meriam instructors manual statics
TRANSCRIPT
INSTRUCTOR 'S MAI\!UAL
for
ENGINEERING l-'1ECHANICSVolume 1 - StaticsVolume 2 - Dynamics
by
J. L. Meriam
John Wiley & Sons, Inc.New York . Santa Barbara . Chichester . Brisbane . Toronto
2 FORCE SYSTEMSr= 4/n.
I
I---r-------- -- -------------2/3 13== faY} -I 6 = 3/.0 °
10
v : T=I!)kiJ 51;" 8= 0.514- c.o:sB= 0.857~--~Ty0--J----x 5= Tcose= /S(O.B-57)=-/2.1?6kAl &= ran-IRy = lan-/J>.;6 = /09.1°
~ ~~~/~:;:=+/;:~~~:) = 772 /rA! 1-2-;;-IO~r--~~-------~-------
RI R rnc05Urc?5-~------/ \ /0 k.AJ &
. \I \...(_0
I \ \
{ " 6~t>_\_ .. x:~ h\1
2/1 I p = - 20 CoS (30°- zoo) = -20 co.!> 10°)L
:: - Iq. 70 kN'
Py=: 20S/~/Oo
= J.47IrN
1-2-/4---rI--F----{}--=-·-t.-;~ = Ij-=-5~. -: -d.-=-S.-3-J---IS-=-3-8-.-I-OY\ ~,.J....., ~:= Fco5ot, F= ~ = _.!.0CJ._
\ 4 //'eJ ~i- ce s o: CoS '38.10
\ .\.- ---\o::::-::tt_~5~_ =1144N
"Y = ;:;:: fa Y} 0< = '100 ra n 38, I U
= 706 AI
z: - /95. 2 N
c = 2 /~" e ~.30"
e cos61 _ Z)< 0, 5"6 (,r+e: S;Y1f:) - 4+ 2vO,:J
z: O.34{' cc= 19.1/°j
C05cJ.. = 0.945
F~ Fcosol = 400(0.945)= 3711 If,
far? ex =
1---,..------_·-_··_-----_·_---------12/9 I !Se -= 10 COj 600
- I? = -3 kAi
R ::10 S/n 6C,"= I? 66 kl\;''Y12=/(-3)'" f(g'6G/ =__9./7~:!
92 )oJ
/09°
s/nA= 4000.7906 =0.3122.r-: /000
;3= /fl.Zo
Z/J>'1 I p= p(~~. -t: 1i) J' r:A8" b(-~'+/ -f If)
M = r» P = f. .; If- A -
Pb -/ I /
oS 4-- 3 o
- Pb (-. . )M --= -3 t T 4.1 - 71r-:A 6 - _ -
'--;;;;J R-=iF= 25"17 k~s&= -/SO(J»! + (/50-IZJ •.,J'.1
=- -450,; I- 360.; kl?-I,.,.
or & = (-".4~O~·-ft!)~3QQi)/.:/~ 16-/'7.------------_. ----
2/91 r i!II &:. -:n" _t - '6i AI·,..,
Mv - 320eo s e s: -J;: = . ~ 0 '7tf/
)< 10:::.'/ V32021 ?O' - ---._ ..
2/92 T~/= - /Sl)(~. 250 -.'61 2S--0)! f ISO (O.l5~):!
:: -75e- .J 22.Sv' lII'm
2/93 /I'vl =(Z5'Osin 60°/'2 +-(Z5'ocos'Oos;'n 40°)(8--(2)o
o ;:25'11i -t ..YeS':' 2903 1;-/1'}.
"~./JM,,~o
. C·
I----------~==========~-------------------2 'OA I - V - 1 - ~ ...-::>/77 AB= /.7. 1'.5 + C/./ = /.304 rY1
T"~· (-1;7 t' f-O,$.I·f- 0.1 6-) kN'- l !Jo.,. - -
7Ok~ !."''' oB =- 0:'-/ f-o.4!f rr: .
~=.!~!."= 2 j.!:. l !r-;1.301 o 0.5 :;.4!
'-I.Z C.S 0./ II
"3- (-0.15i - Q •.,8J -t ~.~&)/, 301 - -
M = -L /o.e) = O. '120 /fA/·mz: 1.3Dt
Z JIc>~ I rzz: I ~z 2 ~_!...~ A8 "Vo.1 - r.» 1-2 "L..62/Yl
I '7 ('. .T:: ~ lO''i?~ ~ /.Si-zk) kt..!- 2.62 - _ -
Til!r If! r:: 0:4 - /. h L.' " Z J.r rr 1
M. =r» T= ? / J.rI. z_ Cl - _
/, b 0 2O. '? 1.5 -2
2.{,Z
,/., 2. -"1\1.=(~ 1= ().-4/57yJ '14.8 /-2.40 = 2,~/ k.','·""," -0 ~.•..
2./96-1 Y0 = .!" Xr S8/~cT r 45 OASo r:::- 1.5·!: r / f?.j IY1
- ./ 2 _ 2CA =14) -f 30 :: 30.34-
T= .3..!-.. (4.S,· - 30 k) kAl- 3034 - -'A _ /.A a: f- /~ .) X _?L ('1.S/.-..1ok):":-'~- ,....,."'!: er~ '],-'/,34 _ _
=J;~'1 (!35!' - al!i - S40!)
L4 = -374l r- 9.3.5j-S6.1 Ir- lr'N,1'Y]I~IO
2/97 T Direction COSines t>f Z /or pOint lJ 4-re,
4.5/L,-4.5/.t)-30~ where 1",/4.52.,.4,"5;-;;;;;=:1940.s '= 30. 7 In
VQctor OB = r: == 4.51:. + 13.5) ,.,
Th"" M = r X I I i. i k I-/J - 2/'" 4.5 /3.5 0 ~
4.S -4.5' -30
={-40S i +/35" j - 815,)3!:7 kll/.""
or ~IJ = -277.3] + 92.4j-5S.5"~ N·",
~ "v1,oo =:: -100.0. zoo).!: = -20t AI'm
~ Ro = 80(0. /6'0 cos 20:)( -j Sin 30· - ~q,s 30°)
- - 6.77j _ 11.72/s N·"'"
IV! ~ - 120 (0.100 cc; S '1sj!! = -,25.46 k N'M_ 120
..J'() /Vl= -20t -6.77)-37.2/s M'm
APPENDIX A-IyI
AI
AZ I=.:. Ad2= 6/5z) =-/50 Y>?.-n4X
J = L f- I=::/ 50 r 170 z: .320o )( y
Iro =-1/ ~/A == '1320/6 .= 7,.30 rnyn
A4 DIsrr/ownon 0/ arC?a In
Ja>r)C' 4~ MQ/ for /"he ~c;<ql?.9/r:'
.r: == .c 6h 3 f =- .: bh3x.3 , x 12
...fa
I= f of- A(o,s)2. j~ y
I =.f r A(0.3\2..Y' -y ')I-I == ° 1-A(O.25-0.o~-:.y 'J/'
0,032 .= 0./6AA=o,2,.,..,Z
A8 I
I
.:.~ Iri "'1 I
1 ' I'- +--~ 0
I_?:!:...,JI rr I
=.!!- (I-~) _ /5"/""}-
._~-> __)( 4(/04) 24 - 64 (/04-)
z: 0.736 (/0-4) tn4-
.so C:=4. rZ;= 2Jx'"I. ",.!...J =: o.scs (10-4)S'- X 2 0
J=.J-Ar2.COl
z: Ar2-A nr(2)==ArZ,(I- -1 ):=. TTbr3(t_!!.)
7T2 2 IT>-
= 6r'(!!- £)2 rr
= '0. 2'1 El6r3
AIi I BC---~I _I r?'A: rV/~_\
o, = 4r/3TT
/?:;r C.OY'rl j:J le le Cl rc/e~ = J
or-Ar:l= ...l....Ar L.+ Ar2
2.
::::2Ar-L2.
FOr hal.! c ;rc;/t:
_ I(] 4) r 4'01- 2: "2 n r ~ ;j7Tr
For ha/:! circle, J = -'!""rrr4o 4JB::--{ f-A(r-?j'= '-i _A;='2.+-A(r_?)2
=~+A(r~2rr)= ~ 1TT4+Tlr4( / _ ~ ) = ,4-e!7 _ ~)
2- s»: 4 3 A/6 II y= b Sin 77"(,
b0i\oO:'--'-'----~- --'I-
r-~ f-dX CZx=a 0
Clb3( )Ct>.5U( .:r.)~ ab] Try . V- -I - Z+Sln U = - cos-(Z+Stn2.~)3// J r» <t.. a.
x= oh3[ 0 3 a._, ~ 1 (2 TO) - (-I)(Z T 0) = 4a-h
917 <JJT
L=)(
~!IIApl~~_ --x-'I".,,,,~
I 40.m",'"
'---40-:--""-,-,,,-' - - '\(.
AII?' I dJ =t;;7.(.??7~d'o) ; J= 21T/~-3dr'...I o <>
-:~f"a,..e.,I ~I-= .i.(40)(40)3~' y .3
4= 85.33(104) m"H
~=z:.,+.z;,=170.7(101 rnY1'/~
Qua,../Cr c "rCu/or a""",,,
~=-i(fTTf4)~ -;(.5'0/= -31.g'/(104) rnr>1.4
/.3 g, 9 (l04) W/ •• ff
-% error: =
z: __ "'_00_:/;_2 _
Z(r)7.+z(r)f-Iar: 4r. I-A-/.-2-2--'1--I--·-~-=-2-[-_-' -4-a.-(-a,-3-)-t--4-a.,-"--(3-Q,-)-1.]--=-':'--"'-a.,-4-'-
.s-rr (]) 12 2. 3
4a. , , L ::J.. C<. (Za) '3 = 4'-a.- 4a.,--X' ® 12 v
= /00/2 = 0.226%.z(/OZj'l-21/0)-/'/error
-I (i)
Cl---{jJ ---)(
/l.. a.TOhl I= 58a4
3
10 la'---------'
( -'690; /.3(1.5+20)
= 10.4 /11,
For a-h-ej
Z. = .: bh'~ .i. (40 r'Z}(40) 3_ 32, 4-1 ~x 12 12 Yz - 3'10/ m ,
Far c/=e-«:
I=-.!... bh3~_...!...(30)(30)3)(. IZ 12 VZ Y2
~ - 27(/04) 171 ••••.••4-16
;:Or ~nf;~ ./Jun:'
I ::2 ( 32 _ 2. 7) 4-le 3 16 10
= /7.'16(/04) n,,...,4
;~Ir.../'--, ~-I\!..J bO{,i80
"'''1 I j mm
-- +i--Xo
80 ~'60
mm
l0 ~m /iJ 1
202 L...l.. ",m
to !tit»
r: ea.-I 1)< '" [2(7. 1'9) t6. 33)(/0 ~= 22. b (lo~) m",4
I!J =[2(4. es) f-Oo/067](IO')
- 9. i/ (10 ') him /-
CJ~L1s~o O.SI">? 0 ---;K-
o 1 3For fnco'l,9ular area/ '-6=24.=2(;2,)(0,5)(0,5)
= - 0.01042. rri: ~
50 :for nef Qrecz/ Jo= 0.0245 -0.0/04 ~ 0.0141 •.•.•.4-
iJ~f(217:4 IS ..L.7T(O.5/_~(O.5)1.= 0.1<t{'4-0,J2f)04- 2 '2.
; 0.07J4 m
i ko=VI.{,/A =";0.0/4-1/0.07/4 = o.445'Y'Y1
J = .: v: =. rr/o.5) 4o 41'2 -,f-
= o.OZ454rn."
~ O·6-m c/"'cle: A = ~(O.6)2= 1./31 ",2
J" = -{ +Ad2; ~ = -i(I./3/)(O.6~-1.131(O.3/:-0.30S''''''
I-m c;r-cle: ~ = i rt:(/-1) = I. $71 'n 4
Net J., = I.S7/- 0.30S = 1.265 ".,1-
Al.'! I cpuarfr:r-c/rculor area
-4 ZG I Q)
!
• I~ (80X2.0/+ r6'O)(2Q){74)z = 7. 119 (IO~) mm"
[!:IQ.: I; (20)(0>0/+ {ZO)(6'O){SO)Z: 1: .5'5(/"')",1'1I"
@ I =..l.-(ZO)(;60/- (,.Il;; (10') m",ofXc) 12-
I" =..!... (16o}(20)'", O./01, 7 (10 ')",'" +JD /2
1-0 0 ,..--,:c-,tQ rl.:J /e: .a .'< d' '"""",'/hOe4'T o/-kn;".:l y_cY'IS7'Y;,cu-/,t/on
Iv::: 3..!...lh3R.ecfo'19/e ,.. 0
TY"/;~/~ (5a •.•..•j>/~ Prob/~,.",.A2)
.I = -(6 -I(, )h3)( .,.
'-2.0
A28 I L A d Adz;,,,.Z '4In. In. In.
'----- L ~-~~I
I I I 9.9 9.9 0.5 2.5I -> s:\ -~ f--- . ..-~- .-
I 2- 9,s 9,s 1.5 2.1.5
~1:- .3 8·7 3.7 2.5 .5'4. /
(~- r ¥- 7. / 7.1 3.5 ~7.5
I 2 -1 .5 4.4- 4.4 4.5 «e.s: I -x.
~ ~ Z .4-~s~
~ 'tI = Z53.tlln.
r = .!... (17r4) _ !!. 54 = 245.4-' ,c-rrQr = U}.g-245,,,. r ooX exact 2 <f - &> -_. J 24S.4
-= of 3 0/0
'50 for E'1?T;Y'c_rc.c r-an.9/e ~x. =-
lv, 7uarkY' c/',-c.,u/ar ar~a-I (' 4' -rr 4J =:1 -TTr)" - (30)
)(1 7 4 16A <7-= - /5; 90 (/0") ,.,..,r>1,.
CP",-vJpos;lc O'-Cq
L = -:,-7,0/(104) f- flS,33 (104/x .;:: 28.3(104) rn """-
Thu~ for
A36 IPari A
in ,2.
?AO 0, 3~ 2.94 0.343 O.6'1b 4.07
2 4. 2.92.35 1t?t76"f!~-~..~_4 r-~I
J d.33 I. flo I a. 5'1 I 0.2c/) o. 7S1-~-----'----'-
TCTlR/~ 13.02 13.61 4."/-37 /I.~-'
- /3.61y= --= /.046 1/7.13.02
I =4 = £.i f z.Ad 2X 0 It
z: 4,437 + 1/.56
= /6.0011').4
~ SJt.<cue,' ~.-:7 ir 'J" 4r/g"
1.' ----1 r Iy !
~~-~ .: J
Ir[1, ---'_-)(
c os U,: 12{; (IO~) = O.171i', LI c 20./1.5',lJ(I,,') s». z
'" ,: z-v;;;'f' Cos ~ '" ? ('1o.z)(0.d"13~) = 16/. / "",.,I 3
b,': '2v'f CD, (~+ 120·)': (-), b3,: zrp' CD& (1+-240') s (_)4-=. <o.ore« 7 r
(j) Ix = /2({IO)(IO)~ = 0.00667(10') mm"' A 42. I dI z: -cr T- cld(d'A) z; 0 + X X (Yclx)~ ---;CoY", X y 2Y /.72. 3
I Y, =-XdxI to 2/;'I b ~ "b 2. 40'"-r, , L r - h ftv 3 / - h b I hl.I'I of, f' , n -)( - - ,...etY- - - - = - bI y'---)/ :y Zb1 2/;24 fI i 0 D ~ Ir ~I~~--_Xf---- X ~ ~d'xf----- b ~
o .T == ~(IO)(5'ol=O.427(IO')'",.,f.1/ j 12
i ® I,,<i(IO)b~)(2).1.667b3-.J' 10il
!C -- =---T -- t-- - -~t-K- I1 = 2(~(6)(;0)'1' b(IO)(45)~
/:,"''''; I j '=0.0-/.07(10')6
LJII Total r; = tota.! IJL----.J
_ID ••• __ IiD IIO~ _ (O.00667)(/O')f 1.66763••~ mm Im~1
= (0.427 +- 0.04071:>)(106)
0'- /;3_0.0244(106)b-o.252(10'),:0
Solve by cubiC fOr'm"/4; (CJ.2~;Z(/CJ.)/< (".dr.~4(I06)3so 3
-, - 't h 2S2( ~I re,,!root--" I..l= __ Hi ere rz r ----!£..:!=126(IO~ _ 24.4(IOJ)
P -Yl 2 , P - ---;---- t /i'./J (10'1)
---------
A 4/ I YT~om~-~:vY1..,----~- - -- -,---X-
I I ' I "0 by Sy h-1rnefry .50: , '/00 IcyI I ImmI ,I C -----, , ,
. 4.: 20 - /0.4--/- = ~ 56 In.
A46' IIx/ ..z; -f ~ ~ A) --{y-:::.z;;y t- a;;,~, A
4y- ~y,= (~ay - a;.o;.)AJ d =- - 4-0 >n»t d,;,= <1'0,..,,,,,whc:~ dx= 20 ",.,rn) ')I=,Jo """');V ) ./
(~o- [-120J)16'= [( 20)(30) - (- 40)(6'0)J AA = soo{/oS) =/.3!{,(I04j I"rlWl2
3800
, '/=, , ',.",..,I ,,I ,,
-- - --
I:::.fx.dvAXy J
= (-/00 )(g-o)(V fox lOO)
:::-/2 lJ.o(tO) ,...,.....,,4
A47
So I ;:I r<!!aordk~S o,f &:X, x v
A52 I A4c! £9:;· AI/ $ y:d6L r r .::I f- I 50 I f- T:(Z5"of-S)IO
Y>UlX n-1,.., J<:Y )( -y= 30(10/') r»nt-"
_AS/ I(a) Ix < I I (f)
y 1 x;y
(c ) I. >I .I.. r-))( )I I )(Y
(4) I «r: 7)( t-r))( '1 Y
A4'1 I I =0 "y ~,,"""'~7'>y~...;,~.z;/',.,./~,.t>~ndC1nl
;j ~ =-.;;. Thu~
bh3= 2(.!... hr!:/)
"1- 12 Zf/"=..!.- b'" b:: ZV3 h12 J2z
h"2y
A§"o Mul-h;y E95.All ;b.J~rh~r and Jet'
I L' '" (-{,.~)2. (1(~-;,)'r4I~)L"..,Ih<_0' -2- - Z
= .: (r.x'Z.I-ZI I -r, 2 -L 2-;- zI I. -I ~-?-T L)-1 « .» J" ~:y.Y ""><y
= L I -.I 2 So L = V T I -I L·'x y !(Y / Xy ~ Y mAX ""''1
Frt:»n rk IVor .£~s. All
(Ix-I;,)2 = [ZZrn4)(- (~r-..(")J2- 4I>£y2.
= [2(2'1 - (30)J~OI2. _ 4(-8'~/Ob)7.= /44('O'Zj
Il£-r; = 12(1°'-)1n1~;J adt:/ t/ ,Jet ZI = 4Z.(;06)I t-T- 30(10" YI-1..... -"x -y- 4
~=ZI(;06) rnnv
, ..; = '1(106) rnm4-
;::::-"-0"'" £'/. AIO
ktn 20( zz ZIxy = 2.(-8).z;-Ix '1-2/
Zcc = 53./3/ 0( = 26.b 0
= 1333
A53
I»»
I------I ::.25(106) ,..,mi"----jY.nOX I
!
A54 Loc.a/C; pi. A t8 /ron?
:r; I .T v",,/w<."'s) y, xy
- I )or. = "2 t24 - 14 = ~1',4
Aa =Yi2."l -IS'
=-13 I~:'-
,-1/2- 0;3= Sin 13 ::.(,7,38)
20(= l'i!o-67.!3g=c 112.6 0
ex = 5"6.3° C/oclr-t-<,/I~r::
Ass 10.z = a.0/3 I = a~ z t: a.YJo/2/ = 7a% I. = - 3a.4,4.x ) y ) 1<y
@J =a.~ I =a.% I ::aY-:!:)(-_3)=a,4/4Y • 1< J Y ) llY 2- 2.
a; @ .sarne 45 @
Q) ~ @ ~O""'~ as (f)a.
@
20< e- - 26. 6 0 0'- 153.40
§~ = fc?n -I f c 53./30). For ro hn"/;;',., /,.-,;>,.,., )(:..y ,
.Yo 10 )/'..0 - Y", The (9 0,/ ;:9. A fa. /5: ,x.' &= -53.13°
" I =-'-S!IO}3:4IG.7rn,.,..4x' 12
-<y' =f..,Jlo)(:5J3=/04.2 1?1"",4
8:-,.,,-..,...,-"---- ;x.I. I,.,-Z,
,cr<J1'Y7£0. A9<l1 )( V --y .5/n 2@f-I,coS28/ 0./0 2 Xy'
416.7 - 104. 2 '( 01 4=- 2 SIn -/06.26/ f" 0 s:-ISO, 0 mm
I"y= ~oyo +c{ <Iy A
= -150,0 +(5.0)(.5:5)(5,10)
4y= 1225,-;,rn4
wher~ a;=-Sr.i-) -t f(~):: 3-fZ = s.O m,..,
~ = S"(~) +f(~) = 4 +/5 =5. 5,..,-
/j;= /00 cooS 30" = 86.G /0
~= /005/11 30'C"5 3d'" 43.3 IQ
;; =- 100-:)ln a.:/ .5/~7 30D= ZS 16
M)( =- 86.'(2 + <1s,r, 30; - ZS-(8)z: f?bb ~ 4 ·200 ' 1% ..,. 16-//).
~,=: 2:'1(6 "'1-co~30o - 43 3( 2 + 451'r, 301c- 236.6 - /73.2 =: '3.1/1.>-1/7"
M'lc c- 16,6(6+ 1co.s30" - 13.3(g)= !j'!9 G- 3-'f-G-f. z: -+7~z ID·/~.
!:f:J~ /46.4.:: +';3.-1./ t-'f7J.2! IJ-;".
?//Ol ID' J'-- IreCCIO'7 Cos/n<i!,; ",I f q,re
Z/RJ
6/£) ~ w;'~re r : Ic?<'+ •• e ; '12.' = //rh4S ~ = SO /e : r 6J' -I- 91:) kN
11 - - -
= £.1 ~ 2 ~ .mm k I!!! = 1:X E =!:. -d - (S"I = ~ (12. i -13Jt- 6k) N'm
/ CJ - 2 \i1/ -,--I=--I __ - __ - __ - _209
So f,,-'r.:e F.: /00 (G i ,t. SJ .•.!!') 16Vi&Z -
Le-!- r=Z4 00
r= (--3-2)=·51-" r: =(-I+Z)=I/~. r= (4-1)=3 In.\( 'J Y ) Z
Thtf~ ! J Is
1
/00 loo (. . \rv! == IX: I~= -5 / '3 z: -- -/4£+23) ·311::1--- m a:z - - /
0 s I I----
: /6-/~J.
7hU5 fo/a/ n-/O»7CCYJT / s
M -= - Z 5'1. I? c .f 32 7. f?J -s-: 87. S'!! Ai· i'Y7-0 -
or :;-10-=- Z60t -I- ~2?j T yg!! N· yV)
2/1031 MOIY/('?nr 0/ c"u~/e /,5 2ifO(-!·C.05 3{)O-!r'S';"3~
= 207.8j - IZO!r AI- rr:
Vv;torJJ£n I "/ force 1:1
1200 co:.> 300(- O.Z50 i + o. Zoo5) f- 12Do .510 3()D~. Zoo)
-z: -25'1.8£ f-- 120J i 2D7-!?!! AI·n,
-----_ .. _._. __ .. - -_._._-_._--.
.!'"xI-o e - 4-SS
-4/5
o 0-2 - 4 20,,/ 7.0'1f:s- (3
~ 20- 7.09 0+ 0 f- 0 -0 -o-~)= -27.0'1 k)/'rn
So ~B = 27. 0'1 klt/'m Se,.,sll.B~A;'
Fi3' (0).' ~8: 2.0 SII") 16fi?O(1.7I'1) = 27-08 1(',v'1rj
-1,;( ..r?~.r- -30 -1-2,;'1-2;")- vr : - - -
Com/1-,m£'lI-r 0./ l??oJnQ,..,-t- Cl;"'''} AB //5
-3 -I o_ 2dof'\1= L"T ~ - 7.77/i7 .$:33 4 4
-3 Z z= 6.24(-2-4 -1-11 f- 0 - 0 f-ID." + 24) =-1"#1.4-----110 - If
BFrom ,or.;)/). 2/8b CA",I vec-?&r ~15 J=~(2j-f-Jr)vS - -
I E= :; (l'.; ~'-1)70k~ r: D,.;
- yD
orr
M:::, =: [J<F.S
~((o.2j. - O.-I~/)X ~ r! f 2/ -k)I ;se v."i-!J}$0 t!J. z -0·1.5~ = ....::..
Do 2
0 2
= fk (0., f 0.4) =- :;;: I F= ~~3C~ 228 N
2j;Dl
c: = 30/ If, F:= - 40> /.6- /1 _ ) -.'3 -
." M:: f:A?:F + /". v L:'"r- - - -A - 1:"'£8
:: (-12.0 3j + 13.'~ ~) .\ 3d:! + (7. '1Si f /3 (;'9/r)>< (-40))=-361.';/(--10'7.1~· -JI7.'l! i-.1"45'.5,·
= 131;·-li - " 7?5 Is /lJ -i'ler: '::1 ; 136) - (,79 fr 1.6-1'1.
"'1:D=M'~ /36.3t'n20"-J-i.79 '''S20Q
z: 46,' I- 63'lD
Iv,' = 6l?S 11,-1;".
;i~~;'R =ZF- R. == ~ + 7- 5'+ 4 +.n- '1 '=: 2:3 kN.~ J
R'J "-ZM>{) 2jjj = (-,f)(~)+4{1'»T7{22)+?(22)
fj =' jjt!,4/23 = /.5: 03",
R,x =£M!Jj 23x = 4(7)-~(/S)+7(2oJ-f- C(20)
X '" 16J>/23 = 7.30 ':!_
2/1// I N=:£~ :: 70?'-30 -li'o-6cJ-50=-90/,b
.-t'y z: EM)' J' +90y ::3:J(12) r- 70(/2) -60(6)- 50(,2;
.y :: 240/90 2.67 ;".
RY.=-[MyJ· -9oX-= + [8'0(''') - 3C(It)) - SO(I>')J
.1:: =-100/'0 = -I. (I I~/
~Z/IOf!2///2 k'ol '" L~)' 7.5'0 : 600,5/;"" 65" -f- f?oo ~-o50S'1;"~5°
. -4007:JO- C"O(~.'1""3i '1400
C05,9 " -- ----. -------.. ;:: 0. S' J6 !6'00 (0. 'ttl6 j) .
('oorc7!~"d~5 "r A art'(
a .0' 3 0\I. Z, o.s co» 30, G. -,51>1 o i
0'- (1.2 0.779 O.1~·)/W = ./~~;-;9i-;'(O.-;-;.4S-l
= 1.5001
Y T /00" . r_ =-, cc (-I.ZI. -O.779JIO.4S",).,,0· - _-r= oB = 0.915. M::./VI : r}(,.6- ," - _
r 91 100(' . ')'." Cl IV! -=-[0. _r X '.5'0 -I. 21: -O.77~ 'f'1.45!'C J'I:
'iD ( \. 9 (0 - -9)= -r-e- -1.2)·I-O.77i'·)·'" () .77 =4'.Bw ...,t.b o _ -/- I. So
.R,,= bOO cas 65"+ ~UO <.oS .33.3"<;05 6.50
c, <SeJO(0.4226) f 11J1J(0. S3.; / )(t)'; L'u,) = 536 /6
R,-,,~"':v " -E'y= 800 Sm 33.3" = ~DO(O.548'6) z: 43 'Ill>r-------------.-- ---_.-- ----
R. = '/.:!'36 -,7 ~3t 'a..' 7Sr;"- ::- 1021 /,6
cos 6) = ,-36/"'7.1 : O.52:J)( - /' -
c~s ~=137//0Zl ::;0.430
Cc5 8", s: -7;,0//,.,2.1:: - 0.734
-,:')0 -z: - 4.> -~ 0 co 5 .30" SH7 3.::>~
t- F S/'7 ~D" s/~' .:)
R z: IF'Y yl
M z: 5bO!:. - 320) } 400!!F= /D3.9 IV N·yYl
_-'1-_/_:_&_" ,,(),"()3~/05, I
.? :.l..(I03.Q<O.'114"" '70)= 2.53 AI':y 2 f f
~---------------If _ 2 L '2.. _ / d N
12:: r So f- 2.53 :"-1::;0 - //. u----
(2 )
N.-_'7
-'/'. /1I .R~: f
/ ~~.I" .
~F c >
2/I!91~=ZJ="::SOOCOS45"/_o) ~ 4Q~ -(o,'OiSOD.5ln<f..5")ts
: 354!. f 40().; - 954!f Ib
I2=Vm:1 -t 4DO \ "tS4 - = iO <;3 le
Mo[SD" Cos 4Y (3; - Go.? (3) - 4D0(' o)]!- + r .:)00 c. •• s is'(6) -;SOO 51/1 15"(7) ~ 600(6,~]}'
-tf SDO SIn -IS (3) -r 40 o (n ]!:!
:: - 473'11: -f 9/96; i no!; /6-:/.1
fA "'Y1739"+ 8/962.;.. 22;:7'l. '" 'f7.14Ib-H
.e" = 20 - ofQS/J., 30°::: 0
le s: -?c - 45.4 - 40et:>s30"::. Cl:YPi. "0
!C<=.5w/rt:l'I"]i' /5 nuT_Q fl"'~~,
/./)( z; 45.1- (,) - 8'0(2 z) =-/_~5'/ Ib-In.
IV! = 20('4.) :280 I~-/,..,.'.Y
M~ = 4Cc 10-1/1.
2/120' R = -/20N' fi: =0 Ri!" -/60 IV.---'7-.-I.....::..x.___ 1;Y /,/ -2 2. •
R=V 120 t-i6o =Z';;~>N/ R=--120~-/6.'..)! N~--------------------------~--------1 -----------:---~ The /~?' /6C-N for.c-es <:"' ••• .31/7v:/'~ 4.
CV'L.'p/.e /60(0. 2S0).:!.· :: 4-oj .·V'Ir;
R. i: Z;:::: 120 L -1li'O./ - IOu~' ,\/
M = I!..V'A:= [120 (0. 25) r- 100 (0.3) + 40]j -I .s-oh= /OOj i·S0t.- N'm
1'v1.v.~:2S - 160 (0.2) =- - 7 N·".,N1y ~ 16o(C1.D?Sj -120(a,/OI!'J-O.07~) ="1 N'''''I
M;;= /20 (t:). 2) ~ 24 A./."""
lv'! = v' 72.+ l z, f 2:ij1 = 2s.';;'- N. n-?
& -::-7~ ;. ~ -f 24 &- A/'1?-7J
~2//2.,IA 55uMe pO.5i/IV(i' u.-~"'t:h &</1'lh dl/"~ch"'r>. C05In::; ec.ua/ 7b "'fiC;U~ ~/ !?=-120~ -160h AIl. . / - -
!0 : "vh/~h ore -l= -0.6) m:OJ
"=-0.0-.J-) I Coorq,-na f~s 0..1 Pore / » y 0 I\.....-{, I J ) /
~~:---7_' 0= 2¥p =- IGO(Y-O.2)! t-160(0.075"-X¥
/~ /-;( Y -120(o.025)J + IZo(o.2-y)ky -
,'X. P r 2S~
::: (IGoy-7)!' +- (9- lr;oX);' +- (Z4-IZOyJ!!
/60y - 7 = - O. G f./l } so/ye
9-/60)1.=0
lA -/2oy z: -0.8""1
,. .!]e.1- !vi=- -IS- N''''''(~'n 11"~D.$ite. 7b te so1}'.1c:1'~~e.,.;r-.clt)
1t!= 0.0.562 rrv 0 r: X = .=6. 2 "., >"Y,
s=er> Dry::/oon-.,...,
;2/12/ I (!::: LE = lOO (.! f-iJ AIA55U","C 'p""",,,,e. """"'~HCJ,I .$0 a';r~~f7;"HCO!5",~S 4' (' ~ ore 'ThDS~ of' 5" 0" (10.) 1~ 0)"-eT C~~"'~""'4:.~S 0..1 p,;, 1(-"Z ,o/ql'r~ 61 >'J l!.
1A./i = /001/ +//'OtIJ)(Q.4-1)-ZO)j- p - -
+-[IOQ(O·1-x) -1<'11(0. 3) ~z: lOO ~!-f (zo - IOO~):!'
f- (10- IO~X-)!:!
£'1"'4/£ tll;'~C7'ID" CtJSIJ?~S
~.feT/00 l =- M/ff '1 wJrf!rt! M IS -rhe20-/o0l.- lw1/ff /"YlQ,h'-ju<le,,:/ £!::!p'J" - /tJD '1- = 0 So/ye ;. :Je.-I- l' ~O. I.,., tJI" x.: lOO "" >'>,
'1= 0';"'" pr 1~/PD""'»1M~lov'2 IJ .•••••.
D/r. C;o.sln~S D:f ~ Ore(/60y-7)/M
J(9-/60)l.)/Ivf, (Z4-IZOY)/M
u..>h~rt!Iv?= JIy'I J£9",q/'~ d'r~c-l,,,,, Co.$,n':S fo "'Ho?"" n v"'/~~r ,.ftr
~2/1~~ ~e-l- ~f!l4 •••,q'N'1q7ts~'/'p;,,, (X,,Y, Dj
D,r.c.-I'io>7 t;~."h.s..,;;:U'r~nc.,,(1 qS3"m~/Jo~/h:--e,q"e 7ho.5~ of .:?=:/2G.!·-/~j-/DDI!r N
lA/HC-YC «: = V7z{J2-;Iio"'r/~-;;;L=.Zga IV-
.50 Co:> ey=/2o/2~g=(l.!i{J3S) C.oS~=-11b/Z3a=-O.7553
If Cp$ S, = -/Do/23? s- - 0.4-19~
,,:!"r~p= IOOy!: + [/OD(O.3-K) +120(0.250) -I- 160(t'.uo)]J·+-(lfox. f IZCJy -{ So)!:! AI·,.,., -
= IOOy!:. -!- (IOO-160X)J f- (.so t'-I~O\( -!-IZoy)I!
£9..,~t4! di~ctio'7 t!.OS/"t!S -lierd Iv1 ;:/~/f/ ,f Jef
IOOy=-O.,s0)5AA i .5olvc '15"( M=-96.5A1·rnlOO - loo X. '" -0.75'53'-/ or Iv? = 96. -5 N. Hl
So T 1'0)l f- 120:/ ; ~o·411f~ 1\.1 t9P/*D s.,Yt!. <h~&..fj.",-/cl<{
Dr k'= 271••••"".,Y'=-18~ n?m
x-="·Z"1,,.....y= -6AI6 rn
3 EQU I LI BRI UM
.3/4 I = 40(9. '?I) = .3'12 IV
.iF. = O· 392 coS 600_ B z, 0
)I. )
8= /% AI
60°f3 .!F=O·A-J92.s'n60<>~O
<. :t ..Y-'A ~ 340 N
AI
I
I
YI-----~------~======~~=====-----·~-~-=---------------p= 200 -/-Cn-? lOO
c- 35. 3 16
P Ib 10
: R- PI 0do
/.2= 2oo/C4:' 10"
:: 203 Ib
~~8I 0.1 Wl
~W A
w z: 30o{9. fi'/) ,., .2943 AI
l.~=O)· 2943(0.4)-8(0.6) = 0
5= 1962 AI 0'- /.9~ kN---A :::2'143 + 1 9{;2
::: 490.5N or 4.91 AN
11 , -I / ::>1 \:J;y, ~= SIn ;.-- -= 17.46·
1.d.I~ o: r 30°= 47.46v 9c?-ex.= 72.54°IT)
; »> «" tF;=o)1---- ---
I':> ',3D" pc 05 47. 460
- 200/<;. g/) Co5 7Z.5"4m ~p=0
) 0.3000p= 200(9.9) 0.6761 z: ~~
3//0 I
p
T
P~ ;-70 Ai (f?71 IV)T~ 25DON (2S/3N_.____ 1
\.'~
25 = 0,' 7; 5/'160°_ 98 l-looO sin 15°'::::-0LF=o'
)
1"4::/:'0)' :;00(0.1 ~) - O. r-« =0A = /2Io N
-'i= /73011/-~
iF.;.=- 0)' ;; t- J7 30 Cos 60°
- 2000 Ct:)SISo = 0
T= /0 (, 7 IIII
r---~-------4f t ;T tT
Ir-----'----t ~
3/3
~--,------~-.~--- --=-==-------13/9 I
A
2'!
LMA =0,'
200(lh) t- 600 (10) f 500(7)
-4.PO(IZ) -8(6)=0
a= 1,317/6I
I
.Y--------
zF=o' A fSt)o r600 fZ"oJ - 400-1317=0, A== 417/6y ,I
~II~ I, f.;1p
"s4~trflOg%
LF=o". R.-4(/S7.o)-O
R:a62~ Iv'
p
3//6 y'IL_-;l
OXltl 600 If:,
S' 0j. 30",
- _I ,
5'14'
SOo /6~C}
L~.::OJ·
40 ( l?) + 40(6 )
+/20 (4) -f 200(3)
-2;=;'::0
~:;~ZO/b
LAd. :::0 . 2 (0.25) - 0.4A = 0i:? ,
A = /.25 kA!
~Fx -x 0,' Ox= 1.25' kN
1"5:0/ g..: 2. kAl
O:VI,Zf5zf 2<- '" 2.36 k/V
3//'1 I
(:::130 I/;
(Cede. 12s; ,;' 16)
ZMg= 0/ (10)0;1.. r: SOD (4)
-600 c;o530v(5) -6P"sm30°(;z)~O ;/,21
Ox.= 420 Ib
LF=o' 0 f-600s;'n:Jo"-5tPO=0.y .J Y
Oy::- 200 /IJ
0= V200 'l- of- 420 2. == 46s- 16
--------p
"'g = 40 (? el) :: 393 N
~M ==0·M-3'13(O.24s;.,30')=0'" .)M = -47. / ._/v. ~
2r= 0./ R. == 3'13 N
ft7:J = 3 "3 N fr",., Sill. to Pr"". SAo~M =0- P(O.24+ tJ.Z4 clS3tJ-.J...q ,
- 3'13 (0.24 $il} atJ")=o
?==IOS:I tI
R == !/OS2-t313'.L' == 4o~ N
~r 6f- '70;
.t » h T.+-L ;;:.F
F; L (f; -I)
.r c t- TfF"=L
- L/ .P,/== (1--;;)
({." 20 CaS 3,f - IS' Sin :'0 ,.
"" ij',j2 m6 c 14 i- (,,/'-2':»<:05 3.;>"
+ 12 S,I') 30"
= 44.25 /n.
lIv/:-o' p{4'12~'te.3z;.:) J •
- 'ZO(g,3'l.)-=O
,0= 11./ /6
3/Zil- / kA/ /,5 kA!
,,-~- I •. 2 kN'mlv' 2m 3"" )"/"",,-(1 ~--- . -=1 7 W=my == 50 (6) '1.81V 3 n-> t;..,t \'\. = 2q43 AJ ol-Z,'I4kN
(1/ 2 1<N
z!":o)' V f2 -1-1.5"-2.94=0" V= 3.~:'N up
~ =- 0, IV1-f- 2 l' 2. (4) - 1(2) - I, 5(5) - 2_94(-1) = 0
/VI: 8. 3 3_/-~_~:.m ~': w
tA./! = c))' A (:;;-S/Yl300) -25{) =0<9
A::- lOO Ib
ZM = o· 60(4sm30") - 5A)(. = 08 J
A = 24 16x
IzT::: r: htn ex = 2' ""'') ra" 0(
_ i re c rc sce II = - !> "" ." . r _. . .. = 3767 IV., il (600 flzul-(5DO) z
Or T= 3·'19 kN
_ 15' 69{' 72{/z ./ _ L _ -'" '= 10'107/11
f 7?e> -fOOor R:: /0. '11 kA/
z; 22. / /rr,
! A'>A = DJ' /3 q - 60(22. i) r 0
Ox = 102 /6
/J~
IZSm"1200 mm
Ren-'ov~ c es+ro r- r",/I~rRCI-?-1ovC riyhi-honc;/ ra//er-ReY>-7ovc u.Ppcr-16fr ~;,*,<:...••.,':J/Qce /o-'"e r- s':<-l'lu1I''t' .6y I"~/I~,.-e~/.;>/t?c~ hln •....~~ ar- ~/~,.;'-~JCj.• e,nd ~'/ r7:?//Ii'r
Rep/ace IoU/er J'upport' .by roc':'-~r
7S",,,,
3/3-11 (A) / 3 5" 3/3'11 L~ = .:)., , X .I
(13) 2, ~ ~ 9) /O} 1I\ ZM =0'\
\ 6 ,;(C) 4; 6) /2
.R,(D) 7 !? /0
/ }
~C05&- Rz5lnG!=o
R,cos(3 (~) - Rc .5In,d (2{) '-'0con->.ol"e Q' .!If9.f-
.3/.3'5" LMA
= 0)- 60('2) - 38 =- 0
8= 40 IDC.
A
,~_: 1.5'/ (J _
// B
T / /' I
V/ ,3//1'60Ib
••. ::::::. .1..2~= 0) TCCJ5,3 !-A -- 60-=0
A= 60- 60.2------±5--V4 2-/- 4_52
60.2 1<,
4'
A -= IS Ih
1119>=2S {'I, SI) -= 245 k!ll
~ It,( =:: 0- T(~ /c••s30-)o J 2 /'
- 245 (4 ~.S .,l) r: 0
T= 14/,6 kN
.-./
3/37 ZM" -0/
L/ (Zb) - "",(6) - T (4 .•1,)T--1"~---'------'.~_______{d
hB_1»1 q ])a
L, =- mq + I d4h2 2 b
D,/L, =- VH, SO
j): D, '" ~ IlnJ + rd-llt..'2 4" I.' h /
ISoo (.,.¥1)(1,,-3) = 14.72 kN
l'> LM ""0. 8 (2400) + 20 (50a)A J
-14.72(!ZOO ~3(JD+SOO s;,,30"j
==0
/3= 3,7.1/- IeNZOkN
=5Jn~
Z 5/1'1(:3
(3 = ° or (3:; 90 u
[ •.[ 30" [,24-I I [
!
ZMo= 0)- M j-"~:J(24 )-12oo{3o)=o
M = 2~600 Ih-In_
(J" IVf= I?QO Ih -.;If
=03/41 ~ (0.35,;" 301 <so == 0
~=333 Ai
Z~ z: O· N t-.333 co e 30° - 58'1y -'
A/= 300 tJ
:::;0
=>.ISO N-n? \1"\ G 0.3".,
\ 4-""_ I'.~- -;-\ W{- c\ B, .3d \ J
F '1f~\Nw=s : 60(9.el)
z Sg'''I tJ
2F=O' F-333s/..,,'0"~ 0X )F=- 166,7 16
{=Vlf,6.72f 30~Z = 34-3 N-
/!V= C. 2(9. E?;j z: bO 8', kill
F\
Zc '" S4 , c~ 27 klV (2.6.7 klV)
F -:::.2. kA! (Z6. 5 k;.J)--_ J
2eW= 60. ~ kN
cx.=fan-I 18cC)s300-6.30 + /8 s/1?3()~
~y\
"/..._--I ,g"~o
ex I IC ICX'Y I I
JO" Ii __ J
A61'
B 420 IJ
l'1:.= OJ' 420(60 C0.5300)+ 8.J!;-'1.3.8/0(;8'5;">130"
-8C05 13.t?1"(18=580'-') = 0
/2.'1'18 :::2IF'Z4/ 8=108011>
EF; ':I!I}' C)L - 1680 J/~ /3.8";'<>=OJ C;<..= 40/ If,
2~=o' C T420-IG!10C~!5/g.f?/o=o C - 12/2 /6Y ) Y , y-
c= l4ii"I.'l-J21Z~ 1276 /6
/A{=~J: 400 (9. i>i) :: 3'12.4 A/
W;=n-12:J= 8or9.8/)~ 74'5/\/
ZM ::0' 785(0.7) -/. 8F = 0o ),c= 305 A./
1Ff -= 0)' R. + 305 - (.3'124 + 75"5)co.530B =0
R1<.= .3773 A/
t
3/47 girl = g/t ="1.6'1/6 ",/sz.i ~9A1= 4d'(9.tfI/(;)= rr.s N
h1;z 1", = 240 (9·tfI/6) ",312 N
'" '" (;,,,-1 ~ -().~ f.t,,-'o.IJ76'V-vo/-IZ
0(= 4.37°Cos <>( '" O. '1'/7/) SIn 0(" ().0763
zM == a, 7~5(2.sc"s4S:J+312 (s C,6j1$)o )
F = 2340 N - 0.076:3 F (2) - 0.1fT! F (o.S)=o0".
3/48/
3/491 zM co· 117.7(6.S)+//7.7(a-S)A .I
- 8(3) "'0
8=275' kill
LF; ,,,OJ Ax - 27.> -117.7/-12',,0
/(ef/"I"c..e. r : b.!:lF= 2T C/)S3()b=7i3
Z'M =0. ma.t - Tffb ==0/) I .J
..l= TB brn~
F---
T
R =f ,F2.,t (h7jP'
=J 3 7 '2.-t (h7 9) '2. '
O.s'"
B
Ax = 3SJ' kNZ-r; = OJ A
J.:: 117.7/ff fill. 7
== 20/ k.NA=,j3St2';'2dT2.'== 410 kN
_8_ = 10
Sin 0<10
) SI/?CX= 8'Yz2./;Z I IOJAI
1 -,
1 "
/f> .(/01. 0 /'i=?k,.j"'"45(31F '",,-18 f3:: /80 - (~t 45·)
I y~- - - 1- = 72. '1 0 Q r: / 7. I "
= O.~'i39
.501. 1(0( = 62. / 0)
~ __ = /05/n 7Z.9" s;,., 6Z.I" )
0.9557.c; = 10 o. ?i'39 :- 10. e I kN
& ::.90 - 7 Z. 'J = /7/0sol. II (01.. = /17. ,,0)
F, /0 F c: /0 o. 2142 = 3. 3 3 k Ai"-/17 /7./° - ,5/" 7i7.9 I I 0.883'1
8=90-/7,1= 7l.'1"
2/14 I Ry r/re prmc,-pltt. of r"'LlI7Snr1 I-ssib//'-IyE may k a.P,P/t"eq" tit" C or E tv/I-hoq rulkr/"'., //$ On A $I;'(S C,/J£ /s Q sl'1..,?le rt.;J/d"
~o...!y. Al'pll~(/f/"" lit 1), hC>Lvever Clrfl'?.J".t- -lire.e//.e.t .$I;',e D 1:S 1),,1" "" -Ihe $""". rig/q iJcdyas Cor C.
L 4/41 Of S"i" •.•
F /s;". 45".4/.•;;,TS·-'45
/'" ,. O.7()7 4 _ 2. 'l2~ kN-45 O.'l~~
r.. /.si" ~O·.•4/s/,. 75"IJc
F: - ~ 4 •• 3. Si'. kN.se O,1~.
R ::6 cos 300 - 4 ?t:>s50oX
=- s: I~b - 2.571:= 2..6.j ,fN
.Ry:- r;, $/;.-do 0 I- 4S/n 50°=..3 + 3.069- = 6.00!rAl
If = 2. b3./ f- 6.06.; kA/
J.... -I {? _I r ,(j:fHn 'Y:/4n "·~~=66.607-:; 2.6.:._
2//,5" I p ..• lOO :a//s'SkN0."6
AT = P ..ri,,30"= //SS to.s)
== .5Z 7 kN
O. I (F/O,S5S!) _ ~F;.;..-_.sin a - oS.tn .33. ~.,"
3/5"01
3oo{;)=Joo lo-JI/ 6'
~
,zM ;: O· 4A -~OO(3)o )-Joo ('1 cos 30°) - 300((,. 5/',-,30")
-300 = 0
A:: 1259 16
30°:,.3oolh I 1.---- •
I
:,y
1,c = o.y J
3/5'1 I W= m.y = 200(9.6'1) ,,/962 AI or 1.%2 J.r",
41"Y1
A ----~-l·- 10(0.'9)A ~ r: r::1 = 4 kAl· m- I.Gmt .-"-..',"y' , I
2 ,t ../// r loA _.L -.:..1 ..2 ",:J0
"., W/ L __ 130 r-ro"1;;=(:>., .••oo #.~) 'I- IOh-/J
x~lr-: ~··IO(O. 2). = 21(A)'n7
Oy 'IOh-AI
LM. == O· (10 COS30°)4 -J- 1.962 (16) --1-(10S/I?))Z~ } .r: 4 I- 2 - 20)(. = 0
Ox. = 30.8 loJ
.2;:; =. 0)' Oy - 10 cos /3 - /.962 - 10 ct:>S ~-3:?0z: 0
S-.::: I!J-. I kA.!
./-- 2 --2 .10= V30. 8 r: IS. / = 34. '3 kN
- - - - (1%.\
3/?-I/ZF=0,' mg==A+tJ+C= 22.0+e2.4T-.fJ.43~47..5'kN
LM =-0.3.43 (3.0)-47..5',}- 20; :J = 0.21Snz.{ )
ZMJ :20j Z2.4(z.4)-22.0(z.4)-t- 47.J>~ ~O
X ~ - 0.0201 ,.,
Vvz = 2/?('1) 0 252 16
W=Z52/02
£/...-1y= 0)' 0;; - /1 'ii /3)::'0) ;:;;=.!i.l.1...5,\/1c -= 0 25 Z (4. 5) + I~ g(l) -11(9)- 6~ "'0 7,;~3/S liJ
x ) ) -----zF.=o- 81+31511-7; -/68~2SZ=O- T=2/1i>l) '- ) C
3/51 I
c = 1.2'1 ffAJ
_3/bZI 4ooA/r-0.9m-1.~
'~~f~::;1~ (J.b Ii. rn ,.,., I
f120 (CfJ?;) :
/0./ L.
tD 8rC
tMBC= Cl)' /.2D -120('" ~/)(O. G) - 400(1.2 - 0.7) = 0
.D = &15'9 AI
Z"1;D"- 0)' / ..213 r 400(0.2) -12o{9. B'/X.:>.6) = 0
8= .522 Ai
2'5 =0;' '8'1rS22 + C - 120(<;.i?1) - 400 -:0
C::: 367 N
tng
#'>Iq •• "O(q.81)~ 1570N
By .sj ••••••~i,-:J
I, + Iz -= Q (0 = TSS N
4-P-=DV?
AZ Z5=Oj'Ay-400:~ Ay=400 Ih
D'-1;=O)' GAz - 400(16)+ (SOOf 300)(6 ) =- Cl
AZ= 2{; 7 1-6
D=;=o;' 4P/r;- +2(;7 - ?oo ::0) p= 29£ 16
A =y(4<JO)'Z.+(Z67)2 = 48/ /0
3/6R I
5",/ve s/rnulraneou<'iy IJet
A ~ 2,041 kN t.ension
Z Mx - 0 i ~~ x [ f (-3 b +Sj -'!! ) + f (~j, i- S1 - 61:) ].1 ~-t 4-!s x(- 23/;0 :l)o,U ••g
-6oI L + '147".i: -Q; T'"' /310 HL --:-__ -:---:--:----:::------
Se .• I.,,.. s••I••./;n,: Lf!i b •.AO SO TY~ - T :
~M>( '" OJ 2T} t (,> - 23&0(4)-0
T- 1~lo N
~ =-A-.-(-i-j-Sk).s:zo - - -
§ =S:~K(-2~+.i+S!s)
C '; -L (-2) + s:;. ).5:39 _ -
8 = {),d'61 kN c"""pressiM
k Iv' C.aln pre SS/OilC-=/,Z/b;
[M ::0' [-60ftZ)-SO(/o)+/SOO-;.1 -j f-My]J
+ [- 50 ( 3) f- Iv1 t J ~-z: q ,My=: -281:) Ih-/I1_AA = /5016-01IV't
0~ -280J f ISO!s- IIJ -/;--/.z;::-::= 9)' (Ry: -s.» j f- {IZ[ (.o)t;r =9--·------
1<)(:::So Ib, RZ =-60 16
3/72..1 >e-lj' L~8:-0.J· IZC-40(Q,:=-o
C = 3016C
36'~ _L(~2'11')::) ~ /b
,yI
48"'I- - - - 1'-------,..,/2"
N"
Y-l:)·l.~= 0) 12 (30) - 4&' Bl:- 0
8l= 7. 5" /6
:1, )(-Y)' 2MA
:; 0)
: - 4'8 f3}1. t: 40(36)
t--B1-50(21) =0
~ By=S /h1i:::":"_
:j' 8 = V6- 7. f 7,5 7.
~!SO /0 =- 9.0/ /6,,;--->- A lf--c.
1---- '__
3/71 Pe,os 20· 2M =0'r .J
(ZOO -100) o, 080- 0./20 P cos 20°= 0
'---;,2) ---x.20 IV·f'Yl {OPl> ast/t!.s~"S~.Ir"n? r~rallon
y-;!' EM:;: o 04t;:J - 20::: 0 81".5J N (=:5o_1-).J A } . I J "
)(-;E J' fMC'" 0,' SO(0.3) i- D.IO - 20 =0 J 0= So N (: 5(J/J
i~ :0/ $O~50 -c :~ C=-/~o.~ (=- -IDOls)
3/73
p= 70.9 N
tM z: e)'Z )
Jv1- O. 260(15. 04 -1. 52) '"0
M= /.Q5:Fk,,}·m
BC -y'4z+32+'l'2 -ltJ.3tJ."r:Z; = -'-(4i:+3j-9k)
117.30 -
z: 2'6 in.
p- /6 COS zoo- itJ.o4 K-I,/,~ = 8 (;pS zo"= 752 k.'V
j=> '" 16 5/;;' :ZOo" 5,47kw3
p= 9 S/n20o", 2.74k~4
L!Jj,,: 0; 41.5. x (-30j)
+ 3) x: ~ (4i -t'3.J- 'l~ )'l.!: = 0- 10.30 -
120i - 30 r;i =>, 7;=45",.5' kl'l- 1/1.30
y-'l, A = &'."'9 j + 16. {,7j +- off)· " 5..
A =/,j/=!t.,f'l2+f6.G72+40.0Z,' =442 kN
2MA = 0; .!..:.l. (/90]\ tr.« : - 2By = o : 8,/:: 7fl5 ,\/:z . 2.33 '.I... , v
fF=o Ay -I- 7.9'.5' - ~ (1107)=0 .4'y-= 5.23 A.!y J 2.33 )
50 A=~y=5.23~ B=v'7"8S2+"i8/2=125~~
A '~.8 8
1. .";1:: .
:: 28,-12! +«:! 124&) =
w= - 2oo!s It
ZMep 0)' (~A x § +.!cE. x l::Y)'.:/ = 0 )' ",,,,,,,,,,t "'/E s: 0
[30~ x 4(-3f+ Zi-l-bb') -t- (q,':' t2oj.1 If(-zo4)].j = 0
(-4000>:.+ 180(/0- 817)/ .•..6coB/7 !;)./=o -/3/7 - ID c 0 B"'-F:: 70 /~ -
8
p ~/Sf?4 AI
S(9.'f{i) kN
3/fiO-'-----'
(Nole t."cd T; .·s "I'm,'n,zied 'n 60l:h mtP..,~ ••.t
et"'''' t/"'II1 s )
•• ;> ''.:.'J-.J/ .»----
!Vote: T T R ••.••J"~av;t'J-fD~t:-~-, J -2.J -) J
reeL",. ••.tl p".s tl.~",,'J!. «- ••"is,.5" {2 ""Ht AI.". Tt.••, C'1 -0.
Cx(3.S)-O.9SI (2)=0, C,,== O.S('I kAl
4j,x T, (-I.Sj) + 2.Sj,XTi(I.Sj)=O 8r.", S1 .•..[, - 1... - ) t, .("
rr; =: 0; - i (4) - T.•.(2.5) + 0.56/ =: 0, ~ + 51•.c I. J21k11
,t.. " f.•.s.r.; rt 'jet 0 :.!:.!...J:.!...f, -:0.347 kN) Tz=!:E.!.l1. =0,43110"16 10
:tF =0. !..:...!.l:.!..fld - 1,121, /,S +1<.0 R = 0,0/"31 "'IV'J J I':; , L, rs :» c; )
~ F : 0; /,/2/ i 2,5 + 03..' f 2,S + C - O.'i!I=O CZ" 0.52' le"a ,t:.' £, 10 2 ~ i! J
Th"s C =/0.S6/2+U,S262' =0.7.8 kN
z".0.' ('U') kN
Z'~6 =OJ
X'11z = 0;
\ \ (i'\.
\ \yI' \\ '.\
.I, = At: =112+ 17"+ 82.'. "'.9S '"~ = BP =";z.sz+ /.Szr2.Sz' •. 3.14 In
I, •.T. (-4i-/.5J·+2.5k)
~ - - -
T1." ~: (-2.Si +1.5:1+2.5/.5)
A
O v' __ 2 - 2
::: 425 i 1717 z:
1-3-;.-8'-5--r1-----_-"-----------s:-O-----2-"'-YF-;--q,-:-s,-o-",-",--I
(I ~ e -13'p ~ T-0'a. 8 SOm,.. : I:,~ .1_
4 ~
/76'7 AJ
A> 8 So A ,-s <Lt /;,.";t,.,,,.J /0"4.1«(2. Df 7.5 kl'/
Z Ma = O. P(300 + 2S) _ 7. S(~) = 0 P"" 0,6&"1 kNv./ € \.y'3' )
,,]/87
2~:=O)' 60-0. 3F= 0
.c= 200 Ai
1{=0)' !,i,COS30o-200=O
.t;;' z 23/ AI
T(4r_1
b
Fedvce fo three. fortesConcvrl"enj" £If O.
b s: '1 + ~ (2) :: 10.33 /'n.
cAllcrr.C1j'/",,6
I},,L-_-'L
.5'0/ Z"1=o, L(6-9) - -4(12) + ,A(fl)::o
L(b-9)=-fA, - ----(1)
ZI:y:=0)_3_C:L]'r;) L ;::3A (lo)
2;:::0' 2-C~2A)t ) r'/3
U)f)(2)v"i,'ve o-9=J, J,;/0.33/n.
3/~ tng .x: o.63S(,o')(9.!I)
= t;.23 (ro ") N'
c
A scale ~ 3. 7S MI{
Ing
= 6.23/.11{
fA" B ~ a.ls, .s~ t7=' o.l4J'
c~s IJ = O. '1ff
,.c = o. J' ~ ) Fa s: O. J ~A
3/T~ "'.9 =' /.3.S(9,,fI)= 132.4kIVJ,!II
p
I,?o{)HA "'''' NB
:ZM =-0. p t».«) -f 132.4 (O.!2-" (o.l4.f) f-{!.J'-o .«j{o."18'i)).4 -'
_~ (I. i) = 0
:EF =-0. P 1- 132.1- (0. 14#) - O.!(~ +/V',s) = 0x .)
'Z. t=; ~ 0.1 ~ r: ~ - 132.4(t). 93'1) = 0
50lve I Jei ~ + Nb = 131.0 k"0p= 5's. / kN
J118 == 124. 7 kIV
3/'13 l70r'1Gfe on ClU.3~"-
F~~
\---~(
z,,, EM =0. P(200)- 4()0(120 GooU'3"~)£ .)
=0p,. 206' AI
T-4oo IV~=j;~;;;t==::::]----xZM4;/:- 0.,' 208 (lOO) -f~"(;6~
-BZ
(zoo) =0
A~ 8z /jz =-424 IV
Z'r; =0; Az -f 424 - 204'- 400 =0-, Az = 1tf'4 N
S'-"a A == f3 '" 0 A --A •• / ~4 N 8" B/! s 424 N~ J.J ~ .J __ --='-- _
L 5 01"18 f/ A60 are 30"a/50 A8= 2r u-hey.::r= rt:l.d,~5 ~/.!Jpl1er~. 7171.15
40:: rjCDS 30":: 2r/1SAC ;: Zr:So OC = r~{2//j)~:: 2rfi/J
£9u,/' 0/ -fop hq-//
Zl::-~o . 3R coS() - rY'/ Q z: 0,? I .J
j,:;:: 2ry2f3 = y-)".'2r
,z:: Yn~/IGL&nper 0&11/
2;::;=0)' P-Rs,"'c9=Op == :!:!.-' 2 "/13 _ .!:!:!2-
vG -z;:- - 3Yz
l: cD=V(4/12)?+4~ = 4'1372 if
i= ~ (-2t'_Z)' r4!J).= T (-i. -J 1- 2t.)4 ,,3/z - - VG - -
.!iV!.Aa=O) 200(2) -7i(z)~O- 2T r: _// = - :: ZOO T=loov6 /0l vG )
T= U51b
3/99 T-I
l(Sj-Zj-14Js) T.2.=~(ZL+6J'-'lk)IS - , - 11 - - -
L GCt-~:1. = '<"it ".,,;£or in AD-dir,
= -J-(2if-{,')140' - d.I
!/
~,'" ",,,,;t: v eat-» •.. "" AC-d,'..-,
= .L: (Si. - 2.i)fi1 - -
ZMAD =0, t.l=X(-IO!)~(Zi +6j}
+14" 1: (5" ) 2i..,.6j~){-! =-2J-14k '~=O
/5 - - .'40- ~ + 47{, T; -0 T 4 kN
.f4O 15W - , ~~'-/~ __ -
= /2't.3 /6
72 .•.•r- - B/\ 0F:. '= --v,.,~6 ~ lrv. 16n 0,5
;:y,= 736N'
!J. p" .500L .;.96S' AI=-- ~-: -!I _
~I y: \ i\ ' 06fo/11 t'nterslcj;on
C !-he n S(;qlr:,c.Oh7 ponc nfSy'
~-::.5PON
Th"s P ~ SOO! + 970/ N
~/77 -/-i -/"00LI<'-7 I g z: -/'Qn- - == 14 040 r = fr;:Tn -" . =~ I~ ""') 300
e<=j3'f'q-:: 47730) cx=QO-7!':S6.31"400mm
p -:: 6005/1'7 56,3(~ .s/» 4- 7.73'"
0.832/P c 600 ...:...--"--"--0.73'17
z: 675 IJ
F- 101:1,/ ~;: F cos(}
= /0 _3 __ 30 ktv'";321'22' v'73
of. == f-an-I : z: 26.57°) ':05(3" 51'nc(~ 0.4472
2 -z --2K z- 900 t- 8'00 - 2 (900)(Ei'O:;)(OA47~
=li'o.{,O{/(4);R.= li'98 /6
/3.:::10-20,57= G3,43°
li'r g 900=--..5/17 '3.L/3v S/n'O '
_ • -/ (900)(0,5"111-)_r-5tn ?98 -
=:G3,7l"
z'"
,/ A2", ./. /'
/' ()
'------'- -- X2m B
;: s: F sfn /} or 1<7_2_ = 20J -YZIl-f!J2' BM13 = 30 2 + 20 Z = /0'0'S ..fi3 -y'i3'
"" 27. 7 ktv',tn CW
kN
2/28' I lOO :~
I-.=rn==YYI==3.~/ 400 III
if. Mo= 100 5/;'" 600(D./ZO)- "'/00 coS 60°(0./_ d.06)
~o60 =41.b-8.0::: 33.6N-rYl cvv
4 STRUCTURES
Joint B
~A8zoo(q.(J/) 4624
N
CO$ B::- S/.,fi'9 = O.9ZfJ5
G=lon-112 = 26.57°
Sin o= ylS I Co:S t!? z/15L5t=O, AG/(5 - 4::: (;1
A&:4ISkAl C.!;:;. =o; A8 - 4t.5(7'rs)::0
AB:8AAI T
4/2 IJo/nL C
'Jom!- D
L1:y=Oj J250({ )-6££1)=0, 8£= I?~O Ib T
~~=o~ BC-3000-1250( -})-1250( ~)=o
451"6 BC =4500 It, co ~ ny::o; CEsl'ne-,psiYl<9co, C£=CD'-
C£ CD LFx=Oj 2C£(J/s)-4500=O,C£=.37,j-O/bT
C.D=3750 /f., C
.f.F;,::O) AB (,;.92805)- 46 'l4.5i,.,4-5°= 0 JOInt D
A8= 3522 tJ rL,c;,:::O)' P£-37SD(~)=O
DE= 225016 T
BC /Y.--",,---' fF =0 . BC cos 30° - 2.. = 0GiOA, X)- ~, i3C=2.3! kt'P5 Tz. k";le
eo 1;:;=0,' co -2.3/ CoS 60D
" 0
CD = /./5' ;",;,s Cy'i -' \(
'x:," - Z 314- i'F=o'
~
10°' ){)60° z,c- =0'
150 y')A8
2.3/ }(
~60\ftO !~/~kAD
,0:)
AB = 2.3/ lops T
.eD: 2.3/ k,ps C
i'~=o; AD +/./5(;05'''°-2.3/~60v'=~
AD=O.5?klps T
A~ 71A8 4kN
.L~=o; 6(4) -,D(IZ) =- 0.D = Z klJ
lr:; = 0)' A -t- Z '" 0, A:: 4 ktJ
zF =0' A8s/;"e-4=0y .J
AB = 4({) :::6.67 kill T
zry, = 0)' A,c- 6.67CosG =0
A,C -=6.67(4/5) =.£,i',j Ir-NC_BFt 6.b7kIJ ,o Lry=OJ' 8F- ~.67J/n & =-0
cB 8;: =6,67(3/5') z: 4- ),-/1./ C
:2.£=0' C!='s/l'1ti+4--6 =0Y J
CF: 2 (5/3) =,J.33/rNf
;..'{~o;cDE f
.Joo o
2 k;.l CD
>1 p
2.2<f/rAJ CF
1:1:;=0; cr-2.24.5/nC7 =0CF= /.00 JrN C
4/6 , 80) GC) er; FZJ ~<> •.•/<>' se ';c:ro /J The-2-kN force r s remcv~.cI
1.1 rJ.te 2-/(/\/ /cI'(e is cZ,.-c,?/t'eq/ 47" G mSreArT
of 8, rh,,- (!hp fy ;cc:rCl-./"orce ""'b-H.~rU/~u/q' be 8G.
~ ~ ~ ~ il
4/ff I Jo/:n/ F ~;:;=o, _Fc_G_=_C! Y::£'5;;0, .e r==o :---x:
Jomf £: -e/£& j3=(-Oh-I..2..=IO.6Zo·t9=lo,,-1-Y4/ ., 16 j
rED c:os(3" O.9fi29,5/n(3=-O./J''l-3
4kN fF=O' E&(j) = ED (0.95'2'1)X) :5
11:;=0)' £6(j:)+ £D(O.lg43)=.4.5o/vt: 1/ :Jc!- Ea = 5. 33 kN T
Jo/nl G Yt~GH5:33 I<J.} GD
21)=0)' GD-S.,33(.~)=O
GD= 3.20 kN C
~. J, I ~ , ,L~=OJ' 40(20) + 60(5)-/58=0
I Y ::, 5"., 8 = 7.3.3 k NI 5m: Srn l.5m :SM~ __ • X; A 1-- -c ~_C'- to
40kiJ B GokN
• .j. A ZF-o A8-o s=;=», AJ= 40 klv' TJO/YiI !. X - > - j .,., •
~
JI [F::: o: J f3 SIn 45°- 40 z: 045° .....".,l )
J!3::: f6.G k:-J CJ8 --- . .:....::....-~
40 kA.' IF = 0)' JI '" 40Vz cos45<>:< = 40 k/'J T
2£=0)' 7.3.3 - 40{2 s/» 45°'.Y _ Bn ,if',] 45"= 0
eH::: 411 kAi C
2Fj = 0; (CIf 2.5)S;'n 60°-4 =0
CJ= 2.12 kM T
4/10 I IrU55 q.3 Q eu,?q/e2M,c=o) 2(a.-f-~)+ 4(Z<z-+rJ-A(3a.) =0
Y. A = /3/3 z: 4. 3-' HA!
f:AB ;r,c=o·A8sln6oo-4.33=O, 60' y JAI- '" AB = 5;00 kill C4.33 kN it;= 0; AI - 5 co5 60
v= 0
,LII=Z,s-okAJ T
.!ty,= 0; 5.00 cos 60°- SI = 0
B£ = 2.50 kiV T
2.5/rN'/ - MUJOII?.L 60" 600--- ---2.50 irA! I HIr4 kN' l.F;=Oj HI+ 2.12 cos6o"
-2.50 - 2,5 co5 60u
'"0
HT:: 2.69/rN T
;[~ ~ oJ 0·8'14 BC -0·81+ (33.5)=0Bc - 33.5 kN (C)
z~, ==~. 0,6'74 BH - 0, 4'94 (10) =0BJ.1"" /0 kN (C)
z;; =0/ CJ.1{O.707)-lo,=O
CH: /4. / kJ./ (r)
-
FrvrY! JO'17f G GF=o)
efc.. ,. F F£ -~o)
r E) £D=O
JO/~f s: ~3~ If, /1-.'SO<? If:, ~
/ / / /. 2eBE. ~F
fJ= = 0 . SOD ( .3... ) - BE. .51'n ze» 0X') 15
.5/~ ze- o. g
B£= 1000 ~ = 5"59 16 Tf5 o.S
Y'
,h",sA / s» from )oi"d B.I
c) CF=O
r 8F=o tEF=Ft$-) r6 =- 14.92 kN (r)
8G =0
4115 I F ---=- F~ ZMA
= 0, - ~OO(2h Cos 30·) -FG(6 'os 30)/\- FG s: /looo I;' " 0
lJ b E/ 6 \/\ ,y----):-'-Ax
1&0·\: I lA400016\ ---X-/ y
C---'BJOin! D ~
I \~~400011; DC
4/)D"\~;' IC£ LFy=O 9IVeS C;;-= 40001,6 T
IJU/~I C '4-C.8 2fi;," 0 :JIVeS CB = 4000 I~ C;y' •
" 8s:~ /a 8 2,\" = a .!1'II"~S 8£ s: 40"0,16 T-IolnlB ~ <--=0,;"".,5 AB=-9"i!7c/6C
~OO Ih "X' Lfy' !J:y'
. , ~ "...''/:..': El' ,"0 .'JM' AC' 0JOIn' 0..:', x: --.: AE ZF ,=0 .51V<O"5 EF= /looo 16 T
4<>00I/) )I - .• - •. ----'-'. .'- - ~..
. 'f I\:/?OOO LFy=O ;J1v't:S AF = gOoo 16 C«/or» F
5'000I/' AF
1;:;' = 0; Ax + 400':> .5;/7 30"-1,'.000 -::0
AJ< s: 6000 16
25~OI' A.:;::4<200 Cos 30o~.J4G4- 10
l5=0 e-r= DC z: 4000 16.. C
iF.". =0 .!j/vIlS DE= "coo /,6 T
25, c 0)' CD= L
2f:x.,=D, c!3 = 2 L c<ps.o" = L
D A---r..~IH DE:
L 60 :8D
y
XIS = oJ BD .. L us 60°=0
8D= /./z~
~·t~:·/~"-: ~8j:
/' 90·.AB
£~,,::O)' LCos60"- fLOS60"
. 8,ccoS.3o·=o!JF= .s: C
213
4/18' I Redunda,,;t-slruclure .6 6~
80) 48) 81~AI)
s-nem f,tlrs J.Vh/~h c::aLt'se.5ror/cQ//y /r7de/e,..",,;nQK/&'/H r-"
I ) vi"
4/191 (a) All but "'18, 8;;; O.C; F/I(6) 8C .:1,.,6/ .as: Dh/y
(c) AI/ .our /--"G(ei) nOrJC
4/20 I j - 1'10. or ./0//7 Is r
(a) [,.,..,+3 = /3]? [2j=/Z]rn no. or 2-fOrc~_e,"ber!1. ~4/23IFor en c rr-e 1i"USS
50 IT7or e rn (!'rYlh~r$ rhonn<!:c~!i50r'y LMI =0/ 30A-SO(O.<f66)(1-I-2-f31-4)S'= 72.2 kN
J2~n70V~ oae rn~rnber conrJec//~o B.C. D. '" ~ hr~e, i,., BP PC DN CN c 0"./ , , ,¥- '- J J ) ,/ 0, /v, N£., EM ,n this c"..,jQJ-
(6) [""+3"/2] = [2j=IZ] .so .5"'ff,c/~nr rro . of' are. Seer} &D be c"'ro.
/71~"'" .6~rs but' r~d.://7d'ancj' '/J/rodac~d by 'I
exf~r/?a/ su~por/s. P/ac~ A or j:"" on A'~: AErO//4r Supporr. ) A£--x
(c) [rn + 3 = q] c- [2) -= 8] :So rn ar-e: rn~""'''er5 ,thon 72.2kN/?t'ces5C1Tj' 4/so S"""PporTs a~ redandonr.R~n7ovt!' AD or CB ono' p/ac~ support a./ Aor B Or? rollers.
(d) [,...,+3= /2J = [2i=IZJ so $.:/r,,"/c/~.nT no ..o.,c
,..,..,~rnbi!'rs) but red4'no'oncy /'a/rod.uc~cT b,-5u?por:fs. P/oc~ 8, 0'-' rol/er!> or
BC = 36J' kN re)
Jo;nt .v~=OJ DE/.,f2'-/ZO=O,1JE3/6'l.7k.V(r)
l.'F rO· BD =120 kN (e)J J
3)VC"> .£8=0
Dli-/3.S'9kA-i Er-y,:o So ::T)~~O
~ \y'c.g
k/;rhour d/QQ.D~4/.s ,FD ~'ov/9" /~I7.!J"'hen I-U' J •
CJ SJo,(},.-/f!H .$0 FJ) IS tc",s,,_ .f CJ ~O
CB= 3.99 /rN C.
.!.ry=o)· H6 s/» 2,.57°- /. 8 CO-5I,5"=-O
!-I(j ~.3. Fl9 !(N C
IF;."'o) HT+/. gSln J5°_3.ffc~526.57°= 0
DE =AE
Z"F"o ar-AEJ ;.~ = 72.2) AE" 144.3 kN (e)
EL "" ISO.a kN (r)
EF -ISo.O (0. (j'66)-/44.3(o.s)~o
EF= ;::02./ kN re)
GL ",so k"; rr)
o EF
EL
Z F = a. XL + So (a.s) f ,,-o(O,S)-ISo.O=O
!J) kL = /00.0 kN (r)
21'v1D== 0
BF(4) - 4(2) "0
BF= '2 kAl C
4/u; I z~=:o; £F(OC(7~.50'j-L(b.5;n30o)=0
CD:xJ/D" bJ)F
--EFC" 60' tL
.£F =- L/13 (C)
~§"0; DFCc's 30° -./.... =- 0
'[)F= ZL/r3 rc)Y,
I
I
I
c8/~~LI(j ~"y I
L
~':;, =0)' c,c CO.536~ - Lc.os 30"/13-L C05600=0
eF= 2L/13 re)
ZA4F z- o~· I. b 2 2 (3) -coi s&os30j
=0CZ; =/, ;'73 kA/ C
LMG=O}' fJC(3cOS30") + 2(3)-1.622 (6)= 0
Bco-/.436 kN C
4/28'1 fe-m 8;'5/12.6 kN. C4St5J= 12/13
~ B 2_4", Z.4,.,.,L~":,,:,._.2:4"""-'p
s-. 8> ! J:'::''O&l4ltZ4), ,(mko. 7!~ p J: ~or aG= 3 kN C'/_- 6
zM =0' G.c(~)·'(4) - 6(2)(2.4)=0 GF= 7.8 kN' C!}) 1:3 -'
EM =0' A8(4)- {,(z)(Z.4) =0 .4B=- 7ZhN TCl ) -' ------ ..
4/311 2Mc=0; IO(S)rIO(IO)-6-H~*O)
61-1 = 42.4 kN (T)
4/301
,I ~!"_'-
"-I \. ..lE,xJI
IJE»:
~
I /'T
I / IS"" / I
I / ISin I".JP»! I
~ /} kN C10 kN
lo",s
Kt:: ,S In IC'151(1'" SO DJ = 0
£N~::: 0)' 40 DE. + 4CJ(30)- 6g(60):tJDS = 72. fOl"s C------_._-_ ...
:z MI '" 0; D£(2.121) -/"'(3)==0
DE = 25: S klY' (C)
Zr;.=-O/ D1 (o.707)-IJ(0.707}==0
DI = 15' !;N re)
By ,'nrr€!CC/on e>!' jOin t Ew,-th :z~ ==0, ~
G
GH
ell
=0
cs ~5'0 ktv' (C)
fO{I") + /o{s) - C;.((sj=o
CH == 30 kN (e)CB
4/10 .:forct! A = 4.33 /-rAJ
llv1p=O; 4.3:,(~ J- 4(a)
'fCIw5 300(~)" 0
CI= 2,12 IpJ rt"1=O)' 4(~) f-HZ(o.. CoS300
)
-4.33{a) = 0
HI= 2.69 .k1V' T
4/.31 s .EMG-::O; ZOD!£. f- 1(2)
-/(ZO) - /(Z2) =0DE = Z t'6ns T
Ely' 0)' PG S/;., 4SO- 3 z: 0
D&·: 4-. Z1 tb"s T
z;; ;':0)' 1/6 - 2 - 4 21c ••s~ D
1-/6~5 10'15 C
4/3G I ,!Iv'! :::0' f?OO//Z)-A8 (i) 6 ::0G) I' v o :
48 = ffooi5 16 T
ZM =0' 1l00(6) -GF(~)6 .::08 J y5
6F=40ors C
1ar7t9=ico-ed):: 2//~
e 51n9~ '/~
floo 11,
f.F=o· B6cosCJ f-GFGt?sey )-AB t:.#StJ= 0
f!JG ::-AB -(!;F:: 4.ooff ~ C
ZMD=o/ gOO(6) -I-BF (/2)
- 8()D{5(~2) -40015(,*}=I3F= 8'00 Ib T
4/37
Z:M =0.E J
SO(J) -50(S-I-6) + S Fe =0
Fe = lOO kN (e)
..>O/eN >OkN
z/.// ::o· 1(4)-2. f3E (4)=0F) 5
13£= 1.6 7 kM CA f-------"~--'l>- - - ~
£
/ irA! I ( 5') - ~ Fe ( 4) ::o"=c z 3.33 kt/ C
. - - (4) L1::1=' -~.~.? '5 - / .• 7 (~) «o£F= 41<11/ T
4/~~ ZMA =0; 648 -4a (100) + z sreo) =0) 8=40 kN
80kN
z « For section)
:EF =0. FN/.f2' +40 -lOO x: 0'J )A" 100 ".1:1'1 _
4"1. : 2a FN = 8'4. i kN (7)
2aIfIIIL x
ZME
= 0; 40(2a)-&,4.Fh
- MN a = 0
B
MtJ=20kN(T)
/00 klo/
40 kN
For seciian thrOl.J:Jh GF !/LM, zr;=O 'Jives
resuit as" FN, soGM = 6'4. f kN (r)
4/40 jA/< /S 5fahco'(;,____"_ /nd~rerl"n/Y1ak
D 10' 10'
LAL s: O· ID CD - 2000(20)1.7 .I
+Zoo o (IOc05 45"):0
CD= 5'414 Ib TCD -,
I. 110D&t'" ", i: "",F '200016
G~ -~~--=~~ ~FG 45"/ 2000 IF.> £
/zOOO/b 2000 10
A
0,466 "'AI-~t~<,-,-,-------'- 3.94 /"-IV
/.731kN zr:;,=o; FC-j.94 -0.466 =0
FC= 4.41 kN C
FI<
wx2101 =0. 125 (30.) -/00 (cH' 3)
<? ) 2
-wx(Zc~R)=o2
WX = /29."1 kN (e)
ZM =0. 100 a.. + 12'1-"1 t?--13<i )
+ JQ ClB _ /25 (3,,-) =02
JQ -= $7.7 kN (c)
~4/43 :;;'10(=0.496, Cos •••.aO.6'6[j'
la "Iv'(I) L Me~0;
C.D(0.868)(4) - CD(0. 4'1';)(',)
-A8(O. 8'68)(6) --48(0.1-96)(/.$)
=0
CD: 3.00 48
ai) 2#1,,- DO,'
/0 (6) + AB (O.86i)(4)-A6{a.4~)(3)
- CD (0. Vor)(6)- Cl) (0. 416)(/.S)-0
60,0 +- I. "le$' AB ~ So "1.5'4-S./Ve si,.,« It,. "~"'./'jf. get AB •.3. 76' kN (c)
......- 4 whDle; .z~ -0.; N"0(24)t-ZOO(,,2)=36Aj _:{1~Fntln-7
Ay = '156 kN
~MA.O I"~""r~ EO=o ( ••/s» c,:.o)
0< • t..••-I:L ~ /0. 30D C40S 0( - a, '1"4/22 J
TZMt: =~. j;T-/;Z(2oo) =0
T= 400' kN
IMF = 0; 200 (ZO) - 100(_) rA,,(:z2}-956 (4) =0
Ax '" 10 I. I kA/ (eo ihQ rf:Jht),
1"MA
=0; ZOO(16)t-t:F(22)--f()o(2K)~0,
cF', 363.' KN (C)
1"F =0· 0·'184· ])':1-200 - '1S6-0!I J
,D,: •• 767. 'I 101 (c)
Sarnl"/e Pr<)/)/en-, 4/-1 !i='c ::: - 5Lk
e- -5L/6.-r o F = -(3t+-4k)
_CE 5 - -
It F = FcS( L)..,..-cB "'7 -3/+ 4tr
F. - r: .- c..•- -'cA.j
50 = fi2.(./ -./)Yz -
fF=-O' (- ~ T FeD)t f(- 3{·'3_F _ »» + (. 2L 1- 4J:;e)k- - J Z iI2 ~ .5 cA 72- - j s _.£yuilt~ Co~ffJ~.iet1t.s m Z'QrD e. .:Jt!.f- :=9
F z: L/12 ,L = 5L 16 F:c - LCD / ) C8 I'.J CA
---Irn,-------------------I~ ~ "4/45r" = no, o,r -'n~rrr o e r:« J c/> rr o 01" ,/'0,,-,1'5 ~ ~
/n-?f-6 = /S)=(3,/'=/5) 50 rru.s.s has Cl D~AD :// .. , r::>
DC =- P t, \ "<./....:. AE! , 'b5"'//lc/~n7" /70. 01' "....,~T77b~rs. TA""re are r'U/o
fefrC1/'~o'rO"'5 wh/~h Jhar~ ,"-h"" SO/77c bQSC lBr_f7:';3,,: .. h. '.,
H~ncc LJ ~ E ore //xed
Alfern QI/v~ pos,'//orJ
4/4(; I The sp<>.ce/r~S5 o6~y$ ?'-he ....,ec~SSQr.Y<:.or,,:7;"'0,,:; for -rra.6,'//j.- .s/nce rne ,...,,,,,,,,,6,,, •... 0/r>1t:n, hers r>?;, 12. q",q' .rh.r hu"..,.6er 0/ >01n15../.: 6 Obl'y fhe Meces SOry ConeT/j/on
n7 'f ~ % 3j Or 12 f- (, = 3(6.), /or ..fJa,t,/I/!y,
P"rfh~r /f /5 observet/ f-Aat ADcB IS a. r;9" d/ ,
fefrahedron Qnd That £130,t:' Qnq' BD,cC are a/so
r'!ll'd fsrrahedrvn5, n"IOffln.!1 rhe err rrr« ffruch"rerl3/d an q' srab/e .
.~ /l/Urr7ber 0/ ,/~/;"r5 JS .r= ~ so n->'f6 =3/:2/t/;n=/S. S"?c~ fhe /t3ure s),o'-""$ o"/y /3 rnf?J'rIbers
E rrror:e art!' I'1l1ce<;5Q,..y 7'b /;"sure S/a.6,II(y'
/nspl'c-It'on sho"Vs fh.::,/- paHe/ ~OGE needs a.c/r a qo rr a i/ SUpport' 46 /n orcTQr 10 ,.EJrevenf/Y}olton 0/ G fOIA./",ra' e: AISo/,c nt?6'ds ;l-heSupport of <'I h"/l'>Y]cer 0;: fo /JX /;'- In Spqce.
-.Jo,nfs £" ahd C /hen 6econ?e FIxed, q,.,d rhp
Iru55 /s r;'gl'd. (ofher poss;6JI/,t?s f2.>vsr for
c.rea//",~ src<6;/,'(y ay <:::Idd';"'3 7'''''''0 n? prn;' e rs)
I-Or rr?'55 a5 Cl <-vhd/t>
«, A z: 0 c;; •....e s DC='P-<-'vIIC ~I
.!~.: 0 <t £Ij =0 5'VC.5 ~.:p
!=or ".",r /3./)£
rMp£ " 0./ tlZZ h - 8< h::: D
B",,=.iJl"" P
y
bA
E3 z: /2.<1S- Ai
ex- =1145/12 = !?5'0 Ai
.= ~ (-1.2.!:'-O.4j-l-O.9k) F :: r; (-/.2i .,.O.4:.;-o.9,(J/,352 - - I AF I.SSZ - :: -
~B = 1.~B2 (-0.31' +1.4!;),. E=2.25; For jo/"tA,Z!,,=o
gives (I :8 (-0.3)I' 2;:; (-/.2;,11: -;-(2.2 + ~B (/.4)f'~(O:9).IK=O, '?32 I.5S2 ~ 1.432 I.S52. '/'--
s.i-; <1 Jet -:;8 ~ -Z.b!.!.... kl'/,.....!, ~363 .1,1'1
Fo •..ces act/n,J on B 4re
E;/i =11~5(-O.9j-O.4j-0.5!f).F = -L (-O.'h+0.4/-0.SI<).v ,-8" r.ro s - _ -
f = ~ (-O a . . ) F.. - C (0'1' . '_)60 1./05 "1. -0.4J. +O.S!; ;-BC -1./05 - . .! fO.4.1" 0.5:5
ra. J";nt B, Zf =0 :J"es(-I.jP I.S'C 03-Z.6il)i +(~ +-f- -1.4~)!! 1-0j=0
/. /05 - 7:7iT f . 1. ..,32. - 1.105 /./05 1,432 -
Solvc (JBt P = 1.620 kN, C ~ - I. 275 kl'/
{E = P = /. 6 Z 0 kN'
F-.-'lE
211{ = 01 400 (1.1) - 8(0, 51/iT=0
~ M,: OJ' 600(200) - 2. 8;400)"1 5
-_18(300) =05
8:: 250 AI
IF =0' Av= 250(4;5) = 200 Ai)( I .---
Lr-=O' A {-.1(Z50)-60C><'U.y I Y 5
A s: 4:TO Ivl
y
4/5~1200 /b -./1
ic=----l~ ---I1 !
2M·::.O~ 6(40c.11'1>30")-200(12);0
13:: 69.3 Ib
.'JI
I,.[M =0· C(4<J '-'>S300)-2CO(40)=08 )
c= 2311b~ ..1_d ~~ ..
200 /ij : !
c *1/'j;; i40", :
.ex - 2 31 CgS 30>"::0
L5x= Zoo 11>
By I- 2.3 1 .s ;;,30·-2Dl'J' :; o
"'!/ f4. 5- u.!3 :::12{;cf~- i1:S t : 217 /6/ /30' : I_.-- - '-dE-- 8 --1-
II -c ..
1-4
-/5
-,-g--'I-~---------------------II"476~ Fra. me Q S Q. whi1/~; -!~ !".,r-- -. '1rl-J l../../A=O/ G(8)-9{.f)-J3.:y&- .• t=>
I B i
(C IcB""" ~m p S'rYl Ay:: /0 kill
r ..8"Ay' -: - G;
(.,.----'7i. ~Nf
ISO N
Hqnd/ej 2Mc =0; 150(110)-8(30) =0, B= SS-a AI
J",o-v; 2. MA =0; SSo((ro)-P(30)=O, p= 1467 IV
l1v1 =0 16 - 1(6)= 0c ) \{By = O.7S 11'''/
fF..=o; C)L1-0.75-6::: 0
Cx:=-.s: 2§ kJv
4/5"9.1
A
~Q A i<..
!2?..k- ..!<. """'i
(I-
'-y
Bt~X/ /uol
'y=1 ;oJoo
He-nolle.' Z-"1,::: 0)' 30 t? -If 0{/50 ) ~ 0,
Jt"W' L~A~O' 20Q-GO('1t7tJ) =0,,",') )
4/631 y,I
'- -- 1& C t<E--£/00 Ai -, 80 ""I~)"I
~
/~m'" 1201-')011""
.. «-- ~ov
A,x ~.D
Ay DI )<
y 1
Q~ 2700 .v01" Q = 2.71-0/
4/.r::~,o')I (;('------"" 0.5 m JP <;" o M P.:..=J I, \ ,========:::::)J, 4 Iv1 =- ) ::: O. 5J./,\ ..;"./
tv1 I P
V-= 2(45'0)
=900 h.- .-O:~5r boo.:"""
YYI. A
, p [MA=O; 900 ((}.05)-: Pb
~ P = 45. :: 4-5 ~;SO Aio 0.3
M= 0.5"45 =0.5(150)-= 75,A/,m6
;vJ IS q"ecr,~.s.d
rr/an..9/e:2 () C: 70 N2A4
A;: 0,· "oC - 140 10D = 0,
8ar..!. ;'v!'£/ D)' 200.E - 70 (~)120 = 0; £~ 2$ Z. AI
1~,:<:=o, D'iCr25:.Z-70(3/5j=O, Dx:/6.f?A!
f ~ = OJ' ~ - 70(4h)-:~.l}: SCD N
D=)f Tly.4-;-42.·o: f'h;.l?2.f-- 5<;.02 ~ 5l?5 Ai
RA(~)= Ma=- /P(?~(s)
~:0300o/8 z:
/2 f- ~25:: /000
{3 .ea = 375"" /6
,Z5 I/'
p= f~ = 900- 300 = SOO N
Py:::. MA= ~OO(I) - 300(2)
Zoo.Y = -;;-- ::: o.~ f7I7-JOO
~- .....
~ 1 I 150N/50 -n,
i/2Q.O y1-"I t'\.1 P',-----
30"'1 Mo = 250 CO.s/5°(O, 2(0) - eso S'-n /S()(O,O.3o)O ':: 4[?,30 - I. '14 z: 46.4 I,.i·m
d"" 4so - &2,S ~S' 20· 2 .39/.~ .••.••
}.f=Fd== 200 (a391)
~ 71',.3 N, h1
2/]'3 I
~
Ol \.
4~00o 16..30"
,-18': M.4=40;t)o0.51>'1300(60sm300+f8)
'-i'~ +40,0 00 cos 30°(00 '-1)530· ~e)r .
:::; 106(0,960 +/.523)0- 2.4fJ(/o') 16-.It
3?~J A_{10" /
CY'31_~v / ' ,so 10
/ I'I"~ / 174 S/ ,C IZ"
7 _ 14. frJ SIn et. = -.L O. S66S,n at. - SIn I Z()" 1 14.8'0
= 0,110eX.::21. r flO
~ =- reo - (2'1, '#1+'10) = 65". fI~
Mo"'-SO(I"f.6'd)= 7'10/h-,,,,
/ ,o - T66"---
~~3~ rG"',;Lph/c,,;!y: E':f v'a.r'-J"on J- pr'nc/plethi!! ;-~sulia>1t' c>f the Lw", ~rc~.> "'/Jot/'4.{,J iJm'J,(:Jh 4 .R
in c>,..der Co f''''''d(Jce/~- - -'7P=S2 kN (4;>/"""-")
Zero ",o",ent. / \ /
/ A.'iL So kN t-'M-\I,/:f-t--+--+-~
A / s= 6ra./ca//J.' Z ~ = 0;
So (2) + p~ (I) - p-E. __3~ -.fT3'
p 2100 ~ -= .:fZS" kN'1- 2
~O
2/37 cl. = /0 +- It) cd S ;'0" .: / ~ 66 1-".
,- --X
r;!V~n: 60(la.6{,)-IOp = 0
)
F= 112,0IIJ
Rx= 112.0-6oc:0530''= 60.0 ~
,fly:- 6051;'30": 30 /6
/? -= Y.5o·;-60 ' = 6 7. I //:,
y,
r~=o;JO(9) - U :0, C..,13SIA
Iv! = ZN70
~1a. I" 8I 1
4/b~Jy:
,, A
00------6
Hand/e .. ~M:: o PI; = (A-8),< Jo I .50. ~P=o' Q=-A-8..la...". .y I
Ph:: Q.:<.Q=P.l!....•.
4/67 £~=:o> 30 /'1.lliY:J.ZS) - :'-0 -/00
i- E(0 ..55)"0
",-" /39.0 V
100 N.,.",
so ~:;;~-- -;- ~",'\i jJ r
, Jo('.II) '" ,:('I'"
I 30c)"., rn : 25.:Jf'VJm 1
.Er=:;' .F - 30(1.11) - 13",:) =0Y )J;:.=. 433.31\..'
( ..../oft! correcf c//;-ecr~"an c;./ ,
reacf,vc- 1>""•. "...,""tp"t $~f}':.)
p
I..~
~11!>'" DE) LMF:::O)'
5:6(24) -b~D(41)- 400 (/g+/5) z: 0
;: = 16!j() It, ';,,..s;.•nAIj .. ,__
From i7:>'7J5 ~s q wl,,'/,.~= ifJ'oo) = 400 10 =. ';
Ft ~D D::..!la ,,!§ l'IcC) = 600 1..6rarn .c.} X / Z .Y l Z f' ,
fFf----§= 1Co to
iF;.=Q)·2;Y=o;
3",8)<=D,,=sP
27 8,:22pa t-P - --p =: 0 <v S.uy .s I J
4E.. -4(3bpl=o E=H'p=7.2Ps / ) ~ _LIV~=O;
s,;'" JO·. 0,173'
Cc. 10' ~ O. 9¥+r
/ So [100 (0. 9S+8) - 20 (0.17~)]
-20(0.1736)"" ;0
A ~ 4103 11/
Fo •..j ••",,;;[M. =: 0; (,0 C - z o (4103) = 0 I C = 13'f IV
ZOOtv'--<----
DlnJt:nJlon5 150/n n?//I/I?7~t&-s
fl~v:v~" yloo" 100 100
250~---'" ~~~~r==f;Dx
A cy Yy
4/731 '10 /6
~,,:
AY _- {- - ~'l u=: --01'
I:; , -: - ~l--I "I I I' I
'----~~'-----,~2CO Ih20" /0" lp,
j Ih i ~ Ih Dy f F ~ Q/0 10" If )
200 Ib . 1 S" L5 2IvlJ3~Cl
C ~iEy
IMA::O;' 3ozy- 90(Zo)-ZOO(10)=0
D:: /e a r«.Y
Ayf-90-/60 ccO
AJ =- 70/b
1.1::;"=O,I"1",:::200/b
8,,= ]~.D 16
ZJO(:O) f-/OC-70(zo)=O
C CC' 4D Ib
"11J::0; ~f4o-70-9t:Fa
B'y= /20 16
!3=r/zoo"{;;o'= 233/6
Z~::O)' 20oe,(- 25'0 (2DO) ::0
Ex" 250 AI
2;)-.~=0 A :: 250;0) )L __ ._
Me...",bl!Y' sDJ'
£~= 0)' 300Ey - 200('50)-2$'0(200)=0
Ey=~Ai
l'Fy:::O; IJy =~
[Fv.:::Oj· D)(.'ZDO-ZSO=O)D)(=450/v'
.50
/=,,,,,..,,, FB()s Dr ?~//l!YS8\L=40011/
C,,= G=loDN
Z/'t(z.;= 0)' "()O('OD) -16)0(200)
-Av (.3Do) =0
Ay =:(;7 Ivl
Ac: ilv1A = oJ'o. 313
y- 0, g(2'14j= 0
8 =: 7i?5 AiY
zr:;,=o) B,,-/47.2-662. =0
/Jx= ,fO'l ;.)
_4:1 791 ~'''-,n,~eC;; - ;; F:: my c $:I (fI, ~/) = 4pa. 5' AI
C = 3 C A 0..1 1x 4 s » :y 4~)l.
0,4 LiV''A=O; tCy(O,7)+ry(O,/)
+ o.~F -6.4F:: °C :: 0.IF(4'1z.S-)= 49,05(11y 2,5
Cy= 2~.5N
c:= } (71.5);; .;,71.9 AI
_f177JsIIL __ -.x:
Ay
(I)f MA'" 0; C (0.325) - S-O = 0, C'" 153, I? N
L F '" O. Ax = o, L F '"o. A = /S3. g AIx ~ ---) J -' -:5"11-------
aais=;». B :153.,f;o,l· LM =0. 153,g(zoo)-]}(lso)=o,/ 'f -' '/ ,8)
ZF :0· Bx = 205;/ Nx I -'-"'--- _
. D,; .~(3)--'c>-1 1- i~', 131 I I=t /8 ,•.---"'---I_~__ 6~'-'-"ii
.7)= 205. I AI
D
10
fMA~O) 20(3)-..;v(6)- c;;;(d;)=o." Y'3
~1 -= 5& /1>
..E'y'= 5v3 .: = ..5 /6V3
s;", /S°.:.- 0, :ZS~8
Cos 15" = O. '165'1
t/V1n=O; 180{f) r40(:3) -6E =0.E;: 53. fl 16
25 0 0 ZJ +.5.3 .1!- !fi''' -"," = 0
J) s: 166.2 11,
[IV/;:" °1.53.fi( 3) - 20(1.5)
- rh = 0
wh~re. h = L{55eLf' z: 2. 7i? .:It·
50 T= 47.2 If,
i53. El 16
For iJC; 6" =6..1 6••." IS·
A" =0.267'1 By
Fe r- AB" XM;l = Oj
Zoo (250) - By (100)(0.256'8)
-0.2{'79 l} (100)(0,965'1)=0
B,:/ = 966 N
Bx = 0.2679 (96",) = 25'1 N
L~ = 0) AI( - 251- zoo (0. 25tft) =0
Ax = .3/ I N
Z F = o. -'1'} +200 (0. '''59) - 9G6 =0'j 1
Ay = 773 N
K • C = B ~ '166 N:; )
r"" en t;re sJstenr
LF=o. 2P= 12.!f '
+ (40+2(3S))('UI)(IO-3)
p= 6.54 kill
4/6'2
By1.tv18=O)· 45(14)-~ 4A;t. = £), AX = 157,5/6
A s:A}(.Vlr To'l'6i =/S7.5 V, f- 0.35.352. = 167.116
~J--:"=O~ 8x f-45"(lh)-/57.6-:(), t5x=11Z.5"lo
2Fy=O)· 8y f- 45(0·'112g) - O.3!}3S(/.51.:5)=~> ay"" 13.3/b
I--_~-----A-D-G-)-·-'[-:-M-A
-: -0-)·-1-0-0-(-4-0-.5-/-..,-3-0--:')----1 /3 = /142.5 Z + ITI z =: _1_4_3_.1_~
-T(32COS 30°):= 0T= 72.2 Ib
EM8-:::C/ 72.2 (20 c..53~1-M:'0 4/6'71IV/= /2S() /.tJ~//7.____ ..__._._.___ r---X,,
'}I
4/6'4 C
~I \
: \ 700 rhr'l1,e1 \
1 \1 \ BI, &0·
AyAll 1"'-'/£ ~o)· Ay (257) - 24(250,. '?(,H 257)
=u
For wh ""j a.IS.""bly
f M = O· 900 A -6.54 (ZSo)oS J
+ 3~('t.YJ)(lo-~(180)=0
A = 1.75. kN
(r.3i)('O-3)k tJ ', I :
~/6"0 ~ 900 mm----;_..."P ,"''' 1 ,
, I ';----- liSt> ••"'--.--.~
BC )'
A'j
A XM =0. 600 (t>.Z) +1200 (0.zJ-Cy(O.2):.O8Cj 8 /
Cj
:. 11100 AIC = ;r-; /)-_0-0--=-2-+-/C-g-O-O~-i = Z 16 0 N
4/nlSOOlb} 3' 3' z,t:.4,7irlrAy
~L~~Y. t-3' 5' /.=.~
I)' Z~=O) U~O())- 4£x.= 0,L F" =0, Ax= 100010
" LN~=O)· .5"oo(rI) +- ~8(2)-1-C(5);OJ SolvC if S~I.5 '"' 8= -1-4444 16L F = C1). .Le -I-/ao o - ";8:;0
y S S C = f 2 7 7 6' 16
2':; "0/ -1 (2 778) f- Ay - i (4<N4) - 5"00 ,. 0) Ay= 18'33 /6
A.: V/oooz r- ;.5'3.32 = 2085' /~
c
Ax~--~----~------------------------1
/ ,,'. 30"
___.~_lE A'y= 44. 2 kA/
rr+r-r r- -------(-"2. _'1
A= 6.57 f 44.2 :: 44.7 JrN
Fr#ll')1e qS a. whole
LM4=O; O.4E-O.6(600)=O, ~z900
ZF.c=o/ Ax= 600 Nj ~r=O. A =10011/f , J
600N
C':J CD,. ~MI> =0
bOO (0. 4)- ex (o.z)=o
ex = IZoo N
_...--""'r-- 0.3 rrr
'7
F ~~:~---;..---.-.~
f::'I--y
B'--.
6°(2) +90 + 48 -100(/) - /80(4.5)=0f28 = /83.8 /sAX f 60/12 -/gJ.8~o) A,,=141.4//'
A -v eo -lOO - GO/v'Z =0, Ay=322.4/6y --._----_ .._-V Z -2A= 141.4 -(-322.4 =~~2_!!,
>Iv' =0'- 'c )2Fy =:0)Z~=o;
[F=o'y ) LMH= 0)' '1-'1-~(3t>OC) - ]'1. 24(2500)
- Z F COS 15''(N)DD) :::0
F-"/3/.!?IrAl
2~:: 0)' 2H.•.- 2(131.1) LOS "1S"~ 0
!-{= 73.2 kAl
IIft:o)' 21-), r9-9.R-3'1.24-2{13I.F)=oVz
I-Iy; 65·1 KIJ
Max. Cl. accu rcs /or Ay " m.-x.
which occurs for B=o.
AC; A ,= Z ;fA!, --B
Xt; 1:...!!.!:!.
EX~"'kl\l
ce s (!J =
(J, 09. -:-1~7!"):. f eo 5 (),,::.1:1.2.5' 13 I t:J
()!.l2 = 2.. S,n" ~ ,£/,75 ::T' s:
~ ".~JO 0 AI
,c,orn AB. Z'1v12""0
8/V~5 T~ 600_lV
- - - ,(
Ill" ol:: '/3J SJ" 0(: 1,f,D, CDSet = 3/.tiO
W,= /,5(lI.11IJ= /4.72 ktJ
Wz = 2 (9.il) = /'7.62 kN
t~=o) :~P-{4.72-19.~2=D
Pc: 3'; Z i<IJ
D./l~-:'~) 372 (f!yy~)-37.21fi)(2.25)
- ..~ (3, o f O.7S' z: 0",/Q '/
f2 0: P(, 7 klJ
[F'!.o·E-5°7/~ 372(5" rY- ) X- r • /1/(> <>», (13):: U
Kx.= 33,2 IfA)
t-y:= c, EY T 37. Z (J2/J3) - 5'l. 7 (3!IID) = 0
Sc22.3kJ>J
40.0/-",\/
fb ,,,SptCf,p.,
CX= 40c:.~ <: /00 NI Dy=Ej= 2C!'..r:!
'X-r p/{:II?~)' fA.~=(); 200 (Ge1o)-JooB}.C=O
Bx=~IF;. =0)' Ax= 600-400=ZDe1;.
y- Z p/QI'/e " ;[~= oJ' 100(3/J0) - Joo By ~ ()
By =0 !!!.:!.!!~'J;=OJ' Ay!-loo-30o=o
~= 2cCJA/
,I
I ,
= ~ - - 3.03---
Sin 24,5° = 0.4147, Cos 21.5°= 0.9100
.)/'7 20.5°~ 0.35(2) c.o520.5D=o.93{,7
f"'10=o)' 2C'; 000 (0.'1100)4'6
- 20,000(0.1117)06)
- 0)( (0.9367)(299) -Se (a.3502)(0',91)=0
CO'([1v/ ) =0' 4Dy, -4(2)~O) f) ~ 2k~j !/ (x" 2lruJ Cl) x. -- --
Dy, {.lMc)/"o; 3Dy-4D,,::'O, Dy=:}Di' f/(./~Cl
4(r?JPi' ~••..-......,1
Dy84/lInc.~ 0 f fi~s 4y,';'$,otl& ""pl?E8' £' = 13 :; / /rAJ} ., r. - ---AC) A.z.=C;= ~
c, A =c.v~:t(O.5)=o.67k/\/y J 3 -----
CO)' Dy~~N
D~=~
.-se" /8,47016
fi-lV/eYHbcrADF; fFi,:o 8,v-e.$
1~-:." "(hv1 ) = 0 tr
D xL;Y =0" -s- ~kN
FI'#", 00. 8'y~Dy =~~
£'11",/ ,f A8[ ,~ ScTt.5f"~ OS d t~,ck·
~A)<= 1.2S-kAJ
Ay ~1.25 kAt
~F=·O; 2P/rz -c s- oC:::f'v2
5co-ne. 0>-1 q.l/ ..2/".:r~~
cM ~o. 4o(zo)·f/iO(S)~ )II II S", ~ s,.,
- IS /j -0v,,,x-- ...J
.8 '" 73.3 kNt60 kN E
r- ,~HI" I", BH, I '
:ZF=o· 0.7078J1-73.3+40=o'J )81-1=47./ kN (C)
ZM[j =0; 1-11(S)- 40 cs ) = 0
I-II ~40 kN (T)
Z;=;' =0; ec - 40 + 47. / (0.707) = 0
t3c= '.7 kN (c)
Joint C; CD=8C ='.7 kN (c)
B + BC
173.3 kN40 kN
11 G· Z-F =0. GoD=0J j )
Theh in ."cc<,,:ss/on
4nd ~'H EG =0J -JF,f.{ = 0
JJoin/:s 11 J a"ve h ••xt Ik=O JK zO./ J ) 0
~k = GC = CA - 10/,!3' icN (C)
KH,.. HD =DB '= 10/-.13' XN (e)
'Vit/, jo"" ifGI=oHJ =0
,For j 0 ,on t 1<.)
;[F =0 'J"v~s
ZMD=0.l· 91)0(30) -IO£x=O
i£x= Z7""/D;~ ~c;.=O; DC=270CI/' C
Hi: ~=-",. 15=90;::> 1-'>
/9' /0; +900 If,
/ L c : ~900 It,oJ01rJr =• ~ IEF
2700 /6 '" 45"~£c.
u:y=o)' t=C/f2 -900 = z>t::c. :; 9':>0rz It,
ZF;. =0)' J.;:-F f 9{/017_ 2700=0rz
VOI;' f F)' FG= E~ FC=O £,c-:: 19"0 16 r:
~{='b==8=(7=J~=:~_~A 2A.1.4=Oj·/O::~ ~-;-:z-~:::2700 10' 10' L _If; T
. 'loo III
\ L=2oro~s
fa
ex =- t.:u-tl.!:!. = 14.04"40
C 0$,,( :::o. 97<J?/
LMF =0/ 40 £:~ i- 20(20 ~ 40 1-GO) - 40(/20) =0,
E:0= 60 f-ons T-------2M,/:' 0; DF (0. '1701)(40) - DF(O. 2425)(20) I- 20(20 1-40)
- 4.0(160) = 0
4//0?1 ~:. EF
1-4-!-/O-C-.-r-If.-U-J-1-oi-=--J::-2-=-f-4.-0-"f-O-----o<---~---p-)-~-8-"----;!y ~: b \_" ..J -' =::. :' ' 30· L_.!- ~'C·:_.h \
cos"" 0 0,970/ 32" 12" .,- ,', A
~-- ----~--:-"'~===:::I! A 30· D /60' ;b '':''f::x£ r }O~~t-()8r-> ;I- : '-"0." mg b -r ,Ay
it B' Y,-54" I},.... I ' •.. £: / 2YY1fJ/(:;
-r" ~/ -+: JOint I\J-- 30·1If-17.3Z=25,32." £D/~' 2>··X'2of3jz = 17.32" !" jU
EA
lid) [lYI +3 =-15]<[2j=I,] So ,nsul?>c,enl'rncrnber:5
/. //}Irodvce '77ern6er FE ('or Se) Or
2 In/roduce .rnel'T7ber E 8 or GH
4;~2Jr-- -x:JWI~J"int r
ZF~O'y )
40 - t3 $/n 6eJ°(o. 'j20):'O
/3 = 14-4. 3 r;A.I' - fi1, 3 G,,5 60"=0
A)(= 7;:.2 ;J
Ay - 141, 3 51'760'" = 0
~~ll~rLCD'
)i. Mc~ a} D(4!s)(o, 320)- 4():; D
Do/56.ZN
ZF=- o L\C,,-IS6.Z(4/s) = 0)( }
ex= 125 ""-
2,~;-~' CY-156.l(3/S)" 0
C.Y ~ 93,11 1'/
Joint: L
IIv1£.:' 0)' (54 i ZS.3z) tJ - :;-4(/ 00) " 0
3= 6'?/ 16
IM =0' 0.970IP(20)- 68./(I7..J2)=CA )
p= 60.816---- .. --.
4/1061 I
l~=o; A' "t:= 130e IV" ---
,1I; ••Of 1(FE «oe) - (,0 = 0
l'~.O; ;(r':-/)E):O
DE '" rE ,. 150/4 kN
flS'O/4 KN r,.c:;..:o. FL - ~ /S'o ~O FL ~ 30 JcN, oS 1 )
FL
rG jkNDL Z F., u 0; DL - ~ !£!!. = 0 DL '" 30 IW
-' oS 4 I
CD
3~~"
GL CL
~f,;=OJ (CL +t;L)f -30-30=0
Z-F : 0, (CL - (J'-) -j: = 0j I
GL 0: 15'0 = 37.5 kN (T)4
fA//=o n->q(2bco5JO')=£F(!!:)A ) ~ <'
EF= 2m3/;;,[j::: z: 0' A ::2mo//3
)l .J X J,
11; = 0/ Ay = rn,
IF~.-;O)' EAc0530"= EJc"~30EA~ EF z: 21?19/t0 c
4//10 r _""O--<.~I"''''__ rs» IV
~
F 0',) "S__• •. •• '. ---====:=::::~'"-,/ r.
J1""MA ~~. 40 F as s 0( = 120/rs»)
, I'M I'" F r cos*< = 4S0 IV
I Mo - 0i +SO (0.0175) gM"ZIlSII/·".
1:M es 0; 57. 5 (/0-3) ~
= 7. J'J'
R ~ /37.0 N
ISo",
ISO IV
5coop; LI'v~o 0 :JIves ;::; = 2~ 5'h-,v'
L!f:::o -=;:::Z!;T,:.7klo...l
25=0 Ey =5/.0 kIJ
For E8AI
..:;7.0 irA!
5 DISTRIBUTED FORCES
••.- ",00./ lo-/~,
= ~OP!l ' 11,-1;' .
Z/1f yI
lOO - I/; ,...6SCf/-/q,.,,' I S -fo~9'" r-/00 16 W c"c/e a" 8
-- \60" 60"/ So d =A8 .::.20""'·
8 /
:--- /~~_~: ~/ )L
/001.1,
A-1 ~ 100 (20)" 2000 Ih-/h.
CoorJ/ncd~5 <>/ Aare -6'.66/~1 -5';7,,---------.
A
I~ M=r,q; I?()o -= a. ()e In/~"f}O
(lY- qI =- ~O J'n joy1
2/431 M-= F~, F=
2/441 70P::: 300(12)
p:: .s(, f kN'
B = 40 ok IV') A = fjx.J
40(4 +4) = S ~Xj B.• *64 k.N
8 .• /(64]2 -i- (40)2' = 75.5" ~N
2::~~I U" 24 (m) - 929 ,y.~
'T 17"''''/2"" ••
2.4 kN 2.4 kN
21St) I p
2.0:- 200(t)./6)- O.30PJ
p;: 4-oN
?= 1-<7.j '"
5/7 I ~:.kb2.)
Y\ x.=k:i ,
:jJJt(1.
0,
dV= ITy 2dt whUl! y=.;; i
'2. 'Z.=rrLcdc
h2",
v= 77;:JZd2 :0
)'/2
So X = if = - ~ = _ 60 (/@) __ 40fi -(2'(3rr/4) - rr
x-I
= -/2.7",,,,
z
JdV =/:r(a. 1_ z 2 t- ca,! tt ~z ~d z
o 3
= IT[a."lz -: f-~(z(aL-z21'als/;'-'f)]~TTa.3[-~. ff]o
JzqJ/ //t.(Z= == - __/</Y 2("tr3lT)
---~ == 21Ta3(1--i)=1Ta."z jrr/ZJd"q z: 2ffC/. ~ (1- c o 5 &)0'6' ::.27TCl2(;-_ I)
D
Z =: fidA -::: «../dA JT-2
S4h7~ •• S forCd""';D I.~ Cd,., e
"5/2 ii I Ja"?e T'••d/(;I /
C/i-CI..I/qr area, So
20
yIII
Tna"1.5ie: A = -~ CLz
.At = a;3A = --'--71'0... 'Z.
4-
x z: 44.1317c.
:;;
3(77-2)---------
5/371
LAy< _Y= ---
~A/41Z
9fT
5/331 A :;;~(4-0)(("o):!ZOOYY>n1zI 2
Y, ,""oM. ,Ij = 30 + J... (60):;; SO rn""-<to'r' I 3 z\\ A
2= i (~O)(40) z: (,oo rY'Y>1
~
/ \\ Yz = ; (30) -: 20 WtY>'
30 ----, _ ZAy 1200(50) f~d6(ZD)2. I y::._o ----~-1- mM. ZA'" - 1200 rbOO
o 60 )
3/391y: a
II
Cl'I
i
v For ,?uori<:>r - o;'-udprI if7n.-a
DICLX = \I:;; a. - 1!!:: :: 4..(/- :t)
c..7c. 3 rr .377
~---. - - ~= 4-0 1'>'1,...-,
:;;~ 10-3TT3 4-TT
Hole;
A = .: (10)(6) s: ...Jo/n,'I 2
Y = ..i-(G.):;; 2 /~., 3 2
A2=-rr(/2)=-3,14,rJ.
Yz = .J'I1.
JOx 2 ~ 3, !47o.! s: /, ~f? /n.30 - 3,14
y = X 6y symmetry
y;:;: lAyc.LA ) Y=
=rTf,zo/'ro) (- i- [1&'O]['1oJ)(- Jj)
1'I'(/;?o/- i (/~O)('iO) b m 6",- 2. iA 2(36) - 3.'0(12.57)
1.14= G.54 rn rn y= = = mZA 3~-/2.57
S/41 IA, f'} IA"!;; , X='I= ZAi
- :'7~ ;' -··~i LA59'-fare ,-~:~) 7GTna",.5/C -18 6 = i7.7 s: 4, Z9 117.
fj c,;'-cle -Zll.3) 2.55 i - 72 II I
To/a!:; 17.7 7G
= 1'9 a(/2) + Tlr(- 2r/n) S/47 1
;:;3 a..tTTr
2 2.2 0 0 ,300 0 () 660.3---1- ---I---I-._--+---+--_..J ---+------
2.5 63.7 0 450 /59.2 0 1125
t~~~~~II~-------------------------------------J/~O~f~a~I.:Sl-?~.9~L--~-----L~~1-/:~5~~~2~47Z~~OJL/~7:?5~
V- I 2/_ - ( .1I - 31Tr '7) hi= h/4 For (}) X = 4 /S'?J= 63.66 rw rrt
18&- 3TT
/V:=-.!..1T(£.)2h h-=.2.+_'(_J,\ - ~mi- /59·2h 2 h 2. 2..3 "). 2") Z 2 4 21 X = ;t.Y¥1 s: ~ = 17. '1 n>W1
1/ 1-
2
('1 - = 5hjg Y= !.•.~ ~ 420"-'" TI =LVh 77r2/'h 7Tr2hsh Z= LmZ _ 1735_if z: = J;;j - 24 T 2rn - ~-LV ------=..!.!. h
TT r"l-h _ TTrLI, 56-:r 24
5/4zl FbrtS;'e,~ A It Ah
..•", In hi '2. w7m mm3
~0
/o» 40 800 IS 12 000
rh ~ 10,:40 800 40 320001 z ® /0.,'/20 2400 70 /6 g 000
@ IO,~ /':;0 /6 o o s 8000
·1 ~/S-' 3600 220 000
jj = L Ai, = 220 000= 39.3 mm
LA S 600
a·2. z--2r::o a=ZrZ ) ---
1,.:;'/441 L - /501- 0707[ - 4 I/.3 mm
X" L.L;;. _ 0+ r e o ts»)Z L " ---~i;i. .3 • -~ 3I. / """
SOn: (go) t- 0--411. 3--- = !!.JL '7"'In
8011 (2 (fo)/7,) + 0-----.------ ..- ..- = 3/, / mm
41/.3
- ZL-y= __ If '"
ZL
Z~?.Lz. =LL
i- r-'?/
S/46 1 ~ron? .Drob. 5/23 .6_ J :y JYn?n?efrjl
~ =: y s: r/e for upper 5ph~r;cQ/ .5echo/7
wlfh area A = 4:r~ /1"r2-
For b<l51!!', 5(= 4rhfT y==o A= 1/r2
J 1 zTJ,Q5 X = .tAl(: z: n-r'1(r/2) +(11'r2/2)(4rhff)
.!...q 17r'l+ ..!.n-rZ =0.475r2 ---
trr Y rh) +- (11',-0/2)(0)-7r2+ ...!...~r2 == r/3
2 --
~ = iTTf.30/(3S) = 49 490 i'>'I""~
~~--iT7(20/'(2.:Y) =-;5 ?of r>1W1~
)(: :: _ 4(ao)=. _ 12,73 mm~"'" GI 377
--- ~ 4!U»)X = - __ :: - ~+9 h'>1-Y1
czr 3FT .
~ z: 17.5 ••••"'" ~ =-iJIO+35)=22,5"''''''ILn.;) 35"",,,,,, cr I a
€]X= .;?Vx" z: (~"I4g't))(-/2,73) -(/5 70g)(- g.4'1)
.1I LV 4946'0 - /$701/20 __ -""'" = -14, 71 ".,....,
t.en;]l}, 25mm Z= lVlc.:: (494f10)(17.5)-(1570i)(2Z,5)
LV 4'14110-/:1'70!
r
I - rr/c;Yl..9/C I Z = ro cl, .3: S~YH/& /rc/e
1?1f1,S5 i Y Z I'YI~1-r9 rn rn I".,I'?" •.•.••.•.•Port
/ 4.2 0 lOO 0 420o o
47.2. ...,..,.,
200.b mY>?
5/491Pa,.t W /6
w,[ W-X; ,Y y.
In. In. . 16-/n. 16-/0.
0 241fT 0 /20
/.3.5 b /66.2 7.1. 'iD;cvlar- It-be
L3r?1C~ga~~
srr/2.3145 a 405 0
~-71 . 2 I"f 3. 9
Y .2Wy IY3.9 ." LW = 73,;2 = 2.66 In.
_ ZW;"X= -=lw'
73.02
~-71. 2 .-- =7.82/;1.73.02 1
v_tmi< 27"" y- -729/' - --" --. ,,347.4 "'m) = _ =-90.5' mm.l,..., j.tJb s.o«
5'/531V.f~ verncal 5rr/'ps
A 2Xc > X:) /n. A .3 . '!
..5fnp It? In. Xc J 111· AYe) I".0-2 /4.2 / 3.5' 14.Z 49,72-4 /6.8' 3 4.2 50.4 70.6
4-~ 17. f, 5' 4.4 rs.o 77.46-8' /4.4 7 5.6 100. £I. 1l0. G
8'-/0 /f.6 9 6.7 104.4 77.7
10-12 'l.G /1 7.r? I 105'.6 73.0 j
12.-/4- e.s 13 8'.'1 //4.4 7 s. 3 I14 -16 7.2 15 10.2 I /08'.0 i 73.4I
Tohls 100.2 685.8 580.7
x;= tAxc = ~= 6. I? In. 5= iAyc= S80.7-- /00. 2 = .5 8 /1'}.L.<:l 100.2 --- ) LA
~ lOA"£' a-,O( A~OI~ A'i Alm~ 1'o'I1T! I ".,....,:lo ITJ'" 3 .•m'34.0 0 : 0 341.7 0
i0 0 ! 0 0 0
!
lzS'~.2
X = :f Ai< = - 2/3.6 (103
)_ -= _ 8.3:f A 2$'IJ'. 2 (ID')
-40 o 0 -512 i 0
I33.3 -213.;; - b4a 12&6'.7
o
® so -2(,.1 - 6'0
- 1A-Y=-'1:=cA- ;fAiZ=-=.cA
-810.3(103) =0 -3/.4..,,,,256".2 (10") -----
26(,. 7 (I{)3) x:
ese.z (la")/0.3 ~>m
5/521~I-----rrI
r I Ir- _, I IS'I I J .t I
21 I I/' I I 1
Ar ea A I x I .4~-;g-, /~--+ ;:~
3ab 3a 9a2b50 /0' 500
25'a'b500
49a2bSO;;81a ZJ;,
500
Port
5'ab 5tf
So 107ab 1 7,;z50 170
9°2 I 9a50 /0
/
2
3
a x.ZAx. /f-9f 25f-4'11- 8/ Cl _ 33a.
X =.EA 1-1-3';' s » 7f-9 10 - aO ==0.66<2
2/3 - 33/ao>< = 2a, Error::: 2'/2 100= 1.00 %Tru~ 3 ,,,
1014/
3d)/z
.s/» 84.90
LD = z
~ 1.506d ,
x = fA; = a.ytZ/z) + (- ~)(4).lA
::
a. 2._ ~h2
2 h'l.ja - 12---2a. -h
=2a.rav'2 =a(2rrz)(f) .51Jr1 /.5 nof re/~va~ll (.5IYC.$ nc-y. a,-cl)
60 h = a (2-(2) = O.586a.
j'l56! ~• I 0
/~ ,~-
0"''''/ /---,- ~~ ~
'"/ -c:- - "'@- zA-y '" ---'1-
ZA- ZAil=-LA
- 4/6.2S(/O~)-14.S ",'"= - .:
2S 635
= 2070.4(103) 73.0 mm.:
2K 63S
x=o ,J
- 2Ai(X=-LA
--?(10( i\ X = 3.82 5/nol j( z Z.SS SIn 0(
, I 2
S = - 6 cos 0( - 4 SI"n 0<
i 0::: 301-6(3,82s/no<)f 1/3-1(?.55~/no()
+ 128(- 6 cos 0( - 4- 5/170( ) = 0
'128.0.5lnO( = 7r;8ctPso( -/z:lnot = 7Gf = 0828/ '128'
0( == 39.60
/lh A = ZT7rL = 2lTfJh~r2Ih C
I •
, r
=/Tr~
S/60[---
A::, 2TTrL ) - 4!Tr2 = 2rr=--- 1f2lT(7Tr) --
Sl611 V = L17rA T= (413)17r3 4r) 2JT (TTr--/z) = ..:J;r-
--
S/63 I A=2'7rL = 211Rr&
I 2." 2" 2 ,.
'5/£71 V= ?&A = (a t: 4"-)l! lTt:I.'317 2 4-
3== 170.(J17r4)
z4
S16t' Ii:,~,~~
'C ,,-! <: ',~+-- ,"-'a a
I~------
:~IT'-7854-
2.4646
'12.4 - 72. {, x to 4-
43D~104
5/691 A=2!TrL V=2nrA S/74 ,I A=277rL) L= IZO 2TT(0.5»=/.6~rn360
! 7\' r=3f2(-i)r2(r3/2):..5:73Z;". I Fron-? SUrH;plt:Proh.~-//)
'i!\J" .' L 04(4) 0 IG ,~. [[:\o.<rn J2 0 o,y, ~ ~hu< cc < 60"--- C . r..... 0<. .,r 0<. = i7/3 reJtT'hi~ A =4(4) =lblJ7.2
/'.\A-" • 120 /0 = o.8'(l'ih) __
A - ( ) ( ) Z ,C \ I 0.662 YY1, 1_30"A - Z 17 .5,732 I{, = S76 I~, 3 1'/ ff/3
V= 217(,5;732)(/6);::~-76 1'7.' r= (o.3fO.f!-O.b6Z) = O.438rn-.J ~ o.3rn
-, , 2.SO A= 2Jr(0.438)(/.68) = 4.62 rYJ~~~I-------------------------.5/70 A:: 27Tr L
;::27T(a -~) 17a.IT 2
:: rra. 2(7T_ 2)
_~ From Proh. 5/.39
V;:: zTlrA
ZOo
5/7S\
-I '
~
' -Lqq--i iI ", ,I I I: I
50 /50 Iso I
Part Area. r Ar32-A mY>1 1""1YY1 rn »1)
10000 225 Z2S. 0 ;1./04
22 SOD 125 281.3;<10.f.r = 10-31T«
~3;:: 2TT ~ 3, fa. 2_ !Taj
4-f'T 3 t' 4
3:: 1T4.- (/0-3")6
~cf.
LJlmen5ions Inn?"II",.,.,<:/~'-s
-;:: ~;:: 433.7'-104= /76.0 "" •.••
R. lA 24{.4'
V= 2niiA .= 2/T(/76.0){Ul..46}= 27 Z x/06
3/721 A :: z rr? L +- TTdh
= 277(6'.2)34 t- 77(~}(/!)
No. <?/ ..:J4/, for 2 ~DarJ -:::
or
z: O.077g ,....,
r :::77. El J"Hn-1
"Z204 1ft
~,. Z = 8. e 2:}I./ I---,I--------------------~..rOe) -----I:5,"!..Y~7.~6:.J .5fe;~rr: : A", eo 2", 6400 rrr Z
le . le' A - I -(7.,,,,2.1IZorn 70"" IOI?7~/'-C. =z:" vi
: .~' =36'48' rn2
I I -2 2I I A/el-an~a. z: 2:,-':' rr:
I I 80 rwI I ;: =- /20 J. 40 '" 160 YY1, I • C $7"", ..e
~
I- -- ;:;. =IZot4(70)"1497-cl,"ck JIT . rnR 4_R. = fAr= 64<:>0(160) -J?4i(/49.7)
2A zssz= 17.5:5 r»
V= &,eA = 5(/75.5":12552) = 469000 J-H3
rrt :~ V = 2.40 (469 0(:,>0) = 1./2G XIOb My
/0.0
5/731 V= 27TrA rr: = V/,) 3!J
U/he"'~ m= /0.0 fr,J> (J=- 2.69>'10 Ir.,j/m6 -3 ZA"'-jIS;ZOOXIO-.= 7.600;(10 n-t.
Vr --- =2rrA
/151b
~I
12
12(175) ='3.5 RzR
2={;OOlb
R ; 42:; /6I
~~1 ~/75
-425
1-.i
~ IIJ-JI
-14<\/7
.5/79J fP :Yy.. - - - 1i-----L------.J01v1: -PL
V= -PtV,,,
~! -=rp
t-1v'7,,~==-[.--,-PL
-------t 2.00I,
/M/ = 6.00 k;J'm••.••O',l
CIf x: " 7,.,.,
5/[10 I ~ 4kAl 21"'1, 4,., ~3>n ~J
ZM ::0R,
7122 -4(4) - /0(2)=0
1Z2z: ,:r.14 kAl
R ,,41-2-5,/4 =O.b'6 kN'I
VS{rN,
0.86 ;.-------.
L- -3.14
~M = e . ~8 f 600(2) -600f4)>'l ) =0
A:: 8:::200 AI
JOTOO/I;
C 2'8=333 I/;
3' t 3'
A
M,.'bH
'~ 1 -1000
-2400
733r-----V; ~b
[240v-~
M = - 2400 - -- J1: 3
=-/667Ib-./f
M =rd.A )fO = ZOO (O./S +XCDSaf) 21S61 k? --ZF z: 6oGos40"f-Sosl;""2o~-3t:)c~si'Ou
)C )(
=: 3"l.?7 kAlo ,r, - -? < ?~" •...:3 (J .$',';, '2P"R = z»: = 60.5;n"1O r 4:/ -50 ~~" <-<./ •
Y Y= 41.?1- kM
,..e = 'h1-.8 72 f- "I/.i·~-2·••.54. .s-t:!:.~
B :::rc<n-I Ry = 1-&1';-'4/.81-" 50.2".---------------------.-1 ){ Rx .71>''1 --~'/.'r:> 1--a . i[3:X) AI "'00' I •_"'I_-:'..=.J I - '-" IV ;2 = 34. '7.!: -f 41,8J k"
__~3"V - __ ~
20"
M=F"L/; 4= 60/yoo=0.'2I'7'7.
2./SI I20~'~
\~\20"''''-\ A
x = 0.266", ~ 266 m".,
_2/~"3J 1 KJ( -I.S ~.5'2t:)' ••2.4 si" 20"
o AI =2.230 KN
X n-t- RJ "..I.S ,si'120'+ 2.4 CdS 20'2()'-
I.SkN / I :;: 2,lbJ' kN
/ 0 R '"1(2.230;2 +(2. 7~ ~p""/ / 'J "3.5'55 k/<.l
/ / 6'" = fa,,-/ ~ _ 5/. /0Id__--.-- e.4 kAl 2.23" --~~ M= /.S(200)=r20·-2.4{12o)cc,q~'
= 1/, 2f N.", CCW1,,/(;,,/ I'oc",c,'",n •••" •• Id b6 CCW.
;::::-<.-
260 /1,-~
~ _L • / [lo _ 0
U =;5 = r&>n /60 - 26.6
,,/1 -= F cl.
200 (0, I ZO) = F (0./60 51;" 26.6)
F- 200 ><0.120- -----. - = 335 N
O./60 -0.4472
1------------------------------------------Z/58 11~.300 166So /6 60" R.
6(;' --~2~~_:;-T3 .. h. 0 I
e - - --
T=- 10 . "'125'SkAJc055f? 9" --'---
R=zF= C;;;SO-2S0-3oG>:::/00/6
Rh~ZA-t .(9)/00h e, ESo (,so) - 3':>0 (9.:»
-2So(.30)
2/60 I 200;..1 Cl
f~fOO-=-~~
I 300 1I'}>""
320 AJ
R= 'iF= 6ElO-b60 ~20 tI./
12c!:: [~
zo« = Gilo(0.8) -6~O(0, 5)
d.. z /0.70 In fr, the /eftorA
~eSClIIr1I7t- pqs.sesrhrouyh A t.f EN~=o
200 (0,8) - 320((1. S'-0.3)
=/60-/60=0
.£/2
fCl.!
v
Si". Id 4.~ i';\MA
8!3C: LMc=~' 1.5(4) - /3(6)=0, B" 1 kN
c= 0.5 hA!1'/==0; c-t/-/.:r~o I
4[3: LM =0' 1(6)-f2(4)-MA;O' A~=/4kA/.,.,.,A ) ~ /
IF =0' A - 2 -I =0 A = 3 kA./) )
~,kN.m,i ~ I
I.' -
5/tf4A rt Zn-1 2,.."., /20"' . .".,
Qt £M-=O' ZA-110 =c>,;3 A=!3=60 AI
VA!) I
II
-6J II
M = -120 A./-rn0.5 rnM:,tJ'rn Irj'-o.5n'l
~: r~_I I -120I/'rh
o.25fY1
'-.-/0.15 kkj.(11
~ kIJ,,,O~,--------~-----,-------,I L I
M) K,u-rn 5: +0./ ~
o~:--------~~----~
2/0'1 I /6(0Ib /000 ID
2" 4' 4' 2't <"rr ' LMA=o; 88 f-SOOSoo Ib-jf\t~. .:- -1600(4) -/000 (10) z: 0
A IZoc> /6 B /3 = /9118
V-14
~ ~/; +6/'2 -I-/ooon
o -Lp-----'-I_---+-_-I--~
2F= Dj' A + !'ffl •.-16"'0 -/0170 ::0
A=: 612 /0
M Ih-Jf /\1950 M" -2000 11;-:/-1) ,
I,,
S/8i I M= fry 2
~
' /+r £F-:=O'-PrLSI"nB=O\, ,," e) .
~
p= LSlnB
i p .-£;:;=0) -V-Lco5&=O
alV f& i/=-LcosB1 / "
: (J / .1M =0' PC?-M=o1 ' 0 ) .
O·L_- IV!= Pec.= La-sIne
i ----
t- -wl1y----- ~-_. __ ._.._--=1--
10
ITllTIM7'~ur
\1 £-'1- -\I
zF=O)' v= w(.£ -x)
L'M=O)' . i-xM f w/R-x) T = 0
/',,1= - W(-f-X/2
750 AI1 O.lS-""
!yIZ50 Ai
300N
M N·m) l
f-.50~
.Dc.f-/n~ Y,f-M 1
~--<~~)et- :
- Zl2.5"
AB = a. ce s 6
{jC =«(1- SIn &)
vfW1. ~
21 ~~I '~ r
£if)'ZF = 0/ - v- -vu)C f -2 == 0
V=tA/(1-~)ZM=O; M+ wx(i)-W1x=-~
I\/? = ~~( L- x.)2.
-w.f2M",ox = 8
t 4'
/oolh
I{; Ib
+100 L:\o '\
4' 4' 1lOO It,
=>-- <k>oM) /~-H
I1
01 I I~
.d 1114'<.x.<8'
F=~=-=f)M100 Ib V
ZF=o' Vf-50(x-4)) - lOO = 0
V= SO(6- x)zM 00' Iv1 f so (X-4)'l-
Y) 2
-/00 X =0
!vJ:oo 25(-X2+12X-IG)
3""/95"1 @!, V o/'PJlVM "d
1971b[g200 FOr ~erv rnoY>78nlfA, on /~/I enAj
i
Ji)
~/"/If
~M :: 200((1) 4- : G400 Ib-ftt 15' 8'
I.2.p 1/600 ~~~200~~;:6 6 J...p V Ib
t 7P G 1{,16..~ , P 7to LF=O/ -v- 1"- f6P=o 'Ml~~V P V::p(L-:f) 1600lb·,'6 6 ..e
I 2F = 0)' V-J-coox-/600
Ifiv'/. O· P 'I- 7V= J M+7'(.Z-6PX. =0
_5P ::0 MJ Ib-it -1-64<;)0 V = /600 -200 X, IG
M= ~(j- -1) #LI
_ . :l,2
~
.2Mv-O) Mf 2002:
,1PJ-- 6-/600 X. =0
M= /600,,- -IOOX.zo 1M' Mma .•.=2P.1 o 4' 8' IG'
z; IOOX(lb-x), (,,At )(= 4; 1v1:: 400(12)
= 46'00 Ib-Et
-«)0£2
tyI',
1/.",+2 kJ./A
MA: -I, 5 kN'n?
w=_dVdx.'
V=2-3X.
!v1= -2 -/.S= -,3,5 kN,..,..,s
sj;oo «..r= 2r 1:.. (4-Z)2
= It-X- kN/_
~= .+3 h-A.l
N1A= I- 2 kAl-1'Mf-X->1 I
A B1--2 rn--,?-\V){ 2JdV = .l": X) =, V=.J - (2)(. +-})
.3 ()For)C=2n-t V=I13=3-(4"i)=-3kN
} ---Ms !t Z '2
/dlv1 =J [3-2)( - ~ }/>c2 a 3 2.
2 X.)tv7B= 2 t- (3)(..-)(. -"6 " '"2.,67 kN' rn
dMV= ell(. )
3/IO/J
t
J X t 1L 13 A
A= L2-I-xt
8::: L-l-X
-Lt
i!=;t.;=-=x =l;::b===~==~~-L (h t x)
t LLL l-)C Z-x.
t-1 ho k----=----,
-L6
-L(t-fh)
mll'SkN/mp~~Mx<2~
1.125"kN
J"F=-o' Vfl,5l<: -/./25 =0)
V =;./?5"-I.5")(
LMv=O' 1V7+/S J.. 2.
/ 2-/.125")( =0
M= 1.125X-O,75X2
r-T----r-,--r-=T-'-i':'"-f-'-+-.--. - LAA;;? = 0 'I }
1.5(3)11.5)-2.122 "0~2: 3.:3 75 f(A)
IF=o R 1-3.375 -/.,13):} I
R,=1.l254-N
-Ins
o~-~---+---=
M !rN-m)1
0,422 .L __I .3
S/103
X-y plane dZIv1, __ p =-_p"<7)(2 - 7"
dM, __ Pox? cd;c. - 2£ +- I
3t'vf = - PoX -+ C ;J( -+ C
1 6.R I 2
, 5/104
I'vf =0 at -,(=0 q ;;<=.R .50 C =0 C '" p,.lI Z ) I l.
FOr X -Z p/O/Jf::
50 A/J = Po lL(f2_X2)1 6 P
r~p/oce. X "y /-x, So
I\/! = P" ~('/-x)(:ll-)()2 6 ~
2r:1~'To.z: w- r 2 [ : - (9 - s/» (f -8 ) ]
::urr2 [f-& - COS'e]
I J- '" -I 1- cL F IS!5(!':nd"1-19 rnOY>'1~>7 c7boU< LJ (;JWe rt»
dM ~ dF ot'n;3 = -t<Jr25/"~ df30/2 -6) TTh-01
IV1 = ec/r Z pI;" j9 d~ = - -a/r 2 COS;9 ]o 0
= _ wr' [SIn (; -I] z: wr2 (1- s/n e)
cL2-M = _ u./ SIn 17x.c/x.2 0 -l
dA/1 j . IT" C.:Ix. :: - t<1, Sin; dJ< f- 1
= u;,P ITx c---;;- Cos 7 I- 1
c:; 2 ~ ••)C. 5/1'7 &
-= ?(U/L)c= UJ!••. '2- -
x: 10 (,,,0 (42.00):: 44.7 (10 (,) Ib
-ur==- fi'O('f.?I)/Zc)O :: 3.92 /rAIl""
T = -i-UX-2. 3.<;2(200)2.o --z;-:; 2(90) = &'72 kN
TrnC/x occurs o/" 1.3 I 15 T;:,,q)l ~ V,.;;;- 2f- (/"u) a
7: = V(87Z/2.1- (3.92 x 200)2 ::: //73 irA!rYOC>)(
S/IIO I Fro rn / ~t r?-Vo :I~n·.,..,s "'/' /he <!xj:>0nS/<>n
fo;- coSh ( ), £'1' 3/1'/ h(!':c",~~s
eoo, 0::> 0 z 594 16/.HID .•.Vlf?/. 25
-_-?/I/' ~Jr--y-=-4--h-x..-2----h-_-_ -.Y-L-2.------~~------ILL) 4X.'
wh<:n ~ == L/4 = 2. ~o Y>1, y:: h - 150, ,.,.,
'-7 = (h ·/50)( 10(0) 2. h:: 200 rrt h!L = ~ = lis. 4- (250)2 r "lOOt.>
FroYl-1 E'1 5//6 5= looo(/f~[,:sl- ~[-;-]~t----):: IOOO( 1.(96) "I09{' rn
h=/6.2Srn,vUL 2.
T=o
T" 15.09 feND
So
~"(1-7)~
tiy z, M/,,(;I:; _ ~ 2) t-C C =0 5N'C'" ~ = 0 ot )(=0.,.Ix 7;; 2.1. ,,' ",x.
T z: -u.I" 1. l
o 3h
or n 2_ s-n 7- /17. 5 - ? ~o12 lOo 32 :IZ J
n 2_ 2. r) + 1...:::012 /60
50 _~ =:: 0.604 Or' O. 22~L
.atA.t 0.604 l..'s /;"1/4/'4' J/nt:~
..5Cr'/:.J /s d .:;'~rJ~H-I/u"" h/L"Y¥'
),:::0.226 L =0.Z26(IO#)-= 22.6:11
7hw~ 'l'z= 41.4 -100 =- -.!>-6'.6 1?"7
AAln,m"'''''' 1~I'1.5I::,n 15 TO' SO(9.gl)(41.4)"2.= 21.o (1()3) IVo 40
Ma'XI>'Y1(.«i-?'1 lenSlon 15 Cl f \(2, Yz i I~
~"')(= V;;;-2,.. (0X-,,)' ='1(21.0"103)2.+(50>9.8'1<.5"8'.6/'
= 35.6(103) N 0'- 35.6 irA!
5/1171
_. - .
u.J .«/ - t<--'t-U= t- --'--"JC0 i..
FrOI'Y1 ~? S//3. d (dY) «, w-w,;:Ix ,;:Ix. = _ of- -'--";.:.
To 7;.1.
C: 0 sina aY -=0 "t ;:=0, cfX.
)[.=0
~ -Ub x)3.,l "t!.{
'l.
T= ~1 (Jo 2h
,.. £.c..j-~)
J «er '"
x: = L/2) .u/ = ...vI
1../~ --tU) . l"hu5 oU/ = ut + 4(k-',-IU.)(.ZLZ I 0) 0 L2
dy I j)t.-=- wc/x:."'x. 7,;
o
j [= -= wJC ~If) 0
2
iy=u:,x,
+ -4/, - -<-V" X. f /0'- x.=L/7 )Thu~ y-=hZT 3 J;, L 2 )
o
t/ h:: UJo L 2 ~-uJo L4 L2
-- 1- = - (sw +u»8T" .1r;L2 IG 48T,; o I
.F///?I £'1' ~---:hr /05 y = To (c",,!, ~" - I),tU- ~
50 H _ 2 ': .300(103) ('cosh 22(9. >-1)(2S0) _ /)22(9.rn) ( , -.100(/0])
= 13'10 (C<Jsh o. 17"/~ -I) ~/3'10(;.OI62 -I)
= 22.5' ,.."
Th w j H = 24.5 >??
x: =- 200 "'", Y = lOO ""-/
IOO,,LA. = c.osh zoo!'- _I
7;; 7;bO/vC' ,3ra.):>hlcqljy Q -':pr Ta/I'" = 21;'- In
r-OJ-Y1 /2:c;. 5/20 5.: Zs =- z(2/5')5""'1, ~ .:460 n-Jr-I. !' Z,5
.k9.5//6, S= 400(1+: [~t- ~2[if.-·)=~7 ....460 - 457100 :; 0.65'?0
460IOKJ
z: 1390 (0.1&,"'8)= 251 n'J
600;(~ =cD~h(1200) _Ir 1;,/;-<-
To/"u ': 1270.lt
12,000 z: 12'10'p + 600/,
,.L<- = 6.35 16/./1
0/0£rror =-
Fron--,
ecr =.3 23 NJf'1'7.
~., - .3"3- 15'.2. (9.tl)"""',ce - .•.- 144.5 AI/..,.
(14.7-13.4 )-1-3-.-4--100 = 10% h/~~
5'//221 L = 2)( z:2 (12.00) =- 2400 /t " h = 600 Jf7;,.,0)<. x: 12 o oo Ih _
j I--e.u(Z40o) / [2400]1-
/29' ..:j7/~a I / Z,000 = ,2 V 1 f- 4(60<» = tu (I 2fJO~)
-cc> z: 12,1000. = 7.07 16/.111200 Vz
(7.07-('.35/00 = 11"/0
6.'5
TY,,, :,-I>'t,-- -- --,,,
,,I: :t,
'\oD ,I
-----'--'X-
,i: :-' h '=- y = 1.5.32 ( / 3.09 - /) = 18. 53 ,..,.,
>S/1271 £'1' 51!'? y= To (C..".sh/l¥ -;)~ Ta
.5u6tJll-'/uf~ y=6oo.fr, ~= ,3,10 11>1h', )(.=1600 /r.
3, /o(G~) = cc;>sh 3,10(/600) _I ) 18'60= c.o~h49to _ 1~ To ~ To
L=RCa/?ul",r~ L d If? #Y VC?rI,,",uS ~.~ ?' p/ol'-o •. .>;,o<£>"
0.2'1 r-,R! 501,,110Y} /5
I Z ~= 6900 /br--~«d----t--'---+----tiL::----~ F=m £5" 5'/2zr----+--=="'""k::-----t------1 "'-'11-1, .y=- 600 off,~r-----------.. 7,:;:; .• .: 6900t-3,IO(600)
= .,760 If,
L-__~i ~ -L!_~_7/0(.-
0.27
0.26
0,25G700 7000
/600= ~Ot>+S:t)O:JJI):/1 =160,.,
s» 11 = .:12. -:1, = ~
p:: 62.4(300)(300)(~OO)2
z; e z46 (;Ob) It
ZMA =0; O,9F-I.¥(I'I.o7)20
F:> 38,/ kN
5/1311
5/132/,;/nf) ::
2//73
P==fJ},-:(h = 150(3) = 450 10//12
IZ = -i»A = -jt450)! 3){4) == 2700 16
I}C 2M=0'3C2_2700(')~0z \ ;,q) v73
3Lt\ c = 2700 V!3= /622 1061'
/>jhab!?:= (J3-"h62( 2 2 3
h 2= 3a.. 'L h = a v3/
= ;,JJ3 h s: i /,0 r=.er) 3-: /4. 72 kN/w·/l
R::: pA~ 14.72 (3){(,)
:: 2G'f,9 kN'
W= f?5(7.1i'1) ::: /i'3.4
C 3 m B
7'~-- ~I~
W <\-R-+~iLn,31'4 A - \.-~ rYl
6YY1
PcIv7C=o) 264.9(3) f- 8>3.4(3) - P(3) = 0
p= 348 kA/
Oe:: iA./f: ell!'ns/ty 0/ ?,""c,.-=kz: /50 /h//f3
Ow:: t.V1. t::te,.,~/}'y 0/ .I~J,Jo{/,::lic:v :: 62.4 //'//11
L "1t:n,3lh "r CY/II,u7c-r :: 6 ftr::: rC7d/~~ t:> /9111,.,,,,/<:,- z: 2 -//
t T Let
---CIJ-B
;:::Oretjui/., T= w-B= 'Y' 77r- '[ - r. 77r l
lie w 2
= lTr2L (n-i r'..".)
:: 77(Z2)(6)(150 _ ~:.4}=- 6'757 /,5
B,+83,=""9
/", "1 b t +/.9 {h-J,H. =/ 'J h t:
h="'~/2 -/"
Q =/r~cose )(COS$) rdeo
. rr=:por(;+ ~e)4 0
I. Z - 't s in tio~ J a'"' /.34'&; '"
T= S. 80 "Ill
c
R 1.(J(Jo('?'!)/. . O('" Z 1'3., .J"'~o"} 3. (,)((j.6)
== 3.3.0 .t N
L~ =0; 33.0 (/.2) - C o.« s';' 6~')=0
C==Z5,4KN
I----,---------~--------.----0,/: ~ = ~ (0. flS)(I. 0)( 2)(2)(0) =4.59IrN
8~O R. :.!..(I.o3)hfhJ(Z.7)=-1.3toJ; kAiw 2
~ZIv1~=-O,' ~ R - h R. = 0 . ~o = !z.
~ .3 o 3w' .If"2wZJ
i h3; 6.60 h13 h ::I, 1?7{; rn)
121= 0.;' = 62/(1)(9)(10)=25,27016
122-= Pzz.A2.= 64(~)(b)(IO)= /1520/62 '
z~= D)' M t: /1,52o(/O)-2~Z7D(C,)=O
/VI = 1/. 22 /ra ") 16-/112,
R, s: i 2.40 (9.!/)(I)(I)(l,$)= /7.66 kN
"2 = Z.4o(9.fl)(I)(O.5)(I.$)z/7.~6kN
Z MA = OJ C (I) = /7. 66 (i) +-17. 6;;(~.f)
C = 10.30 k.N
~ fJ,=;"J3h, = 1.0(9.5'/)(0.25)= 2:45"kPa. Pz.= ;03 IJh z: I.O(9.f?l)(O. 300) = 2. 94 k~
~ 2.00 I R .: hA=: 2.45(0.3)(0.3)=- 0.2.21 klJ
/
I"'Yfno1 0 t 1-,
I -Z(;i-f....Rz..=ip2A =-i'/Z.14Yo,"3:)(O.3)=0.1J2kN
~~ LMA=Oj 27S(0.4)-O.Z2.I(O.2)
.300 -0.132(0.2:)0)=0•...• ",.,~ '8 = 0.0966 kA!
2r-- 01";;;'= 96.6 NlaZ;:::-=o; 2:;;+ 2(O.096{;)-O.22/-o.13l=
~ = O.O~OOkN
0"- lA" 110.0Ai
«/:: 6300 I") ;2"= ;;=- 2(9)=...7-:75.:/1TT
, 12, =:6~.4 (9)(9)(6) == IS; 160 /6X. ->-: c: '
Ay..--t--' RZ
'= 62.4 (9)(9 )(G) = .:J~320 /6
2Iv.1A=0/ 9P -f- 61l00(S. 73)
-15',1<>0(6) -30,320(4.5)
f 2~ 8'20 (.3.6'2) = 0
p= /0, 8'30 16
R-I
pI.
122W= 62. 4 11(92)&
4:: 23,820 16
X.=. !~=- 4('1):.3.82 H3rr
L/ 0= .5'7. 7 = 5. 71 m 3
1.03 (9. <I I)
r",. .1e~! /'s:: 7.~.3 i./..,OJ
" se« ", ••t ee- /,..," 1.03
L.,t V% VO!tJMe of cl. •• ;" =.!!!/,s
lJ ~i",:] V ~ ~,.., fJ I mg.: 93 hgf S /00
T= 13. .5kN
fF=o; 13.S(/O~+I/'()3_I)il_h('1.,fI)"'O h=1704 m, (7. s s / o o ~ --'-''---=--~-
5/14 V:: dl;)?loC.ed vo/u;-ne =- consronr.r= ./ye;$h iA/o-/e,- S z:so /t' t-t/okr
1-------I ~ DJ;piocerneY7T YY14~ 5 rn:: p VV V= 1'Y7:f rY75_ z _ but W1 = Wl + ""'0
Pf I's :5 'f
t.vht:YC ~" ach/':d ""Os 5
So ,,/1':"01 d'·~.b/. z: ~ = ~: W1f: ?t ("'15 - 1'1-10)
2400(O.~f!.!03) 2W7 = <; 211o /03
fj =/.00 M.'}/"",,3 J Ps:: 1.03
21/2
fons r_elY/c)
M,9 /....,J
:: 725'1 2 rrlefr/~ fon s/ _ /.00
~
FOr e9tA ~/, b r"/'u "'" Ut;,.,.. W :: B f- 8v L S L
/3;= den.5liy of slc-c:/:: 7.8'3 /VJ91".,3
Pw = " so/I /ot/4' n:-,.. = /. <'>3 1'v1,3 1r'>1 3
(JL = " /eo cl = 11.3 7 1\.4...;; / rYI 3
r" = j.tJo >'Y1) t= 0.035' rH
V= VCl!Un-Ie 0.;1 /r...o(7c/ m 3L J
al/a:>/ E3 m = /"VIP!>" 17/ /~,;:n:1 = rs: \{W I-L 4- ( -b)3
.so f's9 4rrr2t f- (1;1 ~ = fW'J 3rT rf-'2. +-Pw9 I{
L{J (PL-t"") = 4T7r3 [;(t+t)~w -Ai]m (/ - :t) = 477rz[ -{ (If- zCr);ow -Ps t1
'2.[ I ( 0.0.35)3 )]vn(l- 1,03)=4TT(I) 3' It-z- /.03-7.g3(o.OH/1.37
0.90941'>'\. s: 1./008 m= 1.2./0 /VIJ (yY1dn~'£""'~
r-
h I G:=t_ ~~~JlhhII ~;_ . 3~/6'
S/15/1 A1=-,"et-t-ceni:~) So co,"b,,,,,d c.£nt.~r of ".,ass
c",-"not. bi!!- ah",ve M.
i/m.i
v: = rrr'h v' = 1 n r "I ) If "
s 0 n: r- '2 h (-f) = t rt: r- d(3; ))
h""ax. 0= h 0= rj.,/2
.s//52 C;::CCn Iro;q' 0/ /-npn,.5!.dar area.
J-----_ . 50 J = -5 (3) = 2 f'iI -___ '
--. Cz = C""nIYOI9" Dfn:.1roAca'ron.50 H = Y '" ]: (3) ~2.25' .H
R=r~yA= (62.4)(Z)i,(3)(3)
= 5t;2 /b
,cron-? .54""'p/~ Probk...-. 5//6-
;;Z == f /'3ri ~hc~ rY1<>)(.
p,...e~.$u~ /s ("9'- Rcp/q,,, £y
M: 212; == 2(y,P"r')(;Z,-)
/\/1 z: EPo r34 0
2/67 J R. " t,c- -: (;.5" - 3) i - ZJ1---. 2- klJ - --
Y~' f!.= -;.5"!-·-2:/ kM
, a.5rn'.: y ~X =ZMA +~
t.='kN ro o r/-rn ~k--3ktJ -2x=3(O.3)-/.5(o.2)0.2 rYI / sr.r» :0.3n'1. -2(0.5) - o. /- Cl.O?
-.~ ----xA )l. /!! x.= O.290rn
2/6/ I R. - ZF - (; "' 3,$"-3 - s ~1,$ k/'J
R d =Z~; /, S b '" 3,,5' (~)+ '(12)- 3(7) - S(9)
.i2 =- 1/ In
1-2/6}] E~~ ,? Since: !! f>ilSS'S Thr""-,,h O.
40(6) f· 60(4j - .sPeC's eo" = 0, P'" 1/9.:5 liJ
Moment c/ '10-16 t. 6()'/h forc.ES ""qr.f"ec:te,oI ".1 tJSo res"lt for P IS 1')(7'1' qepeIt4, ••-f Or' &.
~
[
F
300'Mrrr
o /50 +OO~1Y'/J7 I m~ I
.'20 240N' /\/
L Mo = 0 ;:••.r k' :-'0;O"S5 lh"''''.'J)' 0
00()F -/ 200..5P) - 240(250) z: 0.,,:.-=- 2.0 11..
:...< = L~:: (/00 - 600 cos 30'ji'-(I"'O-f6C!OSlaao1./ N
= - 4Z0i - 400J N
- 42.0Jl:: 60 - r oo (0.5)
- 6,)0 C05 30"(0. 3)
Y z: O. /0'1 In ':>"_:,':: 109 mm
3~ ...4-
t-::-;/-=-T--::----------·-2. G"--, ~':?".£F::: (ZL1UO + 4oc'o cO's 600)1.
f- (-5t:JOO -.]000 - 400D .51'" 6v")'/
I! z: 4U,:;o!- - 11,460) la----------- ..::. .. -
/? d = £"""a +)) / t, 460 d '" ~t:Jo(.s) l.3oo0{;.s)
-2000 (8'.66) + 40co{4.33)i: 7~ oO~J
d.= 6. ~/J1_k 1}1e- nj-"'f ~.f B
. 2/6G 1RI( = E ~ = e.s ""J 30' + 10 '" /'2./7 kfl/
RJ
= L-j = e.s sin 30o~ /.2S k.vR. =V(12.17)'+{I.2S)" = /2.23 k./V
M = 6(0.T) .• 4(I.Z)+SfZ.SCD.I30·(I, .•O- 2.S s r» 30~(O.")
M =- /';'.2? kAl·", c!t>ck'VI's~
z~ :::0; r; '"R)<= /27. / kN
ZF = a- F;. == 7(9.il)-/o1./ =- -3S. 4 kN (db..,,, 00Ia.,-4)J J.I
5//5(,J ciA = .zxd'j "': (tl-'j)d'j, p ~iJ (h+J)
dR. = I'J (h+'1) f(a-'j)dj
b ZM =0. Pa. - fJdR. ""0
'VLZ!ll{z'lIlll/'::-;~-;X Pa.: 1';:£\(h+J){a-jJdj
d:t ~I'J-t::f3(h+~)
P::P-?(h+--iJ
o
p I'J
~.s//57 x.=..l.-h/s;ntJ lJ-::,ooA(i.-~)) f l J Jln <7
JVht:,.~A = croSS -s~cr/~nqlarea. ~/ po/~
LM = o : .0 QAll..co~ e;tI ) I I J 2
-!3 (1-1-) ea» tJ = 0
A
rn, x _; 27 (7,~~) =: 0.5"30 mm sin 8 n(loJJ(o.O.Jjj3)
From Tabk C3 Append.x C.• _I ; •• _.J A - lTa/.:J
for e//lr>/"Ica/ ;lua",r-n I - "4
JZ = 4a-/317
ltv1B":.O . IAI w - F 2r) f2r-.rzI"- AV2':o
~= 2~(r-i)= ¥(r- ~)~jnrr-":. t.: //-.3 \
A "2 f' rr )
I. 206 (jlfU],)(f.fl) = G.Lod3
N
m '3" 0.3 (9.[?/)= 2.94 '"N.
I[ >: "''] '" 0·4 «T.g/) = .3.12 AI
T = S.3 Iv'
.zF=o. 6.2ocl~-2.94 -3.'l2.-S,30 =0) d3= l.f7Sm.3
J cl _ I. /35' m
~/,,~I· ,/2) .•.~ ».s«. A = '47T ,6 =. 2tl.27 m.y: = 4 r 4(6)= 6.55 ;n.
',17T
y = 0 i= 4(6) = 2.55/~.I .I1T
..fhe/I: A=- 71(4)(6)= 75.40 ,'".2:;=0 y-= Z(4)=2.5S'/rJ. ';:=3/1'}.1"") Tr J
-_ ~XA _ 6.55(Z8.27) + 0(75.40) .X - - := /. 79 /1'}.
lA z.e.e r f- 7S.41!>
Y= LyA = 0(2'1.27) + 2,55(75.-1-C;)lA 2fl.27f7S.40 = /.fSJ/'}.
2.55(29.27) of 3(75,40) .=. 2. /?:; In.
2B'. 27 of 75. 40
- ziAZ=-=
LA
5//631 c"I>SS -Src/";I>n,,/ q,.e" is
AS'.(O.2){O.2)-lT(O.05)~= 0.0321,..2; F=o.Z".,
m-I V w!(2f[;:: As) = 7. ZI(10~){2rrXO.2){O. 0321) = 2'1/ Kj
A'. 21CF L -2f[ {o. Z) (0.914) =/.149 •••z
,*,h~"e L - GOD + IOOf[ _ 9142 •••'" - 0.914 '"
-r-r, :;; _ 37Cl.'3/al _ 37/ n» .s x: - 76'ii"j '2 - f4 a.
S//6bj £'9' S//6, Z -/ "11; YI - :: Htl'--)IV' appre>x.. ~ + ] = ('!!")'1fL ) (h../= 0.0 Z6 I?
280 L 3 L
"cl 0.v7143 c={-l2.)2(.!.. - !..![O.CZ6&'']'\ I!>..)~ ~AZO2- u/::>p..-v)t. L .3 S '/J Cl. - ~.v D.
3~q a..pprvX. 0.07143 = (lL/(1: - 5Zr".OH6J) (!z)"::oo2.?iI- .].5L ) L- •
4C"-a.-pI'J"-vx. SVn-1<!' as ..3L.cI Se; i?=Vo.",Z6'.f =0./70'-
./ h= 280,,0.170 = 47.:?rYI
x: >6[!Jst 12-)£~:mrr
V kA!I ,
~ "1-----+1
-;» i-~ ~ZF=O; V-O.5(J2-x)= 0
V= 0.:5(12 -x)
iMv=O)' M+O.5U~--,"):c
/'V1 =- -0.25(12- x) zM kN./'Y}
J,
r, ----~~-----~----x1 - -- - '1I /'I /',/
-27 /'
v ~ 1 Vx y' X v,x. j",.! V~P",rt m3 m mi 1'",,.'t m3 WJ ".,4 rvt.z. 74_~ , 6.7 I 49'1 8 97.S-! 32.5 3171)
_ Inzl- 76/.,
2 16,7 /3.3 i 22.# 'f 17.4 3£'.7 639
n.s : SS3-24.2. •••
.3 3/,,. 10 62.7 .5' 7. S! 2.352-
I 4 7·t -;s~3l-~361I /8. e I '//.71 7'74ID /J4Itrljt
! s: 31S:9 20.0 i 6317 /2 ·1 ID.S-"./
, 25:5 42.5, 11786! e 9a.' i 24.'1i- 2'15$ 13 /2.5'1.-..16.7 SSS"
:X ::2.4 11'I
j 7 lo.?j 31.7 338 t. 's 761.'1 1,.fU
RI = O.rrS(2)(G.?4}(Z)f.3.5) = 743 /6
R2.= 0.85 2~2.4)(Z)("!.5)=371 /6
R, ~= 4(O.K5)(b2.4)!3j(3.5): 22U /.6
--R .•. k4= J(~2·4)(3}(3.s) = '18'3/6
!2 I ZIVl =0' 114=74-3(/) -I37/(:!)3' '3 , B .J 3
"--, R_4 +2ZZ8(.3.5} f- 93'3(4)I~I
B ~If
I IZ. -4-,_ 1--.1_
tv1=/2.970/6-/1
.57;"718, ~/o./~~ = I. 03(9. M Ido.'f) 1.(3J 0: 1"/.26> kill1-
B2, -;"'" 9 ~ = I. 03('1. s/) l! (I. i) >-(2.4)= 61.7 k.1v'4
V' = vol. Df bA//asC. t3 "'/,,,,9 a.j =j. g'!!!-3 ) , '" /''-
= /. 03 0. ofl) "'; o.j!'fr>r11.37
Given) F=0.IS(8,+8",+B3)
= o. IS(N zs '"61.7'" a..r.f'1,.,)= 12.1!>-f 0.1333 fYI
,( (m -I- m )3 = 5.7(9.81) = Ss. j 1<1'1I 2
2 F .,. 0>. F + 13, ,.. 82 ,.. I:>:J - ("', + ", 2) J - ""9 = 0
12 . IS + O.13:3 3 IY} ,.. 19. 2 p,.. 6 I. 7 -I- O. S'J' 'I m - 5 S. "I - 1. f I", = 0
g.7'1''''' = 37.2,"., = 4.24 M,q
5/170 I 900 Iv'/m ..
. ~ .. SOON! .: ~
I.T~ . f ~;..6 10.6'"
~=133// /22=90711I
2..M =0' SoO(Z.4)-/.flR2R ./, f- 900(/ 2) (L I. 7) = 0
2' J
R '" 907 AIZ
t.F'" 0 . R s: ~ I/. 2) r 6-(')0- 907) i 2
:= /33 AI
&i1J:; ;«- = -!:z 900 =: 750 x.
~tvM x « 1.2,.,.,/33 N
2.
LF=-O' Vf-7:ro!:. -/33=0) 21/ = /33-37!J)GZ
2tv! =0' IV/+- 375 x.2.1:. -/33X=oV ) 3
NI= 133)L -12:>)'..)
i'vla.x. PO.s;/,yY; M= 52. I? Aj.W!
.5/17/ r LMA =-0 31 .••..e:s T=..5'b30 I/;) He;.=0 f £iji =0 ,g;.-e
.s' ~o. Ay VA
_ AX= 4876 161---- ~ Ay= 9/~J6
r/TII-88-""--':----0-'--~--I-D~' ~.1~3-··~~ 2000/hV
2000/h
200010 II
V; Ib, 1 ~: f t9/So i ..·--------------JO
-2000L. ii1,
Mcm,"cnl U/;/I,
"..,a)(I"'h,.,'rl m(7.3n,·f",/~/.5M,lh·in,
'I I
-36J~-------'-I:------2-~-3-l-() -;---
• - 49, 320
-108,000
M= -/08000 16-/17,i
ot )(,= '1.1t
'1~L~-r3' 4= 4.&ZO (1-0.2)(,)
dA ~ 4.6'lt>(I-tJ. 27£)./;<'
dR=j>dA= O.e« (I. OtJO%9-il )dA
=36.2 (x- 0.2x'L)dx
R = 36.2j(x -0.'2x2)dx = /5/.0 /.eNo
5= 3(;. '2J (x'L_ o.2x~)dx ""37f kl/'m
•378 = 2. So In h:; 1. (5- 2.50)/s/ > S
~M =-fl'",dA"
X = Jp;( ciAJf d.4
Ff7?1'Y1 Qreas Und~r J/'cordICl,jy-aH-1
1
Iv! = - c:0z zMYJ'f/~ o c c a r s
IIf-?
Let A "Cr t> rs- P!L:.t/o"AI a rea: "i CAble.
f'" =: ./8J?''-'!f of W4WjJ- =- "et. Vi!.rC'-c...( /",.d 1'-"" ",are.
of ca.b/e /"":JihI'cA = "., .•••ss of =b/e. ?Qr metre
of /e"Jth
;«- =- ye -4) 9 -1'''' A 9- (ZZ.o -/. 03 (lo·J16tJtJ (lo-")j(9.81)
= /b9.3 N/".,/£1 ,-"l"Jra./ of e'J.S/17J,-,It!!S c!1.."" fA" (} '" ..,ed--
dx. r..160 •
tan 60'= T.3s <tCP soS~Eo70'"30/} (103) )
Ea.S/lO; S '" r;, si,,/' l'>' ~" c- '~J._I (ao7oX 169.3)~ se ~ 1 r=- "~'" =1317I - To 7; 3DD (ID!) •
x." (J.3/7)(3'O){lo~) =- 23# 0 m1(,'1.a 3
T c.o s 60' '" 300(103) N, r = &00 ktVM = TI"/ M = 600 (I) "600 kll.",
C'ls/t9; h::; ~(clSh /.317-1)= ~ ("'lJoo-/}s/7Z0 ""/.317 1.317'" /
~/176
6 FRICTION
L5=~' A!f-50co~60o-IOO=O
N= 751,1;,
.1F;=O)· r (15) - 50s/~ 600,,0
r r.= So (0.81,(,)_ 0/r : 75 - .577
/oo rs
I ~rSOJh
F=jA-A!
tJ
sII1---)(
?2lj \
\\
!F)/.. = 0;PC05/5()-t 200=:530°
-0. 5N- j-o('i.~/).5''r? 30°= 0
25=0)'Ps/", 15° t: /V'- 200 ::;,;"30·
-50('1. ~I)cos300 = 0
...5/H-7~/T4'Heo.v.5y :j"ye: rN= "I-¥-:;- tJ P .: ..305 N
/
~ /00 (9.'61) IV
r-:
-ai' ,,~P- "-,,- i>
7- --',,,
</>/lC ,, ""'3
x.=(h-c)ctl?tj= (b-c)~
6/.0 [t"~I'''b"5°0, JJ r SOcosd. "'00y 01 of"I c~=o)' O.3/\J =so SIn 01.
II---X; £/IYH/ncde AI t/ ,Jef
to. 3(;00 -50co.1' c<) == 50 .),',.,eX
D.3fJ6 - 3cos 0( = la s/;., 0(
IV 59UClYC' .si suw/; l.ule Sin '2."" = I-Co.:; "'0(
36- 36c05d. f- 9c05 7..d.=/00 (I-C05"'ot)
/09C05 Zc( - 36 cc>SC< - 64 -= 0
CoSd. z: 3(, :z:/f.3Gf'-+ 4(109)(64 z: 36:!: 170. q2(109) 21~
=- 0.94'10 or -0.62ir,~/~vanf
0(= /8.40
<jJ == f4rl- /-<- = 14,.,-'0.30 = 16.70°
SlY, l' z: O. 2 ~'7
1: =..f. SIr. "/ d = Z-t (0. 287) = 0.575.l.
;!F=o'y )AI z; q 8'/ CoS 20" - 200 s/n 2o·I---=--~III------~------------
= g53 AI 6/~,.cor e9(·nl. Z;:::;'== 0
9/JIs/n ZOofZoOcos 20°= F
!== 5Z3 N
J:i,...,_)(=~sN == Q.70(?53)=597N >523 AI
Thef""~for~ er-ale- /"~I'H~/~S .r re s r ~/H1
F=S23A.i
=- 0./76
.£'e9d. Yn'YI'rnu ••.•
C 0<:ff. o.r JrI c him
IS
"u = mY7 <1;0 fa., t9:::- 1:>=021
72 _._
zF= 0 .fo>Y- rope:; 2/25/..,19 = 600R. = 300 = 1471 IV
1~/IIS2+ n"Z.
6/7 .LM =0' 100 (3 5/n8) _25(8-35/,.,8)=0l:" ./
.s/n&:J'j/~) B=JZ.2°
;Un''';' = /lvn & = ron 32.2"
= 0.630100 'I;
~ Th~re are I'J-Vo P.:?,SS;bl!/!'I(:S
(a) M/dd/t: 610ck n-<OVt!'s /' .5orl-<>""1 O..,C aeN!S 1'701 .
~
I W, = 10019.rrl) = 98"1 N<----- 0.6"W; WZ = Sa('?!?/) = 4'10. ~ tJ
P .}~O.4fw,-tW:;)W;+~
-r=: p= 0.6 /es») f-o.4('lf?lf 49a.5) = 1177 N
rh) tJorh7;n b/<?c-f rn?J~s U//'fi, mIddle .p/c;~
t J..V,<---o 6 LV ~ = 20 (9. 1i'1) = 196. Z !I)
p----.-! t~ I . I
[_ "'w~ I~.3(W;+~+/i.j)
W;f~f~
L'F=o' P=O.6f9fll) f-O.3(9!?1f490,!):f--/96.2)= IOf9 fI.//
lollg <. 1/77 .50 CqJe Ibj occu~ i p= /08"9.A1
6/11 I
6/12 I Bloc If- ..f/';'s I;: F = jLN 0 r- mJ s,;.., e "r": nt.'j I..D~8
Io</ncn 4'13k n;acJ,es () = fun-/<
f7n:::widcd ~ > ~ fc,•.•/9 or a.;. j-'-b
6//3 I,,
\\
rng
2N c.os ex:ca s t9
£;Y=O,' Zf\lC05o( -"'"13 cose = 0, 2N= I'?1J cos 0(
z~=~· 2;-<-11/- r1-1Js/;"e=Oj 2N= n;!..f/h t!)
Thus .5/1161::: cose _L /J /;«- ~ I Tl'ln <7 = /"'ICO.5o/.
8= 10"'-' (;<-/coso()
1-I
Y,I
IL --X-
po: (,0 liJ
t300lh tz
: 8 t~A- /__ .- __ ._--2~·1--.,.J
A ' !
2MA=:0)' 60(2) f 48 -300(2)=0)
.IfS, :::0/ A T 120 -300 =0,
£'i =-0; /,-(1&'0)-60=0/
8" 120 IJ.,
A=/Ro 16
~ -= o. .3'3
1---,-----··-··-···------·---------16/16 I
''P Zrn ~Zmo.3A ~.-<-~~-/--0\-- --T
A } ~ lm800('l.?1) AiL I
c : P r,--------~!- -LIv1 = O· MO('1. 5'1) 2 - -'fA - Q.3A (4-0.5) z: 0, A =3/03 AI
C )
f.F; = 0; P-0.3(3/08')=0) p= 932 AI
y £~ =- 0; N 5;;,.(5 -i Alco'S/J =0
Ic.n(3 :~-I
(3:mn ~-----
iM=O':.4 )P (r- r 5/;'('» - Y\>I.j r SIVL(3;: 0
p= 1")15 S1v{~1-.:;i"'(9
.5 _, ft-~ p= nT.J ----
.(1+;« 2 -p
A
,r I f3 ;.J", I I~:r-'
IH./
b/18/ ZM-=-o'8 )
tJ(O.'I?66r) _jA-AJ(r-f-o.sr) =0
f"'- -= o. ~66 = 0.577/.5)"-N
2F=o',y )
t-O. 5'tJ .•.o. 'l6' (0.577 IV)
- YYl3 :0, Ai= rh.J
P +0.577"",;) (0.5)
- 0.&'6:6 mj '"0
p= O.577""'J
8P
LMO:::O; M-O.6(17/.~)(2)=O
1v1= 20(, .J'I-/b
6/191 £Fy:::o)' Ncos30°/-0.6N,5;,.,30o-4<)Os;/130o=o
AI= 171. ~ 16
y ....-, 40IIb-,I -,
----+---. froy' \ M~
\ / ,\ /.30.:2
-l'--- L -R/ -...
6/2.0
fF=O)' 17/.5-R.s/n30o~oy'
0.61J /2;: 343 Ib
y .FOrces mC/sl.he cO"lcurrerli. -I f'.
P for e.yuII/br/VN1 50 o(=..5in -''2
ZMG::O; 0.6N,(/)+a6~(O.S)-T(I)=O
~F,.~O; T- O.6~ +~ 0:0
Z"; =0/ /112 +O.6tV, -1962 :<0
Co m 6;ne (get0.6'''1" N,=331 N, IVzc=176f N, 7=727 III
-+-"~~T
6/2/ II IfI I~ I
L_-x
iF:: o ' Pcos 0( r: N - m« = 0y ) J.
ZF".=o)· pJ/ncl -I"-N:: 0
'£/In'1lnafc N Iye!
p= /-<-mj fir>7912.
';;'/1 c( 7,/-', co~ - r, f-jA- y:;2 _ r;2.
AS.,5uffte e9u;h'6n~,.,., 2M ~o, AF(rf-rCC>5ISQ
; =/Jrs/n/So
£ _ O.2S8i'N - /1-0.%5"'1 ::-0.1317
!Jul -;;,,,~~O.;?otV (>0.1317 IV)
So F =o,13/7tV c.an k Su-/,porf~cI
f/ paper roils t-</1'r;,OUt' S/lp-,:n"J
FOrces coY}ct-(r'yenl q/- 01v1,',.1/w,uyn X occurs for,,= faYJ-;U
0. = X fan <f 1" (6f-x) k;n r/>
z; j-L(2x f-h)
;'i- = Cl -/,,-,1,
2;"
A55unH' roll slips a C .8bur 1"101 at- A. rh",,,..,
1;= o,~p
~M::.o·)J }
mJ r51n30" +O.4p(r+ ""51n 30")- p( rcos 30") =0
p( o. F{'6 - 0.4[1 +0.5]) = IZoo('f.d2.
p= 22 /2G ;J Or' p=- 22./ kAlCh",ck (1'" a~:5to"'/Jf7~n'-£0j=0)' ,.e - 1200((j. !?1)cOS 30" - 0.4(z1. 12b)Co5 30°
- Z'2 1210 51n 30" :. vR. = 2.8 '1Z2. ;J
f~ =~. Fz r: -/jr = 0) Sco ;:;=o.4(ZZ /26') = s FSo N(a)
(6)
6/U I """9-/ zoo ('1. [11 ) N~,
F' ,I
P\
_8 G,'r
. )f- A Fz/
/
1- ..-10" R-
rc)eu f(~ == Ilf;so AI) < (O.4IC= If !;-69 IV) .50 a$.Ju"J,.fph?~
01-(
L"1a=O)'I"n'j r .sr» 30"-0.4P (r+ r:51;';30")
-p(rco~30C:»=0
( )/Zoo(9.~/P o. :?6G -I- 0.4 [1+ 0,5] x ----
2
p= 401'::'- IV' (=- hort'f· fo ...c e. on hr~s)
a55u»"prIOH •.
+- a. 4(4015) Cos 30"-IZOof9.f-I) CoS Se>"
_ 4{)15 5/'-130°= 0
A.5.5UYY1e rOIl 5//,0$
bUT I'Ic/ .a t- AF-=o. 4 p,
R..;: la ?IZ AI
z/'vh=o' F r-F,:. o : F. =-F c- 0 4(4015) = 160(, IV<../ ) Z , ..J 2. I '
/3u f (F s: 1606 N) < ( 0.4!?. = 93 Z5' 1/) -:;0 o.55u-tf>h;2 o~
(aJS' ~L/:sN"~ ;;:O.5(QS.3):::4Z7/6~Qr~ ) ~_~ .47. 7 /b > 34,9 .50 t<.Jht:'",1 dO"'$ nol -:S-/Ij:>
4 Cl,5.5IAH--1/J h'oH t'/K U-';;'-I, F= .34,916
(0);::: :..J.{<Ai= 0.3('15,3) ~ 28'.6 Ib <"34.'1165",,,,,;,< / J ,
,50 ,f.-VI1"·cl .51'/15 (,vole: Ft 0.25(9.5:3)~-- ,J,'nct:' AI:/ '15.3 unA'",",
",cce/erah~ "r».,d/1'/6-,..s)
LM =0. 4'10 (Z.4)(j)=AIz(3.0),A J '"
Nz ~ 311 N
'Lr. ==0· 8/4 -490(51..).,. tN-ff.O,5N~~ J .J I.J '
N:: 1,,7. tJ tJI
IF =0· P+ 4'1o!.. -0.5(.314)- -1./57.0", .s .s-; 0.5 (1.57-0) = 0
P2 1'1.62 N
6/29 2M =0' A (Za. Tb) = 8b) *" Za.-r-o.I G) bI 2F =0' (B-A)st',..,B -AL(A +8)cosCJ=oI )<) /
I or fc;n8= J..I.- A+13I g-A
::/" I -f- B/A
~A-/
8A -1se f I.,. (Za +h)/6,I.l = fuY7&
(Za.+b)/b -I
-/ /~1 a +")e = fa rt V----o:-
C/30 20010 3D'= 6 ;;0", 30"
= 6/r'3~===±~;==~;2C-O..5~
~
z~=o,,' 10(200) - /8'IJA -6;.../8=0
2M =0' 4(zoo)_ O.5(~+A/8).f:.. - /2~=0D ) . ~
..5O/ve v/J'?'/U'/rw'7c?oL/s!f !/"ye I A/A = 26.0t 16
/\/8=255.1 16
1;=;'=0)' O.96{;P -O.S(Z6.0!? +255.1) =0
p= /62.3 /b
6/3/ £-5; 0.1' AI == rYl3 == 60(9. e.) = 589 II.J
Zr; =0)' P -O. &>($8"9) -.e =0
p= 47/ r;< - - - - (a)
ZMA=o,,' pP 51',..,6o"-60(9.8'I)!.ws602 2
-R..f S,n GO"= 0
0'- P=2£i 340 ----(b)
O.5Ai COrHoI;"e fa) ~ fb) P ,3ef/Z: 13/ 1V.1 pc: 602 Ai
N
L~=O; B(o.U) I-F(3(o.6R.)=mjrO.3J)re t- 6~B = 3 Yn'j (a.)
B~C • B == .u. A (hJc.rx.=O) 1
Z'FS;= 0)' A +;«-8 :: n->!J
(b) t (e») tJ =,.,u (1'Y13 -;«-8)
8 (J+jL'l.) :r»11
6/321sIII1. J fL),
'0.81,/Cl)
(cl) i (it)
Att-r;~( 8' + G~) = 3m3) .Jj-L 'LT! J-L -3.:: 0
(5p-/)(jA-+3) =0) r='h (;.-<-=-3),....,/n#:5 roof/rr e /<,v.:l rd
//t/.J-/----;~P
fl-4=o' :l...P(Z)-.4h7Q (/.5)=0;4.1S' 5 J
P=mj.£;::: = O' 4 3
)( .) '5 n?9 - F - .5 hf,J ;, 0
F- I- 51-'>-1;;
2;Y~OJ' A/-jY>-1:J -1m3 =0, NrJn-19
./l"""n=F/A/=-Ys/h=.!.:0./4 <0,30 so.. 7 . /../n~I/PH 1$ ...:rv/:/tueN/ *' ~~/;I7Le;./~ e ~U/ •
, a-cs . /5 y-cS. F=i b0(9. EN)= //7. 7 AI
Cy Asswrn~ /~pend,'::1 moll;';'/?reacht!!ct' /,,~st ,d 8.
.50 -:g=o. 5Ala
For Ci3, ~A1:=0t" 9f?/(2.)(0.5} rO.StJ8(4)fo.8t6)
98.110/ ~ -Ne (4)(oS) =-060· FI3 A/
8= 36G N
Nt3CB' ZF.=o· CV=~8 =0.5(366)= /~3./A/.1 X. ) ••.•
25,=0/ cy 1-96'./- 366 =0) Cy=26f5' IV'
AC)' ZA// =0' 8'0 (c;. J>1)Jl. t-q/J.I(Z)(0.5) - 268 (4)(005)A.1 V3
- 183./(4)(vg/Z) =0
h== 2.37/'>'7
ChtXk (?Y/ CI:5:5un-tph;;'",: From /pqc(~;- ~.5 Q U/hc>/~
£):"-0' Mt-366-Z(1f?·I)-80(9.Ei'I)=0 NA=6/5'"v.1- J ~ J
LF:. o : F:= ~ == /8'3. /11/ {50 OSSI.;y."p1/;X I A u ,
-u.t n =04((;15) == 24G N > 18'3./ AI 15 OK. .U A max . .
c;, 351 y:L x
~W>3 (/~.5ln &) = 2rn9sIneJTT
(~-f'-)s/nf) =)i
19 ::0 90<> ?Oh e rt !2:!:.- =- /2-fi)<
-1(!7~ )So &= .5ln -2- rrp.
So
FrorY! :J rc<-p h
8 = 40.60
=0o
= 277r~ (Pox +- jkX3)
But U/h<!n X:=O.IOOY>1.) p=/600kPa.
.50 /600::: 8'00 -I-k (0./00) 2. k = 80 OOD kFtl./WJz)
• 2..3/VIVJJ p:; $00 1- 80000 x.5uo.:lf,fufc ~=1.3 kA/·rI'1, r= =«>, )(=0.10 W1-
t,ye. f /.3" 211(O.05)~ (800 < 0.10 + 1[&,0,000][0. 10]')[fnJ • w\. ] 0 [rYl. 1 J {k Ai m T k Ai L: m 3? = ;'rlJ· m
m' m'm2.l0.>/vc for)-L !/:5~ I- ,P-" 0.77(;
5u bs rl'rtA le In 2 "_cl £7. El .3ef
P=p;lf-2f(I-;J]= (Vz-I)rh1J =o.4/4;<1?rI3
'/z1-1- '/ZI+- i 1r:J,,45°
= 113
2./7() I
1/00 mH"I
/::TN'f'7'~
:45~y 150 IV
M:t~ /)
=40-/5 -t-150Sln4So(o.l)1- eo (e.1) -2005Ih3D
U
(O. I)
z: 33.6 AI·m
0;-- .& = 33.6/ II./-m
~ i--_, R = er: -::loooCos20Q
~ 60010 I .K r4000 I ) = 9:1'1. 7 IhIb~.fl / J I t 7' 1),::z;;:: C;oO- >l.J.J -I IDot) $'17 2Jj
~~-------~L:~--AR.=)/Q3: :~;;::Z'=9So Ib1000 It.
M= fMA " 600(7) - 800(4) + 1000 (10 $/n 3d) + ~"o= ~4Z0 lo-.HCCIV'
2./72 I
s: a5.'t 16
2/~ A8::: ";0. JO ~+/-:s~+- 22 :: 2.62 m
L= O.8/.2.~z J m = /.r/2.~2J n=--2/.z.6Z.~r=l.·:z (0. G,i -I-/...5"./-2}- = 0.-/57(O.S'.,£.· Msi-2(:r) kN
2(~6~JAB -= v'~2 .••.T o. S 2-{- aJZ - /. $of-n'1
1.= -1.'2./1.10f =-0·920
rn:Z 0.5/;.301:= 0.383n = C.1//.301 s: 1:).0767
2 (-O.92o.~·+O.333./+0.{)77!.c)
- kN
2/771 A8 ::::Vz 2.f-3~-f 62 = 7£: - "/7 r»r = -2/'7 n = .9/'7
) ,"/
,L=/40(- .6 i -.3./.;..1. k) /6 = zof- 6.l- 2J -136-) /117- 7 _ 7-
Z/?~ Af3 = ~7..s2-1-S2' -=,1.31'1/4'
1>i~., c~.$i"es of r a.cc'·"J ~n Bare
'iI/.y.3r'1' J -IS/.jjiTj
10/,136"'1'
s a T = .~ (i c - ISj + 10 I<) xIV- 'v3{f - - -
~~----~'-'--~~~=~p-/~~-~=~'~~~:2~~='-~=~='=~)~'~~~~-D-~-N-.~--z: F
;f,- a: = L!2r = 10/.100\ =..5POtV'rz 6 )C 6 t : ~
5=(F~Fx%·~1= YIZt:JO 2_ Joo 2._.:J"ii02
=}I'/./," 10';= )041 f/
P
IVA= ,Je= =» /2
IM .""0' Pa:= F 68.f) A
F.:.pf1A b
Y~ce Fe > ~) 5/1ppln.J
Th'-f5 /" 1'>15/2 = P a/I> )
2~ = 0' P(af'h)c F j,i. ) B
F= p,u-6{3 "
(}Ct:,,,,,-s f,~f Cl I- 6 ",-,,~J, AiA="i13
p= ,-"1->156 r=I!:n12a.2(a.1-6) ) A z(a..+o)
:~6/421 120 1/~'-5 con suppo,-i e'jua / .t0pl'os/le Jon;t:s P prov'-dt:d !<. k,.,-).<
Thus m;ni...,/A-.. d (7CCU''-S ",,/'~17
/- coseIf-cOSt9l
!!\
2
or eo5 e = ~ tu f c.o~6) = d- r11-/,,7. Rf-r
d-r I-,.a 'ZJO -;:;-- ~ __ U/11 /"';:, o/~t:J
"" 1-1" /I-"u" ...,I
d".,,;. = 2r of' (/_;<-<-2)1</,t-~1.
cl cleorly 4"""".:: R.. T 21"
~ Cnflc,,/ 1> :::0(/1-
I:;;-V:XSo
p
~/C06"''' ~COS(~"'2'j=W' Pp= 1<-, .5/~ <? f- R1. .5;'"" (~ + z)
= W( lun<p f f-an [<I>of' 7])
:: ~h'(/03)(9,h'I)[O'2~f-0.2875]= 6327 N
or p= 6,33 /.rN
b/~ Max. hd/x ':?r),3k ;.1 at = "" So
/-c;n 0: =..!:..... = mr7r1 :0,:;;.5 ~= /4.04"2lTr ~
L = 217(Z5)(0, z .,-):: 39,3 ".,n?
M = IIV'rfa,., (0( +- ,p) e- wr f>:>n 21-= (S)l.103)(25)< ID-3) fan 28.(/~o = 66,7 N'I'Y}
~ M = 2Tr !-4"-' (~-",)= fr.;"1-I.!::.. = /0,.,_1 t/:J Ion -10,078.3::: 4,48·
0< 1/7r 21T(/.5S4/:z.j
270 (12)Ion (? -01) = 2(15' 0(0) 1,3,4 = 0,/596) r/>-0(.:: 'l,07 D, ----z</> = ~,07 + 4.48 =-/3.55°
1/:' f,;,n rJ z: ran 13.55 = 0.24/
6/'7 </> = i-a...,- 10.4-0 = 21.5'0°
~"90-21>-5°= 41.40"
p
CO/Ul-HrI l/ u-cd..f~
zF -,,=0ver"
122 c.oS (2/, 5'o-rsy>;: 5 kAln- .5
"<''2 - --- =5.(;0 kNcos 2(;, 5'0"
~~~:Lr;.:.o)' PC05 2d'o"-5.bOCOS 4/,40 =0
P =- s: 60 (0-1,,-01)It), 9285 = 4-.5'3 kN
'f> = m",-/o. 4 = 2/,1100
;3= 90-.p-(",-sO)~ 90-2</>-f-5°
= 51.40°
Co/t-rl'11n -i U/c<{jc
i/::;:'erf, = 0)'
K2'-OS(ZI.i?O-S)" = Sh-Iv'
/2 =~ .=.s.ZZkA!7 "<'5 /6,~()
Wedge,,' 2;=;=0.,'p~O.5 21.110-.5;Z2cos 5/,40=0
p;" J-; 22(0,623'1)/0.9285 =.3,5/ kN'
1100 16 q,~fc;n-10.3o
: 7 = /6.70°/6.706 I:I, ~ZI.700 ! 1 ct..=21.700+16.700
: /6. 70"-f' : ~3?40°
1 I
/;< 1;</ I I
eX! I
~L__Jy ....---\ p
of
Wed,Je: :z '5 = 0J'
/( s/n 3f? 4-° -=. 1100 cos 21. 700
1R =: /64516
I
R. =: /G 45 cos lb. 70 = 157(; 16
IS7(;(?Z)- 4zoox:=-o X=30 . .?,n.1 _
eZ
== 17S Ib-/"r;.
pfj/ocJr: ZIj; :=0)'
'18'/GOS 21.8'00
== Rz cos 53.600
p= /331 IV
b/54! <f = ro",-'O.40 = 21.&'~,,- (3=90{)-(29- -10") = 5""6.400
<j>f-/Ov,=- 3 1.800 »> 'I.'
pBlock: ZF. =0'
y) 0
et?1 cos Z!.~O:: R2c0510
Rz=' 12S- NW~d~e: Lt=: "0'•..• )C')
92!JcoS~6.4o" Pc.OS 21.80For screw" _ p = SS! iJcc = 6.06° f/ </>= 14.04"( hOD. 6/53)
M'=Pr!-cm (cl> f-o() = 551 (0.015') rnrJ 20.09'::: 3.02 N·mNvfr: (1) ~/jn,('" roO
F
Pt
N{~R'A
122 A5.5UnTe a'h~(!1$/.t';.s aT- i3
wh~r::/: !'Jv0'='0)' !-f=F-::: O.3AJj 0.710=-100
ZF:; o· IV':; 1001-!=' N'= 142.9 AI)() Z
I~ =F =0.3 (1'1-], 9)
~1j=O~'.Rz= 1'16. 2 + 42.'1 = 42.9z: 239.1 IV
(~=4').9) «O.25"23r./~6'1.?) So ~~~" __,..,,t,.,,,,.Wed,;;c:: L F = 0' R. CoS 26.700::; /42.9 i? = 15Q co" .,X ) I ) I I. f'J
z;y = oJ' p=42.1+-/~'j,"1 S/nZb.70o= //1.7N
Norl??al pr~ss~r~ re rn a/n» un(/h4I?~t:/
Un;;! p;n .fj,j.s
300lb
NorY>1cr/ f/ In'cllcm forces acfmy over fhe PI',., n->qy 6e~,P/pcJ:d.6y a ..nn,91t: e9wl;"':'/~nl forcc K
70 ..xl ,..tun: :2F""O, 400 =-R, ,51'7 (~rl<jN=- R,co-><f i:5o 400= IV .5;n(~""I-)
=oj
To reYHcve ,bIn: ZF=~ ..300 =.R2 .5/",., (</-_1°)r? -' .5/C, r~-I 'jN = ""2CO~ v: So ..300 = N _.:..c...:_,,-
/ Co.=;l'DIVlcle fJ.3ef 4- 51;'(</-1")= .1.5/;" (rpno)
£>'PC:Hd ,"" 1(slnq.co.=;/o- CO$f.s/n/O)= 3 (SI;" '1eo.s I'-'I-Cosps/"I,t</hlc-h .3/"""s /t::ir'1';' = O'/Zl.'l. _ _
r o.~9 97 - O.JZZ -~
1~6/58"[For e9t.n/. 0/ 5cret.V (re/er f-o I'r,:;h, ;//us/:)
JF-O' w=-,,[R CC>~(o(+Q') = coS(oI. i(} U!!.,) I
~A/J='O)' M =' ~ 12,r .51;'"(ot +rr) = r.Sln. (ot r~) ER,
Ct>yy>i;)In~ $ .J~r !VI= w'r /t;n (01 +~) = Wr la" ol T fe-I? 0-/ - fan 0( ft:ln if'
If.. .5l'n rj;gur l~rI r= / ",.,u/cos {9/2.
!Z Ct>~ rt> cD5 ;3 Z.
cl rei,..,(3IZ
=---.!::::. Cos 0( mn S2 = i=. So ran~ = mH~UJ::'o('I I: 217 ) 2 2J? I 2 z
E/ Co~1= I//If- fO/'/~Ct>~2o(. Thws frl"'?J''l-'-¥ll-fo./!CAS7x
f./en('i:
M/bn 0( f- ~fl +fQn ~-zl9cos>cx
= Wr ~--:-~-;====~==-/-# fa,., a: \ /1 i- ,IQ" 2 <9 Cos "Cl(y '2
25-- = -----/60(0.8'00)
= 0.1953
)'C. r
,,= 11.26<>, )'1-= r~nrj>:: 0./9"1
~= r.s;'n 1> = M/,t<!. == 25/160 -= 0./56 la.
500(9.fI) N
Use ~ = 0.271 ,rmI'YJ Pr1:7b. 6/60r=r.5/nq, =ZSs/n (fc,,.,-IO.271);f
-::.25"05;17 1s. 16 <> = 6.54,.,.., m
L!v1A=O.J·500(9./;,/)(0.3- 0.00654)
-<;8'1(0. 006S4) -1\/1 = 0
M= 1433 N·m CJI'" 1V1=1.433kfJ·".,
500 (9. 8'/) N
6/62 I For COrlsT4nT ;6ressurr: £:1' 6/0240 .gIns
R" R'i )3 )3M=2/,p 0- i. =.'?:rO.35)(1) (ISO -(75 =40.flN.rn3 R/-12/..3 (150)2 -(75)2
For ?</he~/ Ltv1=O,,' F(O.3) - 40.8' s:0) ~:: /36.1 N
M= ..335 N·/'n
6/G41 rs;'n rjJ = rs/ncx.
~ r; = r 5/n q, ;
Jt'JO(9.f?I)
Toj~J\ T
\~~'AISm"" I I
~--'>i r;.
l' -::.fc;n-/O;25~ 14.04-0
:;= 0.01551;'" /4,04D= 0.00364 "'"
ZF=O)' TrT; =SOo(9.l?I)
?'!vfc. .: 0) T(12 5 -3.(4) = r(125 T 3. (4)So r(1 f /21.3{')~.500 (9. 5'/)
J2fJ.64
To= 25':'4/J or T::: 2.52 kiJ
.r; = 5"00(9.8'1) - 25Z4 = 23 fjl AIo r: 7;, :: Z. 3 fi fr-J./
j = 0.00364 rrr
TorE)~.I
p'r 11I,-.~~
!F=a)' Tr':>;;" .:rCJo(9.!?I)
r z~ =-0; T(leS r 3.{,,4) ~ ;;;: (12 5' -3. ('4)
Solve « s= fT= 2.3 &' hA! I ,;;;-= 2 S2 irA!
RC®-tki Ib 2.
( . ,';-r
;,
\) F
P=4FF= .i: 110,. 4/6
4-
M=FE.2
= 4(20)
= 80 /h -/rI.
Lf40
M=: l?rs;Y] 1> ~ L r SI'n "
f?O::::200(2) 5/'.-. .pcp=sin-10. Z =: /1.5'4°, J-L=hn cp = ~
~----,---------- -------_._-------6/6fJ 40 /b 'J- '" rs/n <p = 2 $/n (ron-10.Z)
=251",-11!.3/=- 2(0.1961)
=: 0.3922 /"rJ.
Llv1.=O·o )2/)0 r. - 240 RSlnfJ =01-
51;'&= 200xo.3922240)l 20 =- 0.0163<;
B= 0.9360
240/b
'1 = /1:;,,-'0.15 = 8.53°
5c,-evu: (a.) Iz, rai.se: ~= Wr,0.., (0( -f-,p)
;~(20 t-4.2)rUI) ~o fun (10.35')
:::1410AI'm
(a) ro /ouX?": M5 = wr h;.., (1) - et)e; 2:.2('1.91) I;Oro'1 (6.711
z: '107 AI·m0. =~ p .e/-.e~
c 3J-L ;C:L-.e~o. (250/_(Z5/== 2o./S(U. 2 fl.(7)(9.&'/) 2 z
.3 Z (ZrOl- ('~) 2-
= /8~4 I\.j,,.,.,
ra) !vf=1410 f-18't4= 32'10 AI·",?
(h) Iv? = 907 I- IR8'4 = 27'10 tV· n-,
To-lal "",o""~YIIpc'- :1c; ,,,-n/
6/72 p= Ir J/n 0< I dA = 21Tr a-s 0( r c/o:
= 21Tr z cos 0( ace
00 M= 3::.1Tr'.u (3P ) = aPr.3 I ~/Trz r:
:>lTjA = In -' s: 1.6094-,z:
3 "e"u;3rn.J
~=e~To 1<>#/<:'- ""j a. 48
.LJ/',,-;d~ i.7t::f 3' _ n-1f! rYI_V3(o.41?)=rYI.J- -;;:4? ) - ~6-1
or nJ=/22.3 *5
To ro/se rrr)
0.1223 Nf,9
---,----- - .-6/7&' 1 T= Ter;'3 T= 5016.) ;;= 20Ib)j3:.;r
Z I I 2
50 17;<-< e rr,...,.= 2.!:J I If?-:: In 2. 5"c20 IT,#- = 0.9/63) ~::; 0.292
50
b'/7J' [ T= Te~;S2 1 O. '30(3
16000 z: 240 e 0.30(3e =: (;6.{;7
O.30(3~4.200 I ;3=14.00 nul
.Vo. 0/ furns n:. Ji z: 14,CJO= 2.232ff '7.7T -!urns
r ~Pe /"(;
P o.srr= e =Mt1n;' tr-=Oj' TfP =
Cc>;-,-.bu'7e ~ ..5~f
P (If 4. sra) :: /so /6
P =: /80 z: 3/.0 Ih5:,?/O
-I If)a=cos zs =5.3,/3°
0...-= Jfi'o-53,13 =:12.6.87'-
(3=2ci.= Z(tZG.Fr7)rr = 4.42'1 I"ao'180
~ )<-;3 160 4.4Z9j-(- =e -:. er; ) 40
4.42,,/,-::; /.3 i?6 3.1 )A== 0.3/3
/ s o
6/gZ I J;/r; =ej-l-/-J = e O.2oTT = /. [174 - - - -(It)
;;-7;=166.7 - - - -(b)
~Y: Z/vl-:::o' 26P rsr0) I
-/..3~ = 0 ---(c)
Con·d)/'7C (a) f/(h) tI.3~f
72. z ], fl74(r.-1.,6.7) 1=357 11-2 ) Z o.
7; = 357-/bb.7:- 110.71h
75f '1. 8'/);.J 12. = r c: /-0J J)
,t<I (3 +.!. )Z/T75(9.&'1)-/0 = foe Z
72.6= e,zI.99;"
21.9~ = 4. 2 ~s; ~= 0.195'
t100[9.8'1) N
oA
(2) ~($) r,/~-a.-D):;; (a.>4)eo""'o/ne u.-'/rh r/) $ se;re
L--a.-J) /LA2- =e,Ta.-.!::. J
Z
I-- Da.=-----2. / -re-"?
CrQ$5 -xenon 0./ belt
6/n I f3== ~Tl) -; =e~~;;:= e0.25 (7TrI4) = 3.953
1 T 40I r:« 400+ -: 420
z. «I"'",
/)';5" r;(30r~~ a= rf2 -rz: 420(fi -I)h= 1740 rn rn
h = 96.91'>7,...,
== n'!;n. value
Thus C?wlt6,.,i",..,..., ii'10 sl,/"p,''?,j for
h > 96.9 ""'rn
6/91 I~~..J;lo(~L Zf;0o
__ ~ lA ~- .tF. = O' p= 2UN= ~wLd.. I 0( cvua!) ( S /n Cl'
tJ ' tJ:.Y
2N sin. ex = UJL
N-= -iA..JL
2 S/nd.
~------I'-----------------------------------------------IG/9Z ~~0f9.8/) N P (aJ As.s c-o-rr« e9uil/br/urn
~
/1: »: XF=o Zoo cos 200 r- ~h/5 - \' /!-():_ t t ) r-
- -9&'/J/r; 15°=0
F=- 66,0 IV
-- F LF=o' N+200S;nZoo~'18/c;.osI5°=0F IV n.J AI:: &,79 AI
Ij is"',.,.,,,,,,= 0.3 (If 7'1) = 264 AI > G6.o N' So ~9u'j ClSSU,""",1: 0 K
(6) 5",,1"1 z- /'s AI)' ;: Ii =0.,' Peos 20'_ 5'11IJ,'n/5°~o. 3N =- 0
2.F,.,=O)· Ni-PSI", 2o~~ '1ft'1c.csI5° = 0
501vc. 1/5",1 P=,576 AI
(c)A5.5u;-Y}c sl,pp"'''''y (.<.j=' jJla",ccv/r/., r-;'",n=rKN
:El!:. =0' 600 5/"120· i-A/ - 91i1 C-I?J/5"=0 N':: 742 Nn ) )F:: o.Z (74Z) = 148'. S' AI
jj:: = 000 co~ ZOo - 98"/ S/~ /S"_14t!.S = I (;I.~ AI > 0i-.so 6Iac./r fo'V)CVcS up 'pI&n~ c7J C1SSur>-1~q'
13~'R. 0~- -ZM
F N,,.;?eor po/'r 0/u;/? ct! IS
F:: O. 8';,.)1 :: 3200 5/>7 25. 6°
:: /376 16
LM =0' 2.1\4::137{, rl3)j;zo )Iv1 '" 745 /17 ~Jr pc-r "'-"heel
(;/'18' I AC = 1 (2400) z: /8'00..,.,.,.,- 4
rY1J = /200 (9.?1) N.--f C
/ I
;; jAf3 7; O.25(rr)6 T, O~a~:~:o, 0 "933
~ 7; (/r< -I. s) 0 r, (,. ,-x)
T 0' C.on1b/~e ~,ye I21 ~ /.5-)(.
I --- = 2.1933I"., I X X -OS
---- 6t -.J;x:. - 2.5967 - 0 s I 3 mI. SfYI t /.5 rYI - 3:/933 - _. _
rnJ
120mY>'.r;__er :1..2::::_
. R.51;' t9 = 180 = 4:.
300 ,J
. 6/95 IHe//x angle 0(= tan-I.£, = mn-~ =5.820
. errr: 27TUZ1> = mn -10.25 = /4.04- 0
Jcr~JV': (a) A1s = Wr;",.., (e< 1-4-) = 41¥J -/7;" If.f?6·
z: /?OSN·;n
(b) M = W'r /l:Jr1 1<;. - o() = .-f(3.!) Id'" 5'. Z2'"5 2
= 7.2ZA/·,.,.,
M = -'-.«. P(Ro f-R,) ~ .!.. (0.2,,)(4) ZOt-413 2.1 2. ;z
= 6.00 N·r>'t
/Owl Y>-1'::>;'>7~",1 (a j M= 19.057 &.00 = 24.0"A/.,.,
(6) M= 7,Z2 -fG.<JO = /.3.22 A./ ••.•.•
~ AI/ JrrCTlon qn8/~5 4/'1:
IZOO 16 .jJ = fa,.,-IO. 2 = 11.31°
R,
~ ASSc.une e9uil/6r;t/m.i'!vh=O/ /OO(7)?- -N(IO)=Oj N=56 1.6
.>. .fFv =0; -: F - ~ (56) =-0" .:; .:J
Fe: 4211;
F 42 _ 0LLs . = - = -:=;0 - 0.75 <0.00
/- - n11i'f AI ..:J r.
.50 O.5St.tn-1;>",on /s o e; ,
III I
I loo Ib A _L.i,: 1<-i--B'--j
Ord~r 0.:/ sra,!>/lICO/ cOh.5fruchon
(!) cg) (JJ P=4'lZ 11>I I
N
AI.9~b".q/ca/(y.Jp= rzoo mn2(10· t 2'1-)
=1200(0.6401)2. = 4'1216
5/ab . LF ==0' .uN cos o: '"AlS,'nrx.) x. ) / .~ = fan <X
,f, = a t- d (1-C:,;>50<)If. ,d/z':X:
I 'I '::.-~
6ut
!i(I-c.oSOC)2.
So
II(j.
: IJ
N
6/102-
.;!II
IL X
Lel/J = norlrJol Jora: per UrJl!
kn!jrJ., 0;/ co-ca/ar: jxr;f'heyCl.! d)'un-r~kr d
Mrr-+---+r d 11./ = ,0 D dfJ
2-
CoS (3 = fir L_ (D/2)7. = YI _ (])jU)2
ZF=O; L=JdNCO:5(3D UT
= ~'II-(D/2r/jd&2 0
= TI..Dp VI- (D/2r)Z
M=jdlV/ =.I~dA/ ff =!'-p(lj/j;;o
I j) 2z 277/'-,0
5••b~h·h.le L {..J~f M= i.. }l-DL
2 VI-(D/zr/'
LMo::.~· Pr =jLN,r -I-;U~r) P=.;<-fA/, t-N:z) ---re» 6/105
LF=o' AI -.uN =0 (h)x ) 2 / I
P LF -o AI f-,Lt AI.. t- P = n'1'J .. - -' (~)Y- J '/ Z
.5ubsTth.fe (i) /;'(a) ,(C) $..5"/
Truck:~F=o' F= N(q)-O.3tJ(.!z)= 0.7160(2841)= 203416
I------- )( )
6//03 A".5Urrfe .5/;j,p;ny Q,L .blade bu~ no~ _
ar ,5ro",,,,d. / kNJ~ ~-t\ ..[;46=0' Fr-0.5Pr=0 ,c=0.5P 06N
'J= .;) O.GNz / M~' , 300""",..,
J,O.75f<f.91) tlf=o' P_O.7.5/9.8'I).5't~ZO°-<>.oP=o ' I\ kM ) Nz ~.t:.' Ai - - -J--r _~ - 'f. P z: 7. 36 0.3420::' 5.03 kA/ C. " I I
_ G\, 0.5 " o.6N, 1
o.G"';: mm .5'75/'>11'>11\ Ch~ck: £FC=o)' N-O.75(C..81)c.oS 20° I I I
J -0.5-r;.03) = 0 _L~~. 0 _I j_2251 22S:
Iml'Yl I "''''''
LcHZM=O·I(b75)-1v'.2(375) -O.GA/JZZ5') =0 Al.2'" /.324 kAlOrw> 0) ~)
/?.ljhlZM =0.;·1(675)-N (37.51 fo. 6IV (ZZ5 I::0 AI == 2.8/ J.,-A/arm 0 ,,/ . I '/) I
wheel: £M -=0' M-O.G(1.3Z4 f2.?IY225)=O M=5S8"N,/?')c:.; , _
P=/,-~ (If/a)
!J,(U-/-l") f-P~ Yn.J
)'-.v; EIIh7,'nare IV £/ ,3el,N, .-L- (IT-I'" 'l-j + P -= ""'3
,.«.(If-/",-)
(11)<-'2.)_ p= ~(lf,A)P --- +1 - YI17 (71" 2. myf'- ( If'r-) I +f'L t- Z;",-
A/= '1.43 lriJ
0.'N'i.43)= 7.54 k'N ?( F=0,Ox5,03)
.$0 ossu"""'pf/on v4//d
W::./o,ooo /6
o AI' I ~I 30": / I~p--rr~~=:-~;fF X---~ Y'1/ j:
R "'/ From C}eorn<:lry 0.:/.:10 -60 rr/4n~/~
C AD z: 20(3/2 = 100';/f A-C ~ 10.H_ J
AE z: ±AF =i lolli .:10/(3 ft.Z.
10,000 (10/(5) - 10Y3 ,J - 10 (0. '3 N) ::.0
tJ= 211'41 If,
2(-:~J ,£ =: ('cs /20"", - c.s, h-= C. ~
So ,~=- -o.SF' , ~: o.~P
A/so ~ ""200 AI
P ~ 1i2~Py~+ 11 " ,02= (-OS?)" -t- {200/ -r (o.6P/
0.391"'1 = 40000. p 2:: 102 561;0 = $10.3 AI
~ 200,0Y .: 3:!0:"3 == 0.624 P,0= .320 (-e:>. S!-· .;.O. 624/ + o. &.k) AI
~ -1..= -0.1, """=0..6, J'?2.c=I_..2'_,.,..,'= 1- 0./' - 0.3" ;::0.48
so n= ~-=O·1v:J =: co s ~ J 6>•• =GC'S-'O.4r'3~4G./o
91(/ 'tc::'- ~ = 90- 16.1 = 13.(;0GO,fln ~/$O Ii.-=-FJ;::6cI6 " r= ;::;~ 6~ =?G.6/6
n o.··h3
F =/OO(0.701j-O.707-!..JN
AUnit vector !1= o.707j.-O.70'1j:
F = F.nco --= /00[(0. 107)'J..;0+0]
=so Iv'
z/gf7j Le-I th~ ~ns;4!)'" In ac. b02 T
Z = !:(x (,'+ 4J + -?/;!) " A~ t: - 3! + 2../ -f2 tf ./t:oe - - . -
1: = - Z (y. (: i '1.i + .-(k'· I (-3 c -r Zj -f zlo = 0~~ ~Z - - - .: AB - - -
-3:<. -f R+$ =0, /.-=16;j =s..J;J.!!"
Choose aXt!5 R.5 .5-? ~ urnLer I., = VQ.L+b "+c2. = AB
L 2 =- vi~ 2-+ D 2 z: J5C
2/85 D
J
,1..
c
? z :..o-;/-I vect'o;"
2/9b I F= 2 IrN;
f3
,cor El AB=- v',?:27..,..o-:-42+c:12?'=~"...,
i. e .£:2. -=.L Y>'I:: ~ _ 2-vo:Tf YG) ..t;;.z.., - ff1'7= --1...a:
._" F:.3(/+zi_;") .4-1.'-J vG---
D
For GI,,/; vectb,. ~C1)=V6:2'>.# 0..,2 = '10.10 rv-r
g=o, W1=.2..:.:!;= 3:. 17=.J..IIb.2 VS) Y.?
~:: /s(·2.i~f:!)
1[0=r:: =-*-.(/.,.. 2) -!cl . ~(z.'; f k)(6 - ~-
::,-~(4-/)= 6 =16/5 kw'f3o Y30 ---- ...-
Ir.
CoordIYJ.7rti)s 0./ A arc.
(Q.9c"S30~ 0) 0."1 Sfr? 300)
or (0. 77~ 0, o.f5) h-1
AS ·~/O.7ie;.2+ I.Z~+-(O.'1-0.1S);'
.:: /.~o ,"7
1 = - o. 771;1.$ ~'F ,.2//.:,- ,.,' o.~~ I~ ~ , -
/I/1=rx.r- A - -
-:(-a/+bj)y,cb-
= ,cO.i +- aj)
y/
1T-~IT-'?!.. TT-~
ex:. 0( C.O.$0( e 2 Z CIPSo( c 2-
DeJ R£Jd.2
87,0 1.5/8'4 0.0523 2..36'24 10.~3Z 1.1338'7. Z 1.521'1 O.04IJ,/ z. 380 6 /o.r/e 1.057
87.3 1.5237 o.o-r 7/ 2.57'17 la. 80 Z 1.0/7
If? 4 1.5254 0.0454- 2.3789 10,193 0.95'0
Plot' It ,Je/ ex.;: 87.34° or 87. 3D ,0 "~"'~:1f 0./"--~
\~ If -, /
M cr~~~mq
(3 ;: o: for ert/;//br/uYn or pUI/ry
t J;;: ~ J ti;; ;:2 ~ eo 5 d
i;: :" (ZTT-oi)- = eT.I ;.<-(ZTT-O<)
so m.J = 2n7J cos eXe<1 Jor "M- = o. so)2Co5o( e TT-ol!Z.::: I
7 VIRTUAL WORK
1---.----------------"----- ---7/2. I 6U=O/' -Pax -rnJ6y:O
fMJ ~~2b~/;'&/ dy.=2bCOSCJ,J&
~ y - 2 b U/3 Cl 0- = - 2b S //7 .9 08
:B~'b -~PbC056)/$<9- ,.....:;(-26-5'/;"'<9),[8 =0yl
:8 b /, p=- YY19 -hi" Cl
I, Py-------
" AMoh;n Cl/, ,P0;,-d A 15 CCJJ7Jlned ~ r/;e;-,orlzonro/ So P .::70C5 n->aXI"'>-1~n-? ..vorlr
I
iVht:'n Q.pp/le:qI' In -"or/Zonl-al d/rcchon, Any
v~rflct:7/ COJ-H'pc.>;J~rlrcov/d do no ~L?r/r s/nce
,L] ha.f no ver-Tlco/ d/;,.o/a="J-ff<"""T.
~(JO.vt/ n-;oven-'7en r ) =.; (A~.-?;;';""''''vOY1~>1I)
SV=o; PdX. = Q ~ 6X tuhc'-c rfx. = vlrlwol
dI5p/aCI:"I-?-1f!!"11 aT each h4n"//.::, .50 Q=!i p
7/4~=O -~)'n.Y o(~-s/~-~-~~;~~-~)-t--Vl<SB =0__ '_ I OV' )
M = I-'YIj (/:; c<> S <9 - a. SI',., i9)
- - -- ------------~-~-
Jv= 0)' Pri /e a .5/" &)
fm3 J(2a..c:o~8) f-3""'.3rS(c;"wse)=o
2PC{ CC/58 $61 = 5mJa.. SI;" t9 dB
p= ~"""J Ion f)Z
6U::::O
F(250 oe) - R" (2 [lOO 5,'•.•e7)::::o
250Fdt;;= 2oo/Gcosi9 oaF= 'O.l?RC(>5i9
6U=o; ),cCZ 681- ITod/;::cOce = 20(. . 1:.'1.:;.c/'2"f- cl.
h i0=2c!,fd r-2c[cA
---+--b-.JIIII Thws
T
Fa l& :::T .s, (Z lc.)2d
=T ~ odi92d
Q r-= .es, TZacl
a= 20 I~.
b=60 /~.
C =40 In.d = Z In.
F- bO(4o)so - (2000 )(/6) = 7'60) 000 /62.(20)(2)
Ju= 0)' -n» ,f (Cl.cos &)mg+ f(I'>1+Yr7,)yo(bs,nB)
}m,J' r- I'Vlz;J a(.!jSI;"c9)=-O
o,b
tt 8 I
-rnoas"" (9 la f-!n7r""7,)6COSBcf&
r-rr72"cose,si9 =02
"1otZ h", e :: ,.,..,b + ("1/" ;2)/; -- _(,;
I
~,...,z!} U/J.,~" & = BO) rYI.J = 0 .so
,.,..,o~lan~"(r>7,f-~2)6 - ----(2)
E//Yn,'nak 17), t Yyfz f,.-vri'1 £'9$· (/) t/ (1.) t/ .,Jet
mooTone = I??b f- n?oa h>nSo
rrr i: *' me>(iz:ln& -I'on c;:,)
7//5 tSU=O)' 2C tlC£ + Plc. ;:0
From rohl7~"" 0./ ,>OI-V oho_,"':' J/~~c/ ~/vc)t-
oa. = _6_ ae a/so /j -f:: IenSI'h 0.1d,.C 'Z 2. Z.
c.o,..,necTI;'5 /I'nk ...t:: e f- C
o =2e!;e. « Zc S«: ~c=-~oei c.
Thus 2C.L de T- P(-fte} =0 c= £ e(dfc)df-C I 2 de
7/16 J Lt '" 0; M cS B - W 6h '" 0
MS8 = W<f(Z6s/"8)
~ Zwb Co.J {; cB
So IV! '" 2 W b cos e
l3 •.•.t s/" B = A2b
Thu.r M = 2 mq 60 - (-/f;Y'
~L :: lead 0/ screw)' ,j(Z6 Sir]~) == .00( L7/17 I 2Q-. 8
t.!....~Jn Z >1 WhO/re ex. ", :file Q'1.9/eI fhrou.gh tv},,,;:h file .se rea»
B==~====:;;;olfurn s. rh usM b '8/ I;, 00( = 2btr cos!! dB
L Z17=56 cos!?
~z
f1.70 J(S6cos..£)+AA 2b1r=s.!!.rt9.o./ 2 L 2tn!j
-5m~ s/~~tft9 :f 2f/~Nf,c"S~tfB=O 1'vf=5-.:;LI. ~2 2 L 2 ' ~ 'l,z Z
d(/=O)' M~;3-rnJ<Sh=o
L = -Ux) ~A = 2fT[_tlx 12 TT d(3.) fJ L
X,~ '26 cos6)~l<::.:-26 5/Y;& <f6>
&(3 =- 41Tb51;'t9~8L
oh = 46c.oo5t9 08
- rry (4 b Co~ 19)d6> ::: 0
50
A/50
Thu~
h.: 4-6 ,s/Y} e so
M'4TTb Sin &6&L.
M'= m9 L cfYl BIT
bo( " f"ota.-tlon ",r soc.ket on wrenOh
;9 = r.'Jt:;d:or) of U/"r-'e.r i,.,,,dle (lower handle
i (rtlme tire tak.en 4s fi",ea')
i..)"':);-M d'" - P J-j = 0
/7. sS"" = 40 SB 9' 5'1 = _ J'B ~" <5-0( = - ~o.re 0,052S
'T"n-<s -M(-~) +150 (-J'j)=O M= 7.J'g N.0.052S ' '"
h:: 8 b s.» () oh z: cfb c.os e ,sBI
7hv5 C (8' J>..Z.s/~e cos Cl 08) - my (If c Cos 8 dB)::: 0
C = .lrn!31.::: 1-n!J Y;-:;-"'i;;;'2&'b s/';,8 ,fihfJ
e -----I-IF
T:c d
----- ----~ ~--1--------
1 ,f(a.2+C2)=:;O a6a+cl'c "'0
I··· ~ O(hZ+cZ)=O' 6.56 I- C6C = 0r---h --I J
,sC/=o' Po(ll-a) -2F,fd=o ",h~r~ tfd;££C)
p
.s o P (- f & I- * 6C) - 2F : .re = 0
p= 2.c-ehC(6 -a)
of)::: ccw roTallor} of .iaU' about 0ox z: c[8-r J(bcos <) :::- e$8t ~--h· [8 __ .s°651;"d.~OC=e~e
- - -- - - 0-- ---t Ct:x.- h= bcosQ( + a Sr"nc{
{h::: (-bs;n ex +<t.coSQ)cfc<
aU=o' -Poh t-C~X=OI
PIa. cos cc - b s;" C<)6CX = C ~ b S/~ 0( de(.
C= 3- a. caSe{ - b s/q oC-
be. .s/n 0( P
.12 = (h cosB/ r-(h f bsin af= 2h2(lrf';"B), 2.tll=2h"c.osBJ'B
.)1/=0· -2Wb.s/",B,JB-t2MJII-FJIJ Z
,,0
~7/ZS
F B~t I~om er";;' ~f left -J,.,nd
,I me,.,bl2r M = W!::. s'" B s»-, 1 4 J
------------~Ab
2W~s/.,,8JiJ+2W!:: .rin B,Je-F£a~s8J"B"O2 + .t
S;""I"I,(.'j i 'Jet F= WL f b.., 8/:,2S" h st It" i: e r;r .!= b rzr;'~-;;;:i)~, J id
F- mq L Vz , I-----VI +.1;') 11 "an 8b
pr~S"el1ce of I'n te"'na! work hj NI refl."~~sd;SmQ""bl2rmeni f:<, d"term;ne M, Hence.a. =i»: advllnt*}6 0/ V'-".t"4!-w"rk.mtitl10d ;. INt.
IG ~ I
18,\ I
b I I
V,:'- 0 .~:r 0
(;l:: 0I
d~V&=Ili'O" -:: -1->1<76(_/1) d&1 v j
7/271~v=iVe)' ;;cf(6sl;,,~)='~(;~[Zb~2~cose])
Pb cos 6> dB x: 4 k /; '2.( /- cos 6') .5/~ c9 clc9
p = 4-kb (/- co.:! 8) fa" t9
7/281 v,= c,X4
alV,;. 4C :s = 0 for ~auI/ . £ = 0d~ ,X r, )c/2v,=/2Cx. 2 d3V; s:24C x: d"'l{" 2 ~ c4'xZ I) d;<3 I) OX"! ,
4LJ, order der/vaT/V~ IS A:n.v~ST orc/er
r~".,eNnJ"":J d~rlya.hve a T X = 01 I'-';:s (+)50 SyST~fl? Cl) IS $;/ab/~.
V- =CX3Z 2
o'V:z== 3C '2. d 2VL. ~ d~Vz~X ~ J oI;c.l. - ~x.) dx' - 6Cz.
3 Cc'o r-e/e> d~rlvohv~ .IS /O",~~T order
r~I?7Q/n/;'7 der/vQ t'IV~ a r' x=o ~ ~9u,"hbr/lJ~or sys/,,,,, (2) .'S C/nsIa6/~. J
V= ~ .••~ = i k(Zh/- myh
dvtih= 4kh -YHJ ..:= 0 fo"-~<f"·n/.
h = /?13
4J.r
B= h - r>7J
r 4kr
S/>"':"..7 5/-rclch X- = f:, -s = b - V6 "1.-..1 z
J~ =k.x. 6x. )' oU= -Po(Zs)
6{/=6~)'-2P65 =k(6-5)6(6-5)
P ZP= k(o-s)65
7h ",:5 p:= : (6 - VI."_y ~
ou=,f/.·e; £U=PaU}J'J~=k)(Jx 7/341S'pr,,,,, sr,...~kh x:.=(2r-26cos6I)-(2r-Z6)
= 26(1- coS 8)
6' x: = 2" ~/'n & 0&
rh (45 Pa6"6J =- 46'* (1-=.:>&),51;" & 6&402. ,
P = 7 sin e(I-c<:>s &)
7231] (H~;:o kx dX vUh~y~ .srr« Id-/; of
spr;n'y;$ x. =2 (1,2) ,5/;'';50 b~ ='It!O(2.4),5/;''~ rS(2.4.5/n~) =2.79.5/;';& 68 .J
6U = 5019.8'1) 0 (0.6 SI';, 8) = 2'14- cos & de? J
cSU-::.£l/...e' 2'11-=S& £i} = 25"'l.5/n&£fJ) .
}0ni9= ~;;=1.13.s: & =- 411.60
501. /5 F = k r:=(= h "+ .('2.~)f'f
v' '1"1. 2 .t =- (F;Ir) - h provI4~eI')r < F/J,
x=o or
~---,-----------------------------------7/33 ot.;:;: =kx OX {.Qherc x s: 5-6 =-I,,'2-fu-'2._6
:~ d 6X=(b:;'~2I . -- u&<
I I S 6(J= ,Hf) Pou:= k (.(67.-fti. 7.._b) rz=':o V,6 "+ CL 'L
I pL_u.- - p= ( /- -b-)kt<
Ybzt-u.z
..Y = 2P r;;;;-ky-'p-I
So/vc for .y ~ ,ye f
7235J Take
V~~"':r z:
.50 dV a (2. 2. )_~====--k a -I 11'/ '"'J 2 = a. \ / L- ";, t + 1"'.-) 7..~Lp&l J
k1.,. 2 2 V 'I ~ J
V, a.. +""':J~(f) sfabk
..5,t>rl-"'YcC>n?press;Oh IS
X:::: 2a J/-"~2
6~ = kxcSx :: 2.fra. Sl'n~ cf(2a. .51'nt2.)2 ;2.
z: Zka. "'$'n!l. cos.£ J()Z 2
:::h-a ~/~ c9 J[)
6~ = $(""3 6 CO~ a) = -mjbsl;" If) rf8S~ f &"~:: 0)' ka., '1..:>/;'8 S& -"""'30 $/';'& Se =0
/ /ra: "- rn3 ") $/;" 8~0
/2""'lw/ for a•.•y Cl ,j .4-", ~<z-z
\6 ~\ b . _. peose, \--
e;a ~=O
1<.=2.(6).5/;"8 =/25'",,&7/37
~f_~~~"-~.-!"::SO/b dU=c5'Ve . J"e -=k'J( kx:
I 6" 6" .5-0~(24f';"&):: 2~-(;Z,j/;"&)I2~Si9
C.os B be = 35,;"6) cos!} ,sB~k=2S/1Ib/II-). I
III16'i
77T
o
0/5 e z: ~ B = fo"
:: 19,5"
7/J'li Take ~=o rhrow,.Jh /;ean~
V= v.: = mJ /z» CO 5(9) r ""'.3 (a. COlS 2i!1):J
t: m,ja.(2co:U91- cos2,g)
:::= =s= (-205;" 8 -251;'" ee) =- 21'Y1,F~'(s/;" e ~J';'2e)
".:1:: = -2rn.J4 (C05~ r 2 Cos 28).,(82
. clv ' .ror et',ul. H = 0 So .51;'8:: -Sin 261
or S/ne(If-2CoSe)~0)' .5/;'8",0) (,0519=-'/2
So ~a/5. 0/ I;'rt:'r'c.$l~a re e=.o e =. 18'0", '0B = 120" B = 24<)
2 J
(3= G, d V/de2: -2J->1,ja.(1 r2) = (-) wnsiah/~
e =120~ dZVjele 1:: -21??JQ (- i -z[~J) =(+) siab/e
e:/Jo~ d/vJte2=-2mJtl(-/+2)~ r-)Ur1:Jfo6/c
e= Z40~ d'V/tI,l= -ZI?1JQ..(-/t2[-~])=(+) sfa61e
In. 7/40 I Tafn~ £:5= 0 rh,-Qu..;JhO.
v= v,; +Jj s: jk (26 .s/» !l- n-13(26 s/:., ~)dV=2k61.sl',,~c.os~ -J'Y1!}bCdS~dc9 2 2 2
= o for' <?9u;/.) u>5 ~ :. 0 6J:: iT
.51;'~:: mg 8= 2 ::;/n-I1'>'13
2 Zkb . :Jh-b
dY 2/ 2.& -"8 ~- h-6 rCO.5 -2 -.5/"" :;) t-.!..J?-706 .51;"~4'&-2 - ~ 2./ 2
= !rh' (1- 2.5/,,/1) f j """SO J/",., ~
;::0,. u>~!t =0' dV = Ab YI_ 2) f- .: rY/26 (I) = kb 1""5 _/1e~=.11) dB2 ~ 2k6 '/
: (+) .5W6/c. If /e «: n?,3/Zb(-) un 5lab/~ I:; fr > i?1,J/26
For' SI;' -j = ;:~ J Ir> h1J/Zh ,: :~"': = IrbY I-[z:~r)= (f-) 5/ACk
v==~=m9{2rC05.Cl - fC052c3)
c/V=Mg(-zrs;'n &+- zrs/n 2e)d&
" 2m3 (-r s;'ne I-rs/n 28)dlV-2=21'>1:1 {-rcosB f 2rco5 ze)dB
:;he//;: = zrj17
---'-(__ ---"-__ --L- ~ = 0
For &=0, ~2~=2rnr!l (-/ f- ~;=). -/ - 4 ci2V 9FO r: cV/lndt:r r r - - - =2m/"0 (-I + - ) = (-)
v 3!T } &182 J 03ff
t..o?sf,,6Ie
~r sh~11 ;:/r=3.IT'
d.2j/- =2.mrJ !-I T.i) = (+)d(j2 ,.,.
sl-t16/~
7/41' V=- v: IV .: -'-k(AfD8/+.!.k(4-bfJf+Whc<7.s9e 9 Z 2
=k(4t+b28'J+Wf?cos(},8smal/
s .~7'~-"/// .·.·,.,·4
L et preset: of
sl,rir79s be 4when 8=0.
"7 = 2m3l {!.DJ 4- J ~.: f K/l.v::- ~ + ~ '= Zm!Je c.a.r,f + -}1<}2
d v' 11' ~ ~ dv r:dl = -m'j"" ."''2' + AI; dfl ~ 0 ;rvr »: 0
d2v- == - !!!!i.J1. CbJ E: + Kdj>2. '2 2-
r - m: If K /0,. j3.: 0
E (+) $la/,je ,I K> ~geThw.. K = '!!i.l
",;" 2
I..ef Ll = /",.,/!-/o/ compression '1'1
each 4,PrlnyThI:'/'1 fo/' .51'1-14'// an.3/~5
V= Vef':J '" 2. [fk(t:1 _151;"61)2; jk(1J t-is/noj
f- 2L -leos B
V= 2k(LJ2.+L"s,i-;'8) f 2LLeosB
dV=. 4k.f. ~;n Cl CA.5 Cl - 2.LfS/n {}461
ci2v= 4k£7.u>s 28 -ZL.lC05 Cld8z
dV' -I L,If} = 0 .}Or- ti!yuli. &= 0 /j B= COS ill
fOr &~o) :'~~~4ki.-'Y/)-2L£(') =tr t 5fa61e ,jIr ,;--fi
7/47 6 t{= S( 0.3 my cos 8) = -0. 3(l?o19. Ell) .51'n e ~6!:!J ::- _ 23 Ss,,, & 5"&
,A
__ O.DS51;"& == .5pr,,,:! COYYJpress/ol7 X»>
8
or
6 Ve rt':J = o}o 240 s/'n t9 CoS t9 JB - 23.5 .51'" t3 S tJ s: 0
(;056= Z35=O.'N?/O (J=/1.19°2.4() J
-- 1/= 0--J
7/4'1 V9.o ZWa o.sB, ~ =: ikxz =: ~(2a sfn8)Z
---W- mq k ~ . 1(]Vc ~ + ~ = 2iVa MS a + '2 0 Sin
dv =: _ '2Wa .•,on B + 4ka~.s"n (] c.I>S 8de£.'!" _2#4 a(1S 8 + 41.:02(2 C4S28-t)
d()'".: 'f. dV/'d •• 0 w hie!' alliesr or 6141" '/d8 J
or: c~.s 9 ., ~ ",h~re k > WZJca ~4.S/n9"O
For ~,"a// 8, chan q e: in len9th of e4c.h sl'rin'j 1$
t7pj>rox. r. bB cos 0(
V= Ve + V9 = fk(LJ +bBOl>s-</"'ik:(tJ-b8t:.t> s «).,.l'/bOOS(J
=k(Lj2+6za'CoIJ.sz-<)+ w'h ~.s9
dV = Zkbz8e ..n2ci.-Nbsi,., 8dBd2V = 2kb2&1.sZ«- wb CI.s 8. fD" 8-0, d2~=ZI;I/e.$a.(_~dlJ'l J ,19
Th"s(:~) /s (+J, stable, ,'/ 2kb~c.O$2o(>wbg·o
or k, = W ",.!!!..J.. ( If £)"'1,., Z" c,.['", 2 b ,2
7/.52l Fo,. i' of door ~ = ; f (1- cos 8) where W"""9 ,
L et: x =:7/5"0
rr= IISO """ ~I.
i080"''''~k--9o-J",",~
12 T 0.04(9./11) I-N ii
compressl'on of string (",,,sf. ear;/'}Seen hy cO'7s:der,'nJ A f';xed
I wheels to be m"ved)Th"s x= ~(O.3S-")
I. IS
~+ 0.110 ('I.M kN ~ 6.S4 krJ2
cS~ = 2 (k x dX.) '" 2 (120) o·ot (0. 35-h) ~ (-JI,) 2 -14-?,o(J.3H)ih/.15 1.15
S 1I" cf~ j -12.43 ,fh = -/47.0(0.35- h) ih I h:: 0.26 Sm = 26S",",
With F f/xed)J" ""- z (6.54) ,J-h f:Z (M43) I.od'Sf,
I.IS; (-13.09 +O.HS)Sh
=-/z.43Xh
Thus Wr::Ka"(I_ ~).4 r+a
7/53 Fc.>r1X r/ rnorne",i' C?'ruoi/;briurl-f fA)
(Q)/ (0) 1 rd)YI;-.l-wa/ u->orlr (8)
(c), (e), (:f)
re) oU=cf~
te ) Je/= Jt:[ f Jt-e(f) d2V/tlez mu:;! .1>", (-f')
7/54 I ,eo,..- fy.5kn1 au:=. 0
P ox - P 6)(./3 = 0 p e, 3P = 3 (lOO)1 2 ) Z 1
-z: .300 A/
7/5s-1 dt/=O) /j 6x - T~Y3 = 0, 1= 3~
/ = 3 (IOe» = doo AI
7/S6 r",,:. ke Cloro =-k (277) k:- 0.040 ~l~ J' I rrnuT'
6U=o' Moe-pJx=o P=M~(}-=M/) J oX k
SO p~ TT /0 = 7f1s- AI0.040
7/,5"1' V-=~.::- ik(Za. sl'r,!f)a = 2ka-2SI'n21,
ou= cl~)' po(Zt:l.. .51;'" &)= &(2ka'2Sln~!)2Pcz cos c9 0'& = .2A-a. '2.5/',.,.!!.COS~ .f8
2 22P?7_co~B = ,fa2...5ln61
mn6'= ZP e:: fon-1ZPIra ) Ira.
7/S81 V= /;5/;"7 zt9 re cost9
q'J: = .2 6 SIn t9 Coos c; - C SI;'" G :=. 6 S/~ 2& - c $/n8dt9
d2V :. 26 cos Z& - c aa s &d&2
'/ d//'/J"" 0 so S/~&(2b U's& -c) = 0R:>r~9wI', /a(7=
& =. 0 <9 z: cos -I~ i 19 = 1T) Zb )
:=. (f) sra6/c- IJ C<" 26(-) un"Tr:>6/~ // C >26
-I CIVr i9=CC5 26 ) c «: 2b
f/ ,PV = 26 (zcos2e-1) +c cos O = 26(2 £- -I)-C"::""d8:Z 4bz 2h
= 26 [(ZCh)'I.-I] ~(-) .sro c e C < '26 J i.H1siv6/e
FOr e:: rr; d2V = 26 + C :. (-t) So s-h'';e
de2
dV=Z.kL.~/;"~cos~ - n:J~ 5,'''18de 2 2 2
1. ' .t'-= k-t SIY1 t9 - nfJ'2 SIn f)
:=.p( ki -fl?'1J)s;n e=-o for' e9u,';.19=0 e?Y1e1 h = Y>1J 1~.Iep~nden-l
__ z_.i. 0;1-&