Константинов Н.А., Лалин В.В., Лалина И.И. - Расчёт статически определимых стержневых систем с использованием SCAD (1061793), страница 30
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ɉɨɹɜɥɹɟɬɫɹ ɨɤɧɨ ɫ ɬɚɛɥɢɰɟɣɩɪɨɞɨɥɶɧɵɯ ɭɫɢɥɢɣ N. ɗɬɚ ɬɚɛɥɢɰɚ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɩɟɱɚɬɚɧɚ ɫɪɚɡɭ, ɢɥɢɫɤɨɩɢɪɨɜɚɧɚ ɜ ɨɬɱɟɬ (ɜ ɞɨɤɭɦɟɧɬ ɫ ɪɚɫɲɢɪɟɧɢɟɦ doc).ȼɨɡɦɨɠɧɨ ɩɨɥɭɱɟɧɢɟ ɷɬɨɣ ɬɚɛɥɢɰɵ ɜ ɥɸɛɨɟ ɞɪɭɝɨɟ ɜɪɟɦɹ, ɬɚɤ ɤɚɤɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɫɨɯɪɚɧɹɸɬɫɹ ɜ ɩɚɩɤɟ ɪɚɛɨɱɢɯ ɮɚɣɥɨɜSWORK.ɑɚɫɬɶ ɷɬɨɣ ɬɚɛɥɢɰɵ ɞɥɹ ɩɟɪɜɵɯ ɱɟɬɵɪɟɯ ɷɥɟɦɟɧɬɨɜ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɚ ɜɞɚɧɧɨɦ ɩɨɫɨɛɢɢ ɜ ɜɢɞɟ ɬɚɛɥ. 9.1 (ɡɧɚɱɟɧɢɹ ɭɫɢɥɢɣ ɞɚɧɵ ɜ ɤɇ).Ɍɚɛɥɢɰɚ 9.1123456781761N2Nɍ ɋ ɂ Ʌ ɂ ə /ɇȺɉɊəɀȿɇɂə/ ȼ ɗɅȿɆȿɇɌȺɏ1-11-22-12-23-13-24-111223342233445ɜɟɫɶ ɜɟɪɯɧɢɣ ɩɨɹɫ2.0012.0012.6692.6692.5742.5742.574ɜɟɪɯɧɢɣ ɩɨɹɫ ɫɥɟɜɚ|1.41.41.6681.6681.2871.2871.2874-2452.5741.287ɉɪɢɦɟɱɚɧɢɹ ɤ ɬɚɛɥ.
9.1.1. ȿɫɥɢ ɩɪɢ ɨɮɨɪɦɥɟɧɢɢ ɨɬɱɟɬɚ ɩɨ ɪɚɛɨɬɟ, ɩɪɢɜɟɞɟɧ ɪɟɡɭɥɶɬɚɬ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣɜ ɜɢɞɟ ɷɩɸɪ N (ɫɦ. ɪɢɫ 9.4, ɚ ɢ ɪɢɫ. 9.4, ɛ), ɬɨ ɬɚɛɥɢɰɭ ɫ ɭɫɢɥɢɹɦɢ ɜ ɨɬɱɟɬɟ ɩɨ ɪɚɛɨɬɟ ɦɨɠɧɨɧɟ ɩɪɢɜɨɞɢɬɶ.2. Ɋɚɫɱɟɬ ɮɟɪɦɵ ɛɵɥ ɜɵɩɨɥɧɟɧ ɩɪɢ Ɋ1 = 1 ɢ P2 = 1 (ɫɦ. ɪɢɫ. 9.1).Ɍɚɤ ɤɚɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɚɹ ɮɟɪɦɚ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɥɢɧɟɣɧɨ–ɞɟɮɨɪɦɢɪɭɟɦɨɣ(ɩɨ ɞɨɩɭɳɟɧɢɹɦ, ɩɪɢɧɹɬɵɦ ɩɪɢ ɢɡɭɱɟɧɢɢ ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɢ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ(ɫɦ.
ɩɨɞɪɚɡɞɟɥ 1.1), ɬɨ ɩɪɢ ɤɨɧɤɪɟɬɧɨ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ P1 ɢ P2 ɜɫɟ ɩɨɥɭɱɟɧɧɵɟ ɜɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɨɜ ɭɫɢɥɢɹ ɞɨɥɠɧɵ ɛɵɬɶ ɭɦɧɨɠɟɧɵ: ɜ ɩɟɪɜɨɦ ɡɚɝɪɭɠɟɧɢɢ ɧɚ P1; ɜɨ ɜɬɨɪɨɦɡɚɝɪɭɠɟɧɢɢ ɧɚ P2.3. ȼ ɬɚɛɥ. 9.1 ɫɬɪɨɤɢ ɢɦɟɸɬ ɫɥɟɞɭɸɳɟɟ ɧɚɡɧɚɱɟɧɢɟ.ɋɬɪɨɤɚ 2 í ɧɨɦɟɪɚ ɷɥɟɦɟɧɬɨɜ ɜ ɈɋɄ ɢ ɧɨɦɟɪɚ ɭɡɥɨɜ ɩɨ ɢɯ ɤɨɧɰɚɦ ɜ ɆɋɄ.ɋɬɪɨɤɢ 3 ɢ 4 í ɧɨɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɥɟɜɨɝɨ ɢ ɩɪɚɜɨɝɨ (ɜ ɆɋɄ) ɭɡɥɨɜ ɷɥɟɦɟɧɬɨɜ ɩɨɢɯ ɤɨɧɰɚɦ ɜ ɈɋɄ.ɋɬɪɨɤɢ 5 ɢ 7 í ɧɨɦɟɪɚ ɡɚɝɪɭɠɟɧɢɣ ɢ ɢɯ ɧɚɢɦɟɧɨɜɚɧɢɟ.ɋɬɪɨɤɢ 6 ɢ 8 í ɡɧɚɱɟɧɢɹ ɢ ɡɧɚɤɢ ɩɪɨɞɨɥɶɧɵɯ ɭɫɢɥɢɣ N, ɤɇ ɜ ɫɬɟɪɠɧɹɯ ɮɟɪɦɵ.4.
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɪɢɬɶ, ɧɚɩɪɢɦɟɪ, ɢɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɣɪɚɜɧɨɜɟɫɢɹ (ɫɦ. ɭɱɟɛɧɵɟ ɩɨɫɨɛɢɹ [1, 4]. ɉɨɷɬɨɦɭ ɜɵɩɨɥɧɹɟɬɫɹ ɜɬɨɪɨɣ ɪɚɡɞɟɥ ɪɚɫɱɟɬɧɨɣɪɚɛɨɬɵ 4 (ɫɦ. ɩɨɫɬɚɧɨɜɤɭ ɡɚɞɚɱɢ ɜ ɧɚɱɚɥɟ ɪɚɫɱɟɬɧɨɣ ɪɚɛɨɬɵ 4).9.2. ɂɋɉɈɅɖɁɈȼȺɇɂȿ ɍɊȺȼɇȿɇɂɃ ɊȺȼɇɈȼȿɋɂə ȾɅə ɄɈɇɌɊɈɅəɊȿɁɍɅɖɌȺɌɈȼ ɊȺɋɑȿɌȺ ɎȿɊɆɕɁɚɞɚɧɧɚɹ ɮɟɪɦɚ ɹɜɥɹɟɬɫɹ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ ɫɢɫɬɟɦɨɣ, ɩɨɷɬɨɦɭɭɫɢɥɢɹ ɜ ɟɟ ɫɬɟɪɠɧɹɯ (ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɨɩɨɪɧɵɯ) ɦɨɝɭɬ ɛɵɬɶ ɧɚɣɞɟɧɵ ɫ ɩɨɦɨɳɶɸɬɨɥɶɤɨ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ.ɂɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɥɨɫɤɨɝɨ ɬɟɥɚ, ɤɚɤ ɤɨ ɜɫɟɣ ɮɟɪɦɟ, ɬɚɤ ɢɤ ɥɸɛɵɦ ɨɬɞɟɥɶɧɵɦ ɟɟ ɨɬɫɟɱɟɧɧɵɦ ɱɚɫɬɹɦ, ɜɵɩɨɥɧɢɦ ɤɨɧɬɪɨɥɶ ɭɫɢɥɢɣ ɜɨɬɦɟɱɟɧɧɵɯ ɧɚ ɪɢɫ. 9.1 ɫɬɟɪɠɧɹɯ ɮɟɪɦɵ ɢ ɟɟ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ, ɨɩɪɟɞɟɥɟɧɧɵɯɧɚ ɉɄ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD.
ɉɪɢ ɷɬɨɦ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶɪɚɰɢɨɧɚɥɶɧɵɟ ɫɩɨɫɨɛɵ ɩɪɢɦɟɧɟɧɢɹ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɫ ɭɱɟɬɨɦɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɡɚɞɚɧɧɨɣ ɮɟɪɦɵ.ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɜɫɟɣ ɮɟɪɦɵɍɫɥɨɜɢɟɦ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟɣ ɮɟɪɦɵ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɫɟɯ ɡɚɞɚɧɧɵɯ ɜɧɟɲɧɢɯɫɢɥ ɢ ɜɫɟɯ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɹɜɥɹɟɬɫɹ ɭɞɨɜɥɟɬɜɨɪɟɧɢɟ ɬɪɟɯ ɭɪɚɜɧɟɧɢɣɪɚɜɧɨɜɟɫɢɹ (ɡɚɩɢɲɟɦ ɢɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɛɳɟɣ ɫɢɫɬɟɦɨɣ ɤɨɨɪɞɢɧɚɬ, ɩɪɢɧɹɬɨɣɜ ɩɪɨɝɪɚɦɦɟ SCAD):(9.2)¦ X 0; ¦ Z 0; ¦ M y 0ɉɨɫɤɨɥɶɤɭ ɜ ɡɚɞɚɧɧɨɣ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ ɮɟɪɦɟ (ɫɦ. ɪɢɫ. 9.1)ɢɦɟɸɬɫɹ ɬɨɥɶɤɨ ɬɪɢ ɨɩɨɪɧɵɯ ɫɜɹɡɢ (ɧɟ ɩɟɪɟɫɟɤɚɸɳɢɯɫɹ ɜ ɨɞɧɨɣ ɬɨɱɤɟ ɢ ɧɟɩɚɪɚɥɥɟɥɶɧɵɯ ɞɪɭɝ ɞɪɭɝɭ), ɬɨ ɪɟɚɤɰɢɢ ɜ ɧɢɯ ɦɨɝɭɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɢɡ177ɭɤɚɡɚɧɧɵɯ ɭɪɚɜɧɟɧɢɣ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɥɹ ɩɟɪɜɨɝɨ ɡɚɝɪɭɠɟɧɢɹ ɮɟɪɦɵ ɩɨɥɭɱɢɦ:H1=0; V1=3 ɤɇ; V7=3 ɤɇ.Ɍɚɤɢɟ ɠɟ ɡɧɚɱɟɧɢɹ ɪɟɚɤɰɢɣ ɩɨɥɭɱɢɥɢɫɶ ɩɪɢ ɪɚɫɱɟɬɟ ɆɄɗ ɫ ɩɨɦɨɳɶɸɩɪɨɝɪɚɦɦɵ SCAD. ɉɨɷɬɨɦɭ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ (9.2) ɦɨɝɭɬ ɛɵɬɶɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɤɨɧɬɪɨɥɹ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɧɚɣɞɟɧɧɵɯ ɫ ɩɨɦɨɳɶɸɩɪɨɝɪɚɦɦɵ SCAD: ɩɪɢ ɢɯ ɩɨɞɫɬɚɧɨɜɤɟ ɜ ɷɬɢ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɞɨɥɠɧɵɩɨɥɭɱɢɬɶɫɹ ɬɨɠɞɟɫɬɜɚ.Ɉɩɪɟɞɟɥɟɧɢɟ ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɞɥɹ ɭɡɥɨɜɹɜɧɨ ɧɭɥɟɜɵɯ ɫɬɟɪɠɧɟɣ ɮɟɪɦɵɄɚɤ ɩɨɤɚɡɚɧɨ ɜ ɩɨɞɪɚɡɞɟɥɟ 5.6 ɩɨɫɨɛɢɹ ɢ ɜ ɩɨɫɨɛɢɹɯ [1, 7, 10, 16], ɟɫɬɶɩɪɚɜɢɥɚ ɨɩɪɟɞɟɥɟɧɢɹ ɹɜɧɨ ɧɭɥɟɜɵɯ ɫɬɟɪɠɧɟɣ ɜ ɮɟɪɦɟ, ɩɨɥɭɱɟɧɧɵɟ ɧɚ ɨɫɧɨɜɟɢɫɩɨɥɶɡɨɜɚɧɢɹ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɨɞɧɨɝɨ ɢɡ ɭɡɥɨɜ, ɤ ɤɨɬɨɪɨɦɭɩɪɢɫɨɟɞɢɧɹɟɬɫɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɣ ɫɬɟɪɠɟɧɶ.
ȿɫɥɢ ɜ ɡɚɞɚɧɧɨɣ ɮɟɪɦɟ ɢɦɟɸɬɫɹɫɬɟɪɠɧɢ, ɭɫɢɥɢɹ ɜ ɤɨɬɨɪɵɯ ɹɜɥɹɸɬɫɹ ɹɜɧɨ ɧɭɥɟɜɵɦɢ, ɬɨ ɢ ɩɪɢ ɪɚɫɱɟɬɟ ɦɟɬɨɞɨɦɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɨ ɩɪɨɝɪɚɦɦɟ SCAD ɨɧɢ ɞɨɥɠɧɵ ɩɨɥɭɱɢɬɶɫɹ ɧɭɥɟɜɵɦɢ.ɉɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɷɩɸɪɵ N ɩɨɤɚɡɵɜɚɸɬ ɬɪɢ ɧɭɥɟɜɵɯ ɫɬɟɪɠɧɹ ɜɡɚɞɚɧɧɨɦ ɡɚɝɪɭɠɟɧɢɢ 1 ɮɟɪɦɵ. ɉɨ ɢɡɜɟɫɬɧɵɦ ɩɪɚɜɢɥɚɦ ɨɩɪɟɞɟɥɟɧɢɹ ɹɜɧɨɧɭɥɟɜɵɯ ɫɬɟɪɠɧɟɣ ɤɨɧɫɬɚɬɢɪɭɟɦ, ɱɬɨ ɨɧɢ ɢ ɞɨɥɠɧɵ ɛɵɬɶ ɧɭɥɟɜɵɦɢ.Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɢɥɢɹ N13 (ɫɦ. ɪɢɫ.
9.3) ɢɡ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹɜɵɪɟɡɚɧɧɨɝɨ ɢɡ ɮɟɪɦɵ ɭɡɥɚ 8Ʉɪɨɦɟ ɹɜɧɨ ɧɭɥɟɜɨɝɨ ɫɬɟɪɠɧɹ ɫ ɧɨɦɟɪɨɦ 7, ɧɭɥɟɜɨɟ ɭɫɢɥɢɟ ɜ ɤɨɬɨɪɨɦɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ¦ X 8 0 ɞɥɹ ɭɡɥɚ 8, ɬɚɤɠɟ ɩɪɨɫɬɨɫɩɨɫɨɛɨɦ «ɜɵɪɟɡɚɧɢɹ ɭɡɥɚ 8» ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɢɥɢɟ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɫɬɟɪɠɧɟ 13.0.5Z8N13 = 0.5XɊɢɫ. 9.5ɂɡ ɭɪɚɜɧɟɧɢɹ ¦ Z 8 0 ɧɚɯɨɞɢɦ, ɱɬɨ N13 = 0.5 ɤɇ.Ɍɚɤ ɤɚɤ ɫɬɟɪɠɟɧɶ ɫɠɚɬ, ɬɨ ɩɨ ɩɪɚɜɢɥɭ ɡɧɚɤɨɜ ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ (ɫɦ.ɩɨɞɪɚɡɞɟɥ 4.4 ɩɨɫɨɛɢɹ) ɟɝɨ ɡɧɚɱɟɧɢɟ ɨɛɵɱɧɨ ɩɢɲɭɬ ɫɨ ɡɧɚɤɨɦ ɦɢɧɭɫ, ɱɬɨ ɢɫɞɟɥɚɧɨ ɧɚ ɷɩɸɪɟ N (ɫɦ. ɪɢɫ.
9.4, ɚ).Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɫɢɥɢɟ N13, ɧɚɣɞɟɧɧɨɟ ɩɪɢ ɪɚɫɱɟɬɟ ɩɨ ɩɪɨɝɪɚɦɦɟ SCAD,ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɹɦ ɪɚɜɧɨɜɟɫɢɹ ɭɡɥɚ 8.178ɉɪɨɜɟɪɤɚ ɪɚɜɧɨɜɟɫɢɹ ɜɵɪɟɡɚɧɧɨɝɨ ɢɡ ɮɟɪɦɵ ɭɡɥɚ 1 (ɪɢɫ. 9.6, ɚ)Ɉɩɪɟɞɟɥɟɧɧɨɟ ɭɫɢɥɢɟ N13 ɞɟɣɫɬɜɭɟɬ ɢ ɧɚ ɭɡɟɥ 1. Ʉɪɨɦɟ ɧɟɝɨ ɧɚ ɷɬɨɬ ɭɡɟɥɞɟɣɫɬɜɭɸɬ ɭɫɢɥɢɹ N12.46 ɤɇ ɢ N143.5 ɤɇ ɢ ɭɫɢɥɢɹ ɜ ɞɜɭɯ ɨɩɨɪɧɵɯɫɬɟɪɠɧɹɯ (ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ). Ɋɚɜɧɨɜɟɫɢɟ ɭɡɥɚ ɦɨɠɧɨ ɩɪɨɜɟɪɢɬɶ ɚɧɚɥɢɬɢɱɟɫɤɢɦɫɩɨɫɨɛɨɦ, ɫɨɫɬɚɜɢɜ ɞɜɚ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɢɥɢ – ɝɪɚɮɢɱɟɫɤɢɦ ɫɩɨɫɨɛɨɦ,ɩɨɫɬɪɨɢɜ ɦɧɨɝɨɭɝɨɥɶɧɢɤ ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɭɡɟɥ ɫɢɥ (ɪɢɫ. 9.6, ɛ).ɚ)ɛ)Z2.460.5N13 = 0.53.0N14 = 3.53.5E1V12.5N1 =2.46 X2.463.0Ɋɢɫ. 9.6ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɫɩɨɫɨɛɚ ɭɪɚɜɧɟɧɢɹ ɩɪɢ ɩɨɞɫɬɚɧɨɜɤɟ ɜɧɢɯ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɪɨɟɤɰɢɣ ɫɢɥ ɞɨɥɠɧɵ ɬɨɠɞɟɫɬɜɟɧɧɨ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ, ɚɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɝɪɚɮɢɱɟɫɤɨɝɨ ɫɩɨɫɨɛɚ ɩɨɫɬɪɨɟɧɧɵɣ ɦɧɨɝɨɭɝɨɥɶɧɢɤɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɭɡɟɥ ɫɢɥ ɞɨɥɠɟɧ ɛɵɬɶ ɡɚɦɤɧɭɬɵɦ, ɬɚɤ ɤɚɤ ɩɪɢ ɪɚɜɧɨɜɟɫɢɢ ɫɢɥɢɯ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɚɹ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɧɭɥɸ.
ȼɵɩɨɥɧɢɦ ɨɛɚ ɫɩɨɫɨɛɚɩɪɨɜɟɪɤɢ.Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɫɩɨɫɨɛȾɨɥɠɧɵ ɬɨɠɞɟɫɬɜɟɧɧɨ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ ɞɜɚ ɭɪɚɜɧɟɧɢɹ (ɫɢɥɵ, ɤɇ):¦ X 1 3.5 cosE 2.46 0;¦ Z1 0.5 3,5 sin E 3.0 0.Ɂɧɚɱɟɧɢɹ cosE ɢ sin E ɨɩɪɟɞɟɥɢɦ ɩɨtgE ( y9 y 2 ) /( x2 x1 ) (2.04 0) /(2.0 0) 1.02 .Ɉɬɫɸɞɚ cos E 0.7009 ; sin E 0.7133 ɢ ɨɛɚ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɫɞɨɫɬɚɬɨɱɧɨɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ ɬɨɠɞɟɫɬɜɚ.Ƚɪɚɮɢɱɟɫɤɢɣ ɫɩɨɫɨɛɈɛɯɨɞɹ ɭɡɟɥ (ɫɦ. ɪɢɫ. 9.6, ɚ) ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ (ɧɚɱɢɧɚɹ ɫɜɟɪɬɢɤɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɨɩɨɪɧɨɣ ɪɟɚɤɰɢɢ), ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɛɭɞɟɦɨɬɤɥɚɞɵɜɚɬɶ ɜɫɬɪɟɱɚɸɳɢɟɫɹ ɜɟɤɬɨɪɵ ɫɢɥ ɜ ɭɞɨɛɧɨɦ ɞɥɹ ɪɚɫɱɟɬɚ ɦɚɫɲɬɚɛɟ ɜɬɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɜ ɤɨɬɨɪɨɦ ɨɧɢ ɞɟɣɫɬɜɭɸɬ ɧɚ ɭɡɟɥ.
ɂɧɵɦɢ ɫɥɨɜɚɦɢ: ɛɭɞɟɦ179ɝɟɨɦɟɬɪɢɱɟɫɤɢ ɫɭɦɦɢɪɨɜɚɬɶ ɜɟɤɬɨɪɵ ɫɢɥ (ɪɢɫ. 9.6, ɛ). Ɇɧɨɝɨɭɝɨɥɶɧɢɤ ɫɢɥɩɨɥɭɱɢɥɫɹ ɡɚɦɤɧɭɬɵɦ, ɬ.ɟ. ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɚɹ ɜɫɟɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɭɡɟɥ,ɪɚɜɧɚ ɧɭɥɸ ɢ ɭɡɟɥ ɧɚɯɨɞɢɬɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ.Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɢɥɢɣ N3, N9, ɢ N18 ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹɞɥɹ ɱɚɫɬɢ ɮɟɪɦɵ, ɩɨɥɭɱɟɧɧɨɣ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɫɟɱɟɧɢɹ ɟɟ ɩɨɩɟɪɟɱɧɵɦɫɟɱɟɧɢɟɦ (ɫɩɨɫɨɛ ɫɟɱɟɧɢɣ)ɍɫɢɥɢɟ N 3 . Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɷɬɨɝɨ ɭɫɢɥɢɹ ɛɨɥɟɟ ɪɚɰɢɨɧɚɥɶɧɵɦ ɹɜɥɹɟɬɫɹɢɫɩɨɥɶɡɨɜɚɧɢɟ ɧɟ ɫɩɨɫɨɛɚ ɜɵɪɟɡɚɧɢɹ ɭɡɥɨɜ, ɚ ɫɩɨɫɨɛɚ ɪɚɫɫɟɱɟɧɢɹ ɮɟɪɦɵ ɧɚ ɞɜɟɱɚɫɬɢ. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɷɬɨɝɨ ɪɚɫɱɟɬɚ ɫɥɟɞɭɸɳɚɹ:1. Ɋɚɫɫɟɤɚɟɦ ɮɟɪɦɭ ɫɟɱɟɧɢɟɦ 1-1 ɧɚ ɞɜɟ ɱɚɫɬɢ ɢ ɪɚɫɫɦɨɬɪɢɦ ɪɚɜɧɨɜɟɫɢɟɥɸɛɨɣ ɢɡ ɧɢɯ, ɧɚɩɪɢɦɟɪ, ɥɟɜɨɣ (ɪɢɫ.
9.7). ɇɟɢɡɜɟɫɬɧɵɟ ɭɫɢɥɢɹ ɜ ɪɚɫɫɟɱɟɧɧɵɯɫɬɟɪɠɧɹɯ ɨɛɨɡɧɚɱɢɦ ɤɚɤ ɪɚɫɬɹɝɢɜɚɸɳɢɟ.11h 1.6110.5DN9 Ɉ3D1h3=3.11N18Ɉ18HD1.5D18h9=3.11D185.6Ɉ94.0N31h18=8.0790 oɊɢɫ. 9.72. Ʌɢɧɢɢ ɞɟɣɫɬɜɢɹ ɭɫɢɥɢɣ N9 ɢ N18 ɩɟɪɟɫɟɱɟɦ ɜ ɬɨɱɤɟ Ɉ3.3. ɉɪɢɦɟɧɢɦ ɞɥɹ ɷɬɨɣ ɱɚɫɬɢ ɮɟɪɦɵ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɜɢɞɚ:3 6 0.5 6 1(4 2) N 3 3.11 0 . ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɬɨɥɶɤɨ¦ M Oɥɟɜ3ɨɞɧɨ ɧɟɢɡɜɟɫɬɧɨɟ N3. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɞɚɧɧɵɦ ɭɝɥɨɦ ɧɚɤɥɨɧɚ ɜɟɪɯɧɟɝɨ ɩɨɹɫɚɮɟɪɦɵ ( D 15o ) ɩɨɥɭɱɢɦ tg15oh30.2679 h 0.5L tg15oH h 1.5 1.61 3.11 ɦ. Ɍɨɝɞɚ ɩɨɥɭɱɚɟɦ: N 36 0.2679 1.61 ɦ ɢ2.9 ɤɇ.Ɂɧɚɤ ɩɥɸɫ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɬɟɪɠɟɧɶ 3 ɪɚɫɬɹɧɭɬ.
Ɍɚɤɨɣ ɠɟ ɪɟɡɭɥɶɬɚɬɩɨɥɭɱɢɥɫɹ ɩɪɢ ɪɚɫɱɟɬɟ ɮɟɪɦɵ ɆɄɗ ɩɨ ɩɪɨɝɪɚɦɦɟ SCAD.180ɗɬɨ ɪɚɫɫɟɱɟɧɢɟ ɮɟɪɦɵ ɩɪɢɦɟɧɢɦ ɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɹ N9 ɜ ɫɬɟɪɠɧɟɜɟɪɯɧɟɝɨ ɩɨɹɫɚ ɢ ɭɫɢɥɢɹ N18 ɜ ɪɚɫɤɨɫɟ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɹ N9 ɭɪɚɜɧɟɧɢɟɪɚɜɧɨɜɟɫɢɹ ɫɨɫɬɚɜɢɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɨɦɟɧɬɧɨɣ ɬɨɱɤɢ O9:¦ M Oɥɟɜ9ɉɥɟɱɨ h93 4 0.5 4 1 2 N 9 h90y10 cos 15o = 2.57·0.9659 = 2.48 ɦ. Ɍɨɝɞɚ N 9 = – 3.23 ɤɇ.Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɹ ¦ Z 8ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɨɦɟɧɬɧɨɣ ɬɨɱɤɢ O18 :0 ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɫɨɫɬɚɜɢɦ(3 0.5) 5.6 1(7.6 9.6) N18 h18 0¦ M Oɥɟɜ18Ɍɚɤsin D18ɤɚɤ( y11 y4 ) /( x4 x3 ) 3.11 / 2 1.555sin 57 o15c 0.8410 , h18(5.6 4) sin D18tgD18 ,ɬɨD1857 o15c ,9.6 0.8410 = 8.07 ɦ. ɌɨɝɞɚN18 = 3.2/8.07 = 0.4 ɤɇ.Ʉɚɤ ɜɢɞɢɦ, ɭɫɢɥɢɹ N 9 = – 3.23 ɤɇ ɢ N18 = 0.4 ɤɇ ɩɪɚɤɬɢɱɟɫɤɢ ɬɨɱɧɨɫɨɜɩɚɞɚɸɬ ɫ ɷɬɢɦɢ ɭɫɢɥɢɹɦɢ, ɨɩɪɟɞɟɥɟɧɧɵɦɢ ɪɚɫɱɟɬɨɦ ɧɚ ɉɄ ɫɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD.Ⱥɧɚɥɨɝɢɱɧɨ, ɫɨɫɬɚɜɥɹɹ ɧɟɨɛɯɨɞɢɦɵɟ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɦɨɠɧɨɩɪɨɜɟɪɢɬɶ ɢ ɞɪɭɝɢɟ ɭɫɢɥɢɹ ɜ ɫɬɟɪɠɧɹɯ ɮɟɪɦɵ.Ɂɚɤɥɸɱɟɧɢɟȼɵɩɨɥɧɟɧɧɵɟ ɩɪɨɜɟɪɤɢ ɩɨɡɜɨɥɹɸɬ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɪɚɫɱɟɬ ɮɟɪɦɵ ɩɨɨɩɪɟɞɟɥɟɧɢɸ ɭɫɢɥɢɣ ɜ ɟɟ ɫɬɟɪɠɧɹɯ ɢ ɜ ɨɩɨɪɧɵɯ ɫɜɹɡɹɯ ɜɵɩɨɥɧɟɧ ɩɪɚɜɢɥɶɧɨ.Ɇɟɬɨɞɢɱɟɫɤɨɟ ɭɤɚɡɚɧɢɟ ɭɱɚɳɢɦɫɹ ɩɨ ɨɮɨɪɦɥɟɧɢɸ ɨɬɱɟɬɚ ɩɨ ɪɚɫɱɟɬɧɨɣ ɪɚɛɨɬɟ 4ɉɪɟɞɫɬɚɜɥɟɧɧɵɣ ɡɞɟɫɶ ɭɱɟɛɧɵɣ ɦɚɬɟɪɢɚɥ ɩɨ ɪɚɛɨɬɟ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɧɚ ɱɟɬɵɪɧɚɞɰɚɬɢɫɬɪɚɧɢɰɚɯ.
ȼ ɨɬɱɟɬɟ ɩɨ ɪɚɛɨɬɟ ɭɱɚɳɢɦɫɹ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɞɨɛɢɬɶɫɹ ɪɚɰɢɨɧɚɥɶɧɨɝɨ ɟɝɨ ɨɛɴɟɦɚ,ɢɡɥɚɝɚɹ ɨɫɧɨɜɧɭɸ ɱɚɫɬɶ ɯɨɞɚ ɪɚɫɱɟɬɚ ɢ ɟɝɨ ɪɟɡɭɥɶɬɚɬɵ. Ɇɨɠɧɨ, ɧɚɩɪɢɦɟɪ, ɨɩɭɫɬɢɬɶɩɪɟɞɫɬɚɜɥɟɧɢɟ ɞɢɚɥɨɝɨɜɵɯ ɨɤɨɧ ɩɪɨɝɪɚɦɦɵ SCAD, ɨɩɢɫɚɧɢɟ ɪɚɛɨɬɵ ɫ ɬɚɛɥɢɰɚɦɢɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ.ɉɪɢɦɟɪɧɚɹ ɫɯɟɦɚ ɨɮɨɪɦɥɟɧɢɹ ɨɬɱɟɬɚ ɩɨ ɪɚɛɨɬɟ 4 ɩɪɢɜɟɞɟɧɚ ɜ ɩɨɫɨɛɢɢ [4] ɢ ɜ ɍɆɄ[21].18110. ɉɈɋɌɊɈȿɇɂȿ ɗɉɘɊ ɍɋɂɅɂɃ M, Q, Nȼ ɌɊȿɏɒȺɊɇɂɊɇɈɃ ȺɊɄȿ ȻȿɁ ɁȺɌəɀɄɂɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ ɢ ɚɧɚɥɢɡ ɡɚɞɚɧɧɨɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɚɪɤɢ.Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɜɵɩɨɥɧɟɧɢɹ ɪɚɫɱɟɬɧɨɣ ɪɚɛɨɬɵ 3 ɢɡ ɫɛɨɪɧɢɤɚ ɡɚɞɚɧɢɣ(ɫɦ.
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