beams on elastic foundation-Winkler's model

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v(.)- vo, y/t.1= 0., Y't.) =+-, V'[.)"- + El V"'i*1 + K vC*)= fC^) =+ Y"[^) r !- ytx) = -PG) Fr Er 5av(+1 * slv, *sL$,* * T?.-+i- a4(av[s)= tfi, 4EA (# +q8) Ve'1 = *% +s29"+ s g-+ + rB Gu + a $a) tr-" r-+ff) - - F{4tr) EL (sar+ff1 r t T[. J:":1:,I l,{f*".Ji-{. en,,*}i.^ *,.[.0 L* S'.0'uJ b ,t,:] Li 0"V"'= t'*,.t 6r,,ro-),o. . P fsl (sa + -+84) Yr k-- - / {? (^) = sa Y 4Q1

Transcript of beams on elastic foundation-Winkler's model

Page 1: beams on elastic foundation-Winkler's model

v(.)- vo, y/t.1= 0., Y't.) =+-, V'[.)"- +

El V"'i*1 + K vC*)= fC^) =+ Y"[^) r !- ytx) = -PG)Fr Er

5av(+1 * slv, *sL$,* * T?.-+i- a4(av[s)= tfi,

4EA

(# +q8) Ve'1 = *% +s29"+ s g-+ + rB

Gu + a $a) tr-" r-+ff) - -

F{4tr) EL (sar+ff1 r t

T[. J:":1:,I l,{f*".Ji-{. en,,*}i.^ *,.[.0 L* S'.0'uJ b,t,:] Li 0"V"'= t'*,.t 6r,,ro-),o. .

P fsl(sa + -+84) Yrk-- - /

{? (^) =sa Y 4Q1

Page 2: beams on elastic foundation-Winkler's model

P* I*r"r,.oo'-*,iis , N- , [ono6) , lo-hr" ,,.Ls--:,, Arp_[.J u*lL-*]i"sL J::::*' ", ' iJ'--r, G"L E5r"eer,T J"y-*.1*."Jr-

l"okt *,jiLtr,ir.rsi\ o

Greecei

@

Page 3: beams on elastic foundation-Winkler's model

.Yg+ g.{ =od* ' Ju,.:!'tr e . t=O$e

hl e qSs.rv.tej +L*l ll^. S-{*J... o I }L [ro*.,* e rceo"us

J ; II** l,J. e1*n li.,,r. cev\ b* e xy.essoJ o-s t" {"9 -

* J'11,x) = to, t'1{"*J }t" cLo'o.-lerreiic F5+-

(r* *6 ) C^=o + (ra+8 )=, . .hJ",r']i.

vr"i*[er" "

c.,s'3x"

=L =r tr= F- ("**4r-t f

-=b + Y4=ire-t (.,, T

<x

J,^: = d ^ + ;J'cn) = { e-'* -->

3"C*) = "y' e'x *. J"i*t -- y3erx

(*"(ryL)"t t s,"[,ntr,))

,frtisin+) =1F e",g-)=>

;{=

'l\>4 => f,= irY,=i[f t1t L

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e"[r+r)x-n .](*l+i)x a =".-(l*i)x^ .(r-i)x @

3t.)= /l, e ' ' .:,- Az e

Jcq - A, {d*** Ae.}'Tn].d?"t^. n.ge-*o^

_J (x) = d' ( A, eio^ + A< €"'" ) n a*^(lt, et'L A, d"" )^ tqx

+ i*^ [U,

(*r*^ 1is;n*^) + A3 ( ."ro^* tt,,*)f

= e-^f (^, *A<)e-so,. * [0,*Ar)a si"{+ c*'fi.b*A)c,sc.r

-f- fu*r.z)t 5i4q.xJ, oL"*.,n-,= A,rAa,I,=(fl,-X")n, I.= ArtLt

crrsqx + AaS

x) = eo *Ed"*) ts-*x * [E e^"+h*-*)srno.x

Cx) = E, e-:lr,..xcs5\x a E s,,[t.rx €08qx * brcytln*xsin.*; "t'&t,^L.xs;,rqx

2,,6 ) , Lu.. )*-,* '.1", ,. fl7pfl,.J f[*ll"**],.s r,I P'l{""t. C,t,I Er1i,neexi,,.i J.y*J*.n] , P*Jr"o,

Ces _ox a ,1 Si4 o-;

J(") = a* [U,(-ro^

+ {s,vr,rx) r- Aa(*rrr}- tt,,**f

C.*"^[ S.0o]io^ . f +t" h"5e^eorrs Ji f{"r""Ji"-{ eTus-}i.n-