[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 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] (1 10 3 ) 2 [m 2 ] = 1 10 6 [N/m 2 ] = 1 10 6 [Pa] a b = 1[MPa] F a (a) F b (b) (a) a = 50 [mm 2 ] F a = 20000 [N] 20000 [N] = 50 [mm 2 = 400 [MPa] ] (b) b = 200 [mm 2 ] F a = 40000 [N] 40000 [N] = 200 [mm 2 = 200 [MPa] ] (b) (a)
1 1.2 4.
1 1.2 5. (toughness)
1 1.2 6.
1 1.3 1. 2. 3. 4. 5. 6. 7.
1 1.3 1.
1 1.3 2. C Mn Si P S Cu l Sn P S C 0.02 2.11 % carbon steel steel 1.1 0.6 % SS SS400 1 S steel 2 S structure SC S45C 1 S steel C carbon 100 S45C 0.42 0.48 %
1 1.3 3. Ni Cr Mn Mo V
1 1.3 4. 1 cast iron 2
1 1.3 5. 1 Cu Zn Zn 30 % Zn 40 % 2 Cu Sn P
1 1.3 6. 1/3 2.7 660 C l Cu-Mg Cu-Mg-Mo
1 1.3 7. Cr 12 % stainless steel Cr Cr 17 % Ni C P N l Ti Ni Co
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7
2 2.1 1. (load) 2. (stress)
2 2.1 1. (load) (a) (tension) (b) (compression) (c) (bending) (d) (shear) (e) (torsion) (f) (buckling)
2 2.1 2. (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
1 20 mm 49000 N d = 20 [mm] W = 49000 [N] σ W = σ σ = W = W (π/4)d 2 = 49000 (π/4) 20 2 = 155.9 [N/mm2 ] = 156[MPa] d W W 2 2.5 C W = 8000 [N] 8000 [N] 8000 [N] ϕ25 ϕ20 C 150 200 σ 1 d 1 = 25 [mm] σ 1 = W W = 2 1 (π/4)d = 8000 1 (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 = 8000 2 (π/4) 20 2 = 25.5 [N/mm2 = MPa]
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
3 10 mm 150 mm 1950 N 0.0188 mm d = 10 [mm], l = 150 [mm], W = 1950 [N], λ = 0.0188 [mm] ε ε = λ l = 0.0188 150 = 0.000125 = 1.25 10 4 4 12 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 0.3 0.08 12 = = 0.000576 = 5.76 10 4 [mm] l 500 W d l d l W
2 2.3 1. 2.
W W3 2 2.3 1. 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
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
2 2.3 1. - 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
2 2.3 1. - 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
2 2.3 1. - σ (0.2%) σ 0.2 O 0.002 ε 0.002 0.2 % σ 0.2
2 2.3 2. σ ε σ = Eε (E ) (2.7) E 2.1 E σ [Pa] ε [GPa] 1 [GPa] = 1 10 3 [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
5 20 [mm] 200 [mm] 10000 [N] 192 [GPa] a = 20 [mm] = = a 2 = 20 2 [mm 2 ], l = 200 [mm], W = 10000 [N], E = 192 [GPa] = 192 10 3 [MPa] (2.9) λ = W l E 10000 200 = 20 2 = 0.02604 = 0.0260 [mm] 192 103 200 20 20 6 15 [mm] 800 [mm] 0.2 [mm] 200 [GPa] d = 15 [mm], l = 800 [mm], λ = 0.2 [mm], E = 200 [GPa] = 200 10 3 [MPa] (2.7) (2.4) σ = Eε = E λ l = 200 103 0.2 800 = 50 [MPa] 800 15
7 I 35 [mm] 50 [mm] II 30 [mm] 2.5 120 [kn] 200 [GPa] 100 [GPa] 2.15 I II σ 1 σ 2 1 2 I II W = σ 1 1 + σ 2 2, ε = σ 1 = σ 2 E 1 E 2 120 10 3 = π 4 (502 35 2 )σ 1 + π 4 302 σ 2 50 35 30 σ 1 200 10 3 = σ 2 100 10 3 σ 1 = 2σ 2 σ 2 = 120 10 3 (π/4){(50 2 35 2 ) 2 + 30 2 } σ 1 = 2σ 2 = 88.6 [MPa] = 44.3 [MPa] 1 2 W = 120kN
2 2.4 τ W W W W = τ (2.10) W τ = W (2.10) τ τ [N/mm 2 = MPa] W
8 2.18 18 mm 20000 N d = 18 [mm], W = 20000 [N], a a = π 4 d2 = π 4 182 [mm 2 ], 1 2.19 2 (2.10) a 2 τ = W = W 2a = 20000 ( π ) = 39.29[MPa] 2 4 182 9 2.20 1.5 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 40 1.5) = 65970 = 66000 [N]
W 1 W W 2 W W 3 W W W W 2 2 2 1 = 2 3 2 2 = 4 4 2 3 = 6
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
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] = 80 10 3 [MPa] τ = Gγ γ = tan ϕ ϕ ϕ = τ G = 160 = 0.002 [rad] 80 103
2 2.6 σ a = σ f (2.14) 2.3
2 2.7 1. 2. 3. 4. 5. 6.
2 2.7 1. 2.
2 2.7 3. fatigue 2.24 b S N W öhler 10 7 10 8 σ e JIS Z 2274 90% 50%
2 2.7 4. 2.25 a σ 0 (= W/ ) σ ma = α (2.15) α σ 0 3 2 1 10 5 3 4 10 2.5 r 2
2 2.7 5. creep 623 K 350 C 2.27 1000 1 % 1 10
2 2.7 6.
11 SS400 235 N/mm 2 8000 N 3 σ = 235 [MPa], W = 8000 [N], f = 3 σ a = σ f = 235 3 [MPa] πd 2 (2.1) W = σ a = σ a 4 4W 4 8000 3 d = = = 11.40 12 [mm] πσ a π 235 3 12 10 kn 80 MPa W = 10 [kn], σ a = 80 [MPa] W = σ a = σ a 2 W 10 10 3 = = = 11.18 12 [mm] σ a 80
13 200 MPa 10 kn 5 σ e = 200 [MPa], W = 10 [kn] = 10 10 3 = 10000 [N], f = 5 ( π ) W = σ a = σ a 4 d2 σ a = σ e f 4W 4W f 4 10000 5 d = = = = 17.84 18 [mm] πσ a πσ e π 200 14 2 mm 40 mm 12 kn 2.26 r = 2 [mm], = 40 [mm], W = 12 [kn] = 12 10 3 = 12000 [N] r = 2 40 r = 2.26 α = 2.6 20 W σ ma = ασ 0 = α (π/4) ( 2r) 2 = 2.6 12000 = 30.65 = 30.7 [MPa] (π/4) (40 2 2) 2 α 2.6 3 2 1 20 10 5 3 4 10 2.5 r 2
3 3.1 3.2 3.3 3.4 3.5 3.6
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 2 3.2 sin θ θ = 90 = π/2 [rad] = 1 3.1 σ X p p b W X σ ma 2.1 σ σ ma = W θ = 90 3.3 θ X sin 2θ θ = 45 = π/4 [rad] 3.2 τ 45 τ ma τ ma = W 2 = σ ma 2 θ = 45 3.4 X τ τ p p σ c σ
1 30 mm 10000 N 45 τ ma = σ ma 2 = 10000/ { (π/4) 30 2} 2 = 7.073 [N/mm 2 ] = 7.07 [MPa] W 45 45 τ τ 1 30 mm 10000 N 35 3.1 σ = W sin2 θ = W (π/4)d 2 sin2 θ = = 4.657 [N/mm 2 ] = 4.66 [MPa] 10000 (3.14/4) 30 2 sin2 35 3.2 τ = W sin 2θ 2 = W sin 2θ (π/4)d2 2 = 6.650 [N/mm 2 ] = 6.65 [MPa] = 10000 sin 70 (3.14/4) 302 2
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 3.5 3.6
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)
2 3.9 7.8 ( 7800 [kg/m 3 ] ) σ 1 7.8 10 6 kg/mm 3 σ 1 = 10000 + 7.8 10 6 (π/4) 60 2 800 9.8 (π/4) 60 2 = 3.60 [MPa] σ 2 σ 2 = 10000 + 7.8 10 6 (π/4) (60 2 800 + 80 2 1000) 9.8 (π/4) 80 2 = 2.10 [MPa] L 2 d 2 L 1 d 1 W
3 3.4 λ σ σ λ ( σ = W ) 1 + 1 + 2h 3.9 λ 3.9 h = 0 σ = 2 W = 2σ 3.10 σ σ 2
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
4 70 mm 80 mm 500 mm 50 K 50 C 200 GPa 1.2 10 5 K 1 W W = σ = (Eα t) = 200 10 3 1.2 10 5 50 π ( 80 2 70 2) 4 = 141370 [N] = 141 [kn]
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
6 180 mm 60 mm 3.16 200 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 ( 180 50 10 3 = 200 10 3 60 2 = 0.01475 = 0.0148 [mm] 90 103 60 180 3 10 ) )
4 4.1 4.2 4.3 4.4 4.5
4 4.1 beam a b c d e a b c d e
4 4.2 (SF) (M) 1. 2.
4 4.2 1. { 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 ( )
4 4.2 2. 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
1 b { R 1 R 2 R 1 + R 2 5000 = 0 (a) 1800 R 2 720 5000 = 0 (b) 720 5000 R 2 = = 2000 [N], 1800 R 1 = 5000 R 2 = 3000 [N] c 0 < < l 1 F = R 1 = +3000 [N] d l 1 < < l F = R 1 W = +3000 5000 = 2000 [N] e SF { 0 < < l 1 : F = +3000 [N] l 1 < < l : F = 2000 [N] c a 5000 N l 1 = 720 1080 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 = 3000 3000 N X l 1 < < l : F M = +R 1 W ( l 1 ) [N] (+) 2000 N = (W R 1 ) + W l e 1 0 = (5000 3000) ( ) +5000 720 +3000 N = 2000 + 3600000 M 2, 160 [N m] [N m] C = l 1 f M C = +R 1 l 1 = 3, 000 720 0 = 2, 160, 000 [N mm] = 2, 160 [N m]
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 = 1000 2000 = 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 1000 = 300, 000 [N mm] : M = 700 1000 400 2000 = 1, 500, 000 [N mm] W 1 = 1000 [N] W 2 = 2000 [N] l 1 = 200 l 2 = 300 400 [mm] F 0 M 0 1000 [N] 300 [N m] 3000 [N] l = 900 1, 500 [N m] ( ) ( )
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]
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
2 4.10 SF { R 1 R 2-1 R 1 + R 2 1200 1000 = 0 (a ) 740 R 2 130 1200 (130 + 380) 1000 = 0 (b ) 130 1200 + 510 1000 R 2 = = 900 [N], R 1 = 2200 R 2 = 1300 [N] 740 0 < < l 1 : F = R 1 = +1300 [N] l 1 < < l 1 + l 2 : F = R 1 W 1 = +1300 1200 = +100 [N] l 1 + l 2 < < l : F = R 1 W 1 W 2 = +100 1000 = 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 1 380 1200 = 207, 000 [N mm] : M = +740R 1 610 1200 230 1000 = 0 W 1 = 1200 N W 2 = 1000 N l 1 = 130 l 2 = 380 230 F [N] 0 M l = 740 +1300 N (+) +100 N 900 N ( ) 169 [N m] 207 [N m] [mm] [mm] 0
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] ( )
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 = w2 2 2 + wl 2 = w 2 (2 l) { = w ( ) } 2 l 2 l + + w ( ) 2 l = w ( l ) 2 + w 2 2 2 2 2 2 8 l2 [N mm] w [N] M R 1 [N] wl 2 /2 8 [N m] (+) M 0
3 4.21 w = 5 [N/mm] W = 2000 [N] 700 C 800 1500 [mm] C 0 < < 700 F = F C = w F = 0, F C = 5 700 = 3, 500 [N] M = M C = w2 2 M = 0, M C = 5 7002 2 w [N] = 1, 225, 000 [N mm] W = 2000 [N] /2 C 700 800 1500
C 700 < < 1500 F = F C = w W F C = 3, 500 2, 000 = 5, 500 [N], F = 5 1500 2, 000 = 9, 500 [N] M = M C = w2 2 M = 5 15002 2 W ( 700) 2, 000 800 = 7, 225, 000 [N mm] w [N] C W = 2000 [N] /2 700 800 1500 F 0 ( ) 7500 [N] 2000 [N] M 0 ( ) 5.625 10 6 [N m] 1.6 10 6 [N m]
4 4.23 R, R C F M C M C SF M M ma 3 [N/mm] 600 C 400 1000 [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 = 3 6002 = 540 [N] 2l 2 1000 R 1 = wl 1 R 2 = 3 600 540 = 1260 [N] wl 1 [N] 3 [N/mm] l 1 /2 C R 1 R 600 400 2 1000
C 0 < < 600 F = F C = R 1 w F = R 1 = 1, 260 [N], F C = 1, 260 3 600 = 540 [N] M = M C = R 1 w2 2 M = 0, M C = 1, 260 600 3 6002 = 216, 000 [N mm] 2 w [N] 3 [N/mm] /2 C R 1 R 600 400 2 1000 C 600 < < 1000 F = F C = R 1 wl 1 = 1, 260 3 600 = 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 /2 600 400 R 2 1000
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 400 1000 1260 [N] [mm] 0 M (+) 420 ( ) 540 [N] 2.65 10 5 [N m] 2.16 10 5 [N m] 0 (+)
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
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 1200 1400 = 0 1200 R 200 1200 900 1400 = 0 200 1200 + 900 1400 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 = 1350 200 = 270, 000 [N mm] = 270 [N m]
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 ) = 150 + 240, 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 = 1250 + 1, 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] (+) ( )
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 ) = 1200 + 240, 000 M = 840, 000 [N mm] = 840 [N m]
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 ) = 2600 + 1, 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 0 1200 [N] 2600 [N] ( ) M 0 840 [N m] ( ) 1, 620 [N m]
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 1200 1400 = 0 900 R 200 1200 1200 1400 = 0 200 1200 + 1200 1400 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 = 467 200 = 93, 333 [N mm] = 93.3 [N m]
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 ) = 733 + 240, 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 = 1400 1, 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]
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
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 = 4 400 = 1600 [N] l W = l 1 + l 2 /2 = 150 + 400/2 = 350 [mm] R + R 1600 = 0, 800 R 350 1600 = 0 350 1600 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 = 900 0 = 0 C M C = 900 150 = 135, 000 [N mm]
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 1 900 + 4 150 = = 375 [mm] w 4 M = R W ( l 1 )/2 = 2 2 + 1500 45000 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 = 900 4 400 = 700 [N] M = R W ( l 1 l 2 /2) = 700 + 560, 000 M = 700 550 + 560, 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]
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(550 150) = 1600 [N] M = W ( l 1 )/2 = 2( 150) 2 M = 320, 000 [N mm]
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) = 1600 + 560, 000 M = 720, 000 [N mm] SF M l 1 l 2 C l w [N/mm] F 0 ( ) M 0 1600 [N] ( ) 320 [N m] 720 [N m]
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 (800 150) = 2600 [N] l W = l 1 + (l l 1 )/2 = 150 + (800 150)/2 = 475 [mm] R + R 2600 = 0, (150 + 400) R 475 2600 = 0 475 2600 R = = 2245.455 = 2245 [N], 550 R = 2600 R = 354.5455 = 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 = 355 0 = 0 C M C = 355 150 = 53, 182 [N mm]
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 1 355 + 4 150 = = 238.64 [mm] w 4 F = R wl 2 = 355 4 400 = 1245 [N] M = R W ( l 1 )/2 = 2 2 + 955 45000 M = 238.64 [mm] M ma = 68, 895 [N mm] M = 2 550 2 + 955 550 45000 = 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 = 2600 4 400 = 1000 [N] F = W w(l l 1 ) = 2600 4 (800 150) = 0 M = R + R ( l 1 l 2 ) W ( l 1 )/2 = 2 2 + 3200 1, 279, 750
SF M l 1 l 2 w [N/mm] C F 0 M 355 [N] 238.64 [mm] (+) 0 53.2 [N m] l 1000 [N] (+) ( ) 1245 [N] 68.9 [N m] ( ) 125 [N m]
4 4.3
4 4.4
4 4.5