Size: px
Start display at page:

Download ""

Transcription

1

2

3 6-1

4 6-2

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31 H H

32 H

33

34

35 A A da S x A yda,s y A xda A y 0 I x i x Z x _ y Sx _ x S y A, A I x A y 2 da, I y A x 2 da y x da A x h c b y0 y0 x bh h 2 bh 3 12 h 12 =0.289h bh 2 6! I xy A xyda I p A r 2 da, I p I x I y i x I x i y I y A, A 0 _ x r _ y y x x x0 y0 h c x0 y0 b x bh bh y 0 = b 2 h 2 1 x b 2 2 h 2 0 = b 3 h 3 6(b 2 h 2 ) bh 6(b 2 h 2 ) b 2 h 2 6 b 2 h 2! i p I p A x c d y0 y0 x 4 d 2 =0.785d 2 d 2 64 d 4 d 32 d 3 4 =0.0491d 4 =0.0982d 3 Z 1 y I Z 2 I 1, y 2 S x S x Ay 0, S y S y Ax 0 2 I x I x 2y 0 S x Ay 02, I y I y 2x 0 S y Ax 0 I xy I xy x 0 S x y 0 S y Ax 0 y I x I x Ay 0, I y I y Ax 0 I xy I xy Ax 0 y 0 S x S x cos S y sin S y S x sin S y cos I x I x cos 2 I y sin 2 I xy sin2 I y I x sin 2 I y cos 2 I xy sin2 I xy IxIy sin2 I xy cos2 2 I xy 0x, y tan2 2Ixy I y I x I x 1 (I x I y ) 1 (I x I y ) 2 4I xy I y 1 (I x I y ) 1 (I x I y ) 2 4I xy I x I x cos 2 I y sin 2 I y I x sin 2 I y cos 2 I xy IxIy sin2 2 y' y' G y' y x0 0 y0 0' y 0 y y1 y2 x x' x' x x' x x 0 y0 y0 y0 y0 y2 y1 y1 y2 d1 y0 y0 d 2a 2b h H b B r r r 90 r x 4 (d 2 d 12 ) =0.785 (d 2 d 12 ) ab (BHbh) 4 4 r 2 d 2 a H 2 y 1 =0.4244r y 2 =0.5756r (d 64 4 d 14 ) = (d 4 d 14 ) ba 3 4 d 2 d r r y 1 =0.2234r r r r y 2 =0.7766r a 2 (BH 3 bh 3 ) BH 3 bh (BHbh) 32 d 4 d 1 4 d = d 4 d 1 4 d ba 2 4 (BH 3 bh 3 ) 32H Z 1 =0.1296r 3 Z 2 =0.0956r 3 Z 1 = r 3 Z 2 = r

36 x h h1 A y 0 c b1 b y0 y0 x I x bh bhb 1 h 3 3 h b 1 h i x bh 3 b 1 h (bhb 1 h 1 ) Z x bh 3 b 1 h 1 3 6h x y z y x y y QS x bi x S x I x Q max A y 1! b t x 0 f f x hw d d1 x d w h b 0 t b x b/3 r f y1 y2 y0 y y0 0 x x d/3 e bhw(bt) bf+wt b(dd 1 ) b 2 11 d ed/3 e d 1 r bd 3 b 2 d 2 r0.2358d 1 1+ d1 d1 b 2 th 2 f 2 (bt) y 1 2(bfwt) th3 3 (bt)f 2 Ay 3 1 y 2hy 1 d 2 r d2 e e 2fb 3 wt 3 12 b(d 3 d 13 ) 12 d 2 2 2fb 3 wt 3 12{bhw(bt)} d 2/3d 1/3d I x A d 3 d (dd 1 ) d dd 1 d 1 b/4 r1 r2 b e d/4 r 1d/6 r 2d/12 2fb 3 wt 3 6b b(d 3 d 13 ) 6d d/4 Z 1 I x y 1 I Z x 2 y2 y1 y1 y1 2r y1 y1 h a a t b 2r 2r2 2r1 e max max max max max max 2 max Q bh Q bh 4 Q 3 r 2 4 Q 3 r 2 Q 1 rt Q max rt y 1 h 3 2 Q A (y 10) 2 Q y y a 2 a a 9 Q Q max 8 a A 1 2 (y 1 e a) y 1 r 4 3 Q A (y 10) 2 y 1 r Q 2 A (y 10) r 2 y 1 r 1 4 Q 3 (r 4 2 r 14 ) (r 2 2 y 12 ) r 1 y 1 4 Q r 3 (r 4 2 r 14 ) 2 2 r y 1 (r 2 2 y 12 )(r 2 1 y 12 ) 4 max (r 2 2 r 2 r 1r 12 ) 3(r 2 2 r 12 ) Q(r 2 2 r 2 r 1r 12 ) (r 2 4 r 14 ) A Q 4(r 2 2 r 2 r 1r 12 ) 3(r 2 2 r 12 )! D1D2 2 D e 1 D D 1 e D ed/4 e b 2i2 2 b 2i1 2 h h y1 b2 b1 b1 b2 b1 2 2 b2 b1 h1 h2 max h h 3(b 2h 2 2 b 1 h 12 )(b 2 h 2b 1 h 1 ) y1 2 2(b 2 h 3 2 b 1 h 13 )(b 2b 1 ) b 3Q 2 h 2 2 3Q (h 2 b 1 h 2(b 1 2 h 3 2 b 1 h 13 ) 2 2 4y 12 ) max (b 2 h 3 2 b 1 h 13 ) (b 2b 1 ) 2 h 1 2 y 1 3Q b 2 h b 1 h 1 2 4y 2(b 2 h 3 2 b 1 h 13 ) b 1 2b

37 y! dy x B(y) y H B c1 c2 x 1 Z p B(y)ydy B(y)ydy 0c 0 B(y) y c 1, c 2 Zp BH 2 /4 c 2 H B Zp BH 2 /6 P A A A R M max w B a P b B B R BP R BP R Bw M BP M BPb 1 M B w P 3 A 3 EI 1 P A 6 EI 1 A 8 w 4 EI (3b 2 b 3 )! H BH 2 /12 a a 2 a /6 A B w w R B 2 1 M B w w 4 A 30 EI B R d T R R H B T2 Tf T1 Tw H R B R B Tf Hf H Tw 4 d 3 /6 R T R 3 {1(1 ) 3 } 3 R BT 2 (HT 2 ) 1 (H2T 2 ) 2 T 2 1 BT f (HT f ) 1 (H2T f ) 2 T 4 w R 2 (H2T f0.4467r) 1 1 B 2 2 T f (H2T f )T 2 4 w R 2 (T w0.4467r) H B T H R m B H R m B B Hf H Tw H 2 2 Hf Hf BH 6 2 4R m 2 T 1 A fh f A 4 wh f A f A w 1 A fh f A 4 wh f A f A w A fb 1 4 A wt w A f A w w A M A x A x A x w A x M A x A /2 P /2 C B B w B w B B B B R B 2 w R B0 3 R A w 8 5 R B w 8 1 R A w 10 2 R B w 5 11 R A w 40 9 R B w 40 R AR B 5 R A P R B P 16 3 M 2 1 M B w 3 2 M BM 9 M max 128 w 2 3 (x 8 ) M 1 B 8 w 2 M max (x ) 1 M B 15 M maxm w 2 M max (x0.329 ) 7 M B w M B M 2 5 M C P 32 3 M B P 16 w 2 w 2 11 w 4 A 120 EI 1 A 2 M 2 EI max EI (x ) max (x ) max (x0.402 ) 1 M 2 max 27 EI 1 (x ) 3 max (x ) w 4 w 4 EI w 4 EI P 3 EI

38 R M0 max R CA,CB max A P C /2 /2 B P R AR B 2 P M 0 4 P 3 max 48EI P R AR B 2 P C AC B 8 P 3 max 192EI! x A A a P /3 P C b P /3 B B Pb R A Pa R B R AR BP M C Pab P M 0 3 max max Pb( 2 b 2 ) 3/2 (a>b 9 3 EI x= b 2 3 P 3 EI ) c Pa2 b 2 3EI Pb R 2 A (3ab) 3 Pa R 2 B (3ba) 3 R AR BP Pab C 2 A Pa C 2 b B 2 2P C AC B 9 2 max max 2Pa 3 b 2 2a (x= ) 3EI(3ab) 2 3ab P 3 EI! P P P A /4 /4 B 3P R AR B 2 P M 0 2 max P 3 EI 3P R AR B 2 5P C AC B 16 max 1 96 P 3 EI A w B w R AR B 2 w 2 M 0 8 max w 4 EI w R AR B 2 w 2 C AC B 12 max w 4 EI x A x A A A w C a b c a w /2 /2 w a B w B B B 2cb R Awb 2 2ab R Bwb 2 w R A 6 w R B 3 w R AR B 4 w( a) R AR B 2 R M maxr A (a A ) 2w (xar A /w) M max0.064 (x0.577 ) w M w 2 w M 0 (3 2 4a 2 ) 24 wb C 48EI b 2 b 3 (2 b) } max 120 max {( ac)( ac) max (x0.519 ) EI w 4 EI w 4 w (5 1920EI 2 4a 2 ) 2 wb R A {(b2c) (ac)(2acbcab)} R BwbR A 3w R A 20 7w R B 20 w R AR B 4 w( a) R AR B 2 C wb A {(b2c) (2ab) 1 3 b 2 (2 6c3b)} C wb B {(2ab) (b2c) 1 3 b 2 (2 6a3b)} w C 2 w A, C 2 30 B 20 M max w 2 (x0.548 ) 5w C 2 AC B 96 w M 2 max 32 w a C AC B ( 2 2a 2 3 ) 12 1 x 6EI 7 max 3840 max w {3C A x 2 R A x 3 (xa) 4 } 4 w 4 max (x0.525 ) EI w 4 EI w (5 1920EI 4 20 a 3 16a 4 ) A A w D C E B /4 /4 w C B /6 /6 w R AR B 4 w R AR B 4 w 2 M C 16 5w M 2 D,E 96 7w M 2 C 108 max max w 4 EI w 4 EI R AR B 4 w R AR B 4 w 17 C AC B M C w w 2 37 C AC B w M C w max w 4 768EI max w 4 EI x A a M C b B R AR B M M Ma Mb C or M( 2 3b 2 ) 3/2 max 9 3 EI (x= 2 3b 2 ) 3 6abM R AR B 3 bm C A 2 (2 3b) am C B 2 (2 3a) max b(2ab)3 M 54a 2 EI (x= (3a )/3a) x A M B R AR B M x M xm(1 ) M 2 max 9 3 EI (x=(1 1 3 ) )

39 A x R M max B w C 3 R AR C 8 5 R B w 4 w 1 M B 8 9 M D (x ) 8 w 2 w 2 max w 4 185EI (x0.422 ) f h S B I 2 I 2 D I 1 I 1 C I 1 K1 h I2 K 2 S K 2 kk1! A x P P D B E 2 2 C 5 R A 16 P 5 R C 16 P 11 R B 8 P 3 M B 16 P 5 M DM E 32 P P 3 max 48 5 EI (x= 1 ) 5 7P 3 D E 768EI A w E h 2 (k3)f (3hf ) 3 V A 8 w! A P P P P D E BF G 3 3 C 2 R AR C 3 P 8 R B 3 P 1 M B 3 P 1 M EM F 9 P 2 M DM G 9 P 7 D G P H V A V E H 1 V E 8 H w 2 64 w 8h5f A x w B C 7 R A w 16 1 R C w 16 5 R B w 8 1 M B M D (x ) 16 w 2 w 2 7w 4 O 768EI 1 (x ) 2 w wf -H H V wf f (h 2 ) H wf 16 8h 2 (k3)5f (4hf ) A w1 D B E w2 C 1 R A 16 1 R C 16 5 R B 8 (7w 1w 2 ) (7w 2w 1 ) (w 1w 2 ) 1 M B 16 (w 1w 2 ) 2 1 D 768EI 1 E 768EI (7w 13w 2 ) 4 (7w 23w 1 ) 4 x w V V Vwx (h x 2 ) A I 1 1 w 1 B I 2 2 w 2 C Ww 1 1w 2 2 R BWR AR C R A w (1) 1 (w w 2 22 ) 1 M B 8(1) (w w 2 22 ) 5w M B 2 O 384EI 2 16EI 2 (BC ) b V wx -H H V H wx(hb) 16h k (5h 2 b 2 )6h (2hf ) I 2 1 I1 2 R C w (1) 2 (w w 2 22 ) w wh -H H V wh2 2 wh 2 H 16 5kh6(2hf ) V V

40 H P H P V 2 H P 8 3h2f f h S I 2 I 2 I 1 I 1 I 1 K1 h I2 K 2 S K 2 kk1 (khf) 2 4k (h 2 hff 2 )! H V V A P V H V E V A(1)P V EP P H 4 6h(1)f(34 2 ) H M A V A w M E V E H w 3(4k1) w V E V 32 3k1 A V 2 E H w 2 k(4h5f )f 16 w 2 kh(8h15f )f(6hf ) 3 M A { } 96 2(3k1) w 2 kh(8h15f )f(6hf ) 3 M E { } 96 2(3k1)! P P x V V H P -H P H V H V V 2Ph Ph2 12EK 1 HP Px V Px H 4 4(k1) k x k(3h 2 h )3(2hf ) a w M A M A V V M E wf -H H M E V wx -H H V wf 12k(hf )5f V 8 (3k1) H wf 2kh 2 (k4)10khff 2 (5k1) 4 wf 12h(3k2)3f f{kh(4h9f )f(6hf )} M A [ ] 24 6k2 wf 12h(3k2)3f f{kh(4h9f )f(6hf )} M E [ ] 24 6k2 wa V 3 k 2h 3k1 2h(k2)2fa(k1) H wa3 k 4h wa M 2 2h 2 k(12h3hk4ak12a18f ) A { 24h 3a 2 k(kh2hf )8fk(3hfaf3ha)6hf 2 6h6k(3ha) } 3k1 wa M 2 2h 2 k(12h3hk4ak12a18f ) E { 24h 3a 2 k(kh2hf )8fk(3hfaf3ha)6hf 2 6h6k(3ha) } 3k1 a H x V A P V E H V AP Px V E 3Px H 4h x k(h 2 a 2 )h(2hf ) M V A M E wh- H H V wh 2 k V 2 3k1 H wh2 k{h(k3)2f 2 } 4 wh M 2 12k6 kh 2 (k6)kf (15h16f )6f 2 A { } 24 3k1 wh M 2 12k6 kh 2 (k6)kf (15h16f )6f 2 E { } 24 3k

41 ! H H P M A b P a b a H V M M A V A V M A V x V A P M A H P -H P P P M M E M E M E M E V VE V V V E H H H H H P V 2 P H 4 P M 4 V AP(1) k(3h4f )f kh 2 hf(2k1) 3k(32) V EP 3k1 3k(1)(12) 3k1 HP {3k(hf)4 2 (k1) f3(khf)} P 1 M A [ {2k(1)h 2 2 3(2k)hf(14)f (k2)hf4 2 f 2 } P M E [ (k2)hf4 2 f 2 } (1)(12) 3k1 {2k(1)h 2 3(2k)hf(14)f 2 (1)(12) 3k1 Ph 3k V, HP 3k1 Ph 3k2 M A (M E ), Ph M 2 3k1 B (M D ) 2 Ph2 3k4 12EK 1 3k1 3Pa 2 k 3h(k2)3f2a(k1) V E, Pa H 2 k 2h 3k1 2h Pa h 2 k(4hhk2ak6a6f )a 2 k(hk2hf) M A { 2h 2fk(2hfaf3ah)hf 2 2h3k(2ha) } 6k2 Pa h 2 k(4hhk2ak6a6f )a 2 k(hk2hf) M E { 2h 2fk(2hfaf3ah)hf 2 2h3k(2ha) } 6k2 3Pxk a V a{hfb(k1)} E, V 3Pxk H h 3k1 APV E, h Px h M 2 k(2bk2h3f )bfk(6h3b4f ) A { 2h h(3b 2 k 2 6b 2 kf 2 ) 3bkh } 3k1 Px h M 2 k(2bk2h3f )bfk(6h3b4f ) E { 2h h(3b 2 k 2 6b 2 kf 2 ) 3bkh } 3k1 ] ] 3k 3k1 h P H H B w A V V H I 2 C I 1 I 1 V A V P wh -H w V V D V V D H H H H I 1 K1 h I2 K 2 K 2 k K1 V 2 w H w 2 4h V A(1)P V DP 1 2k3 3P (1) H 2h 2k3 1 V 2 AV D 3P H 8h wh V 2 2 5k6 Hwh 8(2k3) Ph V H P 2 P 2 1 2k3!

42 h B I 2 C I 1 I 1 A D I 1 K1 h I2 K 2 K 2 kk1 h B I 1 A S I 2 C I 1 D n h I 1 K1 h I2 K 2 S K 2 k K1 1nn 2 (1n 3 )k! w V 2 w w V 2 w! H H w V M V A V M A M A P wh -H M M D M D V V D V H H H H w 2 4h M w 2 12 V AP(1) V DPV A H 3P 2h M A P 2 M D P 2 H M A wh k2 1 k2 6k1(12) 6k1 (1) k2 (1) wh V 2 k 6k1 M D wh 8 wh 2 24 (1) 2k3 k2 5k12(k2) (k2)(6k1) 7k32(k2) (k2)(6k1) 5k9 12k 12 k2 6k1 5k9 12k k2 6k1 H H w w V V A V V P wh(n-1) wh -H V V V H V D H H H H w 2 8h V A(1)P 1n V DP P (1) 2n(n1) H 2h 1 P V 2 AV D 2 3P n1 H 16h wh V 2 (n 2 2 1) wh(n1) 8k7n(n4) H 8 wh V 2 2 H wh 8 5k2(n2) P M V H M V H Ph V P H 2 Ph M A 2 3k 6k1 3k1 6k1 P V P-H V H Ph V H P 2 2kn

43 f h B A I 2 I 1 I 1 C D I 1 K1 h I2 K 2 K 2 kk1 5h 2 (2k3)4f (5h2f ) m /2 /2 m K3EI/ 3 m b n, = K48EI/ 3 n= 3EI m 3 3EI n=4 m 3 m b n, = 3EI (m0.23m b ) 3 48EI (m0.5m b ) 3! P H H w w V V V A V wf -H P wh -H w V V V D V H H H H w V 2 H w 2 4 5h4f V wf (2hf ) 2 35h 2 (2k3)16f (7h2f ) H wf 14 V A(1)P V DP 5P H 2 V wh2 2 5wh H 2 8 V Ph 3h 2f {(1)1} h(5k6)4f (1) K 1 l a a a m m b/2 m m m m b b y b /2 /2 b m K x EA EI b EI c m 2 K 2 h h ab 3EI K (ab) 2 192EI K 3 3EI n=8 m 3 m b n, =14 3EI K 3 (ab) 3 2EA K x sin 2 2EA K y cos 2 1 n= ab n= 1 bei K c x h 3 I c b 1 2I b h 2I b b 192EI 1 Ky b 3I c b h 3 8I b h 1 3I c b n= K m nx = ny= K x m K y m m, n= n= K n m 3EI 3 a 3 b 3 m nx = ny= 3EI m EI (m0.375m b ) 3 K x m K y m K (mm, /3) b = 1 K n K 1 K 2 b 2! V - P H V H 5Ph H 2 h(2k3)2f K 2 m 1 K 1 K K 2 m 2 2 n = (1 ) 2 m 1 m 2 m 1 m K 2 4K 1 K 2 1 m (1 m 2 2 m ) 1 m 1 m 2 K Km n EI 3-18

44 ! E : t : M x1 w w 0.40 w Q y1 M x2 M x1 0.5lx M y2 l y w w My2 M x2 Q y1 Q x1 l y M x1 M y1! Q y1 M y1 M y M x1 w Q x1 M y2 l y 0.35 l x l x M x1 M x2 M x M y1 Q y1 l x M y Q x Q y M(wl x 2 ) M x2 M x2 M y (wl x 4 /Et 3 ) Q(wl x ) M(wl x 2 ) (wl x 4 /Et 3 ) Q(wl x ) 0.02 M y M x1 Q y1 M y2max M y2max M y1 Q x1 Q x1 M y l y l x 0 M x2max M x2 Q y1 M y2max l y l y l x l x

45 w w w! w Q y3 M y2 M ymax M x1 l y w M y1 Q x3 M y2 M x1 l y w Q y3 M x2 M y2max M y2 M x1 l y! Q x1 M x2 M x2 Q x1 Qx3 Q x1 Q y1 M y1 Q y1 Q y1 M y1 l x l x l x M x M x M(wl x 2 ) M y1 Q x1 M x1 M x2 M xmax Q y1 M ymax M y1 Q x1 Q y1 M x2 Q x (wl x 4 /Et 3 ) Q(wl x ) M(wl x 2 ) M y1 Q x1 Q y1,q y3 Q x3 M x (wl x 4 /Et 3 ) Q(wl x ) Q x M ymax M y M y2max M y l y l x l y l x l y l x M y

46 0.50 M x1 w w! 0.45 M y1 M y2 M y2 Q x1! w l y w l y M x2 Q x1 M x2 M x1 Q y1 Q y1 l x M y1 l x M(wl x 2 ) w M y2 w M x2 M x1 l y (wl x 4 /Et 3 ) M(wl x 2 ) M x1 Q x1 Q y1 M y1 M x (wl x 4 /Et 3 ) Q(wl x ) 0.15 M y M x2 Q x1 Q x l x M y2max M y M y2max 0.2 M y l y 1.0 l y l x l x 0 M x2max l y l x

47 lk w! M y2! Q x1 M x l y w 0.12 Q y1 l x M y2max M x2 Q y lk l l l l l l l l l 2l l 0.10 Q x lk M(wl x 2 ) (wl x 4 /Et 3 ) Q(wl x ) lk lk lk 0.02 M y2max lk M y l y l x

48

49 " "

50 " "

51 " "

52 " H b/t f D2t f /t w B/t D/t tf tw b b t t D B D "

53 " " E )B E> D

54 " " E )B E> D

55

56 # # FB FB FC FB FB FB FC FB FB FC FB FB FB ,130 1,250 1,350 1,420 1,

57 # # FC FB FB FC FB FB FB FB FC FB FC FB FB FC FC FC FB FB 1,640 1,910 2,030 2,280 2,420 2,650 2,520 2,850 3,030 3,330 3,540 3,840 4,480 5,570 8,17 12, ,120 1,170 1,300 1,530 1,930 2,900 4,

58 # # FB FB FB FB FB FB FB FB FB ,070 1,250 1,700 1,940 2,090 2,490 2,920 2,420 2,820 3,

59 # # FC FC FB FC FB FC FB 3,400 3,890 4,500 4,870 5,640 6,590 6,270 7,160 8,270 9,270 7,610 8,990 10,800 11, , ,040 1,

60 # # FC FB FC FC FB FB FB ,170 1,

61 # # FC FC FC FB 1,260 1,460 1,750 1,650 1,870 2,190 2,240 2,520 2,910 3,

62 # #

63 # # FC FC FC FC FC FC FC 1,130 1,390 1,580 1,760 1,820 1,310 1,610 1,830 2,040 1,910 2,120 2,320 1,950 2,220 2,490 2,560 2,820 3,070 1,500 1,840 2,090 2,330 2,180 2,420 2,

64 # # FB 2,210 2,530 2,830 2,920 3,220 3,500 2,690 3,060 3,430 3,780 3,550 3,900 4,240 4,680 1,700 2,070 2,350 2,620 2,470 2,740 2,990 2,490 2,840 3,180 3,290 3,620 3,

65 # # FB FC FC FC FC FC FC FC FC FC FB FB FB FB FB FB FB 3,030 3,450 3,850 4,250 4,010 4,400 4,780 1,900 2,320 2,620 2,920 2,470 2,770 3,060 3,350 3,630 2,770 3,150 3,300 3,670 4,040 4,390 4,220 4,570 5,

66 # # FC FC FC FC FC FC FC FC 3,840 4,290 4,730 5,160 4,380 4,820 5,250 5,330 5,890 2,110 2,570 2,900 3,220 3,070 3,400 3,710 4,020 3,660 4,060 4,460 4,850 5,

67 # # FC FC FC FB 3,740 4,240 4,730 5,210 4,960 5,440 5,900 6,510 2,370 2,860 3,220 3,580 3,780 4,120 4,460 3,400 3,850 4,060 4,500 4,940 4,640 5,070 5,

68 # # FC FC FC FC 4,690 5,230 5,750 5,360 5,880 6,390 7,060 5,490 6,010 6,520 7, ,440 4,920 5,390 5,070 5,540 5, HBL -H355 HBL -H355 HBL -H FC FC FC FC 5,950 6,560 6,080 6,700 7,300 8,080 8,080 6,830 7,420 8,200 8,200 8,960 8, , ,020 1,140 1,310 1,310 1,020 1,140 1,310 1,310 1,470 1,

69 # # HBL -H355 HBL -H355 HBL -H FB FB FB FB 5,850 6,410 6,970 6,570 7,120 7,840 7,290 7,940 8,790 8,790 8,090 8,940 8,940 9,760 9, ,020 1,140 1,310 1,310 1,140 1,310 1,310 1,470 1, FC FC FC FC FC FC FC FC 5,520 6,020 6,510 5,700 6,200 6,680 7,320 6,350 6,960 7,560 6,530 7,130 7,730 8,

70 # # FC FC FC FC FC FC FC 7,900 8,600 8,070 8,770 9,680 9,680 10,600 10,600 8,340 9,030 9,930 9,930 10,800 10,800 11,700 11,700 1,020 1,140 1,020 1,150 1,310 1,310 1,470 1,470 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1, ,980 6,510 6,180 6,720 7, FC FC FC FC FC FC FC 8,840 9,640 9,010 9,810 10,900 10,900 11,900 11,900 10,100 11,100 11,100 12,100 12,100 13,100 13,100 1,330 1,490 1,330 1,490 1,710 1,710 1,920 1,920 1,500 1,710 1,710 1,920 1,920 2,140 2, HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

71 # # FB 7,070 7,720 8,350 9,180 8,720 9,460 10,400 10,400 9,760 10,700 10,700 11,700 11,700 12,600 12, ,020 1,150 1,310 1,310 1,150 1,310 1,310 1,470 1,470 1,640 1, ,110 6,680 7,250 7, FB 9,720 10,600 11,700 11,700 10,900 12,000 12,000 13,100 13,100 14,200 14,200 1,330 1,490 1,710 1,710 1,500 1,710 1,710 1,920 1,920 2,140 2, HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

72 # # FC FB FB FB FB FB FB FB FB FB 6,930 7,620 8,310 8,990 9,880 7,970 8,650 9,320 10,200 9,370 10,200 11,200 11,200 9,720 10,500 11,500 11,500 12,600 12,600 13,600 13, ,020 1,150 1,310 1,310 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1, FB FB FB FB FB 10,400 11,400 12,600 12,600 11,700 12,900 12,900 14,100 14,100 15,200 15,200 1,340 1,490 1,710 1,710 1,500 1,710 1,710 1,920 1,920 2,140 2, HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

73 # # FC FC FC FC FC FC FC FC FC FC FC FC FC FC FC FC 7,190 7,790 8,390 9,160 8,180 8,760 9,530 10,300 11,000 8,190 8,920 9,640 10,600 9,300 10,000 11,000 11,000 11,900 11,900 12,800 9,190 10,000 10,900 12,000 12,000 10,400 11,300 12,400 12,400 13,500 13,500 14,500 14, ,080 1,080 1, ,020 1,150 1,310 1,310 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1, HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

74 # # FC FC FC FC FC FB FC 10,200 11,200 12,100 13,400 13,400 11,600 12,500 13,800 13,800 15,000 15,000 16,300 16,300 1,180 1,340 1,500 1,710 1,710 1,340 1,500 1,710 1,710 1,920 1,920 2,140 2, ,720 8,350 8,980 9,810 8,780 9,400 10,200 11,000 11,800 8,770 9,540 10,300 11,300 9,970 10,700 11,700 11,700 12,700 12,700 13, ,080 1,080 1, FB FB HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

75 # # FB FB 9,820 10,700 11,600 12,800 12,800 11,200 12,000 13,200 13,200 14,400 14,400 15,500 15, ,020 1,150 1,310 1,310 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1, FB FB FB 10,900 11,900 12,900 14,300 14,300 12,300 13,400 14,700 14,700 16,000 16,000 17,300 17,300 1,180 1,340 1,500 1,710 1,710 1,340 1,500 1,710 1,710 1,920 1,920 2,140 2, HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

76 # #

77 # #

78 # #

79 # #

80 # #

81 # #

82 # #

83 # #

84 # #

85 # #

86 # #

87 # #

88 # #

89 # #

90 # #

91 # #

92 # #

93 # #

94 # #

95 # #

96 # #

97 # #

98 # #

99 # # O O N N J J

100 # #

101 # J #

102 # # kg/m 2

103

104 $ $

105 $ $

106 $ $

107 $ $

108 $ $

109 $ $

110 $ $

111 $ $

112 $ $

113 $ $

114 $ $

115 $ $

116 $ $

117 $ $

118 $ $

119 $ $

120 $ $

121 $ $

122 $ $

123 $ $

124 $ $

125 $ $

126 $ $

127 $ $

128 $ $

129 $ $

130 $ $

131 $ $

132 $ $

133 $ $

134 $ $

135 $ $

136 $ $

137 $ $

138 $ $

139 $ $

140 $ $

141 $ $

142 $ $

143 p p p e p e S s e 3 e 1 S s e 3 p e 2 e 1 e 2 e 1 p e 1 e 2 B $ B e p p p p e G 5-M20 6-M20 8-M20 9-M20 10-M20 5-M20 6-M20 8-M20 10-M20 12-M B M-12 1-M FB PL M-14 1-M FB PL M-16 1-M FB PL M-18 1-M FB PL M-20 1-M FB PL M-22 1-M FB PL M-24 2-M FB PL M-27 2-M FB PL M-30 2-M FB PL M-33 2-M FB PL $

144 B B e p p e e p p p p e FB FB FB FB FB FB FB FB FB FB M16 2-M16 3-M16 3-M16 3-M20 3-M20 3-M20 4-M20 4-M20 5-M L L L L L L L L L L M16 5-M16 5-M20 7-M16 5-M20 5-M20 7-M20 5-M20 6-M20 8-M $ B B $ e p p p p e e p p p p e L L L L L L L L L L M16 5-M16 5-M16 6-M16 5-M20 5-M20 6-M20 4-M20 5-M20 6-M L L L L L L L L L L M M M M M M M M M M

145

146 % %

147 h0 H h l Mtop H Mtop Mmax Mtop l m l m1 H h e l h M 0 /2 Mmax M 0 l m lm1 l H Mmax l m lm1 H l lm1 Mmax M 0 l lm1 m y (1h) 3 1/2 t H y (1h) 3 2 y H 3EI t H t y H 3 12EI 3 2EI t 3 4EI 3 1(h) y y 1h 0 H 0 H y 2EI 3 4EI 0 y y 3 t 0 y t (1h) 2 t H t0 t 0 2EI 2 H t 2EI 2 M 00 1h M 0 2 M 00 H M 0 2 % M max H (12h) M max H (1(h) exp tan 1 exp [ ( ) ] 12h tan 1 1 h M max H e H sin 4 H M max e M 0 % 1 l m tan h 1 l m tan 1 1 h l m 4 l m 2 1 l tan 1 1h h 1 l tan 1 h1 h1 l 2 3 l 4 hd/4ei 1/4 hd/4ei 1/

148 % %

149 % %

150 % %

151 % %

152 % %

153 % %

154 % %

155 % %

156

157 & & A A A-A,

158 & &

159 &

160 & &

161 & &

162 & &

163 & &

164 & &

165 & &

166 & &

167 & &

168 & &

169 & &

170 & &

171 & &

172 qs sc afcec sca Fc Ec Fc Ec10 5 qs D r T FcEc LdL/d d d F & d l d D T l r l' l l l qs= nd bd Hd L Hd sc afcec nd ndnd bd LHd Hd Hd L bdd &

173 & 8-33 B p f f p f p p f t ly/lx lx ly wp lx t wp lx t lx 8-34 &

174 & & A H x x Y Y B H x x Y Y B A H x x Y Y A B

175 M M My Mx M w 2 w M max M 2 8 max 8 wx w cos wy w sin Mx w 2 cos 8 w 2 ft 157 N/mm 2 8 My w Mx My cos sin ( 2 Zx Zy Zx Zy sin 8 ( & 5w 4 w 4 x 384EIx cos x 185EIx 5w 4 w 4 y 384EIy sin y 185EIy w 2 M Zx 8Zx ft cos sin & 5w 4 x 384EIx w 4 x 185EIx

176 & &

177 & &

178 & &

179 & &

180 & &

181 & &

182 & &

183 & &

184 & &

185 & &

186 & &

187 & &

188 & &

189 & &

190 & &

191 & &

192 & &

193 & &

194 & &

195 & &

196 & MEMO

197

198 -1-2

199 J2 A J1 A J1 J2 A J A J J A J A -3-4

200 -5-6

201 -7-8

202 -9-10

203 -11-12

204 L W T P R R L T W R R P D L P R R W B L T P R R r3mm L t b do R R

205 -15-16

206 -17-18

207 -19-20

208

209

210 Cat.No.A1J TEL03(3597)3111X03(3597) TEL 06(6342)0707 X 06(6342) TEL 052(561)8612 X 052(561) TEL 011(251)2551 X 011(251) TEL 022(221)1691 X 022(221) TEL 025(241)9111 X 025(241) TEL 076(441)2056 X 076(441) TEL 082(245)9700 X 082(245) TEL 087(822)5100 X 087(822) TEL 092(263)1651 X 092(263) TEL 043(238)8001 X 043(238) TEL 045(212)9860 X 045(212) TEL 054(288)9910 X 054(288) TEL 086(224)1281 X 086(224) TEL 098(868)9295 X 098(868) R(1003)1-3 SPa

211

Contents

Contents Contents 6-1 6-2 780 630 440 385 355 325 295 205 80 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-10 1-11 1-12 1-13 1-14 1-15 1-16 1-17 1-18 1-19 1-20 1-21 1-22 1-23 1-24 1-25 1-26 1-27 1-28 1-29 1-30 MEMO G

More information

(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

(1.2) 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

More information

76 3 B m n AB P m n AP : PB = m : n A P B P AB m : n m < n n AB Q Q m A B AQ : QB = m : n (m n) m > n m n Q AB m : n A B Q P AB Q AB 3. 3 A(1) B(3) C(

76 3 B m n AB P m n AP : PB = m : n A P B P AB m : n m < n n AB Q Q m A B AQ : QB = m : n (m n) m > n m n Q AB m : n A B Q P AB Q AB 3. 3 A(1) B(3) C( 3 3.1 3.1.1 1 1 A P a 1 a P a P P(a) a P(a) a P(a) a a 0 a = a a < 0 a = a a < b a > b A a b a B b B b a b A a 3.1 A() B(5) AB = 5 = 3 A(3) B(1) AB = 3 1 = A(a) B(b) AB AB = b a 3.1 (1) A(6) B(1) () A(

More information

名古屋工業大の数学 2000 年 ~2015 年 大学入試数学動画解説サイト

名古屋工業大の数学 2000 年 ~2015 年 大学入試数学動画解説サイト 名古屋工業大の数学 年 ~5 年 大学入試数学動画解説サイト http://mathroom.jugem.jp/ 68 i 4 3 III III 3 5 3 ii 5 6 45 99 5 4 3. () r \= S n = r + r + 3r 3 + + nr n () x > f n (x) = e x + e x + 3e 3x + + ne nx f(x) = lim f n(x) lim

More information

O E ( ) A a A A(a) O ( ) (1) O O () 467

O E ( ) A a A A(a) O ( ) (1) O O () 467 1 1.0 16 1 ( 1 1 ) 1 466 1.1 1.1.1 4 O E ( ) A a A A(a) O ( ) (1) O O () 467 ( ) A(a) O A 0 a x ( ) A(3), B( ), C 1, D( 5) DB C A x 5 4 3 1 0 1 3 4 5 16 A(1), B( 3) A(a) B(b) d ( ) A(a) B(b) d AB d = d(a,

More information

熊本県数学問題正解

熊本県数学問題正解 00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (

More information

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4 35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m

More information

( )

( ) 18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................

More information

1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載

1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載 1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります

More information

ORIGINAL TEXT I II A B 1 4 13 21 27 44 54 64 84 98 113 126 138 146 165 175 181 188 198 213 225 234 244 261 268 273 2 281 I II A B 292 3 I II A B c 1 1 (1) x 2 + 4xy + 4y 2 x 2y 2 (2) 8x 2 + 16xy + 6y 2

More information

A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6

A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6 1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67

More information

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s [ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =

More information

i I II I II II IC IIC I II ii 5 8 5 3 7 8 iii I 3........................... 5......................... 7........................... 4........................ 8.3......................... 33.4...................

More information

6. Euler x

6. Euler x ...............................................................................3......................................... 4.4................................... 5.5......................................

More information

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy

More information

入試の軌跡

入試の軌跡 4 y O x 4 Typed by L A TEX ε ) ) ) 6 4 ) 4 75 ) http://kumamoto.s.xrea.com/plan/.. PDF) Ctrl +L) Ctrl +) Ctrl + Ctrl + ) ) Alt + ) Alt + ) ESC. http://kumamoto.s.xrea.com/nyusi/kumadai kiseki ri i.pdf

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n 1 1.1 1.1.1 A 2 P Q 3 R S T R S T P 80 50 60 Q 90 40 70 80 50 60 90 40 70 8 5 6 1 1 2 9 4 7 2 1 2 3 1 2 m n m n m n n n n 1.1 8 5 6 9 4 7 2 6 0 8 2 3 2 2 2 1 2 1 1.1 2 4 7 1 1 3 7 5 2 3 5 0 3 4 1 6 9 1

More information

IMO 1 n, 21n n (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a

IMO 1 n, 21n n (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a 1 40 (1959 1999 ) (IMO) 41 (2000 ) WEB 1 1959 1 IMO 1 n, 21n + 4 13n + 3 2 (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a = 4, b =

More information

20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................

More information

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y [ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)

More information

高校生の就職への数学II

高校生の就職への数学II II O Tped b L A TEX ε . II. 3. 4. 5. http://www.ocn.ne.jp/ oboetene/plan/ 7 9 i .......................................................................................... 3..3...............................

More information

Part () () Γ Part ,

Part () () Γ Part , Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35

More information

x x x 2, A 4 2 Ax.4 A A A A λ λ 4 λ 2 A λe λ λ2 5λ + 6 0,...λ 2, λ 2 3 E 0 E 0 p p Ap λp λ 2 p 4 2 p p 2 p { 4p 2 2p p + 2 p, p 2 λ {

x x x 2, A 4 2 Ax.4 A A A A λ λ 4 λ 2 A λe λ λ2 5λ + 6 0,...λ 2, λ 2 3 E 0 E 0 p p Ap λp λ 2 p 4 2 p p 2 p { 4p 2 2p p + 2 p, p 2 λ { K E N Z OU 2008 8. 4x 2x 2 2 2 x + x 2. x 2 2x 2, 2 2 d 2 x 2 2.2 2 3x 2... d 2 x 2 5 + 6x 0 2 2 d 2 x 2 + P t + P 2tx Qx x x, x 2 2 2 x 2 P 2 tx P tx 2 + Qx x, x 2. d x 4 2 x 2 x x 2.3 x x x 2, A 4 2

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1 ... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =

More information

(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10)

(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) 2017 12 9 4 1 30 4 10 3 1 30 3 30 2 1 30 2 50 1 1 30 2 10 (1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) (1) i 23 c 23 0 1 2 3 4 5 6 7 8 9 a b d e f g h i (2) 23 23 (3) 23 ( 23 ) 23 x 1 x 2 23 x

More information

dynamics-solution2.dvi

dynamics-solution2.dvi 1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj

More information

II (10 4 ) 1. p (x, y) (a, b) ε(x, y; a, b) 0 f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a 2 x a 0 A = f x (

II (10 4 ) 1. p (x, y) (a, b) ε(x, y; a, b) 0 f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a 2 x a 0 A = f x ( II (1 4 ) 1. p.13 1 (x, y) (a, b) ε(x, y; a, b) f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a x a A = f x (a, b) y x 3 3y 3 (x, y) (, ) f (x, y) = x + y (x, y) = (, )

More information

3.300 m m m m m m 0 m m m 0 m 0 m m m he m T m 1.50 m N/ N

3.300 m m m m m m 0 m m m 0 m 0 m m m he m T m 1.50 m N/ N 3.300 m 0.500 m 0.300 m 0.300 m 0.300 m 0.500 m 0 m 1.000 m 2.000 m 0 m 0 m 0.300 m 0.300 m -0.200 he 0.400 m T 0.200 m 1.50 m 0.16 2 24.5 N/ 3 18.0 N/ 3 28.0 18.7 18.7 14.0 14.0 X(m) 1.000 2.000 20 Y(m)

More information

空き容量一覧表(154kV以上)

空き容量一覧表(154kV以上) 1/3 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量 覧 < 留意事項 > (1) 空容量は 安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 熱容量を考慮した空き容量を記載しております その他の要因 ( や系統安定度など ) で連系制約が発 する場合があります (3) 表 は 既に空容量がないため

More information

4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx

4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx 4 4 5 4 I II III A B C, 5 7 I II A B,, 8, 9 I II A B O A,, Bb, b, Cc, c, c b c b b c c c OA BC P BC OP BC P AP BC n f n x xn e x! e n! n f n x f n x f n x f k x k 4 e > f n x dx k k! fx sin x cos x tan

More information

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx

More information

a,, f. a e c a M V N W W c V R MN W e sin V e cos f a b a ba e b W c V e c e F af af F a a c a e be a f a F a b e f F f a b e F e ff a e F a b e e f b e f F F a R b e c e f F M N DD s n s n D s s nd s

More information

2/8 一次二次当該 42 AX 変圧器 なし 43 AY 変圧器 なし 44 BA 変圧器 なし 45 BB 変圧器 なし 46 BC 変圧器 なし

2/8 一次二次当該 42 AX 変圧器 なし 43 AY 変圧器 なし 44 BA 変圧器 なし 45 BB 変圧器 なし 46 BC 変圧器 なし 1/8 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( や系統安定度など ) で連系制約が発生する場合があります (3)

More information

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2 II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh

More information

5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 = 4. () = 8 () = 4

5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 = 4. () = 8 () = 4 ... A F F l F l F(p, 0) = p p > 0 l p 0 P(, ) H P(, ) P l PH F PF = PH PF = PH p O p ( p) + = { ( p)} = 4p l = 4p (p 0) F(p, 0) = p O 3 5 5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 =

More information

dvipsj.8449.dvi

dvipsj.8449.dvi 9 1 9 9.1 9 2 (1) 9.1 9.2 σ a = σ Y FS σ a : σ Y : σ b = M I c = M W FS : M : I : c : = σ b

More information

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

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)

More information

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

More information

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1 I, A 25 8 24 1 1.1 ( 3 ) 3 9 10 3 9 : (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4), (3,3,3) 10 : (1,3,6), (1,4,5), (2,2,6), (2,3,5), (2,4,4), (3,3,4) 6 3 9 10 3 9 : 6 3 + 3 2 + 1 = 25 25 10 : 6 3 + 3 3

More information

HITACHI 液晶プロジェクター CP-AX3505J/CP-AW3005J 取扱説明書 -詳細版- 【技術情報編】

HITACHI 液晶プロジェクター CP-AX3505J/CP-AW3005J 取扱説明書 -詳細版- 【技術情報編】 B A C E D 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 H G I F J M N L K Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01

More information

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi) 0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

More information

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b) 2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................

More information

取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ

取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ B A C D E F K I M L J H G N O Q P Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01 00 00 60 01 00 BE EF 03 06 00 19 D3 02 00

More information

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 + ( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n

More information

211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,

More information

<93FA97A AC C837288EA97972E786C7378>

<93FA97A AC C837288EA97972E786C7378> 日立ブラウン管テレビ一覧 F-500 SF-100 FMB-300 FMB-490 FMB-790 FMB-290 SMB-300 FMB-310G FMB-780 FMY-480 FMY-110 TOMY-100 FMY-520 FMY-320G SMY-110 FMY-510 SMY-490 FMY-770 FY-470 TSY-120 FY-340G FY-280 FY-450 SY-330

More information

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P 6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P

More information

Z 2 10Z MPa MPa MPa MPa 1.5MPa s s s JIS 6g/6H SD SD/B LB LS

Z 2 10Z MPa MPa MPa MPa 1.5MPa s s s JIS 6g/6H SD SD/B LB LS 3 03 0.01MPa 0.1MPa 0.1MPa 0.01MPa 1.MPa 0s 0s 0s JIS g/h SDSD/BLB LS0 F FBTT/BTB TB/BCUCU/B SDLCFTT/B TCTC/BDBD SDSD/BLB LS0 F FBTT/BTB TB/BCUCU/B SDLBFTT/B SKSPLK LP FKFP SKSPLK LP FKFP TKTPDPBDBP TKTPDPBDBP

More information

untitled

untitled ( ) c a sin b c b c a cos a c b c a tan b a b cos sin a c b c a ccos b csin (4) Ma k Mg a (Gal) g(98gal) (Gal) a max (K-E) kh Zck.85.6. 4 Ma g a k a g k D τ f c + σ tanφ σ 3 3 /A τ f3 S S τ A σ /A σ /A

More information

he T N/ N/

he T N/ N/ 6.000 1.000 0.800 0.000 0.500 1.500 3.000 1.200 0.000 0.000 0.000 0.000 0.000-0.100 he 1.500 T 0.100 1.50 0.00 2 24.5 N/ 3 18.0 N/ 3 28.0 18.7 18.7 14.0 14.0 X() 20.000 Y() 0.000 (kn/2) 10.000 0.000 kn

More information

f : R R f(x, y) = x + y axy f = 0, x + y axy = 0 y 直線 x+y+a=0 に漸近し 原点で交叉する美しい形をしている x +y axy=0 X+Y+a=0 o x t x = at 1 + t, y = at (a > 0) 1 + t f(x, y

f : R R f(x, y) = x + y axy f = 0, x + y axy = 0 y 直線 x+y+a=0 に漸近し 原点で交叉する美しい形をしている x +y axy=0 X+Y+a=0 o x t x = at 1 + t, y = at (a > 0) 1 + t f(x, y 017 8 10 f : R R f(x) = x n + x n 1 + 1, f(x) = sin 1, log x x n m :f : R n R m z = f(x, y) R R R R, R R R n R m R n R m R n R m f : R R f (x) = lim h 0 f(x + h) f(x) h f : R n R m m n M Jacobi( ) m n

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

48 * *2

48 * *2 374-1- 17 2 1 1 B A C A C 48 *2 49-2- 2 176 176 *2 -3- B A A B B C A B A C 1 B C B C 2 B C 94 2 B C 3 1 6 2 8 1 177 C B C C C A D A A B A 7 B C C A 3 C A 187 187 C B 10 AC 187-4- 10 C C B B B B A B 2 BC

More information

4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X

4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X 4 4. 4.. 5 5 0 A P P P X X X X +45 45 0 45 60 70 X 60 X 0 P P 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P 0 0 + 60 = 90, 0 + 60 = 750 0 + 60 ( ) = 0 90 750 0 90 0

More information

l µ l µ l 0 (1, x r, y r, z r ) 1 r (1, x r, y r, z r ) l µ g µν η µν 2ml µ l ν 1 2m r 2mx r 2 2my r 2 2mz r 2 2mx r 2 1 2mx2 2mxy 2mxz 2my r 2mz 2 r

l µ l µ l 0 (1, x r, y r, z r ) 1 r (1, x r, y r, z r ) l µ g µν η µν 2ml µ l ν 1 2m r 2mx r 2 2my r 2 2mz r 2 2mx r 2 1 2mx2 2mxy 2mxz 2my r 2mz 2 r 2 1 (7a)(7b) λ i( w w ) + [ w + w ] 1 + w w l 2 0 Re(γ) α (7a)(7b) 2 γ 0, ( w) 2 1, w 1 γ (1) l µ, λ j γ l 2 0 Re(γ) α, λ w + w i( w w ) 1 + w w γ γ 1 w 1 r [x2 + y 2 + z 2 ] 1/2 ( w) 2 x2 + y 2 + z 2

More information

i 6 3 ii 3 7 8 9 3 6 iii 5 8 5 3 7 8 v...................................................... 5.3....................... 7 3........................ 3.................3.......................... 8 3 35

More information

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3 π 9 3 7 4. π 3................................................. 3.3........................ 3.4 π.................... 4.5..................... 4 7...................... 7..................... 9 3 3. p

More information

CALCULUS II (Hiroshi SUZUKI ) f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b)

CALCULUS II (Hiroshi SUZUKI ) f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b) CALCULUS II (Hiroshi SUZUKI ) 16 1 1 1.1 1.1 f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b) lim f(x, y) = lim f(x, y) = lim f(x, y) = c. x a, y b

More information

(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37

(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37 4. 98 () θ a = 5(cm) θ c = 4(cm) b = (cm) () D 0cm 0 60 D 99 () 0m O O 7 sin 7 = 0.60 cos 7 = 0.799 tan 7 = 0.754 () xkm km R km 00 () θ cos θ = sin θ = () θ sin θ = 4 tan θ = () 0 < x < 90 tan x = 4 sin

More information

HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語

HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語 A B C D E F G H I 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 K L J Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C RS-232C RS-232C Cable (cross) LAN cable (CAT-5 or greater) LAN LAN LAN LAN RS-232C BE

More information

December 28, 2018

December 28, 2018 e-mail : kigami@i.kyoto-u.ac.jp December 28, 28 Contents 2............................. 3.2......................... 7.3..................... 9.4................ 4.5............. 2.6.... 22 2 36 2..........................

More information

II K116 : January 14, ,. A = (a ij ) ij m n. ( ). B m n, C n l. A = max{ a ij }. ij A + B A + B, AC n A C (1) 1. m n (A k ) k=1,... m n A, A k k

II K116 : January 14, ,. A = (a ij ) ij m n. ( ). B m n, C n l. A = max{ a ij }. ij A + B A + B, AC n A C (1) 1. m n (A k ) k=1,... m n A, A k k : January 14, 28..,. A = (a ij ) ij m n. ( ). B m n, C n l. A = max{ a ij }. ij A + B A + B, AC n A C (1) 1. m n (A k ) k=1,... m n A, A k k, A. lim k A k = A. A k = (a (k) ij ) ij, A k = (a ij ) ij, i,

More information

0 (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4

0   (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4 0 http://homepage3.nifty.com/yakuikei (18) 1 99 3 2014/12/13 (19) 1 100 3 n Z (n Z ) 5 30 (5 30 ) 37 22 (mod 5) (20) 201 300 3 (37 22 5 ) (12, 8) = 4 (21) 16! 2 (12 8 4) (22) (3 n )! 3 (23) 100! 0 1 (1)

More information

untitled

untitled 5 28 EAR CCLECCN ECCN 1. 2. 3. 4. 5.EAR page 1 of 28 WWW.Agilent.co.jp -> Q&A ECCN 10020A 10070A 10070B 10070C 10071A 10071B 10072A 10073A 10073B 10073C 10074A 10074B 10074C 10076A 10229A 10240B 10430A

More information

1 26 ( ) ( ) 1 4 I II III A B C (120 ) ( ) 1, 5 7 I II III A B C (120 ) 1 (1) 0 x π 0 y π 3 sin x sin y = 3, 3 cos x + cos y = 1 (2) a b c a +

1 26 ( ) ( ) 1 4 I II III A B C (120 ) ( ) 1, 5 7 I II III A B C (120 ) 1 (1) 0 x π 0 y π 3 sin x sin y = 3, 3 cos x + cos y = 1 (2) a b c a + 6 ( ) 6 5 ( ) 4 I II III A B C ( ) ( ), 5 7 I II III A B C ( ) () x π y π sin x sin y =, cos x + cos y = () b c + b + c = + b + = b c c () 4 5 6 n ( ) ( ) ( ) n ( ) n m n + m = 555 n OAB P k m n k PO +

More information

X-FUNX ワークシート関数リファレンス

X-FUNX ワークシート関数リファレンス X-FUNX Level.4a xn n pt 1+ 1 sd npt Bxn3 cin + si + sa ( sd xn) 3 n t1 + n pt xn sd ( t1+ n pt) Bt t t cin + xn si sa ( sd xn) n 1 + +

More information

2001 Mg-Zn-Y LPSO(Long Period Stacking Order) Mg,,,. LPSO ( ), Mg, Zn,Y. Mg Zn, Y fcc( ) L1 2. LPSO Mg,., Mg L1 2, Zn,Y,, Y.,, Zn, Y Mg. Zn,Y., 926, 1

2001 Mg-Zn-Y LPSO(Long Period Stacking Order) Mg,,,. LPSO ( ), Mg, Zn,Y. Mg Zn, Y fcc( ) L1 2. LPSO Mg,., Mg L1 2, Zn,Y,, Y.,, Zn, Y Mg. Zn,Y., 926, 1 Mg-LPSO 2566 2016 3 2001 Mg-Zn-Y LPSO(Long Period Stacking Order) Mg,,,. LPSO ( ), Mg, Zn,Y. Mg Zn, Y fcc( ) L1 2. LPSO Mg,., Mg L1 2, Zn,Y,, Y.,, Zn, Y Mg. Zn,Y., 926, 1 1,.,,., 1 C 8, 2 A 9.., Zn,Y,.

More information

1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1

1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1 ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB + 7 9 AD AB + AD AB + 9 7 4 9 AD () AB sin π = AB = ABD AD

More information

29

29 9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n

More information

untitled

untitled 33 30 1 1955 1-1 1-1 -1- - D.J.Varnes Crown Main ScrapTop Head Transverse CrackMinor Scrap LongitudinalFault Zone Surface of Rupture Foot Transverse RidgeTip ToeRight Flank 1-1 -- ph RpH -3- -5-4- -5-

More information

21 2 26 i 1 1 1.1............................ 1 1.2............................ 3 2 9 2.1................... 9 2.2.......... 9 2.3................... 11 2.4....................... 12 3 15 3.1..........

More information

学習の手順

学習の手順 NAVI 2 MAP 3 ABCD EFGH D F ABCD EFGH CD EH A ABC A BC AD ABC DBA BC//DE x 4 a //b // c x BC//DE EC AD//EF//BC x y AD DB AE EC DE//BC 5 D E AB AC BC 12cm DE 10 AP=PB=BR AQ=CQ BS CS 11 ABCD 1 C AB M BD P

More information

chap1.dvi

chap1.dvi 1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f

More information

2.2 ( y = y(x ( (x 0, y 0 y (x 0 (y 0 = y(x 0 y = y(x ( y (x 0 = F (x 0, y(x 0 = F (x 0, y 0 (x 0, y 0 ( (x 0, y 0 F (x 0, y 0 xy (x, y (, F (x, y ( (

2.2 ( y = y(x ( (x 0, y 0 y (x 0 (y 0 = y(x 0 y = y(x ( y (x 0 = F (x 0, y(x 0 = F (x 0, y 0 (x 0, y 0 ( (x 0, y 0 F (x 0, y 0 xy (x, y (, F (x, y ( ( (. x y y x f y = f(x y x y = y(x y x y dx = d dx y(x = y (x = f (x y = y(x x ( (differential equation ( + y 2 dx + xy = 0 dx = xy + y 2 2 2 x y 2 F (x, y = xy + y 2 y = y(x x x xy(x = F (x, y(x + y(x 2

More information

R R 16 ( 3 )

R R 16   ( 3 ) (017 ) 9 4 7 ( ) ( 3 ) ( 010 ) 1 (P3) 1 11 (P4) 1 1 (P4) 1 (P15) 1 (P16) (P0) 3 (P18) 3 4 (P3) 4 3 4 31 1 5 3 5 4 6 5 9 51 9 5 9 6 9 61 9 6 α β 9 63 û 11 64 R 1 65 13 66 14 7 14 71 15 7 R R 16 http://wwwecoosaka-uacjp/~tazak/class/017

More information

応力とひずみ.ppt

応力とひずみ.ppt in yukawa@numse.nagoya-u.ac.jp 2 3 4 5 x 2 6 Continuum) 7 8 9 F F 10 F L L F L 1 L F L F L F 11 F L F F L F L L L 1 L 2 12 F L F! A A! S! = F S 13 F L L F F n = F " cos# F t = F " sin# S $ = S cos# S S

More information

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+ R 3 R n C n V??,?? k, l K x, y, z K n, i x + y + z x + y + z iv x V, x + x o x V v kx + y kx + ky vi k + lx kx + lx vii klx klx viii x x ii x + y y + x, V iii o K n, x K n, x + o x iv x K n, x + x o x

More information

() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (

() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n ( 3 n nc k+ k + 3 () n C r n C n r nc r C r + C r ( r n ) () n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (4) n C n n C + n C + n C + + n C n (5) k k n C k n C k (6) n C + nc

More information

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1) D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y

More information

16 6 12 1 16 6 23 23 11 16 START 1 Out Ok 1,2 Ok END Out 3 1 1/ H24.2 2 1 L2-1 L2-2 H14.3 3 H9.10 PHC SC 19 1 24 3 18N/mm 2 24N/mm 2 30N/mm 2 25 10 13 12 13 12 11 11 11 11 19 7 25 10 24N 8cm 25(20)mm 45

More information

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............

More information

[] Tle () i ( ) e . () [].....[], ..i.et.. N Z, I Q R C N Z Q R C R i R {,,} N A B X N Z Q R,, c,,, c, A, B, C, L, y, z,, X, L pq p q def f () lim f ( ) f ( ) ( ), p p q r q r p q r p q r c c,, f ( )

More information

17 ( ) II III A B C(100 ) 1, 2, 6, 7 II A B (100 ) 2, 5, 6 II A B (80 ) 8 10 I II III A B C(80 ) 1 a 1 = 1 2 a n+1 = a n + 2n + 1 (n = 1,

17 ( ) II III A B C(100 ) 1, 2, 6, 7 II A B (100 ) 2, 5, 6 II A B (80 ) 8 10 I II III A B C(80 ) 1 a 1 = 1 2 a n+1 = a n + 2n + 1 (n = 1, 17 ( ) 17 5 1 4 II III A B C(1 ) 1,, 6, 7 II A B (1 ), 5, 6 II A B (8 ) 8 1 I II III A B C(8 ) 1 a 1 1 a n+1 a n + n + 1 (n 1,,, ) {a n+1 n } (1) a 4 () a n OA OB AOB 6 OAB AB : 1 P OB Q OP AQ R (1) PQ

More information

PLC HMI High flexibility Simple networking Easy to use 190 HMI 2

PLC HMI High flexibility Simple networking Easy to use 190 HMI 2 PLC HMI High flexibility Simple networking Easy to use 190 HMI 2 Contents 4 11 14 15 3 SIMATIC PLC190 24 S7-1200/ S7-1200 S7-1200 I/OCPU ROM SIMATIC S7-1200PLC 4 S7-1200 CPU 100Mbps HMI-PLCPC-PLCPLC16

More information

limit&derivative

limit&derivative - - 7 )................................................................................ 5.................................. 7.. e ).......................... 9 )..........................................

More information

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C 0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,

More information

i

i i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,

More information

5. [1 ] 1 [], u(x, t) t c u(x, t) x (5.3) ξ x + ct, η x ct (5.4),u(x, t) ξ, η u(ξ, η), ξ t,, ( u(ξ,η) ξ η u(x, t) t ) u(x, t) { ( u(ξ, η) c t ξ ξ { (

5. [1 ] 1 [], u(x, t) t c u(x, t) x (5.3) ξ x + ct, η x ct (5.4),u(x, t) ξ, η u(ξ, η), ξ t,, ( u(ξ,η) ξ η u(x, t) t ) u(x, t) { ( u(ξ, η) c t ξ ξ { ( 5 5.1 [ ] ) d f(t) + a d f(t) + bf(t) : f(t) 1 dt dt ) u(x, t) c u(x, t) : u(x, t) t x : ( ) ) 1 : y + ay, : y + ay + by : ( ) 1 ) : y + ay, : yy + ay 3 ( ): ( ) ) : y + ay, : y + ay b [],,, [ ] au xx

More information

untitled

untitled 20 3 Copyright (2007) by P.W.R.I. All rights reserved. No part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the

More information

untitled

untitled W1A W1B W1C W1D W1E W1F W1G W1H W1I W1J W1K W1L W1N W1O W1P W1Q W1R W2A W2B W2C W2D W2F W2G W2H W2I W2J W2K W2L W2N W2O W2P W2Q W2R W3A W3B W3C W3D W3E W3F W3G W3H W3I W3J W3K W3N W3O W3P W3Q W3R W4A W4B

More information

DVIOUT

DVIOUT A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)

More information

< 1 > (1) f 0 (a) =6a ; g 0 (a) =6a 2 (2) y = f(x) x = 1 f( 1) = 3 ( 1) 2 =3 ; f 0 ( 1) = 6 ( 1) = 6 ; ( 1; 3) 6 x =1 f(1) = 3 ; f 0 (1) = 6 ; (1; 3)

< 1 > (1) f 0 (a) =6a ; g 0 (a) =6a 2 (2) y = f(x) x = 1 f( 1) = 3 ( 1) 2 =3 ; f 0 ( 1) = 6 ( 1) = 6 ; ( 1; 3) 6 x =1 f(1) = 3 ; f 0 (1) = 6 ; (1; 3) < 1 > (1) f 0 (a) =6a ; g 0 (a) =6a 2 (2) y = f(x) x = 1 f( 1) = 3 ( 1) 2 =3 ; f 0 ( 1) = 6 ( 1) = 6 ; ( 1; 3) 6 x =1 f(1) = 3 ; f 0 (1) = 6 ; (1; 3) 6 y = g(x) x = 1 g( 1) = 2 ( 1) 3 = 2 ; g 0 ( 1) =

More information

(u(x)v(x)) = u (x)v(x) + u(x)v (x) ( ) u(x) = u (x)v(x) u(x)v (x) v(x) v(x) 2 y = g(t), t = f(x) y = g(f(x)) dy dx dy dx = dy dt dt dx., y, f, g y = f (g(x))g (x). ( (f(g(x)). ). [ ] y = e ax+b (a, b )

More information

K E N Z OU

K E N Z OU K E N Z OU 11 1 1 1.1..................................... 1.1.1............................ 1.1..................................................................................... 4 1.........................................

More information

body.dvi

body.dvi ..1 f(x) n = 1 b n = 1 f f(x) cos nx dx, n =, 1,,... f(x) sin nx dx, n =1,, 3,... f(x) = + ( n cos nx + b n sin nx) n=1 1 1 5 1.1........................... 5 1.......................... 14 1.3...........................

More information

iii 1 1 1 1................................ 1 2.......................... 3 3.............................. 5 4................................ 7 5................................ 9 6............................

More information

ii

ii ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................

More information

2012 A, N, Z, Q, R, C

2012 A, N, Z, Q, R, C 2012 A, N, Z, Q, R, C 1 2009 9 2 2011 2 3 2012 9 1 2 2 5 3 11 4 16 5 22 6 25 7 29 8 32 1 1 1.1 3 1 1 1 1 1 1? 3 3 3 3 3 3 3 1 1, 1 1 + 1 1 1+1 2 2 1 2+1 3 2 N 1.2 N (i) 2 a b a 1 b a < b a b b a a b (ii)

More information

1/1 lim f(x, y) (x,y) (a,b) ( ) ( ) lim limf(x, y) lim lim f(x, y) x a y b y b x a ( ) ( ) xy x lim lim lim lim x y x y x + y y x x + y x x lim x x 1

1/1 lim f(x, y) (x,y) (a,b) ( ) ( ) lim limf(x, y) lim lim f(x, y) x a y b y b x a ( ) ( ) xy x lim lim lim lim x y x y x + y y x x + y x x lim x x 1 1/5 ( ) Taylor ( 7.1) (x, y) f(x, y) f(x, y) x + y, xy, e x y,... 1 R {(x, y) x, y R} f(x, y) x y,xy e y log x,... R {(x, y, z) (x, y),z f(x, y)} R 3 z 1 (x + y ) z ax + by + c x 1 z ax + by + c y x +

More information