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- このか さかど
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1 [Ver. 0.2]
2
3 1 1.1
4
5 (elasticity) 2. (plasticity) 3. (strength) (toughness) 6.
6 (elasticity) }
7 (plasticity),
8 (strength) a < b F a < F b [N/mm 2 ] = F [N] [mm 2 ] F a F b [N/mm 2 ] [MPa] 1[N/mm 2 ] = 1 [N] 1 [mm 2 ] = 1 [N] ( ) 2 [m 2 ] = [N/m 2 ] = [Pa] a b = 1[MPa] F a (a) F b (b) (a) a = 50 [mm 2 ] F a = [N] [N] = 50 [mm 2 = 400 [MPa] ] (b) b = 200 [mm 2 ] F a = [N] [N] = 200 [mm 2 = 200 [MPa] ] (b) (a)
9
10 (toughness)
11
12
13
14 C Mn Si P S Cu l Sn P S C % carbon steel steel % SS SS400 1 S steel 2 S structure SC S45C 1 S steel C carbon 100 S45C %
15
16 Ni Cr Mn Mo V
17 cast iron 2
18 Cu Zn Zn 30 % Zn 40 % 2 Cu Sn P
19 / C l Cu-Mg Cu-Mg-Mo
20 Cr 12 % stainless steel Cr Cr 17 % Ni C P N l Ti Ni Co
21
22 (load) 2. (stress)
23 (load) (a) (tension) (b) (compression) (c) (bending) (d) (shear) (e) (torsion) (f) (buckling)
24 (stress) W σ [mm 2 ] [N] [N/mm 2 = MPa] [mm 2 ] σ [N] W [N] W = σ [N] (2.1) σ = W [N/mm2 = MPa] (2.1) W σ σ W
25 1 20 mm N d = 20 [mm] W = [N] σ W = σ σ = W = W (π/4)d 2 = (π/4) 20 2 = [N/mm2 ] = 156[MPa] d W W C W = 8000 [N] 8000 [N] 8000 [N] ϕ25 ϕ20 C σ 1 d 1 = 25 [mm] σ 1 = W W = 2 1 (π/4)d = (π/4) 25 2 = 16.3 [N/mm2 = MPa] C σ 2 d 2 = 20 [mm] σ 2 = W W = 2 2 (π/4)d = (π/4) 20 2 = 25.5 [N/mm2 = MPa]
26 2 2.2 ε λ = l l l ε = l l l = λ l (2.4) [mm] [mm] ε δ = d d d ε = d d d = δ d (2.5) W ν (Poison s ratio) d l d l ν = ε ε (2.6) W ν 1/ν
27 3 10 mm 150 mm 1950 N mm d = 10 [mm], l = 150 [mm], W = 1950 [N], λ = [mm] ε ε = λ l = = = mm 500 mm 3800 N 0.08 mm 0.3 d = 12 [mm], l = 500 [mm], W = 3800 [N], λ = 0.08 [mm], ν = ε ε = δ/d = 0.3 δ λ/l δ = νλd = = = [mm] l 500 W d l d l W
28
29 W W W λ W σ ε W λ l 0 W 2 W 1 W 3 l 0 l 1 l 2 l 3 W 1 λ 0 = 0 λ W 2 1 = l 1 l 0 λ W 3 2 = l 2 l 0 λ 3 = l 3 l 0 σ = W σ σ 3 W 2 σ 2 W 1 ε = λ l 0 = σ 1 λ 1 λ 2 λ 3 λ ε 1 ε 2 ε 3 ε
30 W λ W 5 W 4 W 3 W 2 W 1 W 5 l 0 l 1 l 2 l 3 l 4 l 5 W W 4 W 3 W 1 λ 0 = 0 λ W 2 1 = l 1 l 0 λ W 3 2 = l 2 l 0 λ 3 = l 3 l 0 W 4 W 2 W 1 λ 4 = l 4 l 0 W 5 λ 5 = l 5 l 0 λ 1 λ 2 λ 3 λ 4 λ λ 5
31 W λ σ ε W P E σ σe σ P E P E λ O O ε P σ P E σ E E E E O OO
32 σ σ σ Y1 σ Y2 Y 1 M Z E Y 2 P Z O ε Y 1, σ Y1 Y 2 σ Y2 M σ
33 σ (0.2%) σ 0.2 O ε % σ 0.2
34 σ ε σ = Eε (E ) (2.7) E 2.1 E σ [Pa] ε [GPa] 1 [GPa] = [MPa] E (stifness) σ = W/ ε = λ/l σ σ E W = E λ l σ P E P (2.9) σ σ σ Y1 σ Y2 E P Y 1 M Z Y 2 Z ε O ε
35 5 20 [mm] 200 [mm] [N] 192 [GPa] a = 20 [mm] = = a 2 = 20 2 [mm 2 ], l = 200 [mm], W = [N], E = 192 [GPa] = [MPa] (2.9) λ = W l E = 20 2 = = [mm] [mm] 800 [mm] 0.2 [mm] 200 [GPa] d = 15 [mm], l = 800 [mm], λ = 0.2 [mm], E = 200 [GPa] = [MPa] (2.7) (2.4) σ = Eε = E λ l = = 50 [MPa]
36 7 I 35 [mm] 50 [mm] II 30 [mm] [kn] 200 [GPa] 100 [GPa] 2.15 I II σ 1 σ I II W = σ σ 2 2, ε = σ 1 = σ 2 E 1 E = π 4 ( )σ 1 + π σ σ = σ σ 1 = 2σ 2 σ 2 = (π/4){( ) } σ 1 = 2σ 2 = 88.6 [MPa] = 44.3 [MPa] 1 2 W = 120kN
37 2 2.4 τ W W W W = τ (2.10) W τ = W (2.10) τ τ [N/mm 2 = MPa] W
38 mm N d = 18 [mm], W = [N], a a = π 4 d2 = π [mm 2 ], (2.10) a 2 τ = W = W 2a = ( π ) = 39.29[MPa] mm 40 mm 350 MPa d = 40 [mm], t = 1.5 [mm], τ = 350 [MPa], 2.21 = πd t = πdt (2.10) W = τ = τ πdt = 350 (π ) = = [N]
39 W 1 W W 2 W W 3 W W W W = = = 6
40 2 2.5 W W W C W W l W C γ γ = tan ϕ = C ϕ ϕ tan ϕ ϕ γ = C = l l W l ϕ = tan ϕ ϕ (2.11) τ γ τ = Gγ (G ) (2.12) G 2.2 G τ [Pa] E [GPa] C ϕ
41 2 2.5 τ τ C C τ τ C τ τ τ τ 2 τ τ N N N 1 τ τ τ τ τ τ τ = τ (2.13) τ C τ N N τ 10 τ 160 MPa 80 GPa τ = 160 [MPa], G = 80 [GPa] = [MPa] τ = Gγ γ = tan ϕ ϕ ϕ = τ G = 160 = [rad]
42 2 2.6 σ a = σ f (2.14) 2.3
43
44
45 fatigue 2.24 b S N W öhler σ e JIS Z % 50%
46 a σ 0 (= W/ ) σ ma = α (2.15) α σ r 2
47 creep 623 K 350 C % 1 10
48
49 11 SS N/mm N 3 σ = 235 [MPa], W = 8000 [N], f = 3 σ a = σ f = [MPa] πd 2 (2.1) W = σ a = σ a 4 4W d = = = [mm] πσ a π kn 80 MPa W = 10 [kn], σ a = 80 [MPa] W = σ a = σ a 2 W = = = [mm] σ a 80
50 MPa 10 kn 5 σ e = 200 [MPa], W = 10 [kn] = = [N], f = 5 ( π ) W = σ a = σ a 4 d2 σ a = σ e f 4W 4W f d = = = = [mm] πσ a πσ e π mm 40 mm 12 kn 2.26 r = 2 [mm], = 40 [mm], W = 12 [kn] = = [N] r = 2 40 r = 2.26 α = W σ ma = ασ 0 = α (π/4) ( 2r) 2 = = = 30.7 [MPa] (π/4) (40 2 2) 2 α r 2
51
52 3 3.1 a W θ W X X W X X θ X θ X X = / sin θ X X W p X X θ X W = p = p sin θ p c X X σ W a W τ σ = p sin θ = W sin θ sin θ = W sin2 θ 3.1 τ = p cos θ = W sin θ cos θ = W sin 2θ sin θ θ = 90 = π/2 [rad] = σ X p p b W X σ ma 2.1 σ σ ma = W θ = θ X sin 2θ θ = 45 = π/4 [rad] 3.2 τ 45 τ ma τ ma = W 2 = σ ma 2 θ = X τ τ p p σ c σ
53 1 30 mm N 45 τ ma = σ ma 2 = 10000/ { (π/4) 30 2} 2 = [N/mm 2 ] = 7.07 [MPa] W τ τ 1 30 mm N σ = W sin2 θ = W (π/4)d 2 sin2 θ = = [N/mm 2 ] = 4.66 [MPa] (3.14/4) 30 2 sin τ = W sin 2θ 2 = W sin 2θ (π/4)d2 2 = [N/mm 2 ] = 6.65 [MPa] = sin 70 (3.14/4) 302 2
54 3 3.2 τ σ c σ t ( τa 2 ) 2 + ( τa 2 ) 2 = (σ c 2a a ) 2 τ = σ c τ = σ t
55 3 3.3 W W W W (b) w V = m = ρv = ρ w = mg = ρg W + w = σ W + ρg = σ σ = ρg + W (3.7) σ = 0 ( ) = l ( ) { λ ( (3.4) (3.7) W + ρgl + W )} /2 λ = lε = l σ E = l E ρgl + 2W 2 (3.8) l W W (a) σ σ V w W (b)
56 ( 7800 [kg/m 3 ] ) σ kg/mm 3 σ 1 = (π/4) (π/4) 60 2 = 3.60 [MPa] σ 2 σ 2 = (π/4) ( ) 9.8 (π/4) 80 2 = 2.10 [MPa] L 2 d 2 L 1 d 1 W
57 3 3.4 λ σ σ λ ( σ = W ) h 3.9 λ 3.9 h = 0 σ = 2 W = 2σ 3.10 σ σ 2
58 3 3.5 = l t[k] α l l = lα t 3.11 ε ε = l l + l l l l (l + l) l l l l σ = Eε = Eα t 3.12 l l
59 4 70 mm 80 mm 500 mm 50 K 50 C 200 GPa K 1 W W = σ = (Eα t) = π ( ) 4 = [N] = 141 [kn]
60 3 3.6, y, z ε z = σ z E σ + σ y me 3.13 ε = σ E σ y + σ z me, ε y = σ y E σ z + σ me 3.14 σ = σ y = σ z σ ε ε(ε = ε y = ε z ) = σ ( 1 2 ) 3.15 E m
61 6 180 mm 60 mm GPa ( ) 10/3 l z = 180 mm, l = l y = 60 mm l z ε z σ z 90 kn ( σz l z = l z ε z = l z E σ ) y = l ( z me E σ z σ ) y m = l ( z E Wz W y 1 ) = l ( z y z m E Wz W y 1 l l y l l z m ( = = = [mm] ) )
62
63 4 4.1 beam a b c d e a b c d e
64 4 4.2 (SF) (M) 1. 2.
65 { R 1 R 2 R 1 + R 2 W = 0 a l R 2 l 1 W = 0 b l 1 W a b 0 < < l 1 R 1 c F X τ F = +R 1 d F F = +R 1 W e SF l W R 1 R 2 X W a R 1 R 2 b R 1 c F τ W F X a (+) X ( ) X b X d R 1 F [N] e 0 (+) +R 1 R 2 X ( )
66 X b 0 < < l 1 R 1 M = R 1 a R C 1 R l 2 W X c b R 1 R d l 1 < < l R 1 W 2 M = +R 1 W ( l 1 ) M = +R 1 c l 1 W e M 0 < < l 1 :M = +R 1 d l 1 < < l : M = +R 1 R 1 W ( l 1 ) M M +M X (a) M X (b) e 0 l 1 W (+) M = +R 1 X W ( l 1 ) +R 1 l 1 l
67 1 b { R 1 R 2 R 1 + R = 0 (a) 1800 R = 0 (b) R 2 = = 2000 [N], 1800 R 1 = 5000 R 2 = 3000 [N] c 0 < < l 1 F = R 1 = [N] d l 1 < < l F = R 1 W = = 2000 [N] e SF { 0 < < l 1 : F = [N] l 1 < < l : F = 2000 [N] c a 5000 N l 1 = l = 1800 mm 5000 N b C 3000 N 2000 N 3000 N X 5000 N f M d 0 < < l 1 : M = +R 1 = N X l 1 < < l : F M = +R 1 W ( l 1 ) [N] (+) 2000 N = (W R 1 ) + W l e 1 0 = ( ) ( ) N = M 2, 160 [N m] [N m] C = l 1 f M C = +R 1 l 1 = 3, = 2, 160, 000 [N mm] = 2, 160 [N m]
68 1 4.6 SF 0 < < l 1 : F = 0 l 1 < < l 1 + l 2 : F = W 1 = 1000 [N] l 1 + l 2 < < l : F = W 1 W 2 = = 3000 [N] M 0 < < l 1 : M = 0 l 1 < < l 1 + l 2 : M = W 1 ( l 1 ) l 1 + l 2 < < l : M = W 1 ( l 1 ) W 2 ( l 1 l 2 ) C : M C = 0 : M = = 300, 000 [N mm] : M = = 1, 500, 000 [N mm] W 1 = 1000 [N] W 2 = 2000 [N] l 1 = 200 l 2 = [mm] F 0 M [N] 300 [N m] 3000 [N] l = 900 1, 500 [N m] ( ) ( )
69 1 [mm] wl [N] w [N/mm] l [mm] w [N/mm] l [mm] W = wl [N] W = wl [N] l/2 l [mm] W = wl [N] l/2 l [mm]
70 l 1 l 2 l R 1 R 2 1 2{ R 1 + R 2 W 1 W 2 = 0 (a ) l R 2 l 1 W 1 (l 1 + l 2 ) W 2 = 0 (b ) W 1 W 2 2 { W = w l 2 [N] R 1 + R 2 w l 2 = 0 (c ) l R 2 (l 1 + l 2 /2) (w l 2 ) = 0 (d ) w [N/mm] l 1 l 2 l W = w l 2 [N] l 1 + l 2 /2 l 3 W 2 = w l 3 [N] 1 W 1 w [N/mm] l 1 l 2 l 3 l W 1 W 2 l 1 l 2 + l 3 /2 l
71 SF { R 1 R 2-1 R 1 + R = 0 (a ) 740 R ( ) 1000 = 0 (b ) R 2 = = 900 [N], R 1 = 2200 R 2 = 1300 [N] < < l 1 : F = R 1 = [N] l 1 < < l 1 + l 2 : F = R 1 W 1 = = +100 [N] l 1 + l 2 < < l : F = R 1 W 1 W 2 = = 900 [N] M 0 < < l 1 : M = +R 1 l 1 < < l 1 + l 2 : M = +R 1 W 1 ( l 1 ) l 1 + l 2 < < l : M = +R 1 W 1 ( l 1 ) W 2 ( l 1 l 2 ) : M = 0 C : M C = +130R 1 = 169, 000 [N mm] : M = +510R = 207, 000 [N mm] : M = +740R = 0 W 1 = 1200 N W 2 = 1000 N l 1 = 130 l 2 = F [N] 0 M l = N (+) +100 N 900 N ( ) 169 [N m] 207 [N m] [mm] [mm] 0
72 2 p.63 1 SF w F F = w [N] w [N/mm] M F 0 w [N] l wl [N] ( ) [mm] [mm] w w /2 M = w 2 = w2 [N m] 2 w [N] w [N] l M 0 w2 2 [N m] /2 wl2 2 [N m] ( )
73 3 p.64 2 SF R 1 R 2 R 1 = R 2 = wl/2 [N] F F = R 1 w = wl/2 w [N] w [N] w [N/mm] F 0 l +wl/2 w [N] (+) +wl/2 [N] l/2 wl/2 [N] ( ) [mm] M R 1 w R 1 w /2 M = R 1 w 2 = R 1 w2 = w wl 2 = w 2 (2 l) { = w ( ) } 2 l 2 l + + w ( ) 2 l = w ( l ) 2 + w l2 [N mm] w [N] M R 1 [N] wl 2 /2 8 [N m] (+) M 0
74 w = 5 [N/mm] W = 2000 [N] 700 C [mm] C 0 < < 700 F = F C = w F = 0, F C = = 3, 500 [N] M = M C = w2 2 M = 0, M C = w [N] = 1, 225, 000 [N mm] W = 2000 [N] /2 C
75 C 700 < < 1500 F = F C = w W F C = 3, 500 2, 000 = 5, 500 [N], F = , 000 = 9, 500 [N] M = M C = w2 2 M = W ( 700) 2, = 7, 225, 000 [N mm] w [N] C W = 2000 [N] / F 0 ( ) 7500 [N] 2000 [N] M 0 ( ) [N m] [N m]
76 R, R C F M C M C SF M M ma 3 [N/mm] 600 C [mm] l = 1000 [mm], l 1 = 600 [mm] l 1 /2 = 300 [mm] wl 1 R 1 + R 2 wl 1 = 0, lr 2 wl 2 1 /2 = 0 R 2 = wl 1 2 = = 540 [N] 2l R 1 = wl 1 R 2 = = 1260 [N] wl 1 [N] 3 [N/mm] l 1 /2 C R 1 R
77 C 0 < < 600 F = F C = R 1 w F = R 1 = 1, 260 [N], F C = 1, = 540 [N] M = M C = R 1 w2 2 M = 0, M C = 1, = 216, 000 [N mm] 2 w [N] 3 [N/mm] /2 C R 1 R C 600 < < 1000 F = F C = R 1 wl 1 = 1, = 540 [N] M = M C = R 1 wl 1 ( l 1 /2) M = 0 wl 1 [N] 3 [N/mm] C R 1 l 1 / R
78 M ma M C 0 < < 600 F F C F = 0 F = R 1 w = 0 = R 1 1, 260 = = 420 [mm] w 3 F 3 [N/mm] 600 C [N] [mm] 0 M (+) 420 ( ) 540 [N] [N m] [N m] 0 (+)
79 1 SF M W 1 = 1200 N W 2 = 1400 N l = 1200 mm l 1 = 200 mm l 2 = 700 mm (1) W 1 W 2 l 1 l 2 C l (2) W 1 W 2 l 1 l 2 C l (3) W 1 W 2 l 1 l 2 C l
80 1 W 1 = 1200N W 2 = 1400N l = 1200mm l 1 = 200mm l 2 = 700mm (1) W 1 W 2 l 1 l 2 C l R R R W 1 W 2 l 1 l 2 C l R R + R = R = R = = 1250 [N], 1200 R = 2600 R = 1350 [N] F M C 0 < < l 1 R W 1 W 2 l 1 l 2 C X R F = R = 1350 [N] M = R = 1350 C M C = = 270, 000 [N mm] = 270 [N m]
81 C l 1 < < l 1 + l 2 R W 1 W 2 l 1 l 2 C X R F = R W 1 = 150 [N] M = R W 1 ( l 1 ) = , 000 M = 375, 000 [N mm] = 375 [N m] l 1 + l 2 < < l W 1 W 2 l 1 l 2 R C X R F = R W 1 W 2 = 1250 [N] M = R W 1 ( l 1 ) W 2 ( l 1 l 2 ) SF M = , 500, 000 W 1 W 2 l 1 l 2 C l [mm] F 1350 [N] 0 M 0 (+) 150 [N] 270 [N m] 1250 [N] 375 [N m] (+) ( )
82 1 W 1 = 1200N W 2 = 1400N l = 1200mm l 1 = 200mm l 2 = 700mm (2) W 1 W 2 l 1 l 2 C l F M C 0 < < l 1 W 1 W 2 l 1 l 2 C X F = 0 M = 0 C l 1 < < l 1 + l 2 W 1 W 2 l 1 l 2 C X F = W 1 = 1200 [N] M = W 1 ( l 1 ) = , 000 M = 840, 000 [N mm] = 840 [N m]
83 l 1 + l 2 < < l W 1 W 2 l 1 l 2 C X F = W 1 W 2 = 2600 [N] M = W 1 ( l 1 ) W 2 ( l 1 l 2 ) = , 500, 000 M = 1, 620, 000 [N mm] = 1, 620 [N m] SF M W 1 W 2 l 1 l 2 C l F [N] 2600 [N] ( ) M [N m] ( ) 1, 620 [N m]
84 1 W 1 = 1200N W 2 = 1400N l = 1200mm l 1 = 200mm l 2 = 700mm (3) W 1 W 2 l 1 l 2 C l R R R W 1 W 2 l 1 l 2 C l R R + R = R = R = = 2133 [N], 900 R = 2600 R = 467 [N] F M C 0 < < l 1 R W 1 W 2 l 1 l 2 C X R F = R = 467 [N] M = R = 467 C M C = = 93, 333 [N mm] = 93.3 [N m]
85 C l 1 < < l 1 + l 2 R W 1 W 2 l 1 l 2 C X R F = R W 1 = 733 [N] M = R W 1 ( l 1 ) = , 000 M = 420, 000 [N mm] = 420 [N m] l 1 + l 2 < < l R W 1 W 2 l 1 l 2 C R X F = R W 1 + R = 1400 [N] M = R W 1 ( l 1 ) + R ( l 1 l 2 ) SF M = , 680, 000 F 0 M 0 W 1 W 2 l 1 l 2 C 467 [N] ( ) 93.3 [N m] l 1400 [N] ( ) (+) 733 [N] 420 [N m]
86 2 SF M w = 4 N/mm l = 800 mm l 1 = 150 mm l 2 = 400 mm (1) l 1 l 2 C l w [N/mm] (2) l 1 l 2 C l w [N/mm] (3) l 1 l 2 w [N/mm] C l
87 2 w = 4 N/mm l = 800 mm l 1 = 150 mm l 2 = 400 mm (1) l 1 l 2 C l w [N/mm] R R l W W = wl 2 l 1 l 2 /2 l 2 /2 R C l w [N/mm] R W = wl 2 = = 1600 [N] l W = l 1 + l 2 /2 = /2 = 350 [mm] R + R 1600 = 0, 800 R = R = = 700 [N], R = 1600 R = 900 [N] 800 F M C 0 < < l 1 l 1 l 2 R C X w [N/mm] R F = R = 900 [N] M = R = 900 M = = 0 C M C = = 135, 000 [N mm]
88 C l 1 < < l 1 + l 2 W = w( l 1 ) l 1 l 2 R C X w [N/mm] R F = R W = R w( l 1 ) F F = R w( l 1 ) = 0 = R + wl = = 375 [mm] w 4 M = R W ( l 1 )/2 = M = 375 [mm] M ma = 236, 250 [N mm] l 1 + l 2 < < l R l 1 W = wl 2 l 2 /2 l 2 /2 C w [N/mm] X R F = R W = R wl 2 = = 700 [N] M = R W ( l 1 l 2 /2) = , 000 M = , 000 = 175, 000 [N mm] SF M l 1 l 2 F 0 M 0 (+) C 900 [N] = 375 [mm] 700 [N] 236 [N m] 135 [N m] (+) l w [N/mm] ( ) 175 [N m]
89 2 w = 4 N/mm l = 800 mm l 1 = 150 mm l 2 = 400 mm (2) l 1 l 2 C l w [N/mm] F M C 0 < < l 1 l 1 l 2 C X w [N/mm] F = 0 M = 0 C l 1 < < l 1 + l 2 W = w( l 1 ) l 1 l 2 C X w [N/mm] F = W = 4( 150) F = 4( ) = 1600 [N] M = W ( l 1 )/2 = 2( 150) 2 M = 320, 000 [N mm]
90 l 1 + l 2 < < l W = wl 2 l 1 l 2 /2 l 2 /2 C w [N/mm] X F = wl 2 = 1600 [N] M = wl 2 ( l 1 l 2 /2) = , 000 M = 720, 000 [N mm] SF M l 1 l 2 C l w [N/mm] F 0 ( ) M [N] ( ) 320 [N m] 720 [N m]
91 2 w = 4 N/mm l = 800 mm l 1 = 150 mm l 2 = 400 mm (3) l 1 l 2 w [N/mm] C l R R l W W = w(l l 1 ) l 1 (l l 1 )/2 (l l 1 )/2 R C l 2 l R W W = w(l l 1 ) = 4 ( ) = 2600 [N] l W = l 1 + (l l 1 )/2 = ( )/2 = 475 [mm] R + R 2600 = 0, ( ) R = R = = = 2245 [N], 550 R = 2600 R = = 355 [N] F M C 0 < < l 1 l 1 l 2 w [N/mm] R X C R F = R = 355 [N] M = R = 355 M = = 0 C M C = = 53, 182 [N mm]
92 C l 1 < < l 1 + l 2 W = w( l 1 ) l 1 l 2 w [N/mm] R C X R F = R W = R w( l 1 ) F F = R w( l 1 ) = 0 = R + wl = = [mm] w 4 F = R wl 2 = = 1245 [N] M = R W ( l 1 )/2 = M = [mm] M ma = 68, 895 [N mm] M = = 125, 000 [N mm] l 1 + l 2 < < l W = w( l 1 ) l 1 l 2 w [N/mm] R C R X F = R + R W = W w( l 1 ) F = W wl 2 = = 1000 [N] F = W w(l l 1 ) = ( ) = 0 M = R + R ( l 1 l 2 ) W ( l 1 )/2 = , 279, 750
93 SF M l 1 l 2 w [N/mm] C F 0 M 355 [N] [mm] (+) [N m] l 1000 [N] (+) ( ) 1245 [N] 68.9 [N m] ( ) 125 [N m]
94 4 4.3
95 4 4.4
96 4 4.5
19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional
19 σ = P/A o σ B Maximum tensile strength σ 0. 0.% 0.% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional limit ε p = 0.% ε e = σ 0. /E plastic strain ε = ε e
(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
NETES No.CG V
1 2006 6 NETES No.CG-050001-V 2007 5 2 1 2 1 19 5 1 2 19 8 2 i 1 1 1.1 1 1.2 2 1.3 2 2 3 2.1 3 2.2 8 3 9 3.1 9 3.2 10 3.3 13 3.3.1 13 3.3.2 14 3.3.3 14 3.3.4 16 3.3.5 17 3.3.6 18 3.3.7 21 3.3.8 22 3.4
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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9118 154 B-1 B-3 B- 5cm 3cm 5cm 3m18m5.4m.5m.66m1.3m 1.13m 1.134m 1.35m.665m 5 , 4 13 7 56 M 1586.1.18 7.77.9 599.5.8 7 1596.9.5 7.57.75 684.11.9 8.5 165..3 7.9 87.8.11 6.57. 166.6.16 7.57.6 856 6.6.5
1
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64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
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