solution statics by ferdinand l. singer 2ed

. ACIC{OVLEDGEMENT

ctqifu o: Ucrs e of lrirlioC}+l6rip: ncaiF4ao- Tnar6l('lb

'

Oroglir rt : G.,-iti.!oo- Trqr6loli'r&-4rx5-nu*,2r3?t'N

. vtt

l1

'; I a& lba.

coii;Aar tE aoobh' -+oo cr,a <o'

. - so42 lts.Ts'.-a@ €i" ad

- -257.12lb€

p,- 3@;65 --:1508L@,

Ps- :e@ 4^*":P-b-

,17".,s'eE l\Y cotrrr',",nts of cdt of ftE to(€sewvn in Figuee P-aot,congido. lho 7221b lood,r,= -nz (finr)

-j!@r+_tD6-

nb 4+€b bodl

Fg- +1t (*l'7dE) ltu ritorgld@' btoch ehown i Fig' P-M is ebj@d

lolrE loods P'1@br,tF-6@b- f t \D=Sh\Dc=6'L,resolro coolt lood inlo coopr;le ru'md \ lcgcnlirl

.conei&r lt,p i6oo lb lcod j

sinc--L aase-+h- +-'(16co)

' t26ob'

h- Ltl@o\ = S6olhc.,&- l6';6i

' toa-

2

co'isidc,r lhc 2e,b loddtP,= aoo co. e: f-Jg@Pg= 2@ s;n@' | l'73.2't lbs.

i 'r"

- P979.!b ,

"t-- ?9,41 fr-lL_

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

d = .:ryL - ?49 !1,

2+o) lhe shodcd oreo in tig p-z<o Tepre*nle a e|*I plola

of uniform ihichness A lole of + in diomele' hos bea coi

in the plole Locote lle cenlec oasFa"ifv of lhe Plole Hini:

The weiehl of ihe plole ic equtvotenl lo th€ we'ghl of lhe

origrnol plofe minue lhe weiehl oflhe moi€nol cut owog

Rep.eseni lhe orieinal weighi ol lhe plole bv o dowoword

t 2-n

n.et r -AA \ -Ar xzX'1.rc<1)-12,s7(q)

onounl k, posi{ion of lhelhe Fink true6 .sh@n h

R= zcb+ te+ a4o | 'aa +..n t zooaB-a39]! (d i@t€d dodn*o"d )

R'- 2.ht tsoo r aal |eoo r 2oo

L - ]4!@,,s,ta4 d@"-d,t )aMc - 14oo(5) = Toooi] lb-

Rdc - <uc , dc = Taco/.14ro - 3-o6!!.;st.+ or

i) ' 12196 tl. r)g|,t of A

za,) Find the lotue] of p c,)r @ thot lhs ftur fb.ces shoal]n.Fig. P-z+e pr-duce on upword resutionl of w tb oci;nqat + (1. frcm lhe En end of ihe bar

zMp= -f(3) + 2cnG) + i.he) - aoo(z)r= 2oo tb (do\9n*o.n)

.MF-.c 'o(1) - pG)-1oo(s)- 2@(2)p- aoo ib (upword)

; ' ' ' ,

( 1/.rz) - rb (/.d6 - @ (k) 6 - $r(k;k)

4=!94]4:9 ""'

2az) Ihe lhr]je-'lep Pullel shown i^ fkl P-2+7

to ihe s,ien couptes compuie lhe "ol'o of jhe

p)e. A)so delonire )he 6re rciing ot lhe

l 4

c- 3oR(4<b-1oo) flab - (412)R

R: l4 b dncoleA rcrlicattyLJp ol A B do*n oi B.

25o.) The conlileve. lruss shown i\Fig.P-2eo cor.ies ov€rlrbal lood of 24<)c)b. Ihe lrr.:s,s le s.pponied by beo-rings o) A \B which exenl lhe fbrces A-,Ah,\ Bh.Ihefou. forces shown con|lule lwo adple€ which musl hoveoppoeile momenl effecis lo pnevenl movemenl oflhe lruss.Delermlne lhe nlognllude of lhe supporling foecee.

rn o.der !o corelilule o couple

o &:ZtpLb epwod)2400(6) - bh(+)

Bh -Ah = 3600 tb

2.e1) A vertlbo) forcc. Pol A b onolhe. ve"ti&l FotB inFig.P-zst pr,e4"o" o reswitonl of loo lb down ol Db o6€Ba+occlocl.wi.ee aauple c of zo<j tb-n. Find ile magniluoe

\ aireolbn of lorc€€ P q F.

lvb'1ao(1) =-2oo ' PG)P= :o96(do*nwo 'd )

ZM^'-2oo -a.4 (+) -t G)t:29pb ( uPword)

+) . + 2. .T-ptJ )P- , " ro

i,I

i

l 6 tz

e) A tircc .rsLn corEisls of o cbckw€ aa?re ot-p]',:.o 4{o r! rcrc. aicled r4 lo the nghi lha,+ trE o.-dnof, r*,Y oEs ol Ot.xt- Recto<t lhc a."en eyslco ty cn3c"":bil srnqre fo.ce ! canp,te lhe nlercc"t€ oi ilslinc of clion wilh lhe x 3y o,e.-

B'-F, - 2ao @5'= 4ezlelb-(ro ho rirhl)

B"t 'Ft "'o 5 xt'--:-la- (uP*qd)

M - c - F , L ,L, - ao _ ?pllfr aane o

xrz6

it =-:!@'-+!l= t t1 ot ol1'<'

t s) ,Iri-F\-

p-6 o 6.tr6lcm a/f (d@ .E ]]vc(F loo aowcvorlicol

-frrceo ot-r@ b lhuugh ^ ptu6 o counld.ctocxw;canPv d qD b-f'

-tu?F,dfte lho sr9t6 ,bve lhol w.,ll rro..re .tr q'I@t€/l} effei

Aj:@.b downwad

a@(+) -eo - aqtt

r:2JL ridri oFo

o€ €r.own ; F4.I'-2ss-tn sl"ens,th of moloFtot6 il iR

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<X*t* @)dc of ra tb' n

3-t-: sqqlb lo lhe |,aftMn = r4o

oy =eoo(4) -75o

_r: :99]E G,.,E'b bor,w o)

:d. I "*t oo'nF€cs,o., membef, oa-r|s on eooen h-E

l:y P = a@b_ eil-uolea z n_ fmm lho orie of lhe rEmbef,.

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 wi)h lhe oadi|bn ofo poir oi oppositcoriol loode eoch equo) io zoolb )we ae\

F= 2oo lb ldowoword)c'2oo(z) - :@a]bjh cw

zso) A ve"licol shoft nB i6 sfl long h boited loo r;qid sup'

pori a) ils lowe. end A l i)s r.,,pper end 6.re ollached ol

rizonlo) bor Ec whrih is 2t1 long . Al ihe end of C ie oppl;

a farce P - 1@)b. Force P ie perpe|dioolor 1o lhe Plone con-

laining poinls A,B,%c Deleffi:ne )he iwisling etfecl at Pon

lhe €hofi .^8 \ lhe bend'hg erre6) ol porn) A.t f"lDO tD

- / l ' lw,st ,no efrecl - 1so(?)' ; / " B . n f t . b n

1". o"na'"q elocl - lso(s)h = 9oo f l ' l l r

E?) Reptaae )he syelem of lo,r-.s ocling on ihe r.o-e in rigP-2sr by o ros"rionl ,e o) n q, o coople oc);nq ho",%"lolly

R= -so tb (6) neons do*nwo'd)lMa =C

6oG) -r,ch) = r(2)f - fo tb ltu'u B \C oe shown

f li 't l

l

lii

:

l

2s Rcpbce |Ae egolcm of foroee st'4n in Fiq. p_2ss by onoqu;votenl forEe lh.oJqh OV, o coupte o;;"" jii#;,...':i',X"":;3'::"'e:::.:mi:::,,

zF, = |a1.a (rka') t 22+ (46) - t61 (r/JB)

fuaq4r!(lo lhe righl)try = ,+1.+(1k ) -22a(/8) - r61(./JE)€F-t = :3oo.s6 G, ^e"^e doanward )^ - ,/(10a.o0. + (-300 36r

: Pt4.Zg-b(dot!. )o lhe nlght)

0r. lad'zoo, f@,osgj|: !L99'

ol C =<Mo

3F = a6 1 (a/r3) 6) r 3o1 ( s/J:t) ( i r ft1 A(1/.rz)(2) - 141.4 (t/E)b) - 22a (2,/.rs)(1)- 22+ (t ':t")()

3F - 1AO,1

b) +p= 1taa1.lP: 2993 tb-

260.) The effecl ofo ce"loin non_concc,nreni fon:e egelemie aofined by )he fol)owrhg data : .x - +rJorr ,<y - _6otb,onazMo=360lbfi counla-o)ockwi6e. Dele.mine ihe potn) olw/clhe n€sul loni rh)€.eec)6 the yo, ;s .

. -T ' -

l ' , ix-ao zy =.F, Ly

l.r"* Lt - 360/90 ' af l belo|9 o

2or. ) ln o cenlo,n oon.<nocunecl lo f t .e b/ . te !n , t B fau^dl h o ) + x . . s o . b . ? y - , t e b , \ z M o = a a o b

f , I n o o o u n l e . c | o o t .y ,* T. : :

uere.h:nF the pornl o) *n(n )no ree. , lon l rnlor6ects the ) l o) , ; .

L, = +ao/46o:-:4 n;ght ol on,gin

lh.r'4h B eic.

l 8 t 9

l i '

252) Dc\ermine comPlele)'J lhe'|ing

on lhe s]eP PuIeY €hdwn

fis. P-263\ t}€

o' le

ih€ r€sullonl of l}e 6rce sy6lem show^ in

r 1 v inlercePts

R .' = Gs9.e2)2 | (-37s)'

e - Q5+.Ag h dorn lo riqhl

4t, - loti' 81s/oes,52 '44-

Rd- aMo " ztu(|es) - 12so(<,5)-2eo625)

!4:9::4:ojs'R poe€* ihrq,eh lhe

o7*i* - ."o .t"'. t z"teqe) - zz+(e/s)

:-ll9iq(]o the."iqhl), zta - lt co3s) | 2z+(t/r) - 361t4/r.)

res"llon) ol )h€ lorces oc-

in Fg. P-e62.

@ 1ft . z!,o cos.6 | 2so

-: q994zb(lo lhe 'iqhl)

4f:r '7@ strl3o' ' r25o

1,*!arq(- meons doMw

,:-t94! ruPwoftt)R- IEFV-IZFV

. - ft@-eEY t6rzrl''-l!.Ab GP io lhe 'iqhl )

Io"ev - zrt7ar, - ss allae.s-e. r -+an sa.61/149.9

2 M ; - :oa s ' n ' 12 J ' 2 2 " ( / n) e) 3" ' G/ ' r . ) ( t

- -L, r ,6 n 0 ( - neJ.s co"") -Cw/

- 1.67 f+ r )qh\ of O'Ly -- 1oo 6/1+9.9

- 0.67 ft below o

202 l

,6a.) Complele)y dclcrmine ]he resullonl wilh reepec) lo pi.Oof lhe ft.r,e syeiem slnm i^Fig. P- t:A.

,bl___L

zMo- 141.1 (1/.$- 2tto (9/'{-t.

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

R " \EF7-+aF7-'@Ai6Y I Gsri.F

B_-:___sst9_A t!(up lo lhe .,qh) )

9, = | o n' 1 257. o3//+rs.1s

)(a)t eawc<iG) + ao eina(+) + ao( a)G) - lil9.19 rLtLcw

d' zMo/A - J!19!p- - 3.27ll.44.68 -

?e) Cod,pola lhc rcs"llonl of lhe llrcc ,;!e€ sh6en in Ftg p466. l-ocale t)6 inicrecolbn wtlh lha r ts y ores.

1F,. ao(%s) | 72.e48)+d(Eh3o) - A@r11 io lho .igh]

zrr - a@(..,L) - 722(t/,Et

9, . lon-' s1o.1/01o.11

9a:=A49'

:,:gOacnEdn6 do*nwdrd)R- GF? + zrr..

.,/c1_-+rgsloEY

E::4231_doq. 10 nsh+

lMo = 3@(1,1a)Q) - 3so("h)G) + 122(2/r,')(4 - 3oo sineo(3)=&: a4.91 j1:lb cw

Lx - 1121.97 - 4LD, righT o1 O

ty = 1121.q7 - 1,3en. obote Ouo.47

-

iliriiili

iilitrliil,i;Irii

iilliliri

!

i

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

bioee Ab. Far s6>a desiqn, thie r erseolion should oc.our w/rh

lhe didd)e lhind oflle bds@. Ooes l) ?

<rr. rc,ooo - 60(b c'o€ to'. ago:.!a tb ( to the

. iqht)

Zfy- -24oOO -6o1co 5t.l3o

t 27)jA( neans do*n'*ord)

,,/66atf; CeTaad"g, - Ion'zrt/ara

- lp.,' 2n P/[email protected]+"* 2s,91'

Ztt;A = -uooa0t) + poaa(b)'bo.P( )= -228.cea fl lb (- meons ccw)

ZM6 = aFlrbxb - zzeao/2zoco =--€.t]tL(from the lcfl of E \

hence *ilhin lhe nri&le third of.lhe bose)

267) Ihe Ho*; .oof l..,ss sho./h in fig P-2o7 cotrie€ lhegiven loods. The wind )oo& o'e pgrpendiculor to ltte in-

clined m€mb€Fs. Delc"mine ilre mognil:de of lhe resu)-

toni, iie lnolinol.ion wllh ihe horrionlol, \ whar"e li inle-

R = 2?424.02 lb.( down lolri-qht)

zt"-zo<tot++u(1/r)' +oo9,32 lb

u 4s"--fi-f666- rca -<+d",!t)

I :--.9qf.93..b-(- mcons down-*o"d)

^[email protected]:o.)rR - 1A'278.17 lb rdodn )o lho

rrghr I

lb.z.ia)b.ldblb

l o l l o l l o l t o a

22 23

+, - lo 4 z?//zF - loa'| 1&7.oe/a@a,62-+, - 64,2'

zM^ - 4+so (1/F)G) | aeo (',/r)(1,o') | zooo (d + aao (d| 2ooo(2o) | looo(tso) - hoa87 72 O.:E

.t - 16008r. z2fooo7.oa - 1!|L dqhi of A

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

Zr' - Rttr , 11o t tso e/s) - o

ff-:lqqlg Gmea"€ lo thc lcfl€F.t . RJ,

Fr -12or 1Eo(a/s-) - o

? 'rt : 29alb +o Ihe lefl

+ao - -MP + faG) + 120(4>\Ar.2oo ( l - lb (ccw)

. d = 2oo/2oo .{ obove O

26e.) Repeol Prob. 26e f lJ.€ r'gtf onl ic aeo tb di.calca d6lmto 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.

4o(1%s) F | 11o i 1eo(3,,s){E_:j6qlb (1o lho n,'ghl)

Q1 ' ZYy

aeo -reo fr'F) . Fr -12o + rco (1/s)

=t=:=:P. Goq^wora)R - F

+2Fr2 - (60)2 + (-tso)2

i :_21-?.!?&(ddo ro nishr J

_-L

-ga - lE1zJr/.t, - tdr-l @l@' -+r::19-

ua'€Non{*'E't"l, n{'olu)t2) -11o(+) | rfuk) rtrt

l+:,fli:D- dti, = ao/po - Z4!L rtgt'l or oir - @A&o' z@LL eo"B o

zo) IfE ll.Ec tuEca 6l|'m i\ r's' p-27o o'v r€qt'cd ro

ote a lgia,lol .€artd't @ti.g lhrorgh poinf A' tf F =

sr6ID, &l€.niE lhc volucs of P ! r- ,tr. ' Applv UR-€'lt

1o dclc.fia R, lhcn ltn- €rac lo fi.d p. 1fi'ollt €:llF- [h-

-'&, (',/h) 6) Bt (./e') &)' 4 GlR.* +gg-6+ lb.fio llE .i,|l.l

lk ' {va+t-aG) - e*(.A-o)b) - z*,(r's)@

aea-.a (a) - -1 (?t-t,y.'').'6(t6)G)

|;9 th.q,9h p-,1 A. lf I i. Evkr to ba 3515, canFd. the

-xt(+)(a)+eat(16\4=e@)

8:,iqqJ rb (da6word)tth. -€llb

.:@.+e ti = r e/&>(.) - r (.ftY1)

L:-Ec'?,b'

P(.A.'tG)rGE5.ae)O/ra>G)-a'e.ai(h)G')'aoo.at(+)!-:!tgY

Chop lo r 3

Equilibrnrn of Fore Syeloms

l

*a) The cyhM€r C ;^ fiq P-3o2 weigh' looolb D'aw o fBD

of cyl,ido. c q of rod Ab.

( " i ' " F

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

thri:rnoes of lhe .od b o56u-e oll @^lool su'{^o€s to besfuoth

a+) Tne fiv-e che*n i^ f;9. p-3aa i6 surf,orled i^ Pivols 01

3p. Eooh membor wo,ghs €orb Per f l Drcw'o FBD ofac\ '

s<z) A tuotb lood is supponlod by o coble whlch rune o-

ver a pulley b G fo€le"ed lo lhe bor DE in Fig P-eos 0m*

o l6D of bons Ac \DE \ of iho purlev Assunc ol l hrn-

dp. t. r,F G-@lh g heol€o{ lfe ee'9hr of eo' h

26 27

!a) ol!& o FBD df pullq/€ Eq D 3 of lhe bor n D €h4n rnP-.oo. nseu-s otl hinges fo be sm@ih g n€loot th€ w6,9hl of

.<"-Kv".

eo€) Th€ cable q boom shdwn i^ Fig. p-tsos eupporl o tadof 6oolb. Deiern1'he lhe lcoslle Col.@ T ;n lhe cobte b, tocomprEssivc ,Ale C rn the boom.

r Mcthod i (using horizonlot \vc.ri@l^"".)

r@se ' - C .a6as t O

I6'n2o't Cst^aE' - 6ao @eb6l. cq r to2 t.alolo I i. tcms of T)1 6h 30' + (1 es.d/coeq.)(srn4s,) . soo

J,:!!!=?9:4c - 1BlE Go*tVe. e.

S:!4.%s rb.* Melhod-I(using tulotior oies)

- , ) , 2 " r r w - o . c s , n'.'.

- c _ e!1.aazllL

l@ -c

l

l

ztn.o: l - 6oo@6,6d r cc6,zs'. a coset + saz ea6(coeze')

-E34!4-]k'r Melhod tr (u6hg Forcz l"io"gle)

si^B- e 6o-

i. hold ogo:n€+ o sl]@lh in-

rod AE,n f''s. P-3oe. D et. Pqfl c.-*,J A cylindo" woighing aootb

M"thod r (u.i"9 t{\Y o'*)t8 of aanido. b

/-Krltdr

e- )d.\'1-ih.Ot Pc.6&'- llac.f

P - dc63r.'//@.t' @

Psins'r dsin!" * .oo @

[N...a€ (.'",{r/@.F + n.i"aa- ,+oo - l:3!aj6glL

P = n @*/@,e'

- 4e.6os(,o.a4/-. z.'P?194 lU

ll.4n6o' - .oo .t rs'

.Fn-o I P . .q @.6; + il co..o'

p -.roo 6 66' + 41g.6os @1 60'

MathoJ )[ (u5inq Fo.c€ r.io.gb)

;.;- :;.c_g-

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

e - ?s' dcl . ltc volrc of P b lhe nomal p.s.6u€ ^t eqlcd bv

2a 29

FBD of +he blooK

Melhod r (u6ii9 Rololed

Method I (udrg ii\v orce)

' 300 - Nsin60'- Psin+s, o

P.DsL ' llao.6o'

P ' tl cbs6o/c.,.1s' @

,a'6) 3@ - nEi^6o.- H@Edho,n

11- 1@. 7 lbP" 212,1a2 lb

Method [ (us;"g Fo,.e1i.ongte>

sn.E .,flor q:d

<f t =or f i€ ink ' 'BoosrnTs.

d - +oj,ao1 tb<fh'o: P= ri co6,rE'- ioo @ 7s.

P= 4@,el (6k)- scb@1..

nl) If the vdlue of P i^ rb. p-e1o6dtvc il musl be i\.trhed w;lhthe 3oolb b6r in equilibrium.

i6 18o lb, d.r€rmhe iho ongtcthe. Gmooth plone to hojd

r.l6in9 sih€ l.wj q = L

P'r@!

!ir). Datcdinc the nogniludes o' P \ F he@ssar/ to k@P

lhe co@!ft.i For@ .r'Ia6 sh@n in Fb p 31? In equniL'rrum

3oo4^@'+ P6 4' ' 2@ st^lcb'

P- -1t3 245 to

F ' aa/2 a'E 6tS I Pcd z'; - 2@ @s 165'

7 '.uasao'- oa z* (cszo)- zo <'x'*'

F - tu,87 \b.

s1a) Fio 3€ rcpreechts tlc -^cu.Ent fo{Ee €v6lar e}i^g ato

j6i"t of o bridge trus€ Detcmine tho voluos of p k E fo m'n-

to;. e{ullib.lum of thc lorcee

u6ihe Rotoled Are Mettod

'@ 6ih16. + e 6i^i/5' = ao6.'nat { ?oo si^l

F - 412,439 tt)

P14@@"a{ - 2@@1E: t 3d?4 ; ; I Fa ' *

P - 1 @ ' 4 4 t b '

:*) the fwa 10l@6 shown i^ Ra P s ore i' equilib'ium Con-

p" le $e "ou€e of Pt- / -

zast '4t'r 3@ str@' '46 s'n E: t FGh&'

F - - i 4 6 3 3 l D

Z F h = o

P tad@*" | 2@@.60' - r@ra t3@@!d'

&b.lilulo lh€ volue ol f

P,@6sF'to@@e"t% = (aao') r roe:o'

P= -€3 ' 12€ l l ' '

30 3 l

!1..) Ihc aoolb fol% & r}h!1..J lhc aoolb fon@ q thc a@lb firrco sn6rn h Fig_ p_s15 otEfo b6 held in cquilibriun b^/ o lhird fo.€o f <ntinq ol on unkno-wn a.sr6e with lhe ho.izontol_ oeta"-ine thc votu€6 ofFqe

.oo6in!o. = Fsrn€- O

3e-a@@a.. I r.a;a_ @4b6l. O ro .4. @

\tn = aao coszo- +/+@6ta6d\ /. -a)

-@- 4ao c.E o' _ co6s _ cdl6lltoo 6'n !o'

-e.- - -76.93s. - 76.93s bet@ \_oai.

F = .roos'n3o _ aooEna.stn 26.t38

r . 20s.315 lb

v6) Dete.mlne the votqe6 €|1- fhe o.st€s o( \€. so fhotcca EhoM in Fs p.3tb w be n e4ott ibt tun

ihe tu*

2 Go)(14) co6e-

-o- - cos-' o,ezs- e ' 2 8 , 9 6 ' - 2 9 .

_29_ =_L

"n* =t"o ("nzg,)l/n

i r :I

ll, i

.

il

t l

l

./ :r7) Thc ayslcm { l^ndlc' cire dlt?a^ h Fb" P-trz e'FPg't

lhe indiootal $/€ighls' CtnPute tlE lavile fo'Eo i cdrc,,n'

ecn.n ' 'aoor ;canat 'B - 36+ .ao(stn&')

I . 914,162lb.

-s----9---2--

D' &7lb

A -- cc66 | 9..s15'- a<n(a"a1 t q+ra(a-1€)

A ' e16.11 lb-

Fototcd ,tses Malhod

ae) lhr€c barc, hi,yez ot A\D\ fdtu) ot p'C a' do$a

in Fls. p-318,6o a ur-linr ncoroni*r' Dolxtte ltrtd*

of P lhafwill Prevonl rDt'on'

s6,'= .d)an*'

i = 15t2rs b

tFh=o qb<t A

c- w.@+', A46o'

33

<F,. a

. P- 22z.or 6tnr . .

u6hg rotiz t.todgle

-g- 9, - _-LEt 60' .i.r.d .tn$'

v-d^;i- =

#i. -;1_

P = 223.07Gtor, )

P = zo4,7t9 tb

n I R)A stD,g . Boo

t7 - 8oo 4oo6t.e)'

11 . 463,6 = 4s4 tb .

-,1, --. "" toqcd [email protected] o 9tn6tt 6po.e. a.po6t,m lwa

?t,rd6€ eeh

^sasrtnq 4@tb q ;"",, ". ' i l ;r"; ;P ete , ayer frictto^b{s ou 6,s ta |\e;, qht+ ot ?ootD \[email protected]€re':n^: jhe oaebo\rhe nordot pro.€!,! N t4t. the o7tia.de.s \ the sm@ih raatuhtot ^urttu

ec.:t fhc FinR l.us6 €holn in Fig P'322 iE 9"@o ca

ler oi A t') o hmge aI B llg gNen loads ore nordol

i-'i""o ^"^o.' Detc'd,i'e trE paotronc at A \ B

plac<. )ho loodc b.}, fh€i' reculiont

to lhelkl: Ro-

.ona " eao(e'"eo']lat)R^.451A,Alb = a62olb,

Rsv r Ra = gooo sin6o'

P,a< - [email protected]' 161A.e

R e " ' 2 3 o 9 I l b

P-ah - 8@o ct'e'

6e'= Rev'rRen" - (E<n 4)' + (4aoo)2

Re -t(2aas.4)' I uaq'Ra- 461a.e lb 4 4620 lb

+o.O- - 2309,+

4000

e

R6 ",+6zotbs ot 3d" w; lh +he horizontol

l4 a5

32!r) TI€ l.iir66 e,v,'*n i^ Fb. p-32. icdt A b o .olfe. dl p. A lood oF 2@lbttE €oofione ol A b S.

cuplo.'ted q o hi.saic oppbia ol C. Dol.

zMA- oaoRb - 260 (@Eeo)(is) t aa(etnza\<a)

RE . 6s94,76_ 30_

Ra.2tgg.za b * zaoo n

R^\ = 2@ C46 so'&\h - l7Bz,O5 lb

R^v = Ra- 2oao stnaa.R^i - 1199.8s tb

R^"- R^h. + R^.2rs -,/ t11t4,os)x t (fq9,35)2

R^ = 2106 tb

l o n € - - P ^ w , 1 1 q 9 3 sHAn 11a2.bs

'6 . lorta {99,3s1132,Os

€- = z4,aol

R^ - 2106 tb down lo +te tefi al-6 " 84 ,7 '

:z+) A wherl of oin rodius co..'ec o lood of rc@ lb' os 6l'6i/'l

in Fiq.p-32+.(a) oele.mine the honizonlol fo.ce P opplied ol tl'c

cenler which rs neceieory ta slart lhe wheel ovc' +h€ 5-h

bbrK. nleo find the rcoclion ot llle bloch (b) if the fo.ce P

nlcy bo inclined al ony ongle *ith fhe hodzonlol, dolermine

the rnlninurn volud of p lo slod thc wheal over lhc block' I

o"qlii ihai P motr,es wrfh +he horizonlol ;\ lhe reoohbn ol

the blooK

.t e = o/41 - elo =ae

") p-- ,7

,439,Z r 4 d ' o

5P - 1o@(locos3atp ' 1732.651tb

?. Pd .rs3o. -_ i32,o51Ra = 2@Olb

P i6 min iduh i f i l wi l l be -L to Fa

hence,-q ' 60 '

10 pnin = \oao(1o.asso,)

P6\^ -- 866 tb

Ro cog3o' = Prnin cos6ops -lp^;n1nsaod/cas tt

- laeo Gosao'l/ cos to

36 37

tsl Dol.;rn;nc t'hc o,,ount q direct,bn of Jhe smolesl forteP ftqu.tn b E,o.i lhe wh6et ^ Fb. p-3es over brock. whol i€lhe reoclion al lhe bt@r : ,

casq, \y , cb.714 _ %ZMa. A

,aco(a) p.o) p/(o)'a "^t..,",.1.X"'l,r''riL1,l"26t ( t .ae) Pcos- h .6^ F6, " \ / t sq , ,a " ,u i t , . o . t ,q .

Pd{ (d6+) r p6hq(i.6e) . iTso(o6D P('6i"q) l 0,6+ jF a"q l 1.se p coe< + 1.se de 6,nq . o

#1"**" *" ." , "_, . , f , " ," , -* .d 'P * 19 6apa^q - r .eep@ \d 4 l a 4 @ 6 4 + i z q d r q .

Lag C@s- - a.a+p.,n-,

lI1 = fod< = l€1o,6+

o,64

< - 7 1 . 2 9 ' + 7 1 . 3 '

o

h(W .;1s.,1'

P stnso' - "o- 1.tn n, o" '

P = 1es4 h ot / .a"Rsthsd - z.co (€D1s.r1")

R- 641.6 lb ! 6+4 Ib

w',h

iIr ll r

l

l

i

j

ird) Thc c/l;ndcFs i^ Fq. P'326 hov(, the indicated weighl6

r., d;mendone. Ascuning sruolh conlocl surfoc€s ' delc^-

mine lhe rcoolione ol , E, c , \ D on lho cTlindors .

FeQ of Enall c-/litdc.,

er l1b41ao' .R6a6ra@e d - P6

Ft . <o asto'

2e' P.r. stn.d

P |a- f @lir,q oldg lhe rj'ore eto*a h fig. P-327Delernhe lhe votue ol P \F

$(r) aAsti - 1so (6) t ae82)f - 390,15 lb

ts(P)snsz,+ - twg) -dha)p - - 1a7.6,4 tb (- @66 colnptce

10 Mrl

FcG ea'l- P@6t4 - t6.o

zso ra (aseai) - ( 1.'.6,)(@E6a.a) - a<to . o

38 39

tsro) Two wc;9hlle€6 bors p;nnod togelher os shown in Fig p-s2o supporl o lood of .sotb. Delermine fhe fircc p\F octiaqr.specl'rety olong bo€ AA i! AC thoi moi^to,ns equitibrrum

Io^ P' lL ) p.s6.a'

to.o< r j_ i o{i3s,66'

{{z- o(+)fco'o< t (r) fs'ns " ..Eo(s)

a F6o6 se.6dt 2 r(s,"!e.66F so(s)f - 6101 lb.

zPs.np a [email protected] - sso(Io\2P(ane6.a') | 2P(caE66.t1) - zsod

p= 901,39 tb 0c .t6)

E e.) Iwo c.tti^d.re n q, 6, wc&hjng lootb \ zootb ,€dpcclivcty,

7". ?'"-"r"d by o .igd r€d cu.vc, po.ollct {o fhc anoo.lh cr

lnd.icol 'urface Eho\'^ in f tb. P-a2e Dalcrm,hc lhc onato" o<\e thol danned the poirtr'on of equiljbn;m.

e.cd ' -< @

lodl.4s< - aoot@eloocoga . .oo @(eo-a)

rcoa-<-m(-so&,.".an^\loo .G4 - ,oo €nEo 6'rF(

l]!s-i t6< - rod26a@.

- ,o - 26'a3's,4.

&orb-l -a,ltu -opI .{€o(a) roo(+Xe) + R, (1o) - !0066) - o

. R1 I R, = 3oo r rood4) r .oo

RQ - s2o b'-

fnzn .e@ lo on inle4sil/ of 4oo lb pe. n

es) DelcFmlnc lhe reochbre R, \R, oT the be.n in ta P-#3

looded;th o concentmled lood ol rdoolb &) o lood .oeling

Pl= Feo lbs

fo. the tlem looded c 6hown h

t6R.' 16F.2 | 4F1 r1600(a)

r5R, =1600(16) + soo(a) + 1600(3)

R4 = 2loo lbs.

R 1 t R z ' 1 6 c , 0 + S O a t 1 6 a AR1 _ 19oo lt\s.

$Rr -Mo$+gQA.) + 60(6)(6)

R, - .9.ss lb6.

P4i Ra-12o I eo(4) | 1149)

r\trr -l<ooQ)Vr, {t*o("W\- ea

40 a

€s)-The .oof -1tu6s

n I b. p * ,s [email protected] b./ o mlk, ot 4 !,o ht gc al B Fnd the 6jues of lne rsc rrorrc

Rsh.o . . . Rp _ 9s i ,39 the.336) I}E cont,h'@ beom shdn h F,s.p-sec is burft hlo a rcrl

1 , , " ,n 'o . - lho l , l roale oeornet po,n l< A\L rh€ beoh i6 rz .

ons \ h€lgh6 jootbpeFfi n concnltuted tood 6 2@a tb j6 oDottetaI the tree c'4. Comp"l€ the n@chbn€ ol ,t kS.

. 3a R\ = !ioo(10) 1 600 (eo) + ea6s)R^ - 966 .67 tbs.

1M^"a3oRe,- e<,r(1e) | 6oo6a) + soo eo)

Rs" = 9f3.83 lbs.€Fh"o

zRa.e@o(1drtua(12)(6)

R6: re60a lbsP , ^ . R e - z @ a - r b G z )R^ " 1s@-zaza- 12ao

1dR^ -ad(14) , Faa(1) .o

€ o o r 1 9 a o = R ^ r F i e

1'l tP ** beo,n ,h F,o p.ra2 iq €upec.,e<) bv o roaL,,on

;l .:: : : -*.

,ot n whioh_ 6epo.ore€ ,hc upp6r k rowe-b€od6.D€r"- ih€ lhevarus of d; ; i ; ' *"

^**

R1 - 1760 lb

ss) Thc lwo 12f1 b@tns dl('r.n n fQ z-4o oi lhe Poge @ 6c

;; ;-J ho.' zo.lo / with r€ePeol ho ooch olhc' 9 tood'i

tiiJ ," " "^" posi:t;o,, t' CD so ihoi oll lhrcc reoclions

;';; ;;;; i."r *,'r "" q n' nen bo? Ilot tor qilt P

be from D? p.edb

F . 34O ' R1 'R, qRB

zF"- oRc -Ri rRs

Rc - 6ro lb

R6 (Y) =Pa(12)

Y = 320(12)

Y = 6 f t .

tM?.-oloPe - 16oo(t+) - 1o@(4)'o

R4 - 3a4o lb'

toF,l + 1600(4) - lo00(6) 'o

co.sn4ring th€ 'rPPc.. b€om '

PG) - tk 62)PO) ' 6.062)

ga r. " 6a.62)| . 6ao4a-)

960

x . g F l .

. . R r i L R 6 i e 6 f t o P o . l .

P , e a f l . l - r c - O

42 43

a/4 (D/4) ̂ yr(d/r) r p(o/4)'NDA -w{a = PV,

wA @-d) - pD/2

aa;a,w-3L

(o'd)

tto)Forlhe sy€,@ of pu e),e €rfrn h Fb.p-ero, delch.incthe ratio of w ta p to rcintaia cguilibiuh llcaleot orte fnb_I'oa L th€ weighl€ of the putlors

ta) rf_ aah purlg €br. in Ft. p-Bro wei9h6 36 rb \w .7zol4F,hd P lo ooinio.h lho cauilibriun.

r,1' 2s.2b p- e6 | 262)/e

i!1.--

s.r) Ihe *tr€el toods o^ o i@+ orc.gi'o h Fb P'ea oel5'--'*

"t ,Of.* " so thot lhe reaotio" of ll'e bao al A rs

lni@ oG gFAl ..e lhc Eootld ol E-

aa!)ihd we{ghf wof a l.o"eri"g a6ne \c 2oIo s dit'g o56to"^

'^ i,t ,- "nu lo p* *nt the @^e l (tn.lipPtnq 'o lhe r'gl'twh'

- l"*.ttp a @,r P af 2a t''ac'.o..@^td *'ts1 -S,: ::i ,.f

il;';:'il"r"";;" ,r'q *t*t the oo'e*rrr re#'n in e4uirr-

f*- ia^ *i* the @'imum taad P i' opPtied t" wfEn lhe loa

q = 2o +ons

U- 2Rs GPe'ltcA .aii+ion)

tsr.a= 6oaG) + 2aoGt+)

.5p.6 - eaor +eoo - @

RArRe ' 600 t 2oo

' v A - e @ . R 6 ' e @ A " @

b GbVa) " e.ot) + aaa

Limilinq Condtlio's,

\ thq P'o r P.2 'o

\ rh€n P'2o ) R1'o

ztAq-o (* ton P-a

4(x) = zrG)q' = r4oTon6 _-O

aMR,'o ($.6 P'2o)

q ( " s ) . z o ( . ) t e o ( r o ) -qi i\{sl = 22oTons - -el

- 6 f 1

4445

!€) boom AA i6 9uworled r;r o hortzontol posifirn h/ o h,.seA x*. o cable $h,ic\ tun6 fton C o@- o smo puite/ ol D os6hown in F,ir' p-ra€ codpuJe the leo6,bn I th the cdble 1^ iheho.tzonlol !^ve.irbot oomp@ehls of fhe r&otion ol n. n :lq l the. jEe o{ lhe put te/ o l D.

zal.) R'paat pftb ea6po6itb^ at whjoh il islood€ retuln verl,bol.

2oo(z) | rca(6) - r(s663a3')(+)

I = 279.s2 lb.s.

Ph = r.oe63-+a"- (r7e.ez) (.663.ai')

R i r l 6 i ^ € a , + t s ' - 2 a o t r c oP.! - 3oo - (21s 62)(6n6a4z)

Ba - bo,a6 Lb.

ir +be aabte putls {he boo,.1 AB in{o ot cl:ned ol 30' abde +he ho.,z6+at. rbe

6tne' - V4 lon€. - 6/4@ao"

4t .1,t{z).,tet | 1&(6)@ao'

Re+I6h--. = a@ r11x)

R! - 3ab- 216.. (etn6d)

Fa - 1 t2 .5o lbs -

B Eoohftorc etos ;^ f b P 4+s i6 tupPot'tcd h pr''ot6 oi A \

"*"* ".;ut " soi p'tfi d"p"le tho f@'r?io:T'--

n * t " ho.,zonlo! \vaticol oo"poale ol lhe

rrg) The teuse. shryn

&-o hinge ot A solve

Beo) ComFrle lhe lolol @tioas

O E

i^ f ig. Pia is oPPoriel on re e's ol A

fd. the conpo.'€n+6 ol the reoolrorLs

Rsh - z'to lbs'

21R^ | uo(15)'dL) r '+46(56)

q--!4 R^= 71o tDs'

24R6! - @(12) r uok) - 4b62)

ol AqB fo. lho fruso shom ih Frgu

/t /t-. / t / |

/ "l/ ,1,/1. ,,fr>E I

rU ln^ 12@tb

-- 194c

l!.'bl) = s&Q) t4l6) 1'8'h')

lit' ' 2455 67 lbs

nh . Eh =?+66.6? lbs.

&r -^ao+s@r@raoao

46 47

Rsh - soolb6.

R^= toag,7tr p@(eo) - se(^d- a@(ao)bs.

{fv .O

PlNrR^-6o0|12co+sooRa? = 12j4.2e tb6,

e.E - GAAiGTGAF - Pa4.?e trB.tang. ;p1i .ee/eoo . . e - 26.12 '

i. RA a12so.7s tb6 up to |he tefl ol 16.12.3Er) lha b.4m shom in. Fig!,re p-s6r i6 cuppo.te! by d hi.tg,e ot n\ a mlle on a 1la2 6lq,c ol B. De]'eaditn@ lhe resufont rechbne

ft(Ra'\ - a{t<12)

t6(FLw) ' +oo(i)

Br Rol.o \ Ptuporlion,Rsh - r R$- s,(1/.)

KB -Yflgo)' t (3oo)' - 335.+r lbs.

R^ ''Lrr..-ziG'jf - Bo ,, tb6

!6r) A pulley ,+ft. h dioreF. \ sdpp. "r'^g o t@d of ,@tb :e @n-led dr € on o honzonlol b6n Gtq p- e.2\ Thc bam ,6 guppor led b, o

I

. eoo- 2c6Ginao)

R6- loo lb5

Pc(s) = 1co(a)

zF! -a

R^v r Rc ' 1oo lb6

P^v - 1oo - .eo = 60 rb6.

5 f h - o : R ^ h ' T @ 6 & '

P*\ ' 4oo @6a'

' 113 eo tos

rOD of lhe beam,

e - 9 - e . 4 = 0 , 5 6 f l -

R^- @o)a t(18.2o)z ' 1ea27 tb6

lo"$ = soy'tz.to ' r'1o'' , k^= 1oo.21 lbs ot 16no'uPfolhe

ngnr .

sse) The forces octing o^o r-f1 ledshl ofo dom ore sf@n in

Flir' p 35j.The uptlo.d qrou^d |.@ction vo'es un;io'olY ftoh on

' '1i .n"ity ot p, b/n. at-A lap" lbA or B Delemrnt p'r p"\ol-

so +he ho,-,2r.'lol' re€ieldnoe to €lidrng'

R4,Bionce to 6lid,iT,

F - 1oo& - 6dx @e'

F= +eo3.ss lbs a 4600 ros-

R= 6a6tetA3a' | 24o..

R* -- 2to.n(1i r axbG)- rc.|:a (6 )

48 49

A-R/B(r6e,b)-#\tt #E 12 t&_

P,.R/B( '6e/d. tg l 11 s t (s€, l - . :aow.1 9 1

3E+J Cdnprtc the fotot reoonbns ol A\B on thein F(t . Prn5a.

tong- -iolo - 1/4 )e-- 2o,s6o

8oq6r r ac+oG1z6,66')(1o) t2oo(1o) . e2.a/c.Ee6.s6)(6b) |'eo(6o) | o.tu(ao)i bca(ro)

R6\ - 4622.+91b6,<Fh -o ; R^h = 2c'b t 2Z4a s.2866" r 3ooir€ rbc.1M6 -g

ao p,^a - e.,.'rAo) | rc6 (6a)t z@a(ao)+ 3a,t (b) | z2ao(@s 16.

lonq ' 33u-o9

| 224a{€,n "6,s6)(1a)

€F. +an_1 3976, 09!ca1. *)

.'. R^ = -+er7,e7 lbs up |o ihe ri9h1 ol q - j€,e6.

355) Dele.oine lhe.eocib^s al A\Son the niik +ru,ss 6h Fig. p rss Mehbers CD \ F6 arc re€peot&ety pe.pendic, _br lo n E \BE ot thet. midpohl€ .

iX!., ^ = poa(as\ l ao.x)(a 2e)+ +ao \et iQ^ - 536i 27 - 6360 lu€

t!)'r]" ' -""n., , ""*6ets) t <aoa(+t zs\ +oco @e6 56'(+1 26)

Rsv = 6131 67 ! 6130 lb€-

Rsh = .ooo s'n26 66" - R^€r^3o" .

- 4oooatn26 s6' - 5361 27 stnaa

Ran = a92.Og5 lI$

Ihe c,]ntilerer 1.u36 6ho'n in Fq p-a% ; suPPricd-bv o thn'.i

i; , .tt,r BC Determine the reoolim oi A h B

ton + - 13/ta t+'26t6'ac =sa ' ts/cosze Ee'

r ' lc- aa' $17 f)

Ao - 39p9;a: s,.ed

Ao -. BF '> 16 17/cd

Ao" BF = to,75 t ] .

-B^, - -!999-

Q^ - 2ooalbe lP

50

35t The unilonm rEd in F,!t. p-ae7 wc,bhs +2o rt \ bo6 ,lsof em"ib, ol d. Del+mine th. t.";-,;;;;ftX.:tione o'l lhe 6moolh_eurfooee ot A\8.

aM^-O

2I r 440(6) - a f i sh4o ' i 6 r t@€.b!l, stn lE - aosa6.

2T .r 2s2o - t6 tlstd.'.

T - ad@sa5. - 1260 ^. e r ish+s . - t?6o

-

s u b 6 l . d 1 z i a 1 ,

n@94s' - grlcD.+s' -e6a-7n.*16.! - 1260

, r -dcoe.E. @

fi - ?s4,sd tbs.

2R^ r aeo(a) - d 8ha.G) 1 n@*.f6)RA - 6dsn4s.- e+opa - s (2.+.soxsr"+s1 - alo - 2!}o tb6.

js in €quil;bf;um unden ihe @lton of Jhe fveFis. P ess. Detemine p, R \-r.

R(16)i r@se(s){ r6nef6) - 6co(4)

| 4ao(s)r6R 1 9T66e f 6ro@ _ Eooo @=Fw -o

o1! {l'""'u.4 e- 6 .a7 . R '6<b- t@6e @

$ (6c).- Ioase) ! elco.+t 6rs,no. €6@015 (6@_ roo6 36.s7') 1 €.r @sr'e)- + 6r€,n !6_s7- . 6o00

T- 12es.7.t tbs_

R ' 6oa- (128s,7) es #.s>'

R- +2e s7 lb6. (!p*a.!,)

P +1.,t1+ - 1@

o - <a- Gz*z)'a=s ez' -'P ' 37,.qz tr,s (ro rltc lefi )

# '#4'o o - ae.afrE

@.r$ols ' t=P^@4'Gz) A-:|, - "r"^1'*' -1 tuo llF = 1'e 2" tE

*",',^oii-*'i' ,'* as.-'who' .{o\re or 'r ocrirq or '( = 3fl

ftvja b tig NeeP lhc bo' horrbrtlot

& . , 1 4

- t c ' s ; 7 9 f i '

caad - f r t N-+.3e

- o o = + 2 4 - . ' r n l l '

I t a - 6 - 1 ' ? , = 4 ' 6 1 f l

1 6 61') = a@O a")

1 - 60'3 b€

52 53

?6t.> Referdrg Io tM 34 ,-'F f = ?dttb r( r - 3fi r .r6lffii.!€ tlpagle €- ol wh,ch the bo. *tll be ,rc|';€d l., the honzohtat

rl is in o poerlion oFegu;librium." (!4fr!e1sct, " t-*.ffif4d)

Us"9,+brlb,tu@tn," ,s, - n(l-,')

fo. &,!-o = lof.(6)Ga)

3- , 16@-. qR^.b Ro,-g-tzene = - lqd i'-"a,*e)

ft. 'he afd;"ales d pl-o

r 16@ = D (caee + 6ns-) -x

x =gGseCt_6'!9)I * fdn@

fo- a+ p^.

J = .tzGne+e.\e) -\-..3pr.3 = Pta at (cast st'e)

nl'a"*t-pL -'**1 - $q[ sa6€" - "(,..e, e r"o)l| l ' l . . a ' I L . l . t ^@ ]A{ e.t i - 6&e - 27.8e - a,(@.+',na)

1t l@ao 1r+on@

:: og+ - 6o(@cJ eno)1+ aon6o

3B@€+6rlon6o) = @ cGe | @ 6nea6€fal(r 1ro"@) -@-l - "td.6,.o

[=(r **an eo) - oo] = 6.6. (eo)

ldtot = A@26279-O- - 26.6aE'3A7'

-

ChoPlor +

'Anolysie ol S{ruct':rcs

54

'1{,a) Joiat b of lhe lruss sha-n in fis. P- ao2 ts euajecled to

gle of+ degrees wilh thi6 slnoghf line. ghow thal the lor@ in

Bc nrusl ba ze'.. Ae e.alne lhi€ r€sull 1 lh€n €how thol 1fie b.cqs ;^ mSdb€. cO'oE EF,FI,HI.,HKI,\JK t€ obo zelo

Ane. At o jo'nl €uqj6t€d to the @tion

of lh.e€ flembe.€ bul r€ d{ha lood,

il t-o of |he menbe.s o€ corl,'1@.'

the tc/ce i. the thin menber musl tJe

the 6rces ererl,ed br lhe lhrce membeoe n8.6c' \BD. M

AD\DD ore in lhe some elrcighl line'but Fc ls inclined dloho.-

ae) Delen;6e ,he fo.ces ir €ooh ba. of lh€ t.oss 6haah ;n Fg

P-e3 . llkl: Fri.sl daiemine which bqre cd.-/ @ load oihq

p.haiple ddeL'ped in Pnb to2.

c E - c F - o

P - cDdn@'+ aeet 6o'

6'i!€ r CD=OE

P - 2cD e t^e'

c o - o , 5 7 7 P = a E 1 C

CO - BD ! o,gj7 p

BF = BD@s6o'

bF - o.67aP coe 6o"

Br * o 617P (o.s)

BF-- O 2A9P - f

.aa+) Del€.dine #E lorc€€

6ho.t iA Fig. P-31

the membene of lhe rooF tnusE

atrEid6irg lhp rhole libur€,-tu =o I R^v + Ror' =libtfiosrnb'

R^v r RE^/ '160-. .O

FDs - 66.6|b.Brv @ Pr'A

4,.a--lF"'

tfa'O: gr,cinr.,', AB.i^N; '1oo +1e6&'

o.5go t o5y'O'1cDtsopo+ so ' ts(z) ' ta-@

<fh-a: Bo.tE,go'= /.ba6io't 1@ctag'

bD = ̂ 6 ric'l-*@

@ p t B .

.06) Th6 coniilove. l.uss in

lhe fucs in oooh tnemb€r '

R ^ v - o e A 6 - @

Ac' 0.A6 AB-@

F^v - o.e(.oo)= solb.

&- Ao ' oe65(AB)'o,E6cje) ' E6 6lbjr

@ d cAB) Id | /\b ' 4')

^ 6 . 1 @ b - b

,,. E,o- /.E+,loo,, 2ootb - c

. ,Ac - CO ! 46,5 lb, -T

8 C . 1 0 0 j b . , . - T

Ft4 P- 46 i6 hi.€€d ai D \e Find

@ P t ^

AS6neo' = 1dO : ^A'ao.'dtb' 1

<Fh-O I AC 'AEco6so'

t\c - [email protected]' /, .C '1- f t2 lb ' - c /

67

bp . 1.?,12 r

@ p l a zry -o 9c.t.6o' -pD 6.nao, . rooo r AB sn3o.o sBO r o.g66Bc r .rc,oo+ 2oao(o,r)

o.eaD I a.e6ac = 2ooo -. - a<Fh *o : 60 ccs3o'- Eccos5e. { AE @s !o "

0,466 ao- o.6ga + 2oaa (a,366) ___.@q , E l i m , n o l i d n r r \ t

+ r.a sso + o a66B. - 2@a) o,5(o,e66sO-o,eac - 179?) o_€66sa'2a9- o,6(2F@)

bc.966tb.- . c /

@ pLC

o.25 BO + d..+€3 gc - looa

CD6t.6v"- Pt,E|.60' I lococo- g6sfos66) +iooo

cocos6o'+ Ac+ scco.6D'- CF&- 2o2o(o,a) | 17t2+ 86{' (a9) = s1ru ib -. . _ C

^9ana6 - ftoo eo,5o.

Aa = 11321b - . , - ' t

Fg P-a<r, coip-le

l"e lL€ . 'L$7 {"

+oz) In lhe co^lileve. l.uss €ho{o irforoe in m€nber6 AB,BE, \ DE.

@ p l - A

@ P I B

u6,19 F.otdt,b^ of Ax,e,

i ee.rrsiro l- r

+ o,25Bo * d.rqi sc - ioo.

' o?s Ao - o..!e3-bQ E lgoo

i^ eoch nember of lhe wor.en trucs.osJ computc ihc fonce

6hdnn in Fil P-'o€

R* = ABs|n6o'

A6-A!9_

A3 ' asoT 62 < 4910 lrc

coneide.ing the wtd€ nborc:

= M E ' o

R^t(n\ - e@($) t L@l1a) |

R^e ' 4240 lb

ZfJ aot A1s;n6ci - aa@r

rc' -4s11stn6d -2OOa

srn5''

, , rc.2@tb- '- 'T

Agco6so' - Ac

tc- <qto Gosao)

/c ' 2459lb-- 'T

@

4h.o: BO. /\6coe6o' r bc.a66o'

ED - +e1o(o5) r 1600(45)

BD.3755lb- -C /

p i . clFe=O: w6n&'I caen6o' ' +OOO

\EDok @l r co&'06f)' aoe

co = eog94 + 4O2DIb' ''f,

ZFh-o:Bccoe6o'r /€ = oDao6@'ICE

2b.o(o5) r 2ass = 2o2oGs) | CE

c e ' 1 w a r 2 4 s 5 - 1 O 1 OC e ' L r + s l b ' - T

5859

ct = 300 lb-..c

DE6tr|@' , a1st @' r etd

DE- 2o2o(o.e66) t so@

DE- s+94.2 v s+€otb c

ai1.) DolermlrF thd ftrce in n:E]mberc ,,a, /c)BD,co, qcE of tk)econiilev€r lru€6 sho,n in. rQ.p-411.lf lhe loods were oppliedoickE in€l€od ofol E\D, €peoify whioh memb€i6 *ouldhove thoir internal fo.ct ahooged.

ton6-- 9-

@ pl . A,

@ p t B , ZF .O =Fh.O

r.f,l.Fa3,as'-1d) AC- Bcos

AB - 1eo,2g lb r'.c- lsotb

@ p I c

t*/* .

./\B@za.@' .eDa44.@)'

AA - ao - 1eo,29 tb -. :f

ta o -94?

PL- A: I oE'i..e4'

co- aso)b-.- ' l /

Ce - CA.:ocsol2 | /\(a- 2g)< 6s3:12 t 190

A, +De - io+t/6(12o\

... 2OJ = 12or e/s(12o)

2Da - 192

D v - 9 6 | b . = A v

lnta.tonsnq hinge k rclr6'

eppo.t *tll not chonqe ltE fo'ces

in cocl' ba. e,.oopt {ir Ac &' cP

a c " q , t e / , o ( ^ s )= 22a tb6.r'6td\)

co - B,o(s/e)= r2o b({..6€n)

&--

Ac .12s |b (lo^.d^)

66 - 156 16 (a"p.ccaoo)

0 1 D :€ to,.c.

* \ t- e6-

s--+Bo " i6o tb (cdnpc66'o^)

co = so(slo) -oh

b q t , O h ' 9 6 | b

.', Co '321b (la5o'r)

dt C: 2?r-O

AY TDA ' BCgC ' 192 tb0€'€ion)

@6l

aoe) oelcrmo€, lh€ for€e in m6nbat.5 AS,BD,9E,qDE of lhetbwe rof lruss ehown h Fb. p-4o9.

A" (ao) - @o(3o) - €oo(2o) - ..o(ro) = o

H"(1o) -,ro(€o)- ooo(ro) -6.()(4o) =o

Hv: 9r5o lb.

a.

sEsh6o ' -6oo(Eh60) .o

BE - 600 tb (@.nprsi6)

[email protected]. r@(@.6o) - atoo60- rsoo rb (cepr!<,ir,)

t'a) Oelermiie the liJr.e i. €och nerba. ol ih€ pro$ roof lruse ehoM

AS - +s@ lb ---C : FHAC:6H - 366tbr-T

o, E, 'Y /@ u5iae d* ^c,

,Y ' ze" .o &=1s&bc-F64/ l* a lhc at-,s,rct o,6

.aS-ED=DF - asoo tb-..-Cat c. f.d-

E w-.E_,q-_es_g .ti5

:. co= 463.3i rb-.-T " DG

Ac - 2/r-n q) t cEcF . :,64)0 - 7A (ztee.az)(F = EA . 2400 tb --- T

D E = O

aM{-o. ,6oo(ri}rad(€)t€oo(e) = AY(3")

Aa- adttb

'/,

l^w

&=4q-_Aq

a1t) comPuie lhe force in eoch rn€r'be' of lhe lru6€ 6hown in

f,A.p'+to t lhe loods o{ B\o a'e shlfled vecticallv do"

-o.a lo oaa io lhe loods dl d b E' wil\ lh€re ba on/ cho"gp

in the.€oohbne ? Whioh membsrE' if ohY' would underyp o

aho.gB In hte.nol, 6rce '

oonsid6.i.q lhe i?hols fi?u.e.

p,y rp'd - 4,o t2@r2@r eod

P^w i Rry ' 1600 lb -O

1MF.O

9^,Y (eo) "4oa(4o:) r 14("j,o\ t ^blao)

+ a@(?a) ' eealt)@b61. lhe 6l]3 of R^v in 1-

Rt! - 1@o - ego - 12a la

a b o = L A e ,

BO . 9e5Z' -4e2.5< 4 9 2 t b - r c

+eo++,/b = 4'.o te.

l-. {nGe') t k1e8, - a"a t ac

<r., .b Bc- 7o' o+ ='7@lb - - ' r

B^ , -A ,Bs , ^ a3 . @ptc . 5 C( , ' B- 9s3.er { 94elb- -C

<Fh-o tF! 'o l . *Ac - .^a @€6s 43' bc'Gco | 2oo

- se6 @66? .4 ' 7oo - \ c0 | 2oo - Ca' l feo ' /

/c - 44o be | ^At : ' tb - -1 ' ' - t l to)b - -c

<tn-a : /cr Gco ' t F

cE - 4ao+4G612o)' 114a:16 '! 1740 lb - -r

62 63

@ p l E , @ ?t. F,

Rw' YE cF

€hown in rig

DF - [email protected] 4 161o1b,..-athe force in eoch m€mb€. of lhe crsne

@ pl. A,

b ' - 02 |ca - ?occ@Bb. - 6. t e. - z.G>(s) c.E126.

b = l 3 . o a -tn | , 62 -@-os)'t s2,.G.oaXqc.FA

A" 22 ,Ep l

bD6D5o'- Bc6h.ir'

o,5 60 - o.s66Bc '-ta

tzo"o . o.eor(ff-e6) + o.sacBC = 6c0c '26 ! 6000 lb_ . .? ,c

,,,!a = 13O9A 61 - 131OO frr -. t7

1Fh.6

ACc@2aa9'- 6

,'\D- 1t1oo'(6e2.6q" - 12o23.4g tb

tB = 12cbo tb_-_c/

Bo'=*ad = rcsg2 rb ?,+ lA lAAtb- : . -C

@ P l

,^6 -eo@s& +Bcoa6o.12t)Ca - o.a66ao r a,aBc -a

aft) Ocfc.mine thc for€€ in mcmbcr AB'BD'& CD of lh€

lruss 6hown in Fig P_a14

K-,T

" ' T , ' l q 'u, sblb coo lt h

4Mq = o. A"(36) = !oo(27) t .ooQs) r @G)

\k A8= Goo

Ag. 948.99 lb --"C

Z F r ' oAC - ./& AB

AC= qJo tb - t r t

ol B, &taaon "

&$/a rst

r/tio Bo - y'F ^aB A - 6 3 2 . 4 6 l b - " c '

'/It Ae - l/.Fo Ao I eaPa - 4.o li) - _-T

;e -E-c.l"-

CD = 125 lh - - -C)

64

atA}..',@

+1s.) Solve lof th€ fo.cetrusb Ghown in F,i?. p-4rs

in menbe.€ Fri, DF. s, 06 ol the

Fr = 1274.19 a plo tb -. . - C

@ Pt. f, @ F,

/,tz FH - 16 | t/fi DFt/E h2io) - 16 r Xi baz)

F6- Eee. 4 6a'tb

co.r6,cren ng the whote,

Rav I Rhv E too 1n@ r ocroR^w*Rnv! l soo

tuNfr6) = aao(e) r 3606€) ,

R^v = 15Oo-9oO - 6o0 lb.

7.r, FH - 3//.tri6 DFor - A@]li)

(3' tzoF - 9+c.6 4 947 tb_.._c

@ pl. 6,

4/5D6+6t t ) -9c ,0

pa - 3ao (s)

D6 = 3.75 tb _. ,_r

ru) u6inq fho mctthod

be.6 BD,CD' \ c€ oi

ofGsctrbns, dele'oi'e lhe fo'ce In med-

the roof lru66 6hown in rl9 P-ar7'

con6deri.9 lhe Y'hole fiqur€

..28 F^w r FFw . 360 -O

F*(1D 'ao(s)

bo - eob2)

p o - $ a l o - - c

co - s/. Azo)C o ' 2 o o l V - - c

cE' 3zblb - -1

41s) rfE wofco lruss rood* -06:0::l i ::j-^:'":'iffi' a1|(d of oe"lios'. - -^,,^. ^r r- \ a I'nqe o1 A ar 1r'e n

- . . r - rh6 {^ .ce in lhe re -m^e w w\ ,5a t

ooosldding lhe {fEle fEu€'

1?n-o' p-6A ' 6aa ltj

4W-O

6@ Oo.l + 6@(0) i Paabo) 'aobOb)1

P.d (a)

Btu p^eG6) " ze6.)

6667

,l{s

or(2o) - R6v (2o)

DF - SoOJb - , - -C

cE("o) r jooo(to) r R6r (2o) " R6., (eo)

cE "4oieasfu):_ogacsl

c E - 1 0 0 t b - . - T

ap) u6e the rethod olseclionc to dele.mire the to.ces in nenb..ED,co, \cE of lhe wonEn True6.

9C-+47.21a++Al i 'o- - -C

cohcidenilg tfE wiEl€ figurc ,

RvF ("o) - rooo(1o) I sooo(F) r

b.b(.)

3o(s.66) =ooo(.)+ also (ta)

BD - 32E.o/e.66

B D . 3 7 s 2 . e 1 b - . . - C

cE - 231so/e.66

c E - 2 7 4 2 . e t b , . _ I

ri .,"-'ro =.".? | \ e- a.66 n.

l / a \ "

RvE as) - co(1o) - soooco) + 4o00(6)cD- 412s9,4a

c D - 2 1 2 s t b - . . - I

- cD(e.6a) + 31s. .s (e.e<) . z.<,o(.)co = I sooo _ (:zsoo., r+)

CO- 2O2O.A lb .2o2a lb ---'f

aad Od6r'ino lhe focce in ltt6 ndnb"rc Df'06' \Eo of

tb$,e lrure €lto'"n n fiS' P'+b-'

aM.'O|.r'.o\=a@6'2)Df = 40cD|b' '-c

2r ! -o i @ot t / to6- A@

rJ6-76.Db"c

1fh.o'. DF r./to6 -e6

tu+ 1/'4s@)'Eo

E6'a<t@tt"--r

R^Y +Rry r 2a@t14oo

n^v l Rov - 3600 .-O

P^. (16 - 216G) + 12@62)

i ^ r , c ( i ' v -9O'2@=1e 'b '

BE _p@lb.

-w= 24<Xtlb -

.aa) ro- rhe rroe siEm :'q i-rfl'ilff,'fiff t*",b,/ llt€ msltEd oej.ints \ ltF/' €t'€cr rhe r

Li^.. n-t ' 6 opdl. 'e meltod oc se''l;orF' fir't obbin {h6

\oloe of EE bt iftP€cr|oo ^,.. cotr6t,-,i,q the whol6 f.gpc,

aa{a(rd/+

P;o' (126)

68 00

:ir_o**r15B]o.,,[email protected],F- fr,6 | *rten)-.,t'Idil

BF - 2@tb -- . -c

r,|.lrEd of g.olbo , @ 3/sBD-BE t 60- *a6ao)ao= 4@tb.

Pd. EF - 1]E l0+ 21@11,6O

EF = a'g(,db) r 2& | 1zd): 2@

* - q+16,fE-12@'1

gF r 45OO lb -. .- c

{.6) In lhe hiL t.rr.e ct'o.d nr Fir. p-a€B, lho Gb momb€r€I't tF o|c F.perdirlor lo ttla irlctirFj r|lsb€.s al lhej. midp<r^!c.l,rco thc drelhod of, €ellon€ lo dst6.ainc th6 fo.€o in rcmbecDr,DE. lr C€.

, R -

-- '5-

4F;v *a" - lrara+4.r1 -gB.

F ^ y - F 6 v ; 4 x!9 ^e/2l o _ : - i -

..:E--i-6 try.f -r4'5'

EG.E )n(a.6) + t('e.s) - Fe! 6e,.)!F -S.e|!9 ryse4 Fip. _.._ c

&f-o|. +lbllE | + - ,|FDFt a t1DE= arxJ iE - . - -T

connot determine the tb'-

lA Fio P-4?5 Then use

force- i" Uo"s fH 6ri,\EK

* r''\'tn Fig.3

en3o'--PE

DE = lo '

p^,Ua) t NQ, 3-2o\ - Fn($) + 1.t(@)t 'zb('br''

! ' oo(4o-1 ' )

r i = 1 1 o 4 l b - - c

-4".^'"^'44 ; , ; . ' , "*(1.\ ' i aeo4 " ' 6H( ̂E')

*Vi aA ' .eO' ' ) \zqt 'z1s)

r 2@G"

6t1 ' c .19 6. zs2arb - ' - f

70

zilr -aR^v (,) - EK(rz3a) | roo(ao) ) .e(eo -LB) r 26('o'1s) t @(a.-2..6)

ER - .9A,94 ? 699ltt - .-r

{rl) Dol€dinc +h. ft.ce in the lne4b4s Dr, D6, q E6 fd' }hc tb'r€'

rF/ -o, con6id6 rhe *fde fiaurs,

Rr = R^v = 1Cr5 K

PN tu>ao(@)' e(d+ rfglA

+ 4-e+ DF(L')DF -161.67 +162 ktqs - -c

2sfuoF - E6 r 26/(t6e D6

6=.fu(6.)-ryt;@nE6 - 1io.7 7! 1t' Rrpc-.-T

R^\ - 30+60+ .&+ Dr t lkfu D6D6- ia/Ilo, -4=o_ 3t6.+o6')J

6- 3a.61 =sa.., r:7s '*.. -r

<€a.) u6e lhe 'nelhod of s€oiioE lo edpu+e lh€ lor€e id

AB,AD,BC,\bo of lhe lnuss .shown in Fig. P-+32.

6 pn6ta ol .s'- 2<).

lr- \ .

FxG4'zao&i | .d16)

Ag ! 5909.31 i 59lo lb' -c

<Ms.o ;R^v(e) r ?g ^o(c) ! 'tlb AD6€)

D - 3 0 @ l b _ - T

€a) co.npdte fts fo'c6'

lr{.c €hown th.. FriJ' P-a!''

4@r e6ao' W r\sBD- lck @4-41@J

EO r5oo1-Or' + 5OOO rb- -T

<Ftt-Oec - +/@ ^b + 1/s 60

w'tr@s1o)t +h(@)

!E'6a.Dtb -- 'c

AB,^c,or, \oE of ihe 6'i6sa-e

< t - Oe.x <@) '12'(.) 1ia(a) r 14O')t t2(to)

I e(1o)

R^v - lox

/t l"' 6,/"1.^? ^1)

/1'/ r '^--6-

<. / l -{ / r

"!

l*"

- .,*o' zw'o

p.',!(2o)t .,b ^8(i6 = gk|e ^sQ6)e=,L lsor,ot

[e(o)_D6d].

AB . 7o.7s = 7o.e klpe i.,_ c

€ M E . O

R1v66I- a,1; ^cdelta = 6/+ Go) C - 46-02 -i€ xip6 ....-T

eG.,). vQo) | tc(o)r tk oF (22 - 2a)

r y@ DF (a)

Df - e3s - 42.s k?e-..-C

a2r) Usa 'lho melhod of ecclions lo compulc lhe forEe in lhc

mcmbers DF,EF,\EO of lho conlilever lruss desc'rbed 'n

Prob.+11 q Fi9.P-/r11 on Poge 92

oe. ao/3

^-;t

a22) fe. Ia ihe desor,bodpute tha fo.c-€ in me.nbe.s

rMe " o (Rd6olving OF ol D)

3/rE Dr (ao/3) - rco(ao) r 2&(^o)

OF 'a6o.56 lb - ' - |

.MA'o (Resolv inq EF al E)

L ff Go) - zoo ,Jo) | 2.to(2o\ft

EF = 335.44 Ib - -1

Eo (2a) - @t(ao) r qno(qo) + ca(rc)

E6 = 450 lb _"- C

BD, CO, E(cE bYpage a2, t\ com-

Fv(so) - 4oo(ro) r ?ro(ro) r soo(!o)

7eoe4.) = z@(r,) i eoo(2a) + a/.rs bo (ao)BD- 491,93 tb --_c

ZMF -o (p-@t \^S CO dIC)2aa(ad r eoo(2a) - 1 G coho)

co - rn1a.a3 tb ,-_c42.) Use the helhc, of seclion. to detcnmtne lhe force ootingin members 0F. EF.8(E€ of the Howe irues dcgoribed in Fis.P-aas a^ page 91.

rS

cEQo). 72b<a.'tF".@rb cE = 1440 lb _,-.t

:Mc-o (Rc&l"t"d Bo ol F)

A\ (i4) - a@(4) \ xro(b) r <a1o)de = gso lf'

rME .o (R€sotvins oF o+ H)l"(ra) = .oa(1o) + aF (en3d)(,o)

DF = 1€oo tb - -c

ZMH.o (cccotv inq FF a l E)a$(1o) ' EF 6'.b' (2o)

F F - r o o l b - . , c

'ne merLcd or sec ' idq Hi l I . lo oppr , thc _el rod

i" (,o) . Eo (io 1o"3o)

E6 - 16+s.4s tb --*T

.+2+) For.thc l.ves she^ i^ FiT.p-a2a, dd{erm,ne thc fo.€e

?i-ry ]Y fllt :f io,nt E ihen check rhls rc€u[ u€;ne

br, hsp€l,on.

tMo:oAt (16') - 1MG.) r ,ae(91

Aw ' zaOO lb *'

&-a leAaAE ' 25oo rb -'-c

AC,cF =tg.o tD-"-T

21.o(d | 1t@Gr). +/s sF (16)g F " 2 @ b - - - c

76

F6 - 2.24 N

.rt Ocf,a.dnc lhc fdcc in trr.c BO,C,. \DF of lh6 nocottelrui6 €ho'6 f FtO. P- 4z

c"b.)| r.ID(6) " @(2a)t fe(ta')cw r t6oo tb.

tW. o : 2 :4.(.a') = -.(a^ *fi.Xt)- ,(5'n?,.!"Xro) i oF(6n ,..B'XEo) +z(@ e. 6, ) (b). e (@ 2E5't) (....J

DF - 2.s Kip. -..-c

r/& oE ,t 1@ - &et @oE - 512.45 tb -"-T

ot Jornl D,

Zli6 -o (?.ov6g co ol9)1/ft DE 60) = 3/b ez)(co)

co = s@tb-''- T

A,(zo) - 4@s 26.r,.110, zo) + (E ̂ %,sf)(z)(er1o) + ot (1s)

6I - o_,rse Kip3 _.._r<M^ " ot Fo Oo) - 2 (as 26.sa) (.to I 20)

+(z)(d 2GE7'.)(6no)

4k co . r/tasD | y'{ooEBO= [email protected]!5 tb-..-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 robl'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,n26.e7.) + Ay i 2.+6 Kipg

2 l G = o ,s/@ or@4) - 2$'@r) \ ,.bGo) r

a@Q.')oF -- 1256 4 lb - .-T

lefl of B-E

at^t. 'o.5/R rr!o)=1e(4o) r 14o60) \,!t(@) +

4+c1=4<r:,<2o)&@(1t)r'.(t(.6o) tte(go)

A I = ' t 1 6 6 . 6 7 l b - - c F H = 1 5 6 4 6 1 l b " - T

zF,.ot 6\ | 5/.l6iFr = /giFtf \ =2aa.27tb-- -C

rcfl of c-c .zrt^. a : 60 Fa = .k]x(6o) + a.a(ao) r 2.t <2r)

f6 =.733-33 lb -"-T

aeo) The lod& cn ihe Po.he. 1'u66 et)o{n in Fig p-a3o o'€' in

^t". O"" ^t *"r" "r-lb' Delermir€ lhc lorces in menbe's Bo'

z?! -o

Av rJv ' 3o(7) Bul Av'Jv

<Mollhe inlc6el ion of Bo \cE 'o

z?ft;-'s+ or(16a) r :o(rss) = rlo(roc)'

BE = 63- gg siPs _ -T

@ft of b-b:M ol lhe Inlerteolion of ooqce'o

l.usc shc^tn i^ a9'P-429 dclern\^c

0F, FH, Ft,6r, g\ ro.

rco(a) \ $a oE , 30 ($5) =1oe8p)

oe - rc'873 x.tq. - -CCE- 97 .22Ki?6- - -1

1@ (ba) ' 30125)+ s/EA bvr.z )

BD. ,143-41 &tp.- -C

78 79

e+o) For tho lrono loadad o€ shofn in fg.p-44o, &lor -

mirE lh6 lbrizonlal \ vorjiool compcnonts of tf,ro pi" pros-. 61,.D ol B. Spoc;fy di'Eotion"s (vp o" aou,t; l6fl or right)of

tho lorso os il oot6 upon member co

ar@\ - 24(e,) + ab(6)

EV. 590 tt)

:Mr .o

N (.r) - 36G\ - 21bQ)

Av = 360 lb

:Mo-O,a(a\- aso(a)

gn(a) 'B00(6)

8n - t€o rb

bJ - esatb (dorn)

( lcn)

+<t Tho strucfuro sho,q{ho hori&ntol e^ vc.tiool

8r-2.gO-39O-a

is hin96d ot A &,c. Fiddof lho hinqo lbiE€ ol B-

8..)

y''rr"z,-zf

8Br = 1oo(e) + ioo(6)

BH . 125 tt)

<Fx-o j BH.AH - j75 ibZFl-Ot At - 166-|,46 =a

Av - 2OO tb

C d = B ! = 1 7 5 l b

aPA-o. e,D(3/s)- AA-oeo 4'4)AA

Zt ^=oi lzo(4\ " Er(4) . o

EA ' 12O lb

aVr.g.1 l4 t - At-o

E$ 'Aq " 12olb

oi i6olatirg bor A_6

zMa-O I A!(O)'120(4) = o

Av -- 60 lD.

Co.'cira^i.g tho wtPlo Gono i

zF\Fot Av +e! -12O 'O

E ' t2b ' to

E! = 6a lb

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/ohin-

god oI A A' o rollor ol E Compu{o +he horiz'nfol \vo'rF

,1r .o*pr*"t. of lhe h'r4o 6.ccs ol Bg'c os.ihev ocl

bor 6D

i{^za j 42c(1\) - Er <ro) -o

Ev' 26'r tV

z f ! - o : E r - A J ' 2 4 O ' o

Av - -24O1EY

At = 24 tb

2ao(e) - a, G) - o

O' = 360 lb

xo9\- s!(6)'o

Bv = i 20 rtr { upwo.d - /

*p.ol" u". rc]

,p."."-P. ry'

808l

bor CE

cv + EY -Dv -O

Cr - 36a - 264

& = 96 tb {d@n@d *i1h rospedl to^ r 1

:[1o=o:cf(5)rc,€) r , tz) -o "- '

Cr. 2.4(2)- @>

cd-40ro t I 'N1 i ;pk r ro Ac J

zN,,\ -o I Bc(4) i cv(s) - cH(b), B"(z) - oBA = aoAo) +a2o(2) - (e6)(s\

BH = 4€ rb to tho righl

aa5.) Thc frElne shown ln F9.p-+as iE .eupportcd byo hin-96d oi E k, o rollor ot O. Computo iho f'orizonlot \vcrti-ool componenis of .ll-D hinge focce ol C os il ocis upon BD.

o'@\ = 240(3>

Or = 90 lb

E"G) - 24o(e)

Ev - 19O lb16olo1ing bor DA

=M^-og! C6J - 240(4)

& - 160 lb

zMe"o(6)}.v- 24o(2)

A Y - € O l b

CA(3).7oG)t@<r)CH- 2SO lb.

+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'6olole oocb ltu€6 o6 o frcc boaT

N G.) - .6dct - 6aoQD) 'o

A! ' 42o to

A"Go)'3@bd + A,A(3a) ' o

Ai(t) - a@(@) - +2o(4o)

AA - -32o tA

;. AA = 32o 10 Iha .lgl\l

, /c_- _ 24a t r j . 24o tb - . ._1

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'D-

po-onts of lhe hjngo {b.oo ol B tN. }ho.' delarmino lho }/p'

e, mognlludo af forca n bors BO e'BE

z(.'o G,.o.b) + 24o (zc) r AA Oa) - A" (4o)' o

Av(a) -AH = #ao -@

l6.loting lofl lrusc

loro . zFf=orc ) a2D /\,8.\n 36 s7. -o-;.7i

,LB- lao\o c/'\' \

zF"-o: B2o- Ac - Ae @s 36,6i- =o, 76- 326 _ 7a6, (cos za,az.)

gr

".,1 -'

a2 83

AaOo) - Aa(b) - 24o(1o).o

/ * - A A . 1 2 o * @

6q. @ &- @,A" G) - AH : rfi<)

-laLal-:4eLtsA_ - 132a

Aw - .katb

. t \ A - P , w - 1 2 0

= 4a -124

/Ad - 32o ltr

An - 32o tozF" -o

Av -B!-24o-o

&r. 44o- 24o

B a = B . a + E H 2. (m)z + (e2o)2

b - 372,+ lb

a<€) A booh (ar|ig +ta loods shoM n rig p-+aa i€7*,W* { lh.@ ..sma.ts t{ i€ suppo.icd rt br vee _1tc.ct t:c,aLto s \ jo-oa 6, b.o f;cl,o^tace nrngc€ Octcrmirte iho votucg of lhc rDoc+ion6.

@

.n *,e at!2@tb

c. cf r-'lo I ot-- -t) ---1lG f lR+

wl = 100(6)

RaG) -.6c8 (z)

R 4 = 3 a 1 t b = C v

RzOa) = 2o.0a) i 2e&(7) 3ca@)R. - 2120 lt)

R3Gd - 2s.n3> + 3&(14) -4ra(4)R e = l l e o t b .

.s9.) Tho bridgo sho'{n

€oolion6, coch *oighir€

6, hingod ic o unifo'm

@ nanb.r co

i

i^ Fb P'aag

A, B, E, .',\ F.

ocnslsts of lv'o o'd

oonlor ofgrovilY ot

wo;gbihg 12o tone Ctn'

o" (@) - 12o(:,c') | 6oG4)

Dv = 1OO tong

C,Go) ' tzo( tdtaa(eo)C a = A o l o 6

E"(@)-Qtbbo)r(a( lo)e\ = 26A *o^a

zlr\E - o

F" (@) - zaoQ.) ' lctt(2.' )

N Go) - 2ca(2o) - so(2a)Av = ae tong

zvl^. ae.Go) - 2cp6o) t s>(1o)

w = 212 lons

45o) A billboord 8C woighing {ooo lb is subjccicd tc o

wind o.cseuro ol 3oo lb por {l os shown rn Fig P_aso Nca-

locilno lho wdrqhls of lho supporiinq hcmbors' doiormrno

16 66-penonts of ihe hingo fo'cos ot A E( F'

wnd PrcEGu'E = 3oo lbl{+

. 3oo lb/${ x lO }i- 3OOO lo

84 85

"oaa(e) rooa(6) | FN 6).r, g2)

Fv (s) - F{ = g2so --O

tc@(s)- rcca (6)+ AtN(4)= A" (12)

N(3)- AN - 22so -@

CB(1o) . eooo (s)

ca -1s@lb.

Z l ' ' - O : 3 . x A - C a - B A - OgH = looo-1silo = lsoo lb.

:ME.o: O,.r (i,) = Fe C4)F{ - D{ . {sootb

zF =a: e4 -Bao-19ca.o

Ec = i@O lb-F; -O: Fr.t r 3oOO - AH -o

AA = asaatb

@ 1 ,Fr i3) = e2so + 15ca

Fv ' 32SQ 1t)

@ 2 .A!(3)- 22sA + 49cn

Ar = 22sotb.

s@ lb

EaQL)-sko)-2ao6o)E! = 2sq tb

/v62)'2440) - e@G)

A Y F 5 o l D

@ .nombor ' t.rht=o

DH C4) - 24(o)

DH = 4€O tD

zrio=ocica) = 2ao?)

CA '24o)b

E a ' 2 1 A - O

E' l , .21ob

tc'c ll*cn

{ot-Ho

o"G)=e<dtdL)t.p,,A2)Dv = g1O rD_

:F ;O: Dll cBH:a6O lb

EFr'o

8 a ' A '

Cr '56010.

6! - so+ 610 - ry

Bf = 9o tb.

86 87

Choplor 5

Fr icl ion

,05)A btock waiehine w ,o " ,"11^if,";"jjll""l",

3il1l,#;ir'1?:;"d"i''lioill r ie (o) gr.ore't h o n e : ( b ) c q " o ' l o e . I c ) l c € E l h o n e

) ', l i i , i ' l . aiter lhon e- ih€ bloch wirl not siide down

i,i.,""j li *i,, reloin ils poeil'bn be'ou6e ihe f'rci'onol

?,n,'; r ;ff ,:\' ilJl"Jl'*, I T'li"S jit. i:1"

* #.2: :-i,:;^, :: ;::;i,z il :. T;:il#;Tf i,"'il ;;? ,.4'"""o '" 'o""u mation la mpc^d 'f aP"

*lr l,#,i.]:*':t g'*i'tl': lji3'#;::L:1 5

t p t t r y t a \ ) 4 w ' 1 w i l t € l r l l b a i n o _

iir fi.'iq n",i" the r'aro^ot, ta'c'l:ll^:'",11;i:

fii l"[,:,"';tl:: ? iii :.: j';* T ;:iJ i"x',;-" "

io etort the molioAP = <n!2 .,

P = ftatb

P - - + o o l b

P: 239'2 E

#*E-#P^:- - l10 1 lb

8889

5a7) Ihe eoo)b block gflown in Figore is in contocl wilh oab' 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"{

thc bloak up tha inc|ie (u)j"gl prcvcnt molion down thcinojine. (o) Il P-aoc lb, whol ie ihe o-ounl \ dr-ecl'bn ofthc J-.,ct;o^ fb.ce ?

> P - COOIbF.n ;nseq' 6n6o's6'

- ' l*\ P - o.,c.br)t___:g,a

q l ' a 2 s . . s - f t a 4 -'

11 .- N p . 5oottrA\.V r T\ b

4K","- * { -"-^J-"il,i"'r',J41\!\ t!

. t w ^ Pc . ) ^ *e,+at4{P 2+:o :4oa(Los15') t f Isao\ l@sao'\ 'o

'&^" r ' 70 lt tb

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 lheconlac4 €u.foce6 -

zfu =o:N= aao (stnno) | zoo(ar.aoN '37J .21 l b .

<Fa =o: r - $o(cos.n) - zoa(snaa)F . 246 .+1 lb.

l L - F A = 2 4 6 a 1 - a 6 6' ' , t J t 2 i5Oe,) fl,e bloak, 6hown in nA. P-@s are cnnacnled bg fldibinetlendl'to cord6 possihg ovor fi1bt'bnla6s putless. Al Al]rr-cnefftoienl ot frrclton ore f. - a,oo \ fk- a,2o whils ol Blhos orc f . -arc\ fk 'o.@. Canwte +ho nog.; tudout d;rcc -

i,bn of tho friallon lorca oali"g oi each btoo"..oro) Whot weighl W G ne,coe9arlJ lo 610.l tha .essJcm ofhbakc ahow^ i^ fig, P-o1a novirg lo ihe F;ghl 7 lhe cocf-

I

el ..og. r FBOor $oaf, Al

frbr'cnf of fiichon ie o lo, \ lhebo fnrolionlese

pullege are, oesumen lo

M^-L^', i*\" *''21'*'

*rl-o n^ - u*,-" ,..n',1 1 ^ . 2 4 o \ b .

ldc

-tx-

'F l 'o

'tt - 204.6+ lb.

'' r^ ' f. N^ " (o 2X rao)F^- 4b lb

{f-o : nr- 2oo(cos6it,t16. 12O tb

. F. ' f , t lB ' (o. $11o)

Fs - a6 lb.

6 6 . 1 ^6mArd =,nrf

l ^ ' 6o tb

=fg -O: ll. ' JoO co6 ro'

HB' O'1,6.+Jb

FBD of BlooN b:

o5Y"fFD of ElazY,C I

II,

l * l--T--

k-@1)lra4t60rt@

v: ry.!:-l!:

80 9l

!nr) trnd the leosl rolueot P rc.quir?A io cousc lhe sgs_lcfl of blooks 6how in Fig. P-sr1 to horo impendirg rraiionlo the lofl . flv <noffiopnl of fnr'clion \e o.z unao- ea>hblooh .

fbo of block^ , A . o . 2 . . e . t . a 1 '

F (n o l " 9

W{Fs.o: li:roo- Psrrq T = 1oo

r {Fx'oi Trf-Pco6a -O slnrl,rf sin7r,69'62", r(..z)(w ps:,r"$ _p6q "o !!Z99l!_12J.O2 - A2Pstn\ - P(aE <-o

K".zs'a"r+cos"<) - pt e2Ib.- p= 12z.iz-s!L. P(o.acee.s6.<) "o ais, ,- , , -r"' - o . 2 a N q - a h e . o p - 1 2 4 . 0 l o .

o.2 E \trnq - iorqcoso<

, :f! 5L

arz.) A hoingcncous blook of wejghl w resi upon lhc in-- .w , . v r i r vg r , r tY rEDr uPn r l ) c I n -or'ne l9tlown in Fig.P-.et2. If tho aeffioicnl of lriclion ico3o, delerrm o lhc aletel h.,iah+ A ^l *,hi-r ^ c.- !'gleic€l haight h- ol whioh o for€o pporollel fo tha incline "at "pl;.a 60 {hol fhc bl6'ck wirls_tu6 uP tho ;odt;d w/o;t lpp;,4 ove.

<r j -o tn<Fr.or P. F+ Wdo&,r7.

p . (d4 (wcos!#r) +w (enaa,er)

{M^'oP(ti = w.-€ 16.01'(t) +we'^ e6/(.)

oofnalh) . ,.\f 1.6y(h - l_

Fr,Dol ElooKJ :

E6) h fig P-512, lhe honagenoous blook we;gh6 'too lb \ I

cne,fftoteni of fn'alrb^ ie a 44 f n'sitr ' dcleti'na lhe

focoe P ta,q"ce nol@n to rmPe"d

\ rP\l, <F!'D: d'soa cosrb/' = 24o tt '

!=1e!:s1+) Ihe rco tb c.Jlinder.shown in F's P 51a i6 hcld ot rcsl

or the .to' 'noline bg o weighf p 6uq6de<t ftEn a 'tt'd

wrcWcd otaund lho alide. i f s fi PPi n9 i-Pends , deJe'rnr -

na P\ the aoffiaienl al fe'cl(:n1F^'o: Hc'oe e'c' ' f c:oa oo''t+co€6o' - ttta.s*'

,/t- --@999- "o6773

< M . " oq ( 1 ) - F ( l )p = t t l = F

ZF!- t t : t16hta I F6nb' -P '1oo

N(stn6a'I o sln.tBd o..113)=1oo

i ' 1@Z w\r ' 173'22 tb

r = @ +)(24o) - s61b

zvA -o : sP = w 6h e6 s7(4) t \\@€36 a|'(a

sP . Pao)bn36.ef O +.,'za b1'O))

sP ' laaob

P -l,l = (o.s11i07a '22) = loo tb

woig'r€ 12olb' blad< B weighs 2<{jlb's15.) BlocK A ir\ Fig.P-s1s

\tho cord ic po.ollel lo ihe ino|i e lf lhe coeffcic''l

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

12A . R,1;^r.*'

-"'^(a,'4>

R1 - 123 7 sin (4o - e)p1 - t u,1 (sin ga'cose- - cossa'€n e-)

Fl - 123.4 coso-

92 93

fBA o f b , €rx-O I w6rns. &sra1..ar | 8.6n1+.o+.aoo6,ns .(Rj '8.) 6rnl+.o?.. ( \+R4) . 8e1.+.ha A

<F3'o I Ra a<E fi-o+ - R1.pq daf - Wco6e(qL-B') c8la.oa - 2ooco6e

R4-fu ' ao6,2 c<E+ @1'@1: Re - o2+.4sne- -R1 >

a24,16too - R1 -R1 - 2.b6,2(jo64az4,+€ioe--2R1 - ao6.2 c.€d

: tut nj. 1N;7 case - 8a4,+ 6;ne-- 2(1zazot e) - zo6,2c<Ee624 4 €ine- +s3 6 @4e

lon e -ElEsr zo. ez's'6.) Reran;.s to prf.b. sts, il fha coc"tirirbnt of f.;ot,or'rs

o,at V, o- =ro' what farca P apptiad lo B aoling dowrt\ panolrai Io lhe rotine wi,l e{orl rnofion i whol ic thaleneion ti the, ct t dfiaor,ed la A?

Rl , '12ost16 6h6sa+.

fu - 121 ,1e tb

<f!'a: hzcc,saos6 - [email protected]' r R1

R . ' 3 2 3 1 1 l b .1F\-a, P. B2s;nao.a6 t fu 6tn aae6 -

P - 1 2 6 . 6 t b .s1s ) JF lt1 Psto, l4o bjoo\s ore .b^^ei@ bs a sot.:dslNI oi#oc.]ed to eoch bto.t, w,ln lrrcl;onte€s pjo6.,[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 preverrfIrotiort .

lL.A26 :.O - la,O+'

FBO at b: t -a. t- . o- 16,7'

of friot;c,^ ut\aer A to p'ucni rnolion-

w - . e t ' 4 2 e - 1 1 3 '

.ln4.r'

C. 2J7. S+ lb

H -4Ct t Cen.o' <t"-o : r-c@624'

n- aoo | (2s7.s+) s;nzo' F -Ui1%

r l r r / -E "206a6- -o . ie /I r e 1 o o 7

szr) r" fis e-s,o \f J.a 1 urde. both bloois \^ wo6he aoob.rhd he. nor' *eishf of F thdl cnn te 6lo.leA oP lhoirottie b9 appl)nq Io A a e's6l wo.c r'cnzoalol tcr<:z P

y'.!-.o.a z4-o : tl - +o3 I c6in3o'zJr-O: ,Ko. Ca€e6' I F

c . 2 7 0sn$,95' s.z+-o+'

c - 201,9 lb -

\/r' a aOlA

w^ . s98.3 l r t

stc -caeao't @,2o)(+,xt+ cs'"zo')

r b - . ( 1 o j 6 ) - C - 3 7 4 o z t b .

wa . or+.a"(. 'o*", i)

wa = 263,7 tb

g4 95

f i . 1 1 2 , i t b .tF,.o: p_F + c .a6so" "

Vtt te+,e)(o, ca)P"@z)(712.a) r zs1.2sp- +a -7 tb

l.*.) | t":- ot 4oo tb 's ";ffi rhe purb,j shown in

,!: . ' : ' t l" ,pi, '? ie p-etenlea F.on @tdt.:rs o,j ota:: P.opdEn

.:" ly .-d cf the brotf- re,e.. rf ,he @elo|ocr ,on, . r r ihe bdl ,e 6u- foe is a.eo,del the,a lweofp

. ft_ r//rL= zog,iMa-o i . r caob '

P(4b) - h&\- F (B) - fioa(.to) - 2oo (a)pGi) = t+too _ p_ zcoto.

:,-) A

:"o",;-: t", .o-m r.,,re a bu.h:^g 2,:^. ton2.,q ,, t ippez:)

, e ^ t t . . a , t @ . o r 6 h & - . n F : g u - w . t h ea.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 1r F derqnl

A f r - o ) N 1 ' N z

n',t 1-o,zN=o,/tt.

w-- Fl t F.- o.2\ (a)W= O,4 l

2M^'Ow(L-1) t r,@) - tib)- o.al$Fl t o.2(z)M- 2Y - oo ,4L -oA roA-2 -a

L - - L

L - e i n

szs.) A uotlorn lodde. 16ft lotq V, weigaioq wlb i6 Ploc€dV one ed on fhe grcund \ the otne" hond ogo,hst o ve.-

trcol woll Thc orgte f footbn ol otl cnoloal s"nfoces is20'. fthd lho mrnimum volue of lhe onglee ol wk lhe 1oC.

O g.r i l rb

"lr=4,t**t".,'S\ to td tvnro' I

@ (!,d__h(1-a)(!-L6tne)" - to. n'(a-L@ea)

Iaîd r - Letno "lon2o', + ton2o't @a"r,(to to't lo^,a) "1."{; L@se + Lstê

a. Ion zA-L<bEetLetaeIon1a" I Ion 2a'

O<M6.ow(x -5 .e€ - )_o

27on 20' L@6o I zLqtne - L6.t( r o n 7 a ' t t o h 2 a ' )

lLst e'L6the(ran ld t ron2o -

-srr9 = 2,39i2

+-:Po:Ton2r'!od<e1L6,ns

lon 'L.o.r+

t L6nt+2

9697

\?a-1 A . toda6

eo I j torc +. ,gne ebi . , ,

j ,6 ,q at grc, t . t !l ' 8D . f r tn

l fF rDro- fê bdda . . p .o.4J oga.re. a "er t i

Y^*:' f,-yt,ir mo,e€ on ..st. or L. y,1 trJs,o,.a. u.*

^ o t6) tb n a1 .,.mb b-fd_e lE Io l s tpp.oq lhe ar 'e , G , .^- - , - "

; ,? " " l l " : , . ' . : : " " ' ' ' : " : " - f t ' o - d , o , . Lon

@ { . d i 1 b * u . I o . 7 s " x

, ,"-,"trl.)*; aJ ,,^, . -r, :, A \ Z [ ^ " ' " v " ? . o ^ ' ( ^ . . o )

, i \ " lz

Tanzs'\ '1t.tz . -Ion1r, r tolon.re( to 'z ' ' ' 1o" to ' ' , ' ,o

.ng-ec.€ad).$a(x-s) x -sf t .

160x - e40 + ^ _ 5.2s 11.52r) A. hon"gncaaG celincrer rfj. in d''*'a ,, n i,.q "" i;; ,";,"_ o";i::'";J.^l"lf*! .!',.?e-

or f' n'oi G w" to. on co. t..t I eb,,o.ps cad.lpllo t6" noq^l )de ol the cowp,e ratdq rctolrs """.k-;";;.""

' e1u'red Io sio'l the citi'

wqr'3@lb ot cg:Jilibnun <r:.o: d, o6is.. D, @67s,

4! l \" ' . \ l

, - n7 .r , 'co376"l r \R\" qr J.ffir:= Jl___,., t1,"i'c^s::".

4,t\>r4;rr I\n l*,1 <rs.ot 1116t.76.|tj.6t t6.. rao

tl,q_e t/k,@,..\ s,",.. - 3,\,{ M a ' B r I - ,

rt, r.^*.+ -,,J t""rc.) . ",,oo ",r. (1c) r r, t.s) n1 = 2os,7e bB . l2o,a)(1,s) t (eof t ) (1.s) . . . n . , tz6stb

_ 0 : : f U 6 A n . E , a t . . . t , . p h .= (to'6)(%s76) = r"tis.Gt,ts)

- n '77,41b. f?= zo,s tb.sr ' . ) l -s1tuo 9t"

r - "o ' - dFl -_d,n- lhe m,n,mud hc,r rzcnlo I

:,x^:-T:::?, ronee.liolrs ro tha jefl .i rh" t";;il;;,cuti^der ;c^*z ;-,;"""; ,:-.,:71'

or tha rop of rhocounte.ciockwise- ' the calind- ro+oli.

tl

Mm

ili

Ptrd' r;fttd. F,{}FI

P(r€l = ,o 6(1{} r z6(t€I

N r "ooe.o'O " o'gaa

p{tr) = w6)pU t o t6b) - 12o (6. 6)

P = 1o..o2tb - 9j.!9 tb

J- la.r€'7 (t-o\'-'^.d(^4) q'Ion6c7 U-o)- r6ad ('.lo)

i",s\ ' -Idn,f.a t ton.(it, lo^bs'7 = -1a6L')1i1ctan1d

r. (tonzo' tlo"rc|) - ,Dtaooo' r (ro" oe-rton +o)- to lan ro'' l = 2 ,81

< M . - o , p ( 2 , 6 1 - ! ) - o

3 . 2 + - 1 o r x ' o 2 4 1 4 ' O

|= 0-76 tL 83418-"tl ,;6.- pr""K of wctsht W \ totol Ldngih zL i€

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 99

otrJle q al whi.h

"(^ffi#:31*r.*.)."t 2Xor1a,@6o. - ekt^<+ l o ^ q . 1 , 4 6 + 1 ^ d .

g" - r rb ( s -g ) , - - { : - z ; ) o n _ r " . o .U- Ionrs'7 !rzL.ti< - -I@6a'(x-2Lbs") :

@b.. lt .. -t(tane'tr6.b,) - [email protected];,ft<

X' 2Lc41fo^6o-- 2L.;n4fo^1 . . t lan6o.

@2) In Fig.P-!€2 j lwo btock4 eaah wobhing t.b tb oe ca .,ae-td fuo ,itfo.r.n ho/'zoofat Loe whrch wdghs lcotb.If lhean_

€htrng

gto of f.ioltb^ ie E u.dd coch btook, nid p di'l>+ea rs.olto lhc as' i.ottio thct w)| ooueo impendlnq tution lolto |.ll.

O iEdoti^g tho ba.

-s<;._9_

c:n. tao6;n*'t rocqn+' zn.o, r" +a-;zs< - )o-o-*+s. pn. 2e2,8+ tb. (o26s)(.rr.ei t o - p

p:Zq€Arii,l

,,y'a., bo. .^8, wa:tsh:,as a;b 1i€ ro6tq..a be .1

l r lc r ' rn l fs6 p:n- lo o a loc, *e,gr , ,aq zoot t 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.

e.1{ . . / ' .o .26a

l l.r__J1

t " -r-l!_f,__ i

ZFg'at 11 - 2oo I Ar

d. jo1.6 tb

. ' .F!"o : Ar - +2+ tra - so| 6 h

W E D 6 E S, 1 . a

53s ) A *.dge t€ bger'r ta .Pt t tog. rt e ) Iho angte ol fria-

lion br}t'ean lhc \ldgL\lhdlaq,dd lla nor ' ongl'< ollho

, a F ' - o 2 R q . | 6 1 t t ) ' P' - 'ra1-P'**' 'i'"'*P]"eaP - ,Rtd.|ttu"4&) ! (@Y.Y+).al! a

1M^'oa24 (b@'6) r r. ra+E'dB a"s-L'a

tt.\@.+s' | (o.t6t)tt6\.b4t6'-d'\s'na6 -o

f tg.q = O,s1gf lo

N a - 2 8 9 4 l b

Brt Aa ' 116 " 26e'4

Fa /^t15 ' (o %6)(2Bs'4)

' . O : P = A A I F

P- 2a64 | bz)(1o1.6)

cos Y.&EQ 'st^P st'"{'

cas.t/2 - et.dst "t/2 coeq

Ia ' / - &1"1/ '

s.6) h fiqur-, delonninc lhe nrnimum wa'ghl of 9loch B lhol

$tt t heep t l ol 1. ,61 o forco F 510116 gloohA uP lho ) 'c l ino

eurfaco ol F lltc weighl al A te loalb \ lhc ongld of fttc-

lion lbr oll surfoces in oonlooJ is tsFBo ofn iF '

LJ--l ,*F{'l$t L?

I

100 l 0 l

ah'O I Rrcosas ' - F, co67s '

0n.a2) cc &' = R. - 3e,6 a tb

\ ts . B, s ,nrs &s,n4s 'ws . (as6 4)6 n zs - (F1.r4)€jn4r'\ttb - 213.2 tb

$,.) ln riqlro ,dcle"nine the votue of p Jusi .s,fficienl ro€ilorl the 1o'wedge u.de. lne 4oo-lb btoch. Ihe ongte offr'otio^ ;s 20' fat otl aanlo;ct sufiac?,a

r*s

- 81 .". !19.4b,

s38) ln

'-f={--

!::!rJ!=Frg.sst. aelo"mino the yotue ol p oct;ng b te tetlrc4u;.ed to pult Iha \eadgo oul fmn urae. tE 4<>o tb

--EL- ' 3L

_L' -P91:L - p - zoej Ib.

$s.) lf the wedse de€aribcd in llusteofton hod o wdghiof +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<icr tho d)o*.

*"':+n" " #/I vtnr. $a L./1' i--)<--- l V o, - +aa

nW' -;"1or -;*'

dngiE of fnbnb^ ' 19

A*P - +16.7 tb

tr\- a : ?n si..' tW @ts' - o

R, - :&_e:::

R1 '641.1t0.

ar/1y

6't A. R, . 2aa ..ao l;/ a'4 6€

V R t " t " z t v

aFa.a ! zPn 'sn ' ' 'P

P. ..(n e)6,^3o'

3,:::3 e

htcrc*< |\erc ;a.eaecd lo ts@tb ?

!fr,.'p-

<Fg.o , F . @6' I R46D,€ ' ' +oo

a,ryc - 8rslrl/.. r') -w

Rr (ce" 'cnc' io"rc) - +oo

& (o e7a) '+ao

R l ' 4 1 1 . 1 l D .

s+o) ,4s 6hown in Fig p-'io,l-o btoars warllri€ z@tb\Esl-

i9 cr. a ton:anlol qfoae oft lo bo P!€tve orrjl b4 a tc'

w.age' lhe ongk' ot l"ial'b" ic 1s' fo' dll ,@ioot cuFloco6

wroi nr"o ol p ic rwqoirea td €to.f mov€hal o{- thc blo'k6?

t1o* woqld thie ohswr be cr'd€cd il ihe wor'ght ol oe ol fho

to2 103

-&- -_:99-

wb Re- 1og.g1lb1Fa-o

= ql 's ' 2 t .2

P^ - ft,t Ib

P - Oos,b1)c.e't lE.4.nip. - 91,Etb

dron in rhurc P-eat . fhe @"4a of lni4rbn lor o svrtocosn ca,lool ie P'.

fOD of b <t ' -o:B ' . ,1 ; -W5 16' . @

s+i Detornirc tho forco p rcquircd lo €'to.t thc, wcagd

&. A.coslo' -s.rb

afr.ot R..os ' -R.6nni , eooo

(-€inrs. /

R" (costs' .<i €) - sn.-t is' - R. s.|.d. tu )RzGoss'<al€- stnrc') . zoe I soo @! E'

R. (.3.a+d) * !666

R. . 7 l ts .4 lb ._ L - 1 1 , 5 s . 1 1 p - g 1 a . + l b

s..) whol lorco p nuel be rypiea to thc wcages snomrigt o P- s+2 to 6lel ttE,n utu a- +t1o t',och ? lho ot.Eltcf.,,itoi for olt @^l<yl €;tf.,.rE ie tO'.

P - ed ,q

_f_ '_le.u-tb

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'ownh figuro p-gaa . Octo.mine thc n)rco p ncc66cory lo clortthc wadqos if llE anglr, of fiichbn oi ol! surfoaee is 2a'.Ncale. l lhe (r ,ol@ ot lhc FolJc.s

fBD ol B i, ..N

s+.) In itlue. P,oal@+e o1t sa.fbces i^ @ Iac+ dolarnae tho mo,imum wclgcd.g lc . \ lnor w i l l g rve lhe êdqe o ne .ânt .a l od"an lo7e,

R - 23aS.4lb

__ L.__8_

P: !9PLLL

$+ lf tha atgto of fniJto^ G b' ol illre-

t< tL6) .a . \ ) - 1a&. n1 .a '

€ rb l t l l l eP, ' - - P - qa+,sen@'T ;;G;;'4

: . e , 6 " , < p , . 6 s l h o " l h - w c r q s l w o r I n c t l o - | . - .

-l taaa_ - f_1t ::) paas rPo rq ) 6nO, - ) € "1& r< )

(s1ntu';.- -@1;6'"^) hab " baa(6'n .''44 - @s'o.6'n<)

I

l'l*

r04 105

G':,o'* '" - -. . '"*\(et ,r'@s1 a,ee-e.q)

, 1 + st tu'@-@b'6'aq -6'n2o'@6q j

(sDo.-G-&J o4" . (*-"., *" *) ", "_6 ,n< _ Grn2o ' -€ ra2o ' - o+66r

Io^4 = a .446a

c< - 2s"gS!^RE THRE-ÔEO 56]'EW

sas) A s;Bte lhrcodcd jootca@q hoc o piloh oF o,s t^

\ a meon rcdius ar 1.a,5 n. Iho creft oiaj of elaj( trtctbrof 0.1s,\of Alhetic f.iot,o^ ol o.1o (a) Deternine tE torczP opp)teA ol Ihe cra ol a Ie.6 zfl. to^g which witl €+o.tI'rling o *ebht of zbns (b) whot wtue or p wt| yc-p tE

jaak tu* |o.hids ?(a) y'." t."o --p.z (b) r^-o.to ta^ 4 . o.to

4 + - - e - 1 a t e : * ) 6 - b t f

o ' Io'r' 6;'@' P '{l t"^ (P ' e)

f t "a .1e P' 0"4)(,, ') u" (.,t t ".2)

f - a f t - t o^ f . oaaf ' " ' t t '

l ' a s "P"+ :Lro . (o te )n' Ge@hn\ b" (.ata.*')

j ' sj +JbE6a5.) tho d,Aonao bot||$ oalo61 lh.cdds o^ o ,.iple_lhrcoac4 oou"** ie 2/.3 in Tte, h€o^ Mdius i" zin, ltecoemotcr,l ar ff,ot,oa o.ro wtot toad con be roised b9eae.lirg a nonvl ol zaoo tb - ft ?pi lo6. 2/ . ;^ (6,^@ i l j6 lnp l . ihedcd f r " l i ipr9 r ic_p+.h b. . P i lc \ = 2;^

,,6- l" 10^ 6. ?;Gi . o lee

lr - g,a3'z F r l f l - a 6 6 i t l

' 2 1 4 .

r-wr 10^(4le) * 2oootb-tt - w(o.ft67 rt) ton (srf ie.ot2ooo tb - Fl . w (o.o1E6e6u ^)

Pilor. . o.zEi^ (;, @ d1lbto nEadd

@tliPrS bs 2)

loê "-19j14: - o.os314( ' .s ' l r )

I - r,t. ta^ (0 ra)- 14U rgF\jf^) ro^l b.sz'

T " 1 0 2 , 3 l b - f i

€ ' lanr (o ossr) ' o oez'

, " . a - ' )

srn) A 6i^gt? ltuc-ded 6gua@ s.Ef t'x. zvzflraae / i'+'-lt-.odI atanolc,- is a,6;^ \ tte ootElda d'2rt* ie ein . Thecdff'ot^l { f"iol,i'n

',c o.ra. Detcmiê tho rp:r6l r*,<:zset'-

rg io €to.t lill;ng o \"t-li.ral otl'al lod ol <o,o<n lb. wralrnor"eol ie rrrcasory lo elorl. toa;ng lt- tood ? .

P - L - - L P - ' D o - t - ' ' 9 a " 2 , 6 i ^tPr 3'si^

'/1a+ -ne .gL '

1 .- . , n;nE - ^ . i ^ " < e | 2 1 6 + )

lane " o.x€t f 'o.u

e - ' 4 ' 6 ' l o n y ' o 1 'r E - w . r n ( d ' e ) I - " " '

. <oan n ( + *!) l "" (s.z't z.; )Is = 6e1.82-b:fL,T@o ' w. lan (C *e)-

- 4<,@(1i 'f,E) nq/".ti-z.e')

sso ,/\ repo tuttg I v+ turc orcu.d o 6rolioô.j ho^rn-loi dF.h i6 ue.a to s"rlt-l o t<rarg wcAhl. lf lhc coe(ooc''t of f",alro^ ic o.+. whol sagl.l a.^ bo @p+r+n bgc,cofi^g a 60 -tb (bt@ al tv oll* o^d of ll\c .+.?

B€LT FRIATIOII

t(Xi ru

vb o"s;.:r c t"a ic G6o ' e4 - .'eo'

:-.;tu - 1, . 2 ut . 1"o;"-,{*"k)t" f, - 'o 1"' 1+> - 11s7 tbbll l.w ... ri "-j1eLb.

36t ) n ropc "."tppd twiac o.ouit a po€i {ill 6uoDonl aw;'?hl af aooo tb wh€.\ o tz.c€, o/-,so tb ;6 s*led ol ,hc o_!h.. o d. tulu:f,;e tte aetr,otc l cf ftroljon.

t.rorb ongE of co^l&) : /2o.

r ) , "+-J t -L^€?. t ( , * . , t r " )\_-4

laat,tb L^ so - | (lr.s)

I ' Jt-!! '=> Ylo e'st 2 . . 7

%,) A boot .,ert6 o pu| ol +ooo tb on tls hoween Vo iswtupPc.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|Dllfp pull ol lhc olh€. doos ncl arccal srto_

Ln -\-- tp

P L": ,4a - ! t4e'_. tnL. t+,ot -a.t oaa

.11,6t | 1yk = e31j' + 6z7.f ia6d = _?:EJe!r--.

gâ.) A loftlue of zao b,fl oci6 o^ lhc btukcdtuh €hcM rn riP-s53. Jf lh? brcN. bond h in c.nta.i *ilh lhe b_Ed.._lhrcvg^ 2sc' \ ihe coemc,al of lnctron ,s oeo Detah.,nelrE hfta P ol tho e.d or the bmN€ tcv-.

f1 - -14')L@'\ tu)L

JL. e.,az . . r , ,

( r - r 2 l ( r a r - f R ) . 2 + o t b f l

T r . . L . q , 6 o t b

f t (o tcoo) . aa - r t ,4ee.2ab

T r3|a

l

il

plre ^- c*) . r, l?,:^ '+)p(1 .333f l ) . +qa.a3 (o . l / ,61)

P ' 6 1 7 t bss+) Jn F,a p -sE+ , lE acetficjtql of fnot;^ G o,2o b.-+qae^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,- o. .(r4u*) - t ,at' '

f t ' 1 A 7 I z

d1 'wo636 ,57 '

<r\ 'o: Iz - tu " w€i^36..) '12 - (a,.) (q @ 36,6, - w a^a6.?1'

12 - o 16 \ t l

4F3-a | \2 - 1o3o.@e6,6J . t i1T'

rl2 ' sod I rir.€rx=o 1 I r r F l i f " ' Pao 6 i^ r6ar '

\ | 1t:ti t1t t1- - 6aa

H..Boot t1\ ; = 3oO1.+ 2W I ot6vl t a, | 6w' 4oo - 1 6?t

v , t . z 9 2 . q Ls's.) J^ F,s. sss , o fler'ibB bctf .un6 fdm A d€^ rhe 6pe^dpurlca 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 rhdT onoxrhurn weight w lho/ oo be eopr.fted

vaal mlolingtho putle4 P or etipping lhe belt on to p"|eg h.

!z= ut-"'"11-"t 'n,'."i12

but I ' .V21" I1 - 1.6+e (Y'/z)

108 109

Z M p ' o(9T, r rz(z) @n" Pttt --

5 f 2 , - 2 1 3 - 3 1 1 ' o

,s ( ! / , t 2 (a a41)w a(2 . ro ) -o

6 e 1 t w - 6 &, w = 7 0 4 7 \ b

l

l

C h o p l c r 6

Syelome in Spoco

r l 0 l l l

€o2l Dclcminc thc mogniludo of lhc rtsrltonl, ilc point;ng, qils 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 o!r"yrr!'

-a1.4-_4!--3a o

lta/r.rI - ?n/3 ... A. - 1ls.?4 lb.3.4/7.e1- Al4 .'- A' - -1:.2.55 tb.zao/ral - d6 .' . /e. 24.17 b.

-L" -L- gL-,L- lAA6.71

:. Br' .-119 a2 ; pr' 236.46 i Bz- -29A-06

_L"_q"_Q--L-_@z D ,'a7

.'-C\. .-r1a-1s i Cr=r41-l.. iCz- -Aa.s7 .., porhl,iq [email protected],<r - 115.24 -118-23-113.15 - -117.1+ tb. { uprio.d to the left.1t - - 1S3.CS | 234.49 | 141,41 - 226, 2+lb22' 2.a.+2 - 29e.o6 - A+.e7 - - 152.46 lb,€o1) Dolc.minc tho mognitude oflh€ rcultdn{, its pointrng , ondib dieclioq cosines lo. lhe folto*ing s)€tem of m.-c.pto.|or,conorrenl forcos, roo rb(z.3,a) ; B.btb(-3,-a,s) ; 2/btb(a-o_a).

Fd.ca2

-e!=cL"SL - 2e-z +

: .Ct 'a ;C. /=OiCz - 2OO

C.t6e' -a/R - I1zMea.oo" 0,34-9

aGo, - 226'.24//46.00

CGet - $2.a6/2s6.

to gpl lo) uso ot - x'ir't t2

_aL=^L-,aL- lqz 5,345

,'. Ar - 37.1+ : At - s5.7 i Az. 1a.2gs,,/r " Br /-/ . Bzh = 366/z.0-7

: . 6 r - ' 127 , 29O I 81 - - 169-E a Bz ' 212. i6

= ( sojso)' 1 (-11a,a2)z t (aj6.aa)z. R - so7,7 tb. pa;hl;S f..*ord \doMabsoa - zt//F\ = gaiEg/s1z7 - afiBcosor - tr//a - 114.o7/sa7,7 - o.z2sIi)6aa - az/e - +aaA+/s.rJ - o.s3e

<' - 3r.14 -127 2ge 1 0 - -9a 1E6lb

4/ - -111.02 tt1

1t - 7+ zB, 212 46 | ztA ' zre6 44lb.

s" = e/)' t(.r)" r(+,)'

Cosez . +a9.9/s24,se . a,gaA

6('J Dolcrdino th.o mognitude of the r.osultont, its point,nq, \itc d,-.r-o" cosines lor the fo ow,ilq sy61eh .f ,,-,,""pt-"",concurrcrl lorces. 2oo tb ( 4, s, i) ; 4oo tb (- 6, a A F.r. tb ( a,- 2,

- 9

roge+ D vee I D2. a2rr ' ,zeL-AL"!:L..<@^ r z 7 0 z l

,'. A" . 113,15 t Ar - ,t.+i,44 i pn - -s4,el

-L= !:-, -EL - -@z o,17

,'. Br = - 27s.46 ; B) - 152.4 a Bz - - 22P'05

L- -q-SL- pqz s,ag

." ca = 222.63 t Cf - -111 .32 t Cz " - 166.A52t - 113.15 - 2t3.66 | 222,63 . 62.12 tb.2l . 141.1++ 1A2.+1-111,A2 - 21r,..6 tb1z - 'a+.e1 - 229,65 - 166.sO = -17s,a b.R" - 4""+zf2r <2. = (62.12>" r (212.s6) . t ( -a,7s.q)"

R - g2r,5.B tb.Cas+, - 6212/s29,s3 - a,118case.r - 212,s6/s2e.s3 _ a.+a2

.'. poinl,n9 bockwo.ds, \ lpwards 1o ihe

t12 t l 3

6at ) ftr@ oonc"@ai 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;lnoke-s wi{h the reference oxes.

3

whee p 'e lb . , -4 . =60 ' , 6 | - a ) ' : ez . .s .

. . qr ' 16.23 iQ/ .6. rs , qz -e.7+ - co€122Aa/$-6s1t - Fseax . s(cos6o) = 2.s -6" = 46.2'<y - easo, . skoseo') " z.s rj, - @s', e.a6/23.6azz = Rcose, - !" (@sa6') = 3.sa el - 7s 6"

!!--L'lt-= 3!z 4,5e

: . px=8. r3 . p f - + ,37 i9z -11 , raq-4L.-44'_?e

F, . 2,s - +,37 - 6.19

\ - -a .36 tb

F r . 2 , 5 - 1 6 , 2 3 - A , 7 3F\ . -22 ,46 tb .

Fz - a .6+ ,9 , r+ 1z+a

Fz ' 23 .G7 lb .

' (' 12 4)' | ( 6 26)' tC n 6',)

'+e=cos '23 .67 /33 .66

.'. po'nl'ng bockwa.ds, \ do*nerd

60,.) A font ol (n tb i6 di@1ed f.om A rowdrd a in the cubc6h@n in Fiq p-.p7 Deleffiie the rcrcnl of the fole abo,+ cochof lhe aoord'no+e o.ds

t!-' !r-" !L' ig'Y

: . F | - 62 .5 tb i Fy '4 4 \b i Fz '626 tb

1t , . Fr (1-) - Fz (4), , - aa ,eG) - 62 .sG)

tu r = -62 ,4 tb - f l . a \z . - rz (a )

.t$ - F. (a) ' 62,t(a)Zr,4r - 2so tO.ft.

-- -62.s(1)

eooh of tho coa.driold o)las.

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

t -L"EL- @-

rMr - F!O) - 1,+8.6 lb-fl.

= - L8,6<4)

l l h - - 3 9 4 . 1 l D - n .auz.-tu(r)rr 'G')

- 7-+,3 (i) | n1,4(4)4M.- s1o.S lh-{ \ .

ri - {1 i tb.:, Fz - 140.F tb.cos) A for@ of:"oio ieai.ectea Fb- B loenc D in ihe cubo6hown in FIi]. P-6o7. Dele.r,he tfte Frornenl of thc J?rrre oboutdrLh ol the a..di^olc o'es.

-E-'LL'-L=4

.'. F, -o lrt- rgol6 lFe-2ao16.

tMr- 244 tb- ll

- -z.to(+)

atAr - -9@ tb- l I .zMr- tu (4)

- r€o(a)4M2 - 72O b- fl-

r l4 l l 6

6td A fot@ { a@lb i. di.ecl€d frDm C tor.arA E in lhe Eubsctn i" in r,6. r-aro Dclc.'r'i€ the hamen{ of }he forE€ oboutcoch o[ ]he coordino]c ores.

d - a.e fl-

+-++-*:. Fr. 1@31b. i fr. z26,sb i f.- 1fE.a tb.

611) A h@ P,dircakn ftr6 F ta*otn607 , cov.es o momenl My - i6oo lb-ft.obout lhc x hz orc€.

iMx .F (a ) -F i ( . )

. . . 5 ( 4 ) - 1 6 ? 9 ( 4 )

.M'- 6s2.Altj-fl.

tMt-F,<+)rFz@)- $3.a(1) t163.i(2)

1Mf , 979.0 tb-ll.{Mz . -r,(a)-Fy(r)

.-t63a(4)-3 .5(e)<lY1: r - l:06.2 tb-ft.

I in lhe cube sho^n in Fig.p-D e l c m ; . e P q r l s m o o e n l

-!L - !L.- tq3 2 !r9.5d - E,36s f'1.

P / ' g @ t b= -aoo(a)r Foo{.)

M) - -.{ro rb-{l.

: .4=6aotb. ipr"4aotb.4M*--P'a.)+ryQ)

4tiz - -Prc+) .PL- !- .., P-1o17 tb.. -Soo (+)

Mz. -32oo lb- f i .61.) A fot c p is d;ructed f.om o poinl n (a,1ia.) io€.d o poin{ S(-3,a,-r). lf il ccuses a rlomen{ Mz - 1coo tb-ft, Determine themonl of P obool the tt &,y oxes.

d . 0.11 fl.- L a Z - ! L - l Lq,1

... p, - 7p/s,n j Pl . 3p/s.11 i pz = sp//eArztA,-p"(\)+WG)

teoo ' 7/sr\(p, + '&)pA,rP . 9'll lb.

Miliiilldfi{

II

pt - 7elb i ry - aootb t p2- s@tozM,- -PzG) P' (1)

= -g.tO) ' 7..)(1)

r1't - '17oo tb'(l

zttf - PaG),p,(1)- s@(4- 7.b(+)

}'4/ - -8oo lb-{I.

6i+) Ths sheoFleg derrich shoxn in Fig p-61a suppods o \ic.ticallood of zooolb. opelied olA. Poin{e B,c,\Doc in lhesa'ne nori-r.ntol plone li A,0,\ D orc in lhe )(Y plone. Delermine {hein cdch menbe. of lhe dcrick.

Go,,ro) da '(o-o)" ' (5o)'* (o c'5)Y

d^b - lS.7oo fl .

drc" . @' o\" r ks- o)' r (o' o)'

d^c '20616l l .di - Eto- <-zal' *s-o)'.

aw..r- o: '!r$(1a)- ot en) - aa/, = laoo )b

. L. !L' !!-"!ra

Dr . 2cballl ; D.-o

lsololing Top view-

c/ 't @(.t/$

e " 9 L ' L ' 9 2 .

AC.1 !?4 ,s tb

Ba - l2t'ooAo)Y$

-&"

l l 6 tt7

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 xoxi6 i6 opplied ol A. Delcmine the forc6 in eoch nedbc.

d; 'Gr)'.(6af ,@o).

a-1r:of +<crf r (o-<-::)'

a;/.3-oy..(o-f 4e"ol.* , oN. s .a67'

lcolole Right Sidc vi€w,

65) Thc frona$orh shown in Fl9.p-61e con€ists of thr€€

;

.r{oa. r. o : B/G) -1db(5), o

as-, !L. _4_

-1@(D, rcf(3) ,o @(z) -o,(oJ -o

cr .62Slb. Df-a lEtb.e- - AL -6IL - __9u_

Ac.76s.olb. Ao - s22.91tb.

AE.lll€ tb. i gry.5ootb.

616) Refer.ing lo Fig.p'61s. r-Jpta.n hly- looo tb jarca ta v€i,li-col down*ord locd ol ea@tb. Defemine +he lorce n eoch.tE1i1*r rnda. {bis rc/isod lood,ng.

d^a.,@Gioi4o4Y

d& -r'G;F ,G;f t Ga\61ArY

da " e36r ll.

lsolot6 F.onl Vicw,

leololo Righl Sid€ vi&,

-4C-" ,9'-

AB- 1r1O lb-."c612) The poinle B,C,ir,,D of lhe oonliteven frolnsv?orx shown inFig. P-617 ore olloohed lo o v6.tical wolt The aoolb toad id F|orollel io the z oxi6r\ lhe r2oorb tood € veriicor. Compute lfe lorce

qk) - 2a.oe) 'a

- 4 L , _ 9 L

lelole Ftunl view,

'-t\

-lL- -jL. _4aaq

AO = 2382 tt) - -I

(2a&-tuaoxs) -c,G) .a

AC- 53A.3

DrG) - (2ab1o.,aY.3> . o

A O - D .

A O " s 2 2 , 9 l b

d4 "446.)2 | (b o). t(4:a +)t2 - 101t

o^. .,t(1o or | <a-o)? + (+-o)2 - b.n.aô . , t (1ea)1 t (6 o )z +@-ot .1 t 6 '

1 W - a

to.o (4) - Lo(.o) - c, (a) . a

--lr-- . sao

.d* ot/.6) - M(4) - +o.(1o\ ' o

_6q -,qeq

Ag; 1615,5 rb - ._ c

l . l8 I t 9

610)'the un6./nmel.icol contilcwe. fftrrewo.h sho.q in Fig.p-610.suppork d we ical lo(t of 17@tb ol A. pdnl€ C rt- 0 oE in lhebodo .dlicol plone whil6 g i6 3 fl. in lron{ of thi6 ptoi€.fi€ nnce in eoch @mb€..

a^s .t@-ifi6:F-,|77litr' . 6.vt!.d^c - l6al;Gzf-aB-Or - 12'

Isololo F.ont Vie*,

dô. "/(s'a)' I (+<)' ' (o' e))' ' e,16r'

c,C1o) oeG)-@(a).o

1,@(e) -B\(O -e/6) "o

s | (1o) t 6/@). 12..b - " -A

i 6 . g , - b r . g tAre 5

;. bf ' 6/68t - 5,b.,lo I

e,(d) | 6 /sB,G).13(a

b t ' Q a , t b , ' . B r . 1 2 . a l b

. . . nB "r7s5 tb, . -C \

A C - 1 2 6 0 h - - f

fteG) - 34d(.) - 0, (1o) "o

s.16s -

T

A O ' 1 9 a , 3 t 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.619d,â - a.i|s l+., d& = 12 {1.

dô - qf ts f i

,l;,; t:rz

lsololc Frb.'l Viow, leolate Top view,

9' 6.,) | B"t@')'Iloo?) - o

I ' G o ) + R r G ) ' 6 w - - A/ \ B . A r - 8 . . S i

f f i E s . +

,'. sr = 6/59r - s,B.t&1ou + G/e g'G) - 6@

13,6 8, a6g@

g-5@tb. iq-@tb: - o.(1d) -a/i e s.G) +1@@) ' o/\e- 8-/r,3 tb---I i B, -aaolb. U(to) " -5.,/c)14o(3) | E@

O" r21otb

.D= gL :. AO -,1,{€6.+\,.4166 0

aro) Thc fmnc*#tr sho{n in Fis.p-62o suPpo.'ie o €.li@l

l.Dd of 2ooo lb. Pdnls &c,\0 oe in thc sdE ho.;zonlol plcneDelcrmine lhe fo.€a in ea6h nEmbec.

d;- .((-t-1))'t!o4)" r <o4)'d.,b - ao.7zotfl.

- (o-o)'+(io-o)' + (o-(+))'

d^c . loiro3 fl.

q - b t b .- _ L

6

AC - 120lb -- - c

o -.co),g,,6;r &(r) -.,o{n)=,

a,46)- t6{E\ r.@(t) - 3e

i....'a)d,'' - (6a-o\2 +ka-o\' t (o-(sr'

d^o. r+, i+ f t .

r20 t2l

zrA.ro. -o,(te,) + Rf l4).-o

W - 6.6./aot - -@

zMa- o, 2o@(1) - CrG\ -D' 6za) - oat(4) |q02.41. ac<t> - -@.

lsolole Riqht gidovic*,

,.. AA , _95O.r13 ., Ac - W.2S t _Lp_- _jEL1o &fio1 10 lara ^o

AA -ros5,3lb- -o I [email protected] i Ao-6.1c'6lb-C

62t) n ve.licol boa p = @tb oppl'pd lo th€ lripod showi in

fiq-Q-621 @u6f,s a codlp.esgrle lorcc o[ 2i5 lb in leg AB \ ocornpree.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

l$s =o, Df(') - Cf (1) . O

Dr ' +/3 cr - -@ .vb.. +o@in @,

cr<+)t 4. c./ (12.c6) 'oc.o

Ct O+.Pe\ ' adaCr = 56.-2l'1b

in@, o' = ,15 G6..25) - 1$ k)|'rO, q"8,G6hGE) = 9eo.7,t4 tb.

q(rd'qG) -oro . [email protected](6U/4tb

lsolole Righl side v,ew,

' M c . O o-0r(6-2.) , @oG) -W41) -o'aoo (6'zo') | as@ - 21e6.6 - o

- 2100 + 4co7o . _2001 .4

Za . 0 ,997 '

-PL " -01-10 o.t.t,

o ' 'b$bes ' Iy 'oDz' 3s,s6 tb

trO = '(aOf , qa' ttzs.6e.fAO - 432.7 lb - .-C

- & - . L ' @

; 8 t ' 1 9 e , a t t b_9-_q-29L

:. C-/ " 2oo1 lb

ot | \999. .O44-*U-O

4'+ooto

Io _. t '

t c - c , - 2 a 3 _ C "1+t+2 B 1.n2 6 '

Cr = t6o,a lb. ,lCz ' 12o 1 lb.

622.) ln Fig.p.621t tl P'12corb. \ the coordinotee cf Oarc \o-e'!.,zo-2fl, compule +he lorc€ in erch leg of lhe l.ipod

d*- 6-)\ (*'d7 t7oZqYdM - 12,$6l l

d^c = "(o-o)' r (1o-o)'+ (6-o)'

d^a = 1+:1+2 fr-d,a = t6'14)Y t1aifa eeY

d^D = i1.3s6 fl

-i-

t22 t23

lsololo Fronl View,

q Ls) . c/(., - 12(,@t . og/ ' 6<bo -.'(t ) --@

lltlo - O IC, G) | 12@(2) - ot Ao, . o

S./66)-qG) - 2.e - -e)

subs. @ ro @.

Q@'q(a) -Cr(a) - 2a<t-C/(e) - - 96@

q _ 32otb.: 8/. 6@ - (32o)(B) . 36s tb.

6dro:cr6'\o)-qG)- 24@

- -?L

Cr+o,ta./-12@-o32O+ W r&9-12AC,-O '

-4L= _lqc-p.ea6 p

A - 471.31b C /'C- +sz.E tb-C-/ \D = 512\.aso 40

0 = s81.5 tb -C

68.) 9elcr'l'ine the nroxrmum sofe verlicol lood w fhot can besuppo.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

) d."..[:7'TG;F,G_gdo^ - 1.aw'

qu.6,n7 doe' 6i'tf ,G-o\\ PIi|'Cj06 .6 ,C62

dva-"6-o."tcarc(+AoJ o.o= 7211

ll

rI

1

* i f . M" 24eb.,2 @ . - L = A L - 1 q,.103 2 G

., A, - 6445lb i At- 19,:+,* tO i AE.12s2.C1lb.Isolole R,ahl S,ae vi*, leolc,te

tif DE '2.@ | ,

#'+'T-+

(srt N\z -G/G).oq - 2(t 4.p}t 4)-

q . 1.731,e2+ tb.dt ct. jf rc >24.r.tb

*pL - 1731.921tb :. qa = 241.4a trra'211 5 "/ildoetu)c&

n(4'at(A=",& -(1i21.s246) - srds.etb

t t l D C ' 2 e t21Oo - Ct -C i ^C2

A'(1) -B/( '>-o

192+..6G) - BaG)bf - 1539 '@

dEcrK \l Dbr24@hDB = 153q.46o

Ee. 6-

.'.DB- 468.561b ../ tl dclol crd

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 tbdv:k 'f M> 24oa

_w. -22122

DA - 27s+.s tb oo totl .x4t tti6\atle bd@E il er@&s za<Dtb

ct ' 1q6,9 \b.C . ' O

t24 125

EQutuERtuM roR ofl.coilcu^RrNT Sp cE toRcEs62c) the Flole 4arn in fb.p'626 aoti$ o load c,f loootb aoptieioJ 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

D.\ ' 2 167.25 tb.

.. thiE @nndl be o@pl be@|s tl witl eo6edlbc I'mll vhich i. z{.ab.

,. sae dar. vot.e of w i. .sigg.S lb

t*a,r(s)-r ' - (o).oAa" 229,61 tb.

ahec'. \f g > za4otboA - 73s.61

-6G)r 1.,60{6) - B(s) = o

6l-r.L-! _-.]

W.-4,4. ,0o(+)rc io) .oC' 4oo tbT

AtAIC -1atA "A

A - 1<><b - 4oo 4oo

y1()4@ t - 't G)a6)(61 ,/s6) + ,/l@(d?/e.6)

t = 5 n .

s'-3p@\i@@

627.) 6olee prob.6 if,t^ add,l,on 1o ihe loootb,the plo{e w€,bhsj

'U@\@t " Ue)qt)(e,/.\ + 'fG)e^1qe)g r ' b A . h )

j " nb l l .

c. g@lb, - f g- g.o tb .T

ztr.a --A+ 12@r 10.o'g&'a@ 'o

A' 600 lb"l

62c., Refe. lo unsynrnetrrcol conlileve. Go'r€wo'h dosc'ib€d

in pnb.61g on poqp €6 q rep€oled heneosFl9.p_62c.lf lhew:

ibal\lood of 17oolb i6 shrfle, b ool o1 lhe midpo"l ofmem-

ber A9, oomptrl" the componen{s of lhe ceoclion ot I E lhe lb*

oes in lhe bors tC \ nD.

nn6 g,otal , .m 6) - c6o) . o ebG)1.&o G) - @ta) - aLs) -o

dn -.[.e-af ,O+ef '6aY ' s,7" Xa"c- .@$i6 -ofi@-of ' tzfia^p - t6of 'Gaf ,GEiff - sftaq.

^ c - c _ . . c r . e r

A c''cr/2 | C, "Ca

A D . O ' - - 9 t ' 0 2e,.6s g

Q c, = ot lz 1 az 'D. /+

sub. @q@ lo @(o,h 'Gh) j ' ( .^*o ' ) la +a2so

6 , 5 0 , + g s c ^ ' + 2 e OD " r c ' . e d o - . - @

9,6d+6/( ' )-ne(6-2 ' ) . as,(a) l qb) '$3o--@

@t , ct)e)- @, to,)(.b) | noo(z9) . o(0, . c') (i) - (., I o,)Go) { a26o - o - -19

I

a./'

t26 r27

Top viow, LVz'o O

o, ts 02(.) .0,(6) - Q(a) | G (+). o;i:::=-" ut: O! o'/+ t,cr-G,i . ' " / (D' / , ' )Gt - o ' l .o) c,G)tc.<i 'o.V" c ' " s .2so , -@

""{2. qbs.@ b@,x r s 2e D' 'eoo

0' . So lb F.N@ | Ct . t.Lt<eo> . 12o tb,to.fu(c.rcsl/a Ac.kao0z):L/1

lc - 126blb.Relcning lo FrD.t view,

zMo"o 0 "b G) | s.e) - e(.o) . oax(6) | az G). +r.. - -@

zMc" a 9BxG) -62(3) - D,G6), o

9*(4) -bz9) - 600 - -@

^oD (, L@

i n o ,.eoQ)-Be(z)"sat

ii O,s@(.o) | 6, (!) - e3so

br = lasa tb.

ar k) - b{e) - @ae, tn) ,2.6 ' +aoo

b, Go) . soaaB* - 5.b lb.

6ao,) Ihe b.f,,n BE of ltle sf,fl". l% de;|cl(. €hawn i^ Fig p,6sok tuloj€d bNo.d jr' meogurcd in o honzaolot ptone lhe nraslnb 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.cesin the lEc Ec \BD t\ lhe. conponenls of the beoring reootion c*

dao 'dsc . t r2 tg

l

j

riIl:

I

N@)- '[email protected])"o

zw-o oq(6)twG) - s.,Oaa) - o

A(s) rt G) ' 4aaa bq , v / ' a e - - @

." E: - 99L

R,!lh{ Side Vi.*,

aio'a, Cr<i) - ]6at!/l) -o

c, ' 6a3lb

n e4.4. q 1o1 's66

oy = t63 [)

- . - A o . \ 9 1 4 ' ' 2 d 9 t bi a --A,(.t r (c'* o'X.t r soo(s6 6)<1tt X')'o

^" 6r , (G r D")Gs) - o - @

A,tst = (,r,7 i t1)t14A" = 2ag7 tb

oz . 6114/s_- 61 tt)

Cz . 227a(s)/i= 22a2 tb.

Or - 193

<j: 6-PL

Refc..inq to llbhl .q& V'bw,zMb:o: ^z1't(hiaj)(s) + cr G) o/5)'saaG) "o

Az = - <2271 t61)(1st633 (s) r la3ci) | 2w

Az - 166.7 ll).

63r) The boom Bc ofthe ctiff'lea de'rich 6hown n rOP6?1

i6 conto,ned in the XY ptono The mo€l AB ls "e'rtiaol \ rg.s-ls in

o soohel ot A Poinfs A\D ore in the same horiuonlol plore '

Points DkE ore in lhe.eome v€rlicol Plono Detormine the

foroeE in 1r'o 1o9s BE ?^ BD \.!4ryw"""ts ol Ihe bea-

r ing reoclion oi n.

t28 t29

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solution statics by ferdinand l. singer 2ed

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