Static and modal analysis of the structure of an Olympic venue (3)


Result analysis:

(1) It can be seen from Table 1 that due to the suitable thickness (0.15 m), the flexibility is moderate and the general vertical displacement of the plate is 0.025.

Around the meter, the span at the elevation of 6.95 meters is larger, and the vertical displacement is slightly larger, which is 0.032629 meters, meeting the requirements of the specification.

(2) The opening of the structure is not large, the largest is 17.32 meters, and the cross-sectional dimension of the beam is relatively small, and the force is not counted.

Very large, but the stress is relatively large, it is recommended to use prestressing tendons to adjust the stress of the beam to meet the requirements of the specification.

(3) The span of the slab is relatively large, and the temperature difference between the four seasons is relatively large, so the temperature stress of the slab is not negligible.

(4) Since more beams and columns meet at the same node, a large stress concentration will occur, so at the beam-column node

Do a careful treatment.

(5) The calculation results show that the design is basically reasonable for static.

4 Analysis of natural vibration characteristics

Due to the large span of the structure, it is necessary to analyze the dynamic response and seismic performance of the structure. In order to solve the self-vibration characteristics of the structure: frequency, period and mode, generally consider the undamped free vibration, and the structure is considered to be in the linear elastic phase. After the boundary treatment, the structure is simply harmonically vibrated. The vibration equation is:

([K]-ω2[M]){Φ}={0} (3)

Where [K] is the structural total rigid matrix; [M] is the structural mass matrix; ω is the natural vibration frequency of the structure; {Φ} is the vibration mode vector.

The various order frequencies of the structure can be found by:

|K-ω2M|=0 (4)

Because the Olympic venue is a typical three-dimensional structure, the frequency is denser and there are more vibration modes. After repeated trials, the first 40 natural frequencies and vibration modes of the structure are taken (Table 2).

Its first 9-order mode (limited space) is shown in Figure 3.

From the figure, it can be concluded that the vibration mode characteristics of the structure are:

(1) The fundamental frequency is high. The first frequency is 3.3674 Hz, which embodies the relatively large overall rigidity of the structure;

(2) The natural vibration frequency is relatively dense. The first frequency is 3.3674 Hz, and the frequency of the fortieth mode is 7.1814 Hz.

The frequency only differs by 3.814 Hz, the spectrum changes evenly, and the phenomenon of no frequency hopping reflects the complexity of the dynamic performance of the structure.

(3) The vertical vibration mode is dominant. Most of the modes are vertical vibration, mainly on the floor and close to the side.

The reason is that the horizontal stiffness of the beam and column is relatively large, which makes the vertical vibration mode easy to back-excite, which is also a prominent feature of the large-span space;

(4) The local vibration mode is obvious. Most of the modes are shown in the upper part and close to the edge, due to the lower structure.

The stiffness is relatively large and the stiffness of the upper portion is relatively small.

Table 2 The first 40 frequency of the Olympic venue

Order frequency

Order frequency

Order frequency

Order frequency

1

3.3674

11

5.6217

twenty one

6.5090

31

6.8678

2

3.6898

12

5.8762

twenty two

6.5792

32

6.8982

3

3.7910

13

6.0393

twenty three

6.6288

33

6.9581

4

4.3993

14

6.0676

twenty four

6.6395

34

6.9885

5

4.8103

15

6.1310

25

6.6652

35

7.0667

6

4.8897

16

6.1518

26

6.7196

36

7.0909

7

5.0427

17

6.2804

27

6.7481

37

7.1407

8

5.2656

18

6.3562

28

6.7668

38

7.1526

9

5.4175

19

6.4483

29

6.8018

39

7.1647

10

5.4649

20

6.4897

30

6.8424

40

7.1814

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