Solucionário - Beer Johnson, Manuais, Projetos, Pesquisas de Resistência dos materiais

Baixe Solucionário - Beer Johnson e outras Manuais, Projetos, Pesquisas em PDF para Resistência dos materiais, somente na Docsity!

600N.

roblem2.

l l l l

2.1 and 2.2 Determinegraphicallythe magnitudeand^ direction^ of the resultantof the two forcesshown,using(a) the^ parallelogramlaw, (b) the^ fiangle rule.

?anr

'

t l l l l l l l l l l

c( - 47.8" (^) F= / gil ly

l l L - - l (^) l i l l l l l

ft=/s?/N t +7,

2.1 and 2.2 Determinegraphicallythe magnitudeand^ direction^ of the resultantof the (^) two forcesshown,using(a) the parallelogramlaw, (D)the^ trianglerule.

,foo u

Jvott

s{=^ 21,6" ft= 7Olb

R= (^) ?od/l /?r.s' {

Problem2.

trll

T I I - I T l l i l l 2.5 The force F'of magnitude the lines a-a andb-b, Determine componentof F alonghnea-ais I

l l l l l l l l l l l l l lb is to be resolvedinto two componentsalong by nigonometry the angle 4 knowing that the 0 l b. l r l l l l l l l l r r l

l l l l l l l l l l l l l l l r l l r r l l l

tr J a,q , .!a

lfrut oF ,f/NFs F tr"^ Sr, (^) €"'

Sr"*

SlNct F^ = taab frtu2 (^) 1o= 70 /b

'P col? ,/ ,/r !,

/oo // 70 / sln (^) €O' 'l/n^4 cr( = 3?,f" i | - - T | | ] - - T - _ _ - T - - - r

l l

4 , \

b /

Problem2 6^ 2.

th

c(

6 T h e l relines )mpon€

]-l

OICI a-a n t c __l I

-l-l

l F o f r and D- f F alot -n

nag b. rg li -l

nitu Det n e l --i I

d e l EITN

t-b

I

--l-*l- - | I 100N is to be resolve< ine by trigonometrytl is 120N. -Tr-T-n l

pon rwir

-- I I

l a r b /

Af ^ o',/ (^) ,/

• d ^) rI 3 IA := IiTlt- L I t l-[f-[^

g- (^) / ( F ' b t i'-t--1.-i-- (^) -l 5 > t v ; t > (^5) a -t^ ?a N

1'/^ol b t t\

I D^ ru^ 2c^ N/ 5 1 J^

"D( \

B

I?.^ a

L a^

o a 5 2 '

A 3 4 a (^4) a

2.7 Atrolley which movesalong a horizontatbeamis acteduponby two forcesas shown. (a) Ifuowing that a:25o,^ determineby tigonometry the magnitudeof the force P sothat the resultantforce^ exertedon^ the trolley is vertical.^ (b) What^ is the correspondingmagnitudeof the resultant?

Problem2.

l l l l l r l

/6oax'^

Lnw (^) oF Stryas

l 6 o o N _ F (^) _ R

grh 35" gin 1t' grn-8oo

/6'+6go=8oo-

r F=^

37.?8 N

(d ?*3#aN (b) ft=273oil

Problem2.

l l l l

Z.g Adisabledautomobileis pulledby meansof trryoropesasshown. The^ tension inABis 500lb andthe^ angle uit25".^ Krrowingthattheresultantof thetwo forces appliedat A is directedalongthe^ axisofthe automobile,determineby trigonometry tojtft" tensionin ropeAC,(Dthe magnitudeof the^ resultanttwo forcesappliedat A.

lnw 6F s/NES

gao/b

Ttg"

E : 7 1 2 / / b

(ol (^) 6e='172 /b

(b) P= 7d7 /b

/goo- 3oo-4so:^ /2€o

I I^ I^ -_t^ I^ I^ ^ I^ I^ I^ I^ I^ l^ I 2.11 Atrolley whictr^ movesalonga^ horizontalbeamis actd uponby two forcesas shown. Determineby trigonometry*re magnitudeand direction^ of the force P so thatthe resultantis a verticalforceof 2500N. I I I I I

l l l l l l l l l l l l l l l l l r

8= ?fioory

St' d ) 5 or

Lfrw oF cognei (^)? ,

ffi prrr"- z(ttookt*r)^ cosI

o

F= ?3-?d N Lflw o,-sr,,res ,# = ?'! ry" d.=4.5o

16oo 11 ?€74 N

P= ?tu,Y (^) ; d= Jl,so

Problem2.12 2.

fo

12K

rces

no! apl

l l l l l l i l l l l ving that P = 301b, determineby trigonomery the resultantof the two llied at point.,4.

I t-r-1=T-T-T]-l-nl-r-Tl -L-j-j

B = / & " - e r 9 ' + 3. r " = / R o '

I

l iw^ ,ar coguss

fta' go' + 2o'- z(ro/n)as^ l?a'

fr= l?.d u

/t,Pw oF^ ,t/^/r.t P (^) - eo g,F (^) ,5,,

Af A^ o to U=^ V=Bll' ,itn (^) ,ltge .ln^0

l.l3 Solve rt

Prob.2.1 by trigonometry.

l l l l l l l l l r l^ l ' l

2.1 a,nd,7. the two fon

! Lletermrnegraphrcallythe magutude anclclnecflonof the resultantof les shown,using(a) the^ parallelogramlaq (D)the friangle rule. t r t r r r i l l l l l l l l *

6efi

1g'

o( - 3oo"

• z (Iaa*firooru)ias /3,ro

/?=/370.(N {fiw of. ,S/,Y€S

dt -^ 3oo= /?,

R='/g7/ ,VZ+?'8'

/8o'-rtto, (^) /3,io.

tt e

.t

:nsi, rapl

Sol

wo c n i rica

yeProb.2.4 bytrigonomeby.

tltlllrlTl stnrcturalmembersB andC areboltedto the^ bracketl.^ Knowing that^ the n memberB is 2500^ lb and^ that the tensionin C is 2000^ lb, determine lly the magnitudeanddirectionofthe resultantforce^ actingon^ the^ bracket.

p = 84"-^ y7o- tfo=lflio ?€oo lb

4oo (^) R

/fiw o/" (oS/N€

114=(zoaa)?(ts /l)^ z^ (rooou)(zsx' u)' N / 2s

a

R = f i o a o U

l,sa/lt

fnProblem

-l-

ffirrtrttl-l-

2.16through 2.19Determinethex arirdycomponentsof eachof the forcesshown.

| | ttt tr I ll I li_l lllll^ l_l*l_t

/2o*^ // rt,are /i= +3/.1//

F,a=-//S'? /b

6;

-//#?

FJ= -76,f/b

/5O -/A farzer ;

]]

T- I I 2 l i n. I _+r 7 in. I

I

I

-Problem

t l l l t l

z0in.---.

r l l l

Itililllllllll 2;16 through 2.19Determinethex andy componentsof eachof the^ forcesshown. r r r r t t l t t l l l l l l l l l l l l l l

t4d- /b f-oBce:

3 r' l, 2l tn.

Of= zo'rzra , g^ F

2 t n.

J-

| | I I | | I I | | I l I I t L I l_l__L_l_I I I

-l-l--T-Problem

--r---T---T--^ t t l

o

i.16through 2.lg Determinether arfiycomponentsof eachof the^ forcesshonm. --r I^ |^ |^ |^ |^ |^ |^ |^ i^ | | | | | I^ I^ I^ i^ |^ |^ I

?6C -N Foat r ,^ (onf = ps,r)'+(zr)'^ ofr= / f^ >o't

F* :

FI

2csrv (^) f -= +??fN

/ S€nn '?? w*^ /'4-?

nq

Y

E.- +/Io^ n^ { J

w z (ae)'=74o110q'^

OB= &,{t*,a

(^4) = fr^ --3+oil^ /n=-ft6N^ <.

-+{ h7},

'7,f

nry B€v'-r

4=

rSooN {

24

r- I I , i n.

i

I

t_

Problem2.

t t l l

l l 2.20 The tensionin the supportwne^ AB is 65 lb.^ Determinethe horizontaland verticalcomponentsof the^ forceactingon^ the pin at^ A.

lll |t^ illllllll-n-[T

ftat,qE. Tfzln,w/tr &,

'Jt 't//t^ e rf '^ ' '

| rc''

I ;?fr

I

I 2.23 The hydraulic cylinder BD exertson memberABC a force P directedalong line BD. Ifuowing that P musthavea 750-N componentpelpendicularto member ABc,determine (a) the magnitudeofthe forceP, (r) its componentparallelto^ ABC. I I

l l l l l l l l l l l l l ProDlem z.z

rtlllll

2J4 Usingr andy components,solve Prob. Z.l.

-i-t l l l l l l l l r l

2.1 and 22 Determinegraphicallythe magnitudeand^ direction of the resultantof the two forcesshown,using (a) the^ parallelogramlaw, (b) the^ hiangle^ rule. r r r r r r t l l l l l l l l l l l l l l l l

7ma

?oo-N FoeE

• f;6w rf).as3oo=+7.?7,+N' Fu=(7mry)an?oo = ++do,o^ N )

6&-il tuere

m*il) cas?do=f/sf,,JV

4=(6ur)

s,i tf, = +3??,6N

Ey

Pi

= 7.Fn=+ 7'l7,rNt /{ts'Y = +?3*7 il = ZF-= + +daoN +,lr?,6/Y'J=^ =^1 /o?7,6ry

*ad=#=

/o ?7.6Al 731,? N

cl = 1716"

t2- - - -R,^ /oz?,d ly

.9'd SlYt +7'

E= /3?o,7/Y^

. - o 'fl= /g?/N 4^ +7,

F*- 73Y'?N

It- 4oo=fuo

Tsza

S=,€

(a) 7so,v=^ Psi ?oo

F= ?t?s'Y

P=?/?o,N

ftl ?on6-=Pcaszo" (zttstt)cx ?oo

Pa;, ?oto Pg

2.25Usingr andy components,solveProb.2.2. I I (^) | | | ' l^ | | I | | | | | I l ' 2.1 and 2.2 Determinegraphicallythe magnitudeand direction of the rezultantof the two forcesshown,using(a) the parallelogramlaw, (D)the^ niangle^ nrle.

fu -/b^ FoBce 4=(8oou)cas6oa=* 4ootb

fJ =@* U)*n &" =+/?2,

foa - /b ,6ece 1= (ru/l)^ e^sef^ -^ +Io?,t lb $-f,r*uSt;rc!o

= -?a/.slb

Py= 2E --^ +^ qootb + qo?,t lb

Pr= 7 FO=+l7?.8 tI - 284ah

L R = gof,6h

F=7otilZ?!'/'

2.26Determinethe resultantof the threeforcesof Prob.2.17. l l l l l.. l l l l l l r l l l l l l 2.16through 2.19Determinether andy componentsof eachof the^ forcesshown. l l l l l l l l l l l l l l l l l l

E-- +61,3U Fg= -1o'otb

F= +3/.1// Fq= -//5,? lb

f;=

-tt*ttt FJ= -76,f/b

t l r l l l l

30o

1r5"

frpa E"^ Frr

/2d /

ldo U

• 67,28tb
• 31,^06 tb

• //t9l lb
  • (^) lb,o ll
• //€,? 4
• ?4.#/

E P;-t4;st tb FJ=

-Zs7.3b

fry=/4,.57.lb

tarp= (^) 4Y = pb^ t2=J,?/o f K.y^ ?,f?,j (^) lU (^) f

,.-^ O-^ R,^ -^ 2d2,9,h^ .o- cosp.

^ ffi, R17t2,7,,b

R"= 25g tL]78{,7"

Problem 2.

t t t l

IIr rrr | | | | | I (^) I I I I I I r I r r I 2.29 A hoist trolley is subjectedto the three forces shown. Knowing that a^ = 40o, determine(a) the magnitudeof the force^ P for which the^ resultantof the^ three forcesis vertical,^ (b) the conespondingmagnitudeof the resultant'

<'

l l t

l l l l l l l l l l l l l l l r l (a) (^) fi,vce F ,t^ zb^ EF^

y&zrce1, (^) R r=

R* =^ I4 - -(+oo,r)t* loorkau),gn +votP^ = o P= /rT86/b^ p=t7z?/b

(b) (^) ffg=76= -ftuu)s,h +a"'(aoah)cos4E = -1/o,3/i itnce /?r=o, R =^ lRsl (^) F= ?/o /b r r l l l l l

Pr oblem 2.3;

I

I - t r r t l m l l l l l l l l l l 2.30 Ahoist trolley is subjectedto the^ threeforcesshown. Knowing^ that^ P : lb, determine(a) the valueof the^ angle afor which the^ resultantof the^ threeforces is vertical, (D).thecorrespondingmagnitudeof the^ resultant.^ I r t r r i r t t l l l l l l l l l l t

to) Faa (^) E ro

Pn=T|.0au)a,.sot.t(zoo /,ilsind, (^) + ?so (^) b = a ?aso<' i^ sth ot,tr /?€ SAu{6, lu? I 4 cos?4^ :^ sth'd,+ ?,{,sj, u^ + /. i;62f, q (/ '^ -rrn'x (^) ) = srtrtae<*2'9€ind^ +/t'tl?^ €

{-ink r?,f sn 4 - ?..fg?,f =A

USIN6 eunppnrr( FoftMuLft j WE /4xq

€rn d=0,f?/62- d,=Z?.!+7o d =?f.f"_ I

$) ft g= -&U)^ sin^ ??,tro-(nooh)cos'Z?.+r+)o= S ?o,B /b _

{r*ct Pr=o., (^) F= [ \l (^) ff= 371 /A

l| | lll

• • r t T l t r r t r r , f)

&e vffi27a41, /(- = o.

t t l

-Problem

l l t l lt t t l l

l l l l l l l l l l l l l l l l l l l l l l r l 2.314 collar which may slide on a vertical^ rod is subjectedto the three^ forces shown. The direction of the force F may be varied. If possible,determinethe direction of the force F so that the resultant^ of the three forces is horizontal, knowingthat^ the^ magnitudeof F is (a)2.a kl'l' (b) l.4ld{. r r t t t l r t t t t r t l l l l l l l l l l l

r 1200N [email protected]

FoRce Fn^ Fn l 2 @ t t wt/

F

o 67u'8r F.ttnol

/ 200t rooil -Ftase

'ft.,= 672,0t

F.rtaol

,9*ct (^) f ftJ=o

i(() Fon f=

(Dr"n f =

Fr=16o0-Fcosot

/S To^ 8 E^ ,AaBl^ itottr'f^ L,^ W t^ W 2/ 7E

* / 6 O 0 - F c a s d

7 .l kN; t,6bt{z$,/\n fr tf s ( '^ P^ a , ^ J^

F.

• AP a a n- a 61 t D^ 1,'1 7 a^ +i^ tH^ ait

T- l,4tn

uz,?tn

/6oN

a tt

o rt- :rn Ct- \ a l o.^ a^ A r t^ a ) /^ ,J^ r a^ h^ r ) :^ I^ a^ Lta^ +^5 l4^ r <

d= 31,

/ (^) Ooo-i /, t7"-s s,tgo=?f,?go

I r-r ,

-T-]-l--

t t l

te r3t'

II

fr=

6

'tc

fr

! , ) w

L

s o

ttl

-Problem

t l t t l

m l l l l l l l l l l l l l l l l 232 through 2.35 Two cablesanetied togetherat C and loaded^ as shown. Determinethe^ tensionnAC^ andBC.

4t

ffi I-^' t i i n ,

l_

] l l l

o o l L

? ,

3eor)

16l

ru A

Problem2.36 2.36Two

N anda=

c

TTgo

cablesare 1 '60o, deter

v

ied min

togetheratC u e the tensionir

rdloadedasshown. KnowingthatP = 500 t AC andBC. _ l i l l l l l l l l _ l _ -

frc Gc 4so

o(= do"

?roblem 2.

rtlrt

I t T - T T | |^ l^ I^ I^ |^ |^ |^ i^ |^ |^ I^ I^ |^ |^ I^ |^ | 2.37Twoforcesof magnitr,rdeTt=8 kips andTa= 15kips (^) areappliedasshoqmto n rwclrlcrl nnntranfinn lfrtmrrinrr fha+ l4L +lrauv '.^--an+lrrrrvvsrvvuvs ictu irtul anrrililt-i"rmvrluuvrr*Ut rlofamirasvlvrusrA the magnitudesof the forces Ts andTp. I | | | I | | | I | | | I | | | r | | | l , - l I V e e L5 o A^ a-^ lAr^ ,wl^6 ' t^ , p^ J,^ ^l^ I^ r^.^ P , t^ * ,^ o v

fr: t€ /<,pt

7;

l_c

A u"0I .9 l,/ D' o Y =e? c h.,^ '-

t | l l l

LZ Ex=0i^ -B 4,fu+ S-#*s -

+tZE.=o: J t t l

4 siry^ foo- T. = o

7

l l l l l

l, *n^ +oo=Q

(7,rceh,fr) * t t (^) f d o - E^ - O^ T 5 B-, L J^ )<^ d

l-I-Tr T^ g^ IrJ Ir'l^ s^ d

-t--

I I

4,r.-.'l',

Problem2.38 -|

I r t t t

;8Two forcesof magnitudeT,t= 6kips andTc= 9 kips^ areappliedasshownto a lded connection. tinowing that^ the connectionis in equilibrium,^ determinethe^

,gnitudesof the forcesTn^ andTo.^ --+---+-

TB

h

t O

+ff Frzoi

ALfV=o"

'?, (^) ,, I I | r++-f-f+-f-ff -7 k,Ft (^) f 6-