Calculation of earthquake force and house stiffness

1. 1 Understanding and application of the ratio of seismic force to seismic interlayer displacement

(1) code requirements: articles 3.4.2 and 3.4.3 of the code for seismic design and article 4.4.2 of the code for design of high rise buildings stipulate that the lateral stiffness of the floor should not be less than 70% of the lateral stiffness of the upper adjacent floor or 80% of the average lateral stiffness of the upper adjacent three floors< (2) calculation formula: ki = VI/ Δ UI

3 scope of application:

① it can be used to calculate the engineering stiffness ratio specified in article 3.4.2 and 3.4.3 of the code for seismic design and article 4.4.2 of the code for seismic design< It can be used to judge whether the basement roof can be used as the embedded end of the superstructure< (2) understanding and application of shear stiffness (1) code requirements:

Article e.0.1 of the code for design of high rise buildings stipulates that when the large space at the bottom is one floor, the equivalent shear stiffness ratio of the upper and lower structures of the transfer floor can be adopted approximately γ It represents the change of stiffness of upper and lower structure of transfer floor, γ It should be close to 1 in non seismic design γ It should not be more than 3. In seismic design γ It should not be greater than 2. See page 151 of the code for design of tall buildings for calculation formula< (2) article 6.1.14 of the code for seismic design stipulates that when the basement roof is used as the embedded part of the superstructure, the ratio of the lateral stiffness of the basement structure to that of the superstructure should not be less than 2. The calculation method of the lateral stiffness can adopt the shear stiffness according to the provisions. The calculation formula is shown on page 253 of seismic code< (2) the calculation method provided by SATWE software is the method provided by seismic code< (3) application scope: it can be used to calculate the stiffness ratio of the project specified in article e.0.1 of the code for design of high rise buildings and article 6.1.14 of the code for seismic design< (3) understanding and application of shear bending stiffness (1) code requirements:

Article e.0.2 of the code for design of high rise buildings stipulates that when the large space at the bottom is more than one floor, the equivalent lateral stiffness ratio of the upper part of the transfer floor to the lower part of the structure shall be calculated γ E can be calculated by formula (e.0.2) using the calculation model shown in Figure E. γ E should be close to 1 in non seismic design γ E should not be greater than 2, when seismic design γ E should not be greater than 1.3. For the calculation formula, see page 151 of the code for design of tall buildings< (2) article e.0.2 of the code also stipulates that when the transfer floor is set at three or more floors, the floor lateral stiffness ratio shall not be less than 60% of the adjacent upper floors< (2) calculation method adopted by SATWE software: simplified calculation of high lateral displacement stiffness

3) application scope: it can be used to calculate the stiffness ratio of Engineering specified in article e.0.2 of the code for design of tall buildings< (4) the main differences between the application scope of stiffness ratio in Shanghai code and national code are as follows:

(1) article 6.1.19 of Shanghai Code stipulates that the lateral stiffness of basement floor should not be less than 1.5 times of that of upper floor when the basement is used as the embedded end of superstructure< (2) the shear stiffness ratio has been used to calculate the three stiffness ratios in Shanghai code< (5) engineering example:

(1) project overview: a project is a frame supported shear wall structure, with 27 floors (including two floors of basement), and the sixth floor is a frame supported transfer floor. The three-dimensional axonometric drawing, the sixth and seventh floor plan of the structure are shown in Figure 1 (the figure is omitted). The seismic fortification intensity of the project is 8 degrees, and the design basic acceleration is 0.3g.

the calculation results of X-direction stiffness ratio of 1-13 floors:

e to the difficulty in listing, the meaning of each line of numbers below is as follows: the calculation method of three kinds of stiffness is separated by "/", the first section is the algorithm of seismic shear force and seismic interlayer displacement ratio, and the second section is shear stiffness, The third section is shear bending stiffness. The specific data are: layer number, RJX, ratx1, weak layer / RJX, ratx1, weak layer / RJX, ratx1, weak layer

where RJX is the lateral stiffness of the tower in the overall coordinate system of the structure (it should be multiplied by the 7th power of 10); Ratx1 is the smaller of the ratio of the lateral stiffness of the tower on this floor to 70% of the lateral stiffness of the corresponding tower on the upper floor or 80% of the average stiffness of the upper three floors. The specific data are as follows:

1, 7.8225, 2.3367, no / 13.204, 1.6408, no / 11.694, 1.9251, no

2, 4.7283, 3.9602, no / 11.444, 1.5127, no / 8.6776, 1.6336, no

3, 1.7251, 1.6527, no / 9.0995, 1.2496, no / 6.0967, 1.2598, no

4, 1.3407, 1.2595, no / 9.6348, 1.0726, No / 6.9007, 1.1557, no

5, 1.2304, 1.2556, no / 9.6348, 0.9018, yes / 6.9221, 0.9716, yes

6, 1.3433, 1.3534, no / 8.0373, 0.6439, yes / 4.3251, 0.4951, yes

7, 1.4179, 2.2177, no / 16.014, 1.3146, no / 11.145, 1.3066, no

8, 0.9138, 1.9275, no / 16.014, 1.3542, No / 11.247.1.3559, no

9, 0.6770, 1.7992, no / 14.782, 1.2500, no / 10.369, 1.2500, no

10, 0.5375, 1.7193, no / 14.782, 1.2500, no / 10.369, 1.2500, no

11, 0.4466, 1.6676, no / 14.782, 1.2500, no / 10.369, 1.2500, no

12, 0.3812, 1.6107, no / 14.782, 1.2500, No / 10.369, 1.2500, no 13, 0.3310, 1.5464, no / 14.782, 1.2500, no / 10.369, 1.2500, no

note 1: when SATWE software calculates "seismic shear force and seismic interlayer displacement ratio", fill in "0" in "relative stiffness ratio of backfill to basement restraint" in "basement information"

note 2: the number of weak layers and corresponding layer number are not defined separately in SATWE software

note 3: this example is mainly used to illustrate the realization process of the three stiffness ratios in SATWE software, and the rationality of the structural scheme is not discussed< (3) analysis of calculation results (1) the judgment results of weak layer are different when stiffness ratio is calculated by different methods

② in the "adjustment information" of SATWE software, the designer should specify the number of the sixth weak layer of the conversion layer. The designation of weak layer number does not affect the program's automatic judgment of other weak layers

③ when the transfer floor is set at three or more floors, the height regulation also stipulates that the lateral stiffness ratio of the floor should not be less than 60% of the adjacent upper floor. This SATWE software has no direct output results, so designers need to calculate the stiffness of each layer separately according to the program output. For example, the calculation results of this project are as follows:

1.3433 × 107／1.4179 × 107＝94.74％> 60%

meet the specification requirements< (4) whether the basement roof can be used as the embedded end of the superstructure:

A) the ratio of seismic shear force to seismic interlayer displacement

= 4.7283 × 107／1.7251 × The basement roof can be used as the embedded end of the superstructure

b) the shear stiffness ratio

= 11.444 × 107／9.0995 × (107) = 1.25 < 2

the roof of the basement can not be used as the embedded end of the superstructure

⑤ when SATWE software calculates the shear bending stiffness, the value range of H1 includes the height of the basement, and the height of H2 is equal to or less than H1. For the designers who want the value of H1 to be taken from 0.00 or above, or remove the basement and recalculate the shear bending stiffness, or manually calculate the stiffness ratio according to the shear bending stiffness output by the program. Taking the project as an example, H1 is calculated from 0.00, using the stiffness string model, the calculation results are as follows:

the floor number of the transfer floor is 6 (including basement), the starting and ending floor number of the lower part of the transfer floor is 3-6, H1 = 21.9m, the starting and ending floor number of the upper part of the transfer floor is 7-13, h2 = 21.0m.

K1 = [1 / (1 / 6.0967 + 1 / 6.9007 + 1 / 6.9221 + 1 / 4.3251)] × 107=1.4607 × 107

K2=[1/1/11.145+1/11.247+1/10.369 × 107=1.5132 × 107

Δ 1=1/K1 Δ 2 = 1 / K2

then shear bending stiffness ratio γ e= Δ one × H2/ Δ two × (6) discussion on the properties of three kinds of stiffness ratio

(1) ratio of seismic shear force to seismic interlayer displacement: a calculation method related to external force. Specified in the specification Δ UI includes not only the displacement caused by seismic force, but also the displacement caused by overturning moment Mi of the floor and the rigid body rotation displacement of the floor caused by the rotation of the next floor< (2) shear stiffness: the calculation method is mainly the ratio of shear area to the corresponding storey height, which is closely related to the shear area and storey height of vertical members. However, the shear stiffness does not consider the influence of the structural system with braces and the height of shear wall openings< (3) shear bending stiffness: actually, it is the interlayer displacement angle under the action of unit force, and its stiffness ratio is also the ratio of interlayer displacement angle. It can consider the influence of shear deformation and bending deformation at the same time, but does not consider the constraints of upper and lower layers

the properties of the three kinds of stiffness are completely different, and there is no necessary connection between them. Because of this, the code gives them different scope of application.

2.

If it is a rigid floor, when the story shear force is calculated, the shear force of each wall can be obtained by distributing the story shear force according to the proportion of each wall and the total lateral stiffness of the story

the transverse seismic shear force is borne by the transverse wall, and the longitudinal seismic shear force is borne by the longitudinal wall. The seismic shear force is transmitted to the transverse wall through the floor, and the seismic force distributed to each wall is related to the stiffness of the floor and the wall

the cast-in-place reinforced concrete floor or assembled integral reinforced concrete floor is considered as rigid, and the lateral displacement of each wall is the same. Let the shear force of the i-th floor be the shear force of the m-th wall of vi

The deformation of each structure is related to the representative value of gravity load which proces its seismic shear force

because the seismic influence coefficient decreases rapidly in the long period, the calculated structural effect under horizontal earthquake action may be too small for the structure whose basic period is more than 3.5s. For long-period structures, the ground motion velocity and displacement may have a greater impact on the damage of structures under seismic dynamic action, but the mode decomposition response spectrum method adopted in the code can not estimate this

for the sake of structural safety, this paper puts forward the minimum requirements for the total horizontal seismic shear force of the structure and the horizontal seismic shear force of each floor, and specifies the shear coefficient under different intensity. When it is not satisfied, it is necessary to change the structural layout or adjust the total shear force of the structure and the horizontal seismic shear force of each floor to meet the requirements

for example, when the total seismic shear force at the bottom of the structure is slightly less than that specified in this article, and the middle and upper floors meet the minimum value, the following methods can be used to adjust:

if the basic (first) period of the structure is located in the acceleration control section (platform section) of the design response spectrum, each floor shall be multiplied by the same increase factor

if the basic period of the structure is located in the displacement control section (long period section) of the response spectrum, the difference △ of the shear coefficient at the bottom of each floor I should be calculated λ 0 increases the seismic shear force of this layer △ feki = △ λ 0GEi

if the basic period of the structure is located in the velocity control section (parabolic section) of the response spectrum, the increase value should be greater than △ a λ 0gei, the average value of the dynamic displacement and acceleration can be taken as the top added value, and the added value of the middle layers can be approximately linearly distributed

extended data:

shear wall structure is a structure that uses the internal or external walls of a building to make shear walls to bear vertical and horizontal loads. Shear walls are generally reinforced concrete walls with the same height and width as the whole building. Because its main load is horizontal load, it is shear and bending, so it is called shear wall

ring the earthquake, the ground motion is proced by the action of seismic wave, and the superstructure is affected by the foundation of the building, which makes the structure vibrate. The inertial force proced by the vibration of the building is the seismic load. Seismic wave may cause vertical vibration and horizontal vibration of buildings, but generally the damage to buildings is mainly caused by horizontal vibration. Therefore, horizontal seismic force is mainly considered in design

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12

note: the above contents may not be applicable to all procts of the same type / series, and some screen options or operation steps may be different e to different software versions. If you have any questions, please contact the corresponding customer service of ASUS for details

what is BIOS? BIOS is the abbreviation of "basic input output system" in English, and its Chinese name is "basic input output system". It is a set of programs that are fixed to a ROM chip on the main board of the computer. It stores the most important basic input and output programs of the computer, post boot self check program and system self boot program. It can read and write the specific information of system settings from CMOS. Its main function is to provide the most direct hardware setting and control for the computer

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9. First of all, it can be seen that the setting of the building owner is inclined plane fixed

secondly, in fact, this question is given more conditions, because it is known μ And the tilt angle can determine whether the object is uniform or not θ ＞μ mgcos θ ， Therefore, there are too many conditions and contradictions in this problem, which does not exist.

the calculation of the building owner is correct,
but back to the solution, some problems do not give the condition of friction, but give the condition of uniform motion, so we need to solve the friction through balance

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