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Ȼԝɥ ɬɟԙɞɟɭɥɟɪɞɟɝɿ ɬԝɪɚԕɬɵɥɚɪ ɭ ɮɭɧɤɰɢɹɫɵɧɵԙ ɚɪԕɚɥɵԕ ɚɪɚɥɚɪɵɧɵԙ
ɲɟɤɚɪɚɫɵɧɞɚ ԛɡɿɥɿɫɫɿɡɞɿɝɿɧɟɧ ɬɚɛɵɥɚɞɵ.

D1 D2 D3 D4 D5 EI ˜ f0 ,
f0 – ɤɨɨɪɞɢɧɚɬɚ ɛɚɫɵɧɞɚԑɵ ԕɢɦɚɧɵԙ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵ.
ɋɨɧɵɦɟɧ, ɚɥɵɧԑɚɧ ɫɨԙԑɵ ɬɟԙɞɟɭɥɟɪɞɿ ɛɿɪ ɬɟԙɞɟɭ ɪɟɬɿɧɞɟ ɠɚɡɵɩ, ɨɧɵ
ɚɪԕɚɥɵԕɬɵԙ ɫɟɪɩɿɦɞɿ ɫɵɡɵԑɵɧɵԙ ԥɦɛɟɛɚɩ ɬɟԙɞɟɭɿ ɞɟɩ ɚɬɚɣɦɵɡ.

EJ x f EJ x y EJ x f0 EJ xT0 z x M c z a2 Pi z b3 q z c 4 q z d 4 .
24 24
2 II 6 III IV v

ɋɨԙԑɵ ɮɨɪɦɭɥɚɧɵ ԕɨɥɞɚɧɭɞɵԙ ɟɪɟɠɟɫɿ: ɛɿɪɿɧɲɿ ɚɪɚɥɵԕɬɚԑɵ ԕɢɦɚɥɚɪɞɵԙ
ɨɪɵɧ ɚɭɵɫɬɵɪɭɵɧ ɬɚɛɭ ԛɲɿɧ ȱ ɢɧɞɟɤɫɿ ɛɚɪ ɬɿɤ ɫɵɡɵԕԕɚ ɞɟɣɿɧɝɿ ɦԛɲɟɥɟɪ
ɩɚɣɞɚɥɚɧɵɥɚɞɵ, ɚɥ ɟɤɿɧɲɿ ɚɪɚɥɵԕɬɚԑɵ ԕɢɦɚɥɚɪɞɵԙ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵɧ ɬɚɛɭ
ԛɲɿɧ ȱȱ ɢɧɞɟɤɫɿ ɛɚɪ ɬɿɤ ɫɵɡɵԕԕɚ ɞɟɣɿɧɝɿ ɛɚɪɥɵԕ ɦԛɲɟɥɟɪ ɩɚɣɞɚɥɚɧɵɥɚɞɵ,
ԕɚɥԑɚɧ ɚɪɚɥɵԕɬɚɪɞɚԑɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪ ɨɫɵ ɬԥɪɬɿɩɩɟɧ ɬɚɛɵɥɚɞɵ.

§8. ɂɿɥɭɞɟɝɿ ɛɟɪɿɤɬɿɤ ɠԥɧɟ ԕɚɬɚԙɞɵԕ
Ɍɚɡɚ ɢɿɥɭ ɤɟɡɿɧɞɟ ɧɟɝɿɡɝɿ ɟɫɟɩɬɟɭɥɟɪ ɤɟɪɧɟɭɥɟɪ ɚɪԕɵɥɵ ɠԛɪɝɿɡɿɥɟɞɿ.
ɋɨɧɞɵԕɬɚɧ, ɛɟɪɿɤɬɿɤ ɲɚɪɬɵ ɛɨɵɧɲɚ ɟԙ ԛɥɤɟɧ ɤɟɪɧɟɭ; ɹԑɧɢ ԕɚɭiɩɬɿ ԕɢɦɚɞɚԑɵ
ɤɟɪɧɟɭ, ɦԛɦɤɿɧ ɤɟɪɧɟɭɞɟɧ ɚɫɩɚɭ ɤɟɪɟɤ.
V max d >V @ (7.31)

M ˜ ymax (7.32)
> @V max Jx d V

Ȼԝɥ ɮɨɪɦɭɥɚɞɚԑɵ Jx ԕɚɬɵɧɚɫɵ ԕɢɦɚɧɵԙ ɤɟɞɟɪɝi ɦɨɦɟɧɬi ɞɟɩ ɚɬɚɥɵɩ,
ymax

Wx ɫɢɦɜɨɥɵɦɟɧ ɛɟɥɝiɥɟɧɟɞi, ɞɟɦɟɤ

Wx Jx . (7.33)
ymax

ɋɨɧɵɦɟɧ, ɬɚɡɚ ɢiɥɭɞɟɝi ɧɟɝiɡɝi ɛɟɪiɤɬiɤ ɲɚɪɬɵ ɬԧɦɟɧɞɟɝiɞɟɣ ɠɚɡɵɥɵɩ,
ɦɚɬɟɪɢɚɥɞɚɪ ɤɟɞɟɪɝiɫiɧiԙ ԛɲ ɟɫɟɛiɧ ɬɨɥɵԕ ԕɚɦɬɢɞɵ:

M d >V @. (7.34)
Wx

Ʉɟɥɬiɪiɥɝɟɧ ɮɨɪɦɭɥɚɦɟɧ, ɟɫɟɩɬɟɥiɩ ɨɬɵɪԑɚɧ ɷɥɟɦɟɧɬɬiԙ ɛɟɪiɤɬiɝi
ɬɟɤɫɟɪiɥɫɟ, ɬԧɦɟɧɞɟɝi ԧɪɧɟɤ ɚɪԕɵɥɵ ɨɥ ɷɥɟɦɟɧɬɬiԙ ɤԧɥɞɟɧɟԙ ԕɢɦɚɫɵɧɵԙ
ԧɥɲɟɦɞɟɪi ɚɧɵԕɬɚɥɚɞɵ.

Wx t M (7.35)

>V @

ɋɨɧɵɦɟɧ ԕɚɬɚɪ, ԕɚɪɚɫɬɵɪɵɥɵɩ ɨɬɵɪԑɚɧ ɷɥɟɦɟɧɬɬiԙ ɦԛɦɤiɧ ɠԛɤɬɟɦɟɫiɧ ɞɟ
(7.34) ɮɨɪɦɭɥɚɧɵԙ ɤԧɦɟɝiɦɟɧ ɬɚɛɭԑɚ ɛɨɥɚɞɵ.

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