a wind velocity having a specific mean recurrence interval. Mean recurrence intervals of 20 and 50 years are generally used in building design, the former interval for determining the comfort of occupants in tall buildings subject to wind storms, and the latter for designing lateral resisting elements.
In general, wind buffeting against a bluff body gets diverted in three mutually perpendicular directions, giving rise to forces and moments about the three directions. Although all six components, as shown in Fig.1.3, are significant in aeronautical engineering, in civil and structural work, the force and moment corresponding to the vertical axis (lift and yawing moment) are of little significance. Therefore, aside from the uplift forces on large roof areas, the flow of wind is simplified and considered two-dimensional, as shown in Fig.1.4, consisting of along wind and transverse wind.
Along wind—or simply wind—is the term used to refer to drag forces, and transverse wind is the term used to describe crosswind. The crosswind response causing motion in a plane perpendicular to the direction of wind typically dominates over the along-wind response for tall buildings. Consider a prismatic building subjected to a smooth wind flow.
The originally parallel upwind streamlines are displaced on either side of the building, Fig.1.5. This results in spiral vortices being shed periodically from the sides into the downstream flow of wind, called the wake. At relatively low wind speeds of, say, 50 to 60 mph (22.3 to 26.8 m/s), the vortices are shed symmetrically in pairs, one from each side. When the vortices are shed, i.e., break away from the surface of the building, an impulse is applied in the transverse direction.
At low wind speeds, since the shedding occurs at the same instant on either side of the building, there is no tendency for the building to vibrate in the transverse direction. It is therefore subject to along-wind oscillations parallel to the wind direction. At higher speeds, the vortices are shed alternately, first from one and then from the other side. When this occurs, there is an impulse in the along-wind direction as before, but in addition, there is an impulse in the transverse direction. The transverse impulses are, however, applied alternately to the left and then to the right. The frequency of transverse impulse is precisely half that of the along-wind impulse. This type of shedding, which gives rise to structural vibrations in the flow direction as well as in the transverse direction, is called vortex shedding or the Karman vortex street, a phenomenon well known in the field of fluid mechanics.
There is a simple formula to calculate the frequency of the transverse pulsating forces caused by vortex shedding:
where f = frequency of vortex shedding in hertz
V = mean wind speed at the top of the building
S = a dimensionless parameter called the Strouhal number for the shape
D = diameter of the building
In Eq. (1.4), the parameters V and D are expressed in consistent units such as ft/s and ft, respectively.
The Strouhal number is not a constant but varies irregularly with wind velocity. At low air velocities, S is low and increases with the velocity up to a limit of 0.21 for a smooth cylinder. This limit is reached for a velocity of about 50 mph (22.4 m/s) and remains almost a constant at 0.20 for wind velocities between 50 and 115 mph (22.4 and 51 m/s).
Consider for illustration purposes, a circular prismatic-shaped high-rise building having a diameter equal to 110 ft (33.5 m) and a height-to-width ratio of 6 with a natural frequency of vibration equal to 0.16 Hz. Assuming a wind velocity of 60 mph (27 m/s), the vortex-shedding frequency is given by
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