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 + + czc n cin xn czt cin ( D xn) sa ( sd sxn) + ra rd xn sa + ra cin si + sa ( xn + sxn sd) + ra ( rd xn ) czt cin ( rd xn ) czc cin xn
n sa n sa n B sa sd Xn + + B BXn3 cin + n si + n sa ( sd Xn) 3
b Xn α + α + 1 β b1 α S ( B b1) + n sa β S ( B b1) + n sa sd B S3 S b1 ( Xn S) cin + B S Xn + 1 3 cin czc Xn cin czt n D ( Xn) ca cd + n sa sd Xn ca + n sa 1 ca B S + ( b1 + b0) Hd S b1 + b 1 b1 + b0 B S + Hd S + Hd 3 b1 + b0 cd ca fi ci + ca ci 1 1 B S ( Xn cd ) + n si + n sa( sd Xn) 3 fi fzc n D fzt ( Xn) fi Xn S + B S cd 1 + + ( b1 + b0) ( ) + n si + n sa sd Xn 1 b1 + 4b1 b0 + b0 Hd 36 b1 + b0 1 b1 + b0 Hd S + Hd cd 3 b1 + b0 3
n ra n ra n B ra rd Xn + + B BXn3 cin + n ra ( rd Xn) 3 b Xn α + α + 1 β b1 α S ( B b1) + n ra β S ( B b1) + n ra rd B S3 S b1 ( Xn S) cin + B S Xn + + n ra rd 1 3 czc cin Xn cin czt n rd ( Xn) ( Xn)
( ) ( ) ( ) ( ) 3 3 0 1 0 1 3 1 0 1 1 0 1 0 0 1 4 1 36 1 1 1 0 1 0 1 3 1 1 0 1 1 + + + + + + + + + + + + + + + + + + + + + cd Hd b b b b S Hd b b Hd b b b b b b S cd S B S B ci Xn rd ra n cd Xn ca ci fi ca Hd b b b b S Hd b b S S B cd Hd b b S B ca ra n ca rd ra n cd ca Xn ( ) fzc fin n rd Xn fzt fin Xn
n df tf 3 H tf tw dw Ixe Ix + n df tf dw tw e j 3 + 1 j 1 n dw tw tf df Iye Iy 3 3 + df tf e j 1 j 1 Zpxe Zpx n df tf ( H tf ) ( dw tw ei ) i n dw tw Zpye Zpy ( df tf ei ) 4 i b 05. g a ao b b 05. g a 15. g ao b 15. g a 0
fst fto fts fto 14 16.. τ
00.3 10.1 1.5 5 Fc E γ
4 fa min Fc 9 100 6 fa min Fc 135. 100 1 fa min Fc 9 + Fc fa fa 15. 15 75 1 1 fa min Fc 135. + Fc 10 5 fa min Fc 45. 100 Fc 1 Fc fa min. + fa fa. 15 15. 135 15 5 3 3 Fc fa min Fc. + fa fa. 40 4 135 15 5
1 fc Fc fc fc 3 Fc fc min 60 fc fc 45. Fc fc min 70 fc fc 4 Fc fc min 80 fc fc 4
Fc Fc fs min 5 + fs fs 15. 30 100 Fc Fc fs 09. min 5 + fs 15. 30 100 Fc 1 Fc fs min + fs. 45 15. 5 15 100 Fc 3 Fc fs min + fs. 40 4 5 15 100 E G ( 1 +ν )
qs 05. sca Fc Ec Fc Ec 9000 ( / ) bd L qs ( sca Fc Ec ) 085. nd 10. 05. Hb Hd
( ) fb lb iy C ft 1 04. Λ fb lb h Af 900
fb lb h Af 900
( ) fb lb iy C ft 1 04. Λ fb lb h Af 900
λ λ ν λ λ Λ Λ Λ Λ fc F fc F fc fc 1 04 077 15...
1.5 3 1.5 fs fs F fs ft F 15.
F fs 15. 3 F fp1 11. fp 19. F fl 15. F F fb1 13. Λ π E 06. F
K A tan 45 K A cos o φ cos( φ θ) θcos( θ + δ) 1 + sin cos ( φ + δ) sin( φ α) ( θ + δ) cos( θ )
K P tan 45o φ + { γ γ ( )} γ ( ) po Ko H1+ ho H1 + w ho H1 + Koq
Ai i i T T + + 1 1 1 3 α α
α 1 0 4. H Df
k H Z 01 1 40.
T Tc Rt 1 Tc T T Tc Rt 1 0. 1 Tc Tc 16. Tc T Rt T T h ( 00. + 001. α)
P K C q h q h h q h 16 60 16 10 4
Mx Ml x Ml Mr L Qx Ml Mr L
Mx wx lx Mx wx lx wx ly lx ly w 1 1 1 1 18 4 4 4 +
Mx w lx Mx w lx 1 1 4 1 36 Qx w lx Qy w lx 053 046..
1 M w l + ( w w ) l + p l 1 1 1 1 6 1 Q w1 l + ( w w1) l + p
al T o lft Ao ψ
α α + 4 1 1 M Q d
at Md ft j j d 7 8
( ) ba ala a l l a l 05 06 05 01 05.....
M fc N xn1 xn1 1 1 n pt( xn dc xn dc ) xn + + 1 + 1 1 1+ 1 1 BD xn1 3 + BD ( 1 1 1 1 1) M fc 3 xn1 N 1 n pt xn dc xn dc xn + + + 1 BD xn1 3 + BD M ft N 1 xn 1 BD n xn dc + BD M N 1 ft pt( 1 dc1) + dc1 BD BD 3 1 xn1 + n pt ( ) ( xn1 + dc1 xn1 dc1+ 1) 1 1 1 3
xn xn1 r M fc n pg r N ( n pg)( xn ) ( xn ) r xn1 4 1 π r 1 1 1 + r 1 1 3 + π + M fc 1 13 1 1 r N n pg 3 + r ( 1 ) 4 1 + θ cos θ sinθcosθ cos θ + π + cos θ cos 6 r + cosθ θ r M ft 1 13 1 1 r N n pg 3 θ + cos θ sinθcosθ + cos θ + π + cos θ r r 4 1 6 r r n + + cosθ cosθ r M π r 1 N ft pg 3 + r r π r
{ 08. σ 01. } N max N Mu at y D + b D Fc N max 04. b D Fc Mu at y N D + N D 08. σ 05. 1 b D Fc Mu 08. at σy D + 04. N D ag at
{ 05. σ 1 004. ( 1 1)( 36. 1) } N max N Mu ag y g D + + g g b D Fc N max Nb Mu ag y N g D + N D 05. σ 1 05. 1 b D Fc Mu 05. ag σy g1 D + 05. N g1 D
QAL b j α fs { 05 ( 000) } QAS b j fs+. wft pw. { 15 05 ( 000) } Qc b j. fs +. wft pw. { 05 ( 0001) } QAS b j fs+. wft pw.
03. ( Fc + ) ( Q d) + 01. 0. 053 pt 180 B Qsu M 03. ( Fc + ) ( Q d) + 01. 0. 068 pt 180 B Qsu M Qsu BQsu + 01. σo b j σo 04. Fc Qsu 09. + σo 50 Qsu ( ) B + 7. pw σwy b j + 7. pw σwy b j 0. 053 pt 03. ( k Fc + 180) Qsu + 7. pw σwy b j M ( Q d) + 01. Fc k 1 1600 Fc k Fc + 140
γ γ ac at 10.
M Cbd npt fc dc dc C1 ( 1 xn1)( 3 xn1) γ xn1 3 xn1 3xn1 d d pt ft dc dc C ( 1 xn1)( 3 xn1) γ xn1 3 xn1 31 ( xn1) d d
Mu 09. at σy d + 09. sat sσy sd
ptb ft nfc ft fc dc d n dc d + + 1 1 1 1 1 γ γ
{ α 0 5 ( 0 00) } QA b j fs+. wft pw. { α 05 ( 0001) } QAS b j fs+. wft pw.
03. ( Fc + ) ( Q d) + 01. 0. 053 pt 180 Qsu M 03. ( Fc + ) ( Q d) + 01. + 7. pw σwy b j 0. 068 pt 180 Qsu + 7. pw σwy b j M 03. ( k Fc + ) ( Q d) + 01. 0. 053pt 180 Qsu + 7. pw σwy b j M Fc k 1 1600 Fc k Fc + 140
( ) ( ) Qsuo ku kp Fc M Q d He D ps s y b j + + + 0 09 180 01 1 161 7.... σ
x aw pw b
( LD) + 1 ( LD) ( ) Qsu b jt pw σwy + k11 k b D ν Fc pw σwy ν Fc k1 pw σwy k ν Fc Fc ν 07. 07. 000 QB u jt τb Σφ + k1 ( 1 k3) b D ν Fc b k τ Σφ 3 b ν Fc 4. 9 aw h τb k0 0. 307 bi+ 0. 47 + x N db bi min bvibcibsi ( ) 3 ( min 1) ( ) ( ) 1 bvi C db + bci { Cs + Cb db + 1} 1 bsi b N db bi bvi h 0 bi bci h bi bsi h 10. + 085. n N ( ) Fc
Ma at ft j j d 7 8
( ) 1 3 M Q d ψ Q fa j j d 7 8
pt at b d
( ) Vc lb L Mb lb L Mb lc lc + +
Vj T T Vc T Mb j T Mb j +
Vju B bj Dj κ σ
pw aw x b
( ) pwe aw C b + Σ sin cos θ θ
pwt T wft Ao b t wp lx lx + + max,... 8 00 07 06 1 1000 1000 λ λ
λ 07. wp lx t lx + + max 10, 11. 0. 0 06. 1 λ 1000 1000 Q 7 τ j d b j 8
τ ψ a Q j j d 7 8
D A be Σ Σ
N Mwu 09. at σy D + 04. aw σwy D + 05. N D 1 B D Fc Mwu at σt lw + 05. aw σwy lw + 05. N lw
Qw ps t l ft
03. ( Fc + ) ( Q D) + 01. 0. 053 pte 180 Qwsu M 03. ( Fc + ) ( Q D) + 01. 0. 068 pte 180 Qwsu M 7 100at j d pte 8 be d + 7. pwh σwh + 01. σo be j + 7. pwh σwh + 01. σo be j
( ) r r r r lo l r ho lo hl min 1 1 1 1
Td ho lo l Q + ( ) Tv ho l lo Q ( ) Th lo h ho h l Q
σb M ψ1 18. Ze Fc Ze φ Zo φ 1+ n( 15. + γ) Pt b D Zo 6 b D ψ1 050. + 0050. l b D ψ1 075. + 005. l
( ) K E nt Ab dt dc lb BS +
Nu N Nu Tu Nu Mu N dt 1 N Nu Tu N Tu ( N + Tu) D N + Tu Mu Tu dt + 1 Nu Tu N Tu Mu N + Tu dt ( )
( ) ( ) ( ) 1 0 1 1 0.5 0.5 0.5 max + + Tu T Su Qsu Qfu Tu N Tu Tu T N Tu Nu T Tu T Su Qsu Tu Nu Qfu Tu N Qfu Tu N Tu Nu Su Qsu N Qfu Tu Nu N Nu Qsu Qfu Qu
D e 6 N e c 1 6 σ + σt 0 B D D D D dt e + 6 6 3 N σc B D σt 0 3 e D dt + e 6 3 D N e+ dt σc xn B xn D dt 3 N 0 σc 0 M σt at D ( dt) D N e dt 1 σt at D dt xn N ag
θ δ 3 cos l A E P K B
Aj σu A1 bσu A1 Ag A1 Ag Ad A1 Ag Ad hn t b05. g a ao b b05. g a 15. g ao b15. g a 0
Aj σu 075. A fσu A n m 075. π ( d )
Aj σu A3 σu A3 n e t Aj σu A4 σu A4 l gt Ad 3 1 b05. g a ao b b05. g a 15. g ao b15. g a 0
1 Aj σu A5 σu 3 A5 Σ 07. S le Aj σu A5 σu
( ) ( ) 1 tan tan 1 4 + + + K K K K GB GA K GB GA π π π π π ( ) ( ) ( ) K K GB GA K GB GA π π π tan 6 36 +
σc cσb tσb σc + 1 1 fc fb ft σt + tσb cσb σt 1 1 ft fb
C Nd A fc Mx Zx fbx My Zy fby T Mx Zx fbx My Zy fby Nd A fc ft + + + C Mx Zx fbx My Zy fby N A ft T N A ft Mx Zx fbx My Zy fby ft + + +
N Aw Mpc Mp Ny A N Aw N Mpc 114. 1 Mp Ny A Ny N Aw Mpc Mp Ny A N Aw N Nwy Mpc 1 Mp Ny A Ny Nwy N 0. Mpc Mp Ny N N 0. Mpc 15. 1 Mp Ny Ny
Ncr 0 λ 30 10. Ny Ncr 30 λ 10 1 0. 006 ( λ 30) Ny NE λ 10 Ncr 13. Ncr 0λ5 10. Ny Ncr 5λ100 1 0. 007 ( λ 5) Ny NE λ 100 Ncr 13.
( ) λ σ π λ λ λ λ λ E y NE Ncr Ny Ncr Ny Ncr 1 1.3 1.3 0.3 0.545 1 1.3 0.3 1.0 0.3 0
σ τ τ 3 1 1 + ft fs
Qd Qa ft fs + max σ τ τ 3 τ max. Qx Asx Qy Asy 15 τ max Qx Asx Qy Asy τ + Qx Qy A
{ } y s sa Fc ca Qh σ 85 0. min
Mu fmu WMu +
fmu Tf B ( H Tf ) σu σu fmu 14. Sf ( B Sf ) ( H Tf ) 3 σu fmu 07. Sf ( B Sf ) ( H + Sf ) 3 1 wmu Tw { H ( Tf + C) } σu 4 1 u wmu Sw { H ( Tf + C + Sw) } 4 14 σ. 3 1 u wmu Sw { H ( Tf + C + Sw) } 4 07 σ. 3 ( ) Ma min Zc fb Zt ft
Md Ma Mdx Zx fbx Mdy Zy fby +
lb h Mcr 0 300 10. Af Mp lb h Mcr lb h 300 1000 1 0. 00071 300 Af Mp Af lb h Af 1000 Mcr Mp 500 lb h Af
0 0 10 0 76 1 0 00099 0 76 363 lb h Af Mcr Mp lb h Af Mcr Mp lb h Af lb h Af Mcr Mp lb h Af.. y Kv Af h lb Kv Mp Mcr Kv Af lbh Kv Af h lb Kv Mp Mcr Kv Af h lb Kv Mp Mcr Kv Af h lb σ 1198 0. 0.6.8 1 1 0. 0.6 1.0 0.6 0
Qa Aw fs Qd Qa Qdx Aw fs Qdy Af fs max. 15
Mu Zpe σu b 05. g a ao b b 05. g a 15. g ao b 15. g a 0 {( ) ( ) ( ) ( )} Mu B1 d T1 H + T1 + B d T H Tf T σu
b 05. g a ao b 05. g b a 15. g ao b 15. g a 0 ( ) Mu n 075. fa σu H Tf Mu n 075. fa σu H
Mu min( bmu pmu) bmu n e Tf σu ( H Tf ) pmu n e T1 σu H + T1 + n e T σu H Tf T ( ) ( ) u Qu Awe σ 3
σu Qu ( B3 d) T3 3 Qu n 075. fa σu
u t e nw Qu σ 3
Ve hb hc tw Ve hb hc tw Ve A
( btf) ( d tw) + 1 d twkc F ( kf F ) ( kw F )
( ) ( ) ( ) B l K B h K Dy B h Qu M K K K K K K K B cu Qu + + + + + + + + 1 1 1 1 1 1 0.5 1.5 max 1.5 4.5 6 4 4 9 My M B cu My B cu Qu B h B cu Qu + + max 18 7 18 3.5 4.5 1.5 9 3 B l B cu Mo B l B cu Qu My Mo B cu My B l B cu Qu B h B cu Qu + + 3 36 1.5 81 7 18 My M Mo B cu My B cu Qu B cu Qu + max 36 7 3 + + + l h l h Qu M l h B l Kp Qu 1 0.385 max 1 γ My M B Kp My B Kp Qu B h B Kp Qu + max.544 0 4 3 3 γ γ γ 3 3 B l Kp Mo B l Kp Qu γ γ My Mo B Kp My B l B l B Kp Qu 4 3 3 1 γ γ
My M Mo B Kp My B Kp Qu max.38 3 4 3 γ γ
4 d y EI + kh By 0 4 dx Qo βx yx e {( αr) cos βx + αr sin βx} 3 4EIβ Qo βx θx e {( 1 αr) cos βx + sin βx} EIβ Qo βx Mx e { αr cos βx + ( αr) sin βx} β βx Qx Qo e { cos βx ( 1 αr) sin βx}
4 d y EI + kh By 0 4 dx Qo βx βx yx [ e ( C1 cos βx + C sin βx) + e ( C3 cos βx + C4sin βx) ] 3 4EIβ Qo βx βx θx [ e {( C1 + C) cos βx + ( C C1) sin βx} e {( C3 C4) cos βx + ( C3 + C4) sin βx} ] 4EIβ Qo βx βx Mx [ e ( Ccos βx C1sin βx) e ( C4cos βx C3sin βx) ] β Qo βx βx Qx [ e {( C C1) cos βx ( C1 + C) sin βx} + e {( C3 + C4) cos βx ( C3 C4) sin βx} ]
( ) Xn a l a l a l a N M 6 1 1 8 α
l a l Xn a l N Q 4 1 1 8 α
( ) ( ) d D bo d a a bo fs j bo Q PA + + + π π α
4 4 I khe B β x B kh nh I E nh 5 η
4 3 0.8 B Eo kh
l Ep Ap a Kv ( ) ( ) ( ) + + 0.15 0.031 0.36 0.011 0.61 0.013 D l a D l a D l a
fc y Ie M e Ae N fb + + σ ( ) 1 max g d g σ σ σ τ +
Wp Lq qu Ls Ns Ap N Ra Wp Lq qu Ls Ns Ap N Ra + + + + ψ γ β α ψ γ β α 5 15 3 5 15 3 1
+ + 0 50 5 30 3 1 qu Ns Lq qu Ls Ns Ap N Ra ψ + + 10 5 5 0 3 1 qu Ns Lq qu Ls Ns Ap N Ra ψ
( ) + + 10 5 90 4 1 5 110 90 5 90 5 3 1 qu Ns D l D l D D l Lq qu Ls Ns Ap N Ra α α ψ α { } ( ) + 90 4 1 5 110 90 5 90 1.5 3 1 D l D l D D l L Ap N Ra α α ψ α
( ) Rf Rp Ra + 3 1 ( ) ( ) ( ) + + + + 0 1.8 3 3.6 3 7.6 0.6 min 1.8 14 0.4 3.3 min 30 min.1 Nh fh Nh fh Nc fc Nc Nc fc Ns fs Lh fh Lc fc Ls fs Rf Np Rp ( ) ( ) ( ) + + + 1.5 3.6 1.5 7.6 0.6 min 1.8 3 4 14 0.4 3.3 min 3 4 30 min.1 3 4 Nc fc Nc Nc fc Ns fs Lc fc Ls fs Rf Np Rp
0.3.5 1.5 1 1 D β D L 0.08 0. + β
Ms Ts Mc Cc M N ( ) ( ) ( ) + + + λ σ λ σ 1 0 0 rs ro As rs Ms Mc rs ro rs ro As Ts Cc
( ) + + + + o ro rs As rs Ms Z o ro rs n ro Mc o ro rs o As Ts Y o ro rs n ro Cc α σ α σ α α σ α σ cos cos cos cos cos 3 ( ) o ro n As rs Ms Z o ro Mc o o n As Ts Y o ro Cc α σ α σ α α σ α σ cos 1 cos 1 cos 1 cos cos 1 3
( ) + + σ η σ π η σ η σ π η n As rs ro Ms ro ri ro Mc n As Ts ri ro Cc 4 3 4 1 1 8 1 1 1.0 κ κ fs As Qa
( ) ( ) { } µ ν ν ν + E B q F F E B q SE 1 1 1
Nf z N Na + σ 10
( ) + + + + Nq Df Nr B Nc c qa Nq Df Nr B Nc c qa 1 1 3 1 3 1 γ γ β α γ γ β α
q A S E µ H E S E ( H ν ) µ ( H, ν ) µ ( H, ν ) µ ( H, ν ) µ ( H ν ) µ H 1, 1 H H 1 H n n H n 1, + + L+ E1 E En n q A
rd z z g rn z d σ σ α σ τ max
5 3 3 R z P z π σ
( )( ) ( )( ) + + + + + + + + + 1 1 sin 1 1 1 1 n m m n n m n m n m m n q z π σ