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8/19/2019 Rigidez Segun GERE

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1 2 3

SECCIONESB H B H B H

60 120 50 100 40 80

INERCIA(I)-CM4 8640000 4166666.66666667 1706666.66666667LONGITUD(L)- CM 1200 1000 800

RELACION(I/L =R) 7200 4166.6666666667 21 .

E= 15000!"#C$1/2- %G/CM2 217 70.6511&2842

AD800000

AD-ADL08000

-600000 828000-1000000 -1000000

ADL-2508000-1428000

0

% 4E(R1'R2) 2E(R2) 0 &88 118&40.&012 18114220& .27 682E(R2) 4E(R2'R ) 2E(R ) = 18114220& .27 68 5477740410.05&61

0 2E(R ) 4E(R ) 0 &27448111.756124

0.000000000108 58 -0.0000000000 &147-0.0000000000 &147 0.00000000021 580.00000000001&57 -0.0000000001067&2

D =0.000 064602&8654

(AD-ADL) = 0.00015414210678& =-0.0006161847716 1

$( 1)=

$


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GL=

0&27448111.75612418548&622 .51225

0.00000000001&57-0.0000000001067&20.0000000005&2510

0.01755884060.0088 16715

-0.0 5 04704


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1 2

SECCIONESB H B H

50 100 50 100

INERCIA(I)-CM4 4166666.66666667 4166666.66666667

LONGITUD(L)- CM 500 500

RELACION(I/L =R) 8 . 8 .

E= 15000!"#C$1/2- %G/CM2 217 70.6511&2842

AD0

AD-ADL00

ADL14400000-&600000

0

% 4E(R1) 2E(R1) 02E(R1) 8E(R1) 2E(R1) =

0 2E(R1) 4E(R1)

D = (AD-ADL) =

$( 1)=

$( 1)


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3B H GL=0 0

0

800

0

-14400000&600000

0

7245688 7 .0&472 622844186.547 6 0622844186.547 6 144&1 76746.18&4 622844186.547 6

0 622844186.547 6 7245688 7 .0&472

0.000000000161015 -0.000000000046004 0.00000000002 002-0.000000000046004 0.0000000000&200& -0.0000000000460040.00000000002 002 -0.000000000046004 0.000000000161015

-0.0027602622 7 6& -0.15815100670.001545746852&27 = 0.08856456 8

-0.00077287 42646 -0.044282281&


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1 2

SECCIONESB H B H

50 100 50 100

INERCIA(I)-CM4 4166666.66666667 4166666.66666667

LONGITUD(L)- CM 500 500

RELACION(I/L =R) 8 . 8 .

E= 15000!"#C$1/2- %G/CM2 217 70.6511&2842

AD0

AD-ADL00

ADL14400000-&600000

0

% 4E(R1) 2E(R1) 02E(R1) 8E(R1) 2E(R1) =

0 2E(R1) 4E(R1)

D = (AD-ADL) =

$( 1)=

$( 1)


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3B H GL=0 0

0

800

0

-14400000&600000

0

7245688 7 .0&472 622844186.547 6 0622844186.547 6 144&1 76746.18&4 622844186.547 6

0 622844186.547 6 7245688 7 .0&472

0.000000000161015 -0.000000000046004 0.00000000002 002-0.000000000046004 0.0000000000&200& -0.0000000000460040.00000000002 002 -0.000000000046004 0.000000000161015

-0.0027602622 7 6& -0.15815100670.001545746852&27 = 0.08856456 8

-0.00077287 42646 -0.044282281&


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0.41666667 0.080.08 0.41666667

2.5 -0.5 - 2

-0.5 2.5 .

-&6.665&&. 25


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TRAMOS O ELEMENTOS 1SECCIONES

B H B0. 0.7 0.

INERCIA(I)-CM4 0.008575 0.00LONGITUD(L)- CM 4

RELACION(I/L =R) 0.00214 75 0.001

E= 15000!"#C$1/2- %G/CM2 217 70.6511&2842 1410000

1

GH = 6 GL=

D =

2AD =

ADL =

AD - ADL =

% =

GIROS =

DE"INIENDOEL SENTIDODE GIRO EN"UNCION AL

GL

1 2

1

A2

AA

1A

2

1 2

11 1 2 * 1

21 22 * 2

1 ( 2 )

$(1)

=

+( 0 @) 1

2


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12= ( 12) 12 0)4 / ( '(2 12) 12 / ( 1)

21= ( 21) 21 0)2 / ( '(4 21) / 21 ( 1)

2 = ( 2 ) 2 1)4 / ( '(2 2 ) / 2 ( 2)

2= ( 2) 2 1)2 / ( '(4 2) / 2 ( 2)

4= ( 4) 4 2)4 / ( '(2 4) / 4 ( )

4 = ( 4 ) 4 2)2 / ( '(4 4 ) / 4 ( )

45= ( 45) 45 )4 / ( '(2 45) / 45 ( 4)

54= ( 54) 54 )2 / ( '(4 54) / 54 ( 4)


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3 4H B H B H0.7 0. 0.7 0. 0.7

575 0.008575 0.0085758 5

71875 0.001071875 0.001715

0= 0

0

-4= 16

-16

4= -16

16

181 6.125 022.6875 0= 022.6875 120&0.75 022.6875

0 022.6875 15717.&75

5.766252E-005 -1.514 7E-005 2.&12248E-006-1.514 7E-005 &.086215E-005 -1.747 5E-005

2.&12248E-006 -1.747 5E-005 6.6&8171E-005

0 , , 30.00051&5451 3 0.02&767672&-0.0017& &45 3 -0.1027852 84

0.001 62& 2 3 0.0780&008 70 , , 3


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.1408450704

6.2816&01408

-2.2816&01408

-&.274647887

-6.725 521127

2.816&014085

1 .18 0&85&2

6.5&154&2&58


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TRAMOS O ELEMENTOS 1 2 3 MODULO DE EL

SECCIONESB H B H B H E= 15000!"#C$

0.6 1.2 0.5 1 0.4 0.8

INERCIA(I)-M4 0.0864 0.0416666667 0.0170666667LONGITUD(L)- M 12 10 8

RELACION(I/L =R) 0.0072 0.0041666667 0.0021

E 217 706.511&2842

TERMINACION DE GRADO DE LIBERTAD: GIRO EN LOS NUDGL= R- = 6- =

DEFINICION DE LOS SENTIDOS DE GIRO DE LAS DEFORMACIONES ANGULARES, ASOCIADO AL GRADO DE LIBERTAD

MOMENTOS EXISTENTES EN LOS NUDOS DE LA ESTRUCTURA REAL8

= -6-10

MOMENTO DE EMPOTRAMIENTO PERFECTO EN LOS TRAMOS O ELEMENTOS-25.08-14.28

L= 12 L= 10 L= 8 H

:;8 1(

@2@ )<

:D


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0.08

= 8.28-10

MATRIZ DE RIGIDEZ&88 1.18&40& 18114.220& 0

= 18114.220& 54777.404101 &274.48111760 &274.4811176 18548.&622 5

MATRIZ INVERSA1.08 576E-005 - .&1465E-006 1.&57 26E-006- .&1465E-006 2.1 58 4E-005 -1.067&2E-005

1.&57 26E-006 -1.067&2E-005 0.00005&251DETERMINANDO LOS ANGULOS DE GIRO

0 , , 30.000 06460 3

= 0.0001541421 3-0.0006161848 3

MOMENTOS POR TRAMOS EN LA ESTRUCTURA

&.5&2628 544

1&.18525670&

1 .8&474 2&1

11.1 5617&12

12= ( 12) 12 0)4 / ( '( 12) 12 1)2 / ( =2E 1( 0 1)2 +

21= ( 21) 21 0)2 / ( '( 21) 21 1)4 / ( =2 1 0' 1)E ( 2

2 = ( 2 ) 2 1)4 / ( '( 2 ) 2 2)2 / ( =2 E 2( 2 1 + 2)

2= ( 2) 2 1)2 / ( '( 2) 2 2)4 / ( =2 E 2 ( 1' 2 2)

)<

= 1

2

)<

4 )< =

( <


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-2.855617&117

-10

REACCIONES

= '( 4) 4 )2 / ( =2 E ( 2 2 + )

4 = ( 4 ) 4 2)2 / ( '( 4 ) 4 )4 / ( =2 E ( 2' 2 )

=(_)/2

=(_)/2

=( $2_ ( )) $3 + /


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STICIDAD CONCRETO/2 ! 10 T/M2

= 1.2 9 B =0.60 = 1.0 9 B =0.50

= 0.8 9 B =0.40

/11 >? /10≤ @

$ )/12( .


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=( $2_ ' )) $( 3 /


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TRAMOS O ELEMENTOS 1 2SECCIONES

B H B H0. 0.6 0. 0.6

INERCIA(I)-CM4 0.0054 0.0054LONGITUD(L)- CM 6 6

RELACION(I/L =R) 0.000& 0.000&

E= 1580000

1

GH = 6 GL=

D =

2AD = =

ADL = =

AD - ADL = =

% = =

GIROS =

DE"INIENDOEL SENTIDODE GIRO EN"UNCION AL

GL

1 2

1A 2A A

1A

2

1 2

11 12 * 1

21 22 * 2

1 ( 2 )

$(1)

=

+ (0 @) 1

2

:{


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= 4 ( ( 12) 12 1)2 / ( =2E 1 (2 0 ' 1 ) 21= ( 21) 21 0)2 / ( '( 21) 21 1)4 / ( =2E 1 ( 0 '2 1 )

2 = ( 2 ) 2 1)4 / ( '( 2 ) 2 2)2 / ( =2E 2 (2 1 ' 2 )

2= ( 2) 2 1)2 / ( '( 2) 2 2)4 / ( =2E 2 ( 1 '2 2 )

4= ( 4) 4 2)4 / ( '( 4) 4 )2 / ( =2E (2 2 ' )

4 = ( 4 ) 4 2)2 / ( '

( 4 ) 4 )4 / (

=2E

( 2

'2

)


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000

65.25

-11.25

-6-5.25

11.25

5688 2844 0

2844 11 76 28440 2844 5688

0.0002051102 -5.8602&E-005 2.& 0145E-005-5.8602&E-005 0.0001172058 -5.8602&E-005

2.& 0145E-005 -5.8602&E-005 0.0002051102

0 , , 3-0.0005& 544 3-0.000&22&&58 3

0.0024 & 46 3

D


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-6

-6.& 75

1.6875

11.25

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