial compressive stress σ m =8~18MPa, linear elastic stability coefficient η≥4; the arch bridge is a reinforced concrete hingeless arch with a material elastic modulus E≥34.5GPa and a unit weight γ=25~28kN / m 3 .

[0020] Specifically, discretizing the reasonable arch axis of the arch bridge into a series form includes: discretizing the reasonable arch axis using cosine series or polynomial series. The discretized arch axis expression satisfies the force balance requirements under multiple distributed loads and can be accurately adapted to arch bridges with different structural forms such as three-hinged arches and hingeless arches.

[0021] Specifically, for any reasonable arch axis, the distributed load and the arch axis both satisfy the following equation: ; Furthermore, the axis of a reasonable arch can be approximately discretized as: ; get The discrete expression is as follows: .

[0022] Specifically, the initial bending moment amplification factor is the ratio of the total bending moment to the linear bending moment, and the linear bending moment under the reasonable arch axis is... The nonlinear bending moment is The initial bending moment increase factor Represented as: ; Where E represents the elastic modulus of the material. represents the horizontal reaction force, This represents the moment of inertia of the arch crown section.

[0023] Specifically, through analysis of nonlinear bending moments, the control section of the arch crown under symmetrical dead load is obtained, when... When the arch width increases, the expression for the crown moment amplification factor is obtained is: .

[0024] Specifically, the correction formula for the increase factor of the crown bending moment of a variable-height arch under the same parameters is as follows: ; in, , These represent the coefficients for increasing the crown bending moment of arches with varying heights and widths, respectively. , , These represent the antisymmetric first-order stability coefficient of the arch rib, the axial compressive stress under dead load (unit: MPa), and the span (unit: m), respectively. This is a correction factor.

[0025] Specifically, the expression for the correction factor is as follows: .

[0026] In one specific embodiment of the present invention, such as Figure 9 As shown, a system for determining the bending moment amplification factor of an arch bridge includes: The parameter acquisition module is used to acquire the design parameters of the arch bridge; The model building module is used to discretize the reasonable arch axis of the arch bridge into a series form. Based on the principle that elastic compression and compressive strain are equal along the arc length integral, a geometric nonlinear structural response analytical model is established in combination with boundary conditions. The first calculation module is used to calculate the total bending moment and linear bending moment of the arch bridge under symmetrical dead load using the analytical model of the geometric nonlinear structural response. The second calculation module is used to calculate the initial bending moment amplification factor based on the total bending moment and the linear bending moment. The module for determining the bending moment amplification factor of an arch bridge is used to determine the applicable values ​​of the bending moment amplification factor for different regions based on the cross-sectional location distribution of the arch ribs of the arch bridge, thereby completing the determination of the bending moment amplification factor of the arch bridge.

[0027] In a specific embodiment of the present invention, the total bending moment of a long-span arch bridge is expressed as about and The function.

[0028] ; in This indicates the loading process of the structure, when the elastic modulus E of the material is constant. Horizontal reaction force of arch ribs under load and the moment of inertia of the arch section Related, among which The impact can be analyzed by increasing the calculated load, while It is linearly related to the linear elastic stability coefficient, and can be analyzed by setting different linear elastic stability coefficients. The effect on nonlinear bending moment.

[0029] Figure 1 and Figure 2 The calculation results for the total bending moment of the 600m arch rib are given. Considering that current design codes use a safety factor of 1.75 for the ultimate bearing capacity design of large-span arch bridges, the total load is set to 1.75 times the dead load of the arch rib. To analyze the horizontal reaction force of the arch rib... The effect on the total bending moment was calculated by dividing the total load into 10 levels. This was done to analyze the moment of inertia of the arch crown section. Impact on total bending moment Figure 1 and Figure 2 The critical loads for linear elastic instability of the medium structure are designed to be 2 times and 7 times the dead load, respectively.

[0030] Depend on Figure 1 It can be seen that when the load on the arch rib is close to the critical load for instability, the nonlinear effect of the arch rib bending moment is significant. Specifically, the positive bending moment at the arch crown increases nonlinearly with increasing loading force, while the negative bending moment at the arch foot first increases and then decreases. The peak value of the negative bending moment and the inflection point of the arch rib bending moment also shift from the arch foot position to the arch crown position. When the loading force reaches the calculated total load, the peak value of the negative bending moment moves to around L / 8, the inflection point of the arch rib bending moment moves from L / 5 to 2L / 7, and the maximum value of the positive bending moment is located at the arch crown section. Therefore, when the linear elastic instability critical load of the structure is twice that of the load, under the action of 1.75 times the symmetrical dead load, the arch crown section is the control section of the bending moment.

[0031] As can be seen from the expression for the total bending moment of a long-span arch bridge, the total bending moment of the arch structure consists of a cosine term and a polynomial.

[0032] ; As the applied force increases, the horizontal reaction force of the arch rib increases, which in turn leads to a cosine period. As the period decreases, the inflection point of the arch rib bending moment shifts towards the arch crown. When the period is less than l, i.e. At this time, the negative bending moment at the arch foot decreases. (From...) Figure 2 It can be seen that when the load on the arch rib is less than the critical load for instability, the nonlinear effect of the arch rib bending moment is not obvious, and the bending moment of the arch rib across the entire span is approximately linearly increasing. When the loading force reaches the total load, the inflection point of the arch rib bending moment only moves L / 30 towards the top of the arch.

[0033] To further clarify the bending moment variation law of the key sections of the main arch under the reasonable arch axis, a parametric analysis was carried out with the span, axial compressive stress and first-order antisymmetric stability coefficient as variables.

[0034] Figure 3 The results of bending moment calculations under various load levels are as follows: Figure 3 In the figures (a), (b), and (c), the calculation results are shown for arch rib spans of 600m, 800m, and 1000m, respectively. Figure 3 It can be seen that as the stiffness of the arch rib increases, the nonlinear effect of the bending moment is suppressed. When the critical load for the first-order antisymmetric instability of the arch rib reaches 4 times the dead load, the bending moment at the arch crown increases by about 29.5% and the bending moment at the arch foot decreases by about 30% under the action of 1.75 times the dead load. The stress level of the arch rib and the span have little effect on the nonlinear effect of the bending moment; the nonlinear effect of the arch rib bending moment is mainly controlled by the stiffness of the arch rib.

[0035] Specifically, the calculation process for nonlinear incremental bending moment is as follows: To independently analyze the nonlinear incremental effect of the arch structure, the nonlinear effect is isolated from the overall effect and solved separately. The nonlinear bending moment of the arch structure can be expressed as: ; in, ;By boundary conditions ,available: ; From the above equation, we can see that the half-span integral of the arch rib bending moment is equal to 0. This equation is based on the variable-width arch. When the relative rotation angle between the arch crown and the arch foot is 0, it also indicates that a large-span arch bridge with a reasonable arch axis is constructed, and the stiffness of its arch ribs follows the principle of... When distributed, the sum of positive bending moments equals the sum of negative bending moments. This conclusion applies not only to nonlinear bending moments but also to linear bending moments. (The equation is repeated in the original text.) ; Substitute into the following formula: ; get: ; According to the definition of a center of elasticity, we have At the same time, based on nonlinear deflection expression: ; It can be solved The parsing expression is as follows: ; To verify the accuracy of the nonlinear bending moment calculation results of this method, the results of the finite element method and the nonlinear bending moment calculation results of this method are plotted on [the graph]. Figure 4 .

[0036] Depend on Figure 4 It can be seen that the trend of the results obtained by this method is consistent with that of the finite element method, and the numerical values ​​are close. The maximum calculation error is located at the 400m arch rib ( At the mid-span position, the calculated value by this method is 39.8 kN×m, while the simulated value is 45.2 kN×m. The calculated result by this method is 5.4 kN×m smaller than the simulated result, with an error percentage of 11.9%.

[0037] The nonlinear bending moment curves of the arch all exhibit an "M" shape. Within the semi-arch area, the nonlinear bending moment passes through two zero-moment points, exhibiting two positive bending moment peaks at the arch crown and arch foot, and one negative bending moment peak. When the elastic stability coefficient of the arch rib is 2, the two zero-moment points are located near L / 13 and L / 3, respectively, and the negative bending moment peak is located near 3L / 16. When the elastic stability coefficient of the arch rib is 7, the two zero-moment points are located near L / 20 and L / 3, respectively, and the negative bending moment peak is located near L / 6.

[0038] Specifically, the calculation process for the moment amplification factor is as follows: The moment amplification factor is the ratio of the total bending moment to the linear bending moment. The linear bending moment under a reasonable arch axis is... The nonlinear bending moment is Then the bending moment increase factor It can be represented as: ; Through the analysis of nonlinear bending moments, the arch crown section is identified as the controlling section for bending moments under symmetrical dead load. The variation law of the arch crown bending moment amplification factor is further discussed. The bending moment amplification factor... Substitute The analytical expression for the crown moment amplification factor is obtained as follows: ; The aforementioned method describes the nonlinear response analysis for arch bridges with constant height and varying width. However, for arch bridges with constant width and varying height, the equilibrium equations are expressed as follows: ; because For about The function is a second-order differential equation with variable coefficients, and an analytical solution cannot be obtained directly.

[0039] Therefore, to further analyze the moment amplification factor of the equal-width variable-height arch, the moment amplification factors of the variable-width and variable-height arches are compared, and the differences between them are analyzed. The specific parameter ranges of the model are shown in Table 1. The differences in the moment amplification factor at the crown of the 288 variable-width and variable-height arch ribs are statistically analyzed. Figure 5 ,in, Figure 5 In (a) and (b), the range of axial compressive stress of the arch rib under constant load is 8-12 MPa and 14-16 MPa, respectively. The error data in the figure is expressed as (bending moment amplification factor of variable height arch - bending moment amplification factor of variable width arch) / bending moment amplification factor of variable width arch.

[0040] Table 1 Comparison of Stability Coefficient Results

[0041] Depend on Figure 5 It can be seen that, under the same parameters, the increase factor of the crown moment of the variable-height arch is greater than that of the variable-width arch, and the error is less than 9%. The error decreases with the increase of axial compressive stress and arch rib stiffness under dead load, and increases with the increase of span. The error is approximately inversely proportional to the square of the axial compressive stress and the stability coefficient, and approximately directly proportional to the span. Therefore, the corrected calculation formula for the increase factor of the crown moment of the variable-height arch can be obtained as follows: ; in, , These represent the coefficients for increasing the bending moment at the crown of arches with varying heights and widths, respectively. , , These represent the antisymmetric first-order stability coefficient of the arch rib, the axial compressive stress under dead load (unit: MPa), and the span (unit: m), respectively. As a correction factor, based on the calculation results in this paper, it is statistically obtained according to the correction calculation formula for the increase factor of the crown moment of a variable-height arch. The mean is 0.0071.

[0042] .

[0043] Specifically, the applicability analysis of the moment amplification factor is performed as follows: To further analyze the spatial distribution and variation of the moment amplification factor of the arch rib with the loading process, this method was used to calculate the moment amplification factor of a 400m arch rib. The total load was calculated to be 1.75 times the dead load, and the linear elastic stability coefficients of the arch rib under dead load were set to 2, 4, and 6, respectively. The calculation results were plotted on [date missing]. Figure 6 As shown.

[0044] Depend on Figure 7 It can be seen that during the entire loading process, the moment amplification factor at the arch foot is <1, while the moment amplification factor at the arch crown is >1. As the loading force increases, the moment amplification factor at the arch foot decreases while that at the arch crown increases. Consistent with the nonlinear effect of bending moment, the moment amplification factor of the arch rib is also suppressed by stiffness. When the stability coefficient of the arch rib is set to 2, 4, and 6, the moment amplification factor at the arch foot ranges from (0.2 to 1), (0.7 to 1), and (0.8 to 1), while the moment amplification factor at the arch crown ranges from (1 to 2), (1 to 1.3), and (1 to 1.2).

[0045] To further analyze the variation law of the moment amplification factor at key sections, the moment amplification factor at the arch crown section was calculated using this method. Parametric analysis was carried out with span, axial compressive stress, and first-order antisymmetric stability coefficient as variables. The calculation results were plotted on [date missing]. Figure 7 .

[0046] Depend on Figure 7 It can be seen that the moment amplification factor of the arch crown section increases with the increase of the loading force and the axial compressive stress of the arch rib under dead load, and decreases with the increase of the span and the stiffness of the arch rib. When the stability coefficient of the arch rib is set to 2 and the axial compressive stress of the arch rib under dead load is 16MPa, the moment amplification factors of the arch crown section of the 400m, 600m, and 800m arch bridges are 2.3, 2.05, and 1.9, respectively.

[0047] The above analysis shows that the moment amplification factor is a function of the horizontal reaction force of the arch rib. and location The coefficient of change. Looking at the distribution of the moment amplification coefficient across the entire span, during the entire loading process, the moment amplification coefficient increases progressively from the arch foot to L / 16 and is always <1, approximating 1 near L / 16. The moment amplification coefficient in the range from L / 16 to L / 3 initially increases non-linearly from 1, and at the arch's elastic center... (Near L / 4), the linear bending moment is 0, and the bending moment amplification factor increases to positive infinity. Within the range of L / 4 to L / 3, the bending moment amplification factor increases from negative infinity to 1. From L / 3 to the arch crown, the bending moment amplification factor increases progressively and is always greater than 1. At this point, if internal force adjustments are made based on a reasonable arch axis to reduce the linear bending moment during the completed bridge stage under dead load, then a very large bending moment amplification factor will appear on all arch ribs.

[0048] Therefore, the moment amplification factor varies significantly across different sections of the arch rib span, and it does not increase across all sections; some regions have a value less than 1, while others exhibit extremely high values. Furthermore, the moment amplification factor changes differently across different sections with increasing loading force, decreasing at the arch foot and increasing at the arch crown. In this case, the moment amplification factor is no longer suitable for characterizing the nonlinear effect of the bending moment.

[0049] Therefore, in order to achieve refined design of ultra-long span arch bridges, the nonlinear bending moment effect throughout the entire span and loading process needs to be obtained, and the total bending moment expression of long span arch bridges can be used for calculation.

[0050]

[0051] Based on the method of this invention, the incremental bending moment of a long-span arch bridge caused by geometric nonlinearity was analyzed, and an analytical formula for the moment amplification factor under symmetrical dead load was obtained, providing theoretical support for the second-order design of arch bridge sections. Analysis shows that when the dead load linear elastic stability coefficient is 4, the moment amplification factor of the 400m arch rib is <1.3.

[0052] The moment amplification factor varies significantly across different sections of the arch rib span, and it is not amplified across all sections; some regions have a value less than 1, while others exhibit extremely high values. Therefore, for a conservative approach, the nonlinear effect of moment amplification can be disregarded within the range from the arch foot to L / 3. However, for the region from L / 3 to the arch crown, assuming the stiffness meets a factor of 4 times the linear elastic stability coefficient, a moment amplification factor of 1.3 is recommended for the arch crown section.

[0053] Therefore, during rapid design, considering the symmetrical dead load, the moment amplification factor increases progressively from the arch foot to L / 16 and is always <1. Although the moment amplification factor is large in the range from L / 16 to L / 3, the linear elastic moment is small and does not control the design, so it can be conservatively considered as 1, i.e., the moment amplification factor is not considered. However, the moment amplification factor increases progressively from L / 3 to the arch crown and is always >1. In this case, the nonlinear effect of the moment can be approximated by the moment amplification factor.

[0054] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0055] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for determining the bending moment amplification factor of an arch bridge, characterized in that, include: Obtain the design parameters of the arch bridge; The reasonable arch axis of the arch bridge is discretized into a series form. Based on the principle that the integral of elastic compression and compressive strain along the arc length is equal, and combined with the boundary conditions, an analytical model of the geometric nonlinear structural response is established. The total bending moment and linear bending moment of the arch bridge under symmetrical dead load were calculated using the analytical model of the geometric nonlinear structural response. The initial bending moment amplification factor is calculated based on the total bending moment and the linear bending moment. Based on the cross-sectional distribution of the arch ribs of the arch bridge, the applicable values ​​of the moment amplification factor in different regions are determined, thus completing the determination of the moment amplification factor of the arch bridge.

2. The method for determining the bending moment amplification factor of an arch bridge according to claim 1, characterized in that, The design parameters include span, sag, material elastic modulus, unit weight, design axial compressive stress, linear elastic stability coefficient, and sag-to-span ratio.

3. The method for determining the bending moment amplification factor of an arch bridge according to claim 1, characterized in that, Discretizing the reasonable arch axis of the arch bridge into a series form includes: using cosine series or polynomial series to discretize the reasonable arch axis.

4. The method for determining the bending moment amplification factor of an arch bridge according to claim 1, characterized in that, The initial bending moment amplification factor is the ratio of the total bending moment to the linear bending moment. The linear bending moment under the reasonable arch axis is... The nonlinear bending moment is The initial bending moment increase factor Represented as: ； Where E represents the elastic modulus of the material. represents the horizontal reaction force, This represents the moment of inertia of the arch crown section.

5. The method for determining the bending moment amplification factor of an arch bridge according to claim 4, characterized in that, By analyzing the nonlinear bending moment, the control section of the arch crown under symmetrical dead load is obtained. When the arch width increases, the expression for the crown moment amplification factor is obtained is: 。 6. The method for determining the bending moment amplification factor of an arch bridge according to claim 5, characterized in that, The correction formula for the increase factor of the crown bending moment of a variable-height arch under the same parameters is as follows: ； in, , These represent the coefficients for increasing the crown bending moment of arches with varying heights and widths, respectively. , , Let represent the antisymmetric first-order stability coefficient of the arch rib, the axial compressive stress under dead load, and the span, respectively. This is a correction factor.

7. The method for determining the bending moment amplification factor of an arch bridge according to claim 1, characterized in that, The expression for the correction factor is as follows: 。 8. A system for determining the bending moment amplification factor of an arch bridge, characterized in that, include: The parameter acquisition module is used to acquire the design parameters of the arch bridge; The model building module is used to discretize the reasonable arch axis of the arch bridge into a series form. Based on the principle that elastic compression and compressive strain are equal along the arc length integral, a geometric nonlinear structural response analytical model is established in combination with boundary conditions. The first calculation module is used to calculate the total bending moment and linear bending moment of the arch bridge under symmetrical dead load using the analytical model of the geometric nonlinear structural response. The second calculation module is used to calculate the initial bending moment amplification factor based on the total bending moment and the linear bending moment. The module for determining the bending moment amplification factor of an arch bridge is used to determine the applicable values ​​of the bending moment amplification factor for different regions based on the cross-sectional location distribution of the arch ribs of the arch bridge, thereby completing the determination of the bending moment amplification factor of the arch bridge.

Images