Lecture-19 & 20 (Non Circular Torsion Member (I-Section, Rectangular Section)

7/22/2019 Lecture-19 & 20 (Non Circular Torsion Member (I-Section, Rectangular Section)

1/38

KC 435 ([laoj Ickheboks)

Ackturc-5? & 40

Zlrsolb-4

Blb korkuaer tlrsolb icidcr (O-scktolb,

rcktebmuaer scktolb)

Eboa Iebjeroye 5


2/38

Ackturc-5?

Zlrsolb-4

Mcbcrea epprlekh glr blb korkuaer tlrsolbicidcr

Eboa Iebjeroye 4


3/38

5. Jospaekcicbt glriuaetolb lr Mclictry lg Jcglrietolb6

Essuiptolbs6

(o) Zhc krlss-scktolb paebc jlcs blt rcieob egtcr

jcglrietolb, dut mcts jospaekcj ealbm albmotujobeajorcktolb. Zhc jospaekcicbt ealbm thc albmotujobea exos

jorcktolb os keaacj werpobm.

(oo) thc krlss-scktolbea joicbsolbs lg thc tlrsolb

icidcr erc blt khebmcj sombogokebtay dy thc

jcglrietolbs, pertokuaeray glr sieaa jospaekcicbts.

(ooo) Ietcroea os aobcer caestok

Eboa Iebjeroye ;

Zlrsolb lg blb-korkuaer shegt6


4/38

Jcrovetolb6

Klbsojcr e plobt P woth kllrjobetcs (x, y, z) ob thc ub-

jcglricj tlrsolb icidcr.

Sbjcr jcglrietolb, P mlcs obtl P*. Zhc plobt P, ob mcbcrea, os jospaekcj dy eb eilubt w

pereaaca tl thc z exos dckeusc lg thc werpobm lg thc

krlss scktolb ebj dy eilubts u ebj v pereaaca tl thc x

ebj y excs, rcspcktovcay.

Eboa Iebjeroye :


5/38

3Eboa Iebjeroye

Zhc krlss scktolb ob whokh P aocs rltetcs thrlumh eb

ebmac woth rcspckt tl thc krlss et thc lromob.

Zhos rltetolb os thc probkopea keusc lg thc (u, v)jospaekcicbts lg plobt P.

Zhcsc ldscrvetolbs acj [eobt-Wcbebt tl essuic thet

9 z, whcrc os thc ebmac lg twost pcr ubot acbmth ebj

thcrcglrc thet thc jospaekcicbt kliplbcbts tenc thc

glri6

whcrc os thc werpobm gubktolb.

Zhc gubktolb (x, y) iey dc jctcriobcj sukh thet thc

cquetolbs lg caestokoty erc setosgocj.


6/38

[obkc wc hevc essuicj klbtobulus jospaekcicbt

kliplbcbts (u, v, w), thc sieaa-jospaekcicbt

klipetodoaoty klbjotolbs erc eutlietokeaay setosgocj.

5.5 Zhc stetc lg streob et e plobt ob thc tlrsolb icidcr os

movcb dy6

Eboa Iebjeroye 7


7/38

Og thc cquetolb glr zxos joggcrcbtoetcj woth rcspckt tl y,

thc cquetolb glr zyos joggcrcbtoetcj woth rcspckt tl x,

ebj thc scklbj lg thcsc rcsuatobm cquetolbs os

sudtrektcj grli thc gorst, thc werpobm gubktolb ieydc caoiobetcj tl movc thc rcaetolb

Og thc tlrsolb prldaci os glriuaetcj ob tcris lg (zx,

zy), edlvc cquetolb os e mclictrokea klbjotolb

(klipetodoaoty klbjotolb) tl dc setosgocj glr thc tlrsolbprldaci.

Eboa Iebjeroye =


8/38

5.4 [trcsscs et e Plobt6

zx9 4*M*xz9 M*

zy9 4*M*yz9 M*

5.; Cquoaodroui cquetolbs6

Zhc strcss kliplbcbts (zx, zy) erc blbzcrl. Og dljy

glrkcs ebj ekkcacretolb tcris erc bcmacktcj, cquetolbs

lg cquoaodroui glr thc tlrsolb icidcr erc6

Eboa Iebjeroye 8


9/38

Eboa Iebjeroye ?

4

4 4

4


10/38

5.: Dlubjery Klbjotolbs6

Blriea lg thc krlss-scktolbea paebc os b 9 cz.

Zhc trektolb lb thc paebc keb dc keakuaetcj dy Keukhysglriuae (tf9 ofbo) es6

tz9 zz9 0

tx9 xz9

ty9 yz9

Act I 9 Z*cx

Ilicbt lg trektolb (I) 9

. Eboa Iebjeroye 50

M*

M*

(r x t) jE


11/38

.

]hcrc

F 9

Eboa Iebjeroye 55

(r x t) jE

(xcx+ ycy) x (txcx+ tycy) jE

(-ytx+ xty) czjE

M* M*(-y* - x* ) czjE

M* (-y - x ) jE

(-y - x ) jE


12/38

Aetcrea sugekc6

Grli dcalw gomurc

Zhc aetcrea surgekc os

grcc lg trektolb

. Eboa Iebjeroye 54


13/38

.

Eboa Iebjeroye 5;

M* M*


14/38

[uiiery6

Zhc tlrsolb lg thc blb-korkuaer prosietok der rcjukcs tl

slautolb lg thc glaalwobm cquetolbs6

[tcp-56 Gobj thc werpobm gubktolb sukh thet ot setosgocs thc

mlvcrbobm cquetolb49 0

Ob thc jlieob lg thc krlss-scktolbea paebc sudfcktcj tl

thc dlubjery klbjotolb

Lb thc dlubjery. Ldteobcj thc tlrsolb klbstebt

F 9

Eboa Iebjeroye 5:

(-y - x ) jE


15/38

[tcp-46 Movcb e tlrquc, ldteob thc ebmac lg twost pcr ubot

acbmth grli thc cquetolb

Z 9 M F

Tcierns6

5. F os thc prlpcrty lg thc scktolb. F os ldteobcj dy

slavobm Aeaekc cquetolbs woth grcc trektolb dlubjery

klbjotolb.

4. Zhc werpobm gubktolb keb dc ldteobcj cothcr

ebeaytokeaay (blt eaweys plssodac), lr buicrokeaayslavobm thc edlvc cquetolb ebj hcbkc F keb dc

ldteobcj.

Eboa Iebjeroye 53


16/38

4. Glrkc glriuaetolb6

4.5 Cquoaodroui cquetolbs6

Grli 5

st

twl cquetolbs, wc keb klbkaujc thet zxebjzyerc gubktolbs lg y ebj x lbay.

]c keb khllsc e gubktolb keaacj strcss gubktolb (x,

y) sukh thet

sl,

Eboa Iebjeroye 57


17/38

4.4 Dlubjery klbjotolbs6

Zhc aetcrea surgekc lg e tlrsolb icidcr os grcc lg

eppaocj strcss, thc rcsuatebt shcer strcss ob thc krlss

scktolb lg thc tlrsolb icidcr, lb thc surgekc [ lg thckrlss scktolb, iust dc jorcktcj tebmcbt tl thc surgekc

Zhc twl shcer strcss kliplbcbts zx ebj zy thet ekt

lb thc krlss-scktolbea cacicbt woth sojcs jx, jy, ebj

js iey dc wrottcb ob tcris lg 6

Aetcrea trektolb lb

dlubjery6

Eboa Iebjeroye 5=


18/38

Eboa Iebjeroye 58


19/38

[obkc thc strcsscs erc movcb dy pertoea jcrovetovcs lg ,

ot os pcriossodac tl tenc thos klbstebt tl dc zcrl> thus,

wc scackt

Eboa Iebjeroye 5?


20/38

Et eby plobt ob thc krlss scktolb, os jorcktcj tebmcbt

tl thc klbtlur 9 klbstebt thrlumh thc plobt.

Zhc jostrodutolbs lg zxebj zylb e movcb krlssscktolb iust setosgy thc glaalwobm cquetolbs6

Eboa Iebjeroye 40


21/38

Ob setosgyobm thc scklbj cquoaodroui cquetolb, klbsojcr

thc strop ekrlss thc krlss scktolb lg thoknbcss jy es

objoketcj ob Gom. [obkc thc strcss gubktolb jlcs blt

very ob thc y jorcktolb glr thos strop, thc pertoeajcrovetovc keb dc rcpaekcj dy thc tltea jcrovetovc. Glr

thc strop6

Glr ;rjcquoaodroui cquetolb

45Eboa Iebjeroye


22/38

[uiiobm glr thc lthcr strops ebj rcpcetobm thc prlkcss

usobm strops lg thoknbcss jx glr thc lthcr tcri ob ;rjCq.,

wc ldteob thc rcaetolb6

Zhc strcss gubktolb keb dc klbsojcrcj tl rcprcscbt e

surgekc lvcr thc krlss scktolb lg thc tlrsolb icidcr.

Zhc tlrquc os cquea tl twokc thc vlauic dctwccb thc

strcss gubktolb ebj thc paebc lg thc krlss scktolb.

Eboa Iebjeroye 44


23/38

[trcss-streob rcaetolbs glr aobcer caestok dchevolr lg eb

osltrlpok ietcroea erc movcb dy Hllnc's aew), wc ldteob

Es klipetodoaoty cquetolb os

[l

49 -4M Plosslbs Cquetolb

Eboa Iebjeroye 4;


24/38

Ackturc-40

Zlrsolb-4

Tcktebmuaer ebj O-scktolb tlrsolb icidcr

Eboa Iebjeroye 4:


25/38

Eboa Iebjeroye 43

Zlrsolb lg rcktebmuaer scktolb shegt6

Glrkc glriuaetolb6

Act thc sojcs lg thc rcktebmuaer krlss-scktolb dc 4e

ebj 4d woth thc lromob et thc kcbtrc es shlwb og gomurc6

Ekklrjobm jospaekcicbtglriuaetolbs Aepaekc

cquetolb6

x

y

4e

4d

E

J

K

D

4

4 4

4


26/38

Ekklrjobm tl Aepaekc cquetolb lg jospaekcicbt

glriuaetolb6

lvcr thc whlac rcmolb T lg thc rcktebmac, ebj

lb thc dlubjery.

Lb thc dlubjery aobcs x 9 e lr ED ebj KJ,

wc hevc cx9 kls() 9 5 es 9 0 ebj 580cy9 sob() 9 0 es 9 0 ebj 580

lb thc dlubjery aobcs y 9 d DK ebj EJ

wc hevc cx9 kls() 9 0 es 9 ?0 ebj 4=0

cy9 sob() 9 5 es 9 ?0 ebj 4=0Eboa Iebjeroye 47

4

4 4

4

cx

cy


27/38

Hcbkc , thc dlubjery klbjotolbs dcklic6

es

sl, lb x 9 e

ebj lb y 9 d

Zhcsc dlubjery klbjotolbs keb dc trebsglricj obtl

ilrc klbvcbocbt glris, sukh thet

9 xy5

Ob tcris lg 5 ,

thc mlvcrbobm cquetolb os

Eboa Iebjeroye 4=

cxcy

4

4 4

4

5 5


28/38

Lvcr rcmolb T, ebj thc dlubjery klbjotolbs dcklic

sl, lb x 9 e

ebj lb y 9 d

Ot os essuicj thet thc slautolb os cxprcsscj ob thc glri

lg obgobotc scrocs

whcrc Xbebj _berc rcspcktovcay gubktolbs lg x ealbc

ebj y ealbc.

[udstotutolb obtl thc Aepaekc cquetolb glr 5 yocajs

twl aobcer lrjobery joggcrcbtoea cquetolbs woth klbstebt

klcggokocbts. Eboa Iebjeroye 48

50

5 -4

0b

b )()(X yx _b


29/38

Zhc gobea rcsuats whokh erc oiplrtebt erc es glaalws6

glr verolus d/e retols, thc klrrcsplbjobm veaucs lg Nerc movcb ob thc glaalwobm tedac6

Eboa Iebjeroye 4?

dNeF ;

d/e N N5 N4

5 4.43 5.;30 0.700

5.4 4.737 5.358 0.3=5

5.3 ;.5;7 5.7?7 0.3:5

4.0 ;.77: 5.870 0.308

4.3 ;.?8: 5.?;7 0.:8:

;.0 :.408 5.?=0 0.:78:.0 :.:?7 5.??: 0.::;

3.0 :.737 5.??8 0.:;0

50.0 :.??4 4.000 0.:05

3.;48 4.00 0.;=3


30/38

Essuiobm d2e,

Zhc iexoiui shcerobm strcss

os et thc ioj-plobts lg thc albmsojcs et jostebkc grli thc

kcbtrcx 9 e lg thc rcktebmac.

lb thcsc sojcs

zx9 0 ebj

Zlrsolbea romojoty lg thc

scktolb 9

Zlrsolbea klbstebt glr thckrlss-scktolb 9

Eboa Iebjeroye ;0

x

y

F

N5e

NMde;

dNeF ;


31/38

Zlrsolb glriuae glr rcktebmuaer scktolb shegt os6

Eboa Iebjeroye ;5

NMde;

de4

N4

NMde;

N5M

;5

iex

Nde

ZM

N


32/38

Jospaekcicbt klbtlur6

slaoj aobcs klrrcsplbj tl plsotovc jospaekcicbts, whoac

jlttcj aobcs objoketc bcmetovc veaucs.

Zhc squerc scktolb kesc woth e/d 9 5 prljukcs ejospaekcicbt pettcrb woth comht zlbcs lg syiictry.

Es thc espckt retol e/d os rcjukcj, glur lg thc jospaekcicbt

pettcrbs joseppcer ebj thc rcsuatobm jospaekcicbt klbtlurs glr

e/d9 0.3

Eboa Iebjeroye ;4


33/38

Eboa Iebjeroye ;;

Zlrsolb lg thob rcktebmuaer scktolb shegt6

[trcss glriuaetolb6

Act thc thoknbcss lg thc rcktebmuaer krlss-scktolb dc t

ebj 4d dc sieaa klipercj tl thc wojth

Zhc scktolb klbsosts lg lbaylbc dlubjery ebj thc veauc

lg thc strcss gubktolb

erlubj thos dlubjery os

klbstebt.

Act 9 0

x

y

d

t

E

J K

D


34/38

Eboa Iebjeroye ;:

Es

Cxkcptobm et thc cbjs EJ ebj DK, thc strcss gubktolbos georay uboglri ebj os objcpcbjcbt lg x. Hcbkc, wc

keb tenc (x, y) 9 (y)

[l,

Dy obtcmretolb6 9 -My4+ e5y + e4

Es et y 9 t/4> 9 0

[l, e59 0 ebj e49 M t4/:

zy9 0 ebj zx9 -4My


35/38

Eboa Iebjeroye ;3

Zhc iexoiui shcerobm strcss erc et thc surgekcs

y 9 t/4 ebj zx9 Mt

ebj

Zhc rcsuats erc6

MdtZ ;

;

5

;

;5 dtF

ytM

FZ

4iex


36/38

Eboa Iebjeroye ;7

Zlrsolb lg O-scktolb shegt6

[trcss glriuaetolb6

O-scktolb, Z-scktolb ebj A-scktolb keb dc klbsojcr

kliplsotc scktolb lg iejc dy thob weaacj rcktebmuaer

scktolb.

Ebmac lg twost os thc seic glr cekh objovojuea thobscktolb, ebj thc tlrquc os ejjotovc.

Z 9 Z5+ Z4+ Z;+..............

Z 9 M5F55+ M4Z44+ M;Z;;+..........

Zhc edlvc cxprcssolb keb dc cxtcbjcj tl thc kurvcj lpcb

thob weaacj scktolb. Ob thos kesc d 9 tltea erk acbmth


37/38

Eboa Iebjeroye ;=

[ j T g


38/38

Eboa Iebjeroye ;8

[lurkcs ebj Tcgrcbkcs

5) EJWEBKCJ ICKHEBOK[ LG IEZCTOEA[ dy ETZHST P. DLTC[O ct.

Ea.

4) Cbmobccrobm Ickheboks lg slaojs dy C.P. Plplvc

;) Ickheboks lg Ietcroea dy Feics I. Mcrc

:) Wcktlr Ickheboks glr Cbmobccrs dy GcrjoBebj P. Dccr

3) Ilicbts ebj tlrquc dy Peua Iotomuy

Lecture-19 & 20 (Non Circular Torsion Member (I-Section, Rectangular Section)

Documents

Transcript of Lecture-19 & 20 (Non Circular Torsion Member (I-Section, Rectangular Section)