PRACTICA DE LABORATORIO 3 ENSAYO A FLEXIÓN
JUAN FELIPE SOLANO GRANADOS JHON ALEXANDER MENDOZA GALINDO ANDERSON DE JESÚS GUERRERO
UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIA DUITAMA – BOYACÁ 2014
PRACTICA DE LABORATORIO 3 ENSAYO A FLEXIÓN
JUAN FELIPE SOLANO GRANADOS JHON ALEXANDER MENDOZA GALINDO ANDERSON DE JESÚS GUERRERO
TRABAJO PRESENTADO EN LA MATERIA DE RESISTENCIA DE MATERIALES AL INGENIERO ELECTROMECÁNICO FABIÁN LEONARDO HIGUERA.
UNIVERSIDAD PEDAGÓGICA Y TECNOLÓGICA DE COLOMBIA DUITAMA – BOYACÁ 2014
1. OBJETIVOS OBJETIVO GENERAL
Determinar el módulo de rigidez por flexión en la viga
OBJETIVOS ESPECÍFICOS
Comparar la carga vs la deformación vertical por medio de graficas que ilustren el comportamiento de las vigas en los ensayos de flexión. Plantear las dudas que surgieron durante el laboratorio. Analizar graficas de esfuerzo y deformación basándose en la teoría de resistencia y flexión. Comportamiento de una viga con respecto a una carga puntual, análisis de la fuerza cortante, momento flector, elástica de la viga y flexión.
2. EQUIPOS Y MATERIALES
Máquina de Prueba Universal Hidráulica: En esta máquina se pueden realizar ensayos de tracción, compresión y flexión, para así determinar las propiedades mecánicas de muchos materiales. La máquina trabaja hidráulicamente, tiene todo tipo de sensores para así poder determinar con precisión las propiedades mecánicas de los materiales.
Fig.1 – Maquina de Prueba Universal Hidráulica
Además también está conectada a un computador con un software específico para realizar estas pruebas y así poder establecer los parámetros del ensayo a realizar. En el computador también se muestran los resultados de la prueba.
Soportes para ensayo de flexión: Es un elemento utilizado para apoyar en dos puntos a la viga que se va a exponer a una carga para así determinar sus propiedades.
Galga extensiométrica: La galga extensiométrica es un sensor, para medir la deformación, presión, carga, torque, posición, entre otras cosas, que está basado en el efecto piezorresistivo, el cual es la propiedad que tienen ciertos materiales de cambiar el valor nominal de su resistencia cuando se le someten a ciertos esfuerzos y se deforman en dirección de los ejes mecánicos.
Fig.4 – Galga extensiométrica
Calibrador pie de rey: Es un instrumento utilizado para medir dimensiones de objetos relativamente pequeños, desde centímetros hasta fracciones de milímetros
Probeta 1 , Viga de madera para ensayo de Flexión:
Fig.5 – Viga de madera para ensayo de Flexión.
2.1.
Probeta 1, viga de madera para ensayo de flexión:
Fb
20
6,7
B
C
A
5
30
5
6,7
40
Fig.6 – Dimensiones en [cm] de la probeta 1, Viga de madera para el ensayo de flexión.
2.2. Descripción del ensayo de flexión: 1. Se ubican los apoyos inferiores para la viga, en la maquina universal de ensayos. 2. Se fija la carga central y se ubica la viga o cercha.
Fig.8 – Fijación de la carga central y ubicación de la viga.
3. Se inicia el ensayo de Flexión aplicando la carga hasta determinado tiempo, necesario para obtener los suficientes datos para poder hallar el módulo de rigidez por cizalladura. DATOS VIGA Probeta 1, Viga de madera: Anexo1:
E
2.3.
Probeta 2, viga de acero con área cuadrada para ensayo de flexión:
17
2,54
Fb
2,54
B A
4
C
26 34
4
Fig.6 – Dimensiones en [cm] de la probeta 2, Viga de acero para el ensayo de flexión.
2.4. Descripción del ensayo de flexión: 4. Se ubican los apoyos inferiores para la viga, en la maquina universal de ensayos.
Fig.7 – Ubicación de los apoyos.
5. Se fija la carga central y se ubica la viga o cercha.
Fig.8 – Fijación de la carga central y ubicación de la viga.
Probeta 3 , Viga de acero de área circular para ensayo de Flexión:
Fig.5 – Viga de acero de área circular para ensayo de Flexión.
2.5.
Probeta 3, viga de acero de área circular para ensayo de flexión:
17
2,54
Fb B A
26 34
4
Ø2,54
4
C
Fig.6 – Dimensiones en [cm] de la probeta 2, Viga de acero de área circular para el ensayo de flexión.
2.6. Descripción del ensayo de flexión: 6. Se ubican los apoyos inferiores para la viga, en la maquina universal de ensayos.
7. Se fija la carga central y se ubica la viga o cercha.
Fig.8 – Fijación de la carga central y ubicación de la viga.
3.1.1. TABLA DE DATOS DE LA PROBETA 1, VIGA DE MADERA Tiempo
Carga
Alargamiento
seg
kN
mm
0
0
0
0,5
-0,0234375
-0,002
1
0
-0,002
1,5
0,03125
-0,004
2
-0,0078125
-0,002
2,5
0,015625
0,002
3
0,0078125
0,014
3,5
0,0234375
0,03
4
0,0234375
0,046
4,5
0,03125
0,062
5
0,0546875
0,08
5,5
0,0546875
0,096
6
0,078125
0,112
6,5
0,1015625
0,128
7
0,109375
0,146
7,5
0,15625
0,162
8
0,1484375
0,18
8,5
0,203125
0,196
9
0,2109375
0,214
9,5
0,2265625
0,23
10
0,21875
0,248
esfuerzo
esfuerzo cortante
Kpa
Kpa
0
0
-10,8206371
-3,083881579
0
0
14,4275162
2885,503232
-3,60687904
-721,3758079
7,21375808
1442,751616
3,60687904
721,3758079
10,8206371
2164,127424
10,8206371
2164,127424
14,4275162
2885,503232
25,2481533
5049,630656
25,2481533
5049,630656
36,0687904
7213,758079
46,8894275
9377,885503
50,4963066
10099,26131
72,1375808
14427,51616
68,5307018
13706,14035
93,778855
18755,77101
97,3857341
19477,14681
104,599492
20919,89843
100,992613
20198,52262
10,5
0,2421875
0,264
11
0,21875
0,282
11,5
0,2421875
0,298
12
0,2421875
0,314
12,5
0,2421875
0,332
13
0,234375
0,348
13,5
0,25
0,364
14
0,25
0,382
14,5
0,2578125
0,398
15
0,2421875
0,414
15,5
0,265625
0,432
16
0,265625
0,448
16,5
0,2734375
0,464
17
0,265625
0,48
17,5
0,2890625
0,498
18
0,3203125
0,514
18,5
0,3359375
0,53
19
0,34375
0,548
19,5
0,375
0,564
20
0,3515625
0,582
20,5
0,3984375
0,598
21
0,40625
0,614
21,5
0,421875
0,632
22
0,453125
0,648
111,81325
22362,65005
100,992613
20198,52262
111,81325
22362,65005
111,81325
22362,65005
111,81325
22362,65005
108,206371
21641,27424
115,420129
23084,02585
115,420129
23084,02585
119,027008
23805,40166
111,81325
22362,65005
122,633887
24526,77747
122,633887
24526,77747
126,240766
25248,15328
122,633887
24526,77747
133,454524
26690,90489
147,882041
29576,40813
155,095799
31019,15974
158,702678
31740,53555
173,130194
34626,03878
162,309557
32461,91136
183,950831
36790,1662
187,55771
37511,54201
194,771468
38954,29363
209,198984
41839,79686
22,5
0,4921875
0,664
23
0,4921875
0,68
23,5
0,5234375
0,698
24
0,5234375
0,714
24,5
0,5625
0,732
25
0,6015625
0,748
25,5
0,625
0,764
26
0,65625
0,782
26,5
0,671875
0,798
27
0,6640625
0,814
27,5
0,734375
0,832
28
0,6953125
0,848
28,5
0,78125
0,864
29
0,796875
0,882
29,5
0,875
0,898
30
0,8359375
0,916
30,5
0,9140625
0,932
31
0,9375
0,948
31,5
1
0,966
32
0,96875
0,982
32,5
1,039063
1
33
1,078125
1,016
33,5
1,125
1,032
34
1,054688
1,05
227,23338
45446,6759
227,23338
45446,6759
241,660896
48332,17913
241,660896
48332,17913
259,695291
51939,05817
277,729686
55545,93721
288,550323
57710,06464
302,977839
60595,56787
310,191597
62038,31948
306,584718
61316,94367
339,04663
67809,32595
321,012235
64202,44691
360,687904
72137,58079
367,901662
73580,33241
403,970452
80794,09049
385,936057
77187,21145
422,004848
84400,96953
432,825485
86565,09695
461,680517
92336,10342
447,253001
89450,60018
479,715143
95943,02862
497,749307
99549,8615
519,390582
103878,1163
486,928901
97385,78024
34,5
1,164063
1,066
35
1,203125
1,082
35,5
1,25
1,1
36
1,28125
1,116
36,5
1,3125
1,134
37
1,265625
1,15
37,5
1,359375
1,166
38
1,351563
1,184
38,5
1,476563
1,2
39
1,484375
1,216
39,5
1,570313
1,234
40
1,421875
1,25
40,5
1,53125
1,266
41
1,601563
1,284
41,5
1,648438
1,3
42
1,679688
1,318
42,5
1,734375
1,334
43
1,773438
1,352
43,5
1,6875
1,368
44
1,710938
1,384
44,5
1,8125
1,4
45
1,859375
1,418
45,5
1,9375
1,434
46
1,96875
1,452
537,425208
107485,0416
555,459372
111091,8744
577,100646
115420,1293
591,528163
118305,6325
605,955679
121191,1357
584,314404
116862,8809
627,596953
125519,3906
623,990305
124798,0609
681,700369
136340,0739
685,307018
137061,4035
724,982918
144996,5836
656,451985
131290,397
706,948292
141389,6584
739,410434
147882,0868
761,051708
152210,3416
775,479224
155095,8449
800,727147
160145,4294
818,761773
163752,3546
779,085873
155817,1745
789,906741
157981,3481
836,795937
167359,1874
858,437211
171687,4423
894,506002
178901,2004
908,933518
181786,7036
46,5
2,03125
1,468
47
2,070313
1,486
47,5
2,085938
1,502
48
1,921875
1,52
48,5
2
1,534
49
2,070313
1,552
49,5
2,164063
1,568
50
2,195313
1,584
50,5
2,273438
1,602
51
2,28125
1,618
51,5
2,375
1,636
52
2,359375
1,652
52,5
2,40625
1,67
53
2,445313
1,686
53,5
2,234375
1,702
54
2,359375
1,72
54,5
2,414063
1,736
55
2,476563
1,752
55,5
2,53125
1,77
56
2,601563
1,786
56,5
2,664063
1,802
57
2,664063
1,82
57,5
2,6875
1,836
58
2,726563
1,854
937,78855
187557,7101
955,823176
191164,6353
963,036934
192607,3869
887,292244
177458,4488
923,361034
184672,2068
955,823176
191164,6353
999,105725
199821,145
1013,53324
202706,6482
1049,60203
209920,4063
1053,20868
210641,7359
1096,49123
219298,2456
1089,27747
217855,494
1110,91874
222183,7488
1128,95337
225790,6741
1031,56741
206313,4811
1089,27747
217855,494
1114,52585
222905,1708
1143,38089
228676,1773
1168,62881
233725,7618
1201,09095
240218,1902
1229,94598
245989,1967
1229,94598
245989,1967
1240,76639
248153,2779
1258,80102
251760,2031
58,5
2,734375
1,87
59
2,710938
1,888
59,5
2,632813
1,904
60
2,632813
1,92
60,5
2,648438
1,938
61
2,679688
1,954
61,5
2,6875
1,97
62
2,710938
1,986
62,5
2,726563
2,004
63
2,75
2,02
63,5
2,78125
2,036
64
2,820313
2,054
64,5
2,84375
2,07
65
2,882813
2,088
65,5
2,898438
2,104
66
2,914063
2,12
66,5
2,914063
2,138
67
2,96875
2,154
67,5
2,976563
2,17
68
3,023438
2,188
68,5
2,992188
2,204
69
3,09375
2,222
69,5
3,109375
2,238
70
3,164063
2,254
1262,40766
252481,5328
1251,58726
250317,4515
1215,51847
243103,6934
1215,51847
243103,6934
1222,73223
244546,4451
1237,15974
247431,9483
1240,76639
248153,2779
1251,58726
250317,4515
1258,80102
251760,2031
1269,62142
253924,2844
1284,04894
256809,7876
1302,08356
260416,7128
1312,90397
262580,7941
1330,9386
266187,7193
1338,15235
267630,4709
1345,36611
269073,2225
1345,36611
269073,2225
1370,61404
274122,807
1374,22114
274844,229
1395,86242
279172,4838
1381,4349
276286,9806
1428,3241
285664,8199
1435,53786
287107,5716
1460,78624
292157,2484
70,5
3,179688
2,272
71
3,304688
2,288
71,5
3,28125
2,304
72
3,335938
2,322
72,5
3,359375
2,338
73
3,4375
2,356
73,5
3,484375
2,372
74
3,515625
2,39
74,5
3,53125
2,406
75
3,609375
2,422
75,5
3,609375
2,44
76
3,671875
2,456
76,5
3,679688
2,474
77
3,734375
2,49
77,5
3,78125
2,506
78
3,804688
2,524
78,5
3,851563
2,54
79
3,914063
2,558
79,5
3,921875
2,574
80
3,992188
2,59
80,5
4,007813
2,608
81
4,101563
2,624
81,5
4,09375
2,64
82
4,125
2,658
1468
293600
1525,71006
305142,0129
1514,8892
302977,8393
1540,13758
308027,5162
1550,95799
310191,5974
1587,02678
317405,3555
1608,66805
321733,6103
1623,09557
324619,1136
1630,30933
326061,8652
1666,37812
333275,6233
1666,37812
333275,6233
1695,23315
339046,6297
1698,84026
339768,0517
1724,08818
344817,6362
1745,72946
349145,891
1756,55032
351310,0646
1778,1916
355638,3195
1807,04663
361409,3259
1810,65328
362130,6556
1843,11542
368623,084
1850,32918
370065,8356
1893,61173
378722,3453
1890,00462
378000,9234
1904,43213
380886,4266
82,5
4,1875
2,674
83
4,21875
2,692
83,5
4,296875
2,708
84
4,296875
2,726
84,5
4,351563
2,742
85
4,375
2,758
85,5
4,421875
2,776
86
4,460938
2,792
86,5
4,539063
2,81
87
4,546875
2,826
87,5
4,609375
2,842
88
4,664063
2,86
88,5
4,6875
2,876
89
4,71875
2,894
89,5
4,820313
2,91
90
4,75
2,926
90,5
4,875
2,944
91
4,867188
2,96
91,5
4,914063
2,978
92
4,9375
2,994
92,5
4,992188
3,01
93
5,03125
3,028
93,5
5,046875
3,044
94
5,085938
3,062
1933,28717
386657,4331
1947,71468
389542,9363
1983,78347
396756,6944
1983,78347
396756,6944
2009,03186
401806,3712
2019,85226
403970,4524
2041,49354
408298,7073
2059,52816
411905,6325
2095,59695
419119,3906
2099,2036
419840,7202
2128,05863
425611,7267
2153,30702
430661,4035
2164,12742
432825,4848
2178,55494
435710,988
2225,4446
445088,9197
2192,98246
438596,4912
2250,69252
450138,5042
2247,08587
449417,1745
2268,72715
453745,4294
2279,54755
455909,5106
2304,79594
460959,1874
2322,8301
464566,0203
2330,04386
466008,7719
2348,07849
469615,6971
94,5
5,085938
3,078
95
5,15625
3,094
95,5
5,148438
3,112
96
5,21875
3,128
96,5
5,234375
3,146
97
5,304688
3,162
97,5
5,320313
3,178
98
5,398438
3,196
98,5
5,382813
3,212
99
5,484375
3,23
99,5
5,46875
3,246
100
5,570313
3,262
100,5
5,585938
3,28
101
5,65625
3,296
101,5
5,625
3,314
102
5,695313
3,33
102,5
5,726563
3,348
103
5,804688
3,364
103,5
5,820313
3,38
104
5,890625
3,398
104,5
5,890625
3,414
105
5,921875
3,432
105,5
5,960938
3,448
106
6,054688
3,464
2348,07849
469615,6971
2380,54017
476108,0332
2376,93352
475386,7036
2409,3952
481879,0397
2416,60896
483321,7913
2449,0711
489814,2198
2456,28486
491256,9714
2492,35365
498470,7295
2485,13989
497027,9778
2532,02909
506405,8172
2524,81533
504963,0656
2571,70499
514340,9972
2578,91874
515783,7488
2611,38042
522276,0849
2596,95291
519390,5817
2629,41505
525883,0102
2643,84257
528768,5134
2679,91136
535982,2715
2687,12512
537425,0231
2719,5868
543917,3592
2719,5868
543917,3592
2734,01431
546802,8624
2752,04894
550409,7876
2795,33149
559066,2973
106,5
6,046875
3,482
107
6,101563
3,498
107,5
6,148438
3,516
108
6,203125
3,532
108,5
6,203125
3,548
109
6,257813
3,566
109,5
6,289063
3,582
110
6,320313
3,6
110,5
6,367188
3,616
111
6,40625
3,632
111,5
6,453125
3,65
112
6,46875
3,666
112,5
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527
20,96875
17,546
527,5
20,97656
17,562
528
20,96875
17,578
528,5
20,98438
17,594
529
20,99219
17,61
529,5
21,00781
17,628
530
21,02344
17,644
530,5
21,00781
17,66
531
21
17,676
531,5
21,01563
17,692
532
21,01563
17,71
532,5
21,03125
17,726
533
21,02344
17,742
533,5
21,05469
17,758
534
21,0625
17,774
534,5
21,03906
17,792
535
21,07031
17,808
535,5
21,07813
17,824
536
21,05469
17,84
536,5
21,0625
17,856
537
21,03906
17,874
537,5
21,08594
17,89
538
21,09375
17,906
9677,25762
1935451,524
9680,86334
1936172,669
9684,46907
1936893,813
9680,86334
1936172,669
9688,07941
1937615,882
9691,68513
1938337,027
9698,89658
1939779,317
9706,11265
1941222,53
9698,89658
1939779,317
9695,29086
1939058,172
9702,50693
1940501,385
9702,50693
1940501,385
9709,71837
1941943,675
9706,11265
1941222,53
9720,54017
1944108,033
9724,14589
1944829,178
9713,3241
1942664,82
9727,75162
1945550,323
9731,36196
1946272,392
9720,54017
1944108,033
9724,14589
1944829,178
9713,3241
1942664,82
9734,96768
1946993,536
9738,57341
1947714,681
538,5
21,10156
17,922
539
21,10156
17,938
539,5
21,11719
17,956
540
21,14063
17,972
540,5
21,09375
17,988
541
21,13281
18,004
541,5
21,13281
18,022
542
21,16406
18,038
542,5
21,14063
18,054
543
21,14844
18,07
543,5
21,15625
18,086
544
21,14063
18,104
544,5
21,17188
18,12
545
21,17969
18,136
545,5
21,17969
18,152
546
21,19531
18,168
546,5
21,19531
18,186
547
21,17969
18,202
547,5
21,20313
18,218
548
21,21094
18,234
548,5
21,21094
18,25
549
21,20313
18,268
549,5
21,25
18,284
550
21,23438
18,3
9742,17913
1948435,826
9742,17913
1948435,826
9749,3952
1949879,04
9760,21699
1952043,398
9738,57341
1947714,681
9756,60665
1951321,33
9756,60665
1951321,33
9771,03416
1954206,833
9760,21699
1952043,398
9763,82271
1952764,543
9767,42844
1953485,688
9760,21699
1952043,398
9774,64451
1954928,901
9778,25023
1955650,046
9778,25023
1955650,046
9785,46168
1957092,336
9785,46168
1957092,336
9778,25023
1955650,046
9789,07202
1957814,404
9792,67775
1958535,549
9792,67775
1958535,549
9789,07202
1957814,404
9810,71099
1962142,198
9803,49954
1960699,908
550,5
21,24219
18,316
551
21,24219
18,332
551,5
21,24219
18,35
552
21,21875
18,366
552,5
21,24219
18,382
553
21,25781
18,398
553,5
21,25781
18,414
554
21,28125
18,432
554,5
21,28906
18,448
555
21,25
18,464
555,5
21,28125
18,48
556
21,30469
18,496
556,5
21,29688
18,514
557
21,32813
18,53
557,5
21,3125
18,546
558
21,29688
18,562
558,5
21,32031
18,578
559
21,32813
18,596
559,5
21,32813
18,612
560
21,35156
18,628
560,5
21,33594
18,644
561
21,33594
18,66
561,5
21,32813
18,678
562
21,35938
18,694
9807,10526
1961421,053
9807,10526
1961421,053
9807,10526
1961421,053
9796,28347
1959256,694
9807,10526
1961421,053
9814,31671
1962863,343
9814,31671
1962863,343
9825,1385
1965027,701
9828,74423
1965748,846
9810,71099
1962142,198
9825,1385
1965027,701
9835,9603
1967192,059
9832,35457
1966470,914
9846,78209
1969356,417
9839,56602
1967913,204
9832,35457
1966470,914
9843,17175
1968634,349
9846,78209
1969356,417
9846,78209
1969356,417
9857,59926
1971519,852
9850,38781
1970077,562
9850,38781
1970077,562
9846,78209
1969356,417
9861,2096
1972241,921
562,5
21,34375
18,71
563
21,35938
18,726
563,5
21,375
18,742
564
21,36719
18,76
564,5
21,35938
18,776
565
21,35938
18,792
565,5
21,375
18,808
566
21,39063
18,824
566,5
21,40625
18,842
567
21,39063
18,858
567,5
21,40625
18,874
568
21,375
18,89
568,5
21,40625
18,906
569
21,39844
18,924
569,5
21,40625
18,94
570
21,41406
18,956
570,5
21,41406
18,972
571
21,44531
18,988
571,5
21,44531
19,006
572
21,45313
19,022
572,5
21,46094
19,038
573
21,44531
19,054
573,5
21,44531
19,072
574
21,46875
19,088
9853,99354
1970798,707
9861,2096
1972241,921
9868,42105
1973684,211
9864,81533
1972963,066
9861,2096
1972241,921
9861,2096
1972241,921
9868,42105
1973684,211
9875,63712
1975127,424
9882,84857
1976569,714
9875,63712
1975127,424
9882,84857
1976569,714
9868,42105
1973684,211
9882,84857
1976569,714
9879,24284
1975848,569
9882,84857
1976569,714
9886,45429
1977290,859
9886,45429
1977290,859
9900,88181
1980176,362
9900,88181
1980176,362
9904,49215
1980898,43
9908,09788
1981619,575
9900,88181
1980176,362
9900,88181
1980176,362
9911,7036
1982340,72
574,5
21,46875
19,104
575
21,47656
19,12
575,5
21,47656
19,136
576
21,50781
19,154
576,5
21,5
19,17
577
21,5
19,186
577,5
21,48438
19,202
578
21,49219
19,218
578,5
21,51563
19,234
579
21,48438
19,252
579,5
21,5
19,268
580
21,48438
19,284
580,5
21,51563
19,3
581
21,52344
19,318
581,5
21,55469
19,334
582
21,53906
19,35
582,5
21,52344
19,366
583
21,51563
19,382
583,5
21,57031
19,4
584
21,55469
19,416
584,5
21,57031
19,432
585
21,5625
19,448
585,5
21,57031
19,464
586
21,52344
19,482
9911,7036
1982340,72
9915,30933
1983061,865
9915,30933
1983061,865
9929,73684
1985947,368
9926,13112
1985226,223
9926,13112
1985226,223
9918,91967
1983783,934
9922,52539
1984505,078
9933,34718
1986669,437
9918,91967
1983783,934
9926,13112
1985226,223
9918,91967
1983783,934
9933,34718
1986669,437
9936,95291
1987390,582
9951,38042
1990276,085
9944,16436
1988832,872
9936,95291
1987390,582
9933,34718
1986669,437
9958,59187
1991718,375
9951,38042
1990276,085
9958,59187
1991718,375
9954,98615
1990997,23
9958,59187
1991718,375
9936,95291
1987390,582
586,5
21,5625
19,498
587
21,60156
19,514
587,5
21,57813
19,53
588
21,60156
19,546
588,5
21,57031
19,564
589
21,59375
19,58
589,5
21,60938
19,596
590
21,60938
19,612
590,5
21,625
19,628
591
21,60938
19,646
591,5
21,65625
19,662
592
21,64844
19,678
592,5
21,65625
19,694
593
21,64844
19,712
593,5
21,64844
19,728
594
21,64844
19,744
594,5
20,91406
19,76
595
20,96875
19,778
595,5
21,02344
19,794
596
21,04688
19,81
596,5
21,0625
19,826
597
21,10156
19,842
597,5
21,125
19,86
598
21,14844
19,876
9954,98615
1990997,23
9973,01939
1994603,878
9962,20222
1992440,443
9973,01939
1994603,878
9958,59187
1991718,375
9969,41367
1993882,733
9976,62973
1995325,946
9976,62973
1995325,946
9983,84118
1996768,236
9976,62973
1995325,946
9998,2687
1999653,74
9994,66297
1998932,595
9998,2687
1999653,74
9994,66297
1998932,595
9994,66297
1998932,595
9994,66297
1998932,595
9655,61404
1931122,807
9680,86334
1936172,669
9706,11265
1941222,53
9716,93444
1943386,888
9724,14589
1944829,178
9742,17913
1948435,826
9753,00092
1950600,185
9763,82271
1952764,543
9774,64451 598,5
21,17188
1954928,901
19,892
Grafica de esfuerzo VS alargamiento 12000 10000
esfuerzo (KPa)
8000 6000 4000 2000 0 -5
0
5
-2000
10
15
20
25
alargamiento (mm)
Grafica de esfuerzo cortante VS alargamiento 2500000
esfuerzo cortante (kPa)
2000000 1500000 1000000 500000 0 -5
0 -500000
5
10 alargamiento (mm)
15
20
25
3.1.1. TABLA DE DATOS DE LA PROBETA 2, VIGA DE ACERO RECTANGULAR Tiempo seg 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5 13 13,5 14 14,5 15 15,5 16 16,5 17
Carga kN -0,015625 -0,015625 0,0078125 0,015625 0,2265625 0,6328125 0,9765625 1,304688 1,554688 1,84375 2,070313 2,304688 2,515625 2,710938 3,257813 3,765625 4,335938 4,882813 5,476563 6,023438 6,585938 7,125 7,65625 8,179688 8,710938 9,226563 9,742188 10,29688 10,80469 11,32031 11,80469 12,35156 12,89063 13,46875 14
Alargamiento mm 0 0 0,002 0,02 0,052 0,094 0,136 0,18 0,224 0,266 0,308 0,352 0,394 0,436 0,478 0,52 0,564 0,606 0,65 0,694 0,736 0,78 0,824 0,868 0,912 0,956 1 1,042 1,086 1,13 1,172 1,214 1,256 1,298 1,338
esfuerzo Kpa -36,3281977 -36,3281977 18,1640988 36,3281977 526,758866 1471,29201 2270,51235 3033,40567 3614,65683 4286,72732 4813,48735 5358,41032 5848,83982 6302,94346 7574,43037 8755,09564 10081,076 11352,5629 12733,0344 14004,5214 15312,3365 16565,6581 17800,8169 19017,8126 20252,9714 21451,8019 22650,6324 23940,2939 25120,9545 26319,7734 27445,9591 28717,4344 29970,7747 31314,9064 32550,0651
esfuerzo cortante Kpa -5,47617935 -5,47617935 2,738089675 5,47617935 79,40460057 221,7852637 342,2612094 457,261151 544,8800206 646,1891633 725,5939391 807,7366294 881,6648753 950,1172925 1141,78357 1319,759223 1519,639945 1711,306222 1919,401037 2111,067315 2308,209771 2497,137784 2683,327881 2866,780065 3052,970163 3233,684081 3414,398 3608,803944 3786,778897 3967,491063 4137,254375 4328,9189 4517,849716 4720,4666 4906,656698
17,5 18 18,5 19 19,5 20 20,5 21 21,5 22 22,5 23 23,5 24 24,5 25 25,5 26 26,5 27 27,5 28 28,5 29 29,5 30 30,5 31 31,5 32 32,5 33 33,5 34 34,5 35 35,5 36 36,5 37
14,5625 15,13281 15,71875 16,29688 16,86719 17,42969 17,95313 18,55469 19,09375 19,67188 20,19531 20,76563 21,22656 21,71875 22,28125 22,72656 23,24219 23,67188 24,14063 24,53125 24,97656 25,26563 25,66406 26 26,28125 26,54688 26,78125 26,98438 27,19531 27,33594 27,51563 27,67969 27,77344 27,94531 28,00781 28,13281 28,23438 28,35156 28,39844 28,51563
1,38 1,422 1,462 1,504 1,546 1,588 1,628 1,67 1,712 1,754 1,794 1,836 1,878 1,92 1,962 2,002 2,044 2,086 2,128 2,17 2,21 2,252 2,294 2,336 2,378 2,42 2,462 2,502 2,544 2,586 2,628 2,67 2,712 2,754 2,796 2,836 2,878 2,92 2,962 3,004
33857,8802 35183,8536 36546,1668 37890,3218 39216,2952 40524,1103 41741,1107 43139,7405 44393,0575 45737,2125 46954,1897 48280,1863 49351,8507 50496,1947 51804,0099 52839,3577 54038,1998 55037,2311 56127,077 57035,2703 58070,6181 58742,7072 59669,0588 60450,1209 61104,0285 61721,6194 62266,5308 62738,809 63229,2222 63556,1876 63973,9677 64355,408 64573,3771 64972,9757 65118,2885 65408,9141 65645,0648 65917,5088 66026,5051 66298,9723
5103,799154 5303,678824 5509,036426 5711,656814 5911,536484 6108,678941 6292,131826 6502,963854 6691,891166 6894,511554 7077,960934 7277,844109 7439,388771 7611,889296 7809,031753 7965,101988 8145,817659 8296,413468 8460,698848 8597,601579 8753,671815 8854,983761 8994,623706 9112,362438 9210,933667 9304,030468 9386,171406 9457,36349 9531,289282 9580,576649 9643,553588 9701,052595 9733,909671 9794,145891 9816,050609 9859,860043 9895,457838 9936,526554 9952,956845 9994,029066
37,5 38 38,5 39 39,5 40 40,5 41 41,5 42 42,5 43 43,5 44 44,5 45 45,5 46 46,5 47 47,5 48 48,5 49 49,5 50 50,5 51 51,5 52 52,5 53 53,5 54 54,5 55 55,5 56 56,5 57
28,59375 28,69531 28,76563 28,88281 28,91406 29,03125 29,07031 29,17969 29,22656 29,29688 29,36719 29,46094 29,5 29,58594 29,58594 29,72656 29,75 29,82031 29,86719 29,90625 29,96875 30,04688 30,03906 30,14844 30,17969 30,23438 30,28906 30,33594 30,34375 30,45313 30,47656 30,53125 30,5625 30,63281 30,67969 30,67188 30,77344 30,80469 30,85156 30,89063
3,046 3,088 3,13 3,17 3,212 3,254 3,296 3,338 3,38 3,422 3,462 3,504 3,546 3,588 3,63 3,67 3,714 3,754 3,796 3,838 3,88 3,922 3,962 4,004 4,046 4,088 4,13 4,172 4,212 4,254 4,296 4,338 4,38 4,422 4,464 4,504 4,546 4,588 4,63 4,672
66480,6017 66716,7292 66880,2235 67152,6676 67225,324 67497,7912 67588,6059 67842,9149 67951,8879 68115,3822 68278,8533 68496,8225 68587,6372 68787,4481 68787,4481 69114,3902 69168,8883 69332,3594 69441,3556 69532,1703 69677,4831 69859,1357 69840,9542 70095,2632 70167,9196 70295,0741 70422,2053 70531,2016 70549,3598 70803,6689 70858,1437 70985,2982 71057,9546 71221,4257 71330,4219 71312,2636 71548,3911 71621,0475 71730,0205 71820,8584
10021,40821 10057,0025 10081,64794 10122,71665 10133,66901 10174,74123 10188,4308 10226,76581 10243,1926 10267,83803 10292,47996 10325,33704 10339,02661 10369,14648 10369,14648 10418,43034 10426,64548 10451,28741 10467,7177 10481,40728 10503,31199 10530,69464 10527,95392 10566,28893 10577,24129 10596,40879 10615,57279 10632,00308 10634,7403 10673,07531 10681,28695 10700,45445 10711,40681 10736,04874 10752,47903 10749,74182 10785,33611 10796,28846 10812,71525 10826,40833
57,5 58 58,5 59 59,5 60 60,5 61 61,5 62 62,5 63 63,5 64 64,5 65 65,5 66 66,5 67 67,5 68 68,5 69 69,5 70 70,5 71 71,5 72 72,5 73 73,5 74 74,5 75 75,5 76 76,5 77
30,9375 30,96875 31,03125 31,05469 31,10156 31,20313 31,17188 31,21875 31,34375 31,28906 31,33594 31,375 31,42188 31,44531 31,49219 31,52344 31,55469 31,55469 31,67188 31,67188 31,71094 31,71875 31,79688 31,8125 31,90625 31,88281 31,9375 31,96094 31,99219 32,03125 32,0625 32,08594 32,14063 32,14844 32,21094 32,21875 32,25781 32,24219 32,30469 32,32031
4,714 4,754 4,796 4,838 4,88 4,922 4,962 5,004 5,046 5,088 5,13 5,17 5,212 5,254 5,296 5,338 5,378 5,42 5,462 5,504 5,544 5,586 5,628 5,67 5,712 5,754 5,794 5,836 5,878 5,92 5,962 6,002 6,044 6,086 6,128 6,17 6,21 6,252 6,294 6,336
71929,8314 72002,4878 72147,8005 72202,2987 72311,2716 72547,4223 72474,7659 72583,7389 72874,3645 72747,21 72856,2062 72947,0209 73056,0171 73110,492 73219,4882 73292,1446 73364,801 73364,801 73637,2683 73637,2683 73728,083 73746,2412 73927,8939 73964,2104 74182,1796 74127,6815 74254,836 74309,3341 74381,9905 74472,8052 74545,4616 74599,9597 74727,1142 74745,2725 74890,5853 74908,7436 74999,5582 74963,2417 75108,5545 75144,871
10842,83511 10853,78747 10875,69219 10883,90733 10900,33412 10935,93191 10924,97956 10941,40634 10985,21578 10966,04827 10982,47856 10996,16813 11012,59843 11020,81007 11037,24036 11048,19271 11059,14507 11059,14507 11100,21729 11100,21729 11113,90687 11116,64408 11144,02673 11149,50116 11182,35823 11174,14309 11193,31059 11201,52574 11212,4781 11226,16767 11237,12003 11245,33517 11264,50268 11267,23989 11289,14461 11291,88182 11305,57139 11300,09696 11322,00168 11327,47611
77,5 78 78,5 79 79,5 80 80,5 81 81,5 82 82,5 83 83,5 84 84,5 85 85,5 86 86,5 87 87,5 88 88,5 89 89,5 90 90,5 91 91,5 92 92,5 93 93,5 94 94,5 95 95,5 96 96,5 97
32,38281 32,38281 32,45313 32,46094 32,50781 32,53906 32,5625 32,57813 32,60156 32,64844 32,67969 32,71875 32,71875 32,75781 32,78906 32,8125 32,85156 32,89063 32,91406 32,92969 32,95313 32,99219 33 33,04688 33,07813 33,09375 33,10156 33,14844 33,1875 33,21875 33,21875 33,28906 33,27344 33,30469 33,34375 33,35938 33,40625 33,46875 33,41406 33,46094
6,378 6,418 6,46 6,502 6,544 6,586 6,628 6,668 6,71 6,752 6,794 6,834 6,876 6,918 6,96 7,002 7,042 7,084 7,126 7,168 7,21 7,25 7,292 7,334 7,376 7,418 7,46 7,5 7,542 7,584 7,626 7,666 7,708 7,75 7,792 7,834 7,874 7,916 7,958 8
75290,1838 75290,1838 75453,6782 75471,8364 75580,8094 75653,4658 75707,9639 75744,3037 75798,7786 75907,7748 75980,4312 76071,2459 76071,2459 76162,0606 76234,717 76289,2151 76380,0298 76470,8677 76525,3426 76561,6824 76616,1805 76706,9952 76725,1535 76834,1497 76906,8061 76943,1226 76961,2809 77070,2771 77161,0918 77233,7482 77233,7482 77397,2193 77360,9027 77433,5591 77524,3738 77560,7136 77669,6866 77814,9994 77687,8449 77796,8411
11349,38083 11349,38083 11374,02626 11376,76348 11393,19026 11404,14262 11412,35777 11417,8357 11426,04734 11442,47763 11453,42999 11467,11956 11467,11956 11480,80913 11491,76149 11499,97663 11513,66621 11527,35928 11535,57092 11541,04886 11549,264 11562,95357 11565,69079 11582,12108 11593,07344 11598,54786 11601,28508 11617,71537 11631,40494 11642,3573 11642,3573 11666,99923 11661,5248 11672,47716 11686,16673 11691,64466 11708,07145 11729,97617 11710,80866 11727,23895
97,5 98 98,5 99 99,5 100 100,5 101 101,5 102 102,5 103 103,5 104 104,5 105 105,5 106 106,5 107 107,5 108 108,5 109 109,5 110 110,5 111 111,5 112 112,5 113 113,5 114 114,5 115 115,5 116 116,5 117
33,45313 33,50781 33,53906 33,57813 33,5625 33,65625 33,64063 33,69531 33,69531 33,75781 33,71094 33,80469 33,79688 33,8125 33,84375 33,91406 33,88281 33,90625 33,94531 33,97656 33,96094 34 34,03125 34,03906 34,07813 34,10156 34,10938 34,17969 34,14844 34,1875 34,19531 34,23438 34,26563 34,26563 34,28906 34,27344 34,38281 34,35156 34,39844 34,39063
8,042 8,082 8,124 8,166 8,208 8,25 8,292 8,334 8,376 8,418 8,458 8,5 8,542 8,584 8,626 8,668 8,71 8,752 8,794 8,836 8,876 8,918 8,96 9,002 9,044 9,086 9,128 9,17 9,212 9,252 9,294 9,336 9,378 9,42 9,462 9,504 9,546 9,588 9,63 9,672
77778,6828 77905,8141 77978,4705 78069,3084 78032,9686 78250,9378 78214,6212 78341,7524 78341,7524 78487,0652 78378,0923 78596,0614 78577,9032 78614,2197 78686,8761 78850,3472 78777,6908 78832,1889 78923,0036 78995,66 78959,3434 79050,1581 79122,8145 79140,9728 79231,8107 79286,2856 79304,4671 79467,9382 79395,2818 79486,0965 79504,2548 79595,0927 79667,7491 79667,7491 79722,2239 79685,9074 79940,1931 79867,5367 79976,533 79958,3747
11724,50174 11743,66574 11754,6181 11768,31118 11762,83324 11795,69032 11790,21589 11809,37989 11809,37989 11831,28461 11814,85782 11847,7149 11844,97769 11850,45211 11861,40447 11886,0464 11875,09404 11883,30919 11896,99876 11907,95112 11902,47669 11916,16627 11927,11862 11929,85584 11943,54891 11951,76056 11954,50127 11979,1432 11968,19085 11981,88042 11984,61763 11998,31071 12009,26307 12009,26307 12017,47471 12012,00028 12050,33178 12039,37942 12055,80972 12053,0725
117,5 118 118,5 119 119,5 120 120,5 121 121,5 122 122,5 123 123,5 124 124,5 125 125,5 126 126,5 127 127,5 128 128,5 129 129,5 130 130,5 131 131,5 132 132,5 133 133,5 134 134,5 135 135,5 136 136,5 137
34,44531 34,45313 34,47656 34,48438 34,54688 34,5 34,5625 34,57813 34,63281 34,57813 34,67969 34,67188 34,6875 34,71094 34,74219 34,74219 34,78125 34,8125 34,77344 34,82813 34,83594 34,875 34,89063 34,91406 34,9375 34,96094 34,98438 35,00781 35,02344 35,03125 35,04688 35,04688 35,09375 35,10156 35,13281 35,13281 35,17969 35,17188 35,21875 35,20313
9,712 9,754 9,796 9,838 9,88 9,922 9,964 10,006 10,046 10,09 10,13 10,172 10,214 10,256 10,298 10,34 10,382 10,424 10,466 10,506 10,548 10,59 10,632 10,674 10,716 10,758 10,8 10,842 10,884 10,924 10,966 11,008 11,05 11,092 11,134 11,176 11,218 11,26 11,3 11,342
80085,5059 80103,6875 80158,1623 80176,3439 80321,6566 80212,6604 80357,9732 80394,313 80521,4443 80394,313 80630,4405 80612,2822 80648,5988 80703,0969 80775,7533 80775,7533 80866,568 80939,2244 80848,4097 80975,5642 80993,7225 81084,5372 81120,877 81175,3519 81229,85 81284,3481 81338,8462 81393,321 81429,6609 81447,8191 81484,159 81484,159 81593,1319 81611,2902 81683,9466 81683,9466 81792,9428 81774,7845 81883,7575 81847,4409
12072,2365 12074,97722 12083,18886 12085,92958 12107,8343 12091,404 12113,30872 12118,78665 12137,95065 12118,78665 12154,38094 12151,64373 12157,11816 12165,3333 12176,28566 12176,28566 12189,97523 12200,92759 12187,23802 12206,40552 12209,14274 12222,83231 12228,31024 12236,52188 12244,73703 12252,95217 12261,16732 12269,37896 12274,85689 12277,5941 12283,07203 12283,07203 12299,49882 12302,23603 12313,18839 12313,18839 12329,61868 12326,88147 12343,30825 12337,83383
137,5 138 138,5 139 139,5 140 140,5 141 141,5 142 142,5 143 143,5 144 144,5 145 145,5 146 146,5 147 147,5 148 148,5 149 149,5 150 150,5 151 151,5 152 152,5 153 153,5 154 154,5 155 155,5 156 156,5 157
35,25781 35,22656 35,28906 35,30469 35,33594 35,33594 35,36719 35,375 35,39063 35,42188 35,375 35,44531 35,45313 35,5 35,49219 35,53125 35,52344 35,60938 35,52344 35,625 35,60938 35,66406 35,625 35,6875 35,67969 35,70313 35,75 35,72656 35,80469 35,76563 35,78906 35,77344 35,80469 35,8125 35,85156 35,85938 35,89063 35,92969 35,92188 35,9375
11,384 11,426 11,468 11,51 11,552 11,594 11,636 11,678 11,718 11,762 11,802 11,844 11,886 11,928 11,97 12,012 12,054 12,096 12,138 12,178 12,22 12,262 12,304 12,346 12,388 12,43 12,472 12,514 12,556 12,596 12,638 12,68 12,722 12,764 12,806 12,848 12,89 12,932 12,972 13,014
81974,5722 81901,9158 82047,2286 82083,5684 82156,2248 82156,2248 82228,8812 82247,0395 82283,3793 82356,0357 82247,0395 82410,5106 82428,6921 82537,6651 82519,5068 82610,3215 82592,1632 82791,9741 82592,1632 82828,2907 82791,9741 82919,1053 82828,2907 82973,6034 82955,4452 83009,9433 83118,9162 83064,4181 83246,0707 83155,2561 83209,7309 83173,4143 83246,0707 83264,229 83355,0437 83373,2252 83445,8816 83536,6963 83518,538 83554,8546
12356,99783 12346,04547 12367,95019 12373,42812 12384,38048 12384,38048 12395,33283 12398,07005 12403,54798 12414,50034 12398,07005 12422,71198 12425,4527 12441,87948 12439,14227 12452,83184 12450,09463 12480,21449 12450,09463 12485,68892 12480,21449 12499,37849 12485,68892 12507,59364 12504,85642 12513,07157 12529,49835 12521,28321 12548,66586 12534,97628 12543,18792 12537,7135 12548,66586 12551,40307 12565,09264 12567,83336 12578,78572 12592,47529 12589,73808 12595,2125
157,5 158 158,5 159 159,5 160 160,5 161 161,5 162 162,5 163 163,5 164 164,5 165 165,5 166 166,5 167 167,5 168 168,5 169 169,5 170 170,5 171 171,5 172 172,5 173 173,5 174 174,5 175 175,5 176 176,5 177
35,94531 35,97656 35,97656 36 36,00781 36,03125 36,03125 36,0625 36,07813 36,10938 36,125 36,14844 36,17188 36,16406 36,19531 36,20313 36,21094 36,24219 36,24219 36,24219 36,26563 36,28906 36,28906 36,34375 36,35156 36,35938 36,375 36,40625 36,41406 36,42188 36,46094 36,45313 36,48438 36,49219 36,50781 36,52344 36,50781 36,54688 36,5625 36,57031
13,056 13,098 13,14 13,182 13,224 13,266 13,308 13,35 13,39 13,432 13,474 13,516 13,558 13,6 13,642 13,684 13,724 13,766 13,81 13,852 13,892 13,934 13,976 14,018 14,06 14,102 14,144 14,186 14,226 14,268 14,31 14,352 14,394 14,436 14,478 14,52 14,562 14,604 14,644 14,686
83573,0129 83645,6693 83645,6693 83700,1674 83718,3257 83772,8238 83772,8238 83845,4802 83881,82 83954,4764 83990,793 84045,2911 84099,7892 84081,6077 84154,2641 84172,4456 84190,6039 84263,2603 84263,2603 84263,2603 84317,7584 84372,2332 84372,2332 84499,3877 84517,546 84535,7276 84572,0441 84644,7005 84662,8588 84681,0404 84771,855 84753,6968 84826,3532 84844,5114 84880,828 84917,1678 84880,828 84971,6659 85007,9825 85026,1408
12597,94972 12608,90208 12608,90208 12617,11722 12619,85444 12628,06958 12628,06958 12639,02194 12644,49987 12655,45223 12660,92666 12669,1418 12677,35695 12674,61623 12685,56859 12688,30931 12691,04652 12701,99888 12701,99888 12701,99888 12710,21402 12718,42566 12718,42566 12737,59317 12740,33038 12743,0711 12748,54553 12759,49789 12762,2351 12764,97582 12778,66539 12775,92818 12786,88053 12789,61775 12795,09218 12800,57011 12795,09218 12808,78525 12814,25968 12816,99689
177,5 178 178,5 179 179,5 180 180,5 181 181,5 182 182,5 183 183,5 184 184,5 185 185,5 186 186,5 187 187,5 188 188,5 189 189,5 190 190,5 191 191,5 192 192,5 193 193,5 194 194,5 195 195,5 196 196,5 197
36,59375 36,60156 36,64063 36,64844 36,64844 36,6875 36,67969 36,69531 36,6875 36,70313 36,74219 36,75781 36,79688 36,79688 36,78906 36,79688 36,85156 36,84375 36,84375 36,89063 36,89844 36,89063 36,92969 36,9375 36,95313 36,96875 36,9375 37,02344 37,01563 37,02344 37,03906 37,04688 37,05469 37,07813 37,09375 37,08594 37,125 37,13281 37,16406 37,17969
14,728 14,77 14,812 14,854 14,896 14,938 14,98 15,022 15,062 15,104 15,146 15,188 15,23 15,272 15,314 15,356 15,398 15,44 15,48 15,522 15,564 15,606 15,648 15,69 15,732 15,774 15,816 15,856 15,898 15,94 15,982 16,024 16,066 16,108 16,15 16,192 16,234 16,274 16,316 16,358
85080,6389 85098,7972 85189,6351 85207,7934 85207,7934 85298,6081 85280,4498 85316,7664 85298,6081 85334,9479 85425,7626 85462,0792 85552,9171 85552,9171 85534,7356 85552,9171 85680,0484 85661,8901 85661,8901 85770,8863 85789,0446 85770,8863 85861,701 85879,8593 85916,1991 85952,5157 85879,8593 86079,6702 86061,5119 86079,6702 86115,9867 86134,1683 86152,3266 86206,8247 86243,1412 86224,9829 86315,7976 86333,9559 86406,6123 86442,9521
12825,21204 12827,94925 12841,64233 12844,37954 12844,37954 12858,06911 12855,3319 12860,80633 12858,06911 12863,54705 12877,23662 12882,71104 12896,40412 12896,40412 12893,6634 12896,40412 12915,56812 12912,83091 12912,83091 12929,2612 12931,99841 12929,2612 12942,95077 12945,68798 12951,16592 12956,64034 12945,68798 12975,80785 12973,07063 12975,80785 12981,28227 12984,02299 12986,7602 12994,97535 13000,44978 12997,71256 13011,40214 13014,13935 13025,09171 13030,56964
197,5 198 198,5 199 199,5 200 200,5 201 201,5 202 202,5 203 203,5 204 204,5 205 205,5 206 206,5 207 207,5 208 208,5 209 209,5 210 210,5 211 211,5 212 212,5 213 213,5 214 214,5 215 215,5 216 216,5 217
37,15625 37,15625 37,20313 37,21875 37,25 37,23438 37,25 37,25781 37,27344 37,28125 37,3125 37,32031 37,32813 37,33594 37,34375 37,39063 37,39063 37,40625 37,39063 37,44531 37,46094 37,46875 37,46875 37,49219 37,50781 37,53125 37,52344 37,55469 37,55469 37,58594 37,59375 37,60938 37,60938 37,625 37,625 37,67188 37,6875 37,6875 37,69531 37,70313
16,4 16,442 16,484 16,524 16,566 16,606 16,648 16,69 16,732 16,772 16,814 16,856 16,896 16,938 16,98 17,022 17,062 17,104 17,146 17,186 17,228 17,27 17,31 17,352 17,394 17,436 17,476 17,518 17,56 17,6 17,642 17,684 17,724 17,766 17,808 17,848 17,89 17,932 17,974 18,014
86388,454 86388,454 86497,4502 86533,7668 86606,4232 86570,1066 86606,4232 86624,5815 86660,9213 86679,0796 86751,736 86769,8943 86788,0758 86806,2341 86824,3924 86933,3886 86933,3886 86969,7052 86933,3886 87060,5199 87096,8597 87115,018 87115,018 87169,5161 87205,8327 87260,3308 87242,1725 87314,8289 87314,8289 87387,4853 87405,6436 87441,9834 87441,9834 87478,3 87478,3 87587,2962 87623,6127 87623,6127 87641,771 87659,9526
13022,35449 13022,35449 13038,78478 13044,25921 13055,21157 13049,73714 13055,21157 13057,94878 13063,42672 13066,16393 13077,11629 13079,8535 13082,59422 13085,33143 13088,06865 13104,49894 13104,49894 13109,97336 13104,49894 13123,66294 13129,14087 13131,87808 13131,87808 13140,09323 13145,56765 13153,7828 13151,04559 13161,99794 13161,99794 13172,9503 13175,68752 13181,16545 13181,16545 13186,63987 13186,63987 13203,07017 13208,54459 13208,54459 13211,28181 13214,02252
217,5 218 218,5 219 219,5 220 220,5 221 221,5 222 222,5 223 223,5 224 224,5 225 225,5 226 226,5 227 227,5 228 228,5 229 229,5 230 230,5 231 231,5 232 232,5 233 233,5 234 234,5 235 235,5 236 236,5 237
37,71094 37,67969 37,75781 37,76563 37,77344 37,78125 37,79688 37,84375 37,8125 37,84375 37,89063 37,88281 37,89844 37,91406 37,92188 37,9375 37,95313 37,96875 37,96875 37,97656 38,01563 38,02344 38,03125 38,02344 38,03906 38,01563 38,07813 38,07813 38,11719 38,08594 38,13281 38,16406 38,16406 38,15625 38,20313 38,17188 38,23438 38,21875 38,24219 38,24219
18,056 18,098 18,138 18,18 18,222 18,262 18,304 18,346 18,388 18,428 18,47 18,512 18,554 18,594 18,636 18,678 18,718 18,76 18,802 18,842 18,884 18,926 18,968 19,008 19,05 19,092 19,132 19,174 19,216 19,256 19,298 19,34 19,382 19,422 19,464 19,506 19,548 19,588 19,63 19,67
87678,1109 87605,4545 87787,0838 87805,2654 87823,4236 87841,5819 87877,9218 87986,8947 87914,2383 87986,8947 88095,8909 88077,7094 88114,0492 88150,3658 88168,5473 88204,8639 88241,2037 88277,5203 88277,5203 88295,6786 88386,5165 88404,6748 88422,8331 88404,6748 88440,9914 88386,5165 88531,8293 88531,8293 88622,644 88549,9876 88658,9606 88731,617 88731,617 88713,4587 88822,4549 88749,7985 88895,1113 88858,7715 88913,2696 88913,2696
13216,75974 13205,80738 13233,18652 13235,92724 13238,66445 13241,40167 13246,8796 13263,30639 13252,35403 13263,30639 13279,73668 13276,99596 13282,47389 13287,94832 13290,68903 13296,16346 13301,64139 13307,11582 13307,11582 13309,85303 13323,54611 13326,28332 13329,02054 13326,28332 13331,75775 13323,54611 13345,45083 13345,45083 13359,1404 13348,18804 13364,61483 13375,56719 13375,56719 13372,82997 13389,26026 13378,3079 13400,21262 13394,73469 13402,94984 13402,94984
237,5 238 238,5 239 239,5 240 240,5 241 241,5 242 242,5 243 243,5 244 244,5 245 245,5 246 246,5 247 247,5 248 248,5 249 249,5 250 250,5 251 251,5 252 252,5 253 253,5 254 254,5 255 255,5 256 256,5 257
38,26563 38,26563 38,28906 38,29688 38,30469 38,32031 38,33594 38,35156 38,35938 38,35156 38,39063 38,42969 38,39844 38,39844 38,42188 38,4375 38,44531 38,4375 38,46875 38,46094 38,49219 38,49219 38,50781 38,51563 38,5 38,50781 38,54688 38,53906 38,5625 38,58594 38,57031 38,59375 38,60938 38,61719 38,625 38,60156 38,63281 38,64844 38,66406 38,66406
19,712 19,754 19,796 19,836 19,878 19,92 19,962 20,002 20,044 20,086 20,126 20,168 20,21 20,252 20,292 20,334 20,376 20,416 20,458 20,5 20,54 20,582 20,624 20,666 20,706 20,748 20,788 20,83 20,872 20,914 20,956 20,996 21,038 21,078 21,122 21,162 21,204 21,244 21,286 21,328
88967,7677 88967,7677 89022,2425 89040,4241 89058,5824 89094,8989 89131,2388 89167,5553 89185,7369 89167,5553 89258,3933 89349,2079 89276,5516 89276,5516 89331,0497 89367,3662 89385,5245 89367,3662 89440,0226 89421,8643 89494,5207 89494,5207 89530,8373 89549,0188 89512,679 89530,8373 89621,6752 89603,4937 89657,9918 89712,4899 89676,1501 89730,6482 89766,988 89785,1463 89803,3046 89748,8065 89821,4629 89857,8027 89894,1193 89894,1193
13411,16498 13411,16498 13419,37662 13422,11734 13424,85455 13430,32898 13435,80691 13441,28134 13444,02206 13441,28134 13454,97442 13468,66399 13457,71163 13457,71163 13465,92677 13471,4012 13474,13841 13471,4012 13482,35356 13479,61635 13490,5687 13490,5687 13496,04313 13498,78385 13493,30592 13496,04313 13509,73621 13506,99549 13515,21064 13523,42578 13517,94785 13526,16299 13531,64093 13534,37814 13537,11535 13528,90021 13539,85257 13545,3305 13550,80493 13550,80493
257,5 258 258,5 259 259,5 260 260,5 261 261,5 262 262,5 263 263,5 264 264,5 265 265,5 266 266,5 267 267,5 268 268,5 269 269,5 270 270,5 271 271,5 272 272,5 273 273,5 274 274,5 275 275,5 276 276,5 277
38,6875 38,69531 38,69531 38,71875 38,72656 38,74219 38,74219 38,73438 38,75 38,76563 38,76563 38,80469 38,82031 38,78125 38,78125 38,82813 38,82031 38,84375 38,85156 38,85938 38,86719 38,88281 38,91406 38,91406 38,91406 38,86719 38,92969 38,89844 38,95313 38,94531 38,97656 38,95313 38,98438 38,97656 39,02344 39,02344 39,00781 39,02344 39,01563 39,03125
21,37 21,41 21,452 21,494 21,534 21,576 21,618 21,658 21,7 21,742 21,784 21,826 21,866 21,908 21,948 21,99 22,032 22,074 22,114 22,156 22,196 22,238 22,28 22,322 22,364 22,404 22,446 22,488 22,528 22,57 22,61 22,652 22,694 22,736 22,778 22,818 22,86 22,902 22,942 22,984
89948,6174 89966,7757 89966,7757 90021,2738 90039,4321 90075,7719 90075,7719 90057,6136 90093,9302 90130,27 90130,27 90221,0847 90257,4013 90166,5866 90166,5866 90275,5828 90257,4013 90311,8994 90330,0577 90348,2392 90366,3975 90402,7141 90475,3705 90475,3705 90475,3705 90366,3975 90511,7103 90439,0539 90566,2084 90548,0268 90620,6832 90566,2084 90638,8648 90620,6832 90729,6795 90729,6795 90693,3396 90729,6795 90711,5212 90747,8377
13559,02007 13561,75728 13561,75728 13569,97243 13572,70964 13578,18757 13578,18757 13575,45036 13580,92479 13586,40272 13586,40272 13600,09229 13605,56672 13591,87715 13591,87715 13608,30744 13605,56672 13613,78186 13616,51908 13619,2598 13621,99701 13627,47144 13638,42379 13638,42379 13638,42379 13621,99701 13643,90173 13632,94937 13652,11687 13649,37615 13660,32851 13652,11687 13663,06923 13660,32851 13676,7588 13676,7588 13671,28087 13676,7588 13674,02159 13679,49602
277,5 278 278,5 279 279,5 280 280,5 281 281,5 282 282,5 283 283,5 284 284,5 285 285,5 286 286,5 287 287,5 288 288,5 289 289,5 290 290,5 291 291,5 292 292,5 293 293,5 294 294,5 295 295,5 296 296,5 297
39,00781 39,05469 39,0625 39,05469 39,0625 39,09375 39,08594 39,10156 39,11719 39,125 39,125 39,15625 39,15625 39,14844 39,14844 39,17969 39,17188 39,1875 39,1875 39,20313 39,21875 39,20313 39,22656 39,23438 39,25 39,25781 39,26563 39,26563 39,28906 39,28125 39,28125 39,32813 39,29688 39,3125 39,3125 39,34375 39,34375 39,36719 39,38281 39,39844
23,026 23,068 23,108 23,15 23,19 23,232 23,274 23,316 23,356 23,398 23,44 23,482 23,522 23,564 23,606 23,646 23,688 23,73 23,77 23,812 23,854 23,896 23,936 23,978 24,02 24,06 24,102 24,144 24,184 24,226 24,268 24,31 24,35 24,392 24,434 24,474 24,516 24,558 24,6 24,64
90693,3396 90802,3359 90820,4941 90802,3359 90820,4941 90893,1505 90874,9922 90911,3088 90947,6486 90965,8069 90965,8069 91038,4633 91038,4633 91020,305 91020,305 91092,9614 91074,8031 91111,1197 91111,1197 91147,4595 91183,7761 91147,4595 91201,9344 91220,1159 91256,4325 91274,5908 91292,7723 91292,7723 91347,2472 91329,0889 91329,0889 91438,0851 91365,4287 91401,7453 91401,7453 91474,4017 91474,4017 91528,8998 91565,2164 91601,5562
13671,28087 13687,71116 13690,44837 13687,71116 13690,44837 13701,40073 13698,66352 13704,13795 13709,61588 13712,35309 13712,35309 13723,30545 13723,30545 13720,56824 13720,56824 13731,5206 13728,78338 13734,25781 13734,25781 13739,73574 13745,21017 13739,73574 13747,94738 13750,6881 13756,16253 13758,89974 13761,64046 13761,64046 13769,8521 13767,11489 13767,11489 13783,54518 13772,59282 13778,06724 13778,06724 13789,0196 13789,0196 13797,23475 13802,70918 13808,18711
297,5 298 298,5 299 299,5 300 300,5 301 301,5 302 302,5 303 303,5 304 304,5 305 305,5 306 306,5 307 307,5 308 308,5 309 309,5 310 310,5 311 311,5 312 312,5 313 313,5 314 314,5 315 315,5 316 316,5 317
39,36719 39,41406 39,35156 39,40625 39,38281 39,42188 39,42969 39,40625 39,42969 39,41406 39,46094 39,45313 39,48438 39,46875 39,47656 39,49219 39,49219 39,5 39,5 39,53125 39,53906 39,55469 39,53125 39,53125 39,55469 39,5625 39,55469 39,57031 39,57031 39,60938 39,60938 39,61719 39,63281 39,64063 39,63281 39,66406 39,65625 39,625 39,67188 39,65625
24,682 24,724 24,764 24,806 24,848 24,888 24,93 24,972 25,014 25,054 25,096 25,138 25,178 25,22 25,262 25,302 25,344 25,386 25,428 25,468 25,51 25,552 25,594 25,634 25,676 25,718 25,758 25,8 25,842 25,882 25,924 25,966 26,008 26,048 26,09 26,132 26,174 26,214 26,256 26,298
91528,8998 91637,8728 91492,56 91619,7145 91565,2164 91656,0543 91674,2126 91619,7145 91674,2126 91637,8728 91746,869 91728,7107 91801,3671 91765,0273 91783,1856 91819,5254 91819,5254 91837,6837 91837,6837 91910,3401 91928,4984 91964,8382 91910,3401 91910,3401 91964,8382 91982,9965 91964,8382 92001,1548 92001,1548 92091,9927 92091,9927 92110,151 92146,4675 92164,6491 92146,4675 92219,1239 92200,9657 92128,3093 92237,3055 92200,9657
13797,23475 13813,66153 13791,75682 13810,92432 13802,70918 13816,40225 13819,13947 13810,92432 13819,13947 13813,66153 13830,09182 13827,35461 13838,30697 13832,82904 13835,56625 13841,04418 13841,04418 13843,7814 13843,7814 13854,73376 13857,47097 13862,9489 13854,73376 13854,73376 13862,9489 13865,68611 13862,9489 13868,42333 13868,42333 13882,1164 13882,1164 13884,85362 13890,32805 13893,06876 13890,32805 13901,2804 13898,54319 13887,59083 13904,02112 13898,54319
317,5 318 318,5 319 319,5 320 320,5 321 321,5 322 322,5 323 323,5 324 324,5 325 325,5 326 326,5 327 327,5 328 328,5 329 329,5 330 330,5 331 331,5 332 332,5 333 333,5 334 334,5 335 335,5 336 336,5 337
39,69531 39,66406 39,67969 39,67969 39,69531 39,72656 39,72656 39,69531 39,70313 39,71094 39,74219 39,75 39,71875 39,75 39,76563 39,75 39,74219 39,77344 39,75781 39,77344 39,78125 39,82031 39,8125 39,82813 39,8125 39,84375 39,85156 39,85156 39,84375 39,875 39,89844 39,85938 39,85156 39,88281 39,89063 39,89063 39,89063 39,89063 39,91406 39,90625
26,338 26,38 26,42 26,462 26,504 26,546 26,588 26,628 26,67 26,71 26,752 26,794 26,836 26,876 26,918 26,96 27,002 27,042 27,084 27,126 27,166 27,208 27,25 27,29 27,332 27,374 27,416 27,456 27,498 27,54 27,58 27,622 27,664 27,704 27,746 27,788 27,83 27,87 27,912 27,954
92291,7803 92219,1239 92255,4638 92255,4638 92291,7803 92364,4367 92364,4367 92291,7803 92309,9619 92328,1202 92400,7766 92418,9348 92346,2784 92418,9348 92455,2747 92418,9348 92400,7766 92473,4329 92437,0931 92473,4329 92491,5912 92582,4059 92564,2476 92600,5875 92564,2476 92636,904 92655,0623 92655,0623 92636,904 92709,5604 92764,0585 92673,2438 92655,0623 92727,7187 92745,9002 92745,9002 92745,9002 92745,9002 92800,3751 92782,2168
13912,23276 13901,2804 13906,75834 13906,75834 13912,23276 13923,18512 13923,18512 13912,23276 13914,97348 13917,71069 13928,66305 13931,40027 13920,44791 13931,40027 13936,8782 13931,40027 13928,66305 13939,61541 13934,13748 13939,61541 13942,35263 13956,0422 13953,30498 13958,78292 13953,30498 13964,25734 13966,99456 13966,99456 13964,25734 13975,2097 13983,42485 13969,73527 13966,99456 13977,94691 13980,68763 13980,68763 13980,68763 13980,68763 13988,89927 13986,16206
337,5 338 338,5 339 339,5 340 340,5 341 341,5 342 342,5 343 343,5 344 344,5 345 345,5 346 346,5 347 347,5 348 348,5 349 349,5 350 350,5 351 351,5 352 352,5 353 353,5 354 354,5 355 355,5 356 356,5 357
39,92969 39,92188 39,9375 39,92969 39,9375 39,9375 39,94531 39,92969 39,9375 39,96094 39,96094 40 39,96875 40 39,98438 39,99219 40 40,02344 39,99219 40,03906 40,00781 40,01563 40,02344 40,03906 40,04688 40,01563 40,0625 40,01563 40,07813 40,03906 40,0625 40,07031 40,07031 40,05469 40,09375 40,08594 40,08594 40,07031 40,09375 40,10156
27,994 28,036 28,078 28,12 28,16 28,202 28,244 28,284 28,326 28,368 28,408 28,45 28,492 28,534 28,574 28,616 28,658 28,698 28,74 28,782 28,824 28,864 28,906 28,948 28,988 29,03 29,072 29,112 29,154 29,196 29,236 29,278 29,32 29,362 29,402 29,444 29,486 29,528 29,568 29,61
92836,7149 92818,5566 92854,8732 92836,7149 92854,8732 92854,8732 92873,0315 92836,7149 92854,8732 92909,3713 92909,3713 93000,186 92927,5296 93000,186 92963,8694 92982,0277 93000,186 93054,6841 92982,0277 93091,0007 93018,3443 93036,5258 93054,6841 93091,0007 93109,1822 93036,5258 93145,4988 93036,5258 93181,8386 93091,0007 93145,4988 93163,6571 93163,6571 93127,3405 93218,1552 93199,9969 93199,9969 93163,6571 93218,1552 93236,3135
13994,37721 13991,63999 13997,11442 13994,37721 13997,11442 13997,11442 13999,85163 13994,37721 13997,11442 14005,32956 14005,32956 14019,01914 14008,06678 14019,01914 14013,54471 14016,28192 14019,01914 14027,23428 14016,28192 14032,70871 14021,75635 14024,49707 14027,23428 14032,70871 14035,44943 14024,49707 14040,92385 14024,49707 14046,40179 14032,70871 14040,92385 14043,66107 14043,66107 14038,18664 14051,87621 14049,139 14049,139 14043,66107 14051,87621 14054,61343
357,5 358 358,5 359 359,5 360 360,5 361 361,5 362 362,5 363 363,5 364 364,5 365 365,5 366 366,5 367 367,5 368 368,5 369 369,5 370 370,5 371 371,5 372 372,5 373 373,5 374 374,5 375 375,5 376 376,5 377
40,11719 40,09375 40,10938 40,11719 40,10156 40,125 40,13281 40,14844 40,13281 40,14844 40,14063 40,125 40,11719 40,08594 40,04688 39,95313 39,76563 39,23438 37,89844 35,70313 32,9375 32,20313 32,13281 32,26563 32,48438 32,61719 32,78125 32,84375 32,86719 32,79688 32,82031 32,92188 33,03906 33,16406 33,19531 33,22656 33,1875 33,05469 32,9375 33,05469
29,65 29,692 29,734 29,776 29,816 29,858 29,9 29,942 29,982 30,024 30,066 30,106 30,148 30,19 30,232 30,272 30,316 30,358 30,402 30,446 30,488 30,526 30,564 30,604 30,646 30,686 30,728 30,768 30,81 30,85 30,892 30,934 30,974 31,016 31,058 31,098 31,14 31,182 31,224 31,266
93272,6533 93218,1552 93254,495 93272,6533 93236,3135 93290,8116 93308,9699 93345,3097 93308,9699 93345,3097 93327,1514 93290,8116 93272,6533 93199,9969 93109,1822 92891,213 92455,2747 91220,1159 88114,0492 83009,9433 76579,8407 74872,427 74708,9327 75017,7398 75526,3346 75835,1184 76216,5587 76361,8715 76416,3696 76252,8985 76307,3734 76543,5241 76815,9681 77106,5937 77179,2501 77251,9065 77161,0918 76852,308 76579,8407 76852,308
14060,09136 14051,87621 14057,35414 14060,09136 14054,61343 14062,82857 14065,56578 14071,04372 14065,56578 14071,04372 14068,3065 14062,82857 14060,09136 14049,139 14035,44943 14002,59235 13936,8782 13750,6881 13282,47389 12513,07157 11543,78607 11286,40739 11261,76196 11308,31211 11384,97862 11431,52527 11489,02428 11510,92899 11519,14414 11494,50221 11502,71385 11538,31164 11579,38036 11623,18979 11634,14215 11645,09451 11631,40494 11584,85829 11543,78607 11584,85829
377,5 378 378,5 379 379,5 380 380,5 381 381,5 382 382,5 383 383,5 384 384,5 385 385,5 386 386,5 387 387,5 388 388,5 389 389,5 390 390,5 391 391,5 392 392,5 393 393,5 394 394,5 395 395,5 396 396,5 397
33,23438 33,47656 33,71094 34,00781 34,30469 34,57813 34,89063 35,13281 35,42188 35,65625 35,92188 36,10156 36,30469 36,42969 36,53125 36,57813 36,61719 36,65625 36,63281 36,64844 36,66406 36,64844 36,60156 36,66406 36,65625 36,71094 36,74219 36,76563 36,78906 36,77344 36,77344 36,77344 36,74219 36,71875 36,6875 36,625 36,53125 36,48438 36,45313 36,39063
31,308 31,348 31,388 31,43 31,472 31,514 31,554 31,596 31,638 31,68 31,722 31,762 31,804 31,846 31,888 31,928 31,97 32,012 32,054 32,094 32,136 32,178 32,218 32,26 32,302 32,342 32,384 32,426 32,468 32,508 32,55 32,59 32,632 32,674 32,716 32,758 32,8 32,842 32,884 32,926
77270,088 77833,1577 78378,0923 79068,3164 79758,5638 80394,313 81120,877 81683,9466 82356,0357 82900,9471 83518,538 83936,2949 84408,5731 84699,1986 84935,3261 85044,3223 85135,137 85225,9517 85171,4536 85207,7934 85244,11 85207,7934 85098,7972 85244,11 85225,9517 85353,1062 85425,7626 85480,2607 85534,7356 85498,419 85498,419 85498,419 85425,7626 85371,2645 85298,6081 85153,2953 84935,3261 84826,3532 84753,6968 84608,384
11647,83523 11732,71338 11814,85782 11918,90348 12022,95264 12118,78665 12228,31024 12313,18839 12414,50034 12496,64128 12589,73808 12652,71151 12723,9036 12767,71303 12803,30732 12819,73761 12833,42718 12847,11676 12838,90161 12844,37954 12849,85397 12844,37954 12827,94925 12849,85397 12847,11676 12866,28426 12877,23662 12885,45176 12893,6634 12888,18898 12888,18898 12888,18898 12877,23662 12869,02147 12858,06911 12836,1644 12803,30732 12786,88053 12775,92818 12754,02346
397,5 398 398,5 399 399,5 400 400,5 401 401,5 402 402,5 403 403,5 404 404,5 405 405,5 406 406,5 407 407,5 408 408,5 409 409,5 410 410,5 411 411,5 412 412,5 413 413,5 414 414,5 415 415,5 416 416,5 417
36,39063 36,3125 36,28906 36,19531 36,03125 35,76563 35,58594 35,60938 35,72656 35,92188 36,05469 36,16406 36,19531 36,19531 36,16406 36,17188 36,07031 36 35,80469 35,73438 35,59375 35,51563 35,49219 35,60156 35,72656 35,82031 35,8125 35,85938 35,82031 35,8125 35,78125 35,64844 35,57031 35,46094 35,25781 35,05469 34,92969 34,82031 34,69531 34,64063
32,97 33,012 33,054 33,096 33,138 33,182 33,224 33,264 33,306 33,348 33,39 33,432 33,474 33,516 33,56 33,602 33,644 33,686 33,728 33,77 33,814 33,856 33,898 33,94 33,982 34,024 34,066 34,108 34,15 34,192 34,234 34,278 34,32 34,362 34,406 34,448 34,49 34,532 34,574 34,616
84608,384 84426,7314 84372,2332 84154,2641 83772,8238 83155,2561 82737,476 82791,9741 83064,4181 83518,538 83827,3219 84081,6077 84154,2641 84154,2641 84081,6077 84099,7892 83863,6385 83700,1674 83246,0707 83082,5997 82755,6343 82574,0049 82519,5068 82773,7925 83064,4181 83282,3873 83264,229 83373,2252 83282,3873 83264,229 83191,5726 82882,7888 82701,1362 82446,8504 81974,5722 81502,3173 81211,6917 80957,3827 80666,7571 80539,6258
12754,02346 12726,64081 12718,42566 12685,56859 12628,06958 12534,97628 12471,99935 12480,21449 12521,28321 12589,73808 12636,28473 12674,61623 12685,56859 12685,56859 12674,61623 12677,35695 12641,75915 12617,11722 12548,66586 12524,02393 12474,73656 12447,35741 12439,14227 12477,47377 12521,28321 12554,14028 12551,40307 12567,83336 12554,14028 12551,40307 12540,45071 12493,90406 12466,52141 12428,18991 12356,99783 12285,80925 12241,99981 12203,66481 12159,85537 12140,69137
417,5 418 418,5 419 419,5 420 420,5 421 421,5 422 422,5 423 423,5 424 424,5 425 425,5 426 426,5 427 427,5 428 428,5 429 429,5 430 430,5 431 431,5 432 432,5 433 433,5 434 434,5 435 435,5 436 436,5 437
34,625 34,60156 34,53125 34,50781 34,60156 34,70313 34,78906 34,78906 34,70313 34,51563 34,14844 33,63281 33,40625 33,36719 33,41406 33,32031 33,34375 33,25781 33,20313 33,08594 33,05469 33,08594 33,02344 32,9375 32,85938 32,82031 32,71094 32,78125 32,92969 33,16406 33,39063 33,57813 33,71875 33,82813 33,875 33,84375 33,875 33,84375 33,83594 33,85156
34,658 34,7 34,742 34,784 34,826 34,868 34,91 34,952 34,994 35,038 35,08 35,122 35,164 35,206 35,248 35,29 35,332 35,374 35,418 35,46 35,502 35,544 35,586 35,628 35,67 35,712 35,754 35,796 35,838 35,88 35,922 35,962 36,006 36,048 36,09 36,132 36,174 36,218 36,26 36,302
80503,286 80448,7879 80285,3168 80230,8187 80448,7879 80684,9386 80884,7263 80884,7263 80684,9386 80249,0002 79395,2818 78196,4396 77669,6866 77578,8719 77687,8449 77469,8757 77524,3738 77324,5629 77197,4316 76924,9643 76852,308 76924,9643 76779,6516 76579,8407 76398,2113 76307,3734 76053,0876 76216,5587 76561,6824 77106,5937 77633,37 78069,3084 78396,2505 78650,5596 78759,5325 78686,8761 78759,5325 78686,8761 78668,7178 78705,0344
12135,21344 12126,99829 12102,35636 12094,14122 12126,99829 12162,59609 12192,71245 12192,71245 12162,59609 12096,88194 11968,19085 11787,47517 11708,07145 11694,38188 11710,80866 11677,95159 11686,16673 11656,04687 11636,88287 11595,81065 11584,85829 11595,81065 11573,90593 11543,78607 11516,40693 11502,71385 11464,38235 11489,02428 11541,04886 11623,18979 11702,59702 11768,31118 11817,59504 11855,93005 11872,35683 11861,40447 11872,35683 11861,40447 11858,66726 11864,14169
437,5 438
33,85938 33,85156
36,344 36,386
78723,2159 78705,0344
11866,8824 11864,14169
Grafica de Esfuerzo VS alargamiento 100000
esfuerzo (KPa)
80000 60000 40000 20000 0 -10
0 -20000
10
20
30
40
alargamiento (mm)
Grafica de esfuerzo cortante VS alargamiento 16000 14000
esfuerzo cortante (KPa)
12000 10000 8000 6000 4000 2000 0 -10
0 -2000
10
20
alargamiento (mm)
30
40
3.1.1. TABLA DE DATOS DE LA PROBETA 2, VIGA DE ACERO CILINDRICA Tiempo seg 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 6,5 7 7,5 8 8,5 9 9,5 10 10,5 11 11,5 12 12,5 13 13,5 14 14,5 15 15,5 16 16,5 17
Carga kN -0,015625 -0,0078125 0,0078125 0,0234375 0,0078125 0,0625 0,359375 0,671875 0,9453125 1,273438 1,59375 1,859375 2,101563 2,28125 2,640625 2,984375 3,367188 3,75 4,117188 4,523438 4,929688 5,296875 5,6875 6,054688 6,429688 6,789063 7,132813 7,515625 7,835938 8,171875 8,539063 8,875 9,234375 9,554688 9,898438
Alargamiento mm 0 0 0,004 0,024 0,058 0,098 0,14 0,184 0,226 0,27 0,312 0,356 0,398 0,44 0,482 0,524 0,566 0,61 0,652 0,694 0,738 0,78 0,824 0,866 0,908 0,952 0,996 1,038 1,08 1,122 1,166 1,208 1,252 1,294 1,336
esfuerzo Kpa -36,32819766 -18,16409883 18,16409883 54,49229648 18,16409883 145,3127906 835,5485461 1562,112499 2197,855958 2960,749271 3705,476161 4323,055521 4886,143747 5303,916858 6139,465404 6938,685752 7828,727757 8718,767438 9572,481245 10517,01438 11461,54752 12315,25901 13223,46395 14077,17775 14949,0545 15784,60304 16583,82339 17473,86307 18218,59229 18999,64737 19853,36118 20634,41627 21469,96481 22214,69403 23013,91438
esfuerzo cortante KPa -5,42786012 -2,71393006 2,71393006 8,141790181 2,71393006 21,71144048 124,8407828 233,3979852 328,3855373 442,3707735 553,6417323 645,9153543 730,0473599 792,4675776 917,3083604 1036,721283 1169,70403 1302,686429 1430,241315 1571,365679 1712,490042 1840,044581 1975,741084 2103,29597 2233,564613 2358,405396 2477,818319 2610,800718 2722,072024 2838,770843 2966,32573 3083,024548 3207,865331 3319,136637 3438,54956
17,5 18 18,5 19 19,5 20 20,5 21 21,5 22 22,5 23 23,5 24 24,5 25 25,5 26 26,5 27 27,5 28 28,5 29 29,5 30 30,5 31 31,5 32 32,5 33 33,5 34 34,5 35 35,5 36 36,5 37
10,22656 10,53125 10,84375 11,09375 11,35938 11,53906 11,72656 11,86719 11,99219 12,11719 12,25 12,3125 12,46094 12,55469 12,61719 12,67188 12,71875 12,77344 12,82031 12,84375 12,875 12,92969 12,94531 12,96094 12,9375 12,95313 12,90625 12,90625 12,89844 12,94531 12,94531 12,97656 12,96094 12,96875 12,94531 12,98438 12,94531 12,9375 12,96094 12,95313
1,378 1,42 1,464 1,506 1,548 1,592 1,632 1,676 1,718 1,76 1,802 1,844 1,886 1,928 1,97 2,012 2,054 2,094 2,136 2,178 2,22 2,262 2,304 2,346 2,386 2,428 2,47 2,512 2,554 2,596 2,636 2,678 2,72 2,762 2,804 2,846 2,888 2,928 2,97 3,012
23776,79955 24485,20522 25211,76917 25793,02034 26410,61132 26828,36816 27264,30653 27591,27193 27881,89751 28172,5231 28481,30696 28626,61975 28971,74344 29189,71263 29335,02542 29462,17992 29571,15289 29698,3074 29807,28036 29861,77847 29934,43487 30061,58937 30097,90595 30134,24577 30079,74766 30116,08748 30007,09126 30007,09126 29988,93298 30097,90595 30097,90595 30170,56234 30134,24577 30152,40405 30097,90595 30188,74388 30097,90595 30079,74766 30134,24577 30116,08748
3552,53358 3658,377721 3766,934924 3853,780686 3946,056044 4008,47383 4073,608152 4122,46063 4165,883511 4209,306392 4255,442334 4277,153775 4328,719314 4361,286475 4382,997916 4401,996295 4418,278138 4437,276517 4453,55836 4461,701019 4472,556739 4491,555118 4496,981241 4502,410838 4494,26818 4499,697777 4483,412459 4483,412459 4480,699398 4496,981241 4496,981241 4507,836962 4502,410838 4505,1239 4496,981241 4510,553497 4496,981241 4494,26818 4502,410838 4499,697777
37,5 38 38,5 39 39,5 40 40,5 41 41,5 42 42,5 43 43,5 44 44,5 45 45,5 46 46,5 47 47,5 48 48,5 49 49,5 50 50,5 51 51,5 52 52,5 53 53,5 54 54,5 55 55,5 56 56,5 57
12,95313 12,95313 12,95313 12,96094 12,98438 12,97656 12,96094 13 12,94531 12,98438 12,97656 13 12,99219 13,00781 12,94531 13,02344 13,01563 13,02344 13,03125 13,03906 13,0625 13,07031 13,07813 13,07813 13,07813 13,125 13,09375 13,125 13,11719 13,14063 13,11719 13,16406 13,1875 13,25 13,21094 13,21094 13,23438 13,23438 13,27344 13,25
3,054 3,096 3,138 3,178 3,22 3,262 3,304 3,346 3,388 3,43 3,47 3,512 3,554 3,596 3,638 3,68 3,722 3,762 3,804 3,846 3,888 3,93 3,972 4,012 4,054 4,096 4,138 4,18 4,222 4,262 4,304 4,346 4,388 4,43 4,47 4,512 4,554 4,596 4,636 4,678
30116,08748 30116,08748 30116,08748 30134,24577 30188,74388 30170,56234 30134,24577 30225,06045 30097,90595 30188,74388 30170,56234 30225,06045 30206,90216 30243,21874 30097,90595 30279,55856 30261,40027 30279,55856 30297,71685 30315,87513 30370,37324 30388,53153 30406,71306 30406,71306 30406,71306 30515,68603 30443,02964 30515,68603 30497,52775 30552,02585 30497,52775 30606,50071 30660,99882 30806,31161 30715,49693 30715,49693 30769,99504 30769,99504 30860,80972 30806,31161
4499,697777 4499,697777 4499,697777 4502,410838 4510,553497 4507,836962 4502,410838 4515,97962 4496,981241 4510,553497 4507,836962 4515,97962 4513,266559 4518,692682 4496,981241 4524,122279 4521,409217 4524,122279 4526,83534 4529,548402 4537,691061 4540,404122 4543,120658 4543,120658 4543,120658 4559,402501 4548,546781 4559,402501 4556,68944 4564,832098 4556,68944 4572,971283 4581,113942 4602,825382 4589,2566 4589,2566 4597,399259 4597,399259 4610,968041 4602,825382
57,5 58 58,5 59 59,5 60 60,5 61 61,5 62 62,5 63 63,5 64 64,5 65 65,5 66 66,5 67 67,5 68 68,5 69 69,5 70 70,5 71 71,5 72 72,5 73 73,5 74 74,5 75 75,5 76 76,5 77
13,34375 13,28906 13,34375 13,33594 13,375 13,36719 13,35156 13,41406 13,44531 13,42969 13,4375 13,46094 13,48438 13,46094 13,53125 13,49219 13,5625 13,51563 13,5625 13,57813 13,60156 13,59375 13,64844 13,61719 13,63281 13,67969 13,6875 13,70313 13,71094 13,73438 13,72656 13,78906 13,78125 13,78125 13,80469 13,82813 13,84375 13,86719 13,88281 13,88281
4,72 4,762 4,804 4,844 4,886 4,928 4,97 5,012 5,052 5,094 5,136 5,178 5,218 5,26 5,302 5,344 5,386 5,426 5,468 5,51 5,552 5,594 5,636 5,676 5,718 5,76 5,802 5,844 5,884 5,926 5,968 6,01 6,052 6,092 6,134 6,176 6,218 6,26 6,3 6,342
31024,2808 30897,12629 31024,2808 31006,12251 31096,93719 31078,77891 31042,43908 31187,75188 31260,40827 31224,0917 31242,24998 31296,74809 31351,2462 31296,74809 31460,21917 31369,40449 31532,87557 31423,9026 31532,87557 31569,21539 31623,69025 31605,53196 31732,68647 31660,03007 31696,34664 31805,34286 31823,50115 31859,84097 31877,99926 31932,49736 31914,31583 32059,62862 32041,47033 32041,47033 32095,96844 32150,46655 32186,78312 32241,28123 32277,59781 32277,59781
4635,392543 4616,394164 4635,392543 4632,679481 4646,248263 4643,535201 4638,105604 4659,817045 4670,672765 4665,246642 4667,959704 4676,102362 4684,245021 4676,102362 4700,526864 4686,958082 4711,382585 4695,100741 4711,382585 4716,812182 4724,951366 4722,238305 4741,236684 4730,380963 4735,807087 4752,092404 4754,805465 4760,235063 4762,948124 4771,090783 4768,374247 4790,085688 4787,372626 4787,372626 4795,515285 4803,657943 4809,084067 4817,226725 4822,652849 4822,652849
77,5 78 78,5 79 79,5 80 80,5 81 81,5 82 82,5 83 83,5 84 84,5 85 85,5 86 86,5 87 87,5 88 88,5 89 89,5 90 90,5 91 91,5 92 92,5 93 93,5 94 94,5 95 95,5 96 96,5 97
13,90625 13,89844 13,9375 13,96094 14 13,99219 14,01563 14,01563 14,02344 14,03906 14,07031 14,0625 14,07813 14,07813 14,08594 14,10938 14,125 14,14844 14,20313 14,17969 14,16406 14,17969 14,21094 14,23438 14,25 14,25781 14,27344 14,27344 14,29688 14,29688 14,375 14,33594 14,3125 14,35156 14,375 14,39063 14,4375 14,41406 14,45313 14,42969
6,384 6,426 6,466 6,508 6,55 6,592 6,634 6,676 6,716 6,758 6,8 6,842 6,884 6,924 6,966 7,008 7,05 7,09 7,132 7,174 7,216 7,258 7,3 7,34 7,382 7,424 7,466 7,506 7,548 7,59 7,632 7,674 7,714 7,756 7,798 7,84 7,882 7,922 7,964 8,006
32332,09591 32313,93763 32404,75231 32459,25042 32550,0651 32531,90681 32586,40492 32586,40492 32604,56321 32640,87978 32713,53618 32695,37789 32731,71771 32731,71771 32749,876 32804,37411 32840,69068 32895,18879 33022,34329 32967,84519 32931,50536 32967,84519 33040,50158 33094,99969 33131,31626 33149,47455 33185,81437 33185,81437 33240,31248 33240,31248 33421,94184 33331,12716 33276,62905 33367,44373 33421,94184 33458,28167 33567,25463 33512,75653 33603,59446 33549,09635
4830,795507 4828,082446 4841,651227 4849,793886 4863,362668 4860,649606 4868,792265 4868,792265 4871,505327 4876,93145 4887,78717 4885,074108 4890,503705 4890,503705 4893,216767 4901,359426 4906,785549 4914,928208 4933,926586 4925,783928 4920,354331 4925,783928 4936,639648 4944,782307 4950,20843 4952,921491 4958,351088 4958,351088 4966,493747 4966,493747 4993,631311 4980,062529 4971,91987 4985,488652 4993,631311 4999,060908 5015,342751 5007,200093 5020,772348 5012,62969
97,5 98 98,5 99 99,5 100 100,5 101 101,5 102 102,5 103 103,5 104 104,5 105 105,5 106 106,5 107 107,5 108 108,5 109 109,5 110 110,5 111 111,5 112 112,5 113 113,5 114 114,5 115 115,5 116 116,5 117
14,45313 14,45313 14,46094 14,45313 14,51563 14,51563 14,55469 14,50781 14,55469 14,54688 14,59375 14,57813 14,57813 14,59375 14,61719 14,57813 14,67188 14,64063 14,61719 14,61719 14,67188 14,66406 14,67969 14,69531 14,67188 14,70313 14,67969 14,72656 14,76563 14,75781 14,78906 14,79688 14,77344 14,79688 14,78906 14,82031 14,82813 14,83594 14,83594 14,86719
8,048 8,09 8,13 8,172 8,214 8,256 8,298 8,34 8,382 8,424 8,466 8,506 8,548 8,59 8,632 8,674 8,716 8,756 8,8 8,842 8,882 8,924 8,966 9,008 9,05 9,092 9,134 9,176 9,216 9,258 9,3 9,342 9,384 9,426 9,468 9,51 9,552 9,594 9,636 9,678
33603,59446 33603,59446 33621,75274 33603,59446 33748,90725 33748,90725 33839,72193 33730,72571 33839,72193 33821,56364 33930,53661 33894,22004 33894,22004 33930,53661 33985,03472 33894,22004 34112,18922 34039,53283 33985,03472 33985,03472 34112,18922 34094,00769 34130,34751 34166,66408 34112,18922 34184,84562 34130,34751 34239,32048 34330,15841 34311,97687 34384,63327 34402,81481 34348,3167 34402,81481 34384,63327 34457,28966 34475,4712 34493,62949 34493,62949 34566,28588
5020,772348 5020,772348 5023,48541 5020,772348 5042,483789 5042,483789 5056,052571 5039,767253 5056,052571 5053,339509 5069,621352 5064,195229 5064,195229 5069,621352 5077,764011 5064,195229 5096,76239 5085,90667 5077,764011 5077,764011 5096,76239 5094,045855 5099,475452 5104,901575 5096,76239 5107,61811 5099,475452 5115,757295 5129,329551 5126,613015 5137,468736 5140,185271 5132,042612 5140,185271 5137,468736 5148,324456 5151,040991 5153,754053 5153,754053 5164,609773
117,5 118 118,5 119 119,5 120 120,5 121 121,5 122 122,5 123 123,5 124 124,5 125 125,5 126 126,5 127 127,5 128 128,5 129 129,5 130 130,5 131 131,5 132 132,5 133 133,5 134 134,5 135 135,5 136 136,5 137
14,92969 14,88281 14,84375 14,89844 14,90625 14,9375 14,92969 14,98438 14,94531 14,98438 14,99219 14,99219 14,96094 15,03125 15,02344 15,02344 15,03906 15,04688 15,04688 15,07031 15,07813 15,07031 15,10938 15,07031 15,10938 15,125 15,14063 15,11719 15,15625 15,14844 15,20313 15,20313 15,19531 15,21094 15,21875 15,21875 15,25 15,23438 15,23438 15,25
9,718 9,76 9,802 9,844 9,886 9,928 9,97 10,012 10,054 10,096 10,138 10,178 10,22 10,262 10,304 10,346 10,388 10,43 10,47 10,512 10,556 10,596 10,638 10,68 10,722 10,764 10,806 10,848 10,89 10,93 10,972 11,014 11,056 11,098 11,14 11,182 11,224 11,266 11,308 11,348
34711,59867 34602,60246 34511,78777 34638,94228 34657,10056 34729,75696 34711,59867 34838,75318 34747,91525 34838,75318 34856,91146 34856,91146 34784,25507 34947,72615 34929,56786 34929,56786 34965,88443 34984,06597 34984,06597 35038,54083 35056,72236 35038,54083 35129,37876 35038,54083 35129,37876 35165,69533 35202,03515 35147,53705 35238,35173 35220,19344 35347,34794 35347,34794 35329,16641 35365,50623 35383,66452 35383,66452 35456,32091 35420,00434 35420,00434 35456,32091
5186,321214 5170,035896 5156,467114 5175,465493 5178,178555 5189,034275 5186,321214 5205,319592 5191,747337 5205,319592 5208,032654 5208,032654 5197,176934 5221,601436 5218,888374 5218,888374 5224,314497 5227,031033 5227,031033 5235,170218 5237,886753 5235,170218 5248,742473 5235,170218 5248,742473 5254,168597 5259,598194 5251,455535 5265,024317 5262,311255 5281,309634 5281,309634 5278,593099 5284,022696 5286,735757 5286,735757 5297,591478 5292,165354 5292,165354 5297,591478
137,5 138 138,5 139 139,5 140 140,5 141 141,5 142 142,5 143 143,5 144 144,5 145 145,5 146 146,5 147 147,5 148 148,5 149 149,5 150 150,5 151 151,5 152 152,5 153 153,5 154 154,5 155 155,5 156 156,5 157
15,26563 15,29688 15,25781 15,30469 15,32031 15,32813 15,30469 15,40625 15,33594 15,375 15,375 15,39844 15,39844 15,45313 15,41406 15,42969 15,4375 15,41406 15,46094 15,46875 15,50781 15,47656 15,52344 15,50781 15,54688 15,53125 15,55469 15,55469 15,57813 15,58594 15,53906 15,60156 15,61719 15,61719 15,58594 15,625 15,64063 15,65625 15,64063 15,70313
11,39 11,432 11,474 11,516 11,558 11,6 11,642 11,684 11,724 11,766 11,808 11,852 11,892 11,934 11,976 12,018 12,06 12,1 12,144 12,184 12,226 12,268 12,31 12,352 12,394 12,436 12,478 12,52 12,562 12,602 12,644 12,686 12,728 12,77 12,812 12,854 12,896 12,936 12,978 13,02
35492,66074 35565,31713 35474,4792 35583,47542 35619,79199 35637,97353 35583,47542 35819,60289 35656,13181 35746,94649 35746,94649 35801,4446 35801,4446 35928,59911 35837,76118 35874,101 35892,25928 35837,76118 35946,75739 35964,91568 36055,73036 35983,07397 36092,07018 36055,73036 36146,56829 36110,22847 36164,72658 36164,72658 36219,22469 36237,38297 36128,38676 36273,69955 36310,03937 36310,03937 36237,38297 36328,19766 36364,53748 36400,85405 36364,53748 36509,85027
5303,021075 5313,876795 5300,304539 5316,589856 5322,01598 5324,732515 5316,589856 5351,870079 5327,445577 5341,014358 5341,014358 5349,157017 5349,157017 5368,155396 5354,58314 5360,012737 5362,725799 5354,58314 5370,868458 5373,581519 5387,150301 5376,294581 5392,579898 5387,150301 5400,722557 5395,29296 5403,435618 5403,435618 5411,578277 5414,291339 5398,006021 5419,717462 5425,147059 5425,147059 5414,291339 5427,86012 5433,289717 5438,715841 5433,289717 5455,001158
157,5 158 158,5 159 159,5 160 160,5 161 161,5 162 162,5 163 163,5 164 164,5 165 165,5 166 166,5 167 167,5 168 168,5 169 169,5 170 170,5 171 171,5 172 172,5 173 173,5 174 174,5 175 175,5 176 176,5 177
15,69531 15,73438 15,72656 15,72656 15,74219 15,73438 15,77344 15,75 15,78125 15,76563 15,78906 15,80469 15,80469 15,84375 15,85156 15,84375 15,84375 15,85156 15,88281 15,88281 15,875 15,92969 15,92188 15,9375 15,95313 15,9375 15,96875 15,98438 15,98438 16,00781 15,98438 16,01563 16,03125 16,05469 16,03906 16,05469 16,0625 16,0625 16,10156 16,09375
13,062 13,104 13,146 13,188 13,23 13,272 13,312 13,354 13,396 13,44 13,48 13,522 13,564 13,606 13,648 13,69 13,73 13,772 13,816 13,856 13,898 13,94 13,982 14,024 14,066 14,108 14,148 14,19 14,234 14,274 14,316 14,358 14,4 14,442 14,484 14,526 14,568 14,61 14,65 14,692
36491,66873 36582,50667 36564,32513 36564,32513 36600,66495 36582,50667 36673,32135 36618,82324 36691,47963 36655,16306 36709,63792 36745,97774 36745,97774 36836,79242 36854,95071 36836,79242 36836,79242 36854,95071 36927,60711 36927,60711 36909,44882 37036,60332 37018,44504 37054,76161 37091,10143 37054,76161 37127,418 37163,75783 37163,75783 37218,23269 37163,75783 37236,41422 37272,7308 37327,2289 37290,88908 37327,2289 37345,38719 37345,38719 37436,20187 37418,04359
5452,284623 5465,856878 5463,140343 5463,140343 5468,56994 5465,856878 5479,42566 5471,283001 5482,138722 5476,712598 5484,851783 5490,28138 5490,28138 5503,850162 5506,563224 5503,850162 5503,850162 5506,563224 5517,418944 5517,418944 5514,705882 5533,704261 5530,9912 5536,417323 5541,84692 5536,417323 5547,273043 5552,70264 5552,70264 5560,841825 5552,70264 5563,55836 5568,984484 5577,127142 5571,697545 5577,127142 5579,840204 5579,840204 5593,408986 5590,695924
177,5 178 178,5 179 179,5 180 180,5 181 181,5 182 182,5 183 183,5 184 184,5 185 185,5 186 186,5 187 187,5 188 188,5 189 189,5 190 190,5 191 191,5 192 192,5 193 193,5 194 194,5 195 195,5 196 196,5 197
16,10156 16,09375 16,14063 16,10938 16,16406 16,14063 16,17969 16,15625 16,19531 16,17188 16,1875 16,21094 16,24219 16,23438 16,26563 16,24219 16,25 16,24219 16,28906 16,27344 16,28906 16,30469 16,28906 16,32813 16,32813 16,32813 16,35156 16,3125 16,36719 16,35938 16,35938 16,38281 16,40625 16,40625 16,39844 16,45313 16,44531 16,46875 16,48438 16,47656
14,734 14,776 14,818 14,86 14,902 14,944 14,986 15,026 15,068 15,11 15,152 15,194 15,236 15,278 15,32 15,362 15,402 15,444 15,488 15,528 15,57 15,612 15,654 15,696 15,738 15,78 15,82 15,862 15,904 15,946 15,988 16,03 16,072 16,114 16,156 16,196 16,24 16,28 16,322 16,364
37436,20187 37418,04359 37527,0398 37454,38341 37581,51466 37527,0398 37617,85449 37563,35638 37654,17106 37599,6962 37636,01277 37690,51088 37763,16728 37745,00899 37817,66539 37763,16728 37781,32556 37763,16728 37872,14024 37835,82367 37872,14024 37908,48007 37872,14024 37962,97818 37962,97818 37962,97818 38017,45303 37926,63835 38053,79286 38035,63457 38035,63457 38090,10943 38144,60754 38144,60754 38126,44925 38253,60376 38235,42222 38289,92033 38326,26015 38308,07862
5593,408986 5590,695924 5606,981241 5596,125521 5615,120426 5606,981241 5620,550023 5612,407365 5625,976146 5617,836962 5623,263085 5631,405743 5642,261464 5639,548402 5650,404122 5642,261464 5644,974525 5642,261464 5658,543307 5653,117184 5658,543307 5663,972904 5658,543307 5672,115563 5672,115563 5672,115563 5680,254748 5666,685966 5685,684345 5682,971283 5682,971283 5691,110468 5699,253126 5699,253126 5696,540065 5715,538444 5712,821908 5720,964567 5726,394164 5723,677629
197,5 198 198,5 199 199,5 200 200,5 201 201,5 202 202,5 203 203,5 204 204,5 205 205,5 206 206,5 207 207,5 208 208,5 209 209,5 210 210,5 211 211,5 212 212,5 213 213,5 214 214,5 215 215,5 216 216,5 217
16,47656 16,48438 16,48438 16,5 16,5 16,53125 16,50781 16,53125 16,54688 16,54688 16,5625 16,55469 16,53125 16,59375 16,60156 16,625 16,61719 16,60156 16,64063 16,66406 16,64844 16,65625 16,64063 16,67969 16,69531 16,71875 16,72656 16,69531 16,75 16,75781 16,75781 16,75 16,75781 16,78125 16,78906 16,76563 16,78906 16,80469 16,82813 16,82813
16,406 16,446 16,488 16,53 16,572 16,614 16,654 16,696 16,736 16,778 16,82 16,862 16,902 16,944 16,986 17,026 17,068 17,11 17,152 17,192 17,234 17,276 17,316 17,358 17,4 17,44 17,482 17,524 17,566 17,606 17,648 17,69 17,73 17,772 17,814 17,854 17,896 17,938 17,98 18,02
38308,07862 38326,26015 38326,26015 38362,57673 38362,57673 38435,23312 38380,73501 38435,23312 38471,57294 38471,57294 38507,88952 38489,73123 38435,23312 38580,54591 38598,7042 38653,20231 38635,04402 38598,7042 38689,54213 38744,01699 38707,70042 38725,8587 38689,54213 38780,35681 38816,67338 38871,17149 38889,32978 38816,67338 38943,82789 38961,98617 38961,98617 38943,82789 38961,98617 39016,48428 39034,64257 38980,16771 39034,64257 39070,98239 39125,4805 39125,4805
5723,677629 5726,394164 5726,394164 5731,820287 5731,820287 5742,676007 5734,533349 5742,676007 5748,105604 5748,105604 5753,531728 5750,818666 5742,676007 5764,387448 5767,100509 5775,243168 5772,530107 5767,100509 5780,672765 5788,81195 5783,385827 5786,098888 5780,672765 5794,241547 5799,66767 5807,810329 5810,52339 5799,66767 5818,666049 5821,379111 5821,379111 5818,666049 5821,379111 5829,521769 5832,234831 5824,095646 5832,234831 5837,664428 5845,807087 5845,807087
217,5 218 218,5 219 219,5 220 220,5 221 221,5 222 222,5 223 223,5 224 224,5 225 225,5 226 226,5 227 227,5 228 228,5 229 229,5 230 230,5 231 231,5 232 232,5 233 233,5 234 234,5 235 235,5 236 236,5 237
16,84375 16,85938 16,85938 16,86719 16,85156 16,86719 16,89844 16,89844 16,92969 16,9375 16,92969 16,92188 16,96094 16,89844 16,92969 16,96094 16,98438 16,97656 17 16,97656 17,03125 17,02344 17,03906 17,05469 17,04688 17,07031 17,07813 17,07813 17,08594 17,10156 17,07813 17,11719 17,11719 17,14063 17,14844 17,19531 17,19531 17,17188 17,20313 17,22656
18,062 18,104 18,144 18,186 18,228 18,27 18,31 18,352 18,392 18,434 18,476 18,518 18,558 18,6 18,642 18,682 18,724 18,766 18,808 18,848 18,89 18,932 18,972 19,014 19,056 19,098 19,138 19,18 19,22 19,262 19,304 19,346 19,388 19,428 19,47 19,51 19,552 19,594 19,634 19,676
39161,79707 39198,1369 39198,1369 39216,29518 39179,95536 39216,29518 39288,95158 39288,95158 39361,60797 39379,76626 39361,60797 39343,44969 39434,26437 39288,95158 39361,60797 39434,26437 39488,76248 39470,58094 39525,07905 39470,58094 39597,73545 39579,57716 39615,89373 39652,23355 39634,07527 39688,55013 39706,73166 39706,73166 39724,88995 39761,20652 39706,73166 39797,54635 39797,54635 39852,04445 39870,20274 39979,17571 39979,17571 39924,70085 39997,35724 40051,8321
5851,23321 5856,662807 5856,662807 5859,375868 5853,946271 5859,375868 5870,231589 5870,231589 5881,087309 5883,800371 5881,087309 5878,374247 5891,943029 5870,231589 5881,087309 5891,943029 5900,085688 5897,369152 5905,511811 5897,369152 5916,367531 5913,65447 5919,080593 5924,51019 5921,797128 5929,936313 5932,652849 5932,652849 5935,36591 5940,792033 5932,652849 5946,22163 5946,22163 5954,364289 5957,077351 5973,359194 5973,359194 5965,220009 5976,07573 5984,214914
237,5 238 238,5 239 239,5 240 240,5 241 241,5 242 242,5 243 243,5 244 244,5 245 245,5 246 246,5 247 247,5 248 248,5 249 249,5 250 250,5 251 251,5 252 252,5 253 253,5 254 254,5 255 255,5 256 256,5 257
17,22656 17,21875 17,24219 17,25 17,24219 17,23438 17,26563 17,27344 17,29688 17,32031 17,3125 17,32813 17,32813 17,35156 17,33594 17,375 17,36719 17,38281 17,39063 17,42969 17,4375 17,42188 17,4375 17,46094 17,46875 17,47656 17,49219 17,5 17,53125 17,5 17,54688 17,57031 17,57031 17,54688 17,58594 17,60156 17,60156 17,60938 17,64844 17,63281
19,718 19,76 19,8 19,842 19,884 19,926 19,966 20,008 20,048 20,09 20,132 20,174 20,214 20,256 20,298 20,338 20,38 20,422 20,462 20,504 20,546 20,588 20,628 20,67 20,712 20,754 20,794 20,836 20,876 20,918 20,96 21,002 21,042 21,084 21,126 21,166 21,208 21,25 21,29 21,332
40051,8321 40033,67382 40088,17193 40106,33021 40088,17193 40070,01364 40142,67004 40160,82832 40215,32643 40269,80129 40251,643 40287,98283 40287,98283 40342,45768 40306,14111 40396,95579 40378,79751 40415,11408 40433,29562 40524,1103 40542,26858 40505,95201 40542,26858 40596,76669 40614,92498 40633,08327 40669,42309 40687,58138 40760,23777 40687,58138 40796,57759 40851,05245 40851,05245 40796,57759 40887,39227 40923,70885 40923,70885 40941,89038 41032,70507 40996,36524
5984,214914 5981,501853 5989,644511 5992,357573 5989,644511 5986,93145 5997,78717 6000,500232 6008,64289 6016,782075 6014,069013 6019,49861 6019,49861 6027,637795 6022,211672 6035,780454 6033,067392 6038,493516 6041,210051 6054,778833 6057,491894 6052,065771 6057,491894 6065,634553 6068,347615 6071,060676 6076,490273 6079,203335 6090,059055 6079,203335 6095,488652 6103,627837 6103,627837 6095,488652 6109,057434 6114,483557 6114,483557 6117,200093 6130,768874 6125,339277
257,5 258 258,5 259 259,5 260 260,5 261 261,5 262 262,5 263 263,5 264 264,5 265 265,5 266 266,5 267 267,5 268 268,5 269 269,5 270 270,5 271 271,5 272 272,5 273 273,5 274 274,5 275 275,5 276 276,5 277
17,66406 17,66406 17,67969 17,64844 17,70313 17,72656 17,71875 17,73438 17,73438 17,77344 17,76563 17,79688 17,77344 17,80469 17,82813 17,8125 17,83594 17,86719 17,84375 17,875 17,89844 17,89063 17,90625 17,9375 17,92188 17,9375 17,96875 18,00781 17,97656 17,99219 18 18,01563 18,01563 18,03125 18,04688 18,0625 18,07813 18,07813 18,08594 18,10938
21,374 21,416 21,458 21,498 21,54 21,58 21,622 21,664 21,706 21,746 21,788 21,83 21,872 21,912 21,954 21,994 22,038 22,078 22,12 22,16 22,202 22,244 22,284 22,326 22,368 22,41 22,45 22,492 22,534 22,574 22,616 22,658 22,698 22,74 22,782 22,822 22,864 22,906 22,948 22,99
41069,02164 41069,02164 41105,36146 41032,70507 41159,85957 41214,33443 41196,17614 41232,51597 41232,51597 41323,33065 41305,17236 41377,82876 41323,33065 41395,98704 41450,48515 41414,14533 41468,64344 41541,29983 41486,80172 41559,45812 41613,95623 41595,79794 41632,11451 41704,77091 41668,45434 41704,77091 41777,4273 41868,24199 41795,58559 41831,92541 41850,0837 41886,42352 41886,42352 41922,7401 41959,07992 41995,39649 42031,73631 42031,73631 42049,8946 42104,39271
6136,194998 6136,194998 6141,624595 6130,768874 6149,767253 6157,906438 6155,193377 6160,622974 6160,622974 6174,191755 6171,478694 6182,334414 6174,191755 6185,047476 6193,190134 6187,760537 6195,903196 6206,758916 6198,616258 6209,471978 6217,614636 6214,901575 6220,327698 6231,183418 6225,757295 6231,183418 6242,039138 6255,60792 6244,7522 6250,181797 6252,894859 6258,324456 6258,324456 6263,750579 6269,180176 6274,606299 6280,035896 6280,035896 6282,748958 6290,891616
277,5 278 278,5 279 279,5 280 280,5 281 281,5 282 282,5 283 283,5 284 284,5 285 285,5 286 286,5 287 287,5 288 288,5 289 289,5 290 290,5 291 291,5 292 292,5 293 293,5 294 294,5 295 295,5 296 296,5 297
18,11719 18,125 18,125 18,11719 18,14844 18,14063 18,13281 18,14063 18,13281 18,14063 18,14844 18,17188 18,17969 18,17969 18,17969 18,1875 18,21094 18,22656 18,22656 18,21875 18,23438 18,25 18,25 18,23438 18,28125 18,28125 18,28906 18,29688 18,29688 18,3125 18,30469 18,32813 18,32813 18,34375 18,35938 18,36719 18,35938 18,34375 18,35938 18,41406
23,03 23,072 23,112 23,154 23,196 23,236 23,278 23,32 23,362 23,402 23,444 23,486 23,528 23,568 23,61 23,65 23,692 23,734 23,776 23,818 23,858 23,9 23,94 23,982 24,024 24,066 24,106 24,148 24,19 24,23 24,272 24,314 24,354 24,396 24,438 24,48 24,522 24,562 24,604 24,644
42122,551 42140,70928 42140,70928 42122,551 42195,20739 42177,0491 42158,86757 42177,0491 42158,86757 42177,0491 42195,20739 42249,7055 42267,86379 42267,86379 42267,86379 42286,02207 42340,52018 42376,83675 42376,83675 42358,67847 42395,01829 42431,33486 42431,33486 42395,01829 42503,99126 42503,99126 42522,14954 42540,33108 42540,33108 42576,64765 42558,48937 42612,98748 42612,98748 42649,30405 42685,64387 42703,80216 42685,64387 42649,30405 42685,64387 42812,77513
6293,604678 6296,31774 6296,31774 6293,604678 6304,460398 6301,747337 6299,030801 6301,747337 6299,030801 6301,747337 6304,460398 6312,603057 6315,316119 6315,316119 6315,316119 6318,02918 6326,171839 6331,597962 6331,597962 6328,8849 6334,314497 6339,740621 6339,740621 6334,314497 6350,596341 6350,596341 6353,309403 6356,025938 6356,025938 6361,452061 6358,739 6366,881658 6366,881658 6372,307781 6377,737378 6380,45044 6377,737378 6372,307781 6377,737378 6396,732283
297,5 298 298,5 299 299,5 300 300,5 301 301,5 302 302,5 303 303,5 304 304,5 305 305,5 306 306,5 307 307,5 308 308,5 309 309,5 310 310,5 311 311,5 312 312,5 313 313,5 314 314,5 315 315,5 316 316,5 317
18,41406 18,41406 18,42969 18,45313 18,4375 18,45313 18,46094 18,46094 18,46094 18,47656 18,47656 18,46875 18,50781 18,52344 18,50781 18,5625 18,53125 18,55469 18,51563 18,5625 18,58594 18,58594 18,60156 18,59375 18,60156 18,60156 18,61719 18,63281 18,64063 18,60938 18,67969 18,67188 18,67969 18,67188 18,72656 18,72656 18,70313 18,70313 18,72656 18,72656
24,686 24,728 24,77 24,81 24,852 24,894 24,934 24,976 25,018 25,06 25,1 25,142 25,184 25,224 25,266 25,308 25,348 25,39 25,432 25,472 25,514 25,556 25,598 25,638 25,68 25,722 25,762 25,804 25,846 25,886 25,928 25,97 26,012 26,052 26,094 26,136 26,176 26,218 26,26 26,3
42812,77513 42812,77513 42849,11495 42903,61306 42867,27323 42903,61306 42921,77134 42921,77134 42921,77134 42958,08792 42958,08792 42939,92963 43030,74431 43067,08413 43030,74431 43157,89882 43085,24242 43139,74053 43048,92585 43157,89882 43212,39692 43212,39692 43248,7135 43230,55521 43248,7135 43248,7135 43285,05332 43321,36989 43339,55143 43266,89503 43430,36611 43412,20782 43430,36611 43412,20782 43539,33908 43539,33908 43484,86422 43484,86422 43539,33908 43539,33908
6396,732283 6396,732283 6402,161881 6410,304539 6404,874942 6410,304539 6413,017601 6413,017601 6413,017601 6418,443724 6418,443724 6415,730662 6429,299444 6434,729041 6429,299444 6448,297823 6437,442103 6445,584761 6432,01598 6448,297823 6456,440482 6456,440482 6461,866605 6459,153543 6461,866605 6461,866605 6467,296202 6472,722325 6475,438861 6464,58314 6489,007642 6486,294581 6489,007642 6486,294581 6505,289486 6505,289486 6497,150301 6497,150301 6505,289486 6505,289486
317,5 318 318,5 319 319,5 320 320,5 321 321,5 322 322,5 323 323,5 324 324,5 325 325,5 326 326,5 327 327,5 328 328,5 329 329,5 330 330,5 331 331,5 332 332,5 333 333,5 334 334,5 335 335,5 336 336,5 337
18,75 18,75 18,70313 18,77344 18,78906 18,79688 18,78906 18,83594 18,80469 18,82031 18,82813 18,84375 18,84375 18,85938 18,875 18,89063 18,88281 18,92188 18,90625 18,91406 18,92188 18,91406 18,96875 18,89844 18,96094 18,96875 18,97656 19,00781 19 19 19 18,99219 19,02344 19,04688 19,03125 19,03906 19,03125 19,07031 19,0625 19,07813
26,342 26,384 26,426 26,466 26,508 26,55 26,59 26,632 26,674 26,716 26,756 26,798 26,84 26,88 26,922 26,964 27,004 27,046 27,088 27,13 27,17 27,212 27,252 27,294 27,336 27,378 27,42 27,46 27,502 27,544 27,584 27,626 27,668 27,708 27,75 27,792 27,832 27,874 27,916 27,958
43593,83719 43593,83719 43484,86422 43648,3353 43684,65187 43702,83341 43684,65187 43793,64809 43720,99169 43757,30826 43775,4898 43811,80637 43811,80637 43848,1462 43884,46277 43920,80259 43902,62106 43993,45899 43957,11916 43975,27745 43993,45899 43975,27745 44102,43195 43938,96088 44084,27367 44102,43195 44120,59024 44193,24664 44175,08835 44175,08835 44175,08835 44156,93006 44229,58646 44284,08457 44247,74475 44265,90303 44247,74475 44338,55943 44320,40114 44356,74096
6513,432145 6513,432145 6497,150301 6521,574803 6527,000926 6529,717462 6527,000926 6543,286244 6532,430523 6537,856647 6540,573182 6545,999305 6545,999305 6551,428902 6556,855025 6562,284623 6559,568087 6573,140343 6567,710746 6570,423807 6573,140343 6570,423807 6589,422186 6564,997684 6586,709125 6589,422186 6592,135248 6602,990968 6600,277906 6600,277906 6600,277906 6597,564845 6608,420565 6616,563224 6611,133627 6613,846688 6611,133627 6624,702409 6621,989347 6627,418944
337,5 338 338,5 339 339,5 340 340,5 341 341,5 342 342,5 343 343,5 344 344,5 345 345,5 346 346,5 347 347,5 348 348,5 349 349,5 350 350,5 351 351,5 352 352,5 353 353,5 354 354,5 355 355,5 356 356,5 357
19,07031 19,10156 19,07813 19,125 19,10156 19,14063 19,14844 19,13281 19,16406 19,16406 19,16406 19,17969 19,20313 19,19531 19,20313 19,19531 19,22656 19,22656 19,23438 19,19531 19,14844 19,17969 19,13281 19,21875 19,20313 19,22656 19,21094 19,22656 19,20313 19,27344 19,22656 19,25 19,24219 19,22656 19,27344 19,28125 19,28125 19,21875 19,30469 19,3125
27,998 28,04 28,082 28,122 28,164 28,206 28,248 28,288 28,33 28,372 28,412 28,454 28,496 28,536 28,578 28,62 28,662 28,702 28,744 28,786 28,826 28,868 28,91 28,952 28,992 29,034 29,074 29,116 29,158 29,2 29,24 29,282 29,324 29,366 29,406 29,448 29,49 29,53 29,572 29,614
44338,55943 44411,21582 44356,74096 44465,71393 44411,21582 44502,05375 44520,21204 44483,87222 44556,52861 44556,52861 44556,52861 44592,86844 44647,36654 44629,18501 44647,36654 44629,18501 44701,8414 44701,8414 44720,02294 44629,18501 44520,21204 44592,86844 44483,87222 44683,68312 44647,36654 44701,8414 44665,52483 44701,8414 44647,36654 44810,83762 44701,8414 44756,33951 44738,18123 44701,8414 44810,83762 44828,99591 44828,99591 44683,68312 44883,49402 44901,6523
6624,702409 6635,558129 6627,418944 6643,700787 6635,558129 6649,130384 6651,843446 6646,413849 6657,269569 6657,269569 6657,269569 6662,699166 6670,841825 6668,125289 6670,841825 6668,125289 6678,98101 6678,98101 6681,697545 6668,125289 6651,843446 6662,699166 6646,413849 6676,267948 6670,841825 6678,98101 6673,554887 6678,98101 6670,841825 6695,266327 6678,98101 6687,123668 6684,410607 6678,98101 6695,266327 6697,979389 6697,979389 6676,267948 6706,122047 6708,835109
357,5 358 358,5 359 359,5 360 360,5 361 361,5 362 362,5 363 363,5 364 364,5 365 365,5 366 366,5 367 367,5 368 368,5 369 369,5 370 370,5 371 371,5 372 372,5 373 373,5 374 374,5 375 375,5 376 376,5 377
19,3125 19,32031 19,33594 19,34375 19,34375 19,33594 19,35156 19,36719 19,35938 19,39063 19,38281 19,40625 19,42188 19,40625 19,39844 19,46094 19,4375 19,47656 19,40625 19,49219 19,44531 19,46875 19,49219 19,50781 19,5 19,48438 19,51563 19,53125 19,53906 19,53906 19,5625 19,55469 19,57031 19,5625 19,58594 19,57813 19,57813 19,59375 19,61719 19,57813
29,654 29,696 29,738 29,78 29,82 29,862 29,904 29,946 29,986 30,028 30,07 30,112 30,152 30,194 30,234 30,276 30,318 30,36 30,4 30,442 30,484 30,524 30,566 30,608 30,648 30,69 30,732 30,772 30,816 30,856 30,898 30,938 30,98 31,022 31,062 31,104 31,146 31,186 31,228 31,27
44901,6523 44919,81059 44956,15041 44974,3087 44974,3087 44956,15041 44992,46698 45028,80681 45010,64852 45083,30492 45065,12338 45119,62149 45155,96131 45119,62149 45101,4632 45246,77599 45192,27788 45283,09257 45119,62149 45319,43239 45210,43617 45264,93428 45319,43239 45355,74896 45337,59068 45301,2741 45373,9305 45410,24707 45428,40536 45428,40536 45482,90347 45464,74518 45501,06175 45482,90347 45537,40157 45519,24329 45519,24329 45555,55986 45610,05797 45519,24329
6708,835109 6711,54817 6716,977767 6719,690829 6719,690829 6716,977767 6722,403891 6727,833488 6725,120426 6735,976146 6733,259611 6741,40227 6746,831867 6741,40227 6738,689208 6760,400648 6752,25799 6765,826772 6741,40227 6771,256369 6754,971051 6763,11371 6771,256369 6776,682492 6773,96943 6768,543307 6779,399027 6784,825151 6787,538212 6787,538212 6795,680871 6792,967809 6798,393932 6795,680871 6803,823529 6801,110468 6801,110468 6806,536591 6814,67925 6801,110468
377,5 378 378,5 379 379,5 380 380,5 381 381,5 382 382,5 383 383,5 384 384,5 385 385,5 386 386,5 387 387,5 388 388,5 389 389,5 390 390,5 391 391,5 392 392,5 393 393,5 394 394,5 395 395,5 396 396,5 397
19,625 19,63281 19,64063 19,65625 19,65625 19,67188 19,67188 19,66406 19,64844 19,69531 19,70313 19,71094 19,71875 19,72656 19,67188 19,74219 19,75 19,72656 19,75781 19,75 19,77344 19,75781 19,77344 19,75781 19,78906 19,78125 19,8125 19,79688 19,80469 19,8125 19,82813 19,80469 19,82031 19,84375 19,82813 19,84375 19,85156 19,875 19,85938 19,88281
31,312 31,352 31,394 31,436 31,476 31,52 31,56 31,602 31,642 31,684 31,726 31,766 31,808 31,85 31,892 31,932 31,974 32,016 32,056 32,098 32,14 32,18 32,222 32,264 32,306 32,346 32,388 32,43 32,47 32,512 32,554 32,594 32,636 32,678 32,72 32,762 32,804 32,846 32,888 32,93
45628,21626 45646,37454 45664,55608 45700,87265 45700,87265 45737,21247 45737,21247 45719,03094 45682,71437 45791,68733 45809,86887 45828,02716 45846,18544 45864,34373 45737,21247 45900,68355 45918,84184 45864,34373 45937,00012 45918,84184 45973,33995 45937,00012 45973,33995 45937,00012 46009,65652 45991,49823 46064,15463 46027,83806 46045,99634 46064,15463 46100,49445 46045,99634 46082,31291 46136,81102 46100,49445 46136,81102 46154,96931 46209,46742 46173,15085 46227,62571
6817,392311 6820,105373 6822,821908 6828,248031 6828,248031 6833,677629 6833,677629 6830,961093 6825,53497 6841,816813 6844,533349 6847,24641 6849,959472 6852,672534 6833,677629 6858,102131 6860,815192 6852,672534 6863,528254 6860,815192 6868,957851 6863,528254 6868,957851 6863,528254 6874,383974 6871,670912 6882,526633 6877,100509 6879,813571 6882,526633 6887,95623 6879,813571 6885,239694 6893,382353 6887,95623 6893,382353 6896,095415 6904,238073 6898,81195 6906,951135
397,5 398 398,5 399 399,5 400 400,5 401 401,5 402 402,5 403 403,5 404 404,5 405 405,5 406 406,5 407 407,5 408 408,5 409 409,5 410 410,5 411 411,5 412 412,5 413 413,5 414 414,5 415 415,5 416 416,5 417
19,88281 19,89063 19,89844 19,91406 19,91406 19,92188 19,89844 19,9375 19,92188 19,92188 19,9375 19,91406 19,97656 19,96875 19,98438 19,97656 20 19,97656 19,98438 19,99219 19,96094 19,99219 20 20,02344 20 20,05469 20,02344 20,04688 20,03906 20,07031 20,04688 20,0625 20,05469 20,04688 20,08594 20,08594 20,09375 20,07031 20,125 20,09375
32,972 33,014 33,056 33,098 33,14 33,184 33,226 33,268 33,31 33,352 33,394 33,436 33,478 33,52 33,562 33,604 33,648 33,69 33,732 33,774 33,816 33,858 33,9 33,942 33,984 34,028 34,068 34,112 34,154 34,196 34,238 34,28 34,322 34,364 34,406 34,448 34,49 34,534 34,576 34,618
46227,62571 46245,80724 46263,96553 46300,2821 46300,2821 46318,46364 46263,96553 46354,78021 46318,46364 46318,46364 46354,78021 46300,2821 46445,59489 46427,4366 46463,77643 46445,59489 46500,093 46445,59489 46463,77643 46481,93471 46409,27832 46481,93471 46500,093 46554,59111 46500,093 46627,2475 46554,59111 46609,08922 46590,90768 46663,56408 46609,08922 46645,40579 46627,2475 46609,08922 46699,9039 46699,9039 46718,06219 46663,56408 46790,71858 46718,06219
6906,951135 6909,66767 6912,380732 6917,806855 6917,806855 6920,52339 6912,380732 6925,949514 6920,52339 6920,52339 6925,949514 6917,806855 6939,518296 6936,805234 6942,234831 6939,518296 6947,660954 6939,518296 6942,234831 6944,947893 6934,092172 6944,947893 6947,660954 6955,803613 6947,660954 6966,659333 6955,803613 6963,946271 6961,229736 6972,085456 6963,946271 6969,372395 6966,659333 6963,946271 6977,515053 6977,515053 6980,228115 6972,085456 6991,083835 6980,228115
417,5 418 418,5 419 419,5 420 420,5 421 421,5 422 422,5 423 423,5 424 424,5 425 425,5 426 426,5 427 427,5 428 428,5 429 429,5 430 430,5 431 431,5 432 432,5 433 433,5 434 434,5 435 435,5 436 436,5 437
20,11719 20,14063 20,10938 20,11719 20,125 20,15625 20,1875 20,16406 20,16406 20,17969 20,16406 20,19531 20,16406 20,19531 20,19531 20,21094 20,17969 20,21875 20,23438 20,22656 20,21875 20,24219 20,23438 20,28125 20,25 20,25 20,27344 20,25781 20,26563 20,22656 20,28906 20,25781 20,3125 20,28906 20,3125 20,32813 20,30469 20,30469 20,35938 20,32813
34,66 34,702 34,744 34,786 34,828 34,87 34,914 34,956 34,998 35,04 35,082 35,124 35,166 35,208 35,25 35,292 35,336 35,376 35,418 35,462 35,504 35,546 35,588 35,63 35,672 35,714 35,756 35,8 35,842 35,884 35,926 35,968 36,01 36,052 36,094 36,136 36,178 36,22 36,262 36,306
46772,5603 46827,0584 46754,40201 46772,5603 46790,71858 46863,37498 46936,03137 46881,53326 46881,53326 46917,87309 46881,53326 46954,18966 46881,53326 46954,18966 46954,18966 46990,52948 46917,87309 47008,68777 47045,02759 47026,84605 47008,68777 47063,18588 47045,02759 47154,00056 47081,34416 47081,34416 47135,84227 47099,50245 47117,68399 47026,84605 47172,15884 47099,50245 47226,65695 47172,15884 47226,65695 47262,99678 47208,49867 47208,49867 47335,65317 47262,99678
6988,370774 6996,513432 6985,657712 6988,370774 6991,083835 7001,939555 7012,795276 7004,652617 7004,652617 7010,082214 7004,652617 7015,508337 7004,652617 7015,508337 7015,508337 7020,937934 7010,082214 7023,650996 7029,080593 7026,364057 7023,650996 7031,793654 7029,080593 7045,362436 7034,506716 7034,506716 7042,649375 7037,219778 7039,936313 7026,364057 7048,075498 7037,219778 7056,218157 7048,075498 7056,218157 7061,647754 7053,505095 7053,505095 7072,503474 7061,647754
437,5 438 438,5 439 439,5 440 440,5 441 441,5 442 442,5 443 443,5 444 444,5 445 445,5 446 446,5 447 447,5 448 448,5 449 449,5 450 450,5 451 451,5 452 452,5 453 453,5 454 454,5 455 455,5 456 456,5 457
20,32031 20,35938 20,33594 20,34375 20,34375 20,38281 20,35156 20,38281 20,375 20,38281 20,39844 20,41406 20,42188 20,41406 20,39063 20,42188 20,42969 20,45313 20,48438 20,44531 20,5 20,44531 20,47656 20,46094 20,46875 20,46094 20,48438 20,48438 20,5 20,48438 20,50781 20,50781 20,53125 20,52344 20,50781 20,53906 20,53125 20,54688 20,50781 20,55469
36,348 36,39 36,432 36,474 36,516 36,558 36,6 36,642 36,684 36,726 36,77 36,812 36,854 36,896 36,938 36,98 37,022 37,064 37,106 37,148 37,192 37,234 37,276 37,318 37,36 37,402 37,444 37,486 37,528 37,57 37,612 37,656 37,698 37,74 37,782 37,824 37,866 37,908 37,95 37,992
47244,81524 47335,65317 47281,15506 47299,31335 47299,31335 47390,12803 47317,47163 47390,12803 47371,96974 47390,12803 47426,46785 47462,78443 47480,96596 47462,78443 47408,30957 47480,96596 47499,12425 47553,62236 47626,27875 47535,44082 47662,59533 47535,44082 47608,09722 47571,78064 47589,93893 47571,78064 47626,27875 47626,27875 47662,59533 47626,27875 47680,75361 47680,75361 47735,25172 47717,09343 47680,75361 47753,41001 47735,25172 47771,59154 47680,75361 47789,74983
7058,931218 7072,503474 7064,360815 7067,073877 7067,073877 7080,642659 7069,786938 7080,642659 7077,929597 7080,642659 7086,072256 7091,498379 7094,214914 7091,498379 7083,359194 7094,214914 7096,927976 7105,070635 7115,926355 7102,354099 7121,352478 7102,354099 7113,209819 7107,783696 7110,496758 7107,783696 7115,926355 7115,926355 7121,352478 7115,926355 7124,06554 7124,06554 7132,208198 7129,495137 7124,06554 7134,92126 7132,208198 7137,637795 7124,06554 7140,350857
457,5 458 458,5 459 459,5 460 460,5 461 461,5 462 462,5 463 463,5 464 464,5 465 465,5 466 466,5 467 467,5 468 468,5 469 469,5 470 470,5 471 471,5 472 472,5 473 473,5 474 474,5 475 475,5 476 476,5 477
20,53906 20,5625 20,5625 20,58594 20,58594 20,57813 20,58594 20,57031 20,59375 20,58594 20,60156 20,60156 20,63281 20,58594 20,63281 20,59375 20,625 20,625 20,625 20,64844 20,61719 20,64844 20,64844 20,66406 20,66406 20,69531 20,67969 20,69531 20,69531 20,71875 20,71875 20,6875 20,71094 20,70313 20,71094 20,70313 20,71875 20,71875 20,73438 20,71875
38,034 38,076 38,12 38,162 38,204 38,246 38,288 38,33 38,372 38,414 38,456 38,498 38,54 38,584 38,626 38,668 38,71 38,752 38,794 38,836 38,878 38,92 38,962 39,006 39,048 39,09 39,132 39,174 39,216 39,258 39,3 39,342 39,386 39,426 39,468 39,512 39,554 39,596 39,638 39,68
47753,41001 47807,90812 47807,90812 47862,40622 47862,40622 47844,24794 47862,40622 47826,0664 47880,56451 47862,40622 47898,7228 47898,7228 47971,37919 47862,40622 47971,37919 47880,56451 47953,22091 47953,22091 47953,22091 48007,71902 47935,06262 48007,71902 48007,71902 48044,03559 48044,03559 48116,69198 48080,37541 48116,69198 48116,69198 48171,19009 48171,19009 48098,5337 48153,03181 48134,87352 48153,03181 48134,87352 48171,19009 48171,19009 48207,52992 48171,19009
7134,92126 7143,063918 7143,063918 7151,206577 7151,206577 7148,493516 7151,206577 7145,77698 7153,919639 7151,206577 7156,6327 7156,6327 7167,488421 7151,206577 7167,488421 7153,919639 7164,775359 7164,775359 7164,775359 7172,918018 7162,062297 7172,918018 7172,918018 7178,344141 7178,344141 7189,199861 7183,773738 7189,199861 7189,199861 7197,34252 7197,34252 7186,486799 7194,629458 7191,916396 7194,629458 7191,916396 7197,34252 7197,34252 7202,772117 7197,34252
477,5 478 478,5 479 479,5 480 480,5 481 481,5 482 482,5 483 483,5 484 484,5 485 485,5 486 486,5 487 487,5 488 488,5 489 489,5 490 490,5 491 491,5 492 492,5 493 493,5 494 494,5 495 495,5 496 496,5 497
20,75781 20,74219 20,77344 20,74219 20,75781 20,76563 20,76563 20,75781 20,77344 20,78125 20,75781 20,76563 20,78906 20,78906 20,79688 20,82813 20,8125 20,82813 20,82031 20,83594 20,82031 20,85156 20,83594 20,83594 20,79688 20,84375 20,85938 20,82813 20,86719 20,80469 20,85938 20,89063 20,89844 20,86719 20,90625 20,85156 20,92969 20,90625 20,90625 20,89063
39,722 39,764 39,806 39,848 39,89 39,934 39,976 40,018 40,06 40,102 40,144 40,186 40,228 40,27 40,314 40,356 40,398 40,44 40,482 40,524 40,566 40,608 40,65 40,692 40,734 40,778 40,82 40,862 40,904 40,946 40,988 41,03 41,072 41,114 41,156 41,198 41,242 41,284 41,326 41,368
48262,00477 48225,6882 48298,3446 48225,6882 48262,00477 48280,18631 48280,18631 48262,00477 48298,3446 48316,50288 48262,00477 48280,18631 48334,66117 48334,66117 48352,84271 48425,4991 48389,15928 48425,4991 48407,31756 48443,65739 48407,31756 48479,97396 48443,65739 48443,65739 48352,84271 48461,81567 48498,1555 48425,4991 48516,31378 48371,00099 48498,1555 48570,81189 48588,97018 48516,31378 48607,12846 48479,97396 48661,62657 48607,12846 48607,12846 48570,81189
7210,911302 7205,485178 7216,340899 7205,485178 7210,911302 7213,627837 7213,627837 7210,911302 7216,340899 7219,05396 7210,911302 7213,627837 7221,767022 7221,767022 7224,483557 7235,339277 7229,90968 7235,339277 7232,622742 7238,052339 7232,622742 7243,478462 7238,052339 7238,052339 7224,483557 7240,765401 7246,194998 7235,339277 7248,908059 7227,196619 7246,194998 7257,050718 7259,76378 7248,908059 7262,476841 7243,478462 7270,6195 7262,476841 7262,476841 7257,050718
497,5 498 498,5 499 499,5 500 500,5 501 501,5 502 502,5 503 503,5 504 504,5 505 505,5 506 506,5 507 507,5 508 508,5 509 509,5 510 510,5 511 511,5 512 512,5 513 513,5 514 514,5 515 515,5 516 516,5 517
20,91406 20,95313 20,9375 20,92969 20,91406 20,95313 20,89844 21 20,92188 20,9375 20,94531 20,95313 20,95313 20,9375 20,96875 20,96875 20,97656 20,96875 20,98438 20,94531 20,98438 20,9375 20,99219 21,01563 20,99219 21 21,02344 21 20,96875 21,02344 21,03125 21,03906 21,00781 21,05469 21,02344 21,01563 21,05469 21,04688 21,03906 21,03125
41,41 41,452 41,494 41,536 41,578 41,62 41,662 41,706 41,748 41,79 41,832 41,874 41,916 41,958 42 42,042 42,084 42,128 42,17 42,212 42,254 42,296 42,338 42,38 42,422 42,464 42,506 42,55 42,592 42,634 42,676 42,718 42,76 42,802 42,844 42,886 42,928 42,97 43,012 43,056
48625,28675 48716,12468 48679,78486 48661,62657 48625,28675 48716,12468 48588,97018 48825,09765 48643,46829 48679,78486 48697,94315 48716,12468 48716,12468 48679,78486 48752,44125 48752,44125 48770,59954 48752,44125 48788,78108 48697,94315 48788,78108 48679,78486 48806,93936 48861,43747 48806,93936 48825,09765 48879,59576 48825,09765 48752,44125 48879,59576 48897,75405 48915,91233 48843,25594 48952,25215 48879,59576 48861,43747 48952,25215 48934,09387 48915,91233 48897,75405
7265,189903 7278,762158 7273,332561 7270,6195 7265,189903 7278,762158 7259,76378 7295,044002 7267,906438 7273,332561 7276,045623 7278,762158 7278,762158 7273,332561 7284,188282 7284,188282 7286,901343 7284,188282 7289,617879 7276,045623 7289,617879 7273,332561 7292,33094 7300,473599 7292,33094 7295,044002 7303,18666 7295,044002 7284,188282 7303,18666 7305,899722 7308,612784 7297,757063 7314,042381 7303,18666 7300,473599 7314,042381 7311,329319 7308,612784 7305,899722
517,5 518 518,5 519 519,5 520 520,5 521 521,5 522 522,5 523 523,5 524 524,5 525 525,5 526 526,5 527 527,5 528 528,5 529 529,5 530 530,5 531 531,5 532 532,5 533 533,5 534 534,5 535 535,5 536 536,5 537
21,0625 21,05469 21,0625 21,04688 21,07031 21,07031 21,07813 21,07031 21,08594 21,09375 21,08594 21,10156 21,10156 21,10156 21,10938 21,10156 21,10938 21,10938 21,11719 21,11719 21,11719 21,14063 21,14844 21,16406 21,125 21,13281 21,16406 21,15625 21,16406 21,16406 21,16406 21,17188 21,1875 21,17969 21,20313 21,1875 21,17969 21,1875 21,21094 21,1875
43,098 43,14 43,182 43,224 43,266 43,308 43,35 43,392 43,434 43,478 43,52 43,562 43,604 43,646 43,688 43,73 43,772 43,814 43,856 43,9 43,942 43,984 44,026 44,068 44,11 44,152 44,194 44,236 44,278 44,32 44,362 44,404 44,448 44,49 44,532 44,574 44,616 44,658 44,7 44,744
48970,41044 48952,25215 48970,41044 48934,09387 48988,56873 48988,56873 49006,75026 48988,56873 49024,90855 49043,06684 49024,90855 49061,22512 49061,22512 49061,22512 49079,40666 49061,22512 49079,40666 49079,40666 49097,56495 49097,56495 49097,56495 49152,06305 49170,22134 49206,53791 49115,72323 49133,88152 49206,53791 49188,37963 49206,53791 49206,53791 49206,53791 49224,71945 49261,03602 49242,87774 49297,37584 49261,03602 49242,87774 49261,03602 49315,53413 49261,03602
7316,755442 7314,042381 7316,755442 7311,329319 7319,468504 7319,468504 7322,185039 7319,468504 7324,898101 7327,611163 7324,898101 7330,324224 7330,324224 7330,324224 7333,04076 7330,324224 7333,04076 7333,04076 7335,753821 7335,753821 7335,753821 7343,89648 7346,609541 7352,035665 7338,466883 7341,179944 7352,035665 7349,322603 7352,035665 7352,035665 7352,035665 7354,7522 7360,178323 7357,465262 7365,60792 7360,178323 7357,465262 7360,178323 7368,320982 7360,178323
537,5 538 538,5 539 539,5 540 540,5 541 541,5 542 542,5 543 543,5 544 544,5 545 545,5 546 546,5 547 547,5 548 548,5 549 549,5 550 550,5 551 551,5 552 552,5 553 553,5 554 554,5 555 555,5 556 556,5 557
21,21875 21,21094 21,21094 21,21875 21,21094 21,19531 21,19531 21,25781 21,20313 21,23438 21,21094 21,21875 21,22656 21,23438 21,25 21,25 21,20313 21,28125 21,25 21,27344 21,25781 21,26563 21,28906 21,26563 21,27344 21,28125 21,29688 21,28125 21,26563 21,28125 21,28906 21,3125 21,30469 21,3125 21,29688 21,3125 21,32031 21,32813 21,28906 21,33594
44,784 44,826 44,87 44,912 44,954 44,996 45,038 45,08 45,122 45,164 45,206 45,248 45,292 45,334 45,376 45,418 45,46 45,502 45,544 45,586 45,628 45,67 45,712 45,754 45,798 45,84 45,882 45,924 45,966 46,008 46,05 46,092 46,134 46,178 46,218 46,262 46,304 46,346 46,388 46,43
49333,69242 49315,53413 49315,53413 49333,69242 49315,53413 49279,19431 49279,19431 49424,5071 49297,37584 49370,03224 49315,53413 49333,69242 49351,8507 49370,03224 49406,34881 49406,34881 49297,37584 49479,00521 49406,34881 49460,84692 49424,5071 49442,68864 49497,16349 49442,68864 49460,84692 49479,00521 49515,34503 49479,00521 49442,68864 49479,00521 49497,16349 49551,6616 49533,50332 49551,6616 49515,34503 49551,6616 49569,81989 49588,00143 49497,16349 49606,15971
7371,034044 7368,320982 7368,320982 7371,034044 7368,320982 7362,891385 7362,891385 7384,602825 7365,60792 7376,463641 7368,320982 7371,034044 7373,747105 7376,463641 7381,889764 7381,889764 7365,60792 7392,745484 7381,889764 7390,032422 7384,602825 7387,319361 7395,458546 7387,319361 7390,032422 7392,745484 7398,175081 7392,745484 7387,319361 7392,745484 7395,458546 7403,601204 7400,888143 7403,601204 7398,175081 7403,601204 7406,314266 7409,030801 7395,458546 7411,743863
557,5 558 558,5 559 559,5 560 560,5 561 561,5 562 562,5 563 563,5 564 564,5 565 565,5 566 566,5 567 567,5 568 568,5 569 569,5 570 570,5 571 571,5 572 572,5 573 573,5 574 574,5 575 575,5 576 576,5 577
21,3125 21,34375 21,32813 21,35938 21,33594 21,34375 21,32813 21,33594 21,29688 21,36719 21,35938 21,36719 21,39063 21,35156 21,375 21,40625 21,36719 21,35156 21,38281 21,375 21,39844 21,39063 21,39844 21,38281 21,40625 21,42188 21,38281 21,41406 21,40625 21,42188 21,40625 21,4375 21,40625 21,44531 21,42969 21,4375 21,39844 21,4375 21,44531 21,46094
46,472 46,514 46,556 46,598 46,642 46,684 46,726 46,768 46,81 46,852 46,894 46,936 46,978 47,02 47,062 47,106 47,148 47,19 47,232 47,274 47,316 47,358 47,4 47,442 47,484 47,528 47,57 47,612 47,654 47,696 47,738 47,78 47,822 47,864 47,906 47,948 47,992 48,034 48,076 48,118
49551,6616 49624,318 49588,00143 49660,65782 49606,15971 49624,318 49588,00143 49606,15971 49515,34503 49678,81611 49660,65782 49678,81611 49733,31422 49642,47628 49696,97439 49769,63079 49678,81611 49642,47628 49715,13268 49696,97439 49751,4725 49733,31422 49751,4725 49715,13268 49769,63079 49805,97061 49715,13268 49787,78908 49769,63079 49805,97061 49769,63079 49842,28718 49769,63079 49860,44547 49824,1289 49842,28718 49751,4725 49842,28718 49860,44547 49896,78529
7403,601204 7414,456925 7409,030801 7419,886522 7411,743863 7414,456925 7409,030801 7411,743863 7398,175081 7422,599583 7419,886522 7422,599583 7430,742242 7417,169986 7425,312645 7436,168365 7422,599583 7417,169986 7428,025706 7425,312645 7433,455303 7430,742242 7433,455303 7428,025706 7436,168365 7441,597962 7428,025706 7438,881427 7436,168365 7441,597962 7436,168365 7447,024085 7436,168365 7449,737147 7444,311024 7447,024085 7433,455303 7447,024085 7449,737147 7455,166744
577,5 578 578,5 579 579,5 580 580,5 581 581,5 582 582,5 583 583,5 584 584,5 585 585,5 586 586,5 587 587,5 588 588,5 589 589,5 590 590,5 591 591,5 592 592,5 593 593,5 594 594,5 595 595,5 596 596,5 597
21,45313 21,45313 21,41406 21,45313 21,45313 21,41406 21,42188 21,46875 21,46875 21,46875 21,46875 21,47656 21,47656 21,49219 21,45313 21,46875 21,46094 21,48438 21,46094 21,47656 21,49219 21,50781 21,51563 21,46875 21,49219 21,51563 21,52344 21,51563 21,49219 21,52344 21,52344 21,53125 21,52344 21,52344 21,52344 21,57031 21,55469 21,5 21,52344 21,54688
48,16 48,202 48,244 48,286 48,328 48,37 48,412 48,456 48,498 48,54 48,582 48,624 48,666 48,708 48,75 48,792 48,834 48,878 48,92 48,962 49,004 49,046 49,088 49,13 49,172 49,214 49,256 49,298 49,342 49,384 49,426 49,468 49,51 49,552 49,594 49,636 49,678 49,722 49,762 49,806
49878,62701 49878,62701 49787,78908 49878,62701 49878,62701 49787,78908 49805,97061 49914,94358 49914,94358 49914,94358 49914,94358 49933,10187 49933,10187 49969,44169 49878,62701 49914,94358 49896,78529 49951,2834 49896,78529 49933,10187 49969,44169 50005,75826 50023,9398 49914,94358 49969,44169 50023,9398 50042,09808 50023,9398 49969,44169 50042,09808 50042,09808 50060,25637 50042,09808 50042,09808 50042,09808 50151,07105 50114,75448 49987,59998 50042,09808 50096,59619
7452,453682 7452,453682 7438,881427 7452,453682 7452,453682 7438,881427 7441,597962 7457,879805 7457,879805 7457,879805 7457,879805 7460,592867 7460,592867 7466,022464 7452,453682 7457,879805 7455,166744 7463,309403 7455,166744 7460,592867 7466,022464 7471,448587 7474,165123 7457,879805 7466,022464 7474,165123 7476,878184 7474,165123 7466,022464 7476,878184 7476,878184 7479,591246 7476,878184 7476,878184 7476,878184 7493,160028 7487,733905 7468,735526 7476,878184 7485,020843
597,5 598 598,5 599 599,5 600 600,5 601 601,5 602 602,5 603 603,5 604 604,5 605 605,5 606 606,5 607 607,5 608 608,5 609 609,5 610 610,5 611 611,5 612 612,5 613 613,5 614 614,5 615 615,5 616 616,5 617
21,54688 21,54688 21,5625 21,52344 21,55469 21,54688 21,5625 21,55469 21,58594 21,57031 21,57031 21,57031 21,57813 21,57031 21,5625 21,57813 21,58594 21,61719 21,61719 21,59375 21,60938 21,60938 21,60938 21,60938 21,60938 21,60156 21,61719 21,64063 21,61719 21,64063 21,63281 21,60938 21,64063 21,61719 21,64063 21,63281 21,65625 21,63281 21,65625 21,64844
49,848 49,89 49,932 49,974 50,016 50,058 50,1 50,142 50,186 50,228 50,268 50,312 50,354 50,396 50,438 50,48 50,522 50,564 50,606 50,65 50,692 50,734 50,776 50,818 50,86 50,902 50,944 50,986 51,028 51,07 51,114 51,156 51,198 51,24 51,282 51,324 51,366 51,408 51,45 51,492
50096,59619 50096,59619 50132,91277 50042,09808 50114,75448 50096,59619 50132,91277 50114,75448 50187,41087 50151,07105 50151,07105 50151,07105 50169,25259 50151,07105 50132,91277 50169,25259 50187,41087 50260,06727 50260,06727 50205,56916 50241,90898 50241,90898 50241,90898 50241,90898 50241,90898 50223,72745 50260,06727 50314,56538 50260,06727 50314,56538 50296,38384 50241,90898 50314,56538 50260,06727 50314,56538 50296,38384 50350,88195 50296,38384 50350,88195 50332,72367
7485,020843 7485,020843 7490,446966 7476,878184 7487,733905 7485,020843 7490,446966 7487,733905 7498,589625 7493,160028 7493,160028 7493,160028 7495,876563 7493,160028 7490,446966 7495,876563 7498,589625 7509,445345 7509,445345 7501,302686 7506,732283 7506,732283 7506,732283 7506,732283 7506,732283 7504,015748 7509,445345 7517,588004 7509,445345 7517,588004 7514,871468 7506,732283 7517,588004 7509,445345 7517,588004 7514,871468 7523,014127 7514,871468 7523,014127 7520,301065
617,5
21,6875
51,534
50423,53835
7533,869847
Grafica de Esfuerzo VS alargamiento 60000 50000
esfuerzo (KPa)
40000 30000 20000 10000 0 -10
0
10
-10000
20
30
40
50
60
alargamiento (mm)
Grafica de Esfuerzo cortante VS alargamiento 8000
Esfuerzo cortante (KPa)
7000 6000 5000 4000 3000 2000 1000 0 -1000
0
200
400
600
800
alargamiento (mm)
1000
1200
1400
4. CONCLUSIONES:
El modulo de rigidez de dos vigas similares, variara si a una de ellas se le hace un recubrimiento diferente. Al hacer una configuración adecuada con materiales que por sí solos son débiles, se pueden lograr módulos de rigidez los suficientemente grandes como para ser aprovechados en la construcción a baja escala. A la hora de manipular los datos arrojados por los equipos algunos son más manejables que otros como es el caso de los arrojados por las galgas cuyos datos generan dudas sobre su utilidad y la forma de aprovecharlos. Como fue evidente en el laboratorio no se necesita un esfuerzo demasiado grande para tener disponible un maquina donde se puedan hacer ensayos de torsión. Es la falta de recursos tanto económicos, intelectuales, así como la disponibilidad de tiempo para crear un dispositivo sencillo pero preciso.
5. RECOMENDACIONES
Antes de aplicar la primera carga, revisar que las probetas estén bien sujetas al dispositivo de agarre de la maquina universal de ensayos. Llevar las probetas previamente medidas, marcadas, y con las respectivas formas, para garantizar una toma de datos exacta y rápida. Revisar que las probetas no posean mal formaciones hechas previamente. Hacer los montajes respectivos con alta precisión para evitar errores en la toma de datos.
6. BIBLIOGRAFIA
Andrew Pytel, Ferdinand L. Singer, “Resistencia de Materiales”, 4ª edición, Nueva York, Harla, 1982, 615p, ISBN: 968-6356-13-4.
