metodo de las flexibilidades y hoja de calculo

7/23/2019 Metodo de Las Flexibilidades y Hoja de Calculo

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UNIVERSIDAD NACIONAL JFACULTAD D

ANLISIS

ALUMNO: CH

APLICACIN DEL METODO DE LA FLEXIBILIDAD PARA CALC

I.- VIGA HIPERESTATICA DE DOS TRAMOS

1.- ISOSTATIZAMOS LA VIGA

2. -DETERMIAMOS LA ECUACION DE COMPATIBILIDAD

ESTADO 0

ESTADO

:


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ESTABLECEMOS LA ECUACION DE LA COMPATIBILI

Donde:

3.- CALCULO DE REACCIONES Y MOMENTOS INTERNOS (

C!"#$"% &' ('!##)%*'+

C!"#$"% &' ,%,'*-%+

Corte 1-1 (0 < < a)

Corte 2-2 (a < < L1)

Corte 2-2 (0 < < L2)

_01=2_0 ^ _0 _( 1) (24 )/ &

._+__=

+ _1 =0 : + _4 =0 _4 = /

+ =0 :_ _ 1 + _4 = _1 = ))(( /

+ _1 =0 : _0 ) =0 ( / _0= ) ( /

+ _2 =0 : _0+ =0 _ / /

+ _1 =0 : _0 ) )=0 ( / +(

!""

!""

#!

""


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%.- CALCULO DE REACCIONES Y MOMENTOS INTERNOS (

C!"#$"% &' ('!##)%*'+

C!"#$"% &' ,%,'*-%+

Corte 1-1 (0 < < a)

Corte 1-1 (a < < L1)

Corte 2-2 (0 < < L2)

&.- CALCULO DE '#1

$or tanto %e tendra:

+ _1 =0 : 1 _1 _4 =0 _4 = _1 /

+& =0 : _1_ + _41=0 _1 = ( _1 )/

+ _1 =0 : _1 + (( _1 )) =0 / _1 =(( _1 ))/

+ _2 =0 : _1+ _1 =0 / _1 = _1 /

_01=2_0 ^ (' )( / '( _1 ))( / ) (24 +)/ & ) (24 )/ & +24_0*( _ 2) ( )( _1 ))(/ / /

_01=2_0 ^ _0(_1) (24 ) / &

_01= ) _1)) *2 ) 2_0 (( ( ( ^ ( ( _1)) *2 ) 2 *(( _ _ 1) 1) *2 ) 2 0* 2)(24 *2( ( ( &

+ _1 =0 : _1+ ( _1 )) =0 ( / _1=( _1 )) ( / #

!""

!""

!""


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.- CALCULO DE

$or tanto %e tendra:

3$L5367 L67 8L67 9 L CC;69 D C

_ = _ ( ( _1)) *2 )( ( * ..( *

_1) *2 )( ( " *../_0* *( _2 )

_01= ) _1 ) *2 ) *..+( ( ( [ ( (( " " _1 *2)2)(*.. "" *22) _1(

_01= ( _ 2 )' 2 *2 )( " " _1 *2 ( _1 )2 + _2 *2 ( *2 )!

"_11=2_0 ^ _1 _( 1) (24 )/ &

/

"_11=2_0*( _1 ) ((( _1 ))( / > > )((((24 +)& 2_0*( _ 2) (( _1 )( _1 / /

"_11= _1)( *2 *2 )( > >2_0*( _1 ) " " *2 + " " _1 *2

*2 ) 2_0*(( _ 2) " " *2 "_11= _1)( *2 *2 )( > > "*2./_0* *( _1 )+ " " _1 *2 *2() " *2./_0* *( _ 2 )

"_11= _2)( *2 *2 )( > > ' " _1 *..+ " " _1 *2 *2 )(' ( _1 ) *..

"_11=( " _1 *2 " _2 *2 ( _1 + _ 2))( *2 ) =( _1 *2 _2 *2 ())( *2 )

._+__=

1_ _2 )'( 2 *2 )( 2 *2 22' " " 1 *2 " "

_01= ) _1 ) *2 ) *..+( ( ( [ ( ('((2 " " _1 *.. " " _1 *2 2 *.+' ( _2 ) *..

_01= ) _2 ) *2 ) *..+( ( ( [ ( ( _2*2 ( ))? _1) *2 ) ' 2 ( ( _2)( *..

_2 )'( 2 *2 )( " " _1 *2 ( _12( *2 )+(! " " _1 *2 " " _2 *2 ())( *


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CLCL367 L7 CC;697 L7 @L97

).- LINEAS DE IN*LUENCIA PARA LAS REACCIO

SI:

! 3 RA RB4,5 4,5 4T*5 4T*50A00 ?A00 10A000 0A0000A?0 BA40 A.0 1ABE41A20 4A0 A4? .A1B21A0 4A20 ?A2BB 4A?.2A40 .A?0 BA04 ?A01?.A00 .A00 .AE A2B0.A?0 2A40 2AEB. A.044A20 1A0 2A02? EA1424A0 1A20 1A21B EA2BA40 0A?0 0AB.4 10A02??A00 0A00 0A000 10A000

SI:

_ _

+ _1 =0 : _ ) _1 ) =0 (# +_$ (

+ =0 :%_ _ + _# + =0_$

1_ 6/ 6 _2 ) _1 '(( " " _2 *2 )2' " " _1 *2 " " _

1_ / 6 _2 ) _1 '(( 2 " " _2 *2 )2' " " _1 *2 " "

7 7 /___________

/7 7/


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! 3 RA RB4,5 4,5 4T*5 4T*5?A00 BA00 0A000 10A000?AB0 4AB0 -0A.24 EA1.A00 4A00 -0AB4B EA200AB0 .AB0 -0A?? A4

A00 .A00 -0A2. A?00AB0 2AB0 -0A10 ?AB?.EA00 2A00 -0A?.? BA400EAB0 1AB0 -0AB1 4A1.

10A00 1A00 -0A.?4 2A0010AB0 0AB0 -0A1 1A41.11A00 0A00 0A000 0A000

0 1 2 . 4 B ? -2

0

24

?

10

12

0A00 1A00 2A00 .A00 4A00 BA00 ?A00 A000

2

4

?

10

12

?

10

12


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0 1 2 . 4 B ? -2

0

2

4


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S FAUSTINO SNCHEZ CARRIN E INGENIERA CIVIL

ESTRUCTURAL I

VEZ AGREDA KENNy

LO DE LA LINEA DE INFLUENCIA DE LAS REACCIONES DE UNA VIGA


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DAD

F

n el est!" #$

"_11=2_0 ^ _1 _( 1) (24 )/ &

=

_0= ( )/


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n el est!" 1$

2 1_^ (' ( )/'( _1 ))( /

" *2 (24 +)& (24, ( *2 )) )


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63$;;L;DD

_ )2)/_* * _( 1 )

_1)) *2 )( '( " " _1 *..) *2 ) '( ( _2 ) *..

*2 (2)+2 " " _1

_1 )) / > > ))/)) (24 ) / &

" " _1 *2 ( _1 ) *2 ( )+22 + 2 " " _12 *2

_1)) *2 )( . *2)?) _1) *2 )( (

)) *2 ) '(( " " _1 *2 ( _1 )2

) *2 ( + )+2 + 2 " " _1 _2 *2 2 ) 1_ 0


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D%*&':

RC E8!"$!,%+:4T*5 L 1 = ?A00 G0A000 L2 = BA00 G-0A.24 $ = 10A00 n-0A?2-0AE. D%*&':-1A100-1A22-1A2B-1A1?-0AE4.-0AB?00A000

L= _1+ _ 2

*2 )( " " _1 *2 ( _1 ) *2 ( )+ _12 + 2 2 2 *2 *2 +1[

*2 )( " " _1 *2 ( _1 ) *2 ( )+ _12 + 2 2 2 *2 *2

L= _1 + _2


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RC4T*50A0000A?111A.4B2A1E

.A12.4A14BA2.??A.0AB?4AB

10A000

E 10 11

L;9 D ;9@L9C; D

A00 EA00 10A00 11A00

L;9 D ;9@L9C; D

L;9 D ;9@L9C; D


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E 10 11

C


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10


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DATOS

Carga 10 tn 10 tn

TRAMO1 TRAMO2

Longitud 6 m 5 ma!" 0.25 m 0.25 m

A#tura 0.5 m 0.5 m

$% 210 &g'%m2 210 &g'%m2

E 2173706.51193 tn'm2 2173706.51193 tn'm2

I 0.0026041667 m( 0.0026041667 m(

EI 5660.69404148 Tn-m2 5660.69404148 Tn-m2

Matri) d" rigid") In%ognita!

3773.79602765 1886.89801383 0 a

1886.89801383 8302.35126084 2264.27761659 0 2264.27761659 4528.55523318 M12*a%%ion

M21*a%%ion

Matri) In+"r!a M2,*a%%ion

0.0003051344 -8.029854E-005 4.014927E-005 M,2*a%%ion

-8.029854E-005 0.0001605971 -8.029854E-005

4.014927E-005 -8.029854E-005 0.0002609702 M1

M2

M,

M12

M21

M2,

M,2

Di!tan%ia

R1

R2

R,

MA

1

2,

12

,


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10

a

6 5

tramo 1

0 0.1 0.2 0.3 0.4 0.5

0 0.6 1.2 1.8 2.4 3

6 5.4 4.8 4.2 3.6 30 4.86 7.68 8.82 8.64 7.5

0 -0.54 -1.92 -3.78 -5.76 -7.5

0 0 0 0 0 0

0 0 0 0 0 0

0 -4.86 -7.68 -8.82 -8.64 -7.5

0 0.54 1.92 3.78 5.76 7.5

0 0 0 0 0 0

0 -0.0015263146 -0.0024976057 -0.0029948143 -0.0030988812 -0.00289074740 0.0004769733 0.0009250392 0.00131529 0.0016188185 0.0018067171

0 -0.0002384867 -0.0004625196 -0.000657645 -0.0008094093 -0.0009033586

0 0 0 0 0 0

0 -1.62 -3.1418181818 - 4. 4672727273 - 5. 4981818182 -6. 1363636364

0 0.6 1.2 1.8 2.4 3

10 8.73 7.4763636364 6.2554545455 5.0836363636 3.9772727273

0 1.594 3.152 4.638 6.016 7.25

0 -0. 324 -0.6283636364 - 0. 8934545455 - 1. 0996363636 -1. 2272727273

0 -1.62 -3.1418181818 - 4. 4672727273 - 5. 4981818182 -6. 1363636364


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0 20

2

4

?

10

12


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0.6 0.7 0.8 0.9 1 0

3.6 4.2 4.8 5.4 6 0

2.4 1.8 1.2 0.6 0 55.76 3.78 1.92 0.54 0 0

-8.64 -8.82 -7.68 -4.86 0 0

0 0 0 0 0 0

0 0 0 0 0 0

-5.76 -3.78 -1.92 -0.54 0 0

8.64 8.82 7.68 4.86 0 0

0 0 0 0 0 0

-0.0024513538 -0.0018616413 -0.0012025509 -0.0005550235 0 00.0018500783 0.0017199947 0.0013875587 0.000823863 0 0

-0.0009250392 -0.0008599973 -0.0006937794 -0.0004119315 0 0

0 0 0 0 0

-6.2836363636 -5.8418181818 -4.7127272727 -2.7981818182 0

0

0

3.6 4.2 4.8 5.4 6 6

2.9527272727 2.0263636364 1.2145454545 0.5336363636 0 0

8.304 9.142 9.728 10.026 10 10

-1.2567272727 -1.1683636364 -0.9425454545 -0.5596363636 0 0

-6.2836363636 -5.8418181818 -4.7127272727 -2.7981818182 0 0


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4 ?


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tramo 2

0.1 0.2 0.3 0.4 0.5 0.6

0.5 1 1.5 2 2.5 3

4.5 4 3.5 3 2.5 20 0 0 0 0 0

0 0 0 0 0 0

4.05 6.4 7.35 7.2 6.25 4.8

-0.45 -1.6 -3.15 -4.8 -6.25 -7.2

0 0 0 0 0 0

-4.05 -6.4 -7.35 -7.2 -6.25 -4.8

0.45 1.6 3.15 4.8 6.25 7.2

0.0003432762 0.0005781495 0.0007166644 0.000770866 0.0007527988 0.0006745077-0.0006865525 -0.0011562989 -0.0014333289 -0.0015417319 -0.0015055976 -0.0013490154

0.0004426457 0.000931463 0.0014122505 0.0018308067 0.0021329299 0.0022644188

-1.9431818182 -3.2727272727 -4.0568181818 -4.3636363636 -4.2613636364 -3.8181818182

0 0 0 0 0 0

6.5 7 7.5 8 8.5 9

-0.3238636364 -0.5454545455 -0.6761363636 -0.7272727273 -0.7102272727 -0.6363636364

9.7125 9.2 8.4875 7.6 6.5625 5.4

0.6113636364 1.3454545455 2.1886363636 3.1272727273 4.1477272727 5.2363636364

-1.9431818182 -3.2727272727 -4.0568181818 -4.3636363636 -4.2613636364 -3.8181818182


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10


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0.7 0.8 0.9 1

3.5 4 4.5 5

1.5 1 0.5 00 0 0 0

0 0 0 0

3.15 1.6 0.45 0

-7.35 -6.4 -4.05 0

0 0 0 0

-3.15 -1.6 -0.45 0

7.35 6.4 4.05 0

0. 0005480375 0 .000385433 0 .0001987389 0-0.001096075 -0.000770866 -0.0003974778 0

0.0021710717 0.0017986872 0.0010930638 0

-3.1022727273 -2.1818181818 -1.125 0

0 0 0 0

9.5 10 10.5 11

-0.5170454545 -0.3636363636 -0.1875 0

4.1375 2.8 1.4125 0

6.3795454545 7.5636363636 8.775 10

-3.1022727273 -2.1818181818 -1.125 0


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LHnea de ;nIJenKHa de 3oGento%

metodo de las flexibilidades y hoja de calculo

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