Analytical method for deformation of concrete beam under automotive construction machinery

Abstract

The invention relates to a method for analyzing deformation of a concrete beam under an automotive construction machine, which comprises the following steps of: 1, simulating the unevenness of the surface of the beam into a function spectrum form, simplifying an automotive model into a 2-degree-of-freedom 1 / 4 automotive suspension model, simulating an Euler-Bernoulli beam model of unit width by the beam model, and constructing an Euler-Bernoulli beam model; obtaining dynamic tire contact force of the automobile under beams in different function spectrum forms; and 2, applying tire force to the Euler beam model to obtain a stress-strain curve of a certain point on the concrete beam when the automobile runs, so as to obtain the deformation of the concrete beam.

Description

Technical Field

[0001] The invention relates to the field of building engineering construction, in particular to an analytical method for deformation of a concrete beam under a vehicle-type construction machinery. Background Art

[0002] With the rapid development of high-rise building facilities in my country, many building floors will be continuously damaged by construction vehicles during the construction phase, including truck cranes, scissor trucks and spider trucks, which will seriously affect the bearing capacity of concrete floors, construction safety and construction efficiency. The random dynamic loads generated by construction vehicles walking on the floor will continuously change the stress state of the beams and slabs, causing continuous stress and deformation, thereby causing fatigue and damage to the beam and slab structure. This fatigue and damage will cause problems such as cracking, peeling and damage to the floor, aggravate the unevenness of the floor, further aggravate the vibration of the vehicle, seriously affect the safety of construction, and also increase the dynamic load of the vehicle on the floor. Therefore, it is very necessary to verify the floor of truck-type construction machinery.

[0003] At present, the general research idea for the verification of the floor of automobile-type construction machinery is to calculate through finite element software. It is mainly to establish a multi-layer structural system of the building through finite element software such as Midas, discretize a continuous infinite degree of freedom problem into a finite number of small areas, and then take each small area as a finite degree of freedom problem, apply a certain static load to the tire area of ​​a certain plate or a certain beam, and verify it separately, so as to obtain an overall approximate solution.

[0004] The existing calculation has certain limitations for the verification of concrete beams under automobile-type construction machinery. Since it is difficult to simulate the motion state of the automobile, the influence of the vehicle speed on the concrete beam is not considered, and the calculation can only be performed by selecting the tire in the most unfavorable area. In addition, since the number of finite element units is also limited, it is difficult to obtain accurate results. In addition, for the finite element solution, when the boundary conditions at both ends of the beam are insufficiently constrained, the internal force of the beam will show stress singularity, which is very different from the actual situation. Summary of the invention

[0005] The present invention aims to overcome the defects of the prior art, and provides an analytical method for the deformation of a concrete beam under a vehicle-type construction machinery, so as to solve the problem of the deformation of a concrete beam under a vehicle-type construction machinery.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows: An analytical method for deformation of a concrete beam under a vehicle-type construction machine, characterized in that it comprises the following steps: Step 1: The unevenness of the beam surface is simulated in the form of a function spectrum. The car model is simplified to a 2-DOF 1 / 4 car suspension model. The beam model simulates the Euler-Bernoulli beam model of unit width to obtain the dynamic tire contact force of the car under the beam in different function spectrum forms. Step 2: Apply tire force to the Euler beam model to obtain the stress-strain curve of a certain point on the concrete beam when the car is driving, thereby obtaining the deformation of the concrete beam.

[0007] The analytical method for the deformation of concrete beams under a vehicle-type construction machine is characterized in that the function spectrum of the beam unevenness is obtained by the method, IRI method or power spectrum method, assuming that its expression is , is the vibration frequency, and according to the D'Alembert principle, the motion differential equation of the interaction between the car and the beam is established as: Where m1 is the tire mass, m2 is the suspension mass, K1 is the tire stiffness coefficient, K2 is the suspension stiffness coefficient, C1 is the tire damping coefficient, C2 is the suspension damping coefficient, y0 is the floor displacement excitation, y1 is the tire vertical excitation, and y2 is the suspension vertical excitation.

[0008] The analytical method for the deformation of concrete beams under a vehicle-type construction machinery is characterized in that: the above-mentioned differential equation of motion can be transformed from time domain to frequency domain through Fourier transformation, and then the solution of y1 can be obtained by Cramer's law and Fourier inverse transformation.

[0009] The analytical method for the deformation of concrete beams under a vehicle-type construction machine is characterized in that the dynamic tire force is calculated by substituting the beam model and the vehicle model into: .

[0010] The analytical method for the deformation of concrete beams under a vehicle-type construction machine is characterized by establishing a uniform motion differential equation of the Euler-Bernoulli beam under the action of tire force: Where E is the elastic modulus, I is the section inertia moment, m is the mass per unit length, c is the damping coefficient, k is the linear stiffness, is the nonlinear stiffness, is the Dirac function, x is the displacement in the direction of the car's travel, v is the velocity, t is the time, and w is the vertical displacement of the beam.

[0011] The beneficial effects of the present invention are as follows: It can be seen from the above technical scheme that the present application provides an analytical method for the deformation of concrete beams under automobile-type construction machinery, which couples the automobile suspension model, tire model and beam model, and provides a new analytical method for the deformation of concrete beams under automobile-type construction machinery while considering the motion state of the automobile. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the beam model under the action of automobile load; Figure 2 This is the algorithm idea diagram; Figure 3 is a schematic diagram of dynamic tire contact force; Figure 4 Schematic diagram of the first three-order analytical solution; Figure 5 It is a schematic diagram of the spatial domain; Figure 6 It is a time domain diagram. DETAILED DESCRIPTION

[0013] The technical solutions of the embodiments of the present application will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field without creative work based on the embodiments in the embodiments of the present application are within the scope of protection requested by the present application. like Figure 1-6 As shown: An analytical method for the deformation of concrete beams under automobile-type construction machinery. Different from the traditional software verification which only establishes a finite element model, the present invention considers the coupling of the three models of automobile-tire-beam, and considers the influence of the automobile's motion state, namely, the vehicle vibration, on the beam.

[0014] Step 1: The unevenness of the beam surface is simulated in the form of a function spectrum. The car model is simplified to a 2-DOF 1 / 4 car suspension model. The beam model simulates the Euler-Bernoulli beam model of unit width. By inputting the function spectrum, the dynamic tire contact force of the car under the beam in different function spectrum forms is obtained. Step 2: Apply tire force to the Euler beam model, consider the stress-strain relationship of the beam itself, and finally obtain the stress-strain curve of a certain point on the concrete beam when the car is driving, thereby obtaining the deformation of the concrete beam.

[0015] 1. The function spectrum of beam unevenness is obtained by the method, IRI method or power spectrum method. Assume that its expression is , is the vibration frequency, and according to the D'Alembert principle, the motion differential equation of the interaction between the car and the beam is established as: Where m1 is the tire mass, m2 is the suspension mass, K1 is the tire stiffness coefficient, K2 is the suspension stiffness coefficient, C1 is the tire damping coefficient, C2 is the suspension damping coefficient, y0 is the floor displacement excitation, y1 is the tire vertical excitation, and y2 is the suspension vertical excitation.

[0016] For the above differential equation of motion, the time domain can be transformed into the frequency domain through Fourier transform, and then the solution of y1 can be obtained by Cramer's law and Fourier inverse transform.

[0017] 2. Substitute the beam model and the car model, according to Figure 1 The force analysis is performed and the dynamic tire force is calculated as follows: .

[0018] 3. Establish the uniform motion differential equation of the Euler-Bernoulli beam under the action of tire force: Where E is the elastic modulus, I is the section inertia moment, m is the mass per unit length, c is the damping coefficient, k is the linear stiffness, is the nonlinear stiffness, is the Dirac function, x is the displacement in the direction of the car's travel, v is the velocity, t is the time, and w is the vertical displacement of the beam.

[0019] By coupling the above three models, we can obtain the mechanical model of the two-dimensional vehicle-tire-beam system, which is a complex five-parameter coupled system dynamics model containing nonlinear terms. In mathematical form, it is a high-order nonlinear partial differential equation.

[0020] 4. For solving approximate analytical solutions of nonlinear mathematical and physical equations, the Adomian decomposition method can be used for calculation. It can transform complex nonlinear problems into a series of linear problems to solve, and has the advantages of fast calculation speed, high calculation accuracy, and no need for numerical difference. Since the Adomian analytical solution meets the characteristics of fast convergence, for the uniform motion differential equation, it is only necessary to take the superposition of the first three orders of the Adomian analytical solution. The above model can be simplified by the Euler formula and the Adomian decomposition method, and the nonlinear partial differential equation can be transformed into a system of linear partial differential equations. For the system of linear partial differential equations, it can be simplified by the linear superposition principle and the chain rule, and then the closed analytical solution of the first-order Adomian analytical solution can be solved by Fourier transformation and the residue theorem.

[0021] Based on the first-order Adomian analytical solution, the second-order Adomian analytical solution and the third-order Adomian analytical solution can be solved. The second-order and third-order Adomian solutions can be solved by superimposed Duhamel integrals and the response solution of the Euler beam under the impulse function.

[0022] Finally, the three results are linearly superimposed to obtain the analytical solution to the deformation of the concrete beam under the vehicle load.

[0023] The above are only embodiments provided for the present application and are not intended to limit the present application. Although the present application is described in detail with reference to the embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. However, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. An analytical method for the deformation of concrete beams under a vehicle-type construction machine, characterized in that It includes the following steps: Step 1: The unevenness of the beam surface is simulated in the form of a function spectrum. The car model is simplified to a 2-DOF 1 / 4 car suspension model. The beam model simulates the Euler-Bernoulli beam model of unit width to obtain the dynamic tire contact force of the car under the beam in different function spectrum forms. Step 2: Apply tire force to the Euler beam model to obtain the stress-strain curve of a certain point on the concrete beam when the car is driving, thereby obtaining the deformation of the concrete beam.

2. The analytical method for deformation of concrete beams under a vehicle-type construction machine according to claim 1, characterized in that: The function spectrum of beam unevenness is obtained by the method, IRI method or power spectrum method. Assume that its expression is , is the vibration frequency, and according to the D'Alembert principle, the motion differential equation of the interaction between the car and the beam is established as:

3. Where m1 is the tire mass, m2 is the suspension mass, K1 is the tire stiffness coefficient, K2 is the suspension stiffness coefficient, C1 is the tire damping coefficient, C2 is the suspension damping coefficient, y0 is the floor displacement excitation, y1 is the tire vertical excitation, and y2 is the suspension vertical excitation.

4. The analytical method for deformation of concrete beams under a vehicle-type construction machine according to claim 2, characterized in that: For the above differential equation of motion, the time domain can be transformed into the frequency domain through Fourier transform, and then the solution of y1 can be obtained by Cramer's law and Fourier inverse transform.

5. The analytical method for deformation of concrete beams under a vehicle-type construction machine according to claim 1, characterized in that: Substituting the beam model and the car model, the dynamic tire force is calculated as: 。 6. The analytical method for deformation of concrete beams under a vehicle-type construction machine according to claim 1, characterized in that: Establish the uniform motion differential equation of the Euler-Bernoulli beam under the action of tire force:

7. Where E is the elastic modulus, I is the moment of inertia of the area, m is the mass per unit length, c is the damping coefficient, k is the linear stiffness, is the nonlinear stiffness, is the Dirac function, x is the displacement in the direction of the car's travel, v is the velocity, t is the time, and w is the vertical displacement of the beam.

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