2. '*pa;a:paat*
na'i -
Jojo BiIrM forulc@4'l
nBsfs I4.t Bor As.i.ti's f'&d[sdig_ A56diai! 'f
pErpu-g..&*tr-".(Af8t.l1
Hg=ffiH
.f dle ftntlPiD€3 (BDAPT thililP
Asociatim eEPA)
PEPA!trtE atioo.lBd& /t*i{i(G ltdb6tiF A5id
;;e-P",ts.- A.."d"d- 6PPAI ao.i'ti' " sd'rh
iii G* ntu.n-' osEAPt lrrdl'tr5'l hh|;tas
. " Arraieiim PA)
Prbr4dbr n rE( Fi$ltqco4rryic 8+86P ndt'tino St-
s- u*i fildrt " e,,"- cl'.Tds'7r2.al4-7r2'ar4t;
Pd no-?u5+12
T L o b o o k s n t l t l € d L o a r n t n ! c u t d 6 I n E n s l n € 6 r l n r
f:"o.ll:: ":: ,rrr!€o rs t6tr,/r;vr.,e. r.i rr,-'p",p"ii!
o r p r o s o a t r n t l b 6 p r t n c l p l € , r t r d c o n c o D t s o r
E t r l r n 6 € r r n g X € c b a n l c a l t r e v o r y b . ! l c a n d u y ; t o ! . t t c
r p p r o s c n t o n e l p t b o i t u d s n t t u n d € . ! t a n d a n O r e " . "
;;;.,:l:j":; ,ii;li;;
,",, ,r,r d6v6rop rher. ofdo!ry
I t l l h t t r o p r e . € r t € d t o p t c t , r h e u 6 r , w t t t t r a v e r
v o r y c o t r p r a n € r s r v a s t u d y o ( t h 6 a u n d r ! € n t a t p r l t r c l D l € r
o t
. E n s r n e 6 r t n s l i 6 c t a t r r c i , h t c h a r 6 t p p l t c r b r ; t o ; l d 6
v a r r e ( y o r p r a c r 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 d b !
t e € 6 I n r t r o l r d r ' t o d d y r c t t v t t l € 3 .
. E t l r a s t a o r t r r s s : e r t e d ! o l b a t e v 6 r y t h t r t l l
D e p r e s e n t e d t n I v s r J p e r t e c r t y u n d e r s t o o d , b l a t n r
: l : l r : " "
c o n . r a € t e n a u r g e . T b l s , t l l e l t D t n a t € o r
r r t r r e u t e d t d d e n t ' s a t t l t u d e o r h . b l t o t
o e l o r t z r n A t t r € c o n c o p t r t t t o u ! u n d e r ! t r n d t n g .
T h e r o t b o r r s t s l r t o { c r n o , l e d 8 € l b 6 t r l n d e b t e d D 6 s s
t o . u t . n a e l S l o n g c o , J e t t r e y B o r t o n g a n , R o n . t d o
C a t l r d l s , a n d n o r e o l d . t a n o t o r t b € t r " . l u . b l e
t n p r e p ! r l n a , n d i r t t l n A t b e o " n u s c r l p t .
iri
11. 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 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
B-a39]! (d i@t€d dodn*o"d )
R'- 2.ht tsoor 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;nq
at + (1. frcm lhe En end of ihe bar
zMp= -f(3) +2cnG) + i.he) - aoo(z)
r= 2oo tb (do9n*o.n)
.MF-.c'o(1) - pG)-1oo(s)- 2@(2)
p- aoo ib (upword)
12. ;''',
(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
l4
13. c- 3oR
(4<b-1oo)
flab - (412)R
R: l4 b dncoleA rcrlicatty
LJp
ol A B do*n oi B.
25o.)The conlileve. lruss shown iFig.P-2eo cor.ies o
v€rlrbal lood of 24<)c)b.Ihe lrr.:s,sle s.pponied by beo-
rings o) A B which exenl lhe fbrces A-,Ah, Bh.Ihe
fou. forces shown con|lule lwo adple€ which musl hove
oppoeile 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 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<jtb-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
l6 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.-dn
of, r*,Y oEs ol Ot.xt- Recto<t lhc a."en eyslco ty cn
3c"":bil
srnqre fo.ce ! canp,te lhe nlercc"t€ oi ils
linc 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 o
l1'<'
t s)
,Iri-F-
p-6 o 6.tr6lcm a/f (d@ .E ]]vc(F loo aowc
vorlicol
-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 |,aft
Mn=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,.
14. 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 oppositc
oriol 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,noefrecl - 1so(?)
';/"
B.nft.bn
1". o"na'"q
elocl - lso(s)
h = 9oo fl'llr
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
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 l
i '
t l
l
li
i
:
l
2s Rcpbce |Ae egolcm of foroee st'4n in Fiq.p_2ss by on
oqu;votenl forEe lh.oJqh OV, o coupteo
;;""
jii#;,...':i',X"":;3'::"'e:::.:mi:
zF, = |a1.a(rka') t 22+(46) - t61(r/JB)
fuaq4r!(lo lherighl)
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@,os
gj|: !L99'
ol C=<Mo
3F =a61(a/r3) 6) r 3o1
(s/J:t)(i r ft1A
(1/.rz)(2)
- 141.4
(t/E)b) - 22a(2,/.rs)(1)
- 22+(t ':t")()
3F - 1AO,1
b) +p= 1taa1.l
P: 2993 tb-
260.) The effecl ofo ce"loin non_concc,nreni fon:e egelem
ie aofined by )he fol)owrhg data : .x - +rJorr ,<y - _6otb,ona
zMo=360lbfi counla-o)ockwi6e. Dele.mine ihe potn) olw/c
lhe n€sulloni rh)€.eec)6 the yo,;s.
.-T'-
l' ,ix-ao zy =.F, Ly
l.r"*
Lt - 360/90
' afl belo|9o
2or.) ln o cenlo,n oon.<nocunecl loft.e b/.te!n ,t B fau^d
l 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.,lonl rn
lor6ects the )l o),;.
L, = +ao/46o:-:4 n;ght ol on,gin
lh.r'4h B eic.
l 8 t 9
15. li'
252) Dcermine 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!,ocos.6 | 2so
-: q994zb(lo lhe 'iqhl)
4f:r '7@ strl3o' ' r25o
1,*!arq(- meonsdoMw
,:-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' 22" ( / n) e) 3"'G/'r.)( t
- -L,r,6 n 0 (- neJ.s co"")-Cw/
- 1.67f+ r)qh of O
'Ly -- 1oo6/1+9.9
- 0.67 ft below o
20
2l
,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 Ftgp
466.l-ocalet)6 inicrecolbn wtlh lha r tsy 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. 10nsh+
lMo =3@(1,1a)Q) -3so("h)G) +122(2/r,')(4 - 3oosineo(3)
=&: a4.91 j1:lb cw
Lx - 1121.97- 4LD, righT o1 O
ty = 1121.q7
- 1,3en. obote O
uo.47
-
16. ili
r
iii
li
iil
i
trl
iil
,i;
I
rii
iill
i
l
ir
i
!
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@lrbnwllh llle
bioeeAb. Far s6>a desiqn, thie r erseolion should oc.ourw/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-6o1co5t.l3o
t 27)jA( neans do*n'
*ord)
,,/66atf; CeTaad"
g, - Ion'zrt/ara
- lp.,' 2n P/4a@.es
+"* 2s,91'
Ztt;A= -uooa0t) +poaa(b)'bo.P( )
= -228.cea fl lb (- meons ccw)
ZM6 = aFlrb
xb - 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€ lhe
given 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"eli inle-
R = 2?424.02lb.(down lol
ri-qht)
zt"-zo<tot++u(1/r)
' +oo9,32lb
u 4s"--fi-f666- rca -<+d",!t)
I :--.9qf.93..b-(- mcons down-
*o"d)
^l@.seiz-tTiffii:o.)r
R - 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' - Rt
tr , 11o
t tsoe/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 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.
4o(1%s) F | 11oi 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
17. -ga - lE1zJr/.t, - tdr-l @l@
' -+r::19-
ua'€No
n{*'E't"l, n{'olu)t2) -11o(+)
| rfuk) rtrt
l+:,fli:D- dt
i, =ao/po - Z4!L rtgt'l or o
ir - @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
1odclc.fia R, lhcn ltn- €rac lo fi.d p.
1fi'ollt €:llF- [h-
-'&, (',/h) 6) Bt (./e') &)' 4Gl
R.* +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(164=e@)
8:,iqqJ rb (da6word)
tth. -€llb
.:@.+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
18. 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 fl 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 oll hrn-
dp. t. r,F G-@lh g heol€o{ lfe ee'9hr of eo' h
26 27
!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 th€ w6,9hl of
.<
"-Kv".
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 Mcthod
i (usinghorizonlotvc.ri@l
^"".)
r@se' - C.a6ast O
I6'n2o't Cst^aE' - 6ao @
eb6l. cq r to2 t.alolo I i. tcms of T)
1 6h 30' + (1es.d/coeq.)(srn4s,) . soo
J,:!!!=?9:4
c - 1BlE Go*tVe. e.
S:!4.%s rb.
* Melhod-I(using tulotior oies)
-, ) ,2" rrw-o. cs,n
'.'.
- c _ e!1.aazllL
l@ -c
19. l
l
ztn.o: l- 6oo@6,6d
r cc6,zs'
. a coset + sazea6(coeze')
-E34!4-]k'
r Melhodtr (u6hg Forcz l"io"gle)
si^B- e 6o-
i. hold ogo:n€+ o sl]@lh in-
rod AE,n f''s.P-3oe.Det. Pqfl c.-
*,J A cylindo" woighing aootb
M"thodr (u.i"9 t{Y o'*)
t8 of aanido. b
/-K
rltdr
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 +heblooK
Melhod r (u6ii9 Rololed
Method I (udrg iiv 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 lb
P" 212,1a2
lb
Method [ (us;"g Fo,.e1i.ongte>
sn.E .,flor q:d
<ft =or fi€ink''BoosrnTs.
d - +oj,ao1 tb
<fh'o: P= rico6,rE'-
ioo @ 7s.
P= 4@,el (6k)- scb@1..
nl) If the vdlueof P i^ rb. p-e1o
6dtvc il musl be i.trhed w;lh
the 3oolb b6r in equilibrium.
i6 18olb, d.r€rmhe iho ongtc
the. Gmooth plone to hojd
r.l6in9 sih€ l.w
j q = L
P'r@!
20. !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€ ll' '
30 3 l
!1..) Ihc aoolb fol% & r}h
!1..J lhc aoolb fon@ q thc a@lb firrco sn6rn h Fig_p_s15
otE
fo 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 _ cdl6l
ltoo6'n !o'
-e.- - -76.93s. - 76.93s bet@ _oai.
F = .roos'n3o _ aooEna.
stn 26.t38
r . 20s.315lb
v6) Dete.mlne the votqe6€|1-
fhe o.st€s o( €. so fhot
cca EhoM in Fs p.3tb w be n e4ottibttun
ihetu*
2 Go)(14) co6e-
-o- - cos-'o,ezs
- e ' 2 8 , 9 6 ' - 2 9 .
_29_ =_L
"n* =t"o("nzg,)l/n
21. ir:
I
ll
, i
.
i
l
t l
l
./ :r7) Thc ayslcm { l^ndlc' cire dlt?a^ h Fb" P-trz e'FPg't
lhe indiootal $/€ighls' CtnPute tlE lavile fo'Eo i cdrc,,n'
ecn.n''aoor;canat'
B - 36+ .ao(stn&')
I. 914,162lb.
-s----9---2--
D' &7lb
A --cc66 | 9..s15'
- a<n(a"a1 t q+ra(a-1€)
A ' e16.11 lb-
Fototcd ,tses Malhod
ae) lhr€c barc, hi,yez ot AD fdtu) ot p'C a' do$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, - _-L
Et 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 a@u.d o 9tn6tt 6po.e. a.po6t,m lwa
?t,rd6€
eeh
^sasrtnq
4@tb q ;"",, ".'il;r";;
P ete , ayer frictto^b{s ou 6,s ta |e;
, qht+ ot ?ootD
a@tb.
D€re':n^: jhe oaeborhe nordot pro.€!,! N t4t. the o7tia.
de.s the sm@ih raatuhtot ^urttu
22. ec.:t fhc FinR l.us6 €holn in Fig P'322 iE 9"@o ca
ler oi A t') o hmgeaI 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 lhe
lkl: Ro-
.ona " eao(e'"eo']lat)
R^.451A,Alb= a62olb,
Rsv r Ra = gooosin6o'
P,a<
- A@o6t.6o' 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.elb 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. ic
dt A b o .olfe. dl p. A lood oF2@lb
ttE €oofione ol A b S.
cuplo.'ted q o hi.sa
ic oppbia ol C. Dol.
zMA-o
aoRb - 260 (@Eeo)(is) t aa(etnza<a)
RE . 6s94,76
_
30_
Ra.2tgg.za b * zaoo n
R^ = 2@ C46so'
&h - l7Bz,O5lb
R^v = Ra- 2oaostnaa.
R^i - 1199.8s
tb
R^"- R^h. + R^.2
rs -,/ t11t4,os)xt (fq9,35)2
R^ = 2106 tb
l o n € - - P ^ w , 1 1 q 9 3 s
HAn 11a2.bs
'6 . lorta {99,3s
1132,Os
€- = z4,aol
R^ - 2106tb down lo +te tefi al
-6 " 84,7'
23. :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 +hehorizonlol ; lhe reoohbn ol
the blooK
.t e = o/41- elo =ae
") p--,7
,439,
Z r 4 d ' o
5P - 1o@(locos3at
p' 1732.651tb
?. Pd .rs3o. -_i32,o51
Ra = 2@Olb
P i6 miniduh if il will be -L to Fa
hence,
-q' 60'
10pnin = oao(1o.asso,)
P6^ -- 866 tb
Ro cog3o' = Prnincos6o
ps -lp^;n1nsaod/castt
- laeoGosao'l/ cos to
36 37
tsl Dol.;rn;nc t'hc o,,ount q direct,bn of Jhesmolesl forte
P 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,"/tsq,,a " ,uit,. o. t,q.
Pd{ (d6+) r p6hq(i.6e) . iTso
(o6D P('6i"q) l 0,6+
jF a"q l 1.sep coe< + 1.sede 6,nq . o
#1"**" *".","_,.,f,",",-*.
d'P * 196apa^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€1
o,6+
o,64
< - 7 1 . 2 9 ' + 7 1 . 3 '
o
h(
W .;1s.,1'
Pstnso'- "o- 1.tn n, o"
'
P = 1es4h ot /.a"
Rsthsd - z.co(€D1s.r1")
R- 641.6lb ! 6+4 Ib
w',h
24. i
I
r l
l 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.,
erl1b41ao'.R6
a6ra@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-327
Delernhe lhe votue ol P F
$(r) aAsti - 1so
(6) t ae82)
f - 390,15lb
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€6bors p;nnod togelher os shown in Figp-
s2o supporl o lood of .sotb. Delermine fhefircc pF octiaq
r.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 aP@.p - sso(Io
2P(ane6.a') | 2P(caE66.t1)
- zsod
p= 901,39tb 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@e
loocoga . .oo @(eo-a)
rcoa-<-m(-so&,.".an^
loo .G4 - ,oo €nEo 6'rF(
l]!s-i t6< - rod
26a@.
- ,o - 26'a3's,4.
25. &orb-l -a,ltu
-op
I .{€o(a)roo(+Xe) +R,(1o)- !0066) - o
. R1I 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 inta 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
| 4F1r1600(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 A
R1_ 19oolts.
$Rr -Mo$+gQA.) + 60(6)(6)
R, - .9.sslb6.
P4i Ra-12o I eo(4) | 1149)
rtrr -l<ooQ)V
r, {t*o("W- ea
40 a
€s)-The .oof
-1tu6s
n I b.
p * ,s 6up@.rea b./ o mlk, ot 4 !,
o ht gc al B Fnd the 6jues of lne rsc rrorrc
Rsh.o ...Rp _ 9si,39 the.
336) I}E cont,h'@ beom shdn h F,s.p-sec is burft hlo a rcrl
1,, ",n'o. -
lhol ,l roale oeornet po,nl<AL rh€ beoh i6 rz.
ons h€lgh6 jootbpeFfi n concnltuted tood 6 2@a tb j6 oDottet
aI the tree c'4. Comp"l€ the n@chbn€ ol ,t kS.
. 3a R =!ioo(10)1600(eo)+ea6s)
R^ - 966.67 tbs.
1M^"a
3oRe,- e<,r(1e)| 6oo6a) +soo eo)
Rs" = 9f3.83 lbs.
€Fh"o
zRa.e@o(1drtua(12)(6)
R6: re60albs
P , ^ . 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;'*"
^**
26. R1- 1760lb
ss) Thc lwo 12f1b@tns dl('r.n n fQ z-4o oi lhe Poge@ 6c
;; ;-J ho.'zo.lo / with r€ePeol hoooch 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"-o
Rc -Ri rRs
Rc - 6ro lb
R6(Y) =Pa(12)
Y = 320(12)
Y = 6 f t .
tM?.-o
loPe- 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 . gFl.
.. RriLR6 ie 6ft oPo.l.
P,e afl. l-rc- 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.inc
the 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 .7zol4
F,hd P lo ooinio.h lho cauilibriun.
r,1' 2s.2b p- e6 | 262)/e
27. 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 theoo'e*rrrre#'n ine4uirr-
f*- ia^ *i* the @'imum taad P i' opPtiedt" wfEn lhe loa
q = 2o+ons
U- 2RsGPe'ltcA .aii+ion)
tsr.a=6oaG) +2aoGt+)
.5p.6- eaor +eoo - @
RArRe ' 600t 2oo
'vA-e@ .R6'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).zo(.)teo(ro)-
qi i{sl = 22oTons
- -el
- 6 f 1
44
45
!€) boom AA i6 9uworled r;r o hortzontol posifirn h/ o h,.se
A x*. o cable $h,ic tun6 fton C o@- o smo puite/ ol D os
6hown in F,ir'p-ra€ codpuJe the leo6,bn I th the cdble 1^ ihe
ho.tzonlol !^ve.irbot oomp@ehls of fhe r&otion ol n. n :
lql the.jEe o{ lhe putte/ ol D.
zal.) R'paat pftb ea6
po6itb^ at whjoh il is
lood€ retuln verl,bol.
2oo(z) | rca(6) - r(s663a3')(+)
I = 279.s2 lb.s.
Ph = r.oe63-+a"
- (r7e.ez) (.663.ai')
R i r l 6 i ^ € a , + t s ' - 2 a o t r c o
P.! - 3oo - (21s 62)(6n6a4z)
Ba - bo,a6 Lb.
ir +beaabte putls {he boo,.1
AB in{oo
t cl:ned ol 30' abde +he ho.,z6+at. rbe
6tne' - V4 lon€. - 6/4@ao"
4t .1,t{z).,tet | 1&(6)@ao'
Re+I6h--. = a@ r11x)
R! - 3ab- 216.. (etn6d)
Fa - 1t2.5o lbs-
28. B Eooh
ftorc etos ;^ f b P4+s i6 tupPot'tcd h pr''ot6 oi A
"*"* ".;ut " soi p'tfi d"p"le thof@'r?io:T'--
n * t " ho.,zonlo! vaticol oo"poale ol lhe
rrg) The teuse. shryn
&-o hinge ot A solve
Beo)ComFrle lhe lolol @tioas
O E
i^ f ig.
Pia is oPPoriel on re e's ol A
fd. the conpo.'€n+6ol the reoolrorLs
Rsh - z'to lbs'
21R^ | uo(15)'dL) r '+46(56)
q--!4 R^= 71otDs'
24R6! - @(12) r uok) - 4b62)
ol AqB fo. lho fruso shom ih Frgu
/t /t-
. / t / |
/ "l/ ,1,/
1. ,,fr>E I
rU ln^ 12@tb
-- 194
c
l!.'bl) =s&Q) t4l6) 1'8'h')
lit' ' 2455 67 lbs
nh . Eh =?+66.6?lbs.
&r -^ao+s@r@raoao
46 47
Rsh- soolb6.
R^= toag,7t
r p@(eo) - se(^d- a@(ao)
bs.
{fv .O
PlNrR^-6o0|12co+soo
Ra? = 12j4.2e tb6,
e.E- GAAiGTGAF - Pa4.?etrB.
tang.;p1i.ee/eoo .. e - 26.12'
i. RA a12so.7stb6 up to |he tefl ol 16.12.
3Er) lha b.4m shom in. Fig!,re p-s6r i6 cuppo.te! by d hi.tg,eot n
a mlle on a 1la2 6lq,c ol B. De]'eaditn@
lhe resufont rechbne
ft(Ra' - a{t<12)
t6(FLw) ' +oo(i)
Br Rol.o Ptuporlion,
Rsh - r R$- 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
29. I
. eoo- 2c6Ginao)
R6- loo lb5
Pc(s) = 1co(a)
zF! -a
R^v r Rc ' 1oolb6
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 6f l -
R^- @o)at(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 Delemrntp'r p"ol-
so +heho,-,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 raxbG)- rc.|:a(6)
48 49
A-R/B(r6e,b)-#tt
#E 12 t&_
P,.R/B('6e/d.tgl 11st(s€,l
- .:aow.
1 9 1
3E+JCdnprtc the fotot reoonbns ol AB on the
in 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 2Z4as.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_13976,09
!ca1. *)
.'. R^ = -+er7,e7 lbs up |o ihe ri9h1 ol q - j€,e6.
355) Dele.oine lhe.eocib^s al ASon the niik +ru,ss
6
h Fig. p rss Mehbers CD F6 arc re€peot&etype.pendic, _
br lo n E BE ot thet. midpohl€ .
30. iX!., ^ =poa(as
l ao.x)(a
2e)+
+aoet i
Q^ - 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'n2666" - R^€r^3o"
.
- 4oooatn26s6' - 5361 27 stnaa
Ran = a92.Og5 lI$
Ihe c,]ntilerer 1.u366ho'n in Fq p-a% ; suPPricd-bv o thn
'.i
i; , .tt,r BC Determine the reoolim oi A h B
ton+ - 13/tat+'26t6'
ac =sa ' ts/cosze Ee'
r'lc-aa' $17 f)
Ao - 39p9
;a: s,.ed
Ao
-. BF '> 1617/cd
Ao" BF = to,75t].
-B^, - -!999-
Q^ - 2ooalbe lP
50
35t The unilonm rEd in F,!t.p-ae7 wc,bhs +2o rt bo6 ,ls
of em"ib,ol d. Del+mine
th. t.";-,;;;;ftX.:
tione o'l lhe 6moolh_eurfooee
ot A8.
aM^-O
2Ir 440(6)- afish4o'i 6rt@€.
b!l, stn lE - aosa6.
2T .r 2s2o - t6 tlstd.'.
T - ad@sa5. - 1260 ^
. erish+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+o
pa - s (2.+.soxsr"+s1 - alo - 2!}otb6.
js in €quil;bf;um unden ihe @lton of Jhe fve
Fis. P ess. Detemine p, R -r.
R(16)i r@se(s){ r6nef6) - 6co(4)
| 4ao(s)
r6R1 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@0
15(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.!,)
31. 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'
.{ore
or 'r ocrirq or '( =3fl
ftvja b tig NeeP lhc bo' horrbrtlot
& . , 1 4
-tc's;79fi'
caad - fr t N-+.3e
-oo=+ 24-.'rnll'
Ita-6-1'?,=4'61fl
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.!€ tlp
agle €- 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, er"o)l
| l'l..a' I L .l.t^@ ]
A{ e.t i - 6&e - 27.8e - a,(@.+',na)
1tl@ao 1r+on@
:: og+ - 6o(@cJ eno)
1+ aon6o
3B@€+6rlon6o) = @ cGe | @ 6ne
a6€fal(r 1ro"@) -@-l - "td.6,.o
[=(r **an eo)- oo] = 6.6. (eo)
ldtot = A@26279
-O- - 26.6aE'3A7'
32. -
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+ degreeswilh thi6 slnoghf line. ghow thal the lor@ in
Bc nrusl ba ze'.. Ae e.alne lhi€ r€sull 1 lh€n €how thol 1fieb.
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
ADDD ore in lhe someelrcighl line'but Fc ls inclineddloho.-
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.
cE-cF-o
P - cDdn@'+ aeet 6o'
6'i!€ r CD=OE
P - 2cD et^e'
c o - o , 5 7 7 P = a E 1 C
CO- BD ! o,gj7 p
BF = BD@s6o'
bF - o.67aPcoe 6o"
Br * o 617P (o.s)
BF-- O 2A9P -f
33. .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^vr 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'1cDtso
po+so' ts(z) 'ta-@
<fh-a: Bo.tE,go'=/.ba6io't 1@ctag'
bD = ^6 ric'l-*@
@pt B.
.06) Th6coniilove. l.uss in
lhe fucs in oooh tnemb€r '
R^v-oeA6-@
Ac' 0.A6 AB-@
F^v- o.e(.oo)=solb.
&- Ao ' oe65(AB)
'o,E6cje) ' E66lbjr
@ d c
AB) 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'
tc - 2@.189' /
,.C'1-ft2lb'- c /
67
bp . 1.?,12
r
@ p l a zry -o 9c.t.6o' -pD 6.nao,. rooor AB sn3o.
o sBOr o.g66Bcr .rc,oo+
2oao(o,r)
o.eaDI a.e6ac = 2ooo -. - a
<Fh *o : 60 ccs3o'- Eccos5e.{ AE @s!o "
0,466ao- 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_€66
sa'2a9- o,6(2F@)
bc.966tb.-. c /
@ pLC
o.25 BO + d..+€3 gc - looa
CD6t.6v"- Pt,E|.60' I loco
co- g6sfos66) +iooo
cocos6o'+ Ac+ scco.6D'- CF
&- 2o2o(o,a)| 17t2+ 86{'(a9) = s1ruib -. ._ C
^9ana6 - ftoo eo,5o.
Aa = 11321b-. ,-'t
Fg P-a<r, coip-le
l"e lL€ . 'L$7
{"
+oz) In lhe co^lileve. l.uss €ho{o ir
foroe in m€nber6 AB,BE, DE.
@ p l - A
@ P I B
u6,19 F.otdt,b^ of Ax,e,
i ee.rrsiro
l- r
+
o,25Bo* d.rqi sc - ioo.
' o?s Ao - o..!e3-bQ E lgoo
34. i^ eoch nember of lhe wor.en trucs
.osJ computc ihc fonce
6hdnn in Fil P-'o€
R* = ABs|n6o'
A6-A!9_
A3 ' asoT 62 < 4910 lrc
coneide.ingthe wtd€ nborc:
= M E ' o
R^t(n - e@($) 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
/
pi.c
lFe=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
ce'1war24s5-1O1O
Ce'Lr+s lb ' -T
58
59
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)e
coniilev€r lru€6 sho,n in. rQ.p-411.lf lhe loods were opplied
oickE in€l€od ofol ED, €peoify whioh memb€i6 *ould
hove 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
@pI 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
35. 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
ac"q,te/,o(^s)
= 22a tb6.r'6td)
co - B,o(s/e)
= r2ob({..6€n)
&--
Ac .12s |b (lo^.d^)
66 - 15616(a"p.ccaoo)
0 1D :
€ 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' BC
gC ' 192tb0€'€ion)
@
6l
aoe) oelcrmo€, lh€ for€e in m6nbat.5 AS,BD,9E,qDE of lhe
tbwe 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: 9r5olb.
a.
sEsh6o'-6oo(Eh60).o
BE - 600 tb (@.nprsi6)
BorBE@.o. r@(@.6o) - atoo
60- rsoo rb (cepr!<,ir,)
t'a) Oelermiie the liJr.e i. €och nerba. ol ih€ pro$ roof lruse ehoM
AS - +s@ lb ---C : FH
AC:6H - 366tbr-T
o, E, 'Y
/@ u5iae d* ^c,
,Y' ze".o &=1s&bc-F6
4/ l* a lhc at-,s,rcto,6
.aS-ED=DF- asoo tb-..-C
atc.
f.d-
E w-.E
_,q-_es_
g .ti5
:. co= 463.3i rb-.-T " DG
Ac - 2/r-n q) t cE
cF . :,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
36. a1t) comPuie lhe force in eoch rn€r'be' of lhe lru6€ 6hownin
f,A.p'+to t lhe loods o{ Bo a'e shlfled vecticallvdo"
-o.a lo oaa io lhe loods dl d b E' wil lh€re ba on/ cho"gp
in the.€oohbne ? WhiohmembsrE'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"at 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 @€6s43' bc'Gco | 2oo
- se6 @66?.4' 7oo- c0 | 2oo - Ca'lfeo' /
/c - 44obe | ^At:'tb
- -1
'' - tlto)b --c
<tn-a : /cr Gco
't F
cE - 4ao+4G612o)'114a:16
'! 1740lb- -r
62 63
@ p l E , @ ?t. F,
Rw' YEcF
€hown in rig
DF- i@a.924 161o1b,..-a
the force in eoch m€mb€. of lhe crsne
@ pl.A,
b'- 02 |ca - ?occ@B
b. - 6. t e. - z.G>(s)c.E126.
b = l 3 . o a -
tn | , 62 -@-os)'t s2,.G.oaXqc.FA
A" 22,Epl
bD6D5o'- Bc6h.ir'
o,560 - o.s66Bc'-ta
tzo"o . o.eor(ff-e6) + o.sac
BC = 6c0c'26 ! 6000lb_..?,c
,,,!a= 13O9A61 - 131OO
frr-. t7
1Fh.6
ACc@2aa9'- 6
,'D- 1t1oo'(6e2.6q" - 12o23.4g tb
tB = 12cbo tb_-_c/
Bo'=*ad = rcsg2rb
?,
+ lAlAAtb-:.-C
@ P l
,^6 -eo@s& +Bcoa6o.
12t)Ca
- o.a66ao r a,aBc -a
37. aft) Ocfc.mine thc for€€ in mcmbcr AB'BD'& CD of lh€
lruss 6hownin Fig P_a14
K-,
T
" ' T , ' l q '
u, sblb coolt
h
4Mq =o. A"(36) =!oo(27) t .ooQs) r @G)
k A8= Goo
Ag. 948.99lb --"C
Z F r ' o
AC - ./& AB
AC=qJotb- tr t
ol B, &taao
n "
&
$/a rst
r/tio Bo- y'F ^a
BA- 632.46
lb-"c'
'/It Ae - l/.Fo Ao I ea
Pa - 4.o li) - _-T
;e -E-c.
l"-
CD = 125lh -- -C
)
64
atA}..',
@
+1s.) Solve lof th€ fo.ce
trusb Ghown in F,i?.p-4rs
in menbe.€ Fri, DF.s, 06 ol the
Fr = 1274.19a plo tb-. .- C
@ Pt.f, @ F,
/,tz FH- 16 | t/fi DF
t/E h2io) - 16 r Xi baz)
F6- Eee. 4 6a'tb
co.r6,cren
ng the whote,
Rav I Rhv E too 1n@ r ocro
R^w*Rnv! lsoo
tuNfr6) =aao(e)r3606€),
R^v =15Oo-9oO
- 6o0lb.
7.r, FH - 3//.tri6
DF
or - A@]li)
(3' tz
oF - 9+c.64 947tb_.._c
@ pl. 6,
4/5D6+6tt)-9c,0
pa - 3ao (s)
D6 = 3.75tb_.,_r
38. 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)
po- $alo- -c
co - s/. Azo)
Co' 2oolV
- -c
cE' 3zblb- -1
41s)
rfE wofco lruss rood*
-06:0::l i ::j-^:'":'iffi
' a1|(d of oe"lios'
. - -^,,^. ^r r- a I'nqe o1A ar 1r'en
-..r- rh6 {^.ce in lhe re-m^e w w,5at
ooosldding lhe {fEle fEu€'
1?n-o' p-6A ' 6aa ltj
4W-O
6@ Oo.l+6@(0) i Paabo) 'aobOb)1
P.d (a)
Btu p^eG6) " ze6.)
66
67
,l{s
or(2o) - R6v(2o)
DF- SoOJb
-,--C
cE("o) r jooo(to)r R6r (2o)" R6.,(eo)
cE
"4oieasfu):_ogacsl
c E - 1 0 0 t b - . - T
ap) u6e the rethod olseclionc to dele.mire the to.ces in nenb..
ED,co, cE of lhe wonEn True6.
9C-+47.21a++Ali'o---C
cohcidenilg tfE wiEl€ figurc ,
RvF("o) - rooo(1o) I sooo(F) r
b.b(.)
3o(s.66) =ooo(.)+ also (ta)
BD - 32E.o/e.66
B D . 3 7 s 2 . e 1 b - . . - C
cE - 231so/e.66
c E - 2 7 4 2 . e t b , . _ I
ri .,"-'ro =.
".? | e- a.66n.
l/a "
RvEas) - co(1o) - soooco) +4o00(6)
cD- 412s9,4a
c D - 2 1 2 s t b - . . - I
- cD(e.6a)
+ 31s..s(e.e<). z.<,o(.)
co = Isooo_(:zsoo., r+)
CO- 2O2O.Alb .2o2a lb ---'f
39. aad Od6r'ino lhe focce in ltt6 ndnb"rc Df'06' Eo of
tb$,e lrure €lto'"n n fiS' P'+b-'
aM.'O|.r'.o=a@6'2)
Df = 40cD|b' '-c
2r!-oi @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.,,t2@rU.rB
F,F- fr,6 | *rten)-.,t'Idil
BF- 2@tb --.-c
r,|.lrEdof 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 45OOlb -. .- 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/2
l 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 t1
DE= arxJiE
-.- -T
40. 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 -a
R^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
PNtu>ao(@)' e(d+ rfglA
+
4-e+ DF(L')
DF -161.67 +162 ktqs - -c
2sfuoF - E6r 26/(t6eD6
6=.fu(6.)-ryt;@n
E6 - 1io.7 7! 1t' Rrpc-.-T
R^ - 30+60+
.&+ Drt lkfu D6
D6-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<).
41. 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 rs
BD- lck @4-41@J
EOr5oo1-Or' + 5OOO
rb- -T
<Ftt-O
ec - +/@ ^b + 1/s 60
w'tr@s1o)t +h(@)
!E'6a.Dtb --'c
AB,^c,or, oE of ihe 6'i6sa-e
< t - O
e.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; ^cdel
ta = 6/+ Go)
C - 46-02 -i€ xip6 ....-T
eG.,). vQo) | tc(o)r tk oF(22-2a)
r y@ DF
(a)
Df - e3s - 42.sk?e-..-C
42. a2r) Usa 'lho melhod of ecclions lo compulc lhe forEe in lhc
mcmbers DF,EF,EO of lho conlilever lruss desc'rbed 'n
Prob.+11q Fi9.P-/r11
on Poge 92
oe. ao/3
^-;t
a22) fe. Ia ihe desor,bod
pute 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 (Resolvinq 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 bY
page a2, t com-
Fv(so) - 4oo(ro) r ?ro(ro)r soo(!o)
7eoe4.)=z@(r,) i eoo(2a)
+a/.rs
bo(ao)
BD- 491,93tb --_c
ZMF -o (p-@t ^S CO dIC)
2aa(adr eoo(2a)
- 1G coho)
co - rn1a.a3
tb ,-_c
42.) Use the helhc, of seclion. to detcnmtne lhe force ooting
in members0F. EF.8(E€ of the Howeirues dcgoribedin Fis.
P-aas a^ page91.
rS
cEQo). 72b<a.'t
F".@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€sotvinsoF o+ H)
l"(ra) =.oa(1o) + aF(en3d)(,o)
DF = 1€ootb - -c
ZMH.o (cccotvinqFF al E)
a$(1o) ' EF 6'.b' (2o)
F F - r o o l b - . , c
'ne merLcd or sec'idq HilI. lo oppr, thc _elrod
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
rhlsrc€u[u€;ne
43. br, hsp€l,on.
tMo:o
At (16')- 1MG.) r ,ae(91
Aw' zaOO
lb *'
&-aleAa
AE' 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 nocotte
lrui6 €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 ,t1@ - &et @
oE - 512.45 tb -"-T
ot Jornl D,
Zli6 -o (?.ov6g co ol9)
1/ft DE60) =3/bez)(co)
co =s@tb-''- T
A,(zo) - 4@s26.r,.110,zo)+(E^ %,sf)
(z)(er1o) +ot (1s)
6I - o_,rse
Kip3_.._r
<M^"ot FoOo)- 2(as 26.sa)
(.toI 20)
+(z)(d 2GE7'.)(6no)
4kco. r/tasD| y'{ooE
BO=3@.5!5
tb-..-T
,r2G) Uc6 lhc 'Ethod of ccctiorls *o aotrsrmirs +heforce ir.r'nen _
b.,rc Dr, F6, 861.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 26s7) (4) - 2(6n 2o.stX' - z (o)(si,n
26.e7.)+ Ay i 2.+6 Kipg
44. 2 l G = o ,
s/@ or@4)-2$'@r) ,.bGo) r
a@Q.')
oF --12564 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=
/giFt
f =2aa.27tb---C
rcfl of c-c .
zrt^. a : 60Fa=.k]x(6o)
+a.a(ao)r 2.t <2r)
f6 =.733-33lb-"-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 inlc6elion of BocE '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($5) =1oe8p)
oe - rc'873 x.tq.- -C
CE- 97.22Ki?6---1
1@ (ba) ' 30125)+ s/EA bvr.z )
BD. ,143-41 &tp.- -C
78
79
e+o) For tho lrono loadad o€ shofn in fg.p-44o, &lor -
mirE lh6 lbrizonlal vorjiool compcnonts of tf,ropi" pros-
. 61,.Dol B. Spoc;fy di'Eotion"s(vp o" aou,t; l6fl or right)of
tho lorso os il oot6 upon member co
ar@ - 24(e,) +ab(6)
EV. 590 tt)
:Mr .o
N (.r) - 36G - 21bQ)
Av = 360 lb
:Mo-O
,a(a- aso(a)
gn(a) 'B00(6)
8n- t€o rb
bJ - esatb (dorn)
(lcn)
+<t Tho strucfuro sho,q
{ho hori&ntol e^ vc.tiool
8r-2.gO-39O-a
is hin96d ot A &,c. Fidd
of lho hinqo lbiE€ ol B-
8..)
y''rr"
z,-zf
8Br = 1oo(e)
+ ioo(6)
BH . 125tt)
<Fx-o j BH.AH - j75 ib
ZFl-Ot At - 166-|,46=a
Av - 2OOtb
C d = B ! = 1 7 5 l b
45. aPA-o. e,D(3/s)-AA-o
eo 4'4)AA
Zt ^=oi lzo(4 " Er(4). o
EA ' 12Olb
aVr.g.1 l4t- At-o
E$ 'Aq " 12olb
oi i6olatirg bor A_6
zMa-O I A!(O)'120(4) =o
Av -- 60 lD.
Co.'cira^i.g tho wtPlo Gono i
zFFot 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'
80
8l
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;pkr ro Ac J
zN,,-o I Bc(4)i cv(s) - cH(b), B"(z) - o
BA = 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 componenisof .ll-Dhinge focce ol C os il ocis upon BD.
o'@ = 240(3>
Or = 90 lb
E"G) - 24o(e)
Ev - 19Olb
16olo1ing bor DA
=M^-o
g! C6J- 240(4)
& - 160lb
zMe"o
(6)}.v- 24o(2)
A Y - € O l b
CA(3).7oG)t@<r)
CH- 2SOlb.
46. +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
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 .lgll
, /c_- _ 24a trj. 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=o
rc ) a2D /,8.n36 s7. -o
-;.7i
,LB- laoo 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-:4eL
tsA_ - 132a
Aw - .katb
. t A - P , w - 1 2 0
=4a -124
/Ad - 32o ltr
An - 32o to
zF" -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.ctt:c,aLto s jo-oa 6, b.o f;cl,o^tace nrngc€ Octc
rmirte iho votucg of lhc rDoc+ion6.
@
.n *,e
at!2@tb
c. cf r-'lo I o
t-- -t) ---1
lG 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. - 2120lt)
R3Gd - 2s.n3> +3&(14) -4ra(4)
Re = lleo tb.
47. .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 12otone Ctn'
o" (@) - 12o(:,c') | 6oG4)
Dv = 1OOtong
C,Go)'tzo(tdtaa(eo)
C a = A o l o 6
E"(@)-Qtbbo)r(a(lo)
e = 26A *o^a
zlrE - o
F" (@) - zaoQ.) ' lctt(2.' )
N Go) - 2ca(2o)- so(2a)
Av = ae tong
zvl^. a
e.Go) - 2cp6o) t s>(1o)
w = 212 lons
45o) A billboord 8C woighing {ooo lb is subjccicd tc o
wind o.cseuro ol 3oolb 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 - O
gH = looo-1silo = lsoo lb.
:ME.o: O,.r
(i,) = FeC4)
F{ - D{ .{sootb
zF =a: e4 -Bao-19ca.o
Ec = i@O lb
-F; -O: Fr.tr 3oOO
- AH -o
AA = asaatb
@ 1 ,
Fr i3) = e2so + 15ca
Fv ' 32SQ 1t)
@ 2 .
A!(3)- 22sA + 49cn
Ar = 22sotb.
48. s@ lb
EaQL)-sko)-2ao6o)
E! = 2sq tb
/v62)'2440) - e@G)
A Y F 5 o l D
@ .nombor '
t.rht=o
DHC4)- 24(o)
DH= 4€O tD
zrio=o
cica) =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
49. ,05)Abtock
waiehine
w ,o " ,"11^if,";"jjll""l",
3il1l,#;ir'1?:;"d"i''lioill
r ie(o)
gr.ore'
thon e:(b) cq"o' loe.Ic) lc€E lhone
)',l ii,i' l. aiter lhon
e- ih€ blochwirl notsiidedown
i,i.,""j li *i,, reloin ils poeil'bn be'ou6e ihe f'rci'onol
?,n,';
r;ff ,:'ilJl"Jl'*,
IT'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"ther'aro^ot,
ta'c'l:ll^:'",11;i:
fiil"[,:,"';tl::
?iii:.:
j';*
T;:iJ
i"x',;-"
"
io etort the molioA
P = <n!2.,
P= ftatb
P -- +oolb
P: 239'2
E
#*E-#
P^:- - l10 1lb
88
89
5a7) Ihe eoo)b block gflown in Figore is in contocl wilh o
ab' inor:ne.Ie 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 thc
inojine. (o) Il P-aoc lb, whol ie ihe o-ounl dr-ecl'bn of
thc J-.,ct;o^ fb.ce ?
> P - COOIb
F.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 . 5oottr
A.V r T b
4K","- * { -"-^J-"il,i"'r'
,J41! t!
. t w ^ P
c . ) ^ *
e,+at4{P 2+:o :4oa(Los15')t f Isaol@sao''o
'&^" r ' 70lt 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 lhe
conlac4 €u.foce6 -
zfu =o:N=aao(stnno)
| zoo(ar.ao
N'37J.21
lb.
<Fa=o:r - $o(cos.n)-zoa(snaa)
F . 246.+1
lb.
lL- FA = 246a1 - a66
' '
, t J t 2 i
5Oe,)fl,e bloak, 6hown in nA. P-@s are cnnacnled bg fldib
inetlendl'to cord6 possihg ovor fi1bt'bnla6s putless. Al Al]rr-
cnefftoienl ot frrclton ore f.
- a,oo fk- a,2o whils ol B
lhos orc f.-arcfk'o.@. Canwte +honog.;tudout d;rcc -
i,bn of tho friallon lorca oali"g oi each btoo"..
oro) Whot weighl W G ne,coe9arlJlo 610.l tha .essJcmof
hbakc ahow^ i^ fig, P-o1a novirg lo ihe F;ghl 7 lhe cocf-
50. I
el ..og. r FBOor $oaf,Al
frbr'cnfof fiichon ie o lo, lhe
bo fnrolionlese
pullege are,oesumen lo
M^-L^
',
i*" *''21'*'
*rl-o n^-u*,-" ,..n',
11^.24ob.
ldc
-tx-
'Fl'o
'tt - 204.6+ lb.
'' r^ '
f. N^ " (o2X
rao)
F^- 4b lb
{f-o : nr- 2oo(cos6it,
t16.12O
tb
. F.' f,tlB
'(o.(11o)
Fs - a6 lb.
6 6 . 1 ^
6mArd =,nrf
l^' 6otb
=fg -O: ll. ' JoOco6ro'
HB' O'1,6.+Jb
FBDof BlooNb:
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 blooks6howin Fig.P-sr1 to horo impendirg rraiion
lo thelofl . flv <noffiopnl of fnr'clion e o.z unao- ea>h
blooh.
fbo of block^ ,A.o.2.. e. t.a1'
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.2aNq-ahe .o p- 124.0lo.
o.2 E trnq - iorq
coso<
, :f! 5L
arz.) A hoingcncous blook of wejghl w resi upon lhc in-
-.w,. vr irvgr,r tY rEDr uPn rl)c In-
or'ne l9tlown in Fig.P-.et2. If tho aeffioicnl of lriclion ic
o3o, delerrm o lhc aletel h.,iah+A ^l *,hi-r ^ c.- !'
gleic€l haight h- ol whioh o for€o p
porollel fo tha incline "at "pl;.a 60 {hol fhc bl6'ck wirls_
tu6 uP tho ;odt;d w/o;t lpp;,4 ove.
<rj-otn
<Fr.or P. F+Wdo&,r7.
p . (d4 (wcos!#r) +
w (enaa,er)
{M^'o
P(ti =w.-€ 16.01'(t)
+we'^ e6/(.)
oofnalh) . ,.f 1.6y(
h - l_
Fr,Dol ElooKJ :
51. 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
rPl, <F!'D: d'soa cosrb/' = 24o tt'
!=1e!:
s1+) Ihe rco tb c.Jlinder.shownin 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. if s fiPPi
n9 i-Pends , deJe'rnr-
na P the aoffiaienl al fe'cl(:n
1F^'o: Hc'oe
e'c'' f c:oa
oo'
't+co€6o'
-
ttta.s*'
,/t-
--@999- "o6773
<M." o
q ( 1 )- F ( l )
p = t t l = F
ZF!-tt: t16htaI F6nb'-P'1oo
N(stn6a'I o sln.tBd o..113)=1oo
i ' 1@Z wr ' 173'22 tb
r =@+)(24o)- s61b
zvA -o : sP =w 6h e6s7(4)
t @€36a|'(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.)
BlocKA 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-
+hedVle 6 of the rnol,ne ai whroh molion ol' F rinpende
12A . R,1
;^r.*'
-"'^(a,'4>
R1- 123
7 sin (4o- e)
p1- tu,1 (sin ga'cose-- cossa'€n e-)
Fl - 123.4coso-
92
93
fBAof b, €rx-O I w6rns. &sra1..ar | 8.6n1+.o+.
aoo6,ns .(Rj '8.) 6rnl+.o?.
. (+R4) . 8e1.+.ha A
<F3'o I Raa<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(jo64
az4,+€ioe--2R1 - ao6.2c.€d
:tut nj. 1N;7
case- 8a4,+
6;ne--
2(1zazote) - zo6,2c<Ee
6244 €ine- +s36 @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 tha
leneion ti the, ct t dfiaor,ed la A?
Rl , '12o
st16 6h6sa+.
fu - 121
,1etb
<f!'a: hzcc,saos6-z.b@.ao' r R1
R . ' 3 2 3 1 1 l b .
1F-a, P. B2s;nao.a6
t fu 6tnaae6-
P - 1 2 6 . 6t b .
s1s) JF lt1 Psto, l4o bjoos ore .b^^ei@ bs a sot.:d
slNI 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 2rotbFhd ihe min weight d A +opreverrf
Irotiort .
52. lL.A26 :.O - la,O+'
FBO
at b: t-a.t-. o- 16,7'
of friot;c,^ utaer 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 rr / -E "206a6-
-o.ie/
I
r e 1 o o 7
szr) r" fis e-s,o f J.a 1 urde. both bloois^ wo6heaoo
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 z4-o : tl - +o3 I c6in3o'
zJr-O: ,Ko. Ca€e6' I F
c . 2 7 0
sn$,95' s.z+-o+'
c - 201,9 lb-
/r' a aOlA
w^ . s98.3lrt
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
fi.112,i tb.
tF,.o: p_F +c .a6so""
Vtt te+,e)(o,ca)
P"@z)(712.a)
r zs1.2s
p- +a-7tb
l.*.) |
t":- ot 4ootb 's
";ffi rhe purb,j shownin
,!:.':' tl",pi,'? iep-etenlea F.on @tdt.:rso,j o
ta:: P.opdEn
.:"
ly .-d cf the brotf- re,e.. rf ,he @el
o|ocr,on,.rr ihe bdl,e 6u-foe is a.eo,del the,alweofp
. ft_ r//rL=zog,
iMa-o i. rcaob'
P(4b)
- h&- F(B)- fioa(.to)
- 2oo(a)
pGi) = t+too _ p_ zcoto.
:,-)
A
:"o",;-:t",.o-m
r.,,re a bu.h:^g2,:^.ton2.,q,,tippez:)
,e^tt..a,t@. or 6h&- .n F:gu-w.the
a.e1 ot t.ato.^ ba lhe tu6i9V lh..ad E o.iq CD^p.te
:: :,
o:r^ A oi *y' {.,eh, ^ @^ be pto.@ ta ptll"al
6|pPn9 cb'v. thc rcd ,)er,ar 1rF derqnl
53. Afr-o) N1'Nz
n',t 1-o,zN=o,/tt.
w-- Flt F.- o.2 (a)
W= O,4 l
2M^'O
w(L-1)
t r,@)- tib)- o.
al$Fl t o.2(z)M-
2Y - o
o,4L
-oA roA-2 -a
L - - L
L - e i n
szs.) A uotlorn lodde. 16ft lotq V, weigaioq wlb i6 Ploc€d
V one ed on fhe grcund the otne" hond ogo,hst o ve.-
trcol woll Thc orgte f footbn ol otl cnoloal s"nfoces is
20'. fthd lho mrnimum volue of lhe onglee ol wk lhe 1oC.
O g.rilrb
"lr=4,t**t".,'S
to td tvnro' I
@ (!,d__h(1-a)
(!-L6tne)" - to. n'(a-L@ea)
Ia^id r - Letno"lon2o', +ton2o't@a"
r,(to to't lo^,a) "1."{; L@se+ Lst^e
a.Ion zA-L<bEetLetae
Ion1a" I Ion 2a'
O<M6.ow(x-5.e€-)_o
27on20'L@6o I zLqtne - L6.t
( r o n 7 a ' t t o h 2 a ' )
lLst e'L6the(ran ld t ron2o -
-srr9 =2,39i2
+-:Po:
Ton2r'!od<e1L6,ns
lon
'L.o.r+
t L6nt+
2
96
97
?a-1
A
.toda6
eoIj torc +.,gne ebi
.,,
j ,6,q at grc,t.t!
l' 8D
.frtn
lfF rDro- f^e bdda .. p.o.4J oga.re. a "erti
Y^*:' f,-yt,ir
mo,e€
on..st. or L. y,1trJs,o,.a.u.*
^ o t6) tb n a1 .,.mb b-fd_e lE I
ol stpp.oq lhe ar'e , G ,.^- -, -"
;,?""ll":,.'.::""'
'':":"- ft 'o- d, o,.Lon
@ { . d i 1 b * u . I o . 7 s " x
, ,"-,"trl.)*; aJ,,^,
. -r, :
, A Z [ ^ " ' " v " ? . o ^ ' ( ^ . . o )
,i"lz
Tanzs' '1t.tz . -Ion1r, r tolon.re
(to'z'' ' 1o" to'', ' ,o
.ng-ec.€ad).$a(x-s) x -sft.
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..tI eb,,o.ps cad.l
pllo t6" noq^l )de ol the cowp,e rat
dq 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"
lrR" 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.). ",,o
o ",r.(1c)
rr,t.s) n1=2os,7e
b
B .
l2o,a)(1,s)t
(eoft)(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,rrzcnlo
I
:,x^:-T:::?,
ronee.liolrs
ro thajefl .i rh" t";;il;;,
cuti^der
;c^*z ;-,;"""; ,:-.,:71'
or tharopof rho
counte.ciockwise-
' the calind- ro+oli.
tl
M
m
ili
54. 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(2,61-!)
-o
3 . 2 +- 1 o r x ' o 2 4 14 ' O
|= 0-76tL 83418-
"tl ,;6.- pr""K of wctsht W totol LdngihzL 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"-rrb (s-g),--{:-z;) o
n _r".o.
U- Ionrs'7 !rzL.ti< - -I@6a'(x-2Lbs")
:
@b..lt .. -t(tane'tr6.b,) - 2L@6q.toh6d.-21;,ft<
X' 2Lc41fo^6o-- 2L.;n4
fo^1.. tlan6o.
@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.ol
to lhc as' i.ottio thct w)| ooueo impendlnq tution lolto |.ll.
O iEdoti^g tho ba.
-s<;.
_9_
c
:n. tao6;n*'trocqn+' zn.o, r" +a-;zs<
- )o-o-*+s.p
n. 2e2,8+tb. (o26s)(.rr.ei t o - p
p:Zq€A
rii,l
,,y'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.
e.1{ ../'.o.26a
l l
.r__J1
55. t " -
r-l!_f,__ i
ZFg'at 11- 2oo I Ar
d. jo1.6 tb
.'.F!"o: Ar - +2+tra - so| 6h
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 ldgLlhdlaq,dd lla nor ' ongl'< ollho
, a F ' - o 2 R q . | 6 1 t t ) ' P
' - 'ra1-P'**'
'i'"'*P]"e
aP- ,Rtd.|ttu"4&) ! (@Y.Y+).al!
a
1M^'o
a24
(b@'6) r r. ra+E'dB a"s-L'a
tt.@.+s' | (o.t6t)tt6.b4t6'-d's'na6 -o
ftg.q = O,s1gflo
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.d
st "t/2 coeq
Ia'/ - &1"1/'
s.6) h fiqur-, delonninc lhe nrnimum wa'ghl of 9loch B lhol
$ttt heeptl ol 1.,61
o forco F 510116gloohA uP lho )'clino
eurfacool F lltc weighl al A te loalb lhc ongld of fttc-
lion lbr oll surfoces in oonlooJ is ts
FBoofn iF'
LJ--l ,*F{'
l$t L?
I
100 l0l
ah'O I Rrcosas'- F, co67s'
0n.a2) cc &' = R. - 3e,6a tb
ts . B, s,nrs &s,n4s'
ws . (as64)6 nzs - (F1.r4)€jn4r'
ttb- 213.2tb
$,.) ln riqlro ,dcle"nine the votue of p Jusi .s,fficienl ro
€ilorl the1o'wedge u.de. lne 4oo-lb btoch. Ihe ongte of
fr'otio^ ;s 20' fat otl aanlo;ctsufiac?,a
r*s
- 81.".!19.4b,
s38) ln
'-f={-
-
!::!rJ!=
Frg.sst. aelo"mino the yotue ol p oct;ng b te tetl
rc4u;.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 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<icr tho d)o*.
56. *"':+n"" #/
I vtnr. $a L./1
'i--)<---l
V o, - +aa
nW'
-;"1or -;*'
dngiEof fnbnb^ ' 19
A*
P - +16.7tb
tr- a : ?n
si..' tW @ts' - o
R, - :&_e:::
R1'641.1t0.
ar/1y
6't A. R, . 2aa.
.aol;/ 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
& (oe7a)'+ao
Rl '411.1
lD.
s+o) ,4s 6hown in Fig p-'io,l-o btoarswarllri€ z@tbEsl-
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 becr'd€cd il ihe wor'ght ol oe ol fho
to2 103
-&- -_:99-
wb Re- 1og.g1lb
1Fa-o
= ql's' 2t.2
P^ - ft,t Ib
P- Oos,b1)c.e'tlE.4.ni
p. - 91,Etb
dron in rhurc P-eat. fhe @"4aof lni4rbn lor o svrtocos
n 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. . 7lts.4 lb.
_L - 11,5s.1
1p-g1a.+lb
s..) whol lorco p nuel be rypiea to thc wcages snom
rigt o P-s+2 to 6lel ttE,n utua- +t1ot',och ? lho ot.Eltc
f.,,itoi for olt @^l<yl €;tf.,.rE ie tO'.
P - ed,q
_f_ '_le.u-tb
57. 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
fBDol B i, ..N
s+.) In itlue.P,oa
l@+e o1tsa.fbces i^ @ Iac+ dolarnae tho mo,imum wclgc
d.glc. lnor will grve lhe ^edqe o ne.^ant.al od"anlo7e,
R - 23aS.4lb
__ L.__8_
P: !9PLLL
$+ lf tha atgto of fniJto^ G b' ol illre-
t<tL6).a. ) - 1a&. n1.a'
€rbltllleP, '-- P - qa+,s
en@'T ;;G;;'4
: . e , 6 " , < p , . 6 s l h o " l h - w c r q s l w o r I n c t l o - | . - .
-l taaa_ - f_1t ::) paa
srPorq) 6nO,-) €"1&r<)
(s1ntu';.- -@1;6'"^) hab " baa
(6'n .''44 - @s'o.6'n<)
I
l'l*
r04 105
G':,o'*'" - -..'"*
(et ,r'@s1 a,ee-e.q)
, 1 + st tu'@-@b'6'aq -6'n2o'@6q j
(sDo.-G-&J o4" . (*-"., *" *) ", "_
6,n< _ Grn2o'-€ra2o' - o+66r
Io^4 = a.446a
c<- 2s"
gS!^RE THRE-^OEO 56]'EW
sas) A s;Bte lhrcodcd jootca@q hoc o piloh oF o,s t^
a meon rcdius ar 1.a,5
n. Iho creft oiaj of elaj( trtctbr
of 0.1s,of Alhetic f.iot,o^ ol o.1o (a) Deternine tE torcz
P opp)teA
ol Ihecra ol a Ie.6 zfl. to^gwhich witl €+o.t
I'rling o *ebht of zbns (b) whot wtueor p wt| yc-p tE
jaak tu* |o.hids ?
(a) y'." t."o --p.z (b) r^-o.to ta^4 . o.to
4 + - - e - 1 a t e : * ) 6 - b t f
o ' Io'r'6;'@' P'{l
t"^ (P ' e)
ft"a.1e P'0"4)(,,') u" (.,t t".2)
f -aft - to^f . oaa
f ' "'tt'
l ' a s "
P"+:Lro.(ote)
n' Ge@hn b" (.ata.*')
j ' sj +JbE
6a5.)tho d,Aonao bot||$ oalo61 lh.cdds o^ o ,.iple_
lhrcoac4 oou"** ie 2/.3
in 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 ?
pilo6. 2/.;^ (6,^@ il j6 lnpl. ihedcd fr"liipr9ric_p+.h
b
.. Pilc = 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.ft67rt) ton(srfie.ot
2ooo tb- Fl . w (o.o1E6e6u ^)
58. Pilor. . o.zEi^ (;, @ d1lbto nEadd
@tliPrSbs2)
lo^e "-19j14: - o.os31
4('.s'lr)
I - r,t. ta^(0 ra)
- 14U rgFjf^) ro^l b.sz'
T " 102,3lb-fi
€ ' 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 . The
cdff'ot^l { f"iol,i'n
',c
o.ra. Detcmi^e tho rp:r6l r*,<:zset'-
rg io €to.t lill;ng o "t-li.ral otl'al lod ol <o,o<n lb. wral
rnor"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;n
E-^.i^ "<e | 216+)
lane " o.x€t f
'o.u
e- ' 4'6' lony'o1 '
rE- w. rn (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 6rolio^o.j ho^rn-
loi dF.h i6 ue.a to s"rlt-l o t<rarg wcAhl. lf lhc coe(o
oc''t of f",alro^ ic o.+. whol sagl.l a.^ bo @p+r+n bg
c,cofi^g a 60 -tb (bt@ al tv oll* o^d of llc .+.?
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
tb
bll l.w ...ri "-j1eLb.
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_
!h.. o d. tulu:f,;e tte aetr,otc l cf ftroljon.
t.rorb ongEof co^l&) : /2o.
r ) ,"+-Jt-L^€?.t(,*.,tr")
_-4
laat,tb L^ so -
| (lr.s)
I ' Jt-!! '=> Ylo e's
t 2 . . 7
%,) A boot .,ert6 o pu| ol +oootb on tls hoween Vo is
wtupPc.Jobaul o copelen oa rhc dock n thc I.o.3o,ilo.^
no.9 lu.116 mu6l lh6 haa,sa- rckc o@.d rha o;taa @l|Dl
lfp 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--.
g^a.) A loftlue of zao b,fl oci6 o^ lhc 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, ,
( r - r 2 l ( r a r - f R ) . 2 + o t b f l
T r . . L . q , 6 o t b
ft (o tcoo) . aa - rt ,4ee.2ab
T r
3|a
l
il
59. plre
^- c*) . r,l?,:^
'+)
p(1.333fl) . +qa.a3 (o.l/,61)
P ' 6 1 7 t b
ss+) 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^ptdnercirin 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 16tl
4F3-a | 2- 1o3o.@e6,6J.t i1
T'
rl2 ' sod I rir
.€rx=o 1 Ir r Fli f" ' Pao 6i^ r6ar'
| 1t:ti t1t t1- - 6aa
H..Boott1; = 3oO
1.+
2WI 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 h.
!z= ut-"'"11-"t
'n,'."
i
12
butI'.V2
1" I1 - 1.6+e
(Y'/z)
108 109
ZMp'o
(9T,rrz(z) @n"Pttt --
5 f 2 , - 2 1 3 - 3 1 1' o
,s (!/,t 2 (a a41)w a(2.ro)-o
6e 1tw - 6&
, w = 7 0 4 7 b
l
l
60. C h o p l c r 6
Syelome in Spoco
rl0 l l l
€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. 3oolb( e, -a, 6) ; {o lb(-?.+,-6) i @ tb(-a,5
-3t,
FORCE (D)
4
logcl Di6to@(o) le o!r"yrr!'
-a1.4-_4!--3
a o
lta/r.rI - ?n/3 ... A. - 1ls.?4 lb.
3.4/7.e1- Al4 .'- A' - -1:.2.55tb.
zao/ral -
d6 .' . /e. 24.17 b.
-L" -L- gL-,L- lAA
6.71
:. Br' .-119a2 ; 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 bdck@.ds,
<r - 115.24
-118-23-113.15- -117.1+tb. { uprio.d to the left.
1t - - 1S3.CS| 234.49 | 141,41- 226,2+lb
22' 2.a.+2 - 29e.o6- A+.e7 - - 152.46lb,
€o1) Dolc.minc tho mognitude oflh€ rcultdn{, its pointrng , ond
ib 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.ca
2
-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 - $2.a6/2s6.
to gpl lo) uso ot - x'ir't t2
_aL=^L-,aL-lq
z 5,345
,'. Ar - 37.1+ : At - s5.7 i Az. 1a.2g
s,,/r " Br /-/ . Bzh = 366/z.0-7
:. 6r -' 127,
29OI 81 - - 169-Ea Bz' 212.i6
61. = ( sojso)' 1(-11a,a2)zt (aj6.aa)z
. R - so7,7 tb. pa;hl;S f..*ord doM
absoa - zt//F = gaiEg/s1z7 - afiB
cosor - tr//a - 114.o7/sa7,7 - o.z2s
Ii)6aa - az/e - +aaA+/s.rJ - o.s3e
<' - 3r.14 -127 2ge 1 0 - -9a 1E6lb
4/ - -111.02 tt1
1t - 7+ zB, 212 46 | ztA ' zre6 44lb.
s" =e/)' t(.r)" r(+,)'
Cosez . +a9.9/s24,se . a,gaA
6('J Dolcrdino th.omognitudeof the r.osultont, its point,nq,
itc d,-.r-o" cosineslor the fo ow,ilq sy61eh .f ,,-,,""pt-"",
concurrcrl lorces. 2ootb( 4, s, i) ; 4ootb(- 6, a A F.r. tb( a,- 2,
- 9
roge+DveeI D2. a2rr',ze
L-AL"!:L..<@
^ r z 7 0 z l
,'. A" . 113,15
t Ar - ,t.+i,44
i pn - -s4,el
-L= !:-, -EL - -@
z o,17
,'. Br = - 27s.46 ; B) - 152.4 a Bz - - 22P'05
L- -q-SL- pq
z s,ag
." ca =222.63t Cf - -111
.32t Cz" - 166.A5
2t - 113.15
- 2t3.66 | 222,63 . 62.12tb.
2l . 141.1++1A2.+1-111,A2- 21r,..6 tb
1z -'a+.e1 - 229,65- 166.sO
= -17s,a b.
R" - 4""+zf2r <2. = (62.12>"
r(212.s6).t(-a,7s.q)"
R - g2r,5.B tb.
Cas+, - 6212/s29,s3 - a,118
case.r - 212,s6/s2e.s3 _ a.+a2
.'. poinl,n9 bockwo.ds,
lpwards 1oihe
t12 t l 3
6at ) ftr@ oonc"@ai k€aE p, e, F ho€ o Esu[,onl of j tb.
dirc-lcd fotuord up to.ighl ol e, =oo',O,= 56',3", - 1r5".p.-
q@lc zo lbpo6s< through fhe ongin {he poi.f (?,1,a).Tho
olue cf Q is otso uo,b il FDsse€ th.oueh ihe p6i^l G,2,2).
Ddiomlne lhe nog.itude of lhc lhi.d force F the ongtes;l
noke-s wi{h the reference oxes.
3
whee p'elb., -4. =60',6| - a)' : ez..s.
.. qr ' 16.23
iQ/.6.rs, qz -e.7+ - co€122Aa/$-6s
1t - Fseax . s(cos6o) = 2.s -6" = 46.2'
<y - easo, . skoseo') " z.s rj, - @s', e.a6/23.6a
zz = Rcose, - !" (@sa6') = 3.sa el - 7s6"
!!--L'lt-= 3!
z 4,5e
:. px=8.r3. pf - +,37 i9z-11,ra
q-4L.-44'_?e
F, . 2,s - +,37 - 6.19
- -a.36 tb
F r . 2 , 5 - 1 6 , 2 3 - A , 7 3
F . -22,46 tb.
Fz - a.6+,9,r+ 1z+a
Fz' 23.G7lb.
' (' 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 cubc
6h@n in Fiq p-.p7 Deleffiie the rcrcnl of the fole abo,+ coch
of lhe aoord'no+e o.ds
62. t!-' !r-" !L' ig'Y
:. F| - 62.5tb i Fy'4 4bi Fz'626 tb
1t , . Fr (1-) - Fz(4)
,,- aa,eG) - 62.sG)
tur = -62,4tb-fl. az . -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.Slh-{.
ri - {1i tb.:,Fz- 140.F
tb.
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 thea..di^olc o'es.
-E-'LL'-L=4
.'. F, -o lrt- rgol6lFe-2ao16.
tMr- 244 tb-ll
- -z.to(+)
atAr - -9@ tb-lI.
zMr- tu(4)
- r€o(a)
4M2 - 72Ob- fl-
rl4 l l 6
6td A fot@ { a@lb i. di.ecl€d frDm C tor.arA E in lhe Eubs
ctn i" in r,6. r-aro Dclc.'r'i€ the hamen{ of }he forE€ obout
coch o[ ]he coordino]c ores.
d - a.efl-
+-++-*
:. Fr. 1@31b.
i fr. z26,sb
i f.- 1fE.a
tb.
611) A h@ P,dircakn ftr6 F ta*otn
607
, cov.es o momenl My- i6oolb-ft.
obout lhc x hz orc€.
iMx.F (a)-Fi(.)
. . . 5 ( 4 ) - 1 6 ? 9 ( 4 )
.M'- 6s2.Altj-fl.
tMt-F,<+)rFz@)
- $3.a(1) t163.i(2)
1Mf , 979.0 tb-ll.
{Mz . -r,(a)-Fy(r)
.-t63a(4)-3 .5(e)
<lY1:r - l:06.2 tb-ft.
I in lhe cube sho^n in Fig.p-
D e l c m ; . e P q r l s m o o e n l
-!L - !L.- tq
3 2 !r9.5
d - E,36s f'1.
P / ' g @ t b
= -aoo(a)rFoo{.)
M) - -.{ro rb-{l.
:.4=6aotb.ipr"4aotb.
4M*--P'a.)+ryQ)
4tiz - -Prc+) .
PL- !- .., P-1o17tb.
. -Soo(+)
Mz. -32oo lb-fi.
61.) A fot c p is d;ructed f.om o poinl n (a,1ia.) io€.d o poin{ S
(-3,a,-r). lf il ccusesa rlomen{ Mz- 1cootb-ft, Determinethe
monl of P obool the tt&,y oxes.
d . 0.11
fl.
- L a Z - ! L - l L
q,1
... p, - 7p/s,n j Pl . 3p/s.11i pz =sp//eAr
ztA,-p"()+WG)
teoo' 7/sr(p,+'&)pA,r
P . 9'll lb.
63. M
il
iii
ll
d
fi
{
I
I
pt - 7elb i ry- aootbt p2-s@to
zM,- -PzG) P'(1)
= -g.tO) ' 7..)(1)
r1't - '17ootb'(l
zttf - PaG),p,(1)
- s@(4- 7.b(+)
}'4/
- -8oo lb-{I.
6i+) Ths sheoFleg derrich shoxn in Figp-61asuppodso ic.tical
loodof zooolb.opeliedolA. Poin{eB,c,Doc in lhesa'ne nori-
r.ntol ploneli A,0, D orc in lhe )(Y plone. Delermine{he
in cdch menbe. of lhe dcrick.
Go,,ro) da '(o-o)" '(5o)'* (o c'5)Y
d^b - lS.7oo fl .
drc" . @' o"rks- o)' r (o' o)'
d^c'20616ll.
di - Eto-
<-zal'*s-o)'.
aw..r- o: '!r$(1a)-
oten)-a
a/,=laoo )b
. L. !L' !!-"!r
a
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 x
oxi6 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-alEtb.
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.nhly-loootb 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 tGa61ArY
da " e36r ll.
lsolot6 F.onl Vicw,
64. leololo Righl Sid€ vi&,
-4C-" ,9'-
AB- 1r1O
lb-."c
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
qk) - 2a.oe)'a
- 4 L , _ 9 L
lelole Ftunl view,
'-t
-lL- -jL. _4aaq
AO = 2382tt)- -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.
a^o . ,t(1ea)1
t(6 o)z+@-ot .1t 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@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' . 6.vt!.
d^c- l6al;Gzf-aB-Or - 12'
Isololo F.ont Vie*,
d^o. "/(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 t
Are 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 61Aoak 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
,l;
,; t:rz
65. lsololc Frb.'l Viow, leolate Top view,
9' 6.,)| B"t@')'Iloo?) -o
I'Go)+RrG)'6w--A
/ B . A r - 8 . . S i
f f i E s . +
,'. sr =6/59r - s,B.t&
1ou +G/eg'G) - 6@
13,68, a6g@
g-5@tb. iq-@tb: -o.(1d)
-a/i es.G) +1@@)' o
/e- 8-/r,3tb---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 2ooolb. Pdnls &c,0 oe in thc sdE ho.;zonlol plcne
Delcrmine 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-o2 +ka-o' t (o-(sr'
d^o. r+,i+ft.
r20 t2l
zrA.ro. -o,(te,) +Rf l4).-o
W - 6.6./aot - -@
zMa- o, 2o@(1)- CrG -D' 6za) - o
at(4)|q02.41. ac<t>
- -@.
lsolole Riqht gidovic*,
,.. AA , _95O.r13 ., Ac - W.2S t _Lp_- _jEL
1o &fio1 10 lara ^o
AA -ros5,3lb- -o I Ac-@9.ollb-c 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 o
cornpree.i'/e fofte ol 2@ lb le4 lC . 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 ' ada
Cr = 56.-2l'1b
in@, o' = ,15 G6..25) - 1$ k)
|'rO, q"8,G6hGE) = 9eo.7,t4
tb.
66. q(rd'qG) -o
ro . L2@.1(6U/4tb
lsolole Righl side v,ew,
'Mc. Oo
-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'o
Dz' 3s,s6tb
trO= '(aOf , qa' ttzs.6e.f
AO- 432.7lb-.-C
-&-.L'@
; 8 t ' 1 9 e , a t t b
_9-_q-29L
:. C-/" 2oo1lb
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. ,l
Cz ' 12o1 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 t7oZqY
dM - 12,$6ll
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. o
g/ ' 6<bo-.'(t ) --@
lltlo - O I
C,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@-o
32O+W r&9-12AC,-O '
-4L= _lqc-
p.ea6 p
A - 471.31bC /'C- +sz.E tb-C
-/D = 512
.aso 40
0 =s81.5tb-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
) d."..[:7'TG;F,G_g
do^ - 1.aw'
qu.6,n7
doe'6i'tf ,G-o PIi|'
Cj06.6,C62
dva-"6-o."tcarc
(+AoJ o.o= 7211
l
l
r
I
1
67. * if. M" 24eb.,
2@.-L=AL-1q
,.103 2 G
., A, - 6445lb i At- 19,:+,*tOi AE.12s2.C1lb.
Isolole R,ahl S,ae vi*, leolc,te
tif DE '2.@ | ,
#'+'T-+
(srt Nz -G/G).o
q - 2(t 4.p}t 4)-
q . 1.731,e2+
tb.
dt ct. jf rc >24.r.tb
*pL - 1731.921tb :. qa =241.4a trr
a'211 5 "/ildoetu)c&
n(4'at(A="
,&-(1i21.s246)- srds.etb
t tl DC'2e t
21Oo- Ct -Ci ^C2
A'(1) -B/('>-o
192+..6G)- BaG)
bf - 1539'@
dEcrK l Dbr24@h
DB = 153q.46o
Ee. 6-
.'.DB- 468.561b .
./ tl dclol crd
B'. Ees.a tbi gt.11gc.16|At.
$q...tb.
o+ thenbhl 6h6 vi*,
zw-o, Ay(1)- s, &) -o
Ar ) t/a (17a6.rc).2232
-1tb
dv:k 'f M> 24oa
_w. -22122
DA - 27s+.s tb oo totl .x4t tti6
atle bd@E il er@&s za<Dtb
ct ' 1q6,9 b.
C . ' O
t24 125
EQutuERtuM
roRofl.coilcu^RrNT
SpcEtoRcEs
62c) the Flole 4arn in fb.p'626 aoti$ o load c,floootb 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
D. ' 2 167.25 tb.
.. thiE @nndl be o@pl be@|s tl witl eo6ed
lbc I'mll vhich i. z{.ab.
,. sae dar. vot.e of w i. .sigg.S lb
t*a,r(s)-r'-(o).o
Aa" 229,61 tb.
ahec'. f g > za4otb
oA - 73s.61
-6G)r 1.,60{6)
- B(s) = o
6l-r.L-! _-.]
W.-4,4.,0o(+)rcio).o
C' 4ootbT
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.)6oleeprob.6 if,t^ add,l,on1oihe loootb,the plo{ew€,bhsj
'U@@t
" Ue)qt)(e,/.
+'fG)e^1qe)
g r ' b A . h )
j " nbll.
68. c. g@lb,-f g- g.o tb .T
ztr.a -
-A+ 12@r10.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:
iballood of 17oolb
i6 shrfle, b ool o1 lhe midpo"l ofmem-
ber A9, oomptrl" thecomponen{s
of lhe ceoclionot I E lhelb*
oesin lhe borstC nD.
nn6
g,otal
, .m 6) -c6o).o ebG)1.&o G)- @ta) - aLs)-o
dn -.[.e-af
,O+ef '6aY ' s,7" X
a"c- .@$i6 -ofi@-of ' tzfi
a^p-t6of 'Gaf ,GEiff -sftaq.
^ c - c _ . . c r. e r
A c''cr/2 | C, "Ca
A D . O ' - -9 t ' 0 2
e,.6s g
Q c, = otlz 1 az'D./+
sub.@q@ lo @
(o,h 'Gh)j '(.^*o')la +a2so
6 , 5 0 , + g s c ^ ' + 2 e O
D "r c ' . e d o - . - @
9,6d+6/(')-ne(6-2
') . a
s,(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
Topviow, 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' . Solb F.N@ | Ct . t.Lt<eo>. 12o tb
,to.fu(c.rcsl/a Ac.kao0z):L/1
lc - 126blb.
Relcning
lo FrD.tview,
zMo"o 0"
b G)| s.e) -e(.o) . o
ax(6)| azG). +r.. - -@
zMc"a 9
BxG) -62(3) - D,G6),o
9*(4) -bz9) - 600- -@
^oD (, L@
ino,
.eoQ)-Be(z)"sat
ii O,
s@(.o) | 6, (!) - e3so
br = lasa tb.
ar k) - b{e) - @a
e, tn) ,2.6 ' +aoo
b, Go) . soaa
B* - 5.b lb.
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 t lhe.conponenls
of the beoringreootionc*
dao'dsc.tr2tg
l
j
ri
I
l
:
I
69. N@)-'e@t6.6)"o
zw-o o
q(6)twG) -s.,Oaa) - o
A(s) rt G) ' 4aaab
q , 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 b
i a -
-A,(.t r(c'*o'X.t rsoo(s6
6)<1tt X')'o
^" 6r , (GrD")Gs)
-o - @
A,tst =(,r,7 i t1)t14
A" = 2ag7 tb
oz . 6114/s_- 61tt)
Cz . 227a(s)/i= 22a2tb.
Or - 193
<j: 6-PL
Refc..inqto 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 - 166.7ll).
63r) The boom Bc ofthe ctiff'lea de'rich 6hown n rOP6?1
i6 conto,nedin the XY ptono Themo€l AB ls "e'rtiaol rg.s-ls
in
o soohelot A PoinfsAD ore in the same horiuonlol plore '
PointsDkE ore in lhe.eome v€rlicol Plono Detormine the
foroeEin 1r'o1o9sBE ?^BD .!4ryw"""ts
ol Ihe bea-
ring reoclion oi n.
t28 t29
a".' u[-a",c-Y
,<ao-yaif - p;?
ago",6<',o)t'Go ori6Zo-' ' la
lsolale F.rni Vrew, lGolole Rqhl 6,da Vid,
<M' -o; {oo(ro) -Ay(o)- Er(s)-o Zt'/^ -o .
Ay(2)rE" .,tooo-.-@ D'Oa)'E G):Ey6o)-o
A A E . O o / ( L ) ' E z ' E ( . ) . a - @
D(E)ro6a(?o)^ytu)-A,(!)-o e4o '4hs ,,,Et . to/tsE/ '"6'"
tr@)t A<s)- 9,<5)- 2ao@ Dr(t- 1d$E, Er(z) =o
A , ( 4 ) i A , - O ' - . t o d - - @ q ( r ) - a o A , E / ' o
ZM^-o. D, - 4o/3oE/ sub..to @
ro@(io)
- E7(ro)-0r($)-Er(s).o C) 2E,tDr-1do
BUI: E4. " E,lo :- 4- 1.5Er 2E | 4b/3oEr.looo
i@<2)- (5E/)(2)-o'(.)'E -o B!+'4.t.bE)
aEat2a,.e.ao - -@ 2*r a,bo(1bE) - a@o
.'. E,=(.Eo-o;)/z @&.raA +8, ?1o.o ...E,,2sob.
ar/'a -O,ha .'. Or " o//z -.Dbs.1@ Be/@s. r5/1o .'. BE-58.4tb.
AtG) | A"@'r, 'e<'otb -@ *!'rg Et "tse, . a,s12ta1
Ar (.)t A -Df/2 . 4.)&th
^t (.) ! (@;!L) - aaa!)
N | + ) t 1 @ . w . B a a o
ta)Ar or ' Totb --@
-A'(Q.A,(")--B^=
6doo
-{&.a
t€a j_3g)
El ' 375 lb
usn]gq . 4944 - ao/eoGas)
Dr ' soolb
bo//@ ' @/aa ., BD. 612..+
lu.
uahs@ NU)-Df "7eo
Ar &) ' 7c!:4
+s.22
Ar . 7@r/4 :. A-/ =t61stb
U6ins Ez ' 1./16Er .4y'6(379) . 2so1b .
oa'l6e(ot/za ' zsotb.
rcGming 1o tujlhlside Vew I tF: =o-
A z ' E - D z ' 2 . 2 5 a = O
. ' . A z ' o
70. 632,) Thc boor of ihe &rich 6bo* h 7lgp-632- k rolol€d bock
30'f.6n lhe fi rlone. Dek iniie lho {iroce in gc kBD }, {he
1 . 1 0 . 6 , . 0 ' . a . @ t l .
rolt.6' - b/^:6 :, ft -.o$-
.n6o'- 6 /.o .'. 6 . ir.32 n.
1ar,@.
. 1r.r/6^ .-.A . ro fl .
( G e ' - $ / A , . ' . & . 2 0 l t .
de -,GoAfi a.A:ofi6'i-Lry ".a 2t{l L, -10t a 5' - 'e '6 rt -
ae.6il6;f'('+. $r.2e.2. $ @'aoton@" 11''att'
L' "2"'" "' 9c'816 3lo
lnE4O
q I Dt'1132
. q .fi32'3173nA '15444lb
8o - 11e4.6a+ -'.go' 63tr lb
' n A T
-Ai Ga),2db60.6c) L o
zM^'a O
C',o)@- rlro(s..6) ' o
Al +O, - i7z2 - -O
loble Rightgddview,
c,'-trzfi@24
ce.199.96
tb
Dz=g9.ec lb.
P.l. lo Qbhl Etdevie : .F-'o
O . - A , - C z - O
Az - 939,96 -199.96
A z ' s a o t t )
ot'!91e.L9,
02 - 1t9a 6a+G1.32)
<Mo-o: -382 <1rt2) | c' (21.6+)|2@Qr..1)-o
Cr(.1.a4)- pegg.z4l&
r30 l3l
l
of Groviiy
C h o p l o r
Coniroide Contors
71. ihe ccn{fti, of lhe shod€d oreo shown
'|6
barrdcd by lbe l( d'.i€, the line x ' a q
k- e% - b1a
a'.- bay'a
- u- blr&
n-f, aa,
-fi ary*a^
i" rg.
th" pd'
G,b)
7 = 3o/s
4 t - l l e ' 9 ' = b / 8
+
7o6) Detffiir€ lh6 (btroil of the quo.+e,' oircle €ho,n in Fs.
P-7o6 whd6e nddius is n.
A-fed' -("$.+ U'
'N'r"
e J;"+ .,,:;,". ...6,^<
_,/.
.1. N p,.l$qd. ^4^
l.; f, t.t!'-*?.-""e-t
*":e
"l " ^ ('" f -1-a-
^':ld^.('(adl -(fl4,-"""1a, r"*=G-F
{'*'"'.,".. -+t-''al: -+l'^'"d
"#1
) - h . % G ' - ' " ) - L ^ . 1
-'lt'{i,v";l
Ai'l,"a 'hJ'!ad'
' r,(:(" ")d' -t'l'"' 41:
ltt - n.' ^i _;i," ^Zl - ".2
t32 133
7o7.)Oelehine the
6hown in f1:9 P-?o7
cantroid ol lhe qu6d6nt of lh€ ellipse
The eauolion of the eriipse *
*
!fu-,
c 7 b " ' 1 - 7 o '
' d -
,t =b/aq;n-;t)
^r =f iG;,) "f,,(u.e:r)a^
t.f a' =
f w.F:ta, .8"1-,^.wd"-:,l{i
LeJr=o6,a .. slnq='/d - Va[ h@+y,o.]
dr =ocdsqdq yl- Ai - !d = eEI i
J7.V
ac!s-..Fi:F
7 - &/'-
^. rt*")("-"-" ) A,a
'chgud,)
-hr e!
d,
-u"l!!;.a.,,^a^
_
-f h,ll(*4) a^
. o b L h L 1 1 @ a t d 4 _ o , 1 . . 1 a . , _ t % ] :
- 4 f " r € r 3 : l "
-
ib lrh tt'PL' o-'E J 14,tq"4 - s_uZ,
A - obi/
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,tae.
'%.f,1.Ji
"%"i++-"-l
^--f,,(dr.f,.(#)d"
' h4^f!
t" a,
-hA^t#7:
, hr."T-hil: - o'1
-!r = rt"
r =!Gd ut l'i" r i"
nr'
-tf.*a r.(oo)
a'hYb^
edx
.t'4+ai
--L lu--'r1
A - br%r
72. b - !ltl]) - b(nrr) - b(nr1)
; . t l n ' { C c ' d l- u z -
- - e -
7oe.)Deledine the s coorditule of lhe spondEl deso'ibed il
Problem 7oe
^e' [:
'/,eQd")- af' e"a'
" . - - t . " " , ' 1 b
' Y,l: h'i/b-d, ' h:i4l'
L+"'-k
- t/-*^l.tl" - of ratu:<'':s)
) 2 ( t n t ' )
:!qa -:b[ .t = h(a'l)
7,o) L.@fe lhe cstroid of lhe o.eo bounded bg the t ot'6 lt)
the sine cu.ve A= ognayL fiEm '=o to x:L
9'an^u
uf= a's,nn,/L
: ^6-!:'/"eed'
-'/"f"
u'a"
shown in F1b.p-7+.How lor
'E
tha o@^troidof the or€o obow {hebo6l
L(€) r 1(6tE
= [1(6)(atl, ] [1(6Xo
sI
1+a - 4:
t - 3.o7i^
t34
r36
@rdinolcs oF t|€ c&t#d of fhe d€o
with nespec+ to fhe eiven o)(ec.
Ixt x"t, y,rr't] s -Lt^Gxqora:'
, [hn.,]-l# ,e]
41j44 - 30723
q - ".+r i^
al:'+t - l/r(.(e)(k.6)f tlkr6'O1
4-11i ' 96.41
, = 2,31 in-
n6) A slendor homogeneous wire of unib6 cross sct;on ie be4f
inlo ihe 6rope shown i^ Fig.p 115 0et. lhc @rdinoie6 oF ils @n-
[6, rrd r€l t . 6(rr s(4'nr) r r(*{:d)
5 ' 2.+a;n
26.@t = -6(+) 1e a4@s3o'r 4 )
t --rq!: - 3:r-eg: , ae65 ; .
< zo,,/tu
","u'- B/e".; -t. 1.4ts,
n.
l, (, E^ (:4'^ 'l&.)) +2f s -[z(axzr(zo''4o)'t(.plJ
A2Az! '8996
.g-
=1.o36in
i i-o
ttE oenlrc;d of lhe shoded ol@ slEwn in d9. p-rle.
[Gt@(t)t v.(6Y.<t
v'GYq1t.f h6*4@n .6)']
25 st - 3s.1ee
i ' 1 3 t h
,17') L@Ie ll}f @n+K;d of lhc b€.+ *i€ €tan in Fig. p- ti7. Thc w;.c
'F
hon|oq3h€ous q of unifo.n orc.c 6etion .
n5) Dele.fiioe the
st'ovn in Fig. P_715
| | h @G)CA.<)']+
t'/, Gkr(%'c)1
i26 - $2
4 'u,".
a27 "l,h 6.2) ('/'4DlI l,/.Grdch-d1f r{.)@@'.6!.11
t = 5 i n .
73. t,:
,o) Dele.nr'n€d lhe ce^lrcid oF ,h€ l;es thot lom the boundo-
rij of fhe €foded ored i^ Fia.P-a1e
ltz,7-eo rs t.F4 +
-.tr-!,-l
^ = 1r@| I6(8Eb/4(,/r)| W(r,/")('/E
+{nX h"z)('/tr)| 6)l
ao-aeii = 251.322
vdlu€ 6hould the 6ir. width of ihc flonge be cl..onged so lho+ lhe
cenfroid of lhc orgo i6 z,s in. obove the bo6e 7
I1(e) l b(1Yr.r) = 1(s)(ar,) | b(rxo.6)
l[|1
a
F ' 5 2 6 t n
.4e.eiq'1eG),6(.>+@f
g&A,4rr.,(9)Vd,.fr,(WW.n)
4A,3e7 t - 261,65e
t -s.4 i^
of the slEd€d or€o i4 FIq p-72o ie ncquired to
Oelermine lh€ dictonce b lhot will fullflll ihis
t'aGYstlty'.
s7-[htbY6rlr3
d
€s.33i in' = 2inb'?
bt = 42.666s n2
,21) Befe. ro the I_ 6€otion of prcb. ?t+ shown io Fiq.P-7r4.To
? o r a . i b - 4 + o . 6 b
' 2b -20
I b _ 1 0 n .
722.>t@le lE @a+rcid of |he ehoded oreo i^ Fiq. P-122
by cuiting o €@icicle of didmeie. r frod o quonler c,rcle of
f+ +il' =e?X!.,r,(IlL.
X-ei:)
.r".;-,2 #7,"
ll; = rl --i -gL = 0.6.7.
12r
s' ( /,Y,'th'
(-"16)(/,)
o"Zj -.% - .7ts - 16t:: str'
r,%_s- 65#:'
E'-e!]g-r- o 3aer
r36 t37
,!) Locolc tho cenlroid of lh€ shoded o.co
[h(.d(G, +b@ .'Jdt . tl'. r,ttt (,..tt..')
.(1.d'
(.t(,.4) -1'
w (4+)
| 24.4a112
. 4..s
X - t.o+;^.
2+.1a1
12E- 1.*> 6) | ('h)(t.r)@(%n) -
+2-*G - g)
24.4a1+2 I =63.5ee
5 ' 2 6 e ; n
the coordino}ee of the oonlrcid of ihe shod€t o.€o
/9. P-7.a.
?-k@O-%6r&) -!ktJ' -r(eb)-ge)
Q/,Gr
t',) -!!{ G-.!F @-
49)
t4,rs3t - hra.'s1
t . z.ra in.
'41eaa1
, '2^.t(.)-/e(d(dr"rt tp'6a - {t)
'!#("-#)
1++s93 E . Ea,a6e
J ' 5 o € i n .
z26) tr:.afe lhe @l.o:td of the .sho&/ dr€o eotcse! b9 +hecutue
U..o' lhe 6frc;9hf l,ie shos in Fi9.p-1t5. HinI: ob€€Ne ]ha{
lhe tuNe q2. oa retot've to the y 0,,6 € of 'he @me tbFm06 9 "
^xz wilh .esp@l to lhe I a'i6.
, l:!t@-nctuelr
=
ly@k)(E',
[kbtu"X%
aq
12, - s7.6
t - +.€fl.
ni .[.h&doe/a..- lh a>o)
& -d
,t2q- 3€
9 - 3 f t .
zr) Locoll3 lhe lglrc;d of the cutvenl st$*^ 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
, -'+ [r(kJkx')t
1.o-rs(+Ydt,fa&)1.')(./')
r /.it't')
7/A_t - e/!)(4)(1.)(ye.,
I 4 - i,6ft.
74. rrd wifitul usitg ;ntogef;n- c!.nPulc i foi lfE 6so b.u'dod b/
fhe )(o'i€,ltp li,.e 1-t2 ,i.ltg o.,rl€ g'a t t/s-a/ao '
A . (qd: At.€Ad'
^ "ii 1.^r,'/6.t/fla)a, ,"'r - l: (af ,'7e- ^'/ed,
+ - . ,
A . Iz" +i6+ rlr'1. _H,r | ,.h, r7...1"
A- 292 ttil.
252' = 1q1s z
I ' 760 @'ts '
,.e) A rcclor5j:B ;. divided iato two Porle b' il'c 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 cen-
hoij of lha uppecpo"i B i. t(rolea WtB-/,iAEg"24^..
6'to rhotc^erAhbl^
-b-
*n
. b(.rz)-b
r^.644
/r&'
16rit/
FD-*lr"=br' -E{,1
bhni, -)L-EL
=b."!nti;?b'h.
S r-a - b,&'-r-o
16 _lod
2(e2)
#Bt'=bh("'4)-(*)D#}l
'F-5"- b##r
-*ilE".W
5. , h(nrwri .. l. .2rA
7,o) A b@n hae lh6 oro€c eotion shos ,ir F9. P-%o,Cc'nFrle
fia moft€nl of o'€ of ihe sked Po.tion abo,t tha ho"iantol
an+rodor o'i. xo of lte *lire €e,lion. (flole , tt ic e-t'o.. i' 6llq-
€ht df -ol;ole llot th c E€.lte t. laa i^ cr'P'li'q J e n@-
x,itum cheonrg sr"esj.
138 r38
fiO r'(t), la)Ol g . 1i,|,tr...)
|t(11)!j,(1(o,)
.o, - i11
. g -o;7 in.
zW - 1(.)(7,e, (t @)O.cs)
!.t/*.. 72,+ nl
E.) Two 10 in.- 15.?ti 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;uJal
oie 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
g- ,.86 i^
f F{s. p-72r. Rela lo Toblevl-z 0. +t? FoPe.+iesof the o.9t6s
q b.-te,.!"e cntrcid ot t€ bu,n-up cal,;n
[e(i)r r(E) t6,8 i.ft] 5 . €^n@!.') r (i4)t.)
..,s(.-otu) r s,sGrs)
xa5 " ale.ra1s
t- &'sa'^'
enlrcid of lhe buill -up solion €,i,bn €hadn ;r
to lobb vn-? ftn lhe popo',tic* of ltc ebrcnls.
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
l
:
l
l
ri
75. 7e6.)A riqhi t.io.gle of sldes bh t6 rololed oboui ondxte
coinoid'ng wiih €i& h lo gerP.ola o righl cl'culo' c'r€ '
I
A v' ?rt.
t na -Ar.kb-|Abrl
.,"1'
't = '/'rb'h
-,1ij""1*-*" -r-*ion6 l; the6v.fo<,eio@E vorumeeene€
iod b/ rololing o semic,rcleol.odius . dboul ilq d;m'ie'
, kho u-or'4.^@of horr
o,rcre
uW _{.{,r
.+
..L
v '+/er"'
r"l A=2t i L6alh of ("-e
-lV
- 2t.2/k.'t.
I A - +r.'
73e) .sfbw thdl the volure of o Porcboroid i€ eq@l 10o€-hdll
{ha oiccumecn,brg oyllnden ,
1-^.,i A.J-l4 'rd, A; '
["
r i '. 1)a'
+r'.^,' .ft' ?):. ..J.:.th-"%id-
/;-L'o.
*"i::#r: #'ft1i"
o'.n,.{+" iq +. j
,,j""tt_
" - '{;t
. _ ,., _.i
- -i.
A,
2^bh +;.+_+
rPi --!P
VfFbbdldd= dr'i A t -*b
= Y r . l i . 4 b h
{ 2 3
' t h b Q . h
7e.) Delamlncd {he vdluBe of the cllipsoid of ^€"dluiion qcro€-
l6d q rolotihq oo ellip6e obout o)
.,te
mia'a'ic (c"olote ottrpaid)
I b) ik olnon oxis (oblaie etlipsoid. Toke the lo.e{ s@;o'h o. d
thu smoll+ semi-or-'s oe b.
,7b"' ' 'Z'
f .q".G'',)
r > . " ' E
140
t4l
At=Csba,)-fe"d,
'f- okG'-t)"
- ut.l", i'"1
Yepune
- st 4-A
-"*.:+.+
v =;fr"u.
- b/""|d -"%, ""
A4.bTll 4421
"/f,
n . a b
"r
to.'47b.'1
x?o.
- 1-t%"
. t'' o"/6"
(t" -5")
Ai -
t"r,'a./ vdqre
' l',"/v'(t'':')av
_"t/b,lbr.
/%l:,
. o'/b'[bt-b%$'-b%]
-"*'F'P
v -
+ro,b
at . a74[+a)1]
rcht "
+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. Royolviigil 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
,a1) A 6a' ptpe eibow ho6on inlenot diome+.f, oa 4 in. lAe .od
of cu.votu€ of ihe pipei oontrt,re ie ain. F,nd +heinlqnot wl.
v.Atuo xhrrcid rd6io"* +"..*ed . t(4)4- 6 _(er'"r/.d;)
V = 7€.e6 ih:
76. 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-
A-ah . ayi. fta
A - 't.,
/ '
Iotot Lufh6 ^eo .
:
, 1,,
A'i +r."
@.lo.e ole 5 volude 96€^cled br rclot;ng
Fg. p-7€ th.ough one bolulid. oba/l l6cx.ot;
4 a t s ' n
.v. 2r. 6 te . 2(21.s6.)
'
v . 1 6 6 7i . t
th+,t a.[flF t 'rC)(#L,4' ,@ t 2({r;t o"cs..+)
|'fltf,*l t ."t+tt4?,
4,^l+.11,q
l
21.E6.9 - t32 132
,
t-
az.t - 1sd
e6
! - e't'" -
?i+) The rim of o pulle/ hos lho cros6 s@lion shdh h Fiq.p-74-l
,f. tP.T
i:
6odoarst@twc;ehiry
aeotbp.. - fi. i**f--t"e }h.
{.ishi df the Flm ,
14,n, (.,;1)7 4, a(a(.L), (!+2(+- /a)
11.e
1 . 18.5
!
. 1 . 6 1 i ^ -
V . 2 T . ( 1 t r c ) . 1 1 . .
V. o,aess
ll'
W . o.ages
<asa)
W = ztB lb.
t42 143
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 boeediooele.s oF tte eemio,ote*. Co."putJ
lhe surlooe orco 1,)votvhe geoeroled bg o complole re,olu-
l@n
, lthk' '+)f q ' u,!)tl(Q1 r/-/taYfa^.d1
16-6oa
t ' 1A- a.25
to,6oig - 1s.75
. t - 1 a s s ; n .
V - 2I . (1.+se14). 1o,6e.z
246) Dolerdn€ lhc €u"lo@ olg B votume qe@Folcd by o cofrpt
resul,bn oboul lhe r ori€ ot the €hode, oreo of ptub7is.
t'o,n t =!in
A - 2r.s.a1.
(1,* |F;A , ,V;e)
z+) 6-p"le lh. €u.jo@ o.e ,.i"ffi ge@rcte<) b/ o @mplete
@olullon ob,rl tha x or,c of lhe 6hoded ow of prco. ttt
3
-5.oe ,i.
t .2r. E.os l+.s(dt
t/z(c)h.d v@4/+l
v - 779.e2 ;n?
A= 2' g. tangth ol c;N,rtvibina Arca
A- 2v.3.erf
a('Nt er. ' 6., ";l
A =as2.szi.:
r fo" t6elh
J',.,rp.,.r",,-
:lt "6.-,..
-t".",,,5;;,(t+l yr,.)
+ tt)4(6 :t:)a
)
19,Be7
E - 7e,,2s
.5 =3'e+ ia.
