Method for predicting hysteretic characteristics of small-span-high-depth coupling beams based on OpenSees and storage medium

Abstract

The application relates to a small-span-high-ratio coupled beam hysteresis characteristic prediction method based on OpenSees and a storage medium, which is based on a nonlinear finite element calculation software OpenSees platform, a coupled beam model for simulating an actual small-span-high-ratio coupled beam is constructed, low-cycle repeated loading is carried out on the coupled beam model, and a hysteresis characteristic prediction result is obtained; the coupled beam model comprises a fiber beam unit and zero-length nonlinear shear-slip tensile spring unit located at both ends of the fiber beam unit, a ZeroLength Element unit with a nonlinear shear-slip tensile spring stiffness is used to form the zero-length nonlinear shear-slip tensile spring unit, and a fiber unit based on force interpolation with a cross-section nonlinear shear stiffness is used to form the fiber beam unit. Compared with the prior art, the application can effectively consider the nonlinear shear deformation and beam end slip tensile deformation of the small-span-high-ratio coupled beam, and can accurately predict the hysteresis characteristic of the small-span-high-ratio coupled beam.

Description

Technical Field

[0001] This invention relates to the field of structural seismic technology, and in particular to a method and storage medium for predicting the hysteretic characteristics of small span-to-height ratio coupling beams based on OpenSees. Background Technology

[0002] Reinforced concrete coupled shear wall structures are widely used in high-rise building structures due to their good overall performance, high lateral stiffness, and high vertical bearing capacity. Actual seismic tests and experimental results show that the bearing capacity, ductility, and energy dissipation capacity of the coupling beams themselves have a significant impact on the seismic performance of the entire coupled shear wall structure. Therefore, accurately considering the nonlinear hysteretic characteristics of the coupling beams in the finite element model is crucial in the structural analysis and design of high-rise buildings.

[0003] As structural components at the location of building door and window openings, concrete coupling beams generally have a small span-to-depth ratio (less than 2.5). Numerous seismic tests on reinforced concrete coupling beams both domestically and internationally have shown that, due to the small shear span ratio, the performance of coupling beams is significantly affected by shear forces, exhibiting obvious strength and stiffness degradation and significant pinching phenomena. This complex characteristic makes numerical simulation of its hysteresis process quite difficult. Seismic test results of coupling beams show that the deformation of coupling beams under repeated loading mainly consists of the following three parts: (1) bending deformation; (2) shear deformation; (3) interface slip deformation between the coupling beam and the wall. The conventional fiber section simulation ignores nonlinear shear deformation and interface slip deformation, which is suitable for frame beams with large span-to-depth ratios, but has a larger error for coupling beams with small span-to-depth ratios.

[0004] Many scholars at home and abroad have studied shear nonlinearity. According to the object of action, there are three ways to consider shear nonlinearity in reinforced concrete members: (1) material level; (2) section level; (3) element level. Theoretically, considering shear nonlinearity directly from the material level is the most essential and accurate. However, the multidimensional constitutive relationship of concrete is still under research, and whether it can reliably simulate the actual elastoplastic response of the structure needs further demonstration. When a refined model is established using the uniaxial stress-strain relationship of concrete, the simulated monotonic loading effect of the reinforced concrete beam is better, but the simulated cyclic loading results are usually quite different from the experimental results. In addition, considering nonlinearity from the material level also faces the problems of long calculation time and difficulty in convergence. Considering shear nonlinearity from the element level is simple in principle and has a small amount of calculation, but the simulation is not accurate enough because the position of the shear spring is limited. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide an accurate simulation method and storage medium for predicting the hysteresis characteristics of small span-to-height ratio continuous beams based on OpenSees.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for predicting the hysteretic characteristics of small span-to-depth ratio coupling beams based on OpenSees includes the following steps:

[0008] A coupling beam model for simulating a real small-span-to-height coupling beam was constructed based on the OpenSees analysis platform. The coupling beam model was subjected to low-cycle repeated loading, and the shear force at one end and the displacement at the other end were recorded to obtain the load-displacement hysteresis curve of the coupling beam model and obtain the hysteresis characteristic prediction results.

[0009] The connecting beam model includes fiber beam elements and zero-length nonlinear shear-slip tension spring elements located at both ends of the fiber beam elements. The zero-length nonlinear shear-slip tension spring elements are formed by ZeroLength Element elements provided by the OpenSees analysis platform, which have a nonlinear shear-slip spring stiffness. The fiber beam elements are formed by fiber elements based on force interpolation, which have an overall cross-sectional stiffness matrix. The overall cross-sectional stiffness matrix is ​​composed of the nonlinear shear stiffness of the cross-section level and the axial and bending stiffness of the fiber cross-section.

[0010] Furthermore, the force interpolation-based fiber element includes a connecting beam fiber section, the nonlinear shear constitutive structure of which is defined by the Hysteretic Material constitutive structure provided by the OpenSees analysis platform.

[0011] Furthermore, in the fiber cross-section of the connecting beam, the concrete of the connecting beam adopts the Concrete02 constitutive model, and the steel reinforcement of the connecting beam adopts the Steel02 constitutive model.

[0012] Furthermore, the fiber cross-section of the connecting beam is determined based on the cross-sectional dimensions of the connecting beam, the arrangement of the reinforcing bars, and the material strength grade parameters.

[0013] Furthermore, the constitutive skeleton curve of the Hysteretic Material is a three-segmented line model.

[0014] Furthermore, the key constitutive parameters of the Hysteretic Material include the crack point load and strain, the peak point load and strain, and the unloading section stiffness.

[0015] Furthermore, the zero-length nonlinear shear-slip tension spring unit adopts the constitutive definition of Hysteretic Material.

[0016] Furthermore, the skeleton curve of the constitutive model of the Hysteretic Material is a bisegmented line model, and the key parameters include peak load and displacement and unloading segment stiffness.

[0017] Furthermore, the hysteresis characteristics include the initial stiffness of the coupling beam, peak load, stiffness degradation, pinching effect, and hysteresis energy dissipation.

[0018] On the other hand, the present invention also provides a computer-readable storage medium comprising one or more programs executable by one or more processors of an electronic device, said one or more programs comprising instructions for performing the OpenSees-based method for predicting the hysteretic characteristics of small span-to-height beams as described above.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] 1. This invention constructs a reinforced concrete coupling beam model based on the OpenSees analysis platform. The coupling beam model consists of fiber elements with nonlinear shear constitutive structure and nonlinear shear-slip tension spring elements with zero length at both ends. It can not only utilize the fiber section to consider axial force and bending coupling, accurately and efficiently reflecting the compression-bending characteristics of the component, but also consider the nonlinear shear deformation of small span-to-height ratio coupling beams and the slip deformation of the interface between the coupling beam and the wall. This invention can accurately predict the initial stiffness, peak load, stiffness degradation, pinching effect, and hysteretic energy dissipation of small span-to-height ratio coupling beams.

[0021] 2. This invention combines the nonlinear shear stiffness of the cross-section layer with the axial and bending stiffness of the fiber cross-section to obtain the overall stiffness matrix of the cross-section, thereby realizing a fiber cross-section that can simultaneously consider axial shear and bending effects and improving simulation accuracy.

[0022] 3. This invention is based on the OpenSees analysis platform, and the method is simple and reliable. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the implementation process of the method of the present invention;

[0024] Figure 2 This is a schematic diagram of the coupling beam model constructed for this invention;

[0025] Figure 3 This is a schematic diagram of the stress-strain relationship of uniaxial concrete material according to the present invention;

[0026] Figure 4 This is a schematic diagram of the stress-strain relationship of uniaxial steel reinforcement material according to the present invention;

[0027] Figure 5 This is a schematic diagram of the nonlinear shear constitutive relation of the present invention;

[0028] Figure 6This is a schematic diagram of the nonlinear shear-slip stretching relationship of the present invention;

[0029] Figure 7 This is a schematic diagram of the hysteresis rule of the uniaxial Hysteretic Material of the present invention;

[0030] Figure 8 This is a schematic diagram of the Section Aggregator command of the present invention;

[0031] Figure 9 This is a schematic diagram of the fiber cross-section division of the coupling beam of the present invention;

[0032] Figure 10 This is a schematic diagram of the loading regime during the simulation analysis of this invention;

[0033] Figure 11 This is a comparison chart of the load-displacement hysteresis curve obtained by simulation analysis using the present invention and the load-displacement curve of the actual test. Detailed Implementation

[0034] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0035] This embodiment provides a method for predicting the hysteretic characteristics of a small-span-to-height coupling beam based on OpenSees, including the following steps: A coupling beam model is constructed based on the OpenSees analysis platform to simulate an actual small-span-to-height coupling beam; the coupling beam model is subjected to low-cycle reciprocating loading, and the shear force at one end and the displacement at the other end are recorded to obtain the load-displacement hysteresis curve of the coupling beam model, thus obtaining the hysteresis characteristic prediction result; wherein, the coupling beam model includes fiber beam elements and zero-length nonlinear shear-slip tension spring elements located at both ends of the fiber beam elements. The zero-length nonlinear shear-slip tension spring elements are formed by ZeroLength Element elements provided by the OpenSees analysis platform, which have a nonlinear shear-slip spring stiffness; the fiber beam elements are formed by fiber elements based on force interpolation, which have an overall cross-sectional stiffness matrix. The overall cross-sectional stiffness matrix is ​​composed of the nonlinear shear stiffness of the cross-section level and the axial and bending stiffness of the fiber cross-section, and can simultaneously consider the axial shear and bending effects of the fiber cross-section. The above method is based on the nonlinear finite element calculation software OpenSees platform to simulate the hysteretic response of a small-span-to-height coupling beam under low-cycle reciprocating loading.

[0036] like Figure 1 As shown, the simulation construction process of the above-mentioned coupling beam model includes:

[0037] S1. Define nodes ①, ②, ③, ④ and elements A, B, and C in sequence according to the span of the connecting beam.

[0038] In this configuration, node ① and node ② are concurrent; the distance between node ② and node ③ is equal to the span of the connecting beam; and node ③ and node ④ are concurrent, thus creating a zero-length element. Node ① and node ② are connected to form element A; node ② and node ③ are connected to form element B; and node ③ and node ④ are connected to form element C, as shown below. Figure 2 As shown in the figure (the nodes are artificially separated to represent zero-length units between them, but they are actually concurrent).

[0039] S2. Based on the cross-sectional dimensions of the coupling beam, the reinforcement arrangement, and the material strength grade parameters, specifically including the strength grades of concrete, reinforcement, and steel, the fiber cross-section of the coupling beam is defined.

[0040] The concrete of the coupling beam adopts the Concrete02 constitutive model, such as... Figure 3 As shown in the figure: ε0 represents the strain corresponding to the peak stress in the concrete; ε u The compressive strain is the strain corresponding to the concrete stress decreasing to 20% of the peak stress; K is the strength enhancement factor of the stirrups on the concrete; f c ' is the compressive strength (MPa) of the concrete cylinder; E0 is the tangential stiffness at the origin. E 20 f is the unloading stiffness at the start of the horizontal segment on the compressed skeleton curve; t ε represents the peak tensile stress. t For peak tensile strain; λ = E 20 / E0. The coupling beam reinforcement adopts the Steel02 constitutive model, such as... Figure 4 As shown.

[0041] S3. Define the nonlinear shear constitutive relationship of the cross section using the Hysteretic Material constitutive model provided by OpenSees. In a specific implementation, a schematic diagram of the nonlinear shear constitutive relationship is shown below. Figure 5 As shown, there are three key parameters that need to be solved:

[0042] (1) Cracking point load and strain (V) cr γ cr ):

[0043]

[0044]

[0045]

[0046]

[0047] In the formula: f c ' is the compressive strength of a concrete cylinder; ρ sv is the stirrup ratio; b and h0 are the width and effective height of the rectangular beam section, respectively; L is the span of the coupling beam; A is the cross-sectional area of ​​the rectangular beam; G c ν is the shear modulus of concrete; E is the Poisson's ratio; c k is the elastic modulus of concrete. i This represents the initial stiffness.

[0048] (2) Peak load and strain (V) u γ u ):

[0049] V u =min(V u1 V u2 )

[0050]

[0051]

[0052]

[0053]

[0054] Where: M u For the bending bearing capacity of the coupling beam; A sv f is the area of ​​the stirrups; sv s represents the stirrup strength; s represents the stirrup spacing.

[0055] (3) Stiffness k of the unloading section d :

[0056]

[0057] In the formula: τ0 is the nominal shear-compression ratio; β is the shear-stirrup ratio; A s E represents the area of ​​the longitudinal reinforcement. s The elastic modulus of the steel reinforcement; a s This is the distance from the point of application of the resultant force of the reinforcing bars to the edge of the beam.

[0058] Hysteretic Material Hysteresis Rules Figure 7 As shown in the figure. (e) 1p ~e 3p s 1p ~s 3p These are the x and y coordinates of the three key points on the positive axis of the skeleton curve; e 1n ~e 3n s 1n ~s 3nThese are the x and y coordinates of the three key points on the negative side of the skeleton curve. x p is the shrinkage coefficient for deformation (strain) during the unloading process. y This represents the force (stress) compression coefficient during the unloading process. `damage1` is the ductility-based damage coefficient, `damage2` is the energy-based damage coefficient, and `beta` is the exponent for controlling the stiffness degradation during unloading based on ductility. The key parameter value is: p x Take 0.6; p y Set K to 0.15; both damage1 and damage2 are set to 0; beta is set to 0.4. ul The unloading stiffness is calculated using the following formula:

[0059] K ul =μ -0.4 K i

[0060] In the formula: μ is the ductility coefficient; Ki is the initial stiffness.

[0061] S4. Constitutive modeling of Hysteretic Material provided by OpenSees (e.g.) Figure 5 (As shown) This implements the constitutive definition of a nonlinear shear-slip tension material. In a specific embodiment, a schematic diagram of the nonlinear shear-slip tension constitutive relationship is shown below. Figure 7 As shown, there are two key parameters that need to be solved:

[0062] (1) Peak load and strain (V) u s eu ):

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] In the formula: u e For elastic bond stress; u u L represents the peak bond stress. e The length of the elastic segment; l a d is the anchorage length; b The diameter is the longitudinal reinforcement.

[0069] (2) Stiffness k of the unloading section dse :

[0070]

[0071] The above nonlinear shear-slip stretch constitutive model is applied to the ZeroLength Element provided by OpenSees to form element A and element C.

[0072] S5. Using the Section Aggregator command provided by OpenSees, the nonlinear shear stiffness of the section level is combined with the axial and bending stiffness of the fiber section to obtain the overall stiffness matrix of the section, realizing a fiber section that can simultaneously consider axial shear and bending effects. This section property is assigned to the force interpolation-based fiber element to form element B. Among them, the nonlinear shear stiffness is calculated in the aforementioned step S3, and the axial and bending stiffness of the fiber section can be solved by the force interpolation-based fiber element itself in the OpenSees program.

[0073] A diagram of the Section Aggregator command is shown below. Figure 8 As shown.

[0074] S6. Assemble zero-length linear shear-slip spring elements A and C at both ends of fiber beam element B, as follows: Figure 2 As shown.

[0075] If the above methods are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0076] In this embodiment, the simulated coupling beam has a width of 130mm, a height of 700mm, a span of 700mm, a single-sided longitudinal reinforcement ratio of 0.44%, a stirrup ratio of 1.51%, a concrete strength of 24MPa, a longitudinal reinforcement strength of 385MPa, a web reinforcement strength of 364MPa, and a stirrup strength of 364MPa. [Reference source: Pi Tianxiang. Research on seismic performance and design method of coupling beam with small span-to-height ratio in reinforced concrete shear wall [D]. Chongqing: Chongqing University, 2008.]

[0077] Establish nodes ① (0,0,0), ② (0,0,0), ③ (0,0,700), and ④ (0,0,700). Connect nodes ① and ② to form element A, connect nodes ② and ③ to form element B, and connect nodes ③ and ④ to form element C. Node ① is fixed, and the horizontal translational displacement constraint of node ④ is released.

[0078] Define the fiber section of the coupling beam, such as Figure 9 As shown. The concrete fiber is modeled using the Concrete02 constitutive model (…). Figure 3 The steel reinforcement uses Steel02 constitutive structure. Figure 4 ).

[0079] The calculated key point data for the nonlinear shear constitutive model are: crack point coordinates (V... cr γ cr (1.089x10) 5 N, 0.000140015); Peak point coordinates (V u γ u (3.945x10) 5 N, 0.004077239); unloading section stiffness k d 2.509x10 5 N. Assign the above coordinates to the constitutive model of the Hysteretic Material.

[0080] The Section Aggregator command provided by OpenSees is used to combine the nonlinear shear stiffness of the section level with the axial and bending stiffness of the fiber section to obtain the overall stiffness matrix of the section, so as to realize the fiber section that can simultaneously consider axial shear and bending. This section property is then assigned to the fiber element based on force interpolation to form element B.

[0081] The stiffness k of the linear shear slip spring is calculated. s 1.32x10 7 N is assigned to zero-length shear spring elements A and C.

[0082] The above model is subjected to low-cycle iterative loading; the loading regime is as follows: Figure 10 The shear force at node ① and the displacement at node ④ were recorded to obtain the simulated load-displacement hysteresis curve. A comparison graph of the simulated load-displacement hysteresis curve and the actual load-displacement curve from the experiment is shown below. Figure 11 As shown, the initial stiffness, peak load, stiffness degradation, pinching effect, and hysteretic energy dissipation of the coupling beam simulated using the method of this embodiment are basically consistent with the experimental results.

[0083] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An OpenSees-based small-span-high-aspect-ratio coupling beam hysteresis characteristic prediction method, characterized by, Includes the following steps: A coupling beam model for simulating a real small-span-to-height coupling beam is constructed based on the OpenSees analysis platform. The coupling beam model is subjected to low-cycle repeated loading, and the shear force at one end and the displacement at the other end are recorded to obtain the load-displacement hysteresis curve of the coupling beam model. The hysteresis characteristic prediction results are obtained, including the initial stiffness of the coupling beam, peak load, stiffness degradation, pinching effect and hysteresis energy dissipation. The coupling beam model includes fiber beam elements and zero-length nonlinear shear-slip tension spring elements located at both ends of the fiber beam elements. The zero-length nonlinear shear-slip tension spring elements are formed by ZeroLength Element elements provided by the OpenSees analysis platform, which have a nonlinear shear-slip spring stiffness, and are used to simulate the shear deformation of the coupling beam and the slip tension deformation at the interface between the beam end and the wall limb. The fiber beam elements are formed by force interpolation-based fiber elements with an overall cross-sectional stiffness matrix. The overall cross-sectional stiffness matrix is ​​formed by combining the nonlinear shear stiffness of the cross-section level with the axial and bending stiffness of the fiber cross-section using the SectionAggregator command provided by OpenSees. The force interpolation-based fiber element includes a fiber section of a coupling beam. The nonlinear shear constitutive model of this fiber section is defined using the Hysteretic Material constitutive model provided by the OpenSees analysis platform. The skeleton curve of the Hysteretic Material constitutive model is a three-segmented line model. The key parameters of the Hysteretic Material constitutive model include the cracking point load and strain, the peak point load and strain, and the unloading section stiffness. In the fiber section of the coupling beam, the concrete of the coupling beam adopts the Concrete02 constitutive model, and the steel reinforcement of the coupling beam adopts the Steel02 constitutive model. The zero-length nonlinear shear-slip tension spring unit adopts the constitutive definition of Hysteretic Material. The skeleton curve of the Hysteretic Material constitutive model is a bisegmented line model. The key parameters include peak load and displacement and unloading segment stiffness. 2.The OpenSees-based method for predicting the hysteretic behavior of small aspect ratio coupling beams according to claim 1, wherein, The fiber cross-section of the connecting beam is determined based on the cross-sectional dimensions of the connecting beam, the arrangement of the reinforcing bars, and the material strength grade parameters.

3. A computer-readable storage medium, characterized in that, Includes one or more programs that are executed by one or more processors of an electronic device, said one or more programs including instructions for performing the OpenSees-based method for predicting the hysteretic characteristics of small span-to-height beams as described in any one of claims 1-2.

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