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 :

    9.1through9.4 For theloadingshown,determine(a)theequationof theelasticcurveforthecantileverbeamAB, (b)thedeflectionatthefreeend,(c)theslopeatthefreeend.

    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

    9.65and9.66Forthecantileverbeamandloadingshown,determinetheslopeanddeflectionatthefreeend.

    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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