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2 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 Chief Executive of P.W.R.I.

3

4

5 * *

6

7 (1) (2) (3) (1) (2) (3) (4) (5) (6) (7) (1) (2) (3) (1) (2) (3)

8 (4) (5) (1) (2) (3) (4) (5) (1) (2) (3) (1) (2) (3) (4) (5)

9 ) 2 2 2)3) -1.1 U

10 2 2-2-

11 (a) (b)

12 ) ) 1-4-

13

14 c Z ) D E D E 2 F L

15

16

17 (a) (b) (c)

18

19

20 2.4 2 Mφ 50 σ c ε c σ s ε s Mφ V Mφ M u M u P s (N) V 10.5 (2.4.1) (2.4.3) S s S c P = S + S (2.4.1) s c s = c c c τ bd (2.4.2) c e pt c ( sinθ cosθ ) Awσ syd + = (2.4.3) 1.15a S c (N)τ c (N/mm 2 )c c c e d c pt b (mm)d (mm)s s (N)A w a θ (mm 2 )σ sy (N/mm 2 )θ ()a (mm) 10.5 S c 6)7) -12-

21 σ ( ε ) c = σ cc Edes c ε cc 1 ε c σ c = Ecε c 1 n ε cc n σ cc (N/mm 2 )ε cc ε cu E c (N/mm 2 )E des (N/mm 2 ) σ s ε s σ sy (N/mm 2 ) E s (N/mm 2 ) ε cc ε cu 8) Mφ Mφ -13-

22 Mφ XY Y X Mφ X Mφ XY -14-

23 X Y (a) (b) Mφ X, Y Y X (a) (b) Mφ X Y

24 X Y (a) (b) Mφ X Y

25 2.5 T = 2.01 δ (2.5.1) T (s)δ 80% (m) δ V6.2.3δ 2 w( s) u( s) ds δ = (2.5.2) w()() s u s ds w(s) s (kn/m)u(s) s (m)δ ( Wiu ) 2 i i ( Wiu j ) δ = (2.5.3) i W i i (kn)u i i (m) EI y M y φ y (EI y =M y / φ y = M y0 / φ y0 ) V6.2.3U -17-

26 (5.5.1) m d (t/m) m d 7 γ w = b 8 g H h (2.5.4) γ w (kn/m 3 )g (m/s 2 )b (m)h (m)h (m) h 1 h 2 (m) m d (t) m d = h2 h1 7 γ w b 8 g H hdh = 7 12 γ w b g H h 3 2 H h 3 1 (2.5.5) I

27

28 (2.5.5) m d

29 P u : P s : P s0 : P a : S Ps P s < S < P s 0 (2.6.1) P s 0 S S P s P s0 (2.4.2) c c = (2.6.1) 3 P a P a P u P a = P u (2.6.2) P s0 (2.6.2) 2.7 P a k ha = -21-

30 AF k ha P u P c P u P c P u P c P c -22-

31 k ha A B C P s0 D E F P s

32 AB 0CDE µ r (=δ P / δ y ) 2 1 khe µ r = + 1 (2.7.1) 2 khy (2.7.1)µ a 5.8 (6.4.5) c S (=k hy / k he ) c S = 1 2µ 1 a -24- (2.7.2) µ a (10.2.3) µ δ δ u y a = 1 + (2.7.3) αδ y

33 δ u δ y α (2.5.3) α α 2-2 α µ a = ) khw P ag (2.7.4) k h 2k h1 k h2 W (N)P ag (N) k hag P ag = k hag W (2.7.4) k h ( csgcz kh ) khag = 0 (2.7.5) c SG c Z k h

34 k hag c Z k h0 MW M uw (2.7.6) SW P sw 0 (2.7.7) M W (Nmm)M uw (N mm)s W (N)P sw0 RC V10.78) δ R (6.4.9) R R ( µ r )( r) δ y δ = c 1 1 (2.7.8) c R RC0.6µ r r 2RC0δ y (mm) 2 1 c Z kh0 µ = r + 1 (2.7.9) 2 khag δ y δ R δ Ra δ R δ Ra (2.7.10) 2) k haw k haw khaw k hag (2.7.11) khw P aw (2.7.12) P aw (N) k haw P aw = k haw W (2.7.12) -26-

35 k h ( csw cz kh ) khaw = 0 (2.7.13) c SW δ R (2.7.8) 2 1 c Z kh0 µ = r + 1 (2.7.14) 2 khaw δ y δ R (2.7.10) 2 δ Ra1 δ Ra1 δ Ra (2.7.15)(2.7.16) h 4b θ = Ra 2cos (2.7.15) bt + h h + 4t 4b h 4B θ = Ra 2cos (2.7.16) BL + h h + 4L 4B h t b L B (rad )) t rad h h L (a) (b) (2.7.15)(2.7.16)

36 3 3 1/

37 (a) (b) (a) (b) 60% (c) 60%

38 k = hp cdf Pu W (2.8.1) k hp c df (=1.1)P u (N)W (N) c df k hp P u W k hp k hp = cdf khug hp cdf khug k = (2.8.2) k hug k huw c Z k h

39 (2.8.3) (2.8.4) k 1. 5 (2.8.3) hug k h k 1. 5 (2.8.4) huw k h µ Fr δ Fr µ Fr 1 = r 2 { ( 1 r) + 1 r + r( khf khyf ) } ( k k ) 2 { } Fr hf Fr -31- hyf Fy ( r 0) ( r = 0) (2.8.5) δ = µ δ (2.8.6) r 0k hf

40 k hf δ Fy (m) k hf k = c c k (2.8.7) hf D c D 12.42/3 δ µ = δ δ (2.8.8) δ Fr + (2.8.9) δ Fy + (2.8.10) µ Fr 1 = r Z h0 Fr Fr Fy = µ δ Fr Fy δ 0 = δ Fy δ 0 2 { ( 1 r) + 1 r + r( khf khyf ) } ( k k ) 2 { } hf hyf ( r 0) ( r = 0) (2.8.11) µ Fr k h =0δ F =δ 0 δ Fr k h =0δ F =δ 0 (m) D E D E D E F L x (m) R R <R F L 1/3 1/3<F L 2/3 0x10 1/6 0 1/3 1/6 10x20 2/3 1/3 2/3 1/3 0x10 2/3 1/3 1 2/3 10x20 1 2/3 1 2/3 0x10 1 2/ /3<F L 1 10x (2.7.4) rad ( -32-

41 1/60rad) rad ( 1/60rad)

42 (8.7.1) 8.7 U

43 No c Z =

44

45 (1)

46 σ ck = 24 (N/mm 2 ) SD345 σ ck = 24 (N/mm 2 ) SD345 σ ck = 24 (N/mm 2 ) SD

47

48

49

50

51

52

53 (2) PHC = N/mm 2 = 80.0 N/mm 2 = 54 = 1000 mm = mm = 13.9 m = 2.50 m W 0 = 9.06 kn/m W = 5.58 kn/m PC py = N/mm 2 pu = N/mm 2 = N/mM

54 6.9m PHC PHC mm PHC -46-

55 (3) N

56 (m) N (m) N c (kn/m 2 ) (kn/m 3 ) αe 0 (kn/m 2 ) φ () γ t1 γ t

57 4.5Vs i Vs i = 100N 1/3 i (1N i 25) Vs i = 80N 1/3 i (1N i 50) T G = n H i TG 4 =0.420 (s) i= 1 Vsi II H i (m) N Vs i (m/s) H i / Vs i

58 FC 35FC 35 I P 15 D 50 10mm 10 D 10 1mm (m) γ t1 (kn/m 3 ) γ t2 (kn/m 3 ) I P FC (%) D 50 (mm) 10% D 10 (mm) F L F L D E D E

59 -51- G.L.- (m) R F L q u (kn/m 2 ) D E /3 1/3 1/3 1/ /

60 -52- G.L.- (m) R F L q u (kn/m 2 ) D E /3 2/3 2/3 2/ /

61 -53- G.L.- (m) D E /3 2/3 2/3 2/

62

63

64 (1)

65 No. (kn) () γ sat =19.6 (kn/m 3 ) 1729 γ w =9.8 (kn/m 3 ) -57-

66 (1840kN) 1840 (kn) / () () 2= (kn)

67 (2) T.P T.P+3.50 T.P+7.90 T.P (3) γ 9.8 (kn/m 3 ) K 0 = (kn/m 3 ) 1.00 (m) 4.5 (m) = 22.5 (kn/m) (kn/m 3 ) 1.00 (m) (m) = (kn/m)

68 (4) w 1 = 4.4 (m) 9.8 (kn/m 3 ) 15.0 (m) = (kn/m) w 2 = (9.70 (m) 4.40 (m) ) 9.8 (kn/m 3 ) 15.0 (m) (kn/m) (5) -60-

69 (6) ( 5.5.1) 7 pd = γ wkhs H h 8 p d (kn/m 2 )γw (kn/m 3 )k hs H (m)h (m) h 1 h 2 m d m h = 2 d h1 8 7 γ w b g H hdh = 7 12 γ w g b H h 3 2 H h g (m/s 2 )b (m) k hs 1 2 k huw c Z k h (7) 3.2.1(3) -61-

70 (1) (2)1) k H (2.5.5) -62-

71

72 EI (m) (m) (kn) i j (knm 2 ) E E E E E E E E E E E E E E E E E E E E E E E E E E E

73 (s) 1 k h k h = c Z k h0 = = 0.25 k h k hg k hg = c Z k hg0 = = 0.20 k h T=0.245 sec T=0.104sec T=0.060 sec

74 (2) 1) 12.4 R a = γ n ( R W ) + W W u s s R a (kn)n γ R u (kn)w s (kn)w (kn) R u R u = qd A + U Li f i q d (kn/m 2 )A (m 2 )U (m)l i (m)f i (kn/m 2 ) P = 1 Pu n a + W P a (kn)n W (kn) L i (m) f i (kn/m 2 ) D E L i f i (kn/m) L i f i (kn/m) L i f i D E (kn/m) /

75 D mm 1000 t mm 130 A m U m q d kn/m q d A kn 7850 U Σl i f i kn R u kn W s kn 95 W kn 78 γ 1.0 n 3 2 R a kn n 3 P a kn D mm t mm A m U m q d kn/m q d A kn 7854 U ΣLifi kn Ru kn Ws kn 95.0 W kn 77.5 γ 1.0 n 3 2 Ra kn n 3 Pa kn

76 K V A E K = p p V a L = = (kn/m 2 ) A p E p (kn/m 2 )L (m) PHC a a = 0.010(L / D) 0.36 = 0.010(13.9/1.00) = D (m) K H k H = k H 0 BH k H 0 = αe0 0.3 k H (kn/m 3 )k H0 0.3m (kn/m 3 )α B H B H = D β D (m)β = 4 D k H 4EI (1/m) D = (m) E = (kn/m 2 ) I = (m 4 ) B H = (m) () β = (m -1 ) 1/β = (m) 1/β αe 0 = (kn/m 2 ) k H0 = (kn/m 3 ) -68-

77 (m) N αe 0 (kn/m 2 ) D E k H (kn/m 3 ) / K 1 K K = EI, 1 4 β K 2 = 2 β 3 K 1 = 2EIβ, 2 = K 3 = 0 2 = K 3 EI, β K 4 = 2EI K, K 0 4 = K 1 K 3 (kn/m) (knm/m) K 2 K 4 (kn/rad) (knm/rad)

78 K 1 kn/m K 2 kn/rad K 3 knm/m K 4 knm/rad K 1 kn/m K 2 kn/rad K 3 knm/m K 4 knm/rad (S-R) H (kn) V (kn)m (knm)δ x (m)δ y (m)α (rad.) H A xx Axy Axα δ x V = Ayx Ayy Ayα δ y M Aα x Aα y Aαα α A xx = Σ (K 1 cos 2 θ i +K v sin 2 θ i ) A xy =A yx = Σ (K v K 1 ) sinθ i cosθ i A xα =A αx = Σ { (K v K 1 ) x i sinθ i cosθ i K 2 cosθ i } A yy = Σ (K v cos 2 θ i +K 1 sin 2 θ i ) A yα =A αy = Σ { (K v cos 2 θ i +K 1 sin 2 θ i ) x i +K 2 sinθ i } A αα = Σ { (K v cos 2 θ i +K 1 sin 2 θ i ) x 2 i + (K 2 + K 3 ) x i sinθ i + K 4 } x i ix q i i 6 7 A xx Axy Axα Ayx Ayy Ayα = () 7 9 Aα x Aα y Aαα A xx Axy Axα Ayx Ayy Ayα = () 7 9 Aα x Aα y Aαα

79 2) W i H i x i y i W i (kn) x i (m) y i (m) W i x i W i y i y 1 = Σ (W i y i ) / Σ W i = / = (m) W i (kn) x i (m) y i (m) W i x i W i y i y 2 = Σ (Wy i y i ) / Σ W i = / = (m) H i (kn) x i (m) y i (m) W i x i H i y i y 3 = Σ (H i y i ) / Σ H i = / 9666 = (m) -71-

80 W i (kn) x i (m) y i (m) W i x i W i y i (28) (29) (30) y 4 = Σ (W i y i ) / Σ W i = / = (m) W i (kn) x i (m) y i (m) W i x i W i y i H i (kn) x i (m) y i (m) W i x i H i y i y 6 = Σ (H i y i ) / Σ H i = / = (m) M d W i x i W i x i H i y i H i y i M d = = (knm) -72-

81 V (kn) H (kn) M (knm) V = W 1 + W 2 + W 4 + W 5 = = (kn) H = k h (W 1 + W 2 + H 3 + W 4 ) + H 6 = 0.25( ) = (kn) M = k h (W 1 y 1 + W 2 y 2 + H 3 y 3 + W 4 y 4 ) + H 6 y 6 +M d = 0.25( ) = (knm) -73-

82 3) mm P N kn Ra kn P N Ra P N Ra OK OK P N kn Pa kn P N Ra P N Ra OK OK δ mm δ a mm δδ a δδ a OK OK -74-

83 (3) 1)

84 (a) knm(b) kn M S N M S N (knm) (kn) (kn) (knm) (kn) (kn) G A B C D E F

85 2) A B C D M knm N kn S kn b mm h mm d mm mm D29 ctc 250 D29 ctc 250 D29 ctc 250 D29 ctc 250 mm A s mm A w mm 2 4-D19 ctc150 4-D19 ctc150 4-D19 ctc150 4-D19 ctc x mm σ c σ s N/mm τ m σ ca σ sa N/mm τ a A B C D A sreq mm M u knm M c knm M d knm A smin mm OK OK OK OK 1)M u M c 2)1.7MM c 3)A s 500(mm 2 ) 1)2)3)OK -77-

86 3) G M knm N kn S kn b mm h mm d mm mm D32 ctc mm A s mm x mm σ c 1.49 σ s N/mm τ m 0.62 σ ca σ sa N/mm τ a G A sreq mm 2 M u knm M c knm M d knm A smin mm )M u M c 2)1.7MM c 3)A s 500 (mm 2 ) 1)2)3)OK -78-

87 4) E F M knm N kn S kn b mm h mm d mm mm D29 ctc 125 D29 ctc mm A s mm A w mm 2 6-D22 ctc150 6-D22 ctc x mm σ c σ s N/mm τ m σ ca σ sa N/mm τ a E F A sreq mm M u knm M c knm M d knm A smin mm OK OK 1)M u M c 2)1.7MM c 3)A s 500 (mm 2 ) 1)2) 3) OK -79-

88 5) βλ 1.0 (= (m) ) β 3k β = 4 (m -1 ) 3 Eh E (= (kn/m 2 ) )h (= 2.5 (m) ) k k p (kn/m 3 ) nm k = p Kv DB Kv 1 (= (kn/m)n (=9 )m =6 D (= 22.5 (m) )B (=15.0 (m) ) βλ =

89 h M knm mm mm mm 3578 mm D D mm mm σ c N/mm σ s N/mm σ ca N/mm σ sa N/mm

90 mm M u knm M c knm M knm A s mm 2 /m OK OK 1)M u M c 2)1.7MM c 3)A s 500 (mm 2 ) 1)2)3)OK S kn b mm h mm 2500 d mm 2280 a mm 2262 d mm 2280 S h kn τ m N/mm τ a1 N/mm τ a N/mm τ a2 N/mm S ca kn S h kn 0.00 S mm 250 σ sa N/mm c ds d1.15 mm 1983 A w mm 2 /m A wreq mm 2 /m

91 6)

92 (a) knm kn mm mm σ ce N/mm σ c N/mm σ c ' N/mm σ c N/mm σ c ' N/mm (b) knm kn mm mm σ ce N/mm σ c N/mm σ c ' N/mm σ c N/mm σ c ' N/mm

93 (1)

94 , , , ,

95 EI (m) (m) (kn) i j (knm 2 ) E E E E E E E E E E E E E E E E E E E E E

96 (s) k h k h20 k h10 = 0.85 k h20 = 1.56 c S c Z = k h1g k h2g k h1g = c Z k h1g0 = = 0.35 k h2g = c Z k h2g0 = = 0.70 k h1g0 k h2g T=0.335sec T=0.127sec T=0.086 sec

97 (2) 1) , , , , M θ

98 N u M u N-M u M u ε cu 8) ε cc ε cu N-M u N-M u L p 1/2 (10.3.7) L p = 0.2h 0.1D = (m) (0.5D = 1.00(m) ) D (=2.0m)h 1/2 (=4.325m) L p EI y u -90-

99 M θ BD M y = 10587(kNm)θ y = (rad) M u = 10587(kNm)θ u = (rad) AC M y M u = (knm)θ y = (rad) = (knm)θ u = (rad) EI y EI y = n {M yb / (θ yb / L p )+ (M ya / (θ ya / L p )} / 2 = 2 {10587/ ( /0.665) / ( /0.665)} / 2 = (knm 2 ) EI EI = = (knm 2 ) -91-

100

101 2) L p (10.3.7) L p =0.2h 0.1D = =0.320 (m) 0.1D =1.850 (m) L p 0.5D =9.250 (m) L p =1.850 (m) D (=18.5m)h (= (m) ) L p M θ 2 y M y = (knm) θ y = (rad) EI EI= = (knm 2 ) -93-

102

103 3) (1) 2-1 k h δ BADC S c (kn) S c = nc c c e c pt τ c bd / 1000 = / (kn) 2-1 S c nc c c e c pt τ c bd /1000 = / (kn) 2-2 n c c c e d c pt τ c (N/mm 2 )b (mm)d (mm) 5-D19@150 S s (kn) S s = ( sin+ cos ) ( ) A σ syd n w 1.15a = = (kn) A w a θ (mm 2 )σ sy (N/mm 2 )θ ()a (mm) P s (kn) P s = S c + S s = (kn) 2-1 P s = S c + S s = (kn) 2-2 P s0 (kn) -95-

104 P s0 = (kn) S c (kn) S c = c c c e c pt τ c bd / 1000 = / (kn) 2-1 S c c c c e c pt τ c bd / 1000 = / (kn) D19@150 S s (kn) S s = A w σ d sy ( sin+ cos) ( ) a = = (kn) P s (kn) P s = S c + S s = (kN) 2-1 P s = S c + S s = (kN) 2-2 P s0 (kn) P s0 = (kn) 4 S AS= (kN) < P s (kn) BS= (kN) < P s (kn) CS= (kN) < P s (kn) DS= (kn) < P s (kn) P s k hag S AS= (kN) < P s (kn) -96-

105 BS= (kn) < P s (kn) CS= (kN) < P s (kn) DS= (kn) < P s (kn) P s k hag

106 4) k h δ A δ y (m) khug 1.13 δ y = δ y0 = =0.016 (m) k 0.78 hy0 δ y0 1 (m)k hug k hy k h δ θ p δ D -98-

107 0.071m θ p δ -99-

108 δ y δ u µ ag c SG k h δ u δ y µ ag = 1+ = 1+ = α δ y δ u δ y µ ag = 1+ = 1+ = α δ y α c SG c SG = = 1 = 2µ 1 ag 1 = 2µ 1 ag 1 = = k h1 = c SG c Z k h10 = = c Z = k h2 = c SG c Z k h20 = = c Z = (2.7.5) k h1 = 0.47 < k hag = k h2 = 0.66 < k hag =

109 (2.7.10) c Z kh µ r = + 1 = + 1 = khag c Z kh µ r = + 1 = + 1 = khag (2.7.9) δ R 2-1 r δ R = c R (µ r 1)(1 r)δ y = 0.6 (1.4531) (10) = (m) c R (=0.6)r (=0) 2 (2.7.15) θ Ra1 (rad) θ Ra1 = 2cos h 4b 2 4bt + h h + 4t 2 4b 2 =0.017(rad) h (mm)t (mm)b (mm) θ Ra1 θ Ra2 1/100 δ Ra1 (m) δ Ra1 = δ Ra2 = θ Ra2 h = 1/ = (m) h (m) δ R = 0 (m) δ Ra1 = (m) 2-1 δ R = (m) δ Ra1 = (m)

110 5) k hag 1.1 c Z k h W i H i x i y i W i (kn) x i (m) y i (m) W i x i W i y i y 1 = Σ (W i y i ) / Σ W i = / = (m) W i (kn) x i (m) y i (m) W i x i W i y i y 2 = Σ (Wy i y i ) / Σ W i = / = (m) -102-

111 H i (kn) x i (m) y i (m) W i x i H i y i y 3 = Σ (H i y i ) / Σ H i = 39583/ 9666 = (m) H i (kn) x i (m) y i (m) W i x i H i y i y 6 = Σ (H i y i ) / Σ H i = 30930/ 9664 = (m) M d W i x i W i x i M d = = (knm) 2-1 V (kn) H (kn) M (knm) V = W 1 + W 2 = = (kn) H = 1.1k h W 1 + c Z k h10 (W 2 + H 3 ) + H 6 = ( ) = (kn) M = 1.1k h W 1 y 1 + c Z k h10 (W 2 y 2 + H 3 y 3 ) + H 6 y 6 +M d = ( ) = (knm) -103-

112 2-2 V (kn) H (kn) M (kn m) V = W 1 + W 2 = = (kn) H = 1.1k h2 W 1 + c Z k h20 (W 2 + H 3 ) + H 6 = ( ) = (kn) M = 1.1k h W 1 y 1 + c Z k h20 (W 2 y 2 + H 3 y 3 ) + H 6 y 6 +M d = ( ) = (knm) H M S W M W (2.7.7) S W = (kn) P sw0 = (kn) 2-1 M W = (knm) M uw = (kNm) 2-1 S W = (kn) P sw0 = (kn) 2-2 M W = (knm) M uw = (kNm)

113 6) M c M y0 M u M c (knm) M y0 (knm) M u (knm) kN kN kN kN S c (kn) S c = c c c e c pt τ c bd /1000 = / (kn) 7-D22@150 S s (kn) S s = A w σ d sy ( sin+ cos) ( ) a = (kn) 1000 = P s0 (kn) P s0 = S c + S s = (kn) M =17845 (knm) M y0 = (knm) 2-1 M =3771 (knm) M y0 = (knm)

114 M =29032 (knm) M y0 = (knm) 2-1 M =12800 (knm) M y0 = (knm) 2-1 S =20914(kN) P s0 = (kn) 2-1 M =17845 (knm) M y0 = (knm) 2-2 M =3771 (knm) M y0 = (knm) 2-2 M =20932 (knm) M y0 = (knm) 2-2 M =12800 (knm) M y0 = (knm) 2-2 S =20914 (kn) P s0 = (kn)

115 (3) 1)

116 2) K VE P NU P TU P NU R U =q d A + U Σ (L i f i ) = 9358 (kn) P PU = 0.85 σ ck A c + σ y A s PHC SC RC = = (kn) P NU = min (R U, R PU ) 9358 (kn) R U (kn)r PU (kn)q d (kn/m 2 )A (m 2 )U (m)l i (m)f i (kn/m 2 )σ ck (N/mm 2 )A c (m 2 )σ y (N/mm 2 )A s (m 2 ) P TU P U = U Σ (L i f i ) = = 1508 (kn) W = = 78 (kn) P PU = σ y A s = = 5865 (kn) P TU = min (P U + W, P PU ) =1586 (kn) P U (kn)w (kn) P PU (kn) K VE 1 K Ap E p = KV a = (kn/m) L VE = -108-

117 k HE p HU k HE (kn/m 3 ) k HE = η k α k k H η k =2 / 3α k 1.5k H 1 (kn/m 3 ) k HE (m) N k H (kn/m 3 ) η k α k k HE (kn/m 3 ) p HU (kn/m 2 ) p HU = η p α p p U η p α p p U (kn/m 2 ) η p α p = 1.5, η p =

118 η p α p = () / () 1.5 1/2 P U P U =K EP (Σ γh + q)2ck EP K EP 2 cos φ = sin cos E + δ E 1 cosδ E cosα ( φ δ ) sin( φ α ) 2 K EP γ (kn/m 3 )h (m)q (kn/m 2 ) c (kn/m 2 )φ ()δ E () (m) N c (kn/m 2 ) φ () δe () γ t2 (kn/m 3 ) K EP P U (kn/m 2 ) η p α p P HU (kn/m 2 )

119 11 H p Hu k H (kn/m 3 ) k H = α k k H 0 BH α k k H 1.0k H0 0.3m (kn/m 3 ) B H (m) k H k H0 = α E0 0.3 B H B e B ele B H (m) B e 15.0 (m) L e = 2.5 (m) (m) ae 0 (kn/m 2 ) k H0 (kn/m 3 ) k HE (kn/m 3 )

120 p HU (kn/m 2 ) p HU = p p EP α p p EP z(m) (kn/m 2 )α p B e (m) p zB e 3.0 p EP K EP p EP =K EP (Σ γh + q)2ck EP K EP 2 cos φ = sin cos E + δ E 1 cosδ E cosα ( φ δ ) sin( φ α ) 2 K EP γ (kn/m 3 )h (m)q (kn/m 2 ) c (kn/m 2 )φ ()δ E () z (m) N c (kn/m 2 ) φ () δ E () γ t2 (kn/m 3 ) K EP p EP (kn/m 2 ) α p p Hu (kn/m 2 )

121 PHC M φ PHC

122 =967.9kN M c (knm) M y (knm) M u (knm) (m) φ c (1/m) φ y (1/m) φ u (1/m) No No No =0.0kN M c (knm) M y (knm) M u (knm) (m) φ c (1/m) φ y (1/m) φ u (1/m) No No No

123 knm 1/m No.1 knm 1/m No.2 knm 1/m No

124 3) k hg = k hp = c df k hug = = 1.24 k hw = c Z k h20 = = 1.56 k h2g = (α i k h k hp ) α i c Z k h0 α i k hg α i = k hp / (c Z k h0 ) =1.24 / 1.56 =0.795 k hp V 0 H 0 M V 0 = W 1 +W 2 +W 4 +W 5 = =52266 (kn) H 0 = α i c Z k h0 (W 1 + W 2 +H 3 ) + α i k hg W 4 +H 6 =α i 1.56( ) + α i =α i (kn) M 0 = α i c Z k h0 (W 1 y 1 +W 2 y 2 +H 3 y 3 ) + α i k hg W 4 y 4 +H 6 y 6 + M d = α i 1.56( ) + α i =α i (knm) (k hp <α i k h ) k hp α i c Z k h0 α i k hg V 0 H 0 M 0 V 0 = W 1 +W 2 +W 4 +W 5 =52266 (kn) H 0 =k hp W 1 +α i c Z k h0 (W 2 +H 3 ) +α i k hg W 4 +H 6 = α i 1.56( ) +α i =α i (kn) -116-

125 M 0 =k hp W 1 y 1 +α i c Z k h0 (W 2 y 2 +H 3 y 3 )+α i k hg W 4 y 4 +H 6 y 6 + M d = α i 1.56( ) +α i =α i (knm)

126 4) a) b) 0.72 k hp =

127 2 基礎の塑性化を考慮した照査水流方向に対しては 堰柱が十分に大きな耐力を有していること 門柱についても k hu > 1.5k h (1.13> =0.99) であり十分大きな耐力を有することから 基礎の塑性化を考慮した照査を行う 基礎の照査にあたっては 門柱 堰柱躯体には k hf 堰柱床版には k hg に相当する慣性力を作用させる 図 に示す水平震度 - 水平変位関係より 基礎が降伏に達するときの水平震度および水平変位は k hyf =0.72 δ Fy = (m) である ここで 静水圧等により初期変位 δ 0 = (m) が生じることを考慮すると 基礎の応答塑性率および応答変位は 式 (2.8.8)~(2.8.11) により算出することができる すなわち k hf = c D c Z k h0 = 2/ =1.04 δ Fr = δ Fy -δ 0 = = μ Fr = 1/2 {1+(k hf / k hyf ) 2 } = 1/2 {1+(1.04 / 0.72 ) 2 } =1.543 δ Fr = μ Fr δ Fy +δ 0 = = (m) μ Fr = δ Fr / δ Fy = / =1.507 ここに r は基礎の降伏剛性に対する二次剛性の比 ( 橋脚基礎に準じて 0 としてよい ) k hf は基礎の降伏に達するときの水平震度 k hf は基礎の主たる塑性化を考慮する場合に基礎の照査に用いる水平震度 δ Fy は基礎が降伏に達するときの上部構造の慣性力作用位置における水平変位 (m) である 基礎が降伏する点 khf= khyf=0.72 水平震度 δo=2.5 δfy=37.7 δfr=56.8 水平変位 (mm) 図 基礎のプッシュオーバー解析により得られた水平震度 - 水平変位関係 -119-

128 PHC PHC / PHC PHC D mm 1000 Do mm 740 b mm 230 h mm 886 d mm 839 N kn M N.m Ac mm Ic mm y mm 500 Mo N.m CN τc* N/mm Sc kn Aw mm s mm 70 σsy N/mm Ss kn Ps kn n 54 n Ps kn *)CcCeCPtτc= =1.275(N/mm 2 )τc -120-

129 Mmax kn m My kn m MmaxMy MmaxMy MmaxMy P N kn 3840 P NU kn 9358 P N P NU FL Fr FrFL O K F0a rad 0.02 F0 m F0 rad αf0αf0a O K Ss kn S kn kn nps kn Sc kn SnPs O K -121-

130 (4) 1) P NU R U π / (kn) R PU (kn) P NU min(r U, R PU )9194 (kn) (kn) P U +W= =1418 (kn) P PU = = 5865 (kn) P TU =min(p U + W, P PU )=1418 (kn) K VE k HE (m) N αe 0 (kn/m 2 ) k H (kn/m 3 ) D E η k α k k HE (kn/m 3 ) /

131 (m) N c (kn/m 2 ) φ () δe () γ t2 (kn/m 3 ) K EP P U (kn/m 2 ) DE p p / P HU (kn/m 2 ) D E =

132 2) k hp =

133 2 基礎の塑性化を考慮した照査液状化が生じることから 基礎の塑性化を考慮した照査を行う 基礎の照査にあたっては 門柱 堰柱躯体には k hf 堰柱床版には k hg に相当する慣性力を作用させる 図 に示す水平震度 - 水平変位関係より 基礎が降伏に達するときの水平震度および水平変位は k hyf =0.51 δ Fy =0.0461m である ここで 静水圧等により初期変位 δ 0 = (m) が生じることを考慮すると 基礎の応答塑性率および応答変位は 式 (2.8.8)~(2.8.12) により算出することができる すなわち k hf = c D c Z k h0 = 2/ =1.04 δ Fr = δ Fy -δ 0 = = μ Fr = 1/2 {1+(k hf / k hyf ) 2 } = 1/2 {1+(1.04 / 0.51 ) 2 } =2.579 δ Fr = μ Fr δ Fy +δ 0 = = (m) μ Fr = δ Fr / δ Fy = / =2.458 ここに r は基礎の降伏剛性に対する二次剛性の比 ( 橋脚基礎に準じて 0 としてよい ) k hf は基礎の降伏に達するときの水平震度 k hf は基礎の主たる塑性化を考慮する場合に基礎の照査に用いる水平震度 δ Fy は基礎が降伏に達するときの上部構造の慣性力作用位置における水平変位 (m) である khf= 基礎が降伏する点 水平震度 0.60 khyf= δo=3.5 δfy=46.1 δfr=113.3 水平変位 (mm) 図 基礎のプッシュオーバー解析により得られた水平震度 - 水平変位関係 -125-

134 PHC Mmax kn m My kn m MmaxMy MmaxMy MmaxMy P N kn 3133 P NU kn 9194 P N P NU FL Fr FrFL O K F0a rad 0.02 F0 m F0 rad αf0αf0a O K Ss kn S kn kn nps kn Sc kn SnPs O K -126-

135 (5) 2-2 1) m kn.m/m kn.m/m

136 2) / m kn kn

137

138

139 (1) 3.2 (2) 3.2 (3) (4) (5) 3.2.1(3) -131-

140 (1) )

141

142 EI (m) (m) (kn) i j (knm 2 ) E E E E E E E E E E E E E E E E E E E E E E E E E E

143 (s) 1 k h k h = c Z k h0 = = 0.25 k h0 1 1 k hg k hg = c Z k hg0 = = 0.20 k h T=0.433 sec T=0.129sec T=0.075 sec

144 (2) 1) K 1 K K 1 kn/m K 2 kn/rad K 3 knm/m K 4 knm/rad K 1 kn/m K 2 kn/rad K 3 knm/m K 4 knm/rad (S-R) H (kn) V (kn)m (knm) δ x (m)δ y (m)α (rad.) H A xx Axy Axα δ x V = Ayx Ayy Ayα δ y M Aα x Aα y Aαα α 6 7 A xx Axy Axα Ayx Ayy Ayα = () 7 8 Aα x Aα y Aαα A xx Axy Axα Ayx Ayy Ayα = () 7 8 Aα x Aα y Aαα

145 2) W i H i x i y i W i (kn) x i (m) y i (m) W i x i W i y i y 1 = Σ (W i y i ) / Σ W i = / = (m) W i (kn) x i (m) y i (m) W i x i W i y i y 2 = Σ (Wy i y i ) / Σ W i = / = (m) H i (kn) x i (m) y i (m) W i x i H i y i y 3 = Σ (H i y i ) / Σ H i = / 3472 = (m) -137-

146 W i (kn) x i (m) y i (m) W i x i W i y i (28) (29) (30) y 4 = Σ (W i y i ) / Σ W i = / = (m) W i (kn) x i (m) y i (m) W i x i W i y i M d W i x i W i x i M d = 0 (knm) V (kn) H (kn) M (knm) V = W 1 + W 2 + W 4 + W 5 = = (kn) H = k h (W 1 + W 2 + H 3 + W 4 ) = 0.25( ) = (kn) M = k h (W 1 y 1 + W 2 y 2 + H 3 y 3 + W 4 y 4 ) +M d = 0.25( ) + 0 = (knm) -138-

147 3) mm P N kn Ra kn P N Ra P N Ra OK OK P N kn Pa kn P N Ra P N Ra OK OK mm mm OK OK -139-

148 (3) 1)

149 (a) knm(b) kn M S N M S N (knm) (kn) (kn) (knm) (kn) (kn) G E F A C B D

150 2) M knm N kn S kn b mm h mm d mm mm D29 ctc 125 D29 ctc 125 D29 ctc 125 D29 ctc 125 mm D29 ctc 250 D29 ctc 250 D29 ctc 250 D29 ctc A s mm x mm σ c σ s N/mm τ m σ ca σ sa N/mm τ a A B C D A sreq mm M u knm M c knm M d knm A smin mm OK OK OK OK 1)M u M c 2)1.7MM c 3)A s 500(mm 2 ) 1)2)3)OK -142-

151 3) G M knm N kn S kn b mm h mm d mm mm D32 ctc mm A s mm x mm σ c 6.61 σ s N/mm τ m 0.21 σ ca σ sa N/mm τ a E A sreq mm M u knm M c knm M d knm A smin mm OK 1)M u M c 2)1.7MM c 3)A s 500 (mm 2 ) 1)2)3)OK -143-

152 4) E F M knm N kn S kn b mm h mm d mm mm D29 ctc 125 D29 ctc mm A s mm A w mm 2 4-D19 ctc150 4-D19 ctc x mm σ c σ s N/mm τ m σ ca σ sa N/mm τ a E F A sreq mm M u knm M c knm M d knm A smin mm OK OK 1)M u M c 2)1.7MM c 3)A s 500 (mm 2 ) 1)2) 3) OK -144-

153 5) h M knm mm mm mm 2350 mm D32@ D35@ mm mm σ c N/mm σ s N/mm σ ca N/mm σ sa N/mm

154 mm M u knm M c knm M knm A s mm 2 /m OK OK 1)M u M c 2)1.7MM c 3)A s 500 (mm 2 ) 1)2)3)OK S kn b mm h mm 2500 d mm 2248 a mm 2904 d mm 2248 S h kn τ m N/mm τ a1 N/mm τ a N/mm τ a2 N/mm S ca kn S h kn 0.00 S mm 250 σ sa N/mm c ds d1.15 mm 1955 A w mm 2 /m A wreq mm 2 /m

155 6)

156 (a) knm kn mm mm σ ce N/mm σ c N/mm σ c ' N/mm σ c N/mm σ c ' N/mm (b) knm kn mm mm σ ce N/mm σ c N/mm σ c ' N/mm σ c N/mm σ c ' N/mm

157 (1)

158 , , , ,

159 (m) (m) (kn) i j (knm 2 ) E E E E E E E E E E E E E E E E E E E E

160 (s) k h k h20 k h10 = 0.85 k h20 = 1.75 c S c Z = k h1g k h2g k h1g = c Z k h1g0 = = 0.35 k h2g = c Z k h2g0 = = 0.70 k h1g0 k h2g T=0.712 sec T=0.156sec T=0.090 sec

161 (2) 1) , , , , M θ

162 N-M u M u 8) ε cc ε cu N-M u N-M u

163 L p 1/2 L p = 0.2h 0.1D = 0.690(m) (0.5D = 1.00(m) ) D (=1.75m)h 1/2 (=4.325m) M θ y u M θ BD M y = 9407(kNm)θ y = (rad) M u = 9407(kNm)θ u = (rad) AC M y = 9060 (knm)θ y = (rad) M u = 9060 (knm)θ u = (rad) EI y EI y = n {M yb / (θ yb / L p )+ M ya / (θ ya / L p ) }/ 2 = 2 {9407 / ( /0.690) / ( /0.690)} /2 = (knm 2 ) EI EI = = (knm 2 ) -155-

164

1.500 m X Y m m m m m m m m m m m m N/ N/ ( ) qa N/ N/ 2 2

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