最新耐震構造解析 ( 第 3 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/052093 このサンプルページの内容は, 第 3 版 1 刷発行時のものです.
i 3 10 3 2000 2007 26 8 2 SI SI 20 1996 2000 SI 15 3
ii 1 56 6
iii 1 1... 1 1.1 1 1.6 31 1.2 3 1.7 38 1.3 10 1.8 45 1.4 16 1.9 * 47 1.5 25 2... 52 2.1 52 2.5 78 2.2 59 2.6 * 81 2.3 66 2.7 89 2.4 70 3... 97 3.1 97 3.4 3.2 97 (Nigam Jennings ) 112 3.3 Runge Kutta 108 4... 114 4.1 114 4.4 129 4.2 118 4.5 4.3 120 138 5 *... 145 5.1 145 5.4 156 5.2 146 5.5 161 5.3 148
iv 6 *... 168 6.1 168 6.5 178 6.2 169 6.6 181 6.3 171 6.7 186 6.4 175 7... 192 7.1 192 7.4 209 7.2 195 7.5 219 7.3 203 8... 223 8.1 223 8.3 229 8.2 224 8.4 234 9... 245 9.1 245 9.4 261 9.2 247 9.5 269 9.3 254 10... 278 10.1 278 10.4 302 10.2 292 10.5 305 10.3 300... 349... 359
1 1 1 1.1 (mechanical model) 1 1.1 1.1 (mass) 2 (inertia force) 1 1.1 (a) (b) (mass point) P δ P/δ (stiffness) k (restoring force) Q (Q = ky) (linear vibration) 1.1 (b) (c) m k
2 1 1 ( lumped mass system) 1.1 m y 1 (single-degree-of-freedom system) (degree of freedom) 1.1 (c) 1 1 (x, y, z) 1.2 1.1 1 1.2 1.2 (a) m k (a) (b) (c) 1 1 1.2 1 1.1 1 1.3 (multi-degree-of-freedom system multi-mass system) 1.3 (c) 1 ( continuous system, distributed parameter system)
1.2 3 1.3 (non-linear vibration) (principle of superposition) 1 ( 1.4) (inelastic vibration) (damping) P P hardening P k 0 ± 0 softening ± 0 k t ± a b 1.4 c 1.2 Newton 2 d Alembert
4 1 1 Newton 2 m F a F = ma (1.1) F a Fx ẍ F = Fy, a = ÿ Fz z d Alembert F +( ma) =0 (1.2) (1.2) ( ma) 0 1.5 1 d Alembert y ky }{{} +( mÿ) =0 }{{} (1.3) 1.5 ky (free vibration) (1.3) mÿ + ky =0 (1.4) 2 ω 2 = k m (1.5) (1.4) ÿ + ω 2 y =0 (1.6) (1.6) a b
1.2 5 y = a cos ωt + b sin ωt (1.7) a b (initial condition) t =0 d 0 v 0 y(t =0)=a = d 0 (1.8) ẏ(t =0)=bω = v 0 (1.9) (1.6) y = d 0 cos ωt + v 0 ω sin ωt (1.10) y = A cos(ωt θ) (1.11) A θ ( A = d 2 v0 ) 2 0 + (1.12) ω ( ) θ =tan 1 v0 (1.13) ωd 0 (1.10) (1.11) 1.6 ( simple harmonic motion) A (amplitude) (ωt θ) (phase angle) 1.6 ω (natural circular frequency) (natural period) T (natural frequency) f T = 1 f = 2π ω (1.14) T m k m T =2π (1.15) k (1.15) T = 2π mg g k 1 η (1.16) 5
6 1 1 g = 980 cm/s 2 η = mg/k = w/k ( 1g ) cm (1.16) Geiger 1 1.1 1.7 (a) (b) 1 1.7 SI (International System) kg N kn (= 10 3 N ) 1N 1kg 1m/s 2 (1 N = 1 kg 1m/s 2 =1kg m/s 2 ) 1kg 9.8m/s 2 9.8N 1.7 m 98 kn 98 kn 98000 kg m/s2 m = 2 = 9.8m/s 9.8m/s 2 =10 4 kg (1.17) k E s =2.06 10 4 kn/cm 2 2 I =10 5 cm 4 k = 3EI h 3 = 3 2.06 104 kn/cm 2 10 5 cm 4 (500) 3 cm 3 =49.4kN/cm = 49.4 10 5 N/m (1.18) T [s] kg N m T =2π m k =6.28 10 4 49.4 10 5 =0.28 s
1.2 7 Geiger T 98 kn η = =1.98 cm 49.4kN/cm T =0.2 1.98 = 0.28 s 1.2 1.8 2 k = 12EI h 3 (1.19) 1.8 2 E c =2.06 10 3 kn/cm 2 I = 504 12 =5.21 105 cm 4 k =2 12 2.06 103 5.21 10 5 400 3 = 402 kn/cm = 4.02 10 7 N/m 294 kn 294 kn m = 9.8m/s 2 =3 104 kg m T =2π k =6.28 3 10 4 4.02 10 7 =0.17 s 1.3 1 1.9 1 1cm (d) k = 305.4kN/cm = 3.05 10 7 N/m
8 1 1 T T =2π 3 10 4 3.05 10 7 =0.20 s 1.2 1.9
1.4 1.2 9 1.10 1 k = 1 + 1 (1.20) k 1 + k 2 k 3 1.11 1.1 1 K R P δ δ = P ( ) ( ) Ph 1 k + h = K R k + h2 P K R P δ = K = 1 (1.21) 1 k + 1 K R /h 2 K k K R /h 2 ( 1.5 ) 1 K = 1/49.4 + 500 2 /(9.8 10 6 ) = 1 0.02 + 0.026 =21.7kN/cm T =6.28 =21.7 10 5 N/m 10 4 21.7 10 5 =0.43 s 1.10 1.11 1.5 1.12 (a) m mg mg/cos θ mg tan θ y = θh tan θ θ mÿ + ky mg h y = 0 (1.22)
10 1 1 ( k ÿ + T = ) y = 0 (1.23) m g h 2π (1.24) k/m g/h 1.12 k/m = g/h 0 k 3EI/h 3 T = w = mg =3EI/h 2 (π 2 /4) EI/h 2 =2.47EI/h 2 P Δ 1.12 (b) 1.3 2
% 114 4 4.1 1 mÿ + Q(ẏ, y, t) = mÿ 0 (4.1) Q mÿ + cẏ + Q(y) = mÿ 0 (4.2) 4.1 4.4 4.1 [13]
4.1 115 4.2 [13] 4.3 [10] 4.5 (elasto-plastic force-displacement relation) k (OA) (AB) (BC), (CD). 4.6 γk (bilinear) AB AB
116 4 4.4 [12] 4.5 4.6 2δ Y CD C D 4.7 3 (trilinear) 4.8 (Ramberg Osgood) (skeleton curve) [8] 4.8 Jennings [15] 4.9 (slip model) X [9][14]
4.1 117 4.7 4.8 4.9 4.10 4.10 RC [9] k k Y / μ (μ = δ max /δ Y ) 4.11 k k Y /μ a α =0(k = k Y ) Clough [25] α =1(k = k Y /μ) RC 4.12 1 RC 4.11
8 223 8.1 1 ( 8.1) [1][2][3] 8.2 8.3 1 8.1 2 (sway) (rocking) ( 8.2) ( 8.3)
224 8 8.2 8.3 8.4 3 8.2 1 8.4 1 ρ G A x y ABCD ( ) ( ρa dx 2 y t 2 + Q + Q ) x dx Q =0 (8.1) Q = AG y (8.2) x ρ 2 y t 2 2 y t 2 = G 2 y x 2 (8.3) = V 2 2 y x 2 (8.4) V 2 8.4 V 2 = G ρ (8.5) (8.4) 1 (wave
8.2 225 equation) V (shear wave velocity) (8.4) y(x, t) =f(x Vt)+g(x + Vt) (8.6) ( y(x, t) =f t x ) ( + g t + x ) (8.7) V V (8.6) (8.7) d Alembert f g 8.5 f(x Vt) x V g(x + Vt) x 8.5 ( 8.6). y = e iκ(x V t) = e i(κx pt) (8.8) y = e iκ(x+v t) = e i(κx+pt) (8.9) 8.6 κ p κ = p V = 2π (wave number ) (8.10) λ λ = 2π κ = 2πV p = VT (8.11)
226 8 p, T = 2π p V λ T f(x Vt) f(x Vt)= 1 F (iκ)e iκ(x V t) dκ (8.12) 2π F (iκ) F (iκ) = f(z)e iκz dz (f(z) t =0 ) (8.13) f(t x/v ) ( f t x ) = 1 F (ip)e ip(t x/v ) dp (8.14) V 2π F (ip) F (ip) = f(y)e ipy dy (f(y) x =0 ) (8.15) 2 8.7 f 2 = A 0 e ip(t x/v2) = A 0 e iκ 2(V 2 t x) (8.16) g 2 = B 2 e ip(t+x/v2) = B 2 e iκ 2(V 2 t+x) (8.17) f 1 = A 1 e ip(t x/v1) = A 1 e iκ 1(V 1 t x) (8.18) f 2 g 2 f 1 (8.4) (f 2 + g 2 ) x=0 = f 1x=0 (8.20) (f 2 + g 2 ) G 2 f 1 x = G 1 x=0 x (8.21) x=0 { A0 + B 2 = A 1 (8.22) ρ 2 V 2 (A 0 B 2 )=ρ 1 V 1 A 1 (8.23)
8.2 227 8.7 B 2 = 1 α = X A 0 1+α ( 1 X 1) (8.23) A 1 = 2 =1+X A 0 1+α ( 0 1+X 2) (8.24) α α = ρ 1V 1 ρ 2 V 2 (8.25) g 2 f 2 X V 2 f 1 f 2 (1 + X) V 1 (8.12) (8.14) (8.23) (8.24) ( g 2 t + x ) ( = X f 2 t + x ) (8.26) V 2 V 2 f 1 ( t x V 1 ) =(1+X) f 2 ( t x V 1 ) (8.27) (i) 1 V 1 = α = X = 1 0 ( 8.8 (a)) g 2 ( t + x V 2 ) = f 2 ( t + x V 2 ) (8.28) (ii) 1 V 1 =0 α =0 X =1 ( 8.8 (b)) ( g 2 t + x ) ( = f 2 t + x ) (8.29) V 2 V 2
228 8 8.8 y(x, t) =f 2 ( t x V 2 ) + f 2 ( t + x V 2 ) (8.30) x =0 y =2f 2 (t) 2 (8.30) α 0 (t) (= 2f 2 (t)) H α H (t) (8.31) (8.31) 7 [1]. α H (t) = 1 ) )} {α 0 (t HV2 + α 0 (t + HV2 (8.31) 2 (iii) 8.9 8.9
359 172 173 337 333 5 18 147 263 310 1 2 238 60, 89 157 50 30 158 35 39 SEAOC 299 S 211 132 43 FFT 161, 166 174 12 78 261 261 41 169 169 169 168 12 3 252 33 21 348 158 22 1 115 192 204 196 170 3 1 77 149 22 17 209 209 17 179 171 149 208 27 168 331 12 201 11 42 71 68 64 64 262 262 1 67 53 153 292 47 161, 166 179 237 248 5, 60 5 5 89 60 60 189 substitute structure 140 3 36 304 173 174 74
360 73 148, 150, 156, 173 33 206 294 203 195 1 2 1 67 53 271 172 4 262 296 200 2 296 258 103 218 5 192 192 192 192 192 192 309 297 39 24 196 5 147 14 186 223 97 26 Stodola 94 218 160 34 116 60 229 65 296 336 78 252 99 1 130 129 55 225 162 12 247 297 99 33 129 337 333 293 308 14 335 2 52 29 5 129 3 114 263 263 5 9 60 172 41 219 178 16 D 57 31 29 62 20 226 45, 337 75 138 120 140 76 45 55 296 235 116 163 Nigam Jennings 112 314 2 147 2 151 2 170 2 78 Newmark β 104 30 31 261
361 300 11 11 115 147 225 225 227 224 147 151, 157 226 176 90 236 3 3 181 P-Δ 10 P 211 66, 81 170 211 66 66 1 48 19 47 47 19 147 237 150 146 146 150 150 148 148 149 150 170 102 205 35 170 138 9 298 132 33 21 137 262 262 220 190 39 254 175 195 45 177 172 219 78 78 68 87 61 168 163 161 192 339 300 160 168 116 1 146 158 12 12 Runge Kutta 108 67 96 191 149 2
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