Page 1
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
�⁄�^3
�_��
�⁄�^2
�_�
�_ℎ�_��_�
�_��_�
Page 2
DESCRIPCIÓN
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
PARAMETROS SALIDA
Page 3
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
�_� �_� �_�� �_1
�_� �_� �_�� �_1
Page 4
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
�_� �_� �_�� �_1
�_� �_� �_�� �_1
Page 5
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
�_� �_� �_�� �_1
�_� �_� �_�� �_1
Page 6
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
�_� �_� �_�� �_1
�_� �_� �_�� �_1
Page 7
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
�_� �_� �_�� �_1
Page 8
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
�_� �_� �_�� �_1
�_� �_� �_�� �_1
Page 9
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
�_� �_� �_�� �_1
�_� �_� �_�� �_1
Page 10
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
Page 11
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
Page 12
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
Page 13
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
Page 14
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 _⁄� �
Page 15
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 _⁄� �
Page 16
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 _⁄� �
Page 17
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 _⁄� �
Page 18
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 _⁄� �
Page 19
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 _⁄� �
Page 20
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 _⁄� �
Page 21
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 _⁄� �
Page 22
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 _⁄� �
Page 23
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 _⁄� �
Page 24
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 _⁄� �
Page 25
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〗 ^∗)
Page 26
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〗 ^∗)
Page 27
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〗 ^∗)
Page 28
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〗 ^∗)
Page 29
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〗 ^∗)
Page 30
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〗 ^∗)
Page 31
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〗 ^∗)
Page 32
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〗 ^∗)
Page 33
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〗 ^∗)
Page 34
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〗 ^∗)
Page 35
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〗 ^∗)
Page 36
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
Page 37
ESTIMADORES ESTADISTICOS
7.60700918250.08265145227.6320237717
Err:5121.65096146512.72567375935.7898009357
-0.381999098313.938048
013.938048
3035.196663823399
020406080
100120140160180200
Histograma
Frecuencia
Clase
Frecuencia
Page 38
020406080
100120140160180200
Histograma
Frecuencia
Clase
Frecuencia
Page 39
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
Page 40
0
20
40
60
80
100
120
140
Histograma
Frecuencia
Clase
Frecuencia
Page 41
0
20
40
60
80
100
120
140
Histograma
Frecuencia
Clase
Frecuencia
Page 42
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
Page 43
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
Page 44
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
Page 45
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
Page 46
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
Page 47
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
Page 48
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
Page 49
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
Page 50
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
Page 51
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
Page 52
7.23975063 9.177009757.27699831 9.128774427.30920714 9.087058557.33724921 9.050734917.36181534 9.018910367.38345855 8.99086971
Page 53
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
Page 54
0
10
20
30
40
50
60
70
80
90
Histograma
Frecuencia
Clase
Frecuencia
Page 55
0
10
20
30
40
50
60
70
80
90
Histograma
Frecuencia
Clase
Frecuencia
Page 56
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
Page 57
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
Page 58
-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
Page 59
-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
Page 60
-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
Page 61
-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
Page 62
-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
Page 63
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
Page 64
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
Page 65
-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
Page 66
-2.279E-015-2.364E-015-2.444E-015-2.518E-015-2.588E-015-2.653E-015