A parametric study based on AS1170.2 is performed in order to determine the factors affecting building acceleration at both along-wind and crosswind directions. These factors are categorized as follows:
Wind-governed parameters
These are the basic parameters in terms of where the building is located that affect the design wind speed. These parameters are as follows:
a) Region and terrain category type
b) Multipliers (Height, Wind Direction, Shielding, Topography)
Building-governed parameters
These parameters are related to the building size and/or its shape, and can greatly affect the building acceleration. These parameters are as follows:
a) Building dimensions (length, width, height) b) Building properties (stiffness, mass)
c) Damping ratio and its mode shape k, depending on the type of structure
An illustrative example, as shown in Figure 2.14, of a tall building located at a region with relatively high wind speeds was adopted for the purpose of this study. The relevant information about this building is as follows:
• Location at Region B and Terrain category 3
• Dimensions: 46m x 30m x 183m height
• Sway frequencies: na=nc=0.2 Hz
• Average building density of 160 kg/m3 and damping ratio of 1%
Figure 2.14 Illustrative example of a tall building
183m
30m 46m
Along Wind Response
2.2.2.1 Region
Regional wind speeds are based on 3s gust wind data and classified into several regions
— Regions A, W, B, C and D — across Australia. The table below shows a comparison of the building’s accelerations for the same building at different regional wind speeds of 5-year return period.
Along Wind Response Across Wind Response
Region
Wind Speed (m/s)
Base Shear (MN)
Base Moment
(MNm)
Acceleration (mg)
Base Shear (MN)
Base Moment
(MNm)
Acceleration (mg)
A 32 15.8 1533 11.1 5.5 670 21.7
B 28 27.6 2676 7.4 9.4 1140 16.6
C 33 42.5 4120 12.1 14.1 1711 23.1
D 35 71.4 6921 14.5 22.8 2769 25.9
W 39 21.3 2061 20.1 7.3 890 32.2
Table 2.1 Comparison of building accelerations against regional wind speed
Regional Wind Speed VS Building Acceleration
0 5 10 15 20 25 30 35
0 1 2 3 4 5 6
Region
Acceleration (mg)
Along Wind Acceleration Across Wind Acceleration
Figure 2.15 Comparison of regional wind speed with along-wind and crosswind response
From Figure 2.15, Region W has the highest building acceleration although it has a relatively lower base shear and moment compared to other regions. This is due to the 5 year average recurrence interval of the highest wind speed, while its lowest wind speed is at a 1000 years return period. In comparison, Region B has a higher wind speed with a 1000 year return period and a lower wind speed of a 5 year return period, and therefore has a lower building acceleration than the building located at Region W. Likewise, the along-wind acceleration has increased/decreased linearly across the wind acceleration
2.2.2.2 Terrain Category
The surroundings are another factor that affects the wind flow towards a structure and, eventually, the building’s acceleration. According to AS 1170.2, the terrain should be carefully assessed and classified into 4 types. Category 1 is exposed open terrain;
Category 2 is grassland with few scattered obstructions; Category 3 is terrain with numerous closely spaced obstructions, such as areas of suburban housing; and category 4 is terrain with closely spaced obstructions, such as large city centers. The table below shows a comparison of a building located at different regions with parameters set that are similar to the illustrative example.
Along Wind Response Across Wind Response
TC
Base Shear (MN)
Base Moment
(MNm)
Acceleration (mg)
Base Shear (MN)
Base Moment
(MNm)
Acceleration (mg)
1 34.9 3276 8.4 14.2 1733 25.2
2 31.9 3034 8.2 12.0 1461 21.3
3 27.6 2676 7.4 9.4 1140 16.6
4 22.0 2162 5.7 6.2 757 11.0
Table 2.2 Comparison of building accelerations against terrain category
Terrain Category VS Building Acceleration
0 5 10 15 20 25 30
0 1 2 3 4 5
TC
Acceleration (mg)
Along Wind Acceleration Across Wind Acceleration
Figure 2.16 Comparison of terrain categories with along-wind and crosswind response
Clearly from Figure 2.16, the worst building acceleration may occur at terrain category 1, which can be well explained by the unobstructed wind flow around the building.
However, the effect is minimal if along wind accelerations across the 4 terrains are compared. Therefore, it may be concluded that terrain category has a large effect on building crosswind acceleration.
2.2.2.3 Building Dimensions
The dimensions of a building are another important factor that eventually affect acceleration as a result of the change of the crosswind force spectrum coefficient (Cfs) value. A wider or longer building would yield different tip acceleration when compared to a square building of the same height. Therefore, a series of building dimension ratios (H:B:D) are applied to compare the building’s accelerations, setting similar parameters to the illustrative example.
Along Wind Response Across Wind Response Building
Ratio (H:B:D)
Base Shear (MN)
Base Moment (MNm)
Acceleration (mg)
Base Shear (MN)
Base Moment (MNm)
Acceleration (mg)
1 6:2:1 35.6 3456 8.8 7.9 956 19.9
2 6:1.5:1 27.6 2676 7.4 9.4 1140 16.6
3 6:1:1 18.2 1761 4.4 21.3 2589 15.5
4 6:1:1.5 16.6 1614 4.9 15.5 1880 14.5
5 6:1:2 15.1 1479 4.5 11.3 1372 13.7
Table 2.3 Comparison of building accelerations against building dimensions
Building Ratio VS Acceleration
0 5 10 15 20 25
0 1 2 3 4 5 6
Building Ratio
Acceleration (mg)
Along Wind Acceleration Across Wind Acceleration
Figure 2.17 Comparison of building dimensions with along-wind and crosswind response
From Figure 2.17, it can be seen that the highest acceleration may be applied to a building with a rectangular shape; the narrower the short section of the building where the crosswind is applied would result in a larger acceleration at both the along- and cross wind response. The ideal structure would be either a symmetrical or a square building, providing the least acceleration regardless of the wind directionality.
2.2.2.4 Building Mass
In actual fact, building mass is hard to predict because it varies from day-to-day due to the movable live load within the building. In this case, G+0.4Q is adopted to compare the along-wind and across-wind responses. The results shown below are a comparison of building accelerations against ranges of building mass, with the other building parameters similar to those for the illustrative example. Commonly, a typical concrete residential building is ranged from 150-200kg/m3, while an office building is from 250-300kg/m3.
Along Wind Response Across Wind Response
Mass (kg/m3)
Base Shear (MN)
Base Moment (MNm)
Acceleration (mg)
Base Shear (MN)
Base Moment (MNm)
Acceleration (mg)
100 27.0 2621 9.3 6.2 751 27.2
160 27.6 2676 7.4 9.4 1140 16.6
200 27.9 2707 6.5 6.0 724 13.1
250 28.3 2742 5.8 5.9 716 10.4
300 28.6 2773 5.2 5.8 708 8.6
Table 2.4 Comparison of building mass against building dimensions
Building Mass VS Acceleration
0 5 10 15 20 25 30
0 50 100 150 200 250 300 350 400
Building Mass (kg/m3)
Acceleration (mg)
Along Wind Acceleration Across Wind Acceleration
Figure 2.18 Comparison of building mass with along-wind and crosswind response
From Figure 2.18, it is obvious that a building’s mass may have a direct relationship to along-wind acceleration and an exponential relationship to across-wind acceleration.
Therefore, a lighter building, which is the trend in tall building nowadays, may have an adverse effect on human comfort, as a result of an exponential increment in the crosswind acceleration. This has to be specifically taken into consideration in the design of tall buildings. As yet, however, no code/standard provides a uniform guideline for designers in terms of reinforcing the acceleration criteria to ensure that the building remains serviceable during a high windstorm event. This will be discussed later in Chapter 2.4.
2.2.2.5 Building Periods
Theoretically, a building’s period is proportional to its mass and stiffness. By setting the mass as constant, a building period may vary depending on the stiffness of the structure.
Stiffness of structure plays a crucial part in determining the deflection and acceleration of buildings, especially in high-rises. Depending upon the structural system adopted in a building, periods might not be similar, although the building’s width, length, height and mass are the same. Therefore, in the table below a series of building periods are applied to compare building accelerations, setting the other parameters similar to those of the illustrative example.
Along Wind Response Across Wind Response
Periods (s)
Base Shear (MN)
Base Moment (MNm)
Acceleration (mg)
Base Shear (MN)
Base Moment (MNm)
Acceleration (mg)
10 30.1 2922 13.5 8.7 1055 15.4
7 28.7 2781 10.0 9.0 1100 16.0
5 27.6 2676 7.4 9.4 1140 16.6
3 26.5 2574 4.4 9.9 1200 17.5
1 25.8 2505 1.3 10.8 1318 19.2
Table 2.5 Comparison of building periods against building responses
Building Periods VS Acceleration
0 5 10 15 20 25
1 3 5 7 9 11
Period (s)
Acceleration (mg)
Along Wind Acceleration Across Wind Acceleration Resultant Acceleration
Figure 2.19 Comparison of building periods with along-wind and crosswind response
From Figure 2.19, different building periods may have a great effect on both along-wind and across-wind acceleration. Along-wind acceleration tends to increase linearly, while across-wind acceleration decreases slightly with an increasing period. However, the final resultant acceleration from both along-wind and across-wind is approximately similar, for periods less than 5s, while the resultant acceleration tends to increase for periods of more than 5s.