Федоров М.П. и др. Информационно-компьютерные технологии в строительстве. Применение программы SCAD для расчета сооружений на динамические воздействия
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70
ɧɚɠɢɦɚɟɦ ɤɧɨɩɤɭ ɢ ɡɚɞɚɟɦ ɧɚ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɚɯ, ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɯ ɛɚɥɤɭ, ɜɟɫ
ɨɞɧɨɝɨ ɩɨɝɨɧɧɨɝɨ ɦɟɬɪɚ ɛɚɥɤɢ:
Ɉɬɦɟɱɚɟɦ ɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ, ɤ ɤɨɬɨɪɵɦ ɨɬɧɨɫɢɬɫɹ ɷɬɚ ɦɚɫɫɚ. ɉɪɢ ɷɬɨɦ ɧɚ ɪɚɫɱɟɬɧɨɣ
ɫɯɟɦɟ ɆɄɗ ɛɚɥɤɢ (ɫɦ. ɪɢɫ. 1.28) ɩɨɹɜɢɬɫɹ ɢɧɮɨɪɦɚɰɢɹ ɨ ɫɞɟɥɚɧɧɨɦ ɜɜɨɞɟ.
ɉɪɢɦɟɱɚɧɢɟ. ȼ ɩɟɪɜɨɦ ɜɚɪɢɚɧɬɟ ɡɚɝɪɭɠɟɧɢɹ (ɫɦ. ɩɪɢɦɟɪ 4 ɜ ɩɨɞɪɚɡɞɟɥɟ 1.1) ɜ
ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɜ ɭɡɥɟ 2 ɜɦɟɫɬɨ ɧɭɥɟɜɨɝɨ ɡɧɚɱɟɧɢɹ ɛɭɞɟɬ ɜɜɟɞɟɧɨ ɡɧɚɱɟɧɢɟ ɜɟɫɚ ɦɚɫɫɵ ɜ
ɭɡɥɟ 2 ɪɚɜɧɨɟ gmG
ɩɪ,22
= (2.4 ɬ)·(9.81 ɦ/ɫ
2
) = 23.544 ɤɇ, ɩɨɷɬɨɦɭ ɧɚ ɪɢɫ. 1.28 ɜ ɭɡɥɟ 2
ɜɦɟɫɬɨ D0 ɤɇ ɛɭɞɟɬ ɨɛɨɡɧɚɱɟɧɢɟ D23.544 ɤɇ. Ɋɚɫɩɪɟɞɟɥɟɧɧɚɹ ɦɚɫɫɚ ɛɚɥɤɢ ɜ ɜɚɪɢɚɧɬɟ 1 ɧɟ
ɜɜɨɞɢɬɫɹ, ɬɚɤ ɤɚɤ ɨɧɚ ɭɱɬɟɧɚ ɜ ɜɢɞɟ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɣ ɦɚɫɫɵ ɜ ɭɡɥɟ 2. ɉɨɷɬɨɦɭ ɩɪɢɜɟɞɟɧɧɨɝɨ
ɡɞɟɫɶ ɜɬɨɪɨɝɨ ɞɢɚɥɨɝɨɜɨɝɨ ɨɤɧɚ ɩɨ ɜɜɨɞɭ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɵ Ʉɗ ɧɟ ɛɭɞɟɬ, ɢ ɧɚ ɪɢɫ 1.28
ɛɭɞɟɬ ɨɬɫɭɬɫɬɜɨɜɚɬɶ ɭɤɚɡɚɧɢɟ ɧɚ ɜɜɨɞ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ
ɦɚɫɫɵ.
7. ɉɪɢ ɥɸɛɨɦ ɜɚɪɢɚɧɬɟ ɡɚɝɪɭɠɟɧɢɹ ɟɝɨ ɧɚɞɨ ɫɨɯɪɚɧɢɬɶ, ɚ ɡɚɬɟɦ ɡɚɣɬɢ ɜ ɪɚɡɞɟɥ
«ɍɩɪɚɜɥɟɧɢɟ», ɧɚ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɣ ɩɚɧɟɥɢ ɤɨɬɨɪɨɝɨ ɜɵɛɪɚɬɶ ɤɧɨɩɤɭ
«ȼɵɣɬɢ ɜ ɷɤɪɚɧ
ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɟɤɬɨɦ» ɢɧɚ «ɞɟɪɟɜɟ ɩɪɨɟɤɬɚ» ɜ ɪɚɡɞɟɥɟ «Ɋɚɫɱɟɬ» ɜɵɛɪɚɬɶ «Ʌɢɧɟɣɧɵɣ».
8. ɉɨɫɥɟ ɜɵɩɨɥɧɟɧɢɹ ɥɢɧɟɣɧɨɝɨ ɪɚɫɱɟɬɚ ɜɵɛɢɪɚɟɦ ɜ ɪɚɡɞɟɥɟ «Ɋɟɡɭɥɶɬɚɬɵ» ɧɚ «ɞɟɪɟɜɟ
ɩɪɨɟɤɬɚ» ɩɨɞɪɚɡɞɟɥ «ɉɟɱɚɬɶ ɬɚɛɥɢɰ». Ɉɬɤɪɨɟɬɫɹ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɬɚɛɥɢɰ ɫ
ɪɟɡɭɥɶɬɚɬɚɦɢ ɪɚɫɱɟɬɚ.
Ɋɟɡɭɥɶɬɚɬɵ ɪɟɲɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ «ɂɦɩɭɥɶɫ» ɧɚɯɨɞɹɬɫɹ ɜ ɭɠɟ ɢɡɜɟɫɬɧɵɯ ɢɡ
ɡɚɞɚɱɢ ɨ ɪɚɫɱɟɬɟ ɛɚɥɤɢ ɩɪɢ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɹɯ ɱɟɬɵɪɟɯ ɬɚɛɥɢɰɚɯ
ɪɚɡɞɟɥɚ «Ⱦɢɧɚɦɢɤɚ» (ɫɦ. ɩɪɢɦɟɪ 1 ɜ ɩɨɞɪɚɡɞɟɥɟ 1.4).
Ⱦɥɹ ɨɬɤɪɵɬɢɹ ɷɬɢɯ ɬɚɛɥɢɰ ɚɤɬɢɜɢɡɢɪɭɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɫɬɪɨɤɭ ɜ ɩɪɚɜɨɦ ɫɬɨɥɛɰɟ
ɞɢɚɥɨɝɨɜɨɝɨ ɨɤɧɚ ɫ ɧɚɡɜɚɧɢɟɦ «Ⱦɢɧɚɦɢɤɚ». ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɫɥɟ ɪɟɞɚɤɬɢɪɨɜɚɧɢɹ ɬɚɛɥɢɰ ɢ ɫ
ɭɱɟɬɨɦ ɩɟɪɜɨɝɨ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɡɚɝɪɭɠɟɧɢɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɱɢ «Ɇɨɞɚɥɶɧɵɣ ɚɧɚɥɢɡ»
ɩɨɥɭɱɢɦ ɫɧɚɱɚɥɚ ɩɟɪɜɭɸ ɬɚɛɥɢɰɭ:
------------------------------------------------------------------
| ɊȺɋɉɊȿȾȿɅȿɇɂȿ ȼȿɋɈȼ ɆȺɋɋ, ɬɫ |
------------------------------------------------------------------
| 1 2 3 |
------------------------------------------------------------------
| 1 - (ɦɨɞ-1) |
| Z 2.4 |
| 2 - (ɢɦɩɭɥɶɫ-1) |
| Z 2.4 |
------------------------------------------------------------------
ȼɬɨɪɚɹ ɬɚɛɥɢɰɚ ɫɨɞɟɪɠɢɬ ɫɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ
Z
, ɫ
-1
,
SZ
Q 2/
, Ƚɰ, ɢ ɩɟɪɢɨɞ
ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ
Q ZS /1/2T , ɫ.
ȼ ɬɪɟɬɶɟɣ ɬɚɛɥɢɰɟ ɩɪɢɜɨɞɢɬɫɹ ɟɞɢɧɢɱɧɨɟ ɡɧɚɱɟɧɢɟ ɨɪɞɢɧɚɬɵ ɋɎɄ ɜ ɭɡɥɟ 2.
71
-------------------------------------------------------------------------------
|Ɂɚɝpɭ: N : COȻCTB. : ɑ A C T O T ɕ : ɉEPɂOȾɕ |
| : ɉ/ɉ : :-----------------------------:-----------
|ɠɟɧɢɟ: : ɁHAɑEHɂə : 1/C : Ƚɐ : C |
-------------------------------------------------------------------------------
| 1 .0108832 91.88433 14.63126 .0683467 |
| |
| 2 .0108832 91.88433 14.63126 .0683467 |
------------------------------------------------------------------
------------------------------------------------------------------
| ɎɈɊɆɕ ɄɈɅȿȻȺɇɂɃ |
------------------------------------------------------------------
| 1 2 3 |
------------------------------------------------------------------
| 1 (ɦɨɞ-1) |
| Z 1. |
| 2 (ɢɦɩɭɥɶɫ-1) |
| Z 1. |
------------------------------------------------------------------
------------------------------------------------------------------
| ɂɇȿɊɐɂɈɇɇɕȿ ɇȺȽɊɍɁɄɂ, ɬɫ |
------------------------------------------------------------------
| 1 2 3 |
------------------------------------------------------------------
| 2 (ɢɦɩɭɥɶɫ-1) |
| Z -2.8 |
------------------------------------------------------------------
ɑɟɬɜɟɪɬɚɹ ɬɚɛɥɢɰɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɡɧɚɱɟɧɢɟ ɪɚɫɱɟɬɧɨɣ ɫɢɥɵ 8.2
ɪɚɫɱ
P ɬɫ ɜ ɭɡɥɟ 2.
Ⱥɧɚɥɨɝɢɱɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨɥɭɱɢɬɫɹ ɩɪɢ ɪɭɱɧɨɦ ɪɚɫɱɟɬɟ (ɫɦ. ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɮɨɪɦɭɥɵ (1.117)
ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ): 5.187.1
ɪɚɫɱ
P =2.8 ɬɫ.
ɉɪɢɦɟɱɚɧɢɟ ɤ ɩɨɫɥɟɞɧɟɣ ɬɚɛɥɢɰɟ.
ɗɬɚ ɬɚɛɥɢɰɚ ɧɚɡɜɚɧɚ «ɂɧɟɪɰɢɨɧɧɵɟ ɧɚɝɪɭɡɤɢ» ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɚɦɩɥɢɬɭɞɭ
ɪɚɫɱ
P
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɚɦɩɥɢɬɭɞɭ ɢɧɟɪɰɢɨɧɧɨɣ ɫɢɥɵ
AmJ
2
Z = AJ ɩɪɢ ɫɨɛɫɬɜɟɧɧɵɯ
ɤɨɥɟɛɚɧɢɹɯ ɛɚɥɤɢ ɫ ɱɚɫɬɨɬɨɣ
Z ɢ ɚɦɩɥɢɬɭɞɨɣ ɩɟɪɟɦɟɳɟɧɢɣ E
ɫɬ
uA (ɫɦ. ɮɨɪɦɭɥɭ 1.31):
Am
u
PP
o
2
ɫɬ
ɪɚɫɱ
Z E
G
E = AJ .
Ɂɞɟɫɶ
1
2
Z mJ – ɚɦɩɥɢɬɭɞɚ ɢɧɟɪɰɢɨɧɧɨɣ ɫɢɥɵ, ɜɵɡɵɜɚɸɳɟɣ ɞɟɮɨɪɦɚɰɢɸ ɢ
ɩɟɪɟɦɟɳɟɧɢɹ ɛɚɥɤɢ ɩɨ ɩɟɪɜɨɣ ɫɨɛɫɬɜɟɧɧɨɣ ɮɨɪɦɟ ɤɨɥɟɛɚɧɢɣ, ɢɦɟɸɳɟɣ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
ɩɟɪɟɦɟɳɟɧɢɹɯ ɟɞɢɧɢɱɧɵɣ ɩɪɨɝɢɛ ɛɚɥɤɢ ɜ ɭɡɥɟ 2 ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɛɚɥɤɢ ɤɚɤ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ
ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ.
Ⱦɟɣɫɬɜɭɸɳɚɹ ɢɧɟɪɰɢɨɧɧɚɹ ɫɢɥɚ
E
ɫɬ
uJAJJ = ( 1
2
Zm )
2
Z
E
m
P
o
=
ɪɚɫɱ
P ɩɪɢ
ɤɨɥɟɛɚɧɢɹɯ ɛɚɥɤɢ ɢ ɛɭɞɟɬ ɪɚɫɱɟɬɧɨɣ ɫɢɥɨɣ, ɨɬ ɞɟɣɫɬɜɢɹ ɤɨɬɨɪɨɣ ɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɪɚɫɱɟɬɧɨɟ
ɩɟɪɟɦɟɳɟɧɢɟ ɭɡɥɚ 2 ɢ ɪɚɫɱɟɬɧɵɣ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ .
ɉɨɞɪɨɛɧɟɟ ɷɬɨɬ ɜɨɩɪɨɫ ɛɭɞɟɬ ɪɚɫɫɦɨɬɪɟɧ ɜ ɪɚɡɞɟɥɟ 2 ɩɨɫɨɛɢɹ, ɩɨɫɜɹɳɟɧɧɨɝɨ
ɫɢɫɬɟɦɚɦ ɫ ɧɟɫɤɨɥɶɤɢɦɢ ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɨɝɪɚɦɦɵ SCAD ɜɵɱɢɫɥɹɸɬɫɹ ɩɟɪɟɦɟɳɟɧɢɹ ɜ ɭɡɥɚɯ Ʉɗ ɜ ɨɛɳɟɣ
72
ɫɢɫɬɟɦɟ ɨɫɟɣ ɤɨɨɪɞɢɧɚɬ ɢ ɭɫɢɥɢɹ ɜ ɧɚɦɟɱɟɧɧɵɯ ɪɚɫɱɟɬɱɢɤɨɦ ɫɟɱɟɧɢɹɯ. ȼ ɞɚɧɧɨɦ ɩɪɢɦɟɪɟ
ɨɝɪɚɧɢɱɢɦɫɹ ɭɫɢɥɢɹɦɢ ɜ ɭɡɥɚɯ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɪɚɫɱɟɬɧɨɣ ɫɢɥɟ ɩɟɪɟɦɟɳɟɧɢɹ ɭɡɥɚ 2 ɢ
ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɜ ɧɟɦ ɩɪɢɜɟɞɟɧɵ ɜ ɫɥɟɞɭɸɳɢɯ ɬɚɛɥɢɰɚɯ.
------------------------------------------------------------------
| ɉȿɊȿɆȿɓȿɇɂə ɍɁɅɈȼ, ɦɦ |
------------------------------------------------------------------
| 1 2 3 |
------------------------------------------------------------------
| 1 - 1 ( ɢɦɩ=0.5ɬ) |
| Z 1.3 |
------------------------------------------------------------------
------------------------------------------------------------------
| ɍɋɂɅɂə /ɇȺɉɊəɀȿɇɂə/ ȼ ɗɅȿɆȿɇɌȺɏ, ɬɫ*ɦ |
------------------------------------------------------------------
| 2_ 1-1 1-2 2-1 2-2 |
------------------------------------------------------------------
| 2 - 1 (ɢɦɩɭɥɶɫ-1) |
| M -5.6 -5.6 |
------------------------------------------------------------------
Ɍɟɩɟɪɶ ɨɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ ɧɚ ɡɧɚɤɢ ɜɵɱɢɫɥɟɧɧɵɯ ɜɟɥɢɱɢɧ.
ɉɨɫɤɨɥɶɤɭ ɫɨɛɫɬɜɟɧɧɚɹ ɮɨɪɦɚ ɤɨɥɟɛɚɧɢɣ ɛɚɥɤɢ ɫ ɬɨɱɟɱɧɨɣ ɦɚɫɫɨɣ, ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɜ
ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ ɛɚɥɤɢ, ɢɦɟɟɬ ɜɢɞ, ɢɡɨɛɪɚɠɟɧɧɵɣ ɧɚ ɪɢɫ. 1.9, ɫ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɨɪɞɢɧɚɬɨɣ
ɩɟɪɟɦɟɳɟɧɢɹ ɪɚɜɧɨɣ +1, ɬɨ ɜɵɡɵɜɚɸɳɚɹ ɬɚɤɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɛɚɥɤɢ ɫɬɚɬɢɱɟɫɤɚɹ ɫɢɥɚ ɛɭɞɟɬ
ɩɪɟɞɫɬɚɜɥɹɬɶ ɫɨɛɨɣ ɚɦɩɥɢɬɭɞɧɨɟ ɡɧɚɱɟɧɢɟ ɢɧɟɪɰɢɨɧɧɨɣ ɫɢɥɵ 1
2
Z mJ ɢ ɛɭɞɟɬ ɧɚɩɪɚɜɥɟɧɚ
ɜ ɫɬɨɪɨɧɭ ɟɞɢɧɢɱɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ (ɪɢɫ. 1.29).
ɇɚɩɪɚɜɥɟɧɢɟ ɬɚɤɨɣ ɫɢɥɵ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɢɦɟɟɬ ɡɧɚɤ «ɦɢɧɭɫ». ɉɨɫɤɨɥɶɤɭ ɫɢɥɚ ɩɪɢ
ɢɡɝɢɛɟ ɛɚɥɤɢ ɪɚɫɬɹɝɢɜɚɟɬ ɜɟɪɯɧɸɸ ɫɬɨɪɨɧɭ ɛɚɥɤɢ , ɬɨ ɢ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ ɬɚɤɠɟ ɢɦɟɟɬ
ɡɧɚɤ «ɦɢɧɭɫ».
Ɋɢɫ. 1.29
ɂɡ ɮɢɡɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɹɫɧɨ, ɱɬɨ, ɬɚɤ ɤɚɤ ɛɚɥɤɚ ɩɨɫɥɟ ɢɦɩɭɥɶɫɧɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ
ɦɚɫɫɭ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɜɧɢɡ ɧɚɱɧɟɬ ɢɡɝɢɛɚɬɶɫɹ ɜɵɩɭɤɥɨɫɬɶɸ ɜɧɢɡ, ɬɨ ɩɨɥɭɱɟɧɧɨɟ
ɞɢɧɚɦɢɱɟɫɤɨɟ ɪɚɫɱɟɬɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ 3.1)(
ɪɚɫɱɪɚɫɱ
Pu ɦɦ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɨɫɭɦɦɢɪɨɜɚɧɨ
ɫɨ ɫɬɚɬɢɱɟɫɤɢɦ ɩɟɪɟɦɟɳɟɧɢɟɦ ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɛɚɥɤɢ 4.1)(
oɫɬ
Pu ɦɦ. ɗɬɨ ɛɵɥɨ
ɫɞɟɥɚɧɨ ɜɵɲɟ ɩɪɢ ɪɚɫɱɟɬɟ ɜɪɭɱɧɭɸ. Ⱥɧɚɥɨɝɢɱɧɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɫɭɦɦɢɪɨɜɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɣ
ɪɚɫɱɟɬɧɵɣ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ 6.5)(
ɪɚɫɱɪɚɫɱ
PM ɬɫ·ɦ ɫɨ ɫɬɚɬɢɱɟɫɤɢɦ ɢɡɝɢɛɚɸɳɢɦ
ɦɨɦɟɧɬɨɦ 8.4)(
oɫɬ
PM ɬɫ·ɦ. ɗɬɨ ɬɚɤɠɟ ɛɵɥɨ ɜɵɩɨɥɧɟɧɨ ɩɪɢ ɪɭɱɧɨɦ ɪɚɫɱɟɬɟ. Ɋɟɡɭɥɶɬɚɬɵ
ɪɭɱɧɨɝɨ ɪɚɫɱɟɬɚ ɢ ɪɚɫɱɟɬɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD ɫɨɜɩɚɞɚɸɬ.
73
1.6. Ⱦɟɣɫɬɜɢɟ ɭɞɚɪɧɨɣ ɧɚɝɪɭɡɤɢ
ȼ ɩɪɟɞɵɞɭɳɟɦ ɩɨɞɪɚɡɞɟɥɟ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ, ɱɬɨ ɱɢɫɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ
ɢɦɩɭɥɶɫɚ ɨɩɪɟɞɟɥɹɥɨɫɶ ɩɨ ɮɨɪɦɭɥɟ (1.125) ɩɨ ɬɪɟɦ ɭɤɚɡɚɧɧɵɦ ɬɚɦ
ɩɚɪɚɦɟɬɪɚɦ. ȿɫɥɢ ɢɦɩɭɥɶɫ ɫɜɹɡɚɧ ɫ ɭɞɚɪɨɦ ɩɨ ɤɨɧɫɬɪɭɤɰɢɢ ɧɟɤɨɬɨɪɨɝɨ ɬɟɥɚ
ɦɚɫɫɨɣ
m , ɡɧɚɱɟɧɢɟ ɢɦɩɭɥɶɫɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɩɪɢɛɥɢɠɟɧɧɨɣ ɮɨɪɦɭɥɟ
(1.129), ɩɪɢɜɟɞɟɧɧɨɣ ɜ ɫɩɪɚɜɨɱɧɢɤɟ [14] (ɬɚɦ ɢɦɩɭɥɶɫ
p
J ɢɦɟɟɬ ɨɛɨɡɧɚɱɟɧɢɟ
S
):
)1(
oop
kvmJ .
(1.129)
Ɂɞɟɫɶ
o
v
– ɫɤɨɪɨɫɬɶ ɭɞɚɪɹɸɳɟɝɨ ɬɟɥɚ ɜ ɧɚɱɚɥɟ ɭɞɚɪɚ;
o
k
– ɤɨɷɮɮɢɰɢɟɧɬ
ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɩɪɢ ɭɞɚɪɟ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɜɨɣɫɬɜ ɫɨɭɞɚɪɹɸɳɢɯɫɹ ɬɟɥ,
ɩɪɢɛɥɢɠɟɧɧɵɟ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɨɝɨ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 5.1 ɭɤɚɡɚɧɧɨɝɨ
ɫɩɪɚɜɨɱɧɢɤɚ [14].
ɂɡ ɬɪɟɯ ɩɚɪɚɦɟɬɪɨɜ ɢɦɩɭɥɶɫɚ ɪɟɲɚɸɳɟɟ ɜɥɢɹɧɢɟ ɧɚ ɪɟɚɤɰɢɸ ɫɢɫɬɟɦɵ
ɢɦɟɸɬ ɟɝɨ ɜɟɥɢɱɢɧɚ
S
ɢ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ W , ɮɨɪɦɚ ɠɟ ɢɦɩɭɥɶɫɚ ɨɤɚɡɵɜɚɟɬ
ɜɬɨɪɨɫɬɟɩɟɧɧɨɟ ɜɥɢɹɧɢɟ [14].
ȿɫɥɢ ɦɚɫɫɚ ɭɞɚɪɹɸɳɟɝɨ ɬɟɥɚ ɦɚɥɚ ɜ ɫɪɚɜɧɟɧɢɢ ɫ ɦɚɫɫɨɣ ɤɨɧɫɬɪɭɤɰɢɢ,
ɜɨɫɩɪɢɧɢɦɚɸɳɟɣ ɭɞɚɪ, ɪɚɫɱɟɬ ɤɨɧɫɬɪɭɤɰɢɢ ɤɚɤ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ
ɫɜɨɛɨɞɵ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɚ ɭɞɚɪɵ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɩɪɢ ɢɦɩɭɥɶɫɟ ɫɢɥɵ,
ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɨɞɪɚɡɞɟɥɟ.
ȿɫɥɢ ɠɟ ɦɚɫɫɚ ɭɞɚɪɹɸɳɟɝɨ ɬɟɥɚ ɫɪɚɜɧɢɦɚ ɫ ɦɚɫɫɨɣ ɭɞɚɪɹɟɦɨɣ
ɤɨɧɫɬɪɭɤɰɢɢ, ɬɨ, ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɵ ɤɨɧɫɬɪɭɤɰɢɢ ɤɚɤ
ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ, ɟɟ ɩɟɪɟɦɟɳɟɧɢɣ, ɚ ɬɚɤɠɟ ɭɫɢɥɢɣ,
ɫɜɹɡɚɧɧɵɯ ɫ ɤɨɥɟɛɚɧɢɟɦ ɫɢɫɬɟɦɵ, ɫɥɟɞɭɟɬ ɭɱɟɫɬɶ ɦɚɫɫɭ ɭɞɚɪɹɸɳɟɝɨ ɬɟɥɚ ɤɚɤ
ɩɪɢɫɨɟɞɢɧɟɧɧɭɸ ɤ ɦɚɫɫɟ ɤɨɧɫɬɪɭɤɰɢɢ. ɉɪɢ ɷɬɨɦ ɭɱɢɬɵɜɚɟɬɫɹ ɬɨɥɶɤɨ
ɫɨɫɬɚɜɥɹɸɳɚɹ ɭɞɚɪɧɨɝɨ ɢɦɩɭɥɶɫɚ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɹ ɦɚɫɫɵ.
ɉɪɢɦɟɪ 1. Ɋɚɫɫɦɨɬɪɢɦ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɩɪɨɫɬɨɣ ɨɞɧɨɩɪɨɥɟɬɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ
ɛɚɥɤɢ ɫ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɜɞɨɥɶ ɟɟ ɨɫɢ ɦɚɫɫɨɣ ɛɚɥɤɢ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ
ɛ
P (ɫɦ.
ɪɢɫ. 1.30, ɚ).
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɧɚ ɛɚɥɤɭ ɜ ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ ɫ ɜɵɫɨɬɵ
m
h ɭɩɚɥɨ ɬɟɥɨ, ɤɨɬɨɪɨɟ ɜ
ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɦɨɠɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɤɚɤ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ ɦɚɫɫɨɣ m (ɫɦ. ɪɢɫ. 1.30, ɚ).
ɉɪɢɜɟɞɟɦ ɛɚɥɤɭ ɫ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɨɣ ɤ ɫɢɫɬɟɦɟ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ
ɫɜɨɛɨɞɵ (ɪɢɫ. 1.30, ɛ) ɩɪɢɟɦɨɦ, ɪɚɫɫɦɨɬɪɟɧɧɵɦ ɜ ɩɪɢɦɟɪɟ 4 ɩɨɞɪɚɡɞɟɥɚ 1.1 ɢ ɜ ɩɪɢɦɟɪɟ 1
ɩɨɞɪɚɡɞɟɥɚ 1.4. Ɍɨɝɞɚ ɜɦɟɫɬɨ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɛɚɥɤɢ ɫ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɨɣ
(ɫɦ. ɪɢɫ. 1.30, ɚ) ɩɨɥɭɱɢɦ ɧɟɜɟɫɨɦɭɸ ɛɚɥɤɭ ɫ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɣ ɜ ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ ɦɚɫɫɨɣ
ɪɚɜɧɨɣ 0.5
ɛ
m (ɫɦ. ɪɢɫ 1.30, ɛ). ɉɨɫɥɟ ɩɚɞɟɧɢɹ ɝɪɭɡɚ ɧɚ ɫɢɫɬɟɦɭ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ ɤ
74
ɷɬɨɣ ɬɨɱɟɱɧɨɣ ɦɚɫɫɟ ɩɪɢɫɨɟɞɢɧɢɬɫɹ ɦɚɫɫɚ ɭɩɚɜɲɟɝɨ ɝɪɭɡɚ m , ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɜ ɰɟɧɬɪɟ
ɩɪɨɥɟɬɚ ɛɚɥɤɢ ɨɛɪɚɡɭɟɬɫɹ ɫɭɦɦɚɪɧɚɹ ɦɚɫɫɚ mmm
c
ɛ
5.0.
Ɋɢɫ. 1.30
ɉɪɢ ɩɚɞɟɧɢɢ ɦɚɫɫɵ ɧɚ ɛɚɥɤɭ ɩɨɫɥɟɞɧɹɹ ɢɫɩɵɬɚɟɬ ɞɟɣɫɬɜɢɟ ɭɞɚɪɧɨɝɨ ɢɦɩɭɥɶɫɚ
p
J
(1.129), ɝɞɟ
m
ghv 2
o
– ɫɤɨɪɨɫɬɶ, ɦ/ɫ, ɩɚɞɟɧɢɹ ɦɚɫɫɵ ɫ ɜɵɫɨɬɵ
m
h , ɦ, ɫ ɭɫɤɨɪɟɧɢɟɦ
ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ
81.9 g
ɦ/ɫ
2
. ɉɨɫɥɟ ɭɞɚɪɧɨɝɨ ɢɦɩɭɥɶɫɚ ɧɚɱɧɭɬɫɹ ɫɜɨɛɨɞɧɵɟ ɤɨɥɟɛɚɧɢɹ
ɫɢɫɬɟɦɵ ɫ ɭɝɥɨɜɨɣ ɱɚɫɬɨɬɨɣ
ɫɫɬ,ɫɫ
///1 ugGgm G G Z ,
(1.130)
ɝɞɟ
G
ɫɫɫɬ,
Gu
– ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɛɚɥɤɢ ɤɚɤ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ ɨɬ
ɫɬɚɬɢɱɟɫɤɢ ɩɪɢɥɨɠɟɧɧɨɣ ɫɢɥɵ ɜɟɫɚ
gmG
ɫɫ
ɫɭɦɦɚɪɧɨɣ ɦɚɫɫɵ
mmm
c
ɛ
5.0
.
ɂɡ (1.128) ɫɥɟɞɭɟɬ, ɱɬɨ
>@
ɫɫɬ,
o
ɫɫɬ,o
oo
ɪɚɫɱ
2
2
)1(
/2)1(
)1(
u
h
k
g
ugghk
mg
kmv
mg
S
G
P
m
m
Z
Z
E E .
(1.131)
Ɇɚɤɫɢɦɚɥɶɧɨɟ ɱɢɫɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɫɭɦɦɚɪɧɨɣ ɦɚɫɫɵ
ɩɪɢ ɤɨɥɟɛɚɧɢɹɯ ɛɭɞɟɬ ɢɦɟɬɶ ɡɧɚɤɢ
# ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɪɢ ɩɟɪɟɦɟɳɟɧɢɢ ɦɚɫɫɵ ɜɧɢɡ ɢ ɜɜɟɪɯ:
ɫɫɬ,
oɫɬɫɬ
2
)1(
u
h
kuuA
m
E ### .
(1.132)
Ɂɞɟɫɶ
G
Gu
ɫɬ
– ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɛɚɥɤɢ ɤɚɤ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ
ɫɜɨɛɨɞɵ ɨɬ ɫɬɚɬɢɱɟɫɤɢ ɩɪɢɥɨɠɟɧɧɨɣ ɫɢɥɵ ɜɟɫɚ
mgG ɭɞɚɪɹɸɳɟɣ ɦɚɫɫɵ m .
Ɇɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɢɡɝɢɛɚɸɳɟɝɨ ɦɨɦɟɧɬɚ ɜ ɫɪɟɞɧɟɦ ɫɟɱɟɧɢɢ ɛɚɥɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ
ɮɨɪɦɭɥɟ
Er r
ɫɬ
MM
(1.133)
Ɂɞɟɫɶ 4/
ɫɬ
GlM – ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ ɜ ɫɪɟɞɧɟɦ ɫɟɱɟɧɢɢ ɛɚɥɤɢ ɨɬ ɫɬɚɬɢɱɟɫɤɢ
ɩɪɢɥɨɠɟɧɧɨɣ ɫɢɥɵ ɜ ɜɢɞɟ ɜɟɫɚ
mgG ɭɞɚɪɹɸɳɟɣ ɦɚɫɫɵ m .
ɑɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ ɜɪɭɱɧɭɸ
Ɋɚɫɫɦɨɬɪɢɦ ɱɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɡɚɞɚɜ ɛɚɥɤɟ ɩɚɪɚɦɟɬɪɵ, ɢɫɩɨɥɶɡɨɜɚɧɧɵɟ ɜ
ɩɪɢɦɟɪɟ 4 ɩɨɞɪɚɡɞɟɥɚ 1.1 ɢ ɜ ɩɪɢɦɟɪɟ 1 ɩɨɞɪɚɡɞɟɥɚ 1.4: ɞɥɢɧɚ ɩɪɨɥɟɬɚ ɛɚɥɤɢ
ɦ8 l ; ɩɥɨɳɚɞɶ
ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ
2
ɛ
ɦ24.0 A ; ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ
12/
3
bhI
Y
= 0.072 ɫɟɱɟɧɢɹ ɛɚɥɤɢ
ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ Y ; ɩɥɨɬɧɨɫɬɶ ɦɚɬɟɪɢɚɥɚ ɛɚɥɤɢ
33
ɛ
ɬ/ɦ5.2ɤɝ/ɦ2500 U ;. ɦɨɞɭɥɶ
ɭɩɪɭɝɨɫɬɢ E = 3.00186 · 10
7
ɤɇ/ɦ
2
=
26
ɬɫ/ɦ1006.3 ; ɠɟɫɬɤɨɫɬɶ ɛɚɥɤɢ ɩɪɢ ɟɟ ɢɡɝɢɛɧɵɯ
75
ɤɨɥɟɛɚɧɢɹɯ 92.216133
Y
EI ɤɇ·ɦ
2
; ɦɚɫɫɚ ɛɚɥɤɢ
ɛɛɛ
Vm
U
= 4800 ɤɝ = 4.8 ɬɢɟɟɜɟɫ
gmG
ɛɛ
= (4.8 ɬ) · (9.81 ɦ/ɫ
2
)= 47.088 ɤɇ = 4.8 ɬɫ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢɦɟɦ: ɦɚɫɫɚ ɭɞɚɪɹɸɳɟɝɨ
ɛɚɥɤɭ ɝɪɭɡɚ
m = 1.5 ɬ; ɜɵɫɨɬɚ ɩɚɞɟɧɢɹ ɝɪɭɡɚ
m
h = 2 ɫɦ = 0.02 ɦ.
ȼɵɱɢɫɥɢɦ ɫɥɟɞɭɸɳɢɟ ɜɟɥɢɱɢɧɵ:
ɋɬɚɬɢɱɟɫɤɢɣ ɪɚɫɱɟɬ
1. ȼɟɫ mgG ɭɞɚɪɹɸɳɟɣ ɦɚɫɫɵ m : G = (1.5 ɬ) · (9.81 ɦ/ɫ
2
) = 14.715 ɤɇ =1.5 ɬɫ.
2. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɬɥɢɜɨɫɬɢ ɛɚɥɤɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ ɛɚɥɤɢ
EIl 48/
3
G = 8
3
/(48 · 92.216133 ) = 4.93 · 10
–5
ɦ/ɤɇ·
|
48.4 · 10
–5
ɦ/ɬɫ.
(1.134)
3. ɋɬɚɬɢɱɟɫɤɢɣ ɩɪɨɝɢɛ ɛɚɥɤɢ G Gu
ɫɬ
= (1.5 ɬɫ)·· (48.4 · 10
–5
) = 72.6·10
–5
ɦ.
4. ɂɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ ɜ ɫɪɟɞɧɟɦ ɫɟɱɟɧɢɢ ɛɚɥɤɢ ɨɬ ɫɬɚɬɢɱɟɫɤɢ ɩɪɢɥɨɠɟɧɧɨɣ ɫɢɥɵ
G :
4/
ɫɬ
GlM = 1.5·8/4 = 3 ɬɦ.
(1.135)
ȼɟɫ ɫɭɦɦɚɪɧɨɣ ɦɚɫɫɵ ɜ ɫɪɟɞɧɟɦ ɫɟɱɟɧɢɢ ɤɚɤ ɫɭɦɦɚ ɜɟɫɚ ɩɨɥɨɜɢɧɵ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɵ
ɛɚɥɤɢ, ɩɪɢɜɟɞɟɧɧɨɣ ɤ ɬɨɱɟɱɧɨɣ ɦɚɫɫɟ ɜ ɫɪɟɞɧɟɦ ɫɟɱɟɧɢɢ ɛɚɥɤɢ, ɢ ɜɟɫɚ ɭɞɚɪɹɸɳɟɣ ɦɚɫɫɵ:
gmmG )5.0(
ɛɫ
= (2.4+1.5) 9.81 = 38.259 ɤɇ = 3.9 ɬɫ.
(1.136)
5. ɋɬɚɬɢɱɟɫɤɢɣ ɩɪɨɝɢɛ
G
ɫɫɫɬ,
Gu ɛɚɥɤɢ ɨɬ ɫɭɦɦɚɪɧɨɣ ɫɬɚɬɢɱɟɫɤɨɣ ɫɢɥɵ
ɫ
G :
cɫɬ,
u = (3.90 ɬɫ) (0.000484 ɦ/ɬɫ) = 0.00189 ɦ.
(1.137)
Ⱦɢɧɚɦɢɱɟɫɤɢɣ ɪɚɫɱɟɬ
1. ɍɝɥɨɜɚɹ ɫɨɛɫɬɜɟɧɧɚɹ ɱɚɫɬɨɬɚ (1.130) ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ ɫ ɫɭɦɦɚɪɧɨɣ
ɦɚɫɫɨɣ )5.0(
ɛɫ
mmm = gG /
ɫ
:
ɫɬ,ɫɫɫ
///1 ugGgm G G Z
=
00189.0/81.9 = 72.09 ɫ
-1
(1.138)
2. ɋɤɨɪɨɫɬɶ
m
ghv 2
o
ɭɞɚɪɹɸɳɟɣ ɦɚɫɫɵ ɜ ɦɨɦɟɧɬ ɭɞɚɪɚ:
626.002.081.92
o
v ɦ/ɫ
(1.139)
3. ɍɞɚɪɧɵɣ ɢɦɩɭɥɶɫ (1.129) (ɩɪɢ 0
o
k )
op
mvJ = (1.5 ɬ) · (0.626 ɦ/ɫ) = 0.939 ɬ·ɦ/ɫ=0.939 ɤɇ·ɫ.
(1.140)
4. Ⱦɢɧɚɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ (ɩɪɢ 0
o
k )
ɫɬ,ɫ
ɪɚɫɱ
2
2
u
h
mg
J
G
P
m
p
Z
E E = 6.4
00189.0
02.02
.
(1.141)
5. Ɋɚɫɱɟɬɧɚɹ ɫɢɥɚ ɩɪɢ ɦɝɧɨɜɟɧɧɨɦ ɢɦɩɭɥɶɫɟ (1.128)
Z E
p
JGP
ɪɚɫɱ
= (14.715 ɤɇ) · 4.6 | (0.939 ɤɇ·ɫ) · (72.09 ɫ
-1
) = 67.7 ɤɇ
(1.142)
6. Ɇɚɤɫɢɦɚɥɶɧɚɹ ɩɨ ɱɢɫɥɟɧɧɨɦɭ ɡɧɚɱɟɧɢɸ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɦɚɫɫɵ ɩɨɫɥɟ ɭɞɚɪɧɨɣ
ɧɚɝɪɭɡɤɢ ɜ ɜɢɞɟ ɦɝɧɨɜɟɧɧɨɝɨ ɢɦɩɭɥɶɫɚ
E
ɫɬ
uA ## (72.6 ·10
–5
ɦ)·4.6 = # 0.0033 ɦ.
(1.143)
7. Ɇɚɤɫɢɦɚɥɶɧɵɣ ɩɨ ɱɢɫɥɟɧɧɨɦɭ ɡɧɚɱɟɧɢɸ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ ɜ ɫɪɟɞɧɟɦ ɫɟɱɟɧɢɢ
ɛɚɥɤɢ:
Er r
ɫɬ
MM
6.4ɦ)ɬɫ3( r
=
r
13.8 ɬ·ɦ.
(1.144)
76
Ɋɚɫɱɟɬ ɧɚ ɉɄ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD
ɋ ɷɬɨɣ ɰɟɥɶɸ ɫɨɫɬɚɜɢɦ ɧɨɜɨɟ ɡɚɝɪɭɠɟɧɢɟ «ɍɞɚɪ ɫ ɭɱɟɬɨɦ ɦɚɫɫɵ ɭɞɚɪɹɸɳɟɝɨ ɬɟɥɚ». ȼ
ɷɬɨɦ ɫɥɭɱɚɟ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ ɩɪɨɝɪɚɦɦɵ SCAD ɞɥɹ ɡɚɞɚɧɢɹ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢɦɟɟɬ ɜɢɞ:
ɗɬɢ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɨɬɧɨɫɹɬɫɹ ɤ ɭɡɥɭ 2 ɜ ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ ɛɚɥɤɢ.
Ɂɚɬɟɦ ɡɚɞɚɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɦɚɫɫɚ ɧɚ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɚɯ. Ʉɚɪɬɢɧɚ ɫɨɯɪɚɧɟɧɧɵɯ
ɢɧɟɪɰɢɨɧɧɵɯ ɞɚɧɧɵɯ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 1.31.
Ɋɢɫ. 1.31
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɩɪɢɜɟɞɟɧɵ ɧɢɠɟ ɜ ɜɢɞɟ ɞɜɭɯ ɬɚɛɥɢɰ ɢɡ ɪɚɡɞɟɥɚ «Ⱦɢɧɚɦɢɤɚ» ɢ
ɞɜɭɯ ɬɚɛɥɢɰ ɫ ɪɚɫɱɟɬɧɵɦ ɩɟɪɟɦɟɳɟɧɢɟɦ ɢ ɪɚɫɱɟɬɧɵɦ ɢɡɝɢɛɚɸɳɢɦ ɦɨɦɟɧɬɨɦ ɜ ɭɡɥɟ 2:
------------------------------------------------------------------
| ɊȺɋɉɊȿȾȿɅȿɇɂȿ ȼȿɋɈȼ ɆȺɋɋ, ɬɫ |
------------------------------------------------------------------
| 1 2 3
------------------------------------------------------------------
| 1 - ( ɭɞɚɪ-1+)
| Z 3.9
------------------------------------------------------------------
------------------------------------------------------------------
|Ɂɚɝpɭ: N : COȻCTB. : ɑ A C T O T ɕ : ɉEPɂOȾɕ |
| : ɉ/ɉ : :-----------------------------:----------
|ɠɟɧɢɟ: : ɁHAɑEHɂə : 1/C : Ƚɐ : C
------------------------------------------------------------------
| 1 1 .0138734 72.08 11.4777 871254|
------------------------------------------------------------------
123
D1,5 ɬɫ
D0.6 ɬɫ
D0.6 ɬɫ
77
------------------------------------------------------------------
| ɉȿɊȿɆȿɓȿɇɂə ɍɁɅɈȼ, ɦɦ |
------------------------------------------------------------------
| 1 2 3
------------------------------------------------------------------
| 1 - 1 ( ɭɞɚɪ-1+)
| Z -.003388
------------------------------------------------------------------
------------------------------------------------------------------
| ɍɋɂɅɂə /ɇȺɉɊəɀȿɇɂə/ ȼ ɗɅȿɆȿɇɌȺɏ, ɬɫ*ɦ |
------------------------------------------------------------------
| 2_ 1-1 1-2 2-1 2-2
------------------------------------------------------------------
| 1 - 1 ( ɭɞɚɪ-1+)
| M 13.9997 13.9997
| 1 - S1 ( ɭɞɚɪ-1+)
| M 13.9997 13.9997
------------------------------------------------------------------
Ʉɚɤ ɜɢɞɧɨ, ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɜɪɭɱɧɭɸ ɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ
SCAD ɯɨɪɨɲɨ ɫɨɜɩɚɞɚɸɬ.
1.7. Ɋɚɫɱɟɬ ɧɚ ɡɚɞɚɧɧɭɸ ɚɤɫɟɥɟɪɨɝɪɚɦɦɭ ɡɟɦɥɟɬɪɹɫɟɧɢɹ
Ɋɚɫɫɦɨɬɪɢɦ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɜ ɜɢɞɟ ɧɟɜɟɫɨɦɨɣ ɤɨɧɫɨɥɢ ɫ ɬɨɱɟɱɧɨɣ
ɦɚɫɫɨɣ (ɪɢɫ. 1.32). Ɍɚɤɚɹ ɪɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ
ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɪɚɡɥɢɱɧɨɝɨ ɬɢɩɚ ɫɨɨɪɭɠɟɧɢɣ [4-17]. ɉɪɢ ɩɨɩɟɪɟɱɧɵɯ
ɤɨɥɟɛɚɧɢɹɯ ɨɧɚ ɹɜɥɹɟɬɫɹ ɫɢɫɬɟɦɨɣ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ.
Ɋɢɫ. 1.32
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɨɩɨɪɚ ɤɨɧɫɨɥɢ, ɚ ɡɧɚɱɢɬ ɢ ɜɫɹ ɤɨɧɫɨɥɶ, ɜɨ ɜɪɟɦɹ
78
ɡɟɦɥɟɬɪɹɫɟɧɢɹ ɜɦɟɫɬɟ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ Ɂɟɦɥɢ ɫɨɜɟɪɲɚɟɬ ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ
ɤɨɥɟɛɚɧɢɹ ɫ ɭɫɤɨɪɟɧɢɟɦ
)(taa
oo
(ɫɦ. ɪɢɫ. 1.32, ɚ), ɤɨɬɨɪɨɟ ɡɚɞɚɧɨ ɜ ɜɢɞɟ
ɚɤɫɟɥɟɪɨɝɪɚɦɦɵ [4, 6, 16, 17] (ɭɫɥɨɜɧɨ ɨɧɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 1.32, ɝ).
ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɜɢɠɟɧɢɹ ɦɚɫɫɵ ɫ ɡɚɞɚɧɧɵɦ ɭɫɤɨɪɟɧɢɟɦ ɧɚ ɤɨɧɫɨɥɶ ɛɭɞɟɬ
ɞɟɣɫɬɜɨɜɚɬɶ ɜɨɡɦɭɳɚɸɳɚɹ ɫɢɥɚ ɢɧɟɪɰɢɢ
)()( tamtP
o
, ɜɵɡɵɜɚɸɳɚɹ
ɇȾɋ ɤɨɧɫɨɥɢ.
ɍɪɚɜɧɟɧɢɟ (1.86) ɜɵɧɭɠɞɟɧɧɵɯ ɞɜɢɠɟɧɢɣ ɦɚɫɫɵ ɧɚ ɥɢɧɟɣɧɨ
ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɤɨɧɫɨɥɢ ɫ ɭɱɟɬɨɦ (1.80), ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
o
auuu
Z]Z
2
2
,
(1.145)
ȿɝɨ ɪɟɲɟɧɢɟ ɩɪɢ ɧɭɥɟɜɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɞɜɢɠɟɧɢɹ ɢ ɫ ɭɱɟɬɨɦ ɬɨɝɨ,
ɱɬɨ ɞɥɹ ɫɬɪɨɢɬɟɥɶɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ
Z
|Z
D
, ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɝɪɚɥ
WWZW
Z
W]Z
³
dteatu
t
t
o
)(sin)(
1
)(
)(
0
.
(1.146)
ȿɫɥɢ ɭɫɤɨɪɟɧɢɹ ɚɤɫɟɥɟɪɨɝɪɚɦɦɵ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
)()( tfta
o
D
,
(1.147)
ɝɞɟ
D – ɦɚɤɫɢɦɚɥɶɧɚɹ ɚɦɩɥɢɬɭɞɚ ɚɤɫɟɥɟɪɨɝɪɚɦɦɵ; D /)()( tatf
o
– ɮɭɧɤɰɢɹ
ɨɬɧɨɫɢɬɟɥɶɧɵɯ (ɛɟɡɪɚɡɦɟɪɧɵɯ) ɨɪɞɢɧɚɬ ɚɤɫɟɥɟɪɨɝɪɚɦɦɵ, ɢ ɩɨɞɫɬɚɜɢɬɶ (1.147) ɜ
(1.146), ɬɨ ɢɫɤɨɦɨɟ ɪɟɲɟɧɢɟ ɞɥɹ ɩɟɪɟɦɟɳɟɧɢɣ ɦɚɫɫɵ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
(1.89), ɝɞɟ
22
ɫɬɫɬ
)
1
()(
Z
D
Z
D G
m
mPu ;
(1.148)
WWZWZ E
W]Z
³
dtef
u
tu
t
t
t
)(sin)(
)(
)(
)(
0
ɫɬ
.
(1.149)
ȼ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɫɢɫɬɟɦɟ ɜɵɪɚɠɟɧɢɸ (1.89) ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɢɡɦɟɧɹɸɳɟɣɫɹ ɜɨ ɜɪɟɦɟɧɢ ɢɧɟɪɰɢɨɧɧɨɣ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ
ɤɨɧɫɨɥɶ,
)()()(
ɫɬ
tmtPtS ED E
.
(1.150)
ɗɬɚ ɫɢɥɚ ɹɜɥɹɟɬɫɹ ɫɟɣɫɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɨɣ ɧɚ ɤɨɧɫɨɥɶ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ
ɫɨɛɨɣ ɫɭɦɦɚɪɧɭɸ ɢɧɟɪɰɢɨɧɧɭɸ ɫɢɥɭ, ɜɤɥɸɱɚɸɳɭɸ ɜ ɫɟɛɹ ɡɚɞɚɧɧɭɸ
ɜɨɡɦɭɳɚɸɳɭɸ ɢɧɟɪɰɢɨɧɧɭɸ ɫɢɥɭ, ɫɜɹɡɚɧɧɭɸ ɫ ɡɚɞɚɧɧɵɦ ɭɫɤɨɪɟɧɢɟɦ )(ta
o
, ɢ
ɢɧɟɪɰɢɨɧɧɭɸ ɫɢɥɭ, ɫɜɹɡɚɧɧɭɸ ɫ ɭɫɤɨɪɟɧɢɹɦɢ
)(
t
u
ɭɩɪɭɝɢɯ ɤɨɥɟɛɚɧɢɣ ɤɨɧɫɨɥɢ:
)()()()()()(
ɫ
tumtumtamtJtPtS
o
.
(1.151)
ȼɟɥɢɱɢɧɚ )()()(
oɫ
tutatu
ɹɜɥɹɟɬɫɹ ɫɭɦɦɚɪɧɵɦ ɭɫɤɨɪɟɧɢɟɦ ɦɚɫɫɵ ɩɪɢ
79
ɤɨɥɟɛɚɧɢɹɯ, ɤɨɬɨɪɚɹ ɢɡ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɫ (1.150) ɦɨɠɟɬ ɛɵɬɶ ɬɚɤɠɟ
ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ
)()(
ɫ
ttu ED
.
(1.152)
ɉɨ ɫɟɣɫɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɟ
)()(
ɫɬ
tPtS E
ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɩɨɩɟɪɟɱɧɵɯ
ɫɟɱɟɧɢɹɯ ɤɨɧɫɨɥɢ ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɧɨɪɦɚɥɶɧɵɟ
ɧɚɩɪɹɠɟɧɢɹ:
)()(
ɫɬ
tMtM E
;
)()(
ɫɬ
tt EV V
(1.153)
ɚ ɬɚɤɠɟ ɩɨɩɟɪɟɱɧɵɟ ɫɢɥɵ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɤɚɫɚɬɟɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ:
)()(
ɫɬ
tQtQ E
;
)()(
ɫɬ
tt EW W
.
(1.154)
Ɂɞɟɫɶ ɫɬɚɬɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɬɚɬɢɱɟɫɤɢɦ ɪɚɫɱɟɬɨɦ
ɤɨɧɫɨɥɢ ɨɬ ɫɢɥɵ
D mP
ɫɬ
.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɢɧɚɦɢɱɟɫɤɢɣ ɪɚɫɱɟɬ ɤɨɧɫɨɥɢ ɤɚɤ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ
ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ ɜ ɨɫɧɨɜɧɨɦ ɫɜɨɞɢɬɫɹ ɤ ɜɵɱɢɫɥɟɧɢɸ ɢɧɬɟɝɪɚɥɚ Ⱦɸɚɦɟɥɹ ɜ
ɜɢɞɟ (1.149).
ɉɪɨɟɤɬɢɪɨɜɳɢɤɚ ɫɨɨɪɭɠɟɧɢɹ ɱɚɫɬɨ ɢɧɬɟɪɟɫɭɸɬ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ
ɜɫɟɯ ɢɫɤɨɦɵɯ ɜɟɥɢɱɢɧ. Ɍɨɝɞɚ ɜɦɟɫɬɨ ɨɩɪɟɞɟɥɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɤɨɷɮɮɢɰɢɟɧɬɚ )(
t
E ɩɨ ɮɨɪɦɭɥɟ (1.149) ɧɚɯɨɞɹɬ ɬɨɥɶɤɨ ɟɝɨ ɦɚɤɫɢɦɚɥɶɧɨɟ
ɡɧɚɱɟɧɢɟ
)(max t
t
E E , ɤɨɬɨɪɨɟ ɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɨɬ ɬɪɟɯ ɜɟɥɢɱɢɧ: ɮɭɧɤɰɢɢ )(
t
f
;
ɭɝɥɨɜɨɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɵ ɤɨɥɟɛɚɧɢɣ
Z
(ɢɥɢ ɩɟɪɢɨɞɚ ZS
/
2
T
ɷɬɢɯ
ɤɨɥɟɛɚɧɢɣ) ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ;
ɤɨɷɮɮɢɰɢɟɧɬɚ
] (1.81), ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɝɨ ɧɟɭɩɪɭɝɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɚ
ɢ ɤɨɧɫɬɪɭɤɰɢɢ:
]E E E ,),(max)(max Ttft
t
t
.
(1.155)
Ʉɪɨɦɟ ɱɢɫɥɟɧɧɨɝɨ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɗȼɆ, ɡɧɚɱɟɧɢɟ
E
ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ.
ɉɪɟɞɫɬɚɜɢɦ, ɱɬɨ ɤɨɧɫɨɥɶ (ɢɥɢ ɟɟ ɦɨɞɟɥɶ) ɫ ɢɡɜɟɫɬɧɵɦ ɩɟɪɢɨɞɨɦ
ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ
T
ɢ ɤɨɷɮɮɢɰɢɟɧɬɨɦ
]
, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦ ɧɟɭɩɪɭɝɨɟ
ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɚ (1.81), ɭɫɬɚɧɨɜɥɟɧɚ ɧɚ ɩɨɞɜɢɠɧɨɣ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦ
ɧɚɩɪɚɜɥɟɧɢɢ ɩɥɚɬɮɨɪɦɟ, ɤɨɬɨɪɚɹ ɫɨɜɟɪɲɚɟɬ ɞɜɢɠɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɮɭɧɤɰɢɟɣ
)(
t
f
.
Ɍɨɝɞɚ ɩɪɢ ɤɨɥɟɛɚɧɢɹɯ ɦɚɫɫɵ ɦɨɠɟɬ ɛɵɬɶ ɡɚɮɢɤɫɢɪɨɜɚɧɚ ɚɦɩɥɢɬɭɞɚ ɟɟ
ɤɨɥɟɛɚɧɢɣ
E
ɫɬ
)(max utu
t
. Ɍɚɤ ɤɚɤ ɜɟɥɢɱɢɧɚ
ɫɬ
u ɢɡɜɟɫɬɧɚ (1.148), ɬɨ
ɨɩɪɟɞɟɥɢɬɫɹ ɜɟɥɢɱɢɧɚ
ɫɬ
/)(max utu
t
E .
Ɇɨɞɟɥɶɸ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ