18

1.028,084 298,402,9

19 1.145488 350,363,9

.055,0524

407,926,2

.067,530,0

.317,309,8.037,981,82.002,292,79
383,944,8 .050,527,93 .003,356,04
456,926,1065,562,22 .004,751,80

536,253,6 083,305,81006,542,96

.621,927,2.103,978,4

.713,947,1.127,798,5

812,313,1154,982,8

.917,0254185,746,4

,585,902,6

.658,237,9
736,190,1

.008,797,69

011,589,56

014,997,39

.019,105,39

Point
D2

D2

.317,309,8.024,204,82 0,935,87
.383,944,8.032,209,80.00 1,370,09
456,926,104 1,807,40.00 1,940,23
.536,253,6 .053,141,05 .002,672,07
621,927,2.066,353,85.003,593,57
713,947,1.081,588,50.004,734,94
812,313,1.098,987,31.006,128,56

.917,0254.118,692,1 .007,809,11

.024,002,88 1.028,084 .140,844,4
.029,784,5 1.145,488 .165,585,0
.036,549,8 1.269,239 193,054,3
.044,404,3 1.399,336
053,457,8 1.535,780
.063,824,8 1.678,569
.075,626,3 1.827,705
.088,986,9 1,983,186
104,036,9 2.145,014
.120,910.9 2.313,189
139,749,0 2,487,709
160,695,6 2.668,576

044 382,88 1.028,084 ,220,302,8 1.145,488 258,863,5 20 1.269,239 1.269,239 .301,638,0 21 1.399,336 ,471,349,0 .082,007,2 1.399,336 348,834,0 22 1.535,780 540.886,3 .098,683,3 1.535,780 400,656,6 23 1.678,569 .616,786,0 .117,766,2 1.678,569 457,308,8 24 1.827,705 .699,290,5 139,473,3 1.827,705 ,5 18,991,5 25 1.983.186 .788.635,8 164,030,8 1.983.186 26 2.145,014 ,885,051,9 191,671.2 2.145.014 27 2.313,189 .988,76 1,8 222,636,6 2.313,189 28 2.487,709 1.099,982 257,176,9 2.487,709 819,949,3 29 2.668,576 1.218,922 ,295,549,8 2.668,576 .909,702,8 30 2.855,788 1.345,783 .338,020,1 2.855,788 1.005,635 183,900,0 2.855,788 31 3.049,347 1,480,760 .384.860,3 3.049,347 1.107.926 209,516,1 3.049.347 32 3.249.252 1.624,039 436,350,2 3.249,252 1.216,755 33 3.455,504 1,775,803 492,776,8 3.455,504 1.332,296 34 3.668,101 1.936,218 554,433,4 3.668,101 1,454,721 35 3.887,045 2.105,448 .621,620,3 3.887,045 1.584,197 36 4.1 12,335 2.283.648 .694,644,0 4.112,335 1,720,888 37 4.343,971 2,470,963 773,817,7 4.343.971 1.864,955 38 4.581,954 2.667,528 859,459,8 4.581,954 2.016,556 39 4.826.282 2.873,472 .951,894,9 4.826.282 2.175.842 40 5.076,958 3.088,913 1.051,453 5.076,958 2.342,964 41 5.333,978 3,313,960 1.158,470 5.333,978 2.518,066 42 5.597,345 3.548,711 1.273,286 5.597,345 2.701,290 43 5.867,059 3.793,256 1.396,245 5.867,059 2.892,772 44 6.143,118 4.047,675 1.527,698 6.143,118 3.092,644 45 6.425,524 4.312,037 1.667,999 6.425,524 3.301,036 46 6.714,276 4.586,403 1.817,506 6.714,276 3.518,071 47 7.009,374 4.870,820 1.976,580 7.009,374 3.743,868 48 7.310,818 5.165,329 2.145,589 7.310,818 3.978,542 7.618,609 5,469,956 2.324,898 7.618,6094.222,204 50 7.932,746 5.784,720 2.514,881 7.932,746 4.474,958

.009,813,37 1.028,084
012,180,3 1.145488
.0 14,951,1

.060,517,64 .001,901,8

.071,169,06.002,360,9 .083,001,24.002,898,3 .096,075,98.003,522,8

110,455,0 .004,243,2 .126,200,1 .005,068,5

1.269,239

223,392,1
256,737,8

.018,169,5

1.399,336

.021,880,7

1.535,780

,293,229,8 .026,132,4

1.678,569

333,006,4.030,974,9

,376,204,7 .036,460,0

422,961,5042,641,9

2.145,014

.182,247,3 .008,275,7

473,412,5.049,577,0

527,693,2 .057,323,6

2.313,189 2,487,709 2.668,576

.585,937,8.065,942,7
648,279,9.075,496,7 2.855,788
.714,852,4 .086,050,5 3.049,347
237,702,5 3.249,252 .785,787,0.097,671,1 3.249,252
268,622,3 3,455,504 .861,214,8 110,427,4 3.455,504
302,443,1 3.668,101 .941,265,9.124,390,5 3.668,101
339,337,0 3.887,045 1.026,070 .139,633,6 3.887.045
379,480,1 4.112,335 1.115,754
423,053,8 4.343,971 1.210,446
470,242,4 4.581,954 1.310,272
521,235,3 4.826,282
576,225,5 5.076,958
635,410,2 5.333,978
.698,991,5 5.597,345

1.415,357

1.525,826
1.64 1,800
1.763,402

1.890,753

156,231,7 4.112,335
174,262,3 4.343,971
193,804,3 4.581,954

214.939,34.826,282

237,750,2 5.076,958 262,322.5 5.333,978 288,743,5 5.597,345 .766,458,1 .056,281,9 317,101,8 5.867,059 .822,370,9 .061,830,4 840,163,5 6.143,118 2.023,972 347,489,4 6.143,118.880,927,9 .067,779,3

.767,172,3 5.867,059

13.406,34 6.374,755 1.635,565 13.406,34 2,826,279 321,968 13.822.02 6.664,586 1.737.389 13.822,02 2.957,918 .342,192 14.244,04 12.650,18 7,746,632 14.244,04 10.240,93 4.376,572 14.244.04 6.962,649 1.843,839 14.244,04 3.093.543 .363.353 68 14.67241 13.137,75 8.194,027 14.672,41 10.669,60 4.635,994 14.672,41 7.269,028 1.955,048 14.672,41 3.233,211 .385,478 69 15.107.12 13.633,67 8.659,350 15.107,12 11.108,39 4.906,421 15.107,12 7.583.806 2.071,149 15.107,12 3.376.978 408,594 70 15.548.18 14.137,729.142,971 15.548,18 11.55 7.30 5.188,131 15.548,18 7.907,061 2.192,280 15.548,18 3.524,902 432,732 71 15.995,59 14.649,68 9.645,261 15,995,59 12.016,30 5,481,400 15.995,59 8.238,873 2.318,578 15.995,59 3.677,037 457,923 72 16.449,34 15.169,32 10.166,58 16.449,34 12,485,40 5.786,503 16,449,34 8.579,319 2.450,180 16.449,34 3.833,439 484,192 73 16.909,44 15.696,39 10,707,29 16.909,44 12.964,56 6.103,722 16.909,44 8.928,473 2.587,227 16.90944 3.994,165 511,572 74 17.375,89 16.230,65 11.267,75 17.375,89 13.453,77 6.433,336 17.375,89 9.286,407 2.729,862 17.375,89 4,159,269 .540.095 75 17,848,68 16.771,83 11.848.31 17.848,68 13.952,99 6.775,625 17.848,68 9.653,193 2.878,228 17.848,68 4.328,806 .569,790 76 18.327,82 17,319,64 12.449,32 18.327,82 14.462,19 7.130,870 18.327.82 10.028,90 3.032,468 18.327,82 4.502,834 .600,690 77 18.813,30 17.873,80 13.071,13 18.813,30 14.981,32 7.499,354 18.813,30 10.413,60 3.192,728 18.813,30 4,681,404 .632,825 78 19.305,13 18.434,01 13.714,06 19,305,13 15.510,33 7.881,357 19.305,13 10.807,34 3.359,155 19.305,13 4.864,574 .666,227 79 19.803,31 18.999,96 14,378,45 19.803,31 16.049,16 8.277,162 19.803,31 11.210,21 19.803,31 5.052,396 700,930 80 20.307,83 19.571.33 15.064,64 20.307,83 16,597,75 8.687,052 20.307,83 11.622,25 20.307,83 5.244,926 .736,967 20.818,70 20.147,78 15.772,93 20.818,70 17.156,04 9.111,309 20.818,70 12.043,52 3.896,928 20.818,70 5,442,218 .774.371 82 21.335,91 20.728,97 16.503,64 21.335,91 17.723,95 9.550,216 21.335,91 12.474,10 4.089,519 21.335,91 5.644,325 .813,175 83 21.85947 21.314,55 17.257,08 21.859,47 18.30 1,40 10.004,05 21.859,47 12,914,02 4.289,031 21.859,47 5.851,300 .853414 84 22.389,38 21.904,16 18.033.54 22.389,38 18.888,30 10.473,11 22.389,38 13,363,34 4.495,617 22.389,38 6.063,199 85 22.925,63 22.497,42 18.833,33 22.925,63 19.484.56 10.957,65 22.925.63 13.822,11 4.709,435 22.925,63 6.280,073 86 23,468,23 23.093,94 19.656.72 23.468,23 20.090,08 11.457,97 23.468,23 14.290,39 4.930,639 23.468,23 87 24.017,18 23.693,33 20.503,99 24.017,18 20.704,75 11.974,35 24.017,18 14.768,21 5.159,389 24.017,18 88 24.57247 24.295,19 21.375,41 24.572,47 21.328,47 12.507,07 24.572,47 15,255,63 5.395,841 24.572,47 89 25.134,11 24.899,10 22.271,24 25.134,11 21.961,10 13.056 40 25.134,11 15.752,68 5.640,156 25.134,11 90 25.702,10 25.504,64 23.191,73 25.702,10 22.602.54 13.622,62 25.702,10 16.259,41 5.892,496 25.702,10

1.535,780 12 1.827,705 2.145,014 2487,709 .527,693,2 .057,323,6 648,279,9 .075,496,7

.256,7378 .02 1,880,7

1.535,780

.183,808,1.011,306,3

1.269,239.083,001,24.002,898,3

1.535,780 110455,0.004,243,2

.333,0064 .030,974,9

1.827,705

.2385164 .016,009,1

1.827,705

.143,3728.006,009,0

422,961,5 .042,641,9

2.145,014

.303,091,9 .022,044

2.145,014

182,247,3.008,275,7

1.072,507

2487,709

378,337,5 .029,641,9

2487,709

227,5704.011,129,7

1.243,855

.564,029,6 .050,5344 .676,058,6 .064,379,3 4.112,335 .80 1,922,0 .080,886,0 .942,397,1 5.076,958 1.098,255 5.597,345 1.270,259 6.143,118 1459,168 6.7 14,276 1.665,731 7.310,818 1.890,691 7.932,746 2.134,783 8.580,058 2.398,733 9.252,754 2.683,259 9.950836 2.989,070 10.674,30 3.316,867 11.423,15 31 12.197,39 5.553,794 1.356,543 12.197,39 32 12.997,01 6.093,072 1.538,236 12.997,01 .801,761 12.997,01 2.698,570 33 13.822,02 6.664,586 1.737,389 13.822,02 .906,129 13.822,02 2.957,918 .342,192 34 14.672,41 7.269,028 1,955,048 14.67241 1,020,306 14.67241 3.233,211 .385,478 35 15.548,18 7.907,061 2.192,280 15.548,18 5.783,290 1.144,873 15.548,18 3.524,902 432,732 36 16.449,34 8.579,319 2450,180 16.449,34 6.283,742 1.280,431 16.449,34 3.833,439 484,192 17.375,89 9.286407 2.729,862 17.375,89 6.811,411 1,427,593 17.375,89 4.159,269 .540,095 38 18327,82 10.028,90 3.032468 18.327,82 7.366,900 1.586,988 18.327,82 4.502,834 .600,690 9.1 63,907 39 19.305,13 10.807,34 3.359,155 19.305,13 7.950,799 1.759,260 19.305,13 4.864,574 .666,227 9.652,565 40 20.307,83 11.622,25 3.711,105 20.307,83 8.563,689 1.945,064 20.307,83 5.244,926 .736,967 10.153,91 41 21.335,91 12474,10 4.089,519 21.335,91 9.206,134 2.145,075 21.335,91 5.644,325 .813,175 10.667,96 42 22.389,3813.363,34 4.495,617 22.389,38 9.878,688 2.359,975 22.389,38 6.063,199 .895,122 11.194,69 43 23.468,23 14.290,39 4.930,639 23.468,23 10.581,89 2.590,466 23,468,23 6.501,976 .983,086 11.734,12 44 24.572,47 15.255,63 5.395,841 24.57247 11.316,27 2.837,259 24.57247 6.961,080 1.077,350 12.286,24 25.702,10 16.259,41 5.892,496 25.702,10 12.082,33 3.101,078 25.702,10 7,440,932 1.178,205 12.851,05 26.857,10 17.302,05 6.421,893 26.857,10 12.880,58 3.382,662 26.857,10 7.941,946 1.285,946 13.428,55 28.037,50 18.383,82 6.985,340 28.037,50 1.3.71 1,50 3.682,766 28.037,50 1.400,875 14.018,75 48 29.243,27 19.504,96 7.584,153 29.243,27 14.575,55 49 3047443 20.665,69 8.219,670 3047443 15473,19 50 31.730,98 21.866,18

3.249,252

3.668,101

.100,374,1
.123.1804

2.225,894

2454,715

4.112,335
4.581,954
5.076,958
.149,659,3 5.597,345
.180,182,2 6.143,118 .880,927,9 .067,779,3
215,138,5 6.714,276 1.006,214 .080,952,5
254,933,8 7.310,818 1.142,793 .095,955,6 3.655,409
.299,991,6 7.932,746 1.291,140 .112,951 3.966,373
.350,751,0 8.580,058 1.451,729 .132,106 4.290,029
407,668,7 9.252,754 1.625,032 .153,596 4.626,377
471,218,6 9.950,836 1.811,515 .177,602 4.975,418
.541,889 10.674,30 2.01 1,648
.620,185 11423,15
.706,630 12.197,39

483,146,1.030,395,5

2.056,168

.568,048,8 .037,727,9
.662,3254 .046,311,8

2.290,977

.634,619,6 .019,03349.03,317,||| .767,889,7 .025,332,53.0346431

.913,852,3 .032,887,03.03,657,57

.041,810,92.03,905,66 .052,218,05.00 1,218,2 .064,222,27.00 1,605,2 .077,937,31.002,077,9

110,954,5.003,328,3 .1304839.004,131,7

.093,476,86 .002,648,1

2.538,478

.152,178,3.005,072,3

.766458,1.056,281,9

2.798,673

.176,151,3.006,165,2

3.071,559

.202,516,0.007,425,8

3.357,138

.231,385,6 .008,807,3

.262,873,3.010,516,0

297,092,1.012,3808

.334,154,7.014,482,9

374,174,1.016,841,9

417,262,8.019,477,9

1.791,900 15.865,49 1.938,725 16.50646 2.094,331 17.160,12 2.259,070 17.826,47 2.433,262 18.505,51 2.617,277 19.197,24 2.811463 19.901,67 3.016,177 20.618,79 3.231,784 21.348,60 3.458,659 22.091,11 3.697,172 22.846,31 3.947,713 23.614,20 4.210,661 24.394,78 4.486,410 25.188,05 4.775,360 25.994,02 5077,910 26.812,69 5.394,469 27.64403 5.725,452 28.488,08 6.071,275 29.34481 6.432,354 30.214,24 6.809,127 31.096,36 7.202,019 31.99 1,18 7.611,469 32.898,68 8.037,920 33.818,88 8.481,813 34.751,77 8.943,603 35.697,35 9.423,749 36.655,63 9.922,701 37.626,60 10.44093 38.610,26 10.978,90 39.606,61 11.537,10 40.615,66 12.1 15,98 41.637,39 12.716,03 42.671,82 13.337,75 43.718,95 89.557,52 46355,77 13.981,61 44.778,76 91.702,54 47.961,09 14.64811 45.851,27 93.872,94 49.600,52 15.337,75 46.936,47 96.068,72 51.274,26 16.051,02 48034,36 12.350,92 1.802,209 98.289,89 52.982,51 16.78844 49.144,94 12.777,32 1.886,152 100.536,4 54.725,49 17.550,50 50.268,22 13.213,26 1.972,982 102.808,4 56.503,37 18.337,73 51.404,19 13.658,86 2.062,762

50.376,11 20.082,04
51.988,04 21.030,72
53.625,36 22.007,71
55.288,06 23.013,32
56.976,15 24.047,90
58.689,62 25.11 1,75
60.428,48 26205,20
62.192,72 27.328,55
63.982,35 28.482,11
65.797,36 29.666,17
67.637,76 30.881,04
69.503,54 32.126,99
71.394,71 33.404,32
73.311,26 34.713,29
75.253,19 36.054,18
77.220,52 37.427,26
79.213.22 38.832,78
81.231,31 40.271,01

6.746,491 .801,582

7.033,608.847,572

7.328,674 .895,510 7.631,788 .945,447

7.943,056.997,435 8.262,577 1.05 1,534 8.590,455 1.107,797 8.926,789 1.166,281 9.271,682 1.227,043

11.933,96

1.967,950.154,395

2095,865.167,943

2.229,179.182,363

2.368,003.197,691

2.512446.213,964

2.662,614 231,219 2.818,618 249,496

4.723,242 497,484 4.950,511 .529,758 5.184,895 .563,582 5426,500 598,978 5.675,431 .636,022 5.931,791 .674,753 6.195,686 .715,223

9.625,233 1.290,139

9.987,543 1.355,630

10.358,71 1.423,573
10.738,84
11.1 28,03

1.494,031

1.567,062

11.526,37

1.642,726

1.721,088

SHEET 3 OF 5

TABLE 21-Continued

UNIT TWIST LOAD NO. 4

TWIST, RADIAL AND TANGENTIAL DEFLECTIONS

P: 1000 FT-LBS. PER FT.2

CROWN

Point

D

D,

Point
D2 D2

Point

D

D2

D1

D
2.855,788 .279,832,9 .014,664,9 2.115,399.129,119,3.004,347,6 .740,389,6.021,917,40.0362,42
3.455,504 372,308,6 .021,466,4 2.559,633.171,829,0.006,364,9 .895,871,3 .029, 170,88.0 530,64
4,112,335,483,146,1.030,395,5 3.046,174 .223,039,8.009,013,7 1.066,161.037,870,04.0751,51
4.826,282 613,985,204 1,855,2 3.575,024 .283,518,9 .012,413,8 1.251,258.048,146,10.00 1,035,0
5.597,345,766,458,1 .056,281,9 4.146,182.354,032,00 16,695,1 1,451,164.060,130,17.00 1,392,2
1.665,876 .073,953,32.00 1,834,6
1.895,397.089,746,56.002,374,8

6.425,524.942,189,0.074,146,9 4.759,647 435,343,1.021,998,3
1.142,793 095,955,6 5.415,421
1.369,875.122,247,6 6.113,502

7.310,818
8.253,228
9.252,754
10.309.40
11.423,15
12.594,03 2.574,735 .284,215

.528,214,5.028,473,8
.633,406,8.036,282,8

751,678,5 .045,596,0

1,625,032 .153,595,6

1.909,847.190,607,2

2.225,894 233,922

6.853,892
7.636,589
8.46 1,595

.883,786,0.056,595,3

1.030,483.069,472,5

25

26

17.848,68 19,305, 13

4.832,604.820,882

1.778,174.143,947,4

2.139,726,107,640,8 .003,026,5 2.398,862 127,766,8 003,803,7 2.672,806 ,150,255,5.004,721,9

2,961,558

3.265,118

3.583,485

175,237,3.005,796,8

202,843,0007,045,9

233,202,9008,486,7

8.637,496 1.794,255 22.389,38 6.063,199.895,122 29 24.017,18 9.576,196 2.062,389 24.017,18 6.728,961 1.029,412 30 25.702,10 10.578,28 2.359,246 25.702.10 7,440,932

1.565,623.121,439,3 3.916,661 266,447,5.010,137,5

2.009,049.169444,0
2,258,986.198,182

3,464,014,350,937

3.820,227 400,014

14.300,10
15.421,26
2.528.721 230,422
16.584,73 2,818,985 266,438
17.790,50 3.130,508 .306,512
1.178,205 19.038,59
27.444,13 8.200,519 1.342,493 20.328,98
29.243,27 9.009,113 1.523,299 21.661,68
31.099,54 9.868.086 1.721,684 23.036,69
33.012,91 10.778,79 1.938,725 24.454,01
34.983,41 11.742,56 2.175,535 25.913,64
37.01 1,02 12.760,69 2,433,262 27.415,57
13.834,50 2.713,076 28.959,81

39.095,74

41.237,58 14.965,23 3.016,177 30.546,36

39 43.436,54 22.710,50 6.658,582 43,436,54 16.154,14 3.343,790 32.175,22

4.199,864,454,055

4,603,639 .513,382

5.032,264.578,329
5.486,445.649,232

5.966,885 .726,446

6.474,282.810,329
7,009,329,901,253

7.572,717.999,596

40 45.692,61 24.430,50 7.357,083 45.692,61 17,402,45 3.697,172 33.846,38 8.165,131 1.105,749
41 48.005,80 26,229,48 8.108,236 48.005,80 18.711,36 4.077,607 35.559,85 8.787,250
42 50.376,11 28.108,50 8.914,502 50.376,11 20.082,04 4.486,410 37.315,63 9,439,750
43 52.803,53 30.068,58 9.778,347 52.803,53
4.924,909 39.113,72 10.123,30
44 55.288,06 32.110,65 10.702,30 55,288,06
5.394,469 40.954,12 10.838,57
45 57,829,71 34.235,59 11.688,93 57.829,71
46 60.428,48 36.444,22 12.740,82 60.428,48
47 63.084,36 38.737,27 13.860,60 63.084,36
48 65.797,36 41.115,42 15.050.91
49 68.567,48 43.579,29 16.31446
50 71.394,71 46.129,39 17.653,96
51 74.279,05 48.766,21 19.072,15
52 77.220,52 51.490,14 20.571,79
53 80.219,09 54.301,49 22.155,68 80.219.09 39,547,79
54 83.274,79 57.200,53 23.826,62 83.274,79 41.742,18
25.587,45 86.387,60 44.011,24
27.441,01 89.557,52 46.355,77
29.390,18 92.784,56 48.776,53
31,437,82 96.068,72 51.274,26
33.586,84 99.409,99 53.849,65

55

65.797,36
68.567,48
71.394,71 33.404,32
74.279,05 35.379,73
77.220,52 37,427,26

57.200,38
59,421,55

1.220,107 1.34 3,080 1.475,087 1.616,551 14.333,94 11.586,22 1.767,910 14.992,89 6.432,354 44.761,84 12.366,90 1.929,606 15.666,64 7.003,530 46.729,16 13.181,26 2.102,097 16.355,21 7.611,469 48.738,79 14.029,95 2.285,837 17.058,58 8.257,656 50.790,72 14.913.60 2.481,309 17.776,75 8.943,603 52.884,97 15.832,86 2.688,984 18.509,74 9.670,845 55.02 1,52 16.788,34 2.909,361 19.257,53 10.440,93 17.780,66 3.142,929 20.020,13 11.255,44 18.810,45 3.390,201 20.797,54 12.1 15,98 61.685,03 19.878,32 3.651,689 21.589,76 86.387,60 60.187,42 13.024,15 63,990,81 20.984,86 3.927,919 22.396,78 56 89.557,52 63.262,27 13.981,61 66.338,91 22.130,67 4.219,424 23.218,62 57 92.784,56 66,425,1 I 14.990,0I 68.729,31 23.316,34 4.526,745 24.055,26 58 96.068,72 69.675,88 16.051,02 71.162,02 24.54247 4.850,432 24.906,71 59 99,409,99 73.014,47 17.166,36 73.637,03 25.809,61 5.191,036 25.772,96 60 102.808,4 76,440,68 35.840,15 102.808,4 56.503,37 18.337,73 76.154,36 27.118,35 5.549,132 26.654.02 61 106.263,9 79.954,22 38.200,63 106.263,9 59.236,06 19.566,87 78.713,99 28,469,25 5.925,292 27.549,89 62 109.776,5 83.554,75 40.671,24 109.776,5 62.048,32 20.855,53 81.315,93 29.862,87 6.320.090 28,460,57 63 113.346,2 87.241,83 43.254,88 113.346,2 64.940,72 22.205,48 83.960,18 31.299,75 6.734,131 29.386,06 116.973,1 91.014,95 45.95448 116.973,1 67.913,81 23.618,50 86.646,73 32.780,43 7.167,996 30.326,36 65 120.657,1 94.873,53 48.772,98 120.657,1 70.968,07 25.096,40 89.375,59 34.305,47 7.622,303 31,281,46 66 124.398,1 98.816,91 51.713,31 124.398,1 74.104,00 26.640,97 92.146,77 35.875,37 8.097,663 32.251,37 67 128.196,3 102.844,3 54.778,39 128.196,3 77.322,01 28.254,07 94.960,25 37.490,67 8.594,698 33.236,09 132.051,7 80.622,52 29.937,52 97.816,04 39.151,87 9.1 14,033 34.235,61 135.964,1 84.005,88 31.693.19 100.714,1 40.859,48 9.656,303 35.249,95 15.422,3 64.75142 139.933,6 87,472,44 33.522.94 103.654,5 42.614,01 10.222,16 36.279,09 119.776,9 68.344,72 143.960,3 91.022,49 35,428,66 106.637,2 44,415,94 10.812,24 37,323,04 72 148.044.1 124,210,6 72.077,35 148.044,1 94.656,29 37.412,23 109.662,3 11,427,22 38,381,80 73 152.185,0 128.722,3 75.952,14 152.185.0 98.374,06 39.475,56 112.729,6 12.067,76 39,455,36 8.440,177 1.023,489 79.971,99 I56.383,0 102.176.0 41.620,56 115.839,2 12.734,51 40.543,73 8.789,295 1.080,564 106.062,3 43.849,14 118.991,2 13,428,19 41.646,91 9.147,805 1.139,985 164.950,3 I 10.033,0 46.163,29 122.185,4 14.149,45 42.764,90 9.515,825 1.201,817 169,319,7 147.521,1 92.930,20 169.319,7 114.088,2 48.564,87 125.422,0 14.899,01 43.897,70 9.893,471 1,266,122 173,746,2 152.401,4 97.558,51 173.746,2 118.228,0 51.055,88 128.700,9 58.396,15 15.677,55 45.045,30 10.280,86 1.332.966 79 178.229,7 157.350,7 102.345,9 178.229,7 122.452,3 53.638,24 132.022,0 60.593,97 16.485,78 46.207,71 10.678,111,402,412 80 182.770,5 162,367,2 107,295,1 182.770,5 126.761,2 56.313,96 135,385,5 62.843,24 17.32442 47.384,93 11.085,33 1.474,530

187.368,3 131.154,5 59.084,95 138.791,3 65.144,37 18.194,19 48.576,96 11.502,65 1.549,384
192.023,2 135.632,2 61.953,22 142.239,4 67,497,75 19.095,80 49.783,79 11.930,17 1.627,040
196.735,3 140.194,2 64.920,72 145.729,8 69.903,78 20.030,01 51.005,44 12.368,02 1.707,570
201.504,4 144.840,1 67.989,47 149.262,5 72.362,84 20.997,54 52.241,89 12,816,30 1,791,041
206.330,7 149.569,9 71.161,39 152.837,6 74.875,31 21.999,12 53,493,15 13.275,13 1.877.524
21 1.214,1 154.383,3 74,438,53 156.454,9 77.441,54 23.035,55 54.759,21
216.154,6 159.279,9 77.822,85 160.114,5 80.061,88 24.107,50 56.040,09

87 216.154,6 199.200,5 146.693,1
88 221.152,3 204.682,2 153.031,3 221.152,3 164.259,5 81.316,34 163.816,5
89 226.207,0 210.211,7 159.554.4 226.207,0 169.321,5 84.920,97 167.560,7
90 231.318,9 215.786,7 166.264,8 231.318,9 174,465,8 88.638,76 171.347,3
4 OF 5

13.744,631.967,089

14.224,90 2.059,808

14.716,06 2.155,752

15.218,22 2.254,997

15.731,50 2.357,615

28

39.803,3414.205,02

2,811,463

3.322,720.310,856

6,219,272

29

42.697,21 15.751,30

3.231,784

6,671,439

30

45.692,61 17,40245

3.697,172

7.1 39,471

31 48.789.56 19.161,33 32 51.988.04 21.030,72 33 55.288.06 23,013,32 34 58.689,62 25.111,75 35 62.192,72 27.328,55

4,210,661

7.623,368

3.1 73,098 34 98,341 3.839,449 4.196422 4.569,261

.07881885.00 1,949,2

,095,651,18.002,523,3

114,722,7.003,215,6 136,173,0.004,041,5 160,141,3.005,017,0 186,766,8.006,1592 216,188,9.007,4864 .248,5464.009017,2 283,9784010,7712

.322,623,6 012,769,6 .364,620,80 15,033,8 410,108,501 7,5864 459,225,1020,451,0 .512,109,0.023,652,p .568,898,2.027,214,6 .629,730,7.031,165,0 .694,744,5.035,530,4

4.775,360
5,394,469
6,071,275

6.809,127

9.717,613.999,362,5 .057,716,9

1.087,344 .064,597

.108,632

119,613

33.584,07 8595,612 1.231,091 19.901,67 36,025,77 9.539,938 1,415,810 21.348,60 3.689,937 .357,612 38.553,14 10.549,90 1.620,483 22.846,31 4.083,075 409,445 41.166,19 11.627,50 1.846,478 24.394,78 4.502,983 .466,704 43.864,91 12.774,74 2.095,202 25.994,02 4.950,511 46.649,30 13.993,58 2.368,115 27.64403 5,426,500 .598,978 49.519,37 15.285,95 2.666,700 29.344,81 5,931,791 .674,753 52.475,11 16.653,77 2.992,499 31.096,36 6,467,217.757,481 55.516,53 18.098,97 3.347,081 32.898,68 7.033,608.847,572 10.280,84 58.643,61 19.623,24 3.732,067 34,751,77 7.631,788 .945,447 10.859,93 1.180,330 .072,073 61.856,37 21.228,57 4.149,102 36.655,63 8.262,577 1.051,534 11.454,88 1.278,457 .080,179 65.1 54,81 22.916,69 4.599,885 38.610,26 8.926,789 1.166,281 12,065,71 1.381,862 .088,951 81.231,31 40.271,01 68.538,92 24.689,38 5.086,142 40.615,66 9.625,233 1.290,139 12.692,39 1,490,681 .098,423 41 85.343,65 43.246,54 12.716,03 72.008,70 26.548,35 5.609,640 42.671,82 0.358,71 1423,573 13.334,95 1.605,050 42 89.557,52 46.355,77 13.981,61 75.564,16 28.495,32 6.172,201 44.778,76 1.128,03 1.567,062 13.993,36 1,725,104 43 93.872,94 49.600,52 15,337,75 79.205,29 30.531,95 6,775,646 46.936,47 1.933,96 1.721,088 14,667,65 1.850,979 131,406 44 98.289,89 52.982,51 16.788,44 82.932,09 32.659,86 7.421,864 49.144,94 12.777,32 1,886,152 15,357,80 1.982,811 .144,050 45 102.808.4 56.503,37 18.337,73 86.744,57 34.880,66 8.112,773 51.404,19 13.658,86 2.062,762 16.063,81 2.120,734 157,583 46 107.428,4 60.164,61 19.989,72 90.642,72 37,195,91 8.850,317 53.714,20 14.579,37 2.251,435 16.785,69 2.264,884 .172,048 47 112.150,0 63,967,65 21.748,58 94.626,54 39.607,15 9.636480 56.074,99 15.539,62 2452,703 17.523,43 2415,395 187,485 48 116.973,1 67.913,81 23.618,50 98,696,04 42.1 15,85 10,473,28 58.486,54 16.540,36 2,667,106 18.277,05 2.572,400 .203,937 49 121.897,7 72.004,29 25.603,76 102.851,2 44.723,48 11.362,77 60.948,87 17.582,36 2,895,195 19.046,52 2.736,036 .221,448 50 126.923,9 76.240,19 27.708,64 107.092,1 47.431,46 12.307,04 63,461,96 18.666,36 3.137,527 19.831,86 2.906,435 240,060 51 132,051,7 80.622,52 29,937,52 111418,6 50,241,16 13.308,20 66.025,83 19.793,11 3,394,679 20.633,07 3.083,731 .259,821 52 137.280,9 85,152,14 32.294,79 115.830,8 53.153,92 14.368,40 68.640,46 20.963,34 3.667,229 21.450,14 3.268,057 280,775 53 142.611,7 89.829,85 34,784,86 120.328,6 56.171,06 15,489,80 71.305,86 22.177,77 3.955,766 22.283,08 3459,546 302,971 54 148.044,1 94.656,29 37.412,23 124.912,2 59.293,82 16.674,64 74.022,03 23,437,13 4,260,902 23.131,88 3.658,332 .326,454 55 153.5780 99.632,02 40,181,39 129.581,4 62.523,43 17.925.13 76.788,97 24.742,14 4,583,239 23,996,55 3.864,546 .351,275 56 159.213,4 104.757,5 43,096,88 134,336,3 65.861,08 19.243,55 79.606,69 26.093,49 4.923,407 24.877,09 4,078,322 .377,483 57 164.950,3 110.033,0 46.163,29 139.176,8 69.307,89 20.632,19 82475,17 27.491,90 5,282,028 25.773,49 4,299,790 405,128 58 170.788,9 115,458,7 49.385,21 144.103,1 72.864,98 22.093,38 85.39441 28.938,05 5.659,747 26.685,76 4,529,082 434,262 59 176.728,9 121.034,8 52,767,19 149.115,0 76.533,39 23.629,46 88.36443 30,432,63 6.057,224 60 182.770,5 126,761,2 56.313,96 154.212,6 80.314,13 25.242,80 91.385,23 31.976,30 6,475,111 61 188.913,6 132,637,7 60.030.13 159.395,8 84,208,18 26.935,81 94.456,79 33.569,75 6.914,081 164.664,8 88.216,46 28.710,90 97.579,11 35.213,63 7.374,806 1 70.019,4 92.339,84 30.570,52 100.752,21 36.908,60 7.857,990 175.459,6 96.579,18 32.517,16 103.976,1 38.655,29 8.364,315 180.985,6 100,935,2 34.553,29 107.250,7 40.454,35 8.894,500 186.597.2 105,408,8 36.681,42 110.576,1 42.306,39 9449,26 227.904,6 171.027,2 86,147,56 192,294,5 110.000,5 38.904,10 113.952,3 44.212,05 10.029,32 68 234,758,5 177.940,7 91,181,12 198.077,5 114,711,0 41.223,90 117.379.3 46.171,93 10.635,42 69 241.713,9 184,998,9 96.421,72 203.946,1 119.541,0 43.643,35 120.857.0 48.186,63 11.268,28 70 248.770,9 192.200,6 101.874,1 209.9004 124491,0 46.165,08 124.385,5 50.256.74 11.928,68 255.929,4 199.544,3 107.542,9 215.9404 129.561,4 48.791,67 127.964,7 52.382,85 12.617,35 263,189,5 207.028,6 113.432,8 222.066,1 134.752B 51.525,77 131.594,7 54.565,53 13.335,10 270.551,0 214.651,9 119.548,4 228.277,4 140.065,6 54.370,01 135.275,5 56.805,34 14.082,67 74 278.014,2 222412,6 125.894,6 234.574,5 145.500,1 57.327,04 139.007,1 59.102,85 14.860,87 75 285.578,8 230.308,6 132.475,8 240.957,1 151.056,7 60.399,52 142.7894 61.458,60 15,670,48 76 293.245,0 238,338,2 139.296,7 247.425,5 156.735,5 63.590,19 146.622,5 63.873,12 16.512,31 77 301.012,8 246,499,1 146.361,8 253.979,5 162.536,9 66.901,68 150.506,4 66.346,94 17.387, 16 78 308.882,1 254.7892 153.675,8 260.619,2 168,461,0 70.336,73 154.44 1,0 68.880,59 18.295,86 316.8529 263,206,2 161.243,1 267.344,6 174.507,8 73.898,06 158.4264 71.474,56 19.239,22 80 324.925,3 271.747,6 169.068,2 274.155,7 180.677,5 77.588,39 162462,6 74.129,35 20.218.10 81 333.099,2 280,410,8 177.155,5 281.0524 186.970,2 81.410,46 166.549,6 76.845,46 21.233,29 82 341.374,6 289.193,2 185.509,6 288.034,8 193.385,6 85.367,00 170.687,3 79,623,36 22.285,69 83 349.751,6 298.091,9 194.134,6 295.102,9 199.923,8 89.460,78 174.875,8 82,463,51 23.376,15 84 358,230,1 307,104,0 203.035,0 302.256,6 206.584,6 93.694,58 179.115,0 85.366,38 24.505,49 85 366.8102 316.226,5 212,215,1 309.496,1 213.367,8 98.071.12 183,405,1 88.33241 25.674,63 86 375,491,8 325.456,3 221.679,0 316.821,2 220.273,2 102.593,2 187.745,9 91.362,04 26.884,41 384.274,9 334.790,0 231.430,8 324.231,9 227.3004107.263,6 192.137,4 94.455.69 28.135,74 344.2242 241.474,8 331.7284 196,579,8 97.613,79 29.429,48 353.755,5 251.814,9 339.310,5 201.0729 100.836,7 30,766,56 363.380,2 262,455,1 346.978.3 249.109,7 122.1924 205.616,8 104.124,9 32.147.85 SHEET 5 OF 5

TRIGONOMETRIC TABLE FOR ARCH ANALYSIS

206. General Statement.-A convenient table of trigonometric functions is given in table 22. These are used in calculating arch data as described in chapter VI. The trigonometric quantities in the table occur at various places in arch computation forms. Some are necessary in evaluating moments, thrusts, and shears due to applied loads, using formulas for ML, HL, and VL as given in chapter V.

Although all quantities tabulated, except sin2 & and cos2 4, are given in preceding tables, the values are repeated in table 22 for convenience in making arch computations. After arch and load constants are copied from tables 10 and 17 to 21, inclusive, all remaining trigonometric functions needed may be taken from table 22.