Relation: Extreme Wind Speeds and Extreme Wind Loads | Wind Engineering

In this article we will discuss about the relation between extreme wind speeds and extreme wind loads.

Assume that the wind velocity is known at a particular location and elevation near a structure, where it is unaffected by any obstructions and is therefore indicative of the ambient wind environment. The wind pressure at a point on the building surface, or the wind force on a member, is a function of that wind speed and can be determined from results of wind tunnel or full-scale tests.

Turbulence and Flow Separation Effects:

The wind load on a particular member is obtained by integrating the pressures over the member’s tributary area. Since, owing to turbulence and flow separation effects, pressures are time-dependent and imperfectly correlated spatially, with generally unknown correlation, the integration cannot be performed analytically, except for a very few simple cases, and is performed instead by a variety of techniques in wind tunnel or full-scale tests.

When the tributary area is small correlation effects are relatively small, and the fluctuating force excursions may be many times larger than the standard deviation of the fluctuations. The magnitude of the force fluctuation to be specified for design purposes is an issue for which no clear and consistent reliability-based solution appears to be available at this time.

This issue is complicated by questions on the extent to which loads measured on small scale models can provide satisfactory indications on the magnitude of their prototype counterparts, particularly if the results of interest involve large fluctuating pressure excursions.

Wind Direction Effects:

Pressures (and therefore forces) depend on both wind speed and direction.

The dependence is of the form:

p(θ)=^1/2pc(θ)v(θ)² …(1)

where p, c, p, v and θ denote air density, the aerodynamic coefficient, pressure (or force), wind velocity, and direction, respectively. Two methods have been proposed for obtaining extremes of the vector p(θ). The first method relies on techniques for estimating the rate of upcrossing by p(θ) of a limit states s(θ).

p_j(θ_i)=^1/2pc(θ_i)v_j(θ₁)². J=1,2,..,N …(2)

The second method is based on the creation of a set of i (i=1,2,..,8 or i=1,2,..,16) time series based on a set of i recorded time series v_j(θ₁), where θ_i are the eight or sixteen directions for which directional wind speeds are measured.

W_j = (max_i[p_j(θ_i)]^1/2 …(3)

From these sets of time series the single time series is extracted. In Eq. 3 max_i denotes the maximum over all i’s. To within a dimensional constant, W_j may be interpreted as an equivalent wind speed. The time series W_j consists of the largest equivalent wind speeds affecting the structure during the intervals [ t_j-1, t_j] (j = 1,2, . .N).

It is subjected to a statistical analysis and yields the extreme values w, and therefore the extreme pressures (forces) acting on the structure, w², for the mean recurrence intervals of interest. For brevity we refer to the pressures p-w² as actual extreme pressures.

Extreme Loads Calculated Without Regard for Wind Direction Effects.

W_j = ^1/2p(max_i[c(θ_i)] max_i[v_j(θ_i)²])^1/2, …(4)

Extreme load estimation is simplified if the idealized time series obtained by Ignoring direction effects, is considered in lieu of the tine series W_j. For any given mean recurrence interval, depending upon the directional dependence of the aerodynamic coefficient and the wind climate, the extreme values of the variable P=W² are in general larger in many instances much larger — than the actual extreme pressures p=w².

We refer here to the pressures P as idealized extreme pressures. Past experience shows that idealized extreme pressures P (based, say, on a 50- or 100-year extreme wind estimated without regard for direction), used in conjunction with a load factor of 1.3, normally result in acceptably small failure probabilities.

However, use of the smaller actual extreme pressures p (with a 50- or 100-year mean return period) In conjunction with a load factor of 1.3 will result in higher failure probabilities that could well prove to be unacceptable and cannot be justified by invoking past experience.

This issue has not yet been adequately addressed by standard- writing bodies. For example, the ASCE Standard 7-93 as well as the draft ASCE Standard 7-95 allow nominal wind loads to be estimated on the basis of ad-hoc wind tunnel tests. For many special structures estimates of nominal wind loads based on such tests account for wind direction effects.

However, the standard fails to indicate that the use of those estimates in conjunction with the wind load factor specified by the standard generally results in higher failure probabilities than those Implicit in the provisions for ordinary structures. In this writer’s opinion, which was duly communicated to the ASCE Subcommittee on the ASCE 7-95 Standards, this omission could have serious safety repercussions and deserves careful scrutiny.

A similar failure to address the reliability problem in a consistent fashion led recently to a strong increase in effective safety margins for window glass design, which in the writer’s view is largely unwarranted.