Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Recommendations

Info

No information found
MECHANICS OF MATERIALS:An Integrated Learning SystemTimothy A. PhilpotMissouri University of Science and TechnologyRolla, Missouri
Page 3: A research-based,online learning en
Page 8 and 9: VICE PRESIDENT AND DIRECTOREXECUTIV
Page 11 and 12: PrefaceAt the beginning of each sem
Page 13 and 14: topics for students. To help organi
Page 15 and 16: With each of these software feature
Page 17: Second Edition. John Baker, Univers
Page 20 and 21: 8.3 Normal Stresses in Beams 2408.4
Page 23 and 24: CHAPTER1Stress1.1 IntroductionThe t
Page 25 and 26: Greek letter σ (sigma). To determi
Page 27 and 28: ExAmpLE 1.2Rigid bar ABC is support
Page 29 and 30: of) the largest-magnitude internal
Page 31 and 32: 9dIRECT SHEAR STRESSJeffery S. Thom
Page 33 and 34: point O, which is the center of rot
Page 35 and 36: ExAmpLE 1.7A steel pipe column (6.5
Page 37 and 38: The projected area A b is equal to
Page 39 and 40: FIGURE p1.4/5p1.5 Three solid bars,
Page 41 and 42: Determine the shortest allowable le
Page 43 and 44: p1.29 A hollow box beam ABCD is sup
Page 45 and 46: To investigate the stresses acting
Page 47 and 48: ExAmpLE 1.9A 120 mm wide steel bar
Page 49 and 50: ExERcISESm1.12 The bar shown has a
Page 51 and 52: CHAPTER2Strain2.1 Displacement, Def
Page 53 and 54: Accordingly, a positive value of δ
Page 55 and 56: To distinguish clearly bet ween elo
Page 57 and 58:
m2.2 A rigid steel bar AB is pinned
Page 59 and 60:
Sanding sleeveDγ is the specific w
Page 61 and 62:
In the undeformed plate, the angle
Page 63 and 64:
2.4 Thermal StrainWhen unrestrained
Page 65:
pRoBLEmSp2.16 An airplane has a hal
Page 68 and 69:
46MECHANICAL PROPERTIESOF MATERIALS
Page 70 and 71:
3.2 The Stress-Strain Diagrammecmov
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
3.3 Hooke’s LawAs discussed previ
Page 80 and 81:
(b) The lateral strain is0.004 in.
Page 82 and 83:
ExAmpLE 3.340 mm20 mm80 mm(1)PTwo b
Page 84 and 85:
p3.6 A nylon [E = 2,500 MPa; ν = 0
Page 86 and 87:
p3.16 Compound axial member ABC sho
Page 88 and 89:
66dESIgN CONCEPTS• Although their
Page 90 and 91:
4.4 Allowable Stress DesignThe allo
Page 92 and 93:
Note: The resultant force should al
Page 94 and 95:
the design. Substitute the allowabl
Page 96 and 97:
m4.2 The single-shear connection co
Page 98 and 99:
p4.8 Rigid bar ABC is supported by
Page 100 and 101:
78dESIgN CONCEPTSFrequencydistribut
Page 102 and 103:
80dESIgN CONCEPTSFrequencyLoad fact
Page 104 and 105:
The design strength is the product
Page 106 and 107:
84AxIAL dEFORMATIONMore powerful co
Page 108 and 109:
5.3 Deformations in Axially Loaded
Page 110 and 111:
88AxIAL dEFORMATIONEquation (5.5) a
Page 112 and 113:
Now compute the deformations in eac
Page 114 and 115:
The total elongation of the bar is
Page 116 and 117:
p5.9 The assembly shown in Figure P
Page 118 and 119:
yA2.4 m 1.8 mRigid bar(1) (2) (3)de
Page 120 and 121:
xBconfigurations due to a force app
Page 122 and 123:
(b) Member DeformationsThe deformat
Page 124 and 125:
y,va b cabx,uA B C Dp5.18 The truss
Page 126 and 127:
F 1 F 1 F 2Since the axial members
Page 128 and 129:
106AxIAL dEFORMATIONThe five-step p
Page 130 and 131:
Equation Form Comments Typical Prob
Page 132 and 133:
There are still two unknowns in thi
Page 134 and 135:
112AxIAL dEFORMATION(1) (2)Px Bx CA
Page 136 and 137:
114AxIAL dEFORMATIONAn equilibrium
Page 138 and 139:
p5.24 A composite bar is fabricated
Page 140 and 141:
p5.34 A pin-connected structure is
Page 142 and 143:
m5.12 A rigid bar ABC is pinned at
Page 144 and 145:
Step 2 — Geometry of Deformation:
Page 146 and 147:
A(1)L 1+ v BL1100 mmCv BB(Note: Def
Page 148 and 149:
and the deformation of member (2) i
Page 150 and 151:
p5.46 At a temperature of 15°C, a
Page 152 and 153:
130AxIAL dEFORMATIONA A BB CCA A BB
Page 154 and 155:
132AxIAL dEFORMATIONUniform tensile
Page 156 and 157:
pRoBLEmSp5.54 A 100 mm wide by 8 mm
Page 158 and 159:
136TORSIONElectromagneticforcesA(1)
Page 160 and 161:
138TORSIONIf the strain is small, t
Page 162 and 163:
6.4 Stresses on oblique planesThe e
Page 164 and 165:
6.5 Torsional DeformationsIf the sh
Page 166 and 167:
144TORSIONA positive internal torqu
Page 168 and 169:
SOLUTIONThe elastic torsion formula
Page 170 and 171:
Rotation Angle at CThe angles of tw
Page 172 and 173:
yA(1)0.85 m 1.00 m 0.70 m550 N.m900
Page 174 and 175:
pRoBLEmSp6.1 A solid circular steel
Page 176 and 177:
p6.15 Figure P6.15 shows a cutaway
Page 178 and 179:
156TORSIONor in terms of the pitch
Page 180 and 181:
NCR CR BNB= 42 teeth= 54 teethCφ C
Page 182 and 183:
pRoBLEmSp6.18 The gear train system
Page 184 and 185:
162TORSIONAnother common measure of
Page 186 and 187:
Note: Only the magnitude of the tor
Page 188 and 189:
respectively. The bearings shown al
Page 190 and 191:
Step 2 — Geometry of Deformation:
Page 192 and 193:
170TORSIONThe five-step procedure d
Page 194 and 195:
mecmoviesExAmpLESm6.19 A composite
Page 196 and 197:
For stainless steel core (2),τ1Tc
Page 198 and 199:
m6.23 A composite shaft consists of
Page 200 and 201:
R BNB= 40 teethφ BBwhere R B and R
Page 202 and 203:
The angle of twist in shaft (2) isT
Page 204 and 205:
zAyFIGURE p6.42/43L 1(1)T BBp6.43 T
Page 206 and 207:
184TORSION3.02.8T2rT2.6DdStress-con
Page 208 and 209:
p6.52 A stepped shaft has a major d
Page 210 and 211:
188TORSIONabTbTaτ max3T=a 2 bFIGUR
Page 212 and 213:
190TORSIONNote that the shear flow
Page 214 and 215:
36 in. long, and its cross-sectiona
Page 216 and 217:
194EQuILIbRIuM OF bEAMSyA xxAA y(a)
Page 218 and 219:
196EQuILIbRIuM OF bEAMSyP1P2wABCxyA
Page 220 and 221:
The sum of forces in the vertical d
Page 222 and 223:
ExAmpLE 7.3ywDraw the shear-force a
Page 224 and 225:
wx 2LA724 wL x—x3aaV2wL xMload th
Page 226 and 227:
8 kN.m13 kNy8 kN.mAA2 m19 kN(3 kN/m
Page 228 and 229:
206EQuILIbRIuM OF bEAMS from the ri
Page 230 and 231:
208EQuILIbRIuM OF bEAMSw(x)w Aw Bw
Page 232 and 233:
Table 7.1 construction Rules for Sh
Page 234 and 235:
ExAmpLE 7.6AAAyA yy12 kips 10 kipsB
Page 236 and 237:
214EQuILIbRIuM OF bEAMSfunction f (
Page 238 and 239:
fBefore the V diagram is complete,
Page 240 and 241:
e V(10) = +15 kips (Rule 2: ∆V =
Page 242 and 243:
y120 kN.m130 kNV-130 kNM-120 kN.m60
Page 244 and 245:
yA40 kN/m50 kNB60 kN.mxp7.17-p7.18
Page 246 and 247:
y6 kips/ft4 kips/fty25 kN30 kN/mA B
Page 248 and 249:
226EQuILIbRIuM OF bEAMSw(x)w(x)εP
Page 250 and 251:
Table 7.2 Basic Loads Represented b
Page 252 and 253:
Shear-force equation: Using the int
Page 254 and 255:
ExAmpLE 7.129 kips/ftA9 kips/ftA5 k
Page 256 and 257:
9 kips/ft5 kips/ft11 kips/ftBending
Page 258 and 259:
y5 kips/ft9 kips/ft70 kN/m30 kN/m 5
Page 260 and 261:
238bENdINgyLongitudinal plane of sy
Page 262 and 263:
240bENdINgEquation (8.1) indicates
Page 264 and 265:
242bENdINgproduce a resultant force
Page 266 and 267:
244bENdINgyCompressivebending stres
Page 268 and 269:
246bENdINgIn common practice, each
Page 270 and 271:
The controlling section modulus is
Page 272 and 273:
The moment of inertia of the cross
Page 274 and 275:
pRoBLEmSp8.1 During the fabrication
Page 276 and 277:
8.4 Analysis of Bending Stresses in
Page 278 and 279:
256bENdINg“W12 by 50.” This sha
Page 280 and 281:
11.5 in.6 in.Ref. axis0.5 in.1 in.4
Page 282 and 283:
A B C D E F500 mmB y400 mm 600 mm 6
Page 284 and 285:
m8.15 Moment-of-inertia calculation
Page 286 and 287:
p8.22 A WT305 × 41 standard steel
Page 288 and 289:
Table 8.1 Selecting Standard Steel
Page 290 and 291:
55 kip·ft30 kips2.5 kips/ft30 kips
Page 292 and 293:
Ptw2wAaFIGURE p8.32p8.33 The beam s
Page 294 and 295:
272bENdINgSimilarly, the bending st
Page 296 and 297:
274bENdINgas those in the actual cr
Page 298 and 299:
276bENdINgNotice that the bending s
Page 300 and 301:
Maximum Bending MomentThe maximum b
Page 302 and 303:
ExERcISESm8.16 A composite-beam cro
Page 304 and 305:
8.7 Bending Due to an Eccentric Axi
Page 306 and 307:
HyF = 30 kipse = 8 in. 30 kipsM = 2
Page 308 and 309:
Axial StressOn section a-a, the int
Page 310 and 311:
m8.22 A steel inverted tee shape is
Page 312 and 313:
a load P is applied at an eccentric
Page 314 and 315:
outer faces of the flanges. Load P
Page 316 and 317:
294bENdINgTo satisfy equilibrium, t
Page 318 and 319:
296bENdINgEquation (8.24) is useful
Page 320 and 321:
ExAmpLE 8.118 in.8 in.zHK(1)y4 in.(
Page 322 and 323:
8 in.0.859 in.z53.6°H2.859 in.Comp
Page 324 and 325:
(c) the principal moments of inerti
Page 326 and 327:
304bENdINgStress-concentration fact
Page 328 and 329:
p8.71 The notched bar shown in Figu
Page 330 and 331:
308bENdINgThe circumferential norma
Page 332 and 333:
310bENdINgTo remove θ from this ex
Page 334 and 335:
At point A, r = 50 mm. Thus, the be
Page 336 and 337:
SolutioNCentroid location and neutr
Page 338 and 339:
DMr iOABp8.83 The curved tee shape
Page 341 and 342:
CHAPTER9Shear Stress In beams9.1 In
Page 343 and 344:
a maximum intensity of (4.5 MPa −
Page 345 and 346:
I ci (mm 4 ) | d i | (mm) d i 2 A i
Page 347 and 348:
9.3 The Shear Stress Formula325THE
Page 349 and 350:
What is the significance of Equatio
Page 351 and 352:
ad329THE FIRST MOMENT OF AREA, QVb
Page 353 and 354:
9.5 Shear Stresses in Beams of Rect
Page 355 and 356:
mecmoviesExAmpLEm9.2 Derivation of
Page 357 and 358:
(b) Maximum Horizontal Shear Stress
Page 359 and 360:
ywaAaxLFIGURE p9.7a Simply supporte
Page 361 and 362:
the distribution of shear stress ma
Page 363 and 364:
(a) Shear Stress at HBefore proceed
Page 365 and 366:
m9.6 Determine the maximum horizont
Page 367 and 368:
p9.17 The extruded plastic shape sh
Page 369 and 370:
NailA(1)zy(2)Nail CNailB(3)Mz(2)(1)
Page 371 and 372:
Identifying the proper Area for QIn
Page 373 and 374:
Shear Flow FormulaThe shear flow fo
Page 375 and 376:
mecmoviesExAmpLESm9.9 Determine the
Page 377 and 378:
(a) If the screws are uniformly spa
Page 379 and 380:
F(1)dx357SHEAR STRESS ANd SHEARFLOw
Page 381 and 382:
τ xzCutFreesurfaceyFree surfaceCut
Page 383 and 384:
Next, consider the web of the thin-
Page 385 and 386:
Longitudinal planeof symmetryyB′
Page 387 and 388:
The directions and intensities of t
Page 389 and 390:
of Q. However, what is the negative
Page 391 and 392:
used in Equation (b). that is, the
Page 393 and 394:
(b) Distribution of shear stressThe
Page 395 and 396:
Calculation of Shear Stress Distrib
Page 397 and 398:
PA375SHEAR CENTERS OFTHIN-wALLEd OP
Page 399 and 400:
SHEAR CENTERS OFTHIN-wALLEd OPENSEC
Page 401 and 402:
the resultant force F w of the shea
Page 403 and 404:
Distribution of Shear StressThe dis
Page 405 and 406:
ExAmpLE 9.14Find the shear center O
Page 407 and 408:
SHEAR CENTERS OFTHIN-wALLEd OPENSEC
Page 409 and 410:
p9.42 The hat-shape extrusion shown
Page 411 and 412:
btOet (typ.)cOh2beh2aFIGURE p9.54bF
Page 413 and 414:
CHAPTER10beam deflections10.1 Intro
Page 415 and 416:
When the beam is bent, points along
Page 417 and 418:
P395THE dIFFERENTIAL EQuATIONOF THE
Page 419 and 420:
continuity conditionsMany beams are
Page 421 and 422:
integrationEquation (b) will be int
Page 423 and 424:
1 ⎛ 2wx0 ⎞Σ M =⎛ ⎞⎝⎜
Page 425 and 426:
order to complete this FBD, however
Page 427 and 428:
ExAmpLE 10.4The simple beam shown s
Page 429 and 430:
Since C 1 = C 3 ,C2 2Pb( L − b )=
Page 431 and 432:
p10.5 For the beam and loading show
Page 433 and 434:
ExAmpLE 10.5A beam is loaded and su
Page 435 and 436:
p10.15 For the beam and loading sho
Page 437 and 438:
to obtain the shear-force function
Page 439 and 440:
Note that the second term in this e
Page 441 and 442:
ExAmpLE 10.8For the beam shown, use
Page 443 and 444:
pRoBLEmSp10.17 For the beam and loa
Page 445 and 446:
p10.31 For the beam and loading sho
Page 447 and 448:
calculation. Before proceeding, it
Page 449 and 450:
The beam deflection at B can be cal
Page 451 and 452:
mecmoviesExAmpLESm10.8 Determine th
Page 453 and 454:
20 kipsb = 4 ft a=16 ftvxv Cx=10 ft
Page 455 and 456:
MLθ =6EIBy the values defined prev
Page 457 and 458:
The beam deflections at A, C, and E
Page 459 and 460:
The beam deflection at E is compute
Page 461 and 462:
Beam deflection at C: The beam defl
Page 463 and 464:
m10.5 Superposition Warm-up. Exampl
Page 465 and 466:
v4 kips/ft45 kipsvv180 kN.m70 kN80
Page 467 and 468:
CHAPTERStatically Indeterminatebeam
Page 469 and 470:
447P1P2P1P2P1P2THE INTEgRATION METH
Page 471 and 472:
Evaluate ConstantsSubstitute the bo
Page 473 and 474:
integrationIntegrate Equation (f) t
Page 475 and 476:
p11.5 A beam is loaded and supporte
Page 477 and 478:
SolutioN(a) Support ReactionsAn FBD
Page 479 and 480:
ExAmpLE 11.4For the statically inde
Page 481 and 482:
Equation (c) for the beam slope and
Page 483 and 484:
11.5 The Superposition method461THE
Page 485 and 486:
vPvPvAL—2L—2(a) Actual beamxBAS
Page 487 and 488:
Notice that EI appears in both term
Page 489 and 490:
that the roller support is displace
Page 491 and 492:
Case 2—Cantilever Beam with Conce
Page 493 and 494:
wooden beam. Determine an expressio
Page 495 and 496:
ExERcISESm11.1 Propped Cantilevers.
Page 497 and 498:
v60 kN/m125 kNv80 lb/in.140 lb/in.A
Page 499 and 500:
p11.44 A timber [E = 12 GPa] beam i
Page 501 and 502:
Stress TransformationsCHAPTER1212.1
Page 503 and 504:
on the x, y, and z planes. Stresses
Page 505 and 506:
The result of this simple equilibri
Page 507 and 508:
Stresses at HThe forces and moments
Page 509 and 510:
p12.5 An extruded polymer flexural
Page 511 and 512:
also be added together to produce t
Page 513 and 514:
pRoBLEmSp12.11-p12.14 The stresses
Page 515 and 516:
Stress InvarianceThe normal stress
Page 517 and 518:
The choice of either Equation (12.3
Page 519 and 520:
ExERcISESm12.1 the Amazing Stress C
Page 521 and 522:
p12.25-p12.26 The stresses shown in
Page 523 and 524:
In this figure, we will assume that
Page 525 and 526:
Method one. The first method is sim
Page 527 and 528:
p2p2p2σ p2σp2σ p2σp1σp1σp1p1p
Page 529 and 530:
• Substitute the value of θ s in
Page 531 and 532:
Since θ p is negative, the angle i
Page 533 and 534:
(b) The principal stresses and the
Page 535 and 536:
p12.35 A shear wall in a reinforced
Page 537 and 538:
Utility of mohr’s circleMohr’s
Page 539 and 540:
8. Several points on Mohr’s circl
Page 541 and 542:
Since points x and y are always the
Page 543 and 544:
element counterclockwise; therefore
Page 545 and 546:
and the normal stress acting on the
Page 547 and 548:
ExAmpLE 12.10Stresses on an incline
Page 549 and 550:
For element A, the absolute maximum
Page 551 and 552:
pRoBLEmSp12.42 Figure P12.42 shows
Page 553 and 554:
30.0 ksi2,250 psia5.5 ksi680 psiσ1
Page 555 and 556:
The forces on the x, y, and z faces
Page 557 and 558:
where a i , b i , and c i are the c
Page 559 and 560:
Table 12.1 Direction cosines for pl
Page 561 and 562:
p12.66 The stresses at point O in a
Page 563 and 564:
ydx′541PLANE STRAINdxθ′ zxdy
Page 565 and 566:
Next, the displacement vector AA′
Page 567 and 568:
yyπ2γ xyxFIGURE 13.6a Positive sh
Page 569 and 570:
13.4 principal Strains and maximumS
Page 571 and 572:
• When θ p is positive, the elem
Page 573 and 574:
p13.3 The thin rectangular plate sh
Page 575 and 576:
SolutioNPlot point x as (ε x , −
Page 577 and 578:
pRoBLEmSp13.16-p13.17 The principal
Page 579 and 580:
Equations (13.9), (13.10), and (13.
Page 581 and 582:
out-of-plane normal strain e z will
Page 583 and 584:
Although stress is applied only in
Page 585 and 586:
Unit Volume changeConsider an infin
Page 587 and 588:
SolutioN(a) Determine the change in
Page 589 and 590:
Also, Equation (13.17) becomes, sim
Page 591 and 592:
e x and e y in terms of σ x and σ
Page 593 and 594:
ExAmpLE 13.9On the free surface of
Page 595 and 596:
Since the strain measurements were
Page 597 and 598:
ExAmpLE 13.10A 2014-T6 aluminum all
Page 599 and 600:
Whereas elongations and contraction
Page 601 and 602:
ExAmpLE 13.11A unidirectional T-300
Page 603 and 604:
p13.39 A thin brass [E = 100 GPa; G
Page 605 and 606:
(a) Determine the normal strains e
Page 607 and 608:
CHAPTER14Pressure Vessels14.1 Intro
Page 609 and 610:
From this equilibrium equation, an
Page 611 and 612:
yσ hoopzxσ longP = pπr 2σ longF
Page 613 and 614:
τprτ abs max = +2tp2591STRAINS IN
Page 615 and 616:
Stresses in the outlet PipeThe long
Page 617 and 618:
m14.5 A cylindrical steel [E = 200
Page 619 and 620:
diameter of 1,800 mm and a wall thi
Page 621 and 622:
σ θ dr ∆xdθ599STRESSES IN THIC
Page 623 and 624:
The radial stress in the thick-wall
Page 625 and 626:
Similarly, the change in radial str
Page 627 and 628:
External pressure on a Solid circul
Page 629 and 630:
ExAmpLE 14.3An open-ended high-pres
Page 631 and 632:
Then, set σ θ equal to the allowa
Page 633 and 634:
Cylinder shrink fitted on a solid s
Page 635 and 636:
The circumferential stress on the i
Page 637 and 638:
p14.31 An open-ended compound thick
Page 639 and 640:
normal stresses are identical at al
Page 641 and 642:
mecmoviesExAmpLEm15.1 A tubular sha
Page 643 and 644:
15.3 principal Stresses in a Flexur
Page 645 and 646:
a. The normal stresses caused by F
Page 647 and 648:
Shear Force and Bending Moment at H
Page 649 and 650:
mecmoviesExAmpLESm15.2 A cantilever
Page 651 and 652:
The following equilibrium equations
Page 653 and 654:
m15.3 The rectangular tube is subje
Page 655 and 656:
yPPQb ft fAx HHxB C DKx KEyL4FIGURE
Page 657 and 658:
F yyM yy635gENERAL COMbINEdLOAdINgS
Page 659 and 660:
SolutioNSection PropertiesThe cross
Page 661 and 662:
m15.7 A rectangular post has cross-
Page 663 and 664:
Combined Stresses at HThe normal an
Page 665 and 666:
SolutioNEquivalent Force SystemA sy
Page 667 and 668:
The 28,800 lb · ft bending moment
Page 669 and 670:
Stress transformation Results at KT
Page 671 and 672:
The 10.8 kN · m (i.e., 10.8 × 10
Page 673 and 674:
The 8.45 kN · m (i.e., 8.45 × 10
Page 675 and 676:
p15.28 Three loads are applied to t
Page 677 and 678:
P y = 375 lb, and P z = 550 lb. Det
Page 679 and 680:
σ Y(a) Stress element at yieldfor
Page 681 and 682:
where P is some function of δ. The
Page 683 and 684:
When the third term in the brackets
Page 685 and 686:
CompressiontestτTensiontestσσUTp
Page 687 and 688:
ExAmpLE 15.9The stresses on the fre
Page 689 and 690:
CHAPTER16Columns16.1 IntroductionIn
Page 691 and 692:
moment, then the system will tend t
Page 693 and 694:
Buckled configurationIf the compres
Page 695 and 696:
The critical load for an ideal colu
Page 697 and 698:
• The Euler buckling load equatio
Page 699 and 700:
Similarly, the moment of inertia of
Page 701 and 702:
p16.11 An assembly consisting of ti
Page 703 and 704:
P< PcrBxP=PcrBB yPBB yxPBL −x681T
Page 705 and 706:
The equation of the buckled column
Page 707 and 708:
where L is the actual length of the
Page 709 and 710:
Critical StressThe critical load eq
Page 711 and 712:
pRoBLEmSp16.15 An HSS152.4 × 101.6
Page 713 and 714:
column is as shown in Figure 16.8b.
Page 715 and 716:
1.15e = 0693THE SECANT FORMuLAPP cr
Page 717 and 718:
several values of the eccentricity
Page 719 and 720:
graph shows a scattered range of va
Page 721 and 722:
For intermediate-length columns wit
Page 723 and 724:
Controlling slenderness ratio: Sinc
Page 725 and 726:
From this allowable stress, the all
Page 727 and 728:
fixed at base A with respect to ben
Page 729 and 730:
p16.41 A simple pin-connected wood
Page 731 and 732:
ExAmpLE 16.8The W12 × 58 structura
Page 733 and 734:
(b) Magnitude of the largest eccent
Page 735 and 736:
where c is the outside radius of th
Page 737 and 738:
CHAPTER17Energy Methods17.1 Introdu
Page 739 and 740:
deformation vary. This dependency i
Page 741 and 742:
σσModulus oftoughnessFracture719w
Page 743 and 744:
or in terms of the deformation δ a
Page 745 and 746:
strain energies in all the segments
Page 747 and 748:
ExAmpLE 17.3A cantilever beam AB of
Page 749 and 750:
or, since a + b = L,UPab 2 2 2= Ans
Page 751 and 752:
In the loaded system, dynamic loadi
Page 753 and 754:
Special cases. Two extreme situatio
Page 755 and 756:
Plan the SolutionThe axial deformat
Page 757 and 758:
so that the impact factor can be wr
Page 759 and 760:
Multiplying the two factors of the
Page 761 and 762:
SolutioN(a) The areas of the two ro
Page 763 and 764:
This strain-energy density is repre
Page 765 and 766:
pRoBLEmSp17.12 A 19 mm diameter ste
Page 767 and 768:
p17.24 Figure P17.24 shows block D,
Page 769 and 770:
The external work done by a force a
Page 771 and 772:
pRoBLEmSp17.30 Determine the horizo
Page 773 and 774:
PB751METHOd OF VIRTuAL wORkP 2ACδ
Page 775 and 776:
internal forces f 1 and f 2 acting
Page 777 and 778:
17.9 Deflections of Trussesby the V
Page 779 and 780:
The right-hand sides of Equations (
Page 781 and 782:
at B. The right-hand side represent
Page 783 and 784:
MemberL(mm)A(mm 2 )F(kN)f(kN)⎛ FL
Page 785 and 786:
vwPv1763dEFLECTIONS OF bEAMS byTHE
Page 787 and 788:
Pw1765dEFLECTIONS OF bEAMS byTHE VI
Page 789 and 790:
Real Moment M: Remove the virtual l
Page 791 and 792:
BeamSegmentx Coordinateoriginlimits
Page 793 and 794:
For segment CD, draw a free-body di
Page 795 and 796:
P 2P 2P 2P PAC E G HB D F6 mp17.49
Page 797 and 798:
Therefore, the total strain energy
Page 799 and 800:
The terms L, A, and E are constant
Page 801 and 802:
elastic modulus E = 200 GPa; theref
Page 803 and 804:
17.13 Calculating Deflections of Be
Page 805 and 806:
5. Integration: Perform the integra
Page 807 and 808:
ExAmpLE 17.19Compute the deflection
Page 809 and 810:
From Equation (17.40), the beam def
Page 811 and 812:
120 N/mm40 kN/mAB C100 mm 65 mm 65
Page 813 and 814:
Table A.1 properties of plane Figur
Page 815 and 816:
ExAmpLE A.1Determine the location o
Page 817 and 818:
Using the Pythagorean theorem, dist
Page 819 and 820:
SolutioN(a) Moment of inertia About
Page 821 and 822:
A.3 product of Inertia for an AreaT
Page 823 and 824:
1.654 in.y1.654 in.y1.154 in.(1)1.8
Page 825 and 826:
andcos2θ =p∓( I − I )/2x⎛ (
Page 827 and 828:
ExAmpLE A.7Determine the principal
Page 829 and 830:
mecmoviesExAmpLEA.6 The theory and
Page 831 and 832:
geometric Properties ofStructural S
Page 833 and 834:
Wide-Flange Sections or W Shapes—
Page 835 and 836:
x-XYttffXt wdYb fAmerican Standard
Page 837 and 838:
Shapes cut from Wide-Flange Section
Page 839 and 840:
Hollow Structural Sections or HSS S
Page 841 and 842:
Angle Shapes or L ShapesDesignation
Page 843 and 844:
Table of beam Slopesand deflections
Page 845 and 846:
cantilever BeamsBeam Slope Deflecti
Page 847 and 848:
Table D.1a Average properties of Se
Page 849 and 850:
Table D.2 Typical properties of Sel
Page 851 and 852:
Gear relationships between gears A
Page 853 and 854:
thin-walled pressure vesselsTangent
Page 855 and 856:
P3.11 P = 42,000 lbP3.13 (a) E = 30
Page 857 and 858:
P7.1310.0 kips40.00 kip·ftxP7.293.
Page 859 and 860:
(c)(c)P7.45−(a) wx ( ) = 42.09 ki
Page 861 and 862:
P8.83 (a) r n = 112.5 mm(b) σ A =
Page 863 and 864:
P11.23 (a) P = 12.50 kips(b) M = 31
Page 865 and 866:
P12.63 T max = 119.8 N · mP12.65 (
Page 867 and 868:
P15.43 σ x = 1,545 psi, σ z = 0 p
Page 869 and 870:
IndexAAbsolute maximum shear strain
Page 871 and 872:
load, 207, 210, 211load-deflection,
Page 873 and 874:
for indeterminate beam analysis,461
Page 875 and 876:
flexural, 239-240in-plane shear, 54
show all

Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?