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P. 534
Ԧɬɤɟɧ ɩɚɪɚɝɪɚɮɬɚ ɚɣɬɵɥԑɚɧɞɚɣ, ș ɛԝɪɵɲɵɧɵԙ ɬɚɧɝɟɧɫi ɬɵɦ ɚɡ ɲɚɦɚ
ɟɤɟɧiɧ ɟɫɤɟɪɫɟɤ, dy ɲɚɦɚɫɵɧɵԙ ɤɜɚɞɪɚɬɵɧ ¨¨§© §¨ dy ¸· 2 0¹¸¸· ɟɥɟɦɟɭɝɟ ɛɨɥɚɞɵ.
© dz ¹
dz
ɋɨɧɞɚ:
1 d2 y . (7.28)
U dz
2
(7.26) ɠԥɧɟ (7.28) ԧɪɧɟɤɬɟɪɞɟɧ:
d2y M (7.29)
dz2 EJ
Ԕɚɬɚԙɞɵԕɬɵ ɬԝɪɚԕɬɵ ɞɟɩ ɚɥɵɩ (ȿI=const), ɢɸɲɿ ɦɨɦɟɧɬ, ɤԧɥɞɟɧɟԙ ɤԛɲ
ɠԥɧɟ ɬɚɪɚɥԑɚɧ ɤԛɲɬɿԙ ԕɚɪԕɵɧɞɵɥɵԑɵ ɚɪɚɥɚɪɵɧɞɚԑɵ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ
ԕɚɬɵɧɚɫɬɚɪɞɵ ɟɫɤɟɪɫɟɤ:
T d yI , M EJ x d2y , Q EJ x d3y , q EJ x d4y . (7.30)
dz 2 dz3 dz 4
ɋɨԙԑɵ ɬɟԙɞɿɤɬɟɪɞɟɧ ɬɭɵɧɞɚɣɬɵɧ ɬԝɠɵɪɵɦɞɚɪ:
– ɟɝɟɪ q = const ɛɨɥɫɚ, ɨɧɞɚ d 4 y q const, ɛԝɥ ɤɟɡɞɟ ɚɪԕɚɥɵԕɬɵԙ
EJ 1
dz 4
ɢɿɥɝɟɧ ɨɫɿɧɿԙ ɩɿɲɿɧɿ ɬԧɪɬɿɧɲɿ ɞԥɪɟɠɟɥɿ ԕɢɫɵԕ ɫɵɡɵԕ ɛɨɥɚɞɵ;
– ɟɝɟɪ, q = ɨ ɛɨɥɫɚ, ɨɧɞɚ ɚɪԕɚɥɵԕɬɵԙ ɢɿɥɝɟɧ ɨɫɿ ԛɲɿɧɲɿ ɞԥɪɟɠɟɥɿ ԕɢɫɵԕ
ɫɵɡɵԕ;
– ɠɨԑɚɪɵɞɚ ɤɟɥɬɿɪɿɥɝɟɧ ɮɨɪɦɭɥɚɥɚɪɞɵԙ ɞԥɥɞɿɝɿ, ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪɞɵԙ
ԕɚɧɲɚɥɵԕɬɵ ɚɡ ɟɤɟɧɿɧɟ ɛɚɣɥɚɧɵɫɬɵ.
§7. Ⱥɪԕɚɥɵԕɬɵԙ ɫɟɪɩɿɦɞɿ ɫɵɡɵԑɵɧɵԙ ԥɦɛɟɛɚɩ ɬɟԙɞɟɭɿ
Ⱥɪԕɚɥɵԕɬɵԙ ɫɟɪɩɿɦɞɿ ɫɵɡɵԑɵɧɵԙ ɬɟԙɞɟɭɿɧ ɚɧɵԕɬɚɭ, ɨɧɵԙ
ɚɪɚɥɵԕɬɚɪɵɧɵԙ ɫɚɧɵɧɚ ɛɚɣɥɚɧɵɫɬɵ ɟɤɟɧɿ, ɚɪɚɥɵԕ ɫɚɧɵ ɤԧɛɟɣɝɟɧ ɫɚɣɵɧ
ɢɧɬɟɝɪɚɥɞɚɭ ɬԝɪɚԕɬɵɥɚɪɵɧ ɬɚɛɭ ԕɢɵɧɞɚɣ ɛɟɪɟɬɿɧɿ ɠɨԑɚɪɵɞɚ ԕɚɪɚɥԑɚɧ
ɦɵɫɚɥɞɚɪɞɚɧ ɚɣԕɵɧ ɤԧɪɿɧɟɞɿ. Ɇɵɫɚɥɵ, ɚɪԕɚɥɵԕ n ɚɪɚɥɵԕɬɚɧ ɬԝɪɫɚ, ɨɧɞɚ 2n
ɬɟԙɞɟɭɥɟɪɞɟɧ ɬԝɪɚɬɵɧ ɠԛɣɟɧɿ ɲɟɲɭɝɟ ɬɭɪɚ ɤɟɥɟɞɿ. ȿɝɟɪ ԕɚɬɚԙɞɵԑɵ ɬԝɪɚԕɬɵ
(ȿI=const) ɚɪԕɚɥɵԕɬɵԙ ɫɟɪɩɿɦɞɿ ɫɵɡɵԑɵɧɵԙ ɬɟԙɞɟɭɿɧ ɛɟɥɝɿɥɿ ɛɿɪ ɟɪɟɠɟɧɿ
ԝɫɬɚɣ ɨɬɵɪɵɩ ԕԝɪɫɚ, ɨɧɞɚ ɤԧɪɫɟɬɿɥɝɟɧ ԕɢɵɧɞɵԕɬɚɧ ɨԙɚɣ ԕԝɬɵɥɭԑɚ ɛɨɥɚɞɵ.
Ɉɥ ɟɪɟɠɟ:
ɚ) ɤɨɨɪɞɢɧɚɬɚ ɛɚɫɵ, ɚɪԕɚɥɵԕ ɨɫɿɧɿԙ ɬɟɤ ɨԙ ɠɚԕ ɧɟɦɟɫɟ ɫɨɥ ɠɚԕ ɲɟɬɤɿ
ɧԛɤɬɟɫɿɧɞɟ ɛɨɥɭ ɤɟɪɟɤ;
ԥ) ɚɪɚɥɵԕɬɚɪɞɚԑɵ ɢɸ ɦɨɦɟɧɬɬɟɪɿɧ ɚɧɵԕɬɚԑɚɧ ɤɟɡɞɟ, ɚɪԕɚɥɵԕɬɵԙ
ɤɨɨɪɞɢɧɚɬɚ ɛɚɫɵ ɨɪɧɚɥɚɫԕɚɧ ɛԧɥɿɝɿ ԑɚɧɚ ԕɚɪɚɥɭ ɤɟɪɟɤ;
ɛ) ɚɥɞɵԙԑɵ ɚɪɚɥɵԕɬɵԙ ɢɸ ɦɨɦɟɧɬɿɧɿԙ ԧɪɧɟɤɬɟɪɿ, ɤɟɥɟɫɿ ɚɪɚɥɵԕɬɵԙ ɢɸ
ɦɨɦɟɧɬɿɧɿԙ ԧɪɧɟɝɿɧɟ ɟɲ ԧɡɝɟɪɭɫɿɡ ɛԝɪɵɧԑɵ ԕɚɥɩɵɧɞɚ ɤɿɪɭ ɤɟɪɟɤ;
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