Structural anti-seismic test method of partially similar model

Abstract

The invention relates to the technical field of structural engineering, in particular to a structural anti-seismic test method for a partially similar model, which comprises the following steps: S1, determining a geometric similarity ratio S1; s2, making a model; the model is made of a material with the same structure as the prototype, and the material density similarity ratio S rho of the prototype to the model is equal to 1; the model does not need to add a balance weight, the stress similarity ratio S sigma of the prototype and the model is 1, the strain similarity ratio S epsilon is 1, and the force similarity criterion is naturally met without applying the balance weight inertia force; s3, installing a sensor; s4, performing a model test; and determining an input acceleration am and a time axis. The invention provides the similarity criterion suitable for the anti-seismic test of the partially similar structure model made of the same material as the prototype material, so that a designer can more accurately invert the anti-seismic performance of the prototype structure according to the model test result, the redundancy of the structure design is reduced, the structure cost is reduced, and the design efficiency is improved. Therefore, an economical and safe engineering structure is designed.

Description

Technical Field

[0001] The present invention relates to the technical field of structural engineering, and in particular to a structural seismic test method for a partially similar model. Background Art

[0002] The shaking table test is currently the most trusted method for testing the seismic performance of structures. It uses a shaking table to simulate the ground motion caused by an earthquake to verify or validate the seismic resistance of a structure. Chinese regulations require that important structures, such as high-rise buildings, dams, and lifeline projects, undergo shaking table testing before construction. Due to the limitations of the shaking table's size and load-bearing capacity, structural seismic testing can only be conducted using scaled models. Therefore, prior to testing, the similarity between the prototype and the model must be determined so that the prototype's seismic performance indicators, such as seismic resistance level and damage mode, can be calculated based on the model test results.

[0003] The formula for determining the similarity between the prototype and the model is called the similarity criterion. A model that satisfies all parameters involved in the similarity criterion is called a fully similar model, while a model that partially satisfies the criterion is called a partially similar model. Since the models used in structural seismic testing are made of the same materials as the prototype, they cannot meet the similarity criterion currently used in seismic testing. Therefore, the models currently used in structural seismic testing are considered partially similar models.

[0004] The similarity criterion currently used in partial similarity models is based on acceleration equality. However, some similarity models do not meet the required similarity relationship between material density and elastic modulus in this similarity criterion. Consequently, the acceleration responses of the model and prototype are not identical. Since seismic damage to structures is primarily caused by shear stress, stress equality is a necessary requirement for seismic model testing of structures. This is naturally satisfied by models constructed from the same material as the prototype, as strain is a dimensionless geometric parameter. Identical materials imply identical elastic moduli, and therefore, stress equality. However, the current similarity criterion artificially assumes acceleration equality. Therefore, to ensure similar inertial forces and, therefore, stress equality, counterweights must be applied to the model. This increases the inertial forces and, consequently, stresses in the model. Consequently, the resulting seismic performance of the prototype is inaccurate, leading to an underestimation of the prototype's seismic capacity and increased construction costs. Summary of the Invention

[0005] In order to address the deficiencies in the prior art, the present invention provides a structural seismic test method for partially similar models, which is very beneficial for reducing the redundancy of structural seismic design and thus reducing the cost of building structures.

[0006] The method of the present invention comprises the following steps:

[0007] S1. Determine the geometric similarity ratio S l ;

[0008] S2, making models;

[0009] The model is made of the same material as the prototype structure, and the material density similarity ratio between the prototype and the model is S ρ =1; the model does not need to add weight, the strain similarity ratio S between the prototype and the model ε =1, so the stress similarity ratio S between the model and the prototype σ =1, no counterweight inertia force is applied and the similarity criterion of force is naturally satisfied;

[0010] S3, install the sensor;

[0011] S4. Model test; determine the input acceleration a m and determining timelines;

[0012] After completing the above transformation, the shaking table test can be carried out step by step. After each level test, the damage state of the model is recorded, and it is decided whether to increase the level and continue the test according to the damage state.

[0013] After all the tests are completed, the seismic performance of the prototype is determined based on the damage state of the model.

[0014] Furthermore, in step S1, the scale ratio of the model is determined according to the space of the laboratory, the load-bearing capacity of the test bench and the capacity of the power loading equipment, thereby calculating the geometric similarity ratio S between the prototype and the model. l .

[0015] Furthermore, in step S3, the specific operation of installing the sensor is: firmly installing the motion measurement sensor on the model structure, and connecting the output signal of the sensor to the test instrument.

[0016] Furthermore, the specific method for determining the input acceleration is:

[0017] Calculate the acceleration of the model as the input acceleration of the shaker:

[0018] a m =a p S l (16)

[0019] Where: a m ——is the acceleration response of the model;

[0020] a p ——Acceleration response of the prototype;

[0021] S l ——The geometric similarity ratio between the prototype and the model.

[0022] Furthermore, the specific method for determining the time axis is:

[0023] The similarity criteria used are:

[0024] S t =S l (17)

[0025] Where S t —Time similarity ratio between prototype and model;

[0026] S l ——The geometric similarity ratio between the prototype and the model.

[0027] The beneficial effects achieved by the embodiments of the present invention are:

[0028] The present invention proposes a similarity criterion for seismic tests of partially similar structural models made of the same material as the prototype, and inversely derives the seismic index of the prototype structure based on the test results of the model material, and proposes an acceleration similarity ratio S for the model made of the same material as the prototype. a The technical solution that is not equal to 1 can more accurately evaluate the seismic performance of the prototype structure based on the vibration table test results of the structural seismic resistance, reduce the redundancy of the structural design, and reduce the structural cost, thereby designing a more economical and safe seismic-resistant structure. DETAILED DESCRIPTION

[0029] To facilitate those skilled in the art to understand the present invention, specific embodiments of the present invention are described below.

[0030] Structural seismic testing determines whether the seismic resistance of a designed structure meets the requirements for safe service. Due to limitations in the size and load-bearing capacity of a shaking table, structural seismic testing cannot be performed using a full-scale model of the same size as the prototype. Instead, a scaled model (one smaller than the prototype) can be used, leading to similarities between the model and the prototype.

[0031] The similarity between the structural model and its prototype includes geometric similarity, physical and dynamic index similarity. Since the size of the model is determined according to the size of the laboratory site and the load-bearing capacity of the test bench and the loading equipment, the geometric similarity ratio is the ratio of the prototype body size to the corresponding size of the model S. l is determined first, and the other similarity ratios are expressed as geometric similarity ratios.

[0032] The similarity criterion is based on dimensional analysis. Therefore, it is necessary to first select a non-geometric parameter including geometric dimensions as a reference parameter to derive the similarity ratio of all parameters included in the structural test. Since structural tests are usually carried out in a gravity field, the gravitational acceleration of the prototype and the model is the same, that is, the gravitational acceleration similarity ratio S of the prototype and the model is g is 1, and the dimension of acceleration is m / s 2 , is a non-geometric parameter (time dimension) that includes a geometric dimension (length unit m).

[0033] At present, the similarity criterion for structural seismic tests is based on the dimensional analysis of acceleration. This similarity criterion states that since the acceleration due to gravity is equal, all accelerations, including horizontal acceleration, should be equal, that is:

[0034]

[0035] Where: S a — acceleration similarity ratio between the prototype and the model;

[0036] g p , g m ——Gravity acceleration of the prototype and model respectively;

[0037] l p , l m ——length dimensions of prototype and model respectively;

[0038] t p , t m — are the time dimensions of the prototype and model respectively;

[0039] S l —Geometric similarity ratio between the prototype and the model;

[0040] S t ——Time similarity ratio between prototype and model.

[0041] The geometric similarity ratio S between the prototype and the model in formula (1) l It is first determined based on the vibration table, so it is a known parameter. Then the time similarity ratio S between the prototype and the model can be directly obtained by formula (1): t for:

[0042]

[0043] Then, the dynamic characteristics and motion response parameter similarity ratio of the full similarity model can be directly obtained:

[0044]

[0045] S d =Sl (4)

[0046]

[0047] Where: S f ——Frequency similarity ratio between prototype and model;

[0048] S d ——Displacement similarity ratio between prototype and model;

[0049] S v ——Speed similarity ratio between prototype and model.

[0050] The fully similar model must meet the following similarity criteria for the elastic modulus and material density of the model material:

[0051]

[0052] Where: S E — Similarity ratio of elastic modulus between prototype and model;

[0053] E p , E m ——Elastic modulus of the prototype and model respectively;

[0054] S M —Mass similarity ratio between prototype and model;

[0055] S a — acceleration similarity ratio between the prototype and the model;

[0056] S l —Geometric similarity ratio between the prototype and the model;

[0057] S ρ ——Material density similarity ratio between the prototype and the model.

[0058] If we follow the existing method, using the acceleration similarity ratio S a = 1 similarity criterion to deduce the dynamic performance of the prototype structure, then the acceleration similarity ratio S a =1, the elastic modulus and density of the model material can be obtained from formula (7) to satisfy the following relationship:

[0059] S E =S ρ S l (8)

[0060] However, the material that satisfies or substantially satisfies the above-mentioned condition of formula (8) has not yet been discovered or manufactured. The current structural tests usually use the same building materials as the prototype materials to make models, that is, S E =1 and S ρ=1, and we can get the following equation (8):

[0061] S l =1 (8-1)

[0062] Unless the geometric similarity ratio S between the model and the prototype is l =1, that is, full-scale model. Therefore, for the non-full-scale model made of the same material as the prototype structure, the similarity relationship of formula (8) is not satisfied. This type of structural model is called a partial similarity model. From formula (7), it can be seen that the acceleration similarity ratio S of the partial similarity model is a ≠1.

[0063] The current vibration table test of some similar models still uses the acceleration similarity ratio S a = 1 to calculate the seismic performance of the prototype structure. Therefore, in order to meet the stress similarity ratio S between the prototype and the model σ The condition of being equal to 1 requires that a weight be applied to the model to satisfy the force similarity ratio between the prototype and the model:

[0064]

[0065] Where: S F —Force similarity ratio between prototype and model;

[0066] F p , F m — the forces of the prototype and model, respectively;

[0067] σ p ,σ m ——stresses of prototype and model respectively;

[0068] A p , A m ——areas of prototype and model respectively;

[0069] S σ —stress similarity ratio between prototype and model;

[0070] S l ——The geometric similarity ratio between the prototype and the model.

[0071] When the stress similarity ratio S between the prototype and the model is σ =1, the force similarity ratio S between the prototype and the model F for:

[0072]

[0073] The structural force in the shaking table test is the inertia force of the structure, so:

[0074]

[0075] Where: M p , M m — the quality of prototypes and models, respectively;

[0076] a p , a m ——Acceleration responses of the prototype and model respectively;

[0077] S ρ —Material density similarity ratio between prototype and model;

[0078] S l —Geometric similarity ratio between the prototype and the model;

[0079] S a ——The acceleration similarity ratio between the prototype and the model.

[0080] For some similar models whose model materials are the same as the prototype materials, their S ρ =1, according to the current similarity criterion S a =1, formula (11) is simplified to:

[0081]

[0082] Comparing Equation (10) and Equation (12), it can be seen that the forces of some similar models do not meet the similarity criterion. Therefore, the current solution is to add counterweights to the model to make it meet the requirements of Equation (10).

[0083] The current shaking table seismic test method uses the horizontal acceleration response similarity ratio S between the prototype and the model. a The method of adding counterweight to meet the similarity of inertial force is determined to be 1, which leads to an underestimation of the seismic performance of the prototype structure and an increase in construction costs. Therefore, the present invention establishes a structural seismic test method for a partially similar model, comprising the following steps:

[0084] S1. Determine the geometric similarity ratio

[0085] The scale ratio of the model is determined according to the space of the laboratory, the load-bearing capacity of the test bench and the capacity of the power loading equipment, so as to calculate the geometric similarity ratio S between the prototype and the model. l .

[0086] S2. Make a model

[0087] The model is made of the same material as the prototype structure, but no counterweight is required. The structural seismic test verifies the seismic resistance of the structure. To ensure that the stress state of the model is the same as that of the prototype, the stress similarity ratio S of the prototype and the model is required. σ =1, stress is equal to the product of elastic modulus E and strain ε, that is:

[0088]

[0089] Where: E p , E m ——Elastic modulus of the prototype and model respectively;

[0090] ε p , ε m ——strains of prototype and model respectively;

[0091] S E — Similarity ratio of elastic modulus between prototype and model;

[0092] S ε ——Strain similarity ratio between prototype and model.

[0093] Strain is a dimensionless quantity, so the strain similarity ratio S ε = 1. Therefore, formula (13) is a similarity relation that is naturally satisfied. E =1 and S ρ =1Substituting into formula (7) we can get:

[0094]

[0095] Then, Equation (14) and S ρ =1Substituting into formula (11) we can get:

[0096]

[0097] The above formula is the same as formula (10), that is, the force similarity criterion is naturally satisfied without applying the counterweight inertia force.

[0098] S3. Install the sensor

[0099] The motion measurement sensor is firmly mounted on the model structure and the output signal of the sensor is connected to the test instrument.

[0100] S4. Model test

[0101] 4.1 Determining Input Acceleration

[0102] Based on the relationship between the acceleration similarity ratio of the prototype and the model in formula (14), the acceleration of the model is calculated according to the similarity ratio in formula (14) as the input acceleration of the vibration table:

[0103] a m =a p S l (16)

[0104] Where: a m ——is the acceleration response of the model;

[0105] a p——Acceleration response of the prototype;

[0106] S l ——The geometric similarity ratio between the prototype and the model.

[0107] 4.2 Determine the timeline

[0108] The input acceleration of the shaking table test is the acceleration time series of the earthquake that has occurred. Its time must be transformed according to the similarity criterion. The similarity criterion used in this method is:

[0109] S t =S l (17)

[0110] Where S t —Time similarity ratio between prototype and model;

[0111] S l ——The geometric similarity ratio between the prototype and the model.

[0112] After completing the above transformation, the shaking table test can be carried out step by step. After each magnitude test, the damage state of the model is recorded, and it is decided whether to increase the magnitude and continue the test based on the damage state.

[0113] After all the tests are completed, the seismic performance of the prototype is determined based on the damage state of the model.

[0114] The present invention establishes a structural seismic resistance test method for partially similar models and proposes similarity criteria applicable to structural models made of the same material as the prototype. This allows designers to more accurately evaluate the seismic resistance performance of the prototype structure based on the results of the structural seismic table test, thereby designing more economical and safe seismic-resistant structures and reducing structural construction costs while ensuring safety.

[0115] The above-described embodiments of the present invention do not limit the scope of protection of 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 claims of the present invention.

Claims

1. A structural seismic test method for a partially similar model, characterized in that: The following steps are involved: S1. Determine the geometric similarity ratio S l ; S2, making models; The model is made of the same material as the prototype structure, and the material density similarity ratio between the prototype and the model is S ρ =1; the model does not need to add weight, the stress similarity ratio S between the prototype and the model σ = 1 to ensure that the stress state of the model is the same as that of the prototype, and the strain similarity ratio S ε =1, no counterweight inertia force is applied and the similarity criterion of force is naturally satisfied; S3, install the sensor; S4. Model test; determine the input acceleration a m and determining timelines; After completing the above transformation, the shaking table test can be carried out step by step. After each level test, the damage state of the model is recorded, and it is decided whether to increase the level and continue the test according to the damage state. After all the tests are completed, the seismic performance of the prototype is determined based on the damage state of the model.

2. The structural seismic test method of a partially similar model according to claim 1, characterized in that: In step S1, the scale ratio of the model is determined according to the space of the laboratory, the load-bearing capacity of the test bench and the capacity of the power loading equipment, so as to calculate the geometric similarity ratio S between the prototype and the model. l .

3. The structural seismic test method of a partially similar model according to claim 1, characterized in that: In step S3 , the specific operation of installing the sensor is: firmly installing the motion measurement sensor on the model structure, and connecting the output signal of the sensor to the test instrument.

4. The structural seismic test method of a partially similar model according to claim 1, characterized in that: In step S4, the specific method for determining the input acceleration is: Calculate the acceleration of the model as the input acceleration of the shaker: a m =a p S l (16) Where: a m ——is the acceleration response of the model; a p ——Acceleration response of the prototype; S l ——The geometric similarity ratio between the prototype and the model.

5. The structural seismic test method of a partially similar model according to claim 1, characterized in that: The specific method to determine the time axis is: The similarity criteria used are: S t =S l (17) Where S t —Time similarity ratio between prototype and model; S l ——The geometric similarity ratio between the prototype and the model.

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