175606462 Slope Deflection Trabajo Final
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UNIVERSIDAD PERUANA DE CIENCIAS APLICADAS
FACULTAD DE INGENIERÍA
INGENIERIA CIVIL
TRABAJO FINAL: MÉTODO DE ANÁLISIS DE ESTRUCTURA
SLOPE DEFLECTION
CURSO : MECÁNICA DE MATERIALES
PROFESOR : JAVIER MORENO
ALUMNOS : JOSÉ CUYA CALDERÓNJOSÉ DE LA ROCAHENRY FLORES GAMARRARAUL PACO AYUQUE
FECHA : OCTUBRE DEL 2011
LIMA – PERÚ
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TABLA DE CONTENIDO
INTRODUCCION.........................................................................................................1
2. “SLOPE - DEFLECTION” .............................................................................34
2.1 Introducc!n ..................................................................................................34
2.2 SUPOSICIONES B"SICAS DEL #$TODO%.................................................3&
2.2.1 Con'(ncon()% .............................................................................................3&2.3 DEDUCCI*N DE LAS ECUACIONES DEL SLOPE-DEFLECTION% ............3&
2.3.1 #o+(nto) d( (+,otr+(nto .......................................................................3
2.3.2 #o+(nto) /(n(rdo) ,or d(),0+(nto) .................................................41
2.4 PLANTEA#IENTO ENERAL DEL #$TODO DEL SLOPE-DEFLECTION%&3
2.4.1 A,0cc!n d(0 S0o,( D(0(cton (n /) ......................................................&3
2.4.2 A,0cc!n d( S0o,( D(0(cton (n (0 n50)) d( ,!rtco)...............................64
2.& E7ERCICIOS PROPUESTOS% .................................................................18&
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2. “SLOPE - DEFLECTION”
2.1 Introducc!n
E0 ,ro()or (or/( A. #n(9 ,r()(nt! (n 1:1& (0 +;todo d(0 n50)) d( ()tructur)
S0o,(-d(0(cton (n un ,u
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• L) (cucon() und+(nt0() d(0 +;todo ()t
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Fempotramiento Fu(r) /(n(rd) (n 0o) (?tr(+o) d( 0
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⎣ )
empotramientos⎦ #o+(nto) /(n(rdo) (n 0o) (?tr(+o) d( 0
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3,
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F/ur :% / Cr/dJ
A B
S( con)d(rn co+o r(dundnt() 0) r(ccon() d(0 (?tr(+o B )
condcon() (n (0 nodo B )on t0() u(%
θ = - 9 Δ = -
. / . L)
.
Lu(/o%
%⎡ ) 0 )
. .
⎤θ . = 1 -
%
⎢⎣
⎡
⋅& ⋅2 0 )
.
) 0 )
⎥ d = - Ecuc!n 2.3⎦
⎤Δ . = 1- ⎢⎣
⋅& ⋅2 0 /
.
⎥ d = - Ecuc!n 2.4⎦
P0nt(ndo 0 (cuc!n d( +o+(nto) ,r 0 '/ )( t(n(%
4)
- = ) ( " − ) . −
! ⋅
! ⋅
+ ( / . ⋅ 3 " = -
) ( " = ) . +
− ( / . ⋅ 3 " Ecuc!n 2.&
D(r'ndo 0 (cuc!n d( +o+(nto con r(),(cto cd un d( 0) r(dundnt()%
0 ) (
"
0 ) .
= 0 ) (
"
0 / .
= − 3
• Pr (0 c)o d( θ
%⎡ ) 0 )
. %
⎤ %⎡ ! ⋅ ⎤θ . = - = 1 - ⎢⎣
⋅& ⋅2 0 )
.
⎥ d =⎦ 1 -⎢ ⎣
+ ) . − / .⋅ 3 ⋅ [ ] d⎥⎦
37
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- =! ⋅
6
3
+ ) . ⋅ 3 −
3
/ . ⋅ 3
%
-
- =!
⋅%6
/ . ⋅ %+ ) . ⋅ % − Ecuc!n 2.K
D(),(>ndo / . d( 0 nt(ror (cuc!n )( t(n(%
5 ⋅) . ! ⋅%/ . =
%+ Ecuc!n 2.6
3
• Pr (0 c)o d( Δ
%⎡ ) 0 )
. %
⎤ %⎡ ! ⋅ ⎤Δ . = - = 1
3
- ⎢⎣
⋅& ⋅2 0 /
.
4
⎥ d =⎦
1 -%
⎢ − − ) . + / .⋅ 3 ⎥ ⋅ [ − 3 ] d
⎣ ⎦ / ⋅ 3 ! ⋅3 ) . ⋅3
- =. 3 − −
, -
- = / . ⋅ %
3
3 4
! ⋅% ) . ⋅ %− − Ecuc!n 2.
,
D(),(>ndo / . d( 0 nt(ror (cuc!n )( t(n(%
3 3 / = ( ! ⋅% " + ( ) ⋅ % " Ecuc!n 2.:
. , .
I/u0ndo 0) (cucon() 2.6 9 2.: )( (ncu(ntr (0 '0or d( ) . %
3 ⋅ ! ⋅%,
+ 3 ⋅ ) . ⋅ % ⋅ ) . ! ⋅%= + % 3
) . = ! ⋅%
Ecuc!n 2.18
4-
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R((+,0ndo 0 (cuc!n 2.18 (n cu0u(r d( 0) (?,r()on() d( / . )( o
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Aor )( ()tudn 0o) +o+(nto) d(
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F/ur 12% Rotc!n (n (0 nodo d( 0
θi
Mij −θ i M −θ
) i j − θ
i
) ji − θi
i( θ i"
ji j
#o+(nto /(n(rdo (n (0 nodo i d(
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⎛ )− ⎜ ⋅
$ % ⎞ ⎛ ) % ⎞.
⎟ + ⎜ ⋅ ⎟ + θ i = -⎝ &2 ⎠ ⎝ &2 ⎠
⎛ ) % ⎞ ⎛ ()$ " % ⎞−⎜ ⋅
−
$ ⎟ + ⎜ ⋅ ⎟ + θ i = -⎝ &2 ⎠ ⎝ &2 ⎠
⎛ ) $% ⎞⎜ ⋅ ⎟ + θ i = -⎝ 4 &2 ⎠
D(),(>ndo )$ )( o
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Pr (ncontrr 0 r(0c!n (?)t(nt( (ntr( 0o) +o+(nto) /(n(rdo) (n 0o) (?tr(+o) d(
0 d(
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Pr (ncontrr 0 r(0c!n (?)t(nt( (ntr( 0o) +o+(nto) /(n(rdo) (n 0o) (?tr(+o) d(
0 u/d ,r c0cu0r (0 +o+(nto (n
unc!n d(0 d(),0+(nto r(0t'o (ntr( 0o) (?tr(+o) d(0 (0(+(nto.
Pr no )turr (0 do 9 ('tr ,o)
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I+,ortnt(%
E0 )/no d(0 +o+(nto 'r= d(,(nd(ndo ) (0 d(),0+(nto r(0t'o c( /rr 0
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R(to+ndo 0 (cuc!n
) T#T$%&' = ) empotramiento + ) desplazamientos
,0c5ndo0 0 nodo i d( 0 )( t(n(%
) =i j Total
) Total
F
) + )i j i j desplazamientos
F
) ) " ( ) " ( ) "i j i j M ( i j −θ
F 4 &2 &2
i M i j −θ M i j −Δ j /
6 &2
) i j = ) i j + % θi + θ j 9 Δ / Ecuc!n 2.38% %
0o +)+o )( c( (n (0 nodo j o
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2.4 PLANTEA#IENTO ENERAL DEL #$TODO DEL SLOPE-DEFLECTION%
Pr )o0uconr ()tructur) c(ndo u)o d(0 S0o,(-d(0(cton )( )/u(n 0o) )/u(nt(),)o)%
. A,0cr 0) (cucon() (rcco)
t,o.
A0 ()t
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C0cu0r 0o) +o+(nto) (n 0o) (?tr(+o) d( 0)
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T(n(ndo (n cu(nt 0) nt(ror() con)d(rcon() 0) (cucon() u(dn con'(rtd)
(n%
)
)
$ . = 35;55 + 6666;6* ⋅ θ
= − *; + 3333;33⋅
+ 3333;33 ⋅ θ (6"$ .
θ + 6666;6* ⋅ θ ("
)
)
. $
.
$ .
= 66;6* + ---- ⋅ θ (3".
= − 66;6* + 5--- ⋅ θ (4"
. .
@)t ()t( ,unto )( t(n(n (n (0 ))t(+
θ θ ) ) ) ) . 4 (cucon() 9 K nc!/nt)$ . $ . . $ . .
P0nt(ndo 0 condc!n d( (u0
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A)= )u+ndo 0) (cucon() 2 9 3 )( o
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• 4 ). = ). $ + ). = − ,;4, + ,;4, = -
E)to )( c( con (0 n d( '(rcr u( 0 )o0uc!n d(0 ))t(+ d( (cucon() )( o d(
+n(r corr(ct
E)t5tc d( 0 ()tructur%
Conocdo) 0o) +o+(nto) r()u0tnt() (n 0o) (?tr(+o) d( cd (0(+(nto )( ,u(d(n
c0cu0r 0o) cortnt() ,r cd
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• F ?= − ,- + 66;7 + > $ . =
> $ . = 3;-7 HN.
Brr BC%
1.4 n-+
• ) = ,;4, − 57;* − ⎡( 5-
-
&8 n+ -&:.26 n-+
BC CB
< 4 " ⎤ + 4 ⋅ > = -4> .
⎣ ⎦ .
= 74;45 HN.
• F ?= − ( 5- < 4 "+
> .= -5;55 HN.
C0cu0o d( r(ccon()%
Nodo A
74;45 + > .
= -
R A
8
AB
• 4 F 8 = / $ − >$ . = -
57
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/ = > = 3;-7 HN.$ $ .
Nodo B
• 4/.
Nodo C
• 4/
BA BC
-1.4 n-+ 1.4 n-+
RB
F 8 = / . − > . $− > . = -
= 66;7 + -5;55 = *;46 HN.
CB
&:.26 n-+ -&:.26 n-+
RC
F 8 = / − > . = -
= > = 74;45 HN.
•
4 )
.
=
) . − )@ = -
6-
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)@ = ) . = −57;* HN - +.
Eu0
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An0ndo 0 ()tructur d(),u;) d( ocurrdo (0 )(nt+(nto 9 c(ndo u)o d( 0
con'(nc!n ,ro,u()t (n 0 )(cc!n 2.3.2.3 ,r d(t(r+nr (0 )/no d(0 t;r+no d(0
d(),0+(nto r(0t'o )( '( u(%
• L
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63
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) = 66;6* +4 < ---- < ----
⋅ θ + ⋅6 < ----
θ − ⋅ ( -;- ".
) = − 66;6*
+
4
< ----⋅
.
4 44 < ---- 6 < ----
θ + ⋅ θ − ⋅( -;- " . 4 .
4 4
O
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$
.
=
-
--- ⋅ θ − ,;33 (3".
= 5--- ⋅ θ − 4;6* (4" . .
64
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Nu('+(nt( )( ,r()(nt un ))t(+ d( 4 (cucon() 9 0) +)+) K nc!/nt) d(0
(>(+,0o nt(ror θ$ θ ) ) ) ) .
. $ . . $ . .
P0nt(ndo 0 condc!n d( (u0
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- = 6666;6* ⋅ θ
$ + 3333;33 ⋅θ + 6,;,,.
- = 3333;33 ⋅ θ
$ + 6666;6* ⋅ θ − 46;.
R()o0'(ndo (0 ))t(+ )( o
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u( )ur( (0 nodo A +(no) (0 )(nt+(nto u( )ur( (0 nodo B. E)crto (n or+ d(
(cuc!n )( t(n(%
Δ $ − . = Δ − Δ$ .
Δ $ − . 3 c+. - 1 c+.
Δ $ − . 2 c+. 8.82 +.
En (0 c)o d( 0
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) . < ----
= − 66;6* + ⋅4
6 < ----θ − ⋅ ( -;- "
.
4R(cordndoθ = - ,or (0 (+,otr+(nto.
• E'0undo 0o) t;r+no) d( cd (cuc!n )( o
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67
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)$ . = - HN - +.
). $ = − 6-;64 HN - +.
). = 6-;64 HN - +.
) . = − 57;* HN - +.
R(ccon()%
/ $ = 6;56 HN.
/ . = 63;*, HN./ = 77;66 HN.
)@ = − 57;* HN - +.
E>(+,0o 2.4.
C0cu0r 0o) +o+(nto) (n 0o) (?tr(+o) d( 0)
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d( )u(0o ,u(d( ,r()(ntr )(nt+(nto) d(r(nc0() 0 )(r )o+(tdo cr/). S )(
conoc(n 0) ,ro,(dd() d(0 )u(0o )u r/d( ,u(d( )(r r(,r()(ntd con (n r()ort( d(
/u0 r/d( () d(cr 0o) r()ort() )on d(0con() u( (n (0 n50)) ()tructur0 )(
,u(d(n (+,0(r ,r r(,r()(ntr r/d(c().
Co+o )( ,udo '(r (n (0 (>(rcco 2 9 3 0o) )(nt+(nto) u( )ur(ron 0o) ,o9o) (rn
conocdo). En ()t( (>(rcco (0 )(nt+(nto u( ocurr( (n (0 ,o9o A ()
d()conocdo (0 nodo B ,(r+n(c( (n )u ,o)c!n nc0 0u(/o (0 d(),0+(nto
r(0t'o (ntr( 0o) do) nodo) )(r5 Δ .
• P0nt(ndo 0) (cucon() d( +o+(nto ,r cd
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*
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) $= ) $ . = -
- = 35;55 + 6666;6* ⋅ θ $ + 3333;33 ⋅ θ − 666;6* ⋅Δ (6".
) . = ) . $+ ) .
- = − 4;44 + 3333;33
= -
⋅ θ + 6666;6* ⋅ θ − 666;6* ⋅Δ (5"
$ .
O
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4 ). = − ( / $ ⋅6" + ,-⋅ + ). $ = -
D(),(>ndo ). $ %
). $ = / $⋅6 −6-
R(corddo u( 0 u(r d( 0o) r()ort() ()t dd ,or 0 (?,r()!n F= A ⋅ Δ 0
r(cc!n d(0 ,o9o A / $ )( ,u(d( ()cr
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- = ,,;,7 + 3333;33 ⋅ θ $ + 6666;6* ⋅ θ − 3666;6* ⋅Δ (,".
So0uconndo (0 ))t(+ d( (cucon() d( 3?3 )( o
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BIBLIORAFIA
C@A7ES A0(?nd(r. 1::8. Structur0 An50)). N(Q 7(r)9. Edtor0 Pr(ntc( @00
@EAO NORRES Cr0() JILBUR BENSON 7on UTU S(no0 1:6K. E0(+(ntr9
Structur0 An09)) Edtor0 #c rQ @00
S@EPLE Erc.1:&8. Contnu) B(+ Structur() A (/r(( o F?t9 #;tod nd t(
#(tod o +o+(nt D)tr
-
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CA#ARO # Cr0o) *#E Lur. 288K D)(o ()tructur0.
#ALDONADO RONDON E),(rn C@IO C@O u)t'o. 2884. An50)) )=)+c d(
(dccon(). Bucr+n/ Co0o+