PARÁMETROS ENTRADANOMBRE SIMBOLO VALOR UNIDAD

Altura H 320 m

Densidad ρ 2.4

160 MPa

RMR 60 -

k 1.15 -

Gravedad g 9.81

Esfuerzo Vertical 7.53408 MPa

Esfuerzo Horizontal 8.664192 MPa

21 -

2.1140468952 -

Parametro "S" S 0.0019304541 -

Deformación ϵ mm/mm

D 0.6 -

a 0.5040481499 -

E m 9.3346500251 GPa

6.8542772835 MPa

-0.1461049244 MPa

Resistencia a la compresión uniaxial

Rock Mass Rating (1989)

Relacion entre esfuerzo vertical y

horizontal

Parametro "m" Roca Intacta

Parametro "m" Macizo Rocoso

Factor de Disturbación por Voladura

Parametro "a= Macizo Rocoso

Módulo de Young del macizo rocoso

Resistencia a la compresión uniaxial de la masa rocosa

Resistencia a la tracción de la masa

rocosa

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DESCRIPCIÓN

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

PARAMETROS SALIDA

θ(°) 0

r (m) (MPa)

1 0 13.938048 0 13.9380481.2 2.287692 12.34098 0 12.340981.4 3.820070384 11.225026106 0 11.2250261061.6 4.8762291094 10.439142891 0 10.4391428911.8 5.6283401481 9.8723318519 0 9.87233185192 6.1803 9.452916 0 9.452916

2.2 6.5961922732 9.135091297 0 9.1350912972.4 6.91678575 8.88908625 0 8.889086252.6 7.1688376357 8.6950817016 0 8.69508170162.8 7.3704241949 8.5395539275 0 8.53955392753 7.53408 8.413056 0 8.413056

3.2 7.6687021318 8.3088448682 0 8.30884486823.4 7.7807387846 8.2220121081 0 8.22201210813.6 7.8749512593 8.1489207407 0 8.14892074073.8 7.9549145697 8.0868322226 0 8.08683222264 8.02335375 8.03365425 0 8.03365425

4.2 8.082374424 7.9877669638 0 7.98776696384.4 8.1336238353 7.9479010573 0 7.94790105734.6 8.1784052282 7.9130508928 0 7.91305089284.8 8.2177603594 7.8824116406 0 7.88241164065 8.2525298688 7.8553331712 0 7.8553331712

θ(°) 5

r (m) (MPa)

1 0 13.972385881 0 13.8662499131.2 2.2905336186 12.361984132 -0.09244265 12.2694276531.4 3.8223014167 11.2403144 -0.1216193 11.1628472881.6 4.8771282153 10.45165702 -0.12986173 10.3867619581.8 5.6279005228 9.8833695887 -0.13064846 9.82835765252 6.1786904118 9.4631100585 -0.12878374 9.4157981395

2.2 6.5936030361 9.1447751377 -0.12610093 9.1034989232.4 6.9133864885 8.8984469492 -0.12331838 8.86195417272.6 7.164769172 8.7042297335 -0.12070927 8.67157485592.8 7.3658005674 8.5485573869 -0.11836273 8.51901954733 7.5289929065 8.4219584137 -0.11629149 8.3949815321

3.2 7.6632253666 8.3176749421 -0.11447793 8.29282477863.4 7.7749320027 8.230789295 -0.11289413 8.20772268743.6 7.8688629877 8.1576585402 -0.11151051 8.13610121753.8 7.9485845595 8.0955402024 -0.11029938 8.07527062234 8.016814798 8.0423393196 -0.10923621 8.0231767637

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4.2 8.0756537823 7.9964341973 -0.10829978 7.97822989974.4 8.1267443052 7.9565542383 -0.10747204 7.93918469924.6 8.1713860132 7.921692881 -0.1067377 7.90505477334.8 8.2106177342 7.8910446252 -0.10608387 7.87505087195 8.2452777083 7.863958847 -0.10549964 7.848535572

θ(°) 10

r (m) (MPa)

1 0 14.074356186 0 13.6499624181.2 2.2989721334 12.424358329 -0.18207648 12.0567667541.4 3.8289267259 11.285714757 -0.23954325 10.9789364671.6 4.8797982141 10.488819171 -0.25577767 10.2322053771.8 5.6265950045 9.9161474233 -0.25732724 9.69879049132 6.1739105538 9.4933824927 -0.25365445 9.3065332345

2.2 6.5859139973 9.1735324212 -0.24837034 9.01055851772.4 6.903291989 8.9262446266 -0.24288979 8.78217193842.6 7.1526873993 8.7313958708 -0.23775085 8.60247640462.8 7.3520701714 8.5752941993 -0.23312907 8.45867464323 7.5138861947 8.4483951593 -0.22904952 8.3418767157

3.2 7.6469614795 8.3438968668 -0.2254775 8.24576384523.4 7.757688093 8.2568541653 -0.22235802 8.16575154423.6 7.8507831619 8.183606445 -0.21963282 8.09845174633.8 7.929786863 8.1213995543 -0.21724738 8.04131874624 7.9973966248 8.0681306369 -0.21515333 7.992410973

4.2 8.0556960606 8.0221725486 -0.21330893 7.95022745674.4 8.106314746 7.9822508586 -0.2116786 7.9135934994.6 8.1505416433 7.9473562634 -0.21023223 7.88157939334.8 8.1894068837 7.9166812702 -0.20894443 7.85344175025 8.2237415799 7.8895737875 -0.20779373 7.8285805393

θ(°) 15

r (m) (MPa)

1 0 14.240860598 0 13.2869038241.2 2.3127511444 12.526207382 -0.266178 11.7089465441.4 3.8397450051 11.359847708 -0.35018881 10.6810019421.6 4.8841579793 10.549500192 -0.37392195 9.98303325141.8 5.6244632608 9.9696694176 -0.37618726 9.49050216782 6.1661056595 9.54281349 -0.370818 9.1312079559

2.2 6.5733587845 9.220489372 -0.36309315 8.86161866992.4 6.8868089676 8.971634664 -0.35508113 8.6544372612.6 7.132959416 8.7757546842 -0.3475685 8.491924022.8 7.329650198 8.6189519803 -0.3408119 8.36217918623 7.4892188744 8.4915629698 -0.334848 8.2569946471

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3.2 7.6204046407 8.3867139021 -0.32962606 8.17056788563.4 7.729531003 8.2994147511 -0.32506568 8.09870693843.6 7.8212611284 8.2259760412 -0.3210817 8.03832443083.8 7.8990926388 8.1636245549 -0.31759442 7.98710706864 7.9656892416 8.1102445457 -0.31453313 7.943294614

4.2 8.0231076641 8.0641999706 -0.31183679 7.90552891414.4 8.0729558995 8.0242101396 -0.3094534 7.8727487844.6 8.1165054643 7.989261271 -0.30733897 7.84411553264.8 8.1547722888 7.9585426191 -0.30545632 7.81895935435 8.1885758482 7.9313996958 -0.30377411 7.7967401785

θ(°) 20

r (m) (MPa)

1 0 14.466839965 0 12.7745411641.2 2.4673796374 12.664436659 -0.34219184 11.2516509071.4 3.9611480732 11.460460762 -0.45019405 10.2938286641.6 4.9330834009 10.63185632 -0.48070479 9.65623544281.8 5.6005407658 10.042309333 -0.48361702 9.21185808642 6.0785188907 9.6099011145 -0.47671443 8.8903817371

2.2 6.4324637925 9.284219227 -0.46678356 8.65058452322.4 6.7018359844 9.0332379079 -0.4564835 8.46709375552.6 6.9115713689 8.8359583537 -0.44682545 8.32363397942.8 7.0780525535 8.6782042103 -0.43813934 8.20939148763 7.2124014323 8.550150213 -0.43047229 8.1169610776

3.2 7.3223829618 8.4448250742 -0.42375909 8.04113719483.4 7.4135512556 8.3571778706 -0.41789638 7.97817590823.6 7.4899639418 8.28347995 -0.41277468 7.92532975923.8 7.5546410919 8.220932219 -0.40829151 7.88054623884 7.6098679934 8.1674014364 -0.40435599 7.8422673918

4.2 7.6573996565 8.1212394816 -0.40088965 7.80929363134.4 7.6986018779 8.0811571696 -0.39782563 7.78068931664.6 7.7345503952 8.0461346413 -0.39510736 7.75571609364.8 7.7661017783 8.0153567359 -0.39268708 7.73378505785 7.7939449027 7.9881657127 -0.39052446 7.7144219081

θ(°) 25

r (m) (MPa)

1 0 14.745428018 0 12.1118032231.2 2.298620333 12.834846134 -0.40780836 10.6406116071.4 3.8286505177 11.584496843 -0.53652038 9.78825618391.6 4.8796869022 10.733385205 -0.57288166 9.24902561421.8 5.6266494314 10.131860042 -0.57635232 8.88569002542 6.1741098254 9.6926069427 -0.56812614 8.62897169

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2.2 6.5862345523 9.3627855866 -0.55629098 8.44073275372.4 6.9037128272 9.109182575 -0.54401585 8.29853169952.6 7.1531910867 8.910177621 -0.53250583 8.18844580952.8 7.3526425896 8.7512505402 -0.52215413 8.10145722733 7.5145159914 8.6223767453 -0.5130169 8.0315122063

3.2 7.6476395187 8.5164647045 -0.50501642 7.97442212023.4 7.7584069891 8.4283884206 -0.49802952 7.92721284293.6 7.8515369073 8.3543709443 -0.49192571 7.88772471373.8 7.9305705363 8.2915812823 -0.48658288 7.85435841894 7.9982061656 8.2378646256 -0.48189271 7.8259089109

4.2 8.0565280952 8.1915579649 -0.47776168 7.80145411574.4 8.1071664514 8.151361642 -0.47411012 7.78027868274.6 8.1514106421 8.1162483058 -0.47087061 7.76182069934.8 8.190291161 8.0853973526 -0.46798623 7.74563378295 8.2246394181 8.0581470316 -0.46540893 7.7313596778

θ(°) 30

r (m) (MPa)

1 0 15.06816 0 11.301121.2 2.350506211 13.032258 -0.46103382 9.96255305281.4 3.8693875427 11.728187175 -0.60654481 9.23820405521.6 4.8961039183 10.851001945 -0.64765181 8.80139452061.8 5.6186221937 10.235600593 -0.65157545 8.5170751042 6.1447199224 9.788418 -0.64227562 8.3212664806

2.2 6.538956976 9.4538012518 -0.62889579 8.18045045392.4 6.8416447992 9.197161125 -0.61501855 8.0756603562.6 7.0789039163 8.9961573715 -0.60200629 7.9954912642.8 7.2682185327 8.8358714944 -0.59030353 7.93274040023 7.4216293845 8.706048 -0.57997375 7.8826713461

3.2 7.5476377908 8.5994560591 -0.57092908 7.84206240343.4 7.652379398 8.5108827046 -0.56303027 7.80865835743.6 7.740369521 8.436495037 -0.55612982 7.78084110253.8 7.81498918 8.3734251085 -0.55008966 7.75742450244 7.8788096849 8.319493125 -0.54478735 7.7375225775

4.2 7.933814094 8.2730188288 -0.54011716 7.72046246314.4 7.9815512642 8.2326904295 -0.53598902 7.70572553114.6 8.0232449093 8.1974718963 -0.5323267 7.69290670024.8 8.0598720493 8.1665363203 -0.52906587 7.68168577215 8.0922202713 8.1392173056 -0.52615218 7.6718068886

θ(°) 35

r (m) (MPa)

1 0 15.425229864 0 10.350484596

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1.2 2.5580324414 13.250673999 -0.500251 9.26282044131.4 4.0323220743 11.887165803 -0.65813968 8.6845523291.6 4.9617665147 10.981132814 -0.70274339 8.3404591531.8 5.5865159169 10.35037888 -0.70700078 8.11875252622 6.0271700996 9.8944231157 -0.69690988 7.9672547548

2.2 6.3498624178 9.5545007578 -0.68239191 7.85896837542.4 6.5933933601 9.2945003742 -0.66733423 7.77877432352.6 6.7817799778 9.0912851539 -0.6532151 7.71765980092.8 6.9305504245 8.9294959079 -0.64051686 7.66997400993 7.0501138952 8.7986216683 -0.62930839 7.6320237717

3.2 7.1476641872 8.6912774877 -0.61949435 7.60130998863.4 7.2283043485 8.6021541754 -0.61092364 7.57609098093.6 7.2957370027 8.5273569293 -0.60343622 7.55512181933.8 7.3527022517 8.4639769146 -0.59688226 7.53749288934 7.4012635298 8.409806694 -0.59112891 7.5225266731

4.2 7.4429989619 8.3631469263 -0.58606146 7.50970988684.4 7.4791323542 8.3226723979 -0.58158216 7.49864775364.6 7.5106246665 8.287337475 -0.57760832 7.48903251044.8 7.5382390418 8.2563082727 -0.5740701 7.48062129085 7.5625877897 8.2289132553 -0.57090857 7.473220317

θ(°) 40

r (m) (MPa)

1 0 15.805788221 0 9.27521727121.2 2.6612013547 13.48345767 -0.52426832 8.49565855371.4 4.1133228159 12.056602239 -0.68973731 8.09537187911.6 4.9944098036 11.119823851 -0.73648246 7.86365668291.8 5.5705547071 10.472707424 -0.74094426 7.71756835752 5.9687317641 10.007401378 -0.73036888 7.6194474423

2.2 6.2558565659 9.6618244009 -0.7151539 7.55027142842.4 6.4699784494 9.3982427187 -0.69937329 7.49960622322.6 6.6340687521 9.1926705586 -0.6845763 7.46134187942.8 6.7626832026 9.0292790502 -0.67126841 7.43170591323 6.8654198966 8.8972849463 -0.65952181 7.4082650583

3.2 6.9488226145 8.7891390426 -0.6492366 7.38939139113.4 7.0174810617 8.6994295957 -0.6402544 7.37396147623.6 7.0746938428 8.6241958283 -0.6324075 7.36117912233.8 7.122882436 8.5604853297 -0.62553889 7.35046689914 7.1638577918 8.5060612005 -0.61950932 7.3413975026

4.2 7.198996728 8.4592037608 -0.61419857 7.33364905524.4 7.229361456 8.4185734907 -0.60950422 7.32697523914.6 7.2557823111 8.3831145219 -0.60533959 7.32118488364.8 7.2789161098 8.3519855343 -0.6016315 7.31612772665 7.2992880253 8.3245095148 -0.59831819 7.3116843007

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θ(°) 45

r (m) (MPa)

1 0 16.198272 0 8.0991361.2 2.5307585575 13.723536 -0.532356 7.59479127871.4 4.0109086005 12.231348245 -0.70037762 7.42075080671.6 4.9531368873 11.262861 -0.74784389 7.3601550531.8 5.5907354455 10.598869333 -0.75237452 7.34242787092 6.042618943 10.12392 -0.741636 7.3416334715

2.2 6.3747139414 9.7725112066 -0.72618631 7.34742626872.4 6.6260195053 9.505236 -0.71016225 7.35546550272.6 6.8208291321 9.2972330414 -0.69513699 7.36389409522.8 6.9749280473 9.1321890612 -0.68162381 7.37193474923 7.0989398691 8.99904 -0.669696 7.3792939345

3.2 7.2002302344 8.89006725 -0.65925212 7.3858966243.4 7.2840378991 8.799753301 -0.65013136 7.39176423943.6 7.3541722938 8.7240693333 -0.64216341 7.39695740613.8 7.4134577522 8.6600179945 -0.63518883 7.40154904134 7.4640244558 8.605332 -0.62906625 7.4056119779

4.2 7.5075037471 8.5582706939 -0.62367358 7.40921364454.4 7.5451621519 8.5174798017 -0.61890681 7.41241416744.6 7.5779951621 8.4818928998 -0.61467793 7.41526609854.8 7.606794029 8.450661 -0.61091264 7.41781487395 7.6321940982 8.42310144 -0.60754821 7.4200995579

θ(°) 50

r (m) (MPa)

1 0 16.590755779 0 6.85490063581.2 2.3301283225 13.96361433 -0.52426832 6.62050100131.4 3.853388304 12.406094251 -0.68973731 6.70790172961.6 4.8896562271 11.405898149 -0.73648246 6.85671678231.8 5.6217748464 10.725031243 -0.74094426 7.00062980722 6.1562626425 10.240438622 -0.73036888 7.1244728358

2.2 6.5575249797 9.8831980123 -0.7151539 7.22732385632.4 6.8660216701 9.6122292813 -0.69937329 7.31194026412.6 7.108079787 9.4017955243 -0.6845763 7.38161183022.8 7.301375609 9.2350990722 -0.67126841 7.43927323043 7.4581100799 9.1007950537 -0.65952181 7.487325746

3.2 7.5869129102 8.9909954574 -0.6492366 7.52767276163.4 7.6940211415 8.9000770064 -0.6402544 7.5618068713.6 7.7840298903 8.8239428383 -0.6324075 7.59089705883.8 7.8603831113 8.7595506592 -0.62553889 7.61586193714 7.925701985 8.7046027995 -0.61950932 7.6374274572

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4.2 7.9820093317 8.657337627 -0.61419857 7.65617119894.4 8.0308859265 8.6163861126 -0.60950422 7.67255601394.6 8.0735812842 8.5806712777 -0.60533959 7.68695552944.8 8.1110934261 8.5493364657 -0.6016315 7.69967352285 8.1442271507 8.5216933652 -0.59831819 7.7109587068

θ(°) 55

r (m) (MPa)

1 0 16.971314136 0 5.58339142151.2 2.3106687235 14.196398001 -0.500251 5.7508717691.4 3.8381100394 12.575530687 -0.65813968 6.09418443371.6 4.8834990883 11.544589186 -0.70274339 6.41456786841.8 5.624785431 10.847359787 -0.70700078 6.67859637532 6.1672852126 10.353416884 -0.69690988 6.8895993029

2.2 6.5752562529 9.9905216554 -0.68239191 7.05760552832.4 6.8893000454 9.7159716258 -0.66733423 7.19215747842.6 7.1359409047 9.503180929 -0.6532151 7.300917622.8 7.3330385269 9.3348822146 -0.64051686 7.38973597163 7.4929468447 9.1994583317 -0.62930839 7.4630154868

3.2 7.6244181737 9.0888570123 -0.61949435 7.52406953243.4 7.7337863819 8.9973524267 -0.61092364 7.5754064463.6 7.8257227911 8.9207817374 -0.60343622 7.61894159683.8 7.9037314546 8.8560590743 -0.59688226 7.65615179644 7.9704811761 8.800857306 -0.59112891 7.688187082

4.2 8.0280327461 8.7533944614 -0.58606146 7.71595181824.4 8.0779974195 8.7122872054 -0.58158216 7.7401639054.6 8.1216493495 8.6764483246 -0.57760832 7.76139835114.8 8.1600066125 8.6450137273 -0.5740701 7.78011963145 8.1938904426 8.6172896247 -0.57090857 7.796705938

θ(°) 60

r (m) (MPa)

1 0 17.328384 0 4.3320961.2 2.4967595719 14.414814 -0.46103382 5.07700617891.4 3.9842150651 12.734509314 -0.60654481 5.64650541541.6 4.9423793958 11.674720055 -0.64765181 6.06458164261.8 5.5959954111 10.962138074 -0.65157545 6.3732501882 6.0618771096 10.459422 -0.64227562 6.6050363322

2.2 6.4056932694 10.091221161 -0.62889579 6.78243551342.4 6.6666904946 9.813310875 -0.61501855 6.92072390222.6 6.8695068943 9.5983087113 -0.60200629 7.03035460492.8 7.0302481537 9.4285066281 -0.59030353 7.11859491853 7.1598051859 9.292032 -0.57997375 7.1905898894

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3.2 7.265757839 9.1806784409 -0.57092908 7.25004890093.4 7.3535140394 9.0886238975 -0.56303027 7.29969298343.6 7.4270163605 9.0116436296 -0.55612982 7.34155062223.8 7.4891941378 8.9466108804 -0.55008966 7.37715669944 7.5422607578 8.891170875 -0.54478735 7.4076885996

4.2 7.5879139033 8.8435225589 -0.54011716 7.43406088524.4 7.6274733529 8.8022691738 -0.53598902 7.45699220114.6 7.6619776457 8.7663139033 -0.5323267 7.47705326074.8 7.6922530723 8.7347856797 -0.52906587 7.49470174375 7.7189636939 8.7069855744 -0.52615218 7.5103080056

θ(°) 65

r (m) (MPa)

1 0 17.651115982 0 3.15259866591.2 2.6552583547 14.612225866 -0.40780836 4.4784475031.4 4.1086568037 12.878199647 -0.53652038 5.26395302791.6 4.9925294013 11.792336795 -0.57288166 5.76816431791.8 5.5714741456 11.065878624 -0.57635232 6.11129733292 5.9720980788 10.555233057 -0.56812614 6.3554645092

2.2 6.2612717317 10.182236827 -0.55629098 6.53543677172.4 6.4770877112 9.901289425 -0.54401585 6.67193103542.6 6.6425775924 9.6842884618 -0.53250583 6.77792286592.8 6.7723531201 9.5131275822 -0.52215413 6.86187915033 6.8760591132 9.3757032547 -0.5130169 6.9295172976

3.2 6.9602767959 9.2636697955 -0.50501642 6.9848120323.4 7.0296254445 9.1711181815 -0.49802952 7.03059657093.6 7.087426937 9.0937677224 -0.49192571 7.06893487443.8 7.1361211055 9.0284547067 -0.48658288 7.10135950244 7.1775334451 8.9727993744 -0.48189271 7.1290278331

4.2 7.2130523695 8.9249834229 -0.47776168 7.15282718334.4 7.2437493989 8.8835979613 -0.47411012 7.17344708684.6 7.270462393 8.8475374938 -0.47087061 7.19142995864.8 7.2938542934 8.8159246474 -0.46798623 7.20720723445 7.3144552926 8.7880558484 -0.46540893 7.2211255556

θ(°) 70

r (m) (MPa)

1 0 17.929704035 0 2.09737694621.2 2.5875910696 14.782635341 -0.34219184 3.79418358111.4 4.0555293635 13.002235728 -0.45019405 4.81271603871.6 4.9711190494 11.89386568 -0.48070479 5.47193549011.8 5.5819429166 11.155429334 -0.48361702 5.92305394862 6.0104271004 10.637938886 -0.47671443 6.2453170187

�_� �_� �_�� �_1

�_� �_� �_�� �_1

2.2 6.3229290719 10.260803186 -0.46678356 6.48353014922.4 6.5580341094 9.9772340921 -0.4564835 6.66458259272.6 6.7394596599 9.7585077292 -0.44682545 6.80540733612.8 6.8824552701 9.5861739122 -0.43813934 6.91709973373 6.9971977495 9.447929787 -0.43047229 7.0071766838

3.2 7.0906946608 9.3353094258 -0.42375909 7.08087761483.4 7.1679019757 9.2423287315 -0.41789638 7.14194519183.6 7.2324065635 9.1646587167 -0.41277468 7.19311067683.8 7.2868572381 9.0991037699 -0.40829151 7.23640508694 7.3332450954 9.0432625636 -0.40435599 7.2733641189

4.2 7.3730905845 8.9953019061 -0.40088965 7.3051663634.4 7.4075712134 8.9538024337 -0.39782563 7.33272852164.6 7.4376105171 8.9176511583 -0.39510736 7.35677226854.8 7.4639411753 8.8859652641 -0.39268708 7.37787200725 7.4871505324 8.8580371673 -0.39052446 7.3964895197

θ(°) 75

r (m) (MPa)

1 0 18.155683402 0 1.21620017641.2 2.3785341634 14.920864618 -0.266178 3.08562199261.4 3.8913930564 13.102848782 -0.35018881 4.33334918311.6 4.9049721376 11.976221808 -0.37392195 5.19169507471.8 5.6142860036 11.228069249 -0.37618726 5.80224454572 6.1288439494 10.70502651 -0.370818 6.2499810548

2.2 6.5134183572 10.324533041 -0.36309315 6.58716805642.4 6.8081166061 10.038837336 -0.35508113 6.84699329622.6 7.0387751306 9.8187113986 -0.3475685 7.05121130232.8 7.2226139571 9.6454261422 -0.3408119 7.21450564793 7.3714534697 9.5065170302 -0.334848 7.3470516089

3.2 7.4936183971 9.3934205979 -0.32962606 7.4560679843.4 7.5951049258 9.3000918509 -0.32506568 7.54678455313.6 7.6803186106 9.2221626255 -0.3210817 7.62306172343.8 7.7525539109 9.156411434 -0.31759442 7.68779732534 7.8143135444 9.1004194543 -0.31453313 7.7431997419

4.2 7.86752588 9.0523414171 -0.31183679 7.79097507764.4 7.9136958741 9.0107494637 -0.3094534 7.83245782764.6 7.9540117538 8.9745245287 -0.30733897 7.86870366424.8 7.9894216533 8.9427793809 -0.30545632 7.90055635155 8.0206894872 8.9148031842 -0.30377411 7.9286966951

θ(°) 80

r (m) (MPa)

1 0 18.322187814 0 0.5524815643

�_� �_� �_�� �_1

�_� �_� �_�� �_1

1.2 2.2900030012 15.022713671 -0.18207648 2.61166738431.4 3.8218848144 13.176981733 -0.23954325 4.02204688551.6 4.8769603246 12.036902829 -0.25577767 5.00537789151.8 5.6279826143 11.281591243 -0.25732724 5.71044867442 6.1789909714 10.754457507 -0.25365445 6.2302032374

2.2 6.5940865262 10.371489992 -0.24837034 6.62304151712.4 6.9140212351 10.084227373 -0.24288979 6.92654144462.6 7.1655288791 9.863070212 -0.23775085 7.16555412222.8 7.3666639407 9.6890839232 -0.23312907 7.35695863353 7.5299428231 9.5496848407 -0.22904952 7.5125059467

3.2 7.6642480469 9.4362376332 -0.2254775 7.64056222263.4 7.7760163073 9.3426524368 -0.22235802 7.74720524463.6 7.869999855 9.2645322216 -0.21963282 7.83693130233.8 7.9497665668 9.1986364346 -0.21724738 7.91312162274 8.0180358212 9.1425333631 -0.21515333 7.9783567986

4.2 8.0769087326 9.0943688392 -0.21330893 8.03463295944.4 8.1280289248 9.0527087447 -0.2116786 8.08351308944.6 8.1726967162 9.0164295362 -0.21023223 8.12623471484.8 8.2119514817 8.9846407298 -0.20894443 8.16378770995 8.2466319094 8.9566290925 -0.20779373 8.1969713041

θ(°) 85

r (m) (MPa)

1 0 18.424158119 0 0.13995218031.2 2.4329131804 15.085087868 -0.09244265 2.51296816421.4 3.9340875131 13.22238209 -0.1216193 3.98352357661.6 4.9221779985 12.07406498 -0.12986173 4.95395436271.8 5.6058730537 11.314369078 -0.13064846 5.62654862672 6.0980418488 10.784729942 -0.12878374 6.1112794486

2.2 6.4638690729 10.400247275 -0.12610093 6.47187309142.4 6.7430661823 10.112025051 -0.12331838 6.74724319792.6 6.9609184294 9.8902363493 -0.12070927 6.9622089452.8 7.1341332876 9.7158207356 -0.11836273 7.13319063163 7.274103621 9.5761215863 -0.11629149 7.2713962285

3.2 7.3888115428 9.4624595579 -0.11447793 7.38468434553.4 7.4839826629 9.3687173071 -0.11289413 7.47869548083.6 7.5638095831 9.2904801265 -0.11151051 7.55756198973.8 7.6314188202 9.2244957865 -0.11029938 7.62436674274 7.6891800109 9.1683246804 -0.10923621 7.681447108

4.2 7.7389154177 9.1201071904 -0.10829978 7.73060106154.4 7.7820448225 9.078405365 -0.10747204 7.77322981354.6 7.8196876018 9.0420929186 -0.1067377 7.8104383364.8 7.8527358467 9.0102773748 -0.10608387 7.84310740495 7.8819075429 8.982244033 -0.10549964 7.8719460146

�_� �_� �_�� �_1

θ(°) 90

r (m) (MPa)

1 0 18.458496 0 01.2 2.6282207632 15.106092 -6.522E-017 2.62822076321.4 4.0874288495 13.237670384 -8.581E-017 4.08742884951.6 4.9839745383 12.086579109 -9.162E-017 4.98397453831.8 5.5756571175 11.325406815 -9.218E-017 5.57565711752 5.9874130782 10.794924 -9.086E-017 5.9874130782

2.2 6.2859079496 10.409931116 -8.897E-017 6.28590794962.4 6.5094311937 10.12138575 -8.701E-017 6.50943119372.6 6.6812884372 9.8993843812 -8.516E-017 6.68128843722.8 6.8163462692 9.7248241949 -8.351E-017 6.81634626923 6.9244620744 9.585024 -8.205E-017 6.9244620744

3.2 7.0123874275 9.4712896318 -8.077E-017 7.01238742753.4 7.0848761372 9.377494494 -7.965E-017 7.08487613723.6 7.1453559631 9.2992179259 -7.867E-017 7.14535596313.8 7.1963502396 9.2332037663 -7.782E-017 7.19635023964 7.2397506302 9.17700975 -7.707E-017 7.2397506302

4.2 7.2769983056 9.128774424 -7.641E-017 7.27699830564.4 7.3092071353 9.087058546 -7.583E-017 7.30920713534.6 7.3372492119 9.0507349069 -7.531E-017 7.33724921194.8 7.3618153419 9.0189103594 -7.485E-017 7.36181534195 7.383458554 8.9908697088 -7.443E-017 7.383458554

�_� �_� �_�� �_1

α

0 0 1.85 0 0.49176737542.287692 0 1.6380208333 0.30364583 2.4781783008

3.820070384 0 1.4899000416 0.50703873 3.56458947064.8762291094 0 1.3855895996 0.6472229 4.37224580565.6283401481 0 1.3103566529 0.74705075 5.0003692652

6.1803 0 1.2546875 0.8203125 5.49849616876.5961922732 0 1.2125025613 0.87551397 5.898819523

6.91678575 0 1.1798502604 0.91806641 6.22417250337.1688376357 0 1.1540999965 0.95152131 6.49131174757.3704241949 0 1.1334567628 0.97827793 6.7127512843

7.53408 0 1.1166666667 1 6.89795068067.6687021318 0 1.1028347015 1.01786842 7.05413483957.7807387846 0 1.0913093713 1.03273907 7.18687544797.8749512593 0 1.081607939 1.04524391 7.3005094027.9549145697 0 1.0733669171 1.05585746 7.3984429567

8.02335375 0 1.0663085938 1.06494141 7.48337473368.082374424 0 1.0602179647 1.07277523 7.5574606023

8.1336238353 0 1.0549265547 1.07957758 7.62243659688.1784052282 0 1.0503008851 1.08552142 7.67971130788.2177603594 0 1.0462341309 1.09074504 7.73043589988.2525298688 0 1.04264 1.09536 7.775557601

α

0.1061359687 0 1.840470225 0.01408745 0.65858981272.3830900981 -0.52584072 1.6285236755 0.31630804 2.5455350673.8997685286 -0.93903537 1.4816470343 0.51761709 3.62426155564.942023277 -1.33377231 1.3786370675 0.65595577 4.4264624255.682912459 -1.75684962 1.3045199484 0.75429415 5.0494434269

6.2260023308 -2.24200773 1.2497608387 0.82637858 5.54270429416.6348792509 -2.82287966 1.2083092989 0.8806489 5.93854305686.949879265 -3.54125136 1.1762490142 0.92245892 6.2598495812

7.1974240496 -4.45627447 1.150979928 0.95531559 6.52338685947.3953384069 -5.65902084 1.1307312303 0.9815848 6.74164496567.5559697881 -7.29948589 1.1142676388 1.00290544 6.92404518837.6880755301 -9.64106498 1.1007083517 1.02043986 7.07776959597.7979986102 -13.1747149 1.0894127335 1.03502997 7.20834775647.8904203104 -18.8384731 1.079906401 1.04729712 7.32007768977.9688541395 -28.1648763 1.0718323435 1.05770766 7.41633099418.0359773539 -41.6681209 1.0649179148 1.06661694 7.4997760139

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

8.09385808 34.9552023 1.0589521082 1.07429946 7.57254247588.1441138442 25.8141269 1.0537696307 1.08096992 7.6363439918.1880241209 20.2644111 1.0492395586 1.08679814 7.69256998238.2266114875 16.7902877 1.0452571345 1.09191985 7.74235524988.2607009833 14.4787723 1.0417377532 1.09644455 7.7866330476

α

0.4243937678 0 1.811762341 0.05632987 1.02883711752.6665637081 -1.02985892 1.6002971503 0.35393355 2.74556250084.1357050153 -1.83805404 1.4572365129 0.54893298 3.80296106455.136412008 -2.60554387 1.3581227406 0.68175703 4.5888299022

5.8439519364 -3.42078226 1.2873224722 0.77566895 5.19617275846.360759812 -4.34458866 1.2352580852 0.84426497 5.6746316097

6.7488879008 -5.43338659 1.1959732997 0.89578129 6.05687060737.0473646772 -6.75149467 1.1656595017 0.93539817 6.36594978087.2816068655 -8.38106273 1.1418084762 0.96648919 6.61863901667.4686897275 -10.4327105 1.1227216386 0.99132074 6.82734357087.6204046382 -13.0571148 1.1072190255 1.01145789 7.00135925047.7450945011 -16.4525292 1.0944619443 1.028008 7.14773166927.8487907141 -20.8492096 1.083841895 1.04177162 7.27185838197.9359378607 -26.424739 1.0749091789 1.05333868 7.37791687068.0098676711 -33.1012324 1.0673259039 1.0631514 7.46917212688.0731162886 -40.3325869 1.060834365 1.0715464 7.54819991888.1276411524 42.7534731 1.0552353382 1.07878349 7.6170504248.1749721057 36.833447 1.0503729054 1.08506574 7.67736929018.2163185134 32.1041471 1.0461236665 1.09055366 7.73048803268.2526464037 28.4352213 1.0423889513 1.09537547 7.77749214828.2847348281 25.5988737 1.0390891176 1.09963457 7.8192728877

α

0.9539567742 0 1.7635734985 0.12661888 1.4989256583.1300119821 -1.49186396 1.5541309017 0.41544714 3.07442473464.5185907707 -2.66041957 1.4176916017 0.59975349 4.10025538645.4506249196 -3.7598782 1.3250500727 0.72346258 4.85862888066.1036305105 -4.91169617 1.2596763198 0.81013614 5.43907542196.5777111935 -6.19367628 1.2119871246 0.87306097 5.89214398246.9322294866 -7.67026763 1.1762044828 0.92011626 6.25122551687.2040063705 -9.4052909 1.1487052515 0.95618926 6.53964189337.4167900803 -11.4676509 1.1271348353 0.98443208 6.7741241547.5864229921 -13.9321824 1.1099137766 1.0069475 6.96688877017.7237871971 -16.8740335 1.0959526109 1.02517988 7.1269852694

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

7.8365506571 -20.3526249 1.084481169 1.04014699 7.26120487967.9302388157 -24.3816307 1.0749430506 1.05258224 7.37470633688.0089127387 -28.8896835 1.0669284678 1.06302465 7.47145346468.0756101251 -33.6950675 1.0601303767 1.07187741 7.55452509518.1326391734 -38.5292379 1.0543151405 1.07944688 7.62633719488.1817787207 -43.1151858 1.0493024914 1.08596919 7.68880388458.2244172551 42.74831 1.0449515779 1.09162861 7.74345544228.2616512027 39.1522116 1.0411510805 1.09657068 7.7915256998.2943555536 36.0962983 1.0378120957 1.10091153 7.83401741988.3232353654 33.52849 1.0348629399 1.10474476 7.8717516925

α

1.6922988001 0 1.6955674966 0.22461917 2.05537316613.8801653898 -1.91984694 1.493433957 0.51501516 3.58597034655.1277801711 -3.42315884 1.3663020122 0.68061132 4.55717337595.9087042777 -4.78794865 1.2816741318 0.78426354 5.25085084576.4309920123 -6.14243802 1.2226918332 0.8535869 5.76793721686.7980382681 -7.55445232 1.1800222107 0.90230503 6.16356883837.0660984962 -9.06333771 1.1481938768 0.93788472 6.47235974357.2679801368 -10.692549 1.1238391092 0.96468051 6.71743140057.4238957431 -12.4546562 1.1047976633 0.98537522 6.91478962737.5468652762 -14.3530472 1.0896342337 1.00169699 7.07579684137.6455905678 -16.3822039 1.0773659262 1.01480082 7.20868372647.7260708411 -18.5276116 1.0673018066 1.02548298 7.31951692347.7925532181 -20.7660418 1.0589449419 1.0343072 7.41283776637.8481141326 -23.0667272 1.0519306616 1.04168182 7.49209381427.8950270721 -25.3936329 1.0459865357 1.04790858 7.5599360847.935002038 -27.7086324 1.0409057764 1.05321447 7.6184272757

7.9693455068 -29.9750281 1.0365291623 1.05777288 7.66918989087.9990697309 -32.1606958 1.0327325057 1.06171818 7.7135130818.024968943 -34.2402601 1.0294178046 1.06515579 7.7524307324

8.0476734565 -36.1960364 1.0265068937 1.06816937 7.78677922238.0676887073 -38.0178406 1.0239368188 1.07082599 7.8172406224

α

2.6336247942 0 1.6076021523 0.34956156 2.71549021664.4928548591 -2.21323962 1.4123305841 0.59633756 4.10312184735.6248911764 -3.93850477 1.2991972721 0.74659297 5.04162186996.3640464935 -5.5373379 1.2276250868 0.84470121 5.71154858116.8728194482 -7.17591278 1.1793994788 0.91223075 6.20448247187.2377450781 -8.94858931 1.145325201 0.9606674 6.5760801741

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

7.5082873851 -10.9181478 1.1203402079 0.99657654 6.86214109287.7143637027 -13.1293292 1.1014658325 1.02392909 7.08645732067.8749228982 -15.6112445 1.0868541095 1.04524015 7.26525564388.0024359025 -18.3739238 1.075308097 1.06216498 7.40985823718.1053805304 -21.4019975 1.0660242798 1.07582884 7.52832983158.1896821029 -24.6490238 1.0584467009 1.0870182 7.62652397098.2595825668 -28.0369754 1.0521806037 1.09629611 7.70876283668.3181831379 -31.4644991 1.0469393362 1.10407417 7.77828828998.3677933996 -34.8234464 1.0425106209 1.11065895 7.83756697988.4101618803 -38.0179195 1.0387345118 1.11628253 7.8885004848.4466319444 -40.9782511 1.0354886218 1.12112321 7.93257248588.4782494108 -43.6657284 1.0326780022 1.1253198 7.97095346558.5058382487 43.9308538 1.0302280702 1.12898167 8.00457625378.5300547307 41.8027908 1.0280795775 1.13219593 8.03419129078.5514267719 39.9294651 1.0261849725 1.13503265 8.0604075507

α

3.76704 0 1.5 0.5 3.51423993845.4202111583 -2.46682133 1.3223317316 0.71942575 4.85371101466.3593706629 -4.38747915 1.2261887391 0.84408059 5.71591182166.945711343 -6.13588059 1.168210919 0.92190571 6.3008156035

7.3371476823 -7.88091012 1.1304731439 0.97386113 6.71345875027.6118714418 -9.7098097 1.1044834247 1.01032527 7.01429409147.8123077739 -11.6703994 1.0857928843 1.03692923 7.2398266787.9631455681 -13.7866525 1.0718840729 1.05694996 7.41298613658.0795700238 -16.0641685 1.0612432127 1.072403 7.54868526188.1713496269 -18.4917905 1.0529142775 1.08458493 7.65692750438.2450060384 -21.0424616 1.0462686016 1.09436136 7.74460964658.3050314465 -23.6751988 1.0408785682 1.10232855 7.81660358658.3546037452 -26.3391359 1.0364448423 1.10890829 7.87642594378.3960234556 -28.9794748 1.0327526523 1.11440593 7.92666438088.4309897861 -31.5441379 1.0296445621 1.11904702 7.96925605518.4607802324 -33.9894531 1.0270029755 1.12300111 8.00567374698.4863704597 -36.2835863 1.024738583 1.12639771 8.03705291228.5085161625 -38.4073721 1.0227825469 1.12933711 8.06428007898.5278101054 -40.3530581 1.0210811008 1.131898 8.08805542528.5447225976 -42.1218908 1.0195917447 1.1341428 8.10893778648.5596306883 -43.7214044 1.0182805185 1.13612156 8.1273775

α

5.0747452674 0 1.3738219658 0.67357199 4.5065916665

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

6.5458859988 -2.67277827 1.2294560771 0.86883681 5.7928109177.234935548 -4.75648981 1.1527024307 0.96029449 6.5325767163

7.6024401758 -6.57137997 1.1070308721 1.00907346 6.99329223437.8181422704 -8.26592536 1.0776037056 1.03770364 7.29790356367.9543384606 -9.90998627 1.057495375 1.05578099 7.50917764038.0453948002 -11.5340353 1.0431225014 1.06786692 7.66152520198.1091194108 -13.1474275 1.0324783283 1.0763251 7.77494837018.1554053307 -14.7478861 1.024366585 1.08246864 7.86166489488.1900723225 -16.3269864 1.0180372401 1.08707 7.92946017378.2167117918 -17.8736111 1.0130000971 1.09060586 7.9834785388.2376316862 -19.3762196 1.0089234503 1.09338256 8.02722725918.2543675431 -20.8243096 1.0055761262 1.09560391 8.06316335158.2679721127 -22.2092715 1.002792885 1.09740965 8.09304941618.2791862769 -23.5247775 1.0004529935 1.09889811 8.11817656618.2885435507 -24.7668275 0.9984665245 1.1001401 8.13950817718.2964360014 -25.9335672 0.9967653498 1.10118767 8.15777499598.3031569984 -27.0249746 0.9952970706 1.10207975 8.17353953118.3089296312 -28.0424937 0.9940208374 1.10284595 8.18724055868.3139260237 -28.9886687 0.9929044144 1.10350912 8.19922446128.3182807281 -29.8668124 0.9919220817 1.10408713 8.2097676735

α

6.53057095 0 1.2311015109 0.86680404 5.77755476137.6490004711 -2.76697352 1.1276305207 1.01525342 6.88907566188.0745531761 -4.92602335 1.0745003875 1.07173712 7.45294448048.2505769722 -6.76053726 1.0437447814 1.09510079 7.76629158818.3256937733 -8.40986078 1.0243544477 1.10507106 7.9538294458.3566857001 -9.94222108 1.0113308383 1.10918463 8.07315262478.3674095384 -11.3897823 1.0021490916 1.110608 8.15301384738.368614945 -12.7662239 0.9954242885 1.110768 8.208760161

8.3653974313 -14.0760075 0.9903454542 1.11034093 8.24906827648.3602563396 -15.3194298 0.9864118662 1.10965856 8.27909282498.3544397845 -16.4953885 0.9833005567 1.10888652 8.30202997628.3485702659 -17.602835 0.980795451 1.10810746 8.31993660348.3429491812 -18.6414554 0.9787474351 1.10736137 8.33418007518.3377105489 -19.6118987 0.9770508307 1.10666605 8.34569568558.3329008666 -20.5157542 0.9756289951 1.10602766 8.35513949998.3285214897 -21.3554054 0.9744252122 1.10544638 8.36298212038.3245514336 -22.1338363 0.9733967591 1.10491944 8.3695679128.3209597075 -22.8544363 0.9725109422 1.10444271 8.37515340948.3177119493 -23.5208266 0.9717423871 1.10401163 8.37993281458.3147739175 -24.1367172 0.9710711496 1.10362167 8.38405529498.3121132394 -24.7057967 0.9704813727 1.10326851 8.3876369462

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

α

8.099136 0 1.075 1.075 7.46223454138.6595032787 -2.71695274 1.0080582206 1.14937767 8.26378390318.8215060387 -4.83513319 0.9849577927 1.17088032 8.5467302618.8558428343 -6.66776584 0.9769149057 1.17543785 8.63606440078.8471769079 -8.36173743 0.9745619732 1.17428762 8.6521183828.8249054715 -9.98636097 0.9744565324 1.17133153 8.64071832748.7997988793 -11.57203 0.9752254116 1.16799913 8.6199964538.7757900027 -13.1286178 0.9762924607 1.16481243 8.59727474078.7541680783 -14.6551103 0.9774111896 1.16194254 8.57545861858.7351823593 -16.1451019 0.9784784273 1.15942257 8.55559206538.7186859345 -17.5901196 0.9794552134 1.15723299 8.53792729478.7044008603 -18.9816616 0.9803315898 1.15533693 8.52238838778.6920269608 -20.3123897 0.9811103996 1.15369454 8.50877627928.681284221 -21.5767329 0.9817996897 1.15226865 8.4968593925

8.6719267053 -22.7710828 0.9824091384 1.15102663 8.48641246528.6637444779 -23.89372 0.9829484128 1.1499406 8.47723163468.6565607965 -24.9445838 0.9834264628 1.14898711 8.46913871128.6502277861 -25.9249673 0.9838512688 1.14814653 8.46198069818.6446219634 -26.8371981 0.9842298062 1.14740246 8.45562740988.6396401551 -27.6843392 0.9845681057 1.14674123 8.44996851958.6351959803 -28.4699306 0.9848713523 1.14615135 8.4449106337

α

8.2953778894 0 0.9098523822 1.10104723 8.93639785038.6711396424 -2.57510228 0.8787404701 1.15092216 9.48710303998.8194785835 -4.58119282 0.8903411869 1.17061122 9.45376183378.8842596494 -6.36868413 0.9100934397 1.17920962 9.28697665898.9143473037 -8.09614568 0.9291950453 1.18320317 9.11349454398.9287195149 -9.83999544 0.9456327562 1.18511079 8.96325131448.9355153996 -11.6358036 0.9592841935 1.18601281 8.83950519068.9384987654 -13.4957256 0.9705153468 1.18640879 8.73886354478.9395139543 -15.4167987 0.9797628682 1.18654354 8.65693841258.9395057485 -17.3856501 0.9874162778 1.18654245 8.58983448968.9389743798 -19.3818885 0.9937942982 1.18647192 8.53441886998.938190781 -21.381079 0.9991495659 1.18636791 8.4882543504

8.9373034784 -23.3575215 1.0036801933 1.18625014 8.44946307628.9363938666 -25.2867213 1.00754134 1.18612941 8.41659738658.9355057717 -27.1473277 1.0108549335 1.18601153 8.3885354388.9346617124 -28.9223758 1.0137173294 1.1858995 8.3644014592

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

8.9338720523 -30.5997985 1.0162051901 1.18579469 8.34350611178.9331402438 -32.1723138 1.01837995 1.18569756 8.32530216898.9324658744 -33.6368737 1.0202912007 1.18560805 8.30935154658.9318464508 -34.9938801 1.0219792626 1.18552583 8.29530066458.9312784467 -36.2463372 1.0234771474 1.18545044 8.2828619122

α

11.387922715 0 0.7410847007 1.51152134 13.141633789310.756194956 -2.40581451 0.7633144019 1.42767199 12.347341354410.319456293 -4.28355055 0.808882363 1.36970357 11.378439988810.013520406 -5.95730858 0.8514069227 1.32909664 10.625859479.7935488426 -7.57475644 0.8864514812 1.29989977 10.07731217739.6311027939 -9.20788061 0.9144579435 1.27833827 9.6760597655

9.50817238 -10.8911414 0.9367574446 1.26202169 9.37692876069.4131141928 -12.637629 0.9546165528 1.2494046 9.14908525339.3382042136 -14.4466932 0.969052309 1.23946178 8.97196627579.2781847699 -16.3081368 0.9808411872 1.23149539 8.83172703849.2293896895 -18.2050892 0.9905675924 1.22501881 8.71886684999.1892056537 -20.1164479 0.9986713086 1.21968517 8.62672657639.1557323626 -22.0191777 1.0054852677 1.21524225 8.55054110659.1275629318 -23.8904431 1.0112636973 1.21150332 8.48683404569.1036387325 -25.7094136 1.0162026148 1.20832786 8.43302380689.0831514001 -27.4585754 1.0204546649 1.20560857 8.38716210439.0654753893 -29.124469 1.0241398841 1.20326243 8.3477568928

9.05012072 -30.6978735 1.0273535594 1.2012244 8.31365021529.036699323 -32.1735521 1.0301720119 1.19944297 8.2839324417

9.0249007085 -33.5497098 1.0326568913 1.19787694 8.25788107179.0144741293 -34.8273145 1.0348583952 1.19649302 8.2349164027

α

12.996288 0 0.575 1.725 18.281940971211.834567393 -2.21200332 0.6738720824 1.57080458 14.776433096811.072218964 -3.94642151 0.7494618341 1.46961792 12.786331406610.552517808 -5.44531881 0.8049531784 1.40063788 11.581058831910.184883297 -6.82493137 0.8459228184 1.35184167 10.79887963579.9162627774 -8.14171213 0.8766878414 1.31618761 10.26213860089.7144789174 -9.42183588 0.9002340715 1.2894048 9.87730452789.5592774674 -10.6754474 0.918589118 1.26880488 9.59159472869.4374610007 -11.9041092 0.9331404239 1.25263615 9.37340396559.3401598633 -13.1049772 0.944852579 1.23972135 9.20285256579.2612472965 -14.2732624 0.9544084864 1.22924727 9.0669131722

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

9.1963873791 -15.4037127 0.9623004933 1.2206384 8.95674982259.1424449535 -16.4914863 0.9688897627 1.21347861 8.8661915939.0971093679 -17.5326267 0.9744455358 1.20746121 8.79081920959.0586483188 -18.5242699 0.9791715378 1.20235627 8.72739814629.0257430332 -19.4646764 0.9832240432 1.19798874 8.67351543828.997375577 -20.3531536 0.9867244422 1.19422353 8.6273404553

8.9727503256 -21.1899176 0.9897681205 1.19095501 8.58746342238.9512382883 -21.9759297 0.9924308291 1.18809971 8.55278402418.9323370083 -22.7127298 0.9947733159 1.18559094 8.52243305268.9156412627 -23.4022815 0.9968447383 1.18337491 8.4957163258

α

14.498517316 0 0.4184450744 1.92439121 26.775769363112.789036718 -1.9511267 0.5944252653 1.69749149 17.520261871211.722903423 -3.48801564 0.6986855765 1.5559834 14.173920126211.016701878 -4.78223016 0.7656096455 1.46224912 12.480558269310.526055437 -5.92429478 0.8111537617 1.39712552 11.476018557810.171866627 -6.96202042 0.8435621216 1.35011397 10.82119058479.9080717866 -7.92070027 0.8674498773 1.31510042 10.36653896089.7064461007 -8.81376343 0.8855667892 1.2883386 10.03616851939.5489431883 -9.64848703 0.8996351069 1.26743321 9.78765046719.4236015521 -10.4290883 0.9107786419 1.25079659 9.59552355239.3222450703 -11.1583873 0.9197562672 1.23734352 9.44365499039.2391345595 -11.8386735 0.9270955488 1.22631225 9.32137187449.1701470551 -12.4721275 0.9331725401 1.21715552 9.221360539.1122597849 -13.0609973 0.9382611911 1.20947213 9.13846024089.0632163098 -13.6076441 0.9425649187 1.20296258 9.06893799179.0213049865 -14.1145252 0.9462373419 1.19739968 9.01003531638.985208609 -14.5841506 0.9493962346 1.1926086 8.9596757434

8.9539002734 -15.0190335 0.9521331187 1.18845304 8.91627052098.9265699282 -15.4216458 0.954519989 1.18482548 8.87858639148.9025717064 -15.7943812 0.9566141101 1.18164019 8.84565363118.8813855854 -16.1395283 0.9584614917 1.17882815 8.8167008498

α

15.832327089 0 0.2783852768 2.10142806 42.380236681113.57604283 -1.60602978 0.5036027731 1.80195098 21.410444409

12.245049052 -2.87342184 0.6387927974 1.6252879 15.898008735311.39304924 -3.95324432 0.7262911318 1.51220179 13.412785601

10.814318302 -4.92258556 0.7861681783 1.43538671 12.025518857510.403048967 -5.82100893 0.8289422224 1.38079885 11.1544479974

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

10.100202109 -6.66855265 0.8605603005 1.34060192 10.56469421279.8706856088 -7.47494066 0.8845914289 1.31013815 10.14376525729.6925600529 -8.24448732 0.9032831263 1.2864955 9.83130727759.5515294486 -8.97878789 0.9181080814 1.26777648 9.59219388949.4379508527 -9.67821276 0.9300640136 1.25270117 9.40468625049.3451264718 -10.3427281 0.9398463535 1.24038057 9.25466746529.2682855154 -10.9723268 0.9479518656 1.23018146 9.13260749479.2039546034 -11.5672307 0.9547430711 1.2216428 9.03186352429.149555921 -12.127963 0.9604895471 1.21442245 8.9476790144

9.1031435401 -12.6553458 0.9653951271 1.20826213 8.87656901399.0632261276 -13.1504616 0.9696162455 1.20296388 8.81592907519.0286451255 -13.6145991 0.9732745765 1.19837394 8.76377876638.9984894069 -14.0491959 0.976465908 1.19437136 8.71858897038.9720344322 -14.4557846 0.9792664807 1.19085999 8.6791628834

8.94869818 -14.8359471 0.981737587 1.18776256 8.6445523283

α

16.939483226 0 0.1614265015 2.24838112 76.059523136214.213776789 -1.21522292 0.4095552466 1.88659754 27.04154528312.660892655 -2.17401141 0.5751663353 1.68048291 18.001475202511.689498871 -3.01853377 0.6890947634 1.55154961 14.347562458311.040110707 -3.81672453 0.7701331212 1.46535618 12.422388410610.583889405 -4.6027826 0.8295612808 1.40480183 11.256641364710.250783342 -5.3940327 0.8743161815 1.3605886 10.48676815549.9999606459 -6.19866549 0.9088028394 1.32729685 9.94708238939.806275227 -7.01960494 0.9359087377 1.30158894 9.5518523656

9.6535344513 -7.85659668 0.95758283 1.28131563 9.25254295779.530918891 -8.70742347 0.9751756829 1.26504084 9.0197641738

9.4309710111 -9.56866642 0.9896454489 1.25177474 8.83476226479.3484122237 -10.4362156 1.001686278 1.24081669 8.68505737099.2794195127 -11.3056323 1.0118105626 1.23165928 8.56205357249.2211680196 -12.1724156 1.0204029324 1.22392754 8.45965710669.1715332568 -13.032201 1.0277565067 1.21733951 8.37344101989.1288922195 -13.8809071 1.0340977369 1.21167976 8.30012080919.0919875102 -14.7148388 1.0396037509 1.20678139 8.23721451999.0598326183 -15.5307533 1.0444146683 1.20251346 8.18281619699.0316446828 -16.3258959 1.0486424821 1.19877207 8.13544116839.0067959763 -17.0980091 1.0523775557 1.1954739 8.0939180941

α

17.76970625 0 0.0733309925 2.35857679 172.246149483

Factor de Seguridad

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

�_3 �_1 _⁄� �

�_3 _⁄� �

14.701049288 -0.81910058 0.3466471532 1.95127332 32.585119505912.976819662 -1.46581464 0.5338471168 1.72241596 19.674113127311.908485262 -2.04332942 0.664364845 1.58061572 15.04185291311.199125183 -2.60068242 0.7579490362 1.48646221 12.726243970410.703245241 -3.16343915 0.826936167 1.42064396 11.365175082710.342535001 -3.74579606 0.8790776733 1.37276681 10.4832440210.071707164 -4.35591476 0.9193612816 1.33681978 9.87305210359.863044969 -4.99847962 0.9510854839 1.309124 9.4304108385

9.6987892303 -5.67600616 0.9764906443 1.2873223 9.09758214129.5671217171 -6.389545 0.9971364714 1.26984605 8.84016166069.4599234575 -7.13907679 1.0141334075 1.2556176 8.63646931159.3714634995 -7.92374297 1.0282881579 1.24387629 8.47222121369.2976007743 -8.74198838 1.0401975161 1.23407248 8.33765833779.2352813787 -9.59165734 1.0503102731 1.22580081 8.2259085129.1822123857 -10.4700676 1.0589689516 1.21875695 8.13200713139.1366446123 -11.3740762 1.0664384981 1.21270873 8.0522881595

9.09722458 -12.3001464 1.0729263678 1.2074765 7.98399248649.0628915377 -13.2444194 1.078596818 1.20291947 7.92500866519.0328045015 -14.2027924 1.0835812349 1.19892601 7.87369689769.0062896979 -15.1710037 1.0879857002 1.1954067 7.8287668531

α

18.284205938 0 0.0185758819 2.42686644 691.5914191515.005032884 -0.41859971 0.3335467853 1.99162112 34.273556864113.172946026 -0.75004944 0.52873391 1.74844786 20.038250366812.042288616 -1.03990188 0.6575393894 1.59837546 15.296386393211.293693505 -1.31039492 0.7468129654 1.49901428 12.978627784610.771492342 -1.57282699 0.8111513879 1.42970241 11.628640594510.392243257 -1.83295122 0.8590130569 1.3793646 10.7575740610.107848035 -2.09353712 0.8955629882 1.34161676 10.15616567269.8889458337 -2.35568041 0.9240954363 1.31256183 9.72036992599.7167633916 -2.61951691 0.946789871 1.28970802 9.39287301429.5788289789 -2.88463324 0.9651339286 1.27139996 9.13964752039.4665867552 -3.15031373 0.9801706838 1.25650202 8.93929951449.3740044892 -3.415694 0.9926488013 1.24421356 8.77775392949.2967277198 -3.67985848 1.0031167694 1.2339566 8.64540324339.231547864 -3.94190276 1.0119837781 1.22530526 8.5354859381

9.1760575833 -4.20097301 1.0195600668 1.21794002 8.44311914349.1284215466 -4.4562899 1.0260842812 1.21161728 8.36469798329.0872203741 -4.70716191 1.0317424043 1.20614864 8.29750971859.0513421844 -4.95299121 1.0366810992 1.20138652 8.23947851419.0199058165 -5.19327447 1.0410172715 1.19721397 8.18899225518.9922055613 -5.42760004 1.0448450261 1.19353731 8.1447823771

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

α

18.458496 0 0 2.45 DIV/015.106092 -2.995E-016 0.3488442866 2.00503472 32.8998775656

13.237670384 -5.373E-016 0.5425252784 1.75703873 19.584591836612.086579109 -7.391E-016 0.6615239735 1.60425415 15.236539446411.325406815 -9.185E-016 0.7400581249 1.50322359 13.1182371842

10.794924 -1.083E-015 0.7947105789 1.4328125 11.884013169410.409931116 -1.236E-015 0.834329865 1.38171231 11.08661314410.12138575 -1.380E-015 0.8639981516 1.34341363 10.5352554004

9.8993843812 -1.516E-015 0.8868087991 1.31394734 10.13516720039.7248241949 -1.645E-015 0.9047350532 1.29077793 9.8341260274

9.585024 -1.767E-015 0.9190852864 1.27222222 9.60110017539.4712896318 -1.882E-015 0.9307556367 1.25712624 9.41655770469.377494494 -1.991E-015 0.9403770782 1.24467679 9.2676335373

9.2992179259 -2.093E-015 0.948404578 1.23428712 9.14553596419.2332037663 -2.189E-015 0.9551730589 1.22552505 9.0440708415

9.17700975 -2.279E-015 0.9609336017 1.21806641 8.95876047429.128774424 -2.364E-015 0.9658774934 1.21166412 8.88629601479.087058546 -2.444E-015 0.9701525781 1.20612716 8.8241853574

9.0507349069 -2.518E-015 0.9738746087 1.20130592 8.77052001139.0189103594 -2.588E-015 0.9771352762 1.19708184 8.72381677128.9908697088 -2.653E-015 0.9800079843 1.19336 8.6829077587

Factor de Seguridad

�_3 �_1 _⁄� �

�_3 _⁄� �

Resistencia (Mpa)

6.854277283530.583148846840.012609863445.642498717549.365304767951.976822409453.886254887155.327206216856.44248599557.323901594558.032845361558.611712060359.09057695259.491272484259.82996689960.118845232660.367234128760.582371887160.769946420360.934477923461.0795955474

Resistencia

9.13217093331.232258342140.457078278745.97661152449.627735945252.188984780354.061520321955.47450011756.568037465157.432205243358.127231483458.694703081759.164119419559.556893002859.888879802160.1720286479

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

60.415484797260.62634537160.810187057460.971441460561.1136664597

Resistencia

14.043587988133.102606681541.752467914646.953850000350.396590940852.81114766954.575787041755.906865526256.936685970757.750277942658.404475709558.938507373259.380188811559.749703764860.06199384260.328315857460.557283420560.755579703260.928455177761.080081548261.2138075602

Resistencia

19.916081057135.998274871443.794835747248.503853670951.619557082253.802392008955.395976749356.596920475357.525347617358.258372265958.847479219

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

59.328167400559.725585378960.057966918660.338800786760.578243164260.784061423160.962279416761.117627757661.253863786861.3740026965

Resistencia

26.256449119140.348086500246.910761925250.703452041153.133419091854.796479835455.989695025856.877121464557.556177902458.087986356558.512605227758.857239780859.140923678159.377314064559.576425871859.745743800759.890955771660.016448822460.125651795860.221276798260.3054923184

Resistencia

32.889483158843.659725954549.348686444652.826259123755.131108012456.7448096538

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

57.921499082958.807190712859.491152131160.03064956860.463872934560.817121453861.109003761361.352996774661.559060191461.734686231761.885600267362.016239328962.1300856547

62.2299034862.3179099247

Resistencia

39.714847252348.355353485652.804759769655.455963928357.17903238358.36781030859.225043433959.864758262260.355447065860.740418154261.048212547461.298293107661.504319271761.676116019461.820902187861.944081364862.049765322362.141128894262.220655771762.290312020862.3516706907

Resistencia

46.6454076257

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

53.65776737456.732504335558.327268225259.249872993359.827531259560.211684268860.479568748160.673655126560.818753444660.930097982861.017442745161.087259145361.143974228461.190698141661.229667368561.26252354161.290493843661.314510713861.335293072161.3534025755

Resistencia

53.588075707358.527234572760.334357163361.071450748161.38422244661.51296211761.557467506361.562468788261.54911859761.527783102561.503638585961.479267911761.455922809161.43416084161.414176331561.395976052361.379473810361.364541654161.351037447661.338819404361.3277533799

(〖� _1〗 ^∗)

Resistencia

60.437652413562.761713916863.423155478963.562773036963.527555150363.436986889863.334788375263.236957772363.148769084163.071266445863.003875099462.945479621262.894868221962.850907012562.812598046162.779088132262.749658095662.723705611162.700727273562.680302167762.6620776598

Resistencia R E N S1/SV

61.2581193061 1 #REF! #REF! 0.3531819862.809375175 1.2 0.8832105963.4149053555 1.4 1.0307598863.6781687139 1.6 1.0572617163.8002015518 1.8 1.043927363.8584405106 2 1.0186674263.885966742 2.2 0.9915380963.8980482156 2.4 0.9660980163.902158999 2.6 0.9434264163.9021257718 2.8 0.9236477463.8999741324 3 0.9065373663.8968010668 3.2 0.8917669363.8932079452 3.4 0.8790024563.8895243465 3.6 0.8679405563.8859277502 3.8 0.8583187363.8825093675 4 0.84991506

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

63.8793111903 4.2 0.8425439263.8763472231 4.4 0.8360507563.8736158165 4.6 0.8303069663.8711068908 4.8 0.8252054263.8688061793 5 0.82065665

Resistencia

73.374885363971.007976817969.342311860168.16029673167.302300580266.664174615766.178664259765.80166192565.503586668865.264130987665.069038327964.908090596464.773824214764.660692935264.564510367764.482071344464.410889974964.349015314664.294899593664.247302639464.2052216157

Resistencia R E N S1/SV

79.1991233534 1 #REF! #REF! 0.07575.020042135 1.2 0.5332433872.1980895309 1.4 0.71903670.2342767935 1.6 0.8031819968.823961668 1.8 0.8442974467.7817983041 2 0.8654355766.9921810064 2.2 0.8766350366.3807788987 2.4 0.8826246365.8983537323 2.6 0.8857742865.5113795095 2.8 0.8873319865.1964541844 3 0.88798154

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

64.9368742061 3.2 0.888109764.7204765609 3.4 0.8879407164.5382442376 3.6 0.8876069864.3833837033 3.8 0.88718769

64.25070143 4 0.8867304264.1361742216 4.2 0.8862636964.0366477676 4.4 0.8858043463.9496216756 4.6 0.8853620463.8730938599 4.8 0.8849419563.8054463349 5 0.88454648

Resistencia

84.413254771978.463573028374.610849765971.989910876470.133361604668.77369270967.749859919966.96062422166.339939903965.843322999565.43997060865.108030422864.831665720664.599180294864.401788983864.232792546764.087012211663.960394792963.849732165363.752458843263.6665038229

Resistencia R E N S1/SV

88.8873313876 1 #REF! #REF! -0.0178128681.2351566413 1.2 0.2664155776.5126016239 1.4 0.4412474773.3938975509 1.6 0.5561095271.2277969531 1.8 0.6354905269.6630639125 2 0.69258667

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

68.4965134449 2.2 0.7350006667.6039613577 2.4 0.7673563966.9060506702 2.6 0.7925943966.3501617974 2.8 0.8126558765.9002982122 3 0.8288635965.5311676872 3.2 0.8421438165.2245821851 3.4 0.8531606364.9671939468 3.6 0.8624001564.7490299357 3.8 0.8702247764.5625185651 4 0.876909164.4018285379 4.2 0.8826642464.2624105166 4.4 0.8876546664.1406735571 4.6 0.8920164.0337528829 4.8 0.8958335663.9393406991 5 0.89920849

Resistencia

92.503605456583.439986838178.006677863174.488169348272.077735400170.353795269969.078104207968.107606436867.352129357866.752523426166.268672884965.872588068165.544256809165.269062861165.036129276764.837226343364.666034364264.517635343964.388155792164.274511394164.1742216432

Resistencia R E N S1/SV

95.1628221058 1 #REF! #REF! -0.0134931

(〖� _1〗 ^∗)

(〖� _1〗 ^∗)

85.1014938282 1.2 0.35190479.1302054287 1.4 0.445299675.2901580183 1.6 0.4548163472.6725630106 1.8 0.4380982270.807350594 2 0.4145406969.4309603783 2.2 0.3908840668.3861045796 2.4 0.3693455467.5741192579 2.6 0.350463766.9305354778 2.8 0.3341613366.4117670447 3 0.3201580565.9874811587 3.2 0.3081316465.6360366191 3.4 0.2977785165.3416556146 3.6 0.288833165.0926145128 3.8 0.2810706864.8800543824 4 0.2743040264.6971798449 4.2 0.2683781364.5387077694 4.4 0.2631649764.4004805293 4.6 0.258558664.2791899641 4.8 0.254471264.1721772408 5 0.25082967

Resistencia

96.789727015286.128357275179.82284276975.777600105573.024880338171.065872280669.621654087168.526119750867.67524644767.001153788966.457998508466.013905183365.646148643265.338170937465.07767511964.855373127264.664143108764.498449921764.353938855664.227145795164.1152871735

(〖� _1〗 ^∗)

Resistencia R E N S1/SV

97.3373509035 1 0 #REF! 086.468141323 1.2 0 0.0602527580.0506256789 1.4 0 0.1909962175.9385246533 1.6 0 0.3138641573.1427925257 1.8 0 0.4153907971.1544958724 2 0 0.4966400569.6894296962 2.2 0 0.5613869668.5785201373 2.4 0 0.6132697367.7159754241 2.6 0 0.6552235167.032808258 2.8 0 0.6894945666.4824540358 3 0 0.7177759766.0325508579 3.2 0 0.7413430665.660035697 3.4 0 0.7611619565.348109937 3.6 0 0.7779707765.0843013674 3.8 0 0.7923388264.8591917892 4 0 0.8047095964.6655610422 4.2 0 0.8154319264.497798577 4.4 0 0.8247827764.3514910408 4.6 0 0.8329840264.2231281467 4.8 0 0.8402149264.1098895646 5 0 0.84662142

(〖� _1〗 ^∗)

Clase Frecuencia0 1

0.66371657 21.32743314 11.99114971 02.65486629 43.31858286 23.98229943 1

4.646016 65.30973257 75.97344914 106.63716571 207.30088229 587.96459886 172 ESTIMADORES ESTADISTICOS8.62831543 60

9.292032 22 Media9.95574857 9 Error típico10.6194651 7 Mediana11.2831817 6 Moda11.9468983 2 Desviación estándar12.6106149 4 Varianza de la muestra13.2743314 1 Curtosis

y mayor... 4 Coeficiente de asimetríaRangoMínimoMáximoSumaCuenta

ESTIMADORES ESTADISTICOS

7.60700918250.08265145227.6320237717

Err:5121.65096146512.72567375935.7898009357

-0.381999098313.938048

013.938048

3035.196663823399

020406080

100120140160180200

Histograma

Frecuencia

Clase

Frecuencia

020406080

100120140160180200

Histograma

Frecuencia

Clase

Frecuencia

Clase Frecuencia0 1

0.878976 21.757952 22.636928 33.515904 2

4.39488 55.273856 76.152832 87.031808 187.910784 43

8.78976 1169.668736 124

10.547712 29 ESTIMADORES ESTADISTICOS11.426688 1512.305664 7 Media 8.6370665211

13.18464 5 Error típico 0.109345843714.063616 2 Mediana 8.671926705314.942592 3 Moda Err:51215.821568 2 Desviación estándar 2.184181517116.700544 1 Varianza de la mues 4.7706488996

17.57952 1 Curtosis 5.530493802y mayor... 3 Coeficiente de asime 0.1960178183

Rango 18.458496Mínimo 0Máximo 18.458496Suma 3446.1895419009Cuenta 399

0

20

40

60

80

100

120

140

Histograma

Frecuencia

Clase

Frecuencia

0

20

40

60

80

100

120

140

Histograma

Frecuencia

Clase

Frecuencia

0

20

40

60

80

100

120

140

Histograma

Frecuencia

Clase

Frecuencia

SIGMA 1 SIGMA 3

13.938048 012.34098 2.287692

11.2250261 3.8200703810.4391429 4.876229119.87233185 5.62834015

9.452916 6.18039.1350913 6.59619227

8.88908625 6.916785758.6950817 7.16883764

8.53955393 7.370424198.413056 7.53408

8.30884487 7.668702138.22201211 7.780738788.14892074 7.874951268.08683222 7.954914578.03365425 8.023353757.98776696 8.082374427.94790106 8.133623847.91305089 8.178405237.88241164 8.217760367.85533317 8.25252987

13.8662499 0.1061359712.2694277 2.383090111.1628473 3.89976853

10.386762 4.942023289.82835765 5.682912469.41579814 6.226002339.10349892 6.634879258.86195417 6.949879268.67157486 7.197424058.51901955 7.395338418.39498153 7.555969798.29282478 7.688075538.20772269 7.797998618.13610122 7.890420318.07527062 7.968854148.02317676 8.03597735

7.9782299 8.093858087.9391847 8.14411384

7.90505477 8.188024127.87505087 8.226611497.84853557 8.26070098

13.6499624 0.4243937712.0567668 2.6665637110.9789365 4.1357050210.2322054 5.136412019.69879049 5.843951949.30653323 6.360759819.01055852 6.74888798.78217194 7.04736468

8.6024764 7.281606878.45867464 7.468689738.34187672 7.620404648.24576385 7.74509458.16575154 7.848790718.09845175 7.935937868.04131875 8.009867677.99241097 8.073116297.95022746 8.12764115

7.9135935 8.174972117.88157939 8.216318517.85344175 8.25264647.82858054 8.28473483

13.2869038 0.9539567711.7089465 3.1300119810.6810019 4.518590779.98303325 5.450624929.49050217 6.103630519.13120796 6.577711198.86161867 6.932229498.65443726 7.204006378.49192402 7.416790088.36217919 7.586422998.25699465 7.72378728.17056789 7.836550668.09870694 7.930238828.03832443 8.008912747.98710707 8.07561013

7.94329461 8.132639177.90552891 8.181778727.87274878 8.224417267.84411553 8.26165127.81895935 8.294355557.79674018 8.32323537

12.7745412 1.692298811.2516509 3.8801653910.2938287 5.127780179.65623544 5.908704289.21185809 6.430992018.89038174 6.798038278.65058452 7.06609858.46709376 7.267980148.32363398 7.423895748.20939149 7.546865288.11696108 7.645590578.04113719 7.726070847.97817591 7.792553227.92532976 7.848114137.88054624 7.895027077.84226739 7.935002047.80929363 7.969345517.78068932 7.999069737.75571609 8.024968947.73378506 8.047673467.71442191 8.06768871

12.1118032 2.6336247910.6406116 4.492854869.78825618 5.624891189.24902561 6.364046498.88569003 6.872819458.62897169 7.237745088.44073275 7.50828739

8.2985317 7.71436378.18844581 7.87492298.10145723 8.00243598.03151221 8.105380537.97442212 8.1896821

7.92721284 8.259582577.88772471 8.318183147.85435842 8.36779347.82590891 8.410161887.80145412 8.446631947.78027868 8.47824941

7.7618207 8.505838257.74563378 8.530054737.73135968 8.55142677

11.30112 3.767049.96255305 5.420211169.23820406 6.359370668.80139452 6.94571134

8.5170751 7.337147688.32126648 7.611871448.18045045 7.812307778.07566036 7.963145577.99549126 8.07957002

7.9327404 8.171349637.88267135 8.24500604

7.8420624 8.305031457.80865836 8.35460375

7.7808411 8.396023467.7574245 8.43098979

7.73752258 8.460780237.72046246 8.486370467.70572553 8.50851616

7.6929067 8.527810117.68168577 8.54472267.67180689 8.55963069

10.3504846 5.074745279.26282044 6.5458868.68455233 7.234935558.34045915 7.602440188.11875253 7.818142277.96725475 7.954338467.85896838 8.04539487.77877432 8.10911941

7.7176598 8.15540533

7.66997401 8.190072327.63202377 8.216711797.60130999 8.237631697.57609098 8.254367547.55512182 8.267972117.53749289 8.279186287.52252667 8.288543557.50970989 8.2964367.49864775 8.3031577.48903251 8.308929637.48062129 8.313926027.47322032 8.31828073

9.27521727 6.530570958.49565855 7.649000478.09537188 8.074553187.86365668 8.250576977.71756836 8.325693777.61944744 8.35668577.55027143 8.367409547.49960622 8.368614947.46134188 8.365397437.43170591 8.360256347.40826506 8.354439787.38939139 8.348570277.37396148 8.342949187.36117912 8.33771055

7.3504669 8.332900877.3413975 8.32852149

7.33364906 8.324551437.32697524 8.320959717.32118488 8.317711957.31612773 8.31477392

7.3116843 8.31211324

8.099136 8.0991367.59479128 8.659503287.42075081 8.821506047.36015505 8.855842837.34242787 8.847176917.34163347 8.82490547

7.34742627 8.799798887.3554655 8.775797.3638941 8.75416808

7.37193475 8.735182367.37929393 8.718685937.38589662 8.704400867.39176424 8.692026967.39695741 8.681284227.40154904 8.671926717.40561198 8.663744487.40921364 8.65656087.41241417 8.65022779

7.4152661 8.644621967.41781487 8.639640167.42009956 8.63519598

6.85490064 8.295377896.620501 8.67113964

6.70790173 8.819478586.85671678 8.884259657.00062981 8.91434737.12447284 8.928719517.22732386 8.93551547.31194026 8.938498777.38161183 8.939513957.43927323 8.939505757.48732575 8.938974387.52767276 8.938190787.56180687 8.937303487.59089706 8.936393877.61586194 8.935505777.63742746 8.93466171

7.6561712 8.933872057.67255601 8.933140247.68695553 8.932465877.69967352 8.931846457.71095871 8.93127845

5.58339142 11.38792275.75087177 10.7561956.09418443 10.3194563

6.41456787 10.01352046.67859638 9.79354884

6.8895993 9.631102797.05760553 9.508172387.19215748 9.413114197.30091762 9.338204217.38973597 9.278184777.46301549 9.229389697.52406953 9.189205657.57540645 9.15573236

7.6189416 9.127562937.6561518 9.10363873

7.68818708 9.08315147.71595182 9.06547539

7.7401639 9.050120727.76139835 9.036699327.78011963 9.024900717.79670594 9.01447413

4.332096 12.9962885.07700618 11.83456745.64650542 11.0722196.06458164 10.55251786.37325019 10.18488336.60503633 9.916262786.78243551 9.71447892

6.9207239 9.559277477.0303546 9.437461

7.11859492 9.340159867.19058989 9.2612473

7.2500489 9.196387387.29969298 9.142444957.34155062 9.09710937

7.3771567 9.058648327.4076886 9.02574303

7.43406089 8.997375587.4569922 8.97275033

7.47705326 8.951238297.49470174 8.932337017.51030801 8.91564126

3.15259867 14.49851734.4784475 12.7890367

5.26395303 11.72290345.76816432 11.01670196.11129733 10.52605546.35546451 10.17186666.53543677 9.908071796.67193104 9.70644616.77792287 9.548943196.86187915 9.42360155

6.9295173 9.322245076.98481203 9.239134567.03059657 9.170147067.06893487 9.11225978

7.1013595 9.063216317.12902783 9.021304997.15282718 8.985208617.17344709 8.953900277.19142996 8.926569937.20720723 8.902571717.22112556 8.88138559

2.09737695 15.83232713.79418358 13.57604284.81271604 12.24504915.47193549 11.39304925.92305395 10.81431836.24531702 10.4030496.48353015 10.10020216.66458259 9.870685616.80540734 9.692560056.91709973 9.551529457.00717668 9.437950857.08087761 9.345126477.14194519 9.268285527.19311068 9.20395467.23640509 9.149555927.27336412 9.103143547.30516636 9.063226137.33272852 9.028645137.35677227 8.998489417.37787201 8.972034437.39648952 8.94869818

1.21620018 16.93948323.08562199 14.21377684.33334918 12.66089275.19169507 11.68949895.80224455 11.04011076.24998105 10.58388946.58716806 10.2507833

6.8469933 9.999960657.0512113 9.80627523

7.21450565 9.653534457.34705161 9.530918897.45606798 9.430971017.54678455 9.348412227.62306172 9.279419517.68779733 9.221168027.74319974 9.171533267.79097508 9.128892227.83245783 9.091987517.86870366 9.059832627.90055635 9.03164468

7.9286967 9.00679598

0.55248156 17.76970622.61166738 14.70104934.02204689 12.97681975.00537789 11.90848535.71044867 11.19912526.23020324 10.70324526.62304152 10.3425356.92654144 10.07170727.16555412 9.863044977.35695863 9.698789237.51250595 9.567121727.64056222 9.459923467.74720524 9.3714635

7.8369313 9.297600777.91312162 9.23528138

7.9783568 9.182212398.03463296 9.136644618.08351309 9.09722458

8.12623471 9.062891548.16378771 9.0328045

8.1969713 9.0062897

0.13995218 18.28420592.51296816 15.00503293.98352358 13.1729464.95395436 12.04228865.62654863 11.29369356.11127945 10.77149236.47187309 10.3922433

6.7472432 10.1078486.96220895 9.888945837.13319063 9.716763397.27139623 9.578828987.38468435 9.466586767.47869548 9.374004497.55756199 9.296727727.62436674 9.231547867.68144711 9.176057587.73060106 9.128421557.77322981 9.087220377.81043834 9.05134218

7.8431074 9.019905827.87194601 8.99220556

0 18.4584962.62822076 15.1060924.08742885 13.23767044.98397454 12.08657915.57565712 11.32540685.98741308 10.7949246.28590795 10.40993116.50943119 10.12138586.68128844 9.899384386.81634627 9.724824196.92446207 9.5850247.01238743 9.471289637.08487614 9.377494497.14535596 9.299217937.19635024 9.23320377

7.23975063 9.177009757.27699831 9.128774427.30920714 9.087058557.33724921 9.050734917.36181534 9.018910367.38345855 8.99086971

Clase Frecuencia-43.7214044 1-39.5474873 7-35.3735703 7-31.1996532 14-27.0257361 17 ESTIMADORES ESTADISTICOS-22.8518191 24

-18.677902 26 Media -10.2916448127-14.503985 37 Error típico 0.7091230105

-10.3300679 54 Mediana -9.2078806116-6.15615085 49 Moda 0

-1.9822338 68 Desviación estándar 14.16472104052.19168326 78 Varianza de la muestra 200.63932215636.36560032 0 Curtosis 2.847196216910.5395174 0 Coeficiente de asimetrí 0.733340938414.7134344 1 Rango 87.652258206918.8873515 1 Mínimo -43.721404371323.0612685 1 Máximo 43.930853835627.2351856 2 Suma -4106.366280262231.4091027 1 Cuenta 39935.5830197 339.7569368 3

y mayor... 5

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20

30

40

50

60

70

80

90

Histograma

Frecuencia

Clase

Frecuencia

0

10

20

30

40

50

60

70

80

90

Histograma

Frecuencia

Clase

Frecuencia

000000000000000000000

0-0.52584072-0.93903537-1.33377231-1.75684962-2.24200773-2.82287966-3.54125136-4.45627447-5.65902084-7.29948589-9.64106498-13.1747149-18.8384731-28.1648763-41.668120934.955202325.8141269

20.264411116.790287714.4787723

0-1.02985892-1.83805404-2.60554387-3.42078226-4.34458866-5.43338659-6.75149467-8.38106273-10.4327105-13.0571148-16.4525292-20.8492096

-26.424739-33.1012324-40.332586942.7534731

36.83344732.104147128.435221325.5988737

0-1.49186396-2.66041957

-3.7598782-4.91169617-6.19367628-7.67026763

-9.4052909-11.4676509-13.9321824-16.8740335-20.3526249-24.3816307-28.8896835-33.6950675

-38.5292379-43.1151858

42.7483139.152211636.0962983

33.52849

0-1.91984694-3.42315884-4.78794865-6.14243802-7.55445232-9.06333771

-10.692549-12.4546562-14.3530472-16.3822039-18.5276116-20.7660418-23.0667272-25.3936329-27.7086324-29.9750281-32.1606958-34.2402601-36.1960364-38.0178406

0-2.21323962-3.93850477

-5.5373379-7.17591278-8.94858931-10.9181478-13.1293292-15.6112445-18.3739238-21.4019975-24.6490238

-28.0369754-31.4644991-34.8234464-38.0179195-40.9782511-43.665728443.930853841.802790839.9294651

0-2.46682133-4.38747915-6.13588059-7.88091012

-9.7098097-11.6703994-13.7866525-16.0641685-18.4917905-21.0424616-23.6751988-26.3391359-28.9794748-31.5441379-33.9894531-36.2835863-38.4073721-40.3530581-42.1218908-43.7214044

0-2.67277827-4.75648981-6.57137997-8.26592536-9.90998627-11.5340353-13.1474275-14.7478861

-16.3269864-17.8736111-19.3762196-20.8243096-22.2092715-23.5247775-24.7668275-25.9335672-27.0249746-28.0424937-28.9886687-29.8668124

0-2.76697352-4.92602335-6.76053726-8.40986078-9.94222108-11.3897823-12.7662239-14.0760075-15.3194298-16.4953885

-17.602835-18.6414554-19.6118987-20.5157542-21.3554054-22.1338363-22.8544363-23.5208266-24.1367172-24.7057967

0-2.71695274-4.83513319-6.66776584-8.36173743-9.98636097

-11.57203-13.1286178-14.6551103-16.1451019-17.5901196-18.9816616-20.3123897-21.5767329-22.7710828

-23.89372-24.9445838-25.9249673-26.8371981-27.6843392-28.4699306

0-2.57510228-4.58119282-6.36868413-8.09614568-9.83999544-11.6358036-13.4957256-15.4167987-17.3856501-19.3818885

-21.381079-23.3575215-25.2867213-27.1473277-28.9223758-30.5997985-32.1723138-33.6368737-34.9938801-36.2463372

0-2.40581451-4.28355055

-5.95730858-7.57475644-9.20788061-10.8911414

-12.637629-14.4466932-16.3081368-18.2050892-20.1164479-22.0191777-23.8904431-25.7094136-27.4585754

-29.124469-30.6978735-32.1735521-33.5497098-34.8273145

0-2.21200332-3.94642151-5.44531881-6.82493137-8.14171213-9.42183588-10.6754474-11.9041092-13.1049772-14.2732624-15.4037127-16.4914863-17.5326267-18.5242699-19.4646764-20.3531536-21.1899176-21.9759297-22.7127298-23.4022815

0-1.9511267

-3.48801564-4.78223016-5.92429478-6.96202042-7.92070027-8.81376343-9.64848703-10.4290883-11.1583873-11.8386735-12.4721275-13.0609973-13.6076441-14.1145252-14.5841506-15.0190335-15.4216458-15.7943812-16.1395283

0-1.60602978-2.87342184-3.95324432-4.92258556-5.82100893-6.66855265-7.47494066-8.24448732-8.97878789-9.67821276-10.3427281-10.9723268-11.5672307

-12.127963-12.6553458-13.1504616-13.6145991-14.0491959-14.4557846-14.8359471

0-1.21522292-2.17401141-3.01853377-3.81672453

-4.6027826-5.3940327

-6.19866549-7.01960494-7.85659668-8.70742347-9.56866642-10.4362156-11.3056323-12.1724156

-13.032201-13.8809071-14.7148388-15.5307533-16.3258959-17.0980091

0-0.81910058-1.46581464-2.04332942-2.60068242-3.16343915-3.74579606-4.35591476-4.99847962-5.67600616

-6.389545-7.13907679-7.92374297-8.74198838-9.59165734-10.4700676-11.3740762-12.3001464

-13.2444194-14.2027924-15.1710037

0-0.41859971-0.75004944-1.03990188-1.31039492-1.57282699-1.83295122-2.09353712-2.35568041-2.61951691-2.88463324-3.15031373

-3.415694-3.67985848-3.94190276-4.20097301

-4.4562899-4.70716191-4.95299121-5.19327447-5.42760004

0-2.995E-016-5.373E-016-7.391E-016-9.185E-016-1.083E-015-1.236E-015-1.380E-015-1.516E-015-1.645E-015-1.767E-015-1.882E-015-1.991E-015-2.093E-015-2.189E-015

-2.279E-015-2.364E-015-2.444E-015-2.518E-015-2.588E-015-2.653E-015