A control model for the torsional effect of a rectangular planar high-rise structure and its application

Abstract

A control model for the torsional effect of a rectangular planar high-rise structure and its application. The present invention uses the torsional displacement ratio ξ to characterize the model. In the application, by controlling the translational periods in two directions of the rectangular planar structure to have a certain difference, that is, controlling the short-side period to be greater than the long-side period, the purpose of reducing the torsional effect is achieved, breaking through the traditional experience that the dynamic characteristics in two directions need to be kept as consistent as possible, reducing the design difficulty, and improving the seismic performance of the structure.

Description

Technical Field

[0001] The present invention relates to the technical field of high-rise building structure design. Background Art

[0002] Article 3, Paragraph 3, Clause 3.5.3 of the "Code for Seismic Design of Buildings" GB50011-2010 stipulates that: the dynamic characteristics of the structure in two main axis directions should be similar. In actual engineering, when the structural plane is rectangular or elliptical, there is often a certain difference in the vibration periods in two main axis directions, that is, the lateral stiffness difference in two directions is relatively large. Regarding the adverse effects brought by the large difference in dynamic characteristics in two directions, the clause explanation of Article 3.5.3 explains that: "Considering that in some building structures, there are many lateral force resisting members (such as walls) in the transverse direction and few in the longitudinal direction, and in strong earthquakes, the overall collapse often occurs due to longitudinal damage. The 2001 code added the seismic concept that the dynamic characteristics (period and mode shape) of the structure in two main axis directions are similar." From the above explanation, it can be seen that this regulation is mainly to avoid the insufficient seismic capacity in one direction of the structure. This situation often occurs in some shear wall structures of slab-type residential buildings. Due to the need for window opening and daylighting in the longitudinal direction, there are fewer complete walls. Essentially, it is not that the difference in stiffness in two directions will cause adverse effects, but out of consideration for the overall stiffness and bearing capacity of the structure, and to prevent "weakness in the longitudinal direction". When the stiffness in both directions can better meet the requirements, and there is only a difference in the translational stiffness in two directions due to the longer length of the building plane in one direction, especially when "the long direction is stiffer", whether it is also necessary to control according to this article is not clearly stated in the code. In addition, it is generally considered that a long and narrow plane is prone to adverse seismic effects. Therefore, the "Technical Specification for Concrete Structures of High-rise Buildings" JGJ3-2010 has made relevant regulations on the aspect ratio of the structural plane. When the aspect ratio of the structural plane is relatively large, it often leads to a large difference in stiffness in two directions. At this time, it is not clear what kind of impact the coupling of the two effects of a large aspect ratio of the plane and large dynamic characteristic differences will have on the torsion of the structure.

[0003] The situation where the plane dimensions in two main axis directions are quite different, that is, the aspect ratio of the plane is relatively large, often appears not only in multi-story frame structures or high-rise slab-type shear wall residential structures, but also when the plane of a tower-type super high-rise structure is rectangular or elliptical, the two-way dimensions may also be quite different. For example, in the Shenzhen Kingkey Financial Center (rectangular plane, 98 floors, 441.8m high), the dimension ratio in two main axis directions of the plane above the 38th floor reaches 1.9; in the Tianjin CTF Finance Centre (elliptical plane, 75 floors, 336.9m), the ratio of the long axis to the short axis of the plane is 1.7. In the seismic review of ultra-high-rise structures, it is often encountered that the translational periods in two directions of the structure "should be similar", but it is often difficult to achieve in design, and even if it is finally achieved, it may not be economically reasonable. Summary of the Invention

[0004] The object of the present invention is to first disclose a control model for the torsional effect of a rectangular planar high-rise structure, which is characterized in that it is characterized by using the torsional displacement ratio ξ, and the torsional displacement ratio takes the envelope value of the results in two directions.

[0005]

[0006] The torsional displacement ratio ξ is related to three parameters, namely the eccentricity γ, the aspect ratio η1, and the ratio of translational periods in two directions η2.

[0007] The control model for the torsional effect of a rectangular planar high-rise structure is characterized in that the minimum value of the torsional displacement ratio ξ in Equation (9) is obtained by controlling the relevant parameters: when the eccentricity γ is constant and η1η2 is 1.0, the value of ξ is the smallest.

[0008] An application of a control model for the torsional effect of a rectangular planar high-rise structure is characterized in that it has application value in the field of high-rise building structure design for the eccentricity model of the torsional effect of a rectangular structure.

[0009] The application is characterized in that when the product η1η2 of the ratio of translational periods η2 and the aspect ratio η1 of the plane is equal to 1.0, the torsional effect is theoretically the smallest, and the torsional effect is reduced by adjusting the structural scheme to make the product as close to 1.0 as possible.

[0010] The application is characterized in that further, by adjusting the structural scheme to make the product of the ratio of translational periods and the aspect ratio of the plane close to 1.0, it is specifically divided into three cases:

[0011] 1) When the product η1η2 is significantly greater than 1.0 and the ratio of translational periods η2 is also greater than 1.0, the structural scheme is very unreasonable, and the scheme is adjusted by increasing the stiffness in the long direction;

[0012] 2) When the product is significantly less than 1.0, the structural scheme is also obviously unreasonable, and the scheme is adjusted by increasing the stiffness in the short direction or appropriately reducing the stiffness in the long direction;

[0013] 3) When the product is greater than 1.0 and the ratio of translational periods η2 is less than 1.0, there is room for optimization of the structural scheme, and it can be determined whether to adjust the structural scheme according to the satisfaction of other overall indicators with the specifications (including various indicators such as bearing capacity, horizontal displacement, and overall stability).

[0014] The application is characterized in that in case 1), the product η1η2 > 1.5.

[0015] The application is characterized in that in case 2), the product η1η2 < 0.8.

[0016] The application is characterized in that in case 3), it is possible to determine whether to adjust the structural scheme according to the compliance of other overall indicators (including various indicators such as bearing capacity, horizontal displacement, and overall stability). Specifically, when adjusting the structural scheme, such as increasing or decreasing the lateral stiffness in one direction, it is necessary to ensure that other indicators of the structure also meet the relevant requirements of the specification to avoid the deterioration of other indicators due to the adjustment of the structural scheme.

[0017] Another object of the present invention is to provide a method for controlling seismic torsion of a high-rise structure with a rectangular plane. For a high-rise building structure with a large aspect ratio of length to width, by controlling the translational periods in two directions of the structure to have a certain difference, the purpose of reducing the torsional effect of the structure during an earthquake is achieved. Compared with the traditional method that requires the "dynamic characteristics in two directions to be consistent" for such structures, the present invention makes the design more reasonable and economical, and has better seismic performance.

[0018] To achieve the above object, the present invention provides a method for applying seismic torsion control of a high-rise structure with a rectangular plane, which is characterized by including:

[0019] S1. Calculate the aspect ratios of length to width in the two principal axis directions based on the plane dimensions of the main floors of the structure.

[0020] S2. Conduct a dynamic characteristic analysis of the structure to obtain the first-order translational periods in the two principal axis directions respectively.

[0021] S3. Divide the translational periods in the two principal axis directions described in S2 to obtain the translational period ratio.

[0022] S4. Substitute the translational period ratio described in S3 and the aspect ratio of length to width in S1 into the torsional effect model proposed by the present invention to obtain the torsional displacement ratio.

[0023] S5. When the torsional displacement ratio in S4 does not meet the specification requirements or it is necessary to further reduce the torsional effect, the structural scheme can be adjusted to change the translational period ratio in the two principal axis directions so that the product of the translational period ratio and the aspect ratio of length to width is close to 1.0 to achieve the reduction of the torsional effect.

[0024] The described method for controlling seismic torsion of a high-rise structure with a rectangular plane is characterized in that in S3, when obtaining the translational period ratio by dividing the translational periods in the two principal axis directions, it is necessary to use the translational period in the long axis direction as the numerator and the translational period in the short axis direction as the denominator, and the obtained translational period ratio may be greater than 1.0 or less than 1.0.

[0025] The described seismic torsional control method for a rectangular planar high-rise structure is characterized in that in S4, the proposed simplified theoretical formula for torsional effect contains three parameters, namely the aspect ratio of the plane, the ratio of translational periods, and the eccentricity. When the eccentricity is certain, the absolute values and relative magnitudes of the aspect ratio of the plane and the ratio of translational periods jointly determine the magnitude of the structural torsional effect; and this expression can give the maximum value of the torsional displacement ratio when the earthquake acts in two directions.

[0026] In summary, in the seismic torsional control method for a rectangular planar high-rise structure provided by the present invention, for a rectangular planar high-rise building structure with a relatively large aspect ratio (aspect ratio > 1.5), by controlling the translational periods in two directions of the structure to have a certain difference, the purpose of reducing the torsional effect of the structure during an earthquake is achieved. For such structures, the traditional practice of "consistent dynamic characteristics in two directions" is no longer pursued. The calculation and control results are reliable, the design is more reasonable and economical, and the seismic performance is better, which can provide theoretical support for the scheme design of super high-rise building structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Those of ordinary skill in the art should understand that the provided drawings are used to better understand the present invention and do not constitute any limitation to the scope of the present invention. Among them:

[0028] Figure 1 is a schematic plan view of the structural torsional mechanical model of the present invention;

[0029] Figure 2 is a step diagram of the seismic torsional control method for a rectangular planar high-rise structure provided by an embodiment of the present invention;

[0030] Figure 3 is a three-dimensional model and a plan view of the structure provided by an embodiment of the present invention;

[0031] Figure 4 is the internal force diagram of the columns before control provided by an embodiment of the present invention;

[0032] Figure 5 is the internal force diagram of the columns after control provided by an embodiment of the present invention;

[0033] Figure 6 is Table 1: Comparison table of relevant parameters and torsional responses before and after control provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0034] To make the objectives, advantages and features of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the accompanying drawings are all in very simplified forms and are not drawn to scale, and are only used to conveniently and clearly assist in explaining the objectives of the embodiments of the present invention. In addition, the structures shown in the accompanying drawings are often part of the actual structures. In particular, the focus to be shown in each accompanying drawing is different, and sometimes different scales are used. It should also be understood that unless otherwise specified or indicated, the terms "first", "second", "third", etc. in the specification are only used to distinguish the various components, elements, steps, etc. in the specification, rather than to represent the logical relationship or sequential relationship, etc. between the various components, elements, steps.

[0035] Theoretical derivation and application value of the first part of the mechanical model

[0036] To facilitate theoretical analysis and study the torsional effect of the structure, in the preliminary design of the super high-rise building structure, the inconsistency between the structural stiffness center X s and the mass center X m is assumed to be "the rigid center is centered and the mass center is eccentric", and this assumption will not affect the essence of the studied torsional effect.

[0037] Based on the above principles, the following simplified mechanical model is established: The two horizontal dimensions of the structural plane are the plane length a and the plane width b respectively, and it is assumed that a ≤ b. The lateral force resisting members are simplified into four identical corner columns. Considering the difference in stiffness in two directions (X and Y directions), it is assumed that the lateral stiffness of each column in the two horizontal directions is K a and K b respectively, the deviation distance between the mass center and the rigid center is e, and it is assumed that the floor slab is rigid. The plane of the simplified model is shown in Figure 1 .

[0038] For the convenience of formula derivation, the following variables are defined:

[0039] Torsional displacement ratio ξ; eccentricity ratio γ, Plane length-width ratio η1,

[0040] The first translational period T1 along the long direction of the plane;

[0041] The first translational period T2 along the short direction of the plane;

[0042] The translational period ratio η2 in two directions, η2 = T1 / T2.

[0043] Assume that the seismic action is F, and the action direction is the long axis direction (Y direction), and the corresponding torque is M, that is:

[0044] M = Fe = Faγ (1)

[0045] Let the translational displacement under the seismic action in the long-axis direction (Y direction) be u y , then we have:

[0046]

[0047] Define the torsional stiffness of the structure as K θ ,

[0048]

[0049] The torsional angle of the structural plane is

[0050]

[0051] The final y-direction displacement of one side column is

[0052]

[0053] The torsional displacement ratio is

[0054]

[0055] After further simplification, we get

[0056]

[0057] Similarly, the torsional displacement ratio under the seismic action along the short-axis direction can be obtained as

[0058]

[0059] The final torsional displacement ratio should take the envelope value of the results in two directions

[0060]

[0061] From Equations (7) to (9), it can be seen that the torsional displacement ratio ξ is related to three parameters, namely the eccentricity γ, the aspect ratio η1, and the ratio of translational periods in two directions η2η2. The expression form of Equation (9) is concise and has significant mathematical symmetry. It can be judged from this that the minimum value of the torsional displacement ratio ξ can be obtained by controlling the relevant parameters: when the eccentricity γ is constant and η1η2 is 1.0, the value of ξ is the smallest.

[0062] The application value of the eccentricity model of the torsional effect of rectangular structures in the field of high-rise building structure design:

[0063] Optionally, when the product η1η2 of the ratio of translational periods η2 and the aspect ratio η1 of the plane is equal to 1.0, the torsional effect is theoretically the smallest. Therefore, the torsional effect can be reduced by adjusting the structural scheme to make the product as close to 1.0 as possible. However, the stiffness in two directions of the structure should simultaneously meet other control conditions, such as bearing capacity, overall deformation, and stability requirements.

[0064] Furthermore, by adjusting the structural scheme, the product of the translational period ratio and the aspect ratio of the plane is made close to 1.0, which is specifically divided into three cases:

[0065] 1) When the product η1η2 is significantly greater than 1.0 (i.e., η1η2 > 1.5), and the translational period ratio η2 is also greater than 1.0, the structural scheme is very unreasonable and the scheme should be adjusted as much as possible (i.e., by increasing the stiffness in the long direction);

[0066] 2) When the product is significantly less than 1.0 (i.e., η1η2 < 0.8), the structural scheme is also obviously unreasonable and the scheme should be adjusted as much as possible (i.e., by increasing the stiffness in the short direction or appropriately reducing the stiffness in the long direction);

[0067] 3) When the product is greater than 1.0 and the translational period ratio η2 is less than 1.0, there is room for optimization in the structural scheme. It can be determined whether to adjust the structural scheme according to the situation where other overall indicators meet the specifications (including various indicators such as bearing capacity, horizontal displacement, and overall stability).

[0068] As described above, when the plane dimensions of the structure in the two main axis directions differ greatly, that is, the aspect ratio is large, maintaining the translational periods in the two directions basically the same is disadvantageous to the torsion of the structure. For a rectangular plane structure, the translational period ratio should be controlled to be less than 1.0 as much as possible, and the product of the translational period ratio and the aspect ratio of the plane is close to 1.0.

[0069] The second part: Application examples

[0070] As Figure 2 shown, this embodiment provides a method for controlling seismic torsion of a rectangular plane high-rise structure, including:

[0071] Step S1: Calculate the aspect ratios of the planes in the two main axis directions according to the plane dimensions of the main floors of the structure;

[0072] Step S2: Conduct a dynamic characteristic analysis of the structure to obtain the first-order translational periods in the two main axis directions respectively;

[0073] Step S3: Divide the translational periods in the two main axis directions to obtain the translational period ratio;

[0074] Step S4: Substitute the translational period ratio and the aspect ratio of the plane into the torsion effect model proposed by the present invention to calculate the torsion displacement ratio;

[0075] Step S5: When the torsion displacement ratio does not meet the specification requirements or it is necessary to further reduce the torsion effect, adjust the structural scheme according to the following principle: change the translational period ratio in the two main axis directions to make the product of the translational period ratio and the aspect ratio of the plane close to 1.0 to achieve a reduction in the torsion effect.

[0076] First, perform step S1. According to the plane dimensions of the main floors of the structure, calculate the aspect ratios η1 in the two principal axis directions. The specific formula is as follows:

[0077]

[0078] In the formula, η1 is the aspect ratio of the structural plane, a and b are the two horizontal dimensions of the length and width of the structural plane respectively, and a ≤ b.

[0079] Next, perform step S2. Conduct a dynamic characteristic analysis of the structure to obtain the first-order translational periods T1 and T2 in the two principal axis directions respectively; where T1 is the first translational period in the long axis direction, and T2 is the first translational period in the short axis direction.

[0080] Then perform step S3. Divide the translational periods in the two principal axis directions to obtain the translational period ratio η2. The specific formula is as follows:

[0081] η2 = T1 / T2

[0082] In the formula, η2 is the translational period ratio of the structure.

[0083] Then perform step S4. Substitute the translational period ratio and the aspect ratio of the plane into the torsional effect model proposed by the present invention to obtain the torsional displacement ratio; the formula of the torsional effect model is as follows:

[0084]

[0085] In the formula, ξ is the torsional displacement ratio, representing the magnitude of the torsional effect, and γ is the accidental eccentricity of the structure.

[0086] Optionally, the formula (9) of the torsional effect model includes three parameters, namely the aspect ratio of the plane η1, the translational period ratio η2, and the eccentricity γ. When the eccentricity γ is certain, the absolute values and relative magnitudes of the aspect ratio of the plane η1 and the translational period ratio η2 jointly determine the magnitude of the torsional effect of the structure.

[0087] Finally, perform step S5. When the torsional displacement ratio does not meet the code requirements or it is necessary to further reduce the torsional effect, adjust the structural scheme according to the following principle: change the translational period ratio in the two principal axis directions to make the product of the translational period ratio and the aspect ratio of the plane close to 1.0, so as to reduce the torsional effect.

[0088] Optionally, when the product of the translational period ratio and the aspect ratio of the plane is equal to 1.0, the torsional effect is theoretically the smallest. Therefore, the torsional effect can be reduced by adjusting the structural scheme to make the product as close to 1.0 as possible. However, the stiffness in the two directions of the structure should simultaneously meet other control conditions, such as the requirements for overall deformation and stability.

[0089] Optionally, by adjusting the structural scheme, the product of the translational period ratio and the aspect ratio of the plane is made close to 1.0, which is divided into three cases:

[0090] 1) When the product is significantly greater than 1.0 (e.g., >1.5) and the translational period ratio is also greater than 1.0, the structural scheme is very unreasonable and the scheme should be adjusted as much as possible (increase the stiffness in the long direction);

[0091] 2) When the product is significantly less than 1.0 (e.g., <0.8), the structural scheme is also obviously unreasonable and the scheme should be adjusted as much as possible (increase the stiffness in the short direction, or appropriately reduce the stiffness in the long direction);

[0092] 3) When the product is greater than 1.0 and the translational period ratio is less than 1.0, there is room for optimizing the structural scheme, and it can be determined whether to adjust the structural scheme according to the situation where other overall indicators meet the specifications (such as bearing capacity, horizontal displacement, overall stability, etc.).

[0093] The third part: Verification examples

[0094] The present invention will be further elaborated below in conjunction with a specific embodiment to illustrate the achieved effects of adopting the present method.

[0095] Using the seismic torsional control method for rectangular planar high-rise structures provided in the application example of the present invention, a certain 62-story office building is controlled. The structure is 262 m high, the plane is rectangular, and the three-dimensional model and the floor plan are shown in Figure 3 、 Figure 4 。 The aspect ratio of the plane is 1.642. When the dynamic characteristics in two directions are basically the same (Table 1: Model 1), that is, the translational period ratio is 0.991. At this time, the product of the aspect ratio of the plane and the translational period ratio is 1.631, and the maximum torsional displacement ratio of the structure is 1.073. If the stiffness in the long-axis direction is appropriately increased (Table 1: Model 2), the period of the long axis becomes shorter, and the translational period ratio drops to 0.864. At this time, the product of the aspect ratio of the plane and the translational period ratio drops to 1.418, and the torsional displacement ratio also drops from 1.073 to 1.033, indicating that the torsional effect has been improved. The detailed comparison data is shown in Table 1. From Figure 4 and Figure 5 the internal forces of the bottom columns, it can be seen that after controlling the difference in stiffness in two directions, the seismic force is also reduced by about 30%, and the implementation effect is remarkable.

[0096] In summary, in a seismic torsional control method for a rectangular planar high-rise structure provided by the present invention, for a rectangular planar high-rise building structure with a large aspect ratio, by controlling the translational periods in two directions of the structure to have a certain difference, the purpose of reducing the torsional effect of the structure during an earthquake can be achieved. For such structures, the traditional practice of "consistent dynamic characteristics in two directions" is no longer pursued. The calculation and control results are reliable, making the design more reasonable and economical, and the seismic performance is better. It can provide theoretical support for the scheme design of super high-rise building structures.

[0097] In addition, it should also be recognized that although the present invention has been disclosed above with preferred embodiments, the above embodiments are not intended to limit the present invention. For any person skilled in the art, without departing from the scope of the technical solution of the present invention, many possible changes and modifications can be made to the technical solution of the present invention by using the technical content disclosed above, or it can be modified into equivalent embodiments with equivalent changes. Therefore, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still belong to the scope of protection of the technical solution of the present invention.

Claims

1. A seismic torsional control application method for a rectangular planar high-rise structure, characterized in that Including: S1. Calculate the aspect ratio of the plane in two main axis directions based on the plane dimensions of the main floors of the structure; the two horizontal dimensions of the structural plane are the plane length , the plane width , and ; S2, conduct dynamic characteristic analysis on the structure to obtain the first-order translational periods in two main axis directions respectively; the first translational period along the long direction of the plane ; The first translational period along the short direction of the plane ; S3. Divide the translation periods in the two principal axis directions described in S2 to obtain the translation period ratio; the translation period ratios in the two directions along the long side and the short side of the plane , ; S4. Substitute the translational period ratio described in S3 and the aspect ratio of the plane length and width in S1 into the torsional effect model to obtain the torsional displacement ratio. The torsional effect model uses the torsional displacement ratio for characterization, and the torsional displacement ratio takes the envelope value of the results in two directions （9） The torsional displacement ratio is related to three parameters, namely the eccentricity , the aspect ratio , and the ratio of translational periods in two directions ; the eccentricity , ; the planar aspect ratio , ; The deviation distance between the centroid and the rigid centroid is , assuming that the floor slab is rigid; S5. When the torsional displacement ratio in S4 does not meet the code requirements or further reduction of the torsional effect is needed, the structural scheme can be adjusted to change the translational period ratio in the two principal axis directions, making the product of the translational period ratio and the aspect ratio of the plane close to 1.0 to achieve the reduction of the torsional effect.

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