diagrama de interaccion columnas

8/18/2019 Diagrama de Interaccion Columnas

1/142

DIAGRAMA DE INTERACCION COLUMNAS RECTANGULARES

35

5 25 5

25

0 Ø 1/2" 0 Ø 1/2" 0 Ø 1/2"3 Ø 5/8" 2 Ø 5/8" 3 Ø 5/8"0 Ø 3/4" 0 Ø 3/4" 0 Ø 3/4"0 Ø 1" 0 Ø 1" 0 Ø 1"

P1 P2 P3

Es = 2039400 Kg/ !2# = 4200 Kg/ !2

$% = 210 Kg/ !2& = 0'003

DE ORMACION UNITARIA DE LUENCIA EN EL ACEROE() *)+,-. - .* .* ) $ * )

= # / Es = 4200 Kg/ !2 = 0'002059432039400 Kg/ !2

PUNTO 1

CALCULO DE LA UER A DE COMPRESION EN EL CONCRETO

C = 685 $% = 0'85 210 35 25 =

CALCULO DE LA UER A DE COMPRESION DEL ACERO


2/142

P1 = As1 $s1 = 7 4200 = 25200 KgP2 = As2 $s2 = 4 4200 = 17800 KgP3 = As3 $s3 = 7 4200 = 25200 Kg

CALCULO CARGA A IAL NOMINAL

P* = C P1 P2 P3 = 22338:'5 Kg = 223'38:5 T.*

CALCULO DEL MOMENTO LECTOR NOMINAL

M* = 15718:'5 025200 12'517800 0 ;25200 12'5 = 0 Kg; !

0 T; !

0 T;!

PUNTO 2

&1& =

& = &20'003 &3

29':5

5 25 535

CALCULO DE DE ORMACIONES UNITARIAS

&1 = 0'003 30 = 0'0025:143 0'0020594335

&2 = 0'003 1:'5 = 0'0015 0'0020594335

&3 = 0'003 5 = 0'0004285: 0'0020594335

CALCULO DE ES UER OS EN EL ACERO

$s1 = 4200 Kg/ !2


3/142

$s2 = 3059'1 Kg/ !2

$s1 = 8:4'0285:1 Kg/ !2

CALCULO DE LA UER A DE COMPRESION EN EL


4/142


5/142

& =& = &2

0'003 &3

25'5

5 25 530


&1 = 0'003 25 = 0'0025 0'0020594330

&2 = 0'003 12'5 = 0'00125 0'00205943

30

&3 = 0'003 0 = 0 0'0020594330


$s1 = 4200 Kg/ !2

$s2 = 2549'25 Kg/ !2

$s1 = 0 Kg/ !2



6/142

M* = 113:93':5 4':525200 12'51019: 0 ;

0 12'5 = 855520'313 Kg; !855'520313 T; !8'55520313 T;!

) = 5':344058:

PUNTO ) = 10 < = 3'5 ! ENTRE 30 #

&1& =

& = &20'003 &3

25'28:5

5 25 529':5


&1 = 0'003 24':5 = 0'0024958 0'0020594329':5

&2 = 0'003 12'25 = 0'00123529 0'0020594329':5

&3 = 0'003 0'25 = 2'5210E;005 0'0020594329':5


$s1 = 4200 Kg/ !2

$s2 = 2519'25882 Kg/ !2

$s1 = 51'4134454 Kg/ !2



7/142

CALCULO DE LA UER A DE COMPRESION DEL ACERO

P1 = As1 $s1 = 7 4200 = 25200P2 = As2 $s2 = 4 2519'25882 = 100::'0353P3 = As3 $s3 = 7 51'4134454 = 308'4807:2


P* = C P1 P2 ; P3 = 14:814'023 Kg = 147.81402 T.*

CALCULO DEL MOMENTO LECTOR NOMINAL

M* = 112845'479 4'8572525200 12'5

100::'0353 0 ;308'4807:2 12'5 = 866861.82 Kg; !

877'871817 T; !8'77871817 T;!

) = 5'87454381 !

PUNTO 3

&1& =

& = &20'003 &3

22'3125

5 25 527'25


&1 = 0'003 21'25 = 0'0024285: 0'0020594327'25

&2 = 0'003 8':5 = 0'001 0'0020594327'25

&3 = 0'003 3':5 = 0'0004285: 0'0020594327'25


8/142


$s1 = 4200 Kg/ !2

$s2 = 2039'4 Kg/ !2

$s1 = 8:4'0285:1 Kg/ !2



9/142


&1 = 0'003 12'5 = 0'00214287 0'002059431:'5

&2 = 0'003 0 = 0 0'002059431:'5

&3 = 0'003 12'5 = 0'00214287 0'002059431:'5


$s1 = 4200 Kg/ !2

$s2 = 0 Kg/ !2

$s1 = 4200 Kg/ !2



10/142

& =& = &2

0'003 &3

11'9

5 25 514


&1 = 0'003 9 = 0'0019285: 0'0020594314

&2 = 0'003 3'5 = 0'000:5 0'00205943

14

&3 = 0'003 17 = 0'0034285: 0'0020594314


$s1 = 3933'1285: Kg/ !2

$s2 = 1529'55 Kg/ !2

$s1 = 4200 Kg/ !2



11/142

M* = 53103':5 11'5523598'::14 12'5 ;

7118'2 0 ;25200 12'5 = 1223333 Kg; !

1223'33297 T; !)= 27'9549785 12'2333297 T;!

M+ P+ '9 M+ '9 P+ ': M+ ': P++*, 1 0 223'38:5 0 201'048:5 0 157'3:125+*, 2 59:'94121: 1:5'439947 538'14:095 15:'895952 418'558852 122'80:973+*, 3 :34'28501: 172'595487 770'857515 147'33593: 513'999512 113'81784

877'871817 14:'814023 :80'1:5734 133'032721 707'8032:1 103'479817855'520313 149'190:5 :79'978281 134'2:17:5 598'874219 104'433525

+*, E 1012'19737 12:'78297 910'9:7:21 114'914774 :08'53:45 89'3:80:19+*, 4 129:'94571 77'3:978:5 1178'15104 59':41:188 908'571924 47'475:813+*, 5 1223'33297 45'3843214 1100'99977 40'8458893 857'333079 31':79025

L -g > ?+) )@*) +* - B* )* ) $ ,.- ) -) + B* ) )s

'1 $% Ag = 0'1 210 8:5 = 183:518'3:5

POR NO SER UNC 844'4572794419

DIAGRAMA DE INTERACCION

P *.! * 6 M *.! *90 P* M*:0 P* M*L.g - , ! F:0 P* M*) = 10 MA P

Pnominal


12/142

0 200 400 700 800 1000120014000

5077'3:978:5

45'3843214287

MIN P

Mnominal


13/142


14/142


15/142


16/142


17/142


18/142


19/142


20/142


21/142


22/142


23/142

15718:'5 Kg


24/142


25/142

132:59'3:5 Kg

32'5


26/142

1232:7'5725 Kg

30


27/142

113:93':5 Kg


28/142

1:'5

112845'478:5 Kg


29/142


30/142


31/142

773:9'78:5 Kg


32/142

53103':5 Kg


33/142

) = M+ / P+ = 3'5 M M > P M * P0 0 0 113'81784 0 18'3:5

312':425 89'355 519'1:8242 113'81784 519'1:8242 18'3:5312':425 89'355 519'1:8242 113'81784 519'1:8242 18'3:5312':425 89'355 519'1:8242 113'81784 519'1:8242 18'3:5312':425 89'355 519'1:8242 113'81784 519'1:8242 18'3:5

479'113:5 134'0325 ::8':7:373 113'81784 ::8':7:373 18'3:5725'485 1:8':1 1038'35748 113'81784 1038'35748 18'3:5

:81'85725 223'38:5 129:'94571 113'81784 129:'94571 18'3:5

Kg T


34/142


35/142


36/142


37/142


38/142


39/142


40/142


41/142


42/142


43/142


44/142


45/142

DIAGRAMA DE INTERACCION COLUMNAS R

120:'5 105

0 Ø 1/2" Ps0 Ø 5/8"0 Ø 3/4"

17 Ø 1"

Es = 2039400 Kg/ !2# = 4200 Kg/ !2

$% = 210 Kg/ !2& = 0'003

DE ORMACION UNITARIA DE LUENCIA ENE() *)+,-. - .* .* ) $ *

= # / Es = 42002039400

Ag = PI -2 = 11309':33553

PUNTO 1

CALCULO DE LA UER A DE COMPRESION

C = 685 $% = 0'85



46/142

Ps = As $s = 81'7


P* = C Ps =

CALCULO DEL MOMENTO LECTOR NOMIN

M* = 2018:8:'44 0

8400 10'2428400 29'17:8400 43'7528400 51'491

0 00 0

0 00 00 00 00 00 00 00 00 00 0

8400 ;51'4918400 ;43'7528400 ;29'17:8400 ;10'242

PUNTO 2

&1

& =0'003

102


47/142

:'5 105120120


&1 = 0'003 49':5::58094120

&2 = 0'003 30'832572:77120

&3 = 0'003 17'34:845354120

&4 = 0'003 8'508::2::88

120

&5 = 0'003 70120

&7 = 0'003 70120

&: = 0'003 70120

&8 = 0'003 70120

&9 = 0'003 70120

&10 = 0'003 70120

&1 = 0'003 :0'242241907120

&2 = 0'003 89'17:43:234120

&3 = 0'003 103'75215475120


48/142

&4 = 0'003 111'49122:22120

&5 = 0'003 70120

&7 = 0'003 70120

&: = 0'003 70120

&8 = 0'003 70120

&9 = 0'003 70

120

&10 = 0'003 70120


$s1 = 2537'8993 Kg/ !2$s2 = 15:1'99821 Kg/ !2$s3 = 833'494895 Kg/ !2$s4 = 433'819:8 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2

$s1 = 3581'300: Kg/ !2$s2 = 4200 Kg/ !2$s3 = 4200 Kg/ !2$s4 = 4200 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2


49/142

$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2


C = 685 $% As = 0'85

102


P1 = As1 $s1 = 10'2P2 = As2 $s2 = 10'2P3 = As3 $s3 = 10'2P4 = As4 $s4 = 10'2P5 = As5 $s5 = 0P7 = As7 $s7 = 0P8 = As: $s: = 0P8 = As8 $s8 = 0P9 = As9 $s9 = 0P10 = As10 $s10 = 0

P11 = As11 $s11 = 10'2P12 = As12 $s12 = 10'2P13 = As13 $s13 = 10'2P14 = As14 $s14 = 10'2P15 = As15 $s15 = 0P17 = As17 $s17 = 0P1: = As1: $s1: = 0P18 = As18 $s18 = 0P19 = As19 $s19 = 0P20 = As20 $s20 = 0


P* = C SUM P =



50/142

M* = 1828899'88 9258:7'3:28 ;10'2422419117034'3818 ;29'17:43:238501'74:93 ;43'752154754424'971:7 ;51'49122:22

0 00 00 00 00 00 00 0

37529'27:2 10'24224190742840 29'17:43:23442840 43'752154747

42840 51'49122:2210 00 00 00 00 00 0

) = 0'1017703:

PUNTO ) = 10 < = 12

&1

& =0'003

:1'9997:5

:'5 10584':055

120


&1 = 0'003 14'473258094


51/142

84':055

&2 = 0'003 ;4'47193:23484':055

&3 = 0'003 ;18'94775475

84':055

&4 = 0'003 ;27':85:2:2284':055

&5 = 0'003 24':05584':055

&7 = 0'003 24':05584':055

&: = 0'003 24':05584':055

&8 = 0'003 24':05584':055

&9 = 0'003 24':05584':055

&10 = 0'003 24':05584':055

&1 = 0'003 34'94::4190784':055

&2 = 0'003 53'8:293:23484':055

&3 = 0'003 78'35:75474784':055

&4 = 0'003 :7'197:2:22184':055

&5 = 0'003 24':05584':055

&7 = 0'003 24':055


52/142

84':055

&: = 0'003 24':05584':055

&8 = 0'003 24':055

84':055

&9 = 0'003 24':05584':055

&10 = 0'003 24':05584':055


$s1 = 1044'77::: Kg/ !2$s2 = ;322'281704 Kg/ !2$s3 = ;1378'49937 Kg/ !2$s4 = ;1934':0833 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2

$s1 = 2524'24311 Kg/ !2$s2 = 3891'19248 Kg/ !2$s3 = 4200 Kg/ !2$s4 = 4200 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2


C = 685 $% As = 0'85


53/142


54/142

0 00 00 00 00 00 0

25:4:'2:9: 10'24224190739790'1733 29'17:43:234

42840 43'75215474742840 51'49122:221

0 00 00 00 00 00 0

) = 0'2:9:13::

PUNTO 3

&1

& =0'003

:7'5

:'5 10590

120


&1 = 0'003 19':5::5809490

&2 = 0'003 0'832572:77590

&3 = 0'003 ;13'7521547590


55/142

&4 = 0'003 ;21'49122:2290

&5 = 0'003 3090

&7 = 0'003 3090

&: = 0'003 3090

&8 = 0'003 3090

&9 = 0'003 3090

&10 = 0'003 3090

&1 = 0'003 40'24224190790

&2 = 0'003 59'17:43:23490

&3 = 0'003 :3'75215474790

&4 = 0'003 81'49122:22190

&5 = 0'003 3090

&7 = 0'003 3090

&: = 0'003 3090

&8 = 0'003 3090


56/142


57/142


P1 = As1 $s1 = 10'2P2 = As2 $s2 = 10'2

P3 = As3 $s3 = 10'2P4 = As4 $s4 = 10'2P5 = As5 $s5 = 0P7 = As7 $s7 = 0P8 = As: $s: = 0P8 = As8 $s8 = 0P9 = As9 $s9 = 0P10 = As10 $s10 = 0P ,- = As ,- $s ,- = 2P11 = As11 $s11 = 10'2

P12 = As12 $s12 = 10'2P13 = As13 $s13 = 10'2P14 = As14 $s14 = 10'2P15 = As15 $s15 = 0P17 = As17 $s17 = 0P1: = As1: $s1: = 0P18 = As18 $s18 = 0P19 = As19 $s19 = 0P20 = As20 $s20 = 0


P* = C SUM P =


M* = 135831:'08 21':513799'9504 ;10'242241915::'295792 ;29'17:43:23

;9477'34942 ;43'75215475;14901'931 ;51'49122:22

0 00 00 00 00 00 00 0

2:903'8097 10'242241907


58/142


59/142

70

&: = 0'003 070

&8 = 0'003 0

70

&9 = 0'003 070

&10 = 0'003 070

&1 = 0'003 10'24224190770

&2 = 0'003 29'17:43:23470

&3 = 0'003 43'75215474770

&4 = 0'003 51'49122:22170

&5 = 0'003 070

&7 = 0'003 070

&: = 0'003 070

&8 = 0'003 070

&9 = 0'003 070

&10 = 0'003 070


60/142


$s1 = ;1044'40141 Kg/ !2$s2 = ;29:4'2035: Kg/ !2

$s3 = ;4200 Kg/ !2$s4 = ;4200 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2

$s1 = 1044'40141 Kg/ !2

$s2 = 29:4'2035: Kg/ !2$s3 = 4200 Kg/ !2$s4 = 4200 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2


C = 685 $% As = 0'85

51 79


P1 = As1 $s1 = 10'2P2 = As2 $s2 = 10'2P3 = As3 $s3 = 10'2P4 = As4 $s4 = 10'2


61/142

P5 = As5 $s5 = 0P7 = As7 $s7 = 0P8 = As: $s: = 0P8 = As8 $s8 = 0P9 = As9 $s9 = 0P10 = As10 $s10 = 0

P11 = As11 $s11 = 10'2P12 = As12 $s12 = 10'2P13 = As13 $s13 = 10'2P14 = As14 $s14 = 10'2P15 = As15 $s15 = 0P17 = As17 $s17 = 0P1: = As1: $s1: = 0P18 = As18 $s18 = 0P19 = As19 $s19 = 0

P20 = As20 $s20 = 0


P* = C SUM P =


M* = 81:339'104 34'5;10752'8944 ;10'24224191;30337'8:75 ;29'17:43:23

;42840 ;43'75215475;42840 ;51'49122:22

0 00 00 00 00 00 00 0

10752'8944 10'24224190730337'8:75 29'17:43:234

42840 43'75215474742840 51'49122:221

0 00 00 00 00 0


62/142

0 0

) = 0'47905879

PUNTO 5

&1

& =0'003

12'5:00:2

:'5 10514':8832120


&1 = 0'003 ;55'4539219114':8832

&2 = 0'003 ;:4'3:911:2314':8832

&3 = 0'003 ;88'8738347514':8832

&4 = 0'003 ;97':0290:2214':8832

&5 = 0'003 ;45'2117814':8832

&7 = 0'003 ;45'2117814':8832

&: = 0'003 ;45'2117814':8832

&8 = 0'003 ;45'2117814':8832


63/142

&9 = 0'003 ;45'2117814':8832

&10 = 0'003 ;45'2117814':8832

&1 = 0'003 ;34'9794380914':8832

&2 = 0'003 ;17'044242::14':8832

&3 = 0'003 ;1'55952535414':8832

&4 = 0'003 7'2:954:221214':8832

&5 = 0'003 ;45'2117814':8832

&7 = 0'003 ;45'2117814':8832

&: = 0'003 ;45'2117814':8832

&8 = 0'003 ;45'2117814':8832

&9 = 0'003 ;45'2117814':8832

&10 = 0'003 ;45'2117814':8832


$s1 = ;4200 Kg/ !2$s2 = ;4200 Kg/ !2$s3 = ;4200 Kg/ !2


64/142

$s4 = ;4200 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2$s9 = 0 Kg/ !2

$s10 = 0 Kg/ !2

$s1 = ;4200 Kg/ !2$s2 = ;4200 Kg/ !2$s3 = ;745'204325 Kg/ !2$s4 = 259:'97419 Kg/ !2$s5 = 0 Kg/ !2$s7 = 0 Kg/ !2$s: = 0 Kg/ !2$s8 = 0 Kg/ !2

$s9 = 0 Kg/ !2$s10 = 0 Kg/ !2


C = 685 $% As = 0'85

12'5:00:2 10:'429928


P1 = As1 $s1 = 10'2P2 = As2 $s2 = 10'2P3 = As3 $s3 = 10'2P4 = As4 $s4 = 10'2P5 = As5 $s5 = 0P7 = As7 $s7 = 0P8 = As: $s: = 0P8 = As8 $s8 = 0P9 = As9 $s9 = 0P10 = As10 $s10 = 0


65/142

P11 = As11 $s11 = 10'2P12 = As12 $s12 = 10'2P13 = As13 $s13 = 10'2P14 = As14 $s14 = 10'2P15 = As15 $s15 = 0P17 = As17 $s17 = 0

P1: = As1: $s1: = 0P18 = As18 $s18 = 0P19 = As19 $s19 = 0P20 = As20 $s20 = 0


P* = C SUM P =


M* = 112478'887 53':14974;42840 ;10'24224191;42840 ;29'17:43:23;42840 ;43'75215475;42840 ;51'49122:22

0 00 00 00 00 00 00 0

;42840 10'242241907;42840 29'17:43:234

;7581'08411 43'75215474727499'2348 51'49122:221

0 00 00 00 00 00 0

) = ;0'89804558

M+ P+


66/142

+*, 1 0 2371'50:4392+*, 2 208'280402 2048':87517+*, 3 371'251722 1502'8373184+*, 4 383'38001 81:'33910429+*, 5 111'944043 ;124'7529732

L -g > ?+) )@*) +* - B* )*

'1 $% Ag = 0'1

POR NO SER UNC


67/142

ECTANGULARES

:'5

N-. ) - s =40 N-. - s . =

N-. )s .s . =R . ) s,- + .* =A*g+ . *,)-*. =

L.*g *g +! s, +!

1 11'25 10'2422419072 33':5 29'17:43:2343 57'25 43'7521547474 :8':5 51'49122:2215 0 07 0 0: 0 08 0 09 0 0

10 0 0

EL ACERO)

Kg/ !2 = 0'0020594292Kg/ !2

!2

EN EL CONCRETO

210 11309':335529 = 2018:8:'4392 Kg

DEL ACERO


68/142

4200 = 342:20 Kg

237150:'44 Kg = 2371'50:4392 T.*

AL

= 0'000

= 87032'800= 245002'800= 3777:7'800= 432524'400= 0'000= 0'000

= 0'000= 0'000= 0'000= 0'000= 0'000= 0'000= 0'000= 0'000= 0'000= 0'000= ;432524'400= ;3777:7'800= ;245002'800= ;87032'800

0'000 Kg; !0'000 T; !0'000 T;!

& =&2

&3


69/142

:'5

= 0'001243944 1

= 0'000::08141 2

= 0'0004087971 3

= 0'000212:193 4

= 0 5

= 0 7

= 0 :

= 0 8

= 0 9

= 0 10

= 0'001:57057 1

= 0'0022291859 2

= 0'0025913039 3


70/142

= 0'002:8:280: 4

= 0 5

= 0 7

= 0 :

= 0 8

= 0 9

= 0 10


71/142

EN EL


72/142

= 17470098'9704= ;275032'0:011= ;47:781'82383= ;3:1115'25031= ;22:847':1129

= 0= 0= 0= 0= 0= 0= 0= 3:4141'591074= 1249533'01108= 18:0058'30503

= 2205884'1:415= 0= 0= 0= 0= 0= 0

20828040'1872 Kg; !208'280401872T; !

2'0828040187T;!

! ENTRE 0 # 105

& =&2

&3

:'5

= 0'000512242: 1


73/142

= ;0'00015802:: 2

= ;0'0007:10304 3

= ;0'0009487755 4

= 0 5

= 0 7

= 0 :

= 0 8

= 0 9

= 0 10

= 0'00123::381 1

= 0'0019080085 2

= 0'0024210112 3

= 0'0027987473 4

= 0 5

= 0 7


74/142


75/142


76/142

= 0= 0= 0= 0= 0= 0

= 273:09'87:052= 115:770'34771= 18:0058'30503= 2205884'1:415= 0= 0= 0= 0= 0= 0

28980321'7353 Kg; !289'803217353T; !2'8980321735T;!

& =&2

&3

:'5

= 0'0007585919 1

= 2'::5209E;005 2

= ;0'0004550:18 3


77/142

= ;0'000:173:42 4

= 0 5

= 0 7

= 0 :

= 0 8

= 0 9

= 0 10

= 0'0013414081 1

= 0'0019:224:9 2

= 0'0024550:18 3

= 0'002:173:42 4

= 0 5

= 0 7

= 0 :

= 0 8


78/142

= 0 9

= 0 10

EN EL


79/142

DEL ACERO

1343'1324 = 13799'9504315 Kg57'59:7179 = 5::'29579202 Kg

;928'0:34:3 = ;9477'3494228 Kg;1470'9:373 = ;14901'93099 Kg

0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg

2:35'77:7 = 2:903'8095785 Kg

4022'20238 = 41027'474308 Kg4200 = 42840 Kg4200 = 42840 Kg

0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg

144519'23958: Kg

1502837'32 Kg = 1502'8373183: T.*

AL

= 29543397'4735= ;140318'20742= ;17838'235872= 413227'548938= :7:318':14753= 0= 0= 0= 0= 0= 0= 0= 285:9:'57:797


80/142

= 1197737'82272= 18:0058'30503= 2205884'1:415= 0= 0= 0

= 0= 0= 0

37125172'1543 Kg; !371'251721543T; !

3'7125172154T;!

& =&2&3

:'5

= ;0'0005121121 1

= ;0'0014583:19 2

= ;0'00218270:: 3

= ;0'0025:45714 4

= 0 5

= 0 7


81/142


82/142

EN EL


83/142

0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg

1044'40141 = 10752'8943528 Kg29:4'2035: = 30337'8:7472 Kg

4200 = 42840 Kg4200 = 42840 Kg

0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg

0 = 0 Kg;1'45519E;011 Kg

81:339'104 Kg = 81:'339104294 T.*

AL

= 28198199'0981= 109109'520959= 884848'940077= 18:0058'30503= 2205884'1:415= 0= 0= 0= 0= 0= 0= 0= 109109'520959= 884848'940077= 18:0058'30503= 2205884'1:415= 0= 0= 0= 0= 0


84/142

= 038338000'9:85 Kg; !383'380009:85T; !

3'83380009:9T;!

& =&2

&3

:'5

= ;0'01124953:9 1

= ;0'015088:57 2

= ;0'01802:1773 3

= ;0'01971:4225 4

= 0 5

= 0 7

= 0 :

= 0 8


85/142

= 0 9

= 0 10

= ;0'00:0939981 1

= ;0'003254:8 2

= ;0'000317379: 3

= 0'0012:38875 4

= 0 5

= 0 7

= 0 :

= 0 8

= 0 9

= 0 10


86/142

EN EL


87/142

;4200 = ;42840 Kg;4200 = ;42840 Kg

;745'204325 = ;7581'084113: Kg259:'97419 = 27499'234:507 Kg

0 = 0 Kg0 = 0 Kg

0 = 0 Kg0 = 0 Kg0 = 0 Kg0 = 0 Kg

;23:121'84937 Kg

;124752'973 Kg = ;124'75297317 T.*

AL

= 7041272'1:331= 438:::'743247= 1249533'01108= 18:0058'30503= 2205884'1:415= 0= 0= 0= 0= 0= 0= 0= ;438:::'74325= ;1249533'0111= ;28:2:8'5014:= 13744:8'11::3= 0= 0= 0= 0= 0= 0

11194404'2788 Kg; !111'944042788T; !

1'1194404279T;!

'9 M+ '9 P+ ': M+ ': P+ ) = M+ / P+ = 12


88/142

0 2125'35779528 0 1753'05521 0 018:'452372 1843'90:87437 145':97281304 1434'15057 113'35235:08 944'7029:578325'127459 1352'55278753 252'8:713508 1051'98542 1:0'02853572 1417'9044735345'042009 :35'705193874 278'37700785 5:2'13:3:3 227':04:1417 1889'2059514100':49738 ;112'18:77785 :8'3708298813 ;8:'25:0:42 283'380892: 2371'50:4392

) $ ,.- ) -) + B* ) )s

210 4800 = 100800 Kg100'8 T

= 12 !s

12 !s

CARGA

= 100800 Kg100'8 T 0 50

;500

0

500

1000

1500

2000

2500

3000

$F>

DI

Pnominal


89/142

1784

52'522'5

N-. - *,

2222000000


90/142


91/142


92/142


93/142


94/142


95/142


96/142


97/142


98/142


99/142


100/142


101/142


102/142


103/142


104/142


105/142


106/142


107/142


108/142


109/142

M M > P='8 P M * P


110/142

0 1322'4441: 0 100'8153'352004 1322'4441: 153'352004 100'8230'028007 1322'4441: 230'028007 100'8307':04008 1322'4441: 307':04008 100'8

383'38001 1322'4441: 383'38001 100'8

100 150 200 250 300 350 400 450

588'508:48:91 *F> ; 2278':708428907

GRAMA DE INTERACCION

P *.! * 6 M *.! *90 P* M*:0 P* M*L.g - , ! F:0 P* M*MA PMIN P

Mnominal


111/142


112/142

PUNTO 9 90 1092420 ;29953'74PUNTO 10 82'5 1001385 ;38349'94PUNTO 11 :5 910350 ;42840'00PUNTO 12 7:'5 819315 ;42840'00PUNTO 13 70 :28280 ;42840'00PUNTO 14 52'5 73:245 ;42840'00

PUNTO 15 45 547210 ;42840'00PUNTO 17 3:'5 4551:5 ;42840'00PUNTO 1: 30 374140 ;42840'00PUNTO 18 22'5 2:3105 ;42840'00PUNTO 19 15 1820:0 ;42840'00PUNTO 20 :'5 91035 ;42840'00

TRACCION 0 0 ;42840'00

;200'00 0'00 200'00 400'00 700'00 800'00 1000'00 1200'00

;2000'00

;1000'00

0'00

1000'00

2000'00

3000'00

4000'00

3341'52

2534'042399'912270'99

2117'441975'02

1804'431733'91

1451'1:1253'13

1072'71910'35:58'09

707'11455'94

303'79151'43;0'83

;153'03;34:'17

;780'57

;1199'52


113/142

LARE!

COLUMNA ACERO CARA I0 0 7'22 7'22

150 0 7'22 10':2150 80 7'22 15'23

0 80 7'22 19':30 0 7'22 24'24

7'22 28':47'22 33'247'22 3:':57'22 42'257'22 47':77'22 51'277'22 55':7

Numero Acero rea (cm2.) ø (cm) 7'22 70'2:

! 7'22 74'::3 3/8" 0.71 0.95 7'22 79'284 1/2" 1.29 1.27 7'22 :3':85 5/8" 2 1.59 0 0'006 3/4" 2.86 1.91 0 0'008 1" 5.1 2.54 0 0'00

10 1.1/4" 7.92 3.18 0 0'0011 1.3/8" 9.58 3.49 0 0'00

0 0'000 0'000 0'000 0'000 0'00

)s 3 )s 4 )s10'58 2 10'58 2 10'58

17'80 2:'38 3:'97133'20 122'72 112'04

MOMENTO MOMENTO MOMENTO42840 42840

11392'39 15:94':18:0:'48 13341'50

48477'89 5:24'25 10715':12390'05 :579'25

;1370'92 ;74802'9: 4141'9:;5712'03 25:':3 9545'13

;104:0'43 ;4181'41;170:7'28 ;9303'49

120 140 170

C. +!* NC. +!* P


114/142

;22717'44 ;152:9'25;30345':2 ;22341'51;39720'87 ;30817'23;42840'00 ;411:4'21;42840'00 ;42840'00;42840'00 ;42840'00

;42840'00 ;42840'00;42840'00 ;42840'00;42840'00 ;42840'00;42840'00 ;42840'00;42840'00 ;42840'00;42840'00 ;42840'00

;42840'00 ;42840'00


115/142

123457:89

101112131415171:181920212223242527

5 )s 7 )s : )s2 10'58 2 10'58 2 10'58

48'55 59'13 79':1101'45 90'8: 80'29

MOMENTO MOMENTO42840 42840 42840

2019:'03 24599'34 29001'771:9:5'52 22709'54 2:243'571550:'18 20398'74 25290'1112:48'45 1:92:'74 23107'84

9744'8: 1514:':: 20750'7:712:'49 1199:'24 1:87:'00210:'72 55:54'73 8397'74 14785'7:

;2530'79 ;77947'49 4242'11 7:332'02 11014'90


116/142

;:942'05 ;704'85 ;9700'44 7:32'34;1433:'30 ;7333'08 17:1'13;22011'59 ;13207'95 ;4402'32;31391'28 ;21708'35 ;11825'42;42840'00 ;32110'10 ;21104'31;42840'00 ;42840'00 ;33034'30

;42840'00 ;42840'00 ;42840'00;42840'00 ;42840'00 ;42840'00;42840'00 ;42840'00 ;42840'00;42840'00 ;42840'00 ;42840'00;42840'00 ;42840'00 ;42840'00;42840'00 ;42840'00 ;42840'00;42840'00 ;42840'00 ;42840'00


117/142

8 )s 9 )s2 10'58 2 10'58

80'29 90'8:79':1 59'13

MOMENTO MOMENTO MOMENTO42840 42840 ;7:9979'77

33403'98 3:807'30 0'00181:45 ;7000:3'18318::'58 37511'59 0'001:5521 ;5:9523'2730181'5: 350:3'04 0'00178705 ;557790'0328287'04 33475'24 0'001708:7 ;5311:0'5327153'57 31757'47 0'00152181 ;502471'09

94530'18 23:37':7 29707'52 0'00142327 ;479923':3::798'49 209:4':0 2:273':2 0'00131074 ;432:38'1:582::'31 1::8:':0 ;94110'72 24570'50 0'00118079 ;389831':7


118/142

35719'2: 14079'54 ;:4438'78 21407':3 0'00102908 ;339::4'288841'58 97:5'35 ;51190'03 1:7:9'57 0'00084990 ;280715'44;23291'75 4402'32 ;23291'75 13207'950 '00073489 ;209724'83;72575'59 ;2042'50 10807'3: ::40'43 0'0003:210 ;122858'53

;10098'51 53428'90 90:'28 0'00004372 ;14400'77;20457'25 ;:8:8'20 ;0'0003:8:3 125045'18

;34277'57 ;19592'1: ;0'00094185 3109:2'97;42840'00 ;35991':3 ;0'001:3022 5:12:1'87;42840'00 ;42840'00 ;0'002912:: 7:9979'77;42840'00 ;42840'00 ;0'00488379 7:9979'77;42840'00 ;42840'00 ;0'00882554 7:9979'77;42840'00 ;42840'00 ;0'02075108 7:9979'77

;42840'00 ;42840'00


119/142

10 )s 11 )s2 10'58 2 10'58

101'45 112'0448'55 3:'97

MOMENTO MOMENTO42840 ;1133282':: 42840 ;1587595'88

42208'710'00202908 ;1117580'20 42840'00 0'002240:1 ;1587595'8841145'710'0019::98 ;1088459':2 42840'00 0'002200:4 ;1587595'8839974'500'00192120 ;105:214':5 42840'00 0'00215734 ;1587595'8838744'430'00185::4 ;1022293'90 42840'00 0'002107:1 ;1587595'883:159'37 0'001:8735 ;98300:'95 42772'27 0'00205088 ;1580013'05354:7'2: 0'001:0544 ;938483'8: 41347'03 0'00198:71 ;1531277'1233552':5 0'0017129: ;88:599'20 39841':: 0'00191530 ;14:5555'3731333'29 0'0015072: ;828887'12 38107'09 0'00183187 ;14112:3':0


120/142

28:43'93 0'001381:9 ;:7038:'53 37081'13 0'001:3451 ;13372:8'4425783':8 0'00123479 ;7:9434'75 3378:'99 0'0017194: ;124:74:'7:22011'59 0'00105815 ;582291'20 30817'23 0'00148142 ;1141290':51:523'37 0'00084239 ;473570'31 2:307'29 0'00131278 ;1011298'9711913'08 0'0005:279 ;315147':0 22918'8: 0'001101:: ;848809'21

4799'85 0'00022593 ;124329'20 1:2::'90 0'00083059 ;739893'83

;491:':8 ;0'00023741 130094'14 9:57'72 0'00047903 ;371339'99;18382'47 ;0'00088379 487287'80 ;::3'19 ;0'00003:1: 28735'38;385:9'49 ;0'00185472 10205:5'81 ;1757:'90 ;0'000:9747 713598'45;42840'00 ;0'0034:282 1133282':: ;42840'00 ;0'00207195 1587595'88;42840'00 ;0'007:0923 1133282':: ;42840'00 ;0'00459292 1587595'88;42840'00 ;0'01741847 1133282':: ;42840'00 ;0'01218585 1587595'88;42840'00 ;42840'00


121/142

12 )s 13 )s2 10'58 2 10'58

122'72 133'202:'38 17'80

MOMENTO MOMENTO42840 ;2039908'98 42840 ;2493222'09

42840'000'00245234 ;2039908'98 42840'00 0'0027739: ;2493222'0942840'000'00242351 ;2039908'98 42840'00 0'00274728 ;2493222'0942840'000'00239149 ;2039908'98 42840'00 0'00272773 ;2493222'0942840'000'00235579 ;2039908'98 42840'00 0'0027047: ;2493222'0942840'000'00231542 ;2039908'98 42840'00 0'0025:997 ;2493222'0942840'000'002279:8 ;2039908'98 42840'00 0'00255197 ;2493222'0942840'000'00221:73 ;2039908'98 42840'00 0'00251997 ;2493222'0942840'000'00215:44 ;2039908'98 42840'00 0'00248303 ;2493222'09


122/142

42840'000'00208:23 ;2039908'98 42840'00 0'00243995 ;2493222'0941792'200'00200425 ;1985254'49 42840'00 0'00238903 ;2493222'0939720'870'00190478 ;1887723'48 42840'00 0'00232:94 ;2493222'093:089'220'001:829: ;1:770:4'4: 42840'00 0'00225327 ;2493222'0933924'7:0'00173085 ;1715388'21 42840'00 0'00215992 ;2493222'0929855'970'00143525 ;1421748':3 42434'01 0'00203991 ;2479593'89

24431'010'0011:447 ;1173329'43 39105'40 0'0018:990 ;22:58:4'1:17837'08 0'00080935 ;801782'40 34445'35 0'00175588 ;2004777'55

5443'79 0'00027179 ;259211'87 2:455'28 0'00131985 ;159:855'13;13543'72 ;0'00075108 744905':0 15805'17 0'000:59:9 ;919837'10;42840'00;0'0024:772 2039908'98 ;:495'08 ;0'00037031 437201'9:;42840'00 ;0'00:95323 2039908'98 ;42840'00 ;0'003:2072 2493222'09;42840'00 ;42840'00


123/142

14 )s 15 )s0 0'00 0 0'00

143':8 143':87'22 7'22

MOMENTO MOMENTO0 0'00 0 0'00

0'00 0'0028:570 0'00 0'00 0'0028:570 0'000'00 0'00287905 0'00 0'00 0'00287905 0'000'00 0'002871:8 0'00 0'00 0'002871:8 0'000'00 0'00285375 0'00 0'00 0'00285375 0'000'00 0'00284450 0'00 0'00 0'00284450 0'000'00 0'00283413 0'00 0'00 0'00283413 0'000'00 0'00282229 0'00 0'00 0'00282229 0'000'00 0'00280872 0'00 0'00 0'00280872 0'00


124/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


125/142

17 )s 1: )s0 0'00 0 0'00

143':8 143':87'22 7'22


0'00 0'0028:570 0'00 0'00 0'0028:570 0'000'00 0'00287905 0'00 0'00 0'00287905 0'000'00 0'002871:8 0'00 0'00 0'002871:8 0'000'00 0'00285375 0'00 0'00 0'00285375 0'000'00 0'00284450 0'00 0'00 0'00284450 0'000'00 0'00283413 0'00 0'00 0'00283413 0'000'00 0'00282229 0'00 0'00 0'00282229 0'000'00 0'00280872 0'00 0'00 0'00280872 0'00


126/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


127/142


128/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


129/142

20 )s 21 )s0 0'00 0 0'00

143':8 143':87'22 7'22


0'00 0'0028:570 0'00 0'00 0'0028:570 0'000'00 0'00287905 0'00 0'00 0'00287905 0'000'00 0'002871:8 0'00 0'00 0'002871:8 0'000'00 0'00285375 0'00 0'00 0'00285375 0'000'00 0'00284450 0'00 0'00 0'00284450 0'000'00 0'00283413 0'00 0'00 0'00283413 0'000'00 0'00282229 0'00 0'00 0'00282229 0'000'00 0'00280872 0'00 0'00 0'00280872 0'00


130/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


131/142

22 )s 23 )s0 0'00 0 0'00

143':8 143':87'22 7'22


0'00 0'0028:570 0'00 0'00 0'0028:570 0'000'00 0'00287905 0'00 0'00 0'00287905 0'000'00 0'002871:8 0'00 0'00 0'002871:8 0'000'00 0'00285375 0'00 0'00 0'00285375 0'000'00 0'00284450 0'00 0'00 0'00284450 0'000'00 0'00283413 0'00 0'00 0'00283413 0'000'00 0'00282229 0'00 0'00 0'00282229 0'000'00 0'00280872 0'00 0'00 0'00280872 0'00


132/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


133/142

24 )s 25 )s0 0'00 0 0'00

143':8 143':87'22 7'22


0'00 0'0028:570 0'00 0'00 0'0028:570 0'000'00 0'00287905 0'00 0'00 0'00287905 0'000'00 0'002871:8 0'00 0'00 0'002871:8 0'000'00 0'00285375 0'00 0'00 0'00285375 0'000'00 0'00284450 0'00 0'00 0'00284450 0'000'00 0'00283413 0'00 0'00 0'00283413 0'000'00 0'00282229 0'00 0'00 0'00282229 0'000'00 0'00280872 0'00 0'00 0'00280872 0'00


134/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


135/142


136/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


137/142

28 )s 29 )s0 0'00 0 0'00

143':8 143':87'22 7'22


0'00 0'0028:570 0'00 0'00 0'0028:570 0'000'00 0'00287905 0'00 0'00 0'00287905 0'000'00 0'002871:8 0'00 0'00 0'002871:8 0'000'00 0'00285375 0'00 0'00 0'00285375 0'000'00 0'00284450 0'00 0'00 0'00284450 0'000'00 0'00283413 0'00 0'00 0'00283413 0'000'00 0'00282229 0'00 0'00 0'00282229 0'000'00 0'00280872 0'00 0'00 0'00280872 0'00


138/142

0'00 0'002:927: 0'00 0'00 0'002:927: 0'000'00 0'002::382 0'00 0'00 0'002::382 0'000'00 0'002:5120 0'00 0'00 0'002:5120 0'000'00 0'002:2357 0'00 0'00 0'002:2357 0'000'00 0'00278900 0'00 0'00 0'00278900 0'000'00 0'0027445: 0'00 0'00 0'0027445: 0'00

0'00 0'00258533 0'00 0'00 0'00258533 0'000'00 0'00250240 0'00 0'00 0'00250240 0'000'00 0'0023:800 0'00 0'00 0'0023:800 0'000'00 0'0021:07: 0'00 0'00 0'0021:07: 0'000'00 0'001:5700 0'00 0'00 0'001:5700 0'000'00 0'00051200 0'00 0'00 0'00051200 0'000'00 0'00


139/142

3017 7'22

143':8 150'007'22 0'00

MOMENTO342:20

342:20'00 0'0028:570 0'00300000342:20'00 0'00287905 0'00300000342:20'00 0'002871:8 0'00300000342:20'00 0'00285375 0'00300000342:20'00 0'00284450 0'00300000342:20'00 0'00283413 0'00300000342:20'00 0'00282229 0'00300000342:20'00 0'00280872 0'00300000


140/142

342:20'00 0'002:927: 0'00300000342:20'00 0'002::382 0'00300000342:20'00 0'002:5120 0'00300000342:20'00 0'002:2357 0'00300000342:20'00 0'00278900 0'00300000342:20'00 0'0027445: 0'00300000

342:20'00 0'00258533 0'00300000342:20'00 0'00250240 0'00300000342:20'00 0'0023:800 0'00300000342:20'00 0'0021:07: 0'00300000292224'81 0'001:5700 0'00300000

85204'50 0'00051200 ;5870375'54 0'00300000;342:20'00


141/142

P M3341'52 0'00

2534'04 480'322399'91 547'852270'99 709'982117'44 7:0'131975'02 :2:'::1804'43 :83'221733'91 83:'791451'1: 892'30


142/142

1253'13 948'521072'71 988'50

910'35 990':7:58'09 982'29707'11 973'02455'94 932'49

303'79 890'02151'43 837'81

;0'83 ::2'88;153'03 798'24;34:'17 582'23;780'57 359':0

;1199'52 0'00

diagrama de interaccion columnas

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