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Mn
C = T0.85f cba = Asfs0.85f cba = bdEss
s = cu(d cc
)
s
a = 1c
(0.85f cEscu
)a2 + (d)a 1d2 = 0
a
Mn
Mn
= Asbd
cu
!
" " " # $
y = fy/Es
b
cb
d= cucu + y
= 0.0030.003+ fy
29,000,000
= 87,00087,000+ fy
%
Cb = 0.85f cb1cbTb = fyAsb = bbdfy
Cb
Tb
b
b =0.85f c1fy
(cbd
) &
#
b =0.85f c1fy
(87,000
87,000+ fy
) '
( )
" # #
max = 0.75b *
( )
" + ,
min =200
fy
-
. / 0 0 0 1 2 3 4 3 5 6 7 8 8 9 9 3
-
: ; < = > ? @ ? A B C D < E ? F @ G H I D ; ? @ A ;
< ; J K A E L M D ? ? @ A ; N D @ ; B A M O D E D ; G
P Q R S T U V W V X Y Z [ Z Q \ ] Q ^ _ X Y R U [ W \ Q R ` U ]
_ U V a Z b S T U ` R Q Z Z c Z U ` S [ Q W d [ X X _ U ] [ e [ ] U
] [ W S Q S d Q _ U V a Z f
g U V a h ` Q W Z [ Z S Z Q \ S T U ` Q a i R U Z Z [ Q W R U [
W \ Q R ` U a U W S V S S T U S Q i V W ] Z ^ \ j ` [ U W S Z S U U
X V S S T U _ Q S S Q a Z Q S T V S
T1 = Cs k_ U V a l ` Q W Z [ Z S Z Q \ S T U ` Q W ` R U S U d U
_ V W ] S T U R U a V [ W [ W m S U W Z [ X U R U [ W \ Q R ` U a U
W S b V Z Z T Q d W [ W
P [ m ^ R U n f l
P o p q r s n f l t u S R V [ W Z b Z S R U Z Z U Z b V W ] \ Q
R ` U Z [ W _ U V a d [ S T ` Q a i R U Z Z [ Q W R U [ W \ Q R ` U
a U W S f
v w x y z { | } ~ |
Mn | { | } z {
T U V R U V Q \ S U W Z [ Q W Z S U U X [ W _ U V a h [ Z Q _ S
V [ W U ]
_ Y Z U S S [ W m
T1 = Csb d T [ ` T m [ e U Z
As1 = Asf
T U W Q a [ W V X a Q a U W S ` V i V ` [ S Y Q \ _ U V a h [ Z
S T U W
Mn1 = Asfy(d d )
g U V a l ` Q W Z [ Z S Z Q \ S T U ` Q W ` R U S U V W ] S T U
R U a V [ W [ W m Z S U U X b
As2 = AsAs1 = AsAsf
T U ` Q a i R U Z Z [ Q W
\ Q R ` U [ W S T U ` Q W ` R U S U [ Z
C = 0.85f cba
V W ] S T U S U W Z [ Q W \ Q R ` U [ W S T U Z S U U X \ Q R _
U V a l [ Z
T = (As As) fy
T U ] U i S T Q \ S T U ` Q a i R U Z Z [ Q W Z S R U Z Z _ X Q
` [ Z S T U W
a =(As As
)fy
0.85f cb
T U R U \ Q R U b S T U W Q a [ W V X a Q a U W S ` V i V ` [ S
Y \ Q R _ U V a l [ Z
Mn2 =(As As
)fy(d a/2)
T U S Q S V X a Q a U W S ` V i V ` [ S Y \ Q R V ] Q ^ _ X Y R
U [ W \ Q R ` U ] _ U V a d [ S T ` Q a i R U Z Z [ Q W Z S U U X Y
[ U X ] [ W m [ Z S T U
Z ^ a a V S [ Q W Q \ S T U a Q a U W S ` V i V ` [ S Y \ Q R _
U V a h V W ] _ U V a l
k
S T U R U \ Q R U b
Mn = Asfy(d d )+ (As As) fy(d a/2)
-
Mn
T = AsfyCc = 0.85f cbaCs = As
(Es
s
)
s =(1 1d
a
)(0.003)
Cs + Cc = T
0.85f cba + AsEs(1 1d
a
)(0.003) = Asfy
(0.85f cb
)a2 + (0.003AsEs AsFy) a (0.003AsEs1d ) = 0
a
Mn = Cc(d a
2
)+ Cs
(d d )
( )
b= 0.85f
c1
fy
(87,000
87,000+ fy
)
(
f sfy
)b
= 0.85fc1
fy
(87,000
87,000+ fy
)
max = 0.75bmin =
200
fy
f = FA Fey
I My
I
-
! " # $ % " " # + ! " ! " # & ' ! " " " ( ! # ) ! ! ! " ! "
" " !
*
!
$
+ , "
$
!
!
- .
' /
"
%
+
0 $ !
" 1
(
# $
,
! # # 2 0 # 3
"
!
!
$
(
#
1
& 4
"
!
" "
0 $ !
"
2 #
!
#
!
%
"
!
" "
3 !
#
"
"
%
+
- .
' 5 6 & 7
5 6 & 8 9 5 : &
- .
' 5 6 & ; &
0 # %
2 #
#
(
2 #
#
!
,
$
"
=
!
$ #
+
! #
"
! # #
1
! 2 #
!
2 2
3 !
1
# 2 !
"
!
" "
/
"
!
0 ! #
"
% # 2 %
"
!
" "
3
"
!
0 # $ %
!
#
(
2 #
3
"
!
0 &
-
%
"
!
" "
,
$
0 0 2 0
!
"
!
0
"
"
!
" " fps= 3
0 0
(
0
" "
!
!
!
"
0
"
!
3 !
fpu& K #
! 3
1
0
#
" "
/
"
! #
"
!
# $ 0 L
* 1
0
"
!
3 !
"
Mn = Apsfpsd a
2
M N O P N Q
a = Apsfps0.85f cb
M N O P R Q
4
"
!
0
"
!
" " fps
,
2 #
1
,
"
#
"
!
# $ % !
,
0 !
(
#
, ( 1 "
3 % %
#
*
$ !
S 1
! #
"
" 1
"
!
#
"
3 >
- .
' 5 6 & T & ; & 4
S 1
! #
"
- .
'
% % 0
,
0
# 0
(
2 !
2 2
! >
%
"
!
" "
!
"
!
0 =
fse=
S 1
0
" Pe/Aps=
"
# ! 0
" "
!
U & 8
fpu& 4
- .
'
S 1
! #
"
"
2 # 0 0 #
"
&
K #
$
$
, "
!
,
#
!
#
" V
fps = fpu(1 p
1
[fpu
f c+ ddp
( )]) M N O P W Q
' 2
(
# $ %
" "
#
2 #
$
!
"
! )
! # #
1
!
0
1
0 ! 3
fps
!
X S 1
! # 7 & Y < = !
2 # 0 0 #
3 % % 0
" V [pfpu
f c+ ddp
( )] 0.17 M N O P Z Q
d 0.15dp ,
K #
$
$
, "
!
1
,
#
!
#
"
!
"
% / ! # /
% !
! # # 2 Y 8 #
0
" " V
fps = fse + 10,000+f c
100p{
fpyfse + 60,000
}M N O P [ Q
K #
$
$
, "
!
1
,
#
!
#
"
!
"
% / ! # /
% !
! # 3
!
!
Y 8
V
fps = fse + 10,000+f c
300p{
fpyfse + 30,000
}M N O P \ Q
4
L
* 1
0
"
!
3 !
"
!
0
1
0 !
2
# $
X S 1
! # 7 & Y 7 & 4
"
3
"
!
3 !
" S 1
0 ! #
Mn=
= 0.90 2 # L * 1 &
] ^ _ _ _ ` a b c b d e f g g h h b
-
i j k l m n o p j q j l r i s r k n t
u v w x y z { | x y } ~ ~ ~ y ~ ~ { ~ x y } ~ x y } } y x y } ~
x y } } y x y | x y y ~ y y z { ~ y
~ y y ~ x y ~ y } ~ ~ | y } ~ y x | { ~ y ~ y } | } { { }
x { ~ { x y
f c
~ x x | | y y x } | ~ { y ~ y } } y y x y | x y y ~ } {
y { | x | } ~ x | { ~ y y x ~ y ~ y } | y y x ~ y y ~ x y y ~ y
} | y x u v w } y | y } ~ y
| | { { ~ y x y | x y y ~ }
As = 0.004A y x y
A| } ~ y x y ~ y x } } } y ~ | y ~ y y ~ y y { x ~ y } | y ~ y y
~ y x x | ~
~ y x } } x } } } y ~ | u v w | y } ~ y | | { y ~ ~ y y x y | x
y y ~
y } { x y y z { ~ y { ~ | | ~ u v w x | y } ~ y | x y z { | x y
y ~
p
p +(d
dp
) ( )
pw +(d
dp
) (w w
)
0.361
u v w } y ~ y ~ y x } ~ y y ~ } | y ~ y } y ~ y z { ~
a/dp| x y x ~ } | | ~ y
y z { ~ |
y x y | x y y ~ x ~ | x y ~ y x ~
1| } { } y u v w } ~ ~ y } ~ ~ ~ y y } | y ~
} ~ x y ~ } ~ y x y ~ y x ~ ~ y y ~ } ~ x y ~ } y ~ y x y } } |
x ~ | ~ y
y ~ { y
y } y ~ x | { | } } { y ~ y ~ y ~ x | |
P | ~ { | } ~ x | } y y
{ | x x } } ~ y } y ~ | y { } y ~ y } ~ y y x y ~ y x y y ~ y ~
y x ~ y } ~ x | } | ~ y
x y ~ y } ~ y y x y y z { x | y } ~ x | | ~ | } } } | y ~ { ~ y
~ y } ~ x y } } y } | ~ y x y ~ y
} ~ y y { } | ~ y } ~ x y } } } ~ x | { x y } x ~ y ~ ~ y x |
}
y x y } | ~ y x y ~ y } ~ y y x y
y z { ~ ~ y } ~ x y } } y } { ~ | | y ~ y x x y } | x y }
y ~ ~ ~ y { | } ~ y } {
~ y x y } | ~ y x y ~ y } ~ y y
Po = 0.85f c(Ag Ast
)+ fyAst
{ ~ x ~ y y y ~ | | y ~ y ~ } u v w } y | y } ~ ~ ~ y | { y } |
|
{ y x } | x { }
Pn(max) = 0.85[.85f c
(Ag Ast
)+ fyAst ] x ~ | y { }
Pn(max) = 0.80[.85f c
(Ag Ast
)+ fyAst ] x | { y } |
{ y } x y } y | y x ~ | y } | x { }
x y } y ~ | y u v w
x ~ { } x y } { | y ~ } ~ } { ~ ~ } y y x y } } y y ~ } y | x
y
-
P
M
! " # $ % ! # " & ' # ( ) # *
) $ + * , - . / . 0 1 2 ! " # $ % ! # " & + * , 3 4 5 3
. 6 0 7 7 2
8 9
: : ;
<
= >
> = : 3
> : ? >
@
>
= 0.9
= A B A B C = A D @
Pa >
Pb
A
7
f cAg .
Pb
A
7
f cAg >
3 < 6 : 7 B E 1 C F G + * , H ) $ I ! ! J ! " % ! K L M *
N
> 0 O 2
P Q R R S
3 < 7
A
7 7
T
@
T =
@
> T
7 U , & ( ! % ! K L M V
@
lu T 3 < 7
A
7 7 7
> W
O X # & Y K , & ( V
@
k
b >
A
C
7
A
E 3 < 7
A
7 7 O 7 F
@
s 7
E 3 < 7
A
7 7 O O F
@
3 < Z 7
A
7 7 O
3 < [ E F \ E [ F 3 < Z 7
A
7 7 O
@
>
= > ]
=(EcIc/lc)(EbIb/lb)
^ _ ` _ a b
<
=
EI =
EcIg
EI
A
C
EcIg
9 + c & ! ! I " ) # $ ) $ L I " ) # $ " ) M * V
@
3 < 3
> T ]
d e f f f g h i j i k l m n n o o i
-
p q r s t u v w x y z { | } ~ ~ { | ~ { ~ | | ~ { ~ { ~ { | } {
~ ~ } | } w
} q { { } ~ ~ { ~
Q | } { | ~ { } w v |
Q =Pu1u
Huhs 0.04
q { { } { | } { ~ { | } ~ { ~ } { | ~ { ~ {
} { | } { ~ } { ~ { { | w
v w p | } | { } } | | { ~
r } w x
h } | } ~ | } | | { ~
r } w
hw p | { | { ~
r }
I/A
w
w q w w v w } | { { { |
~ | } | }
klu
r< 34 12M1b
M2b
q w w v w } | { { { | ~ | } | }
klu
r< 22
q
klu/r q w w v w x { } { { } { ~ } } | | } } ~ w
-
M2b
M2s
Pu
Mc
Mc = bM2b + sM2s
M2b
l
M2s
b =Cm
1 Pu/Pc 1.0
s =1
1Pu/Pc 1.0
s =
Cm = 0.6+ 0.4M1b
M2b 0.4
M1b/M2b
Cm =
Pc =pi2EI
(klu)2
EI = EcIg/5+ EsIse1+ d
EI = EcIg/2.51+ d
-
b
d = !
" # # " $ $ % " & $ $ " $ # " $
' " # % " & $ "
!
" # # " $ ( ) * + + ,
s
d =- " & $ . . " $ # " & " # . " & . & /
' " # % " & $ # " & " # . " & . & / ( ) * + 0
,
1 %
b &
s . % $ 2 " 3
# . # $ 2 # " & $ 4 1 % &
b &
s
!
$ .
5
4 6
. $ & " . # $ 2 3 # " & # 4
7 8 7 8 7 9 : ; < = > ? < > @ A B C D E F ; G : F @
F > @ H E F D E F ; H A > @ E > I
' " # # " . & % " . $ & 2 "
!
" # 2 $ " $ & . . . " %
% & 3 " & " 2 # .
Pn,Mnx " $
Mny J " / " # . 2
!
& . . $ " .
Pn" " & .
ey = Mnx/Pn" $
ex = Mny/Pn J & .
x" $
y"
!
. 4 ' & / . % % " # & . & % " . "
2 $ K $ 4 1 K & . /
S1 & & " # "
!
. " & $ K $ 2 /
Pn, ex " $
ey L . $
/
S2 3 " & " 2 # . $ K "
!
. " & M N
Pn, ex " $
ey L" $ & $ /
S3 "
!
. " &
Pn,Mnx " $
Mny4 1 & . " " % # #
J
.
O & . # & & & " # # " $ $ " P . .
% & & " # % " # & . & % "
S2 " $ O & . # & # " $ & $ " $ Q R
# " $ &
$ 2 . % " # & . & % "
S34
S T U V W U T X U Y Z [ T \ Y ] W ^ \ ] _ ` U a b \ _
c . " % " # & . & % " % /
S2 O & . # & & . $ % # #
J
d " " . " " . % " &
! e
" " % " # & . & % " & & . $ & . K $ &
.
ex" $
ey f
1
Pni= 1Pnx
+ 1Pny
1P0
( ) * + g ,
J
&
Pni = " # "
!
" # # " $ . & " 3 & / " # 2 "
!
.
Pnx = " # "
!
" # # " $ . & " 3 & / " #
x"
!
.
Pny = " # "
!
" # # " $ . & " 3 & / " #
y"
!
.
P0 = " # "
!
" # # " $ . & % & & & . . h i & & /
j
' . & . # . $ " " k d " l 4 m n " / 2 " & & "
J
. " # # 3 " # . % "
!
" # # " $ " &
3 # 3 $
. " .
J
Pn/P0 . & " % 6 4 6 o & # . . 4 - & . " . . 2 &
. # $ 2
$ . $ % & p
!
& # / 4
S T U V W U T ^ \ ] _ q \ r a \ s T ` U a b \ _
' % " # & . & % "
S3 " 2 % " . " % " # / % & 3 . h # " $ & . j " &
& . $
" . " 3 " # %
Pn4 ' & " # $ . " # d " % & # " $ & " . "
Pn " / 2
!
& . . $ % # #
J
% &
f(Mnx
Mox
)1+(Mny
Moy
)2= 1.0 ( ) * + t ,
J
&
Mnx = Pney ;Mny = Pnex
u v w w w x y z { z | } ~ z
-
Mox = Mnx Pn Mny ex Moy = Mny Pn Mnx ey
1 2
1 = 2 =
Mnx Mny
Mox Moy
Mny
Mnx= MoyMox
=
Pn P0
(Mox
Mox
)+(Moy
Moy
)= 1
2 = 1 = 1/2 = log 0.5
log
(Mnx
Mox
)log0.5/log+(Mny
Moy
)log0.5/log= 1
! " # # $ $
-
% & & ' ( & ) & * + , & ( - + . / * . 0 * /
- & - 1 & 2 & 3 0 4 & 5 6 1 & / 4 . 4 / . 7 8 '
9 * + / ( : 6 8 ' . & - 1 8 6 . 4 / . 7 8 ' 9 . / ' ' + - %
& , 4 & ( 8 . - & (
% ; . / * . 0 * / - 8 ' 9 - 1 & , 4 8 ' . 8 , / * 6 - 4
& 6 6 & 6 ?
= P P
< Q < M 8 6 / 6 A + * * + C 6 D
Tu Tn E F G H F JC 1 & 4 &
Tu8 6 - 1 & - + 4 6 8 + ' / * B + B & ' - ( 0 & - +
A / . - + 4 & ( * + / ( 6 :
8 6 - 1 & 6 - 4 & ' 9 - 1 4 & ( 0 . - 8 + ' A / . -
+ 4 & @ 0 / * - +
K < L M A + 4 - + 4 6 8 + ' : / ' (
Tn8 6 - 1 & ' + B 8 ' / * - + 4 6 8 + ' / * B + B & ' -
6 - 4 & ' 9 - 1 9 8 ) & ' % ;
Tn = Tc + Tc E F G H R JC 1 & 4 &
Tc8 6 - 1 & - + 4 6 8 + ' / * B + B & ' - 6 - 4 & '
9 - 1 , 4 + ) 8 ( & ( % ; - 1 & . + ' . 4 & - & / '
(
Ts8 6 - 1 & - + 4 6 8 + ' / * B + B & ' -
6 - 4 & ' 9 - 1 , 4 + ) 8 ( & ( % ; - 1 & - + 4 6 8
+ ' 4 & 8 ' A + 4 . & B & ' - ?
=
B + ( 8 & 6 @ 0 / - 8 + ' < Q Q / 6 A + * * + C 6 >
?
= P P
< ?
= P P
< < < . + ' - / 8 ' 6 / B + 4 & ( & - / 8 *
& ( . / * . 0 * / - 8 + ' A + 4 - 1 & 6 1 & / 4
6 - 4 & ' 9 - 1 + A B & B % & 4 6 6 0 % & . - -
+ / 3 8 / * . + B , 4 & 6 6 8 + ' ?
= P P
< ? > @ > 9 A B 8 C > ? D @ > E F 8 9 > 8 F
> ? 9 D G H = D 5 ? 8 ; I J K L M > = : 8 ; > ? 8 > ? =
5 N D 8 ; ; @ O > ? 8 P 9 D E 8 I @ F K L M
> ? 8 < = B > ? @ O > ? 8 < 8 Q I < ? = 5 ? 8
R 8 F = ; E F 8 9 > 8 ; >
S
? 8 : = D = : T : 9 F 8 9 @ O ; ? 8 9 F F 8 = D O @ F 5 8 : 8 D
> ; ? 9 A A Q 8 9 > A 8 9 ; >
Av(minU = 50bws
fy
O @ F
Tu < (0.5f c
x2y) V W X Y W Z
[
? 8 D > @ F ; = @ D = ; > @ Q 8 5 @ D ; = B 8 F 8 B = D B
8 ; = E D I > ? 8 ; T : @ O > ? 8 5 A @ ; 8 B ; > = F F T
C ; O @ F ; ? 8 9 F 9 D B > @ F ; = @ D : T ; >
; 9 > = ; O \ > ? 8 O @ A A @ < = D E ]
Av + 2At 50bws
fy
V W X Y ^ Z
< ? 8 F 8
Av= ; > ? 8 9 F 8 9 @ O > < @ A 8 E ; @ O 9 5 A @ ; 8 B
; > = F F T C 9 D B
At= ; > ? 8 9 F 8 9 @ O @ D A \ @ D 8 A 8 E @ O 9 5 A @ ; 8 B
; > = F F T C _
` a b c d e f g h i c j j k l m a c e g f j n a o a e i g f j h
p a q j q e r s f j b c f e
t u v w x y v z { | } x ~ v v {
? 8 9 F F 8 = D O @ F 5 8 : 8 D > = ; > @ Q 8 C F @ R = B
8 B < ? 8 D
Vu VcI ; T 5 ? > ? 9 >
Vs Vu
Vc
V W X Y Z
S
? 8 B 8 ; = E D \ = 8 A B ; > F 8 D E > ? @ O > ? 8 ; ?
8 9 F F 8 = D O @ F 5 8 : 8 D > = ; D @ > > @ 8 5 8 8 B H
I H H H C ; = _
[
? 8 D > ? 8 ; ? 8 9 F F 8 = D O @ F 5 8 : 8 D > = ; C 8 F
C 8 D B = 5 T A 9 F > @ > ? 8 9 = ; @ O > ? 8 : 8 : Q 8 F
I > ? 8 ; ? 8 9 F F 8 ; = ; > 8 B Q \ > ? 8
; > = F F T C ; = ;
Vs =Avfyd
s
V W X Y Y Z
O > ? 8 ; ? 8 9 F F 8 = D O @ F 5 8 : 8 D > = ; = D 5 A =
D 8 B 9 > 9 D 9 D E A 8
I > ? 8 ; ? 8 9 F F 8 ; = ; > 8 B Q \ > ? 8 ; > = F
F T C ; = ;
Vs =Avfy (sin + cos) d
s
V W X Y Z
S
? 8 : 9 = : T : ; ? 8 9 F ; > F 8 D E > ? @ O > ? 8 ; ?
8 9 F F 8 = D O @ F 5 8 : 8 D > = ; D @ > > @ 8 5 8 8
B
f cbwd
9 ; ; > 9 > 8 B = D
G G _ _ _ _
t w ~ z { z z w z } { | } x t u v w x y v z { | } x ~ v v {
G G _ _ _ G ; 8 > ; > ? 8 : 9 = : T : ; C 9 5 = D E @
O
R 8 F > = 5 9 A ; > = F F T C ; 9 ; > ? 8 ; : 9 A A 8 F
@ O
d J @ F J = D 5 ? 8 ; _
S
? 8 : 9 = : T : ; C 9 5 = D E @ O = D 5 A = D 8 B ; > = F F T
C ; = ; ; T 5 ?
> ? 9 > 9 A = D 8 8 > 8 D B = D E O F @ : : = B ? 8 = E
? > @ O > ? 8 : 8 : Q 8 F > @ > ? 8 > 8 D ; = @ D F
8 = D O @ F 5 8 : 8 D > < = A A = D > 8 F 5 8 C >9 >
A 8 9 ; > @ D 8 ; > = F F T C _
O
Vs8 5 8 8 B ;
f cbwd
I > ? 8 : 9 = : T : 9 A A @ < 9 Q A 8 ; C 9 5 = D E ; 9 F
8 F 8 B T 5 8 B > @ @ D 8 ? 9 A O @ O > ? @ ; 8 T ; >
B 8 ; 5 F = Q 8 B _
} x z } { y v z { | } x ~ v v {
S
@ F ; = @ D F 8 = D O @ F 5 8 : 8 D > = ; > @ Q 8 C F @ R
= B 8 B < ? 8 D
Tu TcI ; T 5 ? > ? 9 >
Ts Tu
Tc
V W X Y Z
S
? 8 B 8 ; = E D \ = 8 A B ; > F 8 D E > ? @ O > ? 8
> @ F ; = @ D 9 A F 8 = D O @ F 5 8 : 8 D > = ; D @ > >
@ 8 5 8 8 B H I H H H C ; = _
S
? 8 > @ F ; = @ D 9 A : @ : 8 D > ; > F 8 D E > ? @
O > ? 8 F 8 = D O @ F 5 8 : 8 D > = ; 5 @ : C T > 8 B Q
\
Ts =Attx1y1fy
s
V W X Z
< ? 8 F 8
t = [0.66+ 0.33 (yt/xt )] 1.50V W X Z
-
At
s
Tc
Al 2At(x1 + y1)
s
Al [400xs
fy
(Tu
Tu + Vu3Ct
)= 2At
](x1 + y1s
)
x1 + y1
ln/d <
Vu (Vc + Vs)
Vc
Vs
Vn = 8f cbwd
ln/d < 2
Vn =2
3
(10+ ln
d
)f cbwd
2 ln/d 5
ln
d
Vc = 2f cbwd
Vc =(3.5 2.5Mu
Vud
)(1.9f c + 2500w
Vud
Mu
)bwd 6
f cbwd
(3.5 2.5Mu
Vud
) 2.5
Mu Vu
-
! " # $ % & " ' ! ( ' $ ) * $ + ! , , - "
Vu Vc( . % ' '
Vs =Vu
Vc / 0 1 2 2 3
-
Vs =[Av
s
(1+ ln/d
12
)+ Avh
s2
(11 ln/d
12
)]fyd / 0 1 2 4 3
-
Av " ,
s ' " , ( * % ! " 5 $ # ' + ' ! % 6 ( ! " # $ % & " ' "
,
Avh " ,
s2 # ' $
' $ ! 7 $ " ' 6 ( ! " # $ % & " ' 8
9 : ; < < 8 = 8 > " , < < 8 = 8 < ? @ . !
& ! " ! & . & ! " # $ % & " ' ! " ) $ ' ' + ' ! % 6
" , $ ! 7 $ " ' 6 ( % ' ! $ " (
( # $ 6 6 $ - ( A
B
C + ' ! % 6 , ! % ' ! $ "
Av 0.0015bws / 0 1 4 D 3-
s {
d/5
18! " 8
}/ 0 1 4 E 3
B
) C $ ! 7 $ " ' 6 , ! % ' ! $ "
Avh 0.0025bws2 / 0 1 4 F 3-
s2 {
d/3
18! " 8
}/ 0 1 4 G 3
H I J I K L M N O P M N O O N Q R S T U M N P N V N W X O W T Q
Y T N Z [ W \ ] ^ W _ O ] P M N T ` P a b N O c ` T
9 ' 6 $ , ( " # ! 6 . d * ( ' ( ( , ) & ! ( . ( . 6 6 e + !
6 e % % f , " , ) + ( ( ! & ! 6 6 e ' $ "
$ , ! " e ! " # $ % , % $ " % ' ) & 8 g " e $ # ' @ . ' ! $
" ( , + 6 $ * , * + ! $ . ( 6 e # $ , ( ! 5 " $ # - )
! " # $ % & " ' # $ " $ " * ( ' ( ( , ) & ( % " 6 ( $ )
* * 6 ! , ' $ * ( ' ( ( , ) & ( 8
, ( ! 5 " ! ( ) ( , $ " ' ( & ) ( ! % @ . ' ! $ " ( ) # $
d
Vu (Vc + Vs)-
= ? 8 = h 8i
% ! ' ! % 6 ( % ' ! $ " # $ ( ! ( ' f " ' , ! ( ' " %
h j k# $ & ' # % $ # ' ( . * * $ ' 8 % ' ! $ " ( 6 $ % '
,
' , ! ( ' " % 6 ( ( ' "
h j k , ( ! 5 " , # $ ' ( % $ & * . ' , '
h j k8
l m n o p l q p n r s q m t p u v w x n x y z q m n { u r | p n
q n
i
( # $ % ( ! ( ' , ) e ' % $ " % ' # ' % % f ! " 5 ( $ % % . , !
( ' f " ( @ . 6 ' $ ' (
' ' % . ( , ' } ( ' , ! 5 $ " 6 % % f 8
i
- $ ' e * ( $ # , ! 5 $ " 6 % % f ( + ) " $ ) ( + , ! " ' ( ' (
$ #
* ( ' ( ( , % $ " % ' 8
< 8 ~ 6 . ( % % f ( d $ % % . ! " 5 ' " $ & ! " 6 (
Vcid ( ' ' ( " 6 e + ' ! % 6 . 6 % % f ( '
' ' " ( ! $ " # % $ # ' ) & d ' " ( * , , ! 5 $ " 6 6 e . *
- , ' $ - , ' % $ & * ( ( ! $ " # % 8
k
8 ) ( % % f ( d $ % % . ! " 5 ' " $ & ! " 6 (
Vcwd ( ' ' ! " ' - ) , . ' $ ! 5 , ! 5 $ " 6 ' " ( ! $ " d
' " ( * , , ! 5 $ " 6 6 e ) $ ' . * - , " , , $ - " - , 8
-
Vc =(0.6f c + 700
Vud
Mu
)bwd 2
f cbwd
Vc
Vci
Vcw
Vci = 0.6f cbwd + Vd +
ViMcr
Mmax 1.7
f cbwd
Mcr =(I
yt
)(6f c + fpc fd
)
Vcw =(3.5f c + 0.3fpc
)bwd + Vp
d
h
Av(min = 50bws
fy
Tu < (0.5f c
x2y)
Av(min = Apsfpus
80fyd
d
bw
h
Vs
f cbwd
ld
fy
fy
ldb =0.04Abfy
f c
! " # $ % % & &
-
' ( ) * ( + , - . / ) 0 1
ldb =0.085fy
f c
2 3 4 5 6 5 7
' ( ) * ( + , 8 . / ) 0 1
ldb =0.125fy
f c
2 3 4 5 6 9 7
: ; ( .
/ ?
< D
/ 0 >
; ( K >
;
=
( * K / I > ( ) 0 @
=
E /
=
*
< D
K ) ( G
M N O , P + P + P / *
D
, P + P + Q + , >
;
) ( J @
;
, P + P + Q + R 0
;
/
F F
* ( > .
< F
;
/ *
0.03dbfyf c
2 3 4 5 6 S 7
/ 0 @
=
E
< D
K ) ( G M N O , P + P + P / *
D
, P + P + Q
=
0 >
;
=
B
F
=
< D
. U K / I > ( ) 0 @
=
E
; ( ) 0
=
* M N O , P + P + Q + -
H
, P + P + Q + R
H
/ *
D
, P + P + R / )
=
( * /
F
+
C
; < D < E < F
( B G
F
;
=
0 * ( > > ( .
< F
;
/ * , P
=
* I
; ( .
< F
;
/ * 8
=
* I
;
; ( K >
; ( ) 0 @
=
E
; < ;
( ( ?
=
0 * ( > > ( .
< F
;
/ * 8 . / )
D
=
/ G
? @ A : @ B
= > ? @ C
8 > ? @ ; ? < D : C = 9 : ; < E F : @ B ? F F
G H I
= > ? @
J
: K L @ < = M
H G G H N G H O G H P G H Q
? @ R F L = = ; ? < D : =
S ? = L M T U @ < L ; D : ; > ? @ L F =
V
L B ? < D W L K : K L @ < ? < X
S : @ < D @ Y : Y = L R B L
G H G Z Z G H G [ G G H G [ O G H G I I G H G Q Z G H G O Z G H
G Z Z
\
D = ] : @ < D @ Y : Y = L R B L T T T T T T T
^
: = D < D W L K : K L @ < ? < K D R = > ? @
G H G _ I G H G Z G G H G Z Q G H G [
M
G H G [ P G H G Q _ G H G _ I
S ? = L
_
T ` @ L L R B L R D = ] : @ < D @ Y : Y =
V
L B ? < D W L K : K L @ < ? < X
S : @ < D @ Y : Y = L R B L
G H G [
M
G H G [ O G H G I I G H G Q _ G H G Q N G H G O I G H G [
M
\
D = ] : @ < D @ Y : Y = L R B L
G H G _
M
G H G _ [ G H G _ P G H G Z
M
G H G Z I G H G [ _ G H G _
M
^
: = D < D W L K : K L @ < ? < K D R = > ? @
G H G Z
M
G H G Z Q G H G [
M
G H G [ P G H G I _ G H G Q [ G H G Z
M
S ? = L
Z
T a b : L R B L = R D = ] : @ < D @ Y : Y =
V
L B ? < D W L K : K L @ < ? < X
S : @ < D @ Y : Y = L R B L
G H G [ N G H G I P G H G Q [ G H G P
M
G H G P O G H G N G G H G [ N
\
D = ] : @ < D @ Y : Y = L R B L
G H G _ I G H G _ O G H G Z _ G H G Z Q G H G Z N G H G [ I G H
G _ I
^
: = D < D W L K : K L @ < ? < K D R = > ? @ X
G H G Z P G H G [ Z G H G [ O G H G I [ G H G I N G H G Q O G H
G Z P
S ? = L
[
T a 9 ; L L L R B L = R D = ] : @ < D @ Y : Y =
V
L B ? < D W L K : K L @ < ? < X
S : @ < D @ Y : Y = L R B L
G H G I O G H G Q Q G H G P [ G H G O _ G H G N G G H G N O G H
G I O
\
D = ] : @ < D @ Y : Y = L R B L
G H G _ N G H G Z Z G H G Z P G H G [
M
G H G [ I G H G [ N G H G _ N
^
: = D < D W L K : K L @ < ? < K D R = > ? @ X
G H G [ [ G H G I G G H G I Q G H G Q _ G H G Q O G H G P [ G H
G [ [
S ? = L
I
T c : Y ; L R B L = R D = ] : @ < D @ Y : Y =
V
L B ? < D W L K : K L @ < ? < X
S : @ < D @ Y : Y = L R B L T T T T T T T
\
D = ] : @ < D @ Y : Y = L R B L
G H G Z Z G H G Z O G H G [ Z G H G [ P G H G I Z G H G I I G H
G Z Z
^
: = D < D W L K : K L @ < ? < K D R = > ? @
G H G I G G H G I P G H G Q [ G H G P _ G H G O G G H G O Z G H
G I G
d
e
l1
l2
f g h h h i j k l k m n o p p q q k
-
r s t u v w x y z { | } ~ } } } } y r s } }
y
y
| } s y } y
} } } } } } } y
l2 y
l1 } }
} y } } } y } } } ~ }
} x y } } }
M } } } } }
M = } y wl2s } }
w } } }
ls } } }
l1
l2y }
} } } } } } } }
} } } y
s } }
y
y
} } } } } } }
} } } y r } } } } }
} x y
} } }
y } x y
} y s } x y
ln } } } } }
}
} } } } } } } } } } }
} } } } } y
r } } } } } }
h
h =ln
(0.8+ fy
200, 000
)
36+ 5[m 0.12
(1+ 1
)]
-
h =ln
(0.8+ fy
200, 000
)36+ 9
h =ln
(0.8+ fy
200, 000
)36
m
m <
m
! !
"
#
$
%
&
'
"
( ) * + , - . / 0 1 2 1 3 4 3 5 6 1 7 8 2 9 : : ; ? @ A B C @ D
: = 1 E 6 ; 4 E F 9 @ 3 :
G H I J K
L M N
I
L L O P M
I
N
H Q
N R S T
I J
L
fy U VH
M W
Q X
M
V
H
M W Y T M
I
N
H Q
N
R L
H a I K Z I [ I S \ L I K Z I [ I S \ L b R S T I J L
V
H
M W
Q X
M
K
N
Q
R R S T
I J
L
] ^
U
^ ^ ^
ln _ ` ` ln _ ` a ln_ ` a
a
^
U
^ ^ ^
ln _ `^
ln _ ` ` ln_ ` `
V
H
M W
K
N
Q
R R S T
I J
L
] ^
U
^ ^ ^
ln _ ` a ln _] ^
ln_] ^
a
^
U
^ ^ ^
ln _ ` ` ln _ ` a ln_ ` aa b Q N c S J X I L Q d N I H T d Q N e
I \ I T M f H I J K L M N I L L [ I M g I I T ] ^
U
^ ^ ^
S T
K
a
^
U
^ ^ ^
R L
H
\
H
T
H
\
X
\ M W
H
e h T
I
L L L W S
J J [ I Q [
M S
H
T
I K
[
f
J H
T
I
S N
H
T M
I
N R
Q J
S M
H Q
T i
b j J S [ L g H M W [ I S \ L [ I M g I I T e Q J X \ T L S J Q
T Z I P M I N H Q NI K Z I
L i k W
I
c S
J X I Q d
d Q
N M W
I I K Z I [ I
S \ L W S
J J
T
Q
M
[ I
J I
L L M W S T
^
i l i
b
N
Q
\ m n Y n
Q
\ \
H
M M
I I
` o
l i
o p p q
i r s t u v t w x y z v { | { } s t ~ {
{ w z ~ | { t w z ~ { v y z w ~ { { w v y z
{ w ~ y
| { t { v w v y | | { t { v
I
M N
Q H
M
U
Y i
V
H
M W R
I
N \
H
L L
H Q
T i
'
$ &
$
&
-
Mo
Mo =wul2l
2n
8
Mo Mo
Mo
t
l2/l1
!
! " " # $
# $ # $ # $ % &
# #
'
$ ( ) * + ,
* + , * * + , * * + , * * + -
% . #
/
( ) % . # * + -
* +
, * +
* +
* * +
! $ ( ) * * +
- * +
- * +
* * + -
% . #
0
1 2
'
2
3
+
4 4
+ 5 6 7 8 9 7 : ; < = 9 > ? > @ 6 7 A > B > : C D
E = A ? > 7 : E = A F > 9 < = : F A > C > G : 9
< = B B > : C G A H I J < K L M N O N P Q ? > R 7 D
> 9 P S T G : 9 J < K L M N ? O N P Q ? > R 7 D > 9 P S
T I U V W
'
+ "
+
X Y Z
[
\ Z
'
$ ( ) % . #
`2/`1* +
+ *
+ *
(1`2/`1) =* ,
,
,
(1`2/`1)
+ *
4
* ,
/
( ) % . #
(1`2/`1) =*
Bt =*
* *
* *
* *
Bt
+
,
,
,
(1`2/`1) 1.0 Bt =*
* *
* *
* *
Bt =
+
4
* ,
! $ ( ) % . #
(1`2/`1) = 0- * - * - *
(1`2/`1)
+ *
4
* ,
0
1 2
'
2
3
+
4 4
+ 5 6 7 8 9 7 : ; < = 9 > ? > @ 6 7 A > O
B > : C D E = A ? > 7 : E = A F > 9 < = : F A > C
> G : 9 < = B B > : C G A H I J < K L M N O N P
Q ? > R 7 D > 9 P S T G : 9 J < K L M N ? O N P Q ?
> R 7 D > 9 P S T I U V W
'
+
" +
] ^ _ _ _ ` a b c b d e f g g h h b
-
i j k j l m n o p q r s t u v w x r y t z t v { | }
~
~
~
~
~
~
(1 c2/l2)2
c2
l2 ~
-
1
b
-
! " # $ % & ' ( % ) * + , - , . - & ' ! / & % , 0 1
1 % , , ( 2 2 - - 3 4 5 ! 4 " " 6 !
Bu 7 8 9 7 : ; < = 9 > ? > @ A 7 B > C > : D
EF
= B ? > 7 :
F
= B G > 9 < = : G B > D > H : 9 < = C C > : D
H B I J K < L M N O P O Q R ? > S 7 E > 9 Q T U H : 9 K
< L M N O ? P O Q R ? > S 7 E > 9 Q T U J
V - 2 & % ( 2 W X ! Y ( 2 Z [ - & , ( ' ' ( % ) ! \
( ) ( ] ^ & - ! " ! $ Z - ' 2 ( _ _ ) - ' '
Kt% _ 2 Z - 2 % & ' ( % ) * + , - , . - & ( ' ` * + ` ^
+ * 2 - a . b 2 Z - _ % + + % c ( ) ] - d [ & - ' ' ( % ) #
Kt = 9EcsC
l2
(1 c2
l2
)3 e f g h h i jc Z - & -
Ecs( ' 2 Z - , % a ^ + ^ ' % _ - + * ' 2 ( ` ( 2 b % _ 2 Z - ' +
* . ` % ) ` & - 2 - * ) a 2 % & ' ( % ) * + ` % ) ' 2 * )
2
C, * b . - - k * + ^ * 2 - a . b
a ( k ( a ( ) ] 2 Z - ` & % ' ' l ' - ` 2 ( % ) ( ) 2 % ' -
[ * & * 2 - & - ` 2 * ) ] ^ + * & [ * & 2 ' * ) a `
* & & b ( ) ] % ^ 2 2 Z - _ % + + % c ( ) ] ' ^ , , * 2 ( %
) #
C =(
1 0.63xy
)x3y
3 e f g h h f j
c Z - & -
x* ) a
y* & - 2 Z - ' Z % & 2 - & * ) a + % ) ] - & a (
, - ) ' ( % ) W & - ' [ - ` 2 ( k - + b W % _ - * ` Z & - `
2 * ) ] ^ + * & [ * & 2 ! Y Z - & -
. - * , ' _ & * , - ( ) 2 % ` % + ^ , ) ' ( ) 2 Z - a (
& - ` 2 ( % ) % _ 2 Z - ' [ * ) W 2 Z - ( ) ` & - * ' - a 2
% & ' ( % ) * + ' 2 ( _ _ ) - ' '
Kta( ' % . 2 * ( ) - a
. b , ^ + 2 ( [ + b ( ) ] 2 Z - k * + ^ -
Kt% . 2 * ( ) - a _ & % , m ^ * 2 ( % ) ! 4 4 3 . b 2 Z -
& * 2 ( % % _ / * \ , % , - ) 2 ( ) - & 2 ( * % _ ' + *
.
c ( 2 Z ' ^ ` Z . - * , W 2 % / . \ , % , - ) 2 % _ ( ) - &
2 ( * % _ ' + * . c ( 2 Z % ^ 2 ' ^ ` Z . - * , ! n * & ( % ^ '
c * b ' Z * k - . - - )
' ^ ] ] - ' 2 - a _ % & ( ) ` % & [ % & * 2 ( ) ] 2
% & ' ( % ) * + , - , . - & ' ( ) 2 % * ` % , [ ^ 2 - &
, % a - + % _ * ) - m ^ ( k * + - ) 2 _ & * , - ! $ Z -
, % a - + ( , [ + ( - a . b 2 Z - 0 1 1 % a - ( ' % ) - 2 Z * 2
Z * ' 2 Z - ' + * . . - * , ` % ) ) - ` 2 - a 2 % 2 Z - 2 % & '
( % ) * + , - , . - & ' W
c Z ( ` Z * & - [ & % o - ` 2 - a % ^ 2 % _ 2 Z - [ + *
) - % _ 2 Z - ` % + ^ , ) ' ! p 2 Z - & ' Z * k - ' ^ ] ] - ' 2
- a 2 Z * 2 2 Z - 2 % & ' ( % ) * +
q r s s s t u v w v x y z { { | | v
-
} ~ } ~ ~ ~ ~ } ~ ~ ~ ~ ~ } ~
~ } } ~ } ~ ~ ~ ~ ~ ~ } } ~
~ } ~ ~ ~ ~ } ~
Kec ~ ~ } } ~ ~ ~
~
Kec } ~
Kec =Kct +Kcb
1+ Kct +KcbKta +Kta
~ ~
Kct
Kcb ~ ~ } ~ ~ ~ ~ }
4 e
~ ~ ~ ~ ~ ~ } ~ ~ } ~ } } } ~ ~
~ ~
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}
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~ ~ ~ ~ ~ ~ ~ } ~ ~ ~
-
! " # $ % & ' ( ) ( * + , - % . / (
0
0 1
2
3
4 5 6 7 8 9 8 : 8 ; < = 6 >
1
? @ A B
@ C B
@ D B @ B
3
E F G G G H I J K J L M N O O P P J
-
Q R S T S U V T W X U S S Y S U Z R U X [ U [ R \ ] ^ T _ \ ` ^
[ Y a b c R Y ^ X S R \ c R R c d U c [ e c X R c _ U ^ V S f ` ` U
R ] f c X [ c X R Y S f ` ` U R ] f g
c X [ ^ V \ Y X _ U h U X [ S T i i ^ ] R b ^ X [ Y R Y ^ X S j
\ U ] U R \ U f U Z Y S R k l ^ j U e U ] g V ^ ] ` T W R Y S R ^ ]
f c X [ ` T W R Y m c f V ] c ` U S
Y X j \ Y b \ R \ U ] U c ] U c W c ] _ U X T ` m U ] ^ V ` U `
m U ] S c X [ n ^ Y X R S g c X [ j \ Y b \ j Y W W g Y X _ U X U ]
c W g Y X e ^ W e U R ] c X S W c R Y ^ X
c S j U W W c S ] ^ R c R Y ^ X ^ V R \ U S U n ^ Y X R S g R \
U U V V ^ ] R ] U o T Y ] U [ R ^ S ^ W e U R \ U b ^ ] ] U S i ^ X
[ Y X _ W f W c ] _ U X T ` m U ] ^ V
S Y ` T W R c X U ^ T S U o T c R Y ^ X S Y S i ] ^ \ Y m Y R Y
e U k p R \ U ] ` U R \ ^ [ S ^ V c X c W f S Y S c ] U ` ^ ] U c R
R ] c b R Y e U k
q r s t u v w x y v z x { | v x r u
} \ U ` U R \ ^ [ ^ V ` ^ ` U X R [ Y S R ] Y m T R Y ^ X j c S
[ U e U W ^ i U [ R ^ S ^ W e U i ] ^ m W U ` S Y X V ] c ` U c X c
W f S Y S R \ c R
Y X e ^ W e U ` c X f T X d X ^ j X n ^ Y X R [ Y S i W c b U `
U X R S k } \ Y S ` U R \ ^ [ b c X m U ] U _ c ] [ U [ c S c X Y R
U ] c R Y e U S ^ W T R Y ^ X
^ V R \ U S W ^ i U h [ U ~ U b R Y ^ X U o T c R Y ^ X S k R c
] R Y X _ j Y R \ a Z U [ h U X [ ` ^ ` U X R S V ^ ] U c b \ ` U `
m U ] g R \ U S U c ] U
` ^ [ Y a U [ Y X c S U ] Y U S ^ V b f b W U S g U c b \ b ^ X
e U ] _ Y X _ ^ X R \ U i ] U b Y S U a X c W ] U S T W R g R ^ c b
b ^ T X R V ^ ] ] ^ R c R Y ^ X c X [
R ] c X S W c R Y ^ X ^ V R \ U n ^ Y X R S k } \ U ] U S T W R
Y X _ S U ] Y U S b c X m U R U ] ` Y X c R U [ j \ U X U e U ] ^ X
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U X R Y S U ] ^ c X [
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U W c S R Y b b T ] e U b c X m U W ^ b c R U [ c b b T ] c R U W f
g R \ U S R ] U S S ] U S T W R c X R S V ^ ]
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[ ^ X R \ U m c S Y S ^ V S R c R Y b U o T Y W Y m ] Y T ` c W ^ X
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Q M M F O N R K S M L T P Y H J R H M J N H V J T \ F M L X G W V X
M Y U O N H P Q M M F O N R
t O R L J H u Z v w x H z H ^ F H N P O N R L N P H J F G H F S
M K G M L T P U H X M N K F J L X F H P Z
G H N V X M T L Y N Q M M F O N R X V N N M F
I J M a H X F O N M N H P O J H X F O M N W I H J G V I K U H X
V L K H M Q F G H I J M ^ O Y O F \ M Q V I J M I H J F \ T O N H W
F G H Q M M F O N R Y V \ U H
G H T I H P M L F U \ V N V P a V X H N F Q M M F O N R S O F G
Y M J H K I V X H H O F G H J V X M Y U O N H P Q M M F O N R M J V
K F J V I x X V N F O T H ` H J z
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t O R L J H u Z v w x Q z Y V \ U H L K H P L N P H J F G H F S
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t M J K F J L X F L J H K S O F G G H V ` \ T M V P K J H T V F
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f cbod ^ _ ` a b c d
7 6 ) - )
c. & 3 6 ) - , 3 . 5 5 4 ? 5 / 0 & . * ) 3 5 & 6 5 -
3 & . * ) 5 4 - ) 2 3 , / 0 ' ? , - , - ) , 9
bo. & 3 6 ) 1 ) - . ( ) 3 ) - 5 4 3 6 ) 2 - . 3 . 2 , ?
& ) 2 3 . 5 / 3 , @ ) / , 3
d eB 4 - 5 ( 3 6 ) ? 5 , * ) * , - ) , ; 2 5 ? ' ( / & ) 2 3
. 5 / < 9 , / *
d. & 3 6 ) ) 4 4 ) 2 3 . D ) * ) 1 3 6 5 4 4 5 5 3 . / 0
!
= 6 . & & 6 ) , - . & , ( ) , & ' - ) 5 4 3 6 )
* . , 0 5 / , ? 3 ) / & . 5 / 2 , ' & ) * + > 3 6 ) ) 4
4 ) 2 3 5 4 3 6 ) 2 5 ? ' ( / ? 5 , * 5 / 3 6 ) 4 5 5 3 . / 0 !
/ 2 ? . / ) * 2 - , 2 @ & ( , > 5 2 2 ' - . / 3 6 ) 4 5 5
3 . / 0 , 3 , * . & 3 , / 2 )
d/24 - 5 ( 3 6 ) 4 , 2 ) 5 4 3 6 ) 2 5 ? ' ( / 5 / , ? ? & .
* ) & !
= 6 ) 4 5 5 3 . / 0 7 . ? ? 4 , . ? , & 3 6 ) 2 5 ? ' ( / 3
- . ) & 3 5 1 ' / 2 6 5 ' 3 1
