© 2009 hy ICC. Hibbclcr. Puhlished by Pear~o.;o r,cmH;~ Hall, Pl:al1;on &!ucallon, Inl.:. Upper Saddle River, NJ. All righls f(~seryed Th.is mmerial i~ prolecl.:li unck.-r all copyright laws a1> lhey currently exist No portion of 'his malCriaJ m~y he r~produce<l, 10 any fonn 01 by any lIIeans, wilhout permission in wriring Crom the publisher

©20(J9 hy ~

copyright I~

9-59. Solve Prob. 9-58 Ilsing CasligliiltLC'S theorem.

. .;:;::t:~..,.......I~~ p'

(

J~''',..,J .'olMunj r.~C<j... M{~); lKln_t1 ""'"""""""""'" In 1e'1ll.$ ~r 1Jac: If,ad ,~ a.nd ~., ~ to.6 Nt; .-h..go.,a Q4 Ibc

till..... p C'" ,1,1_', So<u.4 T"fNII' ; Th< b""""'l.II di>91_, ""

"'" t:>o4<l<n'OW:dll,llncliq. ?-H wi.... 0iIl~,) ~ 1.00<" ~ 'd.OOL >nil ......., P' - P.

o.. f1~)~ (OJ), Q FiIf'• (1':r,)(I.I)(lt,)d<,

t J< .~:ii • (nJ/I,OO(.)J!r,

1fL' w w ....

'~u."

9-61. B: by 100 m DClemufi only the e E = 200(

Rtal.'>IoM(,

Virtual :Won

Virrual WorJ

llld Sq 9·15

J.

J kN m· O.

8"

*9-60. Bar ARC has a rCl:tangulal cross section of 300 nun by 100 mm. Attached rod Dil ha~ a Jiameler of 20 mm. Determine the venical displan:ment of poinl C due to lhe loading. Consider only the eJ'kct of bending in ABC and axial Coree in DB. E = 200 lI1'a.

'hal MI"n,nl F"nu111l1 M {.E): As showlI on flg1lfC( a}.

Virtual M"mtnt "u"ctlons m{.fl: A5 shown 1>11 (l5ul1::(b).

Yirtuat W",k EqualtIJl': ror th.e dlsP~Mt at pO"'1 C. combl/1.e

&<.9·18 :lOd Eq.9-15.

fLmM 'lNL

l·~= -dx+~ o EJ A£

1 kN· 6.c -= 2[ ~ J:"' (I.OOxl(20,(k) d.~) 2.50( 50.0) (S)

+--1\""'"£""";"­

'-

'42. The b (CnJpc:rature 0mJ)OOOlIll lop is T, = 5-1\-­Vl.:J'llcal displcKJOOmm

,J gradiclll. The' a dCplh of 14 i

f----- 3 m

1= ~x r·OK~~M():}•.zo.OA

~,.., 3",

(pJ

• 360 k.N . "') 625 k.,'l m 9--63. The top l A c = E1 + AE

·f 1', =- 200"C, . 360(lOOO) 6~.5( IlXlOl Tt. ",,' 30"C. Tf a= +---"-'~--

2oo( 1I)9)[&(O.ll(OYl] WO.01ll](2oo(!{)!'>J JisPlacernelll of =0.017947 m -= 17.9 mrn J.. Am I gradieot. TIK: be,

I

~ '- ­ - 4111 ­

2

© 2()09 by R.C. HlflhcltL P~hll~hed hy I',~ar,un Prel" fiX Hall, I'c~Jsnll Edl)c'ltion, Inc" Upper Saddle Ri ver. NJ. All rigl,'L:, ,·~ser\'ed. Thi" llmh:l'ia/ is PlJ.'t ' oopyrighl laws ilS they cuw:l1lJy L'xisl. Nu p-;lnj·J.I "f Ib.is 1ll;'lwri~1 Ill'll' Ill: 'n.:proJuocd. in any form or by any IlJt'III.'!, "'itholll permission in wriling Jr~, :1:1 *9...{j4. Determine the borizonln[ di~:p[1I(;cm(;ul of

600lb poinl C. £1 is OOnslaui. Tbere is 11 tixed support ill A. Consider only the effect of bend Ing.

u n -f

IR ~al Mo "..IIt FUflclio" M (x): N shown on figlUl'(')'

! Yinu,,1 MO/1lem Functions'" (x): N shown 011 figure(b)_ HI

Yin ..", Work Eq IIMio II : For lhe borimmal dispLx:tmenl 31 POinl C. apply E<j. 9- 18.

llOOlb (mM

II·A", r -deJG EJ .'if!

I flOllb·(dc). =0+- (J.OOJ:l )(4800)d.<1

EI I " ll, ~ ~ I +- r J.OO(rJ +5J(4800+800<,)lU J A

EJ )0

323( 103 ) lb· tI'

(de). =--EJ-- A.",

-t.,,'ft

jib~

-:UooJb

(a)

" ~ - ~,

"'(;:.)00

,rT'JU".... ). J.-; ...(,L

9~. Usc (he method of virl 11111 work and lklerrnine lhe horizontal ddlcclion ill C.The cross-scl:li()llill an.:a of cad1 member is iudicated in Ihe figure. Assumc Ibe members arc pin connected at their end poinls. E = 29( 1(}3) ksi.

:H be.

IJ~ 1 ii'l.' ­I. Ilk\! .1 ': --<I!VIilIIt-"-+ 5 k I

ii

t~ JIl,z2 in.2

'h' i \'f'~ I i\:!I~OI

'('l~-4? ! \\ ( (

,t. '1 ~ "'"717l> A

4ft

'A) ~ I1J'/L _ U3(H,(j1}(4)ll21 (1)(~)(3Hl2) (-8.J.3IH·~tSlI12l ;.u,(" A. - J.., - ~ T + 0 +.

Ali 2(29)( 1011 (IJl1~)(10') U~(2"f t .:::s O.O4Ol tn. -+ AD(

\ .J~ 3ft i

Sok~~6.

2J..:

.-,.-­

H(

A

Ij'--­I

, ...,. II'-,e 11 lIN: Yel1ical d Cl'l.~lufl,1.

258 ---­

.~ ft

1~"'lb

Sf!

I

:d-~-'-1 5iL&ESC' F

~v,J'O""'", 1fT· ,)",~.. j[f"

~ !Ol~

/(1·0 "·It Un

£6n~)I!2l

~)

'bbd.:r. publish~" fly Peurson Prcmicc Hall. P~arson Educallon, Inc.. Upper Saddk River. NJ. All righl'" reservro. Tbi, material is pm{C(;{cd llllrkr all ,C-~'Ihe)' cun'enlly exist. '1\0 portion of Ihis malerial may be reproduuxl, in all)' liJr/ll or by any "\C',lllS. wimout permission in wriling from (he publisher.

SOlw proh. 9-65 llsing Casligliano's theorem.

21;

t= e;:::errr--+ 5 k

h

8Kf~( ( ~

~l'-UU'

I~ I~" U

~ ·U)

,~" [

5.. ..

l> I t I.HI" I.'W "~1 • 1.J.L1 ~

Mc"'ba' I'ffo= <IN

dP All L33P ,. 4661 l.)3

iJ<: P+S I

I r ~- 3fl ­ - ._~ 80 CD

-1,667P - 8.33

0 - 1.667

0

Set P '" O.

,II. ). '" N(JN)!:.... ~ (4,667}(1.331l41{IZ) .. ('sIOl<JIlIZ) + 0 >I­ (---8.JJ)(-1.667){S)( 12)

C i)P A£ 2fZ9)( lo!) (I /(29)( lO') (1)/19000') " 0,0401 Ul, -. "' ­

t-67. Use the method uf virtui11 work and detelmine -me \'trtical deflection at the rocker support D. £1 is CIOIIStllllt.

600lb

-_. -lOfl- ­

H'''''')'' ""'16 '''Ib-, - e

'-loll> rl.}5H

, /1'0 1"10 11. _I-"-~4=~ 1<

b c.

It "..(

A 1I--;- I -'il~

"'w

" (.<)1 ¢«l<J dL f' (IOl(1:>OXj <Iz ~(.:lDl, ~ 1'''''''1 J, £j

..,vdx - +-0 • £1

=+IOl<ft' 1 ....­H

259

([) 20()l) by R.C. Hibbdt:r, Puhlisht:d 11)' Pearson 1'1~,,'i.;e H~Il, Pearson Education, Jnc., Upper Saddle kivt:r, NJ All ril:!ht, reserved. This fnalcrill] j, copyright laws as they currently eXls•.. No portion (.1' Ihis malt:fial may b<: r<:produced. in any form Of by any means. wilh"UI pcnnissioll in wrilin." t: pr~

,;. roOl the ,..,

*10-20. Determine the rcat:tious Dl th~ supports. U is WDstanl.

S(X) l!lift --8'TIl. lJ _ 3k• .. , , 'I '~""'" ."-'", T ,. , IL ..

··--10((-,

(+.1.) 0 '" Ac - c.,fcc (1)

Coroparibility c:qualion

c

1011

t ,

I j

~I( ;t-~ -~fT ~_w_~ --. ~It ~ ~--_. 'I \ I '

, \

lh I

= , I

I I

; I..S C /~c

f

Use vidual work ~

.. _ JLlnM.L._ jIO(J: I )(..J).25G) ....c - -""­ dx ".oEl 0 E1 I

fcc = t~d:xe rO(xY dx = ~ oEl 0 E1 I EI

-625

EJ

~l"

FromEq. I

c, = 1.875 k

A% = 3.00 k

~ = 3.125 k.

o ;: 625 _ 333.33 <; F1 E1

Ana

Aos

AM

';1:,llo/t.

'1 ~,..-l

tn,· "'"

/'I'l~.o·1 P:4,

1 MA '" 6.25 t,. ft ADS

I .oft ......j , iii'

.:f...tt ' ~A,.. : t I • =::-'If­

','75&.

.,." ­

~m

N I ,"' .... I

-{Ill

.L ~~~f~

~ '£1-; '" 0;

(+w, :: 0:

+.!.U; =0:

:.. r.f; = 0;

(+£4t, '" 0;

+./.u; '" OJ

!J

(+1M. '" 0;

(+tIll 0:c:.

Ad

(+tw1 :- 0;

prulJ:(;red ul)lkr all om tho: publisher

19 200-) by R.C. Hlbbeler. PulJhshed by Peafson l'I"entice Hall. Pe~r;vn F.ducalilln, Inc., Upper Saddle River. NJ. All rights =rved. This material i~ prorc;;rtxl !lnller all copyright laws as they cum:ntly exist No portion of (his Illliterial may be reproduced. In any torm or by My means, without permission in writing fr(lill (he publisher.

16-25. Determine tbe reactions at the supporls A and D. Tbe moment of inCrlia ot each segment of Ihe frame is listed in the Ilgure. Take E = 29( 103 ) ksi.

~ kjft

{AD = 600 in.4

I DC 800 in 4

~tA.! I[ , ! , r ~~T

2 k

,1

--10ft .j

r I

(."'.UP • ! ~-H

fill "':.1.if';G. /'1.11.·4 I ~.o.f (1 ! b ~ ..1 U~ , I{t "-l.J JI>Al . ~~.~ I ll.. :SOl(, I .. I-?-I\.

'0'

'0'

6,." r ".;,(dx .: 0 -I- 1'. \Ix}(~J) dl .. J"'l 10)( (7U-~).ir • £/-" • £1,(,' : 0 £kD . MO~ Of1IUI2.S

"'--- JH. PiEra, 1 ",' . J'0 xl f'. 101 IUOk = 5 -4r '" 0 ... --4%.. -dx-­

'!...§l Q El~(,' ~ .£lcD , EJCD ~~JM"'O'I '

lUI2~A,-(l~)", 0 fi.lcD .£1cD.

A,'" - 15.0k AN ... 'tU,=<l. '. '30 + IS To",. 0; I), '" \j.O k Alii

~~::;; O~ n,. =2 k Au

~r.wG '" 0; 15.0< 10) - 2(10) - 30(5) ... Mo '" ~~ /./0= 19.$k·(1 Am

-411

+1:..

4-0"­

'i~CgJ." !B] 'I All .~ ~ ••

F;,fu...~

-4$.133 == --­

E

12.28 := -­

E

i I

311

1

(I)

(...(\.8)(5333)(4) ( LO)( -6.667)(5) + +----­

(I)E 2£

O -48.133 12..28

:= -­ + Fiw -­E E

fil! ::--~:;::4==::=:::::flf>JJry.{. .t'''H ,

A,O =r.nNL = 2(-0.6)(4)(3) A£ (I)E

o ,., .1"0 + F,rJ'.DID

JIo-

NIL 2(-0.6)2(3) 2(-0.8)1(4) 2( I.W(5) I - t--= ­ + + ---,.,...-,-_ IB£nD - /iE - (1)£ (l)E (2)£

Use viIl1Jal work mechod:

From (I)

Cooipanbilily cqualioa :

10-26. Delermim: the force in t:acb m~ IlltJ<::r of the truss, 11le cross-sectional area of each member u; indicated in the figure. Assume the members ,m: pin con n~<.:led at Ihei r cnds. E = 29(103) ksi.

li) 2009. by R.C. Hibbclcr. Published hy PeaJ,,(r~ Pn:ll.:l-:e Hall, PC,anoa EJucalinn. Inc.,Upper Sm.ltlJe Rivtor. NJ. All ri~hl~ r~tor1ic~l. This rnalcrial is~ copynghllaws as IIle}' cum:nrly exrs\. No fKlllrnn "I IIlJS mc.lcmd m.<l:t Ix: r'Cpnxl'uced. In any form or hy any means. wlthoU! pernussron In wriling Ift'rUtlle

F,l) = 3.92 k (T)

4'F,~ - (-) 3.920 -= 0; 1';.. = 3.136k '" 3.14 k (el5,

3' lite +( -) 3.920 - 4.: 0: F,c '" 1.648t: .: l.65 k (T).5

Joint /J

~tF. ~ 0:

+ Tr.r; == 0:

Joint C

+iU; "" 0;

ADS

JSFCA. - 1.648 z: (): FcA ': 2.747" =2.75 Ie (C) ADS

ARli

Aas

~*'Ic~

T,.)

Fe.... j.~,

{

~ '" z·1f1t.

S

II ' .. --}I.

~.H3 J(. .!.M(,.'"

4 5.J~~ - :5(1.747) - 3.136 ;;: 0

;.~ ,. 0;

kti.n1A.

+'tv; =0;

+-11:1; = 0;

4 FeD - '5 (1.747) .: 0;

3 ~D - 5(2.747) :;; 0;

FeD =2.20 k (1)

~D =: 1.65 k: (1)

Cbcck:

Ans

AIU

~

~ 'JU'I:. ~

J. X. Fa,. ,

4/1:.

_---," 1111.',

.. WlJJH )(-13.33)

2

£ • ~,,~ [1( 1.33)1(4

IE E I 311,,­

t FC'If,et '" , '34'(1--;-+F"I- ,..

, \ E , lei" - 3.062 k co

~ F,c - fi S

""c =~. 4.....' -(8.23) ­S

Foe ,. ()

tF, " -3.062+

'0' " !, oJ, ....

FA' - 6

F.. '" l(

3',if, -t -&.23(51 Fa.. "4.~

l'! h\·l{·C. Hibbc: •- :ngll; 'laws as the)

© 2009 by R.C. Hibhcler. Publishcxl by Pe;::u'<;on 1~'cmKe Hall. PearsOIl Edu<:olion, Inc.. UppcrSad(lIc River, NJ. All rights re~crved. This Tllalctial i~ Prill oopyrighllaw~ as lhe;:y currently exis!. No POlli()11 "r'his material may he n:pmduced. in any form or by any nlt'atls, without permission ill \\-riling frolll ~

10-30. Determine the force in memher HB of the lruss. ~ solution \0 Prob. 10 - 29.

'

AE is constant.

Joint A :

4' + i'I.F, -= 0: 2.5 - ( 5} ~H "" 0

F".iI =: 3.125 kN(C)

Joint H;

10kN m - 2.323 + WI),,; '" 0~u; = 0; 3•125 :!

I r:.... £He ;::: 0.7473 kN (1)~ 2.3ZJhJ 5 F""

J. J

-~ -):.

'4' (4)SQ ~ ..-tIE, = 0: (s) 3.125 - 5 0.7473 - Fit. = 0+ 31J.$JQI~Fiu. Z·50/t;,.J ;;'6 Fa. ;::: 1.90 kN (T) AQI

10-31. Determine the for(;C ill mcmbcr HG. A t' is con~tanl.

H G F

4k H 4k

Compalibility eq~QlJ: '

o == 4HG ... ENdHGllG (I)

Use vittml worlt: medIod;

A =: r:!!!:. "" (I )(I2.0)(lS} + (1)(14)(15) ... (l)(ll)( 15) fl(; AE AE AI< AE

(-1.414)( -11.31)(21.2]) (-1.414)( -8.48S}(2LlI) llQ3.97 ... + =-­

AE AE AE

Jj 1IhL 4{ OlflS} 2( -1.414)1(21.'-1) }44..11S ROliC; ,=:rAi ... ----;:e- ... !I.E '" ----xE

1100.91 144.85From Eq.l 0= --+ --F

AE AE HG

-.::-7.621 k; "" 7.62 k (C) Am;FNG

Jsit,5ft

A

'W...32. Detem

,:oJlstan't.

~- - -3 m - ..

tJ.af + FUdBE

INnL ABC;::: AE

i(l4.912 =- '""AE

uh §Rlillt == AE

28..~j

= --~-AE

104912 --- -I- j

Ai

1-.£ "" - 3.621 10

RL\J.

~!lI~~ 6H1J L j