材料力学Ⅱ 2015-2 - JAXA

1 Strength of Materials II.. 2015.. lt ~| `| t t~|.. SFD BMD .. 1 .. 2 .. 3 .. 4 (1).. 5 (2).. 6 .. 7 (1).. 8 (2).. 9 (1).. 10 (2).. 11 .. 12 (1).. 13 (2).. 14 (3).. 15 .. 16 .. JSME .. OB .. 1 .. 1-1..1-1..1-2..1-2..1-2..1-2..1-2..1-2.. 1-3..1-4..1-4..1-5..1-5..1-5. 2 .. 2-1..2-1..2-2..2-3..2-4..2-4..2-4. 3 .. 3-1. curvature ..3-1..3-1..3-2..3-2..3-2..3-3..3-3..3-3 ..3-4..3-4..3-4. 4 (1).. 4-1..4-1..4-2..4-3..4-3. 5 (2).. 5-1..5-1..5-2..5-2..5-4..5-4. 6 .. 6-1..6-1. i .. 6-7.. 6-7. 7 (1) .. 7-1.. 7-1.. 7-1.. 7-2.. 7-3.. 7-3. 8 (2) .. 8-1.. 8-1.. 8-4.. 8-5.. 8-5. 9 (1).. 9-1.. 9-1.. 9-3.. 9-3. 10 (2).. 10-1.. 10-1.. 10-3.. 10-3. 11 .. 11-1.. 11-1.. 11-1.. 11-1.. 11-1. Clapeyron 3 .. 11-7. Bernoulli-Euler .. 11-7. Timoshenko .. 11-7.. 11-9.

2 11-9. 12 (1) .. 12-1.. 12-1.. 12-1.. 12-2. Euler Buckling .. 12-2. Torsional Buckling .. 12-2. Crippling .. 12-3. Lateral Buckling .. 12-3.. 12-3.. 12-3.. 12-4.. 12-4. Euler .. 12-4.. 12-5.. 12-5.. 12-6.. 12-7.. 12-7.. 12-7. ii ..12-8..12-8. 13 (2) ..13-1..13-1..13-2..13-2..13-2..13-2. 14 (3) ..14-1..14-1..14-2. Euler ..14-3. Rankine ..14-3. Johnson ..14-3. Tetomajer ..14-3..14-4..14-5..14-5..14-5..14-5. 15 ..15-1..15-1..15-1..15-1..15-3..15-4..15 -4.. 1-2.. 1-2.. 1-3.. 1-3.. 1-3.. 1-3.. 1-3.. 1-4.. 1-4.. 1-4. BMD SFD (1) .. 1-5. BMD SFD (2) .. 1-5. BMD SFD (3) .. 1-5. BMD SFD (4) .. 1-5.. 2-1.. 2-1.. 2-1.. 2-1.. 2-2.. 3-1.. 3-1.. 3-2.. 3-2.. 3-2. iii .. 3-3.. 3-3.. 4-1.. 4-1.. 4-1.. 4-2.. 4-2.. 4-2.. 4-3.. 5-1.. 5-2.. 5-2.. 5-2.. 5-2.

3 5-3.. 5-3.. 5-3.. 5-3.. 5-3.. 5-4.. 5-4.. 6-1.. 6-2.. 6-2.. 6-2.. 6-3.. 6-3.. 6-3.. 6-3.. 6-3.. 6-4.. 7-1.. 7-1.. 7-2.. 7-2.. 7-2.. 7-2.. 7-2.. 7-3.. 7-3.. 7-3.. 7-3.. 8-1.. 8-1.. 8-1.. 8-1. 4 .. 8-2.. 8-2. 1 .. 8-2.. 8-3. 1 .. 8-3.. 8-3.. 8-4.. 8-4.. 8-4.. 8-5.. 9-1.. 9-1.. 9-1.. 9-1.. 9-1. 1 .. 9-2.. 9-2. iv .. 9-2.. 9-2.. 9-2.. 9-2.. 10-1.. 10-1. 3 .. 10-1.. 10-1. 1 .. 10-1. 2 .. 10-2.. 10-2. 4 .. 10-2.. 10-2. BMD .. 11-1.. 11-1.. 11-2. BMD .. 11-2. BMD .. 11-3. BMD 1 .. 11-3. BMD 2 .. 11-3. BMD 3 .. 11-3. BMD .. 11-4. BMD .. 11-4.. 11-5. BMD .. 11-5. BMD .. 11-6. Bernoulli-Euler .. 11-7.. 11-7.. 11-7. Timoshenko .. 11-7.. 12-1.. 12-1.. 12-1.. 12-1.. 12-1. Euler Wikipedia .. 12-2.. 12-2.. 12-3.. 12-3.. 12-3.. 12-3.. 12-3.. 12-4.. 12-4.

4 12-4. Euler .. 12-4.. 12-4.. 12-5.. 12-5.. 12-6.. 12-7.. 12-7.. 13-1.. 13-1.. 13-1.. 14-1.. 14-1.. 14-1.. 14-2.. 14-2.. 14-2.. 14-2.. 14-2. v . Rankine .. 14-3. Johnson .. 14-3. Johnson .. 14-3. Tetmjer .. 14-4. Tetmajer .. 14-4. A7075-T7451 - 1ksi= MPa .. 14-4. A7075-T7451 .. 14-4. A7075-T7451 .. 14-4.. 15-1.. 15-1.. 15-1.. 15-2.. 15-2.. 15-2.. 15-3.. 15-3.. 15-3.. 15-4.. 1-2.. 4-2.. 7-1. (2) .. 7-1.. 12-2.. 13-2.. 13-2. Rankine .. 14-3. Tetmajer .. 14-4.. BMD SFD (1) .. 1-5. BMD SFD (2) .. 1-5. BMD SFD (3) .. 1-5. BMD SFD (4) .. 1-5.. 2-4.. 2-4.. 2-4.. 3-2. BMD .. 3-4.. 3-4.. 3-4.. 4-1.. 4-2.. 4-2.. 4-2.. 4-3.. 5-1.. 5-2.. 5-2.. 5-2. (1) .. 5-3. (2) .. 5-3.. 5-3.. 5-4.. 5-4. vi . (1) .. 6-1. (2) .. 6-2. (3) .. 6-2. (4) .. 6-3. (5).

5 6-3. (6) .. 6-3. (7) .. 6-3. (8) .. 6-3. (9) .. 6-4. (10) .. 6-4. (11) .. 6-5. (12) .. 6-5. (13) .. 6-6. (14) .. 6-6. (15) .. 6-7. (16) .. 6-7. (1) .. 7-1. (2) .. 7-2. (3) .. 7-2. (4) .. 7-2. (5) .. 7-3. (6) .. 7-3. (7) .. 7-3. (8) .. 7-3. (1) .. 8-1. (2) .. 8-1. (3) .. 8-3. (9) .. 8-4.. 8-4.. 8-5. (1).. 9-1. (2).. 9-1. (3).. 9-2. (4).. 9-2. (5).. 9-2. (6).. 9-2. (7) .. 10-1. (1) .. 10-1. (2) .. 10-2.. 11-1. (9) .. 11-2. (10) .. 11-2. (11) .. 11-3. (12) .. 11-3. (13) .. 11-4. (14) .. 11-4. (15) .. 11-5. (3) .. 11-6. Timoshenko .. 11-8. Timoshenko .. 11-8. (1) .. 13-1.. 14-2.. 14-3.. 15-2. (2) .. 15-3. vii . 1 . bar axial force beam bending moment . shear force BMD Bending moment Diagram SFD Shear Force Diagram .. 3 .. 1) . 2) . 3) . 4).

6 1) .. 4 . 1 . 2 .. A4 .. 1-1 .. y .. Reaction force, R. Reaction moment Bending moment .. Mo M Axial force N Px .. Rx x Ry F. w . y Shear force Distributed force . P . Cross section External force .. fixed . simply supported 2 .. equilibrium .. (a) .. (b) .. (c) .. 0 0 .. 0 Elasticity .. 0 .. 0 internal force . cross 0 section . 0 2 . 1-2 . 2 .. (a) A x = 0 . (b) x = 0 . F M . F . M .. A.. x M. F. (a) . M M F.. x F . (b) . cantilever P . (a) BMD . A concentrated load P w (b) . (b) BMD (c) . BMD . F2 . (b) L. -F + P + F2 = 0 ( ) P.. F2 = F - P ( ) (a) . F2 = F L. P = 0 . P .. w . (b) . A L. P P. x w (a) . (c) . M F M F2 . BMD . F2. x F P (a) (b) (c) .. (b) .. R2 T2.. R2 T2 T2 linear analysis . T2.. deflection . P T1 T1 P. R1 T1 (a) (b).

7 T1 (c) . R1.. 1-3 . M = -P (L - x ) dx x w -PL. (a) BMD x y (a) . x 1. 1 M = - P (L - x )2. - PL2 2. 2. (b) BMD. y x x (b) . 1. M = -P (L - x ) - P (L - x )2 . 1 2. -PL - PL2. 2 dx (c) BMD w M M M + dM M + dM. A'. F. F B'. F + dF F + dF. P . 4 .. 4 A' . 4 . -F + wdx + F + dF = 0. 1N dx ( ). -M - wdx + M + dM - dx (F + dF ) = 0. 2.. dF. = -w ( ). dx . dM wdx = F + dF + ( ). dx 2. ( ) . SFD . w x . SFD . ( ) dx dx 0 . dF dF 0 . (a) . AB x y dM. =F ( ). (b) dx x y .. (c) .. Lagrange .. Euler .. 1-4 .. BMD SFD .. BMD SFD .. 1) .. BMD SFD . BMD SFD (1). BMD SFD . P = 100N q = 20N/m 45 . 1m BMD SFD (1). BMD SFD (2). BMD SFD . 2m q = 20N/m 3m 1m BMD SFD (2). BMD SFD (3). BMD SFD . qo . BMD SFD (3). BMD SFD (4). BMD SFD .. qo BMD SFD (4). 1-5.

8 2 .. torsion .. fo f f + df = = ( ). x x + dx .. d f fo = ( ). dx .. = Rf , AA' = R(f + d f). CC' ( ). dy dy f dq dq R R. x x dy dy f + df dx dq dq R R.. g x x dx dx a b . g = a+b ( ) . ABDC A'B'D'C' .. dx b dy Rf R(f + d f). a dx .. R x g . A dy . B A A' R(f + d f) - Rf Rd f tan g = = ( ). B B' f dx dx dx tan g g . A C B . D C C'. Rd f D D' f + df g= ( ). dx . fo ( ) . Rfo g= ( ).. 2-1 . R moment of inertia of area .. r r < R I p r 2dA ( ). A.. rf g= o ( ) 2p R pR 4. Ip = 0 0 r 2rdrd q =. 2. ( ). t . ( ) . G . T .. R 2. t = Gg ( ) t max = T = T ( ). Ip pR 3.. d . fo 16. t = Gr ( ) t max = T ( ). pd 3. r fo / .. ( ) . fo T . t max = GR ( ) fo = ( ). GI p . do . di . p(do 4 - di 4 ). Ip = ( ). 32. do 16do t max = T = T ( ). 2I p p(do 4 - di 4 ).

9 A .. O a b . 2T. t max = ( ). pab 2.. T . fo = ( ). GI p .. pa 3b 3. T Ip = ( ). a 2 + b2.. T = r tdA ( ). A a b . t dA aT. r t max = ( ). bab 2.. ( ) ( ) T . fo = ( ). G bab 3. fo 2 f T = AG . r dA = GI p o . ( ) . I p polar 2-2 . 8 . 1 . a = 1- . n =1 (2n - 1)2 cosh (2n - 1)pa p2. 2b ( ) . 1 64 b 1 (2n - 1)pa . b= - . 3 p 5 a n =1 (2n - 1)2. tanh 2b GJ . df T = GJ ( ). bk ak k = 1 N dx ak bk ( ) . d f fo bi = ( ). dx . 3bi t max = T ( ) . N. akbk 3 T = GJ. fo ( ). k =1.. 3T ( ) . fo = ( ). N . G akbk 3 . k =1. s . t = t (s ) ( ) . 3t pR 4. t max = T ( ) GJ = GI p = G ( ). t ds 3. 2.. 3T . fo = ( ) ( ) .. G t(s )3ds 0 p(do 4 - di 4 ). GJ = GI p = G ( ). 32. t s . ( ) . A t min . pa 3b 3. GJ = GI p = G ( ). a 2 + b2. 1 . t= T ( ). 2At ( ) a b.

10 Ab 3 . (2n - 1)pa . GJ = G 1 - 192 b 1. tanh ( ). 1 3 5 a 2 2b . p n =1 (2n - 1) . t max = T ( ). 2 Atmin . ( ) ak bk . T ds 1 N. fo =. 4GA 2 t(s ) ( ) GJ = G akbk 3. 3 k =1. ( ). do t s . ( ) t = t (s ) ( ) . T pdo T 4p 1. fo = = ( ). 3 . 3. pd . 2 . 2 t G do 3t GJ = G t(s) ds ( ). 4G o . 4 . t s . ( ) . ( ) . 3T T 3. fo = = ( ). G pdot 3 G pdot 3 4A2. GJ = G ( ). ds ( ) t(s ).. EI . H . I L . 2-3 . ( ) .. T to . d . 2 .. G 2 .. d1 d2 . T . fo .. G 2 . A B A B. B . T B fB . fo .. 1) . 2) .. 2-4 . 3 .. ds = -Rd q ( ). curvature .. ds R=- ( ). dq A arc length ( ) . s A q . 1. k= ( ). R. z .. A k . 1/m .. L L .. L - L. e ( ). dq L. k - ( ). ds DL = L - L. x L. s q L .. y s . q A x . ds dx B A. q + dq u A' B . u + du B' AB . -R s + ds A'B'.