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110
Ɋɢɫ. 1.15
ɉɪɢ ɩɪɨɜɟɪɤɟ ɞɜɭɯ ɞɪɭɝɢɯ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ (1.1) ɫ ɩɨɦɨɳɶɸ ɭɫɢɥɢɣ
(ɫɦ. ɪɢɫ. 1.12) ɜ ɭɡɥɚɯ ɩɨ ɩɨɞɨɲɜɟ, ɩɨɥɭɱɟɧɧɵɯ ɨɬ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɧɚɝɪɭɡɤɢ ɧɚ
ɫɬɟɧɤɭ (ɫɦ. ɪɢɫ. 1.14), ɩɨɝɪɟɲɧɨɫɬɶ ɛɭɞɟɬ ɪɚɜɧɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ 1.3% ɢ 0%.
3. Ʉɨɦɛɢɧɚɰɢɹ ɡɚɝɪɭɠɟɧɢɣ 1 ɢ 2. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɫɢɥɢɹ ɩɨ ɩɨɞɨɲɜɟ
ɫɬɟɧɤɢ ɨɬ ɞɟɣɫɬɜɭɸɳɢɯ ɧɚɝɪɭɡɨɤ ɪɚɜɧɵ:
N
o
= – 475, 3 ɤɇ;
Q
o
= – R
ɝ.ɞ.
= – 0.5·(80·6.5) = – 260 ɤɇ;
M
o
= M
o
(ɫ.ɜ.) + M
o
(ɝ.ɞ.) = – 476.34 ɤɇ·ɦ + 563.3 ɤɇ·ɦ = 86.96 ɤɇ·ɦ.
(1.9)
ɗɩɸɪɵ ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
z
V (NZ) ɢ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
xzzx
W W
(TZX=TXZ) ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ ɨɬ ɤɨɦɛɢɧɚɰɢɢ ɡɚɝɪɭɠɟɧɢɣ ɩɪɢɜɟɞɟɧɵ
ɧɚ ɪɢɫ. 1.8. Ɂɧɚɱɟɧɢɹ ɢɯ ɨɪɞɢɧɚɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɡɥɚɦ ɫɟɬɤɢ ɩɨɤɚɡɚɧɵ ɧɚ
ɪɢɫ. 1.16:
Ɋɢɫ. 1.16.
ɇɚ ɪɢɫ. 1.14 ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɟɣɫɬɜɢɹ ɭɫɢɥɢɣ ɜ ɭɡɥɚɯ,
ɫɟɬɤɢ Ʉɗ, ɥɟɠɚɳɢɯ ɧɚ ɥɢɧɢɢ ɤɨɧɬɚɤɬɚ ɫɬɟɧɤɢ ɫ ɨɫɧɨɜɚɧɢɟɦ, ɩɟɪɟɞɚɸɳɢɯɫɹ ɨɬ
ɫɬɟɧɤɢ ɧɚ ɨɫɧɨɜɚɧɢɟ. ɇɚ ɫɬɟɧɤɭ ɷɬɢ ɭɫɢɥɢɹ ɞɟɣɫɬɜɭɸɬ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
ɉɨɫɤɨɥɶɤɭ ɞɥɹ ɨɛɨɢɯ ɡɚɝɪɭɠɟɧɢɣ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ
ɭɞɨɜɥɟɬɜɨɪɹɸɬɫɹ, ɨɧɢ ɛɭɞɭɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ ɢ ɩɪɢ ɤɨɦɛɢɧɚɰɢɢ ɡɚɝɪɭɠɟɧɢɣ.
ɚ)
ɛ)
ɚ)
ɛ)
111
1.7. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɮɨɪɦɭɥɵ ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ
ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɷɩɸɪ ɧɚɩɪɹɠɟɧɢɣ
z
V (NZ)
ɇɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ
z
V
ɜ ɫɟɱɟɧɢɢ ɫɬɟɧɤɢ ɩɨ ɩɨɞɨɲɜɟ ɜɵɡɵɜɚɸɬɫɹ
ɩɪɨɞɨɥɶɧɨɣ ɫɢɥɨɣ N
o
ɢ ɢɡɝɢɛɚɸɳɢɦ ɦɨɦɟɧɬɨɦ M
o
. Ⱦɥɹ ɩɪɢɛɥɢɠɟɧɧɨɝɨ
ɜɵɱɢɫɥɟɧɢɹ ɷɬɢɯ ɧɚɩɪɹɠɟɧɢɣ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɮɨɪɦɭɥɨɣ ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ
o
o
o
o
z
W
M
A
N
r V
2,1,
,
(1.10)
ɩɨɥɭɱɟɧɧɨɣ ɜ ɤɭɪɫɟ «ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɨɜ» ɞɥɹ ɬɨɧɤɢɯ ɫɬɟɪɠɧɟɣ. ɉɪɢ
ɷɬɨɦ ɩɨɥɭɱɢɦ ɥɢɧɟɣɧɭɸ ɷɩɸɪɭ ɧɚɩɪɹɠɟɧɢɣ
z
V ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ.
Ɂɞɟɫɶ
A
o
= 1·h ɢ W
o
= 1·h
2
/6 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ – ɩɥɨɳɚɞɶ ɢ ɦɨɦɟɧɬ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɫɬɟɧɤɢ ɩɨ ɩɨɞɨɲɜɟ.
ȼɵɱɢɫɥɢɦ ɧɚɩɪɹɠɟɧɢɹ
z
V ɨɬɞɟɥɶɧɨ ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ, ɨɬ ɡɚɞɚɧɧɨɣ
ɜɧɟɲɧɟɣ ɧɚɝɪɭɡɤɢ ɢ ɨɬ ɢɯ ɤɨɦɛɢɧɚɰɢɢ.
ɇɚɩɪɹɠɟɧɢɹ
z
V
ɨɬ ɞɟɣɫɬɜɢɹ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ
ȼɵɱɢɫɥɹɟɦ ɩɥɨɳɚɞɶ ɢ ɦɨɦɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɫɟɱɟɧɢɹ
ɫɥɨɹ ɫɬɟɧɤɢ ɟɞɢɧɢɱɧɨɣ ɬɨɥɳɢɧɵ ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ:
A
o
= b·h = 1·5.5 = 5.5 ɦ
2
;
W
o
=
6
)5.5(1
2
=
6
25.301
= 5.04 ɦ
3
.
ɉɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɢ ɦɨɦɟɧɬ ɜ ɫɟɱɟɧɢɢ ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ ɨɬ ɞɟɣɫɬɜɢɹ
ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ ɛɵɥɢ ɩɨɞɫɱɢɬɚɧɵ ɜ ɩɨɞɪɚɡɞɟɥɟ 1.4 (ɫɦ. ɪɢɫ. 1.10).
ɉɨɷɬɨɦɭ ɜ ɮɨɪɦɭɥɭ (1.10) ɩɨɞɫɬɚɜɥɹɟɦ:
N
o
= N
o
(ɫ.ɜ.) = – 475.3 ɤɇ;
M
o
= M
o
(ɫ.ɜ.) = – 459.38 ɤɇ·ɦ.
ɉɨɫɤɨɥɶɤɭ ɨɛɚ ɭɫɢɥɢɹ ɜ ɬɨɱɤɟ 1 ɩɨɞɨɲɜɵ ɜɵɡɵɜɚɸɬ ɫɠɢɦɚɸɳɢɟ
ɧɚɩɪɹɠɟɧɢɹ
z
V , ɬɨ ɜ ɮɨɪɦɭɥɭ (1.10) ɨɧɢ ɩɨɞɫɬɚɜɥɹɸɬɫɹ ɫɨ ɡɧɚɤɨɦ «ɦɢɧɭɫ»:
04.5
)38.459(
5.5
)3.475(
2,1
r
V = – 86.42
#
91.15 =
.ɤɇ/ɦ7.4
.ɤɇ/ɦ178
2
2
ɗɩɸɪɚ ɷɬɢɯ ɧɚɩɪɹɠɟɧɢɣ ɩɨɤɚɡɚɧɚ ɧɢɠɟ ɜ ɞɜɭɯ ɜɢɞɚɯ: ɤɚɤ ɪɟɚɤɬɢɜɧɵɯ
ɧɚɩɪɹɠɟɧɢɣ, ɞɟɣɫɬɜɭɸɳɢɯ ɫɨ ɫɬɨɪɨɧɵ ɨɫɧɨɜɚɧɢɹ ɧɚ ɫɬɟɧɤɭ, ɢ ɤɚɤ ɧɚɩɪɹɠɟɧɢɣ,
ɩɟɪɟɞɚɸɳɢɯɫɹ ɧɚ ɨɫɧɨɜɚɧɢɟ ɱɟɪɟɡ ɩɨɞɨɲɜɭ ɫɬɟɧɤɢ (ɪɢɫ. 1.17).
ɉɨɫɤɨɥɶɤɭ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ
)ɫ.ɜ.(
o
M ɜɵɡɜɚɧ ɞɟɣɫɬɜɢɟɦ ɫɨɛɫɬɜɟɧɧɨɝɨ
ɜɟɫɚ ɫɬɟɧɤɢ, ɬɨ ɟɝɨ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɞɥɹ ɫɟɱɟɧɢɹ ɫɬɟɪɠɧɹ – ɤɨɧɫɨɥɢ ɜ ɜɢɞɟ:
eGM
o
ɫ.ɜ.)(,
(1.11)
112
ɝɞɟ G – ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɚɹ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ; e – ɷɤɫɰɟɧɬɪɢɫɢɬɟɬ
ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɟɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɟɣɬɪɚɥɶɧɨɣ ɨɫɢ ɩɨɞɨɲɜɵ
ɫɬɟɧɤɢ (ɫɦ. ɪɢɫ. 1.17).
Ɋɢɫ. 1.17
Ɍɚɤ ɤɚɤ ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɜ ɫɟɱɟɧɢɢ ɩɨ ɩɨɞɨɲɜɟ ɪɚɜɧɚ ɜɟɫɭ ɫɬɟɧɤɢ
(
GN
o
ɫ.ɜ.)( ), ɬɨ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɣɬɪɚɥɶɧɨɣ ɨɫɢ
ɩɨɞɨɲɜɵ ɦɨɠɧɨ ɬɚɤɠɟ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
eNM
oo
ɫ.ɜ.)(ɫ.ɜ.)(.
(1.12)
ɉɨɞɫɬɚɜɢɜ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ ɮɨɪɦɭɥɭ ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ (1.10),
ɩɨɥɭɱɢɦ:
)
6
1(
ɫ.ɜ.)(
2,1
h
e
A
N
o
o
r V .
(1.13)
ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɢɦɟɪɟ:
ɫ.ɜ.)(
ɫ.ɜ.)(
o
o
N
M
e =
3.475
38.459
= 0.97 ɦ.
ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ ɜ ɷɬɨɦ ɜɢɞɟ, ɩɨɥɭɱɢɦ
(ɫ ɭɱɟɬɨɦ ɩɨɝɪɟɲɧɨɫɬɟɣ ɩɪɢ ɨɤɪɭɝɥɟɧɢɢ ɡɧɚɱɟɧɢɣ ɜɟɥɢɱɢɧ) ɩɪɢɦɟɪɧɨ ɬɟ ɠɟ
ɡɧɚɱɟɧɢɹ ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
z
V ɜ ɬɨɱɤɚɯ 1 ɢ 2 ɫɟɱɟɧɢɹ ɩɨ ɩɨɞɨɲɜɟ
ɫɬɟɧɤɢ, ɤɨɬɨɪɵɟ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɪɚɧɟɟ (ɫɦ. ɪɢɫ. 1.17):
1
2
Ɉ
G
e
e
N
o
(ɫ.ɜ.)
178
1
V
1
4.7
2
ɗɩɸɪɚ ɞɚɜɥɟɧɢɹ
ɧɚ ɫɬɟɧɤɭ
ɗɩɸɪɚ ɞɚɜɥɟɧɢɹ
ɧɚ ɨɫɧɨɜɚɧɢɟ
Ɉ
N
o
(
ɫ.ɜ.
e
113
)
5.5
97.06
1(
5.5
3.475
2,1
r
V =
ɦ.ɤɇ2.5)06.11(42.86
ɦ;ɤɇ178)06.11(42.86
2
1
V
V
.
ɇɚɩɪɹɠɟɧɢɹ
z
V ɨɬ ɞɟɣɫɬɜɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ
ɪɚɫɩɪɟɞɟɥɟɧɧɨɝɨ ɞɚɜɥɟɧɢɹ
Ƚɨɪɢɡɨɧɬɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɧɟ ɫɨɡɞɚɟɬ ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ ɩɪɨɞɨɥɶɧɨɣ ɫɢɥɵ
(
0ɝ.ɞ.)(
o
N ), ɧɨ ɫɨɡɞɚɟɬ ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ )ɝ.ɞ.(
o
M . Ɍɨɝɞɚ ɜ ɮɨɪɦɭɥɟ
ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ (1.10) ɨɫɬɚɟɬɫɹ ɬɨɥɶɤɨ ɜɬɨɪɨɟ ɫɥɚɝɚɟɦɨɟ ɢ ɨɪɞɢɧɚɬɵ
ɥɢɧɟɣɧɨɣ ɷɩɸɪɵ ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɬɨɱɤɚɯ 1 ɢ 2 ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ
ɨɩɪɟɞɟɥɹɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
o
o
W
M
ɝ.ɞ.)(
2,1
r V ,
(1.14)
ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɩɪɢɦɟɪɟ (ɪɢɫ. 1.18):
o
W
lR
r V
3
ɝ.ɞ.
2,1
=
04.53
5.6)5.6805.0(
r =
04.5
3.563
r =
112r ɤɇ/ɦ
2
.
Ɋɢɫ. 1.18
ɇɚɩɪɹɠɟɧɢɹ
z
V
ɨɬ ɫɭɦɦɚɪɧɨɝɨ ɞɟɣɫɬɜɢɹ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ
ɢ ɨɬ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɝɨ ɞɚɜɥɟɧɢɹ
Ɋɟɡɭɥɶɬɚɬ ɪɚɫɱɟɬɚ ɜ ɞɜɭɯ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜɚɪɢɚɧɬɚɯ ɧɚɞɨ ɩɪɨɫɭɦɦɢɪɨɜɚɬɶ
ɫɨ ɫɜɨɢɦɢ ɡɧɚɤɚɦɢ. Ɍɨɝɞɚ ɩɨɥɭɱɢɦ (ɪɢɫ. 1.19):
1
2
Ɉ
R
ɝ.ɞ.=
260
M
o
(
ɝ.ɞ.
)
= 418.05
112
1
V
1
112
2
V
2
ɗɩɸɪɚ ɞɚɜɥɟɧɢɹ
ɧɚ ɫɬɟɧɤɭ
ɗɩɸɪɚ ɞɚɜɥɟɧɢɹ
ɧɚ ɨɫɧɨɜɚɧɢɟ
Ɉ
112
1
V
l/3
114
.ɤɇ/ɦ1071125
;ɤɇ/ɦ66112178
2
2
2
1
V
V
ɗɬɢ ɠɟ ɧɚɩɪɹɠɟɧɢɹ ɩɨɥɭɱɚɬɫɹ, ɟɫɥɢ ɢɯ ɜɵɱɢɫɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ
ɜɧɟɰɟɧɬɪɟɧɧɨɝɨ ɫɠɚɬɢɹ ɜ ɜɢɞɟ (1.13) ɩɪɢ ɷɤɫɰɟɧɬɪɢɫɢɬɟɬɟ
e , ɩɨɞɫɱɢɬɚɧɧɨɦ ɩɪɢ
ɫɭɦɦɚɪɧɨɦ ɢɡɝɢɛɚɸɳɟɦ ɦɨɦɟɧɬɟ
o
M = – 459.38 + 563.3 = 103.92 ɤɇ·ɦ. Ɍɨɝɞɚ
ɫ.ɜ.)(
o
o
N
M
e
=
3.475
92.103
= – 0.22 ɦ;
)
5.5
)22.0(6
1(
5.5
3.475
2,1
r
V =
¯
®
V
V
.ɤɇ/ɦ2.107)24.01(42.86
;ɤɇ/ɦ7.65)24.01(42.86
2
2
2
1
.
Ɋɢɫ. 1.19
ɉɨɥɭɱɟɧɧɵɟ ɷɩɸɪɵ ɫɨɜɦɟɳɟɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫ ɷɩɸɪɚɦɢ ɧɚɩɪɹɠɟɧɢɣ
z
V (ɫɦ. ɪɢɫ. 1.6 – 1.8), ɩɨɥɭɱɟɧɧɵɯ ɪɚɫɱɟɬɨɦ ɧɚ ɉɄ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɩɪɨɝɪɚɦɦɵ SCAD, ɪɟɚɥɢɡɭɸɳɟɣ ɆɄɗ ɜ ɩɥɨɫɤɨɣ ɡɚɞɚɱɟ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ.
ɗɬɨ ɫɨɩɨɫɬɚɜɥɟɧɢɟ ɨɬɪɚɠɚɟɬ ɪɚɡɥɢɱɢɟ ɪɟɡɭɥɶɬɚɬɨɜ, ɩɨɥɭɱɟɧɧɵɯ
ɪɚɫɫɦɨɬɪɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ. ȼɢɞɧɨ, ɱɬɨ ɦɟɬɨɞ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ ɨɬɪɚɠɚɟɬ
ɜɥɢɹɧɢɟ ɨɫɧɨɜɚɧɢɹ ɧɚ ɤɚɪɬɢɧɭ ɧɚɩɪɹɠɟɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɬɟɧɤɢ ɜɛɥɢɡɢ ɫ ɡɨɧɨɣ
ɤɨɧɬɚɤɬɚ ɫɬɟɧɤɢ ɫ ɨɫɧɨɜɚɧɢɟɦ.
Ȼɨɥɟɟ ɩɨɥɧɨ ɢɫɫɥɟɞɨɜɚɧɢɟ ɜɥɢɹɧɢɹ ɨɫɧɨɜɚɧɢɹ ɛɭɞɟɬ ɜɵɩɨɥɧɟɧɨ ɜɨ ɜɬɨɪɨɦ
ɪɚɡɞɟɥɟ ɪɚɛɨɬɵ ɫ ɩɨɦɨɳɶɸ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɩɪɢɜɟɞɟɧɧɨɣ ɧɚ ɪɢɫ. 1.1 ɩɪɢ
ɢɡɦɟɧɟɧɢɢ ɦɨɞɭɥɹ ɭɩɪɭɝɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɨɫɧɨɜɚɧɢɹ.
1
2
Ɉ
G
e
N
o
(
ɫ.ɜ.
)
66
1
V
107
2
V
ɗɩɸɪɚ ɞɚɜɥɟɧɢɹ
ɧɚ ɫɬɟɧɤɭ
ɗɩɸɪɚ ɞɚɜɥɟɧɢɹ
ɧɚ ɨɫɧɨɜɚɧɢɟ
Ɉ
1
2
e
115
1.8. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɮɨɪɦɭɥɵ ɀɭɪɚɜɫɤɨɝɨ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɷɩɸɪɵ
ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɨ ɜɵɫɨɬɟ ɫɟɱɟɧɢɹ ɛɚɥɤɢ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɮɨɪɦɵ
ȼ ɞɢɫɰɢɩɥɢɧɟ «ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɨɜ» ɞɥɹ ɛɚɥɤɢ ɛɵɥɚ ɩɨɥɭɱɟɧɚ
ɮɨɪɦɭɥɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɥɸɛɨɦ ɟɟ ɩɨɩɟɪɟɱɧɨɦ
ɩɪɹɦɨɭɝɨɥɶɧɨɦ ɫɟɱɟɧɢɢ ɜɵɫɨɬɨɣ
h ɢ ɲɢɪɢɧɨɣ b ɫ ɦɨɦɟɧɬɨɦ ɢɧɟɪɰɢɢ I
y
=
bh
3
/12.
ȿɫɥɢ, ɤɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ (1.7), ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɜɵɞɟɥɟɧɧɵɣ ɜ
ɭɫɥɨɜɢɹɯ ɩɥɨɫɤɨɣ ɡɚɞɚɱɢ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ ɫɥɨɣ ɫɬɟɧɤɢ ɬɨɥɳɢɧɨɣ
b = 1 ɦɤɚɤ
ɫɬɟɪɠɟɧɶ-ɤɨɧɫɨɥɶ, ɡɚɳɟɦɥɟɧɧɵɣ ɜ ɨɫɧɨɜɚɧɢɢ ɜ ɬɨɱɤɟ
O (ɫɦ. ɩɪɢɜɟɞɟɧɧɵɣ ɜ
ɧɚɱɚɥɟ ɨɬɱɟɬɚ ɩɨ ɪɚɛɨɬɟ ɜɢɞ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɫɬɟɧɤɢ ɩɨ ɟɟ ɜɵɫɨɬɟ), ɬɨ
ɩɨɥɭɱɟɧɧɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɫɟɱɟɧɢɹ ɫɬɟɧɤɢ ɩɨ ɩɨɞɨɲɜɟ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
bI
xSQ
x
y
)(
)(
o
W
. (1.15)
Ɂɞɟɫɶ
Q
ɨ
– ɩɨɩɟɪɟɱɧɚɹ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɟɣ ɜ ɫɟɱɟɧɢɢ ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ;
S(x)– ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɱɚɫɬɢ ɫɟɱɟɧɢɹ ɫɬɟɧɤɢ ɩɨ ɩɨɞɨɲɜɟ, ɤɨɬɨɪɚɹ ɧɚ
ɪɢɫ. 1.20 ɡɚɬɟɦɧɟɧɚ.
Ɋɢɫ. 1. 20
Ɍɚɤ ɤɚɤ x
ɤ
= (h/2 –x), ɬɨ
).
4
1(
8
)
2
(
2
1
)
2
()(
2
22
h
xbh
x
h
x
h
bxS
Ɍɨɝɞɚ ɞɥɹ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɫɟɱɟɧɢɹ ɫɬɟɧɤɢ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɟɟ ɤɚɤ
ɫɬɟɪɠɧɹ-ɤɨɧɫɨɥɢ ɮɨɪɦɭɥɚ (1.15) ɩɪɢɦɟɬ ɜɢɞ:
)
4
1(
2
3
)(
2
2
ɨ
h
x
bh
Q
x
W . (1.16)
ɂɡɦɟɧɹɹ ɜ ɮɨɪɦɭɥɟ ɤɨɨɪɞɢɧɚɬɭ
x, ɦɨɠɟɦ ɩɨɫɬɪɨɢɬɶ ɷɩɸɪɭ ɤɚɫɚɬɟɥɶɧɵɯ
ɧɚɩɪɹɠɟɧɢɣ ɩɨ ɥɢɧɢɢ 1 – 2 ɩɨɞɨɲɜɵ ɫɥɨɹ ɫɬɟɧɤɢ, ɥɟɠɚɳɟɣ ɜ ɫɪɟɞɢɧɧɨɣ
ɩɥɨɫɤɨɫɬɢ ɫɥɨɹ, ɤɨɧɰɵ ɨɪɞɢɧɚɬ ɤɨɬɨɪɨɣ ɥɟɠɚɬ ɧɚ ɩɚɪɚɛɨɥɟ, ɨɩɢɫɵɜɚɟɦɨɣ ɷɬɨɣ
ɮɨɪɦɭɥɨɣ. Ɇɚɤɫɢɦɚɥɶɧɚɹ ɨɪɞɢɧɚɬɚ ɷɬɨɣ ɩɚɪɚɛɨɥɵ ɩɪɢ
x = 0 ɛɭɞɟɬ ɪɚɜɧɚ
b
h
Y
h/2
h/2
x
ɤ
O
X
1
2
x
ɤ
116
bh
Q
h
o
max
2
3
)
2
( rW W . (1.17)
ɉɨɞɫɬɚɜɥɹɹ ɜ ɮɨɪɦɭɥɵ (1.16) ɢ (1.17) ɩɚɪɚɦɟɬɪɵ ɫɟɱɟɧɢɹ ɫɥɨɹ ɫɬɟɧɤɢ ɩɨ
ɩɨɞɨɲɜɟ (
b = 1 ɦ; h = 5.5 ɦ), ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨɥɭɱɢɦ:
)132.01(273.0)(
2
o
xQx W . (1.18)
omax
273.0)75.2( Q rW W . (1.19)
Ɉɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ
Q
o
= 0 ɢ ɷɩɸɪɚ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɨ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɮɨɪɦɭɥɟ ɨɬɫɭɬɫɬɜɭɟɬ (ɷɩɸɪɚ ɢɦɟɟɬ ɧɭɥɟɜɵɟ ɨɪɞɢɧɚɬɵ).
Ɉɬ ɞɟɣɫɬɜɢɹ ɡɚɞɚɧɧɨɣ ɧɚ ɫɬɟɧɤɭ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɧɚɝɪɭɡɤɢ ɢ ɨɬ ɟɟ
ɫɭɦɦɚɪɧɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɫ ɫɨɛɫɬɜɟɧɧɵɦ ɜɟɫɨɦ ɩɨɩɟɪɟɱɧɚɹ ɫɢɥɚ ɛɭɞɟɬ
ɨɞɢɧɚɤɨɜɨɣ (
Q
o
= – 260 ɤɇ), ɩɨɷɬɨɦɭ ɷɩɸɪɚ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɫɟɱɟɧɢɢ
ɫɬɟɧɤɢ ɩɨ ɩɨɞɨɲɜɟ ɞɥɹ ɜɬɨɪɨɝɨ ɢ ɫɭɦɦɚɪɧɨɝɨ ɡɚɝɪɭɠɟɧɢɣ ɫɬɟɧɤɢ
ɩɪɢ
ɪɚɫɫɦɨɬɪɟɧɢɢ ɟɟ ɤɚɤ ɫɬɟɪɠɧɹ-ɤɨɧɫɨɥɢ ɢɦɟɟɬ ɨɞɢɧɚɤɨɜɵɣ ɜɢɞ.
Ⱦɥɹ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɷɩɸɪɚɦɢ, ɩɨɫɬɪɨɟɧɧɵɦɢ ɞɥɹ
ɷɬɢɯ ɡɚɝɪɭɠɟɧɢɣ ɩɪɢ ɪɚɫɱɟɬɟ ɱɢɫɥɟɧɧɵɦ ɦɟɬɨɞɨɦ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ
(ɆɄɗ, ɪɟɚɥɢɡɨɜɚɧɧɨɦ ɩɪɢ ɡɚɞɚɧɧɨɣ ɫɟɬɤɟ Ʉɗ ɧɚ ɉɄ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɩɪɨɝɪɚɦɦɵ SCAD) ɨɧɚ ɩɨɫɬɪɨɟɧɚ ɧɚ ɪɢɫ. 1.7 ɢ ɪɢɫ. 1.8.
ɍɠɟ ɩɨ ɜɢɞɭ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɮɨɪɦɭɥɵ ɜɢɞɧɨ, ɱɬɨ,
ɩɨɥɭɱɟɧɧɚɹ ɩɨ ɧɟɣ
ɷɩɸɪɚ ɤɚɫɚɬɟɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɢɧɬɟɝɪɚɥɶɧɨ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɩɟɪɜɨɦɭ
ɭɪɚɜɧɟɧɢɸ (1.1) ɪɚɜɧɨɜɟɫɢɹ ɫɬɟɧɤɢ. Ɉɞɧɚɤɨ ɜɢɞɧɨ ɬɚɤ ɠɟ, ɱɬɨ ɮɨɪɦɭɥɚ ɧɟ
ɭɱɢɬɵɜɚɟɬ ɜɥɢɹɧɢɟ ɧɚ ɇȾɋ ɫɬɟɧɤɢ ɟɟ ɤɨɧɬɚɤɬɚ ɩɨ ɩɨɞɨɲɜɟ ɫ ɠɟɫɬɤɢɦ
ɨɫɧɨɜɚɧɢɟɦ.
Ʉɪɨɦɟ ɬɨɝɨ, ɢɡ ɩɨɥɭɱɟɧɧɨɣ ɷɩɸɪɵ ɜɢɞɧɨ, ɱɬɨ ɨɧɚ ɧɟ ɭɱɢɬɵɜɚɟɬ ɬɨɝɨ, ɱɬɨ
ɩɪɚɜɚɹ ɝɪɚɧɶ ɫɬɟɧɤɢ ɹɜɥɹɟɬɫɹ ɧɚɤɥɨɧɧɨɣ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɜɟɪɬɢɤɚɥɢ ɢ ɧɟ
ɫɨɫɬɚɜɥɹɟɬ ɭɝɥɚ 90
o
. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɜ ɬɨɱɤɚɯ ɧɚ
ɧɚɤɥɨɧɧɨɣ ɝɪɚɧɢ ɫɬɟɧɤɢ (ɫɦ. ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ (2.4) ɜ ɱɚɫɬɢ 1 ɍɆɄ)
ɧɟ ɛɭɞɭɬ ɭɞɨɜɥɟɬɜɨɪɟɧɵ ɩɪɢ ɧɭɥɟɜɵɯ ɨɪɞɢɧɚɬɚɯ, ɩɨɥɭɱɚɟɦɵɯ ɩɨ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɮɨɪɦɭɥɟ.
ɉɪɢɦɟɱɚɧɢɟ. ȼɨɩɪɨɫ ɨɛ ɭɞɨɜɥɟɬɜɨɪɟɧɢɢ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɣ ɹɜɥɹɟɬɫɹ ɧɟ ɩɪɨɫɬɵɦ ɢ
ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɆɄɗ. ɂɡ ɩɪɢɜɟɞɟɧɧɵɯ ɷɩɸɪ ɧɚɩɪɹɠɟɧɢɣ ɜɢɞɧɨ, ɱɬɨ ɩɨɥɭɱɟɧɧɵɟ
ɧɚɩɪɹɠɟɧɢɹ ɜ ɭɡɥɚɯ ɧɚ ɜɟɪɬɢɤɚɥɶɧɨɣ ɢ ɧɚɤɥɨɧɧɨɣ ɝɪɚɧɹɯ ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɝɪɚɧɢɱɧɵɦ
ɭɫɥɨɜɢɹɦ ɧɚ ɷɬɢɯ ɝɪɚɧɹɯ, ɬɚɤ ɤɚɤ ɧɚɩɪɹɠɟɧɢɹ, ɩɨɥɭɱɚɸɳɢɟɫɹ ɩɪɢ ɱɢɫɥɟɧɧɨɦ ɪɚɫɱɟɬɟ ɜ
ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɚɯ, ɩɪɢɦɵɤɚɸɳɢɯ ɤ ɝɪɚɧɹɦ ɫɬɟɧɤɢ, ɹɜɥɹɸɬɫɹ ɨɫɪɟɞɧɟɧɧɵɦɢ. ɉɪɢ
ɭɦɟɧɶɲɟɧɢɢ ɪɚɡɦɟɪɨɜ ɤɨɧɟɱɧɵ ɷɥɟɦɟɧɬɨɜ, ɩɪɢɦɵɤɚɸɳɢɯ ɤ ɝɪɚɧɢɰɚɦ ɫɬɟɧɤɢ, ɩɨɥɭɱɚɸɳɢɟɫɹ
ɜ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɚɯ ɧɚɩɪɹɠɟɧɢɹ ɛɭɞɭɬ ɩɪɢɛɥɢɠɚɬɶɫɹ ɤ ɬɟɦ, ɤɨɬɨɪɵɟ ɭɞɨɜɥɟɬɜɨɪɹɸɬ
ɝɪɚɧɢɱɧɵɦ ɭɫɥɨɜɢɹɦ.
ɗɬɨɬ ɜɨɩɪɨɫ ɬɪɟɛɭɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɤɨɬɨɪɵɟ ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɧɟ
ɩɪɟɞɭɫɦɨɬɪɟɧɵ.
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2. ɊȺɋɑȿɌ ɆȿɌɈȾɈɆ ɄɈɇȿɑɇɕɏ ɗɅȿɆȿɇɌɈȼ
ɇȺɉɊəɀȿɇɇɈȽɈ ɋɈɋɌɈəɇɂə ȻȺɅɄɂ-ɋɌȿɇɄɂ
ɇȺ ɍɉɊɍȽɈɆ ɈɋɇɈȼȺɇɂɂ
2.1. ɉɨɫɬɪɨɟɧɢɟ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
ɫɬɟɧɤɢ ɞɥɹ ɆɄɗ ɩɪɢ ɜɚɪɢɚɧɬɟ 2 ɨɫɧɨɜɚɧɢɹ
ɉɪɨɰɟɞɭɪɭ ɩɨɫɬɪɨɟɧɢɹ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɜ ɜɚɪɢɚɧɬɟ 2 ɢ ɪɚɡɛɢɟɧɢɢ ɟɟ
ɫɟɬɤɨɣ Ʉɗ ɜɵɩɨɥɧɢɦ ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɬɚɤɚɹ ɫɯɟɦɚ ɞɥɹ ɜɚɪɢɚɧɬɚ 1 ɨɫɧɨɜɚɧɢɹ
ɭɠɟ ɩɨɫɬɪɨɟɧɚ.
1.ɋɨɡɞɚɟɦ ɧɨɜɵɣ ɩɪɨɟɤɬ ɢ ɞɚɟɦ ɟɦɭ ɧɚɡɜɚɧɢɟ, ɧɚɩɪɢɦɟɪ,
«ɫɬɟɧɤɚ2-ABCD». Ɍɢɩ ɫɯɟɦɵ, ɤɚɤ ɢ ɩɪɢ ɜɚɪɢɚɧɬɟ 1 ɨɫɧɨɜɚɧɢɹ, ɩɪɢɦɟɦ ɬɨɬ ɠɟ:
«5. ɋɢɫɬɟɦɚ ɨɛɳɟɝɨ ɜɢɞɚ».
2. ȼ ɨɬɤɪɵɜɲɟɦɫɹ ɪɚɛɨɱɟɦ ɨɤɧɟ ɩɪɨɝɪɚɦɦɵ ɜɨɣɞɟɦ ɜ ɪɚɡɞɟɥ «ɋɯɟɦɚ» ɢ,
ɭɱɢɬɵɜɚɹ, ɱɬɨ ɱɚɫɬɶ ɪɚɫɱɟɬɧɨɣ ɨɛɥɚɫɬɢ (ɫɦ. ɪɢɫ. 2) ɜ ɜɢɞɟ ɫɬɟɧɤɢ ɭɠɟ ɩɨɫɬɪɨɟɧɚ
ɜ ɜɚɪɢɚɧɬɟ 1, ɫɨɡɞɚɞɢɦ ɨɫɬɚɜɲɭɸɫɹ ɱɚɫɬɶ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɞɥɹ
ɡɨɧɵ ɨɫɧɨɜɚɧɢɹ.
ɇɚɠɦɟɦ ɜ ɦɟɧɸ ɤɧɨɩɤɭ «Ƚɟɧɟɪɚɰɢɹ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɫɟɬɤɢ ɷɥɟɦɟɧɬɨɜ ɧɚ
ɩɥɨɫɤɨɫɬɢ». Ɉɬɤɪɨɟɬɫɹ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ «Ƚɟɧɟɪɚɰɢɹ ɩɥɚɫɬɢɧɱɚɬɨɣ ɫɯɟɦɵ»
(ɧɢɠɟ ɩɪɢɜɨɞɢɬɫɹ ɬɨɥɶɤɨ ɟɝɨ ɱɚɫɬɶ).
ɍɤɚɡɵɜɚɟɦ ɬɢɩ ɩɥɚɫɬɢɧɱɚɬɨɣ ɫɯɟɦɵ «Ȼɚɥɤɚ-ɫɬɟɧɤɚ», ɜɜɨɞɢɦ ɩɚɪɚɦɟɬɪɵ
Ʉɗ ɫɟɬɤɢ ɢ ɢɯ ɱɢɫɥɨ. ɍɤɚɡɵɜɚɟɦ ɬɢɩ Ʉɗ (ɬɢɩ 21, ɩɪɹɦɨɭɝɨɥɶɧɵɣ Ʉɗ ɛɚɥɤɢ-
ɫɬɟɧɤɢ) ɢ ɡɚɞɚɟɦ ɢɯ ɠɟɫɬɤɨɫɬɶ.
Ⱦɥɹ ɡɚɞɚɧɢɹ ɠɟɫɬɤɨɫɬɢ ɨɬɤɪɵɜɚɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ
(ɧɢɠɟ ɩɪɢɜɟɞɟɧɚ ɟɝɨ ɱɚɫɬɶ). ȼ ɷɬɨɦ ɨɤɧɟ ɜɜɨɞɢɦ:
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– ɨɛɴɟɦɧɵɣ ɜɟɫ ɝɪɭɧɬɚ (ɫɱɢɬɚɟɦ ɝɪɭɧɬ ɨɞɧɨɪɨɞɧɵɦ ɢ ɢɦɟɸɳɢɦ
ɨɛɴɟɦɧɵɣ ɜɟɫ ɪɚɜɧɵɦ 1.8 ɬɫ/ɦ
3
|18 ɤɇ/ɦ
3
);
– ɦɨɞɭɥɶ ɞɟɮɨɪɦɚɰɢɢ ɝɪɭɧɬɚ
o
E = 3e+05 ɤɇ/ɦ
2
;
– ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɚɫɫɨɧɚ ɝɪɭɧɬɚ
3.0 Q
o
;
– ɬɨɥɳɢɧɭ ɩɥɚɫɬɢɧɵ (ɬɨɥɳɢɧɭ ɫɥɨɹ ɩɨɥɭɩɥɨɫɤɨɫɬɢ) 1ɦ.
– ɨɬɦɟɱɚɟɬɫɹ ɬɢɩ ɩɥɨɫɤɨɣ ɡɚɞɚɱɢ (ɩɥɨɫɤɚɹ ɞɟɮɨɪɦɚɰɢɹ).
ɉɨɫɥɟ ɜɵɯɨɞɚ ɢɡ ɞɢɚɥɨɝɨɜɨɝɨ ɨɤɧɚ ɩɨ ɡɚɞɚɧɢɸ ɠɟɫɬɤɨɫɬɢ Ʉɗ ɢ ɜɵɯɨɞɚ ɢɡ
ɨɤɧɚ «Ƚɟɧɟɪɚɰɢɹ ɩɥɚɫɬɢɧɱɚɬɨɣ ɫɯɟɦɵ» ɧɚ ɷɤɪɚɧɟ ɩɨɥɭɱɚɟɦ ɱɚɫɬɶ ɪɚɫɱɟɬɧɨɣ
ɫɯɟɦɵ ɜ ɜɢɞɟ ɱɚɫɬɢ ɩɨɥɭɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɫɟɬɤɨɣ Ʉɗ (ɪɢɫ. 2.1).
ɇɚ ɪɢɫ. 2.1 ɫ ɩɨɦɨɳɶɸ ɮɢɥɶɬɪɚ ɨɬɨɛɪɚɠɟɧɢɹ ɭɤɚɡɚɧ
ɬɢɩ ɢɫɩɨɥɶɡɭɟɦɨɝɨ
ɩɪɢ ɪɚɫɱɟɬɟ Ʉɗ. Ɍɚɤɠɟ ɦɨɝɭɬ ɛɵɬɶ ɭɤɚɡɚɧɵ ɧɨɦɟɪɚ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ,
ɧɨɦɟɪɚ ɭɡɥɨɜ ɫɟɬɤɢ Ʉɗ, ɧɨɦɟɪ ɠɟɫɬɤɨɫɬɢ Ʉɗ. ɗɬɢ ɫɯɟɦɵ ɡɞɟɫɶ ɧɟ ɩɪɢɜɨɞɹɬɫɹ.
ɇɚ ɪɢɫ. 2.1 ɩɨɤɚɡɚɧɨ ɬɚɤɠɟ, ɱɬɨ ɜ ɭɡɥɵ ɫɨɡɞɚɧɧɨɣ ɫɯɟɦɵ, ɧɚɯɨɞɹɳɢɟɫɹ ɧɚ
ɝɪɚɧɢɰɟ 3-4-5-6 (ɫɦ.ɪɢɫ. 1.3), ɜɜɟɞɟɧɵ ɠɟɫɬɤɢɟ ɫɜɹɡɢ ɩɨ ɜɫɟɦ ɜɨɡɦɨɠɧɵɦ
ɧɚɩɪɚɜɥɟɧɢɹɦ ɩɟɪɟɦɟɳɟɧɢɹ ɭɡɥɨɜ ɷɥɟɦɟɧɬɨɜ.
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Ɋɢɫ. 2.1
3. Ɍɟɩɟɪɶ ɜ ɦɟɧɸ ɪɚɡɞɟɥɚ «ɋɯɟɦɚ» ɧɚɠɢɦɚɟɦ ɤɧɨɩɤɭ «Ɋɟɠɢɦ ɫɛɨɪɤɢ». ȼ
ɪɟɡɭɥɶɬɚɬɟ ɨɬɤɪɵɜɚɟɬɫɹ ɪɚɛɨɱɟɟ ɨɤɧɨ ɫ ɫɨɡɞɚɧɧɨɣ ɫɯɟɦɨɣ ɱɚɫɬɢ 3-4-5-6
ɩɨɥɩɨɥɭɩɥɨɫɤɨɫɬɢ, ɪɚɡɛɢɬɨɣ ɫɟɬɤɨɣ ɷɥɟɦɟɧɬɨɜ ɢ ɦɟɧɸ, ɩɨɡɜɨɥɹɸɳɟɟ
ɜɵɩɨɥɧɢɬɶ ɨɩɟɪɚɰɢɢ ɩɨ ɫɨɟɞɢɧɟɧɢɢɸ ɷɬɨɣ ɱɚɫɬɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɫ ɪɚɫɱɟɬɧɨɣ
ɫɯɟɦɨɣ, ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɜ ɜɚɪɢɚɧɬɟ 1.
ȼ ɨɬɤɪɵɜɲɟɦɫɹ ɦɟɧɸ ɧɚɠɢɦɚɟɦ ɤɧɨɩɤɭ «Ɂɚɝɪɭɡɤɚ ɩɨɞɫɯɟɦɵ». ɉɨɹɜɢɬɫɹ
ɨɤɧɨ, ɜ ɤɨɬɨɪɨɦ
ɜɵɛɟɪɟɦ ɮɚɣɥ ɫ ɩɪɨɟɤɬɨɦ «ɫɬɟɧɤɚ1-ABCD». ɋɯɟɦɭ ɫɬɟɧɤɢ,
ɫɨɡɞɚɧɧɭɸ ɜ ɷɬɨɦ ɩɪɨɟɤɬɟ, ɢɫɩɨɥɶɡɭɟɦ ɤɚɤ ɩɨɞɫɯɟɦɭ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ
ɩɪɨɟɤɬɟ «ɫɬɟɧɤɚ2-ABCD», ɩɨɫɤɨɥɶɤɭ ɩɨ ɩɨɞɨɲɜɟ ɫɬɟɧɤɢ ɪɚɡɦɟɪɵ Ʉɗ ɢ ɢɯ
ɱɢɫɥɨ ɫɨɜɩɚɞɚɸɬ ɫ ɪɚɡɦɟɪɚɦɢ Ʉɗ ɩɨɥɭɩɥɨɫɤɨɫɬɢ ɧɚ ɬɨɣ ɠɟ ɞɥɢɧɟ 1-2.
ȼɵɛɢɪɚɟɦ ɮɚɣɥ «ɫɬɟɧɤɚ1-ȺȼCD» ɢ ɜɵɛɢɪɚɟɦ ɮɭɧɤɰɢɸ «Ɉɬɤɪɵɬɶ». ȼ
ɪɟɡɭɥɶɬɚɬɟ ɜ ɪɚɛɨɱɟɦ ɨɤɧɟ ɩɨɹɜɢɬɫɹ ɩɨɞɫɯɟɦɚ
ɜ ɜɢɞɟ ɫɬɟɧɤɢ, ɪɚɡɛɢɬɨɣ ɜ
ɜɚɪɢɚɧɬɟ 1 ɫɟɬɤɨɣ Ʉɗ.
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Ⱦɚɥɟɟ ɜ ɦɟɧɸ ɧɚɠɢɦɚɟɦ ɤɧɨɩɤɭ «ȼɵɛɨɪ ɫɩɨɫɨɛɚ ɫɛɨɪɤɢ». Ɉɬɤɪɨɟɬɫɹ
ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ, ɜ ɤɨɬɨɪɨɦ ɜɵɛɟɪɟɦ ɫɩɨɫɨɛ ɫɛɨɪɤɢ «ɉɪɢɜɹɡɤɚ ɤ ɞɜɭɦ ɭɡɥɚɦ».
Ɉɫɬɚɥɶɧɵɟ ɮɭɧɤɰɢɢ ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɭɤɚɡɚɧɵ «ɩɨ ɭɦɨɥɱɚɧɢɸ».
ɋɨɝɥɚɲɚɟɦɫɹ ɫ ɧɢɦɢ.
Ⱦɜɭɦɹ ɭɡɥɚɦɢ ɞɥɹ ɫɨɟɞɢɧɟɧɢɹ ɫɬɟɧɤɢ ɫ ɨɫɧɨɜɚɧɢɟɦ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɭɡɥɵ
1 ɢ 2 ɫɯɟɦɵ ɫɬɟɧɤɢ (ɨɬɦɟɱɚɟɦ ɢɯ ɧɚ ɩɨɞɫɯɟɦɟ) ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɡɥɵ ɧɚ
ɫɯɟɦɟ ɩɨɥɭɩɥɨɫɤɨɫɬɢ (ɬɚɤɠɟ ɨɬɦɟɱɚɟɦ ɢɯ). ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɫɨɟɞɢɧɹɟɦɵɟ
ɭɡɥɵ ɨɬɦɟɬɹɬɫɹ ɤɪɚɫɧɵɦ ɢ ɡɟɥɟɧɵɦ ɰɜɟɬɨɦ.
Ɂɚɬɟɦ ɧɚɠɢɦɚɟɦ ɤɧɨɩɤɭ «ɈɄ» ɢ
ɩɨɞɬɜɟɪɠɞɚɟɦ ɜɵɛɪɚɧɧɵɣ ɫɩɨɫɨɛ ɫɛɨɪɤɢ
ɞɜɭɯ ɱɚɫɬɟɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɜ ɜɚɪɢɚɧɬɟ 2. ɉɨɹɜɢɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɡɚɩɪɨɫ:
«ɉɨɞɬɜɟɪɞɢɬɶ ɫɛɨɪɤɭ?». ɉɨɞɬɜɟɪɠɞɚɟɦ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɩɨɹɜɢɬɫɹ ɪɚɫɱɟɬɧɚɹ
ɫɯɟɦɚ 2.
ɇɨ ɜ ɩɨɥɭɱɟɧɧɨɣ ɩɪɢ ɫɛɨɪɤɟ ɫɯɟɦɟ ɨɫɬɚɧɭɬɫɹ ɫɜɹɡɢ, ɜɜɟɞɟɧɧɵɟ ɜ ɜɚɪɢɚɧɬɟ
1 ɜ ɭɡɥɵ ɫɬɟɧɤɢ ɩɨ ɥɢɧɢɢ ɩɨɞɨɲɜɵ. ɍɞɚɥɢɦ ɢɯ, ɜɨɣɞɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜ ɪɚɡɞɟɥ
«ɇɚɡɧɚɱɟɧɢɹ» ɢ ɨɬɤɪɵɜ ɨɤɧɨ
«ɍɫɬɚɧɨɜɤɚ ɫɜɹɡɟɣ», ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɝɨ
ɜɜɟɞɟɧɧɵɟ ɜ ɭɡɥɵ ɫɜɹɡɢ ɦɨɠɧɨ ɢ ɭɞɚɥɢɬɶ.
ɉɪɢɦɟɱɚɧɢɟ. Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɩɪɢ ɫɛɨɪɤɟ ɞɜɭɯ ɱɚɫɬɟɣ ɫɯɟɦɵ ɨɧɢ ɜɨɲɥɢ
ɫɨ ɜɫɟɦɢ ɪɚɧɟɟ ɡɚɞɚɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɫ ɪɚɧɟɟ ɡɚɞɚɧɧɵɦɢ ɜɚɪɢɚɧɬɚɦɢ
ɡɚɝɪɭɠɟɧɢɣ ɫɬɟɧɤɢ, ɚ ɬɚɤɠɟ ɡɚɞɚɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɬɢɩɨɜ Ʉɗ ɢ ɢɯ ɠɟɫɬɤɨɫɬɟɣ.
ɍɱɚɳɟɦɭɫɹ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɜɧɢɦɚɬɟɥɶɧɨ ɪɚɡɨɛɪɚɬɶɫɹ ɜɨ ɜɫɟɦ ɷɬɨɦ, ɩɪɟɠɞɟ ɱɟɦ
ɩɟɪɟɯɨɞɢɬɶ ɤ ɪɚɫɱɟɬɭ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɜ ɜɚɪɢɚɧɬɟ 2.
2.2. Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɨ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɜ ɜɢɞɟ ɫɬɟɧɤɢ
ɧɚ ɭɩɪɭɝɨɣ ɩɨɥɭɩɥɨɫɤɨɫɬɢ
ɇɚɩɪɹɠɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɫɬɟɧɤɢ ɩɪɟɞɫɬɚɜɥɟɧɨ ɷɩɸɪɚɦɢ ɧɚɩɪɹɠɟɧɢɣ
z
V
,
xz
W , ɞɟɣɫɬɜɭɸɳɢɯ ɜ ɫɟɱɟɧɢɢ ɫɬɟɧɤɢ ɩɨ ɩɨɞɨɲɜɟ, ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɫɬɟɧɤɢ
(ɪɢɫ. 2.2), ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ (ɪɢɫ. 2.3) ɢ ɨɬ ɤɨɦɛɢɧɚɰɢɢ ɷɬɢɯ