442R_88

+)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), * MCP Application Notes: * * * * 1. Character(s) preceded & followed by these symbols (. -) or (+ ,) * * are super- or subscripted, respectively. * * EXAMPLES: 42m.3- = 42 cubic meters * * CO+2, = carbon dioxide * * * * 2. All table notes (letters and numbers) have been enclosed in square* * brackets in both the table and below the table. The same is * * true for footnotes. * .))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))- ACI 442R-88 (Reapproved 1992) Response of Concrete Buildings to Lateral Forces Reported by ACI-ASCE Committee 442 Richard E. Klingner, Chairman; Daniel P. Abrams, Secretary; C. Michael Allen; Vitelmo V. Bertero; Arnaldo T. Derecho; Mark Fintel; Sigmund A. Freeman; Luis E. Garcia; Satyendra K. Ghosh; Jacob S. Grossman; Mohammad Iqbal; Ignacio Martin; Christian Meyer; Jack P. Moehle; Richard A, Parmelee; Victor M. Pavon; Joseph Schwaighofer; Charles F. Scribner; Shamim A. Sheikh; Richard A. Spencer; M. Daniel Vanderbilt.* * Deceased. The performance of reinforced concrete buildings subjected to wind, blast and earthquake loads is discussed. Building response and basic design approaches corresponding to these loads are briefly reviewed. Performance criteria and approaches for meeting these criteria are outlined. Various structural subassemblies and systems are reviewed, and their behavior is discussed with respect to these performance criteria. The role of analysis in design and in performance evaluation is discussed, and various analytical procedures are reviewed. Techniques for evaluating building response are summarized. General factors contributing to good performance are emphasized. Keywords: beams (supports); blast loads; buildings; columns (supports); earthquake resistant structures; frames; lateral pressure; performance; reinforced concrete; structural analysis; structural design; tube-in-tube; walls; wind pressure. This report supercedes ACI 442R-71 (Revised 1982). This report was submitted to letter ballot of the committee and was approved in accordance with ACI balloting requirements. Copyright (c) 1988, American Concrete Institute. All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by any electronic or mechanical device, printed, written, or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors. CONTENTS Preface Chapter 1--Introduction 1.1--Objectives 1.2--Scope 1.3--Recent examples of reinforced concrete building performance 1.4--Development of the state of the practice Chapter 2--Lateral load categories, building response, and design approaches 2.1--General 2.2--Wind loads 2.3--Blast loads 2.4--Earthquake loads Chapter 3--Performance criteria 3.1--General 3.2--Safety criteria 3.3--Approaches for meeting safety criteria 3.4--Serviceability criteria 3.5--Approaches for meeting serviceability criteria Chapter 4--Structural subassemblies and systems 4.1--General 4.2--Subassemblies 4.3--Structural systems Chapter 5--Methods of analysis 5.1--Objectives and scope 5.2--Introduction 5.3--Approximate analysis for preliminary design of frames 5.4--Linear analysis for static lateral forces 5.5--Nonlinear analysis for static lateral forces 5.6--Analysis for dynamic response Chapter 6--Performance of buildings 6.1--General 6.2--Use of experiments to evaluate structural performance 6.3--Evaluation of results 6.4--Ability of reinforced concrete structures to withstand severe lateral loads Chapter 7--Summary and concluding remarks 7.1--Summary 7.2--Concluding remarks Chapter 8--References Acknowledgments PREFACE This report is intended for professionals interested in the design and construction of reinforced concrete buildings. The purpose of the report is to serve as a primer on issues related to the response of reinforced concrete buildings subjected to lateral forces. Reinforced concrete buildings have generally behaved well under strong lateral loads. Evaluation of the reasons for this good performance, and for occasional examples of poor performance, requires an understanding of the various factors influencing the response of reinforced concrete buildings to lateral loads. Those factors are identified and discussed in this report. While design examples or specific calculations are not included, all aspects of the design process are addressed: characterization of loads; performance criteria and approaches for meeting such criteria; structural systems; analysis techniques; and performance evaluation. To emphasize the innovative possibilities which reinforced concrete offers to the structural engineer, performance criteria are presented in general terms before the characteristics of various structural systems are discussed in detail. CHAPTER 1--INTRODUCTION 1.1--Objectives The purpose of this report is to serve as a primer on issues related to the response of reinforced concrete buildings subjected to lateral loads. The report is neither a discussion of the state of the art of structural engineering research nor a design manual. It assumes previous knowledge and experience in the treatment of problems resulting from lateral loads, and also access to an adequate reference library. The report is oriented primarily to engineering practice in the United States and Canada, but has been written and reviewed by engineers from around the world. 1.2--Scope The organization of this report is intended to reflect various aspects of the design process for lateral loads. In Chapter 2, the three types of lateral loads considered in this report are discussed, structural responses and design approaches for those loads are summarized, and the concept of soil-structure interaction is briefly introduced. In Chapter 3, the criteria used to evaluate structural performance under lateral loads are discussed, and approaches for meeting these criteria are outlined. In Chapter 4, the different types of lateral load-resisting systems and the structural subassemblies comprising them are reviewed. In Chapter 5, techniques are presented for analytically modeling reinforced concrete buildings, and for computing their response to lateral loads. In Chapter 6, techniques are discussed for measuring the response characteristics of reinforced concrete buildings subjected to lateral loads, and for correlating these measured responses with performance under actual loads. In Chapter 7, the principal themes of the report are summarized and discussed. 1.3--Recent examples of reinforced concrete building performance Building codes and techniques for design, analysis and construction evolve continually. Performance of buildings subjected to strong lateral loads provides a reference for the introduction of new behavioral models, new research objectives, new design philosophies, and new structural configurations. In recent years, many opportunities have occurred for observing the behavior of modern reinforced concrete buildings subjected to extreme lateral loads. Some of the lessons learned from that behavior have greatly influenced the evolution of current building codes and practices for design and construction. 1.3.1 Wind--Most of our experience with extreme winds comes from hurricanes and tornadoes. Two recent hurricanes which significantly affected buildings in the United States were Hurricane Iwa in Hawaii (1982),[1] and Hurricane Alicia in Texas (1983).[2] The latter hurricane did produce some structural damage to light construction [Fig. 1.3.1(a)]. While engineered reinforced concrete buildings generally performed well structurally, many suffered nonstructural damage [Fig. 1.3.1(b)]. Storm surges (unusually high tides accompanying hurricanes) resulted in flooding, particularly after glass windows and doors had broken in lower stories. Local wind-induced failures of windows, facades and roofing were common. Although no high-rise buildings suffered structural damage during these two hurricanes, wind-driven debris and gravel from adjacent roofs damaged many panes of glass cladding in high-rise buildings. Recent examples of tornadoes producing significant structural damage include those occurring in Lubbock, Texas (1970)[3] and Xenia, Ohio (1974).[4] Tornadoes interact with structures and cause damage due to pressures caused by wind, pressure differentials caused by rapid changes in atmospheric pressure, and forces caused by impact of wind-borne debris. Much more damage is caused by direct pressure from wind,[5] than by pressure differentials resulting from changes in atmospheric pressure.[6] Generally, impact from debris causes only localized damage, although tornadoes have been known to move articles as large as railroad cars. Impact from a very large object could cause severe structural damage. 1.3.2 Blast--Blast loadings on structures can come from external or internal explosions. External explosions, while not normally considered in building design, have become an important design condition for government and military buildings. Local damage from internal explosions can be significant if it causes progressive collapse of other parts of the structure.[7] 1.3.3 Earthquake--The previous report of ACI-ASCE Committee 4428 was published after destructive earthquakes in Anchorage, Alaska (1964)[9] and Caracas, Venezuela (1967).[10] Significant lessons have since been learned from other earthquakes. Among these earthquakes are: San Fernando, California (1971);[11,12] Qir, Iran (1972);[13] Managua, Nicaragua (1972);[14,15,16] Miyagi-Ken-Oki, Japan (1978);[17] Guatemala City, Guatemala (1976);[18] Tangshan, China (1977);[19,20] Imperial County, California (1979);[21] El-Asnam, Algeria (1980);[22] Italy (1980);[23] Greece (1981);[24] Coalinga, California (1983);[25] Chile (1985);[26] Mexico (1985);[27] and El Salvador (1986).[28] The San Fernando earthquake of 1971 caused only minor damage to most engineered reinforced concrete buildings, but severely damaged a few others [Fig. 1.3.3(a)].[11,12] This event spurred research into the comparative inelastic response of different types of structural systems. The Managua, Nicaragua earthquake of 1972 caused structural damage, in some cases severe, to reinforced concrete buildings [Fig. 1.3.3(b)].[14,15,16] It emphasized the importance of lateral stiffness, the need for adequate vertical and lateral strength, detailing for ductility, engineering attention to nonstructural elements and control of nonstructural damage. The Imperial County, California earthquake of 1979 damaged few buildings, but did cause significant structural damage to a new reinforced concrete building [Fig. 1.3.3(c)].[21] The March 1985 Chilean earthquake caused little damage to most engineered reinforced concrete buildings, but did cause isolated failures of buildings with overall inadequacies in structural configuration.[26] The September 1985 Mexican earthquake severely damaged many engineered reinforced concrete buildings [Fig. 1.3.3(d)]. Damage was due primarily to the following factors: unexpected intensity and duration of ground shaking; dynamic amplification by soil deposits; errors in structural concept; and inadequate detailing.[27] 1.4--Development of the state of the practice The state of the practice of design of buildings for lateral loads has evolved continually throughout the past century. This evolution has been spurred, among other things, by accumulated experience of building performance, by advances in the definition of resistances and loads, and by increased capabilities to compute structural response. The evolution is expected to continue. It follows that current practice as summarized in this document will become dated as further experience stimulates development of a higher level of the state of the practice. A general trend in lateral load analysis and design has been for load levels to increase, resistances to be more explicitly defined, and response analyses to become more intricate. The intended outcome of these enhancements is that the resulting structure be more resistant than a similar structure designed by earlier techniques. This will not always be the case. Some existing structures, while apparently not satisfying current specifications, possess large factors of safety because of the approximate and conservative methods used at the time of their design. A similar structure designed by the current state of the practice may be less safe even though designed for larger forces, simply because current analysis methods enable design of a structure closer to its actual limits of performance. Thus, in introducing this report, there is no pretense that the methods described herein are flawless, that they are universally applicable, or that structures designed by less advanced techniques are less likely to perform satisfactorily under the design lateral loading. Rather, this report is intended simply to document current practice, offer guidance, and present an extensive bibliography of studies related to lateral load analysis and design. The active practitioner is encouraged to use judgment in the application of the information presented herein, and to stay abreast of new developments that are certain to occur following the publication of this document. CHAPTER 2--LATERAL LOAD CATEGORIES, BUILDING RESPONSE, AND DESIGN APPROACHES 2.1--General Many kinds of lateral loads can act on building structures--wind, blast, earthquake, water or soil pressure, and ocean waves. While any or all of these may be significant, wind and earthquake are generally more common. Wind, blast, and earthquake loads are considered in this report. Lateral load analysis requires that the structural engineer assess the magnitude and character of the loads, select a suitable analytical model, and then determine the response of the structure. For each type of lateral load, the structural engineer must judge the degree of analytical sophistication appropriate to a particular structural system. Loads are commonly characterized, and structural response evaluated, using either probabilistic or deterministic approaches. Probabilistic approaches explicitly consider the statistical distributions of loads, of structural parameters, and therefore of structural response as well. Deterministic approaches do not explicitly consider the statistical distributions of those quantities. Because deterministic approaches are simpler than probabilistic ones, and because statistical information sufficient to characterize loads is not always available, deterministic approaches are much more widely used than are probabilistic ones. However, information on the statistical distribution of loads is often used in describing loads deterministically. 2.2--Wind loads 2.2.1 Nature of wind force--Wind is the general term used to describe air which is in motion due to natural causes. In addition to normal winds, some regions are subject to especially strong winds, such as hurricanes or tornadoes. By virtue of its mass and velocity, moving air has kinetic energy. When moving air is stopped or deflected by an obstacle such as a building, some or all of its kinetic energy is transformed into the potential energy of pressure. Wind pressure on any particular structure is proportional to the square of the wind velocity, and total wind force on a structure depends also on the drag characteristics of the structure, air density, and other factors.[29] Wind velocity varies with time. One measure of mean wind velocity used for design purposes, the "fastest mile wind," is obtained by determining the time it takes that wind to travel one mile. Wind gusts are described in terms of fluctuations around that mean velocity. Other procedures for determining a design value for wind speed are based either on the average wind speed over a certain amount of time, or on the speed of gusts of various durations. Typically, gusts lasting about one second are most important for structural design.[29] Mean wind velocity varies with height above the ground, increasing from zero at the ground surface to a maximum value several hundred feet in the air. Wind velocity increases rapidly above the ground in open terrain, and more slowly in rough terrain or in cities. In cities, wind forces on a building can be greatly modified by the placement and configuration of adjacent buildings. The wind pressure at any point on an obstacle struck by wind depends on the velocity and density of the air, on the direction from which it hits the obstacle, and on the obstacle's shape and vibrational characteristics.[29] 2.2.2 Building response to wind--A building struck by wind is subjected to fluctuating pressures. The net wind load on structural elements such as roofs or cladding depends on the difference between the internal pressure, which is usually assumed constant, and the fluctuating external pressure. The net wind load on an entire building is independent of constant internal pressure. Building response consists of static response to the mean wind, plus dynamic response to the wind gusts. If the building is flexible, dynamic response to gusts can be significant. As a result of dynamic amplification, a flexible building can experience significant oscillations in both the along-wind and cross-wind directions. If the gust frequency is close to one of the building's natural frequencies of vibration, a condition of resonance can occur, in which the dynamic response increases to very large values. In addition, when wind strikes a slender building, vortex shedding on alternate sides of the building can create a fluctuating force acting in the cross-wind direction along the height of the building. These fluctuating transverse forces can affect cladding, and also the entire building. If the frequency of vortex shedding is close to one of the building's natural frequencies of vibration, resonance can occur.[29] 2.2.3 Design approaches for wind--Three different approaches are used by current codes for determining design wind loads: Static approach--The design wind force is idealized as an equivalent static load, independent of the dynamic properties of the building. The load varies with geographical location and height above the base of the building. Some codes do not explicitly consider gust effects,[30] while others do.[31,32] The static approach is admissible only for those cases in which the fundamental natural period of vibration of the building is separated from the period of the gusts. Dynamic approach--The design wind force is idealized as an equivalent static load which is dependent on the dynamic properties of the building.[31,32] This approach may be applied to all buildings, and should be applied to buildings with a fundamental period of vibration exceeding about one second. Wind tunnel approach--Design wind forces are determined through the use of boundary-layer wind tunnel tests or other experimental methods.[31,32] This approach is often used for buildings of unusual configuration or high importance (Fig. 2.2.3). Once design forces have been determined, the building and its components must be designed to resist the resulting member actions. If dynamic response is important, dynamic increases in deflections and member actions should be considered, as should the effects of dynamic response on occupant comfort.[33] Because wind is an externally applied force which acts predominantly in one direction, significant inelastic response is generally not permitted. 2.3--Blast loads 2.3.1 Nature of blast forces--The general term blast refers both to vibrations induced in the soil, and to fluctuations in air pressure due to explosions. Soil vibrations due to blasts may be considered using the same procedures as for seismic excitations (see Section 2.4). Blast loads due to fluctuation in air pressures are similar to wind loads in that they produce wind pressures on buildings. However, the pressure variations in space and time are very much different. When an explosion occurs, expanding hot gases produce a pressure wave which starts at the source, and moves outward through the surrounding air at the velocity of sound. A short distance away from the blast, this pressure wave develops an abrupt shock front, whose peak shock overpressure decreases as the front travels outward. When the front strikes an obstacle, the shock overpressure acts on the obstacle's leading surface. Immediately behind the shock front, expanding air from the blast creates a dynamic overpressure, which also acts on the leading surface of the obstacle. Blasts can also occur inside buildings, typically due to utility explosions such as the one which occurred at Ronan Point.[7] Interior blasts produce shock plus dynamic overpressures which act outward on the walls, floor and ceiling surrounding the point of explosion. 2.3.2 Building response to blast--As in the case of wind load, building components are subjected to differences between external and internal pressures. Entire buildings are subjected to the difference between shock plus dynamic overpressure on their windward side (Fig. 2.3.2), and shock overpressure on their other sides.[34] The overall effect is similar to a very strong wind gust. Both overpressures increase almost instantaneously to their peak values, and then return more slowly to zero.[34] If the location and magnitude of a design blast can be specified, the time and space variations of the resulting pressures can be defined. The blast response of buildings or components can then be carried out by conventional methods of structural dynamics,[35] provided that attention is paid to loading rates, which are often high. In addition to the normal dynamic response, these high loading rates cause the propagation of stress waves through the structure at sonic velocities. 2.3.3 Design approaches for blast--Blast design is usually not addressed explicitly by codes. Buildings which must resist external blasts are designed for the overall shears and overturning moments produced by the blast, and also for the resulting member actions. Because blast loads occur very infrequently and are of very short duration (Fig. 2.3.2), some inelastic response is permitted under extreme blast loadings. Also, material strengths are usually increased significantly under the high strain rates associated with blast loads, and this beneficial effect can be included in design. Design of individual components is particularly important in the case of interior blasts. It is important to ensure that local failure of building components does not spread from element to element, eventually causing collapse of all or much of the structure. This undesirable phenomenon, referred to as "progressive collapse," is addressed by modern building code provisions requiring structural integrity and continuity.[7,32] 2.4--Earthquake loads 2.4.1 Nature of earthquake forces--Earthquakes can cause local soil failure and surface ruptures. Though hazardous to buildings, these are not discussed further here. The most significant earthquake effects on buildings usually result from the seismic waves which propagate outward in all directions from the earthquake focus. These waves are of several different types, and can cause significant ground movements up to several hundred miles from the source of a strong earthquake. When the base of a building moves while the upper part tends to remain at rest due to its inertial resistance (mass), the resulting dynamic response causes time-varying member actions which must be considered in design. It is currently impossible to do more than estimate, in general terms, the intensity, sequence, duration and frequency content of the earthquake-induced ground motions to which a structure may be subjected during its lifetime. For design purposes, ground motion is described by the history of hypothesized ground acceleration near the structure, and is most commonly expressed in terms of the response spectrum derived from that history. When records are unavailable or insufficient, smoothed response spectra are used to characterize the ground motion for design purposes (Fig. 2.4.1). Building codes often use simple formulas to describe a smoothed curve which specifies design base shear in terms of a structure's fundamental natural period. Ground motion is usually described in terms of two perpendicular horizontal components and a vertical component, assumed to specify the motion of the entire base of the structure. However, as the base area of a structure increases, its seismic response may also be significantly affected by variations in ground motion along the base at any instant of time.[36] 2.4.2 Building response to earthquake--Given the history of ground shaking at a particular site, or the response spectrum derived from that history, a building's theoretical response can be calculated by established techniques of dynamic analysis, provided that its member properties, mass distribution, and damping characteristics are known.[35,37] Because buildings are more flexible laterally than vertically, and are already designed to resist vertical loads due to gravity, structural response is often computed using only the horizontal components of ground motion, and neglecting vertical ground accelerations. However, this procedure is not always advisable. Vertical accelerations may increase column axial loads above the values due to overturning alone and may significantly affect buildings with cantilevers or long-span girders. The true three-dimensional nature of earthquake input is often simplified in design by assuming that the design horizontal components act nonconcurrently in the direction of each principal axis of a building. A building designed by this approach is tacitly assumed to have adequate resistance against horizontal base accelerations acting in any direction.[37,38] However, this approach may not always be conservative. Several design procedures require that some of the earthquake load be applied simultaneously along both perpendicular building axes,[39] or that the building be designed for an earthquake acting in any direction. Biaxial bending of columns can result either from base motions which do not coincide with the principal directions of the building's framing system, or from nonsymmetrical building response. 2.4.3 Design approaches for earthquake--Several approaches are now available for estimating design forces associated with earthquake loads. Four generally accepted approaches are now discussed: Equivalent static approach--This approach, adopted by most building codes, prescribes a set of equivalent static horizontal forces which are intended to simulate the effect of earthquake loading, and which are used to design the building for earthquake effects.[30,31,32,39,40] The distribution of design forces along the height of a building roughly approximates that of the fundamental mode of vibration of the building (Fig. 2.4.3). The design forces specified by most codes are generally much smaller than the corresponding maximum values which would be indicated by elastic dynamic analyses using the actual earthquake motions[39] Some members within buildings designed to resist such reduced forces will generally yield under severe earthquake conditions. To protect the integrity and stability of a building after such yielding, codes contain provisions intended to ensure adequate inelastic deformation capacity in regions where yielding is likely. This simple method has produced many buildings which have satisfactorily withstood severe earthquakes. It has been developed based on observed performance of structures with small plan eccentricities between their center of mass and their center of stiffness at each floor level, and with uniform distributions of mass, stiffness and strength over their height. It may not be suitable for other types of structures. Reference 40 is the most commonly quoted work on this subject, and References 30, 31 and 32 are similar. The recommendations of Reference 39 are undergoing refinement and testing. Elastic dynamic approach--In this approach, the structure is idealized as a linearly elastic, multi-degree-of-freedom system, whose dynamic response is computed using a structural analysis computer program. Response to dynamic loading may be computed by numerical integration of the structure's equations of motion, but is usually obtained by calculating the maximum modal responses using response spectra, and then combining these modal maxima. Since, as noted previously, typical buildings do not remain elastic under strong earthquakes, member actions computed assuming linear elastic behavior could considerably exceed yield values. For such cases, it is also possible to use an elastic analysis to estimate the inelastic response, using general empirical relationships between the seismic response of linear elastic and idealized inelastic systems. This is most commonly done using modified inelastic design response spectra, obtained by several procedures.[37,41,42,43,44] Inelastic dynamic approach--This approach requires that the structure be idealized as a nonlinear multi-degree-of-freedom system, possibly exhibiting stiffness and strength degradation under repeated load reversals. Using computer programs such as that described in Reference 45, the structure's inelastic response history is calculated using several input ground accelerations. The distribution of member strengths throughout the structure is successively modified until the required inelastic deformations in each member become less than or equal to the corresponding inelastic deformation capacities.[42,46] Modified static approach--In this deterministic procedure, the designer specifies plastic hinge locations where inelastic deformations may occur during the largest seismic event. The collapse strength of the structure is then required to exceed the forces imposed by the design earthquake.[47] An extension of this is the so-called capacity design philosophy, whereby all other regions of the structure (except the plastic hinges) are provided with sufficient reserve strength to ensure that they remain elastic at all times. In designing frames by this approach, for example, the design forces (whether applied statically or derived from dynamic analyses) are used only to determine the required strength of the beams. Design actions for columns are then based on the actual capacities of the adjacent beams, modified to allow for local increases due to dynamic effects.[48] The seismic response of structures so designed is considered to remain relatively insensitive to ground motion characteristics. This very simple design approach, like the previous three, requires judicious detailing of reinforcement in potential plastic hinge regions. 2.4.4 Soil-structure interaction--The response of a structure to lateral loads may be affected in several ways by ground conditions at the site. Under wind loading, consolidation or potential yielding of the foundation structure may have to be considered. Beyond this effect, however, which is essentially static in character, the design of structures for wind loading generally requires little consideration of foundation effects. Much of the recent interest in foundation effects on structures has been related to the dynamic aspects associated with response to earthquake excitation. The foundation effects discussed here are associated with inertial effects due to the passage of seismic waves through the foundation medium. Ground conditions at the site affect the earthquake response of structures in two ways: 1. Local geology amplifies or attenuates the intensity of the transmitted seismic waves, and also modifies their frequency characteristics. 2. Soil properties near a structure affect the structural response. Soil-structure interaction is directly related to the latter aspect, and includes the following effects: the underlying soil modifies the response of a structure compared to what it would have been had the structure been founded on a rigid base; and the presence of the structure modifies the ground motion at the site in relation to the free-field motion. These essential aspects of soil-structure interaction are shown schematically in Fig. 2.4.4. Soil-structure interaction results from two distinct effects: 1. Inertial interaction, caused by relative motion between the foundation and the surrounding soil when inertial forces in the structure are transmitted to the soil. 2. Kinematical interaction, which can occur even in the absence of inertial forces, and which arises when the stiffer structural foundation cannot conform to the distortions of the soil generated by the passage of seismic waves. The phenomenon of soil-structure interaction implies the addition of translational, rocking, vertical, and even torsional degrees of freedom at the base of the structural system. Currently, only the rocking and translational degrees of freedom are generally considered. The effect of soil-structure interaction on the earthquake response of structures has been the subject of a number of analytical studies[49] and limited field observations[50,51] These studies indicate that, for buildings founded on firm or moderately firm ground, the effect of soil-structure interaction is small. This is particularly true for tall, multistory buildings that are relatively flexible compared to the supporting medium. For such cases, the assumption of a structure fixed to a rigid base to which the input motion is applied is justifiable. For stiff structures, particularly those resting on soft ground, the effects of soil-structure interaction can be significant. However, no definite trends are shown by the analytical studies mentioned. Thus, soil-structure interaction may produce an increase in response in one case and a decrease in another, depending upon the properties of the structure, the supporting soil, and the earthquake excitation. Coupling between a structure and its supporting soil generally results in a system that has a longer fundamental period than the same structure fixed to a rigid base. Also, the damping in the soil-structure system, which is due to internal damping within both the structure and the soil immediately adjacent to it, and also to radiation damping resulting from the dissipation of energy through dispersion to the surrounding ground, is generally greater than that corresponding to the structure alone. On the basis of the preceding observations, it has been suggested by Whitman[52] that from a design standpoint, soil-structure interaction always reduces stresses (and therefore deflections as well) in linearly elastic structures. However, a study by Bielak[53] showed that an idealized elasto-plastic structure resting on a linear viscoelastic half-space exhibited larger displacements than would have occurred had the base been rigid. Most soil-structure interaction problems can presently be solved only by linear or equivalent linear methods, and most of the literature on soil-structure interaction refers to linear systems. Excellent summaries of currently available approaches to the analysis of soil-structure interaction problems are given in References 49 and 54. ATC-3,[39] a report representing results of an extensive collaborative effort among design professionals, building code officials and researchers, provides for consideration of site effects and soil-structure interaction effects on the design lateral force or base shear. Formulated as a resource document for future codes, the provisions reflect the need to simplify results of recently available information consistent with the requirements of design practice and the current state of knowledge. The effects of soil-structure interaction are provided for in ATC-3 by modifying the dynamic properties of the fixed-base structure. The modification consists of increasing the fundamental period of the fixed-base system, and changing (usually increasing) its effective damping. The increase in period reflects the flexibility of the foundation soil, while the change in damping accounts for the effect of energy dissipation in the soil due to radiation and material damping. Although ATC-3 recognizes that soil-structure interaction may increase, decrease, or have no effect on the forces in a structure, the net effect of considering soil-structure interaction as specified in ATC-3 for rigidly supported structures is to reduce the design base shear and overturning moment relative to those of a fixed-base structure. As noted earlier, the influence of foundation rocking may cause horizontal displacements relative to the base to be larger than those for the corresponding fixed-base system. This effect may increase both the required spacing between buildings, and the secondary forces associated with P-delta effects. Although such increases are often small, the behavior of many structures during the Mexican earthquake of 1985[27] indicates that certain foundation conditions can encourage very large displacements and even collapse of structures. For conventional building structures, soil-structure interaction produces substantial effects only on the response component associated with the fundamental mode of vibration. Hence, even for the modal analysis procedure stipulated in ATC-3 as an alternative to the equivalent lateral force procedure, only the fundamental period of the fixed-base system is modified in considering soil-structure interaction effects. CHAPTER 3--PERFORMANCE CRITERIA 3.1--General Performance criteria may be listed in two major categories: 1. Safety criteria 2. Serviceability criteria Safety criteria are concerned with the preservation of life under all loads. Serviceability criteria are concerned with structural response to loads or conditions which may cause cosmetic damage, deterioration, temporary loss of function, occupant discomfort, or other forms of distress, but which do not immediately threaten the life safety of the occupants. In this chapter, these two types of criteria are discussed, and approaches for meeting them are reviewed. 3.2--Safety criteria Although most structural systems normally respond in a linear elastic manner under service loads, ultimate conditions must be addressed in the design process. Evaluation of the overall safety of a structure requires criteria defining strength, stability, and ductility. In the rest of this section, the significance of each of these qualities is briefly discussed. In the following section, different design approaches for lateral loads are summarized, and design for earthquake resistance is discussed. 3.2.1 Significance of strength--The strength of a building system subjected to lateral forces depends on the strengths of its various elements and their connections under combinations of flexure, shear, torsion, or axial force. If the members are not strong enough to resist the forces acting on them, they will fail, possibly causing failure of the entire structure. 3.2.2 Significance of stability--For design purposes, most structures are analyzed assuming that loads act at fixed locations (without moving as the structure deflects), and members do not deflect from their original configurations. This is commonly referred to as a "first-order" analysis. In a "second-order" analysis, the possibility of large deflections is considered. In designing buildings for lateral loads, a second-order analysis would commonly consider P-delta effects (secondary moments caused by vertical loads acting on the building's laterally deflected configuration). Instead of using second-order analyses, moment magnifier techniques are often used to approximate column design moments. A laterally loaded structure is usually first designed for sufficient member strength against first-order actions. If the structure sways excessively, however, its member actions (calculated including second-order effects) may still exceed member strengths. Such a structure may become unstable and collapse. 3.2.3 Significance of ductility--If member strengths are less than elastic demands, the structure will respond inelastically. Inelastic response of a structural system is associated with inelastic deformations in so-called "critical regions" of the structure. The strength of an inelastic system is limited by the strengths of its members, and also by the ability of the members to deform inelastically without losing a significant portion of their load-carrying capacity. This characteristic is generally referred to as ductility. Ductility is often quantified using ductility factors, originally defined in terms of elasto-plastic, single-degree-of-freedom systems. For example, the lateral displacement ductility factor for an elasto-plastic, single-degree-of-freedom structure is defined as the ratio between the structure's maximum lateral displacement, and its yield lateral displacement. Ductility factors can also be defined to describe characteristics of elasto-plastic structural elements. For example, the rotational ductility factor for an hinging region is defined as the absolute value between the maximum rotation across the hinging yield rotation. Ductility factors for curvature defined analogously. elasto-plastic of the ratio region, and the and strain are The ductility factor concept is sometimes extended to structures and structural elements which are not elasto-plastic, or which have multiple degrees of freedom. For such structures or elements, ductility factors can still be defined in terms of the ratio of maximum to yield displacement (or other analogous quantity). For example, design procedures of some seismic codes contain provisions that assume implicitly that the structure possesses some minimum available ductility factor. However, because maximum and yield displacements or deformations are difficult to define for systems which are not elasto-plastic, or which have multiple degrees of freedom, there are no universally accepted definitions of ductility factors for such systems. While references are often found in technical literature to ductility factors for systems which are not elasto-plastic, or which have multiple degrees of freedom, such factors are meaningless unless the procedures used to calculate them are explained precisely. Required ductility factors for members in a structure are usually higher than the corresponding required displacement ductility factor for the structure as a whole.[55] Calculating any available ductility factor for a reinforced concrete structure is a complex problem involving bending and shear deformations. The problem becomes even more complex if the structure or its components are subjected to deformation reversals. Available ductility under reversed cyclic loads can be much less than the available ductility under monotonically increasing loads. Under current practice, a member's ultimate deformation capacity can only be predicted approximately given its material and geometrical properties. Detailing requirements are intended to ensure appropriate inelastic deformation capability, but not a specific ductility factor. 3.3--Approaches for meeting safety criteria 3.3.1 Strength design approach--Procedures for strength design of laterally loaded reinforced concrete buildings are prescribed by the general design provisions of ACI 318.[56] Member strengths are assigned according to a distribution of member design actions determined by linear elastic analysis. To ensure stability in laterally flexible structures, member design actions are modified for second-order effects. Although actual member stiffnesses are often uncertain, approximations are justified; elements stiffer than assumed will redistribute internal actions to more flexible elements, provided that sufficient ductility is available. Typical design and detailing provisions (for example, Reference 57, and also Appendix A of Reference 56) are intended to ensure adequate structural ductility. To encourage the formation of plastic hinges in beams rather than columns, for example, a "strong column, weak beam" philosophy is followed. Furthermore, efforts are made to ensure that individual members are sufficiently ductile. For example, a member's flexural capacity is used to calculate member design actions corresponding to brittle failure modes such as shear. 3.3.2 Limit design approach--As an alternative to strength design, limit design procedures assign member strengths which satisfy statics, but which may deviate from those calculated by linear elastic theory. Those members which yield early must possess sufficient ductility so that the system can develop its full lateral-force strength. Furthermore, the lateral deflection needed to develop the full strength of the structure is larger than that corresponding to a strength design. Stability considerations may need to be examined as a result of these large deflections. While limit design is not commonly used in the United States for design of reinforced concrete buildings, it has been used in other countries for design of coupled shear walls and other special types of reinforced concrete structural systems. Its advantage is that a designer, using judgment and experience, may choose a distribution of resistances among structural elements which reduces congestion of reinforcement in heavily stressed regions of a structure, and is more economical than that deduced on the basis of elastic theory.[58] 3.3.3 Approach for earthquake resistance--Because earthquake excitation imposes deformations rather than loads on a structure, member actions are limited by member capacities. Provided that it has sufficient ductility, and that lateral drifts remain within stability-imposed limits, a yielded structure will not collapse under earthquake excitation, and its integrity will be preserved after the earthquake. It is therefore feasible to design a building to respond inelastically during a moderate or strong earthquake. Such a structure dissipates energy during earthquake excitation primarily through inelastic action of its members. When such a structure is subjected to reversed cyclic actions, the relation between force and deflection is usually nonlinear and hysteretic, as shown in Fig. 3.3.3. The energy dissipated per cycle can be related to the area bounded by a hysteresis loop. A structure with adequate energy dissipation can resist many inelastic cycles of reversed deflection with a small loss of strength and stiffness. Performance criteria for earthquake resistance vary with the function of the building and the intensity of the ground motion. Hospitals and other essential facilities should remain functional after any earthquake.[60] Under strong motions, structures may be allowed to undergo damage, provided that collapse and loss of life are prevented. Performance criteria for design of earthquake-resistant structures can be expressed by the following: 1. Buildings should resist frequent minor earthquakes without any damage. To prevent damage to nonstructural elements, the structure should be sufficiently stiff so that lateral deformations are limited. 2. For less frequent, moderate earthquakes, some damage to nonstructural elements is accepted, but damage to the structure itself should not occur. To prevent damage, the structure should be sufficiently strong so that it remains essentially elastic. 3. During rare strong earthquakes, both structural and nonstructural damage is accepted. However, the integrity of the gravity load-carrying structural systems must be preserved, and collapse and associated loss of life must be prevented. To prevent collapse, the structure must be sufficiently ductile to maintain a high level of lateral load resistance while undergoing significant inelastic deformations. This requires that critical regions of reinforced concrete buildings in seismic zones should be detailed for ductile behavior. Detailing of members and connections should be done so that potential plastic zones will be fully utilized. This can be more important than the degree of sophistication or accuracy involved in the mathematical modeling of dynamic response of the structural system. 3.4--Serviceability criteria These criteria are intended to ensure the satisfactory performance of the structure under service condition. Significant lateral-load serviceability considerations include but are not limited to: 1. Lateral deflection 2. Cracking 3. Perception of lateral motion 3.4.1 Significance of lateral deflection--Lateral deflection, or drift, is an important consideration in design of high-rise buildings subjected to lateral forces.[61,62] In addition to the stability criterion addressed previously, excessive lateral drift can cause damage to structural and nonstructural elements. 3.4.2 Significance of cracking--Two aspects of cracking are of concern in the design of buildings for lateral loads; the effects of cracking on lateral stiffness, and appearance. 3.4.3 Significance of perception of lateral motion--If a building's lateral load response causes possible disruption of services, cosmetic distress, or occupant discomfort, the building may be undesirable from a user's viewpoint. This problem most commonly arises with respect to wind loads, but may also be important in zones of high seismicity. 3.5--Approaches for meeting serviceability criteria 3.5.1 Approaches for meeting lateral deflection criteria--The drift ratio is the lateral displacement at the top of the building, divided by its height. The interstory drift ratio is the difference in lateral displacements between any two adjacent levels, divided by the corresponding story height. For seismic design, some codes[30] specify that the maximum interstory drift ratio calculated using the specified design forces (with load factors of unity) should not exceed 1:200. Because of various inelastic response effects that are implicit in the design procedure, this drift limitation does not necessarily reflect the lateral drift to be anticipated under the design loading, Some codes explicitly recognize this fact. For example, the Uniform Building Code[30] recognizes this effect by requiring that structural and nonstructural elements be capable of withstanding lateral drifts at least three times the computed lateral drift. For wind design, most major building codes do not specify a maximum permissible drift ratio. However, many design offices limit the maximum overall drift ratio at the roof level to a value between 1:400 and 1:1000, depending on the structural system, the modeling procedure used in the drift analysis, and the return period of the design wind. Similar ratios are often used to limit interstory drift. As used in wind design, the interstory drift ratio is intended primarily to limit damage in nonstructural components of the building. Drift ratios may also be used to limit peak accelerations, but only if considered together with the building's frequencies of vibration, damping, and mode shapes. The relation between computed drift and actual performance depends on the analytical model used in the analysis, particularly with regard to stiffness assumptions. There is currently no standard modeling procedure, and procedures vary from office to office. Many offices have developed explicit procedures which, while sometimes apparently arbitrary, have nevertheless been proven to produce satisfactory designs for the type of buildings for which they were developed. The adequate performance of these buildings often reflects the fact that three-dimensional framing effects and nonstructural elements not considered in the analytical model are in fact effective in reducing drift. Nonstructural elements can be damaged by large drifts. Cracking of nonstructural elements can cause leakage, loss of acoustical properties, and other serious maintenance problems. Design of structures to satisfy the drift limitations previously discussed will help to reduce damage to nonstructural elements. When large drift is expected, floating partitions capable of accommodating relative movement between skeleton and partition may be required. In selecting the required magnitude of separation, possible detrimental effects of rigid partitions, cladding, or secondary structural components on the adjacent primary structural element must also be considered. Stairs in rigid-jointed ductile frames, for example, should not be permitted to act as braces when inelastic story drift takes place. It is particularly important to design the attachment details of precast concrete facade elements to permit earthquake-induced movements without loss of gravity load-carrying capacity. This is a structural engineering concern.[30,39,40] 3.5.2 Approaches for meeting cracking criteria--Modeling of member stiffness with respect to cracking is discussed in Subsection 5.4.2. As far as control of crack widths for appearance is concerned, it should be understood that properly designed reinforced concrete may crack under service conditions. Crack severity and location should be reviewed by the engineer. 3.5.3 Approaches for meeting perception of motion criteria--Reactions of occupants to building motions may depend on factors such as the following:[63,64,65] 1. The perception of building movement 2. The occupant's body position and orientation 3. Noise 4. The movement of fixtures 5. The reactions of co-workers 6. The expectation of motion 7. Individual psychological differences Several researchers have studied the problem of human perception of motion.[63,64,65] Typical results of such research are summarized in Fig. 3.5.3, which shows that in terms of perceived acceleration level, perceptibility of motion is a function of a building's frequency of vibration, the return period of the wind producing the motion, and the building occupancy. Results of such research are used to establish simple design recommendations and performance criteria.[31] The recommendations of Reference 31 are shown at the right of Fig. 3.5.3. The acceptability of a building design with respect to perception of lateral motion can be assessed through wind tunnel testing of aeroelastic models, or through a dynamic analysis of the building under probable wind exposures. In Reference 31, simple expressions are suggested for estimating accelerations of tall buildings in the crosswind and along-wind directions, based on wind tunnel measurements, and considering the building as an equivalent single-degree-of-freedom system with variations of stiffness and mass. Simplified procedures to account for lateral motion perception need to be developed for conventional buildings. CHAPTER 4--STRUCTURAL SUBASSEMBLIES AND SYSTEMS 4.1--General The purpose of the structural system is to carry all loads safely to the foundation, to prevent excessive deflections of the structure, and to ensure the comfort of the occupants. Structural systems can be made up of one or more basic elements, referred to here as subassemblies. The structural system of a building consists of horizontal floors and sets of vertical elements which perform the dual function of resisting all gravity and lateral loading on the structure. 4.2--Subassemblies 4.2.1 Floor systems General--While the primary function of the floor system is to resist gravity loading, it performs important additional functions in most buildings: 1. The floor system usually provides the in-plane stiffness required to maintain the plan shape of the structure, and distributes horizontal forces to the vertical load-resisting system. 2. The flexural stiffness of the floors may be an integral and necessary part of the lateral load-resisting system. Selection of the floor system significantly affects a structure's cost, and also the performance of its lateral load-carrying system. Structures are commonly analyzed for lateral loads by assuming that the floor system acts as a diaphragm, infinitely stiff in its own plane, which distributes horizontal forces to the lateral load-resisting elements. This assumption is not valid for all configurations and geometries of floor systems. Analyses which take into account the in-plane flexibility of the floor systems can result in a very different distribution of horizontal forces among the various elastic lateral resisting elements than would be obtained using a structural model which assumes rigid floors.[66] Whether or not a diaphragm can be assumed to be rigid depends on the span to depth ratio of the plan dimensions of the slab relative to the location of the lateral load-resisting elements, on the slab thickness, on the locations of openings and discontinuities in the slab, and on the type of floor system used. The flexural stiffness of the floor system may also significantly affect the lateral stiffness of the structure. The designer usually must estimate the effective width of floor system that contributes to frame stiffness. Deformations of the lateral load-resisting elements also affect those parts of the structure which have not been designed to contribute to lateral load resistance. This is important in the design of structures for seismic forces, particularly when the designer assumes ductility of the lateral load-resisting system. A structure designed to respond inelastically under severe design conditions could experience considerably higher lateral drift than that corresponding to elastic response. A floor system that is not part of the ductile system can usually be designed to remain elastic in this situation. Nevertheless, the floor systems must be designed to accommodate the expected motions.[67] Provisions of some codes require the designer to check that the floor slabs can tolerate the out-of-plane deformations associated with several times the lateral deflection calculated for design forces.[30,40] Flat plates--A flat plate [Fig. 4.2.1(a)] is a flat slab without column capitals or drop panels. Because of the relative thickness of the slab and distribution of reinforcement, this system normally acts as a satisfactory shear diaphragm. Although the flat slab and supporting columns are not always considered by design engineers as part of the lateral load-resisting system, their contribution to building stiffness and strength can be significant, particularly for high-rise structures. Even if some effective width of the flat plate is not included as part of the lateral load-resisting system, the design engineer must consider this behavior when designing the structure. As a result of their interaction with the lateral load-resisting system, flat plate elements can be subjected to significant shears and bending moments. When bending moments are transferred from the slab to the column, the combination of direct shear and torsional shear stresses can be high, and may control the design of the slab. In seismic zones, buildings with ductile lateral load-resisting elements may experience high lateral drift due to inelastic response. The effect of this inelastic behavior on the slab-column joints of flat plates can be designed for to some extent by improving the flexural and shear capacity of the slab-column connection. This can be achieved by using shear reinforcement (stirrups or structural steel shearheads) at the slab-column joint, and by concentrating slab flexural steel over the column. However, the relative thinness of flat plates may make placement of such reinforcement difficult. Flat slabs with drop panels and/or column capitals--The shear strength of flat slabs can be improved by thickening the slab around columns with drop panels (either constant-thickness or tapered), column capitals, or both. Like flat plates, flat slab systems [Fig. 4.2.1(b)] normally behave well as diaphragms carrying shear in their own plane. For ductile frames in seismic regions, drop panels improve the ability of the flat slab to participate in the lateral load-resisting system, and to resist high shear and ductility demands. The increased slab thickness at the column allows for the use of closely spaced stirrups radiating out from the column in two directions, which greatly improve the ductility of the slab with respect to bending and punching shear. Given proper attention to proportioning and detailing, flat slab or flat plate frames can have considerable ductility and strength.[68] However, lateral load-resisting systems consisting only of flat slab or flat plate frames, without ductile frames, structural walls or other bracing elements, are not considered suitable in highly seismic areas (Uniform Building Code Zones 3 and 4). Two-way grid (waffle) slabs--For larger spans, a slab system consisting of a grid of ribs intersecting at a constant spacing may be used to achieve acceptable slab depth with minimum dead load [Fig. 4.2.1(c)]. The ribs are formed by special dome or pan forms. The slab thickness between the ribs is normally governed by fire rating requirements. Some pans adjacent to the columns are omitted in order to form a solid concrete drop panel, satisfying requirements for transfer of shear and unbalanced moment. This slab system normally acts as an adequate shear diaphragm. The thicker slab adjacent to the column provides increased shear resistance. Slab flexural ductility can be increased by the addition of closely spaced stirrups radiating out from the column face in two directions. Stirrups may also be used in the ribs. Because a waffle slab behaves similarly to a flat slab, lateral load-resisting systems consisting only of waffle slab frames may not be suitable in highly seismic areas (Uniform Building Code zones 3 and 4). One-way slabs on beams and girders--One-way slabs on beams and girders consist of girders which span between columns and which support beams. The beams, in turn, support one-way slabs. This system provides a satisfactory shear diaphragm, and is suitable for use in structures subjected to lateral loads. Adequate flexural ductility can be obtained by proper detailing of the beam and girder reinforcement. One-way ribbed slabs (joists)--One-way slab systems consist of concrete ribs in one direction, supported by beams on column lines in the other direction. The size of pans available determines rib depth and spacing. As with a two-way ribbed system, the slab thickness between ribs is often determined by fire rating regulations. This system provides a satisfactory shear diaphragm and lends itself to use in a structure whose lateral resistance comes from a moment-resisting frame. One row of pans can be eliminated at column lines, giving a wide, flat beam which may be used as part of the lateral load-resisting frame. Even if the slab system does not form part of the designated lateral load-resisting system, the designer should investigate the actions induced in the ribs by building drift. One-way banded slabs--This floor system involves a drop panel which is continuous from column to column, usually in the short-span direction [Fig. 4.2.1(d)]. The result is a system of shallow, wide beam bands in one direction and a one-way flat slab in the other. Like a flat slab system with drop panels, this system can be reinforced with closely spaced stirrups near the support for improved ductility and shear resistance. Although the presence of the drop panel allows the slab to act like a beam in the short-span direction of the structure, the slab acts like a flat plate in the long-span direction of the structure. A structure using this type of floor system is less stiff laterally than a structure using a ductile moment frame. Lateral load-resisting systems consisting only of flat slab or flat plate frames, without ductile frames, structural walls or other bracing elements, are not considered suitable in highly seismic areas (Uniform Building Code Zones 3 and 4). Two-way slabs with edge beams--This system, in which flat slabs are supported by beams in two directions on the column lines, is very efficient, and is useful where a beam-column frame is required as part of the lateral load-resisting system [Fig. 4.2.1(e)]. For longer spans, a two-way grid (waffle) slab may be used instead of a flat plate. Beams may be detailed to have very high ductility and proportioned to have any desired stiffness. For this reason, two-way slabs with edge beams can provide a structural system with very high diaphragm stiffness, and also sufficient lateral stiffness and strength for use in highly seismic areas. Precast slabs--Precast concrete slabs may be used as a one-way system supported by bearing walls, precast beams or cast-in-place beams. Precast slabs may consist of flat plates, hollow-core slabs, or single- or double-T-sections. Precast slabs are sometimes covered by a thin cast-in-place concrete topping. Welded connections are normally used to transfer in-plane shear forces between slab elements and to the supports. Because precast slabs are individual units interconnected mechanically, the ability of the assembled floor system to act as a shear diaphragm must be critically examined by the designer. Boundary reinforcement may be required, particularly when the lateral load-resisting elements are far apart. In seismic areas, connections between the precast slab system and the lateral load-resisting system must be carefully detailed. A concrete topping bonded to the precast slab improves the ability of the slab system to act as a shear diaphragm, and should be used in highly seismic zones.[69] Composite beam and slab systems--This floor system consists of a one-way slab system resting on beams. Shear connectors are incorporated at the beam-slab interface to ensure composite action. This type of system can have good lateral load resistance, provided that the shear connectors are carefully detailed for sufficient strength and stiffness. Some examples of this type of slab system are: 1. Steel beams supporting a steel deck with a cast-in-place concrete slab, and using steel shear connectors at the top flange of the beams. Composite action of the steel deck with the concrete slab is achieved with embossments on the metal deck. 2. Steel joists with the top chord embedded in a cast-in-place concrete slab. Special wooden formwork is commonly suspended from the joists, temporarily supporting the fresh slab concrete. 3. Precast concrete joists with steel shear connectors between the top of the beam and a cast-in-place concrete slab. The concrete joists are normally designed to support temporary wooden formwork for the cast-in-place slab. In this system, the joists are supported on walls or cast-in-place concrete beams framing directly into columns. 4.2.2 Frames General--The term "frame" denotes a rigid-jointed structure which resists gravity load and some or all of the lateral load through the flexural and axial strength of beams and columns. Components of a frame--Frames consist of vertical column elements and the foundations into which they frame, horizontal beam elements, and connections between the beams and columns. Each of these components requires different design considerations, particularly for ductile frames. Beam elements do not have significant axial loads, and hence are designed for flexure and shear. For ductile frames, special transverse reinforcement is required at beam ends to permit plastic hinges to form there. Column elements are designed for a combination of axial load, bending moment and shear. For ductile frames, the designer usually attempts to ensure that plastic hinges, when required, form in the beams rather than the columns. This "strong column, weak beam" philosophy is based on the need to avoid the formation of plastic hinges at both ends of all columns in a single story or in the structure as a whole, which usually results in a column sidesway mechanism. Such a mechanism requires unrealistically high curvature ductilities in the columns, and as a result, cannot develop significant lateral displacement ductility. Since hinges in the columns cannot be completely prevented, it is important to use adequate detailing in critical regions of columns, even when the "strong column, weak beam" philosophy is followed.[58,59] Beam-column connections must be designed for a combination of tension, compression, and shear, and should be proportioned to prevent excessive bond degradation of reinforcement passing through the joint.[56,57] The strength of joints should never control the total capacity of the frame. Beam-column connections are not suitable for energy dissipation. Sources of lateral drift--In a frame structure, lateral displacement consists of two parts: that due to bending of the columns and beams, and also to local joint deformations; and that due to axial deformations of the columns. The effect of column axial deformations, normally quite small, assumes greater significance as the height-to-width ratio of the building frame increases. Lateral drifts can be significantly increased by foundation deformations, yielding in the frame members, and P-delta effects. Ductile frames--Frames designed in accordance with the provisions of Appendix A of ACI 318[56] may be considered as ductile frames. In designing structures with ductile frames, the designer must be concerned with several factors: 1. Frames are relatively flexible. In a major earthquake, large deformations of the structure can occur if plastic hinges form in a significant number of the beams in the frame. The resulting damage to nonstructural elements can make the building unfit for use. Frame flexibility should be limited without sacrificing ductility. 2. Under loads causing reversed cyclic inelastic response, frames with excessive stiffness degradation can exhibit undesirably large lateral drifts. P-delta effects can lead to frame instability after a few cycles if story drift ratios exceed one or two percent. 4.2.3 Structural walls General--The term "structural walls" (referred to as "shear walls" in the Uniform Building Code[30]), is used here to identify walls designed to resist gravity loads and lateral forces in the plane of the wall. Structural walls act as vertical cantilevers, supporting gravity and lateral loads. Structural walls can have many different cross sections: rectangular, L-shaped, channel-shaped (elevator shafts), and even circular [Fig. 4.2.3(a)]. Walls can be solid or can contain openings. Walls may be coupled by thin flexural elements or deep shear elements, resulting in considerable variation in the behavior of the coupled wall system. Behavior of different types of structural walls--Short structural walls, whose behavior is governed by shear, may be designed to behave like shear brackets. Reinforcement of these walls generally consists of evenly distributed horizontal and vertical steel. Such walls are generally used in structures designed with no special provisions for ductility, although reinforcing details are available to the designer if ductile behavior is required.[55] Structural walls with a height-to-horizontal length ratio greater than two can be designed as beam-column elements subjected to axial load, moment, and shear. Reinforcement can consist of evenly spaced vertical and horizontal bars. Part of the flexural reinforcement may be concentrated at wall ends, where a boundary element may be formed for the purpose of section stability. When analysis shows that large concrete compressive strains may be required to develop the intended ductility of the wall, the ends of the wall should be confined over the length of the plastic hinge.[56] Longitudinal steel in the web contributes to the flexural strength of the wall, and should not be ignored if a capacity design philosophy is used to design the wall for shear. Designers of structural walls must consider overturning resistance provided by the foundation. To ensure ductile response, the foundations of a wall must be capable of resisting the actions generated in the wall, with allowance for the development of overstrength at the base of the wall. Ductile structural walls--The behavior of ductile structural walls should be governed primarily by flexure, and the area of flexural reinforcement should be small enough so that flexural yielding occurs before shearing failure begins. With proper attention to axial load level, confinement of concrete, splicing of reinforcement, treatment of construction joints and prevention of out-of-plane buckling, acceptable ductility can be obtained.[55,70] Coupled walls with shallow coupling beams--In high-rise concrete buildings with flat slab floor systems, such as apartment buildings and hotels, cross walls are commonly used as dividers between residential units, and are coupled by the slab at the interior corridor [Fig. 4.2.3(b)]. The contribution of coupling slabs to the lateral stiffness and strength of the structure should not be neglected by the designer, particularly in high-rise structures where link slabs have short spans. Flexural stiffness of link slabs deteriorates rapidly during inelastic reversed loading, however, and their contribution to energy dissipation and damping of the structures may become negligible.[71] Several studies are available upon which to base assumptions regarding effective slab width, use of noncracked or cracked sections, and effective placement of reinforcement.[71,72] A critical design consideration is the punching shear stress around the ends of the wall caused by shear in the link slabs. Tests have established the distance behind the edge of wall for which the slab can be considered effective for resisting these punching shear stresses.[71] Coupled walls with deep coupling beams--When the central elevator/service core of a high-rise building is pierced by small openings for doors or mechanical ducts, the result is a series of walls connected by deep, short-span link beams [Fig. 4.2.3(c)]. Due to their stiffness and strength, these deep link beams cannot be ignored in the analysis of the shear wall. High axial forces can be developed in the coupled walls, and should be considered to avoid brittle failure of the walls.[55] High shear forces can also be developed in the coupling beams, requiring heavy reinforcement there. Depending on their span to depth ratios, deep link beams must often be designed as deep beams. In seismic zones, where high ductility is desirable, greater ductility can be achieved using main reinforcement running diagonally from corner to corner, confined by spiral reinforcement and designed to resist flexure and shear directly.[55] The ability of the link beams to maintain their load-carrying capacity under reversed inelastic deformation protects the walls, which support the gravity load of the structure. 4.2.4 Infilled frames--An infilled frame consists of a frame surrounding a panel of masonry or concrete which can be designed to be either structural or nonstructural (Fig. 4.2.4). Effects of infilling on the structural response of the frame are often overlooked. However, studies of damage following strong earthquakes have shown that infilling can cause brittle failure of the bounding frame.[10,27] Experimental and analytical research has shown that infilling causes a frame to behave as a braced frame, increasing its lateral stiffness and strength.[73,74,75] The infilling acts as a compressive strut between diagonally opposite frame corners, and creates high shear forces in the columns. In a severe earthquake, these forces can cause the columns to fail in shear. If the infill extends over only part of the story height, this may create a short "captive column" which is vulnerable to shear failure. In addition, deterioration of the infills themselves can involve high nonstructural damage costs, as well as danger to occupants and bystanders. To avoid these undesirable behavior modes, infills should either be sufficiently separated from the bounding frame so that they do not act structurally, or they should be designed to work structurally with the frame. The latter requires that the infills be included in the analytical model of the structure, that the columns have enough shear strength to resist the shear forces produced by the infills, and that the infills themselves have horizontal and vertical reinforcement anchored in reinforced concrete boundary members, to hold them in place after failure.[73,75] When infills are discontinued at a given story level, the resulting structural system acts as a "soft-story" system. Under lateral loads requiring inelastic response, such systems are usually subjected to extreme inelastic deformation demands at the open story, and have generally shown poor resistance to strong earthquakes.[11,12,75] 4.2.5 Tubes General--A tube structure consists of several stiff intersecting frames (often thought of as perforated diaphragms), generally located around the perimeter of the building [Fig. 4.2.5(a)]. While unperforated tubes would behave like walls, the behavior of typical perforated tubes is between that of a frame and a wall. Tube behavior--A tube normally consists of closely spaced columns connected by relatively stiff beams. Tubes exhibit shear lag--the axial stiffness of columns located away from the corners of frames oriented normal to the lateral forces cannot be considered fully effective in resisting overturning moment. The extent of shear lag in the frames normal to the lateral forces depends on the flexibility of the framing elements. To account for shear lag during preliminary design, the effective plan configuration of the equivalent tube may be idealized as two channels, whose flanges are composed of a certain portion of the columns in the sides of the structure normal to the direction of lateral forces [Fig. 4.2.5(b)]. Since tube structures generally consist of girders and columns with low span to depth ratios (in the range of 2 to 4), shearing deformations often contribute to lateral drift, and should be included in analytical models. The tube system is versatile and compatible with various exterior building shapes. The inherent large torsional stiffness of exterior framed tubes allows for a higher degree of plan asymmetry than is possible for other framing systems. Braced tubes--The braced tube is a recently developed system in which a normally proportioned reinforced concrete tube is stiffened and strengthened by infilling in a diagonal pattern over the faces of the building [Fig. 4.2.5(c)].[76] This bracing increases the structure's lateral stiffness, reduces the moments in the columns and girders, and minimizes the effects of shear lag. This increases the efficiency of flange action of the tube faces normal to the wind direction. 4.3--Structural systems 4.3.1 General--Singly or in various combinations, the subassemblies described in Section 4.2 form structural systems for buildings. A structural system is considered efficient if its premium for height is minimized; that is, if the member sizes required for carrying gravity loading only need not be increased appreciably to resist the effect of lateral loading as well. The selection of a building's structural system is strongly influenced by occupancy requirements, architectural considerations, internal traffic flow (particularly in the lower floors), the structure's height and aspect ratio, and also the intensity and types of external loading. A structural system is most efficient when loads are transferred as directly as possible to the foundation, without large torsional effects induced by asymmetry in plan, and also without abrupt changes in member stiffness. Occasionally, a structure may be isolated (usually at its base) from excessive seismic forces. Elastomeric pads or other devices may be used to increase the fundamental period, thereby reducing the elastic seismic response of the structure to typical earthquake motions.[77,78] However, this type of base isolation offers little if any advantage for tall structures, which are characterized by a long fundamental period. Energy dissipators may also be used to reduce the response of the superstructure by providing hysteretic damping at the base. Energy dissipators are usually designed to be replaceable. Base isolators and energy dissipators may be used together.[79] Damper-absorber systems have been used for reducing wind-induced vibrations of tall buildings.[80] 4.3.2 Bearing wall structures--Slender solid or perforated walls are widely used for apartment and hotel structures, where the individual walls enclose the living units and provide acoustic insulation. The main advantages are speed of construction and low steel reinforcement ratios for the walls. In planning multistory bearing wall structures, significant discontinuities in mass, stiffness and geometry should be avoided. Bearing walls should be located close to the plan perimeter and should preferably be symmetric in plan, to counteract torsional effects due to lateral loading. Satisfactory seismic performance has been observed for bearing wall structures whose individual walls and connecting elements are detailed as described in Reference 70. However, because of concerns about the deformability of the system, at least one code[30] has restricted the use of bearing wall construction in earthquake zones to structures less than 160 ft high. 4.3.3 Moment resisting frames--Sets of moment-resisting frames, usually arranged orthogonally to each other and interconnected by floor diaphragms, comprise the structural system of many apartment and office buildings. Floor space requirements of most commercial buildings limit the number of interior columns, favoring large bays, relatively deep beams, and increased story height. Moment-resisting frame structures are economical up to about 15 stories for office buildings, to about 20 stories for apartment buildings. However, these frames may be less economical in seismic zones, where all frames in such a system must be designed in accordance with the provisions of Appendix A of ACI 318.[56] In particular, beam-column connections require careful detailing to achieve ductile behavior of the beams. The flat plate-column system is very effective for commercial and residential buildings in nonseismic zones having low or moderate winds. Portions of the flat plate and the rigidly connected columns act as frames. Simple formwork and reinforcing patterns as well as low construction height are advantages of this system. In designing and detailing plate-column connections, particular attention must be paid to the transfer of shear and unbalanced moment between these two elements. 4.3.4 Dual systems--These consist of two or more basic structural systems in a structure, chosen to achieve specific response characteristics, particularly with respect to seismic behavior. Some of the more common dual systems are discussed as follows. Wall-frame systems--Rigid-jointed frames and isolated or coupled structural walls can be combined to produce a structural system with the gravity load-carrying efficiency of a rigid frame, and the lateral load-resisting efficiency of a structural wall.[81,82] Wall-frame interaction is due to the different characteristic lateral deflected shapes of these two elements. The degree of interaction is dictated principally by geometry and relative stiffness. Wall overturning moment and lateral drift are both greatly reduced by wall-frame interaction. A frame system supported laterally by stiff structural walls receives approximately uniform horizontal shear throughout its height. This allows repetition in the floor framing, with obvious economies in design and construction. Design of the frame elements for gravity loads is also simplified in such cases, as the frame may be assumed to be braced. Wall-frame structures are economical in the range of 30 to 50 stories. For seismic zones, wall-frame systems are superior to isolated walls or frames because of their structural redundancy, which permits the structure to be designed for a desired sequence of yielding under strong ground motion. Beam elements can be designed to experience significant yielding before inelastic action occurs at the bases of the walls. Because of the feasibility of controlling the hinging sequence, and the relative economy with which beams can be repaired, wall-frame structures are appropriate for use in seismic zones. However, designers should be aware that in wall-frame structures, the variation of shears and overturning moments over the height of the wall and frame, is very different under inelastic response conditions, than under elastic response conditions. The difference between elastic and inelastic response is much greater for wall-frame systems than for systems composed of walls or frames alone. Outrigger systems--Outriggers are walls or trusses, one or two stories in height, which couple a wall or a core to a group of perimeter columns, thus increasing the lateral stiffness of the structure [Fig. 4.3.4(a)].[83] Deep, very stiff spandrel girders, sometimes placed around the structure at the outrigger levels, are called "hat" or "top-hat" bracing if located at the top, and "belt bracing" if located at intermediate levels. One or more pairs of outriggers can be used in a bent. A single pair of outriggers is most effective when placed at an elevation of about two-thirds of the height of the building,[84] and two pairs are most effective when placed near the third points. Further reductions in total drift and core bending moments can be achieved by increasing the size and therefore the axial stiffness of the columns, and by adding outriggers at more levels. Outriggers have proven quite effective in structures subjected primarily to wind loading. Design of outrigger-type systems for highly seismic zones must consider the high stiffness of the outriggers. Members framing into the outriggers should be detailed to have high ductility. Tube-core system--Many office buildings require a large service core, formed by a box-like arrangement of solid or perforated walls. Combining the core with a peripheral framed tube enhances the structural characteristics of the tube by reducing its shear deformation.[83] The tube-core system [Fig. 4.3.4(b)] permits large, column-free office space when a long-span floor system connects the core and the outer tube. This system has been used in buildings up to 60 stories in height. Bundled tubes--In a recent innovation, several framed tubes are bundled into one larger structure which behaves as a multicell perforated box.[85] Individual tubes can be terminated at different heights, thus accommodating reduced space requirements in upper floors if desired. The tubes can be slipformed, and may incorporate anchor plates for the floor framing, which spans an entire tube. The bundled tube system offers considerable flexibility in layout, and possesses large torsional and flexural stiffness. It is used in buildings taller than 80 stories. The systematic regularity of bundled tubes is conducive to rapid construction progress through preassembly of the tube reinforcement. Mixed concrete-steel structures--Mixed concrete-steel systems combine interactive concrete and steel assemblies.[86] The resulting structure displays most or all of the advantages of steel structures (large spans and lightweight construction), as well as the favorable characteristics of concrete structures (high lateral stiffness of shear walls and cores, and high damping). Because the erection of steel and concrete structures involves different building trades and equipment, mixed construction may involve scheduling problems and economic penalties. Concrete construction and steel erection should usually be separated, either by working areas or working levels. Two of the more widely used mixed systems are discussed as follows: 1. Core-braced mixed systems. All lateral and torsional resistance is provided by a reinforced concrete service core, while the surrounding steel structure is designed and detailed to accept gravity loading only. Outside the core area, a composite floor system is often used, consisting of a steel deck on steel beams (with or without shear connectors) and a concrete slab. The stiff diaphragm transfers lateral loads from the exterior of the building to the core, and also provides lateral support to the steel columns. The principal advantages of this system are that simple steel framing can be used without moment connections, that high strength steel can be used effectively for columns, and that longer spans can be accommodated. Slipforming of the core (usually in advance of steel erection) results in additional economy. Connections between floor beams and the concrete core must be carefully selected and detailed. Bearing plates, standard T-sections or steel brackets are anchored to the core, and the beams are simply connected to them. Pockets are sometimes chased into the core walls to provide, via bearing plates, support for the ends of the floor beams. This system is economical up to about 35 floors. 2. Composite tubular systems. An exterior framed tube of reinforced concrete is combined with simple structural steel framing in the interior of the building. The peripheral tube resists all lateral and torsional loading, as well as some gravity loading. The interior steel columns carry only gravity loads. The main advantages of this system are the high stiffness of the peripheral tube, the high degree of architectural flexibility in building layout, the easy adaptability to almost any plan configuration, the simplified facade, and the economical window details. Upon completion of the foundation system, the steel framing is erected. To avoid interdependence of steel and concrete construction progress, light peripheral steel columns allow steel erection to be 8 to 10 stories ahead of concrete work on the peripheral tube. These peripheral steel columns (which will eventually be encased in concrete) must therefore be designed to carry full dead load, plus the expected construction loads of 8 to 10 stories. The steel framing above the completed framed tube must resist all lateral loading during construction. Temporary cable or K-bracing is usually provided for this purpose. The floor system, which acts as a horizontal diaphragm, is securely tied to the exterior tube. Construction is expedited by preassembling the reinforcement for the framed tube in a one-story tier at ground level, hoisting it into place, and tying it securely to the small exterior steel columns. 4.3.5 Precast structures--Precast elements are widely used for frame, wall, and wall-frame systems.[69,77] Mixed construction consisting of precast assemblies and cast-in-place concrete cores is also used. The efficiency of such systems depends on the extent of standardization, the ease of manufacture, the simplicity of assembly, and the speed of erection. Precasting is mostly done in large mechanized factories, where high quality control, superior finish, and small dimensional tolerances can be achieved. Much costly onsite labor is replaced by cheaper plant labor. Precast units vary greatly in size from project to project, often reflecting the capacity and range of the lifting equipment available at the construction site. Self-weight of mass-manufactured units is reduced by using lightweight concrete, or by pretensioning. Floor systems include large standardized reinforced (and usually prestressed) concrete slabs with or without cylindrical voids, as well as prefabricated rib slabs. Rigid-jointed frames are usually assembled from H- or T-units; shear walls and cores, from prefabricated single-story panels. Devising and designing appropriate connection details for panels, frame elements and floor assemblies is the single most important operation related to prefabricated structures. Details may significantly affect a system's economy, and also its response to lateral and gravity loading.[69] Three main types of connections are used: 1. Reinforcing steel protruding from adjacent elements is welded together or lapped, and the joint between the elements is filled with cast-in-place concrete. 2. Steel inserts (plates, angles, etc.) provided in the precast elements are bolted or welded together and the gaps are grouted. 3. The individual precast units are post-tensioned across the joint, with or without a mortar bed. The behavior of a precast system subjected to seismic loading depends to a considerable degree on the characteristics of the connections. Because of the great variety of different joint situations in precast structures, specific recommendations cannot be made. Connection details can be developed which ensure satisfactory performance under seismic loadings, provided that the designer pays particular attention to ductility requirements and positive confinement of concrete in the joint area. Welding procedures must be followed which avoid locally brittle conditions. Precast concrete structures, and large-panel structures in particular, are more prone to progressive collapse than are cast-in-place structures. Special attention should therefore be given to the development of connection details which provide continuity and sufficient ductility to assure general structural integrity.[69] It is often difficult to satisfy ductility criteria for strong earthquakes when plastic hinges must occur at connections made onsite, such as at beam-column joints. To overcome this difficulty, it is preferable to locate connections in precast assemblies in areas of low moment demand, where elastic behavior can be assured during earthquake response. Plastic hinge regions can then be designed and detailed as for monolithic cast-in-place structures. 4.3.6 Core-suspended structures--A core-suspended structure (Fig. 4.3.6) consists of a core, usually slipformed, and large cantilevered girders or trusses projecting from the building at one or more levels.[87] The individual floors are attached to hangers suspended from the outer ends of the cantilevers. The hangers are almost always steel (flat bars, pipes, or stranded steel cables), though prestressed concrete hangers have also been used. Core-suspended structures are advantageous in reducing congestion of pedestrian traffic at street level, in avoiding peripheral footings which would interfere with existing basements or service lines, and also in increasing available rental space. To avoid large vertical floor displacements due to temperature changes, all hangers should be located within the building enclosure. Where two or more cores are used, the hangers may be supported more efficiently by an arch or catenary, rather than by cantilevers. The general configuration of core-suspended structures makes them a poor system for use in zones of high seismic risk. CHAPTER 5--METHODS OF ANALYSIS 5.1--Objectives and scope The objective of this chapter is to review modern methods of analysis for reinforced concrete buildings. General analytical techniques are discussed in textbooks on structural analysis. The modeling practices and analytical approaches discussed in this chapter pertain principally to analysis of reinforced concrete structures subjected to lateral forces, and are applicable to all of the structural systems discussed in Chapter 4. This chapter includes a discussion of analysis for static and dynamic response, considering both linear and nonlinear force-deflection behavior for structural systems. 5.2--Introduction Different aspects of structural engineering require different analytical approaches. To select the most suitable analytical model or procedure, a designer must understand the merits and limitations of each technique. Design of new construction generally requires the numerical estimation of member actions in a statically indeterminate structure. These actions are used to establish required member strengths so that the structure will meet the performance criteria discussed in Chapter 3. The true behavior of the indeterminate concrete structure need not be depicted precisely. For preliminary design purposes, regular framed structures may even be made statically determinate by assuming the locations of points of inflection. To estimate the response of an existing structure to external loads or internal deformations (such as thermal movements, differential shrinkage, or foundation settlement), a more detailed analysis is often required. A nonlinear analysis may be necessary to determine realistic internal forces for a particular sequence of events. The response of structures to time-dependent forces must sometimes be computed including the effects of inertial forces. Examples of these problems might include a vibration analysis of a structure containing delicate equipment, or a vulnerability assessment of an existing building for shock, wind or earthquake loading. While linear analysis might be suitable for the equipment problem, nonlinear analysis might be needed for the vulnerability study if extreme loadings were contemplated. Any analytical model of a building must be reduced to its essential parts. The analysis is then carried out, and the results interpreted. This requires substantial competence, judgment and creativity on the part of the designer. More precise analytical techniques are often more difficult to apply. For a given problem, however, more complex analytical techniques are not necessarily better. In a strength design, for example, low-strength members can be neglected even though they may have significant stiffness or mass. Designs considering those members would not necessarily be better in terms of accuracy, safety, or cost-effectiveness. To evaluate the dynamic response of an existing building, on the other hand, the more complex model would be preferable. Selection of a proper analytical model is also influenced by the structure's importance and the consequences of structural distress. Design of nuclear power plants, for example, often requires a nonlinear seismic response analysis, which would not usually be done for a more conventional structure. Analytical models need not be numerical. Although physical modeling is used primarily as a research tool, it may also be appropriate for design of important or complex structures, or those which will be replicated several times. Physical test data can reveal forms of building response not predicted by numerical models. Lateral force distributions from ground shaking or wind pressure can be estimated by experiments using earthquake simulators or wind tunnels. Measured behavior can provide quantitative information on strength and other mechanical characteristics of a given type of structure. Some analytical procedures do not rely on the use of numerical or physical models. Using ambient or forced vibration tests, response of actual buildings can be analyzed directly. This type of experimental analysis is discussed further in Chapter 6. Because of their convenience for engineering analysis and design, numerical analysis techniques only are discussed in the remainder of this chapter. 5.3--Approximate analysis for preliminary design of frames While few reinforced concrete structures can be considered statically determinate, an approximate approach may be useful for preliminary design, because members can be sized independently of their stiffnesses. Traditional approximations such as the portal and cantilever methods may be appropriate for such analyses. Details of these two methods are frequently discussed in textbooks and need not be repeated here. 5.4--Linear analysis for static lateral forces 5.4.1 System modeling Planar analysis--A building can be analyzed as a whole, or divided into parts, each of which is analyzed separately. Many buildings have regular arrangements of widely spaced columns, have few or no structural walls so that little shear is transferred between adjacent columns, and are symmetrical or nearly symmetrical so that negligible twist occurs about a vertical axis when a symmetrical lateral load is applied. These types of buildings can be effectively modeled as a series of parallel planar frames.[88] The complete structure is usually modeled using two orthogonal sets of crossing frames. Compatibility of vertical deflections at crossing points is not enforced, but the consequences of this are usually not significant. Each planar frame is obtained by cutting the structure midway between the parallel vertical planes containing the columns. The slab included within a frame is modeled using beam elements. Because of its relatively high in-plane stiffness, the floor is usually considered rigid in its own plane. Axial deformations of the beams are not considered. This modeling reduces the number of degrees of freedom from three per joint to two per joint (rotation and vertical displacement) plus one per floor (horizontal displacement). For lateral load analysis, all of the parallel plane frames comprising a building are linked into one plane frame to enforce drift compatibility. In this procedure, the linking may be accomplished by requiring that drift of frames be compatible at floor levels. Two identical frames can be modeled as one frame with doubled stiffness, obtained by doubling the modulus of elasticity. Structural walls, if present, must be linked to the frames at floor levels. Because structural walls are usually much stiffer than the frame, all the lateral load is sometimes assigned to the walls, which are then analyzed and designed separately. Walls without openings can be analyzed simply, but such walls almost never occur in real structures. The typical wall consists of solid sections connected by beams, and can be modeled using either combinations of wall and beam elements,[89] membrane elements,[90] or flexural elements connected by equivalent flexible layers (laminae).[91] Three-dimensional analysis--Some buildings with dual systems and buildings with irregular layouts should not be analyzed as planar systems. Recent research has shown that the response to lateral forces of even a very symmetrical building can include complex, three-dimensional interaction of adjacent lateral force-resisting components.[92] Because of the growing availability of special- and general-purpose structural analysis programs capable of computing response in three dimensions, three-dimensional analysis is now commonplace, and will probably replace planar analysis for most applications. Three-dimensional analyses can be conducted using general-purpose programs such as SAP,[93] STRUDL,[94] or ANSYS.[95] To simplify the problem, floors are usually assumed to be rigid in their own planes, reducing the number of dynamic degrees of freedom to only three per floor (two horizontal translations and one rotation about a vertical axis). Special-purpose programs such as ETABS[89] perform this simplification automatically. 5.4.2 Member modeling Beams--Along a beam, the amount and location of flexural reinforcement varies, as does the amount of flexural and shear cracking. Depending on the sense of the moment, a slab cast monolithically with the beam may act in compression or tension. The effective moment of inertia of prismatic concrete members therefore changes from section to section. It may be necessary to make a compromise in modeling by assuming a uniform effective moment of inertia for a member. Allowance for the preceding effects, particularly cracking, may be made by using a reduced stiffness for the beams. In the elastic range of response, beam-column connection regions are usually stiffer than the elements they connect. This should be considered in analysis. Slabs--Slab-column and slab-wall framing may significantly influence the lateral-load stiffness of many structures. Several analytical models to represent lateral-load stiffness of the slab have been proposed.[96] One commonly used model, referred to as the "effective beam width model," represents the slab by an effective beam framing directly between columns and/or walls. Another model, the "equivalent frame model," represents the slab by a beam connected to columns by fictitious torsional members. Research has demonstrated that the slab stiffness may be reduced by as much as 70 percent by cracking under service gravity and lateral loads.[67,96] The analysis should account for this reduction.[67,96] Columns--Columns are subject to all the phenomena previously discussed for beams, and also must resist varying axial loads. Axial compression reduces flexural cracking, and therefore increases the flexural stiffness of short columns. The flexural stiffness of slender columns decreases with axial compression, because of instability effects. However, if a slender column is properly designed, instability effects should be negligible. Axial forces in coupled walls or exterior columns of a frame vary as the structure deflects laterally. The stiffness of these elements therefore changes at different amplitudes of sway, making the structure both asymmetrical and nonlinear. If some degree of inelastic flexural behavior is accepted, however, these effects may be self-compensating for symmetrically placed columns or walls. Walls--Slender walls (those with aspect ratios of total height to width greater than three) can be modeled as column elements, or using the panel elements available in many special-purpose analysis programs. Where beam elements frame into walls modeled as panel elements, rotational compatibility should be enforced between the beam and the panel. When a wall is modeled as a column element, beams framing into the wall should be provided with a rigid end zone to reflect the nonzero width of the wall. Slip of reinforcement at the bases of columns and walls may affect their stiffnesses. This effect may be modeled by placing rotational springs at those locations. The stiffnesses of those springs can be approximated by assuming a linear variation of strain along a limited length of the anchored bars. Omission of these springs is usually conservative for a strength design, but always unconservative for a deflection analysis. Stiffness changes from bar slip can be as significant as those from cracking of the section.[97] 5.4.3 Linear analysis for design--Design of a lateral force-resisting system does not require an exact analytical model. The distribution of member strengths need not agree exactly with the distribution of forces from an elastic analysis. If the strength of a particular member is exceeded, some inelastic deformation will occur, and member actions will be redistributed. Provided that members are sufficiently ductile to assure redistribution, and that sufficient strength is available to resist the lateral loads, collapse will not occur. For reinforced concrete frames with typical member lengths and column dimensions, it is therefore practical to model member stiffness without considering all the previously mentioned phenomena. Consideration of nonprismatic members or inclusion of axial force effects on stiffness may not be necessary. For this reason, reinforced concrete members are commonly modeled as prismatic, with moments of inertia based on their gross section, divided by a factor typically between 1.0 and 3.0 for beams and columns, and typically between 1.0 and 5.0 for walls. These reduction factors can easily be calculated by beam theory, and represent the effects of different percentages of reinforcement, different amounts of cracking, and different axial compressions. Analyses for lateral drift may require a more precise model. Shearing deformations for structural members should be handled consistently with other modeling assumptions. Shearing deformations do not usually have a significant effect on overall structural response for most typical frame members. However, shearing deformations should be included when modeling beams and columns of tube-type structures, and when modeling walls using column elements. 5.5--Nonlinear analysis for static lateral forces The simplest kind of nonlinear analysis is a first-order collapse analysis, carried out using the principles of simple plastic theory. Such analyses can be used for preliminary design. The rest of this section concerns more comprehensive nonlinear analyses, carried out using computer programs. Such a nonlinear analysis may be necessary to predict the behavior of an existing structure under an accidental, unforeseen, or extreme event. Except in the case of very important structures, it is not typically used for design, because of its relative complexity and cost. Nonlinear behavior arises from material and geometrical causes. Cracking and nonlinear stress-strain behavior of concrete, and yielding and slip of reinforcement, are the material-related sources of nonlinearity. As the structure deflects laterally, the product of the vertical loads and the lateral deflections causes increased moments, which in turn cause more lateral deflections. This P-delta effect, which can also be expressed as a reduction of flexural stiffness in members in which axial compression acts, is the principal source of geometrical nonlinearity. Material nonlinearities can be modeled using finite element codes such as NONSAP,[98] ADINA,[99] and ANSYS.[95] Nonlinear analyses are typically accomplished by performing a linear analysis for each increment of load, testing each element to determine changes in state caused by that load increment, iterating to achieve equilibrium, updating local and global stiffness matrices, and then repeating the process for the next load increment. Nonlinear analyses are expensive, and are seldom performed for typical structures.[100] Material-related nonlinear analysis of reinforced concrete is discussed at length in Reference 101. Geometric nonlinearities are also handled using an iterative approach. Computer codes for nonlinear analyses can often accommodate both material and geometric nonlinearities. Simplified procedures for handling P-delta effects are available in some linear analysis programs.[102] In addition to the modeling considerations discussed previously, analysis of nonlinear static response requires a description of the nonlinear force-deformation behavior of each member, including capacity at yield, force-deformation behavior after yield, and ultimate deformation capacity. This topic is discussed further in Subsection 5.6.3. 5.6--Analysis for dynamic response 5.6.1 Introduction--A dynamic analysis is necessary when the inertial forces on a structure are significant compared to its other applied loads. A structure's response to a dynamically applied load may be many times greater than its response to the same load applied statically. The relation between a structure's static and dynamic responses depends primarily on its damping characteristics and on its periods of vibration (which are a function of its mass and stiffness). A structure's longest, or fundamental period, usually has the most important effect on its response. A building's dynamic response can be approximated using its fundamental period and mode shape only. Although empirical formulas have been recommended and can be used to estimate a building's fundamental period in terms of its overall height and width,[30,39] they should be used with caution. The following discussion is intended to summarize the different analytical methods used for dynamic loadings. 5.6.2 Linear dynamic response Single-degree-of-freedom (SDOF) systems--The equilibrium of inertial forces, damping forces, spring forces, and applied loads can be expressed by a differential equation involving the structure's mass, stiffness, and damping, as well as the applied time-dependent load. Because mass usually remains constant, and damping may be expressed in terms of a fraction of critical equivalent viscous damping, the linearity of the equation is dependent on the resisting force. If this is linearly proportional to displacement (corresponding to a linearly elastic system), the differential equation can be solved exactly for arbitrary time-dependent loads. This procedure is discussed in structural dynamics texts. Few modeling considerations for SDOF systems are unique to reinforced concrete buildings. Reinforced concrete buildings are modeled primarily as systems with more than one mass, or with nonlinear force-displacement behavior. Multi-degree-of-freedom (MDOF) systems--For multi-degree-of-freedom systems, masses, stiffnesses, damping factors, and applied forces are best organized in matrix form. While masses may be modeled as being distributed over the height of a structure using continuous functions, this is often unrealistic for concrete buildings, whose mass is concentrated primarily at floor levels. Most computer programs model MDOF systems using lumped masses. A structure's mass usually includes only its dead load. However, permanently applied live loads (such as in libraries and storage facilities) should also be included. Terms of the damping matrix are difficult to model directly. A fixed amount of damping is commonly assigned to each mode of vibration, and is expressed as a percentage of critical viscous damping. Tests have shown that modern reinforced concrete structures with light damage have modal damping ratios ranging from 2 to 3 percent; with moderate damage, from 3 to 5 percent; and with heavy damage, from 5 to 10 percent.[103] The stiffness matrix is identical to that used for static problems, unless strain rate effects are considered, as might be the case for blast loadings or for very stiff structures subject to earthquake motions. Given a building's stiffness and mass matrices, its periods of vibration and corresponding mode shapes can be calculated using computer programs. Once the system is defined, its history of response to the particular dynamic loading can be calculated by computer programs using established techniques of dynamic analysis--either modal superposition, or numerical integration of the simultaneous equations of motion. In most cases, however, response maxima are of more interest than are response histories. The maximum response of linear SDOF systems to given dynamic loadings can easily be computed using response spectra. It is therefore often expedient to calculate the response of MDOF systems by combining the modal maxima obtained using such response spectra. This approach is approximate because the phasing of modal maxima is not known. If modal responses are statistically independent, their most probable maximum combination is the square root of the sum of squares (SRSS). This is a reasonable assumption for lightly damped systems with well-separated periods of vibration. If periods of vibration are very nearly equal, however, the absolute values of those modal responses should be added directly, or more complex combinations should be used.[102] 5.6.3 Nonlinear dynamic response--In computing the nonlinear dynamic response of reinforced concrete structures, it is necessary to distinguish between loadings such as blast, which produce at most only one or two cycles of inelastic deformation, and earthquake loading, which can produce many cycles of reversed inelastic deformation. Deflections of a reinforced concrete structure are not linearly related to forces, because of cracking and inelastic compressive deformation of concrete, and slip and yield of reinforcement. The load-deformation behavior of reinforced concrete members may be asymmetrical, even under symmetrical cyclic reversals of deflection. This is because of the very different mechanical properties of reinforcement and concrete, which result in accumulated inelastic strains and progressive increases in crack widths. Upon deflection reversal, the member actions depend on the extent of crack closure in the concrete, and on the Bauschinger effect in the reinforcement (elimination of the distinct yield point on the stress-strain curve after the first large inelastic strain). Several mathematical models have been formulated to represent the hysteretic behavior of reinforced concrete members and connections.[43,101] The dynamic response of structures with material and geometric nonlinearities can be calculated using modern computer programs such as NONSAP,[98] ADINA,[99] ANSYS,[95] and DRAIN-2D.[45] Nonlinear dynamic analyses involve the same basic steps as nonlinear static analyses, except that the matrix equations are nonlinear. Because the structure's stiffness matrix can change throughout its response, much more computational effort is required than for linear elastic or nonlinear static analyses. Because of the relative complexity of inelastic response history calculations, several simplified methods have been developed to estimate nonlinear dynamic response maxima. The most widely used procedure, developed by Newmark and Hall, approximates the response of an idealized, elasto-plastic SDOF system using its elastic response to spectra which have been modified based on the structure's available displacement ductility.[41] Another method, known as the "substitute structure" method, models inelastic members using elastic members with reduced stiffnesses, and uses artificially large viscous damping factors to represent inelastic energy dissipation.[43] A third method, known as the "Q-Model," describes the inelastic behavior of the system in terms of its response as a nonlinear SDOF system.[43] Other methods have also been proposed. In one of these, the "capacity spectrum method,"[44,128,129] a building's inelastic response characteristics are used to estimate a modified design response spectrum (referred to as a "capacity spectrum"). Nonlinear dynamic analysis has been used primarily as a research tool, and also in the design of structures such as nuclear power plants. Its use has been proposed for conventional reinforced concrete structures.[46] However, nonlinear dynamic analysis is only occasionally used at this time for typical reinforced concrete structures, and the best techniques for applying it are being studied.[104] Two points should be noted with regard to the use of nonlinear dynamic analysis in practice. First, it is important to remember that the results of this type of analysis, and of most computer-based analytical techniques, may be easily misused. Because certain assumptions and approximations are made by the designer when inputting information for an analysis, and by the computer program itself when actually performing the analysis, all output must be carefully checked to be sure that results produced by the analysis are reasonable and consistent with statics and with solutions based on approximate methods of analysis. Second, nonlinear dynamic analysis programs should be considered primarily as research tools at this time. Member characteristics must be described very specifically in order to produce any solution. The computer cost for solution of the problem for a single acceleration history can be high, and in most cases there is no guarantee that the acceleration history used in the analysis even roughly approximates the acceleration history to which the structure may actually be subjected during its lifetime. Judgment and experience must be used to proportion the structure to be analyzed. At best, the nonlinear dynamic analysis of an already-proportioned structure can point out responses that the designer might not have anticipated, either in type or magnitude. CHAPTER 6--PERFORMANCE OF BUILDINGS 6.1--General The purpose of this chapter is to describe the performance of real buildings subjected to lateral forces from wind, blast or earthquake. The actual performance of a building under strong wind, blast, or earthquake loading can differ greatly from the performance implied by design calculations. Reasons for these differences include the following: 1. The code-specified design forces do not accurately represent the forces from severe winds or earthquakes. 2. The design process may not consider the effects of foundation movement, torsion, structural discontinuity, redundancy, load, redistribution, inelastic response, ductility, and nonstructural elements. 3. The design process may not accurately represent the materials, connections, and details of the building as constructed. While design for gravity dead and live loads presumes that the maximum loads experienced by the structure will not exceed design values, design for extreme winds or earthquakes is often based on the assumption that the design forces prescribed by building codes may be exceeded during actual loadings. This is particularly true of strong earthquake loading, where forces on the structure are a function of the strength and stiffness of the building as well as of the motion of the ground. The response of a code-designed building to extreme lateral forces cannot be accurately predicted without investigating its structural performance under forces in excess of those prescribed by the code. As noted in Section 1.3 of this report, structural performance of real buildings subjected to extreme loads can be documented and studied. Alternatively, the performance of real buildings under various loads can be evaluated, or the performance of laboratory specimens can be assessed. 6.2--Use of experiments to evaluate structural performance Much information about the actual performance of buildings subjected to lateral forces has been obtained by instrumenting buildings to measure lateral motion, ranging from small ambient motions to the large motions resulting from severe earthquakes. To supplement data obtained from actual buildings, tests have been conducted on full-sized test structures as well as on scale models. Test results can be correlated with analytical procedures for evaluating building performance. In the rest of this chapter, various aspects of these tests are discussed: types of tests; sources of motion; test instruments; data reduction; performance evaluation; and the application of test results to design codes and practices. 6.2.1 Types of tests--Full-scale structures can include actual buildings, field test structures, and laboratory test structures.[92,104] Testing can involve either naturally occurring or induced motion. Motion in laboratory test structures can be induced by shaking tables or hydraulic actuators. Laboratory test specimens may consist of entire structures, structural assemblages, or structural components. If tests are conducted on reduced-scale models, dimensional similitude must be considered. Each type of test has provided valuable information about structural response to lateral loads. Many buildings responding to the 1971 San Fernando earthquake were instrumented and subsequently analyzed.[12] Response histories have been obtained for Las Vegas high-rise buildings shaken by underground nuclear explosions conducted at the Nevada Test Site.[105,106] Prior to its scheduled demolition, a portion of a St. Louis apartment building was tested using a vibration generator [Fig. 6.2.1(a)].[107] Forced vibration tests have also been performed on several buildings in the Los Angeles area.[108,109,110] During the past decade, extensive laboratory tests have been conducted in many universities around the world.[92,111] Laboratory testing of a full-sized, seven-story reinforced concrete structure has recently been conducted in Japan as part of the U.S.-Japan Cooperative Research Program [Fig. 6.2.1(b)].[92] Small-scale models of that test structure have also been tested at engineering laboratories in the United States, and the results have been compared with those of component tests [Fig. 6.2.1(c)].[92] 6.2.2 Sources of motion--Dynamic responses of buildings can be investigated experimentally using sources of motion such as the following: 1. Ambient motion from vehicular traffic, mild winds, and movement of people and equipment within the building. 2. Forced vibration by occupant motion. Buildings can be excited into their natural modes of vibration by one or more people swaying in resonance with the building.[112,113] 3. Free vibration from initial applied displacement.[110] 4. Forced vibration testing, using specially designed rotating or reciprocating vibration generators.[107,110,114] 5. Wind forces.[115] 6. Explosive devices, placed above or below ground.[116] 7. Earthquakes. Earthquakes are the most difficult of all excitations to record because they generally give no clear advance warning. To obtain satisfactory earthquake records, motion recording instruments must be in place; triggers must be effective; amplitude sensitivities must be properly set; and all equipment must be properly maintained, so that the recording instruments are operational when an earthquake actually occurs. In spite of these difficulties, much valuable information on ground motion characteristics has been recorded during recent earthquakes.[21,27,111] 6.2.3 Instrumentation Types of instruments--Lateral motion recording instrumentation generally consists of two parts, a transducer and a recorder. The transducer is usually a single-degree-of-freedom oscillator that responds in a known fashion to the motion of the object to which it is attached [Fig. 6.2.3(a)]. The motion may be expressed in terms of acceleration, velocity, or displacement [Fig. 6.2.3(b)]. Accelerations are measured using accelerometers. Velocities are measured using velocity transducers. Displacements are measured using electrical transducers or laser beams. Special instruments that measure wind pressures and velocities may also be used. Electronic equipment is generally used to record, amplify and display the measurements. Location of instruments--Instruments are usually placed to measure horizontal motion, while a lesser number are used to measure vertical motion.[117] Instruments are usually placed at the top of the building, where maximum motion generally occurs. It is also important (especially for earthquake data) to measure motion at the ground level, either at the base of the building or at a free-field location away from the building. Permanently placed instruments in high-rise buildings typically measure one vertical and two horizontal components of motion at three levels: at the top floor, at ground level, and at an intermediate floor. More instruments on each floor are needed for buildings that are irregular in plan or in elevation, or have structural discontinuities.[118] A group of temporarily installed instruments can simultaneously record and time-correlate data, or a single temporarily installed instrument can be moved from location to location to record a building's response to ambient vibrations. 6.2.4 Data reduction and analysis of records Types of recordings--Response histories are generally recorded on paper, analog tape, or digitized tape. Paper printouts of taped recordings are useful for visual inspection. If digital computers are to be used to analyze the records, the recordings must be digitized. Raw data generally must be calibrated, and instrumentation corrections applied. Records may be received individually, or as a group of simultaneous recordings correlated to each other in time. Resulting information--The type of information obtainable from instrumentation of buildings depends on the types of instruments being used, their locations, and the type of motion being recorded. Results from low level motion generally differ from those obtained for moderate or high level motion. For example, recorded natural periods of vibration for reinforced concrete structures under ambient motion are generally much shorter than the periods measured during an earthquake or a strong wind. For very small lateral motions, reinforced concrete elements may be essentially uncracked, and nonstructural elements may stiffen the building. For larger motions, some concrete elements will perform as cracked sections, and coefficients of friction between structural and nonstructural elements will be reduced. Modeling assumptions used in analysis and design can be verified or modified based on observations of periods, mode shapes, nonlinear behavior, damping, and amplitude relationships. The mathematical model of the building can be excited by the recorded ground motion, and the response history of stories within the building can be calculated. Comparisons between calculated and measured motion can increase insight into actual building response. Mathematical models of the building can be modified until satisfactory correlation is obtained between calculated and measured results.[12,116,119,120] 6.3--Evaluation of results Response data from full-sized structures can be used to obtain information about many characteristics of reinforced concrete structures: their load-deformation characteristics; their damping characteristics; their cumulative damage resistance; and their ability to withstand severe lateral motion. 6.3.1 Load-deformation characteristics--Reinforced concrete elements can be idealized as linear and elastic only under low load levels. Even under service-level loads, section properties of concrete elements depend on the extent of cracking. Building response also depends on the effective structural stiffness of concrete floor slabs cast integrally with beams and girders, of L- and T-shaped wall sections, and the effective width of flat plates.[121] Nonstructural elements such as partitions, infill walls and exterior cladding can also affect the load-deformation characteristics of reinforced concrete buildings.[72,74,92,122] These factors directly affect lateral displacements from wind and earthquake forces, and can significantly affect a building's periods of vibration, which in turn determine the earthquake forces to which it will be subjected[123] Results from full-scale structures have shown that periods of vibration generally increase with increasing amplitudes of motion.[124,125] At larger displacements, the stiffening effects of nonstructural elements are reduced--their capacities are exceeded, and their stiffnesses are reduced by cracking. Data obtained from studies of ambient motion cannot necessarily be applied to larger amplitudes of motion. 6.3.2 Damping of concrete structures--Damping values can be obtained directly from test results, using the decay of free vibration amplitude. Alternatively, indirect methods can be used which require data both on the forcing function and on the corresponding response of the structure (for example, earthquake ground motion and the response at the roof of the structure). Test results indicate that damping varies with amplitude of motion, partly because of participation of nonstructural elements and cracking of concrete sections. When damping is obtained from indirect methods using data from nonlinear structural behavior, nonlinear effects will reduce amplification of vibrations, resulting in higher apparent damping. When these apparent damping values are used in elastic analyses, they tend to account in an approximate way for inelastic response.[103,114,124,126,127] 6.3.3 Effects of prior loading history--The structural response characteristics of reinforced concrete buildings can change with age. As concrete ages, it usually becomes stronger and stiffer. However, the effects of shrinkage, temperature changes, and differential settlement can cause cracks that reduce the effective lateral stiffness of a structure as it ages. Severe loading conditions can permanently change a structure's properties, as reflected in the periods of vibration. 6.4--Ability of reinforced concrete structures to withstand severe lateral loads As noted in Subsection 2.4.3, inelastic deformations can lead to reduced forces in buildings subjected to earthquake loading. The use of design forces which have been reduced based on such considerations is reasonable if the building and its elements are designed and detailed to develop the required inelastic deformations. In addition to the preceding considerations, reinforced concrete buildings subjected to all types of lateral loads (wind, blast, and earthquake) have been shown to resist forces well in excess of those for which they were designed.[128,129] Some of the sources for this apparent reserve strength are: 1. Gravity loads rather than lateral loads can control the strength of members. 2. The effective tensile flange width of beams is larger than that customarily assumed in design. 3. Material strengths of both steel and concrete exceed those assumed in design. 4. Secondary structural elements, often neglected, do in fact contribute to lateral load resistance. 5. For practical reasons, more reinforcement is provided in beams, columns and walls than that indicated in design. 6. After the formation of plastic hinges, lateral resistance is increased by strain hardening of the steel. 7. Under dynamic actions, capacity may be increased due to high strain rates. CHAPTER 7--SUMMARY AND CONCLUDING REMARKS 7.1--Summary 7.1.1 General--Reinforced concrete buildings have generally behaved very well under strong lateral loads. Evaluation of the reasons for this good performance, and for occasional examples of poor performance, requires an understanding of the various factors influencing the response of reinforced concrete buildings to lateral loads. The following such factors have been identified and discussed in this report: 1. Characteristics of lateral loads, and the relationship between actual lateral loads and the simplified loads used by building codes. 2. Criteria for evaluating the performance of reinforced concrete buildings subjected to lateral loads. 3. Different reinforced concrete structural systems available for resisting lateral loads, and the lateral load response characteristics of each system. 4. The role of analysis in predicting building response. 5. Procedures for measuring the performance of reinforced concrete buildings subjected to lateral loads, and for using these measurements to improve design and analysis approaches. 7.1.2 Uncertainty of lateral loads--It is essential to understand that a high level of uncertainty exists regarding the effects of actual lateral loads on a structure during its useful life. While dead and live loads due to gravity can be defined with a high level of certainty, very few structures are subjected to the extreme wind, blast, or earthquake loads for which they are designed. Nevertheless, the extreme loss associated with structural collapse or major damage requires that structures be designed to minimize the chance of catastrophic collapse under such lateral loads. The basic uncertainty associated with structural response to lateral loads exists regardless of codes and specifications. Structures designed in accordance with existing codes can perform inadequately under extreme lateral loads. Sophisticated mathematical analysis and design do not preclude inadequate performance, but only make it less likely. Thus, analysis and design for lateral loads always require tradeoffs between predictable increases in costs, and less predictable improvements in performance. 7.1.3 Use of this report in the design process--Design examples or specific calculations have not been included in this report. To have done so would have risked misrepresenting the complexity of the design process. Nevertheless, all aspects of that process have been discussed: characterization of loads; performance criteria for safety and serviceability; different structural systems; analysis techniques for predicting response; and procedures for evaluating performance. Designers must determine the relative importance of each aspect, and the order in which each should be addressed. 7.1.4 Variety of reinforced concrete structural systems--Designers of reinforced concrete structures have access to a wide variety of structural systems for resisting lateral loads. In this report, those systems have been discussed, but only after a review of performance criteria. That order of presentation was chosen to emphasize the fact that new structural systems can and will be developed in response to those performance criteria. One of reinforced concrete's chief advantages as a structural material is its flexibility of application. Designers can take advantage of that flexibility if they understand the performance criteria that their designs should meet. 7.2--Concluding remarks In this report, various aspects of the performance of reinforced concrete buildings subjected to lateral loads have been reviewed. Despite uncertainties in every phase of the design process, reinforced concrete buildings have generally behaved well. Specific performance criteria associated with this good performance have been discussed in detail in Chapter 3. Other more general factors, while referred to throughout this report, are repeated here for emphasis. Successful performance of reinforced concrete buildings subjected to lateral loads can be enhanced by the designer's ability to anticipate lateral loads and associated deformations, and to provide ways of resisting them. In general, the ability of reinforced concrete buildings to resist lateral loads which are unanticipated in nature or magnitude depends on several factors, such as the following: 1. Use of a plan layout of structural elements, nonstructural elements, and vertical ducts which minimizes torsional response. 2. Use of multiple structural systems for lateral load resistance. 3. Use of structural systems which transfer internal forces to the foundation smoothly and directly, without sudden changes in stiffness and/or strength of structural elements. 4. Use of structural systems which limit lateral drift. 5. Use of structural systems and elements capable of undergoing some degree of overall and local inelastic deformation without significant loss of load-carrying capacity. This ability, often loosely described as "ductility," is an essential aspect of most reinforced concrete buildings which have performed well under severe lateral loads. 6. Use of connections which are detailed for sufficient strength to resist all loads transmitted by structural elements, and (if inelastic connection behavior is permitted) which are ductile enough to undergo large inelastic deformations without significant loss of strength. This report is intended to serve as a primer on issues related to the response of reinforced concrete buildings subjected to lateral loads. 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Fig. 2.4.3--Applied Technology Council, "Tentative Provisions for the Development of Seismic Regulations for Buildings," Special Publication No. 510 (ATC 3-06) National Bureau of Standards, Washington, D.C., June 1978, 514 pp. Fig. 2.4.4--Lysmer, J.; Udaka, T.; Tsai, C-F.; and Seed, H. B., "FLUSH--A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems," Report No. EERC 75-30, Earthquake Engineering Research Center, University of California, Berkeley, Nov. 1975. Fig. 3.3.3--Earthquake Effects on Reinforced Concrete Structures--U.S.-Japan Research, SP-84, American Concrete Institute, Detroit, 1984, 440 pp. Fig. 3.5.3--Council on Tall Buildings and Urban Habitat, Monograph on Planning and Design of Tall Buildings, American Society of Civil Engineers, New York, 1978, V. CB, p. 402. Fig. 4.2.1(c)--Courtesy of Portland Cement Association. Fig. 4.2.1(d)--Courtesy of Portland Cement Association. Fig. 4.2.3(b)--Figure adapted from: Paulay, T., and Taylor, R. 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O., "Behavior of Multi-Outrigger Braced Tall Building Structures," Reinforced Concrete Structures Subjected to Wind and Earthquake Forces, SP-63, American Concrete Institute, Detroit, 1980, pp. 515-541. Fig. 4.3.4(b)--ACI Committee 442, "Response of Buildings to Lateral Forces," (ACI 442R-71), American Concrete Institute, Detroit, 1971, 26 pp. Fig. 4.3.6--Courtesy of Bogue Babizki & Associates, Structural Engineers, and Rhone & Iredale, Architects (Vancouver, British Columbia, Canada). Fig. 6.2.1(a)--Mayes, Ronald L., and Galambos, Theodore V., "Large-Scale Dynamic Shaking of Eleven-Story Reinforced Concrete Buildings," Proceedings, Workshop on Earthquake-Resistant Reinforced Concrete Building Construction, University of California, Berkeley, June 1979, pp. 1555-1587. Figs. 6.2.1(b) and 6.2.1(c)--Earthquake Effects on Reinforced Concrete Structures--U.S.-Japan Research, SP-84, American Concrete Institute, Detroit, 1984, 440 pp. Figs. 6.2.3(a) and 6.2.3(b)--Reprinted with permission from: Hudson, Donald E., "Ground Motion Measurements," Earthquake Engineering, Prentice-Hall, Englewood Cliffs, 1970, p. 113. ACKNOWLEDGMENTS ACI-ASCE Committee 442 expresses its gratitude and appreciation to the following contributors to this report. The list comprises former and current Committee Members or Associate Members. All gave selflessly of their time, talents and energy: Daniel P. Abrams; Bijan Ahmadi; C. Michael Allen; Jack R. Benjamin; Vitelmo V. Bertero; Finley A. Charney; Arthur N. L. Chiu; Gary Chock; Cinda L. Cibulskas; Arnaldo T. Derecho; Ahmad J. Durrani; Mohammad R. Ehsani; Ugur Ersoy; Mark Fintel; Sigmund A. Freeman; Catherine W. French; Luis E. Garcia; Hans Gesund; Satyendra K. Ghosh; Jacob S. Grossman; Mohammad Iqbal; Milind R. Joglekar; Richard E. Klingner; Ignacio Martin; Mohammad Mehdizadeh; Kishore Mehta; Christian Meyer; Jack P. Moehle; Adrian Moreano; Kenneth Napior; N. Norby Nielsen; James S. Notch; Shunsuke Otani; Robert Park; Richard A. Parmelee; Thomas Paulay; Victor M. Pavon; Murat Saatcioglu; William E. Saul; Joseph Schwaighofer; Charles F. Scribner; Larry G. Selna; Shamim A. Sheikh; George B. Sigal; Foch Simao, Jr.; Parviz Soroushian; Richard A. Spencer; Bryan Stafford-Smith; William C. Stone; Wimal Suaris; Patrick J. Sullivan; M. Daniel Vanderbilt;* S. M. Uzumeri. (* Deceased.)