Сопротивление материалов / Nesmeyanov - Soprotivleniye materialov. Nestandartniye zadachi i podkhodi k ikh resheniyu 2005

ɬɨ ɟɫɬɶ ɜ ɢɫɯɨɞɧɨɣ ɡɚɞɚɱɟ ɞɨɫɬɚɬɨɱɧɨ ɡɧɚɬɶ ɥɢɲɶ ɬɟɦɩɟɪɚɬɭɪɵ, ɧɨ ɫɬɚɬɢɱɟɫɤɭɸ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɪɚɫɤɪɵɬɶ.

ɉɪɢɦɟɪ 9. ɉɭɫɬɶ ɛɚɥɤɚ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɩɨɞɜɟɪɝɚɟɬɫɹ ɬɟɩɥɨɜɨɦɭ ɜɨɡɞɟɣɫɬɜɢɸ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɦɭ ɧɚ ɪɢɫ. 5.33. Ɍɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɫɟɱɟɧɢɹ Ⱥ.

A				ɗɌ						Ɋɟɲɟɧɢɟ. ȼ ɢɫɯɨɞɧɨɣ ɡɚɞɚɱɟ ɫɥɟɞɭɟɬ ɨɩ-
	l								2Ɍɇ	ɪɟɞɟɥɢɬɶ ɥɢɲɶ ɬɟɩɥɨɜɵɟ ɞɟɮɨɪɦɚɰɢɢ ɨɫɟɜɨɣ
l
									Ɍɇ
										ɥɢɧɢɢ – FT ɢ HT0. ɉɨɫɤɨɥɶɤɭ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ
	Ɋɢɫ.5.33									ɫɜɹɡɟɣ ɧɟɬ, ɞɟɮɨɪɦɚɰɢɹ HT0 ɧɟ ɜɥɢɹɟɬ ɧɢ ɧɚ

ɫɢɥɵ, ɧɢ ɧɚ ɢɡɝɢɛ. Ʉɪɢɜɢɡɧɚ ɩɨɫɬɨɹɧɧɚ ɩɨ ɞɥɢɧɟ ɢ ɪɚɜɧɚ – DTH/h. ȼɫɩɨɦɨɝɚɬɟɥɶɧɚɹ ɡɚɞɚɱɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ.5.34ɚ. ɗɬɨ – ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟ-

ɥɢɦɚɹ ɡɚɞɚɱɚ; ɪɚɫɤɪɵɬɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢ (ɫɬɚɧɞɚɪɬɧɵɦ ɨɛɪɚɡɨɦ, ɦɟɬɨɞɨɦ ɫɢɥ) ɞɚɟɬ ɷɩɸɪɭ Mɜɫ (ɪɢɫ.5.34ɛ). ɂɧɬɟɝɪɚɥ Mɜɫ ɩɨ ɞɥɢɧɟ 2l ɪɚɜɟɧ – l/4. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɢɧɬɟɝɪɚɥ Ɇɨɪɚ ɨɩɪɟɞɟɥɹɟɬ ɨɬɜɟɬ

TA=³ȾTɎɜɫdz =³ FTMɜɫdz = (– DTH/h) (– l/4) = DTHl/(4h).

L2l

1 ɚ)

l l

ɛ)

1 4

1

Ɋɢɫ.5.34

Ⱦɚɧɧɵɣ ɩɪɢɟɦ ɷɮɮɟɤɬɢɜɟɧ ɜ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɜ ɤɨɧɫɬɪɭɤɰɢɢ ɦɨɝɭɬ ɜɚɪɶɢɪɨɜɚɬɶɫɹ ɬɟɩɥɨɜɵɟ ɩɨɥɹ, ɚ ɧɚɫ ɢɧɬɟɪɟɫɭɟɬ ɫɦɟɳɟɧɢɟ ɤɨɧɤɪɟɬɧɨɣ ɬɨɱɤɢ (ɧɚɩɪɢɦɟɪ, ɩɨɥɨɠɟɧɢɟ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ). Ɍɨɝɞɚ ɜɫɩɨɦɨɝɚ- ɗɆ ɜɫ ɬɟɥɶɧɚɹ ɡɚɞɚɱɚ ɪɟɲɚɟɬɫɹ ɤɚɤ ɫɥɟɞɭɟɬ, ɧɨ ɨɞɢɧ ɪɚɡ; ɪɟɲɚɬɶ ɬɟɦɩɟɪɚɬɭɪɧɵɟ ɡɚɞɚɱɢ ɞɥɹ ɤɚɠɞɨɝɨ ɩɨɥɹ

ɬɟɦɩɟɪɚɬɭɪ ɧɟ ɧɭɠɧɨ.

Ɇɟɬɨɞ ɨɛɨɛɳɚɟɬɫɹ ɧɚ ɩɪɨɢɡɜɨɥɶɧɵɟ ɬɟɥɚ:

'=³HijT(x)Vijɜɫ(ɯ)dV

V

ɢɥɢ, ɟɫɥɢ ɦɚɬɟɪɢɚɥ ɢɡɨɬɪɨɩɟɧ,

'=3³DT(x)V0Ȋș(ȝ)dV,

V

ɝɞɟ V0 =(Vɯ+Vy+Vz)/3 – ɫɪɟɞɧɟɟ ɧɨɪɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɜ ɬɨɱɤɟ ɤɨɧɫɬɪɭɤɰɢɢ ɯ.

5.9. Ɇɟɬɨɞ ɮɢɤɬɢɜɧɵɯ ɧɚɝɪɭɡɨɤ

Ɂɚɫɥɭɠɢɜɚɟɬ ɜɧɢɦɚɧɢɹ ɞɪɭɝɨɣ ɧɟɫɬɚɧɞɚɪɬɧɵɣ ɩɨɞɯɨɞ ɤ ɪɟɲɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɧɵɯ ɡɚɞɚɱ, ɩɪɟɞɥɨɠɟɧɧɵɣ ɜ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ [3]. Ȼɵɥɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɡɚɞɚɱɚ ɬɟɪɦɨɭɩɪɭɝɨɫɬɢ ɦɨɠɟɬ ɛɵɬɶ ɡɚɦɟɧɟɧɚ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ, ɟɫɥɢ ɞɨɛɚɜɢɬɶ ɮɢɤɬɢɜɧɵɟ ɨɛɴɟɦɧɵɟ ɢ ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɧɚɝɪɭɡɤɢ ɢ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɡɚɩɢɫɵɜɚɬɶ ɞɥɹ ɮɢɤɬɢɜɧɵɯ ɧɚɩɪɹɠɟɧɢɣ, ɤɨɬɨɪɵɟ ɫɜɹɡɚɧɵ ɫ ɞɟɮɨɪɦɚɰɢɹɦɢ (ɞɟɣɫɬɜɢɬɟɥɶɧɵɦɢ, ɧɟ ɮɢɤɬɢɜɧɵɦɢ) ɨɛɵɱɧɵɦ ɢɡɨɬɟɪɦɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ Ƚɭɤɚ. ɉɨɫɥɟ ɪɟɲɟɧɢɹ ɬɚɤɨɣ ɡɚɞɚɱɢ ɨɫɬɚɟɬɫɹ ɥɢɲɶ ɨɬ ɧɚɣɞɟɧɧɵɯ ɮɢɤɬɢɜɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɟɪɟɣɬɢ ɤ ɞɟɣɫɬɜɢɬɟɥɶɧɵɦ, ɚ ɞɟɮɨɪɦɚɰɢɢ ɢ ɫɦɟɳɟɧɢɹ ɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɧɟ ɧɭɠɧɨ.

Ɏɢɤɬɢɜɧɵɟ ɨɛɴɟɦɧɵɟ (ɨɬɧɟɫɟɧɧɵɟ ɤ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ) ɫɢɥɵ ɪɚɜɧɵ – mTc, ɝɞɟ Tc – ɜɟɤɬɨɪ-ɝɪɚɞɢɟɧɬ ɬɟɦɩɟɪɚɬɭɪɵ. Ɉɧ ɧɚɩɪɚɜɥɟɧ ɜ ɫɬɨɪɨɧɭ ɫɤɨɪɟɣɲɟɝɨ ɜɨɡɪɚɫɬɚ-

ɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ, ɢ ɪɚɜɟɧ ɩɨ ɦɨɞɭɥɸ ɫɤɨɪɨɫɬɢ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɢ ɫɦɟɳɟɧɢɢ ɜ ɷɬɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɉɨɞ ɬɟɦɩɟɪɚɬɭɪɨɣ T, ɤɚɤ ɨɛɵɱɧɨ, ɩɨɧɢɦɚɟɬɫɹ ɧɚɝɪɟɜ (ɜ ɝɪɚɞɭɫɚɯ) ɜ ɞɚɧɧɨɣ ɬɨɱɤɟ; m=DE/(1 – 2P), P – ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɚɫɫɨɧɚ.

Ɏɢɤɬɢɜɧɵɟ ɩɨɜɟɪɯɧɨɫɬɧɵɟ (ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ) ɫɢɥɵ ɧɚɩɪɚɜɥɟɧɵ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɢɯ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɪɚɜɧɚ mT. ȿɫɥɢ T! 0, ɷɬɢ ɫɢɥɵ ɧɚɩɪɚɜɥɟɧɵ ɜ ɫɬɨɪɨɧɭ ɪɚɫɬɹɠɟɧɢɹ, ɩɪɢ T 0 – ɜ ɫɬɨɪɨɧɭ ɫɠɚɬɢɹ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɜ ɱɚɫɬɧɨɫɬɢ, ɱɬɨ ɧɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɞɜɭɯ ɦɚɬɟɪɢɚɥɨɜ (ɫ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ m = m1 ɢ m = m2) ɩɨ ɧɨɪɦɚɥɢ ɤ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɢɥɨɠɟɧɚ ɮɢɤɬɢɜɧɚɹ ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɫɢɥɚ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ (m1 – m2)T, ɧɚɩɪɚɜɥɟɧɧɚɹ, ɟɫɥɢ ɷɬɚ ɜɟɥɢɱɢɧɚ ɩɨɥɨɠɢɬɟɥɶɧɚ, ɜ ɫɬɨɪɨɧɭ ɜɬɨɪɨɝɨ ɦɚɬɟɪɢɚɥɚ.

ɉɪɢ ɪɟɲɟɧɢɢ ɨɛɵɱɧɵɯ ɡɚɞɚɱ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɚɬɟɪɢɚɥɨɜ ɷɬɚ ɧɟɫɤɨɥɶɤɨ ɝɪɨɦɨɡɞɤɚɹ ɫɯɟɦɚ ɡɚɦɟɬɧɨ ɭɩɪɨɳɚɟɬɫɹ. ɉɭɫɬɶ ɫɬɟɪɠɟɧɶ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ (buh) ɩɨɞɜɟɪɠɟɧ ɩɟɪɟɦɟɧɧɨɦɭ ɩɨ ɜɵɫɨɬɟ ɧɚɝɪɟɜɭ. Ɋɚɫɫɦɨɬɪɢɦ ɷɥɟɦɟɧɬ ɞɥɢɧɵ ɫɬɟɪɠɧɹ dz (ɪɢɫ.5.35). Ɏɢɤɬɢɜɧɵɟ ɨɛɴɟɦɧɵɟ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɷɥɟ-

y		qB	= mTȼ		ɦɟɧɬ, ɫɜɨɞɹɬɫɹ ɤ ɷɥɟɦɟɧɬɚɪɧɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ
		S		Tȼ	(ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɧɢɡ) ɫɢɥɟ

									dF0=³bdydz(dT/dy)m=bmdz³(dT/dy)dy
				+			y		h
									= =bmdz(TB –TH).
									Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɮɢɤɬɢɜ-
							z		ɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɧɚɝɪɭɡɤɢ dF0/dz ɡɚɜɢɫɢɬ
		dF0							ɥɢɲɶ ɨɬ ɪɚɡɧɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ – ɜ ɜɟɪɯɧɟɣ
					T				ɬɨɱɤɟ (TB) ɢ ɜ ɧɢɠɧɟɣ ɬɨɱɤɟ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟ-
					ɇ				ɱɟɧɢɹ. ɗɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɥɢɲɶ ɞɥɹ ɞɚɧɧɨɝɨ
			b		qSH= mTɇ
x	dz								ɫɥɭɱɚɹ: ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɢɡɦɟɧɹɟɬɫɹ ɢ ɩɨ ɯ,
				Ɋɢɫ.5.35					ɢɥɢ ɫɟɱɟɧɢɟ ɧɟ ɹɜɥɹɟɬɫɹ ɩɪɹɦɨɭɝɨɥɶɧɵɦ, ɬɨ
									ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɮɢɤɬɢɜɧɨɣ ɫɢɥɵ ɛɭɞɟɬ ɢɧɵɦ.

ɉɨ ɱɟɬɵɪɟɦ ɩɨɜɟɪɯɧɨɫɬɧɵɦ ɝɪɚɧɹɦ ɷɥɟɦɟɧɬɚ ɞɥɢɧɵ ɫɬɟɪɠɧɹ «ɩɪɢɥɨɠɟɧɵ» ɮɢɤɬɢɜɧɵɟ ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɫɢɥɵ (ɢɧɬɟɧɫɢɜɧɨɫɬɶ mT) – ɩɨ ɧɨɪɦɚɥɹɦ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ɇɚ ɛɨɤɨɜɵɯ ɝɪɚɧɹɯ ɨɧɢ ɭɪɚɜɧɨɜɟɲɢɜɚɸɬ ɞɪɭɝ ɞɪɭɝɚ, ɢɯ ɫɭɦɦɚɪɧɚɹ ɫɢɥɚ ɪɚɜɧɚ ɧɭɥɸ. ɇɨ ɧɚ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɞɟɣɫɬɜɭɸɬ mTB (ɜɜɟɪɯ) ɢ mTɇ (ɜɧɢɡ). ȼ ɢɬɨɝɟ ɨɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɫɭɦɦɚ ɨɛɴɟɦɧɨɣ ɢ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɦɟɧɬ ɞɥɢɧɵ, ɪɚɜɧɚ ɧɭɥɸ.

Ɉɫɬɚɟɬɫɹ ɪɚɫɫɦɨɬɪɟɬɶ ɮɢɤɬɢɜɧɵɟ ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɫɢɥɵ ɩɨ ɬɨɪɰɚɦ ɫɬɟɪɠɧɹ (ɟɫɥɢ ɨɧɢ ɧɟ ɡɚɳɟɦɥɟɧɵ): ɨɧɢ ɢɦɟɸɬ ɢɧɬɟɧɫɢɜɧɨɫɬɶ, ɪɚɜɧɭɸ mT, ɬɨ ɟɫɬɶ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɡɚɤɨɧɭ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ. ȼ ɢɬɨɝɟ ɨɧɢ ɫɜɨɞɹɬɫɹ ɤ ɮɢɤɬɢɜɧɨɣ ɜɧɟɲɧɟɣ ɫɢɥɟ, ɞɟɣɫɬɜɭɸɳɟɣ ɩɨ ɧɨɪɦɚɥɢ

N *=³mTds=mSTɫɪ	(5.16)
S

(Tɫɪ=1/S³Tds, S – ɩɥɨɳɚɞɶ ɫɟɱɟɧɢɹ, Tɫɪ – ɫɪɟɞɧɹɹ ɩɨ ɫɟɱɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɚ), ɢ ɤ

S

ɮɢɤɬɢɜɧɨɦɭ ɜɧɟɲɧɟɦɭ ɦɨɦɟɧɬɭ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚɥɶɧɨɣ ɨɫɢ x

Ɋɢɫ.5.36

M *=³mTyds= mSxT,	SxT=³Tyds.	(5.17)
S	S

Ɂɞɟɫɶ SxT– ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɬɟɦɩɟɪɚɬɭɪɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ x.

Ɍɨ ɠɟ ɨɬɧɨɫɢɬɫɹ ɢ ɤ ɫɥɭɱɚɸ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɣ ɛɚɥɤɢ: ɟɫɥɢ ɨɧɚ ɧɚɝɪɟɬɚ ɪɚɜɧɨɦɟɪɧɨ ɩɨ ɞɥɢɧɟ (ɢ, ɜɨɡɦɨɠɧɨ, ɧɟɪɚɜɧɨɦɟɪɧɨ ɩɨ ɜɵɫɨɬɟ), ɬɨ ɨɛɴɟɦɧɵɟ ɢ ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɫɢɥɵ ɩɨ ɜɫɟɣ ɞɥɢɧɟ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɭɥɟɜɵɦɢ, ɚ ɧɚ ɬɨɪɰɚɯ ɤɚɠɞɨɦɭ ɢɡ ɦɟɬɚɥɥɨɜ ɫɥɟɞɭɟɬ ɩɪɢɥɨɠɢɬɶ ɮɢɤɬɢɜɧɵɟ ɧɚɝɪɭɡɤɢ (5.16), (5.17). Ⱦɚɥɟɟ ɪɟɲɟɧɢɟ ɨɛɵɱɧɨɣ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɧɚɩɪɹɠɟɧɢɹ, ɞɟɮɨɪɦɚɰɢɢ ɢ ɫɦɟɳɟɧɢɹ; ɩɨɫɥɟɞɧɢɟ – ɢɫɬɢɧɧɵ, ɚ ɧɚɩɪɹɠɟɧɢɹ – ɮɢɤɬɢɜɧɵ, ɢɯ ɧɭɠɧɨ ɤɨɪɪɟɤɬɢ-

ɪɨɜɚɬɶ.

Ɏɢɤɬɢɜɧɵɟ ɧɚɩɪɹɠɟɧɢɹ V ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɢɫɬɢɧɧɵɯ V

mT ɧɚ ɜɫɟɫɬɨɪɨɧɧɟɟ ɪɚɜɧɨɦɟɪɧɨɟ ɪɚɫɬɹɠɟɧɢɟ ɜɟɥɢɱɢɧɨɣ mT.

Ɉɞɧɚɤɨ ɜ ɡɚɞɚɱɚɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɚɬɟɪɢɚɥɨɜ, ɨɛɴɟɤɬɨɦ ɤɨ-

ɬɨɪɵɯ ɹɜɥɹɸɬɫɹ ɫɬɟɪɠɧɟɜɵɟ ɤɨɧɫɬɪɭɤɰɢɢ, ɧɨɪɦɚɥɶɧɵɟ ɧɚ-

ɩɪɹɠɟɧɢɹ ɜ ɩɪɨɞɨɥɶɧɵɯ ɩɥɨɳɚɞɤɚɯ ɪɚɜɧɵ ɧɭɥɸ, ɩɨɷɬɨɦɭ

ɫɯɟɦɭ ɩɟɪɟɫɱɟɬɚ ɧɚɩɪɹɠɟɧɢɣ ɦɨɠɧɨ ɭɩɪɨɫɬɢɬɶ. Ɋɚɫɫɦɨɬɪɢɦ ɫɬɟɪɠɟɧɶ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɫɟɱɟɧɢɹ (ɜɚɪɢɚɧɬ

ɫɟɱɟɧɢɹ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 5.36), ɡɚɳɟɦɥɟɧɧɵɣ ɩɨ ɤɨɧɰɚɦ ɢ ɪɚɜɧɨɦɟɪɧɨ ɧɚɝɪɟɬɵɣ. Ɏɢɤɬɢɜɧɵɟ ɨɛɴɟɦɧɵɟ ɫɢɥɵ ɨɬɫɭɬɫɬɜɭɸɬ, ɮɢɤɬɢɜɧɵɟ ɩɨɜɟɪɯɧɨɫɬɧɵɟ – ɩɨɫɬɨɹɧɧɵɟ ɩɨ ɞɥɢɧɟ ɫɬɟɪɠɧɹ ɢ ɩɨ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ (ɪɢɫ.5.36), ɪɚɜɧɵ mT. Ɉɧɢ ɫɨɡɞɚɸɬ ɜ ɩɥɨɫɤɨɫɬɢ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɮɢɤɬɢɜɧɵɟ ɧɚɩɪɹɠɟɧɢɹ – ɪɚɜɧɨɦɟɪɧɨɟ ɪɚɫɬɹɠɟɧɢɟ Vɯ = Vy = mT. Ɏɢɤɬɢɜɧɵɟ ɩɪɨɞɨɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ Vz ɢ ɢɫɬɢɧɧɵɟ ɩɨɩɟɪɟɱɧɵɟ ɞɟɮɨɪɦɚɰɢɢ Hc ɧɚɯɨɞɢɦ ɢɡ ɡɚɤɨɧɚ Ƚɭɤɚ, ɡɧɚɹ, ɱɬɨ ɩɪɨɞɨɥɶɧɵɟ ɞɟɮɨɪɦɚɰɢɢ Hz ɪɚɜɧɵ ɧɭɥɸ ɩɨ ɭɫɥɨɜɢɹɦ ɡɚɤɪɟɩɥɟɧɢɹ:

Vz =2PEHc/(1 – P – 2P2), Vɯ =mT=E(( – P)Hc+PHc)=EHc/(1 – P – 2P2), Hc=(1 – P – 2P2)mT/E, Vz =2PEHc/(1 – P – 2P2)=2PmT.

Ⱦɟɣɫɬɜɢɬɟɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɪɨɞɨɥɶɧɵɯ ɫɟɱɟɧɢɹɯ: Vc=Vɯ – mT=mT – mT=0, ɜ ɩɨɩɟɪɟɱɧɵɯ – Vz=Vz – mT=2PmT – mT= – (1 – 2P)mT= – DET.

ɂɬɚɤ, ɩɪɢ ɪɟɲɟɧɢɢ ɩɨɞɨɛɧɵɯ ɡɚɞɚɱ ɮɢɤɬɢɜɧɵɟ ɨɛɴɟɦɧɵɟ ɫɢɥɵ ɫɥɟɞɭɟɬ ɫɱɢɬɚɬɶ ɧɭɥɟɜɵɦɢ; ɮɢɤɬɢɜɧɵɟ ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɫɢɥɵ ɩɪɢɤɥɚɞɵɜɚɬɶ ɬɨɥɶɤɨ ɧɚ ɬɨɪɰɚɯ ɫɬɟɪɠɧɹ (ɟɫɥɢ ɨɧɢ ɫɜɨɛɨɞɧɵ) ɢ ɫɱɢɬɚɬɶ ɢɯ ɪɚɜɧɵɦɢ EDT. Ɏɢɤɬɢɜɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɨɩɟɪɟɱɧɵɯ ɫɟɱɟɧɢɹɯ ɫɜɹɡɚɧɧɵ ɫ ɢɫɬɢɧɧɵɦɢ ɩɪɨɞɨɥɶɧɵɦɢ ɞɟɮɨɪɦɚɰɢɹɦɢ ɩɨ ɮɨɪɦɭɥɟ V =EH; ɩɨɫɥɟ ɢɯ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚɯɨɞɢɦ ɢɫɬɢɧɧɵɟ ɧɚɩɪɹɠɟɧɢɹ:

V = V – EDT.

(5.18)

ɉɪɢɦɟɪ 10. ȼ ɪɚɜɧɨɦɟɪɧɨ ɧɚɝɪɟɬɨɦ ɛɢɦɟɬɚɥɥɢɱɟɫɤɨɦ ɫɬɟɪɠɧɟ (ɪɢɫ.5.37ɚ), ɢɦɟɸɳɟɦ ɨɞɢɧɚɤɨɜɵɟ ɪɚɡɦɟɪɵ ɩɨɩɟɪɟɱɧɵɯ ɫɟɱɟɧɢɣ (ɩɪɹɦɨɭɝɨɥɶɧɢɤ buh), ɧɨ ɪɚɡɥɢɱɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɬɟɩɥɨɜɨɝɨ ɪɚɫɲɢɪɟɧɢɹ, ɨɩɪɟɞɟɥɢɬɶ ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɬɨɱɤɢ Ⱥ.

Ɋɟɲɟɧɢɟ. Ɇɨɞɭɥɢ ɭɩɪɭɝɨɫɬɢ ɦɟɬɚɥɥɨɜ ɨɞɢɧɚɤɨɜɵ, ɩɨɷɬɨɦɭ ɧɚɢɛɨɥɟɟ ɭɞɨɛɟɧ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɦɟɬɨɞ ɮɢɤɬɢɜɧɵɯ ɧɚɝɪɭɡɨɤ: ɜ ɢɡɨɬɟɪɦɢɱɟɫɤɨɣ ɡɚɞɚɱɟ ɮɢɝɭɪɢɪɭɟɬ ɨɞɢɧ ɫɬɟɪɠɟɧɶ (ɚ ɧɟ ɞɜɚ) ɫɟɱɟɧɢɟɦ bu2h. ɉɪɚɜɵɣ ɤɨɧɟɰ ɫɜɨɛɨɞɟɧ, ɩɨɷɬɨɦɭ ɜ ɮɢɤɬɢɜɧɨɣ ɡɚɞɚɱɟ ɤ ɧɟɦɭ ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɢɥɨɠɟɧɚ ɮɢɤɬɢɜɧɚɹ ɧɚɝɪɭɡɤɚ

ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ		EDT. Ɉɧɚ ɞɚɟɬ ɞɜɟ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɢɟ				ED1TS1 ɢ ED2TS2
					(ɪɢɫ.5.37ɛ), ɝɞɟ S1=S2=S=bh. Ɇɟɬɨɞɨɦ ɫɟɱɟɧɢɣ
	h				ɧɚɣɞɟɦ ɜɧɭɬɪɟɧɧɢɟ ɫɢɥɨɜɵɟ ɮɚɤɬɨɪɵ, ɩɨɫɬɨɹɧ-
	h			A	ɧɵɟ ɩɨ ɞɥɢɧɟ (ɪɢɫ.5.37ɜ):
	l				N =¦EDiTS= ETS(D1+D2 ),
	ɚ)			E 1T S1	M =ETSh(D2 – D1)/2.
				E 2TS2	ɇɨɪɦɚɥɶɧɚɹ ɫɢɥɚ ɧɟ ɜɥɢɹɟɬ ɧɚ ɜɟɪɬɢɤɚɥɶɧɵɟ ɩɟ-
	ɛ)	z			ɪɟɦɟɳɟɧɢɹ; ɢɡɝɢɛɚɸɳɢɣ (ɮɢɤɬɢɜɧɵɣ) ɦɨɦɟɧɬ
					ɨɩɪɟɞɟɥɹɟɬ ɨɛɵɱɧɵɦ	ɨɛɪɚɡɨɦ	ɤɪɢɜɢɡɧɭ
	N *				F=Ɇ /(EI) (I=b(2h)3/12), ɤɪɢɜɢɡɧɚ ɜ ɷɬɨɦ ɜɵɪɚ-
	M *				ɠɟɧɢɢ ɹɜɥɹɟɬɫɹ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ.
l		ɜ)			ɋɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɩɨɫɬɚɜɥɟɧɧɨɦɭ		ɜɨɩɪɨɫɭ
					ɜɫɩɨɦɨɝɚɬɟɥɶɧɚɹ ɷɩɸɪɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ.5.37ɝ. ȼ
				ɗM ɜɫ
					ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɢɧɬɟɝɪɚɥɨɦ Ɇɨɪɚ
	ɝ)
					XA=³FɆɜɫdz=F l2/2=M
	Ɋɢɫ.5.37
l2/(2EI)=3(D2 – D1 )l2T/(8h).					l
	ɇɚɣɞɟɧɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɹɜɥɹɟɬɫɹ ɢɫɬɢɧɧɵɦ (ɧɟ ɮɢɤɬɢɜɧɵɦ).

ȼ ɫɥɭɱɚɟ, ɤɨɝɞɚ E1z E2, S1 z S2 ɢ Tz const ɡɚɞɚɱɚ ɧɟɫɤɨɥɶɤɨ ɛɨɥɟɟ ɝɪɨɦɨɡɞɤɚ, ɧɨ ɷɬɨ ɩɨɱɬɢ ɫɬɚɧɞɚɪɬɧɚɹ ɡɚɞɚɱɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɚɬɟɪɢɚɥɨɜ. ɉɪɢɦɟɪ ɪɟɲɟɧɢɹ ɬɚɤɨɣ ɡɚɞɚɱɢ ɩɪɢɜɟɞɟɧ ɜ ɪɚɡɞɟɥɟ 3 (ɡɚɞɚɱɚ 9).

ɉɪɢɦɟɪ 11. ɉɭɫɬɶ ɬɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɫɟɱɟɧɢɹ Ⱥɜ ɡɚɞɚɱɟ ɢɡ ɩɪɢɦɟɪɚ 9 (ɪɢɫ.5.33).

Ɋɟɲɟɧɢɟ. Ʉ ɬɨɪɰɚɦ ɛɚɥɤɢ ɩɪɢɤɥɚɞɵɜɚɟɦ ɮɢɤɬɢɜɧɭɸ ɪɚɫɩɪɟɞɟɥɟɧɧɭɸ ɧɚɝɪɭɡɤɭ ɢɧɬɟɧɫɢɜɧɨɫɬɢ q =DTE (ɪɢɫ.5.38ɚ). Ɉɧɚ

2q*						2q*			ɦɨɠɟɬ ɛɵɬɶ ɡɚɦɟɧɟɧɚ ɫɢɥɚɦɢ N =3q S/2 ɢ ɦɨɦɟɧ-
									ɬɚɦɢ M =q bh2/12 (ɪɢɫ.5.38ɛ). Ɋɚɫɤɪɵɜɚɟɦ ɫɬɚɬɢ-
q*								q*	ɱɟɫɤɭɸ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɶ, ɧɚɯɨɞɢɦ ɷɩɸɪɭ ɮɢɤɬɢɜ-
			ɚ) l		l				ɧɵɯ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ (ɪɢɫ.5.38ɜ). Ⱦɥɹ ɨɩɪɟ-
									ɞɟɥɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɫɬɪɨɢɦ	ɷɩɸɪɭ	ɜɫ
M*A								M*			Ɇ
									(ɪɢɫ.5.38ɝ) ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɟ, ɩɪɢɥɨɠɢɜ
N *			ɛ)		M */2			N*	ɟɞɢɧɢɱɧɵɣ ɦɨɦɟɧɬ ɜ ɫɟɱɟɧɢɢ Ⱥ ɢ ɩɪɢɧɹɜ, ɞɥɹ ɩɪɨ-
ɗM *									ɫɬɨɬɵ, ɱɬɨ ɩɪɚɜɚɹ ɨɩɨɪɧɚɹ ɪɟɚɤɰɢɹ	ɪɚɜɧɚ	ɧɭɥɸ
									(ɩɨɫɤɨɥɶɤɭ ɨɫɧɨɜɧɚɹ ɡɚɞɚɱɚ ɪɟɲɟɧɚ ɩɨɥɧɨɫɬɶɸ, ɬɨ
			ɜ)
M *						M *			ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɧɚɱɟɧɢɟ ɏ1ɜɫ ɩɪɨɢɡɜɨɥɶɧɨ).
ɗɆ ɜɫ									Ɉɬɜɟɬ, ɟɫɬɟɫɬɜɟɧɧɨ, ɩɨɥɭɱɚɟɦ ɬɨɬ ɠɟ, ɱɬɨ ɢ ɜ ɩɪɢ-
									ɦɟɪɟ 9.
1			ɝ)	Ɋɢɫ.5.38

Ɋɟɲɢɬɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ

		Ɋ
		Ⱥ	Ɇ
Ɋ		Ɋ Ⱥ	ȼ
	ȼ	ɋ
		Ɋ
		Ɋɢɫ. 5.39	Ɋɢɫ. 5.40

Ⱦɥɹ ɫɢɫɬɟɦ, ɢɡɨɛɪɚɠɟɧɧɵɯ ɧɚ pɢɫ.5.39 ɢ 5.40, ɩɨɫɬɪɨɣɬɟ ɷɩɸɪɵ Ɏ (ɡɚɞɚɱɢ, ɫ ɭɱɟɬɨɦ ɫɢɦɦɟɬ-

ɋɪɢɢ, ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵ). ɑɟɦɭ ɪɚɜɟɧ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɫɟɱɟɧɢɣ A ɢ B, A ɢ C ?

6. ɈɋɈȻȿɇɇɈɋɌɂ ɊȺɋɑȿɌȺ ɎȿɊɆ

Ʉɨɧɫɬɪɭɤɰɢɢ, ɪɚɛɨɬɚɸɳɢɟ ɜ ɭɫɥɨɜɢɹɯ ɪɚɫɬɹɠɟɧɢɹ-ɫɠɚɬɢɹ (ɮɟɪɦɵ), ɡɚɧɢɦɚɸɬ ɜɚɠɧɨɟ ɦɟɫɬɨ ɫɪɟɞɢ ɞɪɭɝɢɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ. Ɉɞɧɨɪɨɞɧɨɫɬɶ ɧɚɩɪɹɠɟɧɧɨɞɟɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɩɪɟɞɟɥɚɯ ɤɚɠɞɨɝɨ ɫɬɟɪɠɧɹ ɡɧɚɱɢɬɟɥɶɧɨ ɭɩɪɨɳɚɟɬ ɪɚɫɱɟɬɵ ɢ ɩɨɡɜɨɥɹɟɬ ɪɟɲɚɬɶ ɜɟɫɶɦɚ ɪɚɡɧɨɨɛɪɚɡɧɵɟ ɡɚɞɚɱɢ, ɜ ɬɨɦ ɱɢɫɥɟ ɫɢɫɬɟɦɵ, ɬɪɟɛɭɸɳɢɟ ɧɟɬɪɢɜɢɚɥɶɧɨɝɨ ɤɢɧɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ.

ɉɪɨɫɬɟɣɲɚɹ ɮɟɪɦɚ – ɷɬɨ ɧɚɛɨɪ ɫɬɟɪɠɧɟɣ, ɲɚɪɧɢɪɧɨ ɫɤɪɟɩɥɟɧɧɵɯ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɩɨ ɤɨɧɰɚɦ (ɭɡɥɚɦ) ɢ ɧɚɝɪɭɠɟɧɧɵɯ (ɢɥɢ ɡɚɤɪɟɩɥɟɧɧɵɯ) ɬɨɥɶɤɨ ɜ ɭɡɥɚɯ (ɧɚɩɪɢɦɟɪ, ɪɢɫ.6.1, ɪɢɫ.6.2). Ɏɟɪɦɵ ɦɨɝɭɬ ɜɤɥɸɱɚɬɶ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɠɟɫɬɤɢɟ ɞɢɫɤɢ – ɷɥɟɦɟɧɬɵ, ɪɚɛɨɬɚɸɳɢɟ ɧɟ ɬɨɥɶɤɨ ɧɚ ɪɚɫɬɹɠɟɧɢɟ (ɫɠɚɬɢɟ), ɧɨ ɢ ɧɚ ɢɡɝɢɛ ɢɥɢ ɤɪɭɱɟɧɢɟ, ɧɨ ɢɯ ɠɟɫɬɤɨɫɬɶ ɧɚɦɧɨɝɨ ɛɨɥɶɲɟ ɠɟɫɬɤɨɫɬɢ ɫɬɟɪɠɧɟɣ. Ⱦɢɫɤɢ ɫɱɢɬɚɸɬ ɚɛɫɨɥɸɬɧɨ ɠɟɫɬɤɢɦɢ (ɧɚɩɪɢɦɟɪ, ɫɬɟɪɠɟɧɶ, ɜɵɞɟɥɟɧɧɵɣ ɞɜɨɣɧɨɣ ɥɢɧɢɟɣ ɧɚ ɪɢɫ.6.3, ɡɚɲɬɪɢɯɨɜɚɧɧɵɣ ɷɥɟɦɟɧɬ ɧɚ ɪɢɫ.6.4).

Ɋ

2P

Ɋ

Ɋ
Ɋɢɫ.6.1	Ɋɢɫ.6.2	Ɋɢɫ.6.3

ȼɫɬɪɟɱɚɸɬɫɹ ɪɚɦɵ, ɪɚɛɨɬɚɸɳɢɟ, ɤɚɤ ɮɟɪɦɵ. Ɉɧɢ ɫɨɫɬɨɹɬ ɢɡ ɩɪɹɦɵɯ ɭɱɚɫɬɤɨɜ ɢ ɧɚɝɪɭɠɟɧɵ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɦɢ ɫɢɥɚɦɢ (ɜ ɬɨɦ ɱɢɫɥɟ, ɨɩɨɪɧɵɦɢ ɪɟɚɤɰɢɹɦɢ) ɧɚ ɤɨɧɰɚɯ ɭɱɚɫɬɤɨɜ (ɪɢɫ.6.5, 6.6). ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɷɬɨ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɟ ɪɚɦɵ. Ɉɞɧɚɤɨ ɢɡ-ɡɚ

	Ɋ	Ɋ		Ɋ ɬɨɝɨ, ɱɬɨ ɠɟɫɬɤɨɫɬɶ
	Ɋ			ɫɬɟɪɠɧɟɣ	ɧɚ	ɫɠɚɬɢɟ
				ɨɛɵɱɧɨ	ɫɭɳɟɫɬɜɟɧɧɨ
				ɜɵɲɟ, ɱɟɦ ɧɚ ɢɡɝɢɛ,
				ɩɪɢ	ɨɩɪɟɞɟɥɟɧɢɢ
	M			ɜɧɭɬɪɟɧɧɢɯ		ɫɢɥɨɜɵɯ
	Ɋɢɫ.6.4	Ɋɢɫ.6.5	Ɋɢɫ.6.6	ɮɚɤɬɨɪɨɜ	(ɪɚɫɤɪɵɬɢɟ
				ɫɬɚɬɢɱɟɫɤɨɣ		ɧɟɨɩɪɟ-

ɞɟɥɢɦɨɫɬɢ) ɩɨɞɚɬɥɢɜɨɫɬɶɸ ɫɬɟɪɠɧɟɣ ɧɚ ɪɚɫɬɹɠɟɧɢɟ-ɫɠɚɬɢɟ ɩɪɟɧɟɛɪɟɝɚɸɬ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɡɝɢɛɧɨɣ. ɗɬɨ ɞɨɩɭɳɟɧɢɟ ɢ ɩɪɢɜɨɞɢɬ ɤ ɨɬɦɟɱɟɧɧɨɦɭ ɫɬɪɚɧɧɨɦɭ ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ ɪɟɡɭɥɶɬɚɬɭ (ɜɩɨɥɧɟ ɫɨɝɥɚɫɭɸɳɟɦɭɫɹ, ɨɞɧɚɤɨ, ɫ ɬɨɣ ɦɨɞɟɥɶɸ, ɤɨɬɨɪɭɸ ɦɵ ɢɫɩɨɥɶɡɭɟɦ ɞɥɹ ɪɚɦ).

ɉɪɢɦɟɪ 1 (ɪɢɫ.6.7 – ɩɥɨɫɤɚɹ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɚɹ ɪɚɦɚ). Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɢɪɚɟɦ ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɫɢɫɬɟɦɭ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɭɸ ɭɫɥɨɜɢɹɦ ɫɢɦɦɟɬɪɢɢ ɢɫɯɨɞɧɨɣ ɡɚɞɚɱɢ (ɪɢɫ.6.8). ɍɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ:

¦X=¦Y=P – A+B=0, ¦MD=2Bl – 2C=0.

			ȼ	Ɉɞɧɨ ɢɡ ɦɧɨɠɟɫɬɜɚ ɪɟɲɟɧɢɣ ɷɬɨɣ ɫɢɫ-
		P		ɬɟɦɵ ɢɦɟɟɬ ɜɢɞ:
	P 2		2
	2l	2l	Ⱥ		A=P+X1, B=X1, C =X1 l.
	l	l	ɋ	Ʉɨɷɮɮɢɰɢɟɧɬɵ ɤɚɧɨɧɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟ-
				ɧɢɹ (G11X1+'1P=0) ɧɚɯɨɞɢɦ ɫ ɢɫɩɨɥɶ-
			"ɗ"
	ɋ	ȼ		ɡɨɜɚɧɢɟɦ	ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ	ɷɩɸɪ
				(ɪɢɫ.6.9).	ɉɪɟɧɟɛɪɟɝɚɹ, ɤɚɤ	ɨɛɵɱɧɨ,

Ⱥɩɨɞɚɬɥɢɜɨɫɬɶɸ ɫɬɟɪɠɧɟɣ ɧɚ ɫɠɚɬɢɟ,

ɩɨɥɭɱɚɟɦ '1P =0, ɬɨ ɟɫɬɶ X1=0; ɝɪɭɡɨ- Ɋɢɫ.6.7 Ɋɢɫ.6.8 ɜɚɹ ɷɩɸɪɚ ɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɪɟɲɟɧɢɟ. Ɋɚɦɚ ɪɚɛɨɬɚɟɬ ɤɚɤ ɮɟɪɦɚ. ɉɨ ɤɨɧɰɚɦ ɭɱɚɫɬɤɨɜ ɦɨɝɭɬ ɛɵɬɶ ɩɨɫɬɚɜɥɟɧɵ ɲɚɪɧɢɪɵ (ɫɧɹɬɨ ɡɚɩɪɟɳɟɧɢɟ ɩɨɜɨɪɨɬɚ), ɷɬɨ ɡɚɞɚɱɢ ɧɟ ɢɡɦɟɧɹɟɬ.

Ɉɰɟɧɢɦ ɩɨɝɪɟɲɧɨɫɬɶ, ɫ ɤɨɬɨɪɨɣ ɪɟɲɟɧɚ ɞɚɧɧɚɹ ɡɚɞɚɱɚ. Ⱦɥɹ ɷɬɨɝɨ, ɜɵɱɢɫɥɹɹ '1P ɢ G11, ɭɱɬɟɦ ɩɨɞɚɬɥɢɜɨɫɬɶ ɩɪɢ ɫɠɚɬɢɢ. ɉɨɥɭɱɢɦ:

'1P = ³N1NɊ /(ES)dz= 2Pl/(ES), G11=³M12/(EI)dz+³N12/(ES)dz=2l(O2/3+1)/(ES).

	ɏ1=0	Ɋ=0
		ɏ1=1
		ɗɆp
		l
		Ɋ

ɗNp

Ɋ 1

Ɋɢɫ.6.9

		l	Ɂɞɟɫɶ O – ɝɢɛɤɨɫɬɶ ɲɚɪɧɢɪɧɨ
			ɨɩɟɪɬɨɝɨ ɫɬɟɪɠɧɹ l/i, ɝɞɟ i –
ɗɆ1			ɪɚɞɢɭɫ ɢɧɟɪɰɢɢ ɫɟɱɟɧɢɹ, ɪɚɜ-
			ɧɵɣ I / S .
			ɉɪɢ ɜɵɱɢɫɥɟɧɢɢ G11 ɜɬɨ-
			ɪɵɦ ɫɥɚɝɚɟɦɵɦ ɦɨɠɧɨ ɩɪɟ-
			ɧɟɛɪɟɱɶ, ɬɚɤ ɤɚɤ ɞɚɠɟ ɞɥɹ
		1	ɨɱɟɧɶ ɠɟɫɬɤɢɯ ɫɬɟɪɠɧɟɣ ɩɨ-
			ɝɪɟɲɧɨɫɬɶ ɧɟ ɛɭɞɟɬ ɛɨɥɶɲɨɣ:
ɗN1			ɩɪɢ O=20 ɨɧɚ ɫɨɫɬɚɜɥɹɟɬ
			0,75%, ɩɪɢ O=200 – ɦɟɧɶɲɟ
			ɫɨɬɨɣ ɩɪɨɰɟɧɬɚ. Ɂɧɚɱɢɬ,
			X1= – '1P /G11= – 3P/O2
			ɢ ɦɚɤɫɢɦɚɥɶɧɵɣ ɢɡɝɢɛɚɸɳɢɣ

ɦɨɦɟɧɬ (ɜ ɡɚɞɟɥɤɚɯ) ɪɚɜɟɧ (M1)maxX1= –3Pl/O2 ɩɪɢ ɧɨɪɦɚɥɶɧɨɣ ɫɢɥɟ, ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɨɣ P (ɬɨɱɧɟɟ, A=P+X1=P(1 – 3/O2)).

Ɇɚɤɫɢɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɜ ɪɚɦɟ

maxV =N/S+Mmax/W=P/S+3Pl/(O2W)

ɞɥɹ ɫɥɭɱɚɹ ɤɪɭɝɥɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɪɚɜɧɨ P(1+6/O)/S, ɢ, ɧɚɩɪɢɦɟɪ, ɩɪɢ

O=200 (l/d=50) ɧɚɣɞɟɦ maxV =1.03P/S.

Ɂɧɚɱɢɬ, ɩɪɟɧɟɛɪɟɝɚɹ ɩɨɞɚɬɥɢɜɨɫɬɶɸ ɧɚ ɫɠɚɬɢɟ, ɦɵ ɨɲɢɛɚɟɦɫɹ ɜ ɞɚɧɧɨɣ ɡɚɞɚɱɟ ɧɚ 0,01% ɜ ɜɟɥɢɱɢɧɟ ɨɩɨɪɧɨɣ ɪɟɚɤɰɢɢ, ɚ ɜ ɡɧɚɱɟɧɢɢ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ – ɧɚ 3% (ɩɪɢ O=200). ȼ ɦɟɧɟɟ ɝɢɛɤɢɯ ɫɬɟɪɠɧɹɯ ɨɲɢɛɤɚ ɨɤɚɠɟɬɫɹ ɛɨɥɶɲɟɣ.

ȼɨɬɥɢɱɢɟ ɨɬ ɪɚɫɫɦɨɬɪɟɧɧɨɝɨ ɩɪɢɦɟɪɚ, ɤɨɧɫɬɪɭɤɰɢɹ, ɩɨɤɚɡɚɧɧɚɹ ɧɚ ɪɢɫ.6.10, ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɛɵɱɧɭɸ ɪɚɦɭ: ɡɞɟɫɶ ɩɪɟɧɟɛɪɟɠɟɧɢɟ ɩɨɞɚɬɥɢɜɨɫɬɶɸ ɧɚ ɫɠɚɬɢɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɢɡɦɟɧɹɟɬ ɡɧɚɱɟɧɢɣ ɧɟɢɡɜɟɫɬɧɵɯ ɦɟɬɨɞɚ ɫɢɥ ɢ ɜɟɥɢɱɢɧ ɢɡɝɢɛɚɸɳɢɯ ɦɨɦɟɧɬɨɜ. ɑɬɨɛɵ ɷɬɨ ɭɜɢɞɟɬɶ, ɞɨɫɬɚɬɨɱɧɨ ɩɪɢ ɜɵɛɨɪɟ ɨɫɧɨɜɧɨɣ ɫɢɫɬɟɦɵ ɜɪɟɡɚɬɶ ɜ ɤɨɧɰɵ ɭɱɚɫɬɤɨɜ ɲɚɪɧɢɪɵ. ȿɫɥɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ ɩɨɥɭɱɚɟɬɫɹ ɨɛɵɱɧɚɹ ɮɟɪɦɚ, ɬɨ ɡɞɟɫɶ – ɦɟɯɚɧɢɡɦ, ɧɟ ɧɚɯɨɞɹɳɢɣɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ. ɇɨ ɩɪɢ ɞɪɭɝɨɣ ɧɚɝɪɭɡɤɟ (ɪɢɫ.6.5) ɷɬɚ ɪɚɦɚ ɪɚɛɨɬɚɟɬ ɤɚɤ ɮɟɪɦɚ.

ȼɪɚɦɚɯ ɢɧɨɝɞɚ ɜɫɬɪɟɱɚɸɬɫɹ ɨɬɞɟɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɮɟɪɦɵ, ɤɨɬɨɪɵɟ ɩɨɥɟɡɧɨ

P				ɜɵɹɜɢɬɶ ɞɥɹ ɭɩɪɨɳɟɧɢɹ ɩɨ-
P				ɫɬɪɨɟɧɢɹ	ɷɩɸɪ	Ɏ.	ɗɬɨ
	1 q		2	q ɫɬɟɪɠɧɢ,	ɲɚɪɧɢɪɧɨ ɡɚɤɪɟɩ-
2P				ɥɟɧɧɵɟ ɩɨ ɤɨɧɰɚɦ ɢ ɧɟ ɢɫɩɵ-
				ɬɵɜɚɸɳɢɟ	ɩɨɩɟɪɟɱɧɨɣ		ɧɚ-
			ɛ)	ɝɪɭɡɤɢ (ɢɥɢ ɩɚɪ ɫɢɥ) ɩɨ ɫɜɨɟɣ
a)				ɞɥɢɧɟ. ɇɚɩɪɢɦɟɪ, ɜ ɬɚɤɢɯ ɭɫ-
Ɋɢɫ.6.10	Ɋɢɫ.6.11			ɥɨɜɢɹɯ ɧɚɯɨɞɹɬɫɹ ɷɥɟɦɟɧɬɵ 1
				ɢ 2 ɧɚ pɢɫ.6.11ɚ,ɛ. ȼɵɛɢɪɚɹ
ɨɫɧɨɜɧɭɸ ɫɢɫɬɟɦɭ, ɩɨɥɟɡɧɨ ɬɚɤɢɟ ɷɥɟɦɟɧɬɵ ɪɚɡɪɟɡɚɬɶ, ɭɱɢɬɵɜɚɹ ɫɪɚɡɭ, ɱɬɨ ɢɡɝɢ-
ɛɚɸɳɢɟ ɦɨɦɟɧɬɵ ɢ ɩɨɩɟɪɟɱɧɵɟ ɫɢɥɵ ɜ ɧɢɯ ɪɚɜɧɵ ɧɭɥɸ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɡɚɞɚɱɟ ɧɚ
ɪɢɫ.5.5 ɦɵ ɧɟ ɞɨɝɚɞɚɥɢɫɶ ɷɬɨɝɨ ɫɞɟɥɚɬɶ, ɨɬɱɟɝɨ ɩɨɹɜɢɥɚɫɶ ɥɢɲɧɹɹ ɧɟɢɡɜɟɫɬɧɚɹ ɪɟ-
X1				ɚɤɰɢɹ ɨɬɛɪɨɲɟɧɧɨɣ ɫɜɹɡɢ ɋ, ɪɚɜɧɚɹ,
P				ɤɚɤ ɷɬɨ ɜɵɹɫɧɢɬɫɹ ɢɡ ɭɫɥɨɜɢɣ ɪɚɜ-
X1			X1 ɧɨɜɟɫɢɹ, ɧɭɥɸ.
X1				ɗɤɜɢɜɚɥɟɧɬɧɵɟ ɡɚɞɚɱɢ ɞɥɹ ɪɚɦ,
2P q	X1	X1	q	ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɧɚ ɪɢɫɭɧɤɚɯ 6.11ɚ ɢ
"ɗ"	"ɗ"			ɛ, ɦɨɝɭɬ ɢɦɟɬɶ ɜɢɞ, ɩɨɤɚɡɚɧɧɵɣ ɧɚ
				pɢɫ.6.12 ɢ 6.13. ɗɬɨ ɡɚɦɟɬɧɨ ɨɛɥɟɝ-
Ɋɢɫ.6.12	Ɋɢɫ.6.13			ɱɚɟɬ ɪɟɲɟɧɢɟ ɡɚɞɚɱ.
				ȼ ɪɚɡɞɟɥɟ 5 ɛɵɥɚ ɞɚɧɚ ɪɟɤɨ-
ɦɟɧɞɚɰɢɹ: ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɜɧɭɬɪɟɧɧɢɯ ɫɢɥɨɜɵɯ ɮɚɤɬɨɪɨɜ ɜ ɮɟɪɦɚɯ ɪɚɡɪɟɡɚɬɶ ɜɫɟ
ɫɬɟɪɠɧɢ. Ɉɞɧɚɤɨ ɟɫɥɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɜɧɟɲɧɢɦ ɫɜɹɡɹɦ ɡɚɞɚɱɚ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟ-
ɞɟɥɢɦɚ, ɬɨ ɜɧɚɱɚɥɟ ɩɨɥɟɡɧɟɟ ɪɚɫɫɦɨɬɪɟɬɶ ɢɯ ɝɥɨɛɚɥɶɧɨ (ɬ.ɟ. ɧɟ ɪɚɡɪɟɡɚɹ ɢ ɧɟ ɢɧɬɟ-
ɪɟɫɭɹɫɶ, ɟɫɬɶ ɥɢ, ɫɤɚɠɟɦ, ɫɬɨɣɤɢ ɢ ɪɚɫɤɨɫɵ ɜ ɮɟɪɦɚɯ) ɢ ɨɩɪɟɞɟɥɢɬɶ ɷɬɢ

P1

P2

P3

P4

P1

P2

P3

P4

		Ɋɢɫ.6.14							Ɋɢɫ.6.15

ɪɟɚɤɰɢɢ. ɇɚɩɪɢɦɟɪ, ɮɟɪɦɭ ɧɚ ɪɢɫ.6.14 ɩɪɟɞɫɬɚɜɢɦ ɜɧɚɱɚɥɟ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ pɢɫ.6.15, ɨɩɪɟɞɟɥɢɦ ɪɟɚɤɰɢɢ ɜɧɟɲɧɢɯ ɫɜɹɡɟɣ, ɚ ɡɚɬɟɦ, ɪɚɫɫɦɚɬɪɢɜɚɹ ɢɯ ɤɚɤ ɜɧɟɲɧɸɸ ɧɚɝɪɭɡɤɭ, ɪɟɲɚɟɦ ɡɚɞɚɱɭ ɨɛɵɱɧɵɦ ɦɟɬɨɞɨɦ. ɉɨɞɨɛɧɵɦ ɠɟ ɨɛɪɚɡɨɦ ɜ ɪɚɦɟ ɧɚ

ɪɢɫ.5.5 ɦɨɠɧɨ ɧɚɣɬɢ ɜɧɚɱɚɥɟ ɪɟɚɤɰɢɸ A (ɪɢɫ.5.6, ɨɱɟɜɢɞɧɨ, A = P) ɢ ɡɚɬɟɦ – ɫɬɪɨɢɬɶ ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɡɚɞɚɱɭ (ɪɢɫ.5.5).

7. ɉɊȿȾȿɅɖɇɈȿ ɋɈɋɌɈəɇɂȿ ɂȾȿȺɅɖɇɈ ɉɅȺɋɌɂɑȿɋɄɈɃ ɄɈɇɋɌɊɍɄɐɂɂ

ɂɞɟɚɥɶɧɨ ɩɥɚɫɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ (ɢɥɢ ɢɞɟɚɥɶɧɨ ɭɩɪɭɝɨɩɥɚɫɬɢɱɟɫɤɢɣ) ɦɨɠɟɬ ɢɦɟɬɶ ɥɸɛɨɟ ɡɧɚɱɟɧɢɟ ɞɟɮɨɪɦɚɰɢɢ, ɧɨ ɟɝɨ ɧɚɩɪɹɠɟɧɢɟ ɩɨ ɦɨɞɭɥɸ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɹ VT, ɟɫɥɢ ɪɟɱɶ ɢɞɟɬ ɨ ɪɚɫɬɹɠɟɧɢɢ-ɫɠɚɬɢɢ. Ⱦɟɮɨɪɦɚɰɢɸ H ɪɚɡɞɟɥɹɸɬ ɧɚ ɭɩɪɭɝɭɸ He { V/E ɢ ɩɥɚɫɬɢɱɟɫɤɭɸ Hp { H – He. ȿɫɥɢ ɧɚɩɪɹɠɟɧɢɟ ɩɨ ɦɨɞɭɥɸ ɧɟ ɞɨɫɬɢɝɥɨ ɡɧɚɱɟɧɢɹ VT, ɬɨ ɩɥɚɫɬɢɱɟɫɤɚɹ ɞɟɮɨɪɦɚɰɢɹ ɩɨɫɬɨɹɧɧɚ; ɩɪɢ ɧɚɱɚɥɶɧɨɦ ɧɚɝɪɭɠɟɧɢɢ ɨɧɚ ɪɚɜɧɚ ɧɭɥɸ. ɉɪɢ V =VT ɭɜɟɥɢɱɟɧɢɟ ɞɟɮɨɪɦɚɰɢɢ ɪɚɜɧɨ ɭɜɟɥɢɱɟɧɢɸ Hp, ɭɦɟɧɶɲɟɧɢɟ H ɪɚɜɧɨ ɭɦɟɧɶɲɟɧɢɸ He. ɉɪɢ V = – VT, ɧɚɨɛɨɪɨɬ, ɭɦɟɧɶɲɟɧɢɟ H ɪɚɜɧɨ ɭɦɟɧɶɲɟɧɢɸ Hp, ɧɨ ɟɫɥɢ ɞɟɮɨɪɦɚɰɢɹ ɜɨɡɪɚɫɬɚɟɬ, ɬɨ ɢɡɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɭɩɪɭɝɚɹ ɞɟɮɨɪɦɚɰɢɹ. Ɉɞɧɨɣ ɢɡ ɝɥɚɜɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɧɟɭɩɪɭɝɨɝɨ ɦɚɬɟɪɢɚɥɚ ɹɜɥɹɟɬɫɹ ɧɟɨɞɧɨɡɧɚɱɧɨɫɬɶ ɫɜɹɡɢ ɦɟɠɞɭ ɧɚɩɪɹɠɟɧɢɟɦ ɢ ɞɟɮɨɪɦɚɰɢɟɣ. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɪɢ ɪɚɫɱɟɬɚɯ ɫɥɟɞɭɟɬ ɡɧɚɬɶ ɧɟ ɬɨɥɶɤɨ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɧɚɝɪɭɡɤɢ, ɧɨ ɢ ɢɫɬɨɪɢɸ ɟɟ ɢɡɦɟɧɟɧɢɹ.

ɉɪɢ ɦɨɧɨɬɨɧɧɨɦ ɜɨɡɪɚɫɬɚɧɢɢ ɩɚɪɚɦɟɬɪɚ ɧɚɝɪɭɡɤɢ (ɧɚɩɪɢɦɟɪ, P) ɤɨɧɫɬɪɭɤɰɢɹ ɜɧɚɱɚɥɟ ɪɚɛɨɬɚɟɬ ɭɩɪɭɝɨ – ɩɨɤɚ ɫɚɦɨɟ ɛɨɥɶɲɨɟ ɧɚɩɪɹɠɟɧɢɟ (ɤɨɬɨɪɨɟ ɧɚɯɨɞɢɬɫɹ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɢɡ ɨɛɵɱɧɨɝɨ ɭɩɪɭɝɨɝɨ ɪɚɫɱɟɬɚ) ɧɟ ɞɨɫɬɢɝɧɟɬ ɩɪɟɞɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ. ȼɟɥɢɱɢɧɚ ɩɚɪɚɦɟɬɪɚ P ɜ ɷɬɨɬ ɦɨɦɟɧɬ ɨɛɨɡɧɚɱɚɟɬɫɹ ɢɧɞɟɤɫɨɦ: P = PɌ. ɋ ɷɬɨɝɨ ɦɨɦɟɧɬɚ ɫɬɚɞɢɹ ɭɩɪɭɝɨɣ ɪɚɛɨɬɵ ɤɨɧɫɬɪɭɤɰɢɢ ɫɦɟɧɹɟɬɫɹ ɭɩɪɭɝɨɩɥɚɫɬɢɱɟɫɤɨɣ: ɜ ɱɚɫɬɢ ɤɨɧɫɬɪɭɤɰɢɢ ɧɚɩɪɹɠɟɧɢɹ ɞɨɫɬɢɝɥɢ ɩɪɟɞɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ, ɢ ɜɨɡɪɚɫɬɚɧɢɟ ɧɚɝɪɭɡɤɢ ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɜɨɡɪɚɫɬɚɧɢɟɦ ɧɚɩɪɹɠɟɧɢɣ ɜ ɞɪɭɝɢɯ ɱɚɫɬɹɯ ɤɨɧɫɬɪɭɤɰɢɢ. ɉɪɨɢɫɯɨɞɢɬ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɟ ɧɚɩɪɹɠɟɧɢɣ – ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɨɥɟɦ ɧɚɩɪɹɠɟɧɢɣ ɜ ɭɩɪɭɝɨɣ ɫɬɚɞɢɢ ɪɚɛɨɬɵ ɤɨɧɫɬɪɭɤɰɢɢ. ɇɚɤɨɧɟɰ, ɜɨɡɧɢɤɚɟɬ ɩɪɟɞɟɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ (P = P0 – ɩɪɟɞɟɥɶɧɚɹ ɧɚɝɪɭɡɤɚ), ɤɨɝɞɚ ɜɨɡɪɚɫɬɚɧɢɟ ɩɟɪɟɦɟɳɟɧɢɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɨɡɪɚɫɬɚɧɢɸ ɩɥɚɫɬɢɱɟɫɤɢɯ ɞɟɮɨɪɦɚɰɢɣ ɩɪɢ ɩɨɫɬɨɹɧɧɵɯ ɭɩɪɭɝɢɯ ɞɟɮɨɪɦɚɰɢɹɯ (ɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɪɢ ɩɨɫɬɨɹɧɧɵɯ ɧɚɩɪɹɠɟɧɢɹɯ ɢ ɩɨɫɬɨɹɧɧɨɣ ɧɚɝɪɭɡɤɟ). Ⱦɨɫɬɢɠɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɤɨɧɫɬɪɭɤɰɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɜɨɡɦɨɠɧɨ ɬɚɤɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɟɣ ɬɟɥɚ – ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɩɥɚɫɬɢɱɟɫɤɢɯ ɞɟɮɨɪɦɚɰɢɣ – ɧɚɡɵɜɚɸɬ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɥɚɫɬɢɱɟɫɤɨɝɨ ɦɟɯɚɧɢɡɦɚ. ɉɪɢ ɷɬɨɦ ɢɡɦɟɧɟɧɢɹ ɩɥɚɫɬɢɱɟɫɤɢɯ ɞɟɮɨɪɦɚɰɢɣ ɤɢɧɟɦɚɬɢɱɟɫɤɢ ɜɨɡɦɨɠɧɵ, ɚ ɧɚɩɪɹɠɟɧɢɹ ɫɬɚɬɢɱɟɫɤɢ ɞɨɩɭɫɬɢɦɵ: ɨɧɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɭɫɥɨɜɢɹɦ ɪɚɜɧɨɜɟɫɢɹ ɢ ɧɟ ɩɪɟɜɵɲɚɸɬ ɩɪɟɞɟɥɶɧɵɯ.

ɋɭɳɟɫɬɜɭɸɬ ɞɜɚ ɷɤɫɬɪɟɦɚɥɶɧɵɯ ɩɪɢɡɧɚɤɚ ɩɪɟɞɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ: ɫɬɚɬɢɱɟɫɤɢɣ ɢ ɤɢɧɟɦɚɬɢɱɟɫɤɢɣ. ɉɨ ɩɟɪɜɨɦɭ ɩɪɟɞɟɥɶɧɚɹ ɧɚɝɪɭɡɤɚ – ɷɬɨ ɧɚɢɛɨɥɶɲɚɹ ɢɡ ɬɚɤɢɯ, ɤɨɬɨɪɵɟ ɭɪɚɜɧɨɜɟɲɢɜɚɸɬɫɹ ɫɬɚɬɢɱɟɫɤɢ ɞɨɩɭɫɬɢɦɵɦɢ ɧɚɩɪɹɠɟɧɢɹɦɢ. ɉɨ ɜɬɨɪɨɦɭ

– ɷɬɨ ɧɚɢɦɟɧɶɲɚɹ ɢɡ ɬɚɤɢɯ, ɩɪɢ ɤɨɬɨɪɵɯ ɜɨɡɦɨɠɟɧ ɩɥɚɫɬɢɱɟɫɤɢɣ ɦɟɯɚɧɢɡɦ. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɟɫɬɶ ɞɜɚ ɦɟɬɨɞɚ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɟɞɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ: ɫɬɚɬɢɱɟɫɤɢɣ ɢ ɤɢɧɟɦɚɬɢɱɟɫɤɢɣ.

ȼ ɫɬɚɬɢɱɟɫɤɨɦ ɦɟɬɨɞɟ ɡɚɞɚɸɬ ɜɨɡɦɨɠɧɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɜ ɤɨɧɫɬɪɭɤɰɢɢ. Ʉɚɠɞɨɦɭ ɢɡ ɧɢɯ ɨɬɜɟɱɚɟɬ ɧɟɤɨɬɨɪɨɟ ɡɧɚɱɟɧɢɟ P; ɧɚɢɛɨɥɶɲɟɟ ɢɡ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɢ ɟɫɬɶ ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ P0.

ɑɚɫɬɨ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɧɟ ɜɫɟ ɦɧɨɠɟɫɬɜɨ ɬɚɤɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɧɚɩɪɹɠɟɧɢɣ, ɚ ɥɢɲɶ ɧɟɤɨɬɨɪɵɣ ɥɟɝɤɨ ɡɚɞɚɜɚɟɦɵɣ ɧɚɛɨɪ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɥɭɱɚɸɬ ɩɪɢɛɥɢɠɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ɩɪɟɞɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ, ɡɚɜɟɞɨɦɨ ɧɟ ɩɪɟɜɵɲɚɸɳɟɟ ɢɫɬɢɧɧɨɟ