Post on 23-Nov-2015
description
C
.
:
, 2013
2013/80
C
1
,
.
,
,
.
,
.
C
2
C
3
.............................................................7
1.1 ....................................................................................................................................... 7
1.2 ..................................................... 8
1.3 ...................................................................................................................... 10
1.4 .................................................................................................................. 12
1.5 ................................................................................... 14
1.6 .............................................. 14
1.7 .................................................................................................................................. 15
................................................................. 18
2.1 .......................................................................................................................... 18
2.2 ........................................................... 19
2.3 .................................................................................................. 20
2.4 ............................................................................................. 21
2.5 .......................................................................................................... 23
2.6 ................................................................................................ 25
............................................................................ 26
3.1 ................................................................................................................................................ 26
3.2 ................................................................................... 26
3.3 ...................................................................................... 28
3.4 ................................................................................................... 31
3.5 ........................................................................................ 32
3.5.1 ................................................................................................................................. 32
3.5.2 ........................................................................................... 32
3.5.3 ................................................................................................ 35
3.5.3.1 ...................................................................................................................................... 35
3.5.3.2 ................................................................................................................. 39
3.6 ........................................................................................ 42
3.6.1 ........................ 42
3.6.2 .......... 44
.............................................................. 45
4.1 ......................................................................................... 45
C
4
4.2 ............................................................................ 47
4.2.1 C ....................................................................................................... 47
4.2.2 C .......................................................... 51
........................................................................................................... 57
5.1 ......................................................................................... 57
5.2 ......................................................................................................... 57
5.3 C3. ......... 58
. 59
6.1 ................................................................................................................................................ 59
6.2 ........................................................................................................................ 59
6.3 FEMAP v10. ......................................... 60
6.3.1 (modeling) .................................................................................... 60
6.3.2 ....................................................................................................................... 63
6.3.2.1 ................................................................................ 65
6.3.3 ( property ) .................................................................................... 65
6.3.4 (mesh generation) ........................................................................................ 67
6.3.5 .................................................................................................... 71
6.3.6 ( loads ).............................................................................................................. 74
6.3.7 ( nalyze ) .......................................................................................... 77
6.4 FEMAP v10 ................................................................ 81
................................................................................. 83
7.1 ............................................................................................................................................ 83
7.2 C ........................................................................................................ 83
7.3 C ............................................................ 87
7.4 C C
........................................................................................................................................... 91
7.5 ........................................................................................................ 93
7.6 ................................................................................... 95
7.7
. .................................................................................................................... 99
................................................................................................................... 101
............................................................................................................................... 102
C
5
2013/80 .. ( : .)
,
C .
C
, . ,
,
.
, .
28 , C ,
, ,
.
,
, ,
.
.
,
,
3 V 1993-1-3.
3.
.
FEMAP v10,
.
, ,
.
.
C
6
National Technical University of Athens
Faculty of Civil Engineering
Institute of Steel Structures
Diploma Thesis
2013/80
Bending of thin-walled beams C and Z section with web perforation
Oikonomou D.E. ( supervised by Raftoyiannis I.)
Abstract
The present study is a preliminary research concerning the detrimental effects of a web
whole, to the load-carrying capacity of lightweight cold-formed steel C and Z section under
bending.
Lightweight steel C and Z-sections are extensively used in constructing light industrial
steel buildings. However, local instabilities as distortional and local buckling can significantly
influence the load carrying capacity of such members, especially in areas of large deformations
and perforations. Due to the limited awareness of the static behavior of perforated cold-formed
steel sections, the research of this phenomenon is essential. In the present study, 28 models
were analyzed of C and Z shaped beams, both with and without stiffeners, with circular and
quadrangular web perforations of three sizes.
In the first part of this study there is a general presentation of cold-formed steel
elements, describing their features, the cold-forming techniques, the usual instabilities and
applications in the construction industry. In the second part the materials are presented.
Following the third part where the types of buckling of lightweight steel members are
presented, focusing on local instabilities based on ENV 1993.1.3.
In the fourth part we present the computation of the moment of one axis bending based
on ENV 1993.1.3. Afterwards we decide which static model will be used to convert the moment
to loads. In the sixth part there is a presentation of FEMAP v10, a finite element analysis
program that has been used for a nonlinear static analysis defining the maximum bending load
of the members.
Finally the results of the above methods are presented along with comparisons and
comments and some final conclusions.
C
7
1
1.1
C Z
.
, ,
.
.
C Z,
, .
.
.
.
.
3, 1993-1-3 ,
,
.
1.1 : C Z
C
8
1.2
.
, ,
,
, .
1.2:
,
. ,
(,
), .
,
(
, , ).
.
, , ,
.
. , .
C
9
,
.
1.3 : Zayed National Museum
1.4 :
C
10
1.3
.
:
1. , ,
2. .
1.5.
,
. (
),
. 50 300mm
1 8mm.
1.5:
C
11
1.6.
.
40 200mm 0,5 2mm.
.
1.6:
,
.
.
1.7 :
1.8 :
C
12
1.4
:
1.
2.
3.
( 6 ).
.
90.
( 1.9) .
.
1.9 : ( folding )
,
.
.
( 90 )
( 1.10).
14 . (extruders)
. ,
, .
C
13
, ,
.
.
1.10 : (press banking)
1.11 : (cold rolling)
C
14
1.5
: 1) , 2)
3) . ,
.
,
.
:
1.
2.
3.
4.
, . . . . . , , , .
1.6
:
,
.
C
15
, .
, , .
.
.
.
1.7 :
1.12 :
C
16
1.13 :
1.14 :
C
17
1.15 :
1.16 :
C
18
2
2.1
.
.
.
2.1 :
fyb(N/mm2) fu(N/mm
2)
. 2:
EN 10025: Part 2 S 235
S 275
S 355
235
275
355
360
430
510
.
3:
/
,
EN 10025: Part 3 S 275 N
S 355 N
S 420 N
S 460 N
S 275 NL
S 355 NL
S 420 NL
S 460 NL
275
355
420
460
275
355
420
460
370
470
520
550
370
470
520
550
C
19
2.1 :
.
4:
,
EN 10025: Part 4 S 275 M
S 355 M
S 420 M
S 460 M
S 275 ML
S 355 ML
S 420 ML
S 460 ML
275
355
420
460
275
355
420
460
360
450
500
530
360
450
500
530
2.2
. , ,
,
.
fya, :
fya = fyb + (fu fyb) 2
g
k n t
A
fya 2
u ybf f
( 2.1)
:
g k k = 7 k = 5 n 90 ri 5t ( 90 n) t
C
20
eff g eff fyb. fya :
i) ii)
iii) , 580C .
2.3
. , b , h r ( ) :
2.1 : , bd , . t .
C
21
2.4 . , . : r 5t r 0.10bp . . r , :
Ag Ag,sh (1 - ) (2.2) Ig Ig,sh (1 2) (2.2)
Iw Iw,sh (1 4) (2.2) :
m
1i
ip,
jn
1j
j
b
90r
43,0
: Ag Ag,sh Ag bp,i i Ig Ig,sh Ig Iw Iw,sh Iw
m n rj j
C
22
2.2 : (2.2) eff , Iy,eff , Iz,eff Iw,eff . , r > 0,04tE/fy .
X
P2
2
rt
bpgr
() X P
2/m trr
)
2sin()
2tan(mr
rg
2.3 : bp ,
C
23
cbp,c
bb
p
cbp,c
bp,d
d
b
bp
() bp
hhwb
p = s
w
sw
() bp (bp = sw)
bp
bp
() bp
bp
bp
() bp
2.3 : bp ,
2.5
,
.
.
.
C
24
2.2: -
b / t 50
b / t 60
c / t 50
b / t 90
c / t 60
d / t 50
b / t 500
45 90
h / t 500 sin
, :
0,2 c / b 0,6
0,1 d / b 0,3
C
25
b , c d 2.2. c/b < 0,2
d/b
C
26
3
3.1
. , , . , , . , . .
3.2
, . , ( thin walled beams) . , . . . . , , . , . , :
C
27
( Local buckling ) ( ). , , . , . ( Distorsional buckling ) , .
,
. ,
.
, , .
.
. ,
.
3.1 :
3.2 : ) ) , )
C
28
, . , , , . . .
3.3
.
( 3.3). ,
x. ,
.
3.3 :
C
29
:
= 1
1 cosn y n y
l ln n
n
n y n yA e B e
l l
(3.1)
n n
. :
2
2x y
, 2
2y x
, 2
xyx y
(3.2)
:
2
2 2 2
1
0 0
2 2 2(1 )2
l
y y y
hdxdy
E
(3.3)
(3.1) (3.2) :
2 23 3
1 21
22 2
nn n n n
n
B A B Anh
l E G G
(3.4)
:
1 2
2cos cos ...o
x xM M M M
l l
(3.5)
= w + Mf
(w) (Mf). Mf = e :
0
2 0N h dy
(3.6)
0
2w xM h e dy M
:
2 2 22
2
0 02 2
l l
wM dxN dx
AE EI (3.7)
C
30
:
1 2 (3.8)
:
0n n
n n.
2 ,
x f.
2 , . c c ,
l, :
wl c
M e
I
, 2 0l ch A
2
42
(3 2 )
l
(3.9)
.
.
.
,
,
beffb .
Von Karman :
cr
y
beff
bp f
(3.10)
Winter :
1 0,22cr cr
y y
beff
bp f f
(3.11)
cr .
C
31
,
.
.
,
,
. ,
,
.
.
. ,
, .
,
:
eff y
M
W fR
, Weff
, 2
1
,
, .
3.4
,
.
.
.
3.4 : ) ) )
C
32
3.5
3.5.1
1993-1-3
, :
.
, .
,
.
,
.
com,Ed,ser
, .
.
3.5.2
:
2
212 1cr
p
t EK
b
: bp t Poisson K , 3.1 3.2
y
p
cr
f
:
C
33
0,673p 1 0,22
1p p
0,673p =1
3.1 :
C
34
3.2 :
max , ,
:
C
35
max1
yf
, 3.1 3.2.
max1
yf
, max p
:
max,max
1
p pyf
. ,
:
p
yf
,
.
:
1. 1 2,
.
2. = 2/1 3.1 3.2 .
3. p
4. , p
5. beff.
6. beff bp.
7. M beff , p t ,
, 5.5.2 EC.3.1.1.
3.5.3
3.5.3.1
,
. .
C
36
, ,
.
3.5 :
.
1993-1-3,
,
, .
,
, .
.
C
37
) C
3.6 :
, ,
. ,
.
,
u :
u
K
,
.
C, C1, C2
,
.
:
C
38
233
12 1
3
p
p
ubb
t
p
ub
C
C
3.6(). 1
1 : 3
1 2 2 3
1 1 1 2
1
4(1 ) 0,5w w f
t
b h b bb h k
:
b1 -
1
( be2 ),
b2 2 ( ).
hw
kf = 0 2 (.. y-y)
2
1
f
Aeffk
Aeff 2 .
eff1 eff2 1 2
.
,
.
d
d :
d = 1,0 0,65d
d = 1,47-0,723 d 0,65 1,38d
d = 0,66
d 1,38d
:
,
yb
d
cr s
f
( cr,s )
C
39
3.5.3.2
( ). , . bp. : 1. 45 135. 2. c : c > 0,2bp 3. bp/t 60 bp/t 90 . , . : .
3.7 :
1. . , n nn-1 (n< n-1), n-1 (n-1) . : i) , com,Ed
=0
yf
. , bp 3.7
C
40
3.5.2 be1 be2. ceff deff : ) : ceff = bp,c
3.5.2
:
, 0,35p c
p
b
b , = 0,5
,0,35 0,6p c
p
b
b , = , 230,5 0,83 ( 0,35)p c
p
b
b
) :
Ceff = bp,c
3.5.2,
( 3.1).
,eff p dd b
3.5.2
. ( 3.2)
ii)
,
.
s :
2( )s e effA t b c (3.12)
2 1 2( )s e e e effA t b c c d (3.13)
,cr s
:
,2 S
cr s
S
KEI
A (3.14)
:
S
iii) 1
3.5.3.1 .
2 ,
com,Ed cr,s.
C
41
3.8 :
, :
C
42
S,red
:
0,
,
yb
s red d s
com Ed
f
A x A
com,Ed
.
s,red tred
s.
t.
3.6
3.6.1
c,Rd
( 3.9) :
el0
Wpl f
yb
Wel f
yb
0
Mc,R
Weff
fyb
3.9 :
effW
elW
M0ybeffRdc, /fWM (3.15)
C
43
effW
Wel
M0elelplelybRdc, /)/1(4)( WWWfM Wplfyb/0 (3.16)
el/
p )3(055,025,05,0el
.
p 673,0el .
d 65,0el .
3.9.
(3.16) :
a) .
b) , .
c) 60.
, :
M0yaelRdc, /fWM (3.17)
3.10 :
Weff , max,Ed
fyb / M0 ,
C
44
, . , .
= 2 / 1 , 3.10.
3.6.2
,
com,Ed = fyb / M0.
. , Wpp,eff
.
C
45
4
4.1
. C ,
, .
l= 1200mm. C
.
.
4.1 :
h (mm) b (mm) c (mm) r (mm) t (mm)
C 100 50 2 2
C 100 50 20 2 2
100 50 2 2
100 50 20 2 2
:
h,
b,
c,
r,
t,
C
46
) )
4.1 : C ) )
4.2 :
C
47
4.3 :
4.2
4.2.1 C
C
( 4.4) S355MC.
S355MC : fyb = 355 N/mm2 fu=430 N/mm2
4.4 : C
C
48
1. .
r=2mm , 5t=10mm r
C
49
2.
,
,
.
,
.
1 = 2 :
= 2/1 = 1
, = 0,43
p :
p = 549 355
1,052 1,052 1,616 0,6732 2,1 10 0,43
p ybb f
t E K
=0,22 1 0,22 1
(1 ) (1 ) 0,53461,616 1,616
p p
beff=bp=0,534549=26,19mm ( 4.6)
4.6 :
3.
,
z ( )
G , :
26,19 2 98 98 2 4942,55
(26,19 98 49) 2Gz
mm
4.
:
C
50
= 2
1
42,550,7674
98 42,55
, 0>>-1 2 27,81 6,92 9,78 7,81 6,92 ( 0,7674) 9,78 0,7674 18,88
:
5
49 3551,052 1,052 0,24 0,673
2 2,1 10 18,88
p yb
p
b f
t E K
= 1,00 ( )
:
9855,45
(1 ) 1 0,7674
p
eff c
hh h mm
1 0,4 22,18eff effh h mm
2 0,6 33,27eff effh h mm
5.
:
21 2 346,38eff eff p eff eff p cA b b h h h h t mm ( < g )
:
,
26,19 2 13,095 49 2 24,58,91
346,38G effY mm
,
26,19 2 98 22,18 2 86,91 33,27 2 59,185 42,55 2 21,28
346,38G effZ
= 42,55mm
:
, 12,25 8,91 3,34YN G G effe Y Y mm ( )
:
, 49 42,55 6,45ZN G G effe Z Y mm ( )
6.
:
, ,
yb
Y Rd eff com
fM W
, Weff=
eff
comz
:
, 1 43,55G effz z mm
100 43,55 56,45comz h z mm
:
C
51
IY,eff=3 3 3 3 32 22,18 2 33,27 2 42,55 49 2 26,19 2
12 12 12 12 12
2 2 226,19 2 98 42,55 49 2 42,55 22,18 2(86,91 42,55)
2
2 442,5522,18 2(86,91 42,55) 42,55 2 503.551,712
mm
Weff,com =3503.551,71 8.920,31
56,45
eff
com
Imm
z
MY,Rd = ,0
3.166.711,39yb
eff com
fW Nmm
=3.166,71kNmm
4.2.2 C
.
.
.
, .
, .
1. .
: r = 2mm , 5t = 10mm r
C
52
4.7 : C
:
22 ( ) 98 2 (48 19) 2 464g p p pA h b c t mm
2 (48 2 24) 2 (19 2 48)17,79
464Gy mm
3 3 32 22 98 48 2 2 192 2 2 (48 2 49 ) 2 (19 2 39,5 )
12 12 12yI
=738.786,67mm4
3 3 32 298 2 2 48 19 22 2 98 2 17,79 2 (48 2 (24 17,79) )
12 12 12zI
+
2 42 (19 2 (48 17,79) ) 175.750,81mm
2.
:
i)45135
= 90
ii)cp>0,2bp c = 20mm > 0,248 = 9,6mm
iii) 60pb
t
4824 60
2
C
53
. ,
, 4.8.
4.8 :
1 : .
) :
1=2 =2/1=1.
= 4
0
355yb
com
fMPa
5
48 3551,052 0,519 0,673
2 2,1 10 4p
= 1,00
beff = 48mm
beff1=beff2=0,548= 24mm
) :
ceff :
Ceff=cp
i) 0,35p
p
c
b =0,5
ii) 0,35 0,6p
p
c
b : 230,5 0,83 ( / 0,35)p pK c b
19
0,39648
p
p
c
b 0,35
C
54
5
19 3551,052 1,052 0,529 0,673
2 2,1 10 0,603
p yb
p
c f
t E K
= 1,00
Ceff=cp=19 mm
As = (beff2+ ceff)t = (24 + 19)2=86mm2
( beff,2 , ceff)
:
Z =24 2 1 19 2 10,5
5,2086
mm
- :
IS()=
3 32 224 2 2 1924 2 (4,20) 19 2 (1 9,5 5,20)
12 12
3.129,49mm4
2 : : 2 3
20,423 0,31 1,5 0,043
p yb ps
s p
h f bI
A b E t
= 0,5
3 : .
S,red ,
:
S,red= 1
,
yb
s
com Ed
f
A
, S,red As
com,Ed .
: s,red=0,586 = 43 mm2
, s,red
:
, 0,5 2 1,00s redreds
t At mm
A
: 2
, , 1 43 2 24 91eff s red effA t b mm
3. :
,
, ,
.
:
24 (2 98 1 98,5) 19 1 86 98 2 49 19 2 10
24 2 24 1 19 1 98 2 46 2 19 2GZ
=44,81mm
C
55
= 2
1
44,810,842
53,19
.
EC3 -1
C
56
Iy,eff=3 32 76,563 2 21,72
12 12
3 3 3 346 2 23 1 1 19 2 19
12 12 12 12
2 276,563 2 (44,43 38,28) 21,72 2(87,284 44,43) 2 223 1 (98,5 44,43) 19 2(44,43 10) 219 1 (88 44,43) 246 2 44,43
2 423 1 (98,5 44,43) 645.788,76mm
Weff,com=, 3645788,76 11.830,67
54,57
y eff
com
Imm
z
MY,Rd=Weff,com0
ybf
11830,67
355
1,00 =4.199.886,58 Nmm = 4.199,89kNmm
4.2 : EC3
EC3(kNmm)
C , Z 3.166,71
C , Z 4.199,89
C
57
5
5.1
(
).
,
Rd.
, ,
- . ,
, .
5.2
5.1.
5.1 :
.
C
58
5.3
C3.
.
1200l mm
h=100mm t=2mm. :
t