Direct calculation method, medium and equipment for load resistance partial coefficient based on moment method

Abstract

The present invention discloses a method, medium and equipment for directly calculating the load resistance partial coefficient based on the moment method, which belongs to the field of ballastless track. By establishing a structural limit state function and setting a corresponding calculation formula, the method can successively complete μ Rcheck 、μ G , σ G , α 3G , β 2Tcheck The calculation of parameters such as , and then the structural resistance design value μ can be calculated R , and on this basis complete the target second-order reliability index β 2T The method of direct calculation of load resistance partial coefficients based on the moment method of the present invention is simple and easy to calculate. It can quickly realize the direct calculation of structural resistance design value and load resistance partial coefficient, simplify the calculation process of engineering structure reliability design, avoid the iterative calculation process of the existing design process, shorten the reliability design cycle, improve the efficiency of reliability design, meet the actual needs of engineering applications, and have good practical value and realistic significance.

Description

Technical Field

[0001] The present invention belongs to the field of ballastless track and relates to a method, medium and equipment for directly calculating a load resistance partial coefficient based on the moment method, and in particular to a method, variable storage medium and computer equipment for directly calculating a load resistance partial coefficient based on the moment method. Background Art

[0002] Under the influence of loads, environmental factors, and internal material factors, the structural performance of engineering structures will gradually decline, reducing their reliability and shortening their service life. However, current structural design theories do not fully consider issues such as structural performance degradation and durability, and cannot accurately reflect the safety of structures throughout their entire life cycle.

[0003] Structural engineering typically consumes enormous amounts of energy and materials. The ever-expanding scale of construction not only damages the ecology and pollutes the environment, but also increases the burden on nature and puts limited resources at risk of depletion. Furthermore, the costs of inspection, repair, and reinforcement due to the lack of durability in structural engineering also place a significant burden on society's further development. Therefore, in order to improve the design reliability of structural engineering, an effective design theory is essential. This is also the fundamental reason for the rapid development of structural reliability theory. Based on this theory, people can determine the safety and reliability strength of structures from a probabilistic perspective, further improving the accuracy of engineering structural design.

[0004] With the development and application of structural reliability theory, the design method has evolved from a structural design method characterized by allowable stress to one characterized by probability theory and limit states. In engineering structure design standards, the use of limit state design methods based on probability theory is a common development trend in the current international structural engineering field. Reliability-based engineering structure design can be achieved by using a full probability method that directly calculates the probability of structural failure or by using the load and resistance partial factor method (LRFD). Since the load and resistance partial factor method does not require the calculation of the failure probability of the structure, it is very practical and effective. This method has been widely used in structural design specifications in various countries. my country's current engineering structure design standards adopt the probabilistic limit state design principle and partial factor design expression.

[0005] At present, the load resistance coefficient is usually determined by the First-Order Reliability Method (FORM). The calculation process is as follows: Figure 2As shown in . Although the FORM design can meet the calculation requirements of load-resistance partial factors to a certain extent, it still has significant limitations. This is because the FORM method is applicable only because the probability distribution functions of all basic random variables involved in structural reliability analysis are known. Its calculation process is complex, requiring derivatives and double iterative loops, and suffers from double convergence problems. It cannot provide explicit calculation formulas for load and resistance partial factors, making the related design process cumbersome and lengthy, and has certain design limitations. Summary of the Invention

[0006] In response to one or more of the above-mentioned defects or improvement needs in the prior art, the present invention provides a method, medium and equipment for directly calculating the load resistance partial coefficient based on the moment method, which can obtain the display calculation formula of the load resistance partial coefficient, realize the direct calculation of the load resistance partial coefficient, reduce the difficulty of obtaining the load resistance partial coefficient, and simplify the reliability design process of engineering structures.

[0007] To achieve the above object, one aspect of the present invention provides a method for directly calculating the load resistance partial coefficient based on the moment method, comprising the following steps:

[0008] S1: Establish the structural limit state function G(X);

[0009] G(X)=R-∑S i (1)

[0010] Where R is the random variable representing resistance, S i is a random variable representing the load effect;

[0011] S2: Calculated resistance value μ Rcheck ;

[0012]

[0013] Where V R is the coefficient of variation of the resistance random variable R, which obeys the lognormal distribution; V R =σ R / μ R , μ R and σ R are the mean and standard deviation of resistance R; μ Si is the load effect S i The mean of

[0014] S3: Calculate the mean μ of the structural limit state function G(X) G , standard deviation σ G and skewness α 3G ;

[0015] μ G =μR -∑μ Si (3)

[0016]

[0017]

[0018] Where μ R and σ R are the mean and standard deviation of resistance R, and μ R The calculated μ Rcheck Substitute into the calculation; μ Si and σ Si are the load effects S i The mean and standard deviation of α 3R , α 3Si are resistance R and load effect S respectively i skewness;

[0019] S4: α obtained in S3 3G Substitute into formula (6) and calculate the target second-order reliability index verification value β 2Tcheck ;

[0020]

[0021] Where, β T It is the target reliability index of structural design, and its value is determined according to the corresponding structural design code;

[0022] S5: Determine the structural resistance design value μ according to formula (7) R ;

[0023] In the formula, the coefficient ω R and ω S are the derived coefficients of resistance R and load effect S respectively;

[0024] S6: μ obtained in S5 R Substituting into equations (3) to (5), calculate μ G , σ G and α 3G , and calculate the resistance R and load effect S according to the following formula i The separation coefficient α R With α Si ;

[0025] α R =σ R / σ G (10)

[0026] α Si =σ Si / σG (11)

[0027] S7: α obtained in S6 3G Substitute into formula (6) to calculate the target second-order reliability index β 2T ;

[0028] S8: Determine the load resistance partial coefficients φ and γ according to formula (12) and formula (13);

[0029]

[0030]

[0031] Where R n is the standard value of resistance, S ni is the standard value of load effect, both of which are determined through actual measurement and data statistics.

[0032] As a further improvement of the present invention, in S4, the applicable range of formula (6) is: |α 3G |≤1.

[0033] As a further improvement of the present invention, in S5, the coefficient ω R and ω S The calculations are obtained by the following formulas:

[0034]

[0035] Where V S To combine all load effects S i As the coefficient of variation of an overall effect random variable S,

[0036] As a further improvement of the present invention, in S4, the structural design target reliability index β 2T The value range is 1.0~3.0.

[0037] Another aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps in the method for directly calculating the load resistance partial coefficient based on the moment method.

[0038] Another aspect of the present invention provides a computer device comprising a memory, a processor and a computer program.

[0039] The computer program is stored in a memory and configured to be executable by a processor, and when the processor executes the computer program, the steps in the method for directly calculating the load resistance partial coefficient based on the moment method are implemented.

[0040] The above-mentioned improved technical features can be combined with each other as long as they do not conflict with each other.

[0041] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0042] (1) The direct calculation method of the load resistance partial coefficient based on the moment method of the present invention is to establish the structural limit state function and set the corresponding calculation formula to complete μ Rcheck 、μ G , σ G , α 3G , β 2Tcheck The calculation of parameters such as , and then the structural resistance design value μ can be calculated R , and on this basis complete the target second-order reliability index β 2T The rapid acquisition of load resistance partial coefficients φ and γ realizes the direct calculation of load resistance partial coefficients, avoids the iterative calculation process in the existing design method, simplifies the calculation process during the reliability design of engineering structures, and is suitable for rapid calculation in engineering applications.

[0043] (2) The method for directly calculating the load resistance partial coefficient based on the moment method of the present invention is simple and easy to calculate. It can quickly determine the structural resistance design value and the load resistance partial coefficient, simplify the calculation process during the reliability design of the engineering structure, avoid the iterative calculation process of the existing design process, shorten the reliability design cycle of the design object, improve the efficiency of the reliability design of the design object, better meet the actual needs of engineering applications, and have good practical value and realistic significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0045] Figure 1 is a flow chart of a method for directly calculating a load resistance partial coefficient based on the moment method in an embodiment of the present invention;

[0046] Figure 2 This is a flow chart for calculating the load resistance partial factor using the verification point method (FORM);

[0047] Figure 3 Schematic diagram of load distribution of a beam fixed at both ends with a uniformly distributed load in a preferred embodiment of the present invention;

[0048] Figures 4 to 9 It is a comparison chart of the calculation results using the calculation method of the present invention and the FORM method in the preferred embodiment. DETAILED DESCRIPTION

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0050] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential" and the like to indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are 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, and therefore should not be understood as limiting the present invention.

[0051] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0052] In the present invention, unless otherwise specified or limited, the terms "installed," "connected," "connect," "fixed," etc. should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, or integration; mechanical connection, electrical connection; direct connection, or indirect connection through an intermediate medium; internal communication between two components, or interaction between two components, unless otherwise specified. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0053] In the present invention, unless otherwise expressly specified or limited, when a first feature is "above" or "below" a second feature, it may mean that the first and second features are in direct contact, or that the first and second features are in indirect contact through an intermediary. Furthermore, when a first feature is "above," "above," or "above" a second feature, it may mean that the first feature is directly above or diagonally above the second feature, or simply means that the first feature is at a higher level than the second feature. When a first feature is "below," "below," or "below" a second feature, it may mean that the first feature is directly below or diagonally below the second feature, or simply means that the first feature is at a lower level than the second feature.

[0054] Example:

[0055] See also Figure 1 In the preferred embodiment of the present invention, the method for directly calculating the load resistance partial coefficient based on the moment method is used to achieve the full life design requirements of the engineering structure. It should be noted that when designing, the average value μ G is the first-order central moment, standard deviation σ G is the second-order central moment, and the skewness is α 3G is the third-order central moment. For existing design / calculation methods, only μ is usually used. G and σ G In the preferred embodiment, it is necessary to use higher-order statistical moments such as the third-order moment and the fourth-order moment, so it is defined as a calculation method based on the moment method.

[0056] Specifically, in a preferred embodiment, the method for directly calculating the load resistance partial coefficient based on the moment method preferably includes the following steps:

[0057] S1: Establish a structural limit state function; in a preferred embodiment, the formula is preferably as shown in the following formula (1):

[0058] G(X)=R-∑S i (1)

[0059] Where R is the random variable representing resistance, S i is a random variable representing the load effect, and the resistance R is related to the load effect S i To be independent of each other.

[0060] S2: For general engineering structures, the resistance random variable R generally obeys the log-normal distribution, so that the resistance calculation value μ proposed by the method of the present invention is Rcheck It can be calculated by formula (2);

[0061]

[0062] Where V R is the coefficient of variation of the resistance random variable R, which obeys the lognormal distribution; V R =σR / μ R , μ R and σ R are the mean and standard deviation of resistance R; μ Si is the load effect S i The mean of

[0063] S3: The resistance value μ determined by S2 Rcheck Substitute into the following formulas (3) to (5) to calculate the mean μ of the structural limit state function G(X) G , standard deviation σ G and the third-order central moment (skewness) α 3G ;

[0064] μ G =μ R -∑μ Si (3)

[0065]

[0066]

[0067] Where μ R and σ R are the mean and standard deviation of resistance R, respectively, and μ in the formula is R The resistance calculation value μ is preferred Rcheck Substitute into the calculation; μ Si and σ Si are the load effects S i The mean and standard deviation of α 3R , α 3Si They are resistance R and load effect S i The third central moment (skewness) of .

[0068] S4: α obtained in S3 3G Substitute into formula (6) to calculate the target second-order reliability index verification value β 2Tcheck ;

[0069]

[0070] Where, β T is the target reliability index of structural design, and its value is determined according to the corresponding structural design code. It should be noted that the applicable range of formula (6) is: |α 3G |≤1.

[0071] S5: Determine the structural resistance design value μ according to formula (7) R ;

[0072] In the formula, the coefficient ω Rand ω S are the derived coefficients of resistance R and load effect S respectively; and can be preferably calculated by formula (8) and formula (9); where V S To combine all load effects S i As the coefficient of variation of an overall effect random variable S,

[0073]

[0074] Thus, the direct calculation method of the load resistance design partial coefficient in the preferred embodiment determines the structural resistance design value μ R ;For engineering design, the structure can be designed directly according to the resistance design value.

[0075] S6: The resistance design value μ determined by S5 R Substitute into equations (3) to (5) and calculate the mean μ of the structural limit state function G(X) G , standard deviation σ G and the third-order central moment (skewness) α 3G , and calculate α according to the following formula R With α Si ;

[0076]

[0077]

[0078] In the formula, the coefficient α R With α Si Represent resistance R and load effect S respectively i The direction cosines of the load, also known as the resistance R and the load effect S i The separation factor.

[0079] S7: α obtained in S6 3G Substitute into formula (6) to calculate the target second-order reliability index β 2T ;

[0080] S8: Determine the load resistance partial coefficients φ and γ according to formula (12) and formula (13).

[0081]

[0082]

[0083] Where R n is the standard value of resistance, S ni It is the standard value of load effect, which is generally determined through actual measurement and statistics of a large amount of data.

[0084] According to the calculation process of steps S1 to S8 above, the load resistance partial coefficient can be directly calculated, avoiding the iterative calculation process in the traditional design process.

[0085] Furthermore, the direct calculation method of the load resistance design partial coefficient in the present invention is further illustrated by the following two specific embodiments.

[0086] Example 1:

[0087] In this embodiment, the design object is as follows Figure 3 The fixed beam shown in the figure bears three uniformly distributed loads, namely, dead load D, live load L, and snow load S. The snow load is the control load and has time-varying properties. The probability parameters of the known resistance and related load effects are listed in Table 1. Table 1 Basic random variable statistical parameters of the fixed beam at both ends

[0088]

[0089] The target reliability index β T =3.0, determine the cross-sectional resistance value and load resistance design partial factor of the ultimate limit state design of the beam. The specific process includes the determination of the structural resistance design value and the load resistance partial factor, which are as follows:

[0090] (1) Determine the design value of structural resistance

[0091] S1: Establish structural limit state function;

[0092] G(X)=R-(D+L+S) (14)

[0093] S2: Calculate the resistance value μ according to formula (2) Rcheck ;

[0094] The resistance calculation value μ Rcheck Substitute into equations (3) to (5) to calculate the mean value μ of the structural limit state function G(X) G ′、Standard deviation verification value σ G ′ and skewness test value α 3G ';

[0095] μ G ′=μ Rcheck -∑μ Si =3.7550-(1+0.175+0.6874)=1.8926

[0096]

[0097]

[0098] S4: The above α 3G Substitute ′ into formula (6) to calculate the target second-order reliability index verification value β 2Tcheck ;

[0099]

[0100] S5: Calculate the coefficient ω according to formulas (8) to (9) R and ω S , and determine the structural resistance design value μ according to formula (7) R ;

[0101]

[0102]

[0103]

[0104]

[0105] (2) Determine the load resistance partial coefficient

[0106] S6: The determined structural resistance design value μ R Substitute into equations (3) to (5) and calculate the mean μ of the structural limit state function G(X) G , standard deviation σ G and the third-order central moment (skewness) α 3G ,

[0107] μ G =μ R -∑μ Si =3.0659-(1+0.175+0.6874)=1.2035

[0108]

[0109]

[0110] Calculate the separation coefficient:

[0111]

[0112]

[0113]

[0114]

[0115] S7: Substitute the above-obtained parameters into formula (6) to calculate the target second-order reliability index β 2T ,

[0116]

[0117] S8: Calculate the load resistance partial coefficient according to formula (12) and formula (13):

[0118]

[0119]

[0120]

[0121]

[0122] Example 2:

[0123] In this embodiment, the load resistance partial coefficient is calculated using the verification point method (FORM) and the method of the present invention, and the calculation results of the two methods are compared.

[0124] Specifically, assuming that the design object in this embodiment is subjected to dead load, live load, snow load and wind load, its limit state function is shown in formula (15):

[0125] G(X)=R-(D+L+S+W) (15)

[0126] Where R is the structural resistance, D is the dead load effect, L is the live load effect, S is the snow load effect, and W is the wind load effect. The probability parameters of the known resistance and related load effects are listed in Table 2.

[0127] Table 2 Basic random variable statistical parameters

[0128]

[0129] The resistance value and load resistance partial factor of the structure in the ultimate state design are calculated using FORM and the method of the present invention respectively. The calculation process of FORM is as follows: Figure 2 As shown in , the calculation method in the present invention refers to Example 1, and the specific calculation process is not described in detail.

[0130] Accordingly, through Figures 4 to 9 By comparing the results of the two calculation methods, we can draw the following conclusions:

[0131] Figure 4 Design the target reliability index β for the structure T When the value is 1.0 to 3.0, the resistance design value determined by FORM and the method of the present invention varies with the target reliability index. Figure 4It can be seen that the resistance design value calculated by the method of the present invention is slightly larger than the resistance design value calculated by the FORM. For engineering structure design, a larger resistance design value is safer for the structural design. This shows that the calculation results of the method of the present invention are safer than those of the FORM when performing structural design.

[0132] Figure 5 Design the target reliability index β for the structure T When the value is 1.0 to 3.0, the number of iterations required to calculate the load resistance partial coefficient of the structure using FORM is 9 to 15, while the number of iterations required by the method of the present invention is 0. Since the calculation process of the method of the present invention is simple and does not require iterative calculations, it is easier for designers to use. Therefore, the method of the present invention is more suitable for practical engineering applications than FORM.

[0133] Figures 6 to 9 Design the target reliability index β for the structure T When the value is 1.0 to 3.0, the load resistance partial coefficient determined by FORM and the method of the present invention varies with the reliability index. Figures 6 to 9 It can be seen that the load resistance partial coefficients calculated using the present invention differ somewhat from those calculated using FORM. This is because different coefficient combinations can yield the same resistance design value. When designing engineering structures, resistance design values are generally derived by combining partial coefficient expressions, and these resistance design values are then used for structural design. Furthermore, if the resistance partial coefficient for a structure is known, the corresponding calculated load partial coefficient should be used.

[0134] Furthermore, in order to facilitate the application of the direct calculation method of the load resistance partial coefficient based on the moment method in the preferred embodiment, a computer-readable storage medium and a computer device are also provided in the preferred embodiment.

[0135] In a preferred embodiment, a computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the aforementioned method for directly calculating a load resistance partial factor based on the moment method. Accordingly, a computer device includes a memory, a processor, and a computer program; wherein the computer program is stored in the memory and configured to be executable by the processor, and when the processor executes the computer program, the steps of the aforementioned method for directly calculating a load resistance partial factor based on the moment method are implemented.

[0136] The direct calculation method of the load resistance partial coefficient based on the moment method in the present invention is simple and easy to calculate. It can quickly determine the structural resistance design value and the load resistance partial coefficient, simplify the calculation process during the reliability design of the engineering structure, avoid the iterative calculation process of the existing design process, shorten the reliability design cycle of the design object, improve the efficiency of the reliability design of the design object, better meet the actual needs of engineering applications, and have good practical value and practical significance.

[0137] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for directly calculating the load resistance partial coefficient based on the moment method, characterized in that: The steps include: S1: Establish the structural limit state function G(X); G(X)=R-∑S i (1) Where R is the random variable representing resistance, S i is a random variable representing the load effect; S2: Calculated resistance value μ Rcheck ; Where V R is the coefficient of variation of the resistance random variable R, which obeys the lognormal distribution; V R =σ R / μ R , μ R and σ R are the mean and standard deviation of resistance R; μ Si is the load effect S i The mean of S3: Calculate the mean μ of the structural limit state function G(X) G , standard deviation σ G and skewness α 3G ; m G =μ R -∑μ Si (3) Where μ R and σ R are the mean and standard deviation of resistance R, and μ R The calculated μ Rcheck Substitute into the calculation; μ Si and σ Si are the load effects S i The mean and standard deviation of 3R , α 3Si are resistance R and load effect S respectively i skewness; S4: α obtained in S3 3G Substitute into formula (6) and calculate the target second-order reliability index verification value β 2Tcheck ; Where, β T It is the target reliability index of structural design, and its value is determined according to the corresponding structural design code; S5: Determine the structural resistance design value μ according to formula (7) R ; In the formula, the coefficient ω R and ω S are the derived coefficients of resistance R and load effect S respectively; S6: μ obtained in S5 R Substituting into equations (3) to (5), calculate μ G , σ G and α 3G , and calculate the resistance R and load effect S according to the following formula i The separation coefficient α R With α Si ; a R =s R / s G (10) a Si =s Si / s G (11) S7: α obtained in S6 3G Substitute into formula (6) to calculate the target second-order reliability index β 2T ; S8: Determine the load resistance partial coefficients φ and γ according to formula (12) and formula (13); Where R n is the standard value of resistance, S ni is the standard value of load effect, both of which are determined through actual measurement and data statistics.

2. The method for directly calculating the load resistance partial coefficient based on the moment method according to claim 1 is characterized in that: In S4, the applicable range of formula (6) is: |α 3G |≤1.

3. The method for directly calculating the load resistance partial coefficient based on the moment method according to claim 1 or 2, characterized in that: In S5, the coefficient ω R and ω S The calculations are obtained by the following formulas: Where V S To combine all load effects S i As the coefficient of variation of an overall effect random variable S, 4. The method for directly calculating the load resistance partial coefficient based on the moment method according to any one of claims 1 to 3, characterized in that: In S4, the structural design target reliability index β 2T The value range is 1.0~3.

0.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for directly calculating the load resistance partial coefficient based on the moment method according to any one of claims 1 to 4 are implemented.

6. A computer device comprising a memory, a processor and a computer program, characterized in that: The computer program is stored in a memory and configured to be executable by a processor, and when the processor executes the computer program, the steps in the method for directly calculating the load resistance partial factor based on the moment method according to any one of claims 1 to 4 are implemented.

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