Apuntes Estructuras Hiperestaticas UMSS

7/24/2019 Apuntes Estructuras Hiperestaticas UMSS

1/59

Fr4,./*\s Hrru.^{l*,T# /(/-&


2/59

l.J g-.,*.^,\Hr-r$"

f7=

.r1.

f\

s/eryLpft J-{. nHon-**

fuuo

l{- *r.-lo

{*r*^ /Ju, ,*r,t/vd,,Vz: (-rn-,s/,v" rou {

: Hrm /* = fln*v^/o

Ff:= I'l=FA = rtY\=hr=a*Hg = fi ll

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L@a Aouro ft"c,V

fJ,=/ );4

('{*

'{,

&)-*

&--.

\\Fue /c,*:,

o,J --FP

Pta

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., 1/ )/

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14/59

#/ro {rq6*Fo ,Oc,r *- : - - / fusk,; u)

u)t,-4-(Jx I t =re. Na) .:o ( Ful.1.7-a ;pfle.fi\tu frt


15/59

r/ UrZc- M fit r?a elahl" /c/ r rt c'/n **,,,{ftoo^Jr// n

f"s

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16/59

@

f +{

\.fob

kJr// / rr-o rot A

= + Pte *1Aaau /^-/ n*'n*nv,/;n-*o Fro ,00, o /a aJu = {fl JAr t P'J4p &J4a

7-,*do

^f,a


17/59

//,# /s ttoo,o[,

lu

i

iQ*, ,-

A/.\t

'tTr- ( P\J: \ PSwr

f-PU--L3 i

u.*,r-= J',ru

J. o Ar*o*uL,/&4 {e r,nrt,

ce6l*/*L'


18/59

Po,u(D

ua {-Cou,o{ #'**uo,4urz-^ /r, /r-

u de /r* r &c."..,g-.4.-^,*a-a

44 *1'n; ^j'iSf.1/: g-t-H= Q

-/;*";l , 14 J,-,;*s u,ter/r**u^ ,u*-{u) '

FncrJ^..{s =1PFren Gs?ir=fr" + F"

Fee 5 -J e

Fe : F -FtT'

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= lfao +(fqc= [/eeJz-\E.a\\,it A.=o+ "rrKfL.G,?art f*n /**e

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+


19/59

dl(s=oIP t B),e,/'

rz=

(p t e-q ) I4/

F' 5%/T",,/

rr/fr, t,^o[*r* ,.g U

--R lue "k **- G,F, /4\J #'*)ra- /*^o ,n 't'r^

m$,*o

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]i

rr = Ur +fJ\r: g* * rtpie=lw\'.d-^9 qr?/ ? )(,)F h %tl)(t

-, '4,5u, = lPo , gfn ra.a + -': = 1o/qt 4, tr,/],-.E, t?t

fl,l,m )n>y

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\r = it"l-te-A

:

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3,

{" c -

(du. = bU

bp

--


20/59

fue "/r*;rrr-6fu., 4o= 4. = /,4t = za c-',y't=*-Pa.'4n-.&

b? = 'lo trrl ---,V/&of ^ H A) ,

fJr +\.i-..+ f&

5y. ) tril=%-* l.f +

/+ 74. oo/

':

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,S, "

^t- /( a o/ooo.)

g olo lHuJ.d * t- t?rr",ffiLt"^)= Trto*ff*Ll=

_,@r7[;1

a--8.ft,


21/59

tlo,*ri*?-q *f)

I( +^# j @

Tf=P*':,/ >E /+

0 .^fro

@q.

J

@ e ,rtr"oy l;"

//

&/^

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f .dPr*tJPrl Wrf

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4t

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f cx)=(p*+a S k: e1

.;'

vo \-0r.Q\

Itont, (,) es

*Jo F A, /'

/fla(q ,sv/, u:4 /*r**.r-{orufu*_J& _Uu.-.. tqq*u,'xra""au uou-)rg /)?-,eo F\

,,f"= '. Ia,S


22/59

,* twr,Fta-v

-tu /r.'

0I _ trTn

' rg='f'?=LL:+.@>$=# U)

q

{r =I^H'& (/

i-

/ -r'/


23/59

tor,na-{*,uot Fr=&

(t 'ru) "o,

{rt*)"o'

(t+ o")

, / :l .u J3o.'' n* J.op A*oh, *n/-/,**,a , nAJ;"r* ono /*,uo 4./"^., // co,,a'r,gl". ,- ,rl J ul l *^r p" -/r)/*;

nf rlr-r)* *oro)*,n./;z*.Ar: (J 4t,h-uv.nJrot*.*^/ zr,r-,*,/oe/ lo//o"-uuA /r""i; J-/ ,t**^A,P**=-g'' =-;z l.loo .= D

+11 w=[PrP")"K

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,+(r*o)*ll.

I f +P"

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f" lu me\S''a " e4

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24/59

/o,, qry la

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}+

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25/59

n(%)J*

Jn

11 Lt)-J'#*"o1,lilu / e64", ro.

fhtu), m ( = -1o Ur' /.*u;: f* "*l",u ai'x

aF-

ta) , rn W

flas -. ho.tfztt-exsJ*u.a " ,N7-1;J^Q-u $= r'.1 L/ry" N7- -4 r4A +/* , ' ^rl/r7/run ol,osturra--t Ll ,\

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26/59

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n cx)

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@

%

q robr"/r*frt'{o./

/ -zn, -f*o '-7' c'=

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2A aL-/2. =: f+?,7F-a,

a,'


27/59

''t\ ,0r-{" ,rA-A* ?En/, )rtaes 'or-tfr*tS c (^'t1 '^ J NJ5 E 5 rw

{o=' Po'4, E7

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+ -t

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29/59

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'ft> c"=;(*q(c)&D;---


30/59

l-' v cp'aT{nJu.r

-wFv* c\. * ,(*?.q/q

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F v f -:1

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31/59

/ co r dri-

l^fr**tb=* .( ?,-./n'14, ?r. ru r( * J'*'j*

'' s *//,tuJ"'

l,b

re*

liq= J-Z'.'.'

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E 9C,)

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t-a' *'(*)( ?., F c, *{*)(fvrrl r q*ei7 ( 7-e"- 7._t?? 6z (


32/59

,/1-Lq // (/rtr.r, nn. 4*n=* A &s*d._

{:

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t\ ?ca'nh(,)=

'-i o,=-F 5 */* s,:iooI

frtorwe44l*uoJ l-tc*)

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q -u'"

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f-t - -z- rT-aZe {?-rt xr r)rt,


33/59

?/ = ?--Q.N- Gd26/1

n

Y5*r,1

fisl=--0t( *7-q%lp*,U't t /n ?-q*(*t 6- 6

tF (? {,7

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+ ,rya*EJo q# orllC;T

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34/59

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{;.* qa-rm A*c

fuL*;;t-[= f 'fl'"1'-*il1\'/ Jo e-

U

r-15,:/*t

q:, zI E-l8

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&-

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=;= 'plT

r. Jr.^3.-qt'{+=


35/59

_/Ju4/ /aH,ta-oa t "-fl

$

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at-L'o'33t/

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[-c'^,6q.

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{= ( 4{-)

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tml/ 3 9"6

f1{''nt

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.F*=-

,rr vdv'] o e-h-+"

IZ

fn=4,ENll ? ?" + J.s?EI

'=?7-q v


36/59

2Vb R a fta*

+a


37/59

gMsn J'*o ,E = c/tte'n rryt'tr?q*lr.{r^,'s,4u *,u/'/'Ju

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t, (a

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d' = {ttCz

')

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I

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fqn' 1 il '\tr

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38/59

Elr \:3{?ql(


39/59

il.c_ hda 4-- c

2 -('c-

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/* {**.,tqF* s-0.-e*er4 L vec/o."-{c's /^{-Y/'

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40/59

n lrrn)ne/P

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7+

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tt t"r$

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rtty i

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/)*c


41/59

rty

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ml'lll

u*

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2n'

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4.

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t6tt=

I

, = | L,yl

b'= f+*-W)


42/59

ru/, u" /r*u

)tu 4Wg'=('*T's i *(o+fr)-a4

fr,rur*/n,"t>p&tJ*J

' kr'*.="k ('i (;-o) frun': t-{en-a) Fjr:=

?:f=

J ,wb, e,,eo-(

J, lo,uo

r/ri o*Jo*J" l*.ryasJ, u.,t "b

C aac)ryw aLr

4 &toIa()e

qd

fn r:tUra,un

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s;,Iadl *

( -J)s/r- (rxl*a):o

3;v ?-0= /A; 6F(e*t-q=_/

6-Q

fr = ;rr


43/59

&o=r- (a-a) :

//{uru{^ft i'r--

uaL'

&rt

Lt //o /4 \\//

A3 :. s- = ?

3't '3Y '(:

ft/."./u*-J,

t/ F'r

e:P J/+: il* J

lYarees sr& J"",4 , /, ,; cin-,s.s cr- (rf omo * ,)

o*-t'?f' ffi,

*sM'

4 ,*b*l.r/4q

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*) ca6ct J &ade :ao"tl =-

k:r/

ft -a)E+ C- u4

f,n uu &


44/59

GpDlo =

;;

F

p

3* r -E:- (

''5=grdr{;*.4= ffbrr" *-,s 4*{s tla "/ .u'VYt

X',- = ?

4: c 6


45/59

.f ,o

l,**M'

--) Sro + S,, - YL--- oX, :- +.. ), o$-tu-

,f^ *J^,-k t J*r.Ka fg) D?n tq _- o;

=...

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I

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I.I\e@r"

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46/59

+) 74rlr*rto Vl'"o'uo-,loo d't;;"*'*J fu '"S,o t 5,, "Y: Q

3 r to*(H)taq)=r \no3: *g-do.(ol?")+ {c.,.*f,- " (20.) (ra)rB

11 u + H, ,MX=s"u.5rt

fie

[-.rryqo)

j-.r__

**t :d

n I 5*E I 5., r ,3? q,J2J

sn* zf1.l \: -t1

9t

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,Uu /,/,/ "q E u,r'vczt-


47/59

t,6u*-f J,*j'* ;, T =&.e

z+-av

Et5^

tr rl*. 2. rz. 1 Q')

\3?- q,- + -LG

/1,*^

/9V

9a

,2q.?*Itl-

///rnu /1, p /i rrr,"o"* ,/, *ffr>it+.

5,0 l$,,X c o

= r+ {rqor/o)a +a * Fr


48/59

qE

flt--.-#-

z?u?

2 ?-q7

-a^ Aav

r /o (u,u


49/59

'* ./ J"y'u'"^ ft/Fz- dW

I *l-nr

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t oft," rade*,

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s /rr*;

o-

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t

I

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re7*

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9- ev

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6,r;NJ'r A Qersr-L*&,' */ ttdut{;'JZ

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I

u)|

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lt-*

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50/59

Tb'i (V

t

I

I

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t-:'**


51/59

fl,prts" 4atb*q.7

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o

f,2 /- /.-

l, clu rTlcrtc*c t/t- /"- J

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cr?

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fdo ntt wtp ff'n ffi'#-"/"

t4o(.:- ttffiJI

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Y=*flna,,y=*r*"i#)

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aF va taory) - S q* IL q" Yq&-K7 qu

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52/59

./.4{

.;f

i t' i *l-L"r{{-(I rylll1 6n'

rj*-:, fd*cL 4

X"'

= f *3=3 & '3-o: AxC ft= gr\-O;J

ooJac\ \J

ffi,r,fiu,1,/" /z'gr\^r,J,*-?

Ifcr trl.rooo*f*;on e,i u ry g ( eu, k-


53/59

YJ 'X,

rt / u'J " ,:"f,'t ',P ltc

.::i";r:;.fiv"*fy-r^(/,11/z: o 7

IY-r Ul


54/59

5= /7 -(ea )tr /^)r4 t Qc^- ( e*) /*Pr-) = ./ 7 /*E

(Jf^)*#* za. (efo)(r) = *?"Ve a

{J',u,

J fJ/FJ J*,

(,t JJo

EJI{fl

d "&t

/ t:, rJ*

a rQ,b Q**

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: +o.*

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: F- &(fol(t) rZ - &Y*(^ )

f

o,2,)

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n.n X, /e 6z Xz az X, J*,/2a Yv: O

K,= o, fs7 PT-= - 0, rE ? Po-

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/a"(-(tolfl")/o 7 /u,

Pe'-#+Sntr +' o

Jo*ut t,qr' i'i ', t tqr tc'- Su:r $"

oF3t$$c"


55/59

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Apuntes Estructuras Hiperestaticas UMSS

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