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Сопротивление материалов. Часть 1. Учебное пособие

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ɗɬɢ ɜɟɥɢɱɢɧɵ ɢ ɤɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɨɜ ɬɹɠɟɫɬɢ ɞɜɭɬɚɜɪɚ ɢ ɭɝɨɥɤɚ ɜ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ Ɉɯɭ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ.1.12,ɚ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ:

ɚ1 7,24 ɫɦ, b1 7,32 ɫɦ, ɚ2 14,55ɫɦ, b2 14,69 ɫɦ.

Ɉɩɪɟɞɟɥɢɦ ɩɨ ɮɨɪɦɭɥɚɦ (1.5) ɦɨɦɟɧɬɵ ɢɧɟɪɰɢɢ ɫɟɱɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚɥɶɧɵɯ ɨɫɟɣ Ɉɯ ɢ Ɉɭ.

J	x	J		F b2		J		F b2
			x1		1 1		x2		2 2
		39727 100 7,322							617 49,8 14,692		56449 ɫɦ4 ;
J	y	J		F a2		J		F a		2
				ɭ1	1 1			y2	2	2
		1043 100 7,242 2026 49,8 14,552									18854 ɫɦ4 ;
J xy		Jx1y1 F1a1b1 J x2 y2 F2a2b2
		100 7,24 7,32 644 49,8 14,55 14,69 15300 ɫɦ4 .

ɉɨ ɮɨɪɦɭɥɚɦ (1.7) ɨɩɪɟɞɟɥɢɦ ɜɟɥɢɱɢɧɵ ɝɥɚɜɧɵɯ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɢ ɭɝɥɵ ɧɚɤɥɨɧɚ ɝɥɚɜɧɵɯ ɨɫɟɣ 1 ɢ 2 ɤ ɨɫɢ Ɉɯ.

J1,2

tg 1

♣ J

∙

♦

♥

≠

	56449 18854				ρ	♣56449 18854			∙	2		2	;
			2		ρ	♦	2		÷	15300			;
			2			♥	2		≠
	J1 = 61889 ɫɦ4 ,						J2 = 13415 ɫɦ4 ;
	Jxy			15300			0,356 ,			1	19,6			ɨ	;
J y J1			18854 61889				0,356 ,			1	19,6				;
J y J1			18854 61889
2		Jxy			15300			2,813	,		2	70,4				ɨ	.
2		J y	J2	18854		13415		2,813	,		2	70,4					.
		J y	J2	18854		13415

ɇɚ ɪɢɫ.1.12,ɛ ɩɪɢɜɟɞɟɧɨ ɝɪɚɮɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧ ɝɥɚɜɧɵɯ ɦɨɦɟɧɬɨɜ ɢɧɟɪɰɢɢ ɢ ɩɨɥɨɠɟɧɢɹ ɝɥɚɜɧɵɯ ɨɫɟɣ.

ȽɅȺȼȺ 2

ɐȿɇɌɊȺɅɖɇɈȿ ɊȺɋɌəɀȿɇɂȿ ɂ ɋɀȺɌɂȿ ɋɌȿɊɀɇȿɃ

2.1. Ɉɫɧɨɜɧɵɟ ɨɩɪɟɞɟɥɟɧɢɹ ɢ ɮɨɪɦɭɥɵ

ɐɟɧɬɪɚɥɶɧɨɟ ɪɚɫɬɹɠɟɧɢɟ ɢ ɫɠɚɬɢɟ ɩɪɹɦɨɝɨ ɫɬɟɪɠɧɹ ɜɵɡɵɜɚɟɬɫɹ ɞɟɣɫɬɜɢɟɦ ɨɫɟɜɵɯ ɧɚɝɪɭɡɨɤ, ɜ ɫɨɫɬɚɜ ɤɨɬɨɪɵɯ ɜɯɨɞɹɬ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɟ ɫɢɥɵ ɢ ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɧɚɝɪɭɡɤɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟɫɹ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ q. ɉɪɢ q = const ɧɚɝɪɭɡɤɚ ɧɚɡɵɜɚɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ, ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɚɹ ɤɨɬɨɪɨɣ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ qɚ, ɝɞɟ ɚ – ɞɥɢɧɚ ɭɱɚɫɬɤɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ.

ȼ ɩɨɩɟɪɟɱɧɵɯ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɹ ɞɟɣɫɬɜɭɸɬ ɬɨɥɶɤɨ ɧɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɢ ɨɞɧɨ ɜɧɭɬɪɟɧɧɟɟ ɭɫɢɥɢɟ – ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ N, ɨɩɪɟɞɟɥɹɟɦɚɹ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ ɫɟɱɟɧɢɣ. ɉɪɢ ɷɬɨɦ ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɪɚɜɧɚ ɫɭɦɦɟ ɩɪɨɟɤɰɢɣ ɧɚ ɨɫɶ Ɉɯ ɧɚɝɪɭɡɨɤ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɨɞɧɨɣ ɢɡ ɱɚɫɬɟɣ ɫɬɟɪɠɧɹ (ɪɢɫ.2.1).

N=P1 P2

m m m m m m

N=P3 qa P2 P2

P1 P1

Ɋɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ N ɞɥɹ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɱɚɫɬɟɣ ɫɬɟɪɠɧɹ ɞɨɥɠɧɵ ɫɨɜɩɚɞɚɬɶ. Ɋɚɫɬɹɝɢɜɚɸɳɚɹ ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɫɱɢɬɚɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɣ, ɚ ɫɠɢɦɚɸɳɚɹ – ɨɬɪɢɰɚɬɟɥɶɧɨɣ. ɉɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɣ ɫɢɥɵ (ɧɚɩɪɢɦɟɪ, ɤɇ).

ɉɨɫɥɟ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ N ɜ ɯɚɪɚɤɬɟɪɧɵɯ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɹ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɷɬɢɯ ɫɢɥ ɩɨ ɞɥɢɧɟ ɫɬɟɪɠɧɹ (ɷɩɸɪɭ N). ɉɪɢ ɟɺ ɩɨɫɬɪɨɟɧɢɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ

dN	q .	(2.1)

dx

ɇɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɰɟɧɬɪɚɥɶɧɨɦ ɪɚɫɬɹɠɟɧɢɢ ɢ ɫɠɚɬɢɢ ɨɞɢɧɚɤɨɜɵ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

Ɋɢɫ.2.1			ς	N	,	(2.2)
				F

ɝɞɟ F – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ.				ɉɚ = ɇ/ɦ2 ,		Ɇɉɚ =
ȼ ɫɢɫɬɟɦɟ ɋɂ ɧɚɩɪɹɠɟɧɢɹ ɢɦɟɸɬ ɪɚɡɦɟɪɧɨɫɬɶ
= 10–1 ɤɇ/ɫɦ2 ɢ ɞɪ.
Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɞɨɥɶɧɚɹ ɞɟɮɨɪɦɚɰɢɹ ɫɬɟɪɠɧɹ ɞɥɢɧɨɣ l ɪɚɜɧɚ
Η	l	,				(2.3)

	l

ɝɞɟ l – ɭɞɥɢɧɟɧɢɟ ɢɥɢ ɭɤɨɪɨɱɟɧɢɟ ɫɬɟɪɠɧɹ.

ȼ ɩɪɟɞɟɥɚɯ ɭɩɪɭɝɢɯ ɞɟɮɨɪɦɚɰɢɣ ɫɩɪɚɜɟɞɥɢɜɨ ɥɢɧɟɣɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɧɚɩɪɹɠɟɧɢɹɦɢ ɢ ɞɟɮɨɪɦɚɰɢɹɦɢ, ɧɚɡɵɜɚɟɦɨɟ ɡɚɤɨɧɨɦ Ƚɭɤɚ

ς EΗ ,

(2.4)

ɝɞɟ ȿ – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ɫɬɟɪɠɧɹ.

ɍɞɥɢɧɟɧɢɟ ɢɥɢ ɭɤɨɪɨɱɟɧɢɟ ɫɬɟɪɠɧɹ, ɡɚɤɪɟɩɥɟɧɧɨɝɨ ɜ ɧɚɱɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɯ = 0, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

	l	N
l	³			dx .	(2.5)

	0	EF

Ⱦɥɹ ɱɚɫɬɧɨɝɨ ɫɥɭɱɚɹ ȿF = const ɢ N = const ɢɦɟɟɦ
l	N l		.		(2.6)

	EF

Ⱦɥɹ ɫɬɟɪɠɧɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɠɟɫɬɤɨɫɬɶɸ ȿF ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɦ ɡɚɤɨɧɟ ɢɡɦɟɧɟɧɢɹ ɩɪɨɞɨɥɶɧɨɣ ɫɢɥɵ N ɜɟɥɢɱɢɧɭ l ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ

l	1	:N	1	:ς	(2.7)

	EF		E
ɝɞɟ :N ɢ :ς – ɩɥɨɳɚɞɢ ɷɩɸɪɵ N ɢɥɢ ɷɩɸɪɵ ς					ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɭɱɚ-
ɫɬɤɟ ɫɬɟɪɠɧɹ.

ɉɨɩɟɪɟɱɧɵɟ ɫɟɱɟɧɢɹ ɫɬɟɪɠɧɹ, ɨɫɬɚɜɚɹɫɶ ɩɥɨɫɤɢɦɢ ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɦɢ ɤ ɨɫɢ, ɩɨɥɭɱɚɸɬ ɨɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ u = u(x). ɗɩɸɪɚ ɨɫɟɜɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɫɬɪɨɢɬɫɹ ɩɨɫɥɟ ɨɩɪɟɞɟɥɟɧɢɹ ɭɞɥɢɧɟɧɢɣ ɢɥɢ ɭɤɨɪɨɱɟɧɢɣ l ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ.

ȿɫɥɢ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ ɢ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɧɟɞɨɫɬɚɬɨɱɧɨ, ɬɨ ɫɬɟɪɠɟɧɶ ɢɥɢ ɫɬɟɪɠɧɟɜɚɹ ɫɢɫɬɟɦɚ ɧɚɡɵɜɚɸɬɫɹ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɦɢ. Ⱦɥɹ ɢɯ ɪɚɫɱɟɬɚ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɫɥɨɜɢɹ ɞɟɮɨɪɦɚɰɢɢ.

Ɋɚɫɱɟɬ ɧɚ ɩɪɨɱɧɨɫɬɶ ɷɥɟɦɟɧɬɨɜ ɫɬɪɨɢɬɟɥɶɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɦɟɬɨɞɭ ɩɪɟɞɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɣ. ȼ ɩɨɩɟɪɟɱɧɵɯ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɹ ɩɪɢ ɰɟɧɬɪɚɥɶɧɨɦ ɪɚɫɬɹɠɟɧɢɢ ɢɥɢ ɫɠɚɬɢɢ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɭɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ

ς	N	δ ϑc R ,	(2.8)

	F

ɝɞɟ R – ɪɚɫɱɟɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɚ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟ ɟɝɨ ɩɪɨɱɧɨɫɬɶ, ɢ ϑɫ – ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɥɨɜɢɣ ɪɚɛɨɬɵ. ȼɟɥɢɱɢɧɚ ɩɪɨɞɨɥɶɧɨɣ ɫɢɥɵ N ɜɵɱɢɫɥɹɟɬɫɹ ɨɬ ɞɟɣɫɬɜɢɹ ɪɚɫɱɟɬɧɵɯ ɧɚɝɪɭɡɨɤ, ɨɩɪɟɞɟɥɹɟɦɵɯ ɫ ɭɱɟɬɨɦ ɤɨɷɮɮɢɰɢɟɧɬɚ ɧɚɞɟɠɧɨɫɬɢ ɩɨ ɧɚɝɪɭɡɤɚɦ ϑf . Ɂɧɚɱɟɧɢɹ R, ϑɫ ɢ ϑf ɩɪɢɜɟɞɟɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɪɚɡɞɟɥɚɯ ɋɇɢɉ.

ɉɨɞɛɨɪ ɫɟɱɟɧɢɹ ɫɬɟɪɠɧɹ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

F τ	N	.	(2.9)

	ϑc R

Ɋɚɫɱɟɬ ɷɥɟɦɟɧɬɨɜ ɦɚɲɢɧɨɫɬɪɨɢɬɟɥɶɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɦɟɬɨɞɭ ɞɨɩɭɫɤɚɟɦɵɯ ɧɚɩɪɹɠɟɧɢɣ. ɍɫɥɨɜɢɟ ɩɪɨɱɧɨɫɬɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɡɚɩɢɫɵɜɚɟɬɫɹ

ɜ ɜɢɞɟ
V	N	d[V] ,	(2.10)
	F

ɝɞɟ [V] – ɞɨɩɭɫɤɚɟɦɨɟ ɧɚɩɪɹɠɟɧɢɟ.

ɉɪɢ ɪɚɫɱɟɬɟ ɫɬɟɪɠɧɟɣ ɢ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɢɡ ɩɥɚɫɬɢɱɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ ɭɩɪɨɳɺɧɧɚɹ ɞɢɚɝɪɚɦɦɚ ɡɚɜɢɫɢɦɨɫɬɢ V = f(H), ɧɚɩɪɢɦɟɪ, ɞɢɚɝɪɚɦɦɚ ɉɪɚɧɞɬɥɹ (ɪɢɫ.2.2). ɋɨɝɥɚɫɧɨ ɷɬɨɣ ɞɢɚɝɪɚɦɦɟ ɩɪɢ ɞɨɫɬɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹɦɢ ɩɪɟɞɟɥɚ ɬɟɤɭɱɟɫɬɢ Vɬ ɞɟɮɨɪɦɚɰɢɢ ɧɟɨɝɪɚɧɢɱɟɧɧɨ ɜɨɡɪɚɫɬɚɸɬ. ɉɪɢ ɷɬɨɦ ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɜ ɫɬɟɪɠɧɟ ɩɪɢɧɢɦɚɟɬ ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ (ɪɚɡɪɭɲɚɸɳɚɹ ɫɢɥɚ)

	ς			N	Nɩɪɟɞ		VɬF .	(2.11)
ςɬ				Ɂɚ ɧɚɱɚɥɨ ɪɚɡɪɭɲɟɧɢɹ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ
ςɬ				Ɂɚ ɧɚɱɚɥɨ ɪɚɡɪɭɲɟɧɢɹ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ
				ɦɨɠɧɨ ɩɪɢɧɹɬɶ ɬɚɤɨɟ ɫɨɫɬɨɹɧɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ ɧɚɩɪɹ-
				ɠɟɧɢɹ ɜɨ ɜɫɟɯ ɫɬɟɪɠɧɹɯ ɞɨɫɬɢɝɧɭɬ ɩɪɟɞɟɥɚ ɬɟɤɭɱɟɫɬɢ.
Ɉ				ɉɪɢ ɷɬɨɦ ɜɟɥɢɱɢɧɚ ɩɪɟɞɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ				5ɩɪɟɞ ɨɩɪɟ-
				ɞɟɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ. Ⱦɨɩɭɫɤɚɟɦɚɹ ɧɚ-
			Η
			Η
		Ɋɢɫ.2.2		ɝɪɭɡɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
		Ɋɢɫ.2.2				ȇɩɪɟɞ
				ȇ		ȇɩɪɟɞ	,	(2.12)
				ȇ			,	(2.12)

ɝɞɟ n – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɩɪɨɱɧɨɫɬɢ.

2.2. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ

Ɂɚɞɚɱɚ 2.1

Ⱦɥɹ ɫɬɟɪɠɧɹ ɫɬɭɩɟɧɱɚɬɨ ɩɨɫɬɨɹɧɧɨɝɨ ɫɟɱɟɧɢɹ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɨɫɟɜɵɯ ɧɚɝɪɭɡɨɤ (ɪɢɫ.2.3,ɚ), ɩɨɫɬɪɨɢɦ ɷɩɸɪɵ N ɢ V. Ɉɩɪɟɞɟɥɢɦ ɭɞɥɢɧɟɧɢɹ (ɭɤɨɪɨɱɟɧɢɹ) ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ ɢ ɜɫɟɝɨ ɫɬɟɪɠɧɹ ɜ ɰɟɥɨɦ ɢ ɩɨɫɬɪɨɢɦ ɷɩɸɪɭ ɨɫɟɜɵɯ ɩɟɪɟɦɟɳɟɧɢɣ. ȼ ɪɚɫɱɟɬɚɯ ɩɪɢɦɟɦ ȿ = 1 105 Ɇɉɚ = 1 104 ɤɇ/ɫɦ2.

Ɉɩɪɟɞɟɥɢɦ ɨɩɨɪɧɭɸ ɪɟɚɤɰɢɸ ɜ ɬɨɱɤɟ ɡɚɤɪɟɩɥɟɧɢɹ ɫɬɟɪɠɧɹ.

6X = 0, – R + 9 + 30 1,2 – 24 = 0, R = 21 ɤɇ .

ɇɚɩɪɚɜɥɟɧɢɟ ɨɩɨɪɧɨɣ ɪɟɚɤɰɢɢ ɜ ɧɚɱɚɥɟ ɪɚɫɱɟɬɚ ɩɪɢɧɹɬɨ ɩɪɚɜɢɥɶɧɨ.

Ɉɩɪɟɞɟɥɢɦ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ ɫɟɱɟɧɢɣ ɩɪɨɞɨɥɶɧɵɟ ɫɢɥɵ ɢ ɧɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɪɟɞɟɥɚɯ ɬɪɟɯ ɯɚɪɚɤɬɟɪɧɵɯ ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ.

ɚ)		R			ɛ)	N (ɤɇ)	ɜ)	ς (Ɇɉɚ) ɝ)	u (ɫɦ)
		R				21		17,5
		Ɉ				21		17,5
	1	Ɉ
ɦ	1					+		+
0,8						+		+
0,8		9ɤɇ
		9ɤɇ							0,014
									0,014
ɦ	2	F1=12ɫɦ		2
0,8		F1=12ɫɦ
0,8									+
						12		10	+
						12		10	0,022
		30ɤɇ/ɦ			ɚ			6	0,0232
ɦ	3	30ɤɇ/ɦ
ɦ	3
1,2		F2=20ɫɦ2				–ɚ
					–	1,2		–
					–			–
		24ɤɇ	24				12		0,0184
		ɯ				Ɋɢɫ.2.3

ɍɱɚɫɬɨɤ 1

(0 d x d0,8 ɦ,

ɪɢɫ.2.4).

R=21ɤɇ

21ɤɇ

6X = 0, – 21 + N = 0 ;

N = 21 ɤɇ (ɪɚɫɬɹɠɟɧɢɟ) ;

21 1,75 ɤɇ/ɫɦ2

9ɤɇ

17,5 Ɇɉɚ .

ɍɱɚɫɬɨɤ 2

(0,8d x d1,6 ɦ, ɪɢɫ.2.5).

6X = 0 , – 21 + 9 + N = 0 ;

Ɋɢɫ.2.4

Ɋɢɫ.2.5

N = 12 ɤɇ (ɪɚɫɬɹɠɟɧɢɟ),

12 1ɤɇ/ɫɦ

10 Ɇɉɚ .

ɍɱɚɫɬɨɤ 3

(1,6 d x d2,8ɦ, ɪɢɫ.2.6).

6X = 0 , – N + 30(2,8 – ɯ) – 24 = 0 , N = 30(2,8 – ɯ) – 24 ;

ɯ = 1,6 ɦ , N =30 1,2 – 24 = 12 ɤɇ (ɪɚɫɬɹɠɟɧɢɟ),

2,8–ɯ

0,6 ɤɇ/ɫɦ

6 Ɇɉɚ .

30ɤɇ/ɦ

ɯ = 2,8 ɦ , N = – 24 ɤɇ (ɫɠɚɬɢɟ) ,

24ɤɇ

1,2 ɤɇ/ɫɦ

12 Ɇɉɚ .

Ɋɢɫ.2.6

ɋɬɪɨɢɦ ɷɩɸɪɵ N ɢ V (ɪɢɫ.2.3,ɛ,ɜ). ȼ ɩɪɟɞɟɥɚɯ ɩɟɪɜɨɝɨ ɢ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɨɜ ɩɪɨɞɨɥɶɧɵɟ ɫɢɥɵ ɢ ɧɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɢɦɟɸɬ ɩɨɫɬɨɹɧɧɵɟ ɡɧɚɱɟɧɢɹ, ɚ ɜ ɩɪɟɞɟɥɚɯ ɬɪɟɬɶɟɝɨ ɭɱɚɫɬɤɚ ɨɧɢ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ. ȼ ɫɟɱɟɧɢɢ ɯ = 0,8 ɦ ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɢɦɟɟɬ ɫɤɚɱɨɤ ɧɚ ɜɟɥɢɱɢɧɭ 9 ɤɇ.

Ɉɩɪɟɞɟɥɢɦ ɜɟɥɢɱɢɧɵ ɭɞɥɢɧɟɧɢɣ (ɭɤɨɪɨɱɟɧɢɣ) ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ.


l1	N1l1			21 80			0,014 ɫɦ (ɭɞɥɢɧɟɧɢɟ) ,
		EF1	1 104 12

l2	12 80					0,008 ɫɦ (ɭɞɥɢɧɟɧɢɟ),
		1 104 12
l3	1		:N		1			24 12	120
		ȿF2				1 104 20		2
						0,0036 ɫɦ ɭɤɨɪɨɱɟɧɢɟ .
Ɉɛɳɟɟ ɭɞɥɢɧɟɧɢɟ ɫɬɟɪɠɧɹ ɪɚɜɧɨ
l l1 l2 l3						0,014 0,008 0,0036 0,0184 ɫɦ.

Ɉɩɪɟɞɟɥɢɦ ɨɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɯɚɪɚɤɬɟɪɧɵɯ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɹ.

ɯ= 0, u = u0 = 0 ;

x= 0,8 ɦ , u1 = u0 + l1 = 0,014 ɫɦ ;

x = 1,6 ɦ , u2 = u1 + l2 = 0,014 + 0,008 = 0,022 ɫɦ ; x = 2,8 ɦ , u3 = u2 + l3 = l = 0,0184 ɫɦ .

ɗɩɸɪɚ u ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.2.3,ɝ. ȼ ɩɪɟɞɟɥɚɯ ɩɟɪɜɨɝɨ ɢ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɨɜ ɨɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ, ɚ ɜ ɩɪɟɞɟɥɚɯ ɬɪɟɬɶɟɝɨ ɭɱɚɫɬɤɚ – ɩɨ ɡɚɤɨɧɭ ɤɜɚɞɪɚɬɧɨɣ ɩɚɪɚɛɨɥɵ. ȼ ɫɟɱɟɧɢɢ, ɝɞɟ N = ς = 0, ɢɦɟɟɬɫɹ ɷɤɫɬɪɟɦɭɦ umax, ɤɨɬɨɪɵɣ ɪɚɜɟɧ:

u	max	u	2	l	0,022	1	1	12 40 0,0232 ɫɦ,

				3		1 104 20	2

ɝɞɟ l3 – ɭɞɥɢɧɟɧɢɟ ɜɟɪɯɧɟɣ ɱɚɫɬɢ ɬɪɟɬɶɟɝɨ ɭɱɚɫɬɤɚ ɫɬɟɪɠɧɹ ɞɥɢɧɨɣ ɚ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɩɪɨɩɨɪɰɢɢ:

24	12 ,	ɚ = 0,4 ɦ.
1,2 ɚ
	ɚ

ȼɫɟ ɩɨɩɟɪɟɱɧɵɟ ɫɟɱɟɧɢɹ ɩɟɪɟɦɟɳɚɸɬɫɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ Ɉɯ, ɬɨ ɟɫɬɶ ɜɧɢɡ.

Ɂɚɞɚɱɚ.2.2

Ⱦɥɹ ɫɬɟɪɠɧɹ ɫɬɭɩɟɧɱɚɬɨ ɩɨɫɬɨɹɧɧɨɝɨ ɫɟɱɟɧɢɹ, ɢɫɩɵɬɵɜɚɸɳɟɝɨ ɰɟɧɬɪɚɥɶɧɨɟ ɪɚɫɬɹɠɟɧɢɟ ɢ ɫɠɚɬɢɟ (ɪɢɫ.2.7,ɚ), ɩɨɫɬɪɨɢɦ ɷɩɸɪɵ N ɢ ς. Ɉɩɪɟɞɟɥɢɦ ɭɞɥɢɧɟɧɢɹ (ɭɤɨɪɨɱɟɧɢɹ) ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ ɢ ɜɫɟɝɨ ɫɬɟɪɠɧɹ ɜ ɰɟɥɨɦ ɢ ɩɨɫɬɪɨɢɦ ɷɩɸɪɭ ɨɫɟɜɵɯ ɩɟɪɟɦɟɳɟɧɢɣ. ȼ ɪɚɫɱɟɬɚɯ ɩɪɢɦɟɦ ȿ = 2·105 Ɇɉɚ = 2·104 ɤɇ/ɫɦ2.

Ɉɩɪɟɞɟɥɢɦ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ ɫɟɱɟɧɢɣ ɡɧɚɱɟɧɢɹ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ ɢ ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɯɚɪɚɤɬɟɪɧɵɯ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɹ, ɧɚɱɢɧɚɹ ɫ ɫɟɱɟɧɢɹ ɜɛɥɢɡɢ ɫɜɨɛɨɞɧɨɝɨ ɬɨɪɰɚ.

ɍɱɚɫɬɨɤ 3 (2 δ ɯδ 3ɦ).

ɯ = 3 ɦ , N = 0, ς = 0 ;

		ɯ = 2 ɦ , N = – 30 1 = –30 ɤɇ (ɫɠɚɬɢɟ) ;
				V	30	2 ɤɇ/ɫɦ2			20 Ɇɉɚ .
					15
ɍɱɚɫɬɨɤ 2 (1,2 d ɯd2 ɦ).
		ɯ = 2 ɦ , N = – 30 ɤɇ ,
				V	30	3 ɤɇ/ɫɦ2			30 Ɇɉɚ .
					10
		ɯ = 1,2 ɦ , N = – 30 ɤɇ ,					V = – 30 Ɇɉɚ .
ɚ)		ɯ	ɛ)	N (ɤɇ)		ɜ)	ς (Ɇɉɚ)		ɝ) u (ɫɦ)
									0,008
	3	F3=15ɫɦ2
1ɦ	3	30ɤɇ/ɦ							–
1ɦ		30ɤɇ/ɦ
						20			0,003
									0,003
ɦ	2	F2=10ɫɦ2		–			–
0,8		60ɤɇ
		60ɤɇ			30			25	0,009
			30		30	30		25	0,009
			30	+		30	+		+
1,2ɦ		F1=12ɫɦ2		+			+
	1	20ɤɇ/ɦ


	Ɉ
		R		6			5
		R
					Ɋɢɫ.2.7
ɍɱɚɫɬɨɤ 1 (0 d ɯd1,2 ɦ).
		ɯ = 1,2 ɦ , N = – 30 + 60 = 30 ɤɇ (ɪɚɫɬɹɠɟɧɢɟ) ;
				V	30	2,5 ɤɇ/ɫɦ2		25 Ɇɉɚ ;
		ɯ = 0 ,			12
		ɯ = 0 ,		N = 30 – 20 1,2 = 6 ɤɇ ;
				V	6	0,5 ɤɇ/ɫɦ2		5 Ɇɉɚ .
					12
ɗɩɸɪɵ		N ɢ V	ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ.2.7,ɛ,ɜ. ȼ ɩɪɟɞɟɥɚɯ ɩɟɪɜɨɝɨ ɢ ɬɪɟɬɶɟɝɨ
ɭɱɚɫɬɤɨɜ ɩɪɨɞɨɥɶɧɵɟ ɫɢɥɵ ɢ ɧɨɪɦɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɥɢɧɟɣɧɨ-
ɦɭ ɡɚɤɨɧɭ, ɚ ɜ ɩɪɟɞɟɥɚɯ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɚ ɨɧɢ ɢɦɟɸɬ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ. ȼ ɫɟ-
ɱɟɧɢɢ ɯ = 1,2 ɦ ɩɪɨɞɨɥɶɧɚɹ ɫɢɥɚ ɢɦɟɟɬ ɫɤɚɱɨɤ ɧɚ ɜɟɥɢɱɢɧɭ 60 ɤɇ.
Ɉɩɨɪɧɚɹ ɪɟɚɤɰɢɹ ɜ ɡɚɤɪɟɩɥɟɧɧɨɦ ɫɟɱɟɧɢɢ ɪɚɜɧɚ R = 6 ɤɇ. ȿɺ ɧɚɩɪɚɜɥɟɧɢɟ
ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ.2.7,ɚ.
Ɉɩɪɟɞɟɥɢɦ ɜɟɥɢɱɢɧɵ ɭɞɥɢɧɟɧɢɣ (ɭɤɨɪɨɱɟɧɢɣ) ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ.

l		1		30 6			120	0,009 ɫɦ;
	2 104		12
1						2
l2		30 80			0,012 ɫɦ;
		2 104 10

l3			1		1	30 100		0,005 ɫɦ;
		2 104 15
					2
l	l1 l2 l3					0,009 0,012 0,005 0,008ɫɦ.

ɋɬɟɪɠɟɧɶ ɜ ɰɟɥɨɦ ɭɤɨɪɚɱɢɜɚɟɬɫɹ.

Ɉɩɪɟɞɟɥɹɟɦ ɨɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɯɚɪɚɤɬɟɪɧɵɯ ɫɟɱɟɧɢɣ ɫɬɟɪɠɧɹ.

ɯ = 0 , u0 = 0 ;

x = 1,2 ɦ , u1 = u0 + l1 = 0,009 ɫɦ ;

x = 2 ɦ , u2 = u1 + l2 = 0,009 – 0,012 = – 0,003 ɫɦ ; x = 3 ɦ , u3 = u2 + l3 = l = – 0,008 ɫɦ .

ɗɩɸɪɚ u ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.2.7,ɝ. ȼ ɩɪɟɞɟɥɚɯ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɚ ɨɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ, ɚ ɜ ɩɪɟɞɟɥɚɯ ɩɟɪɜɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɭɱɚɫɬɤɨɜ – ɩɨ ɤɜɚɞɪɚɬɢɱɧɨɦɭ ɡɚɤɨɧɭ. ȼ ɫɟɱɟɧɢɢ ɯ = 3 ɦ ɤɚɫɚɬɟɥɶɧɚɹ ɤ ɷɩɸɪɟ u ɩɚɪɚɥɥɟɥɶɧɚ ɨɫɢ Ɉɯ. ȼ ɩɪɟɞɟɥɚɯ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɚ ɢɦɟɟɬɫɹ ɫɟɱɟɧɢɟ, ɨɫɟɜɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɤɨɬɨɪɨɝɨ ɪɚɜɧɨ ɧɭɥɸ.

Ɂɚɞɚɱɚ 2.3

ɑɭɝɭɧɧɵɣ ɫɬɟɪɠɟɧɶ ɫɬɭɩɟɧɱɚɬɨ ɩɨɫɬɨɹɧɧɨɝɨ ɫɟɱɟɧɢɹ ɡɚɤɪɟɩɥɟɧ ɧɚ ɨɛɨɢɯ ɬɨɪɰɚɯ ɢ ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɞɜɭɯ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯ ɫɢɥ (ɪɢɫ.2.8,ɚ). ɉɨɫɬɪɨɢɦ ɜ ɨɛɳɟɦ ɜɢɞɟ ɷɩɸɪɵ N, ς ɢ u ɢ ɨɩɪɟɞɟɥɢɦ ɜɟɥɢɱɢɧɭ ɫɢɥɵ 5 ɢɡ ɭɫɥɨɜɢɣ ɩɪɨɱɧɨɫɬɢ ɩɨ ɦɟɬɨɞɭ ɞɨɩɭɫɤɚɟɦɵɯ ɧɚɩɪɹɠɟɧɢɣ. ȼ ɪɚɫɱɟɬɚɯ ɩɪɢɦɟɦ F =

= 10 ɫɦ2 ɢ ɞɨɩɭɫɤɚɟɦɵɟ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɪɚɫɬɹɠɟɧɢɢ ɢ ɫɠɚɬɢɢ [ςɪ] = 80 Ɇɉɚ = = 8 ɤɇ/ɫɦ2 , [ςɫ] = 150 Ɇɉɚ = 15 ɤɇ/ɫɦ2.

	ɚ)	ɛ)		ɜ)	ɝ)
		R1	X=R1	NP	NX	X
		O				X
		O
40ɫɦ	1	F
	1
		P	P
		P	P	P
				P
30ɫɦ	2					+
	2	3P	3P
				4P
				4P
30ɫɦ	3	1,5F		–
	3			–

		R2
18		x	Ɋɢɫ.2.8
18

ȼ ɬɨɱɤɚɯ ɡɚɤɪɟɩɥɟɧɢɹ ɫɬɟɪɠɧɹ ɜɨɡɧɢɤɚɸɬ ɞɜɟ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ R1 ɢ R2. ɋɨɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ:

6ɏ = 0 , – R1 + 5 + 35 – R2 = 0 , R1 + R2 = 45.

ɉɨɥɭɱɢɥɢ ɨɞɧɨ ɭɪɚɜɧɟɧɢɟ ɫ ɞɜɭɦɹ ɧɟɢɡɜɟɫɬɧɵɦɢ. Ⱦɚɧɧɵɣ ɫɬɟɪɠɟɧɶ ɹɜɥɹɟɬɫɹ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɦ, ɢ ɞɥɹ ɟɝɨ ɪɚɫɱɟɬɚ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɫɥɨɜɢɟ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɹ l = 0. Ɋɚɫɤɪɨɟɦ ɷɬɨ ɭɫɥɨɜɢɟ ɫ ɩɨɦɨɳɶɸ ɩɪɢɧɰɢɩɚ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɞɟɣɫɬɜɢɹ ɫɢɥ.

Ɉɬɛɪɨɫɢɦ ɦɵɫɥɟɧɧɨ ɨɞɧɨ ɢɡ ɡɚɤɪɟɩɥɟɧɢɣ, ɧɚɩɪɢɦɟɪ, ɜɟɪɯɧɟɟ, ɢ ɜɜɟɞɟɦ ɜ

ɷɬɨɦ ɫɟɱɟɧɢɢ ɧɟɢɡɜɟɫɬɧɭɸ ɫɢɥɭ ɏ = R1 (ɪɢɫ.2.8,ɛ). ɉɪɨɢɡɜɟɞɟɦ ɪɚɫɱɟɬ ɩɨɥɭɱɟɧɧɨɝɨ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɝɨ ɫɬɟɪɠɧɹ ɪɚɡɞɟɥɶɧɨ ɧɚ ɞɟɣɫɬɜɢɟ ɡɚɞɚɧɧɵɯ ɧɚɝɪɭɡɨɤ ɢ ɫɢɥɵ ɏ. ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɷɩɸɪɵ ɩɪɨɞɨɥɶɧɵɯ ɫɢɥ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ.2.8,ɜ,ɝ. ɉɪɢ ɷɬɨɦ ɜɟɥɢɱɢɧɵ ɭɞɥɢɧɟɧɢɣ ɢ ɭɤɨɪɨɱɟɧɢɣ ɫɬɟɪɠɧɹ ɪɚɜɧɵ:

lɊ

ȇ 30

4ȇ 30

100

;

E 1,5F E 1,5F

lɏ

X 40

X 60

E 1,5F

ɂɫɩɨɥɶɡɭɟɦ ɭɫɥɨɜɢɟ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɹ ɢ ɧɚɯɨɞɢɦ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ.

lɊ lɏ

100

X R1 1,25ȇ,

4ȇ R1

2,75ȇ.

Ɉɩɪɟɞɟɥɹɟɦ ɡɧɚɱɟɧɢɹ N, ς ɢ l

ɜ ɩɪɟɞɟɥɚɯ ɭɱɚɫɬɤɨɜ ɫɬɟɪɠɧɹ.

ɍɱɚɫɬɨɤ 1.

N R 1,25ȇ ,

ς 1,25

;

1,25ȇ 40

ɍɱɚɫɬɨɤ 2.

1,25ȇ ȇ

0,25ȇ ,

0,25

0,167

;

1,5F

0,25ȇ 30 5

E 15, F

ɍɱɚɫɬɨɤ 3.

2,75ȇ , ς 2,75

1,83

;

1,5F

2,75ȇ 30

E 1,5F

ɉɪɨɜɟɪɢɦ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɹ.

l	l l	2	l		ȇ 50 5 55 0.
	1	2	3	EF
				EF
Ɂɚɞɚɱɚ ɪɟɲɟɧɚ ɩɪɚɜɢɥɶɧɨ. ɗɩɸɪɵ N ɢ ς ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ.2.9,ɛ,ɜ.
Ɉɩɪɟɞɟɥɹɟɦ ɨɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɯɚɪɚɤɬɟɪɧɵɯ ɫɟɱɟɧɢɣ.
ɯ = 0 ,			u = u0 = 0 ;			= 50 ȇ ;
ɯ = 40 ɫɦ ,			u1 = u0		+ l1	= 50 ȇ ;
							EF
ɯ = 70 ɫɦ ,			u2 = u1		+ l2	= ȇ 50 5 55 ȇ ;
ɯ = 100 ɫɦ ,			u3 = l = 0 .				EF		EF
ɯ = 100 ɫɦ ,			u3 = l = 0 .
ɚ)			ɛ)	N 1,25Ɋ			ɜ)		ɝ)
	R1=1,25Ɋ			N 1,25Ɋ			ς 1,25	Ɋ	u
O								F
O

1		+	+
	P			50	Ɋ
				50	Ɋ
					ȿF
2	3P			+
	3P	0,25Ɋ	Ɋ		Ɋ
		0,25Ɋ	Ɋ		Ɋ
			0,167F	55ȿF
3		–	–
	R2=2,75Ɋ 2,75Ɋ		Ɋ
	R2=2,75Ɋ 2,75Ɋ		1,83F
	x
		Ɋɢɫ.2.9

ɗɩɸɪɚ u ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.2.9,ɝ. Ɉɫɟɜɵɟ ɩɟɪɟɦɟɳɟɧɢɹ ɢɡɦɟɧɹɸɬɫɹ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ. ȼɫɟ ɩɨɩɟɪɟɱɧɵɟ ɫɟɱɟɧɢɹ ɩɟɪɟɦɟɳɚɸɬɫɹ ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ Ɉɯ, ɬɨ ɟɫɬɶ ɜɧɢɡ.

ɂɫɩɨɥɶɡɭɟɦ ɭɫɥɨɜɢɹ ɩɪɨɱɧɨɫɬɢ ɩɨ ɧɚɢɛɨɥɶɲɢɦ ɪɚɫɬɹɝɢɜɚɸɳɢɦ ɢ ɫɠɢɦɚɸɳɢɦ ɧɚɩɪɹɠɟɧɢɹɦ (ɩɟɪɜɵɣ ɢ ɬɪɟɬɢɣ ɭɱɚɫɬɤɢ) ɢ ɨɩɪɟɞɟɥɢɦ ɞɨɩɭɫɤɚɟɦɵɟ ɡɧɚɱɟɧɢɹ ɫɢɥɵ 5.

ςp

1,25

δ[ςɪ]

8 ɤɇ/ɫɦ2 ,

ȇδ 64 ɤɇ;

ςc

1,83

δ[ςc ]

15 ɤɇ/ɫɦ2 ,

ȇδ81,8ɤɇ.

ɂɡ ɞɜɭɯ ɞɨɩɭɫɤɚɟɦɵɯ ɡɧɚɱɟɧɢɣ ɫɢɥɵ ɧɚɞɨ ɩɪɢɧɹɬɶ ɦɟɧɶɲɟɟ: 5 = 64 ɤɇ.

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