Steel tube concrete parabolic arch out-of-plane stability bearing capacity prediction method and system

Abstract

This invention provides a method and system for predicting the out-of-plane stability bearing capacity of a parabolic arch made of steel-concrete composite tubular (SCCB) structure, belonging to the field of SCCB structures. To address the problem that existing SCCB arch bearing capacity calculation methods only consider in-plane stability and, based on experience, require an elastic stability safety factor of not less than 4, cannot directly obtain the out-of-plane stability bearing capacity, this invention proposes a regularized slenderness ratio calculation method that considers the influence of non-directional forces, considering the factors affecting the out-of-plane stability bearing capacity of the parabolic arch. For initial stress, a method for calculating the initial stress influence amplification factor is proposed; for creep, a method for calculating the creep influence amplification factor is proposed; and a modified Perry formula is used to obtain a stability coefficient calculation method, thereby obtaining the out-of-plane stability bearing capacity. This invention does not rely on parameter analysis, greatly simplifying the parameter analysis process. The stability bearing capacity calculation formula is simple, and the arch is transformed into an axially compressed column, solving the problem of introducing the influence of initial stress and creep into the arch stability bearing capacity formula.

Description

Technical Field

[0001] This invention relates to the field of concrete-filled steel tube structures, and more specifically, to a method and system for predicting the stable bearing capacity of a parabolic arched plane in a concrete-filled steel tube. Background Technology

[0002] Steel-concrete composite arch bridges are widely used in my country due to their high load-bearing capacity, ease of construction, and aesthetic appeal. To date, over 600 such bridges have been built nationwide, with the largest span reaching 575 meters. As the span of steel-concrete composite arch bridges increases, the slenderness ratio of the arch ribs increases while the width-to-span ratio decreases, leading to increasingly apparent out-of-plane stability issues for the arch ribs. For mid- and under-deck steel-concrete composite arch bridges with cable ties, the non-directional forces acting on the bridge deck system must also be considered. Furthermore, the stress process of large-span steel-concrete composite arches is complex, and the initial stress generated during construction and the creep of the core concrete during load-bearing periods significantly impact the out-of-plane stability of the arch ribs. Statistics show that the arch axes of steel-concrete composite arch bridges are predominantly parabolic and catenary, accounting for 97% of the total, with parabolic arches being the most widely used, accounting for 54%. However, most of the design provisions for steel-concrete composite arches in my country focus on in-plane stability design, with only circular arch design provisions including out-of-plane stability design. Specifically, the existing standard, "Technical Specification for Steel-Concrete Composite Arch Bridges" GB50923-2013, only provides the design formula for in-plane stability bearing capacity. Regarding out-of-plane stability design, it only suggests a minimum elastic stability safety factor of 4. This suggested value is empirical and requires finite element analysis; furthermore, it cannot directly determine the out-of-plane stability bearing capacity. This invention aims to address this deficiency.

[0003] Therefore, it is urgent to propose a method for predicting the stable bearing capacity of a parabolic arch of a steel-concrete composite tube that considers non-directional forces and the entire stress process. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] To address the issue that existing methods for calculating the bearing capacity of steel-concrete composite arches only consider in-plane stability and require an elastic stability safety factor of not less than 4, which is an empirical value that needs to be combined with finite element analysis and cannot directly yield the in-plane stable bearing capacity.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for predicting the plane stability bearing capacity of a steel-concrete composite parabola, comprising the following steps:

[0008] S100. Determine the basic parameters affecting the outward plane stability bearing capacity of the steel-concrete composite parabolic arch. The basic parameters include: span, rise-to-span ratio, outer diameter of the steel tube, thickness of the steel tube; elastic modulus of the steel, strength grade of the steel, strength grade of the concrete, elastic modulus of the concrete; axial force at the arch foot during the construction and load-bearing stages.

[0009] S200, Regularized slenderness ratio calculated based on the energy method in stability theory, considering the influence of non-orthotropic forces;

[0010] S300. Based on the formula for the equivalent relative initial bending coefficient proposed through extensive parameter analysis, the equivalent relative initial bending coefficient considering the influence of non-coaxial force is calculated.

[0011] S400, Amplification factor of initial stress influence calculated based on second-order elastic analysis;

[0012] S500, calculation of creep effect amplification factor based on second-order elasticity analysis;

[0013] S600, based on the stable bearing capacity formula modified from the Perry formula, calculates the stable bearing capacity of the parabolic arch-shaped concrete tube considering non-directional forces and the entire stress process.

[0014] Further, in step S200, the regularized aspect ratio is:

[0015]

[0016] In the formula, The regularized slenderness ratio representing a concrete-tube arch; Represents the axial compressive strength of the concrete-filled steel tube section; This represents the critical axial force for buckling of a concrete-filled steel tube arch at the arch foot. Represents the flexural stiffness of the steel-concrete composite section; H represents the equivalent length coefficient of the concrete-filled steel tube arch; H / L represents the rise-to-span ratio.

[0017] Further, in step S300, the equivalent relative initial bending coefficient is,

[0018]

[0019] In the formula, This represents the equivalent relative initial bending coefficient.

[0020] Furthermore, in step S400, the amplification factor for the influence of initial stress is,

[0021]

[0022] In the formula, This represents the amplification factor of the initial stress effect; This represents the axial force borne by the steel pipe at the arch foot during the construction phase; This represents the critical axial force for buckling of a hollow steel tube arch at the arch foot. This represents the bending stiffness of the hollow steel pipe section; This represents the equivalent length coefficient of the hollow steel pipe arch.

[0023] Furthermore, in step S500, the creep effect amplification factor is,

[0024]

[0025] In the formula, This represents the amplification factor of the creep effect; The critical axial force at the arch foot of a steel-concrete composite arch during the load-bearing stage represents the buckling critical axial force. N represents the flexural stiffness of the steel-concrete composite section considering the effects of creep; L This represents the axial force at the arch foot during the load-bearing stage.

[0026] Furthermore, in step S600, the stable bearing capacity of the steel-concrete composite parabolic arch is,

[0027]

[0028] In the formula, Represents the plane stability bearing capacity (N) of the steel-concrete composite parabola. This represents the stability coefficient of the parabolic arch of the steel-concrete composite tube.

[0029] A system for predicting the plane stability bearing capacity of a steel-concrete composite parabola is provided. This system has program modules corresponding to the steps described above, and executes the steps in the method for predicting the plane stability bearing capacity of a steel-concrete composite parabola during operation.

[0030] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of a method for predicting the planar stability bearing capacity of a steel-concrete composite parabolic arch.

[0031] Compared with the prior art, the beneficial effects of the present invention are:

[0032] This invention derives the critical buckling force of a steel-concrete composite parabolic arch-shaped rib considering non-orienting forces using the energy method in stability theory. Based on this definition, the regularized slenderness ratio can effectively reflect the influence of various parameters on the stable bearing capacity of the arch rib, thus simplifying the formula for the fitted equivalent relative initial bending coefficient. Through second-order elastic analysis—that is, by establishing static equilibrium equations for the deformable structure and solving the differential equations—the amplification factors of initial stress and creep are obtained, leading to the stable bearing capacity of the steel-concrete composite parabolic arch-shaped rib considering non-orienting forces and the entire stress process. In summary, the prediction method of this invention has the following advantages:

[0033] (1) The critical buckling force of parabolic arches in previous technologies was obtained by fitting parameters through parameter analysis, which is not applicable outside the range of fitted parameters. However, the critical buckling force of parabolic arches protruding from the plane proposed in this invention is derived from stability theory and does not rely on parameter analysis, making it more practical.

[0034] (2) In the past, the regularized slenderness ratio was derived from the buckling critical force definition, which had an unclear physical meaning and required a lot of parameter analysis to fit the stable bearing capacity calculation formula, and the formula was complicated. However, the regularized slenderness ratio of the present invention, based on the derived buckling critical force definition, greatly simplifies the parameter analysis process and the stable bearing capacity calculation formula is simple.

[0035] (3) Previous technologies that considered the amplification factor of initial stress and creep effects were only applicable to axially compressed columns. The equivalent length factor derived by the present invention based on stability theory can transform the arch into a column, thus solving the problem of introducing the effects of initial stress and creep into the arch stability bearing capacity formula.

[0036] (4) Existing standards require that the elastic stability safety factor be no less than 4, which is an empirical value and is conservative. The formula proposed in this invention makes up for the lack of existing standards on the design formula for out-of-plane stability bearing capacity, and is convenient for optimization design. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch in an embodiment of the present invention.

[0038] Figure 2 This is a schematic diagram of the elevation and cross-section of a steel-concrete composite parabolic arch in an embodiment of the present invention. Detailed Implementation

[0039] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0040] Specific Implementation Plan 1: Combining Figure 1As shown, this invention provides a method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch, comprising the following steps:

[0041] S100. Determine the basic parameters affecting the outward plane stability bearing capacity of the steel-concrete composite parabolic arch: span, rise-to-span ratio, outer diameter of the steel tube, thickness of the steel tube; elastic modulus of the steel, strength grade of the steel, strength grade of the concrete, elastic modulus of the concrete; axial force at the arch foot during the construction and load-bearing stages.

[0042] The span, rise-to-span ratio, outer diameter of the steel pipe, and thickness of the steel pipe; the elastic modulus of the steel and the elastic modulus of the concrete are used to calculate the flexural stiffness of the steel-concrete composite section; the span, rise-to-span ratio, outer diameter of the steel pipe, and thickness of the steel pipe; the strength grade of the steel and the strength grade of the concrete are used to calculate the axial compressive strength of the steel-concrete composite section.

[0043] S200. Calculate the regularized slenderness ratio considering the influence of non-directional forces, based on the formula derived from the energy method in stability theory:

[0044]

[0045] In the formula, The regularized slenderness ratio representing a concrete-tube arch; The axial compressive strength (N) of the steel-concrete composite section is calculated according to the relevant formulas in the standard "Code for Design of Steel-Concrete Composite Structures" GB50936-2014. The critical axial force (N) at the foot of the concrete-filled steel tube arch represents the buckling critical axial force. Represents the flexural stiffness of the steel-concrete composite section (Nmm). 2 ); H / L represents the equivalent length coefficient of the concrete-filled steel tube arch; H / L represents the rise-to-span ratio.

[0046] In this step, the specific derivation process is as follows:

[0047] The key to this step lies in the critical buckling axial force N. cr The derivation is as follows: The detailed derivation process based on the energy method in stability theory is as follows:

[0048] The total potential energy equation for a steel-concrete composite arch experiencing planar instability is:

[0049]

[0050] In the formula, ρ is the total potential energy when the steel-concrete composite arch experiences planar instability; ρ is the radius of curvature of the parabola. For the torsional stiffness of the steel-concrete composite section; θ is the radius of gyration of the steel-concrete composite section; M is the bending moment; N is the axial force; u and ϕ are the buckling shape functions; θ is the angular coordinate of the arch rib, i.e., the angle between the tangent of the arch rib and the horizontal line; α is the angular coordinate of the arch foot; q is the uniformly distributed load acting on the arch rib; Y is the vertical coordinate of the arch.

[0051] The radius of curvature ρ of the parabola in equation A1 can be calculated by the following formula:

[0052]

[0053] The radius of gyration of the steel-concrete composite section in Equation A1 Calculated by the following formula:

[0054]

[0055] The bending moment M and axial force N in equation A1 are solved using the force method:

[0056]

[0057] Solving for the critical axial force N of buckling using the energy method cr A key factor is assuming a reasonable buckling shape function, namely u and ϕ in equation A1. Based on extensive finite element parameter analysis, the following buckling shape function can be used to obtain the critical buckling axial force N with high accuracy. cr Approximate solution:

[0058]

[0059] Where u0 and ϕ0 are the maximum values ​​of lateral displacement and torsional angle when the arch rib experiences planar instability; s and X are the arc length coordinates and span coordinates of each point on the arch rib with the left arch foot as the origin; S is the length of the arch axis; and L is the span of the arch.

[0060] Substituting the buckling shape function into equation A1 transforms the total potential energy equation into equation A2:

[0061]

[0062] It should be noted that the process of transforming equation A1 into A2 involves complex integral calculations, which require programming calculations using mathematical software.

[0063] According to the principle of stationary potential energy, the following equation holds:

[0064]

[0065] The premise for equation A3 to have a non-zero solution is that its coefficient determinant is 0, that is:

[0066]

[0067] Solving equation A4 will yield the critical buckling axial force N. cr Through extensive parameter analysis, it was found that it is strongly correlated with the span-to-span ratio, and the following calculation formula is finally given:

[0068]

[0069] S300. Calculate the equivalent relative initial bending coefficient considering the influence of non-conserving forces, based on the formula for the equivalent relative initial bending coefficient proposed through extensive parameter analysis:

[0070]

[0071] In the formula, Represents the equivalent relative initial bending coefficient;

[0072] S400, Calculate the amplification factor of the initial stress effect, based on second-order elastic analysis:

[0073]

[0074] In the formula, This represents the amplification factor of the initial stress effect; This represents the axial force (N) borne by the steel pipe at the arch foot during the construction phase. This represents the critical axial force for buckling of a hollow steel tube arch at the arch foot. Represents the bending stiffness of the hollow steel pipe section (N / mm²) 2 ); The equivalent length coefficient of the hollow steel pipe arch;

[0075] In this step, the specific derivation process is as follows:

[0076] According to the theory of elastic stability, the equilibrium differential equation for an axially compressed column with an initial defect δ0 is:

[0077]

[0078] In the formula, δ represents the additional deflection when the axially compressed column becomes unstable;

[0079] Solving the above differential equation yields the amplified deflection in the column as follows:

[0080]

[0081] Based on the above conclusions, under axial force N L Under the action of the load, when the effect of the initial stress is not considered, the deflection in the column is: :

[0082]

[0083] When considering the effect of initial stress, since only the steel pipe is working during the initial stress stage, the axial force is N. pre The deflection in the column is :

[0084]

[0085] When the concrete and steel pipe work together, the axial force further increases to N. L At that time, the deflection in the column is :

[0086]

[0087] Therefore, the initial stress amplification factor can be obtained:

[0088]

[0089] S500, Calculate the creep effect amplification factor based on second-order elastic analysis:

[0090]

[0091] In the formula, This represents the amplification factor of the creep effect; The critical axial force (N) at the arch foot of a steel-concrete composite arch during the load-bearing stage represents the buckling critical axial force of the arch. The flexural stiffness (N / mm²) of the steel-concrete composite section considering creep effects. 2 When calculating, simply reduce the concrete elastic modulus by half; N L This represents the axial force at the arch foot during the load-bearing stage;

[0092] In this step, the specific derivation process is as follows:

[0093] Under axial force N u Under the action of creep, the deflection in the column is, without considering the effect of creep. :

[0094]

[0095] When creep is considered, the axial force is N. L At that time, the deflection in the column is :

[0096]

[0097] The axial force is further increased to N. u At that time, the deflection in the column is :

[0098]

[0099] Therefore, the creep amplification factor can be obtained:

[0100]

[0101] S600. Calculate the stable bearing capacity of the parabolic arch of a steel-concrete composite tube considering non-directional forces and the entire stress process. The calculation is based on the stable bearing capacity formula modified from the Perry formula:

[0102]

[0103] In the formula, Represents the plane stability bearing capacity (N) of the steel-concrete composite parabola. This represents the stability coefficient of the parabolic arch of the steel-concrete composite tube.

[0104] Specific Implementation Scheme 2: The present invention provides a system for predicting the stable bearing capacity of a steel-concrete composite parabolic arch. This system has a program module corresponding to the above steps, and executes the steps in the above-described method for predicting the stable bearing capacity of a steel-concrete composite parabolic arch.

[0105] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0106] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, the steps of a method for predicting the stable bearing capacity of a parabolic arch-shaped concrete tube.

[0107] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0108] Example

[0109] For ease of use by designers, combined with Figure 2 As shown, taking the following steel-concrete parabolic arch as an example, the calculation process in the invention is described in detail.

[0110] A steel-concrete parabolic arch has a span L = 120m, a rise-to-span ratio H / L = 0.25, an outer diameter D = 275.5mm, and a thickness t = 2.7mm. What is the yield strength f of the steel? y =355 MPa, concrete compressive strength f c =33.5 MPa, steel elastic modulus E s =2.06×10 5 MPa, elastic modulus of concrete E c =3.28×10 4 MPa. Axial force N at the arch foot during construction phase. pre =4.16×10 7 N, axial force at the arch foot during the load-bearing stageL =1.64×10 8 N, calculate its out-of-plane stable bearing capacity considering non-directional forces and the entire process of force application.

[0111] untie:

[0112] (1) Calculation of regularized slenderness ratio

[0113] The axial compressive strength N0 of the steel-concrete composite section is calculated according to the relevant formula in the standard "Code for Design of Steel-Concrete Composite Structures" GB50936-2014. The calculation result is given here: N0 = 3.42 × 10⁻⁶. 8 N.

[0114] The flexural stiffness of the steel-concrete composite section is:

[0115]

[0116] The equivalent length factor for a steel-concrete composite arch is:

[0117]

[0118] The critical axial force for buckling of a steel-concrete composite arch at the arch foot is:

[0119]

[0120] The regularized slenderness ratio of a steel-concrete composite arch is:

[0121]

[0122] (2) Calculation of equivalent relative initial bending coefficient:

[0123]

[0124] (3) Calculation of the amplification factor of the influence of initial stress.

[0125] The bending stiffness of the hollow steel pipe section is:

[0126]

[0127] The equivalent length factor for an empty steel pipe arch is:

[0128]

[0129] The critical axial force for buckling of a hollow steel tube arch at the arch foot is:

[0130]

[0131] The amplification factor for the effect of initial stress is:

[0132]

[0133] (4) Calculation of creep effect amplification factor,

[0134] The flexural stiffness of the steel-concrete composite section considering creep is:

[0135]

[0136] The critical axial force for buckling at the arch foot of a steel-concrete composite arch during the load-bearing stage is:

[0137]

[0138] The creep effect amplification factor is:

[0139]

[0140] (5) Calculate the plane stability bearing capacity.

[0141] The out-of-plane stability coefficient is:

[0142]

[0143] The out-of-plane stable bearing capacity is:

[0144] .

[0145] The existing standard, "Technical Specification for Steel-Concrete Composite Arch Bridges" GB50923-2013, requires an elastic stability safety factor of not less than 4, i.e., N. cr / N u ≥4, in the example:

[0146] Note that this does not mean that the formula proposed in this invention does not meet the requirements of the specifications. On the contrary, the existing specifications require that the elastic stability safety factor be no less than 4, which is an empirical value and is conservative. The formula proposed in this invention makes up for the lack of existing specifications regarding the design formula for out-of-plane stability bearing capacity and facilitates optimization design.

[0147] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for predicting the planar stability bearing capacity of a steel-concrete composite parabolic arch, characterized in that, Includes the following steps: S100. Determine the basic parameters affecting the outward plane stability bearing capacity of the steel-concrete composite parabolic arch. The basic parameters include: span, rise-to-span ratio, outer diameter of the steel tube, thickness of the steel tube; elastic modulus of the steel, strength grade of the steel, strength grade of the concrete, elastic modulus of the concrete; axial force at the arch foot during the construction and load-bearing stages. S200, Regularized slenderness ratio calculated based on the energy method in stability theory, considering the influence of non-orthotropic forces; S300. Based on the formula for the equivalent relative initial bending coefficient proposed through extensive parameter analysis, the equivalent relative initial bending coefficient considering the influence of non-coaxial force is calculated. S400, Amplification factor of initial stress influence calculated based on second-order elastic analysis; S500, calculation of creep effect amplification factor based on second-order elasticity analysis; S600, based on the stable bearing capacity formula modified from the Perry formula, calculates the stable bearing capacity of the parabolic arch-shaped concrete tube considering non-directional forces and the entire stress process.

2. The method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch as described in claim 1, characterized in that: In step S200, the regularized slenderness ratio is: In the formula, The regularized slenderness ratio representing a concrete-tube arch; Represents the axial compressive strength of the concrete-filled steel tube section; This represents the critical axial force for buckling of a concrete-filled steel tube arch at the arch foot. Represents the flexural stiffness of the steel-concrete composite section; H represents the equivalent length coefficient of the concrete-filled steel tube arch; H / L represents the rise-to-span ratio.

3. The method for predicting the stable bearing capacity of a parabolic arched steel-concrete composite structure according to claim 2, characterized in that: In step S300, the equivalent relative initial bending coefficient is, In the formula, This represents the equivalent relative initial bending coefficient.

4. The method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch as described in claim 3, characterized in that: In step S400, the amplification factor of the initial stress effect is, In the formula, This represents the amplification factor of the initial stress effect; This represents the axial force borne by the steel pipe at the arch foot during the construction phase; This represents the critical axial force for buckling of a hollow steel tube arch at the arch foot. This represents the bending stiffness of the hollow steel pipe section; This represents the equivalent length coefficient of the hollow steel pipe arch.

5. The method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch as described in claim 4, characterized in that: In step S500, the creep effect amplification factor is, In the formula, This represents the amplification factor of the creep effect; The critical axial force at the arch foot of a steel-concrete composite arch during the load-bearing stage represents the buckling critical axial force. N represents the flexural stiffness of the steel-concrete composite section considering the effects of creep; L This represents the axial force at the arch foot during the load-bearing stage.

6. The method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch as described in claim 5, characterized in that: In step S600, the stable bearing capacity of the steel-concrete composite parabolic arch extending outward is: In the formula, Represents the plane stability bearing capacity (N) of the steel-concrete composite parabola. This represents the stability coefficient of the parabolic arch of the steel-concrete composite tube.

7. A system for predicting the planar stability bearing capacity of a steel-concrete composite parabolic arch, characterized in that: The system has a program module corresponding to the steps of any one of the claims 1-6 above, and executes the steps in the above-described method for predicting the stable bearing capacity of a parabolic arched steel tube concrete structure when it is run.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the method for predicting the plane stability bearing capacity of a steel-concrete composite parabolic arch as described in any one of claims 1-6.

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