Федоров М.П. и др. Информационно-компьютерные технологии в строительстве. Применение программы SCAD для расчета сооружений на динамические воздействия
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200
.
Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɤɭɪɫɨɜɨɣ ɪɚɛɨɬɟ (ɞɥɹ ɫɨɤɪɚɳɟɧɢɹ ɟɟ ɨɛɴɟɦɚ) ɭɫɥɨɜɢɦɫɹ ɩɪɢɜɨɞɢɬɶ
ɪɟɡɭɥɶɬɚɬɵ ɨɩɪɟɞɟɥɟɧɢɹ ɬɨɥɶɤɨ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ M. ɉɨɷɬɨɦɭ, ɜ ɨɬɤɪɵɜɲɟɦɫɹ ɩɨɫɥɟ
ɧɚɠɚɬɢɹ ɤɥɚɜɢɲɢ «ɍɫɢɥɢɹ» ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɧɚɡɧɚɱɢɦ ɬɨɥɶɤɨ ɭɤɚɡɚɧɧɨɟ ɭɫɢɥɢɟ:
.
ɉɨɫɥɟ ɫɞɟɥɚɧɧɵɯ ɧɚɡɧɚɱɟɧɢɣ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɦ ɡɚɤɪɵɬɢɢ ɜɫɟɯ ɞɢɚɥɨɝɨɜɵɯ ɨɤɨɧ ɩɨ
ɧɚɡɧɚɱɟɧɢɸ ɩɚɪɚɦɟɬɪɨɜ ɜɵɯɨɞɧɵɯ ɬɚɛɥɢɰ ɢ ɢɫɤɨɦɵɯ ɜɟɥɢɱɢɧ ɫɧɨɜɚ ɩɨɹɜɢɬɫɹ ɨɫɧɨɜɧɨɟ ɨɤɧɨ
ɩɨ ɩɨɞɝɨɬɨɜɤɟ ɢ ɜɵɜɨɞɭ ɬɚɛɥɢɰ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɪɚɫɱɟɬɚ, ɜ ɤɨɬɨɪɨɦ ɩɨɹɜɢɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ
ɨɬɤɪɵɬɶ ɬɚɛɥɢɰɵ ɪɚɡɞɟɥɚ «Ⱦɢɧɚɦɢɤɚ».
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɧɚɠɚɬɢɟɦ ɤɥɚɜɢɲ «Ɏɨɪɦɢɪɨɜɚɧɢɟ ɞɨɤɭɦɟɧɬɚ» ɢ «ɉɪɨɫɦɨɬɪ
ɪɟɡɭɥɶɬɚɬɨɜ» ɨɬɤɪɵɜɚɟɦ ɫɥɟɞɭɸɳɢɟ 4 ɬɚɛɥɢɰɵ ɪɚɡɞɟɥɚ «Ⱦɢɧɚɦɢɤɚ»:
Ɍɚɛɥɢɰɚ 1
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| ɊȺɋɉɊȿȾȿɅȿɇɂȿ ȼȿɋɈȼ ɆȺɋɋ, ɤɇ |
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| 4 5 6 7 8 9
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| 1 - ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| X 192.2 192.2 15.69 184.4 361. 184.4 |
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Ɍɚɛɥɢɰɚ 2
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|Ɂɚɝpɭ: N : COȻCTB. : ɑ A C T O T ɕ : ɉEPɂOȾɕ
| : ɉ/ɉ : :-----------------------------:----------
|ɠɟɧɢɟ: : ɁHAɑEHɂə : 1/C : Ƚɐ : C
------------------------------------------------------------------
| 1 1 .1135605 8.805872 1.402209 .7131604
| 2 .0293393 34.08395 5.427381 .1842509
| 3 .0107959 92.62708 14.74953 .0677987
| 4 .0083913 119.1697 18.97606 .0526979
| 5 .006435 155.4 24.74523 .0404118
| 6 .0056563 176.7923 28.15164 .0355219
| 7 .0055773 179.2974 28.55055 .0350255
| 8 .0040112 249.2958 39.69679 .0251909
| 9 .0039302 254.4345 40.51506 .0246821
| 10 .002663 375.51 59.79459 .0167239
| 11 .0024821 402.8826 64.15328 .0155876
| 12 .0008075 1238.363 197.1916 .0050712
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201
Ɍɚɛɥɢɰɚ 3
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| ɎɈɊɆɕ ɄɈɅȿȻȺɇɂɃ, ɦ |
--------------------------------------------------------------------------------
| 4 5 6 7 8 9 |
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| 1 - 1 ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| X .4724 .4724 .3153 .9961 .9981 1. |
| 1 - 2 |
| X 1. .9999 -.0932 -.2395 -.2486 -.2579 |
| 1 - 3 |
| X .0005 .0005 1. -.0107 -.0079 -.0011 |
| 1 - 4 |
| X -.0046 -.0046 -.0025 .0006 .003 .0054 |
| 1 - 5 |
| X .0026 .0025 .0012 .0035 -.0017 -.0072 |
| 1 - 6 |
| 1 - 7 |
| X -.0014 -.0134 .1134 1. .0029 -.9976 |
| 1 - 8 |
| X 1. -.9999 -.0039 .0672 -.0749 .0794 |
| 1 - 9
| X .1392 -.1393 .0466 -.9822 1. -.9765
| 1 - 10 |
| X .0002 .0002 .0001 8.e-5 -2.e-5 |
| 1 - 11 |
| X -.0003 -.0003 -1.e-5 |
| 1 - 12 |
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Ɍɚɛɥɢɰɚ 4
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| ɂɇȿɊɐɂɈɇɇɕȿ ɇȺȽɊɍɁɄɂ, ɤɇ |
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| 4 5 6 7 8 9 |
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| 1 - 1 ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| X 34.76 34.76 1.894 70.31 137.9 70.59 |
| 1 - 2 |
| X 41.02 41.01 -.3122 -9.424 -19.15 -10.15 |
| 1 - 3 |
| X .0273 .0282 3.972 -.5007 -.7285 -.0528 |
| 1 - 4 |
| X -.0002 -.0002 -1.e-5 3.e-5 .0003 .0002 |
| 1 - 5 |
| X -.0001 -.0001 -.0002 .0002 .0004 |
| 1 - 6 |
| 1 - 7 |
| X -9.e-5 -.0008 .0005 .0605 .0003 -.0604 |
| 1 - 8 |
| X -.0044 .0044 -.0002 .0006 -.0003 |
| 1 - 9 |
202
(ɉɪɨɞɨɥɠɟɧɢɟ ɬɚɛɥɢɰɵ 4)
| X .004 -.004 .0001 -.0276 .055 -.0274 |
| 1 - 10 |
| 1 - 11 |
| 1 - 12 |
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ȼ ɬɚɛɥ. 1 ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɜɟɫɨɜ ɬɨɱɟɱɧɵɯ ɦɚɫɫ (ɜɤɇ) ɜ ɭɡɥɚɯ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
(ɫɦ. ɪɢɫ. 2). ɗɬɢ ɦɚɫɫɵ ɩɨɥɭɱɟɧɵ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɩɪɢɜɟɞɟɧɢɟɦ ɤ ɭɡɥɚɦ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
ɪɚɦɵ ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɜɟɫɨɜ ɦɚɫɫ ɤɨɥɨɧɧ ɢ ɪɢɝɟɥɟɣ (ɫ ɭɱɟɬɨɦ ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɦɚɫɫ ɩɥɢɬ
ɩɟɪɟɤɪɵɬɢɣ, ɨɩɢɪɚɸɳɢɯɫɹ ɧɚ ɪɢɝɟɥɢ). ɉɨɤɚɡɚɧɨ, ɱɬɨ ɜ ɪɟɡɭɥɶɬɚɬɟ ɭɤɚɡɚɧɧɨɝɨ ɜɵɲɟ
ɪɟɞɚɤɬɢɪɨɜɚɧɢɹ ɩɪɢɜɟɞɟɧɧɵɯ ɬɚɛɥɢɰ ɜ ɧɢɯ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɬɨɥɶɤɨ ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ
ɤɨɥɟɛɚɧɢɹ (ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɫɢ X).
ȼ ɬɚɛɥ. 3 ɞɥɹ ɜɫɟɯ 12-ɢ ɋɎɄ ɩɪɢɜɟɞɟɧɵ ɨɪɞɢɧɚɬɵ ɬɨɥɶɤɨ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ
ɨɬɧɨɫɢɬɟɥɶɧɵɯ (ɤ ɟɞɢɧɢɰɟ) ɩɟɪɟɦɟɳɟɧɢɣ ɭɡɥɨɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ.
Ɂɧɚɤɢ ɩɟɪɟɦɟɳɟɧɢɣ ɩɪɢɧɹɬɵ ɜ ɨɛɳɟɣ ɞɥɹ ɜɫɟɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ
(ɈɋɄ) (ɫɦ. ɪɢɫ. 2).
ȼ ɩɪɨɝɪɚɦɦɟ SCAD ɩɨ ɩɪɢɜɟɞɟɧɧɵɦ ɡɧɚɱɟɧɢɹɦ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɫ
ɭɱɟɬɨɦ ɢɯ ɡɧɚɤɨɜ ɜ ɈɋɄ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧɵ ɜɫɟ 12 ɋɎɄ.
ɍɱɢɬɵɜɚɹ ɡɧɚɱɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɬɚɛɥ. 2, ɨɝɪɚɧɢɱɢɦɫɹ ɩɪɟɞɫɬɚɜɥɟɧɢɟɦ ɬɨɥɶɤɨ
ɩɟɪɜɵɯ ɞɜɭɯ ɋɎɄ (ɪɢɫ. 5, 6), ɨɬɜɟɱɚɸɳɢɯ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɟɪɜɵɦ ɬɪɟɦ ɫɨɛɫɬɜɟɧɧɵɦ
ɱɚɫɬɨɬɚɦ ɜ ɫɩɟɤɬɪɟ ɩɨɥɭɱɟɧɧɵɯ 12-ɢ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɪɚɦɵ:
Z
1
8.805872 1/ɫ;
Z
2
34.08395 1/ɫ.
Ɍɚɛɥ. 4 ɨɬɪɚɠɚɟɬ ɪɟɡɭɥɶɬɚɬ ɜɵɩɨɥɧɟɧɢɹ ɩɪɨɝɪɚɦɦɨɣ SCAD ɚɥɝɨɪɢɬɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ
ɧɚ ɷɬɚɩɟ ɜɵɱɢɫɥɟɧɢɹ ɜɟɤɬɨɪɨɜ ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɝɪɭɡɨɤ (10) ɜɨ ɜɫɟɯ 12-ɢɋɎɄ, ɩɨɥɭɱɢɜɲɢɯɫɹ
ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɥɨɠɟɧɢɹ ɩɨ ɋɎɄ ɜɟɤɬɨɪɨɜ ɢɫɤɨɦɵɯ ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɝɪɭɡɨɤ, ɞɟɣɫɬɜɭɸɳɢɯ ɜ
ɭɡɥɚɯ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ ɞɥɹ ɆɄɗ.
ȼ ɬɚɛɥ. 4 ɩɪɢɜɟɞɟɧɵ ɜɟɥɢɱɢɧɵ ɬɨɥɶɤɨ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɫɟɣɫɦɢɱɟɫɤɢɯ ɧɚɝɪɭɡɨɤ (ɜɤɇ)
ɧɚ ɪɚɦɭ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɫɟɦ 12-ɢɋɎɄ. Ɂɧɚɤɢ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯ ɜ ɭɡɥɚɯ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ
ɫɟɣɫɦɢɱɟɫɤɢɯ ɫɢɥ ɩɪɢɧɹɬɵ ɜ ɈɋɄ.
Ɋɢɫ. 5
1
2
3
4
5
6
7
8
9
0.996
0.998
1.
0.472
0.472
0.315
1-ɹɋɎɄ
203
Ɋɢɫ. 6
Ⱥɧɚɥɢɡ ɡɧɚɱɟɧɢɣ ɫɟɣɫɦɢɱɟɫɤɢɯ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɜ
ɭɡɥɚɯ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ ɞɥɹ ɆɄɗ (ɫɦ. ɪɢɫ. 2), ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɧɚɢɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɨɧɢ
ɢɦɟɸɬ ɜ ɩɟɪɜɵɯ ɞɜɭɯ ɋɎɄ. ɂɯ ɞɟɣɫɬɜɢɟ ɧɚ ɪɚɦɭ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 7, 8.
Ɋɢɫ. 7
Ɋɢɫ. 8
ɉɨɫɥɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɜɫɟɯ ɨɬɪɟɞɚɤɬɢɪɨɜɚɧɧɵɯ ɬɚɛɥɢɰ ɢɡ ɪɚɡɞɟɥɚ «Ⱦɢɧɚɦɢɤɚ» ɜ ɬɨɣ ɠɟ
ɨɛɳɟɣ ɬɚɛɥɢɰɟ, ɝɞɟ ɛɵɥ ɜɵɛɪɚɧ ɪɚɡɞɟɥ «Ⱦɢɧɚɦɢɤɚ», ɜɵɛɢɪɚɟɦ ɫɬɪɨɤɭ .
1
23
4 5
6
7
8
9
ɋɟɣɫɦɢɱɟɫɤɚɹ ɧɚɝɪɭɡɤɚ ɜ
1-ɣɋɎɄ
34.76
137.9
70.31
1.894
79.59
34.76
1
2
3
4
5
6
7
8
9
1.
1.
– 0.239
– 0.249
– 0.258
– 0.093
2-ɹɋɎɄ
1 2
3
4
5
6
7
8
9
– 9.424
– 19.15
– 10.15
41.02
41.01
– 0.31
ɋɟɣɫɦɢɱɟɫɤɚɹ ɧɚɝɪɭɡɤɚ ɜɨ
2-ɣɋɎɄ
204
Ⱦɥɹ ɜɵɜɨɞɚ ɬɚɛɥɢɰɵ ɫ ɩɟɪɟɦɟɳɟɧɢɹɦɢ ɭɡɥɨɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ ɧɟɨɛɯɨɞɢɦɨ
ɨɬɪɟɞɚɤɬɢɪɨɜɚɬɶ ɟɟ ɬɚɤɢɦɢ ɠɟ ɞɟɣɫɬɜɢɹɦɢ, ɤɚɤ ɷɬɨ ɛɵɥɨ ɫɞɟɥɚɧɨ ɞɥɹ ɬɚɛɥɢɰ ɪɚɡɞɟɥɚ
«Ⱦɢɧɚɦɢɤɚ». ɉɨɫɥɟ ɪɟɞɚɤɬɢɪɨɜɚɧɢɹ ɩɨɥɭɱɢɦ ɬɚɛɥ. 5.
Ɍɚɛɥɢɰɚ 5
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| ɉȿɊȿɆȿɓȿɇɂə ɍɁɅɈȼ, ɦ |
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| 4 5 6 7 8 9 |
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| 1 - 1 ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| X -.022874 -.022875 -.015269 -.048233 -.048333 -.048421 |
| 1 - 2 |
| X -.001801 -.001801 .000167 .000431 .000447 .000464 |
| 1 - 3 |
| X -1.63e-7 -1.68e-7 -.000289 .000003 .000002 3.25e-7 |
| 1 - 4 |
| 1 - 5 |
| 1 - 6 |
| 1 - 7 |
| X -1.e-7 |
| 1 - 8 |
| 1 - 9 |
| 1 - 10 |
| 1 - 11 |
| 1 - 12 |
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Ɍɚɛɥ. 5 ɨɬɪɚɠɚɟɬ ɪɟɡɭɥɶɬɚɬ ɜɵɩɨɥɧɟɧɢɹ ɩɪɨɝɪɚɦɦɨɣ SCAD ɚɥɝɨɪɢɬɦɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ
ɧɚ ɷɬɚɩɟ ɜɵɱɢɫɥɟɧɢɹ ɜɟɤɬɨɪɨɜ ɩɟɪɟɦɟɳɟɧɢɣ (11) ɜɨ ɜɫɟɯ 12-ɢɋɎɄ, ɩɨɥɭɱɢɜɲɢɯɫɹ ɜ
ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɥɨɠɟɧɢɹ ɩɨ ɋɎɄ ɜɟɤɬɨɪɚ ɢɫɤɨɦɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɭɡɥɨɜ ɪɚɫɱɟɬɧɨɣ ɪɚɦɵ
(ɫɦ. ɪɢɫ. 2) ɞɥɹ ɆɄɗ ɩɪɢ ɫɟɣɫɦɢɱɟɫɤɨɦ ɜɨɡɞɟɣɫɬɜɢɢ.
ȼ ɬɚɛɥ. 5 ɩɪɢɜɟɞɟɧɵ ɩɟɪɟɦɟɳɟɧɢɹ ɭɡɥɨɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ ɞɥɹ ɆɄɗ (ɫɦ. ɪɢɫ. 2)
ɬɨɥɶɤɨ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ (ɩɨ ɨɫɢ X).
ɂɡ ɪɚɫɫɦɨɬɪɟɧɢɹ ɬɚɛɥ. 5 ɫɥɟɞɭɟɬ, ɱɬɨ ɧɚɢɛɨɥɶɲɟɟ ɜɥɢɹɧɢɟ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɪɚɫɱɟɬɧɨɝɨ
ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɥɸɛɨɝɨ ɭɡɥɚ ɪɚɦɵ ɨɤɚɡɵɜɚɸɬ ɩɟɪɜɵɟ ɞɜɟ ɋɎɄ. Ɉɫɬɚɥɶɧɵɦɢ
ɩɪɢ ɷɬɨɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɉɨɷɬɨɦɭ ɜ ɮɨɪɦɭɥɟ (8) ɋɇɢɉ [18] (ɜ ɮɨɪɦɭɥɟ (12) ɞɚɧɧɨɣ
ɩɨɹɫɧɢɬɟɥɶɧɨɣ ɡɚɩɢɫɤɢ) ɦɨɠɧɨ ɩɪɢɧɹɬɶ n* = 2.
Ɋɢɫ. 9
1
23
4
56
7
8
9
ɉɟɪɟɦɟɳɟɧɢɹ ɨɬ
ɫɟɣɫɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ
ɜ 1-ɣɋɎɄ
– 0.023
– 0.048
– 0.048
– 0.023
– 0.015
– 0.048
205
Ɋɢɫ. 10
Ƚɨɪɢɡɨɧɬɚɥɶɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɭɡɥɨɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ (ɫɦ. ɪɢɫ.2) ɨɬ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɟɣɫɦɢɱɟɫɤɢɯ (ɢɧɟɪɰɢɨɧɧɵɯ) ɧɚɝɪɭɡɨɤ ɜ ɩɟɪɜɵɯ ɞɜɭɯ ɋɎɄ (ɫɦ. ɪɢɫ. 7 ɢ 8)
ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 9, 10.
Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɧɨ ɨɬɪɟɞɚɤɬɢɪɨɜɚɬɶ ɬɚɛɥɢɰɭ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɭɫɢɥɢɣ ɜ ɧɚɡɧɚɱɟɧɧɵɯ
ɤɨɧɰɟɜɵɯ ɫɟɱɟɧɢɹɯ Ʉɗ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ ɞɥɹ ɆɄɗ (ɫɦ. ɪɢɫ. 2). Ⱦɥɹ ɷɬɨɝɨ ɜ ɨɫɧɨɜɧɨɦ
ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɩɨ ɪɟɞɚɤɬɢɪɨɜɚɧɢɸ ɬɚɛɥɢɰ ɚɤɬɢɜɢɡɢɪɭɟɦ ɫɬɪɨɤɭ .
ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ ɬɚɛɥ. 6 ɫɥɟɞɭɸɳɟɝɨ ɜɢɞɚ.
ȼ ɬɚɛɥ. 6 ɩɪɢɜɟɞɟɧɵ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɜ ɤɨɧɰɟɜɵɯ ɫɟɱɟɧɢɹɯ Ʉɗ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
ɪɚɦɵ ɞɥɹ ɆɄɗ ɜɨ ɜɫɟɯ 12-ɢɋɎɄ. ȼ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ (ɜɆɋɄ) ɤɨɧɰɟɜɵɟ ɫɟɱɟɧɢɹ
ɤɚɠɞɨɝɨ Ʉɗ ɢɦɟɸɬ ɧɨɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ 1 ɢ 2. ȼ ɬɚɛɥɢɰɟ 6 ɞɥɹ ɤɚɠɞɨɝɨ Ʉɗ ɭɤɚɡɚɧɵ ɢ
ɧɨɦɟɪɚ ɭɡɥɨɜ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɢ ɜ ɨɛɳɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ (ɜɈɋɄ).
ȼ ɬɚɛɥɢɰɟ 6 ɞɥɹ ɤɚɠɞɨɝɨ ɤɨɧɰɟɜɨɝɨ ɫɟɱɟɧɢɹ Ʉɗ ɩɨ ɮɨɪɦɭɥɟ (8) ɋɇɢɉ [18] (ɩɨ
ɮɨɪɦɭɥɟ (12) ɜ ɞɚɧɧɨɣ ɩɨɹɫɧɢɬɟɥɶɧɨɣ ɡɚɩɢɫɤɟ) ɩɨɞɫɱɢɬɚɧɨ ɡɧɚɱɟɧɢɟ ɪɚɫɱɟɬɧɨɝɨ ɦɨɦɟɧɬɚ.
ɗɬɢ ɪɚɫɱɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɜ ɩɨɫɥɟɞɧɟɣ ɫɬɪɨɤɟ ɬɚɛɥɢɰɵ (ɨɧɚ ɢɦɟɟɬ ɨɛɨɡɧɚɱɟɧɢɟ
«s1»). Ɉɧɢ ɩɨɞɫɱɢɬɚɧɵ ɩɨ ɭɤɚɡɚɧɧɵɦ ɮɨɪɦɭɥɚɦ ɫ ɭɱɟɬɨɦ ɜɫɟɯ 12-ɢɋɎɄ.
Ɉɞɧɚɤɨ, ɤɚɤ ɜɢɞɧɨ (ɫɦ. ɬɚɛɥ. 6), ɧɚɢɛɨɥɶɲɢɣ ɜɤɥɚɞ ɜ ɪɚɫɱɟɬɧɵɟ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ,
ɨɩɪɟɞɟɥɹɟɦɵɟ ɩɨ ɮɨɪɦɭɥɟ (8) ɋɇɢɉ [18], ɢɦɟɸɬ ɩɟɪɜɵɟ ɞɜɟ ɋɎɄ. ɉɪɨɞɟɦɨɧɫɬɪɢɪɭɟɦ ɷɬɨ ɧɚ
ɩɪɢɦɟɪɟ ɪɚɫɱɟɬɧɨɝɨ ɢɡɝɢɛɚɸɳɟɝɨ ɦɨɦɟɧɬɚ ɜ ɭɡɥɟ 1 Ʉɗ 1 ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ (ɫɦ. ɪɢɫ. 2).
Ɍɚɛɥɢɰɚ 6
--------------------------------------------------------------------------------
| ɂɁȽɂȻȺɘɓɂȿ ɆɈɅɆȿɇɌɕ ȼ ɄɈɇɐȿȼɕɏ ɋȿɑȿɇɂəɏ 1 ɂ 2 Ʉɗ (ɜ ɆɋɄ), ɤɇ·ɦ |
--------------------------------------------------------------------------------
| 002_ 1-1 1-2 2-1 2-2 3-1 3-2 4-1 |
| 1 1 4 4 2 2 5 |
| 4 4 7 7 5 5 8 |
--------------------------------------------------------------------------------
| 1 - 1 ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| M -403.798 258.266 -231.33 290.276 -403.471 257.598 -232.382 |
| 1 - 2 |
| M -43.3194 43.3752 43.5365 -33.6153 -43.3731 43.4848 43.7091 |
| 1 - 3 |
| M -.012551 .021186 .046994 -.041467 -.009962 .015878 .038628 |
| 1 - 4 |
| M -.000101 .000132 -.000559 .000731 -.000099 .000129 -.000564 |
| 1 - 5 |
| M -.000088 .000117 -.000379 .000488 -.000085 .000112 -.000386 |
1 2
3
4
5
6
7
8
9
0.0004
– 0.002
0.0004
0.0005
0.0002
– 0.002
ɉɟɪɟɦɟɳɟɧɢɹ ɨɬ
ɫɟɣɫɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ
ɜɨ 2-ɣɋɎɄ
206
(ɉɪɨɞɨɥɠɟɧɢɟ ɬɚɛɥɢɰɵ 6)
| 1 - 6 |
| 1 - 7 |
| M .000309 -.000616 -.001271 .001052 -.000002 .000037 -.000233 |
| 1 - 8 |
| M .00008 -.000073 -.000066 .000031 -.00008 .000073 .000066 |
| 1 - 9 |
| M -.000149 .000221 .000301 -.000196 .00015 -.000223 -.000307 |
| 1 - 10 |
| M -.000014 .000023 -.000015 8.29e-7 -.000014 .000023 -.000015 |
| 1 - 11 |
| M -.00001 .000016 -.000006 -.000006 -.00001 .000016 -.000006 |
| 1 - S1 |
| M -406.115 261.883 -235.391 292.216 -405.796 261.243 -236.457 |
--------------------------------------------------------------------------------
(ɉɪɨɞɨɥɠɟɧɢɟ ɬɚɛɥɢɰɵ 6)
--------------------------------------------------------------------------------
| ɂɁȽɂȻȺɘɓɂȿ ɆɈɅɆȿɇɌɕ ȼ ɄɈɇɐȿȼɕɏ ɋȿɑȿɇɂəɏ 1 ɂ 2 Ʉɗ (ɜ ɆɋɄ), ɤɇ·ɦ |
--------------------------------------------------------------------------------
| 002_ 4-2 5-1 5-2 6-1 6-2 7-1 7-2 |
| 5 3 3 6 6 4 4 |
| 8 6 6 9 9 5 5 |
--------------------------------------------------------------------------------
| 1 - 1 ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| M 291.014 -148.196 -70.309 -70.309 -489.597 489.98 |
| 1 - 2 |
| M -33.7363 1.86318 .307102 .307102 .161287 -.224273 |
| 1 - 3 |
| M -.035599 -5.95768 4.96604 4.96604 .025807 -.022749 |
| 1 - 4 |
| M .000734 -.00003 -.000039 -.000039 -.000692 .000694 |
| 1 - 5 |
| M .000493 -.000024 -.000025 -.000025 -.000496 .000498 |
| 1 - 6 |
| 1 - 7 |
| M .000321 -.000577 .00088 .00088 -.000654 .00027 |
| 1 - 8 |
| M -.000031 -.000001 .000002 .000002 .000007 .000007 |
| 1 - 9 |
| M .000202 -.000099 .000173 .000173 .000079 .000083 |
| 1 - 10 |
| M 8.2e-7 -.000001 -7.07e-7 -7.07e-7 -.000038 .000038 |
| 1 - 11 |
| M -.000006 -6.74e-7 -3.37e-7 -3.37e-7 -.000023 .000023 |
| 1 - S1 |
| M 292.963 -148.327 -70.4848 -70.4848 -489.597 489.981 |
--------------------------------------------------------------------------------
(ɉɪɨɞɨɥɠɟɧɢɟ ɬɚɛɥɢɰɵ 6)
--------------------------------------------------------------------------------
| ɂɁȽɂȻȺɘɓɂȿ ɆɈɅɆȿɇɌɕ ȼ ɄɈɇɐȿȼɕɏ ɋȿɑȿɇɂəɏ 1 ɂ 2 Ʉɗ (ɜ ɆɋɄ), ɤɇ·ɦ |
--------------------------------------------------------------------------------
| 2_ 8-1 8-2 9-1 9-2 |
| 7 7 8 8 |
| 8 8 9 9 |
--------------------------------------------------------------------------------
| 1 - 1 ( ɫɟɣɫɦ-2000-ɪɚɫɩɪɟɞɟɥ. ɦɚɫɫɚ Ʉɗ) |
| M -290.276 291.014 |
| 1 - 2 |
| M 33.6153 -33.7363 |
| 1 - 3 |
| M .041467 -.035599 |
| 1 - 4 |
207
(ɉɪɨɞɨɥɠɟɧɢɟ ɬɚɛɥɢɰɵ 6)
| M -.000731 .000734 |
| 1 - 5 |
| M -.000488 .000493 |
| 1 - 6 |
| 1 - 7 |
| M -.001052 .000321 |
| 1 - 8 |
| M -.000031 -.000031 |
| 1 - 9 |
| M .000196 .000202 |
| 1 - 10 |
| M -8.29e-7 8.2e-7 |
| 1 - 11 |
| M .000006 -.000006 |
| 1 - 12 |
| 1 - S1 |
| M -292.216 292.963 |
--------------------------------------------------------------------------------
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɭɱɢɬɵɜɚɹ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɮɨɪɦɭɥɵ ɬɨɥɶɤɨ ɩɟɪɜɵɟ ɞɜɟ ɋɎɄ,
ɩɨɥɭɱɢɦ:
¦
2
1
2
1ɪ1
i
i
MM =
22
)3.43()8.403( = 89.187444.163054 = 33.164929 = 406.115 ɤɇ·ɦ
Ʉɚɤ ɜɢɞɢɦ, ɩɨɥɭɱɢɥɫɹ ɬɚɤɨɣ ɠɟ ɪɟɡɭɥɶɬɚɬ, ɤɚɤ ɢ ɜ ɬɚɛɥ. 6.
ɇɚ ɪɢɫ. 11 ɢ 12 ɩɪɢɜɟɞɟɧɵ ɷɩɸɪɵ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ ɞɥɹ ɩɟɪɜɵɯ ɞɜɭɯ ɋɎɄ.
Ɋɢɫ. 11
Ɋɢɫ. 12
208
ȼ ɢɫɩɨɥɶɡɭɟɦɨɣ ɜ ɋɇɢɉ [18] ɦɟɬɨɞɢɤɟ ɅɋɌ ɡɧɚɤ ɪɚɫɱɟɬɧɨɦɭ ɦɨɦɟɧɬɭ ɜ ɤɚɠɞɨɦ
ɤɨɧɤɪɟɬɧɨɦ ɫɟɱɟɧɢɢ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɬɚɤɨɣ ɠɟ, ɤɚɤɨɣ ɢɦɟɟɬ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ, ɜɧɨɫɹɳɢɣ
ɧɚɢɛɨɥɶɲɢɣ ɜɤɥɚɞ ɜ ɡɧɚɱɟɧɢɟ ɪɚɫɱɟɬɧɨɝɨ ɦɨɦɟɧɬɚ. Ʉɚɤ ɜɢɞɧɨ (ɫɦ. ɬɚɛɥ. 6), ɨɫɧɨɜɧɨɣ ɜɤɥɚɞ ɜ
ɪɚɫɱɟɬɧɵɟ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɪɚɦɵ (ɫɦ. ɪɢɫ.2) ɢɦɟɟɬ
ɩɟɪɜɚɹ ɋɎɄ. ɉɨɷɬɨɦɭ ɜɫɟɦ ɪɚɫɱɟɬɧɵɦ ɦɨɦɟɧɬɚɦ
ɩɪɢɫɜɨɟɧ ɬɚɤɨɣ ɠɟ ɡɧɚɤ, ɤɚɤ ɜ ɩɟɪɜɨɣ ɋɎɄ.
ȼɵɩɨɥɧɟɧɢɟ ɪɚɫɱɟɬɚ ɧɚ ɫɟɣɫɦɢɱɟɫɤɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɡɚɞɚɧɧɨɣ ɪɚɫɱɟɬɧɨɣ
ɫɯɟɦɵ ɪɚɦɵ (ɫɦ. ɪɢɫ. 2) ɩɪɢ ɭɱɟɬɟ ɬɨɥɶɤɨ ɩɟɪɜɵɯ ɞɜɭɯ ɋɎɄ
Ⱥɧɚɥɢɡ ɬɚɛɥɢɰ 4, 5 ɢ 6 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫ ɜɟɥɢɱɢɧɚɦɢ ɧɚɝɪɭɡɨɤ ɢ ɜɵɡɜɚɧɧɵɯ ɢɦɢ
ɩɟɪɟɦɟɳɟɧɢɣ ɢ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ, ɩɨɥɭɱɟɧɧɵɯ ɜɨ ɜɫɟɯ 12-ɢ ɋɎɄ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ
ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɪɚɦɵ (ɫɦ. ɪɢɫ. 2), ɩɨɤɚɡɵɜɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɭɦɟɧɶɲɟɧɢɹ ɜɵɜɨɞɢɦɨɣ
ɢɧɮɨɪɦɚɰɢɢ ɩɪɢ ɪɚɫɱɟɬɟ ɪɚɦɵ, ɟɫɥɢ ɜ ɫɚɦɨɦ ɧɚɱɚɥɟ ɫɨɫɬɚɜɥɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɡɚɝɪɭɠɟɧɢɹ
ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɧɚ ɡɚɩɪɨɫ ɨ ɱɢɫɥɟ ɭɱɢɬɵɜɚɟɦɵɯ ɩɪɢ ɪɚɫɱɟɬɟ ɋɎɄ
ɜɜɟɫɬɢ ɧɟ ɱɢɫɥɨ «12»,
ɤɚɤ ɷɬɨ ɛɵɥɨ ɫɞɟɥɚɧɨ ɜ ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɜɵɲɟ ɩɪɢɦɟɪɟ, ɚ ɜɜɟɫɬɢ ɰɢɮɪɭ «2».
ɉɨɫɬɪɨɢɦ ɬɚɤɨɣ ɪɚɫɱɟɬ, ɫɨɫɬɚɜɢɜ ɧɨɜɨɟ ɞɢɧɚɦɢɱɟɫɤɨɟ ɡɚɝɪɭɠɟɧɢɟ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɪɚɡɞɟɥɟ
«Ɂɚɝɪɭɠɟɧɢɹ» ɫɧɨɜɚ ɧɚɠɦɟɦ ɤɧɨɩɤɭ «Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɜɨɡɞɟɣɫɬɜɢɹ» ɢ ɜɵɛɟɪɟɦ «ɋɨɡɞɚɧɢɟ
ɧɨɜɨɝɨ ɡɚɝɪɭɠɟɧɢɹ».
Ⱦɚɥɟɟ, ɫ ɭɱɟɬɨɦ ɭɠɟ ɜɵɩɨɥɧɟɧɧɨɝɨ ɩɟɪɜɨɝɨ ɩɪɢɦɟɪɚ, ɜɵɩɨɥɧɢɦ ɷɬɨɬ ɧɨɜɵɣ ɪɚɫɱɟɬ ɜ
ɫɨɤɪɚɳɟɧɧɨɣ ɮɨɪɦɟ
. ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɥɜɚ ɩɟɪɜɵɯ ɞɢɚɥɨɝɨɜɵɯ ɨɤɧɚ ɞɢɚɥɨɝɨɜɵɯ ɨɤɧɚ ɩɪɢ
ɡɚɞɚɧɢɢ ɬɟɯ ɠɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ, ɱɬɨ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɪɢɦɟɪɟ ɫ ɨɬɥɢɱɢɟɦ ɬɨɥɶɤɨ
ɭɤɚɡɚɧɧɨɝɨ ɱɢɫɥɚ ɭɱɢɬɵɜɚɟɦɵɯ ɋɎɄ.
209
ȼɟɫɶ ɨɫɬɚɥɶɧɨɣ ɪɚɫɱɟɬ ɜɵɩɨɥɧɢɦ ɜ ɭɠɟ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ.
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɩɪɚɤɬɢɱɟɫɤɢ ɨɫɬɚɧɭɬɫɹ ɛɟɡ ɢɡɦɟɧɟɧɢɹ. Ɉɞɧɚɤɨ ɪɟɡɤɨ ɫɨɤɪɚɬɢɬɫɹ
ɨɛɴɟɦ ɜɵɜɨɞɢɦɵɯ ɬɚɛɥɢɰ.
2. ɄɈɇɌɊɈɅɖɇɕȿ ɊȺɋɑȿɌɕ ȼɊɍɑɇɍɘ
ɉɈ ɎɈɊɆɍɅȺɆ ɑȺɋɌɂ 1 ɍɆɄ, ɉɈɋɈȻɂə [4] ɂ ɋɇɂɉ [18]
Ɋɚɫɱɟɬ, ɜɵɩɨɥɧɟɧɧɵɣ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD ɦɨɠɧɨ ɥɟɝɤɨ
ɩɪɨɜɟɪɢɬɶ ɜɪɭɱɧɭɸ ɩɨ ɮɨɪɦɭɥɚɦ, ɩɪɢɜɟɞɟɧɧɵɦ ɜ ɭɤɚɡɚɧɧɵɯ ɩɨɫɨɛɢɹɯ.
2.1. ɉɪɨɜɟɪɤɚ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɋɎɄ
ɋɜɨɣɫɬɜɨ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɨɬɪɚɠɟɧɨ ɜ ɱɚɫɬɢ 1 ɍɆɄ ɢ ɜ ɩɨɫɨɛɢɢ [4] ɮɨɪɦɭɥɨɣ (2.29):
ij
uɆu
ɬ
)( =
ij
uGu
ɬ
)( = 0.
Ɂɞɟɫɶ
j
u – ɜɟɤɬɨɪ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɥɸɛɨɣ ɋɎɄ ɫ ɧɨɦɟɪɨɦ j;
i
u – ɜɟɤɬɨɪ ɩɟɪɟɦɟɳɟɧɢɣ
ɜ ɥɸɛɨɣ ɞɪɭɝɨɣ ɋɎɄ ɫ ɧɨɦɟɪɨɦ
j
i z .
ɉɪɨɜɟɪɢɦ ɫɨɛɥɸɞɟɧɢɟ ɷɬɨɝɨ ɫɜɨɣɫɬɜɚ ɞɥɹ 1-ɣɢ 2-ɣɋɎɄ, ɩɨɥɭɱɟɧɧɵɯ ɩɪɢ ɪɚɫɱɟɬɟ
(ɫɦ. ɬɚɛɥ. 2):
(0.4724 0.4724 0.3153 0.9961 0.9981 1)·
»
»
»
»
»
»
¼
º
«
«
«
«
«
«
¬
ª
4.184
361
4.184
69.15
2.192
2.192
·
»
»
»
»
»
¼
º
«
«
«
«
«
¬
ª
2579.0
2486.0
2395.0
0932.0
1
1
=
·.
= (90.795 90.795 4.947 183.681 360.314 184.4)·
»
»
»
»
»
¼
º
«
«
«
«
«
¬
ª
2579.0
2486.0
2395.0
0932.0
1
1
= (90.785 90.795 - 0.461 - 43.992 -
- 89.574 -47.557) = 181.59 – 181.58 = 0.
ɋɜɨɣɫɬɜɨ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ 1-ɣɢ 2-ɣ
ɋɎɄ ɫɨɛɥɸɞɚɟɬɫɹ.
2.2. ɉɪɨɜɟɪɤɚ ɪɚɜɟɧɫɬɜɚ ɫɭɦɦɵ ɜɟɤɬɨɪɨɜ
i
ˤ
ɞɥɹ ɜɫɟɯ ɋɎɄ
ɩɪɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦ ɫɟɣɫɦɢɱɟɫɤɨɦ ɜɨɡɞɟɣɫɬɜɢɢ ɟɞɢɧɢɱɧɨɦɭ ɜɟɤɬɨɪɭ
e
ɗɬɨ ɪɚɜɟɧɫɬɜɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ (2.92) ɜ ɱɚɫɬɢ 1 ɍɆɄ ɢ ɜ ɩɨɫɨɛɢɢ [4] (ɮɨɪɦɭɥɚ
(8) ɜ ɞɚɧɧɨɣ ɩɨɹɫɧɢɬɟɥɶɧɨɣ ɡɚɩɢɫɤɟ). ɉɪɨɜɟɪɢɦ ɷɬɨ.
2.2.1. ɋɧɚɱɚɥɚ ɩɨ ɮɨɪɦɭɥɟ (6) ɞɚɧɧɨɣ ɪɚɛɨɬɵ ɩɨɞɫɱɢɬɚɟɦ ɩɨɫɬɨɹɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ
ɞɥɹ 1-ɣɋɎɄ:
1
ɬ
1
ɬ
1
1
ɬ
1
ɬ
1
1
)(
)(
)(
)(
uGu
eGu
uɆu
eɆu
K
.
ɉɪɢ ɷɬɨɦ ɭɱɬɟɦ, ɱɬɨ ɪɟɡɭɥɶɬɚɬ ɩɟɪɟɦɧɨɠɟɧɢɹ ɩɟɪɜɵɯ ɞɜɭɯ ɦɚɬɪɢɰ ɜ ɱɢɫɥɢɬɟɥɟ ɢ
ɡɧɚɦɟɧɚɬɟɥɟ ɷɬɨɝɨ ɜɵɪɚɠɟɧɢɹ ɭɠɟ ɢɦɟɟɬɫɹ ɜ ɬɨɥɶɤɨ ɱɬɨ ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɩɭɧɤɬɟ 2.1.
Ɍɨɝɞɚ ɜ ɱɢɫɥɢɬɟɥɟ ɩɨɥɭɱɢɦ:
(90.795 90.795 4.947 183.681 360.314 184.4)·(1 1 1 1 1 1)
Ɍ
= 90.795 + 90.795 + 4.947 +
+183.681 + 360.314 +184.4) = 914.932.
ȼ ɡɧɚɦɟɧɚɬɟɥɟ ɩɨɥɭɱɢɦ: