材料力学新装版 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. http://www.morikita.co.jp/books/mid/060512 このサンプルページの内容は, 新装版 1 刷発行時のものです.
i 1 1 1
ii 1996 1994 8 1994 18 2014 5
iii 1 1 1.1............................................ 1 1.2........... 3.............................................................. 8 2 9 2.1.................................. 9 2.2................................... 11 2.3.............................................. 14 2.4.............................................. 16 2.5.. 22 2.5.1 22 2.5.2 25............................................................. 29 3 31 3.1..................... 31 3.2........................................... 33 3.3.................. 35 3.4......................................... 38 3.4.1 38 3.4.2 42 3.5......................................... 45 3.6.................................................. 50............................................................. 51
iv 4 53 4.1......................................... 53 4.2................................... 55 4.3............................... 60 4.4.............................................. 61 4.5................................. 65 4.6......................................... 66 4.6.1 66 4.6.2 69 4.7.................................................. 70 4.8............................... 72............................................................. 73 5 74 5.1.................................................. 74 5.2....................................... 75 5.3............................... 77 5.4......................... 83 5.5.................................................... 89 5.6..... 100 5.7............................ 103 5.8........................................ 107............................................................ 111 6 113............................................................ 116 7 117 7.1............................................... 117 7.2...................................... 120 7.3...................................... 127 7.4.................................. 129............................................................ 131
v 132................................................ 132.1 ε ξ γ xy 132.2 γ ξη ε x 133.3 γ ξη ε y 133.4 γ ξη γ xy 134 B................. 134 C............................. 137 C.1 137 C.2 140 C.3 142 D I Z.................... 146 E n......... 148 F.......................................... 150 153 157 α alpha N ν nu B β beta Ξ ξ xi Γ γ gamma O o omicron δ delta Π π pi E ε epsilon P ρ rho Z ζ zeta Σ σ sigma H η eta T τ tau Θ θ theta Υ υ upsilon I ι iota Φ φ phi K κ kappa X χ chi Λ λ lambda Ψ ψ psi M µ mu Ω ω omega
vi SI SI rad SI 180/π µ 10 6 m Å 10 10 M 1/1852 m 2 a 10 2 m 3 l 10 3 s h 1/3600 m/s km/h 3600/1000 kn 3600/1852 m/s 2 G 1/9.80665 kg u 1/(1.6605655 10 27 ) kgf 1/9.80665 N ton 1/(9.80665 10 3 ) dyn 10 5 N m Pa N/m 2 MPa kgf m 1/9.80665 kgf/m 2 1/9.80665 kgf/cm 2 1/(9.80665 10 4 ) kgf/mm 2 1/(9.80665 10 6 ) kgf/mm 2 1/9.80665 kgf/m 2 1/9.80665 Pa mmhg 760/(1.01325 10 5 ) N/m 2 Torr 760/(1.01325 10 5 ) bar 10 5 atm 1/(1.01325 10 5 ) erg 10 7 kgf m 1/9.80665 J kw h 1/(3.6 10 6 ) N m PS h 3.77672 10 7 W J/s ev 6.24146 10 18 K kgf m/s 1/9.80665 kcal/h 1/1.163 PS 1/735.4988 C q( C) = T (K) 273.15
1.1 1 dynamics 2 1 statics 1 2 strength of materials 1.1 1.1 1 external force 2 internal force
2 1 W C θ M B W B B W C 2
1.2 3 1.2 dynamics m F α F = mα equilibrium condition 1.2 W 1.3 R W F = mα F = W R = 0 α = 0 v = 0 1.2 1.3 1.2 W R = 0 R = W 1.1 1.2 1.4 3 P i x y z P ix P iy P iz
4 1 1.5 1.4 1.6 n P ix = 0, i=1 n P iy = 0, i=1 n P iz = 0 i=1 1.2 1.2 1.5 1.6 1.5 1.6 3 1.5 1.6 1.5 1.6 1.2 1.6 1.5 0 1 2 P 0 P a + 1 P 2a = 0 1.3 2 1.3 ( ) ( ) B = B ( ) C + C = 0 1.4 1.6 1.4
1.2 5 = 0 0 (P 12 ) P a + 1 2 P 2a = 1 2 P a 1 2 P a 1.2 x y z 3 1 1.1 1.7 B C P B B B R R B R R B P a b 1.7 1.7 1.8 2 R + R B = P 1.8 P R R B = 0 1.5 1.2 3 1.8 2 1.5 R R B P a + R B (a + b) = 0 1.6 1.6 1 x y z 3 3 3 1.3 1.4 B C 2 R R B 1.7 R R B 1.8
22 2 δ δ = a + 2b 2(a + b) λ a 1 + 2(a + b) λ 2 = 2a2 + 4ab + 5b 2 6E(a + b) 2 P l 2.43 2.5 2.5.1 k P λ 2.23 P = kλ 2.44 2.44 2.24 P W U P P 2.24 2.24 P = kλ U = W = 1 2 P λ = 1 2 kλ2 = P 2 2.45 2k P U 2.45 U = W = 1 2 P λ > 0 2.46 λ = P l E 2.3 P = E l λ 2.47 2.23 2.24
2.5 23 E l k = E l k 2.48 P U = P 2 l 2E 2.49 2.5 2.25 δ V 2.26 P Q R Q sin 60 R sin 30 = 0 2.50 Q cos 60 + R cos 30 P = 0 2.51 R Q 3 R = 2 P, Q = 1 2 P 2.52 2.25 2.26 Q R W = U λ λ = Q 3l E 2.53
24 2 W = U W = 1 2 P δ V, δ V = 3P l 4E U = 1 2 Qλ = Q2 3l 2E 2.54 2.55 δ V 2.27 a b R Q 2.53 λ 2.27 C l B 3l + λ 2.27 c δ V δ H δ V = λ sin 30 = Q 3l E 1 3P l 2 = 2.56 4E δ H = λ cos 30 = Q 3l 3 E 2 = 3P l 2.57 4E C C l l λ 2 2
2.5 25 2.5.2 2.5 δ V P δ H 2 2 3 2 2.28 P Q W U 2 2.28 1 P Q δ P P P P δ QP P B Q δ QQ Q B Q δ P Q Q P P Q 2.29 a b 2.29 W 1 W 1 = 1 2 P δ P P + 1 2 Qδ QQ + P δ P Q 2.58 P δ P Q 1 Q P 2 P δ P Q δ P P P δ QQ δ P Q Q C 1 C 2 C 3 2.58 W 1
26 2 2.29 W 1 = 1 2 C 1P 2 + 1 2 C 2Q 2 + C 3 P Q 2.59 δ δ = δ P P + δ P Q = C 1 P + C 3 Q 2.60 2 Q P Q P 2.30 a b W 2 1 W 2 = 1 2 Qδ QQ + 1 2 P δ P P + Qδ QP 2.61 W 2 = 1 2 C 2Q 2 + 1 2 C 1P 2 + C 3P Q C 3 2.62 1 2 W 1 = W 2 = W 2.63 C 3 = C 3 2.64 δ B = δ QQ + δ QP = C 2 Q + C 3 P 2.65 2.59 2.60 δ W P 2.62 2.65 δ B W Q δ = W P = C 1P + C 3 Q δ B = W Q = C 2Q + C 3 P 2.66 2.67
2.5 27 2.30 2.31 W = U δ = U P δ B = U Q 2.23 U P λ 2.31 P = kλ U U = P λ U C = λ P λ λ = U P 2.31 P = kλ U C P λ = U C P 2.68 P = kλ U C complementary strain energy U + U C = P λ U = U C 2.69 2.70 U C U 2.6 2.25 δ H ( δ V W = 1 2 P δ V δ V = U ) P P Q 2.32 δ H
28 2 δ H = U Q 2.32 δ H U = 1 ( ) 2 P + 3Q 3l 2 2 E δ H = U Q = 3 4 (P + 3Q) l E 2.71 2.72 2.72 δ H P Q P Q Q P 2.32 2.25 2.72 Q 0 (Q 0) δ H 2.25 δ H = U 2.73 Q Q 0 δ H δ H = 3 P l 4 E 2.5 2.74 0 1
29 2 3 U 4 U 0 1 2 3 4 2 3 5 U 6 U 7 4 6 8 5 U δ 9 7 δ 10 δ 0 2.1 2.33 1 B σ 1 BC σ 2 2 B δ B C δ C B d 1 BC d 2 2.33 E 2.2 2.34 B δ B C 2.33 2.3 2.35 C δ C 2.34 2.4 2.36 B δ V δ H 2.5 2.37 C δ C E 2.6 2.38 C δ C E
5.4 83 F = q(l x) O M + 5.19 df = q dx F = qx + C 1 x = l F = 0 C 1 = ql F = q(l x) 5.21 dm dx = F dm = q(l x) dx q(l x)2 M = + C 2 2 x = l M = 0 C 2 = 0 q(l x)2 M = 2 q(l x) (l x) 2 q(l x)2 M = 2 = 0 5.21 5.3 5.22 SFD BMD 5.22 5.4 M 5.23 5.23
84 5 1 5.24 a y = 0 x y 5.24 b 5.23 2 5.24 5.24 M BB B x B y = 0 x neutral plane radius of curvature ρ ρ M dθ OO = ρ dθ y = y B (ρ + y)dθ B = OO = ρ dθ x ε x ε x = = (ρ + y)dθ ρ dθ ρ dθ = y ρ 5.23 B σ x σ x = Eε x = Ey 5.24 ρ
5.4 85 5.25 5.2 5.25 M M = σ x d y = E y 2 d ρ 5.25 d 5.25 b b dy σ x d y M 5.25 y 2 d moment of inertia of area I I I = M = EI ρ y 2 d 1 ρ = M EI 5.26 5.27 2 I h/2 [ ] y 3 h/2 I = y 2 d = by 2 dy = b = bh3 5.28 3 12 h/2 h/2 b h 5.28 σ max 5.24 y = h 2 σ x max = Eh 2ρ = Mh 2I = M I/h/2 5.29
86 5 Z = I h/2 σ max = M Z 5.30 5.31 Z section modulus Z Z = bh2 6 3 5.32 5.26 5.25 y = 0 y > 0 y < 0 ε x = y ρ σ x = Ey ρ 5.33 5.34 5.25 d y M = σ x d y = E y 2 d = EI ρ ρ I C a a I = y 2 d = 2 y 2 z dy = 4 y 2 a 2 y 2 dy = π 4 a4 a 0 5.35 5.36 a y 2 + z 2 = a 2 z = a 2 y 2 y = a sin θ 5.26
5.4 87 d I = π 4 a4 = πd4 64 Z = I d/2 = πd3 32 σ max = M Z = 32M πd 3 5.37 5.38 5.39 4 5.27 y z 5.27 x σ x σ x d = 0 5.40 y = 0 y = 0 e y = e nn y > e y < e y = e ρ ε x y = e ρ 2 σ max y = y σ x y e σ x = σ max 5.41 h/2 e 5.40 y e σ x d = σ max h/2 e d = σ max (y e)d = 0 5.42 h/2 e
88 5 y d y d e = = d 5.43 y e center of gravity 5.43 M M = σ x (y e)d = σ x y d e σ x d = σ x y d ρ σ x = Eε x = E(y e) ρ 5.44 5.45 5.44 M = E (y e)y d 5.46 ρ y e = 0 5.46 M = E y 2 d = EI ρ = EI ρ ρ M 5.47 I 5.47 EI EI 5.4 a I 1 3 O I I = y 2 d = ( 3/6)a ( 3/3)a y 2 2z dy 5.28
5.5 89 ( 3/6)a = 2 ( y 2 1 3 (y + 3/3)a 3 [ ( 1 1 = 2 3 4 y4 + = 1 3 32 3 a4 = 96 a4 ) 3 a dy )] ( 3/6)a 3 9 ay3 ( 3/3)a 5.47 I ρ I I C I D 5.5 5.29 M δ θ 5.29 EI E I δ l x l (2ρ δ)δ = l 2 5.48 δ 2 2