www.EngineeringEBooksPdf.com This page intentionally left blank www.EngineeringEBooksPdf.com bee80288_ifc.indd Page 10/26/10 4:39:07 PM user-f499 /Volumes/201/MHDQ251/bee80288_disk1of1/0073380288/bee80288_pagefiles SI Prefixes Multiplication Factor 12 000 000 000 000 000 000 000 10 000 109 000 106 000 103 100 102 10 101 0.1 1021 0.01 1022 0.001 1023 0.000 001 1026 0.000 000 001 1029 0.000 000 000 001 10212 0.000 000 000 000 001 10215 0.000 000 000 000 000 001 10218 Prefix† Symbol tera giga mega kilo hecto‡ deka‡ deci‡ centi‡ milli micro nano pico femto atto T G M k h da d c m m n p f a † The first syllable of every prefix is accented so that the prefix will retain its identity Thus, the preferred pronunciation of kilometer places the accent on the first syllable, not the second ‡ The use of these prefixes should be avoided, except for the measurement of areas and volumes and for the nontechnical use of centimeter, as for body and clothing measurements U.S Customary Units and Their SI Equivalents Quantity U.S Customary Units SI Equivalent Acceleration ft/s2 in./s2 ft2 in2 ft ? lb kip lb oz lb ? s ft in mi oz mass lb mass slug ton lb ? ft lb ? in 0.3048 m/s2 0.0254 m/s2 0.0929 m2 645.2 mm2 1.356 J 4.448 kN 4.448 N 0.2780 N 4.448 N ? s 0.3048 m 25.40 mm 1.609 km 28.35 g 0.4536 kg 14.59 kg 907.2 kg 1.356 N ? m 0.1130 N ? m in4 lb ? ft ? s2 ft ? lb/s hp lb/ft2 lb/in2 (psi) ft/s in./s mi/h (mph) mi/h (mph) ft3 in3 gal qt ft ? lb 0.4162 106 mm4 1.356 kg ? m2 1.356 W 745.7 W 47.88 Pa 6.895 kPa 0.3048 m/s 0.0254 m/s 0.4470 m/s 1.609 km/h 0.02832 m3 16.39 cm3 3.785 L 0.9464 L 1.356 J Area Energy Force Impulse Length Mass Moment of a force Principal SI Units Used in Mechanics Quantity Unit Symbol Formula Acceleration Angle Angular acceleration Angular velocity Area Density Energy Force Frequency Impulse Length Mass Moment of a force Power Pressure Stress Time Velocity Volume, solids Liquids Work Meter per second squared Radian Radian per second squared Radian per second Square meter Kilogram per cubic meter Joule Newton Hertz Newton-second Meter Kilogram Newton-meter Watt Pascal Pascal Second Meter per second Cubic meter Liter Joule p rad p p p p J N Hz p m kg p W Pa Pa s p p L J m/s2 † rad/s2 rad/s m2 kg/m3 N?m kg ? m/s2 s21 kg ? m/s ‡ ‡ N?m J/s N/m2 N/m2 ‡ m/s m3 1023 m3 N?m † Supplementary unit (1 revolution 2p rad 3608) ‡ Base unit www.EngineeringEBooksPdf.com ISBN: 0073380288 Author: Beer, Johnston, Dewolf, and Mazurek Title: MECHANICS OF MATERIALS Front endsheets Color: Pages: 2, Moment of inertia Of an area Of a mass Power Pressure or stress Velocity Volume, solids Liquids Work bee80288_ifc.indd Page 10/26/10 4:39:07 PM user-f499 /Volumes/201/MHDQ251/bee80288_disk1of1/0073380288/bee80288_pagefiles SI Prefixes Multiplication Factor 12 000 000 000 000 000 000 000 10 000 109 000 106 000 103 100 102 10 101 0.1 1021 0.01 1022 0.001 1023 0.000 001 1026 0.000 000 001 1029 0.000 000 000 001 10212 0.000 000 000 000 001 10215 0.000 000 000 000 000 001 10218 Prefix† Symbol tera giga mega kilo hecto‡ deka‡ deci‡ centi‡ milli micro nano pico femto atto T G M k h da d c m m n p f a † The first syllable of every prefix is accented so that the prefix will retain its identity Thus, the preferred pronunciation of kilometer places the accent on the first syllable, not the second ‡ The use of these prefixes should be avoided, except for the measurement of areas and volumes and for the nontechnical use of centimeter, as for body and clothing measurements U.S Customary Units and Their SI Equivalents Quantity U.S Customary Units SI Equivalent Acceleration ft/s2 in./s2 ft2 in2 ft ? lb kip lb oz lb ? s ft in mi oz mass lb mass slug ton lb ? ft lb ? in 0.3048 m/s2 0.0254 m/s2 0.0929 m2 645.2 mm2 1.356 J 4.448 kN 4.448 N 0.2780 N 4.448 N ? s 0.3048 m 25.40 mm 1.609 km 28.35 g 0.4536 kg 14.59 kg 907.2 kg 1.356 N ? m 0.1130 N ? m in4 lb ? ft ? s2 ft ? lb/s hp lb/ft2 lb/in2 (psi) ft/s in./s mi/h (mph) mi/h (mph) ft3 in3 gal qt ft ? lb 0.4162 106 mm4 1.356 kg ? m2 1.356 W 745.7 W 47.88 Pa 6.895 kPa 0.3048 m/s 0.0254 m/s 0.4470 m/s 1.609 km/h 0.02832 m3 16.39 cm3 3.785 L 0.9464 L 1.356 J Area Energy Force Impulse Length Mass Moment of a force Principal SI Units Used in Mechanics Quantity Unit Symbol Formula Acceleration Angle Angular acceleration Angular velocity Area Density Energy Force Frequency Impulse Length Mass Moment of a force Power Pressure Stress Time Velocity Volume, solids Liquids Work Meter per second squared Radian Radian per second squared Radian per second Square meter Kilogram per cubic meter Joule Newton Hertz Newton-second Meter Kilogram Newton-meter Watt Pascal Pascal Second Meter per second Cubic meter Liter Joule p rad p p p p J N Hz p m kg p W Pa Pa s p p L J m/s2 † rad/s2 rad/s m2 kg/m3 N?m kg ? m/s2 s21 kg ? m/s ‡ ‡ N?m J/s N/m2 N/m2 ‡ m/s m3 1023 m3 N?m Moment of inertia Of an area Of a mass Power Pressure or stress Velocity Volume, solids Liquids Work † Supplementary unit (1 revolution 2p rad 3608) ‡ Base unit www.EngineeringEBooksPdf.com ISBN: 0073380288 Author: Beer, Johnston, Dewolf, and Mazurek Title: MECHANICS OF MATERIALS Front endsheets Color: Pages: 2, bee80288_fm_i-xx_1.indd Page i 11/19/10 7:20:16 PM user-f499 /Users/user-f499/Desktop/Temp Work/Don't Delete Job/MHDQ251:Beer:201/fm MECHANICS OF MATERIALS www.EngineeringEBooksPdf.com This page intentionally left blank www.EngineeringEBooksPdf.com bee80288_fm_i-xx_1.indd Page iii 11/19/10 7:20:16 PM user-f499 /Users/user-f499/Desktop/Temp Work/Don't Delete Job/MHDQ251:Beer:201/fm SIXTH EDITION MECHANICS OF MATERIALS Ferdinand P Beer Late of Lehigh University E Russell Johnston, Jr Late of University of Connecticut John T Dewolf University of Connecticut David F Mazurek United States Coast Guard Academy TM www.EngineeringEBooksPdf.com bee80288_fm_i-xx_1.indd Page iv 11/29/10 6:37:55 PM user-f499 /Users/user-f499/Desktop/Temp Work/Don't Delete Job/MHDQ251:Beer:201 TM MECHANICS OF MATERIALS, SIXTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020 Copyright © 2012 by The McGraw-Hill Companies, Inc All rights reserved Previous editions © 2009, 2006, and 2002 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper QVR/QVR ISBN 978-0-07-338028-5 MHID 0-07-338028-8 Vice President, Editor-in-Chief: Marty Lange Vice President, EDP: Kimberly Meriwether David Senior Director of Development: Kristine Tibbetts Global Publisher: Raghothaman Srinivasan Executive Editor: Bill Stenquist Developmental Editor: Lora Neyens Senior Marketing Manager: Curt Reynolds Lead Project Manager: Sheila M Frank Buyer II: Sherry L Kane Senior Designer: Laurie B Janssen Cover Designer: Ron Bissell Cover Image: (front) © Ervin Photography, Inc Lead Photo Research Coordinator: Carrie K Burger Photo Research: Sabina Dowell Compositor: Aptara®, Inc Typeface: 10.5/12 New Caledonia Printer: Quad/Graphics All credits appearing on page or at the end of the book are considered to be an extension of the copyright page The photos on the front and back cover show the Bob Kerrey Pedestrian Bridge, which spans the Missouri River between Omaha, Nebraska, and Council Bluffs, lowa This S-curved structure utilizes a cable-stayed design, and is the longest pedestrian bridge to connect two states Library of Congress Cataloging-in-Publication Data Mechanics of materials / Ferdinand Beer [et al.] — 6th ed p cm Includes index ISBN 978-0-07-338028-5 ISBN 0-07-338028-8 (alk paper) Strength of materials—Textbooks I Beer, Ferdinand Pierre, 1915– TA405.B39 2012 620.1’12—dc22 2010037852 www.mhhe.com www.EngineeringEBooksPdf.com bee80288_fm_i-xx_1.indd Page v 11/19/10 7:20:17 PM user-f499 /Users/user-f499/Desktop/Temp Work/Don't Delete Job/MHDQ251:Beer:201/fm About the Authors As publishers of the books written by Ferd Beer and Russ Johnston, we are often asked how did they happen to write the books together, with one of them at Lehigh and the other at the University of Connecticut The answer to this question is simple Russ Johnston’s first teaching appointment was in the Department of Civil Engineering and Mechanics at Lehigh University There he met Ferd Beer, who had joined that department two years earlier and was in charge of the courses in mechanics Born in France and educated in France and Switzerland (he held an M.S degree from the Sorbonne and an Sc.D degree in the field of theoretical mechanics from the University of Geneva), Ferd had come to the United States after serving in the French army during the early part of World War II and had taught for four years at Williams College in the Williams-MIT joint arts and engineering program Born in Philadelphia, Russ had obtained a B.S degree in civil engineering from the University of Delaware and an Sc.D degree in the field of structural engineering from MIT Ferd was delighted to discover that the young man who had been hired chiefly to teach graduate structural engineering courses was not only willing but eager to help him reorganize the mechanics courses Both believed that these courses should be taught from a few basic principles and that the various concepts involved would be best understood and remembered by the students if they were presented to them in a graphic way Together they wrote lecture notes in statics and dynamics, to which they later added problems they felt would appeal to future engineers, and soon they produced the manuscript of the first edition of Mechanics for Engineers The second edition of Mechanics for Engineers and the first edition of Vector Mechanics for Engineers found Russ Johnston at Worcester Polytechnic Institute and the next editions at the University of Connecticut In the meantime, both Ferd and Russ had assumed administrative responsibilities in their departments, and both were involved in research, consulting, and supervising graduate students—Ferd in the area of stochastic processes and random vibrations, and Russ in the area of elastic stability and structural analysis and design However, their interest in improving the teaching of the basic mechanics courses had not subsided, and they both taught sections of these courses as they kept revising their texts and began writing together the manuscript of the first edition of Mechanics of Materials Ferd and Russ’s contributions to engineering education earned them a number of honors and awards They were presented with the Western Electric Fund Award for excellence in the instruction of engineering students by their respective regional sections of the American Society for Engineering Education, and they both received the Distinguished Educator Award from the Mechanics Division of the v www.EngineeringEBooksPdf.com bee80288_fm_i-xx_1.indd Page vi 11/20/10 3:27:43 PM user-f499 vi About the Authors /Users/user-f499/Desktop/Temp Work/Don't Delete Job/MHDQ251:Beer:201/fm same society In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engineers, and in 1995 Ferd was awarded an honorary Doctor of Engineering degree by Lehigh University John T DeWolf, Professor of Civil Engineering at the University of Connecticut, joined the Beer and Johnston team as an author on the second edition of Mechanics of Materials John holds a B.S degree in civil engineering from the University of Hawaii and M.E and Ph.D degrees in structural engineering from Cornell University His research interests are in the area of elastic stability, bridge monitoring, and structural analysis and design He is a registered Professional Engineering and a member of the Connecticut Board of Professional Engineers He was selected as the University of Connecticut Teaching Fellow in 2006 David F Mazurek, Professor of Civil Engineering at the United States Coast Guard Academy, joined the team in the fourth edition David holds a B.S degree in ocean engineering and an M.S degree in civil engineering from the Florida Institute of Technology, and a Ph.D degree in civil engineering from the University of Connecticut He is a registered Professional Engineer He has served on the American Railway Engineering & Maintenance of Way Association’s Committee 15—Steel Structures for the past seventeen years Professional interests include bridge engineering, structural forensics, and blastresistant design www.EngineeringEBooksPdf.com bee80288_ndx_I1-I10.indd Page I10 11/24/10 2:54:02 PM user-f499 /Volumes/201/MHDQ251/bee80288_disk1of1/0073380288/bee80288_pagefiles Total work, 695 Toughness, modulus of, 694, 697, 750–751 Transformations of stress and strain, 436–511 application of Mohr’s circle to the three-dimensional analysis of stress, 464–466 computer problems, 510–511 fracture criteria for brittle materials under plane stress, 469–477, 505 general state of stress, 462–463, 504 introduction, 438–440 maximum shearing stress, 443–451, 503 measurements of strain, 494–501, 506 Mohr’s circle for plane stress, 452–462, 489–491, 503, 506 of plane stress, 440–442, 486–488, 502, 506 principal stresses, 503 review problems, 507–509 stresses in thin-walled pressure vessels, 478–485 summary, 502–506 three-dimensional analysis of strain, 491–494 yield criteria for ductile materials under plane stress, 467–469, 504 Transformed sections, drawing, 224 Transmission shafts, 142 design considerations of, 211 design of, 143 Transverse cross section, deformations in, 233–241, 306 Transverse loading, 223, 316 deformations of a beam under, 43, 552–553, 618 Tresca, Henri Edouard, 468 Tresca’s hexagon, 468 True stress and true strain, 61–62 Twisting See also Angle of twist; Permanent twist stresses due to, 419, 531 Two-force members, 4–6 Unsymmetric loadings combined stresses, 419 distribution of stresses over the section, 418–419 equivalent force-couple system at shear center, 419 shear center, 414–426, 429 shearing stresses in flanges, 418 shearing stresses in webs, 418 stresses due to bending, 419 stresses due to twisting, 419 of thin-walled members, 414–426 Upper yield point, 60 U Y Ultimate loads, 31, 33, 667 Ultimate strength of a material, 4, 59 determination of, 30–31, 44 Unequal-leg angle steel, A26–A27 Uniaxial stress, 227 Unknown forces, 43 Unknown loads, 79–80 Unloading, 123 elastic, 193 Unsymmetric bending, 224, 279–283, 308 Yield criteria for ductile materials under plane stress, 439, 467–469, 504 maximum-distortion-energy criterion, 468–469 maximum-shearing-stress criterion, 467–469 Yield points, upper and lower, 60 Yield strength, 58–60, 129, 707 determination by offset method, 60 Yielding, 32 Young, Thomas, 62 Young’s modulus, 62 V von Mises, Richard, 468 von Mises criterion, 468 W Watts (W), 212 Wide-flange beam (W-beam), 231, 388 Wide-flange shaped steel (W shapes), properties of, A16–A19 Winkler, E., 294 Wood See also Timber design of columns under a centric load, 665–667 maximum stress in, 248 Work elementary, 695 total, 695 Work and energy principle of, 725–726 under several loads, 732–734 under a single load, 719–722, 752–753 Working load, 31 I10 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN1 11/24/10 6:24:48 PM user-f494 volume 201/FREE048/work%0/indd%0/ Answers to Problems Answers to problems with a number set in straight type are given on this and the following pages Answers to problems with a number set in italic are not listed CHAPTER 1.1 1.2 1.3 1.4 1.7 1.8 1.9 1.10 1.13 1.14 1.15 1.16 1.18 1.19 1.21 1.22 1.23 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.35 1.36 1.37 1.39 1.40 1.41 1.43 1.44 1.45 1.48 1.49 1.51 1.52 1.53 1.55 1.56 1.57 1.58 1.59 1.61 1.63 1.65 1.67 dl 22.6 mm; d2 15.96 mm (a) 35.7 MPa (b) 42.4 MPa 28.2 kips (a) 12.73 ksi (b) 22.83 ksi (a) 101.6 MPa (b) 221.7 MPa (a) 2640 psi (b) 2320 psi 10.64 ksi 285 mm2 24.97 MPa (a) 17.86 kN (b) 241.4 MPa 5.93 MPa 12.33 in 60.2 mm 63.3 mm 10.82 in (a) 3.33 MPa (b) 525 mm (a) 444 psi (b) 7.50 in (c) 2400 psi (a) 25.9 mm (b) 271 MPa (a) 80.8 MPa (b) 127.0 MPa (c) 203 MPa (a) 10.84 ksi (b) 5.11 ksi s 70.0 psi; t 40.4 psi (a) 1.500 kips (b) 43.3 psi s 489 kPa; t 489 kPa (a) 13.95 kN (b) 620 kPa (a) (tension) at u 908; 54.1 MPa (compression) at u 08 (b) 27.0 MPa at u 458 (a) 706 kN (b) u 458 (c) 18.00 MPa (d) 36.0 MPa (compression) 3.60 (a) 1.141 in (b) 1.549 in (a) 3.35 (b) 1.358 in 168.1 mm2 5.75 in 1.800 10.25 kN 2.50 (a) 1.550 in (b) 8.05 in 1.683 kN 2.06 kN 3.02 3.72 kN 3.97 kN (a) 629 lb (b) 1.689 (a) 362 kg (b) 1.718 14.93 mm (a) 8.92 ksi (b) 22.4 ksi (c) 11.21 ksi 2.25 kips 3.45 (a) 5.57 mm (b) 38.9 MPa (c) 35.0 MPa sall dy4 tall 21.38 < u < 32.38 (a) 27.58 (b) 3.31 (c) 16 mm # d # 22 mm (d ) 18 mm # d # 22 mm (c) 0.70 in # d # 1.10 in (d) 0.85 in # d # 1.25 in (b) For b 38.668, tan b 0.8; BD is perpendicular to BC (c) F.S 3.58 for a 26.68; P is perpendicular to line AC 1.C5 (b) Member of Fig P 1.29, for a 608: (1) 70.0 psi; (2) 40.4 psi; (3) 2.14; (4) 5.30; (5) 2.14 Member of Fig P 1.31, for a 458: (1) 489 kPa; (2) 489 kPa; (3) 2.58; (4) 3.07; (5) 2.58 1.C6 (d) Pall 5.79 kN; stress in links is critical 1.68 1.69 1.70 1.C2 1.C3 1.C4 CHAPTER 2.1 2.2 2.3 2.4 2.6 2.7 2.9 2.11 2.13 2.14 2.15 2.18 2.19 2.20 2.21 2.22 2.23 2.25 2.27 2.28 2.29 2.30 2.35 2.36 2.37 2.38 2.39 2.41 2.42 2.43 2.45 2.46 2.47 (a) 2.45 kN (b) 50.0 mm (a) 0.381 in (b) 17.58 ksi (a) 9.09 ksi (b) 1.760 (a) 9.82 kN (b) 500 MPa (a) 0.546 mm (b) 36.3 MPa 73.7 GPa dmin 0.1701 in.; Lmin 36.7 in 9.21 mm 1.988 kN 1.219 in 0.1812 in (a) 9.53 kips (b) 1.254 1023 in (a) 32.8 kN (b) 0.0728 mmw (a) 0.01819 mmx (b) 0.0919 mmw (a) 0.1767 in (b) 0.1304 in 50.4 kN dAB 22.11 mm; dAC 2.03 mm 4.71 1023 in.w 14.74 kN (a) 80.4 mmx (b) 209 mmw (c) 390 mmw PhypEabw (a) rgL2y2E (b) Wy2 (steel) 215.80 ksi; (concrete) 21.962 ksi (a) 257.1 MPa (b) 285.7 MPa 20.306 mm (a) (steel) 218.01 ksi; (aluminum) 26.27 ksi (b) 26.21 1023 in 177.4 lb (a) 68.2 kN m at A; 37.2 kN m at E (b) 46.3 mm n (a) 45.5 kN m at A; 54.5 kN m at E (b) 48.8 mm n TA Py10; TB Py5; TC 3Py10; TD 2Py5 (a) 9.73 kN (b) 2.02 mm m (a) (BC) 1000 lb; (DE) 2400 lb (b) 2.21 1023 in n (steel) 21.448 ksi; (concrete) 54.2 psi AN1 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN2 11/24/10 6:24:51 PM user-f494 2.49 2.50 2.51 2.52 2.53 2.56 2.57 2.58 2.59 2.61 2.63 2.64 2.66 2.67 2.68 2.69 2.70 2.75 2.76 2.77 2.78 2.81 2.82 2.84 2.85 2.86 2.88 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.101 2.102 2.105 2.106 2.109 2.110 2.111 2.112 2.113 2.114 2.115 2.116 2.117 2.118 2.121 2.122 2.123 2.124 2.128 2.129 2.130 28.15 MPa 256.2 MPa 142.6 kN (a) 298.3 MPa (b) 238.3 MPa (a) (AB) 25.25 ksi; (BC) 211.82 ksi (b) 6.57 1023 in n (a) 21.48C (b) 3.68 MPa 5.70 kN (a) 201.68C (b) 18.0107 in (a) 52.3 kips (b) 9.91 1023 in (a) 1.324 1023 in (b) 299.3 1026 in (c) 212.41 1026 in (d) 212.41 1026 in2 E 205 MPa; G 70.3 MPa; n 0.455 94.9 kips 1.99551 (a) 263.0 MPa (b) 213.50 mm2 (c) 2540 mm3 (a) 10.20 mm (b) 2.40 mm (c) 8.91 mm (a) 5.13 1023 in (b) 20.570 1023 in (a) 7630 lb (compression) (b) 4580 lb (compression) 16.67 MPa 19.00 103 kNym 0.0187 in a 0.818 in.; b 2.42 in a 42.9 mm; b 160.7 mm 75.0 kN; 40.0 mm (a) 16.55 1026 in3 (b) 16.54 1026 in3 (a) 588 1026 in (b) 33.2 1023 in3 (c) 0.0294% (a) 20.0746 mm; 2143.91 mm3 (b) 20.0306 mm; 2521 mm3 3.00 (a) 0.0303 mm (b) sx 40.6 MPa; sy sz 5.48 MPa (a) sx 44.6 MPa; sy 0; sz 3.45 MPa (b) 20.0129 mm (a) 13.31 ksi (b) 18.72 ksi 5.56 kips (a) 11.4 mm (b) 28.8 kN 36.7 mm (a) 92.3 kN; 0.791 mm (b) 180.0 kN; 1.714 mm 189.6 MPa 176.7 kN; 3.84 mm 176.7 kN; 3.16 mm 2.65 kips; 0.1117 in 3.68 kips; 0.1552 in (a) 0.292 mm (b) (AC) 250 MPa; (CB) 2307 MPa (c) 0.0272 mm (a) 990 kN (b) (AC) 250 MPa; (CB) 2316 MPa (c) 0.0313 mm (a) 112.1 kips (b) 50 ksi in low strength steel; 82.9 ksi in high strength steal (c) 0.00906 in (a) 0.0309 in (b) 64 ksi (c) 0.00387 in (a) (AD) 250 MPa; (BE) 124.3 MPa (b) 0.622 mmw (a) (AD) 233 MPa; (BE) 250 MPa (b) 1.322 mmw (a) (AD) 24.70 MPa; (BE) 19.34 MPa (b) 0.0967 mmw (a) 236 ksi (b) 15.84 ksi (a) (AC) 2150 MPa; (CB) 2250 MPa (b) 0.1069 mm n (a) (AC) 56.5 MPa; (CB) 9.41 MPa (b) 0.0424 mm n (a) 9158F (b) 17598F (a) 0.1042 mm (b) (AC) and (CB) 265.2 MPa (a) 0.00788 mm (b) (AC) and (CB) 26.06 MPa 0.429 in 4.678C 30.0 kips (steel) 67.1 MPa; (concrete) 8.38 MPa volume 201/FREE048/work%0/indd%0/ 2.131 2.133 2.135 2.C1 2.C3 2.C5 137.88F (a) 262 mm (b) 21.4 mm (a) AsYymg (b) EAyL Prob 2.126: (a) 11.90 1023 in w (b) 5.66 1023 in x Prob 2.60: (a) 2116.2 MPa (b) 0.363 mm r 0.25 in.: 3.89 kips r 0.75 in.: 2.78 kips 2.C6 (a) 20.40083 (b) 20.10100 (c) 20.00405 CHAPTER 3.1 3.2 3.3 3.5 3.6 3.8 3.10 3.11 3.13 3.14 3.15 3.16 3.19 3.20 3.21 3.22 3.24 3.26 3.27 3.28 3.29 3.30 3.31 3.33 3.34 3.35 3.37 3.38 3.39 3.41 3.42 3.43 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.55 3.56 3.59 3.62 3.63 3.64 3.66 3.68 3.69 3.70 3.73 (a) 53.4 MPa (b) 53.9 MPa (a) 5.17 kN ? m (b) 87.2 MPa 4.12 kip ? in (a) 70.7 MPa (b) 35.4 MPa (c) 6.25% (a) 125.7 N ? m (b) 181.4 N ? m (a) 19.21 kip ? in (b) 2.01 in 39.8 mm (a) CD (b) 85.8 MPa (a) 2.85 ksi (b) 4.46 ksi (c) 5.37 ksi (a) 3.19 ksi (b) 4.75 ksi (c) 5.58 ksi 9.16 kip ? in (a) 1.503 in (b) 1.853 in 3.18 kN ? m 3.37 kN ? m (a) 72.5 MPa (b) 68.7 MPa (a) 59.6 mm (b) 43.9 mm 1.189 in 4.30 kip ? in (a) 55.0 MPa (b) 45.3 MPa (c) 47.7 MPa (a) 20.1 mm (b) 26.9 mm (c) 36.6 mm (a) (C12 C22) tally2rgc2 (b)(Tyw)0 [1 (c1yc2)2] 1.000; 1.025; 1.120; 1.200; 1.000 (a) 4.218 (b) 5.258 0.491 in 7.68 ksi (a) 1.3848 (b) 3.228 (a) 14.438 (b) 46.98 6.028 1.1408 3.778 12.228 (TA lyGJ) (1yn4 1yn2 1) 62.9 mm 42.1 mm (a) 82.1 mm (b) 109.4 mm 22.5 mm 1.285 in 1.483 in (a) 73.6 MPa (b) 34.4 MPa (c) 5.078 4.138 (AB) 9.95 ksi; (CD) 1.849 ksi (AB) 1.086 ksi; (CD) 6.98 ksi 12.24 MPa 0.241 in (a) Ty2ptr12 (a) 46.9 MPa (b) 23.5 MPa 6.69 mm 2.64 mm 40.1 hp (a) 51.7 kW (b) 6.178 0.3125 in AN2 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN3 11/24/10 6:24:52 PM user-f494 3.74 3.75 3.76 3.77 3.78 3.80 3.81 3.83 3.84 3.86 3.87 3.88 3.90 3.91 3.92 3.93 3.94 3.95 3.98 3.99 3.100 3.101 3.104 3.105 3.106 3.107 3.110 3.111 3.112 3.113 3.114 3.115 3.118 3.119 3.120 3.121 3.122 3.123 3.124 3.127 3.128 3.129 3.131 3.132 3.134 3.135 3.136 3.137 3.138 3.141 3.142 3.143 3.144 3.146 3.148 3.149 3.150 3.151 3.153 3.155 (a) 0.799 in (b) 0.947 in (a) 4.08 ksi (b) 6.79 ksi (AB) 15.00 mm; (CD) 20.4 mm; (EF) 27.6 mm 7.11 kW 4.90 Hz d 2.82 in (a) 16.02 Hz (b) 27.2 Hz 33.5 Hz or 2010 rpm (a) 5.36 ksi (b) 5.02 ksi 10.8 mm 42.6 Hz 63.5 kW (a) 2.61 ksi (b) 2.01 ksi (a) 203 N ? m (b) 165.8 N ? m 21.2 N ? m (a) 144.7 kip ? in (b) 148.1 kip ? in (a) 9.64 kN ? m (b) 9.91 kN ? m (a) 18.86 ksi; 1.500 in (b) 21.0 ksi; 0.916 in (a) 2.478 (b) 4.348 (a) 6.728 (b) 18.718 (a) 52.1 kip ? in (b) 80.8 kip ? in (a) 977 N ? m (b) 8.61 mm 145 MPa; 19.758 (a) 1.126 fY (b) 1.587 fY (c) 2.15 fY (a) 5.96 kN ? m; 17.948 (b) 31 kN ? m; 26.98 (a) 43.08 (b) 7.61 kN ? m 671 lb ? in (a) 1.826 kip ? in (b) 22.98 2.32 kN ? m 2.26 kN ? m 5.63 ksi 14.628 68.0 MPa at inner surface 20.28 (a) c 0.75 c (b) 0.221 tYc3 (a) 13.54 kip ? in; 3.088 (b) 17.03 kip ? in; 2.268 (a) 11.08 ksi; 2.848 (b) 8.81 ksi; 1.6618 (a) 40.1 MPa; 0.6538 (b) 50.9 MPa; 0.9178 (a) 2.25 kN ? m; 0.8158 (b) 1.770 kN ? m; 0.9018 59.2 MPa 5.07 MPa 0.944 1.356 1.198 (a) 4.57 kip ? in (b) 4.31 kip ? in (c) 5.77 kip ? in (a) 7.52 ksi (b) 4.618 (a) 70.8 N ? m (b) 8.778 (a) 4.57 ksi (b) 2.96 ksi (c) 5.088 (a) 1009 N ? m (b) 9.078 4.73 MPa at a; 9.46 MPa at b 44.2 MPa at a; 27.6 MPa at b 16.85 N ? m 88.1 kip ? in or 7.34 kip ? ft 1.735 in (a) 12.76 MPa (b) 5.40 kN ? m (b) 0.25%; 1.00%; 4.00% (a) 3cyt (b) 3c2yt2 9.38 ksi 6.37 kip ? in (a) 1105 N ? m at A; 295 N ? m at C (b) 45.0 MPa (c) 27.4 MPa 3.156 127.8 lb ? in volume 201/FREE048/work%0/indd%0/ 3.157 3.158 3.160 3.162 3.C2 3.C5 3.C6 (a) 24.58 (b) 19.378 36.1 mm 8.47 MPa 1.221 Prob 3.44: 2.218 (a) 23.282% (b) 20.853% (c) 20.138% (d) 20.00554% (a) 21.883% (b) 20.484% (c) 20.078% (d) 20.00313% CHAPTER 4.1 4.2 4.3 4.4 4.5 4.6 4.9 4.11 4.12 4.14 4.15 4.17 4.18 4.19 4.21 4.23 4.24 4.25 4.27 4.28 4.29 4.30 4.31 4.32 4.33 4.34 4.37 4.38 4.39 4.40 4.42 4.43 4.44 4.46 4.47 4.48 4.49 4.50 4.51 4.55 4.57 4.59 4.63 4.64 4.65 4.66 4.67 4.68 4.69 4.71 4.72 (a) 22.38 ksi (b) 20.650 ksi (a) 261.6 MPa (b) 91.7 MPa (a) 1.405 kip ? in (b) 3.19 kip ? in 2.38 kN ? m 5.28 kN ? m 4.51 kN ? m 67.8 MPa; 281.8 MPa 15.40 ksi; 210.38 ksi 58.8 kN (a) 8.24 kips (b) 1.332 kips 106.1 N ? m 20.4 kip ? in 4.11 kip ? in 177.8 kN ? m 65.1 ksi (a) 0.602 mm (b) 0.203 N ? m (a) 75.0 MPa; 26.7 m (b) 125.0 MPa; 9.60 m 8.49 Mya3; 12.00 MyEa4 (a) 0.889 h0 (b) 0.949 (a) 1.414 (b) 1.732 (a) 334 ft (b) 0.04648 (a) 1007 in (b) 3470 in (c) 0.013208 (a) 139.6 m (b) 481 m (a) (sx)max (y2 c2)y2rc 1.092 kN ? m 887 N ? m 335 kip ? in 689 kip ? in (a) 66.2 MPa (b) 2112.4 MPa (a) 256.9 MPa (b) 111.9 MPa (a) 22.02 ksi (b) 14.65 ksi 39.8 m 43.7 m 625 ft (a) 212 MPa (b) 215.59 MPa (a) 210 MPa (b) 214.08 MPa 11.73 kN ? m 9.50 kn ? m 33.9 kip ? ft (a) (aluminum) 62.3 MPa; (brass) 62.3 MPa; (steel) 62.3 MPa (b) 33.7 m (a) 222.5 ksi (b) 17.78 ksi (a) 6.15 MPa (b) 28.69 MPa (a) 128 N ? m (b) 142 N ? m (a) 219 MPa (b) 176 MPa (a) 22.8 kip ? in (b) 27.7 kip ? in (a) 12.2 ksi (b) 9.9 ksi (a) 38.4 N ? m (b) 52.8 N ? m (a) 57.6 N ? m (b) 83.2 N ? m (a) 0.521 in (b) 17.50 ft (a) 2.40 kN ? m (b) 3.41 kN ? m (a) 1.778 kN ? m (b) 2.60 kN ? m AN3 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN4 11/24/10 6:24:53 PM user-f494 4.75 4.77 4.78 4.79 4.80 4.81 4.83 4.85 4.86 4.87 4.88 4.91 4.92 4.94 4.96 4.99 4.100 4.102 4.104 4.105 4.106 4.107 4.108 4.109 4.111 4.113 4.114 4.116 4.118 4.119 4.121 4.122 4.124 4.125 4.127 4.128 4.129 4.130 4.131 4.134 4.135 4.137 4.138 4.139 4.141 4.143 4.144 4.145 4.148 4.149 4.150 4.151 4.152 4.153 4.161 4.162 4.163 (a) 3339 kip ? in (b) 4725 kip ? in (a) 29.2 kN ? m (b) 1.500 (a) 27.5 kN ? m (b) 1.443 (a) 4820 kip ? in (b) 1.443 (a) 2840 kip ? in (b) 1.611 1.866 kN ? m 911 N ? m 20.7 kip ? in 212 kip ? in 120.0 MPa 106.4 MPa (a) 106.7 MPa (b) y 231.2 mm, 0, 31.2 mm (c) 24.1 m (a) 13.36 ksi (b) y 21.517 in., 0, 1.517 in (c) 168.8 ft (a) 0.707 rY (b) 6.09 rY 7.29 kN ? m (a) 2212 psi (b) 2637 psi (c) 21061 psi (a) 4.87 ksi (b) 5.17 ksi (a) 112.7 MPa (b) 296.0 MPa (a) (A and B) 28.33 MPa (b) (A) 215.97 MPa; (B) 4.86 MPa 623 lb (a) 288 lb (b) 209 lb (a) 2139.3 MPa (b) 2152.5 MPa 14.40 kN 16.04 mm 0.500 d (a) 2.54 kN (b) 17.01 mm to the right of loads 7.86 kipsw; 9.15 kipsx (a) 1125 kN (b) 817 kN 2.485 in , y , 4.56 in (a) 47.6 MPa (b) 249.4 MPa (c) 9.80 mm below top of section 9.00 kN (a) 30.0 mm (b) 94.5 kN P 75.7 kipsw; Q 87.2 kipsw P 5.98 kipsw; Q 49.0 kipsw (a) 22.80 MPa (b) 0.452 MPa (c) 2.80 MPa (a) 23.37 MPa (b) 218.60 MPa (c) 3.37 MPa (a) 1.149 ksi (b) 0.1479 ksi (c) 21.149 ksi (a) 0.321 ksi (b) 20.107 ksi (c) 0.427 ksi (a) 229.3 MPa (b) 2144.8 MPa (c) 2125.9 MPa (a) 57.8 MPa (b) 256.8 MPa (c) 25.9 MPa (a) 9.598 (b) 77.5 MPa (a) 27.58 (b) 5.07 ksi (a) 10.038 (b) 54.2 MPa (a) 11.38 (b) 15.06 ksi 22.32 ksi 113.0 MPa (a) (A) 31.5 MPa; (B) 210.39 MPa (b) 94.0 mm above point A (a) (A) 22.9 MPa; (B) 8.96 MPa (b) 56.0 mm to the right of point B 0.1638 in 53.9 kips 733 N ? m 1.323 kN ? m 29.1 kip ? in 29.1 kip ? in (a) 12.19 ksi (b) 11.15 ksi (A) 10.77 ksi; (B) 23.22 ksi 60.9 mm volume 201/FREE048/work%0/indd%0/ 4.164 4.167 4.168 4.170 4.171 4.172 4.174 4.175 4.176 4.177 4.178 4.179 4.180 4.183 4.185 4.186 4.192 4.194 4.195 4.197 4.199 4.200 4.202 4.203 4.C1 4.C2 4.C3 4.C4 4.C5 4.C6 4.C7 2148.6 MPa (a) 2154.4 MPa (b) 75.2 MPa 73.2 mm 1128 lb (a) 2172.4 MPa (b) 53.2 MPa (a) 2131.5 MPa (b) 34.7 MPa (a) 3.06 ksi (b) 22.81 ksi (c) 0.529 ksi (a) 245.2 MPa (b) 17.40 MPa (a) 243.3 MPa (b) 14.43 MPa 107.8 N ? m (a) 6.74 ksi (b) 23.45 ksi 1.584 in (a) 232.5 MPa (b) 34.2 MPa (a) 69.3 MPa (b) 258.6 MPa (a) 25.96 ksi (b) 3.61 ksi (a) 26.71 ksi (b) 3.24 ksi 8.82 ksi; 214.71 ksi 4.63 kip ? in (a) 46.9 MPa (b) 18.94 MPa (c) 55.4 m (a) 282.4 MPa (b) 36.6 MPa (a) 9.33 ksi (b) 8.00 ksi (a) 2Py2at (b) 22Pyat (c) 2Py2at (a) 2500 psi (b) 2822 psi (c) 2667 psi (d) 21280 psi (e) 21000 psi (a) (A) 20.5 s1; (B) s1; (C) 2s1; (D) 0.5 s1 (b) 4.333 r1 a mm: sa 50.6 MPa, ss 107.9 MPa; a 14 mm: sa 89.7 MPa, ss 71.8 MPa (a) 111.6 MPa (b) 6.61 mm yY 65 mm, M 52.6 kN ? m, r 43.3; yY 45 mm, M 55.6 kN ? m, r 30.0 m b 308: sA –7.83 ksi, sB –5.27 ksi, sC 7.19 ksi, sD 5.91 ksi; b 1208: sA 1.557 ksi, sB 6.01 ksi, sC 22.67 ksi, sD 24.89 ksi r1 /h 0.529 for 50% increase in smax Prob 4.10: 2102.4 MPa; 73.2 MPa yY 0.8 in.: 76.9 kip ? in., 552 in.; yY 0.2 in.: 95.5 kip ? in., 138.1 in a 0.2 in.: 27.27 ksi, a 0.8 in.: 26.61 ksi For a 0.625 in., s 26.51 ksi CHAPTER 5.1 (b) A to B: V PbyL; M PbxyL B to C: V 2PayL; M Pa(L x)yL 5.2 (b) V w(x 2L)y2; M wx(L x)y2 5.3 (b) A to B: V 2wx; M 2wx2y2 B to C: V 2wa; M 2wa(x ay2) 5.4 (b) V 2w x2y2L; M 2w x3y6L 5.5 (b) A to B: V w(a x); M w(ax x2y2) 5.6 5.7 5.8 5.9 5.11 5.12 5.14 B to C: V 0; M wa2y2 C to D: V w(L x a); M w[a(L x) (L x)2y2] (b) A to B: V w(L 2a)y2; M wx(L 2a)y2 B to C: V w(Ly2 x); M w[(L 2a)x2 (x a)2]y2 C to D: V w(L 2a)y2; M w(L 2a)(L x)y2 (a) 430 lb (b) 1200 lb ? in (a) 300 N (b) 67.5 N ? m (a) 40.0 kN (b) 40.0 kN ? m (a) 120.0 kips (b) 120.0 kip ? ft (a) 85.0 N (b) 21.25 N ? m (a) 900 N (b) 112.5 N ? m AN4 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN5 11/24/10 6:24:54 PM user-f494 5.15 5.16 5.18 5.19 5.21 5.22 5.25 5.26 5.27 5.28 5.30 5.31 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.40 5.41 5.42 5.43 5.46 5.47 5.48 5.49 5.51 5.52 5.54 5.55 5.57 5.58 5.61 5.62 5.63 5.65 5.67 5.69 5.70 5.71 5.72 5.73 5.74 5.76 5.77 5.79 5.80 5.81 5.82 5.83 5.84 5.87 5.88 5.89 5.91 5.92 7.13 MPa 1.013 ksi 139.2 MPa 9.90 ksi 14.17 ksi 116.2 MPa 10.34 ksi |V|max 6.00 kN; |M|max 4.00 kN ? m; smax 14.29 MPa (a) 10.67 kN (b) 9.52 MPa (a) 3.09 ft (b) 12.95 ksi (a) 866 mm (b) 99.2 MPa (a) 819 mm (b) 89.5 MPa (a) 33.3 mm (b) 6.66 mm 1.021 in See 5.1 See 5.2 See 5.3 See 5.4 See 5.5 See 5.6 See 5.7 See 5.8 See 5.9 See 5.10 See 5.15 See 5.16 See 5.18 See 5.19 (a) V w0(L2 3x2)y6L; M w 0(Lx x3yL)y6 (b) 0.0642 w L2 (a) V (w0 Lyp)cos(pxyL); M (w L2yp2) sin(pxyL); (b) w0 L2yp2 |V|max 8.00 kips; |M|max 16.00 kip ? ft; 6.98 ksi |V|max 6.5 kN; |M|max 5.04 kN ? m; 30.3 MPa |V|max 200 kN; |M|max 300 kN ? m; 136.4 MPa |V|max 76 kN; |M|max 67.3 kN ? m; 68.5 MPa |V|max 48 kN; |M|max 12.0 kN ? m; 62.2 MPa |V|max 24.5 kips; |M|max 36.3 kip ? ft; 15.82 ksi |V|max 1150 N; |M|max 221 N ? m; P 500 N; Q 250 N 173.2 mm h 14.27 in h 203 mm b 48.0 mm W27 84 W27 84 W530 66 W530 92 S510 98.2 S15 42.9 12.7 mm C9 15 11.74 in mm W24 68 W610 101 176.8 kN ? m 108.8 kN ? m (a) 6.49 ft (b) W16 31 (a) S15 42.9 (b) W27 84 (a) 1.485 kNym (b) 1.935 m volume 201/FREE048/work%0/indd%0/ 5.94 5.95 5.96 5.97 5.98 5.99 5.101 5.102 5.104 5.105 5.106 5.107 5.108 5.109 5.111 5.114 5.115 5.117 5.119 5.120 5.121 5.122 5.123 5.124 5.126 5.128 5.129 5.130 5.132 5.133 5.134 5.137 5.138 5.139 5.140 5.141 5.143 5.144 5.145 W27 84 123.2% 383 mm 336 mm (a) V 2w0 x w0 x2y2a (w0y2a) Kx aL 2; M 2w0 x2y2 w x3y6a (w0y6a) Kx aL 3; (b) 25w a2y6 (a) V 2w0 x w0 Kx aL1; M 2w x2y2 (w0y2) Kx aL (b) 23w a2y2 (a) V 2w0 Kx aL1 3w0 ay4 1(15w ay4) Kx 2aL 0; M 2(w 0y2) Kx aL 2 3w0 axy4 (15 w ay4) Kx 22aL1 (b) 2w a2y2 (a) V 1.25P P Kx aL P Kx 2aL 0; M 1.25Px P Kx 2aL1 P Kx 2aL1 (b) 0.750Pa (a) V 2P Kx aL 0; M 2P Kx aL1 Pa Kx aL (b) 2Pa (a) V 2P P Kx 2Ly3L 0; M 2Px PLy3 P Kx 2Ly3L1 (PLy3) Kx 2Ly3L (b) 24PLy3 (a) V 21.5x Kx 0.8L Kx 23.2L kN; M 20.75x2 Kx 0.8L1 Kx 3.2L1 kN ? m (b) 600 N ? m (a) V 40 48 Kx 1.5L 60 Kx 3.0L 60 Kx 3.6L kN; M 40x 48 Kx 1.5L1 60 Kx 3.0L1 60 Kx 3.6L1 kN ? m (b) 60.0 kN ? m (a) V 13 3x Kx 3L1 Kx 7L Kx 11L1 kips; M 13x 1.5x2 1.5 Kx 3L 2 Kx 7L1 1.5 Kx 11L kip ? ft (b) 41.5 kip ? ft at point D (a) V 23 9.75 Kx 3L Kx 7L Kx 11L kips; M 23x 9.75 Kx 3L1 Kx 7L1 Kx 11L1 kip ? ft (b) 21.0 kip ? ft at point E (a) V 30 24 Kx 0.75L 224 Kx 1.5L 24 Kx 2.25L 66 Kx 3L kN; M 30x 24 Kx 0.75L1 24 Kx 1.5L1 24 Kx 2.25L1 66 Kx 3L1 kN ? m (b) 87.7 MPa (a) 80.0 kip ? ft at C (b) W14 30 (a) 121.5 kip ? ft at x 6.00 ft (b) W16 40 (a) 0.776 kN ? m at x 1.766 m (b) 120 mm |V|max 15.30 kips; |M|max 38.0 kip ? ft |V|max 89.0 kN; |M|max 178.0 kN ? m |V|max 35.6 kN; |M|max 25.0 kN ? m (a) |V|max 13.80 kN; |M|max 16.14 kN ? m (b) 83.8 MPa (a) |V|max 40.0 kN; |M|max 30.0 kN ? m (b) 40.0 MPa (a) |V|max 3.84 kips; |M|max 3.80 kip ? ft (b) 0.951 ksi (a) h h0 22xyL (b) 60.0 kN (a) h h0 (xyL)1y2 (b) 20.0 kips (a) h h0 [(xyL)(1 xyL)]1y2 (b) 4.44 kipyin (a) h h0 (xyL)3y2 (b) 167.7 mm 1.800 m 1.900 m l1 56.00 ft; l2 4.00 ft d d0 (2xyL)1y3 for ¯ x ¯ Ly2 d d0 [2(L x)yL]1y3 for Ly2 ¯ x ¯ L (a) b0 (1 xyL)2 (b) 160.0 lbyin (a) b0 (1 xyL) (b) 20.8 mm (a) 155.2 MPa (b) 143.3 MPa 193.8 kN (a) 11.16 ft (b) 14.31 in (a) 152.6 MPa (b) 133.6 MPa (a) 4.49 m (b) 211 mm AN5 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN6 11/24/10 6:24:55 PM user-f494 5.146 5.149 5.150 5.151 5.152 5.153 5.156 5.157 5.158 5.159 5.160 5.C4 (a) 25.0 ksi (b) 18.03 ksi (a) 240 mm (b) 150.0 MPa (a) 15.00 in (b) 320 lbyin (a) 30.0 in (b) 12.80 kips (a) 2000 lb (b) 19200 lb ? in |V|max 342 N; |M|max 51.6 N ? m; s 17.19 MPa 73.5 MPa |V|max 30.0 lb; |M|max 24.0 lb ? ft; |s|max 6.95 ksi 6.20 in W250 28.4 7.01 kips For x 13.5 ft: M1 131.25 kip ? ft; M2 156.25 kip ? ft; MC 150.0 kip ? ft 5.C6 Prob 5.112: VA 29.5 kN, Mmax 28.3 kN ? m, at 1.938 m from A volume 201/FREE048/work%0/indd%0/ 6.62 e 0.345a 6.63 (a) e 29.4mm (b) at A, 39.0 MPa at B in AB; 78.0 MPa at B in BD; 104.1 MPa at C 6.64 (a) e 19.06 mm (b) at A; 50.5 MPa at B in AB; 25.3 MPa at B in BD; 59.0 MPa at C 6.67 (a) e 10.22 mm (b) At B, E, G, and J: t 0; 6.68 CHAPTER 6.1 6.2 6.3 6.4 6.5 6.6 6.9 6.10 6.12 6.13 6.15 6.16 6.18 6.19 6.21 6.22 6.23 6.24 6.26 6.28 6.29 6.30 6.32 6.34 6.35 6.36 6.37 6.38 6.40 6.41 6.43 6.44 6.45 6.46 6.48 6.49 6.51 6.52 6.53 6.54 6.57 6.59 6.61 92.6 lb 326 lb 738 N 747 N 193.5 kN 217 kN (a) 7.40 ksi (b) 6.70 ksi (a) 920 kPa (b) 765 kPa (a) 3.17 ksi (a) 2.40 ksi 120.3 kN 14.05 in 88.9 mm (b) h 320 mm; b 97.7 mm 143.3 kips (a) 31.0 MPa (b) 23.2 MPa (a) 1.313 ksi (b) 2.25 ksi 32.7 MPa 3.00 ksi (a) Line at mid-height (b) 1.500 (a) hy4 from neutral axis (b) 1.125 4.28 kN 4.63 kN 189.6 lb (a) 1.583 ksi (b) 7.59 ksi (a) 101.6 MPa (b) 79.6 MPa (a) 41.4 MPa (b) 41.4 MPa (a) 33.7 MPa (b) 75.0 MPa (c) 43.5 MPa (a) 1.167 ksi (b) 0.513 ksi (c) 4.03 ksi (d) 8.40 ksi (a) 18.23 MPa (b) 14.59 MPa (c) 46.2 MPa (a) (b) 1.26 ksi (c) 3.30 ksi (d) 6.84 ksi (e) 7.86 ksi 53.9 kips 20.6 MPa 9.05 mm 0.371 in (a) 23.2 MPa (b) 35.2 MPa (a) 10.76 MPa (b) (c) 11.21 MPa (d) 22.0 MPa (e) 9.35 MPa 1.422 in (a) 2.08 (b) 2.10 (a) 2.25 (b) 2.12 (a) V sin uyprmt (a) 1.323 ksi (b) 1.329 ksi (a) 6.73 MPa (b) 1.515 MPa e 0.714a 6.69 6.70 6.71 6.72 6.75 6.76 6.77 6.78 6.81 6.82 6.83 6.84 6.87 6.88 6.89 6.90 6.92 6.93 6.95 6.96 6.98 6.99 6.C1 6.C2 6.C4 6.C5 At A and H: 41.1 MPa; Just above D and just below F: 68.5 MPa; Just to the right of D or F: 13.71 MPa; Just below D and just above F: 77.7 MPa; At K: 81.1 MPa (a) e 9.12 mm (b) At B, E, G, and J: t 0; Just to the right of A or H: 50.6 MPa; Just below A and just above H: 33.8 MPa; Just above D and just below F: 67.5 MPa; Just to the right of D or E: 16.88 MPa; Just below D and just above F: 84.4 MPa; At K: 88.6 MPa e 1.265 in e 20.2 mm e 6.14 mm e 0.482 in e 2.37 in e 2.21 in and 40.0 mm 40.0 mm 65.9 MPa 106.6 MPa (a) 500 lb; 398 lb ? in (b) 2980 psi (a) 500 lb; 398 lb ? in (b) 6090 psi (maximum) Pyat (maximum) 1.333 Pyat (a) 155.8 N (b) 329 kPa 12.01 ksi 87.3 mm (a) 1.745 ksi (b) 2.82 ksi (a) 146.1 kNym (b) 19.99 MPa (a) 50.9 MPa (b) 62.4 MPa e 3(b2 a2)y(6a 6b h) e 0.433 in (a) h 173.2 mm (b) h 379 mm (a) L 37.5 in.; b 1.250 in (b) L 70.3 in.; b 1.172 in (c) L 59.8 in.; b 1.396 in (a) tmax 2.03 ksi; tB 1.800 ksi (b) 194 psi Prob 6.66: (a) 2.67 in (b) tB 0.917 ksi; tD 3.36 ksi; tmax 4.28 ksi CHAPTER 7.1 7.2 7.3 7.4 7.5 7.6 7.9 7.10 7.11 7.12 7.13 s 5.49 ksi; t 11.83 ksi s 20.521 MPa; t 56.4 MPa s 0.1699 ksi; t 5.10 ksi s 249.2 MPa; t 2.41 MPa (a) 237.08, 53.08 (b) 213.60 MPa, 286.4 MPa (a) 18.48, 108.48 (b) 55.0 ksi, 5.00 ksi (a) 8.08, 98.08 (b) 36.4 MPa (c) 250.0 MPa (a) 226.68, 63.48 (b) 25.0 MPa (c) 30.0 MPa (a) 14.08, 104.08 (b) 17.00 ksi (c) 24.00 ksi (a) 31.78, 121.78 (b) 11.18 ksi (c) 2.00 ksi (a) sx9 22.40 ksi; tx9y9 0.15 ksi, sy9 10.40 ksi (b) sx9 1.95 ksi; tx9y9 6.07 ksi, sy9 6.05 ksi AN6 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN7 11/24/10 6:24:55 PM user-f494 7.15 (a) sx9 9.02 ksi; tx9y9 3.80 ksi, sy9 213.02 ksi 7.17 7.18 7.19 7.21 7.23 7.24 7.25 7.26 7.28 7.30 7.31 7.32 7.33 7.34 7.35 7.37 7.39 7.40 7.41 7.43 7.45 7.46 7.47 7.48 7.50 7.52 7.53 7.55 7.56 7.57 7.59 7.60 7.61 7.62 7.63 7.65 7.66 7.68 7.69 7.71 7.72 7.73 7.74 7.76 7.77 7.78 7.80 7.81 7.82 7.83 7.84 7.87 7.88 7.89 7.90 7.91 (b) sx9 5.34 ksi; tx9y9 29.06 ksi, sy9 29.34 ksi (a) 20.600 MPa (b) 23.84 MPa (a) 346 psi (b) 2200 psi s 24.76 ksi; t 20.467 ksi (a) 47.9 MPa; 102.7 MPa 25.1 ksi, 20.661 ksi; 12.88 ksi 5.12 ksi, 21.640 ksi; 3.38 ksi 12.18 MPa, 248.7 MPa; 30.5 MPa (a) 18.98, 108.98; 18.67 MPa, 2158.5 MPa (b) 88.6 MPa 205 MPa (a) 22.89 MPa (b) 12.77 MPa, 1.226 MPa (a) 237.08, 53.08 (b) 286.4 MPa, 213.6 MPa (a9) 8.08, 98.08; 36.4 MPa (b9) 250.0 MPa (a) 231.08, 59.08 (b) 13.00 ksi, 221.0 ksi (a9) 14.08, 104.08; 17.00 ksi (b9) 24.00 ksi (a) 226.68, 63.48 (b) 25.0 MPa (c) 30.0 MPa (a) 121.78; 31.78 (b) 11.18 ksi (c) 2.00 ksi (a) sx9 22.40 ksi; tx9y9 0.15 ksi, sy9 10.40 ksi (b) sx9 1.95 ksi; tx9y9 6.07 ksi, sy9 6.05 ksi (a) sx9 9.02 ksi; tx9y9 3.80 ksi, sy9 213.02 ksi (b) sx9 5.34 ksi; tx9y9 29.06 ksi, sy9 29.34 ksi (a) 20.600 MPa (b) 23.84 MPa (a) 346 psi (b) 2200 psi s 24.76 ksi; t 20.467 ksi (a) 47.9 MPa (b) 102.7 MPa 25.1 ksi, 20.661 ksi; 12.88 ksi 5.12 ksi, 21.640 ksi; 3.38 ksi 12.18 MPa, 248.7 MPa; 30.5 MPa (a) 18.98, 108.98; 2158.5 MPa, 18.67 MPa (b) 88.6 MPa 205 MPa (a) 22.89 MPa (b) 12.77 MPa, 1.23 MPa (a) 28.66 MPa (b) 17.00 MPa, 23.00 MPa 24.68, 114.68; 72.9 MPa, 27.1 MPa uy2, (u p)y2; s0 s0 cos u, s0 s0 cos u 2308, 608; 13 t0, 13 t0 16.58 # u # 110.18 25.18 # u # 132.08 2120.0 MPa # txy # 120.0 MPa 2141.4 MPa # txy # 141.4 MPa (a) 33.78, 123.78 (b) 18.00 ksi (c) 6.50 ksi (b) |txy| 1sx sy smax smin (a) 11.00 ksi (b) 10.00 ksi (a) 94.3 MPa (b) 105.3 MPa (a) 100.0 MPa (b) 110.0 MPa (a) 6.50 ksi (b) 9.00 ksi (c) 7.00 ksi (a) 85.0 MPa (b) 85.0 MPa (c) 95.0 MPa (a) 97.5 MPa (b) 85.0 MPa (c) 120.0 MPa 2.00 ksi; 9.33 ksi (a) 8.00 ksi (b) 4.50 ksi (a) 40.0 MPa (b) 72.0 MPa 240.0 MPa; 130.0 MPa (a) 45.7 MPa (b) 92.9 MPa (a) 1.228 (b) 1.098 (c) Yielding occurs (a) 1.083 (b) Yielding occurs (c) Yielding occurs (a) 1.287 (b) 1.018 (c) Yielding occurs (a) 1.119 (b) Yielding occurs (c) Yielding occurs 52.9 kips 63.0 kips Rupture will occur Rupture will occur No rupture volume 201/FREE048/work%0/indd%0/ 7.92 7.94 7.95 7.96 7.98 7.100 7.102 7.103 7.104 7.105 7.106 7.108 7.109 7.110 7.112 7.113 7.114 7.115 7.116 7.118 7.120 7.121 7.124 7.125 7.126 7.127 7.128 7.129 7.131 7.132 7.133 7.135 7.136 7.137 7.139 7.140 7.141 7.143 7.146 7.147 7.152 7.153 7.154 7.155 7.156 7.157 7.158 7.160 7.161 7.162 7.164 7.165 7.167 7.169 7.C1 Rupture will occur 68.49 MPa 196.9 N ? M 50.0 MPa smax 72.7 MPa; tmax 36.4 MPa 166.5 psi (a) 202 psi (b) 0.0353 in (a) 95.7 MPa (b) 1.699 mm smax 89.0 MPa; tmax 44.5 MPa 12.55 mm smax 136.0 MPa; tmax 68.0 MPa smax 78.5 MPa; tmax 39.3 MPa 43.3 ft smax 16.62 ksi; tmax 8.31 ksi (a) 33.2 MPa (b) 9.55 MPa 2.17 MPa 22208 # b # 27.08 and 63.08 # b # 117.08 (a) 44.2 MPa (b) 15.39 MPa 56.88 474 psi smax 45.1 MPa; tmax (in-plane) 9.40 MPa smax 45.1 MPa; tmax (in-plane) 7.49 MPa (a) 3.15 ksi (b) 1.993 ksi (a) 1.486 ksi (b) 3.16 ksi (a) 5.64 ksi (b) 282 psi (a) 2.28 ksi (b) 228 psi Px9 2450 m; Py9 199.8 m; gx9y9 375 m Px9 115.0 m; Py9 285 m; gx9y9 25.72 m Px9 36.7 m; Py9 283 m; gx9y9 227 m Px9 2450 m; Py9 199.8 m; gx9y9 375 m Px9 115.0 m; Py9 285 m; gx9y9 25.72 m Px9 36.7 m; Py9 283 m; gx9y9 227 m (a) 233.78, 56.38; 2420 m, 100 m, 160 m (b) 520 m (c) 580 m (a) 230.18, 59.98; 702 m, 298 m, 500 m (b) 403 m (c) 1202 m (a) 226.68, 64.48; 2150 m, 750 m, 2300 m (b) 900 m (c) 1050 m (a) 7.88, 97.88; 56.6 m, 243 m, (b) 186.8 m (c) 243 m (a) 31.08, 121.08; 513 m, 87.5 m, (b) 425 m (c) 513 m (a) 37.98, 127.98; 257.5 m, 2383 m, (b) 325 m (c) 383 m (a) 2300 1026 inyin (b) 435 1026 inyin, 2315 1026 inyin; 750 1026 in/in (a) 30.08, 120.08; 560 1026 inyin, 2140 1026 inyin (b) 700 1026 inyin 1.421 MPa 1.761 MPa 222.58, 67.58; 426 m, 2952 m, 2224 m 229.8 MPa; 270.9 MPa P 69.6 kips; Q 30.3 kips P 34.8 kips; Q 38.4 kips 16.58 kN (a) 18.48 (b) 16.67 ksi 08, 908; s0, 2s0 (a) 39.0 MPa (b) 45.0 MPa (c) 39.0 MPa (a) 1.286 (b) 1.018 (c) Yielding occurs smax 68.6 MPa; tmax 34.3 MPa 3.43 ksi (compression) 415 1026 inyin Prob 7.14: (a) 256.2 MPa, 86.2 MPa, 238.2 MPa (b) 245.2 MPa, 75.2 MPa, 53.8 MPa Prob 7.16: (a) 24.0 MPa, 2104.0 MPa, 21.50 MPa (b) 219.51 MPa, 260.5 MPa, 260.7 MPa AN7 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN8 11/24/10 6:24:56 PM user-f494 7.C4 Prob 7.93: Rupture occurs at t0 3.67 ksi 7.C6 Prob 7.138: (a) 221.68, 68.48; 279m, 2599m, 160.0m (b) 877m (c) 877m 7.C7 Prob 7.142: (a) 11.38, 101.38; 310m, 50.0m, (b) 260m (b) 310m 7.C8 Prob 7.144: Px 253m; Py 307; gxy 2893 Pa 727m; Pb 2167.2; gmax 2894 Prob 7.145: Px 725m; Py 275.0; gxy 173.2 Pa 734m; Pb 284.3; gmax 819 CHAPTER 8.1 8.2 8.3 8.4 8.7 8.8 8.9 8.11 8.12 8.14 8.15 8.16 8.17 8.19 8.22 8.25 8.26 8.27 8.28 8.29 8.30 8.31 8.32 8.34 8.35 8.37 8.38 8.39 8.40 8.42 8.43 8.46 8.47 8.48 8.49 8.50 8.51 8.53 8.55 8.56 8.57 8.59 8.61 8.62 (a) 10.69 ksi (b) 19.18 ksi (c) not acceptable (a) 10.69 ksi (b) 13.08 ksi (c) acceptable (a) 94.6 MPa (b) 93.9 MPa (c) acceptable (a) 91.9 MPa (b) 95.1 MPa (c) acceptable (a) W690 125 (b) 118.2 MPa, 34.7 MPa (c) 122.3 MPa (a) W310 38.7 (b) 147.5 MPa, 18.18 MPa (c) 140.2 MPa (a) 134.3 MPa (b) 132.4 MPa (a) 19.39 ksi (b) 20.7 ksi (a) 17.90 ksi (b) 17.08 ksi (a) 126.0 MPa (b) 115.9 MPa at midspan, 105.1 MPa at B and C 873 lb 1.578 in 1.698 in BC: 21.7 mm; CD: 33.4 mm (a) H: 6880 psi, K: 6760 psi (b) H: 7420 psi, K: 7010 psi 41.3 mm 44.8 mm 37.0 mm 43.9 mm 1.822 in 1.792 in (a) 211.07 ksi; (b) 2.05 ksi; 2.15 ksi (c) 15.17 ksi; (a) 11.87 ksi; (b) 2.05 ksi, 2.15 ksi (c) 27.78 ksi; (a) 232.5 MPa; 14.06 MPa (b) 2126.2 Mpa; (a) 237.9 MPa; 14.06 MPa (b) 2131.6 MPa; (a) 4.79 ksi; 3.07 ksi (b) 22.57 ksi; 3.07 ksi 214.98 MPa; 17.29 MPa 23.96 ksi; 0.938 ksi (a) 79.6 MPa; 7.96 MPa (b) 0; 13.26 MPa (a) 4.3 MPa, 293.4 MPa; 12.18, 102.18 (b) 48.9 MPa (a) 30.0 MPa, 230.0 MPa; 30.0 MPa (b) 7.02 MPa, 296.0 MPa; 51.5 MPa (a) 3.47 ksi; 1.042 ksi (b) 7.81 ksi; 0.781 ksi (c) 12.15 ksi; (a) 18.39 MPa; 0.391 MPa (b) 21.3 MPa; 0.293 MPa (c) 24.1 MPa; (a) 27.98 MPa; 0.391 MPa (b) 25.11 MPa; 0.293 MPa (c) 22.25 MPa; 30.1 MPa, 20.62 MPa; 28.28, 81.88; 15.37 MPa 0.12 MPa, 251.4 MPa; 2.88, 92.88; 25.8 MPa 1506 psi, 24150 psi; 31.18, 121.18; 2830 psi (a) 86.5 MPa; (b) 57.0 MPa; 9.47 MPa 5.59 ksi, 212.24 ksi; 8.91 ksi 5.55 ksi, 216.48 ksi; 11.02 ksi 12.94 MPa, 21.33 MPa; 7.13 MPa (a) 51.0 kN (b) 39.4 kN 12.2 MPa, 212.2 MPa; 12.2 MPa (a) 12.90 ksi, 20.32 ksi; 28.98, 81.18; 6.61 ksi (b) 6.43 ksi 26.43 ksi; 6458; 6.43 ksi volume 201/FREE048/work%0/indd%0/ 8.64 8.65 8.68 8.69 8.71 8.72 8.74 8.76 8.C3 8.C5 0.48 ksi, 44.7 ksi; 22.6 ksi W10 15 (b) 23.5 ksi; 4.89 ksi (c) 23.2 ksi 46.5 mm (a) 11.06 ksi; (b) 20.537 ksi; 1.610 ksi (c) 212.13 ksi; P(2R 4ry3)ypr (a) 3.79 ksi, 28.50 ksi; 33.78, 123.78 (b) 6.15 ksi 25.2 MPa; 20.87 MPa; 13.06 MPa (a) 7.50 MPa (b) 11.25 MPa (c) 56.38; 13.52 MPa Prob 8.18: 37.3 mm Prob 8.45: s 6.00 ksi; t 0.781 ksi CHAPTER 9.1 (a) y 2(w 0yEIL) (L3 x2y6 Lx4y12 x5y120) (b) 11 w0 L 4y120EIw (c) w0 L3y8EI c 9.2 (a) y 2(wy24EI) (x4 4L3 x 3L 4) (b) wL 4y8EIw (c) wL3y6EI a 9.3 (a) y 2(Px2y6EI)(3L x) (b) PL 3y3EIw (c) PL2y2EI c 9.4 (a) y (M0y2EI)(L x)2 (b) M0 L2y2EIx (c) M0 LyEI c 9.6 (a) y (wy72EI)(3x4 16ax3) (b) 10wa 4y9EIw (c) 4wa3y3EI c 9.8 (a) y (w 0yEIL)(L2 x3y48 x5y120 L xy80) 9.9 9.10 9.11 9.12 9.13 9.16 9.17 9.18 9.19 9.20 9.23 9.24 9.25 9.26 9.27 9.28 9.29 9.31 9.33 9.34 9.35 9.36 9.37 9.38 9.41 9.42 (b) w L 4y256EIw (c) w0 L3y120EI a (a) 2.79 1023 rad c (b) 1.859 mmw (a) 3.92 1023 rad c, (b) 0.1806 in.w (a) 0.06415M0 L2yEI at x 0.423L (b) 45.3 kN ? m (a) 0.00652w0 L 4yEI at x 0.519L (b) 0.229 in.w 0.398 in.w (a) (PyEI)(ax2y2 aLxy2 a3y6) (b) 1.976 mmw (a) y w0 (x6 15L2 x4 25L3 x3 11L5 x)y360EIL (b) 11w0 L3y360EI c (c) 0.00916 w L 4yEIw (a) y (w0yEIL2)(x6y90 Lx5y30 L3 x3y18 L5 xy30) (b) w0 L3y30EI c (c) 61w L 4y5760EIw 3M0y2Lx 3wLy8x 9.75 kNx 4.00 kipsx R B 9M0y8Lx; MA M0y8, MC2 27M0y16, MC1 9M0y16 R B 5Py16x; MA 23PLy16, MC 5PLy32, MB R A 7wLy128x; MC 0.02734wL2 , MB 20.07031wL2, M 0.02884wL2 at x 0.555 L R A 21w0Ly160x, RB 19w0Ly160x; MB 20.0354w0L2, MC 0.0240w0 L2 , M 0.0317w L2 at x 0.362L R B 17wLy64x; yC wL 4y1024EI R B 5M0y6Lw; yD 7M0 L2y486EIx R A w0 Ly4x, MA 20.0521w0 L2 , MC 0.03125w0 L2 MA PLy8 l, MB PLy8 i MC PLy8 (a) y (M0y6EIL) {x3 3L Kx aL (3b2 L2) x} (b) M0 (3b2 L2)y6EIL c (c) M0 ab (b a)y3 EILx (a) y (Py6EIL) {bx3 L Kx aL b(L2 b2)x} (b) Pb (L2 b2)y6EIL c (c) Pa2 b2y3 EILw (a) (PyEI) {x3y3 Kx aL 3y6 3ax2y2} (b) 5Pa2y2EI c (c) 7Pa3y2EIw (a) y (PyEI) {2x3y6 Kx aL 3y6 5a2 xy2 7a3y2} (b) 5Pa2y2EI a (c) 7Pa3y2EIw (a) y (wyEI) {ax3y6 x4y24 Kx aL 4y24 Kx 3aL 4y24 5wa3 xy6} (b) 23wa4y24EIw (a) y (wy24EI) {2x4 Kx Ly2L Kx LL Lx3 3L Kx LL L3 xy16} (b) wL 4y768 EIx (c) 5wL 4y256EIw AN8 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN9 11/24/10 6:24:57 PM user-f494 9.44 (a) y w [16x5 32 Kx Ly2L 40 Lx4 40 L2 x3 9.45 9.47 9.48 9.49 9.50 9.52 9.53 9.54 9.56 9.57 9.58 9.59 9.60 9.61 9.62 9.65 9.66 9.67 9.68 9.70 9.72 9.73 9.75 9.76 9.77 9.79 9.81 9.82 9.84 9.85 9.86 9.87 9.88 9.90 9.91 9.93 9.94 9.95 9.96 9.97 9.98 9.101 9.102 9.103 9.104 9.105 9.108 9.109 9.110 9.111 9.113 9.114 9.115 9.117 9.118 9.119 9.121 9.123 9.124 15L x]y960 EIL (b) 3w L 4y640EIw (a) 2.49 1023 rad c (b) 1.078 mmw (a) 5.40 1023 rad c (b) 3.06 mmw (a) 14.00 1023 rad c (b) 0.340 in.w (a) 9M0y8Lx (b) M0 L2y128 EIw (a) 5Py16x (b) 7PL3y168 EIw (a) 2Py3x (b) 5PL3y486 EI (a) 11.54 kNx (b) 4.18 mmw (a) 5.58 kipsx (b) 0.1065 in.w (a) 41.25 kNx (b) 0.705 mmw (a) 20 Py27x; 4PLy27 l (b) 5PL3y1296 EIw (a) wLy32x; wL2y192 l (b) wL 4y768 EIw 1.401 mmw at x 0.857 m 0.281 in.w at x 8.40 ft 3.07 mmw at x 0.942 m 0.341 in.w at x 3.34 ft PL2yEI a; 17PL3y24EIw 5PL2y8EI c; 7PL3y16EIw PL2y24EI c; PL3y48EIw wL3y48EI a; wL 4y384EIx 5PL3y162EIw; (b) PL2y9EI c (a) wL 4y384EIw; (b) 6.32 1023 rad c; 5.55 mmw 7.91 1023 rad a; 0.340 in.w 6.98 1023 rad a; 0.1571 in.w (a) 0.601 1023 rad c; (b) 3.67 mmw R A M0y2Lx; R B 5M0y2Lx; RC 3M0yLw (a) 41wLy128x (b) 23wLy128x; 7wL2y128 i (a) 3M0(L2 a2)y2L3x (b) 3M0(L2 a2)y2L3 w; M0(L2 3a2)y2L2 l 3M0y2Lw; M0y4 l 121.5 Nym (a) 5.06 1023 rad c (b) 0.0477 in.w 0.210 in.w (a) 10.54 mmw (b) 23.4 mmw 43.9 kN 5.63 kNw 0.278 in.w 9.31 mmw (a) PL2y2EI a (b) PL3y3EIw (a) M0 LyEI c (b) M0 L2y2EIw (a) w0 L3y24EI a (b) w0 L 4y30EIw (a) wL3y6EI a (b) wL 4y8EIw (a) 5.84 1023 rad c (b) 0.300 in.w (a) 7.15 1023 rad a (b) 17.67 mmw (a) 16.56 1023 rad c (b) 0.379 in.w (a) 2.55 1023 rad c (b) 6.25 mmw (a) 11PL2y24EI c (b) 11PL3y36EIw (a) 3.43 1023 rad a (b) 6.66 mmw (a) PL2y16EI c (b) PL2y48EIw (a) 5PL2y32EI c (b) 19PL3y384EIw (a) wa2(3L 2a)y12EI c (b) wa2(3L2 2a2)y48EIw (a) M0(L 2a)y2EI c (b) M0(L2 4a2)y8EIw (a) PL2y32EI c (b) PL3y128EIw (a) 5Pa2y8EI c (b) 3Pa3y4EIw (a) 5.21 1023 rad c (b) 21.2 mmw (a) 4.71 1023 rad c (b) 5.84 mmw (a) 4.50 1023 rad c (b) 8.26 mmw 3.84 kNym 0.211 L 0.223 L volume 201/FREE048/work%0/indd%0/ 9.125 9.127 9.128 9.129 9.130 9.131 9.134 9.135 9.137 9.138 9.139 9.140 9.142 9.144 9.145 9.146 9.148 9.149 9.150 9.151 9.153 9.154 9.155 9.156 9.157 9.158 9.160 9.162 9.163 9.165 9.166 9.168 9.C1 9.C2 9.C3 9.C5 9.C7 (a) 5PL3y768EIw (b) 3PL2y128EI c (a) 5w0 L 4y768EIw (b) 7w0 L3y360EI c (a) 5wL 4y768EIw (b) 3wL3y128EI c (a) 8.74 1023 rad c (b) 15.10 mmw (a) 7.48 1023 rad c (b) 5.35 mmw (a) 5.31 1023 rad c (b) 0.204 in.w (a) M0(L 3a)y3EI c (b) M0 a(2L 3a)y6EIw (a) 2.34 1023 rad c (b) 0.1763 in.w (a) 5.33 1023 rad a (b) 0.01421 in.w (a) 3.61 1023 rad c (b) 0.960 mmx (a) 17PL3y972EIw (b) 19PL3y972EIw (a) 9wL3y256EI c (b) 7wL3y256EI a (c) 5wL 4y512EIw 0.00652w L 4yEI at x 0.519L 0.212 in.w at x 5.15 ft 1.841 mm 0.1049 in 5Py16x 7wLy128x M0y8Lx R A 3Py32w; R B 13Py32x; RC 11Py16x 65.2 kNx; MA 0; MD 58.7 kN ? m; MB 282.8 kN ? m 10.18 kipsx; MA 287.9 kip ? ft; MD 46.3 kip ? ft; MB 48EIy7L3 144EIyL3 (a) y w (2x5 5Lx4 10L x 7L5)y120EIL (b) 7w L 4y120EIx (c) w0 L3y12EI c (a) 0.01604 M0 L2yEI at x 0.211L (b) 21.5 ft wLy2x, wL2y12 l; M w[6x (L x) L2]y12 (a) 0.712 1023 rad a (b) 1.068 mmx (a) 10.86 kNx; 1.942 kN ? m l (b) 1.144 kNx; 0.286 kN ? m i (a) 5.20 1023 rad a (b) 10.85 mmw (a) 4.27 1023 rad c (b) 0.1080 in.x (c) 0.206 in.w (a) 6.87 mmx (b) 46.3 kNx Prob 9.74: 5.56 1023 rad c; 2.50 mmw a ft: (a) 3.14 1023 rad c, 0.292 in.w; (b) 0.397 in w at 11.27 ft to the right of A x 1.6 m: (a) 7.90 1023 rad c, 8.16 mmw; (b) 6.05 1023 rad c, 5.79 mmw; (c) 1.021 1023 rad c, 0.314 mmw (a) a ft: 1.586 1023 rad c; 0.1369 in.w; (b) a 1.0 m: 0.293 1023 rad c, 0.479 mmw x 2.5 m: 5.31 mmw; x 5.0 m: 12.28 mmw CHAPTER 10 10.1 10.2 10.3 10.4 10.6 10.8 10.9 10.10 10.11 10.13 10.15 10.17 10.18 10.19 10.21 kL KyL KyL 2kLy9 k 4.91 kNym 8KyL (a) 6.65 lb (b) 21.0 lb 305 kN (a) 6.25% (b) 12.04 kips 1.421 164.0 kN 69.6 kips 335 kips 2.44 (1) 319 kg; (2) 79.8 kg; (3) 319 kg; (4) 653 kg AN9 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN10 11/24/10 6:24:58 PM user-f494 10.22 (a) 2.55 (b) (2):28.3 mm; (3): 14.14 mm; (4):16.72 mm; 10.23 10.26 10.27 10.28 10.29 10.30 10.31 10.33 10.35 10.36 10.37 10.39 10.40 10.41 10.43 10.45 10.46 10.47 10.48 10.49 10.51 10.52 10.53 10.56 10.57 10.58 10.59 10.60 10.62 10.64 10.65 10.68 10.69 10.70 10.71 10.72 10.74 10.75 10.77 10.78 10.79 10.80 10.82 10.84 10.85 1086 10.87 10.88 10.89 10.91 10.93 10.94 10.95 10.97 10.98 10.99 10.101 10.102 10.105 (5): 20.0 mm (a) BC: 4.20 ft; CD: 1.05 ft (b) 4.21 kips 29.5 kips 657 mm (a) 1y2.00 (b) d 28.3 mm; b 14.15 mm (a) 1.658 mm (b) 78.9 MPa (a) 4.32 mm (b) 44.4 MPa (a) 0.410 in (b) 14.43 ksi (a) 0.0399 in (b) 19.89 ksi (a) 13.29 kips (b) 15.50 ksi (a) 370 kN (b) 104.6 MPa (a) 224 kN (b) 63.3 MPa (a) 235 kN (b) 149.6 MPa (a) 151.6 kN (b) 109.5 MPa 58.98F (a) 38.6 kips (b) 0.628 (a) 189 kN (b) 229 kN (a) 147 kN (b) 174 kN 2.16 m 1.302 m (a) 13.68 ft (b) 7.83 ft 2.125 in 2.625 in W200 26.6 3.09 (a) 220 kN (b) 841 kN (a) 86.6 kips (b) 88.1 kips (a) 59.6 kips (b) 31.9 kips (a) 1530 kN (b) 638 kN (a) 231 mm (b) 376 mm (c) 714 mm 35.9 kN 76.3 kips 144.1 kips 39.9 kips 107.7 kN 1.615 in mm 123.1 mm 6.53 in W250 67 W200 46.1 W14 82 3y8 in (a) 30.1 mm (b) 33.5 mm L89 64 12.7 (a) (dead) 433 kN; (live) 321 kN (b) (dead) 896 kN; (live) 664 kN 56.1 kips W310 74 5y16 in 76.7 kN (a) 329 kN (b) 280 kN (a) 18.26 kips (b) 14.20 kips (a) 21.1 kips (b) 18.01 kips (a) 0.0987 in (b) 0.787 in (a) 11.89 mm (b) 6.56 mm 7.78 mm 45.6 in 5.48 m 4.81 m 12 mm volume 201/FREE048/work%0/indd%0/ 10.106 10.107 10.108 10.109 10.110 10.113 10.114 10.115 10.116 10.117 10.118 10.120 10.121 10.123 10.125 10.126 10.128 10.C1 10.C2 10.C3 10.C4 15 mm 48.2 mm 44.3 mm 1y4 in 3y16 in W14 145 W14 68 W250 58 W200 59 ka2y2l 0.384 in DT p2 b2y12L2a 2.77 kN 95.5 kips (a) 4.84 mm (b) 135.7 Mpa W10 54 W8 40 r mm: 9.07 kN r 16 mm: 70.4 kN b 1.0 in.: 3.85 kips b 1.375 in.: 6.07 kips h 5.0 m: 9819 kg h 7.0 m: 13,255 kg P 35 kips: (a) 0.086 in.; (b) 4.69 ksi P 55 kips: (a) 0.146 in.; (b) 7.65 ksi 10.C6 Prob 10.113: Pall 282.6 kips Prob 10.114: Pall 139.9 kips CHAPTER 11 11.1 11.2 11.4 11.5 11.6 11.8 11.9 11.10 11.11 11.14 11.15 11.16 11.18 11.19 11.22 11.23 11.24 11.25 11.26 11.28 11.29 11.30 11.32 11.34 11.36 11.38 11.40 11.41 11.42 11.43 11.44 11.45 11.48 11.49 (a) 177.9 kJym3 (b) 712 kJym3 (c) 160.3 kJym3 (a) 436 in ? lbyin3 (b) 64.7 in ? lbyin3 (c) 6.40 in ? lbyin3 (a) 21.6 kJym3 (b) 336 kJym3 (c) 163.0kJym3 (a) 1296 kJym3 (b) 90 MJym3 (a) 58.0 in ? lbyin3 (b) 20 in ? kipyin3 (a) 150 KJym3 (b) 63 MJym3 (a) 176.2 in ? lb (b) AB: 11.72 in ? lbyin3; BC: 5.65 in ? lbyin3 (a) 12.18 J (b) AB: 15.83 KJym3; BC 38.6 KJym3 (a) 168 in ? lb (b) CD: 882 in ? lbyin3; EF: 5.65 in ? lbyin3 13.73 mm (a) 3.28 (b) 4.25 102.7 in ? lb 1.500 P2 lyEA 1.398 P2 lyEA 1.767 kip ? in 59.8 J w2 L5y40EI w2 L5y240EI M02 (a3 b3)y6EIL2 1048 J 670 J 388 J 15 UyV 14.70 J (a) 2.33 (b) 2.02 22.65 MPa , sz , 122.65 MPa U (2M02 LyEbd3)(1 3Ed2y10GL2) U (Q2y4pGL) ln (R 2yR1) 9.12 lb 25.5 ftys 4.76 kg 5.63 kg (a) 21.0 kN (b) 172 MPa (c) 8.61 mm (a) 7.66 kN (b) 316 MPa (c) 23.5 mm AN10 www.EngineeringEBooksPdf.com bee80288_ans_AN1-AN12.indd Page AN11 11/24/10 6:24:59 PM user-f494 11.50 11.52 11.53 11.54 11.56 11.58 11.59 11.61 11.62 11.63 11.65 11.66 11.68 11.69 11.71 11.73 11.74 11.76 11.77 11.78 11.80 11.82 11.83 11.85 11.86 11.88 11.89 11.90 11.91 11.93 11.94 11.95 11.96 11.98 11.99 11.100 11.09 ftys (a) 15.63 mm (b) 83.8 N ? m (c) 208 MPa (a) 23.6 mm (b) 64.4 N ? m (c) 157.6 MPa (a) 0.1061 in (b) 20.2 ksi (b) 7.12 Pa2(a L)y3EIw Pa2 b2y 3EIw M0(a3 b3)y 3EIL2 c 3Pa3y4EIw 3PL3y16EIw M0 Ly16EI c 32.4 in 386 mm 2.558 3.375 PlyEAw 0.0650 in.w 0.366 in.w 1.111 mmw (a) and (b) P2 L3y6EI PM0 L2y2EI M02 Ly2EI (a) and (b) P2 L3y48EI PM0 L2y8EI M02 Ly2EI (a) and (b) P2 L3y48EI (a) and (b) 5M02 Ly4EI 5PL3y48EIw 3PL2y8EI a 7wL3y48EI a PL3y96EIx wL3y192EI a PL2y48EI a 7.07 1023 rad c 0.317 in.w 3.80 mmw 7.25 mmw 5.12 mmw 2.07 1023 rad a Ply2EA z; 3.80 PlyEAw y ; 2.80PlyEAx volume 201/FREE048/work%0/indd%0/ 11.103 11.104 11.105 11.106 11.107 11.109 11.111 11.112 11.113 11.114 11.117 11.118 11.119 11.120 11.125 11.128 11.129 11.130 11.132 11.134 11.C2 11.C3 11.C4 11.C5 11.C6 0.233 in.w 0.1504 in y (a) 2Pl3y3EI y (b) Pl2y6EI a (a) 5Pl3y3EI y (b) 2PL2yEI l (a) Pl3yEIx (b) 3Pl2yEI a (a) PR3y2EI y (b) pPR3y4EIw 3M0y2Lx; M M0 (3xy2 1) 5Py16x; MA 23PLy16, MC 55PLy32, MB 41wLy128x; MA 0; M 0.0513wL2 at x 548Ly128; MB 27wL2y128 3M0 b (L a)y2L3 x; M 3M0 b (L a) xy2L3 M0 KL aL Py(1 cos3 u) 3Py4 7Py8 0.652P 24.7 mm 11.57 mmw 3.128 0.0447 in.w PL2y6EI l A: wLy6w; B: 3wLy4x; C: 5wLy12x (a) a 15 in.: sD 17.19 ksi, sC 21.0 ksi; a 45 in.: sD 36.2 ksi, sC 14.74 ksi (b) a 18.34 in., s 20.67 ksi (a) L 200 mm: h 2.27 mm; L 800 mm: h 1.076 mm (b) L 440 mm: h 3.23 mm a 300 mm: 1.795 mm, 179.46 MPa; a 600 mm: 2.87 mm, 179.59 MPa a m: (a) 30.0 J; (b) 7.57 mm, 60.8 J a m: (a) 21.9 J; (b) 8.87 mm, 83.4 J a 20 in: (a) 13.26 in.; (b) 99.5 kip ? in.; (c) 803 lb a 50 in: (a) 9.46 in.; (b) 93.7 kip ? in.; (c) 996 lb AN11 www.EngineeringEBooksPdf.com This page intentionally left blank www.EngineeringEBooksPdf.com bee80288_ibc.indd Page 10/26/10 2:20:44 PM user-f499 /Volumes/201/MHDQ251/bee80288_disk1of1/0073380288/bee80288_pagefiles Reactions at Supports and Connections for a Two-Dimensional Structure Support or Connection Reaction Reactions at Supports and Connections for a Three-Dimensional Structure Number of Unknowns F F Rocker Rollers Frictionless surface Force with known line of action Ball Force with known line of action (one unknown) Frictionless surface Short cable Short link Force with known line of action (one unknown) Cable Fy Force with known line of action Fz Roller on rough surface 90º Two force components Wheel on rail Collar on frictionless rod Frictionless pin in slot Fy Force with known line of action Fx Fz or Three force components Rough surface Ball and socket Frictionless pin or hinge Rough surface a Force of unknown direction Mx or Fz a Fixed support My Fy Universal joint Fy Fx Three force components and one couple Mz Fx Three force components and three couples Fixed support Force and couple The first step in the solution of any problem concerning the equilibrium of a rigid body is to construct an appropriate free-body diagram of the body As part of that process, it is necessary to show on the diagram the reactions through which the ground and other bodies oppose a possible motion of the body The figures on this and the facing page summarize the possible reactions exerted on two- and three-dimensional bodies Fz Mx (My) Fy (Mz) Hinge and bearing supporting radial load only Fz Two force components (and two couples) (My) Fy (Mz) Pin and bracket www.EngineeringEBooksPdf.com ISBN: 0073380288 Author: Beer, Johnston, Dewolf, and Mazurek Title: MECHANICS OF MATERIALS Back endsheets Color: Pages: 2, Hinge and bearing supporting axial thrust and radial load Fz Fx Three force components (and two couples) bee80288_ibc.indd Page 10/26/10 2:20:44 PM user-f499 /Volumes/201/MHDQ251/bee80288_disk1of1/0073380288/bee80288_pagefiles Reactions at Supports and Connections for a Two-Dimensional Structure Support or Connection Reaction Reactions at Supports and Connections for a Three-Dimensional Structure Number of Unknowns F F Rocker Rollers Frictionless surface Force with known line of action Ball Force with known line of action (one unknown) Frictionless surface Short cable Short link Force with known line of action (one unknown) Cable Fy Force with known line of action Fz Roller on rough surface 90º Two force components Wheel on rail Collar on frictionless rod Frictionless pin in slot Fy Force with known line of action Fx Fz or Three force components Rough surface Ball and socket Frictionless pin or hinge Rough surface a Force of unknown direction Mx or Fz a Fixed support My Fy Universal joint Fy Fx Three force components and one couple Mz Fx Three force components and three couples Fixed support Force and couple The first step in the solution of any problem concerning the equilibrium of a rigid body is to construct an appropriate free-body diagram of the body As part of that process, it is necessary to show on the diagram the reactions through which the ground and other bodies oppose a possible motion of the body The figures on this and the facing page summarize the possible reactions exerted on two- and three-dimensional bodies Fz Mx (My) Fy (Mz) Hinge and bearing supporting radial load only Fz Two force components (and two couples) (My) Fy (Mz) Pin and bracket Hinge and bearing supporting axial thrust and radial load www.EngineeringEBooksPdf.com ISBN: 0073380288 Author: Beer, Johnston, Dewolf, and Mazurek Title: MECHANICS OF MATERIALS Back endsheets Color: Pages: 2, Fz Fx Three force components (and two couples) ... produced the manuscript of the first edition of Mechanics for Engineers The second edition of Mechanics for Engineers and the first edition of Vector Mechanics for Engineers found Russ Johnston at... dilatation Modulus of elasticity Frequency; function Force Factor of safety Modulus of rigidity; shear modulus Distance; height Force Points Moment of inertia Product of inertia Polar moment of inertia... It follows from Eq (1.6) that the magnitude of the resultant of the distributed internal forces is # dF # s dA A But the conditions of equilibrium of each of the portions of rod shown in Fig