! ” #
**& #’ ( ) *$ %$
0( *!+& * + 0( 1 2 3- ./ 4 ( * *!+& !,- ./
(##/)/:%& ’(& $#!/ /! : )
!”#$ %&’ (&) &* + , 6 ! ,5
– 3 31 – 4 4 5 .- 1 . /*& * /*& &0 – #, & & ! “#, – – :3’ + 6;< – ) =- # 1 /8 (&) &* 9* /*& 1 %. / #) 7 &0 /*& 6#$ 3 1 3D E- 9#3 ( 3 F 3″1 7&3G ” “’ 1 1 /8 @* A# @B .& %> 5, ? #) &! 3!> 5, ? #) – 5< 1 /8 (&) &* /*& +I @* – @* ./ 7 /<- – *H – 1
/3- /3) M – &J + /< #4 GG ! – 9″1 1 J 4 5 K# J L- – NO3 =&3 F 31 35< 1 /8 1 %. K*# . ; 5< 1 /8 4 @ 4 -6#$ @*
3 /$3 6#$3 3 *! /- – &* (&) E- 9# ( /- F*H) :’ – & NO P& & . “1
. & – &, I 5 GG ! K*# !.D J R- S0K*# @ +@ Q” . . /*& /
/- + 5, ? SG + 5< 1 /8 + (&) &* : ! 9 % 78
Theoretical and Analytical Study of Non-linear Behavior of Diagonally Stiffened Steel Plate Shear Walls

E. Alavi, and F. Nateghi Alahi
Structural Engineering Department, International Institute of Earthquake Engineering and Seismology

Abstract: Based on the studies over the recent decades, steel plate shear walls, SPSWs, have been introduced as appropriate seismic load resisting systems, which have come to be used in structural design and in retrofitting of existing buildings with different configurations, both stiffened and un-stiffened. The few investigations carried out on SPSWs have shown that stiffening of a thin steel plate shear wall with the conventional horizontal and vertical stiffeners improves its non-linear behaviour.

763112317

$ **1 , $ +, -. – /0&$ *

However, application of conventional stiffeners, commonly used for precluding incidence of shear elastic buckling in infill plates, is time-consuming and imposes high-fabrication costs. This study was, therefore, carried out to investigate the stiffening of SPSWs with diagonal stiffeners and their non-linear behaviour. The theoretical formulas validated against analytical results are presented that are used to estimate the shear strength capacity of the system and to size the diagonal stiffeners. The results show that diagonal stiffeners reduced the effective lengths of buckling in the inclined infill steel plate strips and, consequently, increased the elastic shear strength of the infill steel plate as well as the ultimate shear capacity of the system when compared to un-stiffened steel shear walls. Good agreement is also observed between theoretical and analytical results.

Keywords: Steel plate shear wall, Diagonal stiffeners, Non-linear analysis, Shear strength.
=2 <B2 . < < T 3 6O<? , U8 F5@ V&.
E<. “\(<& %\(& %\& N -5 N 2N %G8 5h
P<< PH << – @ << T 3 6O<<? , U <<8 V& << . <<j %>P& < F< 2 +P PH %8 2 % : , .[ ] %
-, < – < & > +k 3 2 (5 = a ,(59 %B6B
</ PB< 2 < P& % ’< 3 < 3 % <. +, P<& 2 &W A <[B9 3 E (<5 %<G8 5h – 9 + 3P6 . %
% ’ V9 . l – @ T 3 3 5& N ;P m XM
< N %0<0. ; P5 XS R . %&, 7 %3 3
%>P& < F<2 +P PH / nR 2 = M o ’
3 %< <q & <K 92 .[p]% a ,(59 -5B6B
+P< %<K: _ <8 . +P0& 7 – @ %2 F
%< SR gP< +P< %B52 V5H %& 5] 2 P&2 P2
. [ ]P<B. C< 67 %2 8 2 @ 2 – ‘H CX 67 ;W 3 P 2 +P A /& E (5 = -3 2 – , 4 MG 58 – -, < 5\< – 2 – +P + p- & – P ” /5 & . +P< B0<5H [s] ; <2 7 d 7 ;W %r C5S67 3 –
[t] C<<5\D , % 9P& << 3<<9 <<& =<< cW <<. <<
.P& +P ‘H CAN/CSA[u] 3 AISC- p =5 <H E5S(<7 VB7 2 @ , + O 5q& – [ – 3
@ < % 2 – 9 , / 3 [ ] 5 . & d 7 v<. %< 2 – <9 3 [ ]%c (7 3 . 59 . 7 d 7
< E (<5 – +, < \ 2 -2 [ ] C? &W d7
.P& + P B05H 3 %2 +P0& 7 – @ %2
@ < %2 %M 2 = 3 = ,
%M< 38H P PN E (5 F ;BR 2 – GD +P 7

!# 6:
%2 -3 2 -, 45 67 58 9 :
+ ; 0<& 4 < 5 67 =< /5 & 3 > 4 ? – @ A3 ; B5 : C2 D E (5 F – @ % 2 .
@ %2 . G8 H I: B 1 , – 92 22
<N -&8 < -, A3 9 +, %K: L@M
. % + O +P0& 7 +P 7 4 ? 2 ’< , + O 2 – @ % 2 – 9 3 Q3
<7 – <6& <2 < D 3 <57 PB&9 -R 3 % – 9PBB.
5> <SN +P<BB. <H T 3 6O? U8 V&. , . P& %
. < C? K ; B5 : C. – 5 8 PK 2 ;W ;P5 , 3
@ < %<2 – <9 2 G2[ ];X 9 3 %9 . 7
A </& %7 M G =5[B 3 F\ – 9 +PBB. ’ 2 +P ’ -@ <2 5 ] – +P 7 E (5 . P& ; 0& 3 P&
<< SK – 3 << << 1 , -3 <<5& <<2 2 -^ <<& _‘<<N 3 < CX< S – <N <2 CX< %<.3 3 P< H a , (59 <[ – < , .< 1<5& %\ B %\& N % ’ =5Bb 9
P& 7 % Ec D 3 % +PBB. ’ – , PM7 – N 3 8
< 7 %< 2 < <2 \(<& – 052 B 19 3 + 2 2 ; , <2 < M – 3P<M 4 <M G % : , 3 P 2 +P0&
0<52 4 <5 1N . < <> 4<? +P 7 E (5 $ & < W d<7 E (<5 = -3 2 45 67 B505H e f8 . +P c[ ]C?
g, <& T 3 <2 – @ < %< 2 , + O A3 Q3 2 – @ T 3 %0& . aH 3 2 . +P0& 7
!
, P<M2 – @ < T 3 %0<0. ; P<5 <XS R M<7 C5
.3 %< <. <2 + <5h 3P\5< – < 2 D C<y %0< 8 -2 D
<57 ; <N <7 -3 <2 V&<X 9 3 [z] 3 1& +3R 2
.P<& < %7 <M G – <GD – <9 +P<BB. ’ F . 2 D 3
; 0 & &W % S5S67 3 %9 [0,W 4M G . -: 2
<7 %\<B <XS R – GD – 9 +PBB. ’ .P9 %
57 ; N – GD 7 2 . P&> /5 & 3 P& D 3 57
. % {OK ; Bb 9 T 3 %00. ; P5 XS R T 3 – < D 3 <57 -<2 +P< U B < – < M G =
+P< <7 – @ %2 2 ;6 d7 +P 7
%<G8 5h – 9 =52 N – 73 O7 = > q& 2 – GD _ <D <j ; <. <qB 3 – @ < %< 2 – 9 3 D 3 57 4 <M G | < & +3 <R <2 .P<& +P< + d(2 %& 5H – @
@ < %<2 < %<G8 5h -3 2 %S5S67 3 – q&
<2 A,@ – < =5<Bb 9 .P& +P c – GD +P 7
<9 +PBB. ’ M2 =55M7 3 E (5 = % 2 3 3 2
, 3P<6 – 1<N %<S5S67 P< = PBl .P& +P B05H – GD < &W <\ R 3 P& + P / +P0& 7 – @ % 2 – 9
=5< W %& <\ 3 % SR g P \ M %9 [0 ,W | & F . 2 .< +P< C<? K ; <B5 : ;W , 3 B. %SS =52 – 9 &
’<r 3 -<M2 -\(& 2 – GD – 9 +PBB. ’ a}
-3 <2 %G8 5h -S5S67 3 P& +P r P = 2 oS ’
%\& N ; X 55 7 – 2 -5B6B =5Bb 9 .P& > 4? &W
3 – <q& 4 M G |& L& .P& +P c S5S67 |& 3P
%<S5S67 | < & 2 +P c – d7 q & C2 D -5] .P& + P (
“# ” @ 6?
< V % < & %<2 <5] \<6 -2 . %3
CX< X – <9 +PBB. ’ 2 – GD +P 7 – @ %2
– 1<N %< 2 – < 3 / m 2 +P _ ’ & – <GD +P< 7 – @ % 2 +PB9 C5X07 oS ’ – <GD +P< < 7 – @ < % 2 ( ) CX .

!++9 “=* 6< ;, ) > ” ’ /
<2 %<2 – +, 9 +PBB. ’ P , 7
<9 +P<BB. ’< P<M7 CD P<K <2 +P0& 7 – @ T 3
< 3 V 1< <2 < =< . PB. +O – GD 4? 2
, % & 4 j V9 . + 9 2 – @ T 3 F5 @ PK % 2
<5 ] 3 %< q & % : , . % (5 ;W %S. V& .
– <GD – <9 +P<BB. ’ . 0 C5 2 E (5 %S. %\& N
, +O < +3R2 . P2 \ 2 15& ;W %G8 5h 3 V 1
<2 (< <N 38 < <B 19 V9 . nR 2 E (5 =
3< %< 3 P< 4? 2 +P 7 – @ %2
+O . P98 +9 2 15& 8 CK
9 +, , %wM2 %K: +P 7 – @ %2 ,
< 3 % MB<? – <9 +, < < 3<\7 PBS2 – 9 +, C5\D ,
<9 +, < -<2 + < 2 3 -<XS R -3P6 . %G
P& N3 – @ T 3 6O? , U 8 V& . 2 \(& < <2 \(<& =X N – 9 +, -, A3
<X& %<8 2 . < + x5N <7 +P0<& 7 – @ %2
& < W d<7 – @ %2 E (5 _ ’ & %[& [l %<2 C& H F ;. ’ %S. :2 .P& +P c [ ]C?
_ (<6 P< PN Q3 F< – <GD – <9+ P<BB. 7 d7
%8 2 vS? 4@ f7 ;. 7 Q3 = 3 % & , +O 2 3 [z] ;X 9 3 3 1& 4 M G 2MN 2
– @ < T 3 F5 < @ V& < . v<r 3P6 Cr O7 Q3
; <52 < , 4 <? 2 ; 7% CX X 4 ?2 +P ’ :.
K =11.9+10.1/ +10.9/2( )
( 2 3 = dbCX vr \( & 2 K vr
. – @ T 3 O7 d .- : 2 Vt T 3 %0<& . a<H %< 2 < 3 =5 ’7 qB 2
: % c e f8 = I5 67 B505H , – ?8 P 2 3 C< . %0<0. ; P<5 F< <2 =5< 3 – <2 [ ] B> 3
; <N <2 6O<? F % 2 3 \ 6 – 2 8 BX V& . 5 ] . > /5 & 3 2 . 2 – D – 2 3 g, &
% <. +, P& 2 9 > . g, & % 5B5 W T 3 F % 2 [ ] S<< 2 . ( 5& T 3 % << & 5 ] << +P
-< R – 9 +PBB. ’ 2 D 3 57 -3 %2 4 0,W
<2 <. – q& P F H 2 &W (X 5M 3 A /& < %0<0. – <GD <R <& F< ;P< – N
T 3 <57 – 2 . 0 3 4 j , Q3 = . B05H <. P< +P9 0< . +P q& ? % 2 -3 5& C 67
%0<& . %< 2 VB<7 < q& <. <: ; 9 T 3 57 ; N VB7 , 7 C5 2 3 + . V& . 2 +P %B52 V5H F5 @
.< +P C? K % N 7 C2 D %0&. aH 3 ; N
5K& ;<. V& < . , a<H T 3 <. P<& ; 0<& | < &
– GD %00. wR 2 H 8 F PB&9 F5H $ @
E(5& X 2 C P\7 C& H . P % T O7 % D3 (X 3 PB. % C R ; BR 67 ; B. E9 % H 8 XS R = . F5 H
[]X 3 % .. +P 8 B t%0 0. ; P 5
C<& H -3 % N7 C2 D 5j 7 2 % ’ . PB
<2 ” <\7 %<28 E(5& X P& A & %S58 2 % D3 . -: 2
PB<2 -, % ’ – > . %&’ 9 S2
3 P& < %< </ C<& H <> < l F5H -SfO
-Sf<O , P<R 3 PB<2 < %G< % ’<b& Bl Q3 = . 2 4 5r .P9 % ; 0& %\& N 2 67
: , P& 4 \R 3 9 P& < – <B\ <2 % <. +, P<& <2 -, – & $ T <O7 < &W <7 – <9 <. – <: 2 3 % SR g P
4 <? <2 %0<0. ; P<5 <7 P<& ’< 3 A3 PB O5& .P2 Q (> – @ T 3 8 BX + < 4 <? <2 ;W -, – & 2 – @ T 3 f7 $
.
. =X D jW N C? , +O$
( ) <M CX<<2 s%<2 % < & < 3 v57 7 = P2 : % B05H
V = Vcr + +VtVst + Vsc + Vf( )
;W .
7 – @ T 3 F5@ V&. PK %2 3 : Vcr
– GD +P
T 3 %0 0. ; P 5 XS R , %& %2 3: Vt
@
%00. – GD – 9+ PBB. ’ , %& %2 3 : Vst
0 – GD – 9 +PBB. ’ , %& %2 3 : Vsc
; < <2 <57 f<7 . %7 ? _ D % 2 3 : Vf .P 2 vS?
1 N , A P . 9 2 E.K 4@M c 2
. %8H ( ) M
: %; 52 ( ) M 4? 2 Vcr
Vcr = crbt( )
7 T 3 % 2 F5 @ V& . %& 62 VB7 cr ;W . : [ ]P W% 2 , M , . +P
cr = K.22.D = 12(1K. 2.E2) bt 2 yw = yw ( ) b t

3

3

T 3 R b5(5@ 3P E %0 8 % ’ D ;W .
-<N P<K VB<7 yw; <H vr T 3 ’r t
.P& – @ T 3 F5@ V&. vr K 3 ;P
#

V0. ; P5 -0B7 (_) V&. =5K 0B7 (o )

V&. , aH 0B7 (U)
A 19 ( ! A 19 B 3+ C &-+ ” D 6 ? ;,
& > 59 3 P& C5X07 C& H – 9 > F5H -SfO
C< R Q(<> j -, – wR : %X5H CfO
A15& <<X .P<< 5& <<N3 <<2 +P<<BB. H T 3 %0<<0. ; P<<5 m < <2 =5[B< – < 2 <2 – D 3 57 2 0 15& %[ ’5(>
. +P X 3 %. 4 M G
<2 _ < – <9 & =5<2 v5 3 , 2 /5 & 4 <M G 3 u,1<5 ; < E5S(<7 <5M , + O < 2 3 I d8 +P<B9 ; 0<& <. (s) < M [u] ; <X 9 3 % D –- \?
.P< W %< < <2 < – @ T 3 E5S(7 D3 d xx , yy, xy – 0B7 – 1N 3 5Mr3 ( ) CX
0<B7 – 1<N %B 1[ <N <2 .P<9 %< ; 0& K =
</&W , 3 < % C? K (t) M -, + 3 (s) M . P W % 2 (u) M , t – GD %00. VB7
( xxyy)2 + yy2 + xx2 + 6 xy222yw = 0(s)
3 cr2 + 3 crt sin2 + 2t2yw = 0(t)
100084-11492

3
t = 2 cr sin2 +(u)
[ – 7 3 3 C & H & 9 2 C 6 F5 H ; <X 9 3 3 1& < .[p] < > PB9 8 D C& H – 9 >
; <N %0<0. ; P5 C R -, ( P -2 %. Q3 , [z]
< K – 2 – GD – 9 +PBB. 7 2 +P ’ – D 3 57 C<5\D , – [ ; 6 . P& . + O d % ’ 2 – 2
3< D 3 <57 %00. ; P5 C R 15& [s] ;X 9 37H
.P&. %2 &W (X -(5& X
P< F< M<7 <2 [s] ; 2<7 4 <M G =
@ < %<2 < %2 3 %2 , qB 2 %S5S67
<9 & P< 3 8 H B> 3 . H 2 g, & +P0& 7 – 9 & – F 4 ? 2 % 2 C& H 3 B05H _ v5 3 , [t] g@ . 3 S 57 .. P _ %00. %G8 Q3 = .( ) CX P& . ? Ec D 6 2 9 &
CAN/CSA [u] <& . 0. P& = /& d7 -, ( P
. +P ‘H 15&
_ <D – w<R I5 67 = – q& M G V’2 3 = ,
<7 P<& +P< < ’< %<. +, P<& <2 %&5H – @
😛 W %2 () M L&
1+
st =[

2t + 2t cos2( d)]
+ +[(1) cr cos2( d45)]ys
=[ t (1+cos (2d)sin (2d))
150884-268189

(1cos (2d) +sin2( d))]
+ +[(1) cr sin2 d]
=[ t cos (2d)t sin (2d)]
+ +[(1 ) cr sin2 d] st =+ +[(1t[1 (1)+cr sin2)sin2(d]d ys)] ( ) < M 4 <? 2 15& – GD – 9 +PBB. ’ – 0 VB7 : % – 5> /5 & 3 ? 8 (p)
sc = t[1(1+ )sin2( d + )]()
+ +[(1) cr sin2 d]crs
<GD +P<BB. ’< ;P< -N PK VB7 ys . -: 2
.P<& – GD – 9+PBB. ’ -0 V&. PK VB7 crs 3
<9 +P<BB. ’< -0< V& < . PK VB7 =5 ’7 e f8
1<5& %<G2 3 3 > 4? ;6 d7 %7 M G
’< , +O < C6 2N 7 2 @ %K: – 9 & =5 W
3S<2 <. – <B\ <2 crs </B .P<& +P c 9 +PBB.
%< (s) 4@ M F . 2 [z] ; X 9 3 3 1& 3 ; 5 7 .P W % 2 (z)
36881789643

1072905-3321

crs = ys2for 2 ()
25679482398

crs = ys (1 0.53( 0.45)1.36 ) for 0.45 < 2 (t) crs = ys for < 0.45(u)
: ;W .
614181-45205

= (b / ts s) 12(1 2)( ys / E)( 2kS) ( ) kS = (b / ls )2 +0.425( ) – <GD – 9+PBB. ’ j : l 3 ’r ts B H bs ;W . <9 +PBB. ’ %Mr V& . , – 5> SN – 2 +3 R2 .
B0<5H I<5 67 = +P C? K – PR C5S67 |& 2 N 7 2
– <GD – 9 +PBB. ’btss’r 2 B H \(& . %
= 90( )
: 2 22 v5 ;W .
= tan 1

(z)
; <Ic <57 <G xG< Ab ; G xGAc ;W .
.P &\: O7 hs 3& 9 : L ; %B
.P& +P c ( ) CX 4 f’0 <2 %0<0. ; P<5 C< R , %& Vt %2 3 a}
+P< + ; 0<& (_$ ) CX< <. xy %2 VB7 – B\
: %C? K () M ,
Vt =

tbt sin 2()
Vsc 3 Vst – <GD – 9 +PBB. ’ , % & % 2 – 3 +P< </ – 6 – 93 5& I – – 9 f7 .
( ) 3 ( ) 4@ <M , v57 7 2 P& – GD – 9 +PBB. ’ : P& % /5 &
Vst = Asst cos d()
Vsc = Assc cos d())
– <GD +P<BB. ’< – 0 %00. G xG As ;W . .( ) CX< P<& %< 6 2 – GD – 9+PBB. ’ 3 , d 3
’ -0 -6 VB7 sc 3 %00. -6 VB7 st
; & <D m < 2 3 D jW N , + O 2 . P& – GD – 9 +PBB. V& < . P<K % 2 VB7 .PB W % 2 + C5S67 3 g 9
%0<0. ; P5 XS R , C? K %00. VB7 3 T 3 F5 @ .P<BB. %< < R – 0 %00. – 0B7 9 +PBB. ’ f<7 C<6 T 3 ;P< ’< <2 N 7 2 . 2 A,@ 15& t 3 cr – 0B7 g 9 ; & D I\: T 3 2 9+ PBB. ’
</ T 3 t 3cr -0<B7 – 9 < <2 R 4N
’< <2 \(<& 0B7 j -3, 2 N 7 2 3 = , .P& %
3 ( ) 3 (u) 3 ( ) 4@ <M , 3 t 3 cr =< 3 9 +PBB. VB<7 + F . 2 9+ PBB. ’ – 0B7 j C P\7 3 < , 4@ <M , + O < <2 – GD – 9 +PBB. ’ %00.
#
6E
<7 < \: F< – @ %2 – PR P = PBl
3 – <q& Q3 <7 P<& +P< <> <. 2 +P 7 3 +P0&
%<2 < %<2 < 3 =5< ’7 +P< c 4@M
. P<& 5> <D %2 , 3 %2 – GD +P 7 – @
=5<Bl %<G8 <5h – P<R C<K -2 . ANSYS 1 A & ,
+P< + O < C<5S67 3 -, (< P – <2 v B %Sc ( < <2 %9 [0< ,W – <9 + 2 – PR – P D .
3 < +P +P5/B 3 % 2 ; 6 %S\D 4 M G , +P W C<2 D | < & 2 P& P& %9 [0 ,W – 9 + . % P – 2
– @ % 2 – 9 – 2 \ M – 9 & =5 W – B\ 2 q & D , 3 % 2 ; \ R M +P 7 3 +P0& 7
+P< C<? K ; B5 : +P + . %S @ 2 &W – <2 F57 B5< +P& < ’< %<G8 P<Bl P< , .
3 (p) -SX< I2 <G <& @ < %<G8 5h -, ( P
<731 ;W F5 < @ – < 5>k 3 3 < +P< + O ( ) +, < <2 +P& < < R – <9 2 <b& Bl . < +P<
<2 V& < . +P PH P& f7 – 6O? ;3 L . 4 ? 2 55 7 X&W [ P2 % & M 7 3 P % & T O7 – PR 4 ?
.P& R 5 3 & 4? 2 – 6O? , U8 -SX
| < & 3 ’< H ;W 4 j 3 5 3 & / + 6& r =< E<9 – < , 4 M G 3 – + (> n6\ – +,
%< 2 – <9 – PR CK . > 4 ? e f8 . P& +P > . 2 ; 6 d 7 Q3 = PBl 15& – @
. +P + &W , – PM7 2 , %< & – <D <jW N , 5 3 – f & [ ] 3 3^
3 P<& 3W < 2 +PBB. H T 3 % 2 V& . = PBl <.<2 \: – @ % 2 F 3P6 – 1N C5S67 C 5S67 5 3 – f & [ ] ; X 9 3 .P & 2
V& < . P< =5< 3 < H 2 ; %0,W && 3P6 – 1N
[] ;X 9 3 %&\ 2 . P&. R +PBB. H T 3 %2
V < ,W +P0& 7 – @ %2 \: P F
< 7 – <2 AISC t [u] < & =5<cW <. ( ) < M 2
: 3P6 +P c %r R – 9 +PBB.
722381-3198

E
b / tss0.56() )
<2 <57 4@ f7 5\S? 2 %& 5H -1S _ D % 2 3 + 4 ? 2 4@ f7 > – q& P , 3 %[ (2 ;
Vf vS ? 4@ f<7 -<2 3< Vf = 0 P& < <
C5X0<7 , %<& %[ ’5(<> A15& <X %<2 <5] ;7 %
F -2 . 3W _ (K 2 -, – wR F5H -SfO
<9 57 <XB < 2 – @ %2 \: F ;8
P<BB. < %0<0. ; P<5 <7 P& %. % ’ 33
CX 9 57 XB – N 2, K 2 F5H -SfO
% D $-\? PB W % P PH & =5 H 3 @ 2 & P& 5[2
(<X A15& <X =< -2 [ – , .[u] ;X 9 3
< S5S67 A </& 2 , 5& =X \: PBl -2 D E. K
% K ;W 2 +3R .P2 Vf\6 -2 z %G8 5h %X57
Sf O , -P M7 = X 1 5& \: F _D
.[z] 5&3 2 3 =2 PB W N3 2 57 F5H
<. < + ; 0<& ; >P&[& 4 M G |& K = 2
<2 _ <D %2 5] +P 7 – @ %2 – 9
< F<1& &< – <5 8 C? O C5X07 |&
C<? O C5X0<7 < 2 Vf 3 = , .[] – SR – % : &
. %C? K () M , & – 5 8
Vf = 4Mpc / hs() )
<<2 A /&<< .<< ;<< F5 <<H ; << Mpc ;W <<.
( ) <<M () 3 (–) ( ) – <<9 <<M %B 1[ <<N
<. P< W %< 2 +P oM7 – 9H v(K 2 () M
+P< ’ – @ % 2 % & % 2 3 +PB9 ; 0& : ; 2 57 vS? 4@ f7 2 \: F (CX X) – GD
V = crbt +

tbtsin2 + A (sst + sc)cos d
4Mpc()
+

hs
%< 2 <5 ] 0<& < R E (<5 – <5 3 & & > F<l . – < 5 <N <2 N < <2 C5S67 d 7 +P C? K
< <2 C<5S67 | < & <2 \(<& %) 3PK 7 =X
<2 |& K = .P9 ; 0& V 1 12 -5 N 2 N
+O 4? =2 B2 .P& F1& T 3 C. E5S(7 5]
<N 7 2 vB 5 3 -f & R 2 ( 2 %3 Q3 ,
< <2 | < & % & – SX 55 7 3 %0& . – 9 2 – <2 3 Q3 3 =< , . T E (5 %MD 3 – 5 ]
. 2 E (5 % 2 5 ] =5 ’7 5 3 | & 2 = . 5& E [ H 2 %B r CK Q3 ,Q3 3 9
<2 F5 <H %<9 > < l ; < 3 +P +O zg
< -, (< P -2 Shell 181 + > 9 -,W N V
.< +P< > . 2 – @ %2 – 1N A7 -PM2
< & 2 4 ? 3 2 – ‘> 2 SK 9 %& , – 9 +, 2 =5<5M7 $_ F<57 7 Q3 $o< : P<& o M7 C2 D ANSYS
=5<2 %& < , – <9 +, <2 , L<\ h /B .+’ %&, +, 2
+P< + O % [ 9 CX0 2 \Sh – 2 / p 7 / P<K 3 F , aH % & 2 2 ;P5 > . %BM = P2 .
<2 <SK p <7 =52 3 | P7 2 2 P O52 T O7 %& , 3 <M2 <2 % < & <2 <. % </&W , .< %< R E (5
| < & <2 %<S5S67 | < & 6<? %[ (<2 f & 5MD
<& & <qB =5< 9 <2 .P<& +P< +P5/B \ M %9 [0 ,W 3 C<2 <. , < /p m <5 – . SPSW2 %0 ,W g P< <N 4 R : = > . 2 2 [p3 p] ; X 9
x f< <& & =< .( ) CX< +P _ ’ & : 2
– @ < +P<BB. <H T 3 3 %& <5H _ <D -& %f
-, < – < & E5S(<7 P<K VB7 . -:2 .P& +2 43 O
< +PBB. H T 3 E5S(7 PK VB7 3XH [ z
%<G8 P<Bl – < 5B6B (p) CX< .P& +P qB XH [
C<K . 2 – 9H 3 %f – 9 @ V& .$VB7
<. < %< <qK .P<9 %< ; 0& SPSW2 P – PR

[?H H] SPSW2 3- (F G! 6 E ;,
V& < . – 9 m2 5 3 -f & =5Bb 9 &W P&.
– 1<N P< C<5S67 mm <B y. P<K 2 %2
. P&2 . 2 ;W 3P6
: +P > . 2 C5S67 Q3 3 M G = A </& +, < +k< 3 < V& . C5S67 F 3 Q3 a}< P<& +P< C<? K %0& . – 9 – SX 3 +P
< H <2 C<5& 3 -, < 5\< – <2 %\< B 5 3 – SX 55 7 <2 ‘<> %G8 5h C5S67 3 +P R +, % K %0& .
A /& 8 BX – ‘> 2 67 Fl . -& X 55 7
Q3 <2 5\ 3 6 , %G8 5h – ‘> C5S67 . +P
<[ & 4<j . 43 O7 = 2 %G8 5h %X57 C5S67
.P& R C2 D %S5S67 Q3 = %& , – 5> 2 s 3P6 – 1N % PB9 %G8 5h C5S67 A3 Q3
67 t, -& X 55 7 2 ‘ > C 5S67 F.
%<& 4<j =2 B2 . > 4? 8BX -‘>2
|& – @ – wR %Mr V&. 3 %G8 5h V&. ,
<2 , <5& 3< <2 ;, 5(2 Q3 = =X .P& +P R
=< 3 =< , . u %<[ 9 <2 ;P5< G8 3 %M
. +P +O 3 Q3 , PM2 “@M Q3
%<B d< <2 P .



قیمت: تومان


دیدگاهتان را بنویسید