175606462 Slope Deflection Trabajo Final

8/15/2019 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+

175606462 Slope Deflection Trabajo Final

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