3.-ANALISIS-DE-VIGAS-6-3-2017con-As

03+000 UNIVERSIDAD SAN PEDRO FACULTAD DE INGENIERIA E.A.P. E.A.P. ARQUITECTURA ESTRUCTURAS II 2015 - II

CALCULO DE WU - FUERZAS CORTANTES Y MOMENTO EN VIGAS DE CONCRETO ARMADO Vista en Planta de Viga

 An),( T"i*"i( 1.30

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03+000 UNIVERSIDAD SAN PEDRO FACULTAD DE INGENIERIA E.A.P. E.A.P. ARQUITECTURA ESTRUCTURAS II 2015 - II

DIAGRAMA DE CARGAS 1.00

n),( :ig

An),( T"i*"i( 1.30

WU

VIGA

C(/!n 

0.10 C(/!n 

1.10 L d$ / Vig Planta Viga - Aligead! - ,!l"na

03+000 UNIVERSIDAD SAN PEDRO FACULTAD DE INGENIERIA E.A.P. ARQUITECTURA ESTRUCTURAS II 2015 - II

1.10 Ra %2&'+(5&

g

Ele)a,i!n Viga - ,!l"na

R4 %&'+(5&

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w  1'27 g4!/ wu

P$"/*$ Vig 0.15

VIGA

c o l u m na

c o l u m na 1.10 !


*"))i(n >)$"(?

FUERZAS CORTANTES #V$

w  1'27 g4!/ wu

P$"/*$ Vig 0.15

VIGA

c o l u m na

1.10 !

c o l u m na


c o l

c o l

0.15

1.10 ! Ele)a,i!n Dis8!si,i!n de Esti4!s 8! Es7"e*! ,!tante MOMENTO FLECTOR #M$ w  1'27 g4!/ wu

P$"/*$ Vig 0.15

VIGA

c o l u m na

c o l u m na 1.10 !


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50.' &5.5 '%.10 &5.5 50.' -%.%%

c o l u m na

1.10 !

0.11

0.11

0.11

0.11

0.11

0.11

>3? >? >5? >7? >%? >&? >'? 6>10?

o l u m na 0.11

0.11

0.11

0.11

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DIAGRAMA DE MOMENTO

-1'.21

R 105'.30

g

R 105'.30

g

0.88

1.10

DIAGRAMA DE CORTANTE 

9

0.00

1@05'.30

0 .11

&%.

0.22

735.5&

0.33

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0.&&

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0.''

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1.10

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1500 1000 500 0 0.00 -500 -1000 -1500

0.11

0.22

0.33

0.44

0.55

0.66

0.77

0.99

0.33 0. 0.55 0.77 0.%% 0.&& 0.'' 1.10

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DIAGRA9A 9O9ENTOS CAD 9ULTIPLE LINE

LINE

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0.@0.02 0.55@0 [email protected] 0.%%@-0.0 [email protected] 0.''@-0.0& [email protected]


UNIVERSIDAD SAN PEDRO - FACULTAD DE INGENIERIA - E.A.P. ARQUITECTURA ESTRUCTURAS II - 2015 - II

ELA:ORACION DE DIAGRAMA DE ENVOLVENTES PRIMER TRAMO NOVIE9#RE 2015?

V

201150.00

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1&&&&(&&

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V2

V3

V%

V&

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c o l u m na

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3(&& !

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c o l u m na

5.70

0.&0 !

0.&0 !

0.&0 !

0.&0 !

0.&0 !

1&&&&(&& R 70000.00

DIAGRAMA DE CORTANTE

6>0? >1? >2? >3? >? >5? >7? >%? >&? >'? 6>10?

0.00 0.&0 1.70 2.0 3.20 .00 .&0 5.70 7.0 %.20 &.00

! ! ! ! ! ! ! ! ! ! !

6>0? >1? >2? >3? >? >5? >7? >%? >&? >'? 6>10?

0.00 0.&0 1.70 2.0 3.20 .00 .&0 5.70 7.0 %.20 &.00

! ! ! ! ! ! ! ! ! ! !

R 70000.00 g

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0.&0 !

0.&0 !

0.&0 !

0.&0 !

0.&0 !

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DIAGRAMA DE MOMENTO

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R 70000.00 g


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37.0000 37.1&2'

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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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0.0001 0.0002 0.0003 0.000 0.0005 0.0007 0.000% 0.000& 0.000' 0.0010 0.0011 0.0012 0.0013 0.001 0.0015 0.0017 0.001% 0.001& 0.001' 0.0020 0.0021 0.0022 0.0023 0.002 0.0025 0.0027 0.002% 0.002& 0.002' 0.0030 0.0031 0.0032 0.0033 0.003 0.0035 0.0037 0.003% 0.003& 0.003' 0.000 0.001 0.002 0.003 0.00 0.005 0.007 0.00%

(

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ω= ρ . 〖 f ′ 〗 _y/ 〖 f ′ 〗A_s/(b.d) _c ρ= ρ_b=0.85 . β_1.( 〖 f^′ 〗 _c/ 〖 f^ ′ 〗 _y ).( 6000/(6000+ 〖 f^′ 〗 _y ) )

P"!$*"( D

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9(!$n*( U/*i!( N$g*i:( 125000 g-! A n$g*i:(

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55.00 )!2

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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3  5 7 % & ' 10 11 12 13 1 15 17 1% 1& 1' 20 21 22 23 2 25 27 2% 2& 2' 30 31 32

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.00& 0.00' 0.0050 0.0051 0.0052 0.0053 0.005 0.0055 0.0057 0.005% 0.005& 0.005' 0.0070 0.0071 0.0072 0.0073 0.007 0.0075 0.0077 0.007% 0.007& 0.007' 0.00%0 0.00%1 0.00%2 0.00%3 0.00% 0.00%5 0.00%7 0.00%% 0.00%& 0.00%' 0.00&0 0.00&1 0.00&2 0.00&3 0.00& 0.00&5 0.00&7 0.00&% 0.00&& 0.00&' 0.00'0 0.00'1 0.00'2 0.00'3 0.00' 0.00'5 0.00'7 0.00'% 0.00'& 0.00'' 0.0100 0.0101 0.0102 0.0103 0.010

0.0'70 0.0'&0 0.1000 0.1020 0.100 0.1070 0.10&0 0.1100 0.1120 0.110 0.1170 0.11&0 0.1200 0.1220 0.120 0.1270 0.12&0 0.1300 0.1320 0.130 0.1370 0.13&0 0.100 0.120 0.10 0.170 0.1&0 0.1500 0.1520 0.150 0.1570 0.15&0 0.1700 0.1720 0.170 0.1770 0.17&0 0.1%00 0.1%20 0.1%0 0.1%70 0.1%&0 0.1&00 0.1&20 0.1&0 0.1&70 0.1&&0 0.1'00 0.1'20 0.1'0 0.1'70 0.1'&0 0.2000 0.2020 0.200 0.2070 0.20&0

1%.1173 1%.511 1%.%&' 1&.11%& 1&.'' 1&.%&11 1'.1113 1'.0% 1'.%7'2 20.0'7& 20.235 20.%'3 21.0%3 21.3'&3 21.%21 22.03% 22.3750 22.7&55 23.0050 23.323% 23.715 23.'5& 2.2% 2.5&'5 2.'03% 25.21%1 25.52'5 25.&10 27.151% 27.71 27.%%03 2%.0%&3 2%.3&53 2%.7'15 2%.''7& 2&.3012 2&.70% 2&.'0% 2'.20'1 2'.50'' 2'.&0'' 30.10&' 30.0%1 30.%03 31.000% 31.2'72 31.5'0& 31.&&5 32.1%%3 32.7'2 32.%702 33.050 33.33'7 33.72%' 33.'15 3.2020 3.&%7 Ing. Edwin C. G!"" #""$"


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0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 1 2 3  5 7 % & ' 10 11 12 13 1 15 17 1% 1& 1' 20 21 22 23 2 25 27 2% 2& 2' 30 31 32 33 3 35 37 3% 3& 3' 0 1 2 3  5 7 % & ' 50 51 52

0.0105 0.0107 0.010% 0.010& 0.010' 0.0110 0.0111 0.0112 0.0113 0.011 0.0115 0.0117 0.011% 0.011& 0.011' 0.0120 0.0121 0.0122 0.0123 0.012 0.0125 0.0127 0.012% 0.012& 0.012' 0.0130 0.0131 0.0132 0.0133 0.013 0.0135 0.0137 0.013% 0.013& 0.013' 0.010 0.011 0.012 0.013 0.01 0.015 0.017 0.01% 0.01& 0.01' 0.0150 0.0151 0.0152 0.0153 0.015 0.0155 0.0157 0.015% 0.015& 0.015' 0.0170 0.0171

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'0 '1 '2 '3 ' '5 '7 '% '& '' 100 101 102 103 10 105 107 10% 10& 10' 110 111 112 113 11 115 117 11% 11& 11' 120 121 122 123 12 125 127 12% 12& 12' 130 131 132 133 13 135 137 13% 13& 13' 10 11 12 13 1 15 17

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

53 5 55 57 5% 5& 5' 70 71 72 73 7 75 77 7% 7& 7' %0 %1 %2 %3 % %5 %7 %% %& %' &0 &1 &2 &3 & &5 &7 &% && &' '0 '1 '2 '3 ' '5 '7 '% '& '' 100 101 102 103 10 105 107 10% 10& 10'

0.0172 0.0173 0.017 0.0175 0.0177 0.017% 0.017& 0.017' 0.01%0 0.01%1 0.01%2 0.01%3 0.01% 0.01%5 0.01%7 0.01%% 0.01%& 0.01%' 0.01&0 0.01&1 0.01&2 0.01&3 0.01& 0.01&5 0.01&7 0.01&% 0.01&& 0.01&' 0.01'0 0.01'1 0.01'2 0.01'3 0.01' 0.01'5 0.01'7 0.01'% 0.01'& 0.01'' 0.0200 0.0201 0.0202 0.0203 0.020 0.0205 0.0207 0.020% 0.020& 0.020' 0.0210 0.0211 0.0212 0.0213 0.021 0.0215 0.0217 0.021% 0.021&

0.320 0.3270 0.32&0 0.3300 0.3320 0.330 0.3370 0.33&0 0.300 0.320 0.30 0.370 0.3&0 0.3500 0.3520 0.350 0.3570 0.35&0 0.3700 0.3720 0.370 0.3770 0.37&0 0.3%00 0.3%20 0.3%0 0.3%70 0.3%&0 0.3&00 0.3&20 0.3&0 0.3&70 0.3&&0 0.3'00 0.3'20 0.3'0 0.3'70 0.3'&0 0.000 0.020 0.00 0.070 0.0&0 0.100 0.120 0.10 0.170 0.1&0 0.200 0.220 0.20 0.270 0.2&0 0.300 0.320 0.30 0.370

'.5301 '.%732 '.''53 50.2277 50.57' 50.7&7 50.'150 51.12% 51.37' 51.5'53 51.&20 52.05 52.27%% 52.'00 52.%115 52.'320 53.151% 53.3%0 53.5&&3 53.&053 5.021 5.2377 5.50' 5.773 5.&%7& 55.0&& 55.2''2 55.50'0 55.%1&0 55.'270 57.1332 57.33'5 57.5& 57.%'3 57.'52' 5%.1557 5%.35% 5%.55& 5%.%5& 5%.'5%5 5&.155& 5&.3531 5&.5'7 5&.%52 5&.'3'& 5'.1337 5'.3275 5'.51&5 5'.%0'7 5'.&''' 70.0&'2 70.2%%7 70.752 70.751& 70.&3%7 71.022 71.207 Ing. Edwin C. G!"" #""$"


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1% 1& 1' 150 151 152 153 15 155 157 15% 15& 15' 170 171 172 173 17 175 177 17% 17& 17' 1%0 1%1 1%2 1%3 1% 1%5 1%7 1%% 1%& 1%' 1&0 1&1 1&2 1&3 1& 1&5 1&7 1&% 1&& 1&' 1'0 1'1 1'2 1'3 1' 1'5 1'7 1'% 1'& 1'' 200 201 202 203

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

110 111 112 113 11 115 117 11% 11& 11' 120 121 122 123 12 125 127 12% 12& 12' 130 131 132 133 13 135 137 13% 13& 13' 10 11 12 13 1 15 17 1% 1& 1' 150 151 152 153 15 155 157 15% 15& 15' 170 171 172 173 17 175 177

0.021' 0.0220 0.0221 0.0222 0.0223 0.022 0.0225 0.0227 0.022% 0.022& 0.022' 0.0230 0.0231 0.0232 0.0233 0.023 0.0235 0.0237 0.023% 0.023& 0.023' 0.020 0.021 0.022 0.023 0.02 0.025 0.027 0.02% 0.02& 0.02' 0.0250 0.0251 0.0252 0.0253 0.025 0.0255 0.0257 0.025% 0.025& 0.025' 0.0270 0.0271 0.0272 0.0273 0.027 0.0275 0.0277 0.027% 0.027& 0.027' 0.02%0 0.02%1 0.02%2 0.02%3 0.02% 0.02%5

0.3&0 0.00 0.20 0.0 0.70 0.&0 0.500 0.520 0.50 0.570 0.5&0 0.700 0.720 0.70 0.770 0.7&0 0.%00 0.%20 0.%0 0.%70 0.%&0 0.&00 0.&20 0.&0 0.&70 0.&&0 0.'00 0.'20 0.'0 0.'70 0.'&0 0.5000 0.5020 0.500 0.5070 0.50&0 0.5100 0.5120 0.510 0.5170 0.51&0 0.5200 0.5220 0.520 0.5270 0.52&0 0.5300 0.5320 0.530 0.5370 0.53&0 0.500 0.520 0.50 0.570 0.5&0 0.5500

71.3&'5 71.5%1% 71.%530 71.'33 72.112' 72.2'15 72.7'2 72.771 72.&220 72.''%1 73.1%12 73.35 73.517' 73.7&&3 73.&5&' 7.02&7 7.1'% 7.375 7.532 7.7'&5 7.&73% 75.02&1 75.1'17 75.351 75.515& 75.7%77 75.&37 75.''5 77.1535 77.310& 77.7%1 77.7225 77.%%%0 77.'30% 7%.0&3 7%.2353 7%.3&72 7%.5373 7%.7&55 7%.&33& 7%.'&12 7&.12%% 7&.2%33 7&.1&0 7&.571' 7&.%0& 7&.&7& 7&.'&&0 7'.12&3 7'.27%7 7'.071 7'.53% 7'.7&0 7'.&172 7'.'511 %0.0&51 %0.21&2 Ing. Edwin C. G!"" #""$"


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

20 205 207 20% 20& 20' 210 211 212 213 21 215 217 21% 21& 21' 220 221 222 223 22 225 227 22% 22& 22' 230 231 232 233 23 235 237 23% 23& 23' 20 21 22 23 2 25 27 2% 2& 2' 250 251 252 253 25 255 257 25% 25& 25' 270

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

17% 17& 17' 1%0 1%1 1%2 1%3 1% 1%5 1%7 1%% 1%& 1%' 1&0 1&1 1&2 1&3 1& 1&5 1&7 1&% 1&& 1&' 1'0 1'1 1'2 1'3 1' 1'5 1'7 1'% 1'& 1'' 200 201 202 203 20 205 207 20% 20& 20' 210 211 212 213 21 215 217 21% 21& 21' 220 221 222 223

0.02%7 0.02%% 0.02%& 0.02%' 0.02&0 0.02&1 0.02&2 0.02&3 0.02& 0.02&5 0.02&7 0.02&% 0.02&& 0.02&' 0.02'0 0.02'1 0.02'2 0.02'3 0.02' 0.02'5 0.02'7 0.02'% 0.02'& 0.02'' 0.0300 0.0301 0.0302 0.0303 0.030 0.0305 0.0307 0.030% 0.030& 0.030' 0.0310 0.0311 0.0312 0.0313 0.031 0.0315 0.0317 0.031% 0.031& 0.031' 0.0320 0.0321 0.0322 0.0323 0.032 0.0325 0.0327 0.032% 0.032& 0.032' 0.0330 0.0331 0.0332

0.5520 0.550 0.5570 0.55&0 0.5700 0.5720 0.570 0.5770 0.57&0 0.5%00 0.5%20 0.5%0 0.5%70 0.5%&0 0.5&00 0.5&20 0.5&0 0.5&70 0.5&&0 0.5'00 0.5'20 0.5'0 0.5'70 0.5'&0 0.7000 0.7020 0.700 0.7070 0.70&0 0.7100 0.7120 0.710 0.7170 0.71&0 0.7200 0.7220 0.720 0.7270 0.72&0 0.7300 0.7320 0.730 0.7370 0.73&0 0.700 0.720 0.70 0.770 0.7&0 0.7500 0.7520 0.750 0.7570 0.75&0 0.7700 0.7720 0.770

%0.3505 %0.&1& %0.7122 %0.%1& %0.&%05 %0.''&2 %1.1251 %1.2511 %1.3%72 %1.500 %1.723% %1.%71 %1.&7%% %1.'&&3 %2.10&0 %2.227' %2.3& %2.71' %2.5%&1 %2.7'3 %2.&0%& %2.'213 %3.033' %3.157 %3.257 %3.3773 %3.%5 %3.5&35 %3.7'0& %3.%'%1 %3.'027 %.00%2 %.110' %.213% %.3157 %.177 %.517% %.715' %.%12 %.&11% %.'0&2 %5.003' %5.0'&% %5.1'25 %5.2&55 %5.3%%7 %5.7&& %5.55'1 %5.7&5 %5.%3%0 %5.&2% %5.'11 %5.''%2 %7.0&22 %7.1772 %7.2' %7.331% Ing. Edwin C. G!"" #""$"


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

271 272 273 27 275 277 27% 27& 27' 2%0 2%1 2%2 2%3 2% 2%5 2%7 2%% 2%& 2%' 2&0 2&1 2&2 2&3 2& 2&5 2&7 2&% 2&& 2&' 2'0 2'1 2'2 2'3 2' 2'5 2'7 2'% 2'& 2'' 300 301 302 303 30 305 307 30% 30& 30' 310 311 312 313 31 315 317 31%

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

22 225 227 22% 22& 22' 230 231 232 233 23 235 237 23% 23& 23' 20 21 22 23 2 25 27 2% 2& 2' 250 251 252 253 25 255 257 25% 25& 25' 270 271 272 273 27 275 277 27% 27& 27' 2%0 2%1 2%2 2%3 2% 2%5 2%7 2%% 2%& 2%' 2&0

0.0333 0.033 0.0335 0.0337 0.033% 0.033& 0.033' 0.030 0.031 0.032 0.033 0.03 0.035 0.037 0.03% 0.03& 0.03' 0.0350 0.0351 0.0352 0.0353 0.035 0.0355 0.0357 0.035% 0.035& 0.035' 0.0370 0.0371 0.0372 0.0373 0.037 0.0375 0.0377 0.037% 0.037& 0.037' 0.03%0 0.03%1 0.03%2 0.03%3 0.03% 0.03%5 0.03%7 0.03%% 0.03%& 0.03%' 0.03&0 0.03&1 0.03&2 0.03&3 0.03& 0.03&5 0.03&7 0.03&% 0.03&& 0.03&'

0.7770 0.77&0 0.7%00 0.7%20 0.7%0 0.7%70 0.7%&0 0.7&00 0.7&20 0.7&0 0.7&70 0.7&&0 0.7'00 0.7'20 0.7'0 0.7'70 0.7'&0 0.%000 0.%020 0.%00 0.%070 0.%0&0 0.%100 0.%120 0.%10 0.%170 0.%1&0 0.%200 0.%220 0.%20 0.%270 0.%2&0 0.%300 0.%320 0.%30 0.%370 0.%3&0 0.%00 0.%20 0.%0 0.%70 0.%&0 0.%500 0.%520 0.%50 0.%570 0.%5&0 0.%700 0.%720 0.%70 0.%770 0.%7&0 0.%%00 0.%%20 0.%%0 0.%%70 0.%%&0

%7.131 %7.'37 %7.5%32 %7.751' %7.%2'% %7.&077 %7.&&27 %7.'5%& %%.0320 %%.105 %%.1%%& %%.2' %%.3201 %%.3&'' %%.5&& %%.527& %%.5'3' %%.7701 %%.%25 %%.%&'' %%.&53 %%.'171 %%.'%%& %&.03&% %&.0'&7 %&.15%% %&.215' %&.2%32 %&.32'7 %&.3&51 %&.3'& %&.'35 %&.573 %&.5'&3 %&.7'3 %&.7''5 %&.%&% %&.%'%1 %&.&7 %&.&'12 %&.'37' %&.'&1% %'.0257 %'.07&7 %'.110& %'.1520 %'.1'2 %'.231& %'.2%0 %'.30&1 %'.3& %'.3&0% %'.15% %'.'& %'.&30 %'.515 %'.57& Ing. Edwin C. G!"" #""$"


1 1 1 1 1 1 1 1 1 1 1 1 1

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1 1 1 1 1 1 1 1 1 1 1 1 1

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Ing. Edwin C. G!"" #""$"


9ULTIPLE PL [email protected] 0.&@1&.'15 1.7@1%.%15 2.@17.515 [email protected] @1.115 .&@12.'15 5.7@11.%15 7.@10.515 %.2@'.315 [email protected] &@0 0@0 [email protected]

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3.-ANALISIS-DE-VIGAS-6-3-2017con-As

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