CH 9 solution.pdf

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• Problem9.3

YI

I

L

Wo

A x

L

A

[)(":L..)j-=-O]

['J(-::L;):1;", 0 1""DX

~ TMJ :5x'1.

IIJOXI

~ ~3'\A loE~{J

V

[116=L..) .)'': 0]

(Q.) EiASfi Co C:tJ~lIe-

(6) j @ ?t-=D:

CC) *- @ ~= 0 :

LJ.se ~Neeo.boi t AIa

+.::>L MJ" -::.0: M... w;:. fM -= - ~ 'dr-a

': 0

dZy -= .-.l.. ~x.\$cH., 6 L

.1'~ - -.L wo')!,'f CrJ?t, - 2"f L + I

,.-- , w.x!"c::I ,,= - - ~ + C ~ + C~ r~o L I 1

r"X-=L 6.: (;) ] .. - ,;L Wo L:! -'- CL' .) h . ,11.." T'" Ic. - J... ,01L'3I - ~... VVg

EI - - -L hI L'" ..d- ..1 L'1 C -j - I~o Vo +.t 'I VVo + z - 0C2 - -doWe) Ly.

~r=II~~~.I Co'(~S - -5 1..~?t.+ If LS )~

h. .vJ. . \Ik -::~~iI L (-; ~., ~ L ~I'

- - WoL'f - ""0L" -J,I:fA - 30cI JA - 30EI ~

!L I-=

h,..W L3-2..-'J.~EI e - woL"A - ~tIEX A..

.......

• Problem9.7

L

('1(:;>..)Y::D] [1f:L...Iy =oJ

~J

wiL-

l _un !rk-~

r

• Problem9.12 9.12Forthebeamandloadingshown,(a)expressthemagnitudeandlocationofthemaximumdeflectionin termsofwo, L, E, andI. (b) Calculatethevalueof themaximumdeflection,assumingthatbeamAB is aW 18x 50rolledshapeandthatWo=4.5kips/ft,L =18ft,andE =29X 106psi.

'I U"~

~~'""""" L"'"[1C:O).)'=O] LX: lJ j=O 1 Us; n~ e.1,J..Y'ft be"-",,,o...s0.. -t t'e~ b~)

fA ~W.Lt~sf1:?~ R(\ .

""ox

IAp:1~"'WI) l "

-0 ~Me = 0:

RA = iwol

-RioL +(k'No l )(~) ~ 0

Us;~~ A:r c:...SGl~4! boJy.> V21'1j : {):

- * Wo Lx+(~~X~)(~)+ M ~ 0M -= ~'No l)( - i Wo X. 3... b L

EI ~ - .J..WLx - .1.~ x3~ - 6 0 (. LET h. .L L 2. J..Wo" C-..Ix ~ ,~Wo )( - ~&IT:X -t I

fLy::' -kwoLX3 -I~O ~xS" + C,X ~C2

[x:o)y=o]

[x-:=L.)::J=O]EP",-st-ic. C uN"! &

0 :- 0 - 0 ... 0 + CZ Ca.= 0

0 '= 3" WOL" - ~ Wo l" + e,l 4 0 C, =-- Wof ..LL 3 - ...L~ - ~ L3 1

j - EI l 31:. X I~o L 3,"0 X ~~ - ~ f...L 2.- -'- ~ - ..L L31Df'C' E rl~ Lx :1'1L .3'0

10 ~;Y'lJ jQC.#../t1'0"'1of ~~~MU""" Je.-tJeG-tiC>\I\" set ~: 0

\.5)(: - 30 e~.. 7L'I = 0 x ~:- ~L I.- -I qool" - 9:l~~. ~ 3.0>

• Problem9.15 9.15KnowingthatbeamAE isaW 360x 10I rolledshapeandthatMo=310kNm,L =2.4m,a =0.5m andE =200GPa,detennine(a) theequationof theelasticcurveforportionBD, (b)thedeflectionatpointC.

:Mo Mo

Use c.Q~i; VIu; -l "I

aVlJ SjWlYhef~1

F~oW\ Sft,)lh'c.s j

bDVV\J~"1 Gc,"IJd i O"" c

c., = Mo0. + C3 : -t0o(~L - do)

-l-i'IpC.,*-t:~o.)~ + 0 :::-~~ - ~Mol~ + CotCy-'::" i Mo 0..,"2.

(a) E.P4.Sfic. c;.uYVc.(Q. ~?(,~ L-o..). Elj :" -ft-'I~'"X..1.,!,"tHo Lx +., Moo.:~,,':: Mo

.

('t,1.- L~ -+ a.2.)\oJ 1.e:I

-4

(6) De!'.Ped;0tA ~t x.= ~.

:Jc.:::2~ [(;)L-(L)(~)+a.~1= -lir (L2.-lI~)

'DcJ",: Mo:- 310xIO?#.M J L:: '-JI,/""~ Ct.J' o. SM ..) E ~ ~oo ~/d'l 'P~I .::: go~')I'Oc; WlfIf#\'t ::: 3o:()( )O-c. M" E I,:: bO. Lf-Y 10" tV. M '2.

3/0)(10'!.[(

&.

( )f. "2.J -:!.yc.= - (g)(bO..~)lrotOf R.If) - &f ,.0.5) =- 3.oS)(10Jc. =3..DS ",,",IV>~

....

• Problem9.23

tV =wO(xIL)2 Wo

L =10ft

[x=0 ) 1.:0 ][x=0 J~" 0 1

y ~~I ~ j> -~rLL-' -;RB

~:)( ! : 1.

EI i..tx.. ~

EI~h- -=

EI::J

[x: LJ Y=0]

9.23ForthebeamshowndetenninethereactionattherollersupportwhenWo=1.4kips/ft.

K'ec..ch oV\S C1..V'es-f4"+ice..JJj iVIe:!d e.1I""";V\Glt~.'6C>t)~ok.lI"j C:o",d.-4i"""5 CtV'e SI,GlIoV"\ G\.t left.

Us;,.." -tV'.e~bod.)' Jg> +;>~ MJ" = b:L

- M + S 1* ~2(~- x) J ~ of1(&(L -)c) :: D)(

M ~ r~S: !~('~-)()J.5- Rg(L-x)

= ~: (~!~- t}(~3)1:- Rs(L-)()

: ~~(tLif - t is x +~)( ") - I?C3(l -)( ')

~(t L1/- ~ex of ~x") - Rs (L -)( )~~(~ L/IX - t l\$)( ~ +&~ x\$) - Ra( Lx -tx2) -to CI

~ ~CtL")(2--/~'L3X~+3~O)(C)- Rs (~L)(1.- tx3) -+C.X -+Ca,[)(:o.)~:o]

[)(:o~~:= 0]

h=L.)'j=oJ

D~t~:

0 -=

0 ~

0 f 0 + C1 C,::' 0

0... 0 ~ 0 of C.. c~". 0

l .L - .J...+ .J.. ) w LIf - (.1- .L) 0 L! - 0i 13 3',," :a (8 1"\8 -~ Wo l" - 1.. f?, L3 = 0 R ~ 1J. MI.LIto 3 8 B ~o Q

w~;;- 1.&4k:fS I~t,)

1ft"

3.03 kips 3.o~ k;rs t ~

• Problem9.66

IV u>L"

i . ,- ~Y~ ~~--L~J

Loc..J'V\3 I: Do.vnwt::tv-d J's+v";b.)+~J ioo.Jw ~ppl;e l to portio,"" AB.

CD.5e ~ of Arpa-",'"~"..D t:A.pp.tec1+=>po"..t,o,,",A~.

e '- w(L/:J.)?- _..L.wL'3.Ii . - "E;I - If-csE.r-~(L/:l)" - --L wL"gE.r - ,~~ EX

'1'-Je. -

C Po"...h'oll\ Be.. t'e.""'~I""~ ..si~c"'jht.

~wl"2./~" r...' - r\ I ~ L. wL3

~) "c - "'s '18 E.I,- I J:. ,,: _-,-wL'f LwL"- _L wLYl~ Ye.- Yf3 +{~}~ 122>EI 't~EI - . Jog'tEILoca.Jil1,:tJI: CO"'I'\+e"'c.PoG-kwl~ecovpJ4!. ~}L pi..ee1 t:;~iu"'J

- 1'\I 6. II - - -L 'AJL'!. .J.. wL~ - ..LwP ..:::::::::1.9c. - 1::', + 1:7, - LIS E:r + 2" EI - .,~EI

I ., 7 wL. , \AI L" ,wL" t:1c. ': 1, ... ::Ie. =- - .3-tEX +IJ~r :" m EX

-4a ,I

......

• \...OC..J\ n~ I: Co'"c.edV'-t~d POA.e!CL4'8

Cc...se..I ,,1 AppeV\cli)( D a..ppilee-ito fe.>.rt.'oVlAt?

eI - - 'PL2 - (3)(C>.75 )~- O.8 tf'37S-a - ZEI -- J.I - - EXvi -=- Pl3 - _(.3)(0.75)"3-=- O_4~187f"

J s 3 r' 3 EI EI

PortioVi Be V'e\N\Ct,'V\S,st ('6..,,~J..t

t'\ I ::' 6",' :- - 0.8

• Problem9.78

20kN/m .

Bc

30kN

1.6m0.8m

@c. 8

1~

• Problem9.81

M~,~~,," 2L ", L3" "3

CD

t- ~ Rar~~~

b-4

Mo("~ci) c.

I

ii ~~ )( ~

M.(ff?~ 3.t!JL

L?c

9.81and9.82For theuniformbeamshown,determinethereactionateachof thethreesupports.

SeCtIM i~ 5+.:..+..",11:1i~c\delflM\'rle.+e. -+0{:i",~t Je:1I/'~e.COVIS I'de.", -Rs to b~ t"'~ \"~clv",d4.",T '(\~o..c.+"o"""CtV\d

~ep.fQ.C:ctl,e lo~"YI' by Jo~;...,s .r ...11d..1I.

Loo..ol;V\~I:: Co..se.s o-t Appe",J,')I D.

(" ') =_R5a1.b:z. ~_IfV\Ji)(D.

( '\ - YIo ( ? ;Z) - 1'-10[(.1:.)3 - ~(L.)\':18).11- - bE.!L Y. - l 1-.- - ~ELL 3 L '3 jM L2--~-L-

- g1 EI

s\Jr~pDS;.h()1II a..,ol co"'st~I'lI\t.

j8:' 01'6)1+ (YS)ll = 0

- .JL ~ ~ ~L~21./3 EX 1- 8 , er = 0 1

• Problem9.83 9.83and9.84Forthebeamshown,detenninethereactionatB.

w

A c --'It,

~w

~1'1. +Mt b ~B~t;=--d ~J ~/ 7. c: Ve-A

I BII---U2-J-U2 1

PoM-io""Ac~ S~fe.rf'-:.r+ioV\of' C,,-se~S~,/ I crl Appe J;)( D."" ;: !:1c-(Lh.)' - Vc.(UZ)3 ~ 'M~L"2.- Vc..L~Je.'2:EI .3~r 'iJEr 'lIfEX

e = Mc.(Lh.)- Vr(L/~t:- ~ ~~L3.c: r;I 2 EI ~EX gE'I.

po",.,h'o,,\CB:- Supe.rFr..;,,;.~io"" of' c ses .3J I.) e..~ :z cf: ApreJ~~ 'P.V ::- J"1~(L/..:?)-..+ Vc.(L/~): - w (L/~ )tJ..Jc. ;{E"I .3E.I: 8E"r

:::- He.L'L +- Vc. L'3..8EI 'J...lfEX

e ::-- Me.(L/~) - \Ic.(L./:J..)~+- w'(j-!:~ . wL

Me. ~ M +t2~1=j':" 0 : Rg ~ Vc - ~ = b~ ~ e WL. . \3 t'- J R - ;:;.F- ~ IN L ~ '-3 '" .""LL B- ~ . 3Z ~\/.t-- '" 12~ "'"'2 M.. "0: M.. - M" -v..~.. 1Uf.;f=0

Ma~~We+~wL):t)- wf

MB -: -..1L.wL~ Ma :-t~~wLt ~1'1~

V. :- ~ wlc. 3:t

M ~.J...WL'a.

c. itS

~

~

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