fo:r" o . lpl :r :o s o"a:t:r n ,t r r r !l€b o6 r sp r ttn6ctlrp,l/€r,; v r . , e . r . i r r , - ' p " , p " i i ! rtrd concoDts or
Etrlrn6€rrng X€cbanlca ltr e vory b.!lc and rpproscn to nelp tbo itudsntt und€.!tand
;;;.,:l:j":;
,ii;li;;
,",, ,r,r
uy;to!.ttc anO re"."
d6v6rop rher. ofdo!ry
Itllh ttro pre.€rt€d toptct, rhe u6r, wttt trave r vory cotrpran€rsrvastudy o( th6 aundr!€ntat prltrclDl€r ot li6ctatrrci,htch ar6 tppltcrbr; to v a r r. eE(nys ronre 6prrtancsr t c r l s l t u a t t o n 3 t r o r u a l l y e n c o q n t o r e; dl d 6 b! te€6 In rtrolr dr' to ddy rcttvttl€3.
'*pa;a:paat*
Jojo BiIrM
nBsfs I4.t
na'i
-
The rotborr stslr to {crno,led8€ lb6tr lndebtedD6ss to. ut.nael Slongco, Jettrey Bortongan, Ron.tdo Catlrdls, and noreo ld.tano tor tb€tr ".lu.ble tn prep!rlna,nd irttlnA tbe o"nuscrlpt.
forulc@4'l
Bor As.i.ti's
f'&d[sdig_
Etlra staort rrs s:erted !o lbat ev6rythtr . tll De presented tn I vsrJ pertecrty understood, bla tn r con.ra€ tenaurge. Tbls ,tll eltDtnat€ or :l:lr :"" rrtrreu te dtddent's attltude or h.blt ot oelortzrnA ttr€ concopt rttt ou! under!trndtng.
A56diai!
pErpu-g..&*tr-".(Af8t.l1Hg=ffiH .f dle ftntlPiD€3 (BDAPT thililP
is ebj@d 7dE) ltu ritorgld@' btoch ehown i Fig' P-M f t\D=Sh\Dc=6'L, lolrE loods P'1@br,tF-6@b-
resolro coolt lood inlo coopr;le .conei&r
ru'md \ lcgcnlirl
lt,p i6oo lb lcod j
sinc--L aase-+ h- +-'(16co)' t26ob' h-
Ltl@o\
= S6olhc.
,&- l6';6i ' toa-
2
8
lt
i'r"
n.et r -AA \ -Ar xz X'1.rc<1)-12,s7(q)
onounl k, posi{ion of lhe lhe Fink true6 .sh@n h R= zcb+ te+ a4o | 'aa +..n t zooa (d i@t€d dodn*o"d ) B-a39]!
- P979.!b , R'- 2.ht tsoor aal |eoo r 2oo d@"-d,t L - ]4!@,,s,ta4
"t- ?9,41fr-lL_ d = .:ryL - ?49 !1, a e|*I plola 2+o) lhe shodcd oreo in tig p-z
fo,.:a oclioq ot the center of lhe 1ox!+ in rectongle' Re mt thewe,lht of lhe mole.iol cll oway W on upwoFd lo'€e ocl,hq ol ttp @i3n of the cfule Locole lhe posi|on ol the resurtont of ihes two forces wilh 'qePeol fo fhe left edge
2az) Ihe lhr]je-'lep Pullel shown i^ fkl P-2+7 jhe to ihe s,ien couptes compuie lhe "ol'o of rciing ot lhe )he 6re p)e. A)so delonire
l4
e)
c- 3oR (4
25o.) The conlileve. lruss shown i\Fig.P-2eo cor.ies o v€rlrbal lood of 24<)c)b. Ihe lrr.:s,sle s.pponied by beorings o) A \B which exenl lhe fbrces A-,Ah,\ Bh.Ihe shown con|lule adple€ which musl hove lwo fou. forces pnevenl oppoeile momenl effecis lo movemenl oflhe lruss. Delermlne lhe nlognllude of lhe supporling foecee. rn o.der !o corelilule o couple
o
&:ZtpLb
epwod)
+ ) . + 2 . . T - p t J) P-, "ro
l1'<'
t s) p-6 o 6.tr6lcm a/f (d@ .E ]]vc(F loo aowc ,Iri-F\vorlicol ot-r@ b lhuugh ^ ptu6 o counld.ctocxw; -frrceo qD
canPv d b-f' .re .tr q'I@t€/l}
lho sr9t6
-tu?F,dfte effei Aj:@.b
,bve
lhol w.,ll rro.
downwad
a@(+) -eo
r:2JL
-
aqtt
ridri oFo
t* ) RffiX fitob- 2€ if the s'/stedr reducco io o tarl_ \,.€.d rEnzdlot foi> d 3@tb lh.oir+ pdnl A pt 6 o .*t
3-t-:
sqqlb Mn = r4o
_r: :d. l:y
lo lhe |,aft -75o
=eoo(4)
oy
:99]E
G,.,E'b
bor,w o)
"*t oo'nF€cs,o., membef, oa-r|s I P = a@b_ eil-uolea z n_ fmm lho orie
o€ €r.own ;
l6
= 4ezlelb-(ro ho rirhl)
L, - ao _ ?pllfr aane o xrz6 it =-:!@'-+!l= t t1 ot o
2.e1)A vertlbo) forcc. Pol A b onolhe. ve"ti&l FotB in Fig.P-zst pr,e4"o" o reswitonl of loo lb down ol Db o 6€Ba+occlocl.wi.ee aauple c of zo
corEisls of o cbckw€
- 2ao @5'
B'-F,
B"t 'Ft
I
i
.rsLn
p]',:.o 4{o r! rcrc. aicled r4 lo the nghi lha,+ trE o.-dn of, r*,Y oEs ol Ot.xt- Recto
R: l4 b dncoleA rcrlicatty LJpol A B do*n oi B.
i,
A tircc
F4.I'-2ss-tn
on eooen h-E of lhe rEmbef,.
sl"ens,th of moloFtot6 il iR
tz
rned lho) ibe in)ennol sleeses ore delon.ined lrom lhe equ;.alen} oriol lood \ auple inio wh;ch P moy be re.E tved. Dele.m;ne lhie equi"olenl oriol lood $ couple' I
f l i '
tl l li i
2s Rcpbce |Ae egolcm of foroee st'4n oqu;votenl forEe lh.oJqh OV, o coupte o
;;""jii#;,...':i',X"":;3'::"'e:::.:mi: zF, = |a1.a(rka') t 22+(46) - t61 (r/JB)
E?) Reptaae )he syelem of lo,r-.s ocling on ihe r.o-e in rig P-2sr by o ros"rionl ,e o) n q, o coople oc);nq ho",%"lolly
lh.r'4h B eic.
)o lhe nlght)
0r. lad'zoo, f@,os gj|: !L99' ol C =
a farce P - 1@)b. Force P ie perpe|dioolor 1o lhe Plone conDeleffi:ne )he iwisling etfecl at Pon laining poinls A,B,%c t f"lDO tD
zso) A ve"licol shoft nB i6 sfl long h boited loo r;qid sup' end 6.re ollached ol l i)s r.,,pper pori a) ils lowe. end A . is 2t1 long Al whrih bor Ec ihe end of C ie oppl; rizonlo)
lhe €hofi .^8 \
in Fiq.p_2ss by on
b) +p= 1taa1.l P: 2993 tb260.) The effecl ofo ce"loin non_concc,nreni fon:e egelem ie aofined by )he fol)owrhg data : .x - +rJorr ,
.-T'l' ,ix-ao l.r"*
-so tb (6)neons do*nwo'd) R= lMa =C
6oG) -r,ch) = r(2) f - fo tb ltu'u B \C
l8
oe shown
zy
=.F, Ly Lt - 360/90' afl
belo|9o
2or.) ln o cenlo,n oon.
L, = +ao/46o:-:4 n;ght ol on,gin
t9
li' oc252) Dc\ermine comPlele)'J lhe res"llon) ol )h€ lorces '|ing in Fg. P-e62. on lhe s]eP PuIeY €hdwn
@
zF,- +1a(t/.t4) t *to 'tnoo t za(?f,a) -2ao sinao - :89.79-Jp: zFr l.j.a (/rz) +26o(9'b) t24o caced -.o.Jcos6a'--g:93_E
2 M; - : o a s ' n ' 1 2J ' 2 2" ( / n ) e ) 3 " ' G / ' r . ) ( t - -L,r,6 n 0 (- neJ.s co"")-Cw/ - 1 . 6 7f + r ) q h \ o f O 'Ly -1oo6/1+9.9 - 0.67 ft
z,;o) Delecmino ]he recu)lonl of lhe lhree 6rces oclinq on )he dorn 6hown in F;a. P-za,rtr loo.le lls inlens@lrbn wllh llle bioeeAb. Far s6>a desiqn, thie r erseolion should oc.ourw/rh lhe didd)e lhind oflle bds@. Ooes l) ?
iil i
trl
iil
,i; I rii
iill i
l
,,/66atf;
267) Ihe Ho*; .oof l..,ss sho./h in fig P-2o7 cotrie€ lhe given loods. The wind )oo& o'e pgrpendiculor to ltte inclined m€mb€Fs. Delc"mine ilre mognil:de of lhe resu)toni, iie lnolinol.ion wllh ihe horrionlol, \ whar"e li inle-
Zr' - Rt tr , 11ot tso e/s) - o Gmea"€ lo thc lcfl ff-:lqqlg
CeTaad"
) Ztt;A = -uooa0t) + poaa(b)'bo.P( = -228.cea fl lb (- meons ccw) ZM6 = aFlrb the lcfl of E \ xb - zzeao/2zoco =--€.t]tL(from nri&le hence *ilhin lhe third of.lhe bose)
i
zoe.)The resullon) of four^6.ces, of whbh ihreo orc ahown. in FiT.P-26e, ie ai o oouple of <€o tb-ftl clockwi€e fh €er'6e. lf i*ah sqore ie rfl. onosdo, aets-mine lhe fb""lh fo.ce
26e.) Repeol Prob. 26e f lJ.€ r'gtf onl ic aeo tb di.calca d6lm to lhd ght o1 a .slope of € lo rz passing *hrough po;^l A. Al.Eo d61eFftine the x \ y rlencopLs of tho m,bdrg 6r€e F.
.:@.+eti = r e/&>(.) - r (.ftY1) L:-Ec'?,b' P(.A.'tG)rGE5.ae)O/ra>G)-a'e.ai(h)G')'aoo.at(+) !-:!tgY
Choplor
3
Equilibrnrn of Fore Syeloms
The cyhM€r C ;^ fiq P-3o2 weigh' of cyl,ido. c q of rod Ab. *a)
looolb D'aw
o fBD
("i'"F !a)
ol!& o FBDdf pullq/€ Eq D 3 of lhe bor n D €h4n rn
P-.oo. nseu-s
otl hinges fo be sm@ih g n€loot
3os) the uniform .od i^ Fi9.P-3d3 weglrc a?orb b hoe ilc a6l6 of 9ro"',1/ol O Dmw o FBD of lhe rod ' tlegleol the besfuoth thri:rnoes of lhe .od b o56u-e oll @^lool su'{^o€s to
eo€) Th€ cable q boom shdwn i^ Fig. p-tsos eupporl o tad of 6oolb. Deiern1'he lhe lcoslle Col.@ T ;n lhe cobte b, to comprEssivc ,Ale C rn the boom. r Mcthodi (usinghorizonlot\vc.ri@l ^"".) r@se'
I6'n2o't
- C.a6ast
Cst^aE' - 6ao @
eb6l. cq r to2 t.alolo I i. tcms of T) . soo 1 6h 30' + (1 es.d/coeq.)(srn4s,)
Melhod r (u6ii9 Rololed ,a'6) 3@ - nEi^6o.- H@Edho,n *,J
A
cylindo"
woighing
aootb i. hold ogo:n€+ o sl]@lh inrod AE,n f''s.P-3oe.Det. Pqfl c.-
11- 1@. 7 lb P" 212,1a2 lb Method [ (us;"g sn.E
ll.4n6o'
l
M"thodr (u.i"9 t{\Y o'*) t8 of aanido. b
.Fn-o I P . .q @.6; + il co..o' p -.roo 6 66' + 41g.6os @1 60'
/-K
rltdr e-
MathoJ )[ (u5inq Fo.c€ r.io.gb)
)d.\'1
-ih.Ot
- .oo .t rs'
Pc.6&'- llac.f P - dc63r.'//@.t'
@
dsin!"
* .oo @
P= 4@,el
(6k)-
[N...a€ (.'",{r/@.F - ,+oo- l:3!aj6glL
+ n.i"aa
;.;-
nl) If the vdlue of P i^ rb. p-e1oi6 18o lb, d.r€rmhe iho ongtc 6dtvc il musl be i\.trhed w;lh the. Gmooth plone to hojd 3oolb b6r in equilibrium. the
:;.c
P = n @*/@,e'
- 4e.6os(,o.a4/-. P?194 lU
z.' r.l6in9 sih€ l.w j q = L
B1o) ,oolb bar i6 hcld at r6i on o srpolh plo,g bt o forc,- p irclincd ot on ongle e { thc pla.'c 06 shc'$/n in Fig. P 'eto. If bv e - ?s' dcl . ltc volrc of P b lhe nomal p.s.6u€ ^t eqlcd
2a
q:d
scb@1..
P'r@!
_g-
.,flor
l
Psins'r
Fo,.e1i.ongte>
29
!ir).
Datcdinc lhe co@!ft.i
to k@P the nogniludes o' P \ F he@ssar/ p equniL'rrum 31? In sh@n in Fb For@ .r'Ia6
3oo4^@'+ P-
P6 -1t3
4'
' 2@ st^lcb'
.oo6in!o. = Fsrn€- O
245 to
F ' aa/2 a'E 6tS I Pcd
7 '.uasao'-
z'; - 2@ @s 165'
oa z* (cszo)- zo <'x'*'
F - tu,87 \b. fo{Ee €v6lar e}i^g ato s1a) Fio 3€ rcpreechts tlc -^cu.Ent p k E fo m'nj6i"t of o bridge trus€ Detcmine tho voluos of to;. e{ullib.lum of thc lorcee u6ihe Rotoled
!1..) Ihc !1..J aoolb fon@ lhc aoolb fol% q & thc r}h a@lb firrco sn6rn h Fig_p_s15 otE fo b6 held in cquilibriun b^/ o lhird fo.€o f
Are
Mettod
3e-a@@a.. I r.a;a_ @ ro .4. O @ \tn = aao coszo- +/+@6ta6d\ /. -a)
frictto^b{s ,ou 6,s ta |\e; q h t + o t ? o o t D , \a@tb. D€re':n^: jhe oaebo\rhe nordot pro.€!,! N t4t. the o7tia. de.s \ the sm@ih raatuhtot ^urttu
.d)an*'
s6,'=
i
= 15t2rs
b
qb
A
tFh=o c- w.@+',
A46o'
33
ca ec.:t fhc FinR l.us6 €holn in Fig P'322 iE 9"@o to lhe nordol ore loads gNen ler oi A t') o hmgeaI B llg Ropaotronc at B lkl: A\ ^"^o.' Detc'd,i'e trE i-'i""o plac<.)ho loodc b.}, fh€i' reculiont
32!r) TI€ l.iir66 e,v,'*n i^ Fb. p-32. ic cuplo.'ted q o hi.sa dt A b o .olfe. dl p. A lood oF 2@lb ic oppbia ol C. Dol. ttE €oofione ol A b S.
zMA- o .ona " eao(e'"eo']lat) R^.451A,Alb= a62olb,
E e.) Iwo c.tti^d.re n q, 6, wc&hjng lootb \ zootb ,€dpcclivcty, by o .igd r€d cu.vc, po.ollct {o fhc anoo.lh cr 7". ?'"-"r"d lnd.icol 'urface Eho\'^ in f tb. P-a2e Dalcrm,hc lhc onato" o< thol danned the poirtr'on of equiljbn;m. \e
P.r.stn.d
e.cd'-< P |a-f
@lir,q
lodl.4s< - aoot@e loocoga . .oo @(eo-a)
lhe rj'ore eto*a h fig. P-327 Delernhe lhe votue ol P \F
oldg
@
rcoa-<-m(-so&,.".an^\ loo .G4
$(r) aAsti - 1so(6) t ae82) f - 390,15lb
l]!s-i
t6<
- ,oo €nEo 6'rF(
- rod 26a@.
ts(P)snsz,+ - twg) -dha) p - - 1a7.6,4 tb (- @66
- ,o - 26'a3's,4.
colnptce
10 Mrl FcG
ea'l-
P@6t4
zso ra (aseai)
- t6.o
- ( 1.'.6,)(@E6a.a)
38
- a
39
&orb-l I
€s)-The .oof n I b. p * ,s [email protected] b./ o mlk, -1tu6s o ht gc al B Fnd the 6jues of lne rsc rrorrc
-a,ltu-op
ot 4 !,
.{€o(a)roo(+Xe) +R, (1o)- !0066) - o Pl= Feo lbs
. R1I R, = 3oo r rood4) r .oo RQ- s2o b'es) DelcFmlnc lhe reochbre R,\R, oT the be.n inta P-#3 looded;th o concentmled lood ol rdoolb &) o lood .oeling fnzn .e@ lo on inle4sil/ of 4oo lb pe. n
[email protected]. r@(@.6o) - atoo 60- rsoo rb (cepr!<,ir,) t'a) Oelermiie the liJr.e i. €och nerba. ol ih€ pro$ roof lruse ehoM o, E, 'Y /@ u5iae d* ^c, ze".o &=1s&bc-F6 ,Y' 4/ l* a lhc at-,s,rcto,6 .aS-ED=DF- asoo tb-..-C
at c. E aM{-o.
to,.c.
€oo(e)
,6oo(ri}rad(€)t = AY(3")
Aa- adttb
'/,
s--+
l^w Bo " i6o tb (cdnpc66'o^)
&=4q-_Aq
co = so(slo) -oh
_,q-_es_ g .ti5
:. co= 463.3i rb-.-T
DE=O
6l @
" DG
Ac - 2/r-n q) t cE cF . :,64)0- 7A (ztee.az) (F = EA . 2400 tb --- T
AS - +s@ lb ---C : FH AC:6H - 366tbr-T
b q t ,O h ' 9 6 | b .', Co '321b (la5o'r) dt C: 2?r-O AY TDA ' BC gC ' 192 tb0€'€ion)
f.d-
w-.E
6hownin a1t) comPuie lhe force in eoch rn€r'be' of lhe lru6€ a'e shlfled vecticallv do" f,A.p'+to t lhe loods o{ B\o -o.a lo oaa io lhe loods dl d b E' wil\ lh€re ba on/ cho"gp o in the.€oohbne ? Whioh membsrE' if ohY' would underyp aho.gB In hte.nol,
6rce
@ p l E ,
@ ?t. F,
'
Rw' YEcF
€hown in rig
oonsid6.i.q
DF - [email protected] 161o1b,..-a the force in eoch m€mb€. of lhe crsne
lhe i?hols fi?u.e.
02 |ca - ?occ@B b. - 6. t e. - z.G>(s)c.E126. b = l3.oab'-
- 4,o t2@r2@r eod P^w i Rry ' 1600 lb -O
p,y rp'd
@ pl. A,
1MF.O
tn | ,
A" 22,Epl
9^,Y (eo) "4oa(4o:) r 14("j,o\ t ^blao)
a bo=LAe,
+ a@(?a) ' eealt)
bD6D5o'-
@b61. lhe 6l]3 of R^v in 1Rt! - 1@o - ego - 12a la
+eo++,/b t ac t {nGe') k1e8, a"a Bc- 7o'o+ ='7@lb -
^ 3. B^,-A,Bs,a
-C B - 9 s 3 . e r{ 9 4 e l b
@ptc. tF!'o | 2oo bc'Gco 7oo \ c0 | 2oo ''
AB,^c,or, \oE of ihe 6'i6sa-e < t-O t2(to) e.x <@) '12'(.) 1ia(a) r 14O')t e(1o) I R^v - lox
/t
^?
l"'
6,/"1.
^1)
/1' <{ .// lr/r'
^--6-
oF (22- 2a)
r y@ DF(a) Df - e3s
- 42.s k?e-..-C
'lho melhod of ecclions lo compulc lhe forEe in lhc a2r) Usa desc'rbed 'n mcmbers DF,EF,\EO of lho conlilever lruss Prob.+11 q Fi9.P-/r11on Poge 92
Fv(so) - 4oo(ro) r ?ro(ro) r soo(!o)
oe. ao/3 rS cEQo). 72b
^-;t
F".@rb
7eoe4.)= z@(r,) i eoo(2a)+ a/.rsbo (ao) BD- 491,93tb --_c ZMF -o (p-@t \^S CO dIC)
rMe " o (Rd6olving OF ol D) 3/rE Dr (ao/3) - rco(ao) r 2&(^o) OF 'a6o.56 lb -'- | .MA'o L ft
ff
2aa(adr eoo(2a)- 1G coho) co - rn1a.a3tb ,-_c 42.) Use the helhc, of seclion. to detcnmtne lhe force ooting in members 0F. EF.8(E€ of the Howe irues dcgoribed in Fis. P-aas a^ page91.
A\ (i4) - a@(4) \ xro(b) r
(Resolvinq EF al E) ,Jo) | 2.to(2o\ Go) - zoo EF = 335.44 Ib - -1
Eo (2a) - @t(ao) r qno(qo)+ ca(rc) E6 = 450 lb _"- C
page a2, t\ coma22) fe. Ia ihe desor,bod pute tha fo.c-€ in me.nbe.s BD,CO, E(cE bY
i" (,o) . Eo (io 1o"3o) E6 - 16+s.4s tb --*T
.+2+) For.thc l.ves
?i-ry ]Y 'ne me r L cfllt d or
she^
ZMH.o (cccotvinq FF al E) a$(1o) ' EF 6'.b' (2o) FF - roo lb-.,c i^ FiT.p-a2a,
dd{erm,ne thc fo.€e
E ihencheckrhlsrc€u[u€;ne :f io,nt HilI. lo
sec'idq
oppr, thc _elrod
br, hsp€l,on.
Ocf,a.dnc lhc fdcc in trr.c BO,C,. \DF of lh6 nocotte .rt lrui6 €ho'6 f FtO. P- 4z
tMo:o At (16')- 1MG.) r ,ae(91 Aw ' zaOOlb *'
&-aleAa AE ' 25oorb-'-c
AC,cF =tg.o tD-"-T
c"b.)|
r.ID(6) " @(2a)t cw r t6oo tb.
fe(ta')
r/&
oE ,t 1@ - &et @ oE - 512.45 tb -"-T ot Jornl D, Zli6 -o (?.ov6g co ol9)
1/ft DE60) = 3/b ez)(co) co = s@tb-''- T
4k co . r/tasD| y'{ooE
[email protected]!5tb-..-T ,r2G) Uc6 lhc 'Ethod of ccctiorls *o aotrsrmirs +he force ir.r'nen _ b.,rc Dr, F6, 8\61.ofthe lr;ongulor flowe lrves stbw. ;. p;r. *+re llinl Fircl oobraine b/ inep.,ct,on lhc forcce in ihc rob l'Emb€.4 of the .'ight €iCe of lhe irucs . b], ;nsp@lion *cb tcnbert Jh, r, |lt, \Ho corics no lood + - lo^', rh - 26sa' €vLFo, AaC6o).2c,o62..6r.(t ') + a (@4 26 s 7) (4) - 2 (6n 2o.stX'\ - z (o)(si,n 26.e7.)+
21.o(d | 1t@Gr). +/s sF (16) gF"2@b---c
A,(zo) - [email protected],.110, zo)+(E^ %,sf) (z)(er1o) + ot (1s) tW. o : 2:4.(.a') = -.(a^ *fi.Xt) 6I - o_,rseKip3_.._r - ,(5'n?,.!"Xro) i oF(6n ,..B'XEo) +
76
Ay i 2.+6 Kipg
F6 - 2.24 N
dclern\^c
l.usc shc^tn i^ a9'P-429
0F, FH,Ft,6r, g\ ro.
e+o) For tho lrono loadad o€ shofn in fg.p-44o, &lor mirE lh6 lbrizonlal \ vorjiool compcnonts of tf,ro pi" pros. 61,.Dol B. Spoc;fy di'Eotion"s(vp o" aou,t; l6fl or right)of tho lorso os il oot6 upon member co
2l G=o, s/@ or@4)- 2$'@r) \ ,.bGo) r a@Q.') oF -- 12564
lb -
ar@\ - 24(e,) + ab(6) EV. 590 tt) :Mr .o N (.r) - 36G\ - 21bQ) Av = 360 lb
.-T
lefl of B-E
at^t.'o.
5/R rr!o)=1e(4o) r 14o60)\,!t(@) + 4+c1=4
'B00(6)
8n - t€o rb (lcn) bJ - esatb (dorn) 8r-2.gO-39O-a
+
is hin96d ot A &,c. Fidd of lho hinqo lbiE€ ol B8..)
aa5.) Thc frElne shown ln F9.p-+as iE .eupportcd byo hin96d oi E k, o rollor ot O. Computo iho f'orizonlot \vcrtiool componenisof .ll-Dhinge focce ol C os il ocis upon BD.
j 42c(1\) - Er
2ao(e)- a, G) - o O' = 360 lb
I'N1 i;pkr
BH = 4€ rb to tho righl
of lhe h'r4o 6.ccs ol Bg'c os.ihev ocl
,p."."-P.ry'
t
zN,,\-o I Bc(4) i cv(s) - cH(b), B"(z) - o BA = aoAo) +a2o(2)- (e6)(s\
tho wtPlo Gono i Av +e! -12O 'O E ' t2b'to E! = 6a lb
aPA-o. e,D(3/s)-AA-o eo 4'4)AA BO= 2oo)h --'C 8&\-a '. oo(4| rc'(a) -bD(4/5)(8)=o EC- lCOtb*--T aaa) Thc f.omc etown in Fig P- +aa is suPpo'lcd b/ohingod oI A A' o rollor ol E Compu{o +he horiz'nfol \vo'rF
*i1h rospedl to
^r1 "-' :[1o=o:cf(5)rc,€) r,tz) -o Cr. 2.4(2)- @>
lzo(4\ " Er(4). o EA ' 12Olb aVr.g.1 l4t- At-o E$ 'Aq " 12olb oi i6olatirg bor A_6 zMa-O I A!(O)'120(4) = o Av -- 60 lD.
Zt ^=oi
zMe"o (6)}.v-
24o(2)
AY-€Olb
CA(3).7oG)t@
8l
+a6) n +hr€c-hingcd oroh i6 coflPoscd ol {*o {'uscs h,nocd looelhor ol D in Fig C-+a Co^pwio lhc comPoncnts pt tio .co"llo. ol A \ thon find tho fo'coe oolins in bo's /lB\|Ac. Hinl: Frrsl r'6ololeoocb ltu€6 o6 o frcc boaT
-.._1 /c_- _ 24a trj. 24o tb a+7) Two frusgos orc jo,ned os sho*n in Fig P-+a7 to {brm o +h'!o hlrgcd or€h Campulg the horrzontol kvo'ljoolco'Dpo-onts of lhe hjngo {b.oo ol B tN. }ho.' delarmino lho }/p' e, mognlludo af forca n bors BO e'BE ,
z(.'o ,.o.b)
.n
*,e
c. cf r-'lo I o t-- -t) ---1 at!2@tb
wl = 100(6)
lofl
lrusc gr
lG
f
lR+
RaG) -.6c8 (z) R4= 3a1tb=Cv
G
+ 24o(zc) r AA Oa) - A" (4o)' o Av(a) -AH = #ao -@
l6.loting
a2
@
RzOa) = 2o.0a) i 2e&(7) 3ca@) R. - 2120lt) R3Gd - 2s.n3> + 3&(14) -4ra(4) Re= lleo tb.
83
lv'o o'd Tho bridgo sho'{n i^ Fb P'aag ocnslsts of ot ofgrovilY oonlor €oolion6, coch *oighir€ Ctn' tone 12o wo;gbihg 6, hingod ic o unifo'm A, B, E, .',\ F.
N Go) - 2ca(2o) so(2a) Av = ae tong zvl^. a e.Go) - 2cp6o) t s>(1o) w = 212 lons tc o 45o) A billboord 8C woighing {ooo lb is subjccicd Fig P_aso Ncawind o.cseuro ol 3oo lb por {l os shown rn hcmbors' doiormrno locilno lho wdrqhls of lho supporiinq E( F' 16 66-penonts of ihe hingo fo'cos ot A wnd PrcEGu'E = 3oo lbl{+ . 3oo lb/${ x lO }i
r ie(o)gr.ore' 3il1l,#;ir'1?:;"d"i''lioill l h o n e loe.Ic) lc€E thon e:(b) cq"o'
lhone- ih€ bloch wirl not siide down )',l ii,i' l. aiter ihe f'rci'onol i,i.,""j li *i,, reloin ils poeil'bn be'ou6e
IT'li"S jit. i:1" r ;ff ,:\'ilJl"Jl'*, ?,n,'; ta'c'l:ll^:'",11;i: iir fi.'iq n",i"ther'aro^ot, " j';* i"x',;-" ?iii:.: T;:iJ fiil"[,:,"';tl:: i,"' il :.T;:il#;Tf ::;::;i,z * #.2::-i,:;^, mpc^d 'f aP" tpt tr y ta \)4w'
il
;;?
,.4'"""o
5a7) Ihe eoo)b block gflown in Figore is in contocl wilh o ab' inor:ne.I\e aeffticient ol f.;cl;on is o,za C4^p"1. 11,. valuo of the tuAz.ntat fi.d-.e P ncccseonl io o) j""l s{o"{ prcvcnt molion down thc thc bloak up tha inc|ie (u)j"gl (o) Il P-aoc lb, whol ie ihe o-ounl \ dr-ecl'bn of inojine. thc J-.,ct;o^ fb.ce ? > P - COOIb 6n6o's6' ;nseq' F.n
-'l*\
1 wilt €lrll ba in o_
mation la
'" 'o""u
g'*i'tl':lji3'#;::L:1 5 *lrl,#,i.]:*':t io etort the molioA
P
=
P= ftatb
P -- +oolb
ql'a2s..s-fta4' 11 .-r N
p
. t c.) ^* e,+at4{P
'&^"
T\ b
w
^ 2+:o
P^:- - l10 1lb
88
.
5oottr
-"-^J-"il,i"'r'
*{ 4K",",J41\!\ t! A\.V
P :4oa(Los15')t f
r ' 70lt tb
Isao\l@sao'\'o
5@.) Ihe 2oolb blook shown 'ta fiq. P-soo hoe imponding rrction up tho plone cnoced bA tte tarizonlal far:e, o{ ltD-b.Pel. lhe o:nffloienl of slalio lriolian beiwcch lhe conlac4 €u.foce6 -
5Oe,) fl,e bloak, 6hown in nA. P-@s are cnnacnled bg fldib inetlendl'to cord6 possihg ovor fi1bt'bnla6s putless. Al Al]rrcnefftoienl ot frrclton ore f. - a,oo \ fk- a,2o whils ol B Canwte +ho nog.;tudout d;rcc lhos orc f.-arc\fk'o.@. i,bn of tho friallon lorca oali"g oi each btoo".. oro) Whot weighl W G ne,coe9arlJ lo 610.l tha .essJcmof hbakc ahow^ i^ fig, P-o1a novirg lo ihe F;ghl 7 lhe cocf-
89
frbr'cnfof fiichon ie o lo, \ bo fnrolionlese el
..og.
r
lhe pullege are, oesumen lo FBO or $oaf, Al
M ^ L ^ ', *''21'*' i*\"
*rl-o
!nr) trnd the leosl rolueot P rc.quir?A io cousc lhe sgs_ lcfl of blooks6how in Fig. P-sr1 to horo impendirg rraiion lo the lofl . flv h blooh . fbo of block^
{Fs.o: li:roo- Psrrq = 1oo T slnrl,rf sin7r,69' r {Fx'oi Trf-Pco6a -O 62", r(..z)(w ps:,r"\)_p6q "o !!Z99l!_ - A2Pstn\- P(aE<-o 12J.O2 p= 12z.iz K".zs'a"r+cos"<)- pt e2Ib."o -s!L. P(o.acee.s6.<) ais,,- ,,-r" 'p- 124.0lo. o . 2 a N q- a h e . o o.2 E \trnq - iorq coso<
, :f!
6 6 . 1 ^ 6mArd =,nrf
l^' 6otb =fg -O: ll. ' JoO co6 ro' HB' O'1,6.+Jb
o5Y" fFD of ElazY,CI
l*l
--T--
arz.) A hoingcncous -blook .w,. irvgr,r vof r wejghl w t Y rresi EDr u upon Pn rlhc l ) c Iinnor'ne l9tlown in Fig.P-.et2. If tho aeffioicnl of lriclion ic o3o, delerrm o lhc gleic€l p!' aletel h.,iah+ hA ol ^l *,hi-r ^ for€o c.haight whioh o porollel fo tha incline "at "pl;.a 60 {hol fhc bl6'ck wirls_ tu6 uP tho ;odt;d w/o;t lpp;,4 ove.
p=ttl=F Z F ! - t t : t 1 6 h t aI F 6 n b ' - P ' 1 o o o..113)=1oo N(stn6a'I o sln.tBd ' ' 1@Z 173'22 tb i w\r
P -l,l =(o.s11i07a'22) = loo tb s15.)BlocKA ir\ Fig.P-s1swoig'r€ 12olb' blad< B weighs 2<{jlb' cord ic po.ollel lo ihe ino|i e lf lhe coeffcic''l \tho of fri"tion lor oll eorfooee in co-tooi ie o'25, dcleirlne+he dVle 6 of the rnol,ne ai whroh molion ol' F rinpende
R.'32311lb. 1F\-a, P. B2s;nao.a6 t fu 6tnaae6P - 1 2 6 . 6t b . s1s) JF lt1 Psto, l4o bjoo\s ore .b^^ei@ bs a sot.:d slNI oi#oc.]ed to eoch bto.t, w,ln pjo6., lrrcl;onte€s
[t lt- aeffrc enr of t^,cr,b. u@e. eo.h oto..< i-L.zo \ € we6hs 2rotb\ Fhd ihe min weight d A +o preverrf Irotiort . 12A
;^r.*'
.
R,1 -"'^(a,'4>
R1- 1237 sin (4o - e) p1 - t u,1 (sin ga'cose-- cossa'€n e-) Fl - 123.4coso-
92
93
lL.A26
:.O - la,O+'
c . 2 sn$,95'
7 0 s.z+-o+'
c - 201,9 lb\/r'
a
aOlA
w^ . s98.3lrt
of friot;c,^ ut\aer A to p'ucni w-.e
t'42
rnolion-
e-113'
tF,.o:
.ln4.r' C . 2 J 7 .S + l b
r
/ - Er " 2 0 6 a 6- o- . i e /
l rr
o|ocr,on,.rr
ihe bdl,e 6u-foe
szr) r" fis e-s,o \f J.a 1 urde. both bloois \^ wo6he aoo b.rhd he. nor' *eishf of F thdl cnn te 6lo.leA oP lho irottie b9 appl)nq Io A a e's6l wo.c r'cnzoalol tcr<:z P y'.!-.o.a
at b: t-a.t-. FBO
z4-o : tl - +o3 I c6in3o' zJr-O: ,Ko. Ca€e6' I F stc -caeao't @,2o)(+,xt+cs'"zo') rb-.(1oj6)-C-374oztb.
, e ^ t t . . a , t @ . o r 6 h & - . n F : g u - w .t h e a.e 1 ot t.ato.^ ba lhe tu6i9V lh..ad E o.iq CD^p.te o:r^ A oi *y' {.,eh, ^ @^ be pto.@ ta ptll"a\l :: :, 6|pPn9 cb'v. thc rcd ,)er,ar 1rF derqnl
95
\ ? a - 1A l' 8D
2M^'O
w(L-1)t r,@) - tib)- o. al$Fl t o.2(z)M-2Y - o o , 4 -Lo A r o A - 2 - a
Afr-o) N1'Nz
mo,e€on ..st. or L. y,1trJs,o,.a. u.*
Y^*:' f,-yt,ir
^ o t6) tb n a1 o l s t p p . o q 'l h' :e" :a"r-' e
.,.mb b-fd_e lE I , fGt ', .o^ -- d - ,, o - ", .
;,?""ll":,.'.::""'
L--L
n',t 1-o,zN=o,/tt.
.,, e oI j t o r c + . , g n e e b i j ,6,q .toda6 at grc,t.t! lfF rDrof^e bdda .. p.o.4J oga.re. .frtn a "erti
L-ein
,
w-- Flt F.- o.2\ (a) W= O,4 l
@{. di 1b * u.Io.7s"x
. -r, : aJ ,,^,
, i,"-,"trl.)*; \"lz A\Z
Lon
v "?
[^"'"
.o^ '(^..o)
Tanzs'\ '1t.tz . -Ion1r, r tolon.re (to'z''
tl
' 1o" to'', ' ,o
.ng-ec.€ad).$a(x-s) x -sft. szs.) A uotlorn lodde. 16ft lotq V, weigaioq wlb i6 Ploc€d V one ed on fhe grcund \ the otne" hond ogo,hst o ve.trcol woll Thc orgte f footbn ol otl cnoloal s"nfoces is 20'. fthd lho mrnimum volue of lhe onglee ol wk lhe 1oC.
160x - e40 + ^ _ 5.2s 11. 52r) A. hon"gncaaG celincrer rfj. in
''*'a,, n i,.q"" i;; ,";,"_ d o";i::'";J.^l"lf* or f' n'oi G w"
to. on co. t..t I eb,,o.ps cad.l
! .!',.?et6" noq^l )de ol the cowp,e pllo ' rat e1u'red dq rctolrs """.k-;";;.""
"lr=4,t**t".,'S \ to td tvnro'
O g.rilrb
wqr'3@lb I
ot cg:Jilibnun
qr '.\lJ
lr\R\"
Jl___,.,
4!l\"
.ffir:= 4,t\>r4;rr
I
(!-L6tne)" - to. n'(a-L@ea) Ia^id r - Letno"lon2o', + ton2o't @a" r,(to to't lo^,a) "1."{; L@se+ Lst^e
27on 20' L@6o I zLqtne - L6.t (ron7a'ttoh2a') lLst
e'L6the(ran ld t ron2o -
-srr9 =2,39i2
a.Ion zA-L
O
+-:Po:
Ton2r'!od
'L.o.r+
{Ma'B
o ",r. (1c)r r,t.s) .
B l 2 o , a ) ( 1 , s( e) to f t ) ( 1 . s )
9t"
:,x^:-T:::?, cuti^der;c^*z counte.ciockwise-
t L6nt+
r-"o'-
the citi'
d, o6is..
D, @67s,
t1,"i'c^s::".
n7 .r,'co376"
-,,J t""rc.) ",,o n1=2os,7e b
... n.,tz6stb
. E,at.
_ 0 : : f U 6A n sr'.) l-s1tuo
,-
l*,1
\n
@ (!,d__h(1-a)
Io sio'l
..t,.ph.
=(to'6)(%s76) = r"tis.Gt,ts) n'77,41b. f?= zo,s tb. dFl-_d,n- lhe m,n,mud h c , r r z c n l oI
gto of f.ioltb^ ie E u.dd coch btook, nid p di'l>+ea rs.ol to lhc as' i.ottio thct w)| ooueo impendlnq tution lolto |.ll. iEdoti^g ba. tho O
e.1{
../'.o.26a l
l
.r__J1
-s<;.
_9_ c q'Ion6c7 U-o)- r6ad ('.lo) J- la.r€'7 (t-o\'-'^.d(^4) ' -Idn,f.a t ton.(it, lo^bs'7 = -1a6L')1i1ctan1d i",s\ ,Dtaooo' r (ro" oe-rton+o)- to lan ro' r.(tonzo' tlo"rc|) 'l= 2,81
< M . - o , p ( 2 , 6 1 - !-)o 2 4 14 ' O
3 . 2 +- 1 o r x ' o 83418|= 0-76tL LdngihzL i€ totol "tl ,;6.pr""K of wctsht W \ ploc.d 06 !;ra'a ia fig P szt wilh ll ends ia oonlacl w/ ii;"a'i,a do."a .Ttu orgto of f",cl'bn \c ts'. Oe|ctsioe
98
:n. tao6;n*'t rocqn+' zn.o, r" +a-;zs<)o-o-*+s. p n. 2e2,8+ tb. (o26s)(.rr.ei t o - p
rii,l
,,y'a.,
p:Zq€A bo. .^8, wa:tsh:,as a;b 1i€ ro6tq..abe .1
lrlcr'rnlfs6 p:n- lo o aloc, *e,gr,,aq zoott as 6ha*^ h lhe . ,/a-t @ wat , I a.26a Fhte u oet t1e atocr . r.a.?o Dete.n;no tho fo...o p necica b s,rc{ nlolb,1 +a tho r;ghl.
99
a h ' O I R r c o s a s '- F , c o 6 7 s ' 0n.a2) cc &' = R. - 3e,6a tb
t " r-l!_f,__ i Z F g ' a t 1 1- 2 o o I A r d. jo1.6 tb .O: P=AAIF
'
1M^'o a24(b@'6) r r. ra+E'dB a"s-L'a
P- 2a64| bz)(1o1.6)
-o tt.\@.+s' | (o.t6t)tt6\.b4t6'-d'\s'na6 ftg.q = O,s1gflo Na-2894lb ' " Brt Aa 116 26e'4 ' (o %6)(2Bs'4) Fa /^t15
.'.F!"o : Ar - +2+tra - so| 6 h WED6ES 53s ) A *.dge
$,.) ln riqlro ,dcle"nine the votue of p Jusi .s,fficienl ro €ilorl the 1o'wedge u.de. lne 4oo-lb btoch. Ihe ongte of fr'otio^ ;s 20' fat otl aanlo;ctsufiac?,a
r*s -
, t€ bger'r ta .Pt t tog.
81.".!19.4b,
1. a rt e )
Iho angte ol frialla nor ' ongl'< ollho
lion br}t'ean lhc \ldgL\lhdlaq,dd
!::!rJ!=
s38) ln Frg.sst. aelo"mino the yotue ol p oct;ng b te 2Rq.| - 'ra1-P'**'
,
aF'-o
'
tetl rc4u;.ed to pult Iha \eadgo oul fmn urae. tE 4<>otb
61tt)'P
'i'"'*P]"e
aP - ,Rtd.|ttu"4&) ! (@Y.Y+).al!a cos Y.&EQ 'st^P st'"{' cas.t/2 - et.d st "t/2 coeq
Ia'/ - &1"1/' s.6) h fiqur-, delonninc lhe nrnimum wa'ghl of 9loch B lhol gloohA uP lho )'clino $ttt heeptl ol 1.,61o forco F 510116 eurfaco ol F lltc weighl al A te loalb \ lhc ongld of fttclion lbr oll surfoces in oonlooJ is ts F B oo f n
iF'
LJ--l I
l$t 100
,*F{'
L?
--EL- ' 3L
'-f={-
_L'
-P91:L
-
p - zoej
Ib.
$s.) lf the wedse de€aribcd in llusteofton hod o wdghi of +tttb,whot votua ol p wautd b. re+ui.ed (a) I; stort lhe we/tgo uncle- ihc bjock,\(b) la pu lhe \|edge au1 f.r,m ctn
l0l
*"':+n"" #/ I 'i--)<---l vtnr.
dngiE of fnbnb^
' 19
-&- -_:99-
$a L./1 V o, - +aa -;"1or -;*'
wb
Re- 1og.g1lb 1Fa-o P Oos,b1)c.e't lE.4.ni p. - 91,Etb
nW' R 1' 6 4 1 . 1 t 0 .
!fr,. 'p-
= ql's' 2t.2 P^ - ft,t Ib
s+i Detornirc tho forco p rcquircd lo €'to.t thc, wcagd dron in rhurc P-eat . fhe @"4a of lni4rbn lor o svrtocos n ca,lool ie P'.
A*
fOD of b
P - + 1 6 . 7t b tr\- a : ?nsi..' tW @ts' - o
R, - :&_e:::
F.@6'
afr.ot R..os r') -w
(-€inrs.
_L btoars warllri€ z@tb\Esls+o) ,4s 6hown in Fig p-'io,l-o qfoae bo P!€tve orrjl b4 a tc' oft lo i9 cr. a ton:anlol ic 1s' fo' dll ,@ioot cuFloco6 w.age' lhe ongk' ot l"ial'b" p ic rwqoirea td €to.f mov€hal o{- thc blo'k6? wroi nr"o ol t1o* woqld thie ohswr be cr'd€cd il ihe wor'ght ol oe ol fho
s..) whol lorco p nuel be rypiea to thc wcages snom rigt o P- s+2 to 6lel ttE,n utu a- +t1o t',och ? lho ot.Eltc f.,,itoi for olt @^l
ar/1y
. 6't A. R, . 2aa 6€ a'4 .aol;/
Rt"t"ztv
aFa.a ! zPn'sn'' 'P P. ..(n e)6,^3o'
3,:::3 e
to2
/
- 11,5s.1 p-g1a.+lb
lo ts@tb ?
V
eooo
R" (costs' .
Rr(ce"'cnc'io"rc) - +oo & (o e7a)'+ao R l ' 4 1 1 . l1D .
;a.eaecd
' -R.6nni ,
I R46D,€'' +oo
a,ryc - 8rslrl/..
htcrc*< |\erc
1 6 ' .@
&. A.coslo'-s.rb
P
-
ed,q
_f_ '_le.u-tb
103
sa3\ To adju6l tha wtbol podlion of o posllbn ot o c'rlvn^ €upportilg a 2boa lb laad . lwo s' *adgc6 oro u6cd os ef'own h figuro p-gaa . Octo.mine thc n)rco p ncc66cory lo clort thc wadqos if llE anglr, of fiichbn oi ol! surfoaee is 2a'. Ncale.l lhe (r,ol@ ot lhc FolJc.s
G':,o'*'" - -..'"*\ (et
,r'@s1
,
1 +
st
tu'@-@b'6'aq
-6'n2o'@6q
j
a,ee-e.q)
(sDo.-G-&J
o4"
6,n<
. (*-".,
*"
Grn2o'-€ra2o'
_
*) ", "_ - o+66r
= a.446a c< 2s"
Io^4 gS!^RE
P opp)teAol Ihecra ol a Ie.6 zfl. to^g which witl €+o.t I'rling o *ebht of zbns (b) whot wtue or p wt| yc-p tE
s+.) In itlue. P,oa $+ lf tha atgto of fniJto^ G b' ol illrel@+e o1t sa.fbces i^ @ Iac+ dolarnae tho mo,imum wclgc d.glc. \
lnor will grve
lhe ^edqe
o
ne.^ant.al
56]'EW
sas) A s;Bte lhrcodcd jootca@q hoc o piloh oF o,s t^ a meon rcdius 1.a,5 ar n. Iho creft oiaj \ of elaj( trtctbr of 0.1s,\of Alhetic f.iot,o^ ol o.1o (a) Deternine tE torcz
R - 23aS.4lb
fBDol B i, ..N
THRE-^OEO
od"anlo7e,
ft"a.1e
P' 0"4)(,,') u" (.,t t ".2)
p,.6s lho" lh- wcrqsl w or Inc tlo-|.-.
:.e,6",<
l'as" P"+:Lro.(ote) n' Ge@hn\ b" (.ata.*')
t
j ' sj +JbE 6a5.) tho d,Aonao bot||$ oalo61 lh.cdds o^ o ,.iple_ lhrcoac4 oou"** ie 2/.3in Tte, h€o^ Mdius i" zin, lte coemotcr,l ar ff,ot,oa o.ro wtot toad con be roised b9 eae.lirg a nonvl ol zaoo tb- ft ?
- 1a&. n1.a'
l'l*
pilo6.
€rbltllleP,
taaa_
-l srPorq)
6nO,-)
(s1ntu';.(6'n .''44
- f_1t
'--
P
en@'T ::) "
qa+,s
;;G;;'4
,,6-
paa
€"1&r<)
-@1;6'"^) hab - @s'o.6'n<)
-
2/.;^ .. Pilc\ = 2;^
I baa
l"
(6,^@ il j6 lnpl.
10^6. ?;Gi . o lee lr - g,a3' zFr
lfl '214.
r-wr 10^(4le) *
ihedcd
f r " l i i p r 9 r i c _ p + . hb
f -aft -
- a66itl
2oootb-tt- w(o.ft67rt) ton(srfie.ot
2ooo tb - Fl . w (o.o1E6e6u ^)
r04
to^f . oaa f ' "'tt'
105
vb
o"s;.:r c t"a ic G6o' e4 - .'eo'
- 1, . 2 ut . 1"o;"-,{*"k)
:-.;tu t"
tb f, - 'o 1"' 1+>- 11s7 ... ri "-j1eLb.
bll l.w
36t ) n ropc "."tppd twiac o.ouit a po€i {ill 6uoDonl a w;'?hl af aooo tb wh€.\ o tz.c€, o/-,so tb ;6 s*led ol ,hc o_ Pilor. . o.zEi^ (;,
@ d1lbto
nEadd
@tliPrSbs 2) "-19j14: - o.os31 lo^e 4('.s'lr) € ' lanr (o ossr) ' o oez'
I - r,t. ta^(0 ra)
- 14U rgF\jf^) ro^l b.sz', " . a - ' ) " T 102,3lb-fi srn) A 6i^gt? ltuc-ded 6gua@ s.Ef t'x. zvzflraae / i'+'ie ein . The lt-.odI atanolc,- is a,6;^ \ tte ootElda d'2rt* ',c cdff'ot^l { f"iol,i'n o.ra. Detcmi^e tho rp:r6l r*,<:zset'rg io €to.t lill;ng o \"t-li.ral otl'al lod ol
r E- w . r n ( d ' e )
.
B€LT
'f,E)
I-""'
nq/".ti-z.e')
!h.. o d. tulu:f,;e tte aetr,otc l cf ftroljon. ongEof co^l&) : /2o. t.rorb
,"+-Jt-L^€?.t(,*.,tr")
r\_-4)
L^ so - | (lr.s)
laat,tb
I ' Jt-!! t2..7
'=> Ylo e's
%,) A boot .,ert6 o pu| ol +oootb on tls hoween Vo is wtupPc.J obaul o copelen oa rhc dock n thc I.o.3o,ilo.^ no.9 lu.116 mu6l lh6 haa,sa- rckc [email protected] rha o;taa @l|Dl lfp pull ol lhc olh€. doos ncl arccal srto_
Ln-\-- tp
L":,4a - !t4e'_. oaa t | 1yk = e31j' .11,6t g^a.)
tnL.
P
A
loftlue
of zao b,fl
+
t+,ot -a.
6z7.f ia6d
oci6 o^ lhc
= _?:EJe!r--.
btukcdtuh
€hcM
rn ri
P-s53. Jf lh? brcN. bond h in c.nta.i *ilh lhe b_Ed.._ lhrcvg^ 2sc' \ ihe coemc,al of lnctron ,s oeo Detah.,ne lrE hfta P ol tho e.d or the bmN€ tcv-. f1 - -14')L@'\ tu) L
JL. e.,az .. r, , T r 3|a
l
FRIATIOII
,/\ repo tuttg I v+ turc orcu.d o 6rolio^o.j ho^rnloi dF.h i6 ue.a to s"rlt-l o t
t(Xi
( r-r2l(rar-fR) Tr..L
.q,6otb
ft (o tcoo) . aa
ru
. 2+o tbfl
-
rt ,4ee.2ab
il
plre^- c*) . r, l?,:^ '+) p(1.333fl)
. +qa.a3 (o.l/,61)
ZMp'o
(9T, r rz(z) @n" Pttt -5 f 2 , - 2 1 3 - 3 1 1' o ,s (!/,t 2 (a a41)w
P'617tb ss+) Jn F,a p -sE+ , lE
acetficjtql
G o,2o b.-+qae^
of fnot;^
rdp? b tho fh€d drum I bo&<-n oll ed.tooea i^ conlool. oa.lc^. m'ne the minihuh t€,ghl w fo pl€lal da,v^ptdne rcirin of the -J,-
- t,at
o..(r4u*)
''
,
a(2.ro)-o
6e 1tw - 6& w= 7047\b
ft'1A7Iz d1 'wo636,57'
Iz -tu " w€i^36..)' 12 - (a,.) (q @ 36,6, - w a^a6.?1' 12 - o 16\tl
T'
4F3-a | \2- 1o3o.@e6,6J.t i1
rl2 ' sod I rir .€rx=o 1 Ir r Fli f" ' Pao 6i^ r6ar' \ | 1t:ti t1t t1- 6aa H . . B o o t t 1 \;
= 3oO 1.+2W I ot6vl t a, | 6w' 4oo - 16?t
v,t.z92.qL s's.) J^ F,s. sss , o fler'ibB bctf .un6 fdm A d€^ rhe 6pe^d purlca E q booK o@ P ta o 2&-h wc,€}'t $o avff|o;6t of $tolrcd )e ,ti bciweo lho bslf \ the @apound pu$% p rhd T onoxrhurn weight w lho/ oo be eopr.fted vaal mloling
tho putle4 P or etipping lhe belt on to
p"|eg
i !z= ut-"'"11-"t'n,'."
h.
12
1"
butI'.V2 I1 - 1.6+e(Y'/z) l l
108
109
€o2l Dclcminc thc mogniludo of lhc rtsrltonl, ilc point;ng, q ils dir€clion c.sincs lbr ltro following.sFtdn of n6n -ooplono.. cdcu.rcnl forros. 3oo lb ( e, -a, 6 ) ; {o lb (-?. +,-6) i @ tb(-a,5 -3t, FORCE
(D)
4
logcl
Di6to@(o)
le
-a1.4-_4!--3 a
o!r"yrr!'
o
- ?n/3 lta/r.rI ... A. - 1ls.?4 lb. 3.4/7.e1- Al4 .'- A' - -1:.2.55tb. zao/ral 24.17 b. d6 .' . /e. gL-,L-L" -LlAA
k€aE p, e, \ F ho€ o Esu[,onl of j tb. dirc-lcd fotuord \ up to.ighl ol e, =oo',O,= 56',3", - 1r5".p.q@lc zo lb\po6s< through fhe ongin \{he poi.f (?,1,a).Tho \olue cf Q is otso uo,b \ il FDsse€ th.oueh ihe p6i^l G,2,2). Ddiomlne lhe nog.itude of lhc lhi.d force F \ the ongtes;l noke-s wi{h the reference oxes. 6at ) ftr@ oonc"@ai
6c.0) A foftp ol 2@lb. 16 dirccled f.pm E toword C h the cubc sho{n in Fig.p-5o7. Doterminc ihe rnomenl of ll",c force obout eooh of tho coa.driold o)las. rMr - F!O) - 1,+8.6 lb-fl. = - L8,6<4) llh--394.1lD-n.
auz.-tu(r)rr'G')
t -L"EL- @-
- 7-+,3(i) | n1,4(4) 4M.- s1o.Slh-{\.
ri - {1 i tb.:,Fz- 140.Ftb. cos) A for@ of:"oio ieai.ectea Fb- B loenc D in ihe cubo 6hown in FIi]. P-6o7. Dele.r,he tfte Frornenl of thc J?rrreobout drLh ol the a..di^olc o'es.
611) A h@ P,dircakn ftr6 F ta*otn I in lhe cube sho^n in Fig.p607, cov.es o momenl My - i6oolb-ft. D e l c m ; . e P q r l s m o o e n l obout lhc x hz orc€. -!L - !L.3 2
Mz. -32oo lb-fi. f.om o poinl n (a,1ia.) io€.d o poin{ S
(-3,a,-r). lf il ccusesa rlomen{ Mz- 1cootb-ft, Determine the monl of P obool the tt &,y oxes. - -z.to(+) atAr -9@ tb-lI.
-E-'LL'-L=4 .'. F, -o lrt- rgol6lFe-2ao16.
zMr- tu (4) - r€o(a)
d . 0.11fl. -La
q,1
4M2 - 72Ob- fl-
Z-
!L-
lL
... p, - 7p/s,n j Pl . 3p/s.11i pz =sp//eAr
tMr-
ztA,-p"(\)+WG) teoo' 7/sr\(p,+'&)pA,r
244 tb- ll
P . 9'll lb.
rl4
ll6
M
iliii ll
d
fi {
I
I
pt - 7elb i ry - aootbt p2- s@to zM,- -PzG) P' (1)
65) Thc frona$orh shown in Fl9.p-61e con€ists of thr€€ b6.€ Ab, Ac,q Ao whose tower ends o.€ in the some ho.ir6._ tol plone. horiz.tr,tot fo.@ of 1@ lb oclinq pono et id lhc x oxi6 i6 opplied ol A. Delcmine the forc6 in eoch nedbc.
= -g.tO) ' 7..)(1) r1't - '17oo tb'(l
- PaG),p,(1) - s@(4- 7.b(+) - -8oo lb-{I. }'4/
zttf
d;
6i+) Ths sheoFleg derrich shoxn in Figp-61a suppodso \ic.tical lood of zooolb.opelied olA. Poin{e B,c,\Doc in lhesa'ne norili r.ntol plone A,0,\ D orc in lhe )(Y plone. Delermine {he in cdch menbe. of lhe dcrick.
a-1r:of +
'(o-o)" ' (5o)'* (o c'5)Y Go,,ro) da d^b - lS.7oo fl . drc" . @' o\" r ks- o)' r (o' o)' d^c'20616ll.
di - Eto<-zal'*s-o)'.
'Gr)'.(6af ,@o).
oN. s.a67'
lcolole Right Sidc vi€w, lsolot6 F.onl Vicw,
; lsololing Top view-1@(D, rcf(3) ,o cr.62Slb.
.r{oa. r. o : B/G)-1db(5),o as-, !L. c/ 't @(.t/$
AE.lll€
Ba- l2t'ooAo)Y$
aw..r- o: '!r$(1a)-ot en) - a a/,= laoo )b . L. !L' !!-"!r a Dr . 2cballl ; D.-o
e"9L'L'92. AC.1!?4,s
_4_
e- - AL
@(z)
Df-alEtb.
-6IL - __9u_
Ac.76s.olb.
Ao - s22.91tb.
tb. i gry.5ootb.
616) Refer.ing lo Fig.p'61s.r-Jpta.nhly-looo tb jarca ta v€i,licol down*ord locd ol ea@tb. Defemine +he lorce n eoch .tE1i1*r rnda. {bis rc/isod lood,ng.
tb
d^a.,@Gioi4o4Y
-&"
d& -r'G;F ,G;f t Ga\61ArY da " e36r ll.
ll6
-o,(oJ -o
tt7
leololo Righl Sid€ vi&,
610)'the un6./nmel.icol contilcwe. fftrrewo.h sho.q in Fig.p-610. suppork d we ical lo(t of 17@tbol A. pdnl€ C rt- 0 oE in lhe bodo .dlicol plone whil6 g i6 3 fl. in lron{ of thi6 ptoi€.
fi€ nnce in eoch @mb€..
a^s.t@-ifi6:F-,|77litr' d^c - l6al;Gzf-aB-Or
(2a&-tuaoxs)-c,G) .a qk) - 2a.oe)'a
d^o.
DrG) - (2ab1o.,aY.3>. o
. 6.vt!. - 12'
"/(s'a)'I (+<)' ' (o' e))' ' e,16r'
-4C-" ,9'-4L,_9L
AO -
D.
AB- 1r1O lb-."c A O" s 2 2 , 9 l b 612) The poinle B,C,ir,,D of lhe oonliteven frolnsv?orx shown in Fig. P-617 ore olloohed lo o v6.tical wolt The aoolb toad id F|oro llel io the z oxi6r\ lhe r2oorb tood € veriicor. Compute lfe lorce d4 "446.)2 | (b o). t(4:a +)t2 - 101t o^. .,t(1o or |
Isololo F.ont Vie*,
,; t:rz
,l; c,C1o)oeG)-@(a).o
lelole
1,@(e)-B\(O -e/6) "o s | (1o)t 6/@). 12..b - " -A i6 . g, - br .gt 5 Are
Ftunl view,
'-t\
1W- a .d*
ot/.6) - M(4)
- +o.(1o\ ' o
_6q -,qeq A g ; 1 6 1 5 , 5r b- . _ c to.o (4)- Lo(.o) - c, (a) . a -lL-
-jL.
_4aaq
AO = 2382 tt)- -I
--lr-- . sao AC- 53A.3
l.l8
;. bf ' 6/68t
- 5,b.,lo
I
e,(d) | 6/sB,G).13(a bt'Qa,tb,'.Br.12.alb ... nB "r7s5 tb,.-C \
A C - 1 2 6 0 h -- f fteG)
s.16s
-
- 34d(.) - 0, (1o) "o
T
A O ' 1 9 a , 3t b - - 1
aB) €de P"d. ate tl lhe 11.,tb load i. Fig 61A oak hodzon. oulwo.d froi n ,n ihe drrealicn lrom E leoid A. Ftun Piot.'F.619 d,^a - a.i|s l+., d& = 12{1. d^o - qfts fi
It9
lsololc Frb.'l Viow,
leolate
Top view,
zrA.ro. -o,(te,) + Rf l4).-o W - 6.6./aot - -@ zMa- o, 2o@(1)- CrG\ -D' 6za) at(4)|q02.41.
- o.(1d)-a/i es.G) +1@@)' o U(to) " -5.,/c)14o(3) | E@
g-5@tb. iq-@tb: /\e- 8-/r,3 tb---I i B, -aaolb.
.D= 4166
O" r21otb gL :. AO -,1,{€6.+\,. 0
i....'a)
,..
AA
i Ao-6.1c'6lb-C AA -ros5,3lb- -o I [email protected] in 62t) n ve.licol boa p = @tb oppl'pd lo th€ lripod showi codlp.esgrle fiq-Q-621 @u6f,s a lorcc o[ 2i5 lb in leg AB \ o cornpree.i'/e fofte ol 2@ lb le4 l\C . Deleernine lhe force h leg AD \ lhe ooordiiales ro \eo of ils l6de. cnd D.
d,6 = ]|e,OO6'
d^L- 6ofr (o--eiGi.F
.((-t-1))'t!o4)" r
d,'' - (6a-o\2 +ka-o\' t (o-(sr' d^o. r+,i+ ft.
r20
=o, Df(') - Cf (1) . O
Cr = 56.-2l'1b in@, o' = ,15 G6..25) - 1$ k) = 9eo.7,t4tb. |'rO, q"8,G6hGE) , _95O.r13 ., Ac - W.2S t _Lp_- _jEL ^o 1o &fio1 10 lara
aro) Thc fmnc*#tr sho{n in Fis.p-62o suPpo.'ie o €.li@l 2ooo lb. Pdnls &c,\0 oe in thc sdE ho.;zonlol plcne l.Dd of Delcrmine lhe fo.€a in ea6h nEmbec. d;-
-o -@.
Dr ' +/3 cr - -@ .vb.. +o@ in @, cr<+)t 4. c./(12.c6)'oc.o Ct O+.Pe\ ' ada
o -.co),g,,6;r &(r) -.,o{n)=,
9' 6.,) | B"t@')'Iloo?) - o I'Go)+RrG)'6w--A /\B.Ar-8..Si f f i E s . +
l$s
a c < t >-
t2l
lsolole Righl side v,ew,
lsololo Fronl View,
-i' M c . Oo -0r(6-2.),@oG)-W41) -o 'aoo(6'zo')| as@- 21e6.6 -o
0 = s81.5 tb -C 68.) 9elcr'l'ine the nroxrmum sofe verlicol lood w fhot can be suppo.t€d by the t.!'pod 6ha'n h fiq.p-G23 Arlhoul ett:e*d _ lng o cdmp.essive l6rJ 6 2arblb in dny member. w
62c) the Flole 4arn in fb.p'626 aoti$ o load c,f loootb aoptiei oJ E L) 16 supporleo i^ o ha.tz.nta. po6'r;on b/ th.c. *l,".ic"bl". ofloct€d dr A.B \C. Gopule lhe tef,,e,on:^o..h a.]bte
,&-(1i21.s246)- srds.etb t tl DC'2e t
,
#'+'T-+
2 1 O o- C t
B'. Ees.a tb i gt.11gc.16|At. $q...tb. o+ the nbhl 6h6 vi*, zw-o, Ay(1)- s, &) -o Ar ) t/a (17a6.rc).2232-1 tb dv:k 'f M> 24oa
_w. -22122 DA - 27s+.s tb oo totl .x4t tti6 \atle bd@E il er@&s za
-Ci
^C2
ct ' 1q6,9 \b. C.'O
6l-r.L-!
_-.]
W.-4,4.,0o(+)rcio).o C' 4oo tbT
-6G)r 1.,60{6) - B(s) = o
s'-3p@\i@@
A t A I C - 1 a t A" A - 4oo 4oo A - 1<>
627.)6oleeprob.6 if,t^ add,l,on1oihe loootb,the plo{e w€,bhsj
LVz'o O - Q(a) | G (+). o 02(.).0,(6) o'/+ ut: O! t,cr-G (D'/,')Gt- o'l.o) c,G)tc.
o, ts ;i:::=-" ,i.'"/
nn6g,otal , .m 6) - c6o). o
ebG)1.&o G) - @ta) - aLs) -o
.V" ""{2.
c' " s.2so, -@
qbs.@ b@ ,x r s 2e D' 'eoo 0' . Solb F.N@ | Ct . t.Lt. 12o tb
g- g.o tb .T
c . g @ l b ,- f
ztr.a -
,to.fu(c.rcsl/a
-A+ [email protected]'g&'a@ 'o A' 600 lb"l 62c., Refe. lo unsynrnetrrcol conlileve.
Ac.kao0z):L/1 lc - 126blb.
Go'r€wo'h
dosc'ib€d
in pnb.61g on poqp €6 q rep€oled heneosFl9.p_62c.lf lhew: ibal\lood of 17oolbi6 shrfle, b ool o1 lhe midpo"l ofmem-
ber A9, oomptrl" the componen{sof lhe ceoclion ot I E lhe lb* oes in lhe bors tC \ nD. dn -.[.e-af,O+ef '6aY ' s,7" X a"c- .@$i6 -ofi@-of ' tzfi a^p- t6of 'Gaf ,GEiff - sftaq. I
^ c - c _ . . c r. e r a./' A c''cr/2 | C, "Ca
AD . O' --9t e,.6s g
'02
Relcninglo FrD.t view, zMo"o 0" b G)| s.e) - e(.o) . o ax(6)| azG). +r.. - -@ z M c "a 9
6ao,) Ihe b.f,,n BE of ltle sf,fl". l% de;|cl(. €hawn i^ Fig p,6so k tuloj€d bNo.d jr' meogurcd in o honzaolot ptone lhe nrasl nb i. vc.llcrl ( ls s"pporled ino g>or3.t aI A The poinfs A, C, \ 0 orc in lhc sorle ho.iz..,lot plone. oelemine lire li.ces
in the lEc Ec \BD
l
ii O, s@(.o) | 6, (!) - e3so br = lasa tb.
l :
t\ lhe.conponenlsof the beoring reootion c*
Q c, = otlz 1 az'D./+ sub.@q@ lo @ (o,h 'Gh)j '(.^*o')la +a2so 6,50,+gsc^'+2eO D "r c ' . e d o - . - @
9,6d+6/(')-ne(6-2') . a s,(a)l qb)'$3o--@
dao'dsc.tr2tg I
@t , ct)e)- @, to,)(.b)| noo(z9) . o (0, . c') (i) - (., I o,)Go) { a26o - o - -19
q(6)twG) - s.,Oaa) - o A(s) rt G) ' 4aaa b q, v/'ae --@
q 1o1's66
n e4.4.
oy = t63 [) - . -A o
-A,(.t r (c'* o'X.t r soo(s66)<1tt X')'o -o - @ ^" 6r , (Gr D")Gs) A,tst =(,r,7 i t1)t14 A" = 2ag7 tb oz . 6114/s_- 61 tt) Cz . 227a(s)/i= 22a2tb.
. \91
i a -
4''2d9tb
ZM^-o. r o @ ( i o-) E 7 ( r o ) - 0 r ( $ ) - E r ( s ) . o BUI: E4. " E,lo :- 4- 1.5Er -o i @ < 2 ) - ( \ 5 E / ) ( 2 )- o ' ( . ) ' E a E at 2 a , . e . a o - - @
Or - 193
6-PL
Refc..inq to llbhl .q& V'bw, + cr G) o/5)'saaG) "o zMb:o: ^z1't(hiaj)(s) t61)(1st633(s)r la3ci) | 2w Az = - <2271 Az - 166.7 ll).
n rOP6?1 63r) The boom Bc ofthe ctiff'lea de'rich 6hown rg.s-lsin i6 conto,ned in the XY ptono The mo€l AB ls "e'rtiaol \ ' o soohel ot A PoinfsA\D ore in the same horiuonlol plore the Points DkE ore in lhe.eome v€rlicol Plono Detormine
usn]gq . 4944 - ao/eo Gas) Dr ' soo lb ' bo//@ @/aa . , BD. 612..+ lu. uahs@ NU)-Df "7eo Ar &) ' 7c!:4+s.22 Ar . 7@r/4 :. A-/ = t61stb U6ins Ez ' 1./16Er .4y'6(379) . 2so1b .
oa'l6e(ot/za
' zso tb.
rcGming 1o tujlhlside Vew I tF: =oAz'E -Dz'2. .'. Az'o
t28
t29
25a =O
632,) Thc boor of ihe &rich 6bo* h 7lgp-632- k rolol€d bock 30'f.6n lhe fi rlone. Dek iniie lho {iroce in gc kBD }, {he
1.10.6,.0'.
rolt.6' - b/^:6 .\n6o' - 6 /.o
a.@tl.
:, ft -.o$.'. 6 . ir.32 n.
1ar,@.. 1r.r/6^ .-. A . ro fl . (Ge'-$/A,.'.&.20lt. de -,GoAfi a.A:ofi6'i-Lry ".a 2t{l L, 10t a 5' - 'e '6 rt @'aoton@" 11''att' $r.2e.2. $ ae.6il6;f'('+. 3lo "2"'" 9c'816 "' L'
Choplor
lnE4O q .
'
q
l
I Dt'1132 .fi32'3173nA
8o - 11e4.6a+ n A T
'15444lb
Coniroide \ Contors of Groviiy
-'.go ' \63tr lb
- Ai Ga),2db60.6c) L o
ot'!91e.L9,
zM^'a O
c,'-trzfi@24
C',o)@- rlro(s..6) ' o Al +O, - i7z2 - -O loble Right gddview,
ce .199.96tb
02 - 1t9a 6a+G1.32)
Dz = g9.ec lb. P.l. lo Qbhl Etdevie : .F-'o O.-A,-Cz-O Az - 939,96 -199.96 Az'saott)
Cr (.1.a4) - pegg.z4l&
r30
l3l
ihe ccn{fti, of lhe shod€d oreo shown i" rg. '|6 by barrdcd lbe l( d'.i€, the line x ' a q th" pd'
7o7.)Oelehine the cantroid ol lhe qu6d6nt of lh€ ellipse 6hown in f1:9 P-?o7 The eauolion of the eriipse * !fu-, *
c7b"'1-\7o'
G,b) k- e% - b1a
'
a'.- bay'a- u- blr&
d
-
,t = b/aq;n-;t)
n-f, aa,-fi ary*a^
^r =f iG;,) "f,,(u.e:r)a^
t.f a' =f w.F:ta, .. slnq='/d LeJ r=o6,a dr = ocdsqdq
.8"1-,^.wd"-:,l{i
- Va[ h@+y,o.] Ai - !d = eEI i 7 - &/'\-
ylJ7.V ac!s-..Fi:F
'chgud,)- hr e!d, A,a -f h,ll(*4) a^
^. rt*")("-"-" ) -u"l!!;.a.,,^a^ _ .obL hL11@atd4
_o,1..1a.,_t%]:
-4f"r€r3:l" 7 = 3o/s
- lle +
4t 7o6) Detffiir€ lh6 (btroil P-7o6 whd6e nddius is n.
'N'r" .1.
l.; ^f,\
"l "
^':ld^.('(adl
{'*'"'.,".. )-h.%G'-'")-L
-'l t'{i,v";l
ltt
of the quo.+e,'
- n.'
-
oircle €ho,n
in Fs.
A- fed' -("$.+ U' _,/. ...6,^< .,,:;,".
e J;"+ N
'9'=b/8
p,.l$qd.
^4^
t.t!'-*?.-""e-t*":e ('" f -1-a-(fl4,-"""1a,
' o-'E J ib lrh tt'PL
A - obi/
14,tq"4
7oa) Cfivlle th6 o.eo of lhe spondrel in Fr'g. P-7os bounded by lhe x o,i6, tho tinex .b,q the cuNc g=x,n wheG n Zo.wlEt ;e locolion of lls c€hl.oic fr€m lhe line r -u ? prepo.€ tfe lobke ot o.eoc \ lo@tion of cenl.oid f6'- 6iues of n.o,1,2,ta\e.
r"*=G-F
-+t-''al: -+l'^'"d" #1
a'h\Yb^
^.\1
Ai'l,"a 'hJ'!ad'
' r,(: (" ") d' - t'l'"' 41: ^i _;i," ^Zl - ".2
edx.
^--f,,(dr.f,.(#)d" ' h4^f! t" a, -hA^t#7:
t'4+ai '%.f,1.Ji "%"i++-"-l-!\r --L lu--'r1
, hr."T-hil: - o'1 = rt" r =!Gd nr'
A - br%r
t32
- s_uZ,
133
ut l'i" r i" -tf.*a r.(oo)
;.
-t-l en -' {
7oe.) Deledine Problem 7oe
n5)
- b(nrr) - b(nr1)
b - !ltl])
Dele.fiioe the @rdinolcs oF t|€ c&t#d in Fig. P_715 with nespec+ to fhe eiven
st'ovn
C c ' d l- u z -
, [hn.,]-l# , e] I xt x"t , y,r r't] s -Lt^Gxqora:'
'41eaa1, '2^.t(.)-/e(d(dr"rt tp'6a ,21) Befe. ro the I_ 6€otion of prcb. ?t+ shown io Fiq. P-7r4. To vdlu€ 6hould the 6ir. width of ihc flonge be cl..onged so lho+ lhe cenfroid of lhc orgo i6 z,s in. obove the bo6e 7 I1(e) l b(1Yr.r) = 1(s)(ar,) | b(rxo.6) ?ora.ib-4+o.6b ' 2b -20 I 722.>t@le
lE
b_10n.
@a+rcid
of |he ehoded
oreo i^ Fiq. P-122
by cuiting o €@icicle of didmeie. r frod
o quonler c,rcle of
'!#("-#)
ll;
l[|1 a
= rl
--i -gL 12r
= 0.6.7.
s' ( /,Y,'th'(-"16)(/,)
o"Zj -.% - \.7ts - 16t:: str'
r,%_s- 6 5#:' E'-e!]g-r-
, l:!t@ - n ctuelr=ly@k)(E',\[kbtu"X% aq 12, - s7.6
r36
t - +.€fl.
n i .[.h&doe/a..\ - lh a>o)& -d
,t2q - 3€ 9-3ft. zr) Locoll3 lhe lglrc;d of the cutvenl st$*^ i^Fig.p jz1 tlnl. ln tog.a{,bn ie onneceosd.g tf lho o.€,a i6 €ubdiv;dei into the eloment b be fdrnd in foble vr-1
, -'+
1.o-rs(+Ydt,fa&)1.\')(./') [r(kJkx')t r /.it't') - e/!)(4)(1.)(ye.,\
7/A_t o 3aer
- {t)
1++s93 E . Ea,a6e J'5o€in. z26) tr:.afe lhe @l.o:td of the .sho&/ dr€o eotc\se! b9 +he cutue lhe 6frc;9hf shos l,ie in Fi9.p-1t5. HinI : ob€€Ne ]ha{ U..o' \ lhe tuNe q2. oa retot've to the y 0,,6 € of 'he @me tbFm 06 9 " ^xz wilh .esp@l to lhe I a'i6.
c!.nPulc i foi lfE 6so b.u'dod o.,rl€ g'a\ t t/s-a/ao ' ,"'r
+- ., A . Iz" +\i6+ rlr'1.
A-
,.e)
A
At.€Ad' - l: (af ,'7e- ^'/e\d,
252' = 1q1s z I ' 760 @'ts ' ;. divided
!.t/*..
_H,r | ,.h, r7...1"
292 ttil.
rcclor5j:B
|t(1\1)!j,(1\(o,) fiO r'(t), la)Ol g . 1i,|,tr...) .o, - i11 . g -o;7 in. - 1(.)(7,e\, (t\ @)O.cs) zW
b/
iato
two Porle
b' il'c
E.) cuAr'e g-^r"
oe ehorn h Fb.,P-22e.u€trq #E knd$n bcoiion of t's conl'olt of lhs lo{€,^ poei A oc aivon in loble vn-l' 6t'ow ltlot ttE cenhoij of lha uppecpo"i B i. t(rolea WtB-/,iA\Eg"24^..
Two 10 in.- 15.? ti
72,+ \nl
chonnolc orc werded
ioge{hdn
os €h@n
h
fu. P-7:1. F;d lhe momeniof a"ea of the upre. dhonneloboul the ho.;o"lo j @^|rc;uJaloie rroof ihe o{rro ceul,o. o@
ol roi^- E,e lb - a,ar i^'
2(aaa)6 - a.+a(e+ rrc) ' +.+rG) e.9t5.67seG1
-b6'to rhot c^ *n erAhbl^
g- ,.86 i^
. b(.rz)-b
r^.644
FD-*lr"=br'
\-E{,1
f F{s. p-72r. Rela lo Toble vl-z 0. +t? FoPe.+ies of the o.9t6s q b.-te,.!"e cntrcid ot t€ bu,n-up cal,;n
/r&'
\16rit/
bhni, -)L-EL
6,8 i.ft] [e(i)r r(E) t
=b."!nti;?b'h. S
2(e2)
#Bt'=bh("'4)-(*)D#}l
'F-5"- b##r
-*ilE".W 5. , h(nrwri .. l. .2rA
138
" ale.ra1s t- &'sa'^'
r-a - b\,&'-r-o 16 _ lod
,ir 7,o) A b@n hae lh6 oro€c eotion shos fia moft€nl of o'€ of ihe sked Po.tion an+rodor o'i. xo of lte *lire €e,lion. (flole llot th c E€.lte t. laa i^ €ht df -ol;ole x,itum cheonrg sr"esj.
xa5
5 . €^n@!.') r (i4)t.) ..,s(.-otu) r s,sGrs)
enlrcid of lhe buill -up solion €,i,bn €hadn ;r to lobb vn-? ftn lhe popo',tic* of ltc ebrcnls.
l :
tF''E
{ 4(o.'),(+)j t. B (. n.. -,..,) t..,,(a*,.^ | 6.Yo'Y6.r.) i/6dYo.') 27.7.s 5 = 462.4d J
- e,+e in
F9. P-%o,Cc'nFrle abo,t tha ho"iantol , tt ic e-t'o.. i' 6llqJ e n@cr'P'li'q
r38
l l
ri
t6 rololed oboui ondxte 7e6.) A riqhi t.io.gle of sldes b\h coinoid'ng wiih €i& h lo gerP.ola o righl cl'culo' c'r€ ' I
v ' ? r tt. n a - A r . k b - | A b r l 't = '/'rb'h
A .,"1'\
At=Csba,)-f e"d,
'f- okG'-t)"
v
- ut.l", i'"1\ - b/""|d - "% , ""
-"*.:+.+ =;fr"u.
Yepune- st 4-A
"/f,
A4.bTll 4421
-,1ij""1*-*" -r-*ion6 l; the 6v.fo<,eio@ E vorumeeene€ iod b/ rololing o semic,rcle ol.odius . dboul ilq d;m'ie'
73e) .sfbw thdl the volure of o Porcboroid i€ eq@l 10 o€-hdll {ha oiccumecn,brg oyllnden , i '. 1)a' A; ' r A.J-l4 'r\d,
1-^.,i
o"/6"(t" -5") vdqre
' l',"/v'(t'':')av
A=2t i L6alh of ("-e
\
t''
+o'h
i - 9 7ro) ,A oille of -a;,3t" t;'" 'r lhe xy pronewitb rtc oaltr oi o d,6+dn€ o obovc the x-o:is. Royolviig il oboul ih€ xoxis will gene.ole o doughnul-shope ri.q aoiea a torus, poraea o '. 96al*
thon..
Coopule th€ €urlo.e
a,b
q votume of
-*b
{ 2 3
't
h bQ.h
Delamlncd {he vdluBe of the cllipsoid of ^€"dluiion qcro€.,te (c"olote ottrpaid) mia'a'ic q l6d rolotihq oo ellip6e obout o) I b) ik olnon oxis (oblaie etlipsoid. Toke the lo.e{ s@;o'h o. d \ thu smoll+ semi-or-'s oe b. 7e.)
,7b"' ' 'Z'
r>."'E
f .q".G'',)
140
,a1) A 6a' ptpe eibow ho6 on inlenot diome+.f, oa 4 in. lAe .od of cu.votu€ of ihe pipei oontrt,re ie ain. F,nd +he inlqnot wl. v.Atuo x hrrcid
rd6io"* +"..*ed V = 7€.e6 ih:
t4l
. t(4)4- 6 _ (er' "r/.d;)
7ar.) n;d lha yol!rc of thc Ephedc,l wedqe fo.ned ,y.rlolidl lhrough oh ongle of .6' o cemici.ole of rodid r dboul ilc bos€
\/ -"rh, y?r -r
v-_rc-
z,+!) Tl€ oreo con.loined tEiween h^jo ocicenldc €€oioil.cte6 of roall t.s;tt q.;n. iG .ofor€d obout clrlo:,s +rn.owou,i\ porallel- lo lhe boee diooele.s oF tte eemio,ote*. Co."putJ lhe surlooe orco 1,)votvhe geoeroled bg o complole re,olul@n
7si.) gctenmine tho crntnoid of o hemisplrerc of mdrus n' tching lhe otis of egmmetng os lhe z oxr€'
.
".
tlr':
-rl-I---l
^r.?
$''"1*f 1 '
(e*rrdre)r = r(+)(+)rs(er+@'o) 2..s4t = t4r'elo i -c.5+ in.
!
7!6) Dol..ninc tlE hciqht i of lhc cgtindc. mountcd on lhe h€mi6ph6.icol bo€e s*'6^n in hb.P-7s6.Eo lhol the conDasile Dodgw;lf be h sloblc equilihium on ils bose. flinl: y',e tong os lhe ccnlor of groJlg doos nol lio obovc the I-x plono lh6r€' will ori€f o rcslonhg couptd whon th6 dq ;6 l;ppcd .
r
p-76? zar) A u.ifo"o wirc is bal in'lo lha shope €ho{n in F€ The cleoishl s"4@ols lio in |ho x-z Plo(6' \ thc. e.in l4elh s"grnar.a o" o"qtce of 30' wilh the r orjs. The .enic'"culo' w''c af lhe oool€' of menls is in thc x-Y Pldne Locdte tho sE;'lv
'
1.'2-127 - ++4..2c i. -11 it. frcm opa
;r65€ag " r G\(+) e6,s6cg =32 g ' 1 2 0 +i n ' 26,s662' .(!) + e(aetn3a') 26,66.2 - 3+
z-r2ah. 7e+) tocote the ce.iol g6wiis of o st€ol .ivet hovinq o cgI'hd.icol bodg I in in d;onclo. b 2 in long wilh o hcnispr'e"riol hcod of 1 in,bdiue. Uso lhe.6url of Prob 7s1
r("/h(h/)-\trGfW4a) h' - 2b't h = r.4l+ fl.
?s,.) Fcpaol Ptub-7s6 if lho cyl;d"bol porlion of tho bodq in llq.p-t!6 G raptocadW o r,qhl .t \t:cotpo.l,o. *ilh o 2 ft rodiuG bose q oll'tude h.
A,
\+/
lk efh(v) - 4//0f(//@) h"A=+
h-3+64f!.
7se) sleel ball ;6 dountod o" l,,p ol o Lrnbor c,rtincre. os shovh in rig. p-zso Sleot woighs +eo b po.or n q timtc. *o,qh, 1oolb po. c, ft. D6le..mino lho pos,lion of 'ho ocnlo. ol qovi
ae) A bodg codsi6+s of o nqht ci.oulo. aonc whoe ba6o i612 h. ;n. de.p s in. in d,bncle/\ who€e ollitudo i6 16 in A hole h a ocq a"iled fiom {ho bose lho o.is of lLe lbl" co'rcidog -/ thc o.i6 of lhe aoe. Locnle +he (gfroid of lho el volume. Uee lhe
tbhf)
(rc.o2+te.oa)g = rc.oz(zet/1e)t ta.6s(p x /z) 1a5.1g = 2a6.$ = 3 r.es fi frum boso
tusuli of P.ob. ,{€.
t45 144
*\(60
So4) D€le.mir€ lh3 rnorEnl of irE.lio of o tdlo.Bte of bose b \ olhiude h wilh rospcd bon o.i. ihrough the oper porollel
to the bose. Uce the lrsneG. lcrmulo \ P(& soz. l"- bh'/$ t = 7r ' Ad'
th€, rBarll€ of ilto€ .
' bh/r6 | bh/, (zbh)a
' bv?/& t 2brP/s 1 br?/4 60!) Def6.d,he the norcol of inerlio of lhe guoder onljte in FIg.P.8d9r,lh r€.p€., to th€ g,sn orc6. tt J- lp.d^
Choptor a
r- f,-r(4/.di DY*']P1 . L+/'4p \, l/r . r.
+/.)" +".
j
' i' ri, ' r'76 r, . t.V6 1r - n../.a
Momon{sof lnoilio
' 1, +1,
8od Dete.n;B lhe dorenl of in€rtio of the €ed€Fcte ,h Fig p-ooq with rB6pc.lio thd q;6n ot€c.
1. --! red{
.gfy'^"vyaoay
=f, l' /o2^"+ae
= 1" ./a C a.'ede
[
P/* k-,ed.)];
. r./a C y. r.coe,6)do , t%re - s^,e/a: . r'/. f(l-o) - k'"ry - qho],7 I'
r €o7) Sho"v the momenl of ine'tia ofo s€nicircb of rodi'Js the dbd'etgn is orira with respecl to o ceo{roidol o)'i6 pomllel lo
sla) D6{em,ne the morunt ol ine.lio \ the redius ofg7.otioa,V respe.ctto he Y ore, of the oneo cL,l f"om lhe first q"oaront b' {he curue y . +-r! where i \ y ore in in.h6
nr'-/rr-\' rc' . I' +--u-'\3{ r-. i, rAd? - --z ' o.921ra ' ir I o 26Lg4(+ i, ' o.\og76ra* ot1ra qr'roclercircle €oa) Detcdnir€ tho momenl of rnerl'b fo" lhe sho{n in Fb p-8os wilh respecl to o cenlrorldal X-oxts
r-/"Cfd^ t d .rd,
t
= -(oa) . a
rf6r"-,.4)d"
\'La'(A- f/A: \
+(4t'\e-of- (,-o)'/4
- ("/^)'h
^'frd, .tr'(..")di
t-
32/s -t2//e
- 16o-
= S*-'+
A 4+t - t'h l-
rr'IJ
^ -iy<*a:t -ttl
#=t"*(*f
' 8 ' s / - - -2 + ' 6 ' L A i n r
+ 0 . 1 1 1 4r71 01 3t-7r = oo549r+ = oo55 14 It tfc mo6€nl of iner{ro with 'especl s€e) Dele.-irE *hoee e4"olioi foc lhe o,.e.a e.eb.€d b,/ the s{iPse
,l,lecdeler-i"e the@iis ca gyrclio"
"4 , + , ,
:.,t.1W4,V6.h)=f,6 o11.)Dele.mine
ihe mmenl of nealo w/ r€sp€ol lo the x ax,s PoroLlrlo q8o shadn in Fi9.P'€11.
4.*'' - "'-l'"&7d
,
, - "toV1;
,'i,-Jy,d^ =J./.ardy
i,. +f,f (otow ) at
b= b6'r'e Y _bene e'e4 - a-'7/2 dY'b.ae€de . a b co'€- dd b".ie @/b) (b'- b'"."4) \-+f = +fh o'o " a"+<'x"ede
- is (''r"a ,*n)ca\(, , cx*"")lae
. ab. (t, ex.,e)da l/ - lr(-. ' .66,t de ob"Le ek - 4^'a/s1: (t ob, l"' = ob'5B./+o)-6n'?!-5nolol - "6ii-p - ""*761!"
?,.p-
.. t,.t*rd, -f t'"X"*) a"
>
" =Y1t14"aiy.r atf t,,'(bZ)'
- b/L
148
I, -{faa d^- (a-t\ar ; t -x1" *=x1r" 't/'G-"/sr')d' t -o/b'r' .a/b' . ('6v'- &'(t') ) at
i,'[;;1 - "/t('%t .[2,<"-r"[+utfiuoll 1r. oF/" - ob% - "b%"(s-e) . 2ob/as . e.2) De+smt^e the I/ O. the €hadeJ pa@Wrttcotta of fig.p-o11. rf'l,.dA Ll-\t'bl4odt
8'lo) A rEologle 'e 3in. h5in. Do€nnina *tr poLcnrtrnanl of irF,r.tio\ firc mdiue of gTroiion *,lh r*gccl lo o poldr Q(i' throvgh ona dner
l-f/,///) 'V,/) P
1
6i9) DaLrrnine the monE 'l of ir€plio cf lhe T- 6eolion i^ Fb.p'8@ d/ (f,,rc'i +o'lc cenlddol oxi.
n
r,=!, rAdr t. - Iv+Ad' +.('xe)t ' ar6n1 ,|'*l
rr
. L(6X2r1) t .
s7
I ---f I
shdM
i' - 4Ol | ,(6X..'r'4&f ,z
2
I/ - qFf + 6(!)( 5F ' sa inl
1, - 2so,6, in!
li.r@Ya).3an'.
82o) Oelcmine the rrc nenl 6,f irrorlio of thc oreo etrorn in
- 216+9+-270in1
^ . F 6 . - , @ f f i - 3 . 6 ai n
Ar = 6(l)r{2(r)t€(r) = !oin?
srz) Deteffine +hc .romcnl of ins"l,;, \ rod,us of g/rat'bn wrth reepeci too poloc ceolrodol oxrs of lhe o.gss eclion ofo l'rol_ lo, lubs who€d ou{sde dio.nols i6 6 in q ln.ide diomele' it'+1
8rs) A hollo{ squorE o.l,€6 6a.}'on cdltsist6 oF oo 8in squarc fro.n rhich i5 Eubt.oct€a o con -nl-1.c,J,lll PlcrB cqlat'e 4inbf'+'r' F;^d llp @. na.neal of inerf ;o ,\ the @a" rodius of grrclion lhrpugh one of lho q4e'ile oomers *ilh reEpeol lo o z oi,6 Po*iig
Ii, -gg!*
i, =a{;)' * r2G)t'.z)a+ilgt +jgf
- t/zGa'-t)
A.]E,r1\n
- 4z(i.)(o,e)+ 12(1)(1) | 66Jh3.r)
et
^t
.tut6)(6/z) - 72 na
i' -lgf
, 'rzcaxoxo.Sz +eg3
+ 6&)(a,s)' t" = 19g ;.'
l6l
lil $i.
ii H fii
ilii
8zd thai
- ds6h h.JE-(&Y i,. b(ae6bf - ru+.lo-'ba
i I
I
i
An aquiloh'ol t iongle hos ile bqso b ho''tonlol- srx ltp centcot&l rornenl cf ire"lir x'lh 'espocl tot'o'i-
12.5GP I h(i2,5J&)(6
ofL\Ir.
oea) C.actprtr-lt'e n'a'srl of rls-lb *ilh reepcci roan ox;e tetqrl pascir€ fh'ough i*o opPo€ilc o?crcs cf o .q'W 6 s;de o .o-- aao/6 - G.,. e.ob/o -@cVt b-,y'2
Y.E:6hvh