Константинов Н.А., Лалин В.В., Лалина И.И. - Расчёт статически определимых стержневых систем с использованием SCAD (1061793), страница 35
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12.1, ɛ, ɜ, ɝ).ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜ ɷɬɨɣ ɠɟ ɫɢɫɬɟɦɟ ɩɨɫɬɚɜɥɟɧɚ ɡɚɞɚɱɚ ɨɩɪɟɞɟɥɟɧɢɹɜɟɤɬɨɪɚ (12.20) ɬɟɯ ɠɟ ɬɪɟɯ ɩɟɪɟɦɟɳɟɧɢɣ, ɧɨ ɨɬ ɝɪɭɩɩɵ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯɭɫɢɥɢɣ P1 , P2 , P3 (ɪɢɫ. 12.4, ɚ), ɞɟɣɫɬɜɭɸɳɢɯ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɢɫɤɨɦɵɯɩɟɪɟɦɟɳɟɧɢɣ ɢ ɨɛɪɚɡɭɸɳɢɯ ɜɟɤɬɨɪª P1 º p « P2 » ,« »«¬ P3 »¼ɝɞɟ P3 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɣ ɦɨɦɟɧɬ.(12.21)Ɋɢɫ. 12.4205Ɍɚɤ ɤɚɤ ɬɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɬɚɤɢɟ ɠɟ ɩɟɪɟɦɟɳɟɧɢɹ, ɤɚɤ ɢ ɜ ɡɚɞɚɱɟ,ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ.
12.1, ɚ, ɬɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ ɞɥɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹɮɨɪɦɭɥɵ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ (12.10) ɨɫɬɚɧɭɬɫɹ ɬɚɤɢɦɢ ɠɟ (ɫɦ. ɪɢɫ. 12.1, ɛ, ɜ, ɝ ɢɪɢɫ. 12.4, ɛ, ɜ, ɝ).ȿɫɥɢ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɹɯ ɨɬ ɞɟɣɫɬɜɢɹ ɟɞɢɧɢɱɧɵɯ ɫɢɥɨɩɪɟɞɟɥɹɬɶ ɩɟɪɟɦɟɳɟɧɢɹ G ik ɩɨ ɬɟɦ ɠɟ ɧɚɩɪɚɜɥɟɧɢɹɦ, ɱɬɨ ɢ ɜ ɝɪɭɡɨɜɨɦɫɨɫɬɨɹɧɢɢ, ɬɨ, ɢɫɩɨɥɶɡɭɹ ɡɚɤɨɧ Ƚɭɤɚ ɢ ɩɪɢɧɰɢɩ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɣɫɬɜɢɹ ɫɢɥ,ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɹ:'1 p G11 P1 G12 P2 G13 P3 ;'2 pG 21 P1 G 22 P2 G 23 P3 ;'3 pG 31 P1 G 32 P2 G 33 P3 .(12.22)ȼ ɦɚɬɪɢɱɧɨɣ ɡɚɩɢɫɢ ɷɬɢ ɭɪɚɜɧɟɧɢɹ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:ª '1 p º ª G11 G12 G13 º ª P1 º«» «»« »(12.23)«' 2 p » «G 21 G 22 G 23 » « P2 » ,« ' 3 p » «¬G 31 G 32 G 33 »¼ «¬ P3 »¼¬¼ɢɥɢ ɩɪɢ ɤɨɦɩɚɤɬɧɨɣ ɡɚɩɢɫɢ ɦɚɬɪɢɰ –ɫɬɨɥɛɰɨɜ (12.20) ɢ (12.21) – ɜ ɜɢɞɟ:dpDp ,(12.24)ɝɞɟ(12.25)ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɚɬɪɢɰɭ ɜɥɢɹɧɢɹ ɫɢɥ, ɨɛɪɚɡɭɸɳɢɯ ɜɟɤɬɨɪ p (12.21) ɧɚɩɟɪɟɦɟɳɟɧɢɹ, ɨɛɪɚɡɭɸɳɢɯ ɜɟɤɬɨɪ d p (12.20).
Ɍɚɤɭɸ ɦɚɬɪɢɰɭ ɜ ɫɬɪɨɢɬɟɥɶɧɨɣɦɟɯɚɧɢɤɟ ɧɚɡɵɜɚɸɬ ɦɚɬɪɢɰɟɣ ɩɨɞɚɬɥɢɜɨɫɬɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ (ɜ ɞɚɧɧɨɦɫɥɭɱɚɟ ɪɚɦɵ) ɜ ɧɚɩɪɚɜɥɟɧɢɹɯ ɞɟɣɫɬɜɭɸɳɢɯ ɫɢɥ.Ʉɨɷɮɮɢɰɢɟɧɬɵ ɷɬɨɣ ɦɚɬɪɢɰɵ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɩɟɪɟɦɟɳɟɧɢɹ ɜɨɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɹɯ (ɫɦ. ɪɢɫ. 12.4, ɛ, ɜ, ɝ), ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɬɫɹ ɩɨɮɨɪɦɭɥɟ Ɇɚɤɫɜɟɥɥɚ - Ɇɨɪɚ (ɞɥɹ ɥɸɛɵɯ i 1, 2 , 3 ɢ k 1, 2 , 3 ):QQɆiM kNNdx + P ³L i k dx + ³L i k dx .(12.26)GIEIEAɉɪɢ ɷɬɨɦ ɞɨɤɚɡɵɜɚɸɬɫɹ ɫɪɚɡɭ ɞɜɟ ɬɟɨɪɟɦɵ ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɢ:1. Ɍɟɨɪɟɦɚ ɨ ɜɡɚɢɦɧɨɫɬɢ ɪɚɛɨɬ ɞɥɹ ɥɸɛɵɯ ɞɜɭɯ ɫɨɫɬɨɹɧɢɣ ɪɚɦɵ,ɡɚɝɪɭɠɟɧɧɵɯ ɤɚɤɨɣ-ɬɨ ɧɚɝɪɭɡɤɨɣ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩɪɢ ɟɞɢɧɢɱɧɵɯ ɭɫɢɥɢɹɯ1k Gik2061i Gki = ³Lɫɨɛɥɸɞɚɟɬɫɹ ɪɚɜɟɧɫɬɜɨ ɪɚɛɨɬ 1k Gik1i Gki ).2. Ɍɟɨɪɟɦɚ ɨ ɜɡɚɢɦɧɨɫɬɢ ɩɟɪɟɦɟɳɟɧɢɣ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ G ikG ki ).ɉɟɪɜɵɣ ɢɧɞɟɤɫ ɜ ɜɵɪɚɠɟɧɢɢ G ik = G ki ɩɨɤɚɡɵɜɚɟɬ ɧɨɦɟɪ ɧɚɩɪɚɜɥɟɧɢɹ, ɩɨɤɨɬɨɪɨɦɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɟɪɟɦɟɳɟɧɢɟ.
ȼɬɨɪɨɣ ɢɧɞɟɤɫ ɩɨɤɚɡɵɜɚɟɬ ɧɨɦɟɪɜɫɩɨɦɨɝɚɬɟɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɜ ɤɨɬɨɪɨɦ ɩɪɢɥɨɠɟɧɚ ɟɞɢɧɢɱɧɚɹ ɫɢɥɚ (ɩɨɷɬɨɦɭɩɪɢ ɡɚɩɢɫɢ ɪɚɛɨɬɵ ɫɢɥ ɟɞɢɧɢɱɧɚɹ ɫɢɥɚ ɨɬɦɟɱɟɧɚ ɢɧɞɟɤɫɨɦ ɪɚɜɧɵɦ ɜɬɨɪɨɦɭɢɧɞɟɤɫɭ ɜ ɨɛɨɡɧɚɱɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɹ).Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ ɧɚ ɫɥɟɞɭɸɳɢɟ ɫɜɨɣɫɬɜɚ ɦɚɬɪɢɰɵ ɩɨɞɚɬɥɢɜɨɫɬɢ:1. Ɉɧɚ ɤɜɚɞɪɚɬɧɚɹ ɢ ɢɦɟɟɬ ɩɨɪɹɞɨɤ ( n n ), ɝɞɟ n – ɱɢɫɥɨ ɫɬɪɨɤɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜ ɜɟɤɬɨɪɚɯ d p ɢ p .2.
ɇɚ ɟɟ ɝɥɚɜɧɨɣ ɞɢɚɝɨɧɚɥɢ, ɨɬɦɟɱɟɧɧɨɣ ɜ (12.25) ɲɬɪɢɯɨɜɨɣ ɥɢɧɢɟɣ,ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɷɥɟɦɟɧɬɵ, ɤɨɬɨɪɵɟ ɜɫɟɝɞɚ ɩɨɥɨɠɢɬɟɥɶɧɵ, ɬɚɤ ɤɚɤ ɩɪɢɩɨɞ ɥɸɛɵɦ ɢɡ ɬɪɟɯ ɢɧɬɟɝɪɚɥɨɜ (12.26)ɪɚɜɟɧɫɬɜɟ i kɩɨɞɵɧɬɟɝɪɚɥɶɧɚɹ ɮɭɧɤɰɢɹ ɜɧɭɬɪɟɧɧɟɝɨ ɭɫɢɥɢɹ ɢɦɟɟɬ ɜɬɨɪɭɸ ɫɬɟɩɟɧɶ.3. Ɍɚɤ ɤɚɤ ɷɥɟɦɟɧɬɵ ɦɚɬɪɢɰɵ ɪɚɜɧɵ G ik G ki ɩɪɢ ɥɸɛɵɯ i ɢ k , ɬɨɦɚɬɪɢɰɚ ɫɢɦɦɟɬɪɢɱɧɚ.Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɜɟɤɬɨɪɚ d p (12.20) ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ (ɫɦ. ɪɢɫ. 12.4,ɚ) ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɵɪɚɠɟɧɢɟ (12.19) ɢɥɢ (12.24).ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɡɚɤɨɧɚ Ƚɭɤɚ ɢ ɩɪɢɧɰɢɩɚ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɣɫɬɜɢɹ ɫɢɥɜɟɤɬɨɪ m p ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟmpM p.(12.27)ɉɨɞɫɬɚɜɢɦ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ (6.19) ɢ ɫɨɩɨɫɬɚɜɢɦ ɟɝɨ ɫ (6.24).
Ɍɨɝɞɚ ɞɥɹɜɵɱɢɫɥɟɧɢɹ ɦɚɬɪɢɰɵ ɩɨɞɚɬɥɢɜɨɫɬɢ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ:D(M ) ɬ LM .(12.28)ɋ ɩɪɢɦɟɪɚɦɢ ɪɚɫɱɟɬɨɜ ɦɚɬɪɢɰɵ D ɦɨɠɧɨ ɩɨɡɧɚɤɨɦɢɬɶɫɹ ɜ ɭɱɟɛɧɵɯɩɨɫɨɛɢɹɯ [7, 10].12.7. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɨɬ ɡɚɞɚɧɧɨɣ ɨɫɚɞɤɢ ɨɩɨɪȾɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɨɬ ɜɧɟɲɧɟɝɨɜɨɡɞɟɣɫɬɜɢɹ ɜ ɩɨɞɪɚɡɞɟɥɟ 12.2 ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɮɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ(12.10).ɗɬɚ ɮɨɪɦɭɥɚ ɨɬɪɚɠɚɟɬ ɪɚɛɨɬɭ ɜɧɟɲɧɢɯ ɫɢɥ ɢ ɜɧɭɬɪɟɧɧɢɯ ɭɫɢɥɢɣ ɜɨɫɬɟɪɠɧɟɜɨɣɫɢɫɬɟɦɵɧɚɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦɫɨɫɬɨɹɧɢɢɡɚɞɚɧɧɨɣɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɧɟɲɧɢɦ ɫɢɥɚɦ ɢ ɜɧɭɬɪɟɧɧɢɦ ɭɫɢɥɢɹɦ ɜɨɡɦɨɠɧɵɯɩɟɪɟɦɟɳɟɧɢɹɯ ɢ ɞɟɮɨɪɦɚɰɢɹɯ.207ȼɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢ ɜɨɡɦɨɠɧɵɟ ɞɟɮɨɪɦɚɰɢɢ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦɫɨɫɬɨɹɧɢɢ ɡɚɞɚɧɧɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɩɪɢɧɹɬɵ ɪɚɜɧɵɦɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɞɟɣɫɬɜɢɬɟɥɶɧɵɦ ɩɟɪɟɦɟɳɟɧɢɹɦ ɢ ɞɟɣɫɬɜɢɬɟɥɶɧɵɦ ɞɟɮɨɪɦɚɰɢɹɦ «ɝɪɭɡɨɜɨɝɨ»ɫɨɫɬɨɹɧɢɹ ɡɚɞɚɧɧɨɣ ɪɚɦɵɉɨɞ «ɝɪɭɡɨɜɵɦ» ɫɨɫɬɨɹɧɢɟɦ ɩɨɧɢɦɚɟɬɫɹ ɫɨɫɬɨɹɧɢɟ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵɨɬ ɥɸɛɨɝɨ ɜɧɟɲɧɟɝɨ ɜɨɡɞɟɣɫɬɜɢɹ (ɫɢɥɨɜɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɜ ɜɢɞɟ ɡɚɞɚɧɧɨɣɧɚɝɪɭɡɤɢ, ɡɚɞɚɧɧɨɣ ɨɫɚɞɤɢ ɨɩɨɪ ɢ ɡɚɞɚɧɧɨɝɨ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ).ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɫɜɨɣɫɬɜɚɦɢ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɢɫɬɟɦ (ɫɦ.ɬɚɛɥ.
5.1 ɜ ɩɨɞɪɚɡɞɟɥɟ 5.7) ɨɬ ɡɚɞɚɧɧɨɣ ɨɫɚɞɤɢ ɨɩɨɪ ɜ «ɝɪɭɡɨɜɨɦ» ɫɨɫɬɨɹɧɢɢɪɚɦɵ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɣ ɧɚɝɪɭɡɤɢ ɧɟ ɜɨɡɧɢɤɚɸɬ ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹM p , Q p , N p , ɚ ɡɧɚɱɢɬ (ɫɦ. ɭɪɚɜɧɟɧɢɹ (1.5) ɡɚɤɨɧɚ Ƚɭɤɚ) ɧɟ ɜɨɡɧɢɤɚɸɬ ɢɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɟɣ N p , J p , H p . ɉɨɷɬɨɦɭ ɜɫɟ ɢɧɬɟɝɪɚɥɵ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢɮɨɪɦɭɥɵ (12.10) ɛɭɞɭɬ ɪɚɜɧɵ ɧɭɥɸ.ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɡ ɮɨɪɦɭɥɵ (12.10) ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɭɸ ɮɨɪɦɭɥɭ ɞɥɹɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯɬɨɥɶɤɨ ɨɬ ɟɟ ɡɚɞɚɧɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ («ɨɫɚɞɨɤ») ɨɩɨɪ:1 ' ip = – ¦ m Rmi cmp , i 1, 2 , 3 .(12.29)Ⱦɥɹ ɩɪɢɦɟɧɟɧɢɹ ɷɬɨɣ ɮɨɪɦɭɥɵ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɬɟɯ ɠɟ ɩɟɪɟɦɟɳɟɧɢɣ,ɤɨɬɨɪɵɟ ɭɤɚɡɚɧɵ ɧɚ ɪɢɫ.
12.1, ɚ , ɧɨ ɬɨɥɶɤɨ ɧɟ ɨɬ ɧɚɝɪɭɡɤɢ, ɚ ɨɬ ɡɚɞɚɧɧɵɯɫɦɟɳɟɧɢɣ ɨɩɨɪ (ɪɢɫ. 12.5), ɧɟɨɛɯɨɞɢɦɨ ɫɨɫɬɚɜɢɬɶ ɬɟ ɠɟ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟɫɨɫɬɨɹɧɢɹ (ɫɦ. ɪɢɫ. 12.5, ɛ, ɜ, ɝ), ɱɬɨ ɢ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɣ ɨɬɡɚɞɚɧɧɨɣ ɧɚɝɪɭɡɤɢ (ɫɦ. ɪɢɫ. 12.1, ɛ, ɜ, ɝ).Ɋɢɫ. 12.5ɇɨ ɬɟɩɟɪɶ, ɞɥɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɮɨɪɦɭɥɵ (12.29) ɧɟɨɛɯɨɞɢɦɨ ɜ ɝɪɭɡɨɜɨɦɫɨɫɬɨɹɧɢɢ ɪɚɦɵ ɭɤɚɡɚɬɶ ɡɚɞɚɧɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɨɩɨɪɵ A (ɫɦ. ɪɢɫ.
12.5, ɚ), ɚ ɜɨɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɹɯ ɜɵɱɢɫɥɢɬɶ ɢ ɭɤɚɡɚɬɶ ɧɚɩɪɚɜɥɟɧɢɹ ɪɟɚɤɰɢɣ ɜɫɟɯɨɩɨɪ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ (ɜ ɞɚɧɧɨɦ ɩɪɢɦɟɪɟ ɬɨɥɶɤɨ ɨɞɧɨɣ)208(ɫɦ. ɪɢɫ. 12.5, ɛ, ɜ, ɝ).ȼɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɨ ɮɨɪɦɭɥɟ (12.29) ɜɟɥɢɱɢɧɵ ɭɤɚɡɚɧɵɧɚ ɪɢɫ. 12.5.ȼɵɱɢɫɥɟɧɧɵɟ ɩɨ ɮɨɪɦɭɥɟ (12.29) ɩɟɪɟɦɟɳɟɧɢɹ ɛɭɞɭɬ ɫɜɨɛɨɞɧɵɦɢ (ɧɟɫɬɟɫɧɟɧɧɵɦɢ), ɬɚɤ ɤɚɤ ɩɪɢ ɷɬɢɯ ɩɟɪɟɦɟɳɟɧɢɹɯ ɜ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɟ ɧɟ ɛɭɞɟɬɜɨɡɧɢɤɚɬɶ ɧɢɤɚɤɢɯ ɭɫɢɥɢɣ.
ȿɟ ɷɥɟɦɟɧɬɵ ɩɟɪɟɦɟɫɬɹɬɫɹ ɤɚɤ ɠɟɫɬɤɢɟ ɞɢɫɤɢ ɜɧɟɤɨɬɨɪɨɟ ɧɨɜɨɟ ɧɟɧɚɩɪɹɠɟɧɧɨɟ ɩɨɥɨɠɟɧɢɟ ɤɚɤ ɱɚɫɬɢ ɦɟɯɚɧɢɡɦɚ (ɪɢɫ. 12.6).ȼEDɋFȺɊɢɫ. 12.6ȼɨɩɪɨɫ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɩɨ ɮɨɪɦɭɥɟ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ ɜɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɛɭɞɟɬ ɪɚɫɫɦɨɬɪɟɧ ɜ ɪɚɡɞɟɥɟ 7ɩɨɫɥɟ ɨɡɧɚɤɨɦɥɟɧɢɹ ɫ ɦɟɬɨɞɨɦ ɫɢɥ ɪɚɫɱɟɬɚ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɯɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ.12.8. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɨɬ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɢɯ ɫɬɟɪɠɧɟɣɉɨɥɭɱɟɧɧɚɹ ɨɛɳɚɹ ɮɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ (12.10) ɩɪɢɦɟɧɢɦɚ ɢ ɩɪɢɬɟɦɩɟɪɚɬɭɪɧɵɯ ɜɨɡɞɟɣɫɬɜɢɹɯ ɧɚ ɫɬɟɪɠɧɟɜɵɟ ɫɢɫɬɟɦɵ.Ɍɟɦɩɟɪɚɬɭɪɧɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɟ ɜɵɡɵɜɚɟɬɭɫɢɥɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯdT tBAɫɢɫɬɟɦɚɯ (ɫɦ.
ɬɚɛɥ. 5.1 ɜ ɩɨɞɪɚɡɞɟɥɟ 5.7h/2ɩɨɫɨɛɢɹ). ȼ t ɜ ɬɨɠɟ ɜɪɟɦɹ ɨɬ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨCtoDɜɨɡɞɟɣɫɬɜɢɹ ɩɪɨɢɫɯɨɞɹɬ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɟɣ.h/ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɪɨɢɫɯɨɞɹɳɢɟ ɞɟɮɨɪɦɚɰɢɢ ɢtɧɫɜɹɡɚɧɧɵɟ ɫ ɧɢɦɢ ɩɟɪɟɦɟɳɟɧɢɹ ɹɜɥɹɸɬɫɹdxKLɫɜɨɛɨɞɧɵɦɢ (ɧɟ ɫɬɟɫɧɟɧɧɵɦɢ).Ɋɢɫ. 12.7Ɋɚɫɫɦɨɬɪɢɦ ɜɨɩɪɨɫ ɨɛ ɨɩɪɟɞɟɥɟɧɢɢ ɷɬɢɯɫɜɨɛɨɞɧɵɯ (ɧɟ ɜɵɡɵɜɚɸɳɢɯ ɭɫɢɥɢɣ) ɬɟɦɩɟɪɚɬɭɪɧɵɯ ɞɟɮɨɪɦɚɰɢɹɯ ɫɬɟɪɠɧɟɣ.ɂɡɨɛɪɚɡɢɦ ɧɚ ɪɢɫ. 12.7 ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɷɥɟɦɟɧɬ ɫɬɟɪɠɧɹ ɞɥɢɧɨɣ dx .Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɩɪɨɢɡɨɲɥɨ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɜɟɪɯɧɟɝɨ ɢɧɢɠɧɟɝɨ ɜɨɥɨɤɨɧ ɫɬɟɪɠɧɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɧɚ tɜ ɢ tɧ ɝɪɚɞɭɫɨɜ, ɝɞɟ tɧ ! tɜ ! 0 .Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ ɫɬɟɪɠɟɧɶ ɬɨɧɤɢɦ ɢ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɟɝɨɜɵɫɨɬɟ ɥɢɧɟɣɧɵɦ.
Ɍɨɝɞɚ t ɨ0 .5 (t ɧ t ɜ ) .209ɍɞɥɢɧɟɧɢɹ ɧɢɠɧɟɝɨ, ɫɪɟɞɧɟɝɨ ɢ ɜɟɪɯɧɟɝɨ ɜɨɥɨɤɨɧ ɷɥɟɦɟɧɬɚ dxɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɨɫɬɚɜɥɹɸɬ ' dx, ɧ Dtɧ dx , ' dx, ɨ Dto dx , ' dx, ɜ Dtɜ dx , ɝɞɟ Dɹɜɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɥɢɧɟɣɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɦɚɬɟɪɢɚɥɚ ɫɬɟɪɠɧɹ.Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɪɨɞɨɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɹ ɨɬɫɪɟɞɧɟɣ ɬɟɦɩɟɪɚɬɭɪɵ t ɨ0 .5 (t ɧ t ɜ )Ht oDt o .(12.30)Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɨɢɫɯɨɞɢɬ ɞɟɮɨɪɦɚɰɢɹ ɢɫɤɪɢɜɥɟɧɢɹ ɫɬɟɪɠɧɹ, ɩɪɢ ɤɨɬɨɪɨɣɫɟɱɟɧɢɹ ɷɥɟɦɟɧɬɚ dx ɩɨɜɨɪɚɱɢɜɚɸɬɫɹ ɧɚ ɭɝɨɥ dTt (ɫɦ.
ɪɢɫ. 12.7).ɍɫɥɨɜɧɨ ɞɟɮɨɪɦɢɪɨɜɚɧɧɵɣ ɨɬ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɥɨɤɨɧ ɷɥɟɦɟɧɬɩɨɤɚɡɚɧ ɜ ɜɢɞɟ ɬɪɚɩɟɰɢɢ ABKL. ɐɟɧɬɪ ɤɪɢɜɢɡɧɵ ɫɬɟɪɠɧɹ (ɨɛɨɡɧɚɱɢɦ ɟɝɨ ɬɨɱɤɨɣɈ) ɪɚɫɩɨɥɨɠɟɧ ɞɚɥɟɤɨ ɨɬ ɟɝɨ ɨɫɢ: ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɪɚɞɢɭɫɚ ɤɪɢɜɢɡɧɵ R . ɉɨɷɬɨɦɭɢɫɤɪɢɜɥɟɧɢɟ ɜɨɥɨɤɨɧ ɫɬɟɪɠɧɹ ɧɚ ɪɢɫ. 12.7 ɧɟ ɩɨɤɚɡɚɧɨ. ɉɪɢɛɥɢɠɟɧɧɨKL (1 Dtɧ )dx , CD (1 Dt o )dx ,.
AB (1 Dt ɜ )dx . Ɍɨɝɞɚ(12.KL AB D(tɧ tɜ )dx31)hhɈɬɫɸɞɚ ɩɨɥɭɱɚɟɦ ɞɟɮɨɪɦɚɰɢɸ ɢɫɤɪɢɜɥɟɧɢɹ ɫɬɟɪɠɧɹ:dTt D(tɧ tɜ )NtDW12.3dxh2)Ɂɞɟɫɶ ɜɟɥɢɱɢɧɚ(12(tɧ tɜ )W.33hɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɝɪɚɞɢɟɧɬ ɬɟɦɩɟɪɚɬɭɪ ɩɨ ɬɨɥɳɢɧɟ h ɫɬɟɪɠɧɹ, ɪɚɜɧɵɣɬɚɧɝɟɧɫɭ ɭɝɥɚ ɧɚɤɥɨɧɚ ɥɢɧɟɣɧɨɣ ɷɩɸɪɵ ɬɟɦɩɟɪɚɬɭɪ ɤ ɜɟɪɬɢɤɚɥɢ.Ɂɚɩɢɲɟɦ ɬɟɩɟɪɶ ɮɨɪɦɭɥɭ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɬɟɯ ɠɟɩɟɪɟɦɟɳɟɧɢɣ ɜ ɪɚɦɟ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ.
12.1, ɚ ɢ ɧɚ ɪɢɫ. 12.5, ɧɨ ɬɨɥɶɤɨ ɨɬɭɤɚɡɚɧɧɨɝɨ ɡɞɟɫɶ ɜɨɡɞɟɣɫɬɜɢɹ ɬɟɦɩɟɪɚɬɭɪɵ.Ɏɨɪɦɭɥɭ ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ (12.8). ɉɪɢ ɷɬɨɦ ɡɚɩɢɲɟɦ ɟɟ ɞɥɹ ɥɸɛɨɝɨɩɟɪɟɦɟɳɟɧɢɹ ɫ ɧɨɦɟɪɨɦ i , ɭɱɬɟɦ, ɱɬɨ ɧɚ ɪɚɦɭ ɧɟ ɜɨɡɞɟɣɫɬɜɭɸɬ ɧɢ ɧɚɝɪɭɡɤɢ,ɧɢ ɨɫɚɞɤɢ ɨɩɨɪ. Ⱦɟɮɨɪɦɚɰɢɢ ɜ «ɝɪɭɡɨɜɨɦ» ɫɨɫɬɨɹɧɢɢ ɡɚɦɟɧɢɦ ɭɤɚɡɚɧɧɵɦɢɬɟɦɩɟɪɚɬɭɪɧɵɦɢ ɞɟɮɨɪɦɚɰɢɹɦɢ. Ɍɨɝɞɚ ɞɥɹ ɬɨɧɤɢɯ ɫɬɟɪɠɧɟɣ ɩɨɥɭɱɢɦ:1 ' it = ³L M i Nt dx + ³L N i H o dx .(12.34)dTt | tgdTtȼɨɩɪɨɫ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɯɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɛɭɞɟɬ ɪɚɫɫɦɨɬɪɟɧ ɜɨ ɜɬɨɪɨɣ ɱɚɫɬɢ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹɩɨɫɥɟ ɢɡɭɱɟɧɢɹ ɦɟɬɨɞɚ ɫɢɥ ɪɚɫɱɟɬɚ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯɫɢɫɬɟɦ.21013. ɉɊɂɆȿɊ ɈɉɊȿȾȿɅȿɇɂə ɉȿɊȿɆȿɓȿɇɂɃȼ ɋɌȺɌɂɑȿɋɄɂɈɉɊȿȾȿɅɂɆɈɃ ɊȺɆȿɋ ɂɋɉɈɅɖɁɈȼȺɇɂȿɆ ɉɊɈȽɊȺɆɆɕ SCAD13.1.
ȼɜɟɞɟɧɢɟɉɟɪɟɦɟɳɟɧɢɹ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɟɣ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɧɚɩɪɢɦɟɪ, ɫɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ Ɇɚɤɫɜɟɥɥɚ-Ɇɨɪɚ (ɫɦ. ɩɪɟɞɵɞɭɳɢɣ ɪɚɡɞɟɥ) ɚ ɬɚɤɠɟ ɩɪɢɪɚɫɱɟɬɟ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɆɄɗ.Ɏɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ-Ɇɨɪɚ (12.10) ɞɥɹ ɩɥɨɫɤɢɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɩɪɢɨɩɪɟɞɟɥɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɣ ɨɬ ɡɚɞɚɧɧɨɣ ɧɚɝɪɭɡɤɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɦɦɭɬɪɟɯ ɢɧɬɟɝɪɚɥɨɜ, ɨɬɪɚɠɚɸɳɢɯ ɜɥɢɹɧɢɟ ɧɚ ɢɫɤɨɦɨɟ ɩɟɪɟɦɟɳɟɧɢɟɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɢɡɝɢɛɧɵɯ (ɜɥɢɹɧɢɟ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ), ɫɞɜɢɝɨɜɵɯ(ɜɥɢɹɧɢɟ ɩɨɩɟɪɟɱɧɵɯ ɫɢɥ) ɢ ɩɪɨɞɨɥɶɧɵɯ (ɜɥɢɹɧɢɟ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ)ɞɟɮɨɪɦɚɰɢɣ ɫɬɟɪɠɧɟɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ.Ɉɛɵɱɧɨ ɜ ɫɬɪɨɢɬɟɥɶɧɵɯ ɤɨɧɫɬɪɭɤɰɢɹɯ ɫɬɟɪɠɧɢ ɹɜɥɹɸɬɫɹ ɬɨɧɤɢɦɢ. ȼ ɧɢɯɜɥɢɹɧɢɟɦ ɫɞɜɢɝɨɜɵɯ ɞɟɮɨɪɦɚɰɢɣ ɧɚ ɩɟɪɟɦɟɳɟɧɢɹ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɟɣɩɪɟɧɟɛɪɟɝɚɸɬ. Ɍɨɝɞɚ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɩɟɪɟɦɟɳɟɧɢɣ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɟɣ ɩɥɨɫɤɨɣɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɤɚɤ ɜɢɞɧɨ ɢɡ ɨɫɬɚɜɲɢɯɫɹ ɜ ɮɨɪɦɭɥɟ ɞɜɭɯ ɢɧɬɟɝɪɚɥɨɜ,ɩɨɬɪɟɛɭɟɬɫɹ ɡɚɞɚɧɢɟ ɠɟɫɬɤɨɫɬɟɣ ɫɬɟɪɠɧɟɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɧɚ ɢɡɝɢɛ (EIyi )ɢ ɧɚ ɪɚɫɬɹɠɟɧɢɟ-ɫɠɚɬɢɟ (EFi), ɝɞɟ i – ɧɨɦɟɪ ɫɬɟɪɠɧɹ.Ⱦɨ ɫɢɯ ɩɨɪ ɜ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɩɪɨɝɪɚɦɦɚ SCAD ɩɪɢɦɟɧɹɥɚɫɶɬɨɥɶɤɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯɫɢɫɬɟɦɚɯ.ɉɪɢ ɬɚɤɨɣ ɩɨɫɬɚɧɨɜɤɟ ɡɚɞɚɱɢ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɨɝɪɚɦɦɵ SCADɠɟɫɬɤɨɫɬɶ ɩɥɨɫɤɢɯ ɫɬɟɪɠɧɟɜɵɯ ɷɥɟɦɟɧɬɨɜ ɬɢɩɚ 2 ɧɚ ɢɡɝɢɛ EIyi ɢ ɩɪɨɞɨɥɶɧɚɹɠɟɫɬɤɨɫɬɶ EFi ɞɥɹ ɷɥɟɦɟɧɬɨɜ ɬɢɩɚ 1 ɢ 2 ɦɨɝɥɢ ɛɵɬɶ ɡɚɞɚɧɵ ɜ ɜɢɞɟɩɪɨɢɡɜɨɥɶɧɵɯ ɡɧɚɱɟɧɢɣ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɪɚɜɧɵɦɢ ɟɞɢɧɢɰɟ (ɫɦ.
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