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(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

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(

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

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

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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

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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

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6. Euler x

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学習の手順

chap1.dvi

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DVIOUT

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Transcription:

6-1

6-2

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

2-1 2-2

2-3 2-4

2-5 2-6

2-7 2-8

2-9 2-10

2-11 2-12

2-13 2-14

2-15 2-16 H H

H 2-17 2-18

2-19 2-20

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 0 0 2 2 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 2 2 2 I y 1 (I x I y ) 1 (I x I y ) 2 4I xy 2 2 2 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 ) =0.0491 (d 4 d 14 ) ba 3 4 d 2 d 1 2 4 0.055r 4 0.2643r y 1 =0.2234r 0.2146r 2 0.0075r 4 0.187r y 2 =0.7766r a 2 (BH 3 bh 3 ) BH 3 bh 3 64 16(BHbh) 32 d 4 d 1 4 d =0.0982 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 =0.03357r 3 Z 2 =0.00966r 3 3-1 3-2

x h h1 A y 0 c b1 b y0 y0 x I x bh bhb 1 h 3 3 h b 1 h 1 1 2 12 i x bh 3 b 1 h 1 3 12(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 3 1+ 2 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 1 3 12(dd 1 ) d 2 2 0.289 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 3 2 3 max 2 max Q bh Q bh 4 Q 3 r 2 4 Q 3 r 2 Q 1 rt Q max rt 1 1 2 2y 1 h 3 2 Q A (y 10) 2 Q y y 1 2 1 4 1 a 2 a a 9 Q Q max 8 a 1.125 2 A 1 2 (y 1 e a) 4 8 2 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 2 2 1 2y 1 (r 2 2 y 12 )(r 2 1 y 12 ) 4 max 3 3 2 9 8 4 3 2 4(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 4 1+ 2 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 ) 2 1 2 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 2 2 2 b 1 h 1 2 4y 2(b 2 h 3 2 b 1 h 13 ) b 1 2b 1 3-3 3-4

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 2 2 1 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 6 2 1 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 3 3 4 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 0.4292R 2 (H2T f0.4467r) 1 1 B 2 2 T f (H2T f )T 2 4 w 0.4292R 2 (T w0.4467r) H B T H R m B H R m B B Hf H Tw H 2 2 Hf Hf 1 2 2 2 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 16 11 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 max0.0298 (x0.4474 ) 1 M B 15 M maxm w 2 M max0.0423 (x0.329 ) 7 M B w 120 2 1 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 max0.00541 EI (x0.4215 ) max0.002385 (x0.4472 ) max0.003045 (x0.402 ) 1 M 2 max 27 EI 1 (x ) 3 max0.00932 (x0.4472 ) w 4 w 4 EI w 4 EI P 3 EI 3-5 3-6

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= 23 648 2 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 5 648 P 3 EI! P P P A /4 /4 B 3P R AR B 2 P M 0 2 max 19 384 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 5 384 w 4 EI w R AR B 2 w 2 C AC B 12 max 1 384 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 2 0 12 w 2 w M 0 (3 2 4a 2 ) 24 wb C 48EI b 2 b 3 (2 b) } 2 4 16 1 max 120 max {( ac)( ac) max0.00652 (x0.519 ) EI w 4 EI w 4 w (5 1920EI 2 4a 2 ) 2 wb R A {(b2c) 2 2 3 (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) 8 2 2 (2ab) 1 3 b 2 (2 6c3b)} C wb B {(2ab) 8 2 2 (b2c) 1 3 b 2 (2 6a3b)} w C 2 w A, C 2 30 B 20 M max0.0215 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 max0.00131 (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 7 1024 259 38880 w 4 EI w 4 EI R AR B 4 w R AR B 4 w 17 C AC B 384 7 M C w 2 384 w 2 37 C AC B w 2 864 19 M C w 2 864 max w 4 768EI max 407 311040 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 ) ) 3-7 3-8

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 128 3 (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 3 486 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 16 49 M D 512 7 (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 2 1 8(1) 1 (w 1 1 2 w 2 22 ) 1 M B 8(1) (w 1 1 2 w 2 22 ) 5w 2 2 4 2 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 2 2 2 1 8(1) 2 (w 1 1 2 w 2 22 ) w wh -H H V wh2 2 wh 2 H 16 5kh6(2hf ) V V 3-9 3-10

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 3k1 3-11 3-12

! 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 2 4 2 (k2)hf4 2 f 2 } P M E [ 2 1 4 2 (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! 3-13 3-14

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 2 24 1 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 2kn2 3-15 3-16

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 2 1 1 = 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 1 2 1 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 1 3-17 Km n EI 3-18

! 0.10 0.09 0.08 E : t : M x1 w 0.50 0.45 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 y1 0.07 M x1 w Q x1 M y2 l y 0.35 l x l x M x1 M x2 M x1 0.06 M y1 Q y1 l x M y1 0.6 0.30 1.2 3.0 Q x1 0.05 Q y1 0.5 0.25 1.0 2.5 M(wl x 2 ) 0.04 0.03 M x2 M x2 M y1 0.04 0.03 (wl x 4 /Et 3 ) 0.4 0.3 Q(wl x ) M(wl x 2 ) 0.20 0.15 0.8 0.6 (wl x 4 /Et 3 ) 2.0 1.5 Q(wl x ) 0.02 M y2 0.02 0.2 0.10 M x1 Q y1 M y2max 0.4 1.0 0.01 M y2max 0.01 0.1 0.05 M y1 Q x1 Q x1 M y2 0.2 0.5 0 0 1.0 1.5 2.0 2.5 3.0 l y l x 0 M x2max M x2 Q y1 M y2max 0 2.0 1.5 1.0 1.5 2.0 2.5 3.0 3.5 0 4.0 l y l y l x l x 0 3-19 3-20

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 0.12 0.12 0.12 0.12 0.10 M x1 0.10 1.0 0.10 M x1 0.10 1.0 M(wl x 2 ) 0.08 0.06 0.04 M y1 Q x1 M x1 M x2 M xmax Q y1 M ymax M y1 Q x1 Q y1 M x2 Q x3 0.08 0.06 0.04 (wl x 4 /Et 3 ) 0.8 0.6 0.4 Q(wl x ) M(wl x 2 ) 0.08 0.06 0.04 M y1 Q x1 Q y1,q y3 Q x3 M x2 0.08 0.06 0.04 (wl x 4 /Et 3 ) 0.8 0.6 0.4 Q(wl x ) Q x3 0.02 M ymax M y2 0.02 0.2 0.02 M y2max 0.02 0.2 M y2 0 0 2.0 1.5 1.0 1.5 2.0 l y l x l y l x 0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 0 2.0 l y l x M y2 0 3-21 3-22

0.50 M x1 w w! 0.45 M y1 M y2 M y2 Q x1! w l y w l y 0.40 1.6 M x2 Q x1 M x2 M x1 Q y1 Q y1 l x M y1 l x 0.35 1.4 0.12 0.12 M(wl x 2 ) 0.30 0.25 0.20 w M y2 w M x2 M x1 l y 1.2 1.0 0.8 (wl x 4 /Et 3 ) M(wl x 2 ) 0.10 0.08 0.06 M x1 Q x1 Q y1 M y1 M x2 0.10 0.08 0.06 (wl x 4 /Et 3 ) 1.0 0.8 0.6 Q(wl x ) 0.15 M y1 0.6 0.04 M x2 Q x1 Q x1 0.04 0.4 0.10 l x 0.4 0.02 M y2max M y2 0.02 0.2 0.05 M y2max 0.2 M y2 0 0 2.0 1.5 l y 1.0 l y 1.5 2.0 l x l x 0 M x2max 0 1.0 1.5 2.0 2.5 l y 3.0 3.5 4.0 l x 3-23 3-24

lk w! M y2! Q x1 M x2 0.16 l y w 0.12 Q y1 l x M y2max M x2 Q y1 0.14 0.12 0.6 lk l l l l l l l l l 2l l 0.10 Q x1 0.10 0.5 lk M(wl x 2 ) 0.08 0.06 0.08 0.06 (wl x 4 /Et 3 ) 0.4 0.3 Q(wl x ) lk 0.04 0.04 0.2 lk lk 0.02 M y2max 0.02 0.1 lk M y2 0 0 1 2 3 4 l y l x 0 3-25 3-26

" " 4-1 4-2

" " 4-3 4-4

" " 4-5 4-6

" H b/t f D2t f /t w B/t D/t tf tw b b t t D B D " 4-7 4-8

" " 4-9 4-10 E )B E> D + 2.2 + 1.4 + 1.2 + 1.0 + 2.0 + 1.8 + 1.6 + 2.3

" " 4-11 4-12 E + 2.3 + 2.2 + 2.0 + 1.8 + 1.6 + 1.4 + 1.2 + 1.0 )B E> D

# # 5-1 5-2 4.54 5.11 5.68 6.25 6.82 6.95 8.83 6.45 7.41 7.95 8.11 7.00 7.98 8.52 8.66 9.56 FB FB FC FB FB FB FC FB FB FC FB FB FB 75.6 134 216 331 472 498 628 713 794 860 912 1,130 1,250 1,350 1,420 1,520 26.7 46.9 75.1 112 160 167 218 233 269 292 304 365 417 450 466 514 21.59 30.00 39.65 51.43 63.53 71.53 83.69 81.31 83.95 91.43 103.9 106.3 109.5 118.5 133.5 133.5

# # 5-3 5-4 7.67 9.20 9.35 10.8 11.0 12.4 8.83 10.3 10.5 11.9 12.2 13.5 15.6 18.9 25.9 34.5 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 12,000 534 646 669 776 808 909 809 951 985 1,120 1,170 1,300 1,530 1,930 2,900 4,370 133.3 144.0 164.7 171.9 196.4 200.0 178.5 186.8 214.4 218.7 250.7 254.9 295.4 360.7 528.6 770.1

# # 5-5 5-6 3.45 3.95 4.48 4.64 5.36 5.05 5.85 6.16 6.99 5.87 6.97 8.08 5.30 6.29 7.29 FB FB FB FB FB FB FB FB FB 135 271 495 756 878 1,070 1,250 1,700 1,940 2,090 2,490 2,920 2,420 2,820 3,310 30.1 67.6 112 160 189 248 292 417 480 447 540 639 450 540 639 26.35 38.11 55.49 71.05 82.03 86.17 99.53 117.4 133.3 131.6 153.9 180.8 141.2 159.2 187.1

# # 5-7 5-8 4.98 5.80 6.64 4.93 5.84 6.78 4.73 5.54 6.37 7.17 4.39 5.30 6.40 6.94 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 11,700 511 601 700 601 721 853 661 781 914 1,040 687 842 1,040 1,140 169.2 187.2 217.1 207.5 231.5 269.7 233.8 257.8 303.7 336.0 253.6 299.3 360.1 387.4

# # 5-9 5-10 1.99 2.34 1.99 2.27 2.27 2.56 2.27 2.56 2.57 3.12 3.67 3.14 3.69 4.24 FC FB FC FC FB FB FB 88.8 138 156 181 278 317 424 481 638 771 906 999 1,170 1,350 13.2 21.7 22.9 26.7 41.1 47.0 59.3 67.7 91.0 112 134 145 174 202 17.85 22.90 22.69 26.67 31.99 36.97 40.80 46.78 51.59 62.91 73.45 70.54 83.37 95.41

# # 5-11 5-12 3.04 3.53 4.26 3.19 3.64 4.29 2.85 3.22 3.77 4.31 FC FC FC FB 1,260 1,460 1,750 1,650 1,870 2,190 2,240 2,520 2,910 3,310 159 187 229 185 214 257 199 227 270 314 81.98 95.43 112.0 98.35 112.3 129.3 111.7 130.3 149.8 168.0

# # 5-13 5-14

# # 5-15 5-16 3.41 4.54 5.40 6.25 6.25 3.03 4.04 4.80 5.55 4.80 5.55 6.31 5.05 6.00 6.94 6.94 7.89 8.84 2.73 3.64 4.32 5.00 4.32 5.00 5.68 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 2,650 160 214 254 294 294 160 214 254 294 254 294 334 334 396 459 459 521 584 160 214 254 294 254 294 334 83.29 98.57 110.00 121.50 132.20 87.79 103.1 114.5 126.0 126.9 138.2 149.5 119.1 133.5 148.0 160.2 174.5 188.7 90.63 106.6 118.6 130.5 132.9 144.2 155.5

# # 5-17 5-18 4.54 5.40 6.25 6.25 7.10 7.95 5.45 6.48 7.50 8.52 7.50 8.52 9.54 10.9 2.48 3.31 3.92 4.54 3.92 4.54 5.16 4.13 4.91 5.68 5.68 6.46 7.23 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 3,940 334 396 459 459 521 584 481 571 661 751 661 751 841 961 160 214 254 294 254 294 334 334 396 459 459 522 584 122.6 137.6 152.5 166.2 180.5 194.7 153.6 170.9 188.2 205.5 206.4 223.5 240.5 236.2 90.63 106.6 118.6 130.6 138.9 150.2 161.5 122.6 137.6 152.6 172.2 186.5 200.7

# # 5-19 5-20 4.96 5.89 6.82 7.75 6.82 7.75 8.68 2.27 3.03 3.60 4.17 3.03 3.60 4.17 4.73 5.30 3.79 4.50 4.50 5.21 5.92 6.63 5.92 6.63 7.57 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 5,020 481 571 661 751 661 751 841 160 214 254 294 214 254 294 334 374 334 396 397 459 522 584 522 585 668 159.6 176.9 194.2 211.5 214.4 231.5 248.5 90.63 106.6 118.6 130.6 133.6 144.9 156.2 167.5 178.7 122.6 137.6 163.9 178.2 192.5 206.7 214.5 228.5 247.2

# # 5-21 5-22 5.40 6.25 7.10 7.95 6.25 7.10 7.95 7.95 9.09 2.10 2.80 3.32 3.85 3.32 3.85 4.37 4.89 4.15 4.81 5.46 6.12 6.12 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 5,070 571 661 751 841 661 751 841 841 961 160 214 254 294 254 294 334 374 397 459 522 584 585 182.9 200.2 217.5 234.7 211.3 228.5 245.6 256.5 279.2 90.63 106.6 118.6 130.6 149.6 161.6 173.5 184.7 168.6 183.6 198.5 212.7 236.5

# # 5-23 5-24 4.20 4.98 5.77 6.55 5.77 6.55 7.34 8.39 1.95 2.60 3.08 3.57 3.57 4.06 4.54 3.25 3.85 3.85 4.46 5.07 4.46 5.07 5.68 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 5,490 481 571 661 751 661 751 841 961 161 214 254 294 295 335 375 334 396 397 459 522 460 522 585 169.6 187.6 205.6 223.5 230.4 247.5 264.5 287.2 92.86 108.9 120.9 132.9 164.1 176.1 188.1 124.9 139.9 171.1 186.1 201.1 204.6 218.8 232.9

# # 5-25 5-26 4.63 5.36 6.09 5.36 6.09 6.82 7.79 5.36 6.09 6.82 7.79 FC FC FC FC 4,690 5,230 5,750 5,360 5,880 6,390 7,060 5,490 6,010 6,520 7,180 571 661 751 661 751 841 961 662 752 842 962 190.1 208.1 226.1 226.6 243.8 260.9 283.8 239.7 256.8 273.8 296.5 3.60 4.17 4.73 4.17 4.73 5.30 4,440 4,920 5,390 5,070 5,540 5,990 397 459 522 460 522 585 171.1 186.1 201.1 211.6 225.8 239.9 HBL -H355 HBL -H355 HBL -H355 6.25 7.10 6.25 7.10 7.95 9.09 6.02 7.10 7.95 9.09 6.02 10.2 6.77 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 8,960 899 1,020 899 1,020 1,140 1,310 1,310 1,020 1,140 1,310 1,310 1,470 1,470 230.1 251.1 248.6 268.8 288.9 315.8 308.3 281.8 301.8 328.5 328.5 355.3 355.3

# # 5-27 5-28 HBL -H355 HBL -H355 HBL -H355 5.00 5.68 6.36 5.68 6.36 7.27 6.63 7.42 8.48 5.62 7.42 8.48 5.62 9.54 6.32 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 9,760 661 751 841 752 842 962 1,020 1,140 1,310 1,310 1,140 1,310 1,310 1,470 1,470 233.6 250.8 267.9 264.8 281.8 304.5 275.8 295.9 322.8 308.3 309.8 336.5 332.4 363.3 360.4 3.91 4.44 4.97 3.91 4.44 4.97 5.68 4.69 5.33 5.96 4.69 5.33 5.96 6.82 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 8,500 460 523 585 461 523 586 669 661 751 841 662 752 842 962 211.8 226.8 241.8 233.7 247.8 261.8 280.5 233.8 251.8 269.8 255.7 272.8 289.8 312.5

# # 5-29 5-30 6.21 6.96 6.21 6.96 7.95 5.26 8.95 5.92 6.21 6.96 7.95 5.26 8.95 5.92 9.94 6.58 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 1,640 276.8 297.8 297.8 317.8 344.5 332.4 371.3 360.4 320.3 340.1 366.6 366.6 393.1 393.1 419.6 419.6 3.68 4.18 3.68 4.18 4.68 5,980 6,510 6,180 6,720 7,240 460 523 461 523 586 211.8 226.8 241.3 255.8 269.8 7.10 7.95 7.10 7.95 9.09 6.02 10.2 6.77 7.95 9.09 6.02 10.2 6.77 11.4 7.52 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 2,140 301.8 325.8 322.8 345.8 376.5 364.4 407.3 396.4 368.1 398.6 398.6 429.1 429.1 459.6 459.6 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

# # 5-31 5-32 4.41 5.01 5.61 6.42 5.85 6.55 7.49 4.96 6.55 7.49 4.96 8.42 5.57 9.36 6.19 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 12,600 662 752 842 962 1,020 1,150 1,310 1,310 1,150 1,310 1,310 1,470 1,470 1,640 1,640 263.3 280.8 297.8 320.5 305.8 325.8 352.5 332.4 349.6 376.1 374.4 402.6 402.4 429.1 429.1 3.00 3.47 3.95 4.42 6,110 6,680 7,250 7,810 399 461 524 586 226.3 241.3 256.3 271.3 6.68 7.49 8.55 5.66 7.49 8.55 5.66 9.62 6.37 10.7 7.08 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 2,140 330.8 353.8 384.5 364.4 377.6 408.1 406.4 438.6 438.4 469.1 469.1 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

# # 5-33 5-34 3.60 4.17 4.73 5.30 6.06 4.17 4.73 5.30 6.06 5.52 6.19 7.07 4.68 5.52 6.19 7.07 4.68 7.95 5.26 8.84 5.85 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 13,600 572 662 752 842 962 664 754 844 964 1,020 1,150 1,310 1,310 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1,640 245.3 263.3 281.3 299.3 323.3 297.4 314.3 331.1 353.6 306.3 327.3 355.3 332.4 339.3 359.1 385.6 374.4 412.1 402.4 438.6 430.4 6.31 7.07 8.08 5.35 7.07 8.08 5.35 9.09 6.02 10.1 6.69 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 2,140 331.3 355.3 387.3 364.4 387.1 417.6 406.4 448.1 438.4 478.6 470.4 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

# # 5-35 5-36 3.29 3.74 4.19 4.78 3.74 4.19 4.78 5.38 5.98 3.95 4.48 5.02 5.74 4.48 5.02 5.74 3.80 6.46 4.28 7.18 4.60 5.23 5.86 6.70 4.43 5.23 5.86 6.70 4.43 7.53 4.99 8.37 5.54 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 14,500 461 524 586 669 525 588 671 754 838 662 752 842 962 754 844 964 964 1,080 1,080 1,200 900 1,020 1,150 1,310 1,310 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1,640 241.3 256.3 271.3 291.3 298.8 312.6 331.1 349.6 368.1 263.3 281.3 299.3 323.3 323.8 340.6 363.1 342.4 385.6 366.4 408.1 285.3 306.3 327.3 355.3 332.4 348.8 368.6 395.1 374.4 421.6 402.4 448.1 430.4 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

# # 5-37 5-38 5.26 5.98 6.70 7.65 5.07 5.98 6.70 7.65 5.07 8.61 5.7 9.57 6.33 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 2,140 307.3 331.3 355.3 387.3 364.4 373.8 396.6 427.1 406.4 457.6 438.4 488.1 470.4 3.12 3.55 3.98 4.54 3.55 3.98 4.54 5.11 5.68 3.75 4.26 4.77 5.45 4.26 4.77 5.45 3.61 6.14 4.06 6.82 7,720 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 13,600 461 524 586 670 526 588 671 755 838 662 752 842 962 754 844 964 964 1,080 1,080 1,200 241.3 256.3 271.3 291.3 307.7 322.1 340.6 359.1 377.6 263.3 281.3 299.3 323.3 332.7 350.1 372.6 342.4 395.1 366.4 417.6 FB FB HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

# # 5-39 5-40 4.37 4.97 5.57 6.36 4.21 4.97 5.57 6.36 4.21 7.16 4.74 7.95 5.26 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 15,500 900 1,020 1,150 1,310 1,310 1,020 1,150 1,310 1,310 1,470 1,470 1,640 1,640 285.3 306.3 327.3 355.3 332.4 357.7 378.1 404.6 374.4 431.1 402.4 457.6 430.4 5.00 5.68 6.36 7.27 4.81 5.68 6.36 7.27 4.81 8.18 5.42 9.09 6.02 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 2,140 307.3 331.3 355.3 387.3 364.4 382.7 406.1 436.6 406.4 467.1 438.4 497.6 470.4 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355 HBL -H355

# # 5-41 5-42

# # 5-43 5-44

# # 5-45 5-46

# # 5-47 5-48

# # 5-49 5-50

# # 5-51 5-52

# # 5-53 5-54

# # 5-55 5-56

# # 5-57 5-58

# # 5-59 5-60

# # 5-61 5-62

# 5-63 5-64 #

# # 5-65 5-66

# # 5-67 5-68

# # 5-69 5-70

# # 5-71 5-72

# # 5-73 5-74

# # 5-75 5-76

# # 5-77 5-78

# 5-79 5-80 #

# # 5-81 5-82

# # 5-83 5-84

# # 5-85 5-86

# # 5-87 5-88 O O N N J J

# # 5-89 5-90

# J # 5-91 5-92

# # 5-93 5-94 7.85kg/m 2

$ $ 6-1 6-2

$ $ 6-3 6-4

$ $ 6-5 6-6

$ $ 6-7 6-8

$ $ 6-9 6-10

6-11 6-12 $ $

6-13 6-14 $ $

6-15 6-16 $ $

6-17 6-18 $ $

6-19 6-20 $ $

6-21 6-22 $ $

6-23 6-24 $ $

6-25 6-26 $ $

6-27 6-28 $ $

6-29 6-30 $ $

6-31 6-32 $ $

6-33 6-34 $ $

6-35 6-36 $ $

6-37 6-38 $ $

6-39 6-40 $ $

6-41 6-42 $ $

6-43 6-44 $ $

6-45 6-46 $ $

6-47 6-48 $ $

6-49 6-50 $ $

6-51 6-52 $ $

6-53 6-54 $ $

6-55 6-56 $ $

6-57 6-58 $ $

6-59 6-60 $ $

6-61 6-62 $ $

6-63 6-64 $ $

6-65 6-66 $ $

6-67 6-68 $ $

6-69 6-70 $ $

6-71 6-72 $ $

6-73 6-74 $ $

$ $ 6-75 6-76

$ $ 6-77 6-78

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 -100505.0 7.5-125656.0 8.0-150756.510.0-150759.012.5-200908.013.5 2-100505.0 7.5 2-125656.0 8.0 2-150756.510.0 2-150759.012.5 2-200908.013.5 1 1 2 1 1 2 G 5-M20 6-M20 8-M20 9-M20 10-M20 5-M20 6-M20 8-M20 10-M20 12-M20 9 9 9 9 12 12 16 16 16 19 B 130 180 240 300 300 205 220 305 380 410 8 8 8 8 10 10 13 13 13 16 161 229 295 382 394 288 327 440 557 565 177 245 311 398 414 308 353 466 583 597 166.1 248.8 334.7 434.5 540.0 508.5 742.1 1022.0 1309.8 1618.2 M-12 1-M12 100 FB-4.5 19 35 PL-4.5 22 47 40 M-14 1-M16 115 FB-6 25 40 PL-6 28 52 50 M-16 1-M16 125 FB-6 25 45 PL-6 28 59 55 M-18 1-M20 140 FB-9 32.5 50 PL-9 34 66 60 M-20 1-M20 150 FB-9 32.5 50 PL-9 34 66 75 M-22 1-M22 165 FB-9 37.5 55 PL-9 38 73 85 M-24 2-M20 175 FB-9 37.5 50 PL-9 38 70 85 M-27 2-M20 200 FB-9 45 50 PL-9 45 72 90 M-30 2-M22 200 FB-12 45 55 PL-12 45 83 95 M-33 2-M22 225 FB-12 50 55 PL-12 50 90 110 6 6 9 9 9 12 12 12 12 12 60 60 70 70 80 80 90 90 100 110 6 6 8 8 8 10 10 10 10 10 60 61 80 80 97 100 112 145 177 217 42 43 56 56 65 70 76 93 109 129 54 55 72 72 81 90 96 113 129 149 21.0 28.7 38.6 48.0 60.6 74.7 87.7 114 139 172 $ 6-79 6-80

B B e p p e e p p p p e FB- 65 6 FB- 75 6 FB- 65 9 FB- 75 9 FB- 90 9 FB-100 9 FB- 90 12 FB-100 12 FB- 90 16 FB-100 16 2-M16 2-M16 3-M16 3-M16 3-M20 3-M20 3-M20 4-M20 4-M20 5-M20 6 6 9 9 9 9 12 12 12 12 65 75 65 75 90 100 90 100 115 130 6 117 71 83 6 142 83 95 8 131 82 98 8 159 96 112 8 190 111 127 8 218 125 141 10 202 121 141 10 232 136 156 10 270 155 175 10 309 175 195 66.3 80.4 99.4 120.6 143.8 165.0 191.8 220.0 255.7 293.3 2L- 65 65 6 2L- 75 75 6 2L- 75 75 9 2L- 75 75 12 2L- 90 90 7 2L- 90 90 10 2L- 90 90 13 2L-100 100 7 2L-100 100 10 2L-100 100 13 5-M16 5-M16 5-M20 7-M16 5-M20 5-M20 7-M20 5-M20 6-M20 8-M20 9 9 12 12 12 12 12 12 12 12 165 8 339 216 232 190 8 474 253 269 205 10 531 286 306 260 10 667 354 374 205 10 529 285 305 270 10 733 387 407 340 10 933 487 507 225 10 598 319 339 305 10 832 436 456 385 10 1062 551 571 303.0 359.4 503.4 633.2 502.0 695.6 886.0 567.8 789.6 1008.2 $ B B $ e p p p p e e p p p p e L- 65 65 6 L- 75 75 6 L- 75 75 9 L- 75 75 12 L- 90 90 7 L- 90 90 10 L- 90 90 13 L-100 100 7 L-100 100 10 L-100 100 13 5-M16 5-M16 5-M16 6-M16 5-M20 5-M20 6-M20 4-M20 5-M20 6-M20 9 9 9 9 9 9 12 9 9 12 90 8 170 101 117 95 8 202 117 133 125 8 291 162 178 160 8 362 197 213 125 8 282 157 173 165 8 389 211 227 160 10 395 218 238 135 8 303 168 184 185 8 443 238 254 180 10 448 244 264 105.6 126.8 180.8 232.6 176.9 242.0 305.5 201.6 277.3 351.3 2L- 65 65 6 2L- 75 75 6 2L- 75 75 9 2L- 75 75 12 2L- 90 90 7 2L- 90 90 10 2L- 90 90 13 2L-100 100 7 2L-100 100 10 2L-100 100 13 5 2-M16 5 2-M16 5 2-M16 6 2-M16 5 2-M20 5 2-M20 6 2-M20 4 2-M20 5 2-M20 6 2-M20 9 9 9 9 9 9 12 9 9 12 160 8 339 186 202 185 8 404 218 234 250 8 581 307 323 315 8 723 378 394 250 8 564 298 314 330 8 777 405 421 320 10 789 415 435 270 8 605 319 335 370 8 885 459 475 355 10 896 468 488 211.3 253.6 361.6 465.3 353.9 484.1 611.0 403.2 554.6 702.6 6-81 6-82

% % 7-1 7-2

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) 2 2 1 M max H (1(h) 2 2 1 exp tan 1 exp [ ( ) ] 12h tan 1 1 h M max H e 4 0.3224H sin 4 H M max e 2 2 0.2079M 0 % 1 l m tan 1 1 12h 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 1/4 7-3 7-4

% % 7-5 7-6

% % 7-7 7-8

% 7-9 7-10 %

% 7-11 7-12 %

% % 7-13 7-14

% % 7-15 7-16

% % 7-17 7-18

% % 7-19 7-20

& & 8-1 8-2 A A A-A,

& & 8-3 8-4

&, @,@ @, & 8-5 8-6

& & 8-7 8-8 @ @ @, @ @ @ @ @ @, @ @ @ @ @ @ @ @ @, @ @ @ @ @ @ @ @, @ @ @ @

& & 8-9 8-10

& & 8-11 8-12

& & 8-13 8-14

& & 8-15 8-16

& 8-17 8-18 &

& 8-19 8-20 &

& & 8-21 8-22

& 8-23 8-24 &

& & 8-25 8-26

& & 8-27 8-28

& & 8-29 8-30

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 & 8-31 8-32

& 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 &

& & 8-35 8-36 A H x x Y Y B H x x Y Y B A H x x Y Y A B

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 8-37 8-38

& & 8-39 8-40

& & 8-41 8-42

& & 8-43 8-44

& & 8-45 8-46

& & 8-47 8-48

& 8-49 8-50 &

& & 8-51 8-52

& & 8-53 8-54

& & 8-55 8-56

& & 8-57 8-58

& & 8-59 8-60

& & 8-61 8-62

& 8-63 8-64 &

& & 8-65 8-66

& 8-67 8-68 &

& 8-69 8-70 &

& & 8-71 8-72

& & 8-73 8-74

& & 8-75 8-76

& & 8-77 8-78

& 8-79 8-80 MEMO

-1-2

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

-5-6

-7-8

-9-10

-11-12

-13-14 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 R0.25 0.025 2 2 R0.25 0.025 10 0.05 10 0.05 8 0.05 55 0.6 27.5 0.4 27.5 0.4 45 2 45 2

-15-16

-17-18

-19-20

Cat.No.A1J-001-02 http://www.jfe-steel.co.jp 100-0011 2 2 3 TEL03(3597)3111X03(3597)4860 530-8353 1 6 2010 TEL 06(6342)0707 X 06(6342)0706 451-6018 6 1 18 TEL 052(561)8612 X 052(561)3374 060-0005 2 5 17 TEL 011(251)2551 X 011(251)7130 980-0811 4 1 25 3 TEL 022(221)1691 X 022(221)1695 950-0087 1 3 1 4 TEL 025(241)9111 X 025(241)7443 930-00043 1 3 TEL 076(441)2056 X 076(441)2058 730-0036 4 21 7 TEL 082(245)9700 X 082(245)9611 760-0019 2 1 23 TEL 087(822)5100 X 087(822)5105 812-0025 1 3527 TEL 092(263)1651 X 092(263)1656 260-0028 313 5 TEL 043(238)8001 X 043(238)8008 231-0011 1 10 4 TEL 045(212)9860 X 045(212)9873 422-8061 1 3513 TEL 054(288)9910 X 054(288)9877 700-0821 1 8 45 18 TEL 086(224)1281 X 086(224)1285 900-0015 3 21 1 TEL 098(868)9295 X 098(868)5458 1308R(1003)1-3 SPa