Shigley's Mechanical Engineering Design.pdf

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Mechanical
Engineering

Contents

Bucynss-Nabet_ © Shit Mechanical Engineering Design, Eighth Elton

Lies
don
eduction to Mechanical Engineering Design
A Ses Analysis
and Siles

A ole Prevention
3. Falles Resulting rom State Loading
1, Fatigue Fallure Resuling from Variable Loading

Design ot Mechanics Somone
Inroducion
7 Shafts and Shaft Components

he Design of Nonpermanent joints
the Design of Permanent Joints

Rolling Contact Bearings
and Joumal Bearings
14. Spur and Hal Gears
15, Bevel and Worm Gears
16. Chuches Brakes, Couplings. and Fiyéhecs
Teile Mechanical Elements
18: Power Transmision Case Sty

Aan Tots
19. Finite-Element Analysis
20, Saisical Considerations

Beteee

efeeges 5338

Fy

2558 885

Back Maser m

Appendix A: Useful Tables m
Appendix B Answers to Selected Problems sn

Cons Tee sun 1@

Lacets

Objectives

“his et end or students beginning the dy of mechanical ngnetng
design Te fo on lending fundamental development of concep wth Pac
Si ecc al componen. tans o ns vn shod nd that Inh
inte em no family with both te ba fr dilo andthe standards ol
Inatal componen For hs eso, sents tanos pci engines,
thy il nd at text pen a rec et Te bss are

2 Cover the uses of machine design including he design proces, engineering me-
‘hans and materials fale prevention under sti: and variable loading and ehar-

teils ofthe principal types of mechanical elements

(te practical approach othe subject through a wide range of eal-woel appic-

on and examples

+ Encourage readers to link design and analysis.

“+ Encourage madero ink fundamental concepts wit pracikal component specification.

New to This Edition

“Tis cipht ition contains the following significant enhancements:

2 New chapter on the Finite Element Method. I response to many requests fom
"viewer this edition presents an introducir; chapter on the ie element metho.
‘The polo hs chapter so provide an overview oh terminology mehod, ep
tiles and applications ofthis (ol inthe design environment.

+ New transmission case study: The tional separation of tops nto chape
Somaines leaves stents a los when it comes time o integral dependen topics
ina age design proces. comprehensive ease study is Incorporated rough stand.
alone example problems in mlileckapers. hen culminated wih a new chapter
{that discuss and demonsrts tb integration ofthe parts iat compete design
pres. Example problems rca to e cas stoy ae presented on engineering
ape background to quickly identify them a pr ofthe case stud

+ Reise and expanded coverage of shaf design. Complementing the new wansnis-
‘Son case study fa siria revised and expandd chapter focusing on ue rl.
(ranto haft design. The moivaig goal isto provide a meaning resentation th
los a new designer to progress through th entire shal design process om ger-
a shal layout 10 spcising dimensions. The chapter ha been moved nd
‘ely follow the fig chapter, peovling an opportunity to seamlessly wanton
from te ftgue coverage tos application inthe design of sas.

+ Availabilty f information to complete the details e a design. Additonal fous is
‘placed on ensuring the designer can cry the process trough to competion

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By assigning larger design problems in clas, the authors have identified where the
talents lek det, For example, formation 1 now povided or such details as
‘Specifying keys to transit torque, sess concentration Factors fr keyways ad r-
{sining ing groove, and allowable deletions for gears and bearing. The we of
eres catalogs and engineering component search engines is emphasized to obtain
tent component specifications.

+ Streanining of presentation. Coverage of material continues to be sreamlined to
focus on presenting stsightforward concept development and a clear design proce
ur fo dent deinen.

Content Changes and Reorganization

A new Pt: Anas Tots has en added at the end ofthe book to inh the new
chape on inte elements andthe chapter on Statistical considerations. Based on a sur
‘ey of inicios the consensus wa 10 move these chaper 10 Ihe end of the back
ere they are avaible o thse Inructes wishing owe then. Moving he stats
‘al copter fom its former location aus the renumbering of the former chapters 2
"hough 7. Since the shalt chapter has ben moved o immedi Follow the fatigue
chap. he component capers (Chapters 8 tough 17) mana hei same number

ing. The new organizo, alongwith brief comments on content changes, I given
below

Part 1: Basies

Pat | provides logic ad unified introducio1 the background material need for

machine design The chain in Pat ha received a thorough cleanup to strain

and sharpen he focus, and limite late,

+ Chapter 1 traduction, Some outed and unnecessary materi hasbeen remove.
‘A now section en problem specication itrdaces the wansmision as st.

+ Chapter 2, Materials. New mate is included on selecting materials in a design
proces. The Ashby chars are include and referenced as a design oo.

+ Chapter 3, Load and Sres Anos. Sever sections have ben reiten to im

prove lr, Bending two planes is specifically lese long witha example

problem.

‘Chapter 4. Deflection and ies. Several secions have ben rewrite o improve

‘lan. new example problem fr deletion la sepped af include. A new

Sections included on else sil of Scar! members in compresion

Part 2: Failure Prevention
‘This section cover alle hy state and dynamic loading. These chapters ave received
extensive cleanup and claricaton targeting siden designers.

= Chapter Fairs Rsuting rom Sai Loading, tn ation o extensive emu
for improved car, a summary ol impora design equations à provided at he end
ofthe chapter

+ Chapter 6, Fatigue Rllre Resulting from Variable Loading. Confusing mail on
‘obtaining an using the S-N diagram clarified, The mpl methods for abtaning
‘notch servit are condensed The ston on combination loading serie or
greater lat chapter summary is prova to overview the analysis roadmap and
Important design equation sed nthe process of fatigue aay

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Part 3: Design of Mechanical Elements

Par cover the design of pei machine component. AN chapter have recived
general cleanup. The shal chapter hasbeen moved to te Beginning fe section. The
arrangement copter long wit any significant changes. is desc elo:

+ Chapter 7, Shas and Shot Components, This chape significantly expanded and
‘erento comprehensive in designing shat. Instructor that previously did not
‘Spsiclly cover te shat chapter are encouraged 1 us this chapter immediatly
Following be coverage of fie falle. The design af shal provides a natura pro
_resson fom te are prevention section no aplicuon toward components. This
Shape i an essential par of the new transmission case stay. The coverage of
Stscrews, ay pts, al retaining rings, previous, placed i the chapter on bolted
ns as teen moved ino this chapter The coverage of limits and fs, reel
‘placed in he copter on sti, has Been moved int this chat.

+ Chapter 8, Screws Fasteners, and the Design of Nonpermanent Joints. The se.
tion on sserews, keys, nd pins, ha been moved from hi chapter to Chapter 7.
‘The coverage of boled and ete joint loaded in hear has bn returned to hin
chapter

= Chapter 9, Welding, Bonding, andthe Design of Permanent dis. The section on
‘bolted ad ice Ji loaded in sear has een moved to Cape 8

+ Chapter 10, Mechanical Springs.

2 Chapter 11, Roling-Contat Bearings

+ Chapter 12, Lubrication and Journal Bearings

+ Chapter 13, Gears - General. New example problems a included ass design
‘of compound gear tain to achieve specifi gear aos. The discussion ofthe rel
"ini been or, pee, and power s cai,

+ Chapter 4, Spur and Helical Gears. The curent AGMA standard (ANSUAGMA
2001-D04) has hen reviewed ensure upo-dt information in he gear chapter
Al references is clear updated o elec the ce saad

+ Chapter 15, Bevel and Worm Gears

+ Chapter 16, Clutches, Brakes. Couplings. and Flywheels

+ Chapter 17, leile Mechanical Elements.

+ Chapter 18, Power Transmssion Case Stab. This new copter provides complete
‘ase study a double reduction power ransmission The Focus so providing an ex
ample für student designers ofthe proces integran topics from multiple chap-
{ers Insects ae encourage 1 include oe ofthe varios ol his case sty as
‘design project inthe cour. Stdn frdback consistently shows tht thi Pe of
projets ons ofthe mos valuable aspects of a fist couse in machine design. This
‘Shaper canbe wills in ol fashion for stents working though a similar
sin

Part 4: Analysis Tools

Par includes à new chapter on inte clement methods, and anew location forthe

chape on iii consideras, Instructors can reference these capter an ned

+ Chapter 19, Finite Element Analysis. This chapter i intended 1 provide an into-
ucion wo the fie element method, and prtculary its application vo the machine
design proces.

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+ Chapter 20, Sail Considerations. Tis capter is related and organize as a

tcl sha more naar sep i te mane pe
proces Mi per sul te di SO er Cap IT acto be
Le

Supplements

‘The eto of Shige's Mechanical Engineering Design festes McGraw Hi' ARIS
Assessment Review and Inston System) ARIS makes homework meaningful and
manageable for to and stant stats can assign nd grade tetpeci
Romeo within the industry's most robust and versal homework management sy
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‘The amay of tools availble 1 users of Shigeys Mechanical Engincering Design
incl

‘Student Supplements

2 Tatoias—Presemaion of major concepts, wih visuals. Among the topes covered
se pressure Vessel design, pes an shi fs, contact ses, and design for state
fare

+ MATLAB? for machine design. Inlodes visual simulations and accompanying source
‘ode. The simulations are inked o examples and problems inthe text and demonstrate
‘th ways computational software can be used in mechanical design and analy

+ Fundamentals of engineering (FE) exam questions for machine desig. Ineactive
problems and soliton serve as festive, ten problem as wel as excelent
reparation forthe FE exam,

+ Algorithmic Problems. Allow step-by-step problem solving using a recursive com
tonal procedure (lgoihm) to crete an inte number ol problems

Instructor Supplements (under password protection)

Solos manual. Theinsrcior’s manual contin sion © most en-ofchapter
ondesen problems.

+ PowerPoint slides. Slides importan igre and tables from the test are provided
in PowerPoint format for ne in eures.

= Tae ou O

Lacets

“Ti as of common symbols usd in machine design and in this ook, Specialized
use in a subjetmater aca oflen trie fore and post subscripts and upon
“To make the uble bet enough to be useful the symbol hemels ae Ted. Se
“Table 14-1. pp. JIS-716 for spur and helical gearing Symbol, and Table 15-1.
Pp 769-790 or bevel gear symbol,

Are coccion
Distance egresion constant

Regression constant estimate

Distance variate

Coie

Briel ardness

Viriato

Distance, Weill shape parameter range number. regression consta
wi

Regression constant estimate

Distance arte

Base lad rating, bolted joint constant, center distance, cocino
‘arian, column end condition, orton far, soci het capacity.
seine index

Distance, viscous damping, velocity coeicen

Cumulative distrito function

Coclicient of ition

Distance variate

Helin diameter

Diameter distance

Modulus of esti, energy or

Distance, een, efcenc: Naperan logarithmic base

Fee fundamental dimension free

Coeieien of tion. frequen. funcion

Figure of met

‘Torsional modus of ei

“Acceleration dueto grvi funcion

Heat, power

nll hardness

Rockwell Cale hardness

Distance im Biches

‘Combined orl coefficient of sometion and on heat runter
Integral. ner impulse, mas moment o nea second moment o rea
Inder

Unit vector in adición

cagar»

rongegasn ages eter gg

Pr}

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Dram ti ane

Banane west eset IN gern

gett

Es Stan

Mechanical equal of heat, polar second momen of area, geometry
cor

Unit veto in the etn

‘Service acta, stese-concentrion facto, rss genio factor,
torque coefcient

‘Marin endurance iit mailing fc, spring rate
variate, unit vector in he: dirt

Length life, fundamental dimension length
Logo discuto:

Length

Fundamental dimension mass, moment

Moment vector, moment atte

Mass, ope, stain tengthenng exponent

Normal fre, number, tana pee

Normal dsibation

Load actor. ational sp, safety Factor

Design ator

Fore, pressure, amet pitch

Probability density function

Pic, pressure, probably

Fist moment of aca imaginary fre, volume
Diebe load, nich sensi

Radius, reaction force, rl Rockwell hess, ses tio
‘este ration fore

Correlation colcient radis

Disanse vector

Sommerfeld number, regi

Svarine

Distance, sample standard deviation, stress
“Temperature, tolerance oque, fundamental dimension time
‘Torque vete tote varie

Distance, Sten esac, tie, tolerance

Stain energy

Uniform erben.

Stain energy per unit volume

near vest her ce

near velocity

CCoi-vork factor load weight

‘Weibull discos

Distance, gap, ad intensity

Vector distance

Coin. tnncsed number

(Coordinate, tre vale of «number, Weitl parameter
Coordinate

(Coordinate, deñection

Cooint, section mus, viscosity

‘Standard deviation ofthe uni normal disribuion
Via of

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ensrnaguanese

[nate oe)

‘Coon, coton of inca thermal expansion end-condition for
rings ead angle

Bearing angle coeicient,

‘Change defecion

Deviation. clngation

Brceniiy ratio, engineering normal) sain

Normal stitution wih a mean oO nd a standard deviation of à
‘Tracer lozaihnic normal stain

Gamma anton

Pitch angle, heu rin, specie weight

‘Slendernes ratio for springs

Unit lognormal witha mean ol and standard deviation equal to COV
Absolute viscosity, population mean

Poisson ratio

Angular el. circula frequency

Anglo, wavelength

‘Slope integral

Ra of curate

Normal tes

Von Mises tes

Standard deviation

Shea sess

Sheu sess varie

‘Angle, Weibull characterise parameter

(Cox pe uni weight

Cou

CES set

Dea ti an

PART Basics

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Introduction to Mechanical
Engineering Design

mw
12
73
14
15
16
17
18
19
1-10
in
12
113
1-18
"15
116

ial Enginesting Design 5
Fhoses ond Inerctons of the Design Roces 5
Design Tools ond Rosouces 8

The Design Engroors Polosionel Responsibilities 10
js ond Codes 12

Economics 12

Solty and Probe! ob 15

Sros ond Singh 15

u
Design Factor and Factor of Salay 17
Raobity 18
Dimensions ond Tlrances 19

Son

ny 16

Us a
CCaleatons ond Significa Figues 22
Power Torsmissen Caso Sul Spocticaons 23

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Mechanical espn i complex undertaking. requiring many sls. Extensive relation.
ships nce o be su ledit a eric of simple asks. The compleit ofthe subject.
requires a Sequence in which das are introduced and het

‘We fist adress the nature of design in general, and then mechanical engineering
design in parkcular. Design an leave proces with many interactive planen Many
reses existo support the designe. main many sources of information and an
Ahunlanc of computational design tok, The design engineer news not oly I develop
‘competence in thi field but mus also clio a tong sense of responsibil and
Proesional werk ee

“Ther re oes o be payed by codes and standard, ver present economic, sales,
and considerations of produc ibility The survival ofa mechanical component soften
felted through stress and strength, Mater of unceraint are eer: preset in engine:
ing design ad re typically address by he design Tato and [actor of safe, cier
in the form of a determine (absolut) o¢stastcal sense. The later, statstial
“approach, deal witha design's ibility and require good sica! data

Tn mechanical design, other consideras inclue dimensions and tolerances,
units, and calculations.

The book consi of four prs Par 1, Bases, begin by expaning some die.
‘ences between design and analysis and inducing some fundamental moins and
approaches to design. I continues with thre chapters reviewing material properties
‘ress analysis, and illness and dllection analysis, which ar the hey prie ne
say or the remainder ofthe book.

Par 2, Faire Prevention, consists of wo chapters on he prevention of fr of
mechanical ps. Why machine pars al and how hey an be designed wo preven al
tre are dificu questions, and so we take two chapirs o answer hem. one on Pre.
verting fare due to ste Tous, athe her on preventing fatigue failure due to
time-varying, cele loa

In Pat 3, Design of Mechanical Element, the material of Pats nd 2s applied
Lo the analysis selection, and design of specie mechanical elements such as sas,
Fasteners, weldments, sings. oling contact bearings, it bearings, ges, el,
chain and wire opos

Par 4, ltr Tol, provides inrodocions1o Luo imposant metas wo in
mechanical design iio element analysis and sica analysis This i opina stoy
ner bt some sections and examples in Part 10 3 demons th we ofthese tl

There ae to appendixes a th endothe book. Appendix contains many use
ful ables referenced thoughout the Book. Appendix B contains answers 10 selected
ceof-chaptr problems

Design
‘To desig scr 1 Formule a plan fr the sisi o ascii need ro sine
problem. If plan ress nthe ection of someting having apical eli hen
‘he product st be funcional sae reliable, compete, usable manufactura, and
make

‘Design à an innovative and highly eve process Is alo a decision. making
proces, Deciions sometimes have oe made with too litle iaormatlon, occasion:
aly with just he ight amount of informatio, o with an excess o pasty coticry
information, Decision re sometimes made tentatively, with height reserved to je
5 move Bones known, The oi ls tthe engineering designer hs o be peony
‘comfortable witha decision-making, problem-solving le

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Design a communication intensive activity in which both words and pitres are
sd, and rien and oral forms are employo Engineers hive 1 communica lc.
tively and work wih people of many disciplines. These are importan sis, and an
‘engineers succes depends on them

A designers person sources fran communica ability and problem
solving skill ae intertwined with Knowledge of technology and frst principles
Engineering tok (sch as mathematics, ais computer, graphic. and languages)
ase combined t produce à plan ha, wen cared ut, produces a product a sano.
tional safe, liable compete, wahl, manyfacurabe, and marketable, reales
fof who Bild or ho ses

Mechanical Engineering Design
Mechanical engines ar associated wi tb produc and processing of energy and
‘ith proving he means of proton the Wels of transportation, a the techniques.
Of automation. The sil and knowledge base ae exensne- Among he discipline
bases are mechanics of solids and uds, mas and momentum transport, manufactr
ing process, ad electra! and information theory. Mechanical engineering design
involves all he disciplines of mechanical engineering

Real problem eit comparimenaiation, A simple jor bearing involves id
ow, he taser, in, enemy transport, materal election, thermomechanical
treatments, salina descriptions and soon. A Biking e cvionmemaly controled
"The hen entiation, and airconditioning considerations are sucky specialized
tat seme speak of rating, ventilating. ad air-conditning design as i i separate
and stint om mechanical engineering design Similar. inem combustión engine
‘esign,turbomachinery design, and jevengine design are sometimes considered i
ct ttes. Hee the leading sing of words recding the word design is merely à
Product descriptor, Simi, thre are phrase such as machine dein, machine clement
design, machine-component design, systems design, and Avid poner design. All of
those phrases ae smen hat more Focused examples of mechanical engincering design.
“The all daw on the same bodies of knowledge are similar organized, and require
similar ls

Phases and Interactions of the De:

[What is the design process? How does it begin? Dos the engineer simply sit down at
a desk witha Blank set of pape and jt down some ideas? What happens next? What
factors influence or contol the decisions that veto be made? Finl ow docs the
‘design process end?

“The complete design process, rm sat 0 Finish, soften outline as in Fig. 1-1
“The process begins with an identification of ned and decision wo do something
about After many iterations, the process ends with the presentation ofthe plans
for satisfying the ned, Depending on the nature ofthe design ask, several design
phases may be epetedthughout the fe of the product, rom inception to er
ation, Inthe next several subsections, we shall examine thee steps In the design
process in detail

Tiemficuin of eed generally sas the design proces. Recognition ofthe nes
and phrasing the nee often constitute a highly creative at, because the need may be
‘nla vague discutent eig of uncasies, ra sein ht something o ig
‘The ped is often ot evident a al: recognition i usualy wiggerd by particular

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Figure 1-1 a
The pois ds,
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adverse cisustanos or st of random cumstances that rss almost imulanscuah.
For example ih ned todo somthing about food packaging machine maybe indi
‘te by the oie le. by a variation in package weight abd by sgh but perceptible
varias in he quality ofthe packaging e weap.

"Tere a dnc irnos between the sitement ofthe ned and the definition
‘ofthe problem. The definition of prblem is more poc and mus include the spc
cations forthe bjt hat so be designe Te specification are the input and at
‘ut quits, the characters ad dimension o the space the obje mus occur,
“aná al the listas on tse quais. We can regard the object to be designed as.
Something ina black box. mths ease we must pci the inputs and upto the ox,
{ogether with ei charıtertis and limits The pecas deine th cos, the
umber be manufactured, be expected if. he unge, be operating temperature and
{he real. Spied characterise cn include the speeds, feds, temperature i
ions, maximo range, expected variations nthe variables, dimensional and weight
Timitaons, te

“There are many implied specifications that result citer from the designers par
"cular envionment or rom the mature of the problem set, The manufacturing
processes that are avaiable together wih the faites ofa cei plan, constitute
restriion on a designers freedom, and hence ar a part ofthe implied specific.
"ss. It may be that a Small lat, or stance, does no oe cold working machin.
er. Knowing this, the designer might select oler metal processing methods that,
an be performed in the plat. The labor skills avaiable and the compte si
ion also constitu implied constants. Anything tha its the designer's freedom
of choice isa constraint. Many materials and sizes are listed in supplier's catalog,
for instance, but thse are otal easly available and shortages frequently occur.
Funhermore, inventory economics requies that a manufacturer stock a minimum
numberof materials and sizes. An example ofa specification is given in Sec. 1-16
"is example s fora case stay a power transmision Alar ls presented Uwoughout
Anis text

‘The syntess of a scheme cometing possible system elements is sometimes
called the invention a he concept or concept design. This ie is and most impor
{ant ste inthe synthesis ak, Various schemes must be propose investigated, and

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unid in tems of etbshed metrics Ash chin ou of scheme progresses,
hates mus he performed to ass whether the stem perfomance i salt or
Iter, ad, if stat, jst how well il pero. System schemes that do nut
survive analysis ar reise improve, o discarded. Those wih potential ae optimized
(o determine the bes performance of which the scheme is capable. Competing schemes
are compared so hat he pt leading othe mos compe product can be chain
Figure 1-1 shows tht mets and analysis and optimalen age imately and
iteratively elite

We have noted, and we empliz, at design isan trate proces in which we
proces hah several eps, crate the result, and then retum an salir phase
‘ofthe procedure. Thu, we may sym several component ol assim, ande and
“plie them nd return 1 posi o se what effet is has onthe remain pats
‘ofthe system. For example. be design fa st to transmit power requires atetion
to the design and selection of individual components (eg. gar, beings shal)
However asis en he case in design, these components are ns independent nore
to design he hat fr tres and defection it cena to now he applied force,
be forces re transite through gen, ii ncenay 0 ow the gear peca:
Bons in ondr to determine the Fes that wil be transmitido A sha But sock
ear come with certain ore sizes qui knowlege ofthe necessary shalt ame
Her. Cleary rough estime wll ned o be made in onder wo proceed though the
proces. refining and erating unl inal design caine that istsfatry fr each
{nil component a wel a for the over design specifications. Throughout the
teat we wl elaborate on his proces fr he case study a power transmision design

Both analysis and optimization require at we constructor devise boat mals
‘of he system tat will ait some form of mathematical anal. Weel hee mod:
‘els mathematical modes In creating them tour hope that We an ind one that wll
Simulate the real physical system very weil, As indie in Fig. 1=L, evolution ia
Significant phase ofthe wal design paces. valuation ithe al prot ofa success
ful design and usally imolvs the testing of a protaype inthe abort. Here we
wish discover ifthe design realy sas the need. IA reliable? Wil compete
successfully wih similar products? I i economical o manufacture ad 1 use? Ts
«sil maintained and adjusted? Can a profit be made from is al or use? How key
is ito ress in product abi lawsuits? And à insurance easily and cheaply
‘blaine Is likely tha rca wl be need o replace deli pars or systems?

‘Communicating the design to others i the Ana, vial presentaron Sp inthe
“design paces. Undoubtedly, many great design, imentions, and creative Werks have
been lou to posterity simply Became the oiginator were unable or unwilling 10
explain their accomplishments to others, Presentation isa sling job. The engineer,
en presenting anew solution to administran, munagemen super pesos,
is atempúng 1 el oto prove to them that this Slatin isa better ne. Unless his ean
be done cfa, the time and effort spent on obtaining the solution have Been
largely wasted. When designers sell anew ies, they also sl themselves, [hey are
repeatedly successful in seing ¡cas designs, and new solos to management they
ein to receive sry increases and promotions in fat this how anyone scores
inhi ore profession.

ne ef tay St Poh ot rm Mel fr
‘Sen ras Eg ring Rn We. 1 À Son Paine a et

O li men Baer
Pres De ==
ar =

. | atta Da

Det cosida

Sometimes the strength eid of an clement ia stem san important factor in the
¿determinan of be geome and th dimension othe clement I sch a tion
ve say that strength an important design consideration, When we se the expression
design comidertio, we ae refering to ame characters that inloenes the design
‘ofthe elemento, perp, he entre system. Usually quite a numberof such chars
teristics mus be considered and pirized in a given design tation. Many of the
important ones aes follows (nt necessarily in ondo ponte)

1 Functionliy 14 Noise
2 Strenge 15 Spine

3 Distosion/detetionsitness 16 Shape

4 Wear 17 Sie

5 Comoion 18 Cool

6 Say 19 Thermal popes

7 Reliab 20 Surface

$ Manufcturbiiy 21 Labicaion

5 Vil 22 Mañeubiiy

10 Cont 23 Maintenance

11 Recto 24 Volume

12 Weight 25 Laity

13 Lite 26. Remanufocuringhesource recovery

Some of these characteristics have 0 do diet with he dimensions. the materi the
processing and the oiing ol he elements ofthe system, Several charter may
Be teed, which affects the coniguation of te ttl system

Design Tools and Resources
"Today, he engineer has great variety of tol and resources available oasis in the
solo of design problems. Inexpensive microcomputers and robust computer sol
are packages ode tol of immense cali or the design, analysis an ie
Inn of mechanical components, I addon 1 these ol, he engines always needs
{echnical infomation, ciber nthe form of ani siencuengincerng behavior or the
‘haraterisis of sii ofthe sel components Here the sources can ange fom
Scienclenincering texooks to manufactures’ brochures e catalogs. Here 10, the
Computer an play major rl in gathering infomation.”

Computational Tools
Computed design (CAD) software allows the development of tree dimension
(6:D) designs fom which comentional o dimensional athaeraphi views with ut
mas dimensoning can be produced Manufetring tool ahs an be genera rom the
FD mode, an in some cases part can be reed dl froma SD database y sing
à api potryping and manulatucing med (srcolidigraphy) paperless manufac

turing! noter advantage la 3 dts is that allows rap and accra cle
‘ons of mas propre sich amas vation ofthe center of gravity and mas momen
of inertia, Other geometric properties Such a areas and distances between points are
Tikewise easily oa, Ter are a great many CAD software packages available such

Anni competido de pren lata ema” ceo in
up à Get. De Engines Dig A Marlon Pig pach be

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as Aries, AutoCAD, CaiKey, Des. Unigrapics, Solid Works, and Proginer 10
ante a

"The tem computer-aided engineering (CAE) generally applis o all computer
reed engineering aplicas With his dehition. CAD can he considere as ab.
set oi CAE. Some computer solwarepuclaes perform specie engipering analysis
nor simulation asks that sist the designer, but they are ot considered a Wal for he
ration ol the design tht CAD is, Such stare its Into two cateporieenginceing-
sed and non-engincerng-speife Some examples of enginecring-tasd sofware or
mechanical engineering application Sofware that migh lo e inkgrted within a
CCAD system includo Ame_lement says (FEA) programs for aalis of stes
and defection (Sc Chap. 19) vibration and beat waster e. AIN ANSYS, and
MSCINASTRAN): computational id dynamics (CFD) programs fr vid: low analy
sis and simulan (eg, CFD++, FIDAP and Fent; and programs fr simulation of
rame ore and motion in mechanisms (eg, ADAMS. DADS, and Woking Mose,

Examples of non engineering specie compter aide application include sf
are for word processing, great software (3. Excl, Lotus, and Quatro ro),
and mahemaial save e. Maple. MathCad, Matlab Mathematica, and TK 0.

"Your nitritos care of inomuton about progr hat muy be ale
to yovand cin commend thse hat ae well or specie sks. One caution, however
Computer sofware no subsite fr the human oa process. Yow are the der ee:
the computer the veil av you on Your joue 1 a soho. Number gente
bya computer can ef fom the nl you entered cores pi you misinterpreted
the aplication othe pat of te program. if the program contained bugs, e is your
responsi 0 assure he ality Fhe sul so be cra to check the aplican and
ress crea. perform benchmark texting by submiting problems with known sok
tions. and monitor software company and user group Rate.

“Acquiring Technical Information
We carey ive in wh ee 0 Ihe formation ae, ber infomation gone
erat an astounding pace. Is il hu extremely important 1 hep ¿beso as
an cuen development in ane el study and oscupain. The refrene in Foot
2 provides an excelent desc ofthe inomtinal recurs avaible and i high
recommended radins for he serious design engine. Some sures of infomation a

2 Libraries comuni; unes, and private) Enginerng dictionaries and encycl-
pedis, textbooks, monngnphs, handbooks, indeing and sac service, joua,
{rants technical report, patents and business source Gr AE

+ Govemmen sources Departments of Defense, Commerce, Ben and Transparent
NASA: Gonemment Pting Oi; US. Pant and Trudemark Ofc National

Technical Information Serie and Nan Ins for Standards and Technology

Profesional secc, American Society of Mechanical Engineers, Society of

Manufacturing Engineers. Society of Automatve Engineers, American Society for

‘Testing and Materials, and American Welding Society

Comercial vendors. Catalogs, technical traue, test data, samples. and cost

infomation,

Internet, Te computer network gateway o websites associated with mos of the

sega lied ove?

"See al mo, ome fe nae geo vane,

Orne

1

rer Feen cone
ea ti a toe

‘This is isnot complet. The reader is urged to explo the various sources of
information on a regular basis and Keep socal f the knowledge ited

The Design Engineer’s Professional Responsi 2
In general, ih design enginer i required to satiny he ns of customers (man:
agement, lents, consumer, te) and is expected to do o in competen responsi
ble, ethical, and profesional manner Much of enincering couse wok and practical
experience focuses on competence. but when does one begin o develop engineering
‘esponsibility and professionalism? To star on the road to success, you should sta
{o develop these characteristics early in your educational program You ned to cul
tivate your professional work ethic and process skills before raluation, s that
‘when you bein your oral engineering caret you will e prepared 10 mec the
challenges.

Its not bein to some student, bt communication skills play age ol er
‘and its the wis student who continously works to improve these skill even i
ls nor direct requirement ofa course assignment! Success in engineetng(acieve-
mens promotions en, et.) may in argo par be dueto competence hu iyo can-
not communicate you des clearly and concisely, your technical polen may be
compromise

You can sar 0 develop your communication sills by Keeping net and clar
Jourallogbook of your actives, entering dated entries Frequently. (Many companies
require lei engnges to keep a joumal for patent and bit concer) Separate
auras shouldbe used for eich design poet or couse subject, When stating a
project or problem inthe definition tage, make ural entre ui requ. Other,
{swell as yourself may ater question why you made certain decision. Good chrono.
Topica end will make it easier o expan our decisions at a er dat

‘Many engineering sudens sc themselves afer gradation a practicing engincers
signing, developing and anayzing produc and processes ad consider the need of
18008 communication skill iter eal or wang, as Secondary. This is fr from the
tru. Mest practicing engineers spend a good dea of tie communicating wih others
‘writing proposal an tecnica) pot, and giving presentation and erating with
enginering and nonengincring suport personnel. You have the tine now to sarpen
ou communication skills, When ghen assignment wo write or make any presenta
tion, technical or montechnial, accep it cthussical, and werk on impeoing your
‘communication skill I wl etme well spent to lear the sil now rather an on.
the jo,

"When you are woking on a design poble, iis important tat you develo a
systematic approach. Cael ation tthe following action tps wil cp you Lo
manie your solo processing chi,

+ Understand he problem. Probe fui is probably he mos significant sep ine
engincering design pros. Curly rad understand, and reine problem tement.
dent he known. From the reine problem statement, describo concisely what
information is known and reiean.
enti the kwon and formate he slain sue. Sie what must be deter
‘mind, in what onder, soa Lo aie st solution othe problem Sketch the compo-
nen or system under investigation, identifying known and unknown parameter
(Crete owchar ofthe steps necessary to reach the fal solo, The step may
require the we of rey diagrams: material properties rom tables: equations

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from fit principles etbooks or handbooks latin the known and unknown
parameter: experimental namely based chart specie computational ls
dieu in Sc, tice
Ste al asuepñons and decisions. Real design problems general do not have
unique ea closed form solutions. Selections such as choke o material, and het
eaters, require decisions. Analyses require assumptions reed to the modeling
‘ofthe vel components or system. All assumptions and decisions shouldbe ened
and corded
‘Anas he problem. Using your soon state in conjunction with your decisions
“and asumpions, excite analysis of the problem, Reference the source of all
‘uations, tables, char, solar resus, ic, Cook the eet of your res
{Check the ower of malte, dimensional, ends signs te
+ Esaluate your solution Evaluate ach sepia the solution, noting how changes in
areas decisions, assumptions, and execwion might change terest, in positive
nat ways I possible corporate the pone change in your ial slain,
Presea your solution. Here is where your communication sI are importar. At
‘is pin, you ae selling yourself and your technical bles, I you Camo sil
Taly expli what you hve done, sme ral f your wock may Be misunderstood
and unsseped. Know your audience,

A stat air al design processes ae iterative and iterative. Thus, it may bonos
‘essary to sepa some o al the above steps more than nee fess than satisfactory
‘evs ar band

In order we effete, all profesional must Keep eurent in their els of
‘ender: The design engineer an sts this in a number of way by? Being an ce
member of à professional society such as the American Society of Mechanical
Engineer (ASME), the Society of Automotive Engincer (SAE), and Ihe Society of
Manufacturing Engineers (SME); sending mectigs, conferees, and scminan of
societies, manufactures universe ing pelle graduate courses or prog
an universes: eulry reading technical ad professional joumals ete An engine's
duc ain docs nt endl gration,

‘Te design engineer profesional obligations include conducting cites in an
‘tial manner. Reproduced her is he Enginers*Creed rom the National Seely of
Profesional Engineers (NSPE)

As a Professional Engineer I dedicate my profesional knowledge and kil the
‘advancoment and betterment of human welfare
Toles:
To give the umost of performance
To participate nome bu honest enterprise;
To liv nd work according tothe Lans of man and he highest standards of pro
Fesioal cond
place service before prof, he honor and standing of the profession before
personal change, and he publi welfare above al ther consierations.
A humilis and with need fr Divine Guidace. make is pledge

pe N Sc Pn Engines Jn 194 Te Ege Cl” Rp
y pero Nil Pons En Tish en pram sd)
SE ori cet ren Jama) 206. he ee pe. i
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1-6

Standards and Codes

A standard is à et of specification for pas. materials. or processes intended 10
achieve uno, elicheney, and a speied qual. One ofthe important purposes
fa standar so plac limit on te number of ems inthe specications so as o
raide a reasonable ventory of toting. sizes, shapes. and varie.

"A cae x à se of specications fee the analysis, design, manucure, and com
stron of something. The purpose ofa code ist achive a specie degre ose,
‘fceney. and performance or quai. Is important 1 observe that safety codes do
Int imply absolute safety In [aabt safety i impossible wo obtain. Sometimes
{the unexpected event really does happen. Designing abating to withstand a 120 ih
ind dos ot mean that he designers think 130 mi wind impossible simply
ness that ey think tis highly improbable,

"Al ofthe organizations and societies Hd below have established specifications
for standards and safety or design codos The amo ofthe organization provides ace
to the nate ofthe standard or code. Some of the standards and codes, as well as
adresses, can e obtained in most wesc libraries The organizations of interest to
mechanical engine ae:

Aluminum Assocation (AA)

‘American Gear Manufacturer Assocation (AGMA)

American tte of Stel Construction (AISC)

American Iron ad Set Insite (AIS)

‘American National Standard Insitute (ANS

[ASM Imemationa

‘America Society of Mechanical Engineers (ASME)

‘American Society of Testing and Materials (ASTM)

‘American Welling Society (AWS)

American Bearing Manufacturers Assocation (ABMAY?

Brith Standards Instaon (BSD)

Industrial Fasteners Insite II)
stitution of Mechanical Engineer, (1. Mech)

Imerntionä Barca of Weights and Mesures (BIPM)

Iermationa Standards Organization 150)

Nationa nte for Standards and Technology (NIST)

Society of Automotive Engineers (SAE)

Economics

‘Te consideration of cot plays such an important ole inthe design decision process ha
ve cou easly spend as much ine i studing the cos Fete ssi he dy ofthe
‘ie subject of design Here we induce only à feu gene concepts and simple res

‘Sena nine USAS) Te, ane war api angel Ana Nat Ses
loma Amaia Soy ol ASA, Caron be syn AS nein.
A (A FRA cane man Ain
eat Manco ii ABM

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oracion Mech Enger Onion | 23

First observe that nothing can be aid in an absolute sense concerning costs
Material nd abor usualy show an increasing cos rom yer Lo sz. Bu the cosa
‘of processing the materials can be expected to exhibit a decreasing wend because of
the ue of automated machine took and robots, The cost of manufacturing a single
product will vary rom city 1 cy and from ene plan Lo another because of oer
head. abr, ts, and eight ifeenials andthe inevitable slight manufacturing

Standard Sizes
“The us of standard stock sizes ia principe f ost reduction. An engines who
species an AISI 1020 bar of otro tc 3 mm square hs ded onto the ood
ue provide that a bar 50 or 60 mm square, both of which are peered sizes. woul
‘do exa well, The Sem sie can be obtained by special ode or by rong or
machining a 60-1 square but these approaches add cost he product o ensue tat
andar or peered ie respected, designer mus ave cos ck isso the
Inara thy employ.

À farther word of cation regarding the selection of preferred sizes is necessary
Alnough a great many sizes are uly td in eatalgs they are nt al aly val
able. Some sizes ae used so inrequenly that hey are nat stoked. À rsh ode or
‘ch sizes may mean more on expense and deay Tus yu should abo Rave ses 10
list sdch as those in Tale A-17 for preferred inch nd milimete size.

"Tere are many purchase pat, such as motors, pumps, bearings, and fastener,
that are specified by designers In the ease of these oo, you sould mal a special
«o 10 specify pus that are realy available. Pats that are made nd soldi age
anti ua got someuhat les than the od sizes. The costo rolling brings
Toc example, depends more onthe quantity of production by the Bring manufacturer
than o the iz ofthe bearing.

Large Tolerances
Among the eet of design specifications on co, olrances ae perhaps mos sig
ica Tolerances, manulscuia processes, and surface nish are intel and
inoece he produciilay ofthe end product in many ways. Close tolerances may
neces atom ps in procesng and inspection or even sender à part com.
Petey impractical to produce economically. Tolerances over dimensional variation
and surface rghnes range and also the variation in mechanical properties resulting
From heat timer and other proesing operations.

‘Since parte having large tolerances can offen be produced by machines with
higher production rats, cons il be signant smaller Also, eee such pas wil
Iho rjeted in the inspection process ad hey are usally eae toascembl. A plot
of cost venus olerance/machining process shown in Fig. 1-2 and stats the
tie increase in manulscturin con as toleran diminishes with Finer machining
processing.

Breakeven Points
Sometimes it happens ta, wen two or more design approaches are compared fr cost
the choice between the two depends on a set f Condon such ase quan of pro.
cto, speed ofthe assembly lines, somo ther condition, Tere then occur a
Pont corresponding to equal cost which call the breukeren point

Figure 1-2
Fem Dd Une, he
chr Dv Pac,
You 2003),

EULEENEDEREE

Figure 1-3

Asan example, considera station in which a etai prt can be manufacture a
the ate of 25 part per hour om an automa stew machine o 1 pas per hour on à
and screw machine: Let us soposs 00, that the sep me forthe automat hand
that he abr cost for cie machine i 20 per hour, including overea Figure 1-31.
graph of cost versus production by the to methods, The breakeven po for this
sample comespons to SO pars. Ihe died production i restr dan $0 ars, the
“tomatic chin should e sc,

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Cost Estimates

“Ther are many ways of obtaining relative ost figures 0 ha tuo or more designs
‘canbe roughly compared. A cern amount of Judgment may be required in some
instances. For example, we can compare the eae value of two automobiles by
‘comparing the dolla cost per pound of weight. Ane way to compar the on of
‘one design with another is simply o cout the numberof pars. The design having
the smaller number of pars is Ikely 1 os es. Many other cos estimators can be
‘sed depending upon the aplication, such as ac, volume, horsepower tone
‘capacity, speed, and various performance ration?

Safety and Product Liability

“The strict lai concep of product ibility general prevail in the United States
“This concept tts that the manufacturer of an nice abe Fran damage o har
that et Dem of defect. And docs! mater wheter the manufacturer new
shout the defect, or even could have known alot For example, suppose an ale
as manufactured sy, 10 ear ago And suppose aa tine the nice ou nt have
ce conser dfecive onthe his fal technological knowledge then available,
“Ten year ate, scoring o the concept of sit bi he manufacturer i sl
liable. Thus, under this concept. the plan needs only o prove that the article was
delete an thatthe defect case some damage or harm. Negligence of he man
Facturer nce at be proved

"Te best approaches tothe prevention o pdt ability are good engineing in
analysis and design. quality control nd comprehensive testing procedures. Advertsing
managers len make glowing promises in he warranties and ses rte fr a po
ct These satements should be reviewed carly bythe engineering a to imite
‘excesie promises ando insert adequate wiring and introctins fore.

Stress and Strength

‘The survival of many products depends on how the designer adjusts the maximum.
stresse in comparen toe Jess than he component renga sei ations of

fees. The designer must allow the mani stesso be less han the regi by a
Silat marin so that despite the unceraines, failure ru.

In focusing on the ses sirength comparison at rial (contin) location,
we often lok for "strength in the geometry and condi of use” Strengths ae the
magnitudes of treses a which something o interes occurs such as the proportional
Tit, 02 percent ot yelling o Fracture. I many eases, sch evens represen the
sites level at which loss of function eur.

"Srengh ica pmper of a material or ofa mechanical element. The strength of an
clement depends on the choice, the tresiment, and the processing of the material
Consider, for example, shipment of spins. We can asocia a tenth with a pe
‘ie spring. When is springs incorporate ito machin, extra forces are applied.
that esl in induced stresses nthe spring, the magnitudes of which depend nis
came and ae independent ofthe material amd is processing. I the spring is
Femoved from the machine unarmed he stress dee othe extemal forces wl earn

iu ei lso amd ne Cap. 11, a han See DE

Opera

rer
ea ti a

1er, But the strength remains as one ofthe propenis ofthe sping. Remember. then,
{hat sien isan inherent property of part a property Dl to Le par Because of
the use ofa prtcular materia ad process.

Various metalworking und heat rating process, such as forging. rling, and
col arming cause vatios in the tents fom pont opi thoughout pur The
‘Spring ited above is quit Hey o have a strength o he ouside of he cis diferen.
From a strength on the inside Because the spring as ben formed by a col wining
process, and the two sides may not have been deformed by the same amount
Remember oo therfore at strength vale given for par may apply only apar.
car point or se of points onthe par

In is book we shall use the capital eter $ 10 denote srengih, with appropriate
subsp to denote the type of sirength. Ths. $, isa sar strength S, a yield
cent, and $, an dim uen

In accordance wih accepted engineering practice, we shall employ the Grek let
ters (Sigma) and rau) o designate normal and shear stresses respectively, Again,
Various subscripts wil indicate some special characters For example y a prin
Pal stesso, a tess component in hey direction. and o, à Srs componer inthe
‘adil direction,

Sres i a tte propery at a specific point within ody. wich i funcion of
ead geomet. temperature. and manufacturing processing. na elementary our in
mechanics of material, ses reed to hal and geometry emphasized wih some
scusion of thermal wresse. However, ae due to het mens, molding
"stembl, et are ao important and are sometimes pd. A review of ress analy.
‘Serbs oad tts and geometry i given in Chap. 3.

Uncertainty
Uncen machin dig shout Esa ol cosine conning sess
anden ide

+ Compos of mae and he eco vaa on propi.

+ Varios in proper rom place pla wi

+ fet of posing lca, maby. on poe.
1 et fey some sch ween dik sonst conten
+ et of hemes estes on proper

2 Intensity nd dit of ain

2 aly of mathe modes wed eps ely

+ nny of es menos

+ are of tie on eg an geome.

+ Efanofamaie

a of sock

+ let of we.
+ Uncertainty as othe length any ist of uncertainties,

Engineers must accommodate uncetny. Uscersinty always acompanis change.
Material properties, od variably icon fee, and tality of mathemati
modes ae among concer 1 designer.

"Tere ae mathematical methods o ess mncensinics. The primary techniques
are the deleminisic and stochastic mets. The dteminiie method stable a

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Provera Pre he conan
Encres =
ein fc bau one abe mesas of of futon parameter nd a
‘mania allowable pace, He de armer can De lod see, deln. s.
“Ts te design facto tied as
Los funcio aro
"4 aim allowable parameter my
Ira ters lo, then he maxima allowable lod can b ou rom
Maximum aa load = SE ot ua
EXAMPLE 1-1 Consider the maximum oad on astute town wih an unse 420 or
ent andthe ad easing run vin 215 pren od sng hl
‘res nominal) 20001 determine te dig factor and maxima alone ad
ft he bse uma
Selon To acco ors unsern, De oso funcion land mus rest 1/085, whereas
the maximum allowable fad mus ders 01/12 Tha fc abate une
ties the design fst Sul be
ass
wee nan WOR ag
From E, (1-2) te maximum allowable ads found tbe
Anne Maximum allowable oat = 22 - yoo ne

14

‘Stochastic method (see Chap. 20) ae has om th sica nature ofthe design
parameter and ocu on the probably of survival ofthe digs function Uh on
Fab), Sections 5-13 and 6-17 demons how ss accomplished

Design Factor and Factor of Safety

A general aprech tote allowable od vers soft od problem se
ermine design fr med, and sometimes ele the casa mato of
‘sign. The fundamental equations (1-1) te nce e desi factor A
lol funcion modes mu E na, ande mode leling othe sale desen
factor gore Aer he designs complete fe aut design factor may huge ss
a res of changes sacha romding up toa standard io for rss econ o sng.
ba components wi ihe aings Ita o enpying wa need
by wing tn desen actor. The actor ls then feed ote factor of safer m The
tetra ay has he ue dehnen se den aco, Du etal ies
sme

Since ess may na vary net wi load (ce Sc. 3-19) using land a he
tos afan prat may tbe cepa. e mor common hen expres

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‘he design factor in terms of a stress and relevant strength Thu Bi. (1-1

ande

us

Fe

‘The sess and strength tems in Bg, (1-3) must be ofthe same type and units. As, e
stress and tenth must apply tothe sme cial location in he part

A od with rose setional are of and loadin tension with an xi! oro of P
2000 IBF undengos à stes of © = P/A. Using a material strength of 24 pui and a
design acer of 30, deemine the minimum dameter of a solid calar ro. Using
MAI, loc prefered rational diameter and determine he was acto of aes

Since A = da, ando = Sng then

S_ 24000 P_ 2000

us A A

„(aan
(aaa,
Fo ee hie peris = 62 To congo
e

ws? rames

ar aa
"Tas rounding he diameter has increase the act design actor

"sti

= 368

Reliability
In these daysof greatly increasing numbers of ibility lawsuits and th ned 0 confor
‘regulations ised by governmental agencies such as EPA and OSHA. itis ery important
forte designe and be manure 1 kaw the reality ftir produce The li
iy method of designs one in which we obtain he distribution of stesses an the dis
‘om ol strength and thn rele these wo in oder 0 achieve an acceptable sucess te.
he isa measure ofthe probably that a mechanical element ill a fala
ae isc lled the relly of hat element The rely R cn be expressed by am
ber having the range 0 << |, Arelaility of R = 0.90 means that there is 90 per.
cet chance ht the par wil perform is proper function without Fle. Te ail of
{6 pars out of every 1000 manufactured might be considered an acceptable hr ate
Tora cern cls of product. This represents ob of

6
CORTE

1994 percent

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Inthe reliably method of design the designe’ ash sto make a judicious stc
tion of materials, processes, and geomet (ize) s a 0 achieve a spi ab
goal. Ts, ifthe objective reality isto be 9.4 percent as above, what combination
‘Of material, processing, and dimensions is needed to meet his gel?

“Analyse that lead 1 a assessment of reliability aes uncerins, o their
‘estimates, in parameters tht describe te station. Stochastic variables such as
Str, strength, load, or size ae describe in terms of thee means, standar devia.
tion, and distibuions bearing balls ae produced y a manufacturing proces ln
which a diameter distribution is created, we can say upon choosing a al that there
is uncertiiy as to size. we wishto consider weight or momento! inertia ling,
this size uncertain an be considered 1 be propagate to ou knowledge of Weight
‘or ina, There ae ways of extimatng the Satna parameters desenbing weight
Ad inertia rom thse desrbing sie and density. These thas are variously called
propagation of ero propagation of uncenaint or propagation of dispersion. These
methode re integral prs of analysis rsyuhesis tasks when probity of ares
involved

Tes imporanı to note that good statistical data and estimates ae essential opor
Forman acceptable eibity analysis. Ti require à go del ol esting and valida:
i ofthe data. In many cases, this not peatland a deterministic approach o the
sen most be underüken

Dimensions and Tolerances

“The following tems are used generally in dimensioning:

+ Nomina size. The size we we in speaking of an element. or example, we may spe
À a Thin pipe ora ¿in ball iter the Uso ze or the acta! measured ie

may be quit diferent. The theoretical size fa Lin pipes 1.900 infor ie tide
diameter And the diameter ofthe ¿cin bol sa, muy atl mesure 092i,
Linie The stated maximum and minimum dimension

Tolerance. The rence between the two mis,

‘Bilateral tolerance. Te vacation in bath detins from the basic dimension. That
is he base size in Denen the two límit, or example, 1.005 0.02 in. The two
ar ofthe tlean need nt he equal

Ultra tolerance. Te basic dimension taken as on ofthe Tis and variation
is permite in only one direcion, fr example,

1005 in

(Clearance. genera tem ha refers 1 he mating of linda par such as a bolt
nd abe. The word clearance bed nl when he internal members smaller tha
{he external member. The dame carence she mere iron nie wo
ameter. The radial clearance the dllcen nthe two ab

Incerference. The opposite of clearance, formating eylindrial parts in which the
internal member ger han the extemal meme.

Allowance. Te minimum stated clearance o he maximum sed interference for
ating pars

‘When several prs ac asembed th gap (o interference) depends on the dimen
sions ad olrances of the individual par

ad Feen cone
Dt ane toe

EXAMPLE 1-3 À shouldered screw contains the hollow sight iclar clindical pars on the crew
‘before a u is tightened agains the sult To sustain the function. te gap must
qual or exceed 0003 in. The pus in he seb depiced in Fig. 1-4 have dimes
‘Sons and wolrunes a follows

1.730 0.008 in 02502 0001 in

0.120-£0005in d = 08750001 in

Figure 1-4 A
oven ee

dic dal lg
2h ond con dl bt
Anke a De gp

cn [S.L

A put excep the prt withthe dimension are supplied by vendons. Th part com
taining the dimension ds made in house

a) Etat he mean and tolerance an he op a,

(6) What base value of wil su that a > 0.008 in?

Solon (a) The mean value of is gen by
Answer

#=a-5-:-

1750 = 0750 - 0120-0875 = 0005 in

For equal tral olernces, he tolerance of he gap is

i

0.003 + 0.001 + 0.005 + 0.001 =0.010in

“Then, = 0.005 0.010, and
wa =e
ae =~ te = 0.005 — 0010 = 0005 in

“This, bh clearance and interference ar possible
(VM a 10 Be 0.003 in, the, = Wan + fe = 0.008 + 0.010 = 0.013 in Tos

005 +0.010 = 0.015 in

Answer dea-b-

350 - 0250 - 0120-0013 = 0867 in

“Tae previous example represented an absolute tolerance sytem. Susi gp
dimensions ear he gp iit are rare evens. Using atric tolerance system, the
‘probity ht he ga fs within gs mis determined" his proa deals
tit the ic dirias of the ini dimensions Fo example, if the ich

‘bons the dimensions inthe previous example were norma andthe tolerances Wee

"Seater 20 radon stl amin

Et tr ie
ad
Dt ane

raser Mecanico Enguera | a

ive in tems o standar devions of he dimension distan. the sana dei
sof water = [LE Hower is ane or on

forthe individual dimensions, rre occurence. To ind the sett a andlor tbe
probably of observing values of within ena iis egies a computr simulation
In mos cases, Monte Carlo computer simulations are sed to determine the distan
‘ow by the loin approach

1 Generate an instance foreach dimension in the problem by selecting the value of
‘each dimension based on its probably distan

2 Gault using the vals ofthe dimensions obsined in sep 1

3, Repeat eps and 2 times to generate the dstietion ofa As the number of
increases, ebay of the ihn inreses

Units
Inthe symbolic nits equation for

tons second aw, F = ma,

Pamir. a
stands fr fre, M for mass, L for length, and 7 fr me. Unis chosen for any hee
‘ofthese quam a cal ae nit. Theft tre having bn chosen, he Furth
Unt is ale derived unit When foc length, and ane ar chosen as ase units, the
mass is the derived unit and the system tat resus i ale gravitational system of
tnt. When mass leg and time are chosen a Bae ums, force he derived unt
{nd the syste th ets called an abso tem of ni

In some English speaking counties, the US. customary four pound second system
(699 ande ick pound second system ips) arth wo standar raion systems
mos use hy engines ae fps system the uni of assis

FT! _ (poundfoceXccond)?
we mer dus US)
“Ts, length time, and Face ae the e base ani in he ps grava system

“The un of force inthe ps system the pound, more propery the prune We
stall le abbreviate this nit If Ihe abbreviation Ibs permisible ower sins
e hal be desing only wi the US. customary geaiatonal system. In somo as
Of engineering itis sel to represen 1000 I a à ilopound nd 0 abbreviate as
Kip, Notes In, (1-9) the derived ni of mas inthe fps gravitational system i the
Inf and is aed a sls there 0 area or slug

‘The uni of as in the ps gravitational stem e

FT? _ (pound-owoeXsccond?
T inch
“The mass uni If in as no ofl name.

‘The International System of Units (SD isan absolute system. The base units athe
ree, logan (for mis) the seven. The uni of force i dete by wing
‘Newt's second law an is aid the norton The mis consti the newton (N) are

ML logan) (meter)

ET Go
“The weight fan object isthe Face exerted upon y gravity. Designating he weight
a Wad the aceleran due o gravity ag we hate

W=ng us

tor

m wr. sin 027

[EME on

Crea

2

ad
Dt ane

=

Inthe fps system, standar gravity sg = 32.1740 For most cases hiss rounded
1 222 Ths the weight of mass ol 1 lug inthe fps system à

tor a) = 322 100

In the ps system, standard ge 386.088 or about 386i Ts, in his system,
‘unit mas weighs

wen

W = (IRE $n) 386 ns) = ANG

‘With St units, standard gravity i 9.806 or about 981 ms Thus. the weight of LK

WP = (HN SEM) = SIN

A series of names and symbol form miles and subrogee o S uns as
‘boon sable to provide an alemane tothe wrling of power of 10, Table A1
inclades the preies and symbol

"Number having fou or more digs are placed in groups fre and separated by
space instead comuna, Hower the space may Be etd fore poca ease of
‘numbers having four digi period is wel sa decimal point These resend
{ions ano he confusion caused by coria European counties in which à comma
is used as a decimal pin and bythe English use of centered period. Examples of
amet and inet usage area lan

1024 or 1928 bat no 1924
(0.1924 960.1924 but vot 0.1924
102424618 5 ba nt 19223 61850

“The decimal point should always be preceded bya zero for numbers les than uni

Calculations and Significant Figures

‘The discussion in is section applies tral numbers, not itegen. The acer of el
number depends onthe number of sigicant gues describing he number Una ak
ot ah the oe our signin ures are nen lor engineering accuracy Unless
‘teri st, no ls an he significant figures shouldbe win your calculations.
‘The number of significant figures usually infeed by the number of figures given
(cepo ling zero) For example, 76, 3.1, and O 19 ae assume be num
es ith hee significan figures. For walling eros, a litle more ciation is ecos
a. To display 706 four inca figures inset a ling ero and display either
76.0, 7.060 10, 0.7060» 10. Alo, onidera number sch as 9160. Sia
notation souk! be used cai the acom, Forte significant gues expres the
‘umber 91. x 10) For four significant Agur expres it 9160 > 10

Compte an cacao display calculations many gica figures. However,
ou should never report a number of igniicat figures ofa calculan any ger han
‘he smallest number of significant igus ofthe numbers wa for the calculan OF
‘oun, you should use the reais accuracy posible when perfrming a calculation. For
example determine the ccunfereceof sll shat witha diameter fd = 040 in The
‘reumfeence given by C = xd. ice lien with uo signant gues, C shuld
por wih only two significan igus. Now i we used only two significant figures
For ur alclato would give C = 3.1 (0.40) = 1.24 in This rounds oto igi.
ica figures as C12 in However, ing = 314159254 a programme in the
caler, € 2 3.141592 654 (040) = 1.256 637061 in. This rounds off 0 C = 13,
in. which 8.3 percent higher an the fr calculation, Note, however, ine dis given

Ett sige | mn

ad
ea ti a

oracion Mech Enger Onion | 23

with wo spin figures it isp that he range of dis 040 + 0.005. This means
that te calculation of Cis nly cur o within 1008/00 = 20.0128 = 41.25%

“The calculation cold also be one na sere of calculos, and rounding ach calcula
tion separa may lead ton accumulaion of peter inceuney. Ths, coders
food engine pace to make sl culations to the pretest asuacy possible and
reporte sults within he aceuracy ofthe gen inp

A use sty incorporating the many facets ofthe design process fr a power tans
Som speed reducer wil be considered throughout this textbook. The problem will be
induced herewith the definition and specification Tor the product tobe designed
Further et and component analysis will he presented in subsequent chapter.
Cape 18 peovies an overview ofthe ene roces, focusing om te design sequence
the imeratontetween he component designs and other details perinent to wansmis
sion of power I also contains a complete ease study ofthe power transmission speed.
reduce ind here.

Many india applications reir machinery o be powered by engines or le
tse moon. The power source uly runs ment ein a à aros range loa.
tina peed When he application requires power to e delivered at slower sped han
supplied he motor a speed rede is introduce, The sped reducer should trans
the power fom he mode lo the application wih site energy los as practical. whe
roducing the spol and consequently increasing the toque. For example assume tht a.
‘Company visos o provide he bel ped reducers sais capaci and speed
Fais tosellto wide variety age aplican. The marketing cam has determined.
A med for nc ofthese spec ede to ay the following customer requirements
Design Requirements

Power he delivered: 20 hp

Input sped: 1750 rev

put spect: $ rin

“Targeted for umilormly loaded applications, such as comeyo bel, lowers,
and generators

Opa shat and input shat nin

Base mounted with 4 bol

Conimous operation

car fe, wi 8 hound, 5 day

Low maintenance

Compa cost

‘Nominal operating conditions of indie locations
put and output sats standard size for yal couplings

In reali the company woul ly design for a whole range of speed ratios or
‘each power capacity obtainable by interchanging ger sizes wii the same overall
‘design. For simplicity, in this ase say only ne sped ratio wil be considered.
Notice ht the fis of customer requirements includes some numerical species bat
also includes some genre requirements «2 low muircrnce and comple co.
‘Thee general equemens give some guidance on what needs oe consiered in the
sin pres bat are ico achieve with any cortan In or opin dow se
bulo requirements, esto farther develop the cistomer gure no. set of
product specifications dat re mess, This sk usualy chs hough the work
‘of team including engineering, marketing, management, ad customer, Varias to,

| unteres | Lai rates PT
O cee es ==>
= =

28 | Mech Egeo Dos

12

1

14

15

may be used (se Feamot 1) proie he requirments, determine suitable mets to
e achica, and o esbli get als fe each meto The gal of is eos sto
bin a produc specication hat Westies precisely what he produc mus Ss. The
Following protection pode an apropia framework or is design En,

Design Specifications
Power be delivered: 20
Power len 5958
Seay ste put sped 1750 efi
Miu apt pct 240 vi
Stenystat up sed: 82-88 ein
Usually tow shock eves ocasional modeste shook
Ing an up sa diet tance: 2000) in
‘Op at and int hf inne: omen 40.005 in, ligan
20001 rad
Maxim loable on apt sb ai, 50 ane, 100 Bf
Maximum loable ds on pa sat ai SO Banc, 00 BE
Bs mounted wi ts
Munn onion ely wi eon boom
100% aay ee
Mana sched: an check ve) 200 bou change of abc
ton every 890 hous o operation: eas and Daring ie > 12,00 bors
inte taf ie gas bearings. and sats epee
‘Aces occ dra and el Min when em a peng of
guidon.
Maulcting co per uni < 3500
Pen: 10000 un per ea
Operating temperature range: „10° 10120
Sl gain water and dan rom peal weather
Noise! hom Ya

PROBLEMS

‘Sekt ect componen rom Fat f hi ok ol bing igs) poto pur
lumii’ rary or the appropriate tr Website and wing the Thomas Reiter of
‘Ameria Matane et nthe fran one on ve manures a spp

‘Sekt mest compone rom Pr fi ook ler bearings ping cc. pot e
‘such engine, po onthe information stun on mama ot

‘Sekt an organ ie in See. 1-6. poeme and wt feat ave
onthe onan

{Goto Ie nd comet NSPE webs (wre, Reh fll enon of

ig tome wate opal ans in he same diction experiencia the erage
saving Denen sik mene with ped: Dt a New Yor tos sow hat een
"Sand 35 mie suce teen ves (in is) 0320/21) whee vs the
etc’ spa ins or ate

da) apor e lento isda vei, wht psd wil ge he fel eng volume

16

17

ren Medical Egg Onion | 25

(0) Does ican he eg fhe veces ut he nel capacity pcs spicy?
Ansa the average eile nth 18
(6) Fer pa (dos the etna ed change much?

Ti ng des mus cas im rl si he en
Tomson atte ee mete otal ea A
‘rasan ness chs as amt wc a ae
cu nn rook soc nia fox oye ay Wee
SR an teva en a e
np pees er aon sida
poss Pena weet Tol oe
ee ret i hs esc
Stacy gant ee loco
Tre e ns hb ma i pres
‘user ag: y msi cs anima ny cda
‘erent pene oop ape bane ae
cas

th (Lata

a)

ere W nthe wight fhe hist and aan Ss he alla eso or compres es
ine ink mtr (sume S = A] nd o ena Pci ato). Wt dene
ange crespnding the minimal cos?

<<

see where con may arte By vii res soin wo be sed toa proxima o
ti us vals flows ht e cor I ed a a =X he
(a) Show tht me X, + Xe

(0) Stow hat he ema ina ice ~ Xy
OS
(6) Sh terna pst XX

ne Xe

26 | Mech grag Dos

18

19

10

12

113

Feen cone
toe
se the me vais) = VB and = VE

(0) Demon be comtes fe core fo Pr 1-7 or in ee ora
pe ar wolf XX

(0) Demons he costes fe eme an fer don wing te ig san
under for Kan

Come ie allowing so appro St nits:
(0) A foe of 0

(© Acond momen of ae of 174i
0) Amare f 36m

9 À mods af sic of21 Mp

(0) A speedo 8 mi

À volume on

Conve te allowing so pri pe
(a) Amor 1.

(6) Apres of 10 Pa.

(0 A seston modul. 1.8 10 m
(Aden of 08 mm

@ Avec of 612m

(0) Austin of 1021 nm.
Avon of 301.

Geely al des ssl ae oun a sto re ds sate tegen dats ca

o poner thn o digit e et of he deal pi. Using these rks. as ts hs or

the chr of pets oe eli on

(a) 0 M/Z wher M

D 0 = Fake

0 y= PP/SEI whee P1200 800mm. E = 207 GPa and = 4 10 me.

DEZ TG. 2 OO Nm. =289 mm G = 793 GPL and
26m Convert rs ders ange

Rept Pr 1-11 othe lowing:

(a) 0 = Future F = 600 Nw = 20 mm and = 6.

0) 1= Win. me B= df= 34

lo) 1a dt. where d= 32

(a) += 167/20. whee T =16N manta

Repos Pr 1

(a) = F/A, where A= ma, F = ON, nl d=20 mm.

0) 0 = 32 Far he E = SON, = 800 mm an d= nm

(o) Ze r/320Na! 4) ord M ad = Bm

(k= GED) whore d= 16 mm, G = 73 GPa
mets amer}

192 mm aod N 23

CPE Ders Stein

ad
Dt ane

‘The selection ofa material für a machine par ora structural member oe ofthe mos
importan decisions the designer is calle on o make. The decison is usualy made
‘before the dimensions of the part re established. Aer choosing he process of er
ing he deed geometry and the material two ann be divoroo) he designer an
‘proportion the member so that bss union an be avoided os the chance of Is of
Funcion can be held o an asepabe ik.

In Chaps. 3 and 4, methods or estimating sreses and detections of machine
member are presented. These simates are based on the properties of the mural
from which the member willbe mate. For deletions and stability vations. for
example. he elastic (Ines) properties ofthe material re require, and evaluations
‘of sites at a rta location In a machine member require a comparison with the
Streng ofthe mater at that location inthe geomety and condon of se, THis
Strength is amaral property fund by testing and is adjusted he geometry and. on.
Aton of use as neces

"As important a sexs and defection ae in he design of mechanical pan, the
selection of a material ot always sc on these ators: Many pai cae no loads
‘on them whatever Parts may be designed merely ffl up space o fo aesthetic qua
ties. Members mut frequently he designe to alo ress corrosion. Sometimes tempe.
tr elects are more important in design than tess and tan. So many ter actors
‘besides tes and sin may gover the design of parts hat the designer mus ave the
‘erat hat come only witha Bond background in materias and presses

Material Strength and Stiffness

‘The standard tensile testis use 10 ob a variety of material characteristics and
strengths hat are used in desig, Figure 2-1 strates a typical tension test specimen
fads characteristic dimensions The eiginal diameter d, and the gauge lng o
td to mesure the decias, ar recorded before the tests begun The specimen it
‘then mounted in the ts machine and slowly loaded i tension wile the load P and
‘defection ae observed. Th oa I comen 1 sess by the caution

en

where An = jr se original ars ole specimen,

LI
Figure 2-1

Al wr cian, Sone ls od

Ett sige | mn
ad
Dt ane

Figure 2-2
Bias a opener in
‘Sa egos ceed
tote ino he
‘sine in th
Gl te crest

oso | 29

‘The deflection, or extension ofthe gage length is given by 1 In where is the
ge agi conespening (oe load P The normal sins callate rom

ent en
And con ur, te he i hd arr
frm ge gsc oss aon as aa
Soman chm one a

Teme sac te pron a ve
coe pave rs aha mt ae
DE en al mop ec ae

one es

here the constant of prapotiomly E, be slope ofthe linear pat ft tes
carve, i alo Young's modas ot the modules of east. E sa measure ofthe
fins ol a material and since sain is dimensiones, th wis of E ae the same.
Stes, Se, for example, has a mals of clics of aboot 30 Mps (207 GPa)
Fesandes of heat eument, carbon content, or alpine, Stainless ee is about
275 Mi (190 GPa)

Pot el in Fig. 2-2 scale the elas mi. be specimens loaded beyond this
nt the deformations ait e plastic andthe material wil ke n apermanent et
hen the loads removed. Busen pl and el he diagram not a perfectly sag ne
‘eventhough the specimen is east

During the tension tt many materials each a pint which the strain begins 10
increase very rapidly witha coesponding increase in tess This point sce the
Sie point. Nal all materials have an obvious yield point especially for rte
mails. For this reason. yield strength 8, soften defined by an oft method as.
‘Shown in ig. 2-2, uher ne ay is dea slope E Pit a corp toa det
or sated amount of permanent st, sully 02 percent of the orginal guge length
(€ = 0002 although 001, 0.1, and US percent are sometimes wed

‘The ulate. o ems, nen , OS, comespond o pin in Fig. 2-2 and
{isthe maximum ses ch onthe sesesrsindigram.* As shown in Fig 2-20

‘ge ae Fr an in gente om ln nen he bc 5 ra
Mon in mir sad e tem ne eng we

mac; == a

ad
Dt ane

20 | scare Eng Du

Figure 2-3

some materials exhibit a downward rend afer the maximum stress reached and fa
ce a point fon the diagram. Others, sch a some of the ca ion and high ire
‘ce, cr while the restrain ace is stil rising, us shown in Fig: 2-2, where
points a and fare ideal.

"AS ot in See 1-9, srngi, a used in this boa, a bu property of ame
Fa. or of à mechanical clement, because ofthe lin of particular maria or
processor both, The teng of connecting rod a the eral catión nthe om.
ley and condon o use. or example she sae no mater wheter its led an ele
men in an operating machin or whether tis yng on workbench avating assembly
with ther ps. On the ter hand, ses something ha occur in pat usual as
result of is being asembled into a machine and loaded, However, sess may be
‘tnt a par by processing or handling For example sho eening produces a om
presse ses inthe utr surface of à part, and abo improves the fag strength oF
{he part. Thus, in hs ook we willbe very caref in distinguishing between regi
este by Sand ss, designated by 0 OF.

“Te diagrams in Fig. 2.2 are called engineering ses sr diagrams because te
stresses ad stains calculated in gs. (2-1) and (2-2 are not rue values. The tes
‘lel in By. 2-1) ane on the ign ares Afore he lai pid. ral
Hye the load applied the ara reduces so ha the tal re stress sarge han
‘the engineering sess, To bain he te stress fr the dram the Toad ad the cos
‘ction area mus he messredsimltancouy during the test. Figure 22a repens
4 ductile material where the sues appears to decrease frm pont o. Tilly
‘beyond pinta the specimen begins to neck” a cation of weakness where the arca
edocs ematical as shown in Fig. 2-3. For dis eus, he te res ch high
than the engineering sues at he necked section.

“The enginerng stan given by Eq 2-2) is based on net change in length fom the
original Tema In poing te tre ses diagram, cudamacy to we tem
‘alle ne sra o, sometimes logarithme sai. Tc sain the um ofthe te
‘mental elongation divided bythe current page length a nd, 0

"a
LT

here ie symbol is se to represen ie stain. The most important characteristic
‘of tre reset diagram (Fig, 2) at ve re coin incre al
{the way ace. Ths, as shown ia Fig. 2-4, thee face stesso is rater han
‘he trv ultimate stesso Contr this with Fig. 2-2 whee the engineering fate
strong 5 e les than the engineering ultimate song 5,

"Compression tts are moe dificult to conduct, and he geometry ofthe tet sp
mens ir from the geomery of thse used in tension ess. The reason or thsi at
the specimen may hackle daring testing ori maybe illo stat the esse.
enemy, Other difficulties oscur bocase ducüle materials will bulge after yielding.
However, the results can he paid on a sess-rsn diagram also, and he same
"strength definition an be applied suse intense testing. Por mou decile meri
the compresive sient are about the same as he tensile songs. When substantia
irons occur between ei and compresve sens, however ssh cas wih

|

e

ñ

Ett sige | mn
ad
Dt ane

Figure 2-4

Coon

moras | at

the cast ions, the tensile and compresive sens should be sated separate; a
Sa where Sis reported asa patie quam
‘Torsional sre are foun y twit solid circular and recording he ome
athe wis ange, The result ar them pled as à orgues diagram. The seat
Stresses inthe specimen are linea wth respect 1 radia catión, being zero at the cen
lero the pecimen and mani at he ut ras Gee Chap 3). The maximum sar
stress fae elated 1 he angle of twist 0 y
= Lo es
where sn adas, rs e radis ofthe specimen os the gage length, and Gis
the mata ses property called the shear modulus othe modulus frig. The
‘maximum sar ses also related 1 the appli torque Ys
Tr
7
Were J = {ris the polar second moment o re ofthe rss section.
“Te trguetwist diagram wil be similar Fi. 2-2, and wing Eqs, (2-5) nd
(2-6), the modulos of il can be Found a weil se elas mil ad the orina!
Yield song Sy. The maximum pont on a toquetwia diagram, comesponding lo
poi wom ig. 22 i Ty. The equation

21

Er
7

deines the mals of ruprae for be torio est. Note Bal tis incor 0 al 5,
the ultimate orinal strength, as he outerost region of he ha is in a paste tae st
the toque 7, andthe tess dito I no longer line.

“lof he stesses and sengis defined the suess-stain diagram of 2-2 and
similar diagrams ae spciicay known as engineering stresses ad strengths or nomi
nl steve and sen. These ar the values normal wed inal engineering design
salon. The aijectivesengincering ad nominal re used here 1 emphaiz at
the sesos re computed by un he origina or unstressed eos ecioal area the
specimen. In this book we shall se these mais only wben we specially wish 0
‘ll tenon to hs dsncton

5 en

CPS Es Stan

2

ad
Dt ane

2-2

Css frere fi] 2

The Statistical Significance of Material Properties
“Theres some sult in he des resented the previos ston hat shou be por
dered erty before continuing Figur 2-2 depic thereat fa singe tension ts
{one specimen, now fracture} Is common for engines to consider tse poeta
"ress ales (pots pl el, ah) popes ato denote them as sens
with a special main, upercse 5, in ie of lowercase sigma o, wih subscripts
added: Sy for proportional lini, for ye tenth, 9, Tor late tensile tenth
(Sor Sif tensile or compresive sensei importan,

ere were 1000 nominally ideal specimens the values of strength obtained
wou be db been some minimum and maximum vale, follows ha the
enr of eng, a material property i stitution and hu is aia in.
nae, Chapter 20 provides move del o statistical considerations in design. Her we
Wil simply describe he results fone example Ex. 20-4, Consider the following table
Which ia ira report containing be maximum sess of 100 tensile est on.
1.1020 sel tom a single heat Hee we are eckng the ultimate tensile strength S,
‘The oan frequency is the number of oscumences within a 1 Aps range given by the
lass midpoint This, 18 mania Ses vales occured in the range of 9 10 $8 Ap

18 23 91 83 109 138 151 199 190 82 49 28 11 4 2

o Mpa
ps

1563 57:5 58.5 595 605 01.5 625 033 O45 655 665 675 695 WS 705 715

“Tae probably density is din asthe number of ocumences divido bythe ta
‘sample number The ar chart in Fig. 2-5 dpi the histogram of e probability den“
‘Sigs If the data i athe form of a Ganson normal diri, he probably
¿ense function determined in Ex. 20-4 is
(S88)
RU]

where the mean srss i 63.62 ps and the standard deviation i 2594 kp. plot
Of FC) is included in Fig. 2-5, The description ofthe tenth then expressed
in terms of is saistical parameter and ls distrihuien (ype. In ths case
So = N62, 2598) kp,

Note thatthe est program has described 1020 property Sa. or only one eat of
‘ove suplir. Testing isan imohcd and expensive process. Tes of proper ae
‘often prepared 1 be helpful o other persons. À sata quantity is described by is.
rea standard deviation, nd dits type, Many tables display à single mame
Which is ote the mean, minimum. or Some pernil, such as the 99th percentile.
‘Aways ead the fonots tothe tbl no qualification is made ina single etry tbl
‘te table subj to serous dou

Since itis o surprise ths useful descriptions ofa property re tts in mature
engine when orderin proper tet, sould couch the instrcions so the data ge
‘rated are enough for hem to observe he tit parameters and 1 nly the dis
Aibatiooa characterise. The tensile test program on 1000 specimens of 1020 see isa
large ene If you were faced wäh puting something in a le of ulimate tensile
Strengths and constrained to single number, what would tbe and js how would your
Footote rea?

10 ap

HS

Ett sige | mn

ad
Dt ane

Figure 2-5
go fr 1000 te
one 1020 mo

Figure 2-6
ong ende od
pos ego gan

omic | a8

‘ene si

Strength and Cold Work

Cold working ise proces of plastic sing below the relation temperature
inthe pla region of the aies rai diagram, Materials can be defomed plialy
by the pplication of heat sin blacksmithing or hot ong bu the esulng mechan
ical properties are quit diferent rom those obtained by cold working. The purpose of
this section sto explain what happens tothe significan mechanical properties of a
‘materi whe that material cold work.

‘Conse the ess diagram of Fi. 2-6, Here a material hasbeen stressed
Beyond the ie rent a 1 Some point , in the plastic region, and the the load
‘emoved. At this pont he material as à permanent pase deformation ¢ the oad
‘omesponding to pnt snow reapplied, he material willbe elatally deformed by

CPS Es Stan

a

ad
Dt ane

‘the amount Thus at point the toa uni strain consis ofthe wo components and
“ans given bythe equation

egte la

‘This material can be unloaded an reloaded any number of mes from and to pont
and found that the action alway cu along the sgh in hat point
Iy paralelo the inal elastic Hine Oy. Thus

a wi

‘The materia now has a higher ied point, es tile a a rs of a redaction in
ain capaci, and sido be strai-hardeed be process is continue, increasing
“the material an become bite and exhibit soe Facture.

Tes possible 1 core a similar gram sin Fig. 2-0), where the abs x
the are deformation and the ordinae is the applied la. The reduction in area cor
sponding othe lad Py, at fractures defined as

wher Ay the orginal rc. The quantity Rin EQ
ent and that in Is of mechanical properties as a measure of daily. See
“Appendix Table A-20 for example. Ductlty i an important popery because it me
‘sires the ability ola material 1 absorb overload and 1 be col-worked. Ths such
Operations as bending, dig. beading, and sete forming ae metal processing
‘operations require ductile materials.

Figure 2-69 ca also be used 10 define he quantity of cold work The court
foci Wis dined as

do dom
A “A

1

where A corresponde 1 he arca ar the lad Phas ben released. The approxi
ion in Eq. (2-9) results because ofthe iu of measuring the small ame
changes inthe ela regio. Ihe amount of cold work is known. then Eq (29) can
es forthe area A, The esx

4

Aw) eo

(Cold working material produce a new st of vales für the sun, as can
be sen from satin diagrams. Dato” describes the pls region ol he te
res tue sain diagram by he equation

omo em

Tp Dan Sold MAIN Ci 2 lg Me nf on 1
ph Da New ka Merl Seg Main D ot Sm 3 Fa 6 188 88S

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co | as

whore o tue stress
= à suengthcoefiient, or stain suenptening coccion
= ue pla stain
Im = sain-stengtening exponent
Ita be sown! hat

mae an

provide that the Load defomation curve eis a stationary point (a place of ero
slop

ificles aie when sing the gage length to evaluate the ru strain in the
plastic range, since necking cases tbe stain 10 he nonuniform. A more Saisactory
Featon ca be obtained by using the area the nec. Asuming that he change in vl
tame of the material stall, A = gl. Ths do = Ao/A, and the tre stain is
en by

1
mi
u

CE]

Returning 0 Fig: 2-6, point isto the et of pont ati < Pa then he
now yok strengths

A
en

at er ea

Because ofthe reduced ara, ati, becas A = An the ulmato sing aso
‘anges ands

la

Since P= o, we find, with Eg. (2-10) hat

ya Sto .
a Me (os)
‘which vali omy when point it he et of point u.

Fo points tothe gh of the yield rengc approaching the ultimate regi,

and, with sal os in au.
KES Sou ace en

‘ith wil veal ha ar wil ave he same ulómate loan enon after
Being ri strengihned in tension asd before. The new sen i of intrest 10
vs no ca the sti ultimate load nens, but—sine fatigue strength ar cr
Felted with the loc) ltimatestenghs-—becase the aigue strength improve, AO
the yield srengih increases, giving larger range of sustainable lst loading

PSS SANE Shi an RM Masi ei Dion ho Mem,

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Answer
Answer

24

‘An annealed ASI 1018 sel (se Table A-22) has 5; = 320 Kpsi $, = 49.5 kp

19; = 911 Aa, = 90 ps = 0.28, and ey = 1.08 ini. Find the new values of

{he sens if the material is given 15 percent cold work,

From Bq, (2-12), we nd the vo sain corresponding to the ultimate sento be
=m =025

‘The ratio A0/A, is, from Eg, 2-9),

1
0

w

‘The tue san coresponding 1015 percent ok work is blind fom Fig. (2-19. Ts

= in À = 101.176 =0.1605

Since < u Bas. (2-14) and (2-18) apply. Therefore,
5, = out = 9001629" = 57.1 kp
Sos

CRE

al

$82 aps

Hardness

‘The resistance ofa material to penetration by pointed oo called hardness. Though
‘here are many hanesemeasurngspsems, we Shall consider here only the two in
retest use.

‘Rockwell harness et are described by ASTM standard hardness method E-18
and measurement are quickly ad easly made, they hve good reproduciili, ande
{est machine fo them as to se Inc the hardness number ead dry fom
dial Rockwell harness les are designated a A, BC... et The indenters are
“escri a a diamond, à in diameter bal nd diamond for scales A,B, and C,
respectively, where the load applied ister 6. 100.0 150 kg Ths the Rockwell B
al, designated Ry, ses 10-45 lead aa No 2 nde, wich sa
Ball The Rockwell Cscale Re uses à diamond one, which is he No. Tete, and
load of 150 kg. Hardness numbers so obtained ae relative. Therefore a hardness
‘Re = SO meaning only in rein another hardness number asin the sre sale.

‘Te Briel hardness is anather est in ery general use In testing, the indenting
1001 trough which Force is appli a al and ie harness number pi found a
‘number equal othe applied loa divided bythe phericl surface aca oF the inden
ation, Thus the unis of Hg ae the same as tose of sues, though hey ar seldom
‘so Brinll hardness testing akes more tims, Since fp must be computed rom the
{est data The primary advantage of boh methods tha they ae nondestracine in
mos ase. Both are empircally and dirty elated othe ultimate eng ofthe

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‘materi tested. This means that he strength of parts could if desied be ested pat
ty par during manufacture
Fü stes, he relationship between the minimum ultimate stent andthe Briel
hardness number for 200 Hy < 480i fon 1 be
04950 ps er
PTE 2
Similar ainsi for as rm an be dived rom data supplied by Kruse.
Data from 72 est of gay on produce by one found ad poured in vo zes est
bars ar reported in graph form. The minimum tenth s defined bythe ASTM, I
Found rom Uhse data be
O2 = 125 gsi
(Er as
Wat shows char rom which he SAE minimum sengú can be obtained The
resis
5, =02878Hy— 16 psi ea
‘which seven mor comerse than the vales obtained fom Eg (2-18,
EXAMPLE 2-2 Its necessary to ensure ha a certain pat supplic by a foundry always mecs or
‘exceeds ASTM No, 2 specfiuons for cst ron (ee Table A-28) What harness
Soul be specified?
Schsion Frm Bg. (2-18), wih (n= 20 paie ae
Haw SES 204125 ay

25

C0 a

AS he foundry can contro the hardness within 20 point, routinely, then specify
145 = Hy = 105. This impone no harsh onthe Foundry and assure the designer
that ASTM grade 20 will always e supplied aa predictable cost.

Impact Properties
An sel ore applied a ste o pat scale an poc oa ithe ine of
pliz es an one hl te Ki nt period of aon he pa or
ice Oir called singly lt

FD E Keane “Gay A Unie Engine Mur” ASTM pl bn 5.190.

COS Ders Stein

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Figure 2-7
She on pa
tengo, chr ded ot
nee pas fc he
15%. Weal The cone
tongue e ian on
Veatch con ed

Figure 2-8

‘The Char (Commonly ts) and an eel sed ore ar tests lie bas of
pi geomet o determine tenes and impar strength, These tests ar ela
in omparing several material and in the determination of low-temperature lene
‘bath ests the specimen is suck by a pendulum released rom a ned high. and te
energy absorbed bythe specimen, called the impo value, can be computed rom the
‘ei of swing alter tre, bt rea om a il that essential “comptes” the esl
‘The effect of temperature on impact values i shown in Fig. 2-7 fora materia
stoning dette itl transition. or all materials show this transition. Notice the
arrow region of rial temperature where the impact value incas very rapidly In
{he low-tmpeatre region the future appears sail, shatering type, whereas the
“appearance tough, ering type above the eval temperature pon. The enc
Temperature seems 1 e dependent on hath the material nl ie geometry of the th.
For this reason designers shoul not rey 10 heavily on he ess of notches bar est.
“The avenge nin rte wed in bling the sesamin digan is about
0.001 iin: Y rl When ern rates nen, ts under impact condition,
he ent nee, shown in Fig, 2-8 Im fact. al very high stn rates the yield
strength seems o apecich the timate srengh as mi But note hat he cures show
Title change in the elongation. This means tha the ductility remains about the same.
lso, in view of the har increase in yield según, a mild sel cold be expected lo.
chine elastically throughout pecially ete suengh range unde impact conos

Deere

fre |

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26

Figure 2-9

Apache mada sun
A coten pd do mat
Soneg be dre
danger en bo fl
Sug dro
Sur 3. Pecado ta
od tenechthe
00442 284 20152 le
Sad 00 2a son
EL owen A
Borde Sal Me
fre oc he
Bci onde, 1989
pe 22128022131)

omic | a9

‘The Charpy and dt really rove ong data under dynam. rather han
static, conditions. may wel be hat impact data obtained from these ests ar as depen
“den the notch geomet as they are onthe stain at. Frese rason may Be et
ter to une the concept of nach semi Facture toughness, and facture mechanic,
discussed ia Chaps Sand 6,1 ass the poil of eacking or Facture.

Temperature Effects

Strength an dy, crees, ar peris fee by the tempera fhe
pong eninnnen.

Th lle fener e papers of secs pied be sen
Nena empersur ea Fp 2-9 Nath he ik engine nal
hvu um or per rel Att plo id, E
Strength however dees cota th emitan iempere ls na
‘Terao mre dy igh sped th ger emporte

"ny ts hn hn neo fora mea ted Con de ong
Per me ated temperate The psi were oo be pene
ac amg de cee gh at tse al ees wee los an e
$A seg of hc mal aie om chore et mal ae sane emp
ATi comin eration nd lon ced omen

‘Och mnt ul ou have bn dv eng mer der
constat od pe 210 ists a cane ats Dal of is Kind es The
Sore ane a const sd empero À mmr of et ely un
Stay a der sess men Te cane eas the dine ein
inde tar nd ei ande pls eat Ti ng ss
À deny cep rch e de ss lin, The rind se shows
2 canst ini ep rt en y ami et. the hid age he
‘reine ns a are reden im a, the A ari, nd à
Maher cep eva adv ste

hen the opening tempranos ar toner an the wann tempera
(Fig 2". polig ae ta ar sol a yt cr. Ti
Sify caused Ch à

| nat Sil | Lai Mal PT
E
=

20 | tram Dan

Figure 2-10

27

(OF course, heat restent vil e shown, sued to make substantia changes in
the mechanical properties of à meri

Heating duet electric and gas welling also changes the mechanical properties.
‘och changes may be due to clamping during the welding proces, as wel as heating:
‘the esting sesos then remain when Be ars have cooled andthe lamps ave bee
rem. Hardness fests an be set lear wheter the strength hs been changed by
Welling, bt such ets wil no reveal he presence of rsd sesos

Numbering Systems
‘The Society of Automotive Engineers (SAB) waste fis wo recognize the need. ad to
apt a system. fr he numbering of sts Later he American Ion and Sie Insite
{AISI adopted similar system. In 1975 the SAE published the United Numbering
‘System for Metals and Alloys (UNS); is system also consis cross reference num
‘bers or otber material specications.” The UNS uses ter prefix 1 designate the
material. a for example, G forthe carbo and ally sel, A fr ih aluminum loys,
{Corte copperbase alloys and $ fr the stainless or comsion stan sees. For
‘some mate o enough agreements ss yt developed in he sry o ara
the eablisiment fa designation.

For he tel the fist two numbers allowing the eer prefix indicate the compo
‘ion, exlaing the carbon comet. The varus composition used are a Follows

GIO Fancobon 46 — Nidelnalbdon |
GN Fewcutngcarten sed wth 648 Nilo

cs hao postor CH Chona
13 Mongo St Chonim
23 Nebel 052 Chemin
625 Nelo 01 Chonimenodım
G31 Nietos Go ee
33 Nidelchomm G37 _ Chontmmicalmefelenn
0 Mohan 92 Mongonesesicon
SH Cromermayideran 694 Nedelchemimmahbdenn

GA Nekkchonkmmohtrun

Fa fie mas dcs ac gr a li be Ai ae Be u

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Table 2-1

Alurirum Aloy
Designations

28

Ami 99.00% pure ord gos Ach

Copper alloys Ron
Norma alo pe
icon los Bud
Mognesun los pene
Magresumalicon loys pea
re llos Ton

“The second number par refers othe approsimat carbon coment Thus, 61040 is a
sin carbon sec witha nominal carbon content o 0.40 percent (0.37 100-4 pesen,
‘The th amber following the pets nse for special ions. or example, the ld
<esignaion AISI 52100 represnt a chron allay with abou 100 points of catho,
“The UNS designations G52986.

‘The UNS designations forthe sinless sc, rl $, lize the oder AIS des
ignaios forthe fist thee numbers following the pre. The next two numbers are
reserved for special purposes. Theft number o group indicate the apposite
‘composition. Tun 2 à choniunaickl-manganese sec, is a chrome
Sel ands chromium ally wel. Sometimes stainless cs are refered toby ir
alloy content This 530200 i fen call an 1.8 salen ic, meaning 18 percent
‘wom and 8 percent ike

“The pets forthe aluminum groups the ete A. The frst number following the
prefs indices the processing. Fo example, AY is a weought aluminum, wile AO is
A casting alloy. The second number designates the main alloy group as shown in
“Table 2-1, The third number inthe group i use to modi the orginal alloy or 10
esigate the impurity limits, The at two numbers eer ober alloys wed withthe
base group.

“The America Society or Testing and Materials (ASTM) numbering system for
‘astro i in widsprad se. Thi system base onthe tense strength. Thus ASTM
[ATS speaks of lances eg. 30 as won ha a minimum tensile strength of 30 Kai Not
from Appendix A 24, however, ha the pica tes sg i 3 psi You sould
Be call to designe which of the two values sus in design and problem work
because ofthe seance of factor of safety

Sand Casting

Sand casting sa tase low-cost proces, and it ends isl 1 economical production
in large quads with practically no limi 10 he sie, shape. ce compleiyofhe pat
produced

In sand casting, he casting is made by pouring molten metal into sand molds. À
pattern commet of etl or wood, is wet form avi nto wich he mien
nota i poured, Roces res he casting ae produced by sand cores inoue.
imo the mold, The designer should make an effort visualize the ptr and casting
inthe moll nhs way the problems of core setting, pater removal, ral, and sl
ication ca b tic. Casings 1 be usadas est Drs o ston are east ea
and properties may vay

Crea == a

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22 l'on agree Dago

‘Ste castings are the most ficult fal to produce, because sel has he highest,
meing temperate ofall materials normaly usd for casting. Ths high empece
‘egrivates al sing problems

“The following ls wil be fund quite useful in he design of any and eating:

1 Allsctons should be designed witha uniform thickness.

2. The casing should be designed so as to produce a gral change from section
to section wher this isses,

3 Adjoining sections shoul! be designed with generous iets or adi

4 complicated par should be designed as tuo or more simple castings 1 Be
assembled by isteners oy welding

‘Sec, gay ro, bas, bronze, and alominum ae mos ofen und in castings. The
ini wall chess foe any ol these materials abou mun, though with parc
tar ar, inner sections can be obtained with some materi

Shell Molding

‘The selh-molding process employs à bated metal pater, usually made of ext rn,
laminum. or brass which spaced in shell mokding machine containing a mixto
‘of dy sand and hermoseting resin. The ho aten melts the pat which together
withthe san form shell about 51010 mm hick around he pte Th hell sen
‘ake at from 40010 00°F fora sor tine while tl on the pate, en ripped
From the tem and placed i storage for sein esting.

Inthe net sip the shells ae assembled by clamping. bling. or posting: hy are
place in a Backup material, such as tc shot ad the men metal is poured it the
‘avy. The hin sll permis the sat e conducted avay so that soliton aes
le rap. As soliton as place the plastic bond ured andthe mol ol
Taps. The penneabiity ofthe backup materia allows the gases to escape and the as
ing 1 aro Al his asin obtaining a fine-grain. rss fe casting

Shell mol easings fur a smooth suce a rl thats que al, and lose
tolerances. In general, he ules governing sad csing lso apply 1 held cas,

Investment Casting
Investment casting uses pate that may be made om was pst, or ter mate
Aire molds made, he pte meted out Thus a mechanized method o sting
‘great many pates is necessary. The mold material is dependent upon the melting
Pt of the cist metal Thus à plaster mold cn be used for some materials wile
‘thers would require a ceramic mol. After the pate is meld ou, the mods baked
‘rire: when frig is completed the mien metal may De poured int the ho mold
“allowed to coo

Iranımberof castings are 1 be made. then metal or permanent molds may be sit
ble, Such mods have he advantage hat the surfaces re sooth bight and accurate,
So that ei any, machining is required. Metal mol castings re also known as de
castings and conga castings

Powder-Metallurgy Process

‘The powdermetalugy process is a quaniy-prouctin process hat nes powders
from a single metal several met, ra mitre of metal and oneal I consis
scaly of mechanically mixin th power. comparing em indies thigh ess,

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Figure 2-11

Connon hopes vole

oma | aa

and heating the compacted part temperature les than the meling point ofthe major
ingresen The palos ar united ino a single in par Similar o what woul be
‘obtained by meling the same ingredients together The advantages ae (1) the elimi
tin of sopor wate material, (2) he cimination of machining operations (3) th lose
unit cost when mas-pradcnd, and (4) the exact Control of composition. Some of the
<isodvantages ae (1) he high cos of is, (2) te Tower physical properties. 3) the
higher cot of mater, (4) the limitations on he design, nd (5) he mite ange of
materials hat canbe use. Pats commonly made by is process are oiimpregnated
bearings incandescent lamp fament.comentd-carbi tip for o: and permanent
‘magnet Some products can be made only by powder metallurgy surgical plant, or
sample. The structure i dire rom what can be obsined by meling the same
ingrdiens.

Hot-Working Processes

By hor working are meant such process as rolling, Forging. ht euro, ad hor
pressing in which the metal i aed above rc allo temperature

Hot ring is wally we o rate à bar of material of à prior shape and
dimension. Figure 2-11 shows some ofthe various shapes that are commonly produced
by the hotsollig proves. Ao them ae available in many different sizes a well as
in irn materi. The materials mon salable in he hot elle ba ies are sic
aluminum, magnesium, and copper alloys.

“Tubing can be manufactured by hot rling sripor plat. The edges ofthe ip ae
ollo og creating seas are eter ut welled rap welt. Sales ub-
ing is manufaturedby rol iccing a soli heated od with peeing mare

Erion is the process hy which get pesones aplico ated met il
‘or blank, causing ito low though a resco ore. Ths proces is more common.
‘with materials oFlow meling poin such a alumi, copper. magnesium, kad. in,
and zinc Stiles tel extrusions ae avaiable on à more line ha.

‘Forging isthe bot working af metal by hammers, pesses,c orgias machines. In
‘common with ater hot-working process, forging produces a reed gran sucre
that esl in increased strength and dat. Compared ith casting. fering have
reer sen forthe same weight In ation ro forgings can be made smoother
and more accurate than and castings otha ess machining I necessary. However. the

ntl coat af the forging dis is usually geste than the cost of pas for caga,
although the greater uni suengih rather than the cost is usualy the deciding cir
sen these to procesos

mac; == a

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Figure 2-12

RECORD.

Cold-Working Processes

By cold working is meant the Forming ofthe metal we aa ow temperate (sly
‘oom temperature), In contrast to prs produced by hot working cold med ps
have a bright new fish, re more acute, and equ es machining

Coldimishe bars and shafts produced by rolling. drawing. turing. grinding.
and polishing. O hee metods, y far the largest percentage of products re made by
the coding and col-deawing procesos. Col rolling is now used mest forte
ration of wide flats and secs Practical al cld-hnishe har are made by cold
ravi bat exe so ae sometimes mistakenly called "colo bars” Inthe ding
process the hol Ban ae fist leaned sal and ten dawn by pling them
rough adie Ut edaces the size aout sh 1 1 in. This proces dos no remove
aerial rom the bar but reduces, "draws down, the size. Many dire shapes ol
hotell bars may be used for ol drawing.

(Cl ling and col dang have the same effct upon the mechanical proper
ties. The cold working process does nt change the grain size But merely dso i
(Cold working resul in large increase in yield strength, an increase intimate
‘rength and hades, and a estas in duel. In ig. 2-12 the props of aol
‘drawn Bar are compared with ose of ahold ar o the same mate

Heading a cold woring process in which th metal i gatered. or ope. THis
‘operation i commonly used to make screw and ives beads ands capable of producing
a Wide variety of shapes Roll reading isthe process o rolling heads by squeezing
androllngablan between wo erate dis Spimöngi ih operation of working hee
hel round a rotting form into a cular shape. Stamping isthe etm und 10
¿describe punch-press operations such as Banking. coining, forming, and sallow
demi.

The Heat Treatment of Steel
Heat eament of sel fers tme: and temperture controlled processes at relie
‘residual stress andor modifs material properties suchas hardness (tren) ds
{ii and toughness. Other mechanical or chemical operations are sometimes grouped
‘under the healing of es eaten, The common hat testing operations are anes
ing. quenching, tempering. and case hardening

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Annealing
When mater scold: o ht worked eda tease are built in, and, ination,
the material ually as a igher fanless asa real thse working operations. These
‘operations change the sce ofthe mail o tht sno longer represent by the
Slim diagram. ull nnealing and normalzing à a heating operation bat permits
the material 10 tansform according o the equilieum diagram. The material to be
anale seated oa temperate hts approximately JOD above thecal em
erature. I held at this temperate forte that is suchen fr the carbon lo
Become disolved and diused though he mater. The objc being wate is then
allow tocol slowly, usual in the face in which it was tated, IT Ue transfor.
tation s complete he itis si o have a fl anneal. Annealing is used 0 son a
Iter and make it more di, to relive residual ies, and o reine the gain

"Te ermanncalng includes the process called norman. Paso be nomalizad
may be heated à slightly higher temperature han in ol aneaing This produces a
‘oan gran sroture, which mv easly machined ifthe materi low-carbon
Stel In henormalzing proces the paris cold in sl arat room emer Since
this cooling is more pid than he low cooling used in fall annealing es tine is nal
able for equim, andthe material is hard thn fly annealed ie. Norman
is aten used asthe final eating operation fr scl, The cooling i sl amount 10
slow quench,

Quenching
Eutcetid sto ha is fly annealed consis ently of peut, which is obtained
From austenite under conditions of equilibrium. A fllyanealed Iypocuecci tel
‘woul const of patie pls fet, wile hyperetccoi tec nthe fly anealed
‘condion wouk Cosi of parte pls cementite. Th hardcss of sel of a given
Garon content depends upon the rte that replaces the partite when ull ana
ing isnot cried ot

"The absence of fll amesing indistes a more rapid rate of cooling, The rate of
‘cooling i the factor that determines the hanes. A controlled cooling rt à called
“quenching. À mil quench bind by coking in air, which, as we have een is
haine bythe normalizing process. The two most widely used medi Tor quenching
Are water and ol. The cl quench quit sow bu prevents quenching rocks cased by
rapid expansion othe objet ein reed. Quenching in water suse For carbon eh
{nd for medium carton lowly sec

"Te effectiveness ol quenching depends upon the fat hat when austenite is cook d
it des mo aston ito pare inantaneouly bu requires me o init and co
Piste the proces. Since the transformation ceases at bout SO, can be prevented
by rapidly coming the material à lower temperatur. When the material cole
rapily to AU ores, the austenite is wansormed no a structure called martensite
Marne supra sai solo of carbon in ere and à he hardest and
stenges fom of ic

Te steel spay cooled 10 a temperature hetwcen 400 and 800°F and held ere
Fora seen length of tne, he auenie is transormed ino a meri tr gener
ily aio ines Ban is a tue intermediate between pes and mares
‘Although thre ae several tures that canbe int Between the temperatures
given. depending upon the temperature used, they are coletiely Kn as aii. By
the choice of hs transformation tempera almost any variation of state may be
obtained, These range all he way from corse parto fine martensite

Ce Ders Stein

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Figure 2-13

The li ol arc
ech popes AS
1340 ed. pd e
tered Nel Cogan)

Tempering
When a tel specimen has ben fll hardened. is very hard ad bite and has igh
sk sees. The self unstable and tends to conc on aging. This tendency
is increased when the specimen is subjected 10 extemal applied loads. becuse the
san sess conte sl more to the instbiy. Ths intel sees can
Be reve by a moles eating process calle tes liens o combination of
‘tres eleving and softening ale tempering ox draning. Ar he specimen has een
Fully hardened by being quenchd fom shove thecal temperate, i reheat 10
some temperature Below the eral temperature fo a certain period of ime and hen
flowed ooo! in il ai. The temperate o which tis reheated depends upon the
‘composition and he degree of hanines or wighnes desred* This schaing operation
less the carbon ei in the martensie, foming carbide crystals. The structure
‘obtained is called tempered martensite, is now essentially soperine dispersión of
iron carbides in ine grained er

‘Te effet of hea train operations upon the various mechanical proper of
How ally ste shown prptialy in Fig. 2-13,

RCE | Emptor [ct
omitió | stents | seme | rca | "inn | ards,
tet | it | ae [ue

“Tere quae apc feng pi con mil yl se Cats. Miche
ne Sung ist! an Ho Termos So Chap. Ju Cl
Miche an hms Dan. Jo) Sunn aloof acne Dee, Me

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Caso Hardening
“The purpose of ese hardening i produce a hard aute surface ona specimen of low
can sel while at the same ine scan the ducliy and unes ide core
Fi is done by increasing the carbon content a the surface. Ether soi, Hi or
sous crturising material may he usd, The proves consis frein the prt
to be carbuczed into he carburizing materia or à stated tie and a tated tempers
tur. depending upon the dep of esse desire nd the composition a the pun. The part
ay then be quenced dre rm the castizo temperature and tempered, in
Some cases must undergo a double beat treament in order o ensure hat ol the oro
{nde case ae in proper condition, Some ofthe more cl ame ardenin process
ase pk chaine, gas carburizing, ning, cyaniding, induction hardeing, and
flame hardning. Inthe at wo cases carbon add he sic in question. ge
ralla medium carbon el for example SABIAISE HL,

Quantitative Estimation of Properties of Heat Treated Steals
<Counes in metal (os materia! since) fo mechanical engineers wally present the
dion etd Cats a Lament or the edition of he wet properties one
Tominy sfr Pan caro sts? 1 this snot Benin your presque express,
then reer toe Sandar Handbook of Machine Design, whet be ln meh son.
‘red wth examples I ook atexbook fra machine clement cours, is good
las projet any hands make ight wor) to stay the method and reporto he las
Few lowalloy ste, de multiplican method of Grossman and Field” À
‘xplind inthe Sndond Handbook of Machine Design (Sees. 29.6 and 3.0)
Moden Stes and Their Prpertes Handbook explain how o pea he Jominy
‘are by the meta of Groseman and Field From alae analysis and grin se
Bethlehem Sie has developed ail plat ide ile ati comento purpose.

Alloy Steels

Although a plan crbon see isan alloy of ron and carbon with small amounts ol
manganese, icon, sul, and phosphors, he tr alloy sels applied when one or.
‘more elements other than Carton are introduced insulin quantities 10 modiy is
Properics substantial. The alloy sels not only poses more desible phyical
Properties but also permit greater latitude in he herein proces.

Chromium
“The addon of chromium results inthe formation of various rides of chromium hat
are very hard, ye the resting sel sore date than see ofthe same ares ro
‘cel by simple increase incon content Chromium alo refines the grain tte
So tt these two combined ffs esl in both increased toughness and increased hard
mes. The ation of cromium increase the cial ange of temperature and moves
the cueca pois tothe let Chromium is thus avery sal lying element.

"Cuts ice. nn Sih. Chae Me Tie Bas, (A
‘Sunn Hao Main Deg Gr Ne Ve 0 33,

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Nickel
“The ation of chelo steel also cases the eut pont to moe tthe and
increases the clica rage of temperatures. Nickel i solble in Fert and does ot
form caries or oxides This increases the streng witout decreasing the dict
‘Case hardening of nike sees rel na beter coe than ean be obtained with plan
(ron sec, Chromium i reguenly used in combination with nickel to ola dhe
Loue and dut provided by the nickel and the wear resistance and andes
‘one by the chroma,

‘Manganese
Manganese is add tal tes a a eoxiiing and desulfurkzing gent, bat if the sal
Fur coments ow and the manganese conte is ver 1 percent he ic is ls à
manganese alo. Manganese disolves nthe ere and also forms carte. cases
the enectid point o move tothe lel and lowers the eral ange of temperatures.
inernsesthe im rue or transformation so hat oi quenching becomes practicable,

Silicon
Silicon is added 0 a sels a a deondizing agent. When aed o ver-1ow-crbon
tel, produce à ite materia with low bytes os and à high magnetic
pemeabliy. The principal use of sce is with other alloying element. such as
manganese, chromium, and vanadium, 1 Sail he carbides.

‘Molybdenum
‘While molyhdenum used alone ina few sels it ind its greatest use when combined
with oer alloying elements, sch as niche, chromium, or both. Mol ena forms
«abi and also solves erie o some exten, x hat tas both hardness und
{oughnes, Molybdenam increases the cial ange of temperature and sbi
lowers the wansormation pont. Because ofthis lowering the transformation po,
molybdenum is mos effective in producing desirable o-hanening ad a-harening
properties. Except for carton, it has the pestes hardening e, and because I ao
‘Sonesta fine grin sie, this esas in he retetion o a great ea toutes

Vonadium
Vanadiam has a very song tendency 1 fom cutis; hnos i use only in small
amounts Iisa strong deoxiizing agent and promote a ine gran size. Since some vana
¿amis dial nthe frie, bo aghen he sel Van gives a wide halen
ing range o sel, nd he alloy can be hardened fom a higher temperature. Is very
<tc soften vanadium see by tempering: Pee. is widely wed ol cs.

Tungsten
Tungsten is widely sed in oo sels because the to! wil mana its hardnes ven
teed heal Tungsten produces fine, dense ste and als both toughness hard
Nes ect similar 1 that of molybdenum excep that must be added in preter
vanities.

Corrosion-Resistant Steels

Irontas alloys containing a lest 12 percent chromium ae called saints sets
“The mod imporan characteristic of tes tess ther resistance to many but not al
comes conditions. The four types availble are the fer chromium ste the

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austeniie chromium nickel cs, and the martensite and precipitation hardenable
Maines tec

"Te e chromium sss hac chromium content ranging rom 12027 per
‘ent. Thor ori resistance ia union of the chromium content so tht alloys
‘containing less than 12 percent sl exi some corosion resistance, although hey
may rust The quench-haenäili o hese steels a Función of both the cromium
{nd he carbon content, The very high carbon sel ave goa quench arab up
to about 18 percent chromo, wile inthe wer carton range I ceases at about
13 percent a ite nick add, hese cl retain some degre of hunenabilty up
Lo 20 percent chromium. I the comio content exceeds 18 pre, hey become di
cult to weld and at the very high chromium levels te hardness becomes s pea that
very cael attention must be paid he service conditions Since chromium expen
Se. he designe will choose the loves cream comen content wi the como-
sive conditions

‘The chvomiomnickel sinless ses ren the austenite srt a room em
erature; hence, they are not amenable wo ha! resumen, Te singh ofthese sees
an be rely improved by cold working. They ae ot mugne unless col- worked
‘Ther work ardenbility propres alo case them to be dial to machine. All
the chromium cel tes maybe welded. They have greater comesion resistant pop-
‘ties than the plain chromium sch. When more chromium i a fo rete co.
rosin resistance, more nickel mus abo be add if he austenitic properties re 10 be
resin.

Casting Materials
Gray Cast Iron
‘OF all the cast mat, gay as ro isthe most widely use, This is Because a has
avery lo cost is easily as In large quant, and is easy to machine. Te principal
objetos tothe use 0 gray cst ion a tht bite and ha is weak im tension,
In din toa high carbon coment (ve 7 erent and usally greater than 2 percent
ut icon also Has a high shcon content wth low percentages of sul, manganese,
and phosphorus The result alloy is composcd of peat, Tre, and graphite, and
under ein conditions the petite may decompose into graphite and fr. The
resuling product then contains al fete and graph, The graphite. in the form of
thin Maes dite evenly thoughoutthesracture, darkens enc, the mame grey
‘Gray cast iron i not edly welded, Because may erick, bu his tndeney may
Droste parts ar rected, ouh the eating are generally wed in
the ascast condition. a mik ame) reduces cooling stresses and improves the machin
sili. teni srengthof gay cst ion varies rom 100 o 400 MPa St 60 ps)
and the compressive strengths are 3 10 4 mes the tensile strengths. The module ol
lin varies widely, with values extending alte way from 75 to 180 GPa (I 10
22 ps

Ductile and Nodular Cast Iron
Because ofthe lng heat treatment required to produce mallahe cast ion, engineers
have long desired cast irn that would combine the dut popes of malleable
iron with he ease of casting and machining of gay ion and athe same time would
uses tes properties inthe act nd. A proces fr puduing such a ei
Using magnesian-contining mara seems 1 ull these requirements.

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"acti cast on, nodular cas iron as is sometimes called is een the
same as maleble cst rn, because bth contin graphite in the form of sper
However, dite cas ion in the as-cast condition exhibis properties very clone to
‘those of malleable on. ad a simple Ich annals given andi followed by a slow
‘ool ei even move ductility lan th malleable predict: Duce wns made by
“ali MaFeSi the mel since magnesium boi at hs temperature iis necessary
Lol it with other elements Before is introduced

Duc iron as a high modulus o elastiity (172 GPs or 25 Mp as compared
with gray cast ion, and ii elastic inthe seme that a potion ofthe testa
curve a rag ine. Gray cst ion, the oer Rand, does ot obey Hooke law;
because the modules of elasticity stcadily decreases with increase in ses. Like
gra cast ion. however, nodular iron has a compresive strength that i higher han
etes strength, although the ference in an rest I 0 year thas become
extensively wd

White Cast Iron
AFal ie carbon in cas ion inthe form of cementite and pet, with no graphite
present herein cr white and Aion as white cast rn. This may Be
produced in two ways. The composition may he aljusted by Leeing the carbon and
Silicon coment Tow or the gray-cast ra composition may be cast against cn ower
Lo promote api cooling. By eher method, casting wit age amount of cement
is produced, and a sul he produc ey rt and ard o mache ba also very
‘resistant to wear. cil s say used in the production of gay rn castings in order
Lo provide a very har surface within a particular area o be esting, while at the same
time einig the more derbe gray ttre within the remaining potion. This pro
doves a elie tough casting witha wear essa ae

Malleable Cast Iron
AE white cat ion within a crsin composition range is ames, product called
‘malleable cast ion is formed, The ane ain process res the caren or is pr
Sea as graphite jst asin gay cas ion bt in dire frm In gray cast iron the
{rapt present in thin Make form, while in malleable cast ro i has «nodular
Form and is known as temper carbon. À god grade of malleable cat ron may have
‘tensile strength of over 350 MPa (50 kp wih an elongation of as moch as IS pe.
Sem. The percentage elongation ol gray cst ion on theater Rand seem Over
Y percent Because ofthe time required for annealing (up 106 day for lage and
‘heavy Castings). malleable iron is necesarly somewhat more expensive than gay

Alloy Cast Irons
Nickel chromium, and molybdenum ae the most common alloying elements used in
astro, Nickel is a general purpose alloying lement sally ae in amount up 10
S percent Nickel increases the wrengih adden. improves the wearing quals and
‘ales the machina the nickel content is ase o 1010 18 pee anausteniti
irre with valable heat amd coroion resistant properties resus. Chromium
increases the Hades and wea resistance and, when usd with a cl, increases the
Lendeney to form wt ion. When chou and nickel are Both added, the hardness
“and strength are improved without eduction inthe machinabiity rating. Molybenom
ale in quant up o 1.28 percent increases the ss, hares, teni regi,
ná impact resistance. Ii a wey used alloying clement,

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Cast Steels
“The adratage of the casting proves is tht prs having comple shapes can be man
fact at costs ls than fahren by ether means, such as welling Thus the
choice of tel castings is lgial when he pu is complex and when it must aso have
à high eng The higher meling temperatures for sec do agravte the esting
problems and quie csr attention to such deals a ore design section thickness,
Fils, and the progress a cooling. The same alloying elements used for the wrought
sel an be used forcast tel 1 improve the stent and ter mechanical proer-
tis, Castel parts can also be Retreat to air the mechanical popes, nd
nik the cas ions, hey can Be welded

Nonferrous Metals

Aluminum

“The oustanding characterises of aluminum and its alloys ae er swengh-weight
rai, thee resistance o cocon ad thee high thermal and elcrcl conductivity,
‘The density o aluminum about 2770 gn" (0.10 in) compared with 7750 kp?
(0.28 fin’) or ee are aluminum as tes eng of aout 90 MPa (13 pl
but this can be improved consdeably by cold woking ad als by alloying with er
ater, The modelos of elsicky ol aluminum, s well sof alloys, 717 GPA
(104 Mpa, wich means that it hs about one the ses of ste

‘Considering the cost and strength of aluminum andi alloys, ey ae among the
‘mos versa material rm the standpoint fiction Aluminum can be processed.
bysandensing. de casting. hot cod working, rent. llyscan be ached
pres. worked, soldered, brazed, or welded. Pure aluminom mel a 660°C (1215°P,
Which males it very desable far the production of either permanent ce sand mol
‘costings, I is commercially avilable the form of plat, ar, ost fi od, and tube
nd in Sintra and exuded shapes, Cetin précautions mast he taken in joing
aluminum by song, raing, or Welding these ining methods re not recommended
forall alloys.

"The corrosion resistance ofthe aluminum loys depends pon the formation of à
thin oxide coating. This im forms spontaneously because aluminum inerenty very
reactive. Constat erosion or abrasion removes hs fim and allows corrosion o tk
place. An exasheay onde lm muy be prime bythe proces called ani. In
this proces the specimen is mae to come the ande ina lectus, which may Be
‘homie aci, orale aco suri ack tis possible inthis poses to cool the
‘olor ofthe resulting fl very accurate

"The most useful alloying elements for aluminum are copper silicon, manganese.
‘magnesia, and sin. Aluminum alloys re lasibed as cating alloys wrought
‘alloys. The esting alloys have greater percentages of alloying element o Aita
casting. but this makes cold working dic. Many ofthe casing alos, and some of
the wrought alloys, cannot be ardened by hestrstmont. The alloys tha ar bete
treble use an alloying clement hat disolves in the aluminum. The est weateat
‘consists of eating the specimen fo temperature that penis the alloying element to
pass into sohn, then quenching so raily thatthe alloying element sma preci
tated. The aging process may be aceerated by heating sigh. which suis neve
fester hardness and strength, One ofthe eter known heat resähealoys i dr
tin, or 2017 (4 percent Cu, 0S percent Mg. . percent Ma). This alley barns in
‘days a room temperature. sans ofthis rapid aging. he alloy mus be tore under

One == a

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refrigeration afer quenching and before forming o it must be formed immediately
te quenching Other alo (sch as $083) have Dee developed that age-handen much
tor slow, tht ony mild refrigeration i ried before forming. Afr foming
‘ey are alii aged in fuma and poses approximately the same srength and
"hands as he 2024 alos. Thos alloys aluminum hat canot be eat reed can
‘be arden only by cold working. BOB work Hardening and tb hardening produced
‘by eat teuiment may Be moved y an anealing process.

Magnesium
“The density of magnesium is about 1800 Kg" (0068 hin’, wich is uo id ha
of aluminum and one-fourth that of sel. Since itis te get of al commercial met
si retest wei inthe areraf nd automate int, Du ther ne are now
‘being ound for Although he magnesium lys do nt lave get streng, beaute
of thei lightweight he stenth-weight ratio compares favorably withthe stronger
lumina and el los. Even 50 magnesium alls ind thse genes use in app
(tions where streng is ot an importan consideration, Magnesia wll ot wilstand
eva temperatures: the yield pin is defintely reduced when the temperate 1
‘ied hal of ing water

"Magnesium and alloys havea mods of lsc of 45 GPa (6.5 Mpa inten
‘sion and in compression, laugh ome alloys are not as strong in compression a in
{ensin. Curl enough, co! working race he modus feasts À range of
‘ast magnesium alloys ae lso salable
Titanium
Titanium and ls los ar similar in strength o modert-sengih sel bu weigh all
as much as See. The materi ets very good reiten to orosion, has low th
mal conti, is nonmagacic, and has high tomperaue wrenih. is modul of
‘lant is Btwcen those of sel and aluminum at 16.5 Mpsi (113 GP. Because of
it many advantages over tel and aluminum, pplication el: aerospace and mil
itary leal tetes and components, marie hardware, chemical nk and process
ing equipment. Ad handling systems, and human internal replacement devices. The
“advantages of nium aes high cos compared to steel and aluminum ad he.
elt of machining i

Copper-Base Alloys
Wen coppe is alloyed with zn, sully called rss. Is aloyed with another
elemen. is on cll bros, Sometimes he ter clement ect, fore
“ample tin Bronce o phaspor ron. Thee are hundreds varias in ac eg.

Brass with $ to 15 Percent Zine
‘The losin basses are easy 10 cold wor, especialy those wi the higher ine on
{ent They re decile bt olen hand o machine, The corrosion resistance I goa, Alloys
inch in group ar lin ras (Speren Zn), comma brome (percent Za,
and red ras (18 percent Za) Giking Das is wed mosly or evel and nice to
be ok thas the sme diy a copper bu greaer tenth, accompanied by
ove machining characteris, Commercial onze se Fr jewel and fo fogings
and stamping, because of i du is machining properties ae poor, bt as
‘excellent cold working properties, Red ass his guod Cocoon resistance 2 well as.
igh-emperature senil, Because oh sud a great dealin he form of tubing or
Piping to cry bot water in such applations as ritos or condenser

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rss with 201036 Percent Zinc
Included in ie iermedisein group are ow brass (20 pers Zu) cartridge bras
(G0 percent Za). and lou bras (3 percent Za), Sige zine is cheaper than coppe,
thos alloys cst les han hoe with mor copper and les in. They alo have bar
Imachinabity and slightly greater tenths hs soe, however, by pos corrosion
resistance andthe possibility of racking at pins o residual sec, Low Wass is very
Similar o eed bras and suse for aces requivin deep drawing operations. OF the
oppetzne alloys, caigo bres has the best combination of duc and sien,
Cage caes were originally manufatured eniely by cold working he process
‘conse of series ol dep draws cach ra hing followed by am anal o place the
‘teri in condition for he next draw, hen te name cartridge bras, Alu he
hot working bility of yellow bass poor, can he ud i practical anyother ab
Fin proces and is ere employed in à ge variety of products.

"When small mounts of cd are od 1 thease, hr mactinabiliy is grey
improved and ihre I some improvement in thir ais o be hutworke. The
ition fea impair bah the cold working and welding propre. In his 2roup are
lowsteaded brass (32) percent Zn. | percent Pb) ile brass (34 percent Zu
2 percent PO) and Je cuting brass SS] percent Za. 3 percent PO). The loca:
rs sno only easy to machine but has good old-working proper. usd or
various serew-macine parts, High ead bras, sometimes called engravers ras.
‘sed for ise Tock, and walch pus Frecuing brass also used fr er
machine arts and has ood corroson resistance wilh excellent mechanical proper.

‘Admiralty metal (2 percent Zn) contains 1 percent tn, which imparts excellent
con resistance, especially o saltwater. I has good wrengih and duc but only
Falrmachining and working characters. Became o is coroion resistance used
in powerplan and chemical equipment. Aluminum bras (22 perent Zu) cons
2 percent aluminum and is se for he same purposes a admiralty mea, because à
has nearly te same properties and characteristics. Ine form o bing or piping is
Favored over admiral metal because has ets resistance 10 rin cad y high:
eh water

Brass with 36 1040 Percent Zine
Brases with more han 38 percent ine are les dct than carie bras nd cannot
be co-worked as severely. They ae frequent two and etude, Mint: etl
(GO percent Zu) slow in ost an ily corista Natal ras has the same
‘composition as Munt metal exept forthe ado of 0.75 percent i, which com
tributes to the comio resistance

Bronze
Silicon broce,cotsning 3 percent con and percent manganese in addition to the
‘oppet las mechanical properties equal 1 those o mid sel swell as god cam
Sion rias. an be ht or ol-worked, machined, or well. It is wel wher
‘ver corrosion resistance combined with seg à require

Phosphor ron, made wih p to 11 percent in and containing small ants of
phosphors especially resistant fatigue and comosion. I has high tee streng
nd high capacity 10 absorb energy md i also resta 1 wear. These properties
make it very useful sa spring material

"Amina bronce saat eat aly conning po 12 percent alominom This
alloy has Sent and corsioneistance properties that are beter han thse of bss a
ination, it properties may be vail ver wie range by col working, est rain

| unteres | Lai Mal PT
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Lacets

88 Loan Eng Dog

Table 2-2

2-19

The Themoplasics
pd by nov, Cala. or mére uns re ped sow ey 2 yo el cor on
Pee sce of ono petra of mona

or changing the composition, When on sain mounts up 04 percent he alo as
‘high endrance ini a high shook resistance, ad excellent wear rn.

‘Benilum bronze is anther ea retable alloy, containing about 2 percent beryl
Fm. This ly is very corrosion resistant an ha high tenth, aros, and esi
tance to wear Alough tis expensive, it used fr spring and ter par subjected
10 tue loading whee corosion resistance i required

‘Wa sight medica mos copper based alloys are available in es om,

lastics
‘The erm shermopasies is seo mea any plat that ows or ismodable ben bet

is applied oí he terms sometimes applied to pastis moldable under pressure Sch
plastics ca be remolded when heated.

A thermoset ia psi for which the polymerization proces is hd in a ho
‘molding ress whore the plat que under pressure Thermos plane cannot
creme

Table 2-2 Its some ofthe most widely wd thermoplastic, together with some
ofthe characteristics and the range of thei properties, Table 2-3, ising some of the

Sp: Te don om ten lied ton he Machine sn Metre ac bn,

SE Hardness Hongation Dimensional Mc
Nome kai Mei Rodwell Stability R

Asp 28 01009 IE 350 Good

Alam 8-10 041-052 80-96 4040 Exelon Good

ene 510 020047 92-110M 275 Hah A

Floplosc 0.507 50-200 100-200 Hoh alt

oP

Non $14 016-048 1121208 10-200 few for Goad
Peine 7-18 035-092 1158 108K 5-40 Eales God for EM
ps

Pératonte 8-16 024-086 62.01M 10125 Emule Ecler ENS
Poe 8-18 0216 65-90M 1300 cee) An Erlen CUR
Pido 650 80-120 Veyb El alent Ecelent CINE
Pebghemfeos 14-19 01 NR 10 God Eole Es M
“ie

Perens 15-12 014080 10:00 05-40 Peu Por OA
oP

Pagano 10 03 V2 S000 Ex cl) Exe? EM
Paint 1.575 095-080 05-850 20-450 Po Pet EM
‘oie

“i ols alte

Mcg.

Clos | m Es Ellos les 5 Sue Flo Poder. Th

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Table 2-3

The Themaets Sam Pes door bend hom ba Machi Das oo elenco
(plied by han / FC Ci Tas domes tare om mal ete o Eyes oro
classe o gua vere mau

E, Hardness. Elongation Heot
Ad 39 008-030 ome Sealer Good ok m
Abe 410 105-120 Bien malen Gert OM
Amro $8 013024 110-120 010090 Good Gent En

oy 5-20 001010 80-120 1-10 Gala Elan Gaede OUR
faces 59 010.025 70.95 eater scan) Goad ER
Sons 56 20.00 Eck! Ecole CI
nacos.

Camp ais. es Ess MM 5 Se Ffm Pesada 1 og

themmoses is similar These tbls ae presented for infomation ony and should mot
busto mae a al design decision, The range of properties and characteris tar
San be obtained with pasties is very seat. Te influence of many fotos such ascos
rol: enfin fin. western, impact eng, and thet file
and reinforcements, must be considered, Manufacturer catalog will be found quite
ep in making posible selections

2-20 Composite Materials'*

‘Composite materia ae formed frm tw or mae dissimilar teri, ach of which.
‘contest the fal properties. Unlike metalic alloy, the materi in a compose
remain distinct from eachother the mactscop lve

Mos engineering composes con! of to mater: à reinforcement called a
{filer anda matrix. The fil provides stillness and Sung he mates hls he mate
altogether and serves otansfer load among the discontinuous rinforcements The
mos common reiforcmens sate in Fi. 2-1, are continus üben, ciber
Sag or woven, sho chopped fibers, and paticults. The most commen matrices
are various plastic resins although ater materials including metals are used.

Metal and other tion engineering materials are uniform or isoropi, in
nature. This means that material properties, such a strength, tes, nd hemal com
“oct ar independent of bth poston wäh he material andthe choice of coor
‘inate sytem, The discontinuos nature of compesierinforcemens hough means
that material propres can vary with ath postion and direction. For example, an

"eft LM. Dare ad Oh Enger Mecano ape Mar One

| nat Sil | Lai mama. PT
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Figure 2-14

Creme

2-21

«epoxy resin enforced with continuous graphie über will ive very high strength and
Siles in the ection ofthe ers, but er low properties noma or anses to
the üben. Fr this reason, cures of composite materials are normally constructed
‘of mate plies (Laminates) where each ply rene (0 achte optimal sutra
les and eng performance

High enge weight ratios, up 1 $ times greater than hos of high-srenih
ee, canbe achieved. High ss o- weight rio can aso e bic, as muchas
‘times greater thin thos of structural metal. Fo hi reason, composi materials ae
becoming very popular in automate, arf, and spacecraft applications where
weigh a premium.

"Te dectionaliy of properties of composite materials increases the compliy of
structural analyses, Rorpie meri ar uly defined by two engineering constants
Young's modulus E and Poisson's ao v. A single ply of à composite material, haw
ver, requires four constants. defined with respect 16 the ply coordinate system. The
‘oman are two Yocng' modal he longtinal modus inthe diction of he
ben, andthe transverse modulus nomal tothe übers, Es) one Poisson's aio
(called the major Poisson's ratio). and one shear mvs (6. ith constant,
the minor Poisons rato, 1. is determined through the reciprocity relation,
y/o = vi E. Combining his with muliple plis ind at irn angles makes
Serra analysis of complex tres unapproactable by manual technique. For
{His esos, compar sofware i available to salculae the properties of a laminated
compost sonsmcten 1

Materials Selection

As sted ate, section oa material ora machine pr or structural member is
‘ove fe most importa decision th designer i cal onto make. Up to this point
inthis chapter we hve discussed many important materi physical properties various
characterises of typical engineering materials, and various material production
processes. The actual selection ofa material fra particular design application canbe
“an csy one, say, Base on previous aplications (1020 steal is always à good and
‘ate because of is many positive ait}, othe selection process can be as
involved and daunting as any desig problem withthe evaluation ofthe many material
physical economical and processing parameters. Thre re systematic and qui
Sppreaches to material selection, Here, fr ration, we wil only Took at how
10 approach some material properties. One tsi technique i 0 Hist all he important
material properties associated withthe design. eg sent, sli, and cost This
‘ante prorlizedby singa weighting measure depending on what properties ar more

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Table 2-4

Maseñol Farias and
Coses

important an ers. Net for ch property. all available materials and rank
them in oder beginning with the bet material: 3. fr strength, high teng tel
sch as 4340 tel shouldbe near th top ofthe Is. For completenes of available
materi. his might require large source o material data, Once thelist ar formed
Selecta manageable amount f materials rom the top ofeach is. rom each reduced
Hist cc the materials that are contained within every lst fr Further review, The
‘materi nthe reduce is cam be graded within he Int an hen weighted accord
Ing tothe importance ofeach proper.

MF Ashby fas developed a power systematic method using materials selec
tion charts! This med Ras alo been implemented in a solano package calle
(CES pack.” The charts display data of various properties forte fies and
‘lasses of materi ste in Table 2-4, For example. considering material stress
Properties, à simple far char ploting Youngs mules on the y axis i shown
ln Fig 215. Each vertical ine represents the range of values of E fora pariculr
material, Only some of the materials are labeled. Now. more mata information|
can be played if the x as repesnts another maria propery, say densi.

pra rares
Merl Nan
St enon oe
low mn
pt
Noe
ur Sos
conte ss
o e
enti Tae
pee Walon
pera nan
pu 4
m Ant nor
saone immo nie M
EEE, ae se
ne se
ce su
toa we
jai =o te
{porous coromics of Concrete en
os = =
e)

A Mr Sein Mech Di Elo Dee ci,
"aed Gt Dei Lin Sewanee com

Cr = ES
ET

38 | radar Eng Dun

re cer pr
ae we oe
‘Stica gloss Silica gloss
ae. ae.
his, gener ye 8
De :
tase Gee =
pa =
os tore
Polycarbonate rc
a Se
Polyehoretherkytone PEEK
Fos 5
ethene me
De Tem
Somme 5
Soc à
Dares a
aaa je
PORN ane soie
Sun, à E
Es, m =
Le laws
A Neen
or x
Be os
Hybrids (Coton red polen CP
pan en Se
oo E
ho rr Lee
ee me
nee -- E
Eo Eo
= =

For Sec cs, nr Bret ce, 05, Ib,
wo

Ti ur mn 1Q

Mechanical Engine a
=
ul
—
cae
[je cs aia
| es? E
one
a. | I
i rn "||| mtn
fo 8
JM
os |
\ ln
Ba

Figur 2-16, cll tube car represents Young’ modulus pleted agains density
2p Te ie ranges fer each motera proper plated two dimensonaly now Kom elipse,
tubes Ths pos mare uel ha the to separas ha las f each proper. Non,
e also sce how Ses we fr various materials ele. Figure 2-16 abo shows
oups files ulna according othe material amics of The 2-4 In bio, ds
tedlinc inthe loner ight coe of he cha indie ados Ep, which sit in mae
Fa selection fr minimum mass desen Lines drawn parallel these Ins represent
ie ales Fc El /p For example ever prall Sed lies are ow in Fig 2-16
that represent dien values of £/0(8 = D. Sine (Ep) represents te eed of
sou in a material each dtd ln, Bp represents a diferent sped as inated

"To sec how ffi ino the mi, conside the following. The performance mec P
of a situa element depends on (1) the functional requirements, (2) the geomet.
and (3) the material properties ofthe ture Thats,

e [mn panes chupe)

‘or symbolically.

(FGM) (220)

(AS né et

A

Figure 2-16

ad

Macher Exit Dig

Young ms Eve deny rois moi Pl omy Po He Aly, Gon Des, Camb, UK}

the functions separable, which ofen is we can writ Ea. (2-20 as
P= SD AAG) UMD, pa

For optimum design, we desire to maximize or minimize P. With regards to material
Properties alone, this à done by maximizing or minimizing JA). called the material
Dein code

Forllastation, ay we wantt design ight si e-4oade cantilever bea with
arr eo section, Fü thi we tl so the mas the ear fo the performance
uc mire. The stifles ofthe beam la ots material and promet The
less of Beam is given by k= F/d where Fand ae th end load and dio,
espece} (ce Chap. The end dein fan end ade caneve ea given
in Table A-9, beam 1363 = Ym = (FINE), whee Es Young's moduli. tbe
second moment ofthe aca nd the eng ofthe Beam. This. he es gen hy

en ea
Fron Tie Ate second monet he weno che sec
me e

a

Ett sige | mn

Dt ane

Figure 2-17

pri
Al Mai ben
Héron Oder, 2005)

aer D nd are the diameter and are ofthe ross section respectively. Substnting
Eq, (2-23) in 2-22) and solving lr, we obtain

CL
(5) En
em tamis ty
nm 229
Seng. 2-20 2a an yl
nato (La) om
bern 29e om 2-2, he Tn arn

can be socie wi any Toon y JF). Ths fF) = DIR he
Functional requirement fies: (6) = (0%), the geomet parameter, length: and
the material cine coccion

fs = am

Ea

isthe material ropeny in ems of density and Youngs modulus. To minimize m we
ant minimize A) or maximize

ga

” (2-28)

where Mis called he material inder and =

§. Reming to Fi. 2-16, dra lines of
various vales of Ep as shown in Fig. 2-17. Lines of increasing M move up and 10
the lel ax shown. Ths we Se tat god candles or a Hight, sti, edited can
Ale beam witha crular cos section ar certain woods composes, and ceric,

‘Other imitslonsraints may warn fuer investigation, Say for fre tra
tion, the design requirements indicate that we nc a Youngs modus greater than
SOPA. Figure 2-18 shows how thi futher ests the search eon. This eliminates
‘woods as a possible material

132.7

| nat Sil | Lai Mal PT
O a ==>

| nica Eine Dar

Figure 2-18
The ch gion fi 2-16
Khe dandy estan
SOC Po
A, Maw Sato

en $

Eater i
i

ms

Sra veu dy pr rn maa, Fr mi $ #02 ps cat ed eng Fr poe Sit À para
ugh arcas and uns She comp rang Meg fo corpses hr au. Fer one See
Iren. fae cooky Mia Aloy roto Dns, Cont, UK)

EM

Serer

Ett sige | mn

ad
Dt ane

21
22
23
24
25

24

27

28

29

oso | 6

Conan. i a given design exer, Ihre will be aber considerations such as
«teng, environment, an cost and ter chats may De necessary 1 imestgate. For
example, Fig 2-19 represents enn versus density or e material fais. As,
tee have no brought in the material proces selection pat ofthe picture done prop.
‘ly materia selection ca el go dela bookkeeping hiss where soltar
packages such as CES Fsupock become very effective

PROBLEMS

teins he minime end anil rats fr SAE 102) cold te
atin the minime tn el sons fr UNS 1000 Pt

Forte mata ob, 2-1 and 22, compare he lowing properties minimum ne and
$id went deta ns,

sung you were soci an AISI ID sl ora pp her yo devi omar
nize te yell sent, bon won jo pe a?

Asuming you were song a AS 10 kloan pion er you ded o max
mine the dct how mold you psy?

acme he kth toi ent ats (all pei sena) in wits ins
Determine he fae 4- viga deny ra (ad pei mada) in wis ich fe
[UNS GOES aoa sc, 2024-74 miu, Te 6AT-AV ann ly and ASTM Na 20
ey sation

sain for a mena non Fora homogenen, ati meal the med o ii ©
Is a Yong modes as

E
m

Using te tuted vals o nd. eine Poisons ui for ste sin blu

‘operand gy a

A pen of man st ang an inl distro 0.503 in as ts in ion

ing agagelegt 12 m The loving a were tine or las las at

late State Plastic State

load”. Elongation, WM Load P, Area A,
‘br 3 ‘bf py

emo om

400 0019 mm ox

so oe vo 00

u oo 1800 où

AS né et

ad
Dt ane

64 ln trans Daan

2-12

Not tt rs some verlo In dat Plt te engnsing nominal san dar
ing two sale forthe ant Mi eo o o oc OO ai und the er fo eo
o maximum sin From hs dram nd he modo feast. 02 porc sb ih
ten. lim sei andthe cent etn in a.

Compe wo ss and th logic in wing he at of Pr 2-9 and phat a on
loo paper Tin nd plc eng oie o the ss scr cp
Fa ye eh andthe llaga decias hal 20 pret cl wor,

“Th ares data ron tn et on cion spine ae

Goimeirgwen | 020 où 080 10 15 20 28 24 40 50
bare

Patte csi cea nd 0 pent et cd rn and mgt malas
fai a 20 tess at 20s

| singh ar of rary cos ein and sks his ol formol oa radios bos
an av ss inthe gure. Se src at dan N having a ri! ng Le wil
‘ein ected kg aer Being Ts legis

“The kent of the eter al ner suc ater ang. re
DEEE
‘Using Eee ol tee tint be

+

Ett sige | mn

Dt ane

210
215

2-16
2-17

218
2-19
220

221

222

anni)
Ate no Mo: Demi eof eel
Ase entra ito

He hares es were mad a a random sample of 10 sel part daring proce. The
rls were vals of 2522) 260. 284257 2). 2493). nl 25. Eva een and
nda deviation fe ime enh in Ks

5, Estimate he ait sen of ie in MPa

Repeat Pd. 2-18 sing be male ast ca.

Zan heheh sgh so ete pn um
Pie df seua rs nde he seein curve face ur = de Tes ae,
fale the ms of ones i de ain ce por un Yume ie o us the
ri cir. A iar cr but in with he cla Es e mat cale
Ihe medita rio. = [3 de wh he stain at yt I he tes ain
Hart = 5 then tan be sown ht

mods ugs sing tt he st at pit on to tr.

Search weh ia Sos 2-20 and eet your ings

Reseach the mtr one rely deso in Table AS. Compa ao varios ren and
alo chin es ng di. and ness, What makes is mas spc?

Pick aspect mata sve inthe bis (2024-4 aluminum, SAE 1040 se), am con
sal aa repo dto esi et Yo Pagos the Tata Regist) o
‘kin a much infomation as ou cn bra cos nd aay of he alan in what
form (ape).

Coser eo tanning a tem foe F Te caring en ars is gen by
fo Fe Aste ll cos ein Th itn oe rd sien CB
‘hich = (FO/CAE). we isthe eth ofthe Using e Asi chs of Fs 2-16
1082-19, xls Sve mea a os sited for ap, sf nd tog rd:
Case es ad sect spa, Frase fe 2-16 poeta = Foru ol
2-19, the apli tn ss the mei streng

CEE
ETS

2 tant sem As | © eo 1

Load and Stress Analysis

a
32

cere

37

3-10
an
312
313
3-14
3-15
3-16
3-17
3-18
3-19

Chapter Out
Equlbiun and FreeBody Diogroms. 68
Shoor Force and Bending Momens in Booms 71

Sing funcions 73
Ses 78

Canes Sress Components 73

Mohs Cle fr Plane Stess 76
Gererol TreeDinensinal Sess 82
Eadie Stain 89

Uniformly Dieibued Suecses 08
Normal Sresse fr Beams in Banding 85
Shoor Stesses for Beoms in Bending 90.
Tonion 95

Sross Corcentaton 108.

Sroses in Pressuized Cyinders 107
Srosos in Rotating Rings 10

Pros ond Shink Fis 110

Tomperctuo Ec 114

Cunod Booms in Bonding 112

Core Stessos 117

Summary 121

e

pre pre] rel -)

ad
ea ti a

(One te main objective of his bok sto dssribe how specific machine components
funcio and how t design ec them so that the function safely without ling
nca. though arc discusion as describ structural suemg in ers of
Toad or tes vere song alr of fenton for sitar reason may aio fom
‘ter (car such as excessive deformation o deletions,

Here itis asumed tht the ear has completed basic courses in sais of iid
boxes and mechani of materi and is qui foie wit the analy fads, and
the ses and deformations asccined with be basic ad states of simple rm
‘ements In is chapter and Chap. 4 we will review and extend es topics brie
‘Complete derivation il not be peste hee, andthe wader is urge 1 retum to
basi textbooks and notes on these subjects.

“Tis chape begins with review of quil and fr body digrams associated
with load-carrying components, One must understand the nature af foren before
temps to perfor an extensive rss or deflection analysis of à mechanical som
ponent. An extremely useful too! in handling discontimows loading of structures
Employs Macaulay oe sinulariy funcions. Singularity funcions se described in
‘Se. 3-3 as appli tothe shear forces nd bending moments in Bans I Chap. 4 the
ae of singularity function wll be expand 10 show thir eal power in handling
‘elections of complex geomet and tcl indterminate poblems

"Machine components transi forces and motion rum one point to anote. The
transmision of force can he envisioned a a How or force dirias that ca e ur
{her visualized by song internal surfaces within the component. Force distibted
¡vera surface leas othe concep of ses stress Components, and tes transforma
‘ons (Mobs cre) forall posible surfaces at point

"The remainder ofthe chapter is devoted to the reses associated with the base
Honig of prismatic elements, such a uniform bang ending, and ton, and topics
with major design ramifications such as ses concerts, Ni: and he Ava
Pressurized cylinder ring rines pres ad sink i, mal stress cuve ham,
nd contact ees,

Equilibrium and Free-Body
Equilibrium
“The word sien wil be ed 1 dene any ae pr or pain of machine oc
arc nchräng al of (dela ve wi 10 say A ae under ie
‘ction may comi fa parie sever partis apa fa righ a. m ee
‘Spd bly, or en sve ged tie

ve ame that he stem tbe sede atone oa os, has conan
vel. nthe system ha zer section Under is condo hye an
10Be ner, The phrase ur equi tio wed pi athe Sten
is are For equi, Ue oes and moments tng on she ales each
EN

grams

E

Emo oa

=0 on

Which sates ha the sum ofl force ande su of ll moment vectors acting upon a
‘stem in quil era

| nat Sil | Lai
© ae
=

à stands Ais | Senna

Free-Body Diagrams

Wecan ral simplif ih ana fa ery complex tractor machine by susshely

isolating each clement and sling and aalyzng le y the we of re ha dara

‘When al te members hve Been ee in his ner, hno canbe assemb

10 yd nfomaton concemig the lane he total sytem. Th, ebay pra

ming i essentially a meats of breaking complicated proben to manageable cent,

ani se snp problems and en, ol ping the ifo together ai,
Using echo iagrams for force analysis see the following important
purpose:

+ The diagram establishes the direction of reference ane, provides a place recon
the dimensions ofthe subsystem and the magnitudes and direction of the known
Forces, and helps in assuming the dictions of unknown forces.

2 The diagram simplifies our thinking because provides pac to tre one thought
while proceeding othe next

“The diagram provides a means of communicating your hough cea and unam.

guy 1 er people

Cael and complet construction ofthe diagram clarifies faze hiking by binging

out various points hat are no always apparent In he statement or in he geomery

‘ofthe ttl problem. Ths the gra al in understanding al aes ofthe probe.

‘The diagram ps nthe planning of à lgia attack on the problem and in ein

up the mathematical relations.

+The diagram helps in recording progress in the solution and in iustaing the
mods usd

+The diagram allows others o follow your reasoning, showing al forces

Figure 3-1a shows a simplifie endo o a gar reduce wher the input and output
shalt AB an CD ae tating a constant specs and respectively The input and
‘utp torques (sonal moments) ae = 240 Ib in and respectively. The stats
are supported inthe housing by Bearings a A,B,C. and D. The pitch adi of gears Gi
and Grae r = 0.78 in and ro = 1. respectively. Daw the lee body dira of
‘ich member and determine the ne reaction forces and moments tal points

Fst, we wl ist al

impiying assumptions

1 Gear Gi and Gare simple spr gears witha standard pressure angle 6 = 20°
Gee See 13-5)

2 The bearings re ealigning and he shafts can be considered tobe singly
supported.

3. The weight each members negligible

4 eiions negligible

5 The mounting bol at EF Had Jar the same sie.

“The separa rc body diagrams of te members are shown in Figs. 3-Ibd Note hat
estonio, called the aw of action and reaction. is used extensively where
‘ich member nates. The force ram Been the sur gears wot tangential but
the pressure angle @ Ths. N= Fan 4.

pre pre] amu O

corp
Figure 3-1
[alu reir obi dos Dans eo un ae

Summing moments bout de x axis of hat AB in Fg. 3-4 gives

Lan = F005) 240,
ET

“The normal force is N = 320 an 20° = 16 Ib.

ing theequlitrum equations for Figs. 3-Ie andthe reader shuld verify hat
Ray = 1926 Rac = 69:9 BK, Rp, = 12519, Re. = 4661, Rey = 192 I, Re. =
CIL Roy = LAC Ro: = 466K, Ty = 4901 in. The direcion fhe op
{oe soppy, esse iti the sive done tem appoint mono

"Note in Fig. 3-10 the net ore from the Bering rectos i exo wheres Uh ne
moment out the ans is 225 (192) + 225 (128) = 7201. This vale he same
a T+ Ta 240 + NO = 72010 in, as shown in Fig, 3-la, The reaction forces
Fe, Rr, hy, ao Rj, fom de mounting bols can be determined from the
qulicium equations as thre are too many unknowns. Only thee equations ae
aille, E, = E = DM, = 0. Incase you were wondering abot assumption
‘chore where we will une A (se Se. 8-12). The gar bon tends orate about the
xs because of pur torsional moment of 720 Bin The bol forces must provide

| nat Sil | Lai
O ae
=

3-2

Figure 3-2

Seen prone dc

Figure 3-3

Sn conto brig

Figure 3-4

à stands Ais | Senna

lend Ses ns | 71

an cul bt opposite sol moment. The center frotan eave othe Boks is at
the cei ofthe bol coneseconal aras Ts Ue bl rasa gu the centr
flan a the center ofthe fr ol aime ol A/D PB = 3202 in
Tromeach bitte bol cs a equal (Ry = Ry = Ry = Ry = amd aho bolt re
is pepedclar tt in rom the ol to ener rain. Tis snes pe wre
fromthe far bol ARCS 202) = 720. Ths, Re = Ry = Ry = Ry = 562216.

Shear Force and Bending Moments in Beams
Figure 3-20 shows a beam supported by reactions Ry and R; and loaded by the con
‘cette ores Fi, a, a FI the Beam set at sone section located atx = x and
the left portion is moved 3 a fee boy an intemal shear fre Y and bending
‘moment Mans ac 0 the cut suce 1 ensure equi (se Fig, 3-20) The bear
fore is obtained by suming the forces on the isolated section. The bending moment is
thes ofthe moments the forces Ur Il ofthe secon ken abot a ai heh
the bolted section. The sign comes tse for bending moment and shear oo in is
ook re shown in Fig, 3-3. Shear force and ending moment ae relied by the equation
au
a
Sometimes the fending is caused by ibn load g(. shown in Fig. 3-4
0) à called the loa intensity with nits of fr per ni length and positive in e

wa

=> EA
at ek

à stands Ais | Senna
rer es

72 | meo grag sr

postive y direton I can be shown ht differentiating Eg. 3-3) els in
a eM
a ae

on

Normally the applied ish oad is directed downward and able (eg. see
Fig 3-6) la hi ee

Equations (3-3) and 3-4) reveal addtional relations if hey re integrated. Ths
it we integrate between, sy. x and x, We ain

For [Tonnen os

hich states that hecha in ser force fom A 1 Bis equal 1 he aca ofthe load
in diagram been xa ad
f "var

‘wa similar manner,
f am

ich its dat echange in moment from A 0 Bis equal te area ofthe shear

Tore diagram einen ad Sp

Ma My 0)

Table 3-1 Function

Graph of Mana
‘Singularity Macaukay') Conconnoed ra? wa 7=0 x#0
Fencns ene tando une
een
5 fiado
pa Ha eo we
(atin) eae ae
forge ona?
— CES
Us dep wre 152
— pa
| Je-aPde= 0-0)
fonp tes

=

cdo cs Resp oben op HIN

Care pre] =

rer
Dt ane

3-3

teat nd Sens | 78

Singularity Functions

“Tee four ing union dled in Table 3-1 const awe and xy mens
ingl acs decile. By Ur, general prions Tr hear fre
‘nd ening men in eamacan De writen when de am oo) by omens
tomers ot res Arti ate ble te concen moment nd oc actions
fr zer fra aes ol x ot egal 102. Te ons ae unto for values of
ee No th the a ap and rnp ful nro nl for ae of hte
ies than a The imgrain peri Abo the ale onsite ar of he ma
‘matical deition o The ft nations ut 469 for Vx) and MG) de ot
Tes costar ol negation provide e lou a the Dam ae arcu fh la
¿Me example ar flow ow bow es cons a cd

| Figure 3-5

i

Dese expressions forthe ling, hear force ad bending moment grams for he
beam of Fig 3-5.

Using Table 3-1 and g() ore king funcion, we find

= Rt)! = ea ma TES] w
Next we use Bg, (3-5) 0 get the shea face

vero re Gi

Note that V = 0 a =0"
"A second integration, in accordance with Eg. (3-6) yes

un [vorn nm Ama eo 0

‘The reactions Rs and Rs can be fund by taking à summation of moments and forces
as wal or hey can be found by mating thal he sear force and bending moment mus
be zem every except the region O = x= J This means that Eg. (2) should give
V =O atx slg larger than Ts

Wo ABER
Since the bending moment should abo be zr inthe same region, we ae, rom, (3),

Rul Flay) ~ Fala) =0 iS
uations 4) an (5) can now he solve or he reactions Ry and.

| stan Sie | Bs à stands Ais | Senna

Dt ane

EXAMPLE 3-3

Solon

Answers

Figure 9-6
loco dogo ico
Snap.

la edrgmenes dagen

Figure 3-64 shows the lading diagram for a beam caiesred at A with a uniform
oad of 20 Ibn acting onthe portion Sin < x = 7 in anda concentrated counter:
clockwise moment of 240 If im atx = 10 in, Deiv the shearfore and bending
moment lations andthe support reacons M and R,

Following the procedure of Example 3-2 we ind th loa intensity Function to be
MO RAG! 20020) = A OY (N

Nowe tat the 204 — 7? erm was necessary to um of he uniform lal at €
Imegrating successively gives

Mi + Rife)" 200 3) + 2000-7! O 10)"F (2)
Mo at Rye)" = 10] = 3) 107 ~ HOKE 10" (3)

‘The eations are Found by making slightly ger than 10 in. where Both Vand Mare
ei hi gion. Equation (2) will hen ve

MO) + RCD ~2000— 3) + 20(10 — 7) — 2400) =

which ils Ry = 80 DE
From Eq (3) we ast
Mi) 480110) — 1040 3) + 1000-7? — MOD =0

Which cl My = 160 fin
"Figures 3-6b and show the seur-foreand bending moment diagrams, Note ha
‘the impulse terms in E. (2. M(x) and 240% = 10), are physical not forces

8

à be

mac;

ad
a an
3-4
3-5
Figure 3-7

Ss cargar en sacs

à stands Ais | Senna

leaded ee ds | 78

and are no shown in the V diagram. Abo not that hot the My and 240 bin
‘moments ar cunerlockwise and noie singularity functions weer by the con
‘tion showa in Fig. 3-2 the and 240 Ih in are negative and poste bending
moments, especies, which efleted in Fig. 3.60

Stress

When an internal surface is ltd asin Fig 3-2 the net force and momen at
the surface manifest temelves force ditrhuton across the entire area. The force
“isbn acting a a pi! onthe surface is unique and wi have components inthe
normal and tangential dietions called normal wre and tangent sear sess,

respectively Nomal and sber suesis re labeled by the Greek symbols a and €

respect te diteton of is outwanl rom the surface is considered to been

les anda positive normal stes, o isn the surface i compresive ese
and commonly considered 10 be à negativo quant The unis of ses in US.
‘Customary unis are pounds per square inch (ps), For SL units res is in netos pr
square meter (N/m) IN/m = pascal (Pa.

Cartesian Stress Components

“The Cartesian ress components are established by defining the mally rthogo-
ral surges at a point within the body. The normals to each surfe will establish the
xx 2 Caesian ases In general, uch suce will have a normal and hear ses
‘The shear tes may have components along two Cartesian aes. For example Fig,
3-7 shows an infinitesimal surface rea isolation at a point within a body where
the surface normal ls the a direction. The normal sus ls labeled 0,- Th symbol o
indicates a normal stress andthe subscript indicates the direction of the surface
normal. Te net sear stes acting on the surface $ (ax which ca e resolved nto
Components in the y and x direction, labeled as fy and ty. respectively (ce
Fig. 8-7) Noe that double subscripts ae necessary forthe shea. The fest subscript
indicates the direction ofthe surface normal whores the second subscript ithe
‘iection ofthe shear sess.

‘The tat of ses at a point describe bythe mutaly perpendicular sacs is
sown in Fig 3-43 can be shown tough coole wanslomation hiss so
cient wo determine the sate of rss on any surface intersting the point. As he

Ett sige | mn

ad
Dt ane

à stands Ais | Senna

Figure 3-8
lo Gare din

Sr Pro men

36

VE

dimensions of the cube in Fig 3-8 approach zero. be stresses the biden faces
‘become equal and opposite 1 those on the opposng Visible faces. Thu, in gener a

complete state of tess is defined by mine stress Components, 03. 0). 0 Yo
hes fee fr oy
For eit, in most cases, “roscas” ae equal, ence
tte ohh ESS on

‘Tis reduces the number of ses components for most hrs dimensional states of
stress rom met six quis 2,0, Spe and

A very common sate of sires occur when the sires on one surface re zero
Wben this occu este o rss is calle plane srs. Figur 3-8 shows à se of
plane stress, array assuming that he normal forte Srs fee surface is the
2 direcion sich Bat 9, = fu = ty =O. I important lo ote Wal the element in
Fig 3-8 il ae dimensional cube Alo, hr its assumed that heros La
a equal such that fy = fy nd ys = By = es = Ee

Mohr Circle for Plane Stress

‘Suppose the dx dy d element of Fig 3-80 eu by an obige plan with a normal at
an ru angle counterclockwise Irom he x axis shown in ig 3-9 Ti section
ISconsemed with he see oan that act upon hi obligue plan. By summing the
Forces cass by all the sos component to eo, res a and rar found tobe

SE 26 + ty sin26

z

os

26-4 60826 0

a

uations (3-8) and (3-9) ae call te plane sms transformation equations.
Dire Eg. 3-8) with respect and seting e result equal er gives

2

ano, 0)

Lu tt Sil
On
=

1 Figure 3-9

à stands Ais | Senna

À

Equation (3-10) define wo patil valu for the angle 29. one of which defines
the maximum normal stesso andthe abe. the minimum normal rss 0, These tuo.
Stress are cae the prin pl stress, and hair comesponding diecons, the prac
pal directions. The angle between the principal directions 190° tis important 1 noe
that Eg (3-10) can be writen in the form

Pa) ro,

o la

Comparing this wih Bq, 0-9). we see hat €
ing principal seses have er shear stress

In a Similar manner, we diferente Eg, (3-9) set the result equal 1 zero, and
ain

meaning tha the surfaces coma

tan2o,

EU

Equation (3-11) define the wo values of 29, a which the sear sess reaches am
‘exteme sl, The angle between he surface containing the maximum she resis
500" Equation (3-11) can alo be writen as

5 00829, + 1,5020, = 0 wo

EE]

Equation (3-12) lls ws at he two surfaces conan
also contain equal normal trees o o, 7/2.

Comparing Bs. (3-10) and (3-11, we ce that tan 29, i the negative reciprocal
‘of tan 29. This means hat 29, and 29, ae ales 90" pun, nd ius the angles
beeen the surfaces conning the maximun sear stresses and the surfaces coin
ing the principal stresses ae +45

Formulas forthe two principal sreses can be obsined by substiuing the
angle 29, from Eg, (3-10) in Eg (3-8, The ros is

the maximum shear sesos

EE]

pre pre] coe O

ad
Dt ane

Ina similar manner the extreme alu sar sesos are ford be

oa

Your particular tention i lle o the fat that an extreme alu o he sear stress
‘may not be the same a he actual maximum alu, See Ss. 3-7

tis important wo note hat the equations given 10 this poi are quit scent for
Performing ny plane sires transformation, However, extreme cae mus exercised
‘when applying them. Fo example, say you are atempüng to determine he principal
Sac otre fora problem where, = 14 MPa, 9, = 10 MPa, and, = 16 MPa.
Equation (3-10) yes d, = —26.7" and 6345" to locate the prin Sres surfaces,
whereas, Eq. (3-13) gine = 22 MPa ad o; = 18 MPa forthe principal Sres
Tall we wanted was th principal stresses, we would be finished. However, what i
‘we wanted toda the element containing the principal stresses properly oriente re
sive othe x,y axes? Wall we have to values ly and two tales forthe princi
pal ses. How do we know which salu of, Comesponds to which value of the
‘Principal sires? To clear this up we would need to subte one of the vales of 9
Into Eq. 3-8) o determine the normal stexsconesponding 1 hat angle

A graphical met for expressing the ations developed in this section, called
Mohr site dagrom is a ery elective means of iii he Ses ste a point
“and Kpin track ofthe discos of the various components associated with plane
Stress Equation (3-8) and (3-9) canbe shown to be ae of parametric equations for
‘and ¢ where he parameters 29, Thorens between o and ¢ that of cr
‘plod in theo, plane, where the cen of the Ge locatd C (2,2) =
160, +0,)/2.0) aná as a ads of R = les ~0,)/2P + A problem aries in
the sign of the shear tess. The tansfortation equations are based on à positive $
‘being eounterlockwise.a shown in ig. 3-9. I pose Y were plated above the
‘sai, points would rotate clockwise onthe circle 26 inthe opposite direction of
Totton on the element. I would be convenient the rotations were in he same
‘isto. One could solve the problem easily by ploting ponte + Below Ihe axis
However the classical approach 19 Mohs cele uses a dire comention fr the
shear res,

Mohr Circle Shear Convention
“This comenion i followed in drawing Mohr’ ctl:

+ Shear tresses tending 1 rot the element clockwise (ew) are pte above the
+ Shearsteses tending orotate the element counerlockwise (ow at plated Below
theo ai

For example, consider height fice ofthe element in Fg. 3-8. By Mobs ice con
‘entin the hear stress shown lo below te au because end 1 ete the
lement counterclockwise, The her ses onthe ap face ofthe clement ls pled
ne the ai sae endo tate the element loki

In Fig. 3-10 we cent a coordinat system with normal tease plated long the
bscisa and shea tresses plated asthe edits. On the abscissa, tensile (pst)
normal Srsses ae plo tothe ight fe origin O and compres (negate) no:
mal stresses tothe left On te ait, clockwise (cu) shear ASS re pled up:
‘ountrclockwis (Gow) abr sesos are plo down,

AS à stands Ais | Senna

rer
Dt ane

Figure 3-10

Using he tes sate of Fig. 3-8, we plot Mohs cis, Fig. 3-10 by fst lok
ing tthe ight surface of he element containing o, 10 she sign of, and the
eu or cow direction of the shear rss The right Tae is called the x face wher
8 =07- Io, is postive andthe hear sts ty iscew a shown in Fig. 3-80, we can
«sabi point A with coordinates (o, 5") in Fig. 3-10. Next we look atthe op
face, where = 90". which comas 0, and sept he process to wba pin Bw
“cortinas (or) a shown in Fig. 3-10. The tuo sates of tess forthe element
ase A9 = 90° rom each eter on ih elements they will De 249 = 180 from each
‘theron Mohr ce, Point À and are the same vertical distance rom theo ais
“Thus, AB mos eon the diameter ofthe srl, and the center ofthe cle Cs where
AB intersects theo ax. With points Aand Bon the ie and center Cie complete
re can then be drawn, Note Wat he extended ends of ine AB ae abel x andy
fs rofeences tothe normal to the surface fr which points À and represen the
“The cre Mohs circle represent the sae of ses a single point in as
lure. Eich point onthe eile represents the sow sate fora specie surface tenet
ing he pin in the scr. Each par of points on he ctl 180 apart rprsen the
sate fes on a clement whose surfaces are 90" apa, Once he cre fs dw he
Sates of sens can be wald or various suce intersecting he pit Bing ana.
Iyzed For example, be principal rss 0, and o; ae pins D and E, respectively,
and their values obviously agree with Eg (3-13) We ls se thatthe shear stresses
ase seo on he surface containing 0 ande. The tw extremo value shear ses, one
‘clockwise nd one sountrlockwise,oscur at F and G with magnitudes cal to the
radis ofthe cle. The surfaces at F and G eich also contin normal stresses of
(o, + 9,2 a note cir in Bq. (3-12) Fall, the tte of sess on an arbitrar
surface located at an angle counter from hex face span H,

pre pre] em O

ad
Dt ane

At oe time, Moir’ circle was wed graphically where was drawn to sel very
“accuracy and ales were measured by wing scale and perc: Hee, Weare sey
thing Mobr creas a visualization aidan will wea somiepbicl approach, calcula
ing vale fom the properties of he circ, Tis lost by the Flowing example,

EXAMPLE 3-4

Solon

i

i

A as element has, = 80 MPa and £, =50 MPa ew as shown in Fig. 3-11
(a) Using Mohr’ rel, ind be principal stresses and directions, and show these
‘ona sess clement comely algu wi respect be xy cordiales, Draw another
Srs cemento show ead td coesponding normal reses, and abel the
raving complete
(Repost ar using he wansformain equations on.

(a) Inthe semigraphical approach used here, we fst make an approximate freehand
sketch of Mo cicle and then use the geometry of the igre ¥ obtain the desired
information,

‘Daw Ab and as fist (Fg. 3-11) and frm the «face loca, = 80 MPa
long the ax. On he «Tae ofthe clement, we seta he har ess SO MPa in
te ew ction. Thin, or th fae, this establishes point A (80, 50") MP,
Corespondin 1 the y ac, theses io = 0 and = 50 MPa inte cow diet.
‘Ti locates pont (0, 50°”) MPa Te ine AB Toes he diameter o required ir
‘le, which can now be drawn. The intersction ofthe cise with the ais deine 0
ando as shown, Now, nating the tangle ACD. indie on the she the length le
lees AD and CD as 0 apd 40 MPa, respectively Te length of he hyptenue AC e

VER F GO = 640 MPa

and hs shold be labeled onthe sketch to, Since intersection Cs 40 MPa from the
gin, the principal tresses are now fund wo be

2) =40464=100MP and oy = 4064 = -24 MPO

‘The angle 26 rom the x ai won is

2, = un! SL

“To daw the principal es clement (Fig, 3-119, skh the wand anes parle
Lo the original axes. The angle 9, om the ess clement must be measured inthe same
Aietion asi the ange 29, onthe Mob cle, Thus, rom x measure 25.7 (al of
1.37 clockwise to oct Be aus. The xis i 90 from the ani ad the tess.
lement can now be completed and labeled as shown. Note tht thee are o Shear
‘reson is clement

"The two maximum shea sresss occur at points E nd Fin Fig. 3-11. The two
normal stresses comesponing to these shear stesses are each 40 MPa, as indicated
Point is 387° ce fom point Aon Mohr cicle Therefore, in Fig. 3-1 dr a
stress element ented 19. (half of 3877 cow frm x The clement shoul hen be
Tabled with magnitudes and directions as shown.

In consretng these stress elements iis important 1 indicate the nd y irc
tions ofthe original reference system. This completes ih Ink between the original
machine element and the ornato of is principal tresses

Ce sul nues
ES =

Figure 3-11

vo,

From Bq, (3-8) forthe fis angle 0, = 257

m+0 0-0

ei

OLI) + (-$0)sin(2(-25.0)] = 108.03 MPa
“The shear on tis surface i bind from Bg, (3-9) as

DO 2259) + (521-257) <0 MPa

which ons that 104.03 MP is a principal stress From Eg. (38), for, = 64.

8040, 90
ar

O cost 2064.3] + (SO) SiN2I64:3) = 24.08 MPa

pre pre] em 1

ad
Dt ane

Answer

Substiing 9, = 64.3 ino Ba. (8-9) again ils x = 0, nating hat - 2408 MPa
is ls a principal rss. Once the principal are ar aula they can e oder
such hat > 0. Ths, où = 10403 MPa and o; = — 24,03 MPa.

Since for oy = 10403 MPa, 0, = 25.7, and ine ¢ is tine postie cow inthe
"transformation equations, we rate clokwise 257 forthe surface containing 1. We
ein Fi, 3-1 eta his ally gres wäh he semigraphica meth

"o dteine y and r, we fst use Eg. (3-11) o cuca $

Ce

Ford, = 19.3, Bg. 0-8) and (3-9 yield

1
= Lun

) 93.103

o #40, #00

= +7

22 su2t19 31 + 6-80) 24193)

eos20193)14 ($0) sn2(19 3) = 400 MPa

610 MP

Remember hat Eg. (3-8) and (3-9) ae coordinate transformation equation. Imagine
‘that we ae rotting th x ya 19.3 caunerlockwine and y wil now point up and
to the let Soa negative shear sus onthe aed x face wil pont down and to the
‘ight as shown in Fig. 3-11 Thus again els gre with he semigraphial method,

Ford, = 109.3, Bas. (3-8) and (3.9) phe o = 40.0 MPa and y = +640 MPa
Using the same logs forthe coordinate transformation we find Wat results agan gr
with Fig. 3-11

General Three-Dimensional Stress

Asin becas of plane rss, a particular venation of stress element occurs in space
forsbich al sar tres component ar zero. When an clement has his particu or
ento, he noms to the faces re mutual cbogonal and core the pin
‘Spal icons andthe nomma sesos associated wäh these faves ae the principal
‘stresses Sine thee ae thre faces, here are tre principal directions and tre pi
‘Spa tesses 1.03, and oy. For plano rss, the see suce conti the tid
‘Principal stress which zero.

In our studies of plane stress we were able to specify any stress ste 0, and
‘uy and find the principal stresses and principal directions. But six components of
SS are required to specify à general sate of stress in three dimensions. and the
problem of termining the principal stresses and dictions is more delt. In
design, three-dimcnsonal transformations ae rarely performed since most max
rum sires ates occur under plane stes conditions, One notable exceptions con
{Get stes, which snot a ee ol plane sess, where the tre principal stress age
given in Sec. 3-19. In fat, all states of stress are uly three dimensional where
‘hey might be described one. € two-dimensionall with espe to specie cond
alates Here sis most importa o understand the relationship amongst the re
Principal stresses. The process in finding the thee pricipal stes from the sin.

O ns

ad
Dt ane

Figure 3-12

3-8

Kamin à stands a | Senna

AS

stress components 9.0, 4 y: fs and a involves Finding the roots ofthe cubic
equation"

Boe

o as

In ploting Mohs ces for redimesional ses, ie principal normal
stresses are ordered so that 0} > 0 > os. Then the esl appears sin Fig. 3-12a. Th
Stes coordinates er. or an) aia lated plan wi lays on the bound:
ties or within the shaded aca,

Figure 3-12 also shows the Ihre principal shear smeses ty. u. and ty?
ac ofthese occur on the to planes, oe of which shawn ia Fig. 3-13 Te ig
ure sows ta tbe pipa hear stresses ae given by the equations

0 = (0, +9, +00) + (010, roto

na + Brita orto a)

22 nel paid

OF cous, ta = he the normal principal stresses ae ordre (0 > 0 > a),
so always omer your principal res, Do this in any computer ode you generate and
you aways generate Ta

Elastic Strain

Normal sain ¢ is defined and discussed in Sec. 21 forthe tensile specimen and is
given by Eq. (2-2) as € = 3/1. where is he ttl elongation ofthe Bar wii the
Teng Hook's forthe tne specimen given by Bg. (2-3) 36

on
where the constant Eis called Yung’ madalus othe mad of elasticity

“Fame of hs quin rer crane dimen random
ic Bop Amel Sagan Aled Ses Ais mde, Men A N Yo
"Neth oe bre un dr Te im
el pice tis ro psi dc

pre pre] amu O

ad
Dt ane

3-9

"When a mater spaced in tension there exists not only an axial train a alo
negative sean (cotrckn) perpendicular w the axial sain. Assuming à Hear,
homogencous, kotrope material, is era rains proportional to he ail rin. I
‘he ail direcion i hen he leal sii aro €, = €. = ve, The constant of pro
orinal ws al Poisson's ratio, which is abou 0.3 For most sacral mea
‘See Table AS for values of fr common materi

Ifthe ail ste i in the x rection, then fom Ba, (3-17)

aho yaa oe)

For astres clement undergoing 9,9, and 0, simultaneously he normal strains
are given by

Hono

= Mere +00] om

een

Shea sin y isthe change in a right angle ofa rss element hen subjected o
pure sar ses and Hooke for shear given by

100

‘whore the constant Gis the shear modales of elasticity e modulus o igi.
canbe shawn Fra near stop, homogeneous mater ete elas com
‘ans are lo ch ther by

E

20040 ea

Uniformly Distributed Stresses
‘The assumption of a uniform distin of sues is frequently made in design. Me
results then on called pure tension. pure compression. o pure hear, depending
upon how the externa lu plc oe body under tds The woe simple some:
times used instead of pure 1 indicate tat there ac no other complicating effects
“The tension rad sopa, Her a tension lad F is applied though pn at ends of
the tar The asumpion of uniform sess means tha if we cut ie bar a a Seton
‘emote rom te ends and remove oe piece, we can replac its eet by applying aun

formly dite force of magnitud 0 to the cut end. So the sexe Is ad o Be
any sb. cles om the equation

e. pa

"This assumpion of nem stress distribution requires hat

The bare right and oa homogeneous material

+ Thelin of action ofthe fre sonins he cet ofthe section

+ The section he tan remote fom the ends and ram any discontinuity or abrupt
change in rss section

mac;

ad
ea ti a

Figure 3-13

Ss

à stands Ais | Senna

For simple compression. Eq (3-22) is applicable with F noemally being con
sidered negative quant. Also, sender bar In compression may fil y Bling,
and this possibilty must be eliminated from consideration before Eq. (3-22) à
wed?

Use ofthe equation

a

fora body say a ol, in shear assumes a uniform sess dstibation wo. ls very
<ul in prose to obtain a uniform distribution of Shar stress, The gain fs
¿nctaded became ocasion dosis in which hs sum id

Normal Stresses for Beams in Bending

“The equations for he normal heading stress in straight beams ae base on the fl
lowing assumptions

1 Tre sams subjected to pre bending. This cans that the shar frei zero
that no sen or il load re present

2 The materials sowopi and homogenous

3 The materia obeys Hook's av.

E The beam sitll straight with cross section thats constant throughout he
beam Ing

The beam haan as of symmetry inthe plane of bending

{6 The proportions of the Beam are such ht woud fal by bending uber than by
rushing, wrinking, or siewise ocn,

7. Plane cross sections of he beam remain plane during bending

n Fig. 3-13 we visualize a ponion of a straight beam acted upon by a positive
bending moment A shown bythe curve arrow showing the physical action ofthe
moment together with a ait ros nating the moment vector, The x axis is
‘coincident wit the neutral air of the section, and the xz plane, which contains the
neutral axes of ll ros section, called the neutral plane, Elements of he eam
‘Coincident with this plane have Zero ses. The location ofthe outa ans with
respect 1 the cross section is coinciden With the centoidal aus of the cross.

pre pre] sms 10)

ad
Dt ane

Figure 3-14

¡PA
A O A

‘The bending stes varies linearly with the distance from he neta as, and
sven by
My

u 1024

her the second moment af rca abou he as. Tats
Im f yaa 625

‘The ares distan given by Eg (3-2) shown in Fig. 3-14. The maximum magn
de ofthe bending ses wil ru whee y as te geet agite. Diga In
asthe maximum magne of Be bending tes, ná cas be maximum mage oy
pare (9-266)
7
Fan (3-24) can sill be used o ace a 1 whether qa ses or compressive
Equation (3-260 is often writen as

m

(9-268)

where Z= eis called the section modal.

A beam having aT section wih th dimensions shown in Fig. 3-18 is subjected 0 à
‘ening moment of 1600 Nm ha cass tension at the top surface, Locate the nt
‘eatin and ind the maximum teni ad compressive Bening sees.

‘The area fe compost sections A = 1956 mm’. Now divide the section into 40
rectangles numbered 1 and 2, ad sum he moment of thse aras aout the op ed.
Wethen tive

andhence cı
[Next we calculate the second mamen of area ol each rectangle about its own ce.
teca axis: Using Table A-18, we nd fü te top cage

Horse! = 1080 10

| nat Sil | Lai
O rn
=

Figure 3-15

à stands Ais | Senna

lend ten cs | 07

For the tom rectangle, we have

SAIS x 10" m

nn keane

We now employ the parle theorem o obtain the second moment of re of the
‘composite eue about its own Getridl axis. This there tes
Kem hg Ade

whore fg the second moment of aca about its a central axis and is the so
‘ond moment of arca abou any parle axis a distance removed, For the ep recta
Be the distance is

di = 3299-62 2600 mm
and forthe boton sctngle

dy = 67.01 44 = 2801 mm
Using the paralekais theorem for bt rectangles, we now find that
1.080 x 10 + 125/2699] 416815 x 108 + 128892300
907 x 1 mt

Final, the maximun tensile ses, which occurs the top surface, is ound 10 be

Mey _ 1600032.0910°°
PRET NI]

7.681) Pa = 27,68 MPa

Similar the maximum compresive ses atthe lower surface is fund tobe

Mes __ 160067.00 10°

“ 5622110") Pa = -5622 MPa

pre pre] amu O

ad
Dt ane

Two-Plane Bending
Qi fe. in mechani dsg, bending ocur in oth yal planes. Cons
‘con ston with one o to plane ofaymmeny ony he bending sess a ven by

mn om

er the fist term onthe ih ie of he equation is identical 0 Ba, 8-20 M, i
the bending moment in the a plane (moment ecos in y direction). is he distance
From the petal y ais a I, she second area moment about the ya.

For noncirclar cos sections, Eg. 3-27 she superposition of ese cased
bythe two Bending moment componen The maximum tense and compressive bend
ing stresses occur where the summation gives the greatest postive and negative sess
cx respectively For sold circular cross sehn, leal aes ae the same and the
Plan contain the momen corresponding to the vector sum of M, and M, contains
{the maximum bending stresses. Fora beam of diameter dhe maximum distance fom
‘the nota ais id, and rom Tale A-I8 = 4/6, The maximus bending tees
fora sol ru cos section is then

Me _ (+ MORIA a
7 ado a

age eae

EXAMPLE 3-6 As shown in Fig. 3-16, beam OC is badd in he x plane by a uniform load of 50

Figure 3-16
find
pones og od
Beringmoner doors
inane où
Ligne doom
ne

Tio ndin he plane by a concentrated foro of 10 I at ed € The beam 8 in
long

LA sonia
+

CES pre] =

Dt ane

Solon

lend te tops | 89

For the cos ection shown determine the musimum tensile and compressive
ending tess and where hey ac

() Ihe eros section was solid ica od of Samat, d = 1.25 in, determine
the magnitude of he mas bending ses.

(0) The reactions at O nd the beingmomen grams in they and xe panes re
Shown in Figs. 316 anc respectively, The mani moment bo planes oscar
AO ver

Uno ==}

E

(SOS = —16001Ein M) = 1008) = OO Cin
“The second moments of ae in bo planes are

OS OO 1, = ¿079 = 0087
“The maximum esi ses occur al pint A shown in Fig 3-16 where fe mas
mu me ss ut oboe ALA yy = 0.75 nay = GS in Thu
from Bs. 6-27)

1600075) , 30000875)

(a= Gao +

= 1 Mops = HAS

‘The maximum compressive bending ses occurs at point B where. y = 0.5 and
0.37 i. Thos

1600-075) , 9001-03375,
020 + CUS

(©) For a solid ile cos seston o diameter, = 1.25 in. the maximum bending
stes a end Os given by Eq 28) 36

(oon

11380 psi = 11 pi

ES 2
aa [0 + ean

9326psi = 9.320400

Beams with Asymmetrical Sections

“The relations developed cali inthis scton can ls be applied to cams having
asymmetrical sections, provided that th plane of Being cones wih ne of the two.
pricipal aes othe stone hve found the rss ta distance from the new
res

° la

=== al sus -)
Pres
ar

90 | chica Ent air

| Figure 3-17

3-11

‘Thing moment ofthis force about the ax andintegraing cross the section gives

mn four focan=M frcan “

We recognize tha the last itgral in Eq, () isthe product neta. the bending
moment on he Beam sin the plane of one a the pesca ne, Sy th x plane, then

tna fredazo a

Wit is rico, the relations develope in Se. 3-10 oll fr any cross-sectional
shape. OF cours, his mens that the designer has special reponse that
‘he Bening lod do in fat come ont the Dem n'a principal plane!

Shear Stresses for Beams in Bending

Most beams ave both shear ores and hending maments present tis only occasion:
aly that we encounter beams subject 10 pure Bening thal 10 sy. Deams having
et shear ore. The Mesure formula is developed onthe assumption of pre bending,
“Tiss done. however 1 eliminae Ihe complicating eect of shea ore inthe deve
‘opment. For engincring purposes, the Mesure Formula valid mo mater whether
‘Shear forces present or no. For this reason, we sal ize the same normal bending
‘sro distin [Egy (3-24) and (3-26) when hear forces ar ao present

a Fi. IK we show a beam segment ol constant cross section subjected 1 à
sear fore V and a bending moment Mat x. Because of external ling and Y the
hear force and ending moment change with respec 0x. AL + de the shear fore
aná bending moment are V + dV and M + dM, spectively. Conskering fomes in he
direction ony, Fig. 3-18 shows the ares diunbaton m dee to the bending
moments I dM is postive, withthe bending momen increasing, the tse on the
rit face for a given value of y. af larger in magnitude tan the stesses onthe et
Fac, Ife further lt he element by making lic at y = y (68 Fig. 3-18) tbe
met ore inte x decton will be decd 1 he let wih vale of

fa

shown nthe oad view of Fig. 3-18 For cir, shear oros onthe boom
face, dicted othe ight required. This sear fre gives ise to a shear ses Y.
whee, assume nil, the lr eb dx. Ts

ware Wen

Ce à stands a | Senna

CPE

Figure 3-18
Gas nn
raton erat

e cane me oii eng an di
a toon Seo aia HAE
© san om

In this equation ib integral the st moment of he area A’ with espe to he neu
tal avs ce Fig. 3-180) This integral is usally designated as Q. Ths

o-fua-va eo

whore forthe sated area is the distance in te y direction rom he neutral
ane fo the centro ofthe ara A. With is, Eg. (3-29) cn be wre as
ve
cm
In using his equation, mote at is he wih o the section a y = 31 Aso 1s the
second momen of aca ofthe etre section about he neutral ai
cae eons shar ree ae As fi, he ar sess given by
Fa, @-31)an shown on area A” in Fig. le cour only ay =. The shear tes
on he lateral area vas wth y(nonnally maximum tthe neural axis Where y =0,
nd ema the eter bers ofthe Beam whee = A

on

A beam 12 in ong to support load o 48 I cn 3 in from the eft support
‘own in Fi, 3-19. Basing the design only on bending ses, designer has selected
à in ahuminum chanel wih the rss section dimensions shown, I be direc shear
Is ngeced the stress in the beam muy be actualy higher han the designer thins.
Determine the principal sesses considering bending and direct shear and compare
thom wah hat considering bending only.

| stan Sie | Bs à stands Ais | Senna

rer
eam tn an

a | Mae grag Dog

| Figure 3-19

‘The loin, share, and being moment diagrams ae shown in Fig 3-19). 1F
the direct sear force included inthe analysis the maximum stress tthe top and
‘bottom of the Beam wll be the same aif only bending were considered. The maximum
ending sesos are

£992 pst

However, the maximum stes due 1 the combined bending and dirt shear
stresses may be maimom atthe point (8°, 1.27) hat jst he et ofthe applied
Toa, where the web joins the Nang. To simplify the calculations we asume cross
‘ction wih square comes (Fig. 3190. The nomal stress at section ab. withx = 3

al

7 1
For the shear res at schon ab, considering tear bone ab and ing q. (30) gives

| nat Sil | Lai
O ae
=

à stands Ais | Senna

lead meins | 98,

Using Eg. 0-30 with V = 36618, 1 = 1.66i0%, © = 0.525, and b= 0.170 in
seus

3000820) r
Ta = “61 PS

“The negative sign coms rom recognizing tht the shear ses is down on an x face of
a dx dy elemente local being considered

"The principal stresses a the pont can now be determined. Using Eq, 2-13). we
find ha ann 3 yy 1227 in,

ara. [ese

: fe

CNE pe

Foca pont at x 7
7 ps. Thun we os that the maximun pincipal esse re £1200 pu, 21 percent
higher than thought bythe designe.

‘Shear Stresses in Standard-Section Beams
‘The shear tes distribution in a beam depends on how Q/b varies a a function of
y. Here we wil show how o determine he shear sess distuibution fora Beam with
à rectangular eros section and provide elt of maximum values of shear stress for
‘ther standard cross sections Figure 3-20 shows portion ol a Beam with arctan
ar cross section, subjected 1 a shear force V and a tending moment M AS a
result ofthe Bending moment, a normal ses. is developed on across ection such
As AA, which sin compression above the neural aus and in tension below. TO
investigate the shear stress at a distance yy above the neural axis, we select an
element of area d sa distance y above the net axis. Then, dA = bly, ad 80
Eg, (3-30) becomes

EN]

Sabin di vale o into E, (3-3) gies

y
Le ea
‘hiss the general quo for ter ses in a estan Dam. T er same
thing ot Te us ma ome sb From Tale AN, the econ moment
Sf arc fa a arr scene 7/1: sai À 22e and A=
de ees

ws

94 | choc Engin Daan

Figure 3-20

à stands Ais | Senna

I we now ets value of for E, (3-32) and earange, we et

30)

‘We note that te maximum hearts exists when y = 0, which sat the ending eu
tea ain Ts

(333

av
a
for a rectangular section. As we move away from the neural as, he shea stress
decrees parbolcally uni is zero athe outer surfaces here y = ras shown
im Fig. 3-206. 1s particularly interesting and significant hee io observe thal the
Shea tess is maximum atthe bending neutral ais where the normal tess due 1
ending is zer, ad tht the shea Ars i zero atthe outer Surfen, here the
bending stress is maximum, Horizomal shar tes Is always accompanied by
vertical shear stes ofthe same magnitude. and so the distribution can be dia
{rammed a shown in Fig 320d Figure 3-20e shows that the shee on the vr
a surfaces varies with 3 We are almos always interested in the horizontal sea,
in Fig. 3.204, whichis nearly uniform wih constant y, The maximum horizontal
‘shear curs where the vera hear ages. Thins usually a the neutral ais ut
may nt be ifthe width bis smaller somewhere else. Furthermore, if the section is
Such that can be minimized on a plane not horizontal then the horizontal shear
ess occum on an inclined plane. For example, with tubing, the horizontal shear
Stress occurs. a radial plane and ie corresponding "vertical shea is ot vertical
but tangential

Formulas forthe maximum flexural shear ses for the most commonly used
shapes ar sed in Table 3-2.

0a

On pre] =

rer
ea ti a

Table 3-2

Fess fr Maximum
Shear Stress Duelo
Bonding

3-12

| Figure 3-21

dond sie tains | 98

eam Shope Formula

2v

Halo, hinwaled nd

Cedar Sr beam thine

Torsion

[Any moment vector tht is colina wih an axis of a mechanical element i ele a
torque vector because the momen causes the element 1 be twisted about that ais A
Bar subjected to such a moment i alo si o he in torsion.

“As shown ia Fig. 3-21 the torque T applied oa bar can be designated by desing
ows onthe surface of th bar to indicate ction or by drawing torque sector rows
along the axes of twist ofthe br, Torque vectors are the hallo arrows shown onthe
axis in Fig 3-21, Noe thi hey cononm tothe gba al or vector

“The angle of wis in rdians fra soli ound har is

1

es

where T= tone
ES
= modos of igi
= polar second moment of aa

0.

pre pre] a

ad
Dt ane

Shear stress develop throughout he crs section. For à rund bar in torsion
‘these srese are proportional oth ais p and are given by

7
me (0-36)
Designating ras he ais othe outer surface, we have
m
ten oan

“The assumptions used in the analysis are

1 The bar is sted upon by a pre torque, and the sections under consideration ae
‘emote fom the point of aplication of head and rom a change in dante.

+ Adjacent cos sections originally plane ad pri remain plane and parallel er
‘isting, and any radial ne remais sight

+ The material obeys Hooke' law
Equation 3-37 applies only 1 circular sections. For a sli und section,

xa
wat 38

“where isthe diameter ofthe bar Fa hollow round section,
= Zui-a ts

‘where be sbscripls oa refer 1 the utide and inside diameter, espectely

Tsing Eq, 0-37 is often neceaury to aba the torque 7 from a considers
‘ion ofthe power and speed ofa ring shalt For convenience when U.S. Customary
vns a ed the forms ofthis relation aro

FV _ anta Te

35000 © Boy © GOs il
hat speed, vin
velit Amin
‘When SI units are usd. the equation is.
H=To oan

where = power, W
T= tore, Nom
(0 = angular velocity. ls

© casi | Laie à stands Ais | Senna

Dt ane

lead sie tains | 977
“The tone Tcoresponing othe power in wats given approximately by

r

st om

whore mis in rosas por minute
“There ae some aplication in machinery for poncirulacrss section members
nd shall here à regular polygoal cross section is sel i asii toque 19
car or ley that can ave an ail change in postion, Because no hey or yay fs
esd, the posibili o à a hey is anode. Saint Venant (185) showed tht the
maximum staring sess in rectangular x e section ar occurs in tbe middle of he
lenges side band i ofthe magnitude
Tr,
me GB) (os)
where isthe longe ie, he shorter si, and a actor that i funcio ofthe rato
‘je a shown i the allowing ale" The angle of wit is gen by

1
BG oe
where funcion fe, 2 town inthe tbe

175 200 250 300 400 600 800 10 06

o

= [0208 021

029 0246 0258 027 0282 02m 0307 0313 03%

# Tora 016

0214 0228 029 0263 0281 029 0307 033 09%

Im Bas. 8-43) and (3-44) band care the width ong side) and hikes (sor sie)
‘ofthe bar, especie They cannot he intrhanged. Equation (3-13) alo appr
rey ali or equal sided angles: tes can be considered as two rectangles ach of
‘which is capa of crying al the torque +

[5a Sf Maa Pu LD Yan otra Coop Now Ya SR D

Teer esse WC. Wang and Gas art's omo o a Si The

Figure 3-2 shows a crank loaded by afore F = 300 IF that causes twisting and
bending ofa ¿in diameer hal eto suport athe ergo he reference syn.
actualy, the support may bean inertia that we wish to role, Bt for the purposes
‘ofa stes analysis we can consider this states problem.

(0 Dew separate Tce bay diagram of th ha AB andthe arm BC. and com
pe the valves ofall forces, moment, and torques at ct Label the dictions ofthe
‘ooninae anos on these diagrams

"0 Compute the maxima of he torsional tes and the bending rss in thea
BC and indicate where these a

| stan Sie | Bs à stands Ais | Senna

rer
Dt ane

9 | erica Ente Dn

| Figure 3-22

Solón

| Figure 3-23

a
<<

(0 Locate a ses clement on the op surface ofthe sta at A and cleat al the
ares components hu ct pon ths element
(4) Detemine the maximum normal and shear srsses at,

(0) The two fee body diagrams are shown in Fig. 3-23, The ests are
Aena Cofamm BC:
tend Bo arm BC

[At end Bof shift AB
Mendo hat AB:

4504 bin
12081, Ty = Sb in
BOOT, = 12008 in My = —4SOK in
0, My 19SOK Tin Ta = 120081 in

Opera

rer

Dt ane

à stands Ais | Senna

london sc | 99

(0) For um BC, he ending moment wil reach a maximum ner te shaft a
A we assume this i 1200 IB hen the Bening ses for a rectangular sc-
tion wil be

‘OF couse. his nor exactly corea, because a B the moment satay being ta
fered into the sa probably ouh à elder
othe torsional tess use Eq. (3-43). Thus

1 (4,18) ___ 40 18
nn (+) Tom (+ caps) = om

“ris ses occurs the middle ofthe in side
(0 Fora sees element at A tbe Being ste is ese and is

M _ 32M _ 320980)
EE

“The orinal ts is

a

here ie reader should verify at the negative sign accounts for te direcion of
(ad) Bin Asin a sae of plane sess hee the sees ao in the x= plane, Ths
the pineal stresses ae gen by Eg. (3-13) wih seit coesponding lo the

‘The maximum normal ses then given by

yee

AED (EG

ec esta

“The maximum shear stress at A cur om surface diferent than the surfaces contain
ing the pricipal sueses or the surfaces containing the bending and tosional shear
sess The maximum shear ses is given by Eg. (3-14) ain with modif sub
sers ans given by

(E

1457 = 27.7 kp

=== al sus 1@
Pres ==
ar

100 | stacks Egg Deion

EXAMPLE 3-9 — The. Siniametr solid el shaft shown in Fig. 3-2 simply suppor at th nds
‘Two pales ae keyed he shaft where pulley B sof diameter 4.0 in and pulley Cis of
ameter KO in. Considering being anftonona reves only: determine the ations
and magnitudes of he greatest ens compressive nd shear Suess in the sal

Selsion Figue 3-24 stows the nt forces, ection, an nal moments on esa
“Aloe hss re dimensional problem and vecs might ce apre, we
ok th component 0 he mont ver y oo a o plane sal
Figure 3 2e shows he ang in ie 2 pla id own the an, whee nd
ing moment a actly eto in zen Thos we abel momen gran
A M vers «Forth x pte, we lok dow the anand the moment agra
ay vea a shown in 324d

“The net moment a ecto e vtr sum of th components. Thats

w= (Mp ui
My = VIF OE
Me = VOD ADO = $657 in

“Thus the maximum bending momen is 8246 If in ad the maximum bending sess
at pulley Bis

At poi

246 brin
AX poin €,

Map _ 32M _ 326046)
a a OR
‘The maximum sional shear sress ocur between Band Candis

Tf _ 167 _ 1601600)
rue ETE

An psi

‘The maximum bending and osional shear tease ocur justo ie rg of pulley
‘points E ad Fs shown in Fig. 3-2. At point E maximum tes ses will
bem given by

At point E, he maximum compressive ses willbe o gen by

+e

a)

“The extreme shear ses lo cur at E and Fandi

pre pre] mu 10

ad
Dt ane

Figure 3-25
The cod ston
fete eat of

EXAMPLE 3-10

Closed Thin-Walled Tubes (+ « 1%

Incl in alt cab han hl he ptf ea rs mes ches
fe wall Teco meaning ht the sear sss rely ropa de
Wellness Teta np Tona ute ach as diced nig 325% pen by

r Jriras= cn frauen Lane

‘where A the arca enclosed by he section median lin, Solving for x gives
r

u as)
For constant wal ickness the angular ist (radins pr uni of eth ofthe tube
Orient

hee Ls he perimeter ofthe section median line. These equations presume the
‘buckling o the ube is prevented by is sers, bulkhend, and soon and that he
stresses below the proportional mi

Ses FP MoE tnd. aT D Mech of Mari A, Maan

A Welded steel tube is 40 in long, has à Lin wall thickness and a 2: by 3 in
‘rectangular cross section as shown in Fig. 3-26. Assume an alowable sear sues of
11500 ps and shear modul of 11.8010) pi

(a) Estate te allowable ton T.

(©) Estimate he ang of wis due the toque.

(a) Wain the section mean ine, he aca enclosed is
Au = 25~01125)8.6 0.125)

andthe length of the mean perimeters
La = 2125 ~ 0.125) +8.6~ 0.25)

CPS autos amie | crues 1

rer es
Dt ane
endend Srs pipa | 108
Figure 3-26
con soso
pode by wee,
‘Answer From Eq, 15) the torque Tis
T = 2Aqre = 26253)0125(11 500) = 237301 in
‘Answer (b) Te angle of twist rm ag, (16)
Tin 237300170) a
DO O = OOM a = 167
EXAMPLE 3-11 Compare the shearstress on aislar ideal tube with an outside dimeer fin
and an insid diameter of 09 in, predicted by Eq. (3-37) lo ha estimated by
Ea 6-45).
Selvion From Ex 037)
Tr Te 105)

Row =F PEA) NA A

From Eq. 0-45),
A =
Bags OI
“Taking Eg, (3-37) as crec the eo inthe thin wall esimat is 4 percent

sr

(Open Thin-Walled Sections

en ihe mean wal ine sot closed itis said 1 be open. Figure 3-27 presents
some examples. Open sections in sion where the walls hin. have relations derived
from the membrane analogy theory esting in

ar
rene 3 un

‘SS Time an N. Ge Too aci SoM Non ck. 1705109.

| stan Sie | Bs à stands Ais | Senna

rer
Dt ane

Figure 3-27

ts

¡Ko

where «i the hear stress Gis the shea modulus, y ls the amp of twist po uit
length Tis torque and Lis the length ofthe median line. The wal thickness is
<esigated e (rather ihn ) o remind you that you are in open sections. By study
ing the table that follows Eq. (44) you will discover that membrane theory pre
sumes be = 0. Note hat open thin-walled sections in torsion shouldbe avoided
in design. AS indi (3-47) te shear tes and the angle of tit are
inversely proportional to & and ©, respective. Ths, for small wall thickness
stress and twist ean become quite large. For example, consider the thin round tube
with a alt in Fig. 3-27. For a raio of wall thickness of outside diameter of
{je =0., the open section has greater magnitudes of stress and angle of twist by
factors of 123 and 615 respectively. compared 10 a closed section of the same
dimension.

EXAMPLE 3-12

[he
Figure 2-28

The crac in sp
food weed
‘esr mame

A I2indong sip of sel i hick ad 1 in wide, as shown in Fig. 3-28 1 tbe
llowable shear ses is 1 SOD psi athe shear modulus i 11.8109 pa, ind the
{oxque comesponding to the allowable sar sess and he angle of tv in degrees
(a) using Eg (3-17) and () using Egy G3) amd (3-44),

(a) The length ofthe median ln sn. From Eg. (3-47),

From Eg, (3-40) with be 1/0128 = 8,

¿TL sm
SSA

= 8572/0097 = S7416F-inkad

0 00970 ad = 56

Creer

rer

Dt ane

à stands Ais | Senna

Stress Concentration

Inthe development ofthe base stress equations Fr tension compression. ending. and
torio, was assumed hat no geometric iepularies occurred inthe member under
‘consideration, But iti qui dit to design a machine without peemiting some
Changes inthe cross sections of the members, Rotting hais mus have showers
designed on hem so hat the bearing can be propel seated and so tat hey will the
est oud: and tb sas must have Rey sks machined no them fr securing pl
leys angers. A bot as a head on one end and screw ted on he eer en oth
of which account fo brut change inthe eros section. Other parts equ les, ll
roves, and noch ol various kinds. Any dscominuiy, in a machine part aller he
Ses tution inthe neighborhood ofthe discontinuity so hat the elementary rss
uno o longer describe he sate of rss in the ara these locations. Such dis
‘ontinaies are called sires raisers ad the regions in which they ocur ar called
Areas of sree concentration

"The sion of elit sess across a section ofa member may be uniform as
ina tar in tension. linear as a beam in bending. or even rapid and cunaous as na
sharply curved beam, Sites concerts an are rum some regularity ink
nta the member, sich as tol marks, ols, notches, grooves, Ihre. Te nom
al stress sao eis i the member i fe oF the sires ar This definition ot
twas Honored, chck the denon on the srexeconcentaton har or abe you
are uso.

"A theoretical, o geomeri, res concentration factor Ko Kis we to relate
the actual maximo stews athe discon to the nomial res. The ators are
“fine by the equations

e

here Ki wed for normal stresses aK fo her stress The nominal ses or
{is more dieu deine. General, isthe sues aku by sing the elem
tary stes equations and the net asa or et cos ston But sometimes the Bross
‘ros sections we insta, ans it ila wine to double chck your source ol Ay
tk Bore calculating te maximum ses

“The subscript in A, means that this Stress concentran facto depends fr its
value cy mb eamery fe part. Tats, he particular materia used has no lest
‘on the vale OA This why ls call à heretic Srs concentration face

“Tn ali ol geometric pesto determine stres-cosentmonfcirs sai
cult peche, and nt many solas can be found. Mos sues-concetion toes
are found by sing experimental techniques Though he finite-element method has
been und, the fat at he elements ar indeed finite prevents finding tb rv maxi
rum sess. Experimental approaches gesell used include photoelastic. grid
methods, rite cating methods, and els srain-gauge methods. OF cours, he
id ad sain gage mods bo str rom the same na a the nie element
method

‘Stres-concentration factors for a varie of geometries may be found in
Tables ALIS and A6.

| stan Sie | Bs à stands Ais | Senna

rer
Dt ane

Figure 3-29

‘art tl Pense
heat Fam nore

EXAMPLE 3-13

‘An example à shown in ig 3-29, hat of thin ple tool in tension where the
plate contin centrally local ole.

"sui loading. steseconcetation factors are applied 2 follows. date
(ey = 008) materia, tbe res concentration facto iso sly applic wo pedi tbe
ical ses, because plato stain in the region of the sess is Mel and
as a strengthening effect In brinle materials (ey < 005). the geomet sts
concentran ates pli th nomial es before comparing i with tenth,
(Gray st ron asso many rent ses sers hat he sess ases nce by the
designer hive only a modes hu aie él

Be Alert to Viewpoint
‘On "sue" odend (or lg) a oad same through a pin to arectngularcross
section rod or sp. The theoretical or geometric sess-oncentraton far fo this
geometry now as follows on the ani ofthe et ren À = (w= dt a shown in
Fig 330.

dw] 01S 020 025 030 035 040 045 050
Kiya sa 46 37 32 28 26 245

As presented inthe able, Ks decreasing monotone This rod en similar to the
‘squae-ended lug depicted in Fig. A-I5-12 of apendi A.

am = Kt la
KE Lg
“A in
His instal to hase theses concentration air on the ached ar. Let
i
ma a

By equating as. () and () and solving for K; we on

1

Figure 3-30

feats coco ed
The msm o ai
eg ac rte À
od hart

An lud bad te
iment Kate on
boheme ig tal

à stands Ais | Senna

A power regresión curves or he daa in the above able in the form Kı = aa)?

which sa decreasing monotone and unexcing). However, rom Eg.)

ne By 0)

oc another able from Eq.)
Ww] 0.15 020 025 030 035 040 045 050 055 040
x; 18.507 6907 5980 5403 5038 4817 4707 4092 476 4946

ich shows a tation point minimum for K This can be foun by iris

Eq, (7) with respect to du and sting equal 0 zero:
aK; ajo Jo?" + atajo.
aan era

here b= 0935, rom which

NL ar
Che

it corresponding K; 4687. Knowing he section x Hes tbe designer spect the
Strongest ag mediately by speiying a pn diameter 010.483 (a a rule of hub,
‘Fal wäh), The theoretical; ati original for, ra plo based onthe daa
‘sing net area, would nt sugges his The righ viewpoint can suggest valuable nas

3-14

Figure 3-31

And bec oh
al ondes peu.

Stresses in Pressurized Cylinders
Clinical pressure veses dr ide, gon bares and pies camping id
a high pesares develop both dial and Langen! ares with vals that depend
‘pon he rao the element under consieraon In deemining radial rss 9,
tnd the tangential Ses, we male ue of the asumpion hal the longi
‘longa is constant round the ccumfeenc ofthe elinder I oer wor ight
Section ofthe cylinder remains plane afr sessing

Referingw Fig. we designate the inside dis ole pin by the ou
side dis by rhe intra pressure by fa the extra ress by Po Then can
be shown at angen an ail stress eit whose magnitude a

po)

vn

See, Bop Aoc Senthil Se Ana nd MC Hl New

| unser Sil | Lai néant as | PT 1
=== =D.
=

108 | stacks Egg Deion

Figure 3-32

to el presse.

As usual, posive vales indicas tension and negative vales, compression,
“Te special ae of p =O gies

(9-50)

‘The equations of et (3-50) ar plein Fig 3-32 1 how the disibuton of esses
‘over the wall hicktes. I hou be realized that longitudinal stresses est when the
nd recio the internal pressure ae taken bythe presse vessel el TR tes
iefound ote

Werther pote that Eq. (3-49), (3-50) and (3-S1) apply only 1 sections uken sis
icant distance from the eds and away from any ares of ses concentration

en

Thin-Walled Vessels
When the wall thickness of clinical pressure vessels about one awenteth, or ls
Fits rats the radial stress that results (om pressurizing the vese is quie small
Sompare wil th tangent Sres Under these condition the agent Sres can be
‘obtained as follows: Let an interna pressure pte exert onthe wall o à eylindr of
ticknes and inside diameter dí The fore tending 1 spare two ales fa it
Teng ofthe ylner à pu. This force sessed by the tangent stes lo called
the hop stes, acing unfamly ver he steel area. We ten have pd, = 210, or
coda E en
‘Thisequatongivesthe avenge angenalstress and is vl regards ofthe wall ick“
nes ora thin-walled veel an apeoximation tthe maximum agent res is

MEN WS

Cid

where +1 ithe verge diameter

Opera

à stands a | Senna

= =
=a
its Les
Ich ot eg st i ee se m un
ARS
m
Pe os
AMPLIAS mie o mo Soi
TT
(ns e eno ar pi et
ee
Beer eee
TE
Sie) nd = 42029 sn. = 192378 ud == mn
PI an Y cia
Ra
E ts oe poe Ta
rada. 20200200"
dr 75+025 aan:
‘oy 0 a gp ans ur
mans
a OP
pee eee eee ore
Rens
ha (3) ng ni = ops
Sn na bn on ecg st. 6-0)
SE
bon ene
ni pa e am
ne. mien
Answer TE 5620 pt

FF

‘These the ses, 0, and ate principal stresses, since hee is no shear on
those surfaces. Noe that here ism sigan ference inthe tangent stesses in
pais () and (b), ab othe in alcoy ean be considered tt.

pre pre] rel.)

ad
Dt ane

3-15

Stresses in Rotating Rings

Many ron elements such as ywhcel and blowers can be simple oa ong
ring determine he stresses. When this done ts found tht these tungen and
‘ail ess exist a In the theory fr thckewaled eines excep at they are
ase by inertial ore xing on al he ars of the ing The tangential and rd
re 0 found re sujet the flowing resins

+ The ose aio the ing or kare compared withthe hicks, = 10
+ The thickness ofthe ring or disk is cons

+ The stresses ae constant ver the tikes.

“The stress are”

1055)

where ri the ads to the sess clement under consideration, pis he mass density
and te angular velocity ofthe ing in rains per second. or arta sk ie
= ii hese equations

Press and Shrink Fits
When two clinical parts ar assemble by raking or pres ing one pat upon
another, a contact pressure is eresed between the two paris. Te stresses resulting fom
{his prete may easily be determined with the equations ofthe preceding section
Figure 3-33 shows two cylindrical member tht ve ben assembled wih a ik
Bi Prior taser the ut rads ofthe inner member wa larger than inc aos
‘ofthe eter member y the radia interference à, Aer assembly an inefrence cont
pressure p develops betwcen the members the nominal vals, casing radial tes
50, = =p in ah member a tbe contacting surface, This press is given by"

LOA ENCEINTE | Te) LIT 2

A tale"
here the subscripts and on he material properties correspond tt outer and inner
members, respectively. If the two members are of the same material with

(0-56)

Boney Eee de aon simpli
bs fed = RMR)
He] en

For Es (3-56) or (8-57), diameters can be usd in place of Rand a
‘he diametal interlerene (ice the rail interference

CES

rer

Dt ane

Figure 3-33

che sert

à stands Ais | Senna

Er
EI®

‘each member. Forte inner member, = p and py =0,Füiheoutermembe. py ~0
and p = p. For example, the magnitudes of the tangential stresses atthe transition
radis Rare maximum for both members, or the inser member

(os
and forthe outer member

wo

vo,
Assumptions

se so ene an Eg ne at ts
ann np ie vote acess
Bu nf ec ave cul niga
Fc cr. Te ae Ren un cen pu md
Bee oma tater babe wn on pao

‘Temperature Effects

When the temperature of an unrestrained body is uniformly increased, the body
expands and Ihe nal sain it

san 0

whores the coolen of thermal expansion and 27 is ie temperature change in
“degrees. In his action the ody experiences a simple volume Increase wih the compo
ens of shear min al zero.

Tra straight bar is rstnind at the ens o as 1 prevent lengthwise expansion and
hens subjected 1 a union increase in temperature a compresivstess Will develop
cae ofthe axial const The ses is

0=-<E = Wane es

In asimila manner ¡a uniform Mt ple à reine atthe edge and sete
10 auf temperate se, the compeesive sues developed is gen by the catión.

(DE
ET

(6)

à stands Ais | Senna

112 | moco Engreg Des

Table 3-3

Cadi kato
3-18
Figure 3-34

Material Cosius Scale (*C 1) Fahrenheit Sal
Aion ENT 13 nor
Bo cot 18107 ore
Coben sed 10810. énor+
Cas on 10.9101 same
Negre 25.2107 nono
Nell ses are 7.00}
Soi sed 17.310r* senior
gen agnor? 2410

‘Te stresses expresse by E (3-61) and (3-62) ae called heat see. They
aise bene of temperature change na clampod or restrined member Such tres
for example, ocur during Welding, sin pars 1 be welded must be clamped before
‘welding Table 3-3 It approximate vales of the coefciens of heal expansion,

Curved Beams in Bending

‘The distribution of sues i a cured flexural member is determined by using the
Following assumptions

+ The eros section has an axis of symmetry in a plane along the eng othe beam.
2 Plan cross sections remain plane ae ending.
+ The modulus of elasticity à he same in tension as in compression.

We tl nd that sta nis andthe conri! axis fa curved beam, ve

‘he aves of straight bam, are no incident und also tht the tess does ol sy Ti
ar from te neural ax. The noto shown in Fi, 3-34 defined follows

re = radis oF mer fiber
dis ofinne fiber

Creer

rer
Dt ane

EXAMPLE 3-15

à stands Ais | Senna

lead Shes Aine | 19

= depth of section
2 = distance rm neta avis to ute fiber

+ = distance from neta visto inner fir

a = rans of net si.

= adas o ential as

+= distance from ential asisto neutral is

M = bending moment: positive M decreases cunatue

Figure 3-34 shows thatthe neutral and onda anes are not coinciden urs out
tha the locaton ofthe neal ans with espet othe center of curvatr Oi given by
the equation

ss

“The ses distin can be fund by balancing the extemal applied moment against
the imermal resisting moment. Te est is found 10 be
oe My
Ae)

where Mi pose in the dition shown in Fig. 3-3. Equation (3-63) shows that he
Sues distin is hyperbole. The eal ses occa he ier and outer su
faces where y = 1 and = 0. respectively ond are

He mM (9-65)
‘These equation ae vai fr pure bending Inthe usual and more general case such as
à crane ok, the U frame ofa press, othe Fae af clamp, he Bending moment is.
ue 1 ores ating o one side the cross section under aideront case the
bending moment is compued aboot the cena ai. no th neutral ac. Alo, a
tional axial tie or compressive sess must he added o the Bening reses
given by Eqs. (3-64) and (3-68) 1 on the rela Sres ating onthe section

sa

"ecole ep of asin ine Rar O Ds Aon Seg
a A Ana And. ep, No Y. MI

Pot the distribution of sresses ass seston AA of the crane hook shown in
Fig.3-3$ The cross section rectangle with b= 075 in adh = ian the load.

Since A = bh, we have A

dr and, rom Ba, (3-63),

eae)
nn m
ul aos

pre pre] em ©

ad
Dt ane

114 | neceneattngreing Des

Figure 3-35

(a Pon vo ear hc
hosen an an
leen am xn,

Thee ro men

nad À = Fin! Ts, fom

From Fg 338, we seth
EX

Diner = Gin

a4
M7 © ME
and soie ece nity is = 1, — ry =4 — 3.641 = 0.389 in The moment Mis pos
Aie andis = Fr, = $0003) = 20.000 in, Adding he ain component of rs
10 By. 3-68) ges

” 681 in

E, My _ 5000, Got =")
AY ae EE
Substiuing values of + from 2 0 6 in resus in the stes dstibaton shown in

3-35r estress lth mer and outer adi are found de 169 and —5.6 kp,
respectively as shown,

° a

pu
rum

ou

Se.

Nate inthe hook example, th symmetical rectangular rss section causes he
maximum tile ses to Be 3 tines greater than the maximum compressive sess. IE
e wanted wo design the hook o use material more cc} we would use more
mei athe ine rasan es material a he ote ran. For this eon, ap
“oil. or unsymmetie [ess sections are commonly used. Sections most ie
‘oentyeocouneed in he ses analysis f curved beams ar shown in Table 34

Table 3-4

exon Scion ch

à stands Ais | Senna

Mi

beit 2er +e?
Test bal
ba + bee

ee

pee plo —
ba,

APN

Tt, peat E

DE bul

AT]

TS 7:

CET

pre pre] mw O

ad
Dt ane

EXAMPLE 3-16

i

i

Amar Cleans for
Cea sl ml md cig e tin ee
cra ty a nr yey ag hn
Ssh entire. lh geome rao
SUNOS Attn ands cal Seat
a tains sa

sat, oe
ie etn gt i a tg at tn i ir
Shite co's moby Behn rans

Mor

Tr
ry 2 re which it shoul bet use Bg, (3-67). then its oly necessary tocar.
and to measure y From this axis. Deteminingr fra complex cross section canbe done
ily by most CAD programs oe numerical a shown nthe Before mentioned eer:
fence: Obsere that a the curvar increases, rf, and Eg. (3-67) Becomes the
Straight-eam formulation Eq. 3-24) Noe thatthe negative signi missing because y
in ip. 3-34 vertically downward, opposite that or the aight ear equation

oon

Consider he iclar section in Table 3-4 wih = 3 and R = in. Determine eby
‘sing the formula fom the ble and approximately by using Eq (3-66). Compare de
‘ess ofthe two solos.

Using the formula rom Tale 3-4 gives

E 1
__ 291421 in
MA) IN
‘This gives an een of
3291421 08879 in

“Tae approximate method sing E (366) cis
1 ak

AT FG

ee
5710
“Thin dlrs rom e ext solution by 29 percent

AS à stands Ais | Senna
en”

3-19 Contact Stresses

When two hadies having curved surfaces are presse together. point or line contact
changes o area contact, and the wresen developed in he two bodies ae ree
dimensional. Conaetstress problems arse in the contact of a wheel and a al,
in automotive valve cams and tappes, in mating ger th, and in the ation of
rolling being, Typical failures ze scen serach, pi, or king in the sure
material,

“The mos general case of cnet Sres oscum when each contacting Hay has a
double radis of curate: at is, when the ais in he plane of ling is rent
From the radius ina perpendicular plane. bth planes an rough he axis fte con
tacing fore. Here we sal consider only the two special ese of entcting spheres
nd contacting clinders The sls presented hee ae due o Herz and so ae fe
‘quently known as Merion sess.

Spherical Contact
When two sold spheres of diameters dí amd d ar pressed together witha force
Fa icular are of contact of radis ai obtained. Specifying Ei. vı and Es

as the respective elastic constants of he two spheres, the ads i given BY the

‘equation
EE (oss)
y AL

“The pressure dation within he contact re of cach she hemipberical, shown
in Fig 3-36. The maximum pressure occur atthe ene fhe cote ara ads

se

Pan wo

Fsquatios (3-68) and (3-69) ae perfectly general nd lso apply to he contact of
à sphere and plan surface oo sphere and an internal spherical surface. For a plane

Surface, use d'= 0. Foran intra surface, the diameter is expressed as a negative
quant

"The maximum sesos occu on the aus, an these ae principal stresses. Their
sales are

Send Ahonen Maton of ara New Yor 3 SO,

pre pre] rel -)

ad
Dt ane

Figure 3-36
La an

$

"Tee equations ae valid fr either sphere. but the value used for Poisson's ratio
mus correspond withthe sere under consideration. The equations are even mae
plat when sues sae ff axis a 1 be determined, oca er lx andy
Soorinses most abo be included, Bu (es are not required or design purposes
ecu the mia occur on the za

‘Mohs ces forthe rss state described by Eqs. 3-70) and (3-7) ae à point,
and wo coincidences. Since, = 05, we ive nun = 0 and

ora

Figure 3-37 a lt of Es. (3-70), 3-71), and (3-72) or a distance 1 3 below the
sure, Not thal he sear ses reaches a maximum sale lig Below the src
AU the opinion of many aulhorkies that hs mama shear sex is responsible for
the surface fatigue fale of contacting element. The explanation hata cack oi
ines a pin of maximum shear ses below the surfae and progress he sur
Face and al the pres of the labra wedges the chip lose

Cylindrical Contact
Figure 3-38 lsats à imitation in which he contacting element ae two.
(yinder llegir and diameter di and d As shown in Fig. 38D, the area con
{act a mur rectangle of with 2 and Ten L and the pressure distan i
lil The avi bis given by he equation

073

| unser Sil | Lai
© ae
=

Figure 3-37

comparas bobo ae
te cag ire
es à igh de

PATENTS
pino Op he
‘ora talon Pour

(ai 4020 Now hte

Figure 3-38

Pal acon bees
‘fede gh Como
Pepe

à stands a | Senna

NL

‘The maximum pressures

2e
Das = 2 wu
Equations (3-73) and (3-74 apply oa einer ad a plane surface, such aa il. by
making. = 20 fo the plane surface, The equations lo apply tothe comet oa yin
(er and an internal linda surface: in hs case dis made negative fr ie interna
Surface,

ct A)

Figure 3-39

congrats blow ce
Solid fe moi
rd aus val
1a ca 12/0 = 070,
One Mo ot td
notant 4030.

“The ste state along the = xis given by he equations

es

74

om

‘These tree equations ae led in Fig. 339 yp toa distance of 3 below the surfe.
Fie = 2 2 046,04 = 9 nd fn = lo, — 2 = lo, — 0/2. Fors = 04365,
91 = 3, al fu = (0, —2.)/2-A plot fff alo included in Fig. 3-39, whee he
gres sale occu at = 0786 witha vale of 0300 Ps

Hert (1681) rosal the preceding mathematical model ofthe ses ld when
‘he contact zoe i ee of shear sess. Another important onac tes casein of
antact wih fiction providing the sharing sess onthe contact zone. Such shearing
‘esses are smal wid cams and elles bt in cams wit atfaced followers wheel
‘contac, nd gear tc, te tresses are certe above the Heian el. Imestg ations
‘ofthe lic om theses field de to normal and hear reses nthe cont zone were
‘begun theoretically by Lundbers (193, and continued by Minin (1949), Smäh-Liu
(1949), and Party (1949) independent; For farther dei, se he reference cd in
Foote 14

AKL |
N

1

H

NR KIT
e | II —

Crea

rer

Dt ane

à stands Ais | Senna

leaden Stes pois | var

3-20 Summary

E

32

“Te bay o quay be res codon at acia location in machine clement
is an important si of We engine. Wiy? Weiher the member fas eet
‘awed ly comparing the (dumagıp ses ea location with de core:
‘ponding tate sag ths scaton Tie chap as sed he ein
Lies

Sins co be eed with grs presio where the potty i sicily
simple a hor erly pros he area quate Ron. In ar
‘tes, approximations ae sed. Tere re ome approximations sich Be
Sont aay (FEA, se Cap. 19, os eal tend comege on ue val
te The a caprina measurement se aug. Foren. losing ier
ce of sees om ie entre sin conto, Waster e nebo, on
Fes rbas den ofthe sen codi tial locaton,

“The nature of escarola undniandag In any Re that the longer
ve won ithe moe Ile things em o be and ew apprnche ss a
15 hip wi he completion: As newer schemes ae IE engine ae
for de Improsemen the new approach promises, Begin o wne the approach
Optimism mal reales a ue expsence as concer. Tsk th promised
to extend the capabilites of he noneapet evenly show that experi 1 no
ion
ass analysis, the computer can be helpful if the necessary equations are avail-
abi. Secas any can ql reduce complice) claim or parame
Sin ely handing "ah 4” quo ring nd fg. ion ol cl)
ri! or oe of cheaper metia), un cen gie img no opinion
paran

"Wen the nes equis are at alle, then nett sch as FEA ae
state, bl cautions we In ode. Even when you have ases lo a poweril FEA
ove, ou shld be near an spe hile youre kang. Ter ae mins questo
SF convergen disco. sie analysis Is mc susi hn clip
tna The els ren bet bare mowing of wal that was se o foma
ite the problem Cher 9 provides an dent wha tect any amd”
lia be wedi eign Ths che Ib no can compete In Il semen
ther and ie spe e fine len pie Bah si ss regule mach
‘xpos and experience to be dep

PROBLEMS

‘The mot Wis sed in esas gr ars 1 psi he weight fa le at
Five, sume te prs ae weighs, For each gre ar skeich a re body saga of ech
ment, ici he me Ty 1 a oc e proper dci, a do compa
mag

‘Using the ge ar st y yo ins, eich eb digi fach ment in
the fue. Comput he magna und rec of cc Fre win an agai or vor

Fin he actos athe supports and pt esa fre nd edit gras oca
‘ofthe ems sown inte gue on page 123 abl he dagas ope

Dt ane

ma

ct A)

37

nani testo cose bi using pan ring. and pan ie vols as
inte gue

(a) Att positions, xy. an shld he pen ings be tado san wes?
BI he tie state? 0. joy sage arm

3-12

For cacho plan es state Inte elos, dew a Mohs ci diga poet lable,
And epic ona daa re, nd din gi mn dex so Dre
ss lents al 3-11 and da ae ei

Repeat Pr 3-8

Dann den

Repeat Pb or
Ga, = 20.9 = 1 = Bow
we in, = cow

For cc of he ses us iste blo: al ee incl mal nd ar rss ra
‘comple Mase sce gra an abe a ts erst

we. 4
Who, = 101, = teen
(0020 = bey

we,

Rept Pb. 3:11
(ha, = We, = 30.9, = 30e
Wha 2300, =a, = Wow
ya, 00 = 20.4, = 00

3-17

3-18
3-19

à stands Ais | Senna

tenons ras | 125

ses the tt deformation hut sai andthe chang he 4 diameter,

in agonal aint aly tension rods 1 mm in deter ar sd in a rectangular ae
topes clase. The as cn sky sopor tens sess F138 MP ie ud a
ally 3 in eh, bom mt ey Rear deep his ees?

ital aves wre id oa nt specie determine the sein oi
"e estores, = DUI ande = 0067. Ende, ad, he mal econ ss

An engine wishes wo determine te searing stent cota epoxy ment. The poten
isto devise att sprinen sch Jl ect ar shew Te shown in eg
tein which 10 Ban ft a a age 0 soto or he alg ec Fal With

the aight shanks scm to accompa is pros Using he cena as 4 ad seating
Se me shearing nh he engine ci

sax omo
or a ip
5 (ie) owe

Rosle the dsr, Whats our posto?

‘Teste of sresta pits, = 2.9,
Determine principal sess, draw acompte Mohr ecc daar being
‘of nest and ep he matin ars ors ea

Rogen Pad. 3-17 with, = 10.0, 20 64 = 104.00
Repeat P 3-17 wie, ty =D tye =A at = 2

10,

Te Roman meta fr asie ie in ein as I Bla copy o ds ha as
sic and ad pone dale Bough the ety Romans lc ae the lc
tls da wit sang sn up or down. yu do, Cons asin appr tanga cn
‘son eam coco, as edit pu

pre pre] nn 1@
an =>

126 | eer Engin eign

Sen atthe es quan

Jee Since th Roman mtd at
one signet /0 = Expres Fines of le

3-21 Un ur exerce wth concert ing single cam. Pb 3-20 cosido au
formyl simple ear Tate A-9-7,
da) Stow Gant he ses ea unto focal rs sein bes ven by

(0 Strip every prance ihm (for mod) an ie be ode tion ito de pto
ype etn, sole the xl ctr in Pod 320 sting = Bay We
And ei ms ek actor, and commen cn wha you be kam

3-22 Tie Chicago No She & Milas Rall ws an coa may ring ten the
ein carte ie Ia pasenge cr as sho nthe gre. which weighed 104 kip
al 32. icon, 7 boss cl, 28 cp egihorSS 8 3 in, Comer
cas of single con à long, simply support deck pl ik bis
(a) What wa de lps hdi men in e bee?

(0 Wat as the positon fhe cae he ie?
(A) Under wich ales the being ment?

Coaches 752-776

(AS “ated nn | m |
Er

dond ná Srs ph | 127

13-23 Foren schen lin dh ac mom of ra e can fhe et an and
ineditos rm te teal a o e tp and otr sacs. Sapos a pose ena
sen O Epi apli: de rol oe ath pan ot surface an
‘ery bmp ehange in cos seien.

nr in

mo JL

13-24 From baie mechanic of mute, inthe dra he bondi sn, ti and ha he
rales comal af muta as gen by p= EI/M. Finden nd yon
‘be comerof um comerla de pls hr the bom sn e mos, foreach Bam
¿born in be gre. The bam se oth made o Dels Table À 5 an hae rca

(3-25 Forcach beam irn e gr fn th tons ad magie of te masia e
sl cdi ss athe matin ser rs ue Y

| stan Sie | Bs à stands Ais | Senna

rer es
Dt ane

3-26

i ul
Y the
aa

AMAIA 5 ara a Oe

Te ie tres number of am esti. an lab eg es FL hp for
wand 12 ia nd fi he masia af fry ret ad a ch bs
a amy he he Inh ae toc ingle pons

(a) Wood ois 1 1 9 iad 12 long

(0) Setra, 20 OD by Ln al ici 8 in ne

leal te be none menden, food om cin mata an wel in
Set nes 3x 3 4 iman 72 ing

LCA SA intel han, in eng

PDA in x ir 72 ang

CIS autos amie | crues 1
= come
Sonne na

endend Sres pipa | 129

13-27 Ani a kml nt campings ee ad Feet somo on acom o soi
mg e btn of con and Kad a shown nr Df: gre. Th ua es
és mamie foin oi pat abr noms choc te oigo in pr
Aa = OS in 0781n.d 05 in ad = OO M, sima e masia bending us
do maxima sear sxe du o Y ah approximation,

3-28 figure lxs in gy Ae o a ol a aban member A wl ana
isons ta atumesconcote ratios and nc rm Sapos be man.
Fe ruine long distance o,f the song momen ration rer or sale an
the concen resto? What he ain emi 97 Wht do you thik of ing he
sa sample

13-29 For e team shown, determino (a the mac lene ad compr Henig res
(8) maxima shea rss ue o Va (the im shea sess th bem

Fern — 4

no

ct A)

3-30

ss

332

3-99

3-9

335

Constr ly spp beam of rectangles etn of cons With and var
‘eth. pornos he wir sah rer ras do eric
‘Stet. hen jected ad at dans fr th po an dane th
ig por. Show Bt he pi a ato ie By
ico
nn [BX ozrse
Vie

In Pr. 3-30 0 a à + wich amt Gr Fe mai hr rs nd
it cristo cont in th ein show ht he depth at an en by

3 Fe ETA
2h <The

»

Coie a singly np sai eam lala cos sein o met do propio
Voy Sri entr ch ht the mani rs, a safe de end om
ta ben joc à tay al cated a à tance a um the suppor a a
{ane ben th igh pp Sho hat the dame data ations gen Dy

aa” Osxsa

"Tosen al es intenso qual enga to compar, The sf qu cos
con id nth and wall hikes Tesco ound of Since band wl bc
ne The get alba sar ss a ano e se int ca How oc
le fs por ná og compre ah ee?

Begin with in aqua alte, al hikes = 0.05 Je Din en no
duc ome ad ie ral, with loable sear sess of SO pu ea nd
‘FILS isn fam sb, Use ctr fin core ain e go 0 27 = 04S
in Usa aun inode medan is radios. pi meda ie La ae Sd
Voy man cure, tog , and th anlar The cos co wil vary un ss
rca wand copter program willed ie alone. Sty he ale Wave
you karat?

e nn e ne Se
Bun

Crea

rer
Dt ane

3-36

3-97

338

3-40

31

à stands Ais | Senna

CET ET

i
=

In Prob 3-38 te angle has ne le ichs in aná cb |
‘The allowable er sess a = 1200 po hs ange
(a) Find te oq aed uch ep an te arg shear es in
(0) in ange a st per ani eng of deci.

sh boa gts in,

‘Two 12 in og in rectangular ip ae pase iger as shown Using main
allowable cat sou of 12 0p demi main te and agua ist nd
tana pring rt. Compare hse ih a sige ui of rs sia iy lo

q

Using «maximum allowable ser sos of 0 MP the nf ameter oc o nani
36h when

lay Te sat pes 200 ei,

(0) Te a est 200 revi.

À 15m arte ser st ew a tos ing. theta tes in th a
nai co 110 MPa when cn is ste epg ange hat at eth eth
orth?

A lame solistas as oque site epic witha alow shat
hing al hicks. Ibo materias ave ese sng wht porc |
‘eduction que ain? Wha sth centage ection in a Weigh

A bol set sal st asi 40 Nm of og and toe sid so hat he sonal
Sens de mece 10 MPa.

Use peter sis
(oy Wa ste on he iid of the sa whe al ones pid?

12

ct A)

32

3-49

3

3-45

3-46

a vin by ager moter oe Fad at hp. Demi site tft dance de for

noble tonnes ol LL.

da) What wou bee tess at ouvert ring qu tic te
‘wong ae?

Ge bending sess Be} bea problem? Wht the effet of int ll gt on
Being

=n u

“Te comeyer re rl in the Sg or Pra 3-4 150 mem in meer and en ot
rein y gered mio sone peda | RW, Fi sao al diameter e base an
loable inal ss of 7 MPa

Forte sane eosesetonl aa A=? = nor queen ston ars a à
cular rss section aa shal ion which has higher masa her es an by
‘et mug ie

Forte sme ses aa A = = nd, fora uae rss clonal asta a à
‘cular roseta aa shat ah eth, trio wich hs ptr gl
cand y wht mpi peter?

Ine igre, ha AB is tating at 100 simi and arms 10 pt shaft CD teh a
determino be (co = = PAM = 362 + 808.4 I. For tail) daw aie aly
‘dag and determino reaction at Cand D som simple pps anu alo tat
tearing Cs ars Dar) (dram he sete force nd bending moment Gagan, nd
(0 min ta the sat diameter 1.28 i, determin the maximum tens and sar

ad cone
Dt ane
endend Sres Anion | 183

13-47 Repeat do aliado Mat AB, Lette diameter at in ant ase
that aig ia ns Dig.

3-48 toro! = 10m pin ul EG, ii oiga cons ed anon
tim ps Gs Penis te a ABCD sg gs €, dins th cn re
at Banting o Ps a Sp ger € and gear Fhe pc date 0 1
fn especie: The cont foe eve he eas stan ah the pese angle
= Remington mas and coming I bears 4.0.2 we simple
Sheer hoch ont m a ABCD a contas he maximo bc nd a
ter shear res Fe is, domine sima tl ad ha ese a

ru

3-49 Iren de pi f Fig 3-2 is infinity wie, on te ses ae ng in he
la com e dere in placenta

Se Daya Add og ant Ad Ses ni 2 Mam, Nowe,

na

à stands a | Senna

3-50

351

352

353
358

355

fort dungen and ar copos spe. Her ste dance fon cn.
da) Find ie ns componen ah tp and ida the ol er = 2
(©) Hd = ¡Om hota rap ungen ss diria, ofr = ro

(6) Repeat par) fr =

Cosina sess concerto a i inh Fie Sterne he maimumnomal and

Develo formats for te maximum dala tri resin hick mld finder
ecto ral posar on

Rep P51 whe then su 10 era reste ely. A wt ad do he

Develop teres elon fra in nll spl presse ec
A promener a iumeerof 150 mona as e al hice, What pro an
a vs cary ithe mai cr rs e pot ccoo 25 Mpa?

A indica pesar el as note mt of 10 nan a al ihnen ie
ina ese 80 pi are masa sar teste esl wa?

| nat Sil | Lai
© ae
=

356
357
258
359

3-60

31

3-62 to
3-67

3-68 10
an

à stands a | Senna

tendon Srs pci | 135
An AISI 108 oh rs ss tbe hs a ID of 1 na a OD of 1 in What masia
‘Sct fhe nina yield stent of he ate?

inca reste cn his abe ake ihe at ip Nol res is nt 1 en 3 pe
et ofthe minima yield strength of he mater?
gauge (00747 and won ¿inst The sks nom Wha e maim

‘The maximum roce speed fora 300 ameter abrasive ng whee is 200
‘of 3320 Km’ andi the maximum ene rest his sp.

a base ctf west ha aster of 6 in hick, and hs are. he
mama str aes dp od

A rt an er lattes at 30 rv. Te stc ade as a im cos cn.
{in ick by 1 im wie and hs {ameter ol in he ener sahen the ie

a RT
un

“Te be se maxima ad mim boe sd sh mass fr vay o saca
Dres an shrink. The matias ar th hol cl. ide main nd minimum.
80 mm fr mete is for os in inch

Problem hf
Number ie
282 MO Mmm AG 4000 AU? 4008
sa USM 15m 100 100 1.016 1500
Fon wor Mm 100 mom was am
3 US Nm 100 1000 1.929 18017
on MI Men 1005 Mom AUS 4060
ra USA 15m 1000 1500 1500 102

Deere

“The le give dt concerning the sink it oft elder of ering matt and
dimension spin dich lac comia for diferent materias may he feng in
tangential oma tcs o oth sso o ue. imemonal kun given

196

pre pre] rel.)

Dt ane

372

3-73

3-74

375

Probl Inner Cylinder Outer Cvlindor

ie dd Mater D D,
+8 Pe 10 20
19 en 100 20
in Sed 0 1007100 Se 1000/1001 200
in Sed 0 200820 Am 200/20 400

Feces ofa fan per aan nie ato pes. Animas fem
face and ns aa oft dl Asn cn ni fe at
mom oe rd A an hai kth or 1

(a) Show dat he mat othe ana forces Fi = 2 Rp,

(0) Stow te eit ofthe oe opc a the Bin T = 2p

‘What arte arose sin a o ss at hen AA he ad 1 R?

‘The ste gebt shown ne gr i al wih os Ff 10. The ba ome of
Lin amet wie toa ais int eye nd athe shank sat e sess the er

‘Sho in the fue in age (0.109) y Jin Ming sping at support a oa of
[FB The id rai fh bed} im sia th secs a he ner andr te
faces tte etal ston

| cyan ies Bain à stands Ais | omar |
= = ==

todo hes ph | 197.

9-76 Ticas tla ar dpc inte ge i et upon by fes of 301 an Fi
in Exim he stress a the mer andr sacs th cred pin the ne.

3-77 Toe ne book dsc in Fig. 3-38 as in amater ole inthe er of eet sco.
Fale hip ia ten tessa hin ade sas atte cil stn,

13-78. A 2Okiplodiscoriedby crane hook sown inte gre. Te crs seston fhe ak es
two ate nt The withthe ros ston en = bee ithe ais om
the comer The nid ais e 2 ad he ote ie = Fin he oss ae

“Eon pagan

pre pre] sus 10)

Dt ane

3-79

3-0

3.

3-82

3-83

3-88

A of eme na sa am burton wih a ey a shen in Agr
‘The crm secon tthe cil loan e litical wih ma ais of and amine a
of in Fea la of 20 ip tie he ese at te emer and er sure of he ia

tte ram a nn inthe gt ating rs seston of Tay ai with
Zar nd 0d oooO Bestia ac and ut Surface rat he tt
(Cie ble 3-4 can be sl to determine 7 o sion. Prom he bl he ita
FAA] cn be vta or a scanle an à cie y uta 4/, foreach ape (ce
En. 60). Stating 4/7, al th cle rom tat of rang sks J JA/r forte ©
frame and, cn nte los

“To cron sc lls, uch 25min ameter ae psd tpt by a fre Eterno
‘he face Fd he anim aes of he ipl al he main shear ES

‘On of he lin Pro 3-81 spacey a a carbon ste pla FF

IAN. att det

Aa sons al ole wih mt inn gh 2 oth o te ini oa cei ng
‘ing an me rat of 4 in wich 2 Im ick. Fad he mime cont fre Fate

Te u sos hip pte contain om as een in a eed vi in the
‘fan to which toe ts wl go 0 fr Jorge sing bn than at aloe by
inte gues br agit he ctf or traf he a othe fa tip.
‘Waking wilde several mili res tations per ear oan rage pon, oh is
anger ta the pote wl one he cement md that tal rc ma xc a
‘of th many eins of ares: Proc His made many ile snes Ya

Ca pre] en

endend Srs pci | 139

a

ds YZ

ne)

pra OT

isons a al itr 50 mm cn dace Sm, tom ng 15 um ot mm.
nd ken 9 rem. Develop an ui fl in aking compte xs ana of i
Protos Describe mata properties neo, equal oie anim he ng
Foe dfs

3-85 Simply qs 3-70, (5-71). a (3-72 by sein <=0 nd ing M/F 9a
Pu, od Y5/pon ad fr ein. check the onda ise of the rin

3-86 A Gin dim nina wc. in id, on ut cure Gaia an ODM on
(a) de Herz wen 2,25 2. a8
(by What aporte sees pit A ats 010i ow the whe im saco di |
areolar

Ett sige | mn
ea ti a

Deflection and Stiffness

Chapter Outline
Spring Rots 14a

Tension, Compression, and Torsion 148
Defcon Du to Bending 144
Boom Deflocson Mohods 146
Beam Deflectors by Suparpesiion
Boom Deflecsons by Siguldy Functions 180
Srain Energy 156

Costighono's Theorem 188
Deflection of Curved Members 168

Saicoly ndetminate Pcbloms 168
Compression Members—Generl 173

Long Columns with Cental loading 173
Inemecioelengih Colum wih Centl loading
Columns wih Eecenic Loading 176

Siu or Shot Compresion Members 180
otic Schily 182

Shock ord Impact 183

Suddenly Applied loading 184

ve

Crea = a

ad
Dean ti ane

142 | mecha Enjoi Di

Figure 4-1

All wal bis dem under oa her elastically plc. A Body can be sl
en insensitive o deformation hat a prsumpion iii does ot et an analy
Sisenough o waran a nonrigid raten. Ifthe ody deforma ler proves tbe ot
eligible, then declaring iit was a poor decision, not a por assumption. À wire
‘ope seve, but in tension it canbe obus gi and it dis enormously under
‘emp al compresshe loading, The same body cn b bh gd and nrg

‘Detection analysis enter int design Suc in many ways. A ta ing eta
ing ring, mus be exible enough be bent wien permanent deformation and
semble with ter put and hen muse gi enough 1 hold he amd pts
together na transmision, he gers mu be supported by aii shal the hat bonds
{oo mic, Ua fits too exe, the tet wll a proper nd the es will
be exces impact. noise, wer, and a ile. In ling set or strip tel pre
ciones the rolls mus crown ht i, cure he ished prot.
wil bof union Us. Thu, 1 design the roll iti acer o know exactly how
much he will end when a het Sel rolled between tem. Sometimes mechanical
Siemens must be designed to have a paricuarforcedfecton charters. The
Suspension system of an automobile, or example, mst be designed win a ery ao
range oacticve an optimum vibration frequency or all conto of vie loading,
‘cause the human body is comforabe ony within a mie range of frequen.

"Te sizeof load bearing component is len determined on dllectons, eather
‘han limits on ess.

“Tis chapter considers distortion of single bodies dus 1 geometry (shape) and
leading, hen, ri. the Behave of groups oF bodies.

Spring Rates
tasty is at property oa material tht enable A 1 regi its original configuration
alain ben deforma. À spring ia mechanical element tha exert a force when
‘eformed: Figure 4-1 shows Sight team of length Simply supported athe nds
“nd Toad by the transverse forse F. The defection is liar rel 10 he fore,
Jong ste elastic limit of the mural not exceeded diated bythe graph Tis
Beam can be described lina sprig

Tn Fig. 4-18 straight beam is supported on two cinders such ha the length
een supp decreases as the heu le deflected by the fre FA lage fe is
required 10 deflect a shor beam than a Jong ne. and hence the mor this beam is
cd, til becomes. Alo, the ore ot eel else othe deletion,
“ná Dene this beam can be serie as nonlinear stifening spring.

| unser Sil | Lai “Coated Stee PT 1
=== =D
=

Daemon | 143

Figure d-1eisan edge-vew ola dish shaped round disk. The force necessary 10
fan the disk increse u fist and then dereses as the disk approaches at con
Furation, a shown bythe graph Any mechanical element having such characters
is called a nanlnar soning spring

Ir we designate the general ratio tween or and deco by the equation

Fer la

them spring rates defined as
ar dE

4092 jim E en

whee mt be measured in the diction o and at he point of application of F Most
‘ofthe frce-deflecton problems encountered in his bok are linea as in Fg La, For
these. a constant als called he spring constant consequent Eg. (4-1) writen

at a

We night noo that Bs (4-1) an (4-2) are qu general and apply equally weil or
torques and moment, provided angular meastrements ae used for y. For linear dis
placements, the uni af are olen Pound per inch or mentos per meer, and or
Angular displacement, pou inches pe cin or newton metes pe aan.

4-2 Tension, Compression, and Torsion
“Te wa exteson of cnacon of» uniform bar in pre eo or compro.
peavey. gen by
A
Tri egal dcs nt apply oa og bar dein comp re possi

iy of clin (ce Secs. 4-1 o 4.19), Using Egy (4-2 and (4-3) we ser Ua the
spring constant fan ana oad Dr is

us

ae
T

‘The angular deflection of a uniform round bar subjected to a tvn moment T
as gin in Eq 38), and is

ua

wher isn radians. Fe multi E. (4-5) by 180/x and substitute Y
fora sl round hr, we bain

ses

wher sin depres.
uation (5) canbe rearangd o giveth torsional sping atea

1_6L
rier

en

CES ere Stan

rer
Dt ane

4-3

Deflection Due to Bending
“The proben fing of tans probly oc mor fen an an oir ong
‘role mecha design Shales cs Ivers pings aces, bc
[Sve many ae elements met on be weeds burs he ei an aly
Of mechanical uns and systems. Me bj ending, however ne a
os shoud Rave sd a pri ral this an ris for sen a
‘etna er only if res tesa om ae and coments abe
so tosh hin Bok
"me Gina of beam sitet to bending momen igen by

1.2
one

ws)
here p isthe rats of curvature. From studies in mathomatie We also lear ha tbe
‘urate of plane curve given by the equation
1 dv
PRET TU

ua

where the interpretation eres tha i the ea ein of he Deam a any point
along its length. The slope ofthe beam a any pin ci.
a

ont la
as

For many problems in ending, the slope i very smal. and fo these the denominator
‘oF Bq. (4-9) ean be an as iy. Equation (48) can then be rien

m

4.8 w
one Bs 0-3) and 6-0 and cel iii Ble
2 ta
4-4 a
comen 1 play es ons i gop lle
wo
wein
wein
win

tal

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Shigley's Mechanical Engineering Design.pdf