i HANDBOOK OF CIVIL ENGINEERING CALCULATIONS ii ABOUT THE AUTHOR Tyler G. Hicks, ., is editor of Standard Handbook of Engineering Calculations, Standard Handbook of Mechanical Engineering Calculations, McGraw-Hill’s Interactive Chemical Engineer’s Solutions Suite, McGraw-Hill’s Interactive Civil Engineer’s Solutions Suite, and other bestselling titles. He is also a consulting engineer with International Engineering Associates. A graduate mechanical engineer, he has taught at several universities and lectured throughout the world. iii HANDBOOK OF CIVIL ENGINEERING CALCULATIONS Tyler G. Hicks, ., Editor International Engineering Associates Member: American Society of Mechanical Engineers United States Naval Institute S. David Hicks, Coordinating Editor Second Edition New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto iv Library of Congress Cataloging-in-Publication Data Hicks, Tyler Gregory, 1921-Handbook of civil engineering calculations / Tyler G. Hicks.—2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-07-147293-2 (alk. paper) 1. Engineering mathematics—Handbooks, manuals, etc. 2. Civil engineering—Mathematics—Handbooks, manuals, etc. I. Title. 2007 '51—dc22 2007012838 McGraw-Hill books are available at special quantity discoun