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LATERAL-FORCE DESIGN
SECTION LATERAL-FORCE DESIGN Charles W Roeder, P.E Professor of Civil Engineering, University of Washington, Seattle, Washington Design of buildings for lateral forces requires a greater understanding of the load mechanism than many other aspects of structural design To fulfill this need, this section provides a basic overview of current practice in seismic and wind design It also discusses recent changes in design provisions and recent developments that will have an impact on future design There are fundamental differences between design methods for wind and earth-quake loading Wind-loading design is concerned with safety, but occupant comfort and serviceability is a dominant concern Wind loading does not require any greater understanding of structural behavior beyond that required for gravity and other loading As a result, the primary emphasis of the treatment of wind loading in this section is on the loading and the distribution of loading Design for seismic loading is primarily concerned with structural safety during major earthquakes, but serviceability and the potential for economic loss are also of concern Earthquake loading requires an understanding of the behavior of structural systems under large, inelastic, cyclic deformations Much more detailed analysis of structural behavior is needed for application of earthquake design provisions, because structural behavior is fundamentally different for seismic loading, and there are a number of detailed requirements and provisions needed to assure acceptable seismic performance Because of these different concerns, the two types of loading are discussed separately in the following 9.1 DESCRIPTION OF WIND FORCES The magnitude and distribution of wind velocity are the key elements in determining wind design forces Mountainous or highly developed urban areas provide a rough surface, which slows wind velocity near the surface of the earth and causes wind velocity to increase rapidly with height above the earth’s surface Large, level open areas and bodies of water provide little resistance to the surface wind speed, and wind velocity increases more slowly with height Wind velocity increases with height in all cases but does not increase appreciably above the critical heights of about 950 ft for open terrain to 1500 ft for rough terrain This variation of wind speed over height has been modeled as a power law: V2 ⫽ V 冉冊 z zg n (9.1) 9.1 9.2 SECTION NINE where V is the basic wind velocity, or velocity measured at a height zg above ground and Vz is the velocity at height z above ground The coefficient n varies with the surface roughness It generally ranges from 0.33 for open terrain to 0.14 for rough terrain The wind speeds Vz and V are the fastest-mile wind speeds, which are approximately the fastest average wind speeds maintained over a distance of mile Basic wind speeds are measured at an elevation zg above the surface of the earth at an open site Design wind loads are based on a statistical analysis of the maximum fastest-mile wind speed expected within a given recurrence interval, such as 50 years Statistical maps of wind speeds have been developed and are the basis of present design methods However, the maps consider only regional variations in wind speed and not consider tornadoes, tropical storms, or local wind currents The wind speed data are maintained for open sites and must be corrected for other site conditions (Wind speeds for elevations higher than the critical elevations mentioned previously are not affected by surface conditions.) Wind speeds Vw are translated into pressure q by the equation q ⫽ CD p V w (9.2) where CD is a drag coefficient and p is the density of air at standard atmospheric pressure The drag coefficient CD depends on the shape of the body or structure and is less than if the wind flows around the body The pressure q is the stagnation pressure qs if CD ⫽ 1.0, since the structure effectively stops the forward movement of the wind Thus, on substitution in Eq (9.2) of CD ⫽ 1.0 and air density at standard atmospheric pressure, qs ⫽ 0.00256Vw2 (9.3) where the wind speed is in miles per hour and pressure, in psf The shape and geometry of the building have other effects on the wind pressure and pressure distribution Large inward pressures develop on the windward walls of enclosed buildings and outward pressures develop on leeward walls, as illustrated in Fig 9.1a Buildings with openings on the windward side will allow air to flow into the building, and internal pressures may develop as depicted in Fig 9.1b These internal pressures cause loads on the over-all structure and structural frame More important, these pressures place great demands on the attachment of roofing and external cladding Openings in a side wall or leeward wall may cause an internal pressure in the building as illustrated in Fig 9.1c and d This buildup of internal pressure depends on the size of the openings for all walls and the geometry of the structure Slopes of roofs may affect the pressure distribution, as illustrated in Fig 9.1e Projections and overhangs (Fig 9.2) may also restrict the airflow and accumulate pressure These effects must be considered in design The velocity used in the pressure calculation is the velocity of the wind relative to the structure Thus, vibrations or movements of the structure occasionally may affect the magnitude of the relative velocity and pressure Structures with vibration characteristics which cause significant changes in the relative velocity and pressure distribution are regarded as sensitive to aerodynamic effects They may be susceptible to dynamic instability due to vortex shedding and flutter These may occur where local airflow around the structure causes dynamic amplification of the structural response because of the interaction of the structural response with the airflow These undesirable conditions require special analysis that takes into account the shape of the body, airflow around the body, dynamic characteristics of the structure, wind speed, and other related factors As a result, dynamic instability is not included in the simplified methods included in this section The fastest-mile wind speed is smaller than the short-duration wind speed due to gusting Corrections are made in design calculations for the effect of gusting through use of gust factors, which increase design wind pressure to account for short-duration increases in wind speed The gust factors are largely affected by the roughness of the surface of the earth They decrease with increasing height, reduced surface roughness, and duration of gusting FIGURE 9.1 Plan view of a building indicating the wind loading on it with changes in velocity and direction of wind (a) High pressure on a solid wall on the windward side but outward or reduced inward pressure on the leeward side (b) Wind entering through an opening in the windward wall induces outward pressure on the interior of the walls (c) and (d ) Wind entering through openings in a side wall or a leeward wall produce internal pressures in the building (e) On a slopng roof, high inward pressure develops on the windward side, outward or reduced inward pressure on the leeward side 9.3 9.4 SECTION NINE FIGURE 9.2 Roof overhang restricts airflow, creates large local forces on the structure Although gusting provides only a short-duration dynamic loading to the structure, a major concern may be the vibration, rocking, or buffeting caused by the dynamic effect The pressure distribution caused by these combined effects must be applied to the building as a wind load 9.2 DETERMINATION OF WIND LOADS Wind loading as described in Art 9.1 is the basis for design wind loads specified in ‘‘Minimum Design Loads for Buildings and Other Structures,’’ ASCE 7-88, American Society of Civil Engineers Model building codes specify simplified methods based on these provisions for determining wind loads These methods can be used for most structures One such method is incorporated in the ‘‘Uniform Building Code’’ (UBC) of the International Conference of Building Officials, Inc (See Art 6.6 for ASCE 7-95.) 9.2.1 Wind-Load Provisions in the UBC The basic wind speeds specified by the UBC for the continental United States and Alaska are shown in Fig 9.3 The contours on the map indicate wind speeds that have a 2% probability of being exceeded in a year at a height 10 m above ground on open sites (These are wind speeds that are expected to occur once in 50 years.) The effects of extreme conditions, such as tornadoes, hurricanes, or local wind currents in mountainous regions are not covered by this map Further, special wind regions are identified in the map where local wind velocity may significantly exceed the indicated values for the location The possibility of occurrence of these local variations should be considered in design LATERAL-FORCE DESIGN 9.5 FIGURE 9.3 Contours indicate for regions of the continental United States and Alaska the basic wind speeds, mph, the fastest-mile speeds 10 m above ground in open terrain with a 2% annual probability of occurrence (Based on data in ‘‘Minimum Design Loads for Buildings and Other Structures,’’ ASCE 7-88, American Society of Civil Engineers and the ‘‘Uniform Building Code,’’ International Conference of Building Officials.) The stagnation pressures qs [Eq (9.3)] at a height of 10 m above ground are provided in tabular form in the UBC: Basic wind speeds, mph Pressure qs, psf 70 12.6 80 16.4 90 20.8 100 25.6 110 31.0 120 36.9 130 43.3 The UBC integrates the combined effects of gusting, changes of wind velocity with height above ground, and the local terrain or surface roughness of the earth in a coefficient, Ce Values of Ce are given in the UBC for specific exposure conditions as a stepwise function of height (Table 9.1) The UBC defines three exposure conditions, B to D Exposure C represents open terrain (assumed in Fig 9.3) Exposure B applies to protected sites Exposure D is an extreme exposure primarily intended for open shorelines and coastal regions Coefficient Ce as well as stagnation pressure qs are factors used in determination of design wind pressures The UBC also specifies an importance factor I to be assigned to a building so that more important structures are designed for larger forces to assure their serviceability after an 9.6 SECTION NINE TABLE 9.1 Coefficient Ce for Eq (9.4) Exposure Height, ft* C D 0–15 20 25 30 40 60 80 100 120 160 200 300 400 1.06 1.13 1.19 1.23 1.31 1.43 1.53 1.61 1.67 1.79 1.87 2.05 2.19 1.39 1.45 1.50 1.54 1.62 1.73 1.81 1.88 1.93 2.02 2.10 2.23 2.34 * Height above average level of adjoining ground extreme windstorm For most buildings, I ⫽ 1.0 For such buildings as hospitals, fire and police stations, and communications centers, and where the primary occupancy is for assembly of 300 or more persons, I ⫽ 1.15 A final factor Cq depends on the geometry of the structure and its appendages and on the component or portion of the structure to be loaded It is intended to account for the pressure distribution on buildings, which may affect the major load elements The design pressure p, psf, is then given by p ⫽ CeCqqs I (9.4) The UBC presents two methods of distributing the pressures to the primary load-resisting system Method (Fig 9.4b) is a normal-force method, which distributes pressures normal to the various parts of the building The pressures act simultaneously in a direction normal to the plane of roofs or walls In this method, Cq ⫽ 0.8 inward for all windward walls and 0.5 outward for all leeward walls For winds parallel to the ridge line of sloped roofs and for flat roofs, Cq ⫽ 0.7 outward For winds perpendicular to the ridge line, C ⫽ outward on the leeward side On the windward side: Cq ⫽ 0.7 ⫽ 0.9 ⫽ 0.4 ⫽ 0.7 outward with roof slope less than 2:12 outward or 0.3 inward with roof slope between 2:12 and 9:12 inward with roof slope between 9:12 and 12:12 inward with roof slope greater than 12:12 Method (Fig 9.4c) uses a projected-area approach with horizontal and vertical pressures applied simultaneously to the vertical and horizontal projections of the building, respectively For this case, Cq ⫽ 1.4 on the vertical projected area of any structure over 40 ft tall, 1.3 on the vertical projected area of any shorter structure, and 0.7 upward (uplift) on any horizontal projection LATERAL-FORCE DESIGN 9.7 FIGURE 9.4 Distribution of wind pressure on a single-story building with sloping roof (a) Buildmg in open terrain subjected to a 70-mph wind; (b) pressures computed by the normal-force method; (c) pressures computed by the projected-area method Individual components and local areas may have local pressure concentrations due to local disturbance of the airflow (Fig 9.2) These normally not affect the design of load frames and major load-carrying elements, but they may require increased resistance for architectural elements, local structural members supporting these elements, and attachment details The UBC also contains values of Cq for these local conditions Some of these component requirements for Cq for wall elements include: 1.2 inward for all wall elements 1.2 outward for wall elements of enclosed and unenclosed structures 9.8 SECTION NINE 1.6 outward for wall elements of open structures 1.3 inward and outward for all parapet walls An unenclosed structure is a structure with openings in one or more walls, but the sums of the openings on each side are within 15% of each other An open structure has similar wall openings but the sum of the openings on one wall is more than 15% greater that the sum of the openings of other walls Open structures may accumulate larger internal pressures than enclosed or unenclosed structures (Fig 9.1) and must be designed for larger outward pressures There are similar component requirements for Cq for roof elements These include: Cq ⫽ 1.7 outward for roof elements of open structures with slope less than 2:12 ⫽ 1.6 outward or 0.8 inward for roof elements of open structures with slope greater than 2:12 but less than 7:12 ⫽ 1.7 inward and outward for roof elements of open structures with slope greater than 7:12 ⫽ 1.3 outward for roof elements of enclosed and unenclosed structures with roof slope less than 7:12 ⫽ 1.3 outward or inward for roof elements of enclosed and unenclosed structures with roof slope greater than 7:12 Corners of wall elements must also be subjected to Cq ⫽ 1.5 outward or 1.2 inward for the lesser of 10 ft or 10% of the least width of the structure Roof eaves and other projections are also collectors of concentrated wind pressure (Fig 9.2) Building codes require considerations of these local pressure distributions with Cq ⫽ 2.3 upward of roof rakes, ridges, and eaves without overhang and slope less than 2:12 ⫽ 2.6 upward of roof rakes, ridges, and eaves without overhang and slope greater than 2:12 but less than 7:12 ⫽ 1.6 upward of roof rakes, ridges, and eaves without overhang and slope greater than 7:12 ⫽ 0.5 greater coefficient for overhanging elements and canopies These factors combine to produce a complex distribution of design pressures Some of the distributions are illustrated in Fig 9.5 These localized distributions affect the strength of local elements and the strength of attachment details of local elements, but they not affect the global strength requirements of the structure 9.2.2 Other Provisions for Wind Loads Alternative methods for determining wind loads, such as that in ASCE Standard 7-88, are available, and give more detailed provisions than those in the UBC (Art 9.2.1) for defining and distributing wind loads Tabulated data may be more detailed in these other methods, and more equations may be required However the pressure distributions are similar to that provided by the UBC These methods provide basic wind loads for buildings, but they not specify how to estimate or control aerodynamic effects Aerodynamic effects may result in interaction between the dynamic response of a structure and the wind flow around it This interaction may amplify the dynamic response and cause considerable occupant discomfort during some windstorms LATERAL-FORCE DESIGN 9.9 FIGURE 9.5 Typical distributions of local wind pressures Furthermore, local variations in wind velocity can be caused by adjacent buildings The wind may be funneled onto the structure, or the structure may be protected by surrounding structures Wind tunnel testing is often required for designing for these effects Local wind variations are most likely to be significant for tall, slender structures As a general rule, buildings with unusual geometry or a height more than times the base dimension are logical candidates for a wind tunnel test Such a test can reveal the predominant wind speeds and directions for the site, local effects such as channeling of the wind by surrounding buildings, effects of the new building on existing surrounding structures, the dynamic response of the building, and the interaction of the response with the wind velocity The model used for the test can include the stiffness of the building, and wind pressures can be measured at critical locations Major structures often are based on wind-tunnel-test results, since greater economy and more predictable structural performance are possible Special structures, such as antennas, transmission lines, and supports for signs and lighting, may also be susceptible to aerodynamic effects and require special analysis Aerodynamic effects are beyond the scope of this section, but analytical methods of dealing with these are available Wind tunnel testing may also be required for these systems (E Simu and R H Scanlan, Wind Effects on Structures, Wiley-lnterscience, New York.) 9.3 SEISMIC LOADS IN MODEL CODES The ‘‘Uniform Building Code’’ (UBC) of the International Conference of Building Officials has been the primary source of seismic design provisions for the United States It adopts 9.10 SECTION NINE provisions based on recommendations of the Structural Engineers Association of California (SEAOC) The UBC and SEAOC define design forces and establish detailed requirements for seismic design of many structural types Another model code is the ‘‘National Earthquake Hazard Reduction Program (NEHRP) Recommended Provisions for the Development of Seismic Regulations for New Buildings,’’ of the Building Seismic Safety Council (BSSC), Federal Emergency Management Agency (FEMA), Washington, D.C There have historically been considerable similarities between the UBC and NEHRP recommendations, since the rationale is similar for both documents and many engineers participate in the development of both documents However, there have also been differences in the detailed approach used by the UBC and NEHRP provisions, and in recent years efforts have been made to resolve these differences, because of the move toward an International Building Code (IBC) As a result, the 1997 edition of the UBC has much greater similarity with NEHRP than has past editions ‘‘Minimum Design Loads for Buildings and Other Structures,’’ ASCE 7-95, American Society of Civil Engineers adopts seismic force requirements similar to those included in the NEHRP provisions The American Institute of Steel Construction (AISC) promulgates ‘‘Seismic Design Provisions for Structural Steel Buildings.’’ This document does not establish design forces, but it provides detailed design requirement for steel structures The detailed seismic design provisions provided in the UBC and NEHRP provisions include most of the AISC seismic provisions, since the AISC seismic provisions are often directly inserted into the model codes or are referenced in the seismic design provisions As a result, there is great similarity between the UBC, NEHRP, ASCE and AISC LRFD provisions The UBC and AISC provisions are emphasized in the following, but several issues that are better understood by examining NEHRP provisions are noted 9.4 EQUIVALENT STATIC FORCES FOR SEISMIC DESIGN The UBC offers two methods for determining and distributing seismic design loads One is the dynamic method, which is required to be used for a structure that is irregular or of unusual proportions (Art 9.5) The other specifies equivalent static forces and is the most widely used, because of its relative simplicity The equivalent-static-force method defines the static shear at the base of the building as being the smaller of CV I W RT (9.5a) 2.5 Ca I W R (9.5b) V ⫽ 0.11 Ca I W (9.6a) V⫽ or V⫽ but not less than in all seismic regions and not less than V⫽ 0.8 Z NV I W R (9.6b) in seismic zone In these equations, W ⫽ total dead load, including permanent equipment, plus a minimum of 10 psf for partition loads, snow loads exceeding 30 psf, and at least 25% ... LATERAL-FORCE DESIGN FIGURE 9. 9 Hysteretic behavior of three steel frames (a) Moment-resisting frame: (b) concentric braced frame: (c) eccentric braced frame 9. 19 9.20 SECTION NINE FIGURE 9. 9 Continued... 9. 6 SECTION NINE TABLE 9. 1 Coefficient Ce for Eq (9. 4) Exposure Height, ft* C D 0–15 20 25 30 40 60 80 100 120 160 200 300 400 1.06 1.13 1. 19 1.23 1.31 1.43 1.53 1.61 1.67 1. 79 1.87 2.05 2. 19. .. vol 9, pp 187– 194 , 198 1.) The method degenerates into a variation of the square root of the sum of the squares (SRSS) method LATERAL-FORCE DESIGN 9. 17 when the modes of vibration are well-separated