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1

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6 GL

7

8 (a) (b)

9 Ph l P N P h l l Ph Ph Ph Ph l l l l P Ph l P N h l P l

10 .9 αl B βlt D E. 5.5 L r..8

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13 e g s e,e l l W l s l g W W s g l l W W e s g e s g r e l ( s ) l ( l s ) r e l ( s ) l ( l s ) e R e r e e R e r e

14 g g W W W W ( A i i ) 8( A i i ) A i 8 A i ( A i i ) 8( A i i ) A i 8 A i, (, ) i i i i i, i R e R e R e R e ( B C.R ( e.5

15 αl B βlt p L r q D

16

17

18 .8m.8m.8m.8m.8m.9m.8m.8m.8m.96m kg/m.96m 888kg 8.N.8m 6.8m kg/m 6.8m 9kg 95.N

19 z

20 s s s 5..6 s..

21 A W 5 Ai i W 5 A.96 G i W G W W W A i A A i i i i G A i W A i i G W A i A A

22 e S G e S G r e l ( s) l ( l s ) r e l ( s) l ( l s ) e.75 R e. 86 r. e R e r e e.7 R e R e (.5.) B C.R.5 B C B C e e S G e S G..

23 r e l ( s ) l ( l s ) r e l ( s ) l ( l s ) R e e r e e R e r.9 e R e R e (.5.) B C.R.5 e B C B C B C. 5 B C.

24 αl B L r.5a.8a m.8m αl B m.6m.8m αl B m.8m αl B..8.8m αl B m.6 D E m αl B..8.8m m.8m αl B m m.8m αl B m m.8m αl B m αl B m

25 5. D E L r

26

27 W W kg / m kg / m kg kg

28 .9m.8m A F E A G F E I.8m H B C (a) D B C D (b) PmαFPP P P P αw P αw P α kg/m P P P P P αw αw 6kg 588N

29 P PA P P A B A B C B A.9.7.m C C A B C A A A A B C.5.9.5m.5.9.5m.9.9.8m abc A A a A A B b A A C c A B A C m m m P P P A B C P a 98N P b 9N P c 9N.9m.9m z.8m

30 N N.8m /rad 8cm.59cm 9cm δ P P u P u P l l rad rad u

31 k -ku ku ( - ) ku -ku ( - )

32 ku - ku -ku ku k k k u k u {} [K] k k k k {} u u {} [ K]{} δ { } vj, vj pj, pj j pi pj k k k δ k δ vi δ vj δ vi vj pi pj pi pi i vi vi pi vi vj k k pj k k δ δ δ δ pi vi pj vj

33 pi vi i cos θ i sin θ sin θ cos θ i i pj vj j cos θ j sin θ sin θ cos θ j j δ δ pi vi u pi cos θ v vi sin θ u sin θ v cos θ pi vi δ δ pj vj u pj cos θ v vj sin θ u sin θ v cos θ pj vj pi vi pj vj cos θ sin θ sin θ cos θ cos θ sin θ sin θ cos θ i i j j δ pi cosθ δ vi sin θ δ pj δ vj sin θ cosθ cosθ sin θ u v sin θ u cosθ v pi vi pj vj {} pi vi pj vj,{ } i i j j,{ δ} δpi δ vi δ pj δ vj,{ δ} δ δ δ δ i i j j u pi v vi, u pj v vj [ K] k k cosθ sin θ sin θ cosθ [ T] k k cosθ sin θ sin θ cosθ { } [ K ] { δ}

34 {} [ T]{} {} δ [ T]{} δ [ T]{} [ K ][ T]{} δ T {} [ T] [ K ][ T]{} δ [ K ]{} δ [ K] [ T] π θ [ ] T a θ [ T] [ K] [ T] [ K][ T] k u v u v

35 v u v u k v u u v u v k v u v u v u k F F,

36 v u 5 k F δ K K bb ba ab aa b a 5 k F K K { } [ ]{} δ aa a K { } [ ]{} δ ba b K {} [ ] { } a aa K δ δ K K bb ba ab aa b a { } [ ]{} δ aa a K { } [ ]{} δ ba b K {} [ ] { } a aa K δ K K F k 5 k k k v u k F k 5F v u

37 k k k u k v k kv F ku kv F F ku kv σ σ, σ z, τ, τ, τ z, τ z, τz,, τ z

38 X z Y dz Z σ τ z τ P X σz σz dz z τz τz dz z τz τz dz z τ σ z τz d τ τ σ z τ σ d z d τ z τ τ τ d τ d σ σ d τ z τ z d Y σ z d Z σ,,z), τ (,,z), τ (,,z) ( z σ,,z), τ (,,z), τ (,,z) ( z σ,,z), τ (,,z), τ (,,z) z( z z σ d,,z), τ ( d,,z), τ ( d,,z) ( z σ, d,z), τ (, d, z), τ (, d,z) ( z σ,,z dz), τ (,,z dz), τ (,,z dz) z ( z z ( d, d,z dz) (,,z) d d dz z

39 σ τ τ z σ τ τ z σ τ τ z z z ( d,,z) σ (,,z) ( d,,z) τ (,,z) σ d, τ d, τ z ( d,,z) τ (,,z) d z (, d,z) σ ( (, d,z) τ (,,z) z σ,,z) d, τ z d, (, d,z) τ (,,z) d (,, z d) σ (,, z) (,, z d) τ (,, z) z z τ σ z dz, z τ z dz, z τ z (,, z d) τ (,, z) dz z z σ ddz τ ddz τ dd σ τ τ σ d ddz d ddz z τ τ z F dddz z z dz dd

40 Z Y τ z d ddz τ X d X σ τz d ddz σ σ d ddz τz τ z dz dd z Y τ ddz d dddz σ τ τ z z F τ τ z σ τ z τ z z σ z z F F z ddz σ τ z dd τ τ zdd τ z dd ddz σ ddz σ ddz dd ddz σ τ z

41 d σ ddz σ d τzdd d ddz τz d τzdd τ τ τ dd d τ z ddz d τ dd d σ ddz ddz d d σ ddz d τ z τ z τz τ z σ τ τ z τ σ τ z τ z z τ z z σ z z F, F, F z ε u u τ τ

42 D D C v u γ θ θ B A v u v u ε γ A u B ε ε z v w z γ γ z z w v z u w z C σ Eε σ ε' ε E ε σ E σ ε ε E σ ε z ε E ε ε σ,ε σ,ε ε z ε

43 { σ ( σ σ )}, ε E ε z E ε z z E { σ ( σ σ )}, { σ ( σ σ )} τ τ τ z z E γ ( ) E ( ) E ( ) γ γ z z z γ G τ γ z τ z G γ z τ z G ε ε ε z γ E γ z γ z ( ) ( ) σ σ σ z τ τ ( ) τ z z

44 ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) z z z z E E γ τ γ τ z z z E E E E γ τ ε ε ε σ σ ε ε ε σ z ε ε ε ( ) ( )( ) ( ) ( ) ( ) z z γ τ τ z z z E γ γ ε ε ε τ σ σ σ z { } σ z τ σ σ σ { } z z τ τ ε z γ ε ε ε z z γ γ { } [ ]{} ε σ D {} [ ] { } D σ ε

45 W u W u du u O u u W du u du U W u u U du u dσ ddz σ ddz u ε d W O k, u U z d d W u u u u dz

46 U u σ ε dddz U σ ε dddz σ ε V dv U σ ε dv V τ u γ d ddz U u U τ γ dddz τγ dv V U ( σ ε σ ε σzεz τγ τ zγ z τzγ z ) V dz { σ } σ σ σ z τ τ z τ z { ε} ε ε ε z γ γ z γ z T U {}{ ε σ }dv V dv U z d d u γ

47 δu δv δw z z ( Pδu Pδv Pzδw ) ds ( F δu Fδv Fz δw) dddz ( σδε σ δε σzδεz τδγ τ zδγ z τzδγ z ) dddz δε δε δε δε z δε δε δγ ( δu) ( δv) ( δu) ( δv) ( δw) ( δv) ( δw) ( δu) ( δw) z δγ δγ δγ z z z z z δγ z δγ z P F δu * {} P P, {} F F, { δ } δv δ Pz Fz w

48 { } { }, z z z z z z * τ τ τ σ σ σ σ δγ δγ δγ δε δε δε ε { } {} { } {} { }{ } σ ε δ δ dv dv F ds P T T

49 E

50 8t/cm σ kg/cm. mm W W 8.N / m 95.N / m ( kg)

51 .8m8.59.cm 9. cm P αα P P 588N P 9N P P 76N P 8N 588N.96m A.5m.5 PA N P B 588 9N.96. PC 588 5N.96 B 6.8m.m C

52 9N 6.8m D.6m P P P D E F N N N 6.8 E F.m.6m 76N.96m G H I J P P P P G H I J. 76 9N N N N.96.m.86m.m.6m K L 8N 6.8m P P K L. 8 9N N 6.8.m.m

53 cm N min 6.5. uz min -.5cm uz ma.9 - cm (m)

54 N min -.9kN (N) M mi -.6kN n M ma.8kn (Nm)

55 u ma

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58 (N)

59 α P P u P PP /rad cm 9cmP P P u P u 5kN P 5kN P 68kN P u 8kN

60 P 75kN P kn P 5kN P u 77kN α P W P u 5kN α u W 5.88 P u P u 7kN () P 68kN α P W 68.9.

61 P u 8kN α u P u W P75kN P Pu77kN α W α u P u W () P kn α P W.9 P u 7kN α u 578. W.9 P u α α u

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[Ver. 0.2] 1 2 3 4 5 6 7 1 1.1 1.2 1.3 1.4 1.5 1 1.1 1 1.2 1. (elasticity) 2. (plasticity) 3. (strength) 4. 5. (toughness) 6. 1 1.2 1. (elasticity) } 1 1.2 2. (plasticity), 1 1.2 3. (strength) a < b F

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(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0 1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45

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66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI 65 8. K 8 8 7 8 K 6 7 8 K 6 M Q σ (6.4) M O ρ dθ D N d N 1 P Q B C (1 + ε)d M N N h 2 h 1 ( ) B (+) M 8.1: σ = E ρ (E, 1/ρ ) (8.1) 66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3)

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.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

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