Sustainable Technology 2 - Part 2

8/10/2019 Sustainable Technology 2 - Part 2

1/72


2/72

Module

itle:

Module

ode;

Pre-rsqulsites:

Co-roqulsit:

Somg3tsr/Acad6mic

ear:

Crsdit alue:

Lsvol

of

study:

Module

eader:

Intgrnal

Modrator:

Module

uide

Sustainable

echnology

ET2006

None

None

2006t07

15

Level

2

Kadda

ahiaoui

Room:

MA109

Phone:

664

Fax:01902322743

E-mail:

[email protected],uk

GrahamOakes

I Rationale

The

principal

im

of

this module

s

to use

case

studies

f sustainable

technologies

o:

.

Further

evelop-

nowledge

nd

understanding

f the

screntific

rinciples

hat

qovern

thebehaviour

f

products

nd ngineering

ysiems.

.

Further

evetop

nowledge

nd understanding

f

methods

or the

anatvsjs

f

engineering

omponents

ndsystems,

hich

r;

thenapptieC

o sotve

ett-i-Rnea

proDtems.

By

successful

ompletion

f hemodule,

tudents

ill

beable:

1.

Apply

scientific

and mathernaticai rinciples

o

the

design

and evaluation

t

engineering

omponents

nd

systems.

2. AppJy

outine

olution

methods

o the synthesis

nd analysis

f engineeing

ystems

and

components.

@The niversilyl Wotverhampton

Schooi

f Engineering

nd he

BuiltEnvironment

School

ssessment

andbook

Learning

utcomoa


3/72

3. Evaluate

he strength

and retiability

f

comp.essior

hear.bendng

ano

torsion

metnoos.

rigid

body

systems

subject

o tension,

by using

analyUcal

nd

finjte

eiements

3 Weekly

opic

guide

(Piease

ote

haton

occasionst

maybe necessary

o amend

he schedule)

Il", Td 9_y'l-1"

tqught

usrng n..

pprications

pproach,

hereby

he

scientiric

rjnciptes

f

prooucrs

no

engtneenng

ystens

willbe

deveroped

or

vai6u5

aah;.a

technoloqies

l.e

case

studies

irr

oncenkate

n sustainabre

echnologies

n which

he

emphasis

i

be o

demonstrate

how

he application

f

scientjfic

rinciples.

an mprove

he

pedofmance

nd

efficiency

f

these

products

nd

engineedng

ystems.

sing

hisapproach,

he

olbwing

opics

illbe

addiesseo:

[/]odelling

ngineering

ystems

.

Behaviollral

odels

or

engineering

ystems

decomposition

nto ub_systems

,

.

Static

ndDynamic

orces

frce

body iagrams

Design

or

Skength

ndReljabitity

.

Stress ystems

axial,

ending,

jrect

hear,

o|sional

hear,ongitudinal

hear

nd

contact

(Hertzian)stress.

. Cornbinedtfessesprincipalhesses, aximumhear tfessesndMohlsctrcte

.

Theories

ffailure yielding

n

complextress

ystems

.

Fatigue

cyclicoading,

-N urves

^

.

Skess

oncentration

actors

strategies

or educlng

tress

Designor

Rigidity

ndStability

.

Factors

ffectingigidity-

oad,material

roperties

nd

eometfic

roperties

.

Euckling

odes

Eulr

ndRankine

ooets

_. . _.Vib|atior

principles

f natural

ibration

nd

whirling

f shafts

Finite

lement

oolications

.

Th.finite

lement

nalysis

ethod

element

hoice,

eshing

tretegies,

onstratnts,

oads,

solution

nd

pogt-processing

.

ADplicatio[of

EA

o welLdefined

esiqn

roblems.

llst Resource3

School rovided

3D

solidmodelling

ADsoftware

IntegEted

inite

lement

modelling

oftwafe

Graphical

resentation

oftwa

5

Specialist

esourcesStudent

rovided

with

cost

ndicaGd)-

NotAppljcable

6 lndicativ

Readi

and

LearninE

u ort

List

Lecture

otes nd

utorial

Ashby,4ike.

Materials

0750643579

Shigley,

.E. Mechanical

0071181865

handouts

Selection

n

Engineering

esign.

ButteMorth-Heinemann,

999.

_

Engineering

esign

Mccraw-Hill

ducation

EuroDe.

001.

Ogrodni(Peter

.

-

Fundamentat

ngneering

\,,techanics

Longman,

997.

0582297990

ylll?l,

D"ulq

G

-

The \,4echanical

esign

rocess.

2nd

ed.

_

New

york;

London:

vccraw_

Hi[,1997.

0071155767

)1/-liSlrl,-l-anlil9lq.

-

Design

Methods

n Engineedng

nd

product

Design

London:

\rccraw-

Hi||, 998.

0077093763

Dreter

GeorgeElrwold

Engh-ering

esign:

Materials

rd

Frocessirg

Approach

3ro

eo.;

London

VlcGraw-Hll l .

000.

0071162046

OThe ,hjversllyiwolverhampton

3

or 6

Schoolor

ngineerngnd

heBuittEnvironmenl

School

ssessmentandbook


4/72

Fagan,

. J.

-

Finite

lement

natysis:

heory nd

Practice.

Technical,

992.

0582022479

Mottram,

. Toby,

James

Toby;

lvccfaw-Hill,

996.

0077090934

-

HarJow:

ongman

cientific

mechanical

esign.

London:

sing inite

elements

n

)kldams,

V

;

Building

ettef

roducts

jth

FiniteEtement

na\, ]e

_Onwordpress,

1998.

8 A$Eslmont

7 Teaching

and Learning

Methods

.........

-'

--

Thismodule

ntroduces

he

student

o udher

cientific

rinciples

nd

provides

n

opportunrry

to apply injte

lenent

methods

nd

echniques

o analise

well

defined

eslqn

.ooi.ir..

fn"

mooL,te

tfluse

case

studies

fsustiainable

echnoiogies

o demonstrate

oir

hese

rincrptes

can

beappljed

n he

design

f

products

ndengineering

ystems.

It s core

o the

CAPD nd

CAED

pathways.

LilgiiTt_f|.::f"l:

ancr eminar

ctivity

ilt nvotveou

n

investigarions,

resentatrons,

orscussrons

no/or

xerctses

n

set opics

ndmay

nvolve

elf

rd

peer

ssessment.

This

approch

ees the leam,ng

needs

as the

focus

of the

leaming

actjvity

wttn

rne

unoersranqrng

nat

you

wil need

o

akeon some

esponsibility

or

your

own

earnind

1,2,3

1.Lecture

To

ptovide

hetneoM

the

pafticular

ubject

overed

within

het

S .ecifrc

ine

perbd,

2.

Case tudies

To show

how

ne

knowteage-mA-$

mplanented

nto

p.8'ctical

iluations

nd

vaious

cenarios.

3.Tutodals To suppottke lectureateiat.- aii

enaura

that

tudenb

have

gained

enough

und1rctanding

f

the subject

na$er

4. Projct

ork

To

atlow

student{-

-ifipty-ien

Knowtedge

nd

sfills

to salve

a Drcblem.

E,l

Msthods:

Learning

utcome

Leaming

ctivity

Explanation

8.2

Asssssment

omponents

nd

W-igh

ffi

To

pass

the module

you

must achieve

a

minimumgrade

of

E4 for

Cgq[

Element

f

Assessrnent 4

a minimum rade

f

DS or

Caq[

Compo;ent

f Assessm"nT-

- - -

@Ths nive|sityf WoJvedampron

Schoolor

ngineeg

and heBuitr

nvnonmenl

School

ssessment

andbook

Learning

utcome

Assssment

Tasks

%

weighting

hahd-in

te

(university

weeK)

Rationale

or he

ask

1t

Componeni.

In

class

openbook

examination

50%

I

Toptovidehe oiiortunnlx

apply

routine

analyticat

methods

o

solve well

defin^d

QrcOtens.

1,3

Component

.

Design

and

analysis project

usinqFEA

methods

500/"

Tp

.

provide

oppottunity

A

oesrgn

ysfems

and

pafts

by

application

f FEA

nethods


5/72

The

assignments

hould

be handed

n at

the City

Carnpus

tudent

egistry[4T

Block

)

anda

receipt

btained.

8.5

Extensions

Extensjons

ill

onlybe allowedn

exceptronal

irc mstances

nd

you

must

have

a valid

ause

(normally

overed,

or

exan]ple,

y a medical

edificate).

pplications

or

extensions

eed

o

be rnade

sing heAU33

ormobtainabte

rom

he

CttyCampus

tudent

egistry,lvli

atock;.

As6ignm6nts

ubmlttod ate

without

a sanctioned

xtenBlon

lll

bo maif"jfb.

lf

yo

are unable

o submit

ourwork

y hedeadline

r wtthin

nyextension ranted;

r fyou

consider

our

performance

as been

affected

y some

exceptional

ircumsta_nces

ou

"nou,q

onsrder

pplying

or Extenuating/M

t

gating

Circumstances.

nsuchcases ousho'uldonsuttyour seEonatutofor a unNersttvounsellotor advice

8.6

Return

of Coursework

The

pink

copy

f the Student

ssessrfient

orm

wi nomalty

e returned

o

you

wthin

mree

wofking eeks.

tudent ork

s notnofmally

eturned

nd

;u

areadvtsed

o'keep

our wn

hard nd

oft opy

f anywork

ubmitted.

8.7 Rstrieval

f

Failurs

Regllationsoverning

etrieval

f failure ary

dependjng

n

your

award,

n

particutar

pon

whether

ou.are

,studying

ora degree

r a higher

ational

uatification.

ease efer

o

your

Award andbook

r the

Universirys,Undergfaduate

odular

cheme

uide,for

tud;nts

2406t07.

8,8 Moderation

A representative

ample

fall

elemenls

f assessment

ithin

he

module ill

bemoderaieo

n

accordance

ith he

procedures

etout n

heSchool

ssessment

andbook.

8.3

Marking

Criteria

Full

etai ls f

thenarking

ritea wll

be ssued

o

start

of thernodule.

you

as

part

f

heassignment

rief t

he

8.4

Submission

f Coursework

Award

Handbook

ndAcademic

Plagiarisrn

nd collusjon

re

very serious

offences

hat

can resllt

in

expulsion

fom

rne

University. hrs

s

because hose

oJnd

guirty

t

ptagiansm

r

colJusiolw,

-ot

onlv ave

anempted

o

present

omeore

lse'swork

as theirowl

buthave

also

soLght

o

gain

a; unfar.

advanlage

ver

hek ellow

tudents.

9,1 Avoiding

Plagiarism

ndCollusion

1. In the caseof groupworkyouafe actively

ncouraged

o work

n

a team.

However

he

sections

ftheassignment

hat

ou

answer

ust

e

Vour

wn ndividualwork.

2. You

sho,uld

make it

very clear

what

solrces of

information

ave

been

used;

wherc

mate

allinformation

rom

hese

sources

s

quoted

t

must

be clearly

eferenced

sing

ne

Harvard

Referencing

ystem.

Details

an

be obtained

rom

Learning

entres

r

on_lne

yi9

..

the

Learning

Centre

no-me

page:

httpi//asp.wlv.ac.

k/Level5.asp?userType=4&Level5=31

5).

3. Never

ttempt

o copyor

paraphfase

notner

tudent work.

oTheUniveEllyf Wotverhampron

School f Engineeang

.d ihe BuiltEnvirofmeni

School

ssessment

andbook

larism

Collusion

ulations

or Students

006/07


6/72

tl

Module

artlcipantr

Module

eader:

Kadda

ahiaoui

RoomrMA109Phone:1664

Fat

2743

E-mailr

[email protected]

NotAppllcable

odule

eam:

12

Reqlrtatlon

Lo,"""jjpT r9

tllt

gnty

tudents

ho eve

orma

registered

s

participants

na

modute

w[ De

aore c

gatn

rudf8.

13

lloblle Phone

This module_guide

houtd

e read

n conjunction

ith

he

erms

and conditions

ontaineo

n

your

Awaro

pahway

cuide

and he

University's

Undergraduate

lrlodular

cheme

Guide,

or

Students

006/07.

ln

the nterest

f courtogy

o other

tudents

nd

stfl

please

nEuE

tatmobile

hon$

are

swrcneo

r ounng

ctures

nd

utorlallassss.

n

xcepflonal

lrcumotanceE

he

module

leader

rey

allowndtvlduathoneE

o b kept

n f va

d reason

8

glven.

nv

siuajnt

wno

consEers

gynave

a va ct rgason

must

discuss

hj6

wfth

he ec{urer

rior

o

th ecture

startlng.

@Th.Unlvollyot Wolv.rh.mplon

School

t Enginocdng

nd hr Buitt

EnvtEnm.nr

School

At363sm.nt

Handbook

I

t

I

t

I

I

l -

I

l -

l

6 ol6


7/72

UNIVERSITY

F

WOLVERHAMPTON

Schoolof

Engineeringnd he BuiltEnvironment

ASSESSMENTRIEF

Moduleitler

SustainablE

Tochnology 2

Module ode: ET 2006

Componentumber:

1of2

Element umber

I of

'l

Weightingr

50%

Assignmentne-coursework:

inite Elemgnt AsSlgnment

Learning utcomes

o beassessedl

1. Use

nformationechnologyise ommercialevel oftware

^

To

provide

heopportunity

oanalfze

arts

rcomponentsyapplicalionf

-

FEAmethods

r

Analyse: ompare

ith outinenalyticalethodsndapply ppropriate

- solutions

lvlarkingriteria:

Seeassignmentrief

or

detail

Th.

mlnlmumiBE

mrrk or hl. componlnt 05.

lfthisB sn elem6nt,

ou

wlllp.ss h. modul6fyouachi.vs minimum

rad

f E

torthis

lenonlandan

av.Bg6

g| d

of D5

or

h.

wholc ompon.nl.

Assignmntandedut We3k 7

Latest ate orsubmission:

We6k1l

&sllnmont3

ubmilt d 5fi$ th. d.adlin.snd

without

n

althoftd

gxtsrclon

f 0mswlllbt maiGdF0.

Plo|semr*your alllgnmsnt or he.ttontlon tr Kadda

You hould mrk. lt

v.ry

cllar what ourc63

of ntoinationh.v b6nu3.di wharumat.dallnfomatlon iom th$.

sourc6 B

quotcd

r musl b. cl .rly blonced

using h He ad Roblcnclng swtlm.

(o.tall

c.n b. oblain.d rom

lhe .sslgnmontmustbo handgd

n

o

siudontReglltry,MTBlock, lty campus.

A signed

eceipt ustbe

btained

henheassignmentsresubmitted.

ou.hould oop

your

gcglPtn a.ef6

plac6.

You

areadvised

o keep

our

wrl lectronic

hard'

opy

f anywork ubmitted.

@

The

UnivaBit

of Wolverhampton

schooloiEnginaering

nd heBuiltEnvionrnenl

Scnool ssessmeniandbook


8/72

lt)...'^.V

"

I

ov

". . , ,1.

:

. io"

: , ' t

n .>;2

3iroqvi

?n'-K,-

"

/rtJ

( to ' i t?\

8T2006:

Sustairable echtrolog/

Assignment 1: Finit Element

Modelling

.K-

.

t .

'

lc z. t -= F\. t t t

.s

-- .-

cl ."*

Ltyc" 'hI t .

' . . \ .^ '9

c-nq

Geometricmodelling of complex

pafis

can

be ime consuming

t the

or"-o'rocJ#t?,|

*

I

stageofa Finite Element

Analysis.Consequently,

he

geometry

hosen

or this

assig nent s not socomplex.

heaimofthis exercise

s to assess

ou

understanding

of the FE methodand ts application o

solveengineering

roblems.

Fig. showsa slottedbar madeof steelhavinga Young's modulusof 200GPa"a

Poissol's atio

of 0.3anda

eld

stessof250 MPa,

t will be assumed

hat he

bar

will be ully frxed

(encastre)

t

one endand subjected

o a tensile oad

hat

you

will

decideat the other.

pledicted

values.

Commenton both setsof

data.

(r0%)

4) Next try to investigate

he effectof meshdensity

on

youl

FE

results.Repeat

the.exercise

ith.

at east, ou.r iffelent

mesh ensiries.

n rhis

part

ofrhe

asslgnment.oumaychooseo use ewerelementscoarse esh) r a laJger

number felements

a

inermesh)lroughour,

r elecl o usemapped

meshiq-Jou are ree-6EEElTeasonable

number

of el.-.Ei*

The outcome rom this

part

ofthe assignment ill

be

plots

ofthe thrce

main

variables

ono., off'r and SCFagainst

umberof elements

sed.Comment

on

.

",-",,t

.

glnt

Each tudent ill

be

given

a setofdimensionso

complete isArer

pecific

eomeLry.

r , |

. t

. t

|e" . , - t ' - - t r " , l , l

I

l tLr154"-

vl

)

After creatinghe

gometry,

elect

lane

stresVwithhickness

lement

pe

6g

anduse hesrnart ize acility

o meshhemodel.

Note ie number

felemenrs

thathavebeen utomatically

enerated.

ext,apply

heappropriate

oundary

conditions nd oading nd

perform

staticelastic nalysis. rom hepost

processing

ession,

roduce

hardcopy

f themagnified'deformed

hape'

/

and

some otrtour

lots

hat

you

considq

mportant.

(20%\

2)

From he

FE output, etemine he elevant

tessesn the

argeand educed

, r

\

6

sections nd he

peak

tress t theslotend.Deduce

hevalue

ofthe stless

^

^t

4

bL

'

concentrationactor

SCF).

:r'',r

.,9r."(lSZ)

J

"

3)

Using

your

echue otes, r a reference

ook, ind the

nominal tesses

ad

SCF or the

gometryou

were

allocated

ndcomparehesewith

theFE

the esults.

(20%)

5) Discusshow

you

would

expect he SCF o vary

ifthe slot width were

o be

reduced.Considering

he time to

perform

a static

inear stess ofsuch

simple

component,

ou

areadvised

o modela casewith

a

'cmck

like'

slot

to

compare

our

results. (20%)

6) By referenceo the

Arsys o ine element ibrary

documentation,nvestigate

whethersomeother ype

ofelementscould have

beenused o analyse his

problem

and ndicate he relative

meritsofthe altemative

elements,f any.

Iut ,yo6


9/72

Also,by considerationf the

gcornetry

fthe modeland he oadingo which

it wassubjcctcd,ould ymmetry avcben xploitedo simp[ry hc analysis?

Provide xplanationsndskctphesemonstating ow his can

bedone.

(10%\

Your cportshould ontain omorc han3 or 4 sides

ftext besidcsh equcstcd

idomution i both abular nd

gmphical

orE. For anyhand alculation,

he

formulae sed ndoatculationetailsmustb ncludcd.Hardcopiesfthc

meshes,

dcformcd

hapc

nd

somc

ontour

lots

arealso

equested.

Wibcsscd ffod at thc computcrerminal arics l0% of the inal malk o this

compotrcot

Thc eport hould

c

handcdnto registy by thc

ducdate, nda datcdccsipt

obt&ired.t should nalked or thcattlNrtionf KaddaWork

handedn aftcr his

datewill Dotbc assesscddess herc s a valid reason.

This

piece

of workcoDtibutes ooloowads heovcrallassc$mcntor

thismodule,

lJarc or tssuc: wccK /

IIad-iD Dat : Wcek l1

Dr, K. Yahiaoui


10/72

i i

i .r

-,. , , ,",

I ' tr: : '

,

Cc,.c

e'rfr

"tr.,,1

;c"ct" '^;

ibsnu


11/72

Introduction

o Stress

oncentation

acrors

Page

of2

Home

Introduction

to

SCF'

Iadex

-J

. =Foinlol maximurntress

http://www.engineering.ucsb.edu,/-me1

web/scf,/intoduction

o

The

profile

ofthe

stress

t he

section

thtough

he

center

fthe

hole

has

he

form

shown

n Fig

2b when

he

diameter

is

small

by

comDarison

o

with

the

width W.

Notice

he

maximum

tress iq

3o and

occurs

t he

edge

f the

hole

In

theexpression

-msr

--

The

actor

3 is

known

as he

stress

cotrcertration

actor (SCF).

Refening o Fig2 t canbeseenhat

rocarised

oa region hose

ize

sapproxim.,.tf

:T#[ti3':ser

6

aJe re

Fajlurcs

5u"1l

lutttue

brittle_cracking

nd

plastic

eformation

equently

occur

at

ponts

ot stess

concentalion.

l is for

tlis reason

hat

stxess

oncennariorrfactors

play

an mportant

ole

in design.

The

value

fSCFs

depend

n

fte shape

nd

dimensions

frhe

comDonent

eine

deslgned

ndcante

calculared

sing

Lnire

lemeut

methods.

ur

here

remari

e\amptesrhere

ie

equations

reknown

and

hevalues

an

beeasily

alculared.

Introduction

o

Stress

Concentration

Factors

Figl

-

Uniform

Plate

The

unifom plate

hown

n the

Figl

is subjecred

o a tensile

orce

p.

Thesrress

m

ue

plate

s unltorm

everywhere

ith:

o = PA\II

It

is often

necessary

o

drill a

hole n

the

plate

Fig

2a).

When

he

oad

p

is applied

the

presence

fthe

hole

disturbs

heuniform

streJses

n

the

plate.

tig

?a

F,s b

_stress

oncentration...

8/1

/2005


12/72

Intro,luction

o

Stess

Concentation

Facrors

Page

2

of 2

SCFFOR

COMPONENTS

WITH

HOLES

Holes

e

necessary

or anumber f purproses.orexample oles renecessaryo

accommooate

flebolts

or

nvets

whicb

ratrsmit

oad

berween

diacenr

lementi.

Some

ypical

examples

re llustrated

n

the accompanying

iagiams:

r

einforcing

ing.

@@

fi*;"'"o'*oed

in orsion

ith

through

ircular

ole

Reidorcing

ing

?

Cylindrical ressure

essel

ith

r) l

lnl8rnal

I

Pressure

Plate

oaded

y

tension

in

hrough

ole.

Load

P

n

\

Pi

t

ad

http://www.engineering.ucsb.edu,/^-mel

web/sc?intoduction

to

_srress

otrcentratlon...

8/l /2005


13/72

oy-

ho,-

w4\\ tl1. {Jeor'le.tz

ytsiaii'

l"enl-6

.

ii

n.Cry'J

F1"

r\c''\f,

"l

ovecL;

i=

6-

p"'oFeYtJ

o[

or-

g\-9"

ll'r

i. ur.l

tr

p'eJ".t it

v"ti.tn,'""

t"

b..L,-.

*^J

d"(L.t,t,

.71,u

s"*"&

mnn


14/72

Qr)

Ro=50

na

Kt

=

45

-*.

w=

loo

KI

xc.6t

-/62

=181

N

P=

IK"J

r)

I=

rc

(D,\

-

D.\)

rc ttooq-qoe1

,-+

6q

I =

.+x\od

-*+

f=5om'"

t\=L+5

N.m

(

-

Lt+5

o

o5

-+. ' t -

Alo-

o=;7; ; ' ; ;a=

' ' "

n

2)

forsi.n"I

SLress-'Z.

N=

IOOo

rPn

Bend*r,a t+,ve*$ =?

A6,^\

-1-

> D=_--=-

fY'r

-.r'

l'

_ ,- -- -=

dKo

. lL

t '*r

\

c\: '

J--E

1""

-

* '

J=1xt.(1

x\o- ' --r

4 P

looo

,--

6"

-G-

=

cJ=\ooo*L.n =\o5 -34

J

ot

* T.R"

-:.> L = -----


15/72

6y,--

b"il'n

-

(,)

3't{


16/72


17/72


18/72


19/72

i-

t*z+5xlo-5

-

6il

-

gor

o6i. ,rrro-?

4o.6

r ro=

.

lco*to5.

.s)^ld?

,"r.1

.a


20/72

A

CAD

htpj

rs

,*f

o

FEn

m"/" .

DESIGNING

COMPONENTS

TO WITHSTAND

STATIC

LOADS

st ' esses

due

to external

loading

can

fo l l owing

types:

-

be

divided

into

the

{a )

axial

loading stresses I(b)

bending

stresses

)

(c)

direct

shear

stresses

I

ld)

torsional

shear

st lesses

t

(e)

longi tudinal

shea

stresses

(f)

contact

or

l lertz ian

st lesses

Lonltl,-sk"K

V,

\,.^k\ '=t" ' i*

AxiaI

Loadinq

Stre

sses

loees

t=

nuss

it"uittr

w=h0

lr-

raJ+

-t,1

$

a

=

The

simplest

type

of

stress

encountered

t=

stress

=

load

atea

be

subjected

to bendinq

st

r^.r -

resses

due

to

the

eqcejl t lqj l ty

of

the

Apart

fron

assumptions

about

the mater ia l ,

th is

equat ion

assumes

that

the

load'P'

is

axia l ly

appl ied

wit i ,ouianv- l""ah+Fi^ i+ ,

I: :ll:

^i"-"-'.^?ri?n

.s.

not

c6rredr,

n."

lt

"-i"ipi;;;=;ii

i"jiJ;

6 e'

=a-.fr..

,lo^

1's

v^.Julus

3

A

load.

(for

a

qircular

i,.,

un

iio.-Jr-it-ii

.?if,fi#ffiJi

iffE

oad

wil l

cause

an

Bt

increase

in naximum

"tr." . i " '7-- '

ro nraxrmum

sEle

/

"t

pr

g,,t"o-.**o1"fu,5

-

C"-*r-

|

)'l'


21/72

Bendinq

S resses

When

a

comp

one

nt

oencls. the stress

st lesses

are g iven

is

subjected

distr i .but ion

by

the

s

mple

/"

-g/

t?-" .

r jg lgyef:C load and hence

Lrs,trnear,

as

shown,

and

the

Dendt

ng

equati

on:

c,r=

hrhere

M

=

appl ied

bending

moment

(N-m)

I

=

second

moment

f

area

i ;4 i '

y

=

distance

from

neutral

a* j .s

io

wt.r .

stress

1s req-d

The

above

formula

appl j^es

straisht.

-a; ; ; ;

" ; ; ; ; ; : - - t :

cornponents

-which

are.. in i t ia l lv

;j::*lj.::#li.'=:"i#:,:",i.:,":?,:,,i'i"',"i,i.".'"Tl:

*"i:";i,".

:a;";

My

I

For

components

subjected

to

assumed

that

the

shear st lesssection and is given

by

f=

,d ir-ect

shear-forces

i t

is

usual ly

ts uni formly distr ibuted across the

=

appl ied

shear

fo(ce

(N)

=

area

ih

shear

(mz)

F

A

In

.pract ice

the

shear

st

:

*,",":

,

."''?

*.,

ru;

I

]i,

'.r:if

1T

,*'

j

1,.,.3;

i

:;1":,;:j:"f":,"T:','"#1::1.ff

.lJ::*:',"":.'::.ff

:\".iJ,.''li


22/72

Tors iona

1 shea

S re

ss

es

l1r

8"

(l.t"t(,-

e\4i

zr

-'r

-Y-Z-

r-

.

r'"4('-''

,e"

r

-a-

(J

E

k,

RtT

-

E

='

FiaTg;&&

",.

:{-x-=-

For

a

so

teotoa-Kt

.\,

".

EU6T)

bar

subjecred

.o

"

. ' i* i / f f i ) . , , - , , - -

y '

mome

)

the

tors

io

na

"

".

-"I,'"="HLL""

I

n frffi:?li's

n

to

be given

byr-

T'

-

GgY'*""

---:--

e

---==-

= =:-4

lt .t . I .,

, t Y l , r* , t (hrrh

ol

S^^iE

U

^

'',-

|)

r-#;

f

whele

T

,t

where

for

for

a hol

low

shaf, t

o-pplieJ,

-1-

or1.g,

1.r^

p.l^.

s"--) *.^..t

*

uI

a.c*.,

J."r

Irs

p.le

a

sol1d

shaft

=

appl

j .ed

torque

{N

f t)

=

polar

Eecond

honent

of

=

radius

to l rhere

stress

Z1-

E

-P ' .h)

Roa

" l

\

lne


23/72

-i

F'

At

=

o(pp[

J

'f

o


24/72

f

-

ner/'rl

7arq,y6,,

N,rt

j

--

f. ^"

s"*noL'

mote"r

o/

(

= Sl.^"

Strse

d,t

ro"L:w

Y-

fi -

y^&,s

1""," .ih. go\e, ,..

G

=

AoJ,, lu '

{

4,r l ry

t{

lL

=

YL

o(

ta''ist',

@:=

t-

-

X.3t\

"{

sA^{q

n

^utarrL -

l jJ.

sl*tt=r=

rcJh

IJ

VL

.

rl-/t=j=

-(d,+-rL+)

&=r=

=*--

Ri

-nR"

T

./l-

|

2T

rc tRo4-

R,'+

tzt4q-"+p )

R-

+*

a1-

17

Lr-oa)t

Power

fir

Rev

?-rc

-:-- A

rv.n

0o


25/72

Rosrer

,*U

-==>

U)

I ll

be.

t

ve4

\^ \ '

s\c+tsr

tc-

d8

rqn

T-ur brvls-

-

IJ

kkh;* sfeel-

-r^

Ua4k

--

mae3

4

^A'

"L

Pr-*A,

^

HoUo,.t

.z

r -D

d?A2

^?\

LLr\o - rr( ,,

.-J -

h)

SolJ

3

9s

NH

{ t

t - -

o

.--ii----

w1

-=

wfi

Ro'-

Rr'

4d

13

(e

-=

i^

R

t tJ

Ti

T't

:

j* Ro

7ir-rll-=

Ts xR"

'Js.Tu R4

s' ;t

sLdt

r+,il..

"eU+

i

$\;,8d- -=

-1.4 R

u7"

(Ro+-

R;"a)

':)>

SeF

.t*".bt:

=

,

l

.trlrc.

*;,ry;, il;i,"

strass

is

"

s^-a

-4"

b,t|'

sh.fu

K.

=-_

--

3c,rL(t)

x' 6r'","


26/72

6.

A solid

ircular

haft

f250mrr

iamcter

s o bc

ceraccq

lvjlhgqow

$"ft-q*

**

material, heratio ofcidlmal to iatcrlal diaincters eiag2l F-| d -e srzcot $' loxow

il;'F,L

.;;;;il

strcss

s thc

sarnc

or botb

shafts

Calculate

lso

6e ntio

of

wights

of the

holow o

solid

shaft.

{A.ns$sr:

OD

=

255.5

mn'

lD

=

127

75 N'

0'7E2'l)

Dob

Dr'|

=Oo

D3

6. A solid steel haftof 300mmdiameters to be eplacedy a hollowshaft,heratioof

extemal o intcmal

diaEretels

eing 1.5:1.

Fhd th

sizc of the

bollow

shaft

f thc

maximumshear

tcss is to

be thc same

as for the

solid shaft.

What

pcrcetrtage

cconomyn weight

will this change

ffcct?

Als D

=

327

ur andd=2186111

34%

, tL

R"

-

/4t

_

oj

-

oi'

+pi'-

pi

^.

z

$)=" '

PV

D2

Ef

6.

D=

lss

-'.

Djr-GiD)4_n

_---...--.-.d_---o

D-

b"4.

-

(o.

o)4

t

ooq

)

Ts=r-u

5{

B

D

3

-->

Do

D. -zo1

Ts--

(t

. .4r .

^

r

t - lo

Ll-o. . /

=

f)o

.-v

7g

xf 6147

/n a


27/72

Quutrctn:

Hoat

Jou

uoull

ol*e,;-

tl"

lu'.,g

Or*l

^,1

An-scLer

uetlA

l/,e brK

to

Xef

ty

ma-{;,

:r?-*tv

re

d'"

Vo[u"'.

ol tf"

',c,t


28/72

''

rcJ$

L=_:67

3

gcor\f,

(^orer't

"

|

6{ee\.

D=too

a=Bo3-

uJ3

\x tL

t=

u,t'

-

r t3

Ail dimensions

n

mm

+

' -

50

6tg

ra

76

k- : -----4


29/72

f9-bin.,l,

t>tY'e93'"

+\"o

,6,

alYas'i

J

?t"est.s

t

J

3t-r.as


30/72

I f

a ho

j .

zonta

I bea

m,

or

other

component

is

suD

ected

to

ansverse

or vert ical

loads,a

shear. for i .

a i i j ru*

m"a-y

e

aer vea

and

the value

of

the vert ical

stre"r

to iJe-at

l ,oy

sect ion

dete mined.

?hi .s

force

tends

to

p."do;;- ; -r ; ; j ive

sr ia ing

between

eelt ica l

secr ions

ot

the beaml-

-a;; t I

; : ' ; ; ; " , la ter i r

. l i l l P:

accornt lanied by complementarv

"t . . ,

" f , ic i ' i -n

th is

case

hrl l t

be

hor i .zontal .

1o i l lustrate

th is,

consider

two.

rectangular

sect ion

beams

Lying

one on

top of

the

other

and

rest ing

on

s-irnptu

"ulports

as

shoe/n

be1ow.

If some vert ical toading.

. is.

appl ied the beams

wit

I

bend

ndependent ly

and as

a

resulr

the

l t" " i - "u. i - " . - " 'J i ' in"

top

u." .

iIl

slide

retarive

ro

the

upper

surtucJ

o

-t

ti-

I oiru-"r''o"u..

I f

thelefore

the

beams

ale

replaced.

by

a

single

sol id

bar

of

the

ame overal l d j .mensions as h_e _wobeims thei there rnusc De some

nternal

system

of

forces

(and

he;; ;-s-h;; ; ' " i i "1""t

"" t

up

i th in

the

beam

to

Drevent

the

abovern"rt .""Ji i i " ln9

taking

1ace.

The

horizontjl

shea

stress

in

tfre

Ueam

is

-a-cLmpanied

by

:.J:I:i".t

shear

srress

of

esua]

u.io..

"itiJ*."frirlilnt.ry

sr,eui

The

way

in which

the

shear

be

calculated

by

using

the

where

stresses

vary

ac oss

the

sect i .on

can

equat

t-on

B=

= snear stress (N,/mz

)

=

shea_r

orce

appl ied

(N)

second

monent

of

area

of cr6


31/72

: udy

ol the

above-

equat ion

indicates

that

for

a

given

stze

of

beam and

shear

load

the maxi_murn.

a Iue

of

shear

streis

wil l

occur

where

-Z.Ay

is

a maxinun

and

this is

at

the

nerrt .a l

ixrs.

et

the

oute

f ib _es,

l rhere tAf

is zero,

the

sne"r

"tre is- is.

oUvioui iy

ze o.

consequent ly,

i t may

be

seen

that

the

naxlrnum

shear

stress

occurs

where

the b":9-11_9

-s-t ] e6

i :s

," .o

"nd, ' .onuersely,

hat

tbe_maxinum

berding

stress occuls where the shea stress iszero. I t is therefore

usual

to conaider

the

bending

and

shear

stresses

sepa_rate ly

and

enaure

that

they

are

te ls

than

the

respect ive

al IowabIe

stres.ses,

At

any

intLr.eaiate

poin i

between

the

neulral

axis

and

th_e.

outer

edg'e

ine-corii inea

etfect

of

the

shea

streaE

al ld thr

bu

th s

r equ

e ;

i ;;" rd

s:"

i'

lrt

rl'.'r?""i

?l

j:

":t

";r"".'"r,i:

3i

of

the next

l ecture.

For

eonvenience

the results_.o-btained

fron

the

above

equatton

may

be compared

to

the average

shear

stress

obtainect

irorn-

I

^,,

=

F

\

ctrcular

section

l(

{

n".tans,-,

at

""ction

Lrhin

tube

For

sone

common

gectionE

thrs r el at lo ng hi p

isr

t '^n

I

tav

Z7x

Shear streEE dist ibution in sone exanple sections

o

l-

I

I

i

I


32/72

Contact

o Hertzian

Stresses

When

two

elast ic

bodies

e

exrer-n

-r

y

a

pp

ed r

"ia,

ii3"i'.3;;::::

r"#:i.:::*':l:'":i

il

and

deformation

of the

sur. face

-occurE.

Even

though

the

external ly

appl ied

force

may-be qui te

smal l ,

the

consequent ia l

: : : l?":_: . : : ""s

may.

neverrheless

be quire

high

owing

to

ihe very

snarl

arg_a

ot

.qonracl^

Further,

these

stresses

are

very

local

i i

nature,

since

the effect ive

area

over which

the

force

i

d i f fused

r.ncreases

rapid ly

with

j .ncrease

beneath

the

surface,

r 'ne

crassrcal

soLut ion

for point

contact

under

Ioad

is

due

to

Hertz

and for

th is

reason

tha

st.resses

are

ott n ie ierrea to as

""""'*r".lLli"-:"::""'%

:e\et'sof

'l'ti*)

-ns^t

Stress

Conceniration

The

effect

of

a sudden

change

in Bection

due

to a

sharp

corner,

a

hole

or-

_a

key,way,

i .s

to cjuse

a

local

increi""

-o i -" . .""" .

rn.

exact

e.f fect

depends

upon

the

shape

and

aj .mensions-of ' tn"

"" tr"""

: l - i^"^"_.

and

is

expresEed

in

teins

of

a

stresJ

concentrat ion

actor.

lncbr'

K

=

I t is general ly

vely

di f f icu l t

to

calculate,

sEregs

concentrat i -on

factor

and

so most

i la ta

experinantal ly

(usuaLly

Uy

pnoto-etast ic i tv) .-

reference

books

on

stress

-and

strain

formuiie

on a wide

variety

of

stress

concentrations

but

ale

as fo l

lows.

theoret ical ly.

the

has

been

o b a i ned

There

are

standard

which

contain

data

the most

important

n4ximun

local

ised


33/72


34/72

(c)

Keyways and spl ines

Another feature which needs

spl ine in a shaft subject to

factoi variea fron between

2

ke ' ,ay.

ca efu l at tent ion

j .s

the keyway

or

torsion.

The stre6s

co ncent rat

ion

and 4 depending

on the depth

of

lhe

(d)

Gear teeth

The streas distr ibut ion in a laaded

gear

taath iB a

cornplex

problen.

fhere i8 a Btresa

concentration

at

the

poj.nt

of maling

of lhe two teeth

due

lo

the contact

stresses and

a further stress

concent at1on at the root f i l le ts of a

tooth, the tat ter

being

the nore aerious.

(e)

screw

threads

A connon

cause

of machinely

or

plant

breakdown ls

the fat igue

fai lure

of bol ts or Eluda due

p incipal ly

to the h igh

stress

concentration at the loot of

the thread. For situationE where

a

bolt ls to be highly

stressed then Epecia l designs of

bol t have

been

produqei l

to

le l ieve

the high streaE concenlrat ion

of the

normal bolt.


35/72


36/72

UNIVESRI

TY OF WOLVERHAMPTON

SCHOOL

OF CONSTRUCTION.

ENGINEERING

AND

TECHNOLOGY

B

Sc COMPUTSR

IDED

PRODUCT ESIGN

TUTORIAL

SHEET

I)

SIRESS ANALYSIS.

2J

What' type

of stresses

ale

present

in

the fot

lowinq

products

and which

is

the

most.

signi f icant

?

- -

(D

(c

(d

In a f loor

jo ist

n 'hele

wit l

t .he maximum

bending

stress

occur

? Where will

the maxinum

shear

stress occur ;

Hence

where

is the best

place

to dr i l l

a hole

throuqh

the

jo ist

? at

the centre

o near

the

edge ?

If a V

notch is

to be

cut in

the

top of

the

io isl-

whereabouts

should

th is be

placed

for

least-effect

?

which ra'ouId

be

nore significant,

shaft or a f law

at

the surface

?

a

plyh'ood

topped table

Ari^[ L-^aL"1

-r--t"":;

a conventional

ironinq

board

l-^.1it.i{;-jl

s\Itets

a ladder

b""cl.r

"sitr]

an

electlic m&or

shaft

T".si"^-[

S\*r at-..e >a ball bearing

Cont


37/72

/

*,o.r'

"rr,i'.'

"r:u:,

ut of 5 mm

hick

aluminiun

plate

and

30

kN. What must

the width

of the

i r

ba

not

f the maxinqn al lowable stress

in

the aluminiurn must

exceed 50 MN/m

?

Ans

100

nlrr

A

chai

Ieg nust carry a

begding moment

of

200

N n

and

a

bending stress of

50

l"lN/n" must

not

be exceeded.

A

rectangula sect ion of deplh 40

mm s

to be

uaed so wnac

nust be the bleadth to satisfy

this requirement

?

Ans 15 mm

A socket set

b lace is intended

to

carry

a torque of I00

N m

and to be

Sade

of a s ee1 lrith a maximun allowable stless

of 300 UN/mz. Calculate a sui table

dianete of

bar from

which to rnake the brace.

AnE 15 mn

Ans 15 kN

-

tr*AtY

i'= ----'

.

i


38/72


39/72


40/72

The

angles

at rrh ich

the

pt incipal

stresses occu cqn be

calculated

from the

formul a:

(o-or)

7

Ih is

fo lmula

gives

an

angle from

the in j . t ia l datum axiE to the

neL'

p lane.

The

planes

on

which the

princiPal

stresses

The

----e:W -

\a

new

PIane.

lne

Pranes

on

wnfcn tne

PrrncrPar

sErer

predictabty referred to as the princiDal p langs.

act

a e

It a lso

the

th'o

appens

that the

two

Pl incipal

p lanes

(corresponding

to

orincioal

g lanes)

ale a lr . 'ays

perpindicular

(

ie a lways

t

r i . i rc ipal

p lanes) a le i lwayj

peip indicuLar

(

ib a lwjys

at 90o

to

Plr,ncrpar

Pr

each

othe

)

.

Another cur lous

faqt is that

there is

never

any thear

stress

act ing on

a

principal

p lane,

so th is

fact

is sometines

usef,u l in

ident i fy ing

princiPal

s tresses.

Shear StresEea

and Shear

Planes

It has been abserved that some netal l ic rnater ia ls fa l l due to

shear

rather than

tension

and hence

for these mater ia ls

we are

tnterested

in

how the

shear EtresE

varlea and ln

part icular

the

maxinurn

value

of shear 9t less

that

may occu and also

posslb ly

the

plane

(or

angle)

on which i t

occurs.

bul

i f

usefu I

the

principal

stregaes

have

already

been

found then a

^r-

+

fhe

planes

o

maxLnum

( le

the

pla

neg

on whlch the naximurn

shear

glre gse

But

i f t

p lanes

are a I readv known tHen

the rnax shear

plane

are

i t is nuc h

aIwayE atu icker

to

uEe the

fact that

, i5o to the prinqipal p lanes.

(da-tr : )a

+

4"1e

(d,

-

6.r)

g=9p:45


41/72


42/72


43/72

Ans

(a)

.

A

conponent. is

subjectd

to

the sCress

system

shown.

what

1s.

lne

-haxrmun

permissable

value

for

.S.^

i f

the

greater

pr lncrpal

stress

is

not

to exceed

100

MN,/nz

?

-

I

.


44/72

Is i t

possib le

to state

without

calqulat ion

what

ale

( i )

the

pri .ncipal

stresses

( i i )

the naximlrn

shear

sEresses

for

the

stresE systems

shown

t -

._Tf--l

__:s""r.'

l-1,.

I l l I

l - l

45H

r^a

-l--ls''r"l-l

-

|156y| -e

(r l i ) i I5,-45,

+45

MN/m.

A shaf l is

subJect

to a tongitqdinal

thrus

which

prodrices

a

complesEive

streEs

of 100

MN/mz.

,An

appl ied

tor iue

gives

lise

to a

shear

stress of

55 lttt,/mz.

find

the

'prin;ipat

stresses and

the

planes

on which

they

act.

Ans 124.33

MN,/ml compresBive

t.

24.33

MN/m.

tensi le

at

I

i--l-

L_j

?sh l*

t

4

5|a.,l-t

AnE

Je)

(

1) ls , l5

,

* ts

l , rn7.2

(

r

)

No

113.850

23,86c


45/72

Examples

f

twodimensional

tress

systems

Intemal

ressure

n

a

thincvlinder

Tension

Compression

14"*,1^

orsion

Combined

oadino

eg

gnsion

nd

orsion

_fFE+

loP

middle

bottom

-ry/

- [ ] -


46/72

C"w.bit .ol- ,

Stre-"s

?

g0roe

t

Xy=

she'.'

/

In

tl^e

o'ctlr\'l


47/72

t

t

oS

l l 'at tor

c l

Li"",t

fu^

{


48/72

Principal

Stress

or

theCase fPlaneStress

Principal

Directions, Principal Stress

The normal stresses

6x,

and

oy,)

and the

shear stress

(rx,y,)

vary

smoothly

,,rith

espect

ta

the

rotatign

angle

0,

in accordancewith the

coordinate ransformation

quations.

Thereexlst

a

cauple

of

particular

angleswhere he stresses ake

on speclalvalues.

First/ here exlsts an angleep wherethe shear stress rxy, becomes ero.That angle s

found

by setting rx,y, o zero n the above shear ransformation

equation and solving or

(set

equal o e/. The result s,

,'u,| .

=

'"o

Theangle

epdeflnes he

pflnclpal

lrectlans herc h. onlystfesses

re normEl

stresses. hese tresses re called

nhclpal

tresses

nd are ound rom

he original

stresses

expressed

n he x,y,z directions) ia,

6x+6y

,

ot,z

=

---i--

Page1 of2

The ransformationo the

Drincloal

lrections

anbe

llustrated

s:

Strssesn

glven

oordlr|ab svstem

PrlrclDal

tresses

MaximumShar

Stresg

Direction

Another mportant

angle, 0s, s where he maxlmum shear stress

occurs.Thls is found

by finding the maximum

of the shear stress ransformationequation,

and solving or 6.

The result s.

I

L-

3-ll,Lllt

-, '=*

, l l l l

q.

'-t1

,

'

' - -

' l *

\ ,

:--

I \

,\r_a

http://www.efunda.com/formulae/solid*mechanics/mat_mechanicVplaDe-stessjrinclpal,c,..

/312007


49/72

-

rincipal

Stress

or

the CaseofPlane Strcss

The

ransformatlono the maxlmum hear tress

lrectlon anbe llustrated

st

Page2

of2

tuzes:-oJ:2

zNq

+As

=AP

+4f

Themaximum hear tresss equal o one-half he dlfference etweenhe two princlpal

svesses,

ef

_b.

-lFfl-:

"T

Strllscs In

glvrn

ffil{lrEE systcm

Maxlrum

shcrrstrcss

c

nng

gP*45"

http;//wwwefunda,con/formula,/solid_mechanics/mat_mechanicVplane_stosslrincipat.c...

/32007


50/72

THEORIES

OF

EI,AS?

C FAlLIJRE

French

9F9rtl e9.It_-Fe

r i Tresca

(I814-I885).

Introduction

We

have seen that \ ,{hen

nater ia l .s

are loaded

in

simple

tension

rhaw hah:wo in: l iFAAr h:FhAr

' r^l- .

+ha al: .+i- l i -

poj.nE r.t chere is one). ,rha happens when tle I o;d-* i?:t'.::::

further depends on whether

the

mater ia l is

duct i le

or

br i t t le .

Duct i le

mater ia ls,

at

Ieast

under stat ic Ioading,

shor.r large

amounts

of

p]_aseic

defornat ion before fa l lure

eg

necking

of

tensi le testp ieces. Obse vat ion seems to suggest

that

fa i lure

occurs a1on9

planes

at 45e

to the

di lect ion

of the load

and

hence

it appears that shear

stresses cause the fa i lure.

Bri t t le

mater ia ls, however d isplay very

1i t t le

plast ic

deformation

before

fa i lure occurs and the fracture occurs on

planes

at

9Oo

to the

direct ion of the Ioad thus suggest ing that

pr incipal

strcsses

cause the fa i lure '

Duit l \e

+

s\e ' l

" ' ' - t "

'

BYittl'e'

.--

priu

c,p']l

sLrz$5e4'

When

designing

components in Eimple tension the a l lowable

tensiLe

stress comes direct ly from measurements dur idg a tensi le test on

the

mater ia l and

thus

this can be used

f,or low

dr. i . i I i+w

mate ia ls. Simi la 1y,

fo duct i le marer ia ls.

Ctr"

Ji ,J" i ^r i ' "" i

can be derj .Ved,

in

pr incip le,

fron a shea

test at though

in

pract j .ce

half the

tbnsi le strength is of ten

used.

When

designing cotnponents

subjected to 2D or 3D stress

systems

,.e

would l ike a way of

comparing the severi ty of

the combined

effect

of the seve a1

st esses with that of simple

tension

because

it

would be extremely

expensive

to

ca ry out

a

mate i .a l

te6t for

every

possib le

combinat ion of 2D ot 3D stresses.

Yi. 1d or fa i lure c i ter ia

A

yie ld

or fa i lu le

cr i ter ion is a theoret ical formula,

which

can

only be ve i f ied by

cornpa ison with expe imental

resul ts obtained

f lom

3D

atress tests.

I t

should be

Eehehbered that

yie ld

or

fa i lure theo ies

refer to the change fron

elast ic

to 'p last ic

condit ions, which

is what we would norrnal ly

consider as fa i , lu e,

rather than out l ight

fracture of a componen .

AIthough a nunber

of theories have been developed

over the

past

ceDtu y o so we 1{ i11

only consider those which have

proved

to

be

el iable and are

current ly in conmon use. The

theol ies are

expressed

in terms of

the

principal

stresses.

Yie ld or fa i lure theories for duct i le nater ia ls

MaximuF Shear Stress

Theoly

(Tresca)

t ' f t

ts cbnic. c,r' 've

a.

ee\

b

^PPl1

Ye-Uevdnt

o drttile

t-ral9

This theory states that fa i lure wi l l occur in a

conplex stress

si tuat ion

when

the

absolute rnaxinum shear stress becones

equal to

the absolute shear

stress at

the

elast ic l ih i t

point

in a simple

tensi le test.

I t is of ten known as

Tlesca's theory after the

C.r

q>

q-)ot

( r

5;6q:5

lr wsu,A4 tk L;k* o.;-A\'*

",-

r'^6+i*"h s\..^r

\ . t f l \ r

g5e

"qth

dl{o

"s

o.

('n

Y\orn

f

"fug.

{\^:

V c.,\l.u-

l ) -4

{.,-'

\*L:

.[

sL"--

st""^'1t1" k

kiltl"

tn,ll._

tenii 'z

rest.'

';llir-io",,-

n

^is

a7'p*:tat"

+o

clv','

tL.

yir "|

(oht

*'*

i7"iiJ

+*U...


51/72

t s4 .StI{t - .*gi-

(

von

Mises

The

alternat ive

name

for

^thr. ,

-r l :orr_,-

the

Distort ion.

Energy

heory,

which

is

ofEen

,. . : :

] l

rh, .

USA,

best

descr loes

rhe

i: r.

il:lilii_=',1:;,.l =ffi

l:".'.,,:,t"ii:iii.?..".

ili'.";"il: t :?T:liX'.'.?T:'-"- cri ic.ai ;;;;; ;;;' :i" maera .

**'":

*,*

;

1ii"

, ,

:+,""i.:fr;

.''"

"".

'

i:"

ai

;

ili'-*i:ilil::xTli:'.*"...T+ii3:ii:: .il.

er nan-American

mathemati

rhe

rheory

s

e*p."s""a'.1; i i i t i " t i i r i ' " lvonMi

es

(

ss

-

r s

s

)."

. *-Z

=

LUv

Another way of expressinq

i&,a*+:

#

t ":;.1;::

::'4;"Q

;i:'$J'i*

r.,__=+=

i,,es

rerrr9cr

rq

ai.

ln

ef f

ective

\

I ) r -

-rr) ' -_5-rL/d_cf" l /Zt

AL

--

.L-,

E I

(

r-

ar-,)

+

(nz

-/

\

-

.)

)

vz

I

and

take

fai lure

to

occur

vi

:i:

"Eilrii.::i:

ill,

'v: l :i:'=:t"::*";:i:":"

i:

eq

.va

en

t o

*,

"

-"

o-.-p

'.

"

"^.jii

]ri

:t,

: :

1

n"t.".:ui"#l

"

ti:.

r

;

j;

It :

p.

:i

i'.i"'.?

r,

n'

,

""nn

'.J

".1".d.,',1 :li ;,; i*: "

3,1"t'in"

"t

o#}t, il*iirilt"ut"ttd in fj.nite .r.r""",t -.t1'"'."sofr$,are

(c

"f

n

".-

F

(n-,i1'

(Rankine

)

This

theoly

assumes

that

f? i l : : :

" f

a

br i t t le

mater ia l

wit t

occur_hen

he greatest

pr inciDa

"

r

a"

i

+-rffii

-5',iriiiE iuf|ii:";.:L"

s.'.

.,ar

.

u"

ihe

6f

{

>qjqt

a;

'

'*r-

/ et,.reat

p.,....r,

t.,og

( o l= qt \ or= '*--

li: ::::^"f:: i:ii:'::^:'

":?'":"il:.;1"'?.'Hsn

predicts

ai,ure


52/72

Mohr

Fai lure

Theorv

the

fot lowing

formulaf

,-

2]D

st ic)," ' '

Tn i ts

sin. :1 i f ied

form

for two

princiPal

stresses

this

Ji- lo" i

ro.

-d i f fe ing

tensiLe

and

cor ' ; ressj 've

Prope t ies

theo y

- t

dr"t

62l

a-

- '

I

cLc

s.*-4-R

Sumnar

The

theori

es

of

fa i lu e

ref

er

to

el

ast ic

fa i lure

ie

the

i ;"-"" i t - r ; ;

f rom

elast ic

to

Plast ic

condlt ions

an' l

not

the

f,racture

of

the

nater ia l .

For

br i t t le

naler ia ls

the

naxir(ru ln

pr incipal

stress

theory

is

i i ir"-' l 'r" ii i ioii rniierrat where he;e is a -rna ked if f e ence in

; ; ; ; I ; - " ;e

conPressive

PloPertLes

he

Moh

fai lure

theory

should

be

used.

For

tnost

other

nater ia ls

the

von Mises

{distort ion

energy"

theory

i -

"on+a-.""a

to

be

the

mo

t--?6lfiu

i e theory

but. the

tresca

; ;* i ; ; ;

"h. . t

" t t " " "

theorv

gives

the

mogt conservat ive

( ie

safe)

; ; ; ; i i ;

ina

tn i"

tosethei

*1th.

i ts

easi lv

aPpt ie l

and

simple

iormula,

probably exPlains

i ts

widesPread

use

rn

lnous ry '

L

, . .

ln

ln

t

,

+hre

.

orrq

tl,V-

n;".p*

t

*,_,ti"

"

,

,"-,t

il"."

p';^"ig.[

4\u*-s.

6,,e,

o^oL

.

.

61

6

--

pti^"i

9^Q

gL-..$t

eB

6t

=o",,*-^l-t

6

c"

u-o*l$

Le^srov,

tvlph

A,^?v'+sio

^


53/72

UNIVERSITY

OF WOIVERHAMPTON

SCHOO],

OF CONSTRUCTION,

ENGINEERING

AND IECHNOLOGY

B Sc

COMPUTER

IDED PRODUCT

DESIGN

TUIoRIAL

SHEE

-

Theolies

of fal lure

2l

(a)

E:


54/72

The

+ree

prinqipal

stresses. in

a car component

are I70

MN/m',

-B5MN/rnz

and

30MN/mz.

Find

the

voo

Mises

equivalent stress.

Ans 221,19

MN/m'

The three.

pr incipal

Ftresses

rn

I05 MN,/nz,

-60

MN,/nz

4nd

zero.

known to be 320 MN,/mz. Find

yie ld ing

acco dj .ng to

the

Tresca

a

cohPonent are

known

o

be

fhe

elast ic l i In i t

stress is

the safety factors

agains

and von

Mises

cl i te l ia .

-

-174-

=

l.q+

=s"2tcD

Hint: F of s

=

elast ic l in i t shea stress

Largestsmax shear st less

?to

^N/^1

VZo

el ast ic l imit st less

von Mises equivalenC

stress

Vo^ \aae 9

Ans I .94

and 2.212

A fo lk l i f t

t luck has hydlaul ic rams that may

be considered

to

be

thin wal led cyl inders subjected

to an

internal

pressure.

The

principal

st lesses wi l l

be

given

by:

,

P=

r..r",*.r

Po"""-

(r..t

l.')

6" --

(d

Oi=

lg dc:o

rrL


55/72

3t,,e


56/72

iv(aX

3

D

stre-ss

sf,stPis

3

Thep*'*

"I

,'hr'-

vo''fu"z

1

''

"t"1*Q-

?'"Y-b

I

*\tut"-

----->-

St"estu*

I

'

(

IPY'"QI

et'-5t{'

I

y;ril

9"en1th

or

rl"

'

/t.//

poi.

,1,

/"{,"-l

tn

e,4i.*,iry

anJ

^*r-.1,

*tente

os l.le

st'zes

d7

.kA

o

.,--,;1

brr;*

*"

r,

'l(

a.le/",

3

pvin lpL

3trcs6.s

6w.**-dr

5i*-6n

5;"-(-

Lb,f-tu)

22

'Ptro:nL

r"j,"n

{ r -6n

(

It\o\r's

Crt

\


57/72

Von

{tlrse

Sustainable Technology 2 - Part 2

Documents

Transcript of Sustainable Technology 2 - Part 2