Константинов Н.А., Лалин В.В., Лалина И.И. - Расчёт статически определимых стержневых систем с использованием SCAD (1061793), страница 33
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ȼ ɷɬɨɦ ɫɟɱɟɧɢɢ ɢɡɜɟɫɬɧɚ ɚɛɫɰɢɫɫɚ x8 = 12.5 ɦ. Ɍɨɝɞɚ ɢɡ (5.11)ɧɚɯɨɞɢɦ:sin D 8(0.5l x8 ) / r = (0.5 20 12.5) / 12.5 = – 0.2;cos D 8z8194(1 sin 2 D 80.9798 ;f r (1 cos D 8 ) = 5– 12.5(1 – 0.9798) = 4.75 ɦ.( z*ɉɨ ɮɨɪɦɭɥɚɦ (5.15) – (5.17) ɨɩɪɟɞɟɥɹɟɦ ɭɫɢɥɢɹ ɜ ɫɟɱɟɧɢɢ 8 ɚɪɤɢz8 a 4.75 2.5 2,25 ɦ):M8Q8N8M 8o H * z8* = 240.6 – 95·2.25 = 26.9 ɤɇ·ɦ;Q8o cos D 8 H * sin D 8 = (–11.25·0.9798 – 95·(– 0.2) = 8 ɤɇ;(Q8o sin D 8 H * cos D 8 ) = – (– 0.056·(– 0.2) + 0.476·0.9798) ql = – 0.478 ql == – 95.6 ɤɇ.Ⱦɥɹ ɤɨɧɬɪɨɥɹ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɨɜ ɭɫɢɥɢɣ ɩɨ ɩɪɨɝɪɚɦɦɟ ARKA ɧɚɷɩɸɪɚɯ ɭɫɢɥɢɣ (ɫɦ. ɪɢɫ. 11.2) ɜ ɫɟɱɟɧɢɹɯ 3 ɢ 8 ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɭɫɢɥɢɣ,ɩɨɥɭɱɟɧɧɵɟ ɪɚɫɱɟɬɨɦ ɩɨ ɩɪɨɝɪɚɦɦɟ ɢ ɪɚɫɱɟɬɨɦ ɜɪɭɱɧɭɸ (ɜ ɫɤɨɛɤɚɯ).
ȼɢɞɢɦ,ɱɬɨ ɪɟɡɭɥɶɬɚɬɵ ɛɥɢɡɤɨ ɫɨɜɩɚɞɚɸɬ.Ʉɨɧɬɪɨɥɶ ɷɩɸɪ M ɢ Q ɜ ɫɜɹɡɢ ɫ ɢɦɟɸɳɟɣɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ ɜ ɜɢɞɟɭɪɚɜɧɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ dM / ds Q ɩɨɤɚɡɵɜɚɟɬ ɢɯ ɩɨɥɧɨɟ ɫɨɨɬɜɟɬɫɬɜɢɟ.ɋɨɩɨɫɬɚɜɥɟɧɢɟ ɷɩɸɪ M ɜ ɚɪɤɟ ɢ ɛɚɥɤɟɗɬɨ ɫɨɩɨɫɬɚɜɥɟɧɢɟ ɩɨɤɚɡɵɜɚɟɬ:x ɢɡɝɢɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɜ ɚɪɤɟ ( M max | 90 ɤɇ·ɦ ) ɡɧɚɱɢɬɟɥɶɧɨ (ɞɥɹɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɚɪɤɢ ɩɪɢɦɟɪɧɨ ɜ ɬɪɢ ɪɚɡɚ) ɦɟɧɶɲɟ, ɱɟɦ ɜ ɛɚɥɤɟMmax | 240 ɤɇ·ɦ).x ɩɪɢ ɡɚɞɚɧɧɨɣ ɧɚɝɪɭɡɤɟ ɚɪɤɚ ɫɠɚɬɚ (ɞɨɜɨɥɶɧɨ ɪɚɜɧɨɦɟɪɧɨ: | ɨɬ 93 ɤɇɞɨ 102 ɤɇ), ɚ ɜ ɛɚɥɤɟ ɩɪɨɞɨɥɶɧɵɟ ɫɢɥɵ ɨɬɫɭɬɫɬɜɭɸɬ.Ɂɧɚɱɢɬɟɥɶɧɨɟ ɭɦɟɧɶɲɟɧɢɟ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ ɜ ɚɪɤɟ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɛɚɥɤɨɣ (ɫɦ. ɪɢɫ. 11.1) ɢ ɧɚɥɢɱɢɟ ɫɠɢɦɚɸɳɢɯ ɭɫɢɥɢɣ ɜɫɟɱɟɧɢɹɯ ɚɪɤɢ ɩɪɢɜɨɞɢɬ ɤ ɛɨɥɟɟ ɛɥɚɝɨɩɪɢɹɬɧɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɧɨɪɦɚɥɶɧɵɯɧɚɩɪɹɠɟɧɢɣ ɜ ɫɟɱɟɧɢɹɯ ɚɪɤɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɛɚɥɤɨɣ (ɫɦ. ɪɢɫ.
5.8, ɜ, ɝ).Ɂɚɤɥɸɱɟɧɢɟȼɵɩɨɥɧɟɧɧɵɟ ɩɪɨɜɟɪɤɢ ɩɨɡɜɨɥɹɸɬ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɪɚɫɱɟɬ ɚɪɤɢ ɩɨɨɩɪɟɞɟɥɟɧɢɸ ɭɫɢɥɢɣ ɜ ɟɟ ɫɟɱɟɧɢɹɯ ɢ ɜ ɨɩɨɪɧɵɯ ɫɜɹɡɹɯ ɜɵɩɨɥɧɟɧ ɩɪɚɜɢɥɶɧɨ.19512. ɈɉɊȿȾȿɅȿɇɂȿ ɉȿɊȿɆȿɓȿɇɂɃ ɋȿɑȿɇɂɃ ɋɌȿɊɀɇȿɃɅɂɇȿɃɇɈ ȾȿɎɈɊɆɂɊɍȿɆɕɏ ɋɌȿɊɀɇȿȼɕɏ ɋɂɋɌȿɆ12.1. ȼɜɟɞɟɧɢɟɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɨɩɪɟɞɟɥɟɧɢɹ ɇȾɋ ɩɥɨɫɤɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɨɬɫɬɚɬɢɱɟɫɤɢ ɩɪɢɥɨɠɟɧɧɨɣ ɜɧɟɲɧɟɣ ɧɚɝɪɭɡɤɢ ɞɥɹ ɤɚɠɞɨɝɨ ɫɟɱɟɧɢɹ ɢɦɟɟɦ 9ɧɟɢɡɜɟɫɬɧɵɯ ɜɟɥɢɱɢɧ (ɫɦ. ɪɢɫ. 1.5):M ,Q , N – ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹ ɜ ɫɟɱɟɧɢɢ;N, J, H – ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɞɟɮɨɪɦɚɰɢɢ ɜ ɫɟɱɟɧɢɢ;u , w, T – ɩɟɪɟɦɟɳɟɧɢɹ ɫɟɱɟɧɢɹ.Ⱦɨ ɫɢɯ ɩɨɪ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɨɛ ɨɩɪɟɞɟɥɟɧɢɢ ɇȾɋ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɫɬɚɜɢɥɚɫɶ ɬɨɥɶɤɨ ɱɚɫɬɶ ɷɬɨɣ ɡɚɞɚɱɢ, ɚ ɢɦɟɧɧɨ: ɡɚɞɚɱɚ ɨɩɪɟɞɟɥɟɧɢɹ ɜɧɭɬɪɟɧɧɢɯɭɫɢɥɢɣ M ,Q , N ɜ ɫɟɱɟɧɢɹɯ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ.ɉɨɫɥɟ ɨɩɪɟɞɟɥɟɧɢɹ ɭɤɚɡɚɧɧɵɯ ɭɫɢɥɢɣ ɦɨɠɧɨ ɢɡ ɭɪɚɜɧɟɧɢɣ, ɨɬɪɚɠɚɸɳɢɯɡɚɤɨɧ Ƚɭɤɚ (1.5), ɨɩɪɟɞɟɥɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɟɥɢɱɢɧɵ, ɨɬɪɚɠɚɸɳɢɟɞɟɮɨɪɦɚɰɢɢ ɢɡɝɢɛɚ N , ɩɨɩɟɪɟɱɧɵɟ ɞɟɮɨɪɦɚɰɢɢ (ɞɟɮɨɪɦɚɰɢɢ ɫɞɜɢɝɚ) J ɢɩɪɨɞɨɥɶɧɵɟ ɞɟɮɨɪɦɚɰɢɢ H .Ɍɪɢ ɩɟɪɟɦɟɳɟɧɢɹ ɫɟɱɟɧɢɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɡɚɬɟɦ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (1.4) ɩɪɢ ɡɚɞɚɧɧɵɯ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ.ȼ ɤɭɪɫɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɚɬɟɪɢɚɥɨɜ ɬɚɤɨɣ ɫɩɨɫɨɛ ɨɩɪɟɞɟɥɟɧɢɹɩɟɪɟɦɟɳɟɧɢɣ ɛɵɥ ɩɪɨɢɥɥɸɫɬɪɢɪɨɜɚɧ ɧɚ ɩɪɢɦɟɪɚɯ ɪɚɫɫɦɨɬɪɟɧɢɹ ɇȾɋ ɩɪɹɦɵɯɫɬɟɪɠɧɟɣ ɩɪɢ ɩɪɨɞɨɥɶɧɵɯ ɢ ɢɡɝɢɛɧɵɯ ɞɟɮɨɪɦɚɰɢɹɯ.Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɤɭɪɫɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɚɬɟɪɢɚɥɨɜ ɪɚɫɫɦɚɬɪɢɜɚɥɫɹ ɬɚɤɠɟɦɟɬɨɞ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ ɜɵɱɢɫɥɟɧɢɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣɷɧɟɪɝɢɢ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ.
Ɉɧ ɛɵɥ ɪɟɚɥɢɡɨɜɚɧ ɜ ɜɢɞɟ ɮɨɪɦɭɥɵɄɚɫɬɢɥɶɹɧɨ, ɢɡ ɤɨɬɨɪɨɣ ɡɚɬɟɦ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɟɣɩɨɥɭɱɚɟɬɫɹ ɮɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ.ȼ ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɟ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɫɟɱɟɧɢɣɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɮɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ. ȼɨɩɪɨɫ ɨɟɟ ɩɨɥɭɱɟɧɢɹ ɛɚɡɢɪɭɟɬɫɹ ɧɚ ɡɚɤɨɧɟ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɩɪɢ ɞɟɮɨɪɦɚɰɢɢɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɪɟɚɥɢɡɭɟɦɨɝɨ ɜ ɮɨɪɦɟɩɪɢɧɰɢɩɚ (ɧɚɱɚɥɚ) ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ (ɉȼɉ).196Ɂɞɟɫɶ ɜɨɩɪɨɫ ɨ ɩɨɥɭɱɟɧɢɢ ɷɬɨɣ ɮɨɪɦɭɥɵ ɪɚɫɫɦɨɬɪɟɧ ɜ ɫɨɤɪɚɳɟɧɧɨɣɮɨɪɦɟ.
Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɫ ɧɢɦ ɦɨɠɧɨ ɩɨɡɧɚɤɨɦɢɬɶɫɹ ɜ ɭɱɟɛɧɢɤɚɯ ɩɨɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɟ, ɧɚɩɪɢɦɟɪ, [7, 8, 10, 11].12.2. Ɏɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ-Ɇɨɪɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɞɟɣɫɬɜɢɬɟɥɶɧɵɯɩɟɪɟɦɟɳɟɧɢɣ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦȾɟɣɫɬɜɢɬɟɥɶɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢ ɞɟɮɨɪɦɚɰɢɢɊɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɨɟ ɝɪɭɡɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɨɣɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɜ ɜɢɞɟ ɪɚɦɵ (ɪɢɫ. 12.1, ɚ).Ɋɢɫ. 12.1ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɩɪɢɥɨɠɟɧɧɨɣ ɜɧɟɲɧɟɣ ɫɬɚɬɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ ɜ ɥɸɛɨɦɫɟɱɟɧɢɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɜɨɡɧɢɤɚɸɬ ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹ M p ,Q p , N p ,ɞɟɮɨɪɦɚɰɢɢ N p , J p , H p ɢ ɩɟɪɟɦɟɳɟɧɢɹ u p , w p , T p .
ɂɧɞɟɤɫ p ɭ ɨɛɨɡɧɚɱɟɧɢɣɜɟɥɢɱɢɧ ɭɫɢɥɢɣ, ɞɟɮɨɪɦɚɰɢɣ ɢ ɩɟɪɟɦɟɳɟɧɢɣ ɩɨɤɚɡɵɜɚɟɬ ɢɯ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶɝɪɭɡɨɜɨɦɭ ɫɨɫɬɨɹɧɢɸ. ɋɚɦɨ ɝɪɭɡɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɧɚ ɪɢɫ. 12.1, ɚ ɬɚɤɠɟ ɨɬɦɟɱɟɧɨɤɚɤ ɫɨɫɬɨɹɧɢɟ «p».ȼɫɟ ɭɤɚɡɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɜ ɪɚɦɟ ɹɜɥɹɸɬɫɹ ɞɟɣɫɬɜɢɬɟɥɶɧɵɦɢ ɢɥɢ ɢɫɬɢɧɧɵɦɢ.Ɂɚɞɚɧɧɚɹ ɪɚɦɚ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɚ, ɩɨɷɬɨɦɭ ɞɟɣɫɬɜɢɬɟɥɶɧɵɟ ɭɫɢɥɢɹM p ,Q p , N p ɜ ɥɸɛɵɯ ɟɟ ɫɟɱɟɧɢɹɯ ɨɬ ɡɚɞɚɧɧɨɣ ɧɚɝɪɭɡɤɢ ɥɟɝɤɨ ɨɩɪɟɞɟɥɹɸɬɫɹ. ɉɨɮɨɪɦɭɥɚɦ (1.5) ɡɚɤɨɧɚ Ƚɭɤɚ ɥɟɝɤɨ ɨɩɪɟɞɟɥɹɸɬɫɹ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟɞɟɣɫɬɜɢɬɟɥɶɧɵɟ ɞɟɮɨɪɦɚɰɢɢ:MpQpNp(12.1)Np; Jp P; Hp.EIESGSɊɚɫɫɦɨɬɪɢɦ ɦɟɬɨɞɢɤɭ ɨɩɪɟɞɟɥɟɧɢɹ ɞɟɣɫɬɜɢɬɟɥɶɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣɥɸɛɨɝɨ ɫɟɱɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɝɪɭɡɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɪɚɦɵ ɫɧɚɱɚɥɚ ɧɚɩɪɢɦɟɪɟ ɨɩɪɟɞɟɥɟɧɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ '1 p ɫɟɱɟɧɢɹ B ɪɚɦɵ(ɫɦ. ɪɢɫ. 12.1, ɚ).197ȼɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢ ɞɟɮɨɪɦɚɰɢɢɂɡɨɛɪɚɡɢɦ ɧɟɤɨɬɨɪɨɟ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ 1 ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣɪɚɦɵ (ɪɢɫ.
12.1, ɛ), ɜ ɤɨɬɨɪɨɦ ɜɧɟɲɧɟɣ ɧɚɝɪɭɡɤɨɣ ɛɭɞɟɦ ɩɨɥɚɝɚɬɶ ɟɞɢɧɢɱɧɭɸɫɢɥɭ, ɞɟɣɫɬɜɭɸɳɭɸ ɜ ɫɟɱɟɧɢɢ B ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɢɫɤɨɦɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ '1 p ɜɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ ɪɚɦɵ. Ɉɬ ɷɬɨɣ ɟɞɢɧɢɱɧɨɣ ɫɢɥɵ ɜ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɟɣ ɪɚɦɵɜɨɡɧɢɤɧɭɬ ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹ M 1 ,Q1 , N1 .ȼɜɟɞɟɦ ɞɥɹ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɪɚɦɵ ɩɨɧɹɬɢɹ «ɜɨɡɦɨɠɧɵɟɩɟɪɟɦɟɳɟɧɢɹ» ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ «ɜɨɡɦɨɠɧɵɟ ɞɟɮɨɪɦɚɰɢɢ». ɉɨɞ ɧɢɦɢɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɥɸɛɵɟ ɦɚɥɵɟ ɩɟɪɟɦɟɳɟɧɢɹ u*, w*,T * ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦɦɚɥɵɟ ɞɟɮɨɪɦɚɰɢɢdT *dw *du *,N*; J* T * ; H*(12.2)dxdxdxɞɨɩɭɫɤɚɟɦɵɟ ɧɚɥɨɠɟɧɧɵɦɢ ɧɚ ɪɚɦɭ ɫɜɹɡɹɦɢ.ɇɚɩɪɢɦɟɪ, ɬɚɤɢɦɢ ɜɨɡɦɨɠɧɵɦɢ ɩɟɪɟɦɟɳɟɧɢɹɦɢ ɢ ɞɟɮɨɪɦɚɰɢɹɦɢ ɜɨɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ ɪɚɦɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɞɟɣɫɬɜɢɬɟɥɶɧɵɟ ɭɩɪɭɝɢɟɩɟɪɟɦɟɳɟɧɢɹɦɢ ɢ ɞɟɮɨɪɦɚɰɢɹɦɢ ɪɚɦɵ, ɜɵɡɜɚɧɧɵɟ ɡɚɞɚɧɧɵɦɢ ɜ ɝɪɭɡɨɜɨɦɫɨɫɬɨɹɧɢɢ ɪɚɦɵ ɧɚɝɪɭɡɤɚɦɢ (ɫɦ.
ɪɢɫ. 12.1, ɚ).ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ ɪɚɦɵ ɡɚɞɚɧɵɜɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ u*, w*, T * ɢ ɜɨɡɦɨɠɧɵɟ ɞɟɮɨɪɦɚɰɢɢ (12.2)ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɪɚɜɧɵɟɞɟɣɫɬɜɢɬɟɥɶɧɵɦɩɟɪɟɦɟɳɟɧɢɹɦu p , wp , T pɢɞɟɣɫɬɜɢɬɟɥɶɧɵɦ ɞɟɮɨɪɦɚɰɢɹɦ ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ, ɬ.ɟ. ɡɚɞɚɧɵ ɜɨɡɦɨɠɧɵɟɩɟɪɟɦɟɳɟɧɢɹ ɢ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɢɞɟ:u* u p ; w* w p ; T* T p ;(12.3)N* N p ;J* J p ; H* H p .(12.4)ɉɪɢɧɰɢɩ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɞɥɹ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɨɣɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵȾɥɹ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɡɚɤɨɧɨɦ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ «ɉɪɢɧɰɢɩ(ɇɚɱɚɥɨ) ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ» (ɉȼɉ ɢɥɢ ɇȼɉ) ɜ ɫɥɟɞɭɸɳɟɣɮɨɪɦɭɥɢɪɨɜɤɟ.Ⱦɥɹ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɧɚɯɨɞɹɳɟɣɫɹ ɜɪɚɜɧɨɜɟɫɢɢ, ɫɭɦɦɚ ɪɚɛɨɬɵ A , ɫɨɜɟɪɲɚɟɦɨɣ ɩɪɢɥɨɠɟɧɧɵɦɢ ɤ ɫɢɫɬɟɦɟɜɧɟɲɧɢɦɢ ɫɢɥɚɦɢ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɬɢɦ ɫɢɥɚɦ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɹɯ,ɢ ɪɚɛɨɬɵ B , ɫɨɜɟɪɲɚɟɦɨɣ ɜɧɭɬɪɟɧɧɢɦɢ ɭɫɢɥɢɹɦɢ ɫɢɫɬɟɦɵ ɧɚɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɨɡɦɨɠɧɵɯ ɞɟɮɨɪɦɚɰɢɹɯ, ɪɚɜɧɚ ɧɭɥɸ:198A B 0.(12.5)ɉɪɢɦɟɧɢɜ ɉȼɉ ɤ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɨɦɭ ɷɥɟɦɟɧɬɭ ɞɥɢɧɨɣ dx (ɫɦ.
ɪɢɫ. 1.5), ɢɢɫɩɨɥɶɡɨɜɚɜ ɭɪɚɜɧɟɧɢɹ (1.3) – (1.5), ɩɨɫɥɟ ɩɪɟɧɟɛɪɟɠɟɧɢɹ ɫɥɚɝɚɟɦɵɦɢ ɜɬɨɪɨɝɨɩɨɪɹɞɤɚ ɦɚɥɨɫɬɢ (ɫɦ. [7, 10]), ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɪɚɛɨɬɵ Adx ɜɧɟɲɧɢɯ ɫɢɥ,ɤ ɤɨɬɨɪɵɦ ɨɬɧɨɫɹɬɫɹ ɢ ɧɚɝɪɭɡɤɢ ɩɨ ɞɥɢɧɟ ɷɥɟɦɟɧɬɚ (ɫɦ. ɪɢɫ. 1.5,ɚ) ɢ ɜɧɭɬɪɟɧɧɢɟɭɫɢɥɢɹ ɩɨ ɟɝɨ ɤɨɧɰɚɦ (ɫɦ. ɪɢɫ. 1.5, ɛ), ɜ ɜɢɞɟAdx ( M N * Q J * N H*)dx .(12.6)Ⱦɥɹ ɜɫɟɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɩɨɫɥɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɨ ɞɥɢɧɟ L ɜɫɟɯɫɬɟɪɠɧɟɣ, ɩɨɥɭɱɢɦ:A ³L ( M N * Q J * N H*)dx = ³L M N * dx + ³L Q J * dx + ³L N H * dx .(12.7)Ɂɞɟɫɶ: A – ɪɚɛɨɬɚ ɜɧɟɲɧɢɯ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɟ, ɧɚɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɢɦ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɹɯ; M ,Q.N – ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹɜ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɟ, ɞɥɹ ɤɨɬɨɪɨɣ ɩɪɢɦɟɧɟɧ ɉȼɉ; N*, J*, H * – ɜɨɡɦɨɠɧɵɟɞɟɮɨɪɦɚɰɢɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɨɡɦɨɠɧɵɦ ɩɟɪɟɦɟɳɟɧɢɹɦ (12.2).Ɏɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣɍɪɚɜɧɟɧɢɟ (12.7) ɨɬɪɚɠɚɟɬ ɩɪɢɧɰɢɩ ɜɨɡɦɨɠɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɥɸɛɨɣ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢɪɭɟɦɨɣ ɫɢɫɬɟɦɟ. Ɂɧɚɱɢɬ ɨɧɨɩɪɢɦɟɧɢɦɨ ɢ ɤ ɪɚɦɟ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ 1 (ɫɦ.
ɪɢɫ. 12.1, ɛ).Ɍɨɝɞɚ ɜ ɮɨɪɦɭɥɟ (12.7) M M 1; Q Q1; N N1 . ɉɪɢ ɷɬɨɦ ɡɚɜɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢ ɞɟɮɨɪɦɚɰɢɢ ɪɚɦɵ ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɞɟɣɫɬɜɢɬɟɥɶɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢ ɞɟɮɨɪɦɚɰɢɢ ɪɚɦɵ ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ, ɬ.ɟ.ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢ ɡɚɩɢɫɢ ɭɪɚɜɧɟɧɢɹ (12.7) ɪɚɜɟɧɫɬɜɚ (12.3), (12.4), ɚ ɬɚɤɠɟɪɚɜɟɧɫɬɜɨ A A1 p 1 '1 p ¦ m Rm1 cmp .ȼ ɷɬɨɦ ɪɚɜɟɧɫɬɜɟ ɫɥɚɝɚɟɦɨɟ ɜ ɜɢɞɟ ɫɭɦɦɵ ɨɬɪɚɠɚɟɬ ɪɚɛɨɬɭ ɜɫɟɯ mɫɨɫɬɚɜɥɹɸɳɢɯ Rm1 ɪɟɚɤɰɢɣ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ 1 ɧɚɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɢɦ ɩɟɪɟɦɟɳɟɧɢɹɯ cmp ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ p . Ɍɨɝɞɚɩɨɥɭɱɢɦ ɮɨɪɦɭɥɭ (12.7) ɜ ɜɢɞɟ:1 '1 p = ³L M 1 N p dx + ³L Q1 J p dx + ³L N1 H p dx – ¦ m Rm1 cmp .(12.8)Ɏɨɪɦɭɥɚ (12.8) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɮɨɪɦɭɥɭ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ ɞɥɹɨɩɪɟɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɹ '1 p ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ ɪɚɦɵ (ɫɦ.
ɪɢɫ. 12.1).ɉɨɫɤɨɥɶɤɭ ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ ɪɚɦɵ ɞɟɮɨɪɦɚɰɢɢ ɫɜɹɡɚɧɵ ɫɜɧɭɬɪɟɧɧɢɦɢ ɭɫɢɥɢɹɦɢ ɮɨɪɦɭɥɚɦɢ ɡɚɤɨɧɚ Ƚɭɤɚ (12.1), ɬɨ ɮɨɪɦɭɥɚ Ɇɚɤɫɜɟɥɥɚ –Ɇɨɪɚ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɚ ɢ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ:1991 '1 p = ³LɆ 1M pEIdx + P ³LQ1Q pGIdx + ³LN1 N pEAdx – ¦ m Rm1 cmp .(12.9)ɋɨɨɬɜɟɬɫɬɜɢɟ ɟɞɢɧɢɱɧɨɣ ɫɢɥɵ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɢɫɤɨɦɨɦɭ ɩɟɪɟɦɟɳɟɧɢɸ ɜ ɟɟ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢɂɡ ɮɨɪɦɭɥɵ Ɇɚɤɫɜɟɥɥɚ – Ɇɨɪɚ ɜ ɜɢɞɟ (12.8) ɢɥɢ (12.9) ɜɢɞɧɨ, ɱɬɨ ɜ ɥɟɜɨɣɟɟ ɱɚɫɬɢ ɨɬɪɚɠɚɟɬɫɹ ɪɚɛɨɬɚ ɟɞɢɧɢɱɧɨɣ ɜɧɟɲɧɟɣ ɫɢɥɵ, ɩɪɢɥɨɠɟɧɧɨɣ ɜɨɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɷɬɨɣ ɫɢɥɟ ɞɟɣɫɬɜɢɬɟɥɶɧɵɯɩɟɪɟɦɟɳɟɧɢɹɯ ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ.ȿɫɥɢ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ (ɜ ɞɚɧɧɨɦɫɥɭɱɚɟ ɪɚɦɵ) ɜɫɟɝɞɚ ɩɪɢɤɥɚɞɵɜɚɬɶ ɟɞɢɧɢɱɧɭɸ ɫɢɥɭ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸɢɫɤɨɦɨɦɭ ɩɟɪɟɦɟɳɟɧɢɸ, ɬɨ ɥɟɜɚɹ ɱɚɫɬɶ ɮɨɪɦɭɥɵ ɜɫɟɝɞɚ ɛɭɞɟɬ ɢɦɟɬɶ ɬɚɤɨɣ ɠɟɜɢɞ, ɤɚɤ ɢ ɜ ɮɨɪɦɭɥɚɯ (12.8) ɢ (12.9).
ɋɭɦɦɚ ɪɚɛɨɬ ɨɫɬɚɥɶɧɵɯ ɜɧɟɲɧɢɯ ɫɢɥɜɫɩɨɦɨɝɚɬɟɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ, ɜɵɡɜɚɧɧɵɟɟɞɢɧɢɱɧɨɣ ɫɢɥɨɣ, ɩɟɪɟɧɟɫɟɧɚ ɫ ɨɛɪɚɬɧɵɦ ɡɧɚɤɨɦ ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɮɨɪɦɭɥɵɆɚɤɫɜɟɥɥɚ –Ɇɨɪɚ.ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɵɪɚɠɟɧɢɹ (12.8) ɢ (12.9) ɮɨɪɦɭɥɵ Ɇɚɤɫɜɟɥɥɚ –Ɇɨɪɚɹɜɥɹɟɬɫɹ ɨɛɳɢɦɢ ɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɞɪɭɝɢɯ ɩɟɪɟɦɟɳɟɧɢɣ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɟɣ.ɇɟɨɛɯɨɞɢɦɨ ɬɨɥɶɤɨ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɫɨɫɬɨɹɧɢɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵɩɪɢɥɨɠɢɬɶ ɟɞɢɧɢɱɧɭɸ ɫɢɥɭ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɢɫɤɨɦɨɦɭ ɩɟɪɟɦɟɳɟɧɢɸ ɜɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ.ɇɚ ɪɢɫ. 12.1, ɜ ɢ ɪɢɫ.
12.1, ɝ ɢɡɨɛɪɚɠɟɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟɫɨɫɬɨɹɧɢɹ 2 ɢ 3 ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɪɚɦɵ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɟɪɬɢɤɚɥɶɧɨɝɨɩɟɪɟɦɟɳɟɧɢɹ ' 2 p ɢ ɭɝɥɚ ɩɨɜɨɪɨɬɚ ' 3 p ɫɟɱɟɧɢɹ B ɪɚɦɵ ɜ ɫɨɫɬɨɹɧɢɢ p ɪɚɦɵ.ȼɫɟ ɩɟɪɟɦɟɳɟɧɢɹ ɫɟɱɟɧɢɣ ɪɚɦɵ ɛɭɞɟɦ ɨɬɧɨɫɢɬɶ ɤ ɧɟɤɨɬɨɪɨɣ ɨɛɳɟɣɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 12.1, ɚ. Ƚɨɪɢɡɨɧɬɚɥɶɧɭɸ ɢɜɟɪɬɢɤɚɥɶɧɭɸ ɨɫɶ ɨɬɦɟɬɢɦ ɰɢɮɪɚɦɢ 1 ɢ 2, ɚ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɟɣɛɭɞɟɦ ɨɬɦɟɱɚɬɶ ɰɢɮɪɨɣ 3 ɤɚɤ ɩɨɜɨɪɨɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ (ɲɬɪɢɯɨɜɚɹ ɥɢɧɢɹ ɧɚɪɢɫ. 12.1, ɚ), ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɜ ɤɨɬɨɪɨɣ ɥɟɠɚɬ ɨɫɢ 1 ɢ 2..Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɫɟɯ ɬɪɟɯ ɢɫɤɨɦɵɯ ɞɟɣɫɬɜɢɬɟɥɶɧɵɯɩɟɪɟɦɟɳɟɧɢɣ '1 p , ' 2 p , ' 3 p ɜ ɝɪɭɡɨɜɨɦ ɫɨɫɬɨɹɧɢɢ ɪɚɦɵ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶɨɞɧɭ ɨɛɳɭɸ ɮɨɪɦɭɥɵ Ɇɚɤɫɜɟɥɥɭ –Ɇɨɪɚ ɜ ɜɢɞɟ:ɆiM pQi Q pNi N p1 ' ip = ³Ldx + P ³Ldx + ³Ldx – ¦ m Rmi cmp , i 1, 2 , 3 .
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