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WIND LOAD DESIGN ANALYSIS: ASCE 7-98
Loren Pittack and Julio de Blas (Partnership)
CAE614 Structural Dynamics
University of Miami College of Engineering: Civil, Architectural, and Environmental Engineering Dept
Professor Fahmy
December 12, 2000 Simple concepts have frequently been used in estimating live loads for structural design. Now, however, live loads on buildings, such as wind, snow, earthquake and floor loads, are receiving increased attention to match more accurate structural analyses that are possible. Wind loads have become particularly significant because of increasing number of high-rise buildings. Other factors have also contributed to importance of wind in design: lightweight low-slope roofs, curtain wall construction and appearance of special structures having "aerodynamic shapes." Some tall buildings that extend into regions of high wind velocity have swayed excessively in strong winds. Wind forces have blown off improperly anchored lightweight roofs, and roofing materials have been lifted by high local suctions and eventually peeled from large areas of roofs. These and many other problems have emphasized the importance of a clearer understanding of wind and its effects. With the old simplified approach, merely a uniform lateral pressure on windward side of a building and suction on leeward wall often represented total effect of wind. Crossly simplified rules were also used to calculate pressures or suctions on roofs. Only horizontal shear and overturning moment were calculated. For low or medium height buildings, such simple methods may have been reasonably satisfactory, but for tall buildings, the greater importance of wind loading calls for more accuracy. Wind is not constant either with height or with time, is not uniform over the side of a building, and does not always cause positive pressure. In fact, wind is a very complicated phenomenon; it is air in turbulent flow, which means that motion of individual air particles is so erratic that in studying wind, one ought to be concerned with statistical distributions of speeds and directions rather than with simple averages or fixed physical quantities.
Architects and engineers are concerned with and responsible for not only structural design, but also the choice of exterior cladding materials and components, operation of mechanical services such as heating and ventilating equipment, and with details of openings to limit infiltration. Wind has important effects on each of these aspects of design; one might even conclude that of the manifestations of nature with which the architect has to contend, apart from gravity, the effects of wind are ubiquitous.
Development of Wind
Wind usually refers to movement of air parallel to the earth's surface. Driving forces for such movements are pressure differences caused by unequal heating of the air. For a steady wind, however, direction of flow does not follow the steepest pressure gradient from a "high" to, a low" as one might expect. In fact, direction of flow is more nearly parallel to the isobars (lines connecting points of equal pressure) rather than perpendicular to them. This is because every object moving across the earth's surface deflects to the right in the northern hemisphere (to the left in the southern) because of rotation of earth. This deviating effect, called the Coriolis force, is small and is usually disregarded except in the atmosphere and ocean. Pressure gradient causing wind, however, is also small. Normally, wind requires several hours to develop, and although flow begins perpendicular to the isobars, it gradually deflects to the right as time passes, so that when a steady state is attained, wind blows more nearly parallel to the isobars. The Coriolis force and frictional drag force then balance the pressure gradient, plus or minus centrifugal force if path happens to curve.
Velocity Profile
The roughness of the earth's surface, which causes drag on wind, converts some of wind's energy into mechanical turbulence. Since turbulence generates at the surface, surface wind speed is much less than wind speed at higher levels. Turbulence includes vertical as well as horizontal air movement and hence the effect of surface frictional drag is propagated upwards. Mechanical turbulence and effect of frictional drag gradually decrease with height and at gradient level (around 1000 to 2000 feet) the frictional effect is negligible. Pressure gradient at this level balance by the Coriolis force (and possibly centrifugal force), and the wind blows almost parallel to the isobars. For strong winds, the shape of the vertical profile of wind speed depends mainly on degree of roughness of surface, which means over-all drag effect of buildings, trees and any other projections that impede flow of wind at the surface. Three typical velocity profiles are shown in Fig. 1, where the effect of variable surface roughness on mean wind speeds is shown for an arbitrarily selected gradient wind of 100mph. Velocity profiles have been determined by fitting curves to observed mind speeds at several levels. It is convenient and sufficiently accurate to describe these profiles by a power law of the form: v_h = v_r*(h/h_r)^k, where v_h is mean wind speed at height h above ground, v_r is the mean speed at reference height h_r, above ground; k is the exponent for best-fitting curve. A reference height of 10 meters or about 30ft is internationally recommended as the standard and anemometers are usually mounted as close to this height as is practical. Exponents for mean wind speeds vary from about 1/7 for flat open country to about ½ for centers of large cities.
Figure 1 - Mean velocity profiles over terrain with 3 different roughness characteristics for gradient wind of 100mph. Courtesy Meteorological Division, Dept of Transport
Turbulence in Surface Winds
Velocity profile (Figure 1) describes only one aspect of wind at lower levels. Superimposed on mean speed are gusts and lulls, which are deviations above and below the mean. These gusts have a random distribution over a wide range of frequencies and amplitudes, in both time and space. Figure 2 shows clearly the unsteady nature of wind speed measured by an anemometer. Gusts are frequently the result of the introduction of fast moving parcels of air from higher levels into slower moving strata of air. This mixing or turbulence is produced by surface roughness and thermal instability. In such cases dynamic instability of flow may result when eddies separate first from one side and then form. Turbulence caused by surface roughness is similar to the turbulent boundary layer flow at the walls of pipes. Flow near surface encounters small obstacles that change wind speed and introduce random vertical and horizontal velocity components at right angles to main direction of flow. Turbulence generated by obstacles may persist downwind from projections as much as 100 times their height. Large scale topographical features are not included in the above-mentioned surface roughness. They can influence the flow, so they are given special consideration in design. For instance, wind is usually much stronger over the brow of a hill or ridge because flow lines converge over the obstructing feature and to pass the same quantity of air a higher speed is required. Large valleys often have a strong funnelling effect that increases wind speed along the axis of the valley. Thermal stability of air has a considerable effect on the intensity of turbulence. Cold surface air tends to damp out mechanical turbulence; heated surface air tends to rise and to increase turbulence. When wind is strong, air near the surface becomes thoroughly mixed and thermal stability becomes neutral. Under these conditions, temperature differences neither damp out nor increase mechanical turbulence caused by surface roughness. Figure 2 - Typical pressure tube anemometer record.
Dynamic effects
Every structure has a natural frequencyof vibration, and should dynamic loading occur at or near it, structural damage out of all proportion to size of load may result. For example, bridges capable of carrying far greater loads than the weight of a company of soldiers have been known to break down under dynamic loading of men marching over them in step. Similarly, certain periodic gusts within the wide spectrum of gustiness in wind may find resonance with natural vibration frequency of a building, and although the total force caused by that particular gust frequency would be much less than the static design load for the building, dangerous oscillations may be set up. This applies not only to the structure as a whole, but also to components such as curtain wall panels and sheets of glass. A second dynamic effect is caused by instability of flow around certain structures. Long narrow structures such as smoke stacks, light standards and suspension bridges are particularly susceptible to this sort of loading the other side of the object, causing an alternating pattern of eddies to form in its wake. A side thrust is thus exerted on the object similar to the lift on an aerofoil, and since this thrust alternates in direction, a vibration may result. Side-to-side wobbling effect of a straight stick pulled through water is an example of this phenomenon. As research gradually provides a better understanding of the structure of wind and the complex interactions between wind and buildings, one can look forward to greater economy in the use of building materials through greater precision in estimating static load; and to greater safety because of the inclusion of dynamic load in design.
Minimum Wind Design Loads for Building & Other Structures
ASCE Standard A7-98, Minimum Design Loads for Buildings and Other Structures (A7 Standard) provides a basis for determining wind loads and other loads on structures in the United States. All model-building codes include this standard as a reference and the new International Building Code has adopted the A7 Standard as the recommended design method. Evaluation of wind loads can be a very complicated process and the A7 Standard has provided the best information currently available for dealing with these problems for rigid structures and a limited class of flexible structures. Unfortunately, complication of wind loading also can lead to a relatively complicated procedure for code-based evaluation of wind loads. A full evaluation of the structure, parts and portion loadings for even a relatively simple structure can lead to lengthy and tedious calculations using the A7 Standard. The Wind Loads on Structures program recently released by the Standards Design Group removes much of the tedious computation for manual analysis and reduces evaluation of A7-98 to relatively simple steps. All buildings and other structures must be design to resist environmental loads. This is a wind load. Design wind loads can determined using 3 procedures: Simplified procedure, Analytical procedure and Wind tunnel procedure. There are definitions one must know in order to understand procedures of determining wind loads. These definitions are based on a dynamic point of view:
Flexible building or structure: A building or other structure is considered flexible if it contains a significant dynamic response. Resonant response depends on the gust structure contained in the approaching wind, on wind loading pressures generated by the wind flow about the building, and on dynamic properties of the building or structure. Gust energy in wind is smaller at frequencies about 1 Hz; therefore resonant response of most buildings and structures with lowest natural frequency above 1 Hz will be sufficiently small that resonant response can often be ignored. When buildings or other structures have a height exceeding 4 times the least horizontal dimension or when there is reason to believe that the natural frequency is less than 1 Hz (natural period greater than 1sec.), the natural frequency should be investigated.
Rigid building or structure: Building or other structure whose fundamental frequency is greater or equal than 1 Hz. A general guidance is that the most rigid buildings and structures have height to minimum width less than 4.
Design Force, F: Equivalent static force is used in determination of wind loads for open buildings and other structures.
Design pressure, P: Equivalent static pressure to be used in the determination of wind loads for buildings.
Main wind-force resisting system: An assemblage of structural elements that provide stability and support for overall structure.
Wind Load Design Analytical Procedure
Gust effect factor G
For rigid structures, gust effect factor shall be taken as 0.85 or calculated by: G = 0.925*[(1+1.7g_QI_zQ)/(1+1.7g_vI_z)]. I_z = c(33/)^1/6, where I_z is the intensity of turbulence at height (equivalent height of structure defined as 0.6h); g_Q and g_v shall be taken as 3.4. Refer to ASCE 7-98 for values. Background response Q = SQRT(1/[1+0.63*((B+h)/L_z)^0.63]), where L_z = l(/33)^
Flexible or Dynamically Sensitive Structures
For dynamically sensitive structures, gust factor shall be calculated by: G_f = 0.925*[(1+1.7*I_z*SQRT(g_Q²Q²+g_R²R²))/(1+1.7g_vI_z)]
g_Q and g_v shall be taken as is given by: g_R = SQRT(2*ln(3600n₁))+[0.577/SQRT(2*ln(3600n₁))], where n₁ = Building natural frequency (Hz). The resonant response factor = R = SQRT(R_nR_hR_b(0.53+0.47R_l)/B), where R_n = 7.47*N₁/(1+10.3N₁)^5/3. Reduced the frequency, N₁ = n₁L_z/. R_l = 1/n - (1 - e^-2n)/(2n²), for n > 0. q = q_z = 1, for n = 0, where subscript l shall be taken as h, B and L respectively: q = q_z setting n = 4.6n₁h/
q = q_z setting n = 4.6n₁B/
q = q_z setting n = 4.6n₁L/ B = Damping ratio (% of critical damping). Mean hourly wind speed (ft/s), = (/33)^*V(88/60), whereandare constants.
Velocity pressure
Velocity pressure, q_z, evaluated at height z shall be calculated using following equation: q_z = 0.00256K_zK_ztK_dV²I (psf) where K_d = wind directionality factor, K_z = velocity pressure exposure coefficient, K_zt = topographic factor and q_h = velocity pressure at mean roof height h.
Pressure and Force Coefficients
Main Force Resisting System & Rigid buildings of all heights
Design wind pressures for main wind force resisting system of buildings of all heights shall be determined by following equation: p = qGC_p - q_i(GC_pi) (pssf), where q = q_z for windward walls. q = q_h for leeward walls, side walls and roofs. q_i = q_h for windward walls, side walls, leeward walls and roofs of enclosed buildings. q_i = q_z for positive internal pressure evaluation in partially enclosed buildings. G = Gust effect factor. C_p = External pressure coefficient. (GC_pi) = Internal pressure coefficient.
Low Rise Buildings
Design wind pressures for main wind force resisting system of low-rise buildings shall be determined using  equation: p = q_h[(GC_pf) - (GC_pi)] (psf), where (GC_pf) = External pressure coefficient.
Flexible Buildings
Design wind pressures for main wind force resisting system of flexible buildings shall be determined from following equation: p = qG_fC_p - q_i(GC_pi) (pssf)
Wind Loads Commentary
Maximum Along-Wind Displacement
Maximum along-wind displacement as a function of height above ground surface is: X_max(z) = p*B*h*C_fx²/[2m₁(2*PI*n₁)²]*KG, where fundamental model shape = = (z/h)^. = Mode exponent. p = Air density. C_fx = Mean along-wind force coefficient. Modal mass = , where µ(z) = Mass per unit height. K = 1.65^â/(â++1). (3-sec. gust speed) = V(z/33)^â, where V is 3-sec. gust speed in Exposure C at reference height;  and â are terrain exposure constants given in tables.
RMS Along-Wind Acceleration
RMS Along-wind acceleration as a function of height above ground surface is:.
Maximum Along-Wind Acceleration
Maximum along-wind acceleration as a function of height above ground surface is:. g_x = SQRT(2*ln(n₁T)) + 0.5772/SQRT(2*ln(n₁T)), where T = time length over which minimum acceleration is computed, usually taken to be 3600sec. to represent 1hr.