00 04 2009 taranath reinforced concrete design of tall buildings

Reinforced Concrete Design of Tall Buildings Reinforced Concrete Design of Tall Buildings Bungale S Taranath, Ph.D., P.E., S.E Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number: 978-1-4398-0480-3 (Hardback) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Taranath, Bungale S Reinforced concrete design of tall buildings / by Bungale S Taranath p cm Includes bibliographical references and index ISBN 978-1-4398-0480-3 (alk paper) Reinforced concrete construction Tall buildings Design and construction Tall buildings Design and construction Case studies I Title TH1501.T37 2010 691’.3 dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com 2009024350 This book is dedicated to my wife SAROJA Without whose patience and devotion, this book would not be Contents List of Figures xxi List of Tables xlvii Foreword li ICC Foreword lv Preface lvii Acknowledgments lxi A Special Acknowledgment lxiii Author .lxv Chapter Design Concept 1.1 1.2 1.3 1.4 Characteristics of Reinforced Concrete 1.1.1 Confined Concrete 1.1.2 Ductility 1.1.3 Hysteresis .5 1.1.4 Redundancy 1.1.5 Detailing .6 Behavior of Reinforced Concrete Elements 1.2.1 Tension 1.2.2 Compression 1.2.3 Bending 1.2.3.1 Thumb Rules for Beam Design 1.2.4 Shear 14 1.2.5 Sliding Shear (Shear Friction) 18 1.2.6 Punching Shear 21 1.2.7 Torsion 22 1.2.7.1 Elemental Torsion 22 1.2.7.2 Overall Building Torsion 25 External Loads 26 1.3.1 Earthquakes Loads .26 1.3.2 Wind Loads 27 1.3.2.1 Extreme Wind Conditions 29 1.3.3 Explosion Effects 31 1.3.4 Floods 32 1.3.5 Vehicle Impact Loads 32 Lateral Load-Resisting Systems 32 1.4.1 Shear Walls 33 1.4.2 Coupled Shear Walls 36 1.4.3 Moment-Resistant Frames 37 1.4.4 Dual Systems 38 1.4.5 Diaphragm 38 1.4.6 Strength and Serviceability 39 1.4.7 Self-Straining Forces 40 1.4.8 Abnormal Loads 40 vii viii Contents 1.5 1.6 Chapter Collapse Patterns .40 1.5.1 Earthquake Collapse Patterns 41 1.5.1.1 Unintended Addition of Stiffness 41 1.5.1.2 Inadequate Beam–Column Joint Strength 42 1.5.1.3 Tension/Compression Failures 42 1.5.1.4 Wall-to-Roof Interconnection Failure 43 1.5.1.5 Local Column Failure 43 1.5.1.6 Heavy Floor Collapse 44 1.5.1.7 Torsion Effects 44 1.5.1.8 Soft First-Story Collapse 45 1.5.1.9 Midstory Collapse 45 1.5.1.10 Pounding 45 1.5.1.11 P-Δ Effect 45 1.5.2 Collapse due to Wind Storms 47 1.5.3 Explosion Effects 47 1.5.4 Progressive Collapse 47 1.5.4.1 Design Alternatives for Reducing Progressive Collapse 49 1.5.4.2 Guidelines for Achieving Structural Integrity 49 1.5.5 Blast Protection of Buildings: The New SEI Standard 50 Buckling of a Tall Building under Its Own Weight 50 1.6.1 Circular Building 51 1.6.1.1 Building Characteristics 52 1.6.2 Rectangular Building 53 1.6.2.1 Building Characteristics 53 1.6.3 Comments on Stability Analysis 53 Gravity Systems 55 2.1 2.2 2.3 Formwork Considerations 55 2.1.1 Design Repetition 58 2.1.2 Dimensional Standards 58 2.1.3 Dimensional Consistency 59 2.1.4 Horizontal Design Techniques 60 2.1.5 Vertical Design Strategy 63 Floor Systems 65 2.2.1 Flat Plates 65 2.2.2 Flat Slabs 65 2.2.2.1 Column Capitals and Drop Panels 66 2.2.2.2 Comments on Two-Way Slab Systems 67 2.2.3 Waffle Systems 67 2.2.4 One-Way Concrete Ribbed Slabs 67 2.2.5 Skip Joist System 67 2.2.6 Band Beam System 68 2.2.7 Haunch Girder and Joist System 70 2.2.8 Beam and Slab System 73 Design Methods 73 2.3.1 One-Way and Two-Way Slab Subassemblies 73 2.3.2 Direct Design Method for Two-Way Systems 74 2.3.3 Equivalent Frame Method 75 Contents ix 2.3.4 2.4 2.5 2.6 2.7 2.8 Yield-Line Method 77 2.3.4.1 Design Example: One-Way Simply Supported Slab 78 2.3.4.2 Yield-Line Analysis of a Simply Supported Square Slab 81 2.3.4.3 Skewed Yield Lines 82 2.3.4.4 Limitations of Yield-Line Method 83 2.3.5 Deep Beams 83 2.3.6 Strut-and-Tie Method 85 One-Way Slab, T-Beams, and Two-Way Slabs: Hand Calculations 92 2.4.1 One-Way Slab; Analysis by ACI 318-05 Provisions 92 2.4.2 T-Beam Design 97 2.4.2.1 Design for Flexure 97 2.4.2.2 Design for Shear 100 2.4.3 Two-Way Slabs 103 2.4.3.1 Two-Way Slab Design Example 106 Prestressed Concrete Systems 108 2.5.1 Prestressing Methods 111 2.5.2 Materials 111 2.5.2.1 Posttensioning Steel 111 2.5.2.2 Concrete 112 2.5.3 PT Design 113 2.5.3.1 Gravity Systems 113 2.5.3.2 Design Thumb Rules 115 2.5.3.3 Building Examples 118 2.5.4 Cracking Problems in Posttensioned Floors 120 2.5.5 Cutting of Prestressed Tendons 121 2.5.6 Concept of Secondary Moments 123 2.5.6.1 Secondary Moment Design Examples 124 2.5.7 Strength Design for Flexure 133 2.5.7.1 Strength Design Examples 134 2.5.8 Economics of Posttensioning 142 2.5.9 Posttensioned Floor Systems in High-Rise Buildings 143 2.5.9.1 Transfer Girder Example 144 2.5.10 Preliminary Design of PT Floor Systems; Hand Calculations 146 2.5.10.1 Preview 146 2.5.10.2 Simple Span Beam 149 2.5.10.3 Continuous Spans 152 2.5.11 Typical Posttensioning Details 172 Foundations 172 2.6.1 Pile Foundations 178 2.6.2 Mat Foundations 179 2.6.2.1 General Considerations 179 2.6.2.2 Analysis 182 2.6.2.3 Mat for a 25-Story Building 183 2.6.2.4 Mat for an 85-Story Building 185 Guidelines for Thinking on Your Feet 187 Unit Quantities 187 2.8.1 Unit Quantity of Reinforcement in Columns 188 2.8.2 Unit Quantity of Reinforcement and Concrete in Floor Framing Systems 197 332 Reinforced Concrete Design of Tall Buildings In wind-tunnel tests, accelerations are measured directly by accelerometers Two accelerometers are typically used to measure components in the x and y directions, while a third records the torsional component Peak acceleration is evaluated from the expression: a= a x2 + a2y + az2 where a is the peak acceleration ax and ay are the accelerations due to the sway components in the x and y directions az is the acceleration due to torsional component The peak accelerations measured for a series of wind directions and speeds are combined with the meteorological data to predict frequency of occurrence of human discomfort, for various levels of accelerations A commonly accepted criterion is that for human comfort, the maximum acceleration in upper floors should not exceed 2.0% of gravitational acceleration for a 10 year return-period storm Shown in Figure 4.51 is a comparison of predicted peak accelerations from wind-tunnel tests and full-scale measurements for a 70 plus-story steel building The measurements were taken on August 18, 1983 during Hurricane Alicia 4.6.3 LOAD COMBINATION FACTORS The determination of the wind loads by BLWT treats the load direction independently It should be recognized that wind loads in all three principal directions of a building will occur simultaneously although the peak loads in each respective direction will not all occur at the same time Therefore, load combination factors are used to specify the required simultaneous application of loads in the three principal directions such that the major load effects are reproduced for design purposes These can be in the form of (1) general load reduction factors applied to all three load directions or (2) a combination of load factors where the full application of the load in the main load direction is accompanied by reduced loads in the other load directions This information is generally provided to the design engineer by the wind tunnel consultant 4.6.4 PEDESTRIAN WIND STUDIES A sheet of air moving over the earth’s surface is reluctant to rise when it meets an obstacle such as a tall building If the topography permits, it prefers to flow around the building rather than over it Some examples are shown in Figure 4.1 There are good physical reasons for this tendency, the predominant one being that wind, if it has to pass an obstacle, will find the path of least resistance, that is, a path that requires minimum expenditure of energy As a rule, it requires less energy for wind to flow around an obstacle at the same level than for it to rise Also, if wind has to go up or down, additional energy is required to compress the column of air above or below it Generally, wind will try to seek a gap at the same level However, during high winds when the air stream is blocked by the broadside of a tall, flat building, its tendency is to drift in a vertical direction rather than to go around the building at the same level; the circuitous path around the building would require expenditure of more energy Thus, wind is driven in two directions Some of it will be deflected upward, but most of it will spiral to the ground, creating a so-called standing vortex or mini tornado at sidewalk level Buildings and their smooth walls are not the only victims of wind buffeting Pedestrians who walk past tall, smooth-skinned skyscrapers may be subjected to what is called the Mary Poppins effect, referring to the tendency of the wind to lift the pedestrian literally off his or her feet Another effect, known humorously as the Marilyn Monroe effect, refers to the billowing action of women’s skirts in the turbulence of wind around and in the vicinity of a building The point is that during Wind Loads 333 windy days, even a simple activity such as crossing a plaza or taking an afternoon stroll becomes an extremely unpleasant experience to pedestrians, especially during winter months in cold climates Walking may become irregular, and the only way to keep walking in the direction of the wind is to bend the upper body windward (see Figure 4.54a through d) Although one can get some idea of wind flow patterns from the preceding examples, analytically it is impossible to estimate pedestrian-level wind conditions in the outdoor areas of building complexes This is because there are innumerable variations in building location, orientation, shape, and topography, making it impossible to formulate an analytical solution Based on actual field experience and results of wind-tunnel studies, it is, however, possible to qualitatively recognize situations that adversely affect pedestrian comfort within a building complex Model studies can provide reliable estimates of pedestrian-level wind conditions based on considerations of both safety and comfort From pedestrian-level wind speed measurements taken at specific locations of the model, acceptance criteria can be established in terms of how often wind speed occurrence is permitted to occur for various levels of activity The criterion is given for both summer and winter seasons, with the acceptance criteria being more severe during the winter months For example, the occurrence once a week of a mean speed of 15 mph (6.7 m/s) may be considered acceptable for walking during the summer, whereas only 10 mph (4.47 m/s) would be considered acceptable during winter months (a) (b) (c) (d) FIGURE 4.54 Pedestrian reactions (a–d) 334 Reinforced Concrete Design of Tall Buildings The pedestrian-level wind speed test is usually performed using the same model that was used for the cladding loads test, and may include some landscaping details The model is instrumented with omnidirectional wind speed sensors at various locations around the development where measurements of the mean and fluctuating wind speed are made for a full range of wind angles, usually at 10° intervals The scaling involved is the same as that of the modeled wind flow Thus, the ratio of wind speed near the ground to a reference wind speed near the top of the building is assumed to be the same in model and full scale, and to be invariant with both test speed and prototype speed Since the thermal effects in the full-scale wind are neglected, strictly speaking, the results are only applicable to neutrally stable flows which are usually associated with stronger wind speeds However, near tall buildings, local acceleration effects due to the local geometry are usually dominant over thermal effects, and are also the most important for design considerations The measured aerodynamic data is combined with the statistics of the full-scale wind climate at the site, to provide predictions of wind speeds at the site Two types of predictions are typically provided: Wind speeds exceeded for various percentages of the time on an annual basis Wind speeds exceeded 5% of the time can be compared to comfort criteria for various levels of activity Very roughly, this is equivalent to a storm of several hours duration occurring about once a week Predictions of wind speeds exceed during events or storms with different frequencies of occurrence Wind speeds exceeded once per year can be compared to criteria for pedestrian safety Other, nonquantitative techniques are also available to determine levels of windiness over a project site One of these techniques is a scour technique in which a granular material is spread uniformly over the area of interest The wind speed is then slowly increased in increments The areas where the granular material is scoured away first are the windiest areas; areas that are scoured later as the wind speed increases represent progressively less windy areas Photographs of the scour patterns at increasing wind speeds can be superimposed using image processing technology to develop contour diagrams of windiness This information can be used to determine locations for quantitative measurements, or simply to identify problem area where remedial measures are necessary Testing several configurations can provide comparative information for use in evaluating the effects of various architectural or landscaping details The advantage of the scour technique is that it can provide continuous information on windiness over a broad area, as opposed to the quantitative techniques which provide wind speeds as discrete points An even more qualitative technique is to introduce smoke to visualize flow paths and accelerations at arbitrary places This can be a useful exploratory technique to understand the flow mechanisms and how best to alter them Pedestrian comfort depends largely on the magnitude of the ground-level wind speed regardless of the local wind direction As a result, quantitative evaluation of the pedestrian-level wind environment at the wind-tunnel laboratory is normally restricted to measurements of the magnitude of ground-level wind speeds unless information on local wind direction is of special interest Measurements are made of coefficients of wind speed (pedestrian-level wind speed as a fraction of an upper level reference speed) for a full range of wind directions at various locations near the site, and in some cases, at a location well away from the building to provide a form of calibration with existing experience These wind speed coefficients are subsequently combined with the design probability distribution of gradient wind speed and direction for the area to provide predictions of the full-scale pedestrian-level wind environment Wind Loads 4.6.5 335 MOTION PERCEPTION: HUMAN RESPONSE TO BUILDING MOTIONS Every building must satisfy a strength criterion typically requiring each member be sized to carry its design load without buckling, yielding, or fracture It should also satisfy the intended function (serviceability) without excessive deflection and vibration While strength requirements are traditionally specified, serviceability limit states are generally not included in building codes The reasons for not codifying the serviceability requirements are several: Failure to meet serviceability limits is generally not catastrophic; it is a matter of judgment as to the requirements’ application, and entails the perceptions and expectations of the user or owner because the benefits themselves are often subjective and difficult to quantify However, the fact that serviceability limits are not codified should not diminish their importance A building that is designed for code loads may nonetheless be too flexible for its occupants, due to lack of deflection criteria Excessive building drifts can cause safety-related frame stability problems because of large PΔ effects It can also cause portions of building cladding to fall, potentially injuring pedestrians below Perception of building motion under the action of wind is a serviceability issue In locations where buildings are close together, the relative motion of an adjacent building may make occupants of the other buildings more sensitive to an otherwise imperceptible motion Human response to building motions is a complex phenomenon encompassing many physiological and psychological factors Some people are more sensitive than others to building motions Although building motion can be described by various physical quantities, including maximum values of velocity, acceleration, and rate of change of acceleration—sometimes called jerk—it is generally agreed that acceleration, especially when associated with torsional rotations, is the best standard for evaluation of motion perception in tall buildings A commonly used criterion is to limit the acceleration of a building’s upper floors to no more than 2.0% of gravity (20 milli-g) for a 10 year return period The building motions associated with this acceleration are believed to not seriously affect the comfort and equanimity of the building’s occupants There are few comparisons of full scale measurements of peak accelerations with tunnel results However, based on available measurements, it appears that the full scale measured peak accelerations are in good agreement with those predicted from wind tunnel test data (see Figure 4.55) The Council on Tall Buildings and Urban Habitat (CTBUH) recommends 10 year peak resultant accelerations of 10–15 milli-g for residential buildings, 15–20 milli-g for hotels and 20–25 milli-g for office buildings Generally, more stringent requirements are suggested for residential buildings, which would have continuous occupancy in comparison to office buildings usually occupied only part of the time and whose occupants have the option of leaving the building before a windstorm occurs However, on some of the extremely slender towers this proves difficult to achieve structurally even after doing all that it is practically possible in terms of adding stiffness and mass It seems the only remaining measure that can be taken is to install a supplementary damping system 4.6.6 STRUCTURAL PROPERTIES REQUIRED FOR WIND-TUNNEL DATA ANALYSIS For a rigorous interpretation of wind-tunnel test results, certain dynamic properties of a structure are required These are furnished by the structural engineer and consist of Natural frequencies of the first six modes of vibration Mode shapes for the first six modes of vibration Mass distribution, mass moments of inertia, and centroid location for each floor Damping ratio Miscellaneous information such as origin and orientation of the global coordinate system, floor heights, and reference elevation for “base” overturning moments 336 Reinforced Concrete Design of Tall Buildings 70 nt lta u es 60 R Acceleration (mg) 50 Building plan Full-scale measurements 40 From wind tunnel data 30 20 Likely range 10 FIGURE 4.55 0300 2200 0600 0100 1000 0500 Time August 18, 1983 1400 0900 1800 1300 GMT CDT Measured peak accelerations for the Allied Bank Tower during hurricane Alicia 4.6.6.1 Natural Frequencies The natural frequencies (or periods) are the fundamental result of a dynamic analysis of the structure Usually this is performed by a 3D computer program, which has the capability of performing an “eigenvalue” or model analysis Generally, only the first three modes are used as these will correspond to the fundamental modes in each of the sway (x, y) and torsional (z) directions It should be noted that if the structure or mass distribution is unsymmetrical, then at least two of these components will be coupled together in some modes Normally, the higher modes (four through six) are required only to insure that all of the fundamental directions have been included 4.6.6.2 Mode Shapes Each mode of vibration is described by both a natural frequency and a shape The mode shapes consist of tabulated values of the x, y, and z deformations of each degree of freedom in the structure For wind-engineering purposes, the floor diaphragm is typically considered rigid, and a single set of x, y, and z deformations is established for each floor Mode shapes have no units They are of indeterminate magnitude and can be scaled to any desired size However, it should be remembered that when multidimensional mode shapes include both translational and rotational (twist) components, the same scaling factor must be applied to all components The significance of this is illustrated in Figure 4.56 The two shapes shown, derived from the same numerical data but with different units, are obviously different: the left depiction can be described as dominated by translation whereas the right is apparently dominated by twist Another aspect of mode shapes concerns the reference system used in conveying the mode shapes Most commercial programs specify the components with respect to the center of mass of each floor If the shape consists of coupled twist and displacement, then the displacement magnitude is dependent on the location of the reference origin If the centers of mass not align on a straight Wind Loads 337 + (a) FIGURE 4.56 by twist ++ + (b) Mode shapes using different units (a) Mode dominated by translation, (b) mode dominated vertical axis—as in setbacks or shear wall drop-offs—then the displacements will contain offsets or “kinks.” It is essential, therefore, that the wind engineer knows the reference system used in the modal data received from the structure engineer 4.6.6.3 Mass Distribution The mass and the mass moment of inertia, MMI, are required at each floor, which typically include the structure’s dead weight and some allowance of live load The MMI is taken about a vertical axis through the centroid (center of mass) of each floor The location of the centroid is also needed All of the mass in the structure should be included since it will affect the natural frequency, which in turn, will influence the loads determined from the wind-tunnel tests As a crude rule of thumb, an x percent change in the natural frequency may cause the loads to change by 0.5x to 2x percent The mass distribution is needed for two reasons First, the mass and mode shape are used together with the natural frequency to determine the generalized stiffness of each mode The stiffness is combined with the generalized load (measured on the wind-tunnel model) to determine the fluctuating displacement response in each mode This is needed to evaluate the acceleration at the top of the building and to determine inertial wind loads Second, the static-equivalent loads from the wind-tunnel analysis consist of mean, background, and resonant contributions The resonant contributions (which in many cases are the single largest contributor) are applied to the structure as concentrated forces at each concentrated mass, and are in proportion to the mass (and also to the modal displacement of that mass) Thus, the accuracy of the wind-tunnel load distribution (i.e., the floor-by-floor forces) is dependent on the relative mass throughout the structure 4.6.6.4 Damping Ratio Currently there is no simple method to compute the damping ratio Therefore, assumptions are made based on analysis of available field data The customary practice in many parts of the world is to use a value of 0.01 for a steel frame structure, and 0.02 for a concrete structure for the prediction of 50–100 year loads For special structures, for example, a mixed or composite frame, or those with extreme aspect ratios, other values may be appropriate It should be noted that wind design is based on different principles from earthquake design, for which very high values of damping, usually 0.05, are considered This value comes from those schooled in seismic design, based on ultimate conditions that not apply to wind design Therefore, wind engineers strongly encourage structural engineers to consider a lower value As stated above, a service-level damping ratio of 0.01 or 0.02 is still the most used to determine the service load effects An extreme damping level (say, 0.03 to 0.05) in combination with wind speeds that have recurrence interval of approximately 500–1000 years could also be used For the prediction of low return-period accelerations such as a 10 year return period, it may be appropriate to use a lower damping value 338 Reinforced Concrete Design of Tall Buildings 4.6.6.5 Miscellaneous Information • Global coordinate system The engineer typically creates and uses this system when inputting nodal point locations in the horizontal (usually x, y) plane Computer output will report the center of masses using this same system A supplemental sketch is required to define both the origin and coordinate directions relative to the structure • Floor heights Provide a tabulation of the relative floor heights and some reference to an absolute height (datum) • Reference “base” elevation In addition to concentrated floor forces and torques to be applied at each floor level, a summary of information will be provided by the wind engineer as “base” overturning moments and torques These moments are typically evaluated at “ground” level or “foundation” level (top of footing or pile caps, etc.) but they can be reported by the wind engineer at any elevation desired by the structural engineer 4.6.6.6 Example The typical floor plan of a high-rise building shown in Figure 4.57 is referenced here to illustrate the typical format used when reporting the computer-generated structural dynamic properties for analyses of wind-tunnel test data First, the structural engineer provides the wind engineer a floor-by-floor tabulation of the building properties For each diaphragm, the mass, the center-ofmass’s location, the center-of-rotation’s location, and the mass-moment of inertia are given See Figure 4.58 The mass should account for the weights of structural slabs, beams, columns, and walls; and nonstructural components such as floor topping, roofing, fireproofing material, fixed electrical and mechanical equipment, partitions, and ceilings When partition locations are subjected to change (as in office buildings), a uniform distributed dead load of at least 10 psf of floor area is used in calculating the mass Typical miscellaneous items such as ducts, piping, and conduits can be accounted for by using an additional 2–5 psf In storage areas, 25% of the design live load is included in the calculation of seismic weight In areas of heavy snow, a load of 30 psf should be used where the snow load is greater than 30 psf However, it may be reduced to as little as 7.5 psf when approved by building officials Recall that mass moment of inertia, MMI, is a structural property of the floor system that, in a manner of speaking, defines the rotational characteristics of the floor about the center of rotation The larger the MMI, the more prone the building is to torsional rotations 18 ft in 33 ft 10 in 33 ft in 18 ft in 343 ft in FIGURE 4.57 Building typical floor plan Wind Loads 339 Story Mass X [kip-s2/ft] Mass Y [kip-s2/ft] XCM [ft] YCM [ft] XCR [ft] YCR [ft] Mass Moment of Inertia [kip-s2/ft] HI RF 193.2 193.2 157.0 −30.3 156.1 −18.4 1.111E+06 46 278.1 278.1 156.8 −30.9 156.4 −18.1 1.537E+06 45 138.0 138.0 156.7 −31.4 156.4 −18.0 7.577E+05 44 138.0 138.0 156.7 −31.4 156.5 −18.0 7.577E+05 43 138.0 138.0 156.7 −31.4 156.6 −18.0 7.577E+05 42 138.6 138.6 156.7 −31.5 156.6 −18.0 7.634E+05 41 153.7 153.7 156.4 −31.9 156.6 −18.0 1.030E+06 40 155.0 155.0 156.2 −32.0 156.6 −18.1 1.055E+06 39 155.0 155.0 156.2 −32.0 156.6 −18.1 1.055E+06 38 158.4 158.4 156.2 −32.1 156.6 −18.1 1.103E+06 37 184.1 184.1 155.9 −32.6 156.6 −18.1 1.531E+06 36 185.4 185.4 155.7 −32.6 156.6 −18.1 1.564E+06 35 185.4 185.4 155.7 −32.6 156.6 −18.2 1.564E+06 34 185.7 185.7 155.7 −32.7 156.6 −18.2 1.564E+06 33 187.9 187.9 155.9 −32.7 156.6 −18.3 1.618E+06 32 187.9 187.9 155.9 −32.7 156.6 −18.3 1.618E+06 31 187.9 187.9 155.9 −32.7 156.6 −18.4 1.618E+06 30 187.9 187.9 155.9 −32.7 156.6 −18.4 1.618E+06 29 187.9 187.9 155.9 −32.7 156.6 −18.5 1.618E+06 28 187.9 187.9 155.9 −32.7 156.5 −18.6 1.618E+06 27 187.9 187.9 155.9 −32.7 156.5 −18.7 1.618E+06 26 193.6 193.6 154.9 −32.2 156.5 −18.8 1.628E+06 25 192.6 192.6 155.0 −32.3 156.4 −18.9 1.628E+06 24 193.7 193.7 155.0 −32.4 156.4 −19.0 1.640E+06 23 194.7 194.7 154.9 −32.5 156.3 −19.2 1.652E+06 22 194.7 194.7 154.9 −32.5 156.3 −19.3 1.652E+06 21 194.7 194.7 154.9 −32.5 156.2 −19.4 1.652E+06 20 194.7 194.7 154.9 −32.5 156.2 −19.6 1.652E+06 19 194.7 194.7 154.9 −32.5 156.1 −19.7 1.652E+06 18 194.7 194.7 154.9 −32.5 156.1 −19.8 1.652E+06 17 194.7 194.7 154.9 −32.5 156.1 −20.0 1.652E+06 16 194.7 194.7 154.9 −32.5 156.0 −20.1 1.652E+06 15 194.7 194.7 154.9 −32.5 156.0 −20.2 1.652E+06 14 195.0 195.0 155.0 −32.5 156.0 −20.3 1.655E+06 13 195.2 195.2 155.0 −32.5 155.9 −20.4 1.659E+06 12 198.0 198.0 152.9 −32.6 155.9 −20.4 1.720E+06 FIGURE 4.58 Tabulation of building properites (continued) 340 Reinforced Concrete Design of Tall Buildings Mass moment of Inertia [kip-s2/ft] Mass X [kip-s2/ft] Mass Y [kip-s2/ft] XCM [ft] YCM [ft] XCR [ft] YCR [ft] 11 199.2 199.2 151.7 −32.6 155.8 −20.4 1.766E+06 10 199.8 199.8 151.3 −32.6 155.8 −20.3 1.780E+06 199.8 199.8 151.3 −32.6 155.8 −20.2 1.780E+06 199.8 199.8 151.3 −32.6 155.7 −19.9 1.780E+06 199.8 199.8 151.3 −32.6 155.7 −19.6 1.780E+06 199.8 199.8 151.3 −32.6 155.7 −19.1 1.780E+06 199.8 199.8 151.3 −32.6 155.6 −18.5 1.780E+06 210.6 210.6 153.3 −32.8 155.6 −17.9 1.910E+06 210.4 210.4 153.2 −32.8 155.6 −17.2 1.908E+06 210.4 210.4 153.2 −32.8 155.5 −16.5 1.908E+06 251.1 251.1 160.1 −33.1 155.5 −16.1 2.429E+06 PODIUM 291.9 291.9 159.6 −32.1 155.5 −16.0 2.747E+06 PODIUM 3M 329.7 329.7 153.6 −31.1 155.5 −16.1 2.869E+06 PODIUM 3M 348.4 348.4 153.6 −30.8 155.4 −16.2 3.010E+06 PODIUM 348.4 348.4 153.6 −30.8 155.4 −16.0 3.010E+06 PODIUM 343.6 343.6 153.6 −31.0 155.3 −13.3 2.968E+06 Story Shown here is a table listing the mass, the center of mass, the center of rigidity and the mass-moment of inertia for a building with a floor plan similar to Figure 4.55; the difference is that the shear wall core is located on the northern half of the floor plan The origin is located at the plan’s northwest corner FIGURE 4.58 (continued) Next, we turn our attention to the modal information shown in Figures 4.59 and 4.60 to understand the dynamic deformations likely to be experienced by the building when subjected to ground motions Take, for example, the numbers shown in row Figure 4.60 The fundamental period of the building, 7.07 s as given in column 2, is the period at which the building “wants” to vibrate when set in motion by some sort of disturbance such as a seismic or wind event Columns through 13 give the mode shapes, (also shown in Figure 4.59) and the percentage of modal partition in each of the mode shapes Ux, Uy shown in the table represent the familiar transitional displacements Uz, refers to axial displacement in the vertical, z, direction which for dynamic analysis purposes is considered zero The value of Rz = 2.4 indicates that the torsional rotation of the building is small in the first mode The last three columns, sum R x, etc., record of summation of modal participation up to and including that level A study of the modal graphs along with the numerical values of Figure 4.60 will clarify the procedure for interpreting the computer results The sixth through eighth columns show the percentage of mass participating in the translational x and y directions, and the vertical up and down movement in the z direction The mass participation in the x direction is 56% as implied by the number 56 in column Our building wants to oscillate principally in the x direction, because the percentage of participation in the y direction is zero as given in column Note the building does not vibrate up and down, hence Uz is zero for the entire period range R x and Ry are the building rotational components in the x and y directions while Rz is the rotation about the z-axis Observe the R x component is large for the first mode because the Y displacement of the building is dominant in that mode Wind Loads 4.6.7 341 PERIOD DETERMINATION AND DAMPING VALUES FOR WIND DESIGN Many simple formulas have been proposed over the years to estimate a tall building’s fundamental period, for preliminary design purposes, until a rigorous calculation can be made Sometimes this rough approximation is the only calculation of fundamental period that can be made when the Mode 700.00 600 600.00 500 500.00 400 400.00 0.00004 600.00 600.00 500.00 500.00 400.00 100.00 0.00 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.00004 100.00 0.00002 200.00 300.00 200.00 0.00 –0.002 0.00016 700.00 300.00 0.00016 700.00 400.00 0.000035 Torsion Mode Height Height x, y component Mode 0.00014 0.00 0.00012 0.025 0.00014 0.02 0.00012 0.015 0.00003 0.01 0.0001 0.005 x, y component 0.00008 0.00006 –0.005 0.0001 100.00 0.00002 100 0.000025 200.00 0.000015 200 0.00001 300.00 300 0.000005 Height Height Mode 700 Torsion Mode Mode 700.00 700.00 600.00 600.00 500.00 500.00 Height Height 400.00 400.00 300.00 300.00 200.00 200.00 100.00 100.00 (a) FIGURE 4.59 x, y component 0.00008 0.00006 0.00004 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.00002 0.00 0.00 –0.002 Torsion Modes shapes: (a) Modes 1, 2, and (continued) 342 Reinforced Concrete Design of Tall Buildings Mode 700.00 600.00 600.00 500.00 500.00 400.00 400.00 Height 700.00 300.00 200.00 200.00 100.00 100.00 700.00 400.00 Height 300.00 300.00 200.00 200.00 100.00 100.00 700.00 600.00 600.00 500.00 500.00 400.00 400.00 Height 700.00 x, y component 0.00025 0.0002 0.0001 0.00015 0.0005 0.00014 0.00012 0.0001 0.00008 0.00004 0.00 –0.00002 0.005 0.01 0.015 –0.00004 100.00 –0.00006 100.00 –0.00008 200.00 300.00 200.00 0.00 –0.025 –0.02 –0.015 –0.01 –0.005 Torsion Mode 0.00002 300.00 –0.0001 x, y component Mode –0.0005 –0.00015 0.01 0.00 0.012 0.008 0.006 0.004 0.002 –0.002 –0.004 –0.006 0.00 –0.008 0.0002 500.00 400.00 Height 0.0001 600.00 500.00 Height Torsion Mode 700.00 600.00 (b) 0.00015 x, y component Mode 0.00 0.005 0.01 0.015 –0.0005 0.00 –0.025 –0.02 –0.015 –0.01 –0.004 0.0005 300.00 –0.0001 Height Mode Torsion FIGURE 4.59 (continued) (b) modes 4, 5, and wind-tunnel engineer is asked to perform a “desktop” prediction of the eventual loads The formula most widely recognized today for wind design is T= H (ft) 150 (4.40) FIGURE 4.60 Period 7.07 6.86 5.50 1.99 1.54 1.38 0.97 0.73 0.59 0.57 0.43 0.41 0.32 0.31 0.29 0.24 0.21 0.20 0.19 0.15 0.15 0.14 0.12 0.12 UX 18.01 15.70 26.53 10.07 2.95 0.15 4.87 0.95 4.20 0.13 0.01 4.81 0.02 3.20 0.52 1.96 0.06 0.02 1.08 0.07 0.53 0.00 0.35 0.12 UY 23.95 33.41 0.17 0.11 2.57 16.68 0.06 0.47 0.09 8.33 0.20 0.01 4.46 0.17 0.22 0.00 1.06 1.37 0.00 0.00 0.01 1.30 0.00 0.00 Tabulation of dynamic properties Mode 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 UZ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SumUX 18.01 33.71 60.24 70.31 73.25 73.41 78.28 79.23 83.42 83.56 83.56 88.37 88.39 91.59 92.11 94.07 94.13 94.15 95.23 95.30 95.83 95.83 96.18 96.30 SumUY 23.95 57.36 57.53 57.64 60.21 76.89 76.95 77.42 77.51 85.84 86.04 86.05 90.51 90.68 90.90 90.90 91.96 93.33 93.33 93.33 93.34 94.64 94.64 94.65 SumUZ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 RX 39.34 55.04 0.28 0.03 0.58 3.51 0.01 0.05 0.01 0.79 0.01 0.00 0.22 0.01 0.01 0.00 0.03 0.04 0.00 0.00 0.00 0.02 0.00 0.00 RY 28.84 25.09 42.32 1.47 0.44 0.02 0.65 0.13 0.35 0.01 0.00 0.37 0.00 0.16 0.03 0.07 0.00 0.00 0.02 0.00 0.01 0.00 0.00 0.00 RZ 16.17 8.96 31.60 3.40 9.29 2.21 1.50 6.66 0.90 0.34 6.07 0.02 0.44 0.12 3.61 0.00 1.27 0.69 0.01 0.74 0.26 0.00 0.17 0.58 SumRX 39.34 94.38 94.66 94.69 95.27 98.78 98.79 98.84 98.85 99.64 99.65 99.65 99.87 99.88 99.89 99.89 99.92 99.96 99.96 99.96 99.96 99.98 99.98 99.98 SumRY 28.84 53.93 96.25 97.72 98.16 98.19 98.84 98.97 99.32 99.33 99.33 99.70 99.70 99.86 99.89 99.96 99.96 99.96 99.99 99.99 100.00 100.00 100.00 100.00 (continued) SumRZ 16.17 25.12 56.73 60.13 69.42 71.63 73.13 79.80 80.70 81.04 87.11 87.14 87.57 87.69 91.31 91.31 92.58 93.27 93.28 94.02 94.28 94.28 94.44 95.02 Wind Loads 343 FIGURE 4.60 (continued) Mode 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Period 0.11 0.10 0.10 0.09 0.09 0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.04 UX 0.00 0.41 0.04 0.58 0.00 0.09 0.51 0.01 0.33 0.06 0.20 0.00 0.04 0.12 0.02 0.00 0.12 0.00 0.07 0.07 0.17 0.01 0.00 0.16 0.00 0.12 UY 0.87 0.00 0.01 0.00 0.77 0.00 0.00 0.75 0.02 0.00 0.00 0.63 0.06 0.00 0.00 0.47 0.00 0.00 0.15 0.13 0.00 0.01 0.19 0.00 0.01 0.00 UZ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SumUX 96.30 96.71 96.74 97.32 97.32 97.41 97.93 97.94 98.27 98.33 98.54 98.54 98.58 98.70 98.72 98.72 98.83 98.84 98.90 98.97 99.15 99.15 99.15 99.32 99.32 99.44 SumUY 95.52 95.52 95.53 95.53 96.30 96.30 96.30 97.06 97.08 97.08 97.08 97.70 97.77 97.77 97.77 98.24 98.24 98.24 98.39 98.52 98.52 98.53 98.72 98.72 98.73 98.73 SumUZ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 RX 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 RY 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 RZ 0.00 0.08 0.64 0.07 0.00 0.65 0.11 0.00 0.03 0.70 0.00 0.04 0.57 0.00 0.38 0.00 0.00 0.21 0.00 0.00 0.02 0.12 0.00 0.01 0.12 0.00 SumRX 99.99 99.99 99.99 99.99 99.99 99.99 99.99 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 SumRY 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 SumRZ 95.03 95.11 95.75 95.82 95.83 96.47 96.58 96.59 96.61 97.31 97.31 97.35 97.92 97.92 98.30 98.30 98.30 98.51 98.52 98.52 98.54 98.66 98.67 98.68 98.80 98.80 344 Reinforced Concrete Design of Tall Buildings Wind Loads 345 which is apparently in reasonable agreement with many field measurements However, this value is not in good agreement with the generally accepted eigenvalue analyses It is not known if this observed discrepancy is due to Errors in the field measurements Computer modeling inaccuracies and oversimplified modeling assumptions Wind-tunnel engineers are typically hesitant to “outguess” the design engineer or substitute their own estimate of the structure’s period They are most likely to produce loads consistent with the modal properties provided the engineer So, this is an issue worthy of further research Until then, it is appropriate for discussion between the wind-tunnel engineer and design engineer Another consideration that goes hand-in-hand with the determination of building periods is the value of damping for the structure Damping for buildings is any effect that reduces its amplitude of vibrations It results from many conditions ranging from the presence of interior partition walls, to concrete cracking, to deliberately engineered damping devices While for seismic design, 5% of critical damping is typically assumed for systems without engineered damping devices, the corresponding values for wind design are much lower as buildings subject to wind loads generally respond within the elastic range as opposed to inelastic range for seismic loading The additional damping for seismic design is assumed to come from severe concrete cracking and plastic hinging The ASCE 7-05 Commentary suggests a damping value of 1% for steel buildings and 2% for concrete buildings These wind damping values are typically associated with determining wind loads for serviceability check Without recommending specific values, the commentary implicitly suggests that higher values may be appropriate for checking the survivability states So, what design values are engineers supposed to use for ultimate level (1.6W) wind loads? Several resources are available as for example, the references cited in the ASCE 7-05 Commentary, but the values vary greatly depending upon which reference, is used The type of lateral force resisting system influences the damping value that may vary from a low of 0.5% to a high of 10% or more Although the level of damping has only a minor effect on the overall base shear for wind design for a large majority of low- and mid-rise buildings, for tall buildings, a more in-depth study of damping criteria is typically warranted While the use of the fundamental building period for seismic design calculations is well established, the parameters used for wind design have not been as clear For wind design, the building period is only relevant for those buildings designated as “flexible” (having a fundamental building period exceeding s) When a building is designated as flexible, the natural frequency (inverse of the building’s fundamental period) is introduced into the gust-effect factor, G f Prior to ASCE 7-05, designers typically used either the approximate equations within the seismic section or the values provided by a computer eigenvalue analysis The first can actually be unconservative because the approximate seismic equations are intentionally skewed toward shorter building periods Thus for wind design, where longer periods equate to higher base shears, their use can provide potentially unconservative results Also, the results of an eigenvalue analysis can yield building periods much longer than those observed in actual tests, thus providing potentially overly conservative results The period determination for wind analysis is therefore, a point at issue worthy of further research In summary, the choice of building period and damping for initial design continues to be a subject of discussion for building engineers This choice is compounded by our increasing complexity of structures, including buildings linked at top For many of these projects there may be no way around performing an initial Finite Element Analysis, FEA, to obtain a starting point for wind load determination Ongoing research into damping mechanisms combined with an increase in buildings with monitoring systems will help the design community make more informed decisions regarding the value of damping to use in design