Structural Elements for Architects and Builders This page intentionally left blank Structural Elements for Architects and Builders Design of Columns, Beams and Tension Elements in Wood, Steel and Reinforced Concrete Jonathan Ochshorn Department of Architecture, Cornell University AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Butterworth-Heinemann is an imprint of Elsevier Butterworth -Heinemann is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA Linacre House, Jordan Hill, Oxford OX2 8DP, UK Copyright © 2010 E lsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. 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ISBN : 978-1-85617-771-9 For information on all Butterworth-Heinemann publications visit our Web site at www.elsevierdirect.com Printed in the United States of America 09 10 11 12 13 10 9 8 7 6 5 4 3 2 1 Contents Preface ....................................................................................................................... v ii List of examples. .........................................................................................................ix List of appendices ...................................................................................................... x i CHAPTER 1 Statics ............................................................................................... 1 Tributary areas ................................................................................... 2 Equilibrium ........................................................................................ 7 Reactions .......................................................................................... 1 0 Internal forces and moments ........................................................... 1 7 Indeterminate structures .................................................................. 3 1 Strength of materials ........................................................................ 3 3 CHAPTER 2 Loads ............................................................................................... 39 Dead loads ........................................................................................ 3 9 Live loads ......................................................................................... 4 1 Environmental loads. ........................................................................ 46 CHAPTER 3 Material properties ...................................................................... 6 1 Wood ................................................................................................ 63 Steel .................................................................................................. 6 8 Reinforced concrete ........................................................................ 7 0 CHAPTER 4 Sectional properties .................................................................... 73 Wood ................................................................................................ 73 Steel .................................................................................................. 7 4 Reinforced concrete ........................................................................ 7 5 CHAPTER 5 Design approaches ...................................................................... 79 Allowable stress design .................................................................... 7 9 Strength design ................................................................................ 8 0 CHAPTER 6 Tension elements ......................................................................... 87 Wood ................................................................................................ 89 Steel .................................................................................................. 9 6 Reinforced concrete ...................................................................... 1 04 CHAPTER 7 Columns ........................................................................................ 1 07 Wood .............................................................................................. 109 Steel ................................................................................................ 1 15 Reinforced concrete ...................................................................... 1 20 v vi Contents CHAPTER 8 Beams ........................................................................................... 129 Defl ection ....................................................................................... 129 Bending stress ................................................................................ 1 30 Shear stress .....................................................................................136 Wood .............................................................................................. 139 Steel ................................................................................................ 1 50 Reinforced concrete ...................................................................... 1 64 CHAPTER 9 Connections ................................................................................. 1 93 Wood .............................................................................................. 194 Steel ................................................................................................ 2 26 Reinforced concrete ...................................................................... 2 38 Appendix 1: Tables for Chapter 1 (statics) ......................................................... 2 49 Appendix 2: Tables for Chapter 2 (loads) ............................................................ 2 51 Appendix 3: Tables for Chapter 3 (material properties) ...................................... 2 65 Appendix 4: Tables for Chapter 4 (sectional properties). .................................... 287 Appendix 5: Tables for Chapter 5 (design approaches) ...................................... 3 09 Appendix 6: Tables for Chapter 6 (tension elements) ......................................... 3 11 Appendix 7: Tables for Chapter 7 (columns) ....................................................... 3 15 Appendix 8: Tables for Chapter 8 (beams) .......................................................... 3 29 Appendix 9: Tables for Chapter 9 (connections) ................................................. 3 45 Appendix 10: Unit abbreviations and conversion .................................................. 3 73 References ............................................................................................................... 3 75 Glossary ................................................................................................................... 3 77 Index ....................................................................................................................... 3 83 Preface As is well known, architects and builders rarely design the structural elements and systems within their buildings, instead engaging the services of (and, it is to be hoped, collaborating with) structural engineers, or relying upon standard practices sanctioned by building codes. Where architects or builders wish to be adventurous with their structures, some knowledge of structural behavior and the potential of structural materials is certainly useful. On the other hand, where they are content to employ generic structural systems— platform framing in wood, simple skeletal frames in steel or reinforced concrete— one can get by with little actual knowledge of structural design, relying instead on the expertise of structural consultants and the knowledge of common spans, heights, and cross-sectional dimensions around which many ordinary buildings can be planned. The heroic stage of modernism, in which architects often sought to reconcile structural behavior and overall building form— some fi nding inspiration in the struc- tural frame or the load-bearing wall— was also the heroic stage of structural educa- tion for architects: it was hardly necessary, in that context, to explain why architects needed to learn about structures. Some of the same excitement about the potential of structure in architecture still remains, but it is also true that a “ mannerist ” ten- dency has emerged, interested not necessarily in renouncing the role of structure in architecture, but rather reveling in its potential to distort, twist, fragment, and other- wise subvert modernist conventions and the architectural forms they support. Yet all structures, whether hidden from view or boldly expressed, follow the same laws of equilibrium, are exposed to the same types of forces, and are con- strained by the same material properties and manufacturing practices. It is, there- fore, appropriate for architects and builders to study structures in such a way that the basic principles underlying all structural form become clear. This can be accom- plished in three phases: (1) by studying the concepts of statics and strength of materials, (2) by learning how these concepts are applied to the design of common structural elements fabricated from real materials, and (3) by gaining insight into the design of structural systems comprised of structural elements interconnected in a coherent pattern. Much of the material presented in this text can be found elsewhere; the basic conditions of equilibrium, historical insights into structural behavior that form the basis for structural design, and recommendations for design procedures incorpo- rated into building codes are all widely disseminated through industry-published manuals, government-sanctioned codes, and academic texts. Many excellent struc- tures texts have been written specifi cally for architects and builders. Thus, the ques- tion naturally arises: Why write another one? The primary motivation for writing this text is to organize the material in a man- ner consistent with the structures curriculum developed within the Department viii Preface of Architecture at Cornell University, based on the three sequential “ phases ” just described — structural concepts, elements, and systems. While this text does contain a concise introduction to structural concepts (statics), it is primarily concerned with the design and analysis of structural elements: columns, beams, and tension mem- bers, and their connections. This material is organized into a single volume that is concise, comprehensive, and self-suffi cient, including all necessary data for the pre- liminary design and analysis of these structural elements in wood, steel, and rein- forced concrete. A second motivation for writing this text is to present material in a manner con- sistent with my own priorities and sensibilities. Every chapter contains insight, spec- ulation, or forms of presentation developed by the author and generally not found elsewhere. Additionally, the Appendices included at the end of the text contain numerous tables and graphs, based on material contained in industry publications, but reorganized and formatted especially for this text to improve clarity and simplicity— without sacrifi cing comprehensiveness. Methods for designing structures and modeling loads are constantly being refi ned. Within the past several years, important changes have occurred in the design of wood, steel, and reinforced concrete structures, as well as in the model- ing of loads. These changes include revised procedures for beam and column design in wood; the replacement of the standard specifi cation for 36-ksi steel with a new standard based on 50-ksi steel for wide-fl ange sections; a major modifi cation in the load factors used in reinforced concrete design, aligning them with those recom- mended by SEI/ASCE 7 and already used in the design of wood and steel structures; and numerous refi nements in the modeling of environmental loads. These changes have all been incorporated into this text. Finally , a disclaimer: This text is intended to be used only for the preliminary (schematic) design and understanding of structural elements. For the design of an actual structure, a competent professional should be consulted. List of examples 1 .1 Find reactions for simply supported beam 1 .2 Find reactions for three-hinged arch 1 .3 Find reactions for a cable 1 .4 Find internal shear and bending moment for simply supported beam with “ point ” loads 1 .5 Find internal shear and bending moments for a simply supported cantilever beam with distributed loads 1 .6 Find internal axial forces in a truss (section method) 1 .7 Find internal axial forces in a three-hinged arch 1 .8 Find internal axial forces in a cable 2 .1 Calculate dead loads 2 .2 Calculate live loads 2 .3 Calculate snow loads 2 .4 Calculate wind loads 2 .5 Calculate seismic loads 5 .1 Load combinations (Part I) 5 .2 Load combinations (Part II) 5 .3 Load combinations (Part III) 6 .1 Find elongation in tension element 6 .2 Analyze wood tension element 6 .3 Design wood tension element 6 .4 Analyze steel tension element 6 .5 Design steel tension element 7 .1 Analyze wood column 7 .2 Design wood column 7 .3 Analyze steel column 7 .4 Design steel column 7 .5 Analyze axially loaded reinforced concrete column 7 .6 Design axially loaded reinforced concrete column with cross-sectional dimen- sions assumed 7 .7 Design axially loaded reinforced concrete column with reinforcement ratio assumed 8 .1 Analyze wood beam, dimension lumber 8 .2 Analyze wood beam, timbers 8 .3 Design wood beam, glulam ix