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Effects of Topography on Wind Load

In this section, we will discuss the effects of topography on wind load on structures by calculating the topographic factor Kzt using ASCE 7-16. Speed-up effects due to abrupt changes in topography must be considered in calculating the design wind pressures.

Topographic Factor, Kzt

For ASCE 7-16, section 26.8 details the conditions in calculating the topography factor, Kzt . These are:

  • “The hill, ridge, or escarpment is isolated and unobstructed upwind by other similar topographic features of comparable height for 100 times the height of the topographic feature (100H) or 2 mi (3.22 km), whichever is less. This distance shall be measured horizontally from the point at which the height H of the hill, ridge, or escarpment is determined.”
  • “The hill, ridge, or escarpment protrudes above the height of upwind terrain features within a 2-mi (3.22-km) radius in any quadrant by a factor of 2 or more.”
For Hills or Ridge
For Escarpment
  • “The building or other structure is located as shown in Fig. 26.8-1 in the upper one-half of a hill or ridge or near the crest of an escarpment.”
  • H/Lh ≥ 0.2
  • H is greater than or equal to 15 ft (4.5 m) for Exposure C and D and 60 ft (18 m) for Exposure B.

Where:
H = Height of hill or escarpment relative to the upwind terrain, in ft (m).
Lh = Distance upwind of the crest to where the difference in ground elevation is half the height of hill or escarpment, in ft (m).

Lh distance for Hills or Ridge
Lh distance for Escarpment

Satisfying these conditions, Kzt needs to be considered. Otherwise, Kzt is equal to 1.0.

Case Study

To illustrate the calculation of Kzt, we will consider Gilt Edge Stage Rd, Lewistown, MT 59457, USA (lat: 47.09082818472724, lng:-109.22439642402344) with wind coming from South for our case study in calculating Kzt. The site is classified as Exposure C since there it is an open terrain.

Location of structure and the corresponding wind source direction (Google Maps, 2021).
Elevation profile of terrain S-N direction (Google Maps, 2021).

From the map image, we can deduce that the location of the structure is a plateau and can be considered as escarpment due to its flat surface on top. Getting the elevation data from Google Maps and setting the location of the structure as our starting point (negative distance means upwind and positive means downwind location), we can deduce the following points for Figure 26.8-1:

Point Definition Elevation, ft Location, ft
Structure 5197.18 0
Foot of Escarpment 4615.73 -7708.69
Peak of Escarpment 5443.89 3695.94
Middle 5029.81 -5279.76

From our date above, we can get H, Lh, and x:

Topo Diagram for Escarpment based on Figure 26.8-1.


H = 828.16 ft > 60 ft – difference in elevation of peak and foot
Lh = 1583.85 ft – difference of location of peak and location of middle
x = 3695.94 ft – distance of structure to peak of escarpment (negative for upwind, positive for downwind)
H/Lh = 0.5229 > 0.2

The topographic factor, Kzt, can be solved using the equation in Figure 26.8-1:

Kzt = (1+K1K2K3)2
K2 = 1 – |x|/μLh
K3 = eγz/Lh

Where:
K1 = Factor to account for the shape of topographic feature and maximum speed-up effect.
K2 = Factor to account for the reduction in speed-up with distance upwind or downwind of crest.
K3 = Factor to account for the reduction in speed-up with height above local terrain.
x = Distance (upwind or downwind) from the crest to the site of the building or other structure, in ft (m).
z = Height above the ground surface at the site of the building or other structure, in ft (m).
μ = Horizontal attenuation factor.
γ = Height attenuation factor.

For our case study, using Figure 26.8-1, where hill shape is “2D Escarpment.” Moreover, since H/Lh > 0.5, Lh should be equal to 2H:

K1/(H/Lh) = 0.85 (Exposure C)
K1 = 0.425
Lh = 2(828.16) = 1656.32 ft
γ = 2.5
μupwind = 1.5
μdownwind = 4 (adopted due to location of structure)

Since the structure is on the upwind side:

K2 = 1 – |x|/μLh = 1 – |(3695.94)|/(4)(1583.85) = 0.442
K3 = e-γz/Lh = e-(2.5)z/(1583.85)

Note that K3 varies depending on the elevation from ground of the height being considered. Hence, the corresponding Kzt values per elevation z, are tabulated below:

z, ft K1 K2 K3 Kzt
0 0.425 0.442 1.000 1.411
10 0.425 0.442 0.985 1.404
20 0.425 0.442 0.970 1.398
30 0.425 0.442 0.956 1.391
40 0.425 0.442 0.941 1.385
50 0.425 0.442 0.927 1.379
60 0.425 0.442 0.913 1.373
70 0.425 0.442 0.900 1.367
80 0.425 0.442 0.886 1.361
90 0.425 0.442 0.873 1.355
100 0.425 0.442 0.860 1.349
Tabulated values of topo factor Kzt for corresponding z elevation.

It can be observed that as the height above the ground, z, is increasing, the Kzt value is decreasing.

SkyCiv Load Generator

Using the SkyCiv Load Generator, the topography factor Kzt is calculated automatically. All you need to to is put the Project Address, select the Exposure Category and Wind Source Direction and the software will process the elevation data taken from Google Maps.

Location of the structure using the SkyCiv Load Generator.
Elevation data from Google Maps using the SkyCiv Load Generator.

The points for upwind foot, midheight, and peak of the terrain is automatically detected by our software. As the algorithm may not be always accurate, you can overwrite and these values by using the Edit Peak and Edit Upwind Foot buttons for better result of the topo factor. The values on the table are automatically filled up.

Kzt parameters in SkyCiv Load Generator.

The step-by-step calculation of Kzt that we did above is shown on the detailed wind load calculation of the SkyCiv Load Generator.

Step-by-step calculation and formula of Kzt on the detailed wind load calculation report from SkyCiv Load Generator.
The calculated topographic factor Kzt per level from SkyCiv Load Generator report. Similarly, the topographic/orographic factor can also be calculated in a similar manner for EN 1991, AS/NZS 1170, NBCC 2015, NSCP 2015, and IS 875.

Using the Free Wind Load Calculator, you can generate the design wind pressures up to 3 times per day and is limited only to Gable roof profile.

However, the detailed wind load calculation report can only be accessed using a Professional account along with all the full capabilities of SkyCiv modules. The standalone load generator only version can also be purchased thru this link.

Patrick Aylsworth Garcia Structural Engineer, Product Development
Patrick Aylsworth Garcia
Structural Engineer, Product Development
MS Civil Engineering

References:

  • Minimum Design Loads for Buildings and Other Structures. (2017). ASCE/SEI 7-16. American Society of Civil Engineers.
  • Google Maps

 

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