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8/12/2019 enisxisi
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1:
............................................................... 1
1.1 ........................................... 1
1.2 ................................................................ 2
1.2.1 ..................................................... 31.2.1.1 ..................5
1.2.1.2 ....5
1.2.1.3 ..........................6
1.2.1.4 .....................................7
1.2.2 ................................... 10
1.2.3 ................................................. 11
1.2.4 ......................... 11
2:
............................................................... 13
2.1 .................................. 13
2.2
...................................................................................... 14
2.3 ..................................................... 182.4 ..................................... 19
2.4.1 .............................................. 20
2.4.2 ............................................... 25
2.4.3 ................................................ 29
2.5 ........................................................ 30
2.6 ..... 30
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3: .......................33
3.1 : ........33
3.1.1
................................................33
3.1.2 .............................................................35
3.2 ...............36
3.3 ...................................38
3.3.1 ...............................38
3.3.1.1 ........39
3.3.1.2 ..............................................41
3.3.1.3 ............................43
3.3.2 .................................44
3.3.2.1 ........................45
3.3.2.2 ...................47
3.3.2.3 .........................47
3.4 .........................................49
3.4.1 ........49
3.4.2
.......................................................................51
3.4.3 .............51
3.5 ..............................................................55
3.5.1 ....................56
3.5.2 .........................................................58
3.5.3 ..................................................59
3.6 ...............................................61
4:
..........................64
4.1 : .................................64
4.2 ......................................................65
4.2.1 .....................66
4.2.2 ............................67
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4.3 ...................................................... 67
4.3.1 ................................................................ 68
4.3.2
................................................................ 70
4.3.2.1
........................................................ 71
4.3.2.2 .... 72
4.3.2.3 .... 75
4.3.2.4
................................................................ 76
4.3.2.5
......................................... 77
4.3.2.6 ................................ 80
4.3.2.7
......................................................... 81
4.4 ..................................... 82
4.4.1 ............................................... 82
4.4.2 ................................................ 85
4.4.2.1 ... 85
4.4.2.2 ............. 90
4.4.2.3 ......................... 92
4.5 ............................................ 94
4.5.1 ...................................................... 94
4.5.2 ...................................................... 95
4.5.2.1 ....95
4.5.2.2 .................... 98
4.6 .......... 98
4.6.1 .................................. 99
4.6.2 ................... 103
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4.6.3
........................................................................104
4.6.4 ...................................................................105
4.6.5 ....108
4.6.6 ..........110
4.7 ............112
4.7.1
...................................................................112
4.7.1.1 .........................113
4.7.1.2 ....................................................114
4.7.1.3 ......................................117
4.7.1.4 ......................................117
4.7.1.5
( ) .......................................................... 118
4.7.1.6
() .........................................................121
4.7.1.7 .....................126
5: , ..................133
5.1 : ,
.............................................................133
5.2 ...................................134
5.3 ............................................138
5.3.1 .................................................................138
5.3.2
........................................................143
5.3.3 ...............................................................144
5.3.3.1 ................................................144
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5.3.3.2
.......................................... 149
5.3.3.3
.............................. 150
5.3.3.4
......................... 152
5.3.4
...................................... 152
5.4 ............ 158
5.5 ............................................................... 159
6:
...................................................... 161
6.1 : ................. 161
6.2 ..................................................... 164
6.3 .......... 166
6.3.1 ........................................................................ 167
6.3.2 ............................................... 169
6.3.3 ............................................. 171
6.4 ...................................... 172
6.5 ...... 174
6.5.1 ......................................................... 174
6.5.2 ............................................. 175
6.5.3 ......... 176
6.5.4 .................................................... 177
6.5.5 ................................................... 178
6.5.6 ....................................................... 179
6.5.7 .......................................................................... 179
6.5.8 ........................... 180
6.5.9 ............................................................................ 180
6.5.10 .............................................................................. 181
6.6 .................................. 181
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6.6.1 ..................................181
6.6.2 ......................182
6.6.3
.............................184
6.7
..........................................................................184
6.7.1
...............................................................185
6.7.1.1 ............186
6.7.1.2 .........................................187
6.7.2 .........................................190
6.7.3
..............................................................194
6.7.4 ..............................................201
6.7.5
...............................................................................203
6.7.6
...............................................................................206
7: .........210
7.1 : .............................210
7.2 .................................211
7.3 .......................................212
7.3.1 ...........................212
7.3.2 ..............................215
7.3.3
...........................................217
7.4 ...............................219
7.5 .........223
7.5.1 ........................223
7.5.2 ..........................227
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7.6
..................................................................................... 235
8: ........................ 238
8.1 - .................. 238
8.2
........................................................................................ 239
8.3
......................................................................................... 242
8.3.1 .. 243
8.3.2 ..................... 247
8.3.3 ............. 252
8.3.3.1
........................................................... 252
8.3.3.2 ..... 254
8.3.4
................................................. 256
8.3.4.1 ..................... 256
8.3.4.2 ........................ 256
8.3.4.3 ........................................ 256
8.3.4.4 .......................................... 256
8.3.4.5 .................................. 257
8.3.5 ................................ 258
8.3.5.1 ............................................ 258
8.3.5.2 .......................... 261
8.4 ................................... 264
8.4.1 ............................................. 264
8.4.1.1 ................................... 265
8.4.1.2 .......................... 267
8.4.2 ...................................................... 268
8.4.2.1 .................................. 268
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8.4.2.2 ..........................270
8.5
....................................................................................271
8.6 ...................................................................274
9: ...................278
9.1 ........................................278
9.2 .......................................280
9.3 ....................................................280
9.3.1 ....................................................280
9.3.2 ....................................................280
9.4 ..................................................................281
9.5 ......................................................................................281
9.5.1 K................................284
9.5.2 .................................284
9.6 ................................................................286
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1
1.1
1970.
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8/12/2019 enisxisi
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,
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1.2
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8/12/2019 enisxisi
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,
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1.2.1
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8/12/2019 enisxisi
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: ()
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(s)
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1.1.: .
8/12/2019 enisxisi
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. .
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8/12/2019 enisxisi
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,
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1.2.:
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1.2.1.3
8/12/2019 enisxisi
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,
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: () , () , ()
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( 1.3),
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,
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pilotis.
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1.2.1.4
.
: () ()
8/12/2019 enisxisi
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/
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1.3.:
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/
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8/12/2019 enisxisi
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10
1.2.2
,
:
1. ,
.
,
.
2. ,
, .
3. ,
.
,
.
.
. ,
1980
.
,
.
o
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.
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11
1.2.3
,
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.
,
,
.
,
,
.
1.2.4
.
:
.
, , ,
, ,
.
,
.
,
,
.
1. Nuti, C., Vanzi, I. (2003), To retrofit or not to retrofit, Engineering
Structures, 25, 6, pp. 701-711.
2. Foo, S., Davenport, A. (2003), Seismic hazard mitigation for buildings,Natural Hazards, 28, 2-3, pp. 517-535.
8/12/2019 enisxisi
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12
3. Martinez-Rodrigo, M., Romero, M.L. (2003), An optimum retrofit
strategy for moment resisting frames with nonlinear viscous dampers for
seismic applications,Engineering Structures, 25, 7, pp. 913-925.
4. Bruneau, M., Bhagwagar, T. (2002), Seismic retrofit of flexible steelframes using thin infill panels,Engineering Structures, 24, 4, pp. 443-453.
5. Wasti, S.T., Sucuoglu, H., Utku, M. (2001), Structural rehabilitation of
damaged RC buildings after the 1 October 1995 Dinar Earthquake, Journal
of Earthquake Engineering, 5, 2, pp. 131-151.
6. Dolsek, M., Fajfar, P. (2001), Soft storey effects in uniformly infilled
reinforced concrete frames,Journal of Earthquake Engineering, 5, 1, pp. 1-
12.
7. Federal Emergency Management Agency (2000), FEMA 356:
Prestandard and Commentary for the Seismic Rehabilitation of Buildings,
Chapters 2 and 3, Washington D.C., November.8. Fukuyama, H., Sugano, S. (2000), Japanese seismic rehabilitation of
concrete buildings after the Hyogoken-Nanbu Earthquake, Cement and
Concrete Composites, 22, 1, pp. 59-79.
9. Kappos, A.J., Stylianidis, K.C., Pitilakis, K. (1998), Development of
seismic risk scenarios based on a hybrid method of vulnerability assessment,
Natural Hazards, 17, 2, pp. 177-192.
10. Ziyaeifar, M., Noguchi, H. (1998), Partial mass isolation in tall
buildings,Earthquake Engineering and Structural Dynamics, 27, 1, pp. 49-
65.11. Penelis, G. and Kappos, A. (1997), Earthquake Resistant Concrete
Structures, E and FN Spon, London.
12. Bracci, J.M., Kunnath, S.K., Reinhorn, A.M. (1997), Seismic
performance and retrofit evaluation of reinforced concrete structures, ASCE
Journal of Structural Engineering, 123, 1, pp. 3-10.
13. American Technology Council (1996), ATC 40: Seismic Evaluation and
Retrofit of Concrete Buildings, Report No. SSC 96-01, Volume 1, Chapter 8,
November.
14. Hart, G.C. (1996), Design criteria for the seismic rehabilitation of
buildings, Structural Design of Tall Buildings, 5, 3, pp. 205-216.15. Priestley, M.J.N., Seible, F. (1995), Design of seismic retrofit measures
for concrete and masonry structures, Construction and Building Materials, 9,
6, pp. 365-377.
16. Pincheira, J.A., Jirsa, J.O. (1995), Seismic response of RC frames
retrofitted with steel braces or walls, ASCE Journal of Structural
Engineering, 121, 8, pp. 1225-1235.
8/12/2019 enisxisi
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2
2.1
. ,
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2.3
.
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2.2
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:
1. ( ):
(< 2 mm) (..
, , .)
(< 0.5 mm),
(
2.1). .
, ,
, ()
.
8/12/2019 enisxisi
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2.1.:
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2. ( ): ,
( 2.2).
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8/12/2019 enisxisi
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( 2.3). ,
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2.3.:
.
2.4
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2.5. 2.6 2.7
pilotis.
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2.4.:
.
2.5.: .
2.6.:
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8/12/2019 enisxisi
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2.7.:
pilotis.
2.3
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8/12/2019 enisxisi
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.
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30 mm.
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2.8.: . 2.9.:
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8/12/2019 enisxisi
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5 mm
.
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3. :
( 2.10).
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2.10.: .
,
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.
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4. :
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10%
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2.11.: .
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8/12/2019 enisxisi
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6. :
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8/12/2019 enisxisi
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1. :
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cm,
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8/12/2019 enisxisi
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8/12/2019 enisxisi
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8/12/2019 enisxisi
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8/12/2019 enisxisi
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2.5
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3.1 :
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10% 50
50% 50 . 475 , 72 .
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10% 50
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*4.2.3 2000.
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.
50% 10% 50 .
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. ,
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8/12/2019 enisxisi
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() .
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3.3
3.3.1
,
( 3.1).
3.1
, 3.1. ,
,
.
1 sec. ,
.
, FEMA 356,
,
3.1.: () . ()
() ()
zi
,
V
,
Fi
8/12/2019 enisxisi
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90% .
.
130%
.
,
,
33%.
3.1.1.
.
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.
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3.3.1.1
,
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8/12/2019 enisxisi
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.
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.
:
1.
Fi= [mizi/ mjzj] Vo (3.1)
mi i, zi
i Vo , ,
3.3.1.2 ,
( 3.2).
75%
.
2.
Fi= [mi i1/ mj j1] Vo (3.2)
i1
i. ,
* FEMA 356
8/12/2019 enisxisi
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41
75%
.
3.
,
.
90%
.
1
sec,
.
:
1.
,
.
2.
.
.
.
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3.3.1.2
,
.
8/12/2019 enisxisi
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100% ( 1 3.2).
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8/12/2019 enisxisi
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.
K
1
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3.2.: .
3.3.1.3
,
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. 3.3
.
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3.3.
.
20%,
.
8/12/2019 enisxisi
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3.3.: ()
. ()
.
3.3.2
.
,
,
.
()
()
8/12/2019 enisxisi
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45
:
(capacity spectrum method).
(displacement coefficient
method).
(equal displacement method).
3.3.2.1
,
.
S, Sv,
Sd .
S
S Sd,
S .
:
Sdi =
i2
2
4Si
g (3.3)
g .
,
. Voi
Si
Sdi
:
Si
= Voi/*1 (3.4)
Sdi =/ 1,1 (3.5)
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*1 1
, ,
,1
. 1
*1 :
1 = mj j1/ mj j2
1 (3.6)
*1 = [mj j1]
2/ mj j2
1 (3.7)
, ,
.
,
.
,
.
.
3.4,
.*
p
.
.**
*ATC 40 FEMA 356.**
50%
.
,
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47
3.4.: .
3.3.2.2
,
3.4,
.
t.
3.3.2.3
,
,
. ,
.
. , constant ductility spectra,
,
.
S
p
1
1 p
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. 3.5,
( 0-2-3 3.5) el
(0-1 3.5).
3.5.: .
(n> 1 sec),
. ,
0.5 sec,
.
,
.
, ,
.
3.4, t
( 3.6).
V
0
1
2
3
el
8/12/2019 enisxisi
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3.6.: .
3.4
3.4.1
Ke
Vy ,
, (
3.7).
Ke
Ke. 3.7
( )
.
,
.
Ke
60% Vy .
, ,
V
el
8/12/2019 enisxisi
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, ,
t.
3.7.: .
. () .
()
()
V
Vt
Vy
0.6 Vy
V
Vt
Vy
0.6 Vy
t
t
e
e
Ko
e
e
Ko
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Vy
.
3.4.2
. e
:
e= T0K
K
e
0 (3.8)
T0
, K0 Ke
.
3.4.3
,
:
t= C0 C1C2 C3 e
Te2
2
4g (3.9)
C0, C1, C2 C3 e
e
.
C0
.
:
,
.
C0.
,
.
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52
3.1.
3.1.: C01
2
1 1.00 1.00 1.00
2 1.20 1.15 1.20
3 1.20 1.20 1.30
5 1.30 1.20 1.40
10 1.30 1.20 1.50
1. .2. , , . .
3.1,
, ,
.
.
C1 ( )
.
:
C1= 1.0 e 2 C1= [1.0 + (R1) 2/ e] /R 0.1 < e < 2 (3.10)
C1= 1.5 e 0.1 sec
2
.*, R
:
* 2000 2 0.40 sec, 0.60 sec, 0.80 sec 1.20
sec , , , .
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53
R= CWV
gm
y
e (3.11)
Cm W .*,**
Cm
1.0
, 0.9
, 0.8
, 0.9
1.0
. *1 ,
(3.7).
1.0 sec, Cm 1.0.
C2
. C2
3.2.
3.2.: C23
e 0.1 sec e 2
11
22
11
22
1.0 1.0 1.0 1.0
1.3 1.0 1.1 1.0
1.5 1.0 1.2 1.0
1.
2. .
3. .
* 3.5.2 2000.
** , R
,
.
.
.
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54
,
,
. .
1
.
3.2, C2
.
, , .
, ,
. ..
,
C2 .
.
C3 ( ).
, C3 1.0.
,
C3 :
C3= 1 +T
e
(R 1)3/2 (3.12)
a ,
.
, C3
.*
< 0.1, C3 = 1.0.
0.1, C3
* (4.2) 2000.
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55
C3= 1 + 5 ( 0.1) / e (3.13)
.
1. , a,
.
2. e.
3. ,R,
.
4.
.5. .
6. .
,
.
(3.12) (3.13) .
*
t .
n
. n
.
3.5
,
20 m( 3.8).
W = 46882 kN
. :
.
2000
* 3.3.3[7] 2000.
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56
= 0.16g (
: ), = 1.00
n= 1.00, =
1.00 B. g= 9.800 m/sec2.
2.65m
2.65m
2.65m
2.65m
2.65m
4.10m
20.00m
2.65m
w = 6272 kN
w = 8140 kN
w = 6494 kN
w = 6494 kN
w = 6494 kN
w = 6494 kN
w = 6494 kN
3.8.: .
3.5.1
: , , .
0 = 0.88 sec. B
2= 0.60 sec. , 0= 0.88 sec > 2= 0.60
sec,
2000 e(0) = 0.273g.
,
8/12/2019 enisxisi
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57
, 3.3.
3.3
1.0.
1 *
1 (3.6) (3.7),
. 3.3
3.3.:
zi
(m)
zi(m)
wi(kN)
mi(kN sec
2/m)
1mi i1/
mj j1
Fi()
7 20.00 6272 640 1.000 0.211 2234
6 17.352.65 6494 662 0.938 0.205 2170
5 14.70 2.65 6494 662 0.839 0.184 1941
4 12.052.65 6494 662 0.703 0.154 1626
3 9.402.65 6494 662 0.535 0.117 1237
2 6.752.65 6494 662 0.351 0.077 812
1 4.102.65 8140 830 0.188 0.052 545
0 0.004.10 0.00 0.00 0.000 0.000 0
20.00 46882 4780 10565
1 = mj j1/ mj j2
1 = 3024.33 / 2316.21 = 1.31
*1 = [mj j1]
2/ mj j2
1 = 3024.332/ 2316.21 = 3948.94 kN sec2/m
:
Vo= *1 e (0) = (3948.94)(0.273g) = 10565 kN (3.14)
Fi 3
,
, (3.2).
*1 = 3948.94 kN sec2/m > 0.75x mi= 0.75x4780 = 3585.00 kN
sec2/m,
, (3.2).
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58
3.5.2
3.3.1.2. 3.9
.
,
.
( ), Vo= 10565 kN
Vo
= 9786 kN, 3.3.1.2. = 6.95 cm,
Vo= 10565 kN, = 6.38 cm Vo
= 9786 kN.
. ,
3.9,
1779 kN .
2.76 cm. ,
Vo = 11565 kN = 9.14 cm.
Vo = 12454 kN
= 12.95 cm.
890 kN Vo= 13344 kN
14.74 cm,
.
, , ,
.
2.65 m
5.1 cm,
0.02
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59
,
.*
0
4000
8000
12000
16000
0 5 10 15 20 25 30
, roof(cm)
,Vo(
kN)
3.9.: .
3.5.3
3.9,
Ke K0,
K0= A
AoV = 9786 / 6.38 = 1534 kN/m
T0 0.88 sec. ,
e (3.8)
e= T0K
K
e
0= 0.88
1534
1534= 0.88 sec
*ATC 40 FEMA 356.
9786
6.38
(cm)
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60
t
C0, C1, C2 C3:
1 = 1.31
71= 1.00 ( 3.3)
C0 = 1.31x1.00 = 1.31.
e = 0.88 sec > 2 = 0.60 sec, (3.10)
C1= 1.0.
1,
e> 2, 3.2 C2= 1.1.
C3 1.0.
e : e (e) = 0.273g
( 3.10), (3.9)
0.0
0.2
0.4
0.6
0.8
0 1 2 3
T (sec)
e(
g)
3.10.: .
B
e=
0.8
8sec
0.273g
0.545g
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t = C0 C1 C2 C3 e
Te2
2
4g = 1.31x1.0x1.1x1.0x0.273x
2
2
4
88.0x9.800
x100 = 7.56 cm
, =
0.24g, ,
, 10, : e (e) = 0.545g,
t = 15.12 cm,
.
3.6
.
:
,
20%
. ,
,
.*
.
,
, ,
, , .
,
,
,
.
* FEMA 356, ATC40 .
8/12/2019 enisxisi
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62
.
,
.
1. Lin, Y.Y., Chang, K.C., Wang, Y.L. (2004), Comparison ofdisplacement coefficient method and capacity spectrum method with
experimental results of RC columns,Earthquake Engineering and Structural
Dynamics, 33, 1, pp. 35-48.
2. Jan, T.S., Liu, M.W., Kao, Y.C. (2004), An upper-bound pushover
analysis procedure for estimating the seismic demands of high-rise
buildings,Engineering Structures, 26, 1, pp. 117-128.
3. (2002),
, -0, .
4. Chopra, A.K., Goel, R.K. (2002), A modal pushover analysis procedure
for estimating seismic demands for buildings, Earthquake Engineering andStructural Dynamics, 31, 3, pp. 561-582.
5. Elnashai, A.S. (2002), Do we really need inelastic dynamic analysis,
Journal of Earthquake Engineering, 6, pp. 123-130, Special Issue S1.
6. Panagiotakos, T.B., Fardis, M.N. (2001), A displacement-based seismic
design procedure for RC buildings and comparison with EC8, Earthquake
Engineering and Structural Dynamics, 30, 10, pp. 1439-1462.
7. Lu, Y., Hao, H., Carydis, P.G. (2001), Seismic performance of RC
frames designed for three different ductility levels, Engineering Structures,
23,5, pp. 537-547.8. Xue, Q. (2001), A direct displacement-based seismic design procedure
of inelastic structures,Engineering Structures, 23, 11, pp. 1453-1460.
9. Federal Emergency Management Agency (2000), FEMA 356:
Prestandard and Commentary for the Seismic Rehabilitation of Buildings,
Chapters 2 and 3, Washington D.C., November.
10. (2000),
2000, .
11. Ekwueme, C.G. (1999), Determination of displacement limits for the
seismic rehabilitation of concrete buildings, Structural Design of Tall
Buildings, 8, 2, pp. 79-115.
8/12/2019 enisxisi
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63
12. Whittaker, A., Constantinou, M., Tsopelas, P. (1998), Displacement
estimates for performance-based seismic design,ASCE Journal of Structural
Engineering, 124, 8, pp. 905-912.
13. Krawinkler, H. and Seneviratna, G.D.P.K. (1998), Pros and Cons of aPushover Analysis of Seismic Performance Evaluation, Engineering
Structures, 20, (4-6), pp. 452-464.
14. American Technology Council (1996), ATC 40: Seismic Evaluation and
Retrofit of Concrete Buildings, Report No. SSC 96-01, Volume 1, Chapter 8,
November.
15. Spyrakos, C.C. (1995), Finite Element Modeling in Engineering
Practice, Algor Publishing Division, Pittsburgh, PA.
8/12/2019 enisxisi
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4
4.1 :
.
,
* . ,
,
,
.
.
.
, ,
,
,
. ,
,
* 3 4 2000.
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65
. ,
.
,
.
,
.
.
. ,
(, , .) () .
.
. ,
.
4.2
2.2
.
-.
,
.
8/12/2019 enisxisi
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66
.
kk kr.
.
kk < kr,
.
,
.
,
.
.
, ..
,
. ,
,
.
.
4.2.1
kk= 1""
(4.1)
8/12/2019 enisxisi
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67
kk
,
.4.2.2
,
, ,
kr= 1
""
(4.2)
,
Sd krRd (4.3)
Sd Rd ,
, .
.
4.3
,
.
, , , .
,
.
,
.
8/12/2019 enisxisi
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68
4.3.1
. ,
.
,
( 4.1).
,
.
,
, .
4.1.: .
,
:
.
.
( 4.2).
.
,
,
. ,
8/12/2019 enisxisi
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69
.
( 4.3).
.
4.2.:
.
4.3.:
.
,
,
( 4.4).
,
, 4.4, .
,
.
4.4.: .
, .
8/12/2019 enisxisi
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70
,
.
,
, :
.
( 4.5)
.
.
( 4.5).
.
.
(prepacked concrete).
() ()
4.5.: . () .
() .
, ,
.
kk kr .
4.3.2
. ,
,
min 20 cm min 20 cm
min 30 cm min 30 cm
8/12/2019 enisxisi
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71
/
, 3.
,
.
4.3.2.1
o ,
.
7 - 10 cm.
, .
4.6.
.
4.6.:
.
,
. ,
. ,
,
.
. ,
.
.
8/12/2019 enisxisi
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72
.
,
.
, ,
,
.
,
, .
. ,
,
.
.
kk= 0.85 kr= 0.90. , ,
.
4.3.2.2
.
,
.
,
(
4.7). ,
,
.
8/12/2019 enisxisi
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73
,
.
,
.
.
.
.
,
.
,
. U
. 4.8,
,
. ,
4.7.: .
L/2 L/2
L
8/12/2019 enisxisi
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74
.
4.8. , U , .
.
.
4.8
.
,
.
() ()
4.8.: .
() . () .
.
,
,
,
U
U
8/12/2019 enisxisi
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75
.
.
4.3.2.3
,
, ,
,
.
.
,
.
.
.
.
.
,
( 4.9).
,
.
4.9.: .
8/12/2019 enisxisi
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76
.
,
. ,
.
4.3.2.4
,
.
4.10
.
.
4.10.: .
.
8/12/2019 enisxisi
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77
.
.
,
.
,
.
.
.
,
.
. ,
, ,
.
.
4.3.2.5
,
.
. ,
,
. ,
.
, .
,
8/12/2019 enisxisi
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78
,
.
:
.
.
,
.
.
.
.
.
, .
( 4.11).
.
( 4.12).
,
. ,
, .
.
8/12/2019 enisxisi
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79
.
.
4.11.:
.
4.12.:
.
.
.
.
,
.
,
.
, .
.
,
4 mm 2% .
.
8/12/2019 enisxisi
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80
.
.
:
lb = max (200 mm, 140 / bl, 200 tl) (4.4)
bl tl mm,.
,
.
4.3.2.6
.
.
..
,
( 4.13).
,
.
.
45 ( 4.14).
.
(> 0.5 mm),
.
,
.
4.15,
.
8/12/2019 enisxisi
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81
.
4.13.:
.
4.14.:
.
4.15.:
.
4.3.2.7
,
.
4.3.1,
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82
.
,
.
,
,
.
,
.
,
kk 0.75, kr 0.90 0.80
, .
4.4
,
,
. ,
,
,
.
,
,
,
.
4.4.1
.
() .
,
,
,
.
8/12/2019 enisxisi
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83
() .
,
:
. .
.
.
( 4.16). ,
.
,
(
).
4.16.: .
.
,
.
() .
,
,
:
~ 15 cm
min 8/7.5
8/12/2019 enisxisi
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84
.
30 cm( 4.17).
, .
. .
.
4.17.:
.
,
.
,
,
,
.
.
, ,
,
.
,
, 4.17.
min30cm
8/12/2019 enisxisi
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85
.
,
kk kr .
4.4.2
.
.
. .
.
.
4.4.2.1
, .
. ,
.
,
,
. 4.18
.
8/12/2019 enisxisi
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86
,
:
1. .
8 cm. .
4.18.:
.
2. .
10 cm. ,
. .
,
,
.
3. .
.
. 10-15 mm.
, ,
8/12/2019 enisxisi
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87
,
.
.4. .
.
.
4.19
, 4.19
.
/ (
). 4.19 4.19 .
,
,
. , , 6 mm, .
.
.
.
,
,
.
,
15 cm .
,
8/12/2019 enisxisi
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88
, 4.19.
,
,
4.20.
() ()
4.19.: .
() . ()
.
( 4.19),
, .
,
.
,
.
.. ( 4.21),
. 4.22 4.22
. ,
.
8/12/2019 enisxisi
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89
4.20.: .
4.21.:
.
. ,
, ,
kk= 0.70~1.00 kr= 0.80~1.00.
8/12/2019 enisxisi
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90
() ()
4.22.: . ()
. ()
.
,
,
,
.
.
kr = 0.70,
kk= 1.00. ,
5 cm , 8~12 cm 12 cm .
4.4.2.2
.
( 4.23),
,
.
.
8/12/2019 enisxisi
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91
. ,
200-400C, .
.
. (h/d3),
.
L50x5. T
,
25 60 mm.
15 cm.
4.23.:
.
, ,
1-2 mm, ( 4.24).
,
,
.
,
.
, .
8/12/2019 enisxisi
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92
,
,
. .
.
.
4.24.:
.
4.4.2.3
.
.
. ,
.
,
.
.
,
.
,
. ,
.
8/12/2019 enisxisi
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93
, ,
.
.
, .
,
. ,
,
.
, ,
. ,
.
,
4.25.
4.25.: .
, ,
.
,
,
.
8/12/2019 enisxisi
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94
4.5
. ,
,
.
4.5.1
,
.
.
,
.
.
, ,
. :
.
.
,
.
.
.
12 .
.
,
.
8/12/2019 enisxisi
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95
kk kr .
4.5.2
.
.
4.5.2.1
.
,
,
.
,
.
( 4.26)
.
,
4.26. 4.26
.
, kk= 0.70~1.00 kr= 0.80~1.00.
kk kr ,
.
8/12/2019 enisxisi
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8/12/2019 enisxisi
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97
.
. ,
,
.
:
VSd krVRd2,. (4.5)
VRd2,. .
*
VSd krVRd3,. (4.6)
VRd3,.= Vcd,.+ Vwd,.+ Vwd,. (4.7)
(4.7) Vcd,.
,** Vwd,. Vwd,.
, .***
, 5 cm. , 8 cm.
* (11.7) 2000.
** (11.1) 2000.***
Vwd,. Vwd,. (11.11) 2000.
8/12/2019 enisxisi
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98
.
. ( 4.26)
( 314/m2), ( 4.26).
4.5.2.2
,
.
.
.
,
.
,
30 cm , .
4.6
,
.
.
,
.
,
8/12/2019 enisxisi
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99
.
,
pilotis. , .
,
.
,
,
.
,
,
.
,
,
.
.
4.6.1
.
,
:
. .
( 4.27
4.28). ,
8/12/2019 enisxisi
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100
, .
, .
,
, . ,
,
10%.
() ()
4.27.: . () . () .
4.28.:
.
,
,
( 4.29
8/12/2019 enisxisi
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101
4.30).
( 4.29)
, , .
() ()
4.29.: . () . () .
. ,
, . ,
.
4.30.:
2004.
8/12/2019 enisxisi
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102
,
. 4.31,
V, , .
V , ,
.
() ()
4.31.: () V. () .
4.32.
2 ,
.
,
.
. ,
,
,
, .
8/12/2019 enisxisi
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103
,
.. ,
.
4.32.: .
4.6.2
:
.
.
. .
. 2mm
.
.
.
.
. ,
.
.
.
8/12/2019 enisxisi
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104
4.6.3
.
.
,
.
.
.
,
b t , ..
2000
. ,
.
.
.
,
, :
net/A 1.262fy/fu (4.8)
netA , , fy fu .
.
8/12/2019 enisxisi
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105
, .
,
20%. ,
.
.
,
.
,
,
.
4.6.4
,
.
,
.
. , V ,
, ,
.
, :
( ) 501NfA cry 50 .. = (4.9)
fy , , Ncr=
2 /l2 Euler
.
,
(.. ).
,
8/12/2019 enisxisi
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106
1.2,*
.
l
.
,
.
4.33,
.
,
100% 80% ,
. ,
, 100% 90%*.
,
,
, .
4.33.: .
:
: ,
,
* : .
8/12/2019 enisxisi
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107
. , :
( )
,
.
,
. 4.1
q
.
4.1.: q
V
()1 1
4 2 6 3
q 4.1 , :
,
.
,
,
.
25%.
,
8/12/2019 enisxisi
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108
: ()
,()
.
1.2. V ,
,
30%
.*
,
.
,
.
, 20%
. ,
,
, .*
4.6.5
,
.
,
.
c
= 2 pc / Vpc, pc Vpc
* : .
8/12/2019 enisxisi
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109
, .
:
c / Io 0.80: . 0.80 c / Io 1.30:
.
c / Io 1.30: .
. , c / Io 1.40 .
60 cm, .
,
( )
( ).
,
. q
4.2.
4.2.: q
()
1
5
7.5
, , , ,
.
.
8/12/2019 enisxisi
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110
.
,
, .
4.6.4.
,
.
0.12 rad 0.03 rad,
, .
4.6.6
7.5 m 5 m ,
, 4.34.
160
Fe 360 (S235). , , s
= 323 kN. H Ed= 287 kN
vd = 36 kN. :
.
3.5.
:
MO
ypd
fAN = =
11
523838
.
.. = 828.91 kN >s= 323 kN
8/12/2019 enisxisi
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111
4.34.:
.
,
cd= (1.20NpdNvd) /NEd= (1.20x828.91 36) / 287 = 3.34 < q= 3.5
: 4.1
q = 4. 4 > q 2, 1
2000, 38 22 .
160
() : b/t= 104/6 = 17.33 < 38 = 33() : b/t= 160/9 = 17.78 < 22 = 20
,
l= 55.722+ / 2 = 4.51 m
()
(
) Euler
7.5 m
5 m
HEA 160
8/12/2019 enisxisi
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112
cr= =
=451
1670210002
2
2
2
l
IE y1701.70 kN
(4.9)
( ) ( ) 50.1732.070.17015.238.38NfA 5.0cry5.0 ===
5.5.3 EC3, b, 5.5.2
0.765.
()
( ) Euler
cr= =
=451
616210002
2
2
2
l
IE z 627.69 kN
( ) ( ) 50.1205.169.6275.238.38NfA 5.0cry 5.0 ===
5.5.3 EC 3, c,
5.5.2
0.431.
(5.45) EC 3
1M
yAmin
bRd
fA
N = = 1.15.238.381431.0
= 357.26 kN >s= 323 kN
4.7
4.7.1
B
o C20/25, 10 cm
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114
d(T)= 0.24 g
+ 151
52
150
1401
.
.
.
.= 0.39 g
4.37.: .
422
316
8/30
4.38.: .
GK + 2QK , 2= 0.3 M= 66.15 Mgr.
50%
1/3 .
.
VO = d(T) M VO = 3.966.15 = 258 kN
4.7.1.2
10 cm 4.39
4.36.: .
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115
A
B B
A
J1 J2
J3
4.39.: .
: J1= 0.0171 m4, J2= 0.05 m
4, J3= 0.1067 m4
. : g= 36.75 kN/m
[M]173
281 370
281
84 [V]-76 76
251
-264
[N]-251 -264
-76 -76
370
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116
II. : q= 35 kN/m
[M]165
267 353
267
80 [V]-72 72
239
-251
[N]-239 -251
-72 -72
353
. : F= 258 kN(J3=J3/2 = 0.0534 m
4, )
[M] [V]92 166
[N]-43 -43
297 655
255
342
342
-43 -43
-166 -166
255
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117
:
. : k= 1, kr= 0.9. q =1.5, .
.
,
.
4.7.1.3
q= 1.5 , d 0.65
*
sd= max { }=+=+ 90432513026430 ./))(.)((k/)NN.N( rEqg = - 424.8 kN
vd =
==
51
200001600
8424
..
.
fA
N
cdc
sd 0.05 < 0.65
4.7.1.4
.
- vd
* : q = 1.5,
2000 2000,
.
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Nsd= (1.35Ng + 1.50Nq )/ kr= (1.35(-264)+1.5(-251))/0.9 = - 814.3 kN
vd =
==
51
200001600
3814
..
.fA
Ncdc
sd 0.10
-
: lo lc= 6.00 m
= lo/i = lo/ =
=
160
126016
3
.
/./
A
I20.78
-
max =
=
100
1525max
1525
.,,
d47.4
= 20.78 < 47.4,
.
4.7.1.5 ( )
:
- Sd = S(1,35G+ 1,50Q) / kr (1
)
- Sd = S(G+ 0,30Q ) / kr (2 3)
1
Msd= (1.35370+1.5353)/0.9 = 1143.3 kmNsd = (1.35(-264)+1.5(-251))/0.9 = - 814.3 kN
2Msd= (370+0.3353+342)/0.9 = 908.8 kNmNsd = ((-264)+0.3(-251)-43)/0.9 = - 424.8 kN
3Msd= (370+0.3353-342)/0.9 = 148.8 kNm
Nsd = ((-264)+0.3(-251)+43)/0.9 = -329.2 kN
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Ng= -(264+2560.61)/0.9 = -393.3 kN
1Msd= (1.3584+1.580)/0.9 = 259.3 kNmNsd = 1.35(-393.3)+1.5(-251)/0.9 = -949.3 kN
2Msd= (84+0.380+655)/0.9 = 847.8 kNmNsd = -393.3+(0.3(-251)-43)/0.9 = -524.7 kN
3
Msd= (84+0.380-655)/0.9 = -607.8 kNmNsd = -393.3+(0.3(-251)+43)/0.9 = -429.2 kN
+ 4.3
4.3.:
1 2 3 1 2 3
Msd 1143.3 908.8 148.8 259.3 847.8 -607.8Nsd -814.3 -424.8 -329.2 -949.3 -524.7 -429.2
cnom = 3 cm.
3 cm + + L/2 5 cm 8 18 ( 4.41).
- . C20/25, S500s d1/h = 5/100 = 0.05.
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1
=
===
=
===
1020
51
20000160
38143814
1430
5120000160
3114331143
22
.
..
.
bhf
N.N
.
..
.
fbh
M.M
cd
ddsd
cd
ddsd
tot= 0.24
2
====
05308424
11408908
..N
..M
dsd
dsd
tot= 0.20
3
====
04102329
01908148
..N
..M
dsd
dsd
tot= 0.05
1
==
==
11903949
03203259
..N
..M
dsd
dsd
tot 0
2
====
06607524
10608847
..N
..M
dsd
dsd
tot= 0.20
3
====
05402429
07608607
..N
..M
dsd
dsd
tot= 0.17
As,tot2m1644
51
20
151
500
60100240 c.
..
.f/f
bh
cdyd
tot =
==
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0.00860100 = 48cm2
2422 (=30.40 cm2) :
0.5(48-30.40) = 8.80 cm2/ : 418/ (=10.17 cm2)
4.7.1.6 ()
lcr =
==
==
cm60
cm12056005
cm100
max //H
h
120 cm
1Vsd= (1.35Vg + 1.50Vq ) / kr= (1.3576+1.572)/0.9 = 234 kN
2
Vsd= (Vg + 0.30Vq+ VE) / kr = (76+0.372+166)/0.9 = 293 kN3Vsd= (Vg + 0.30Vq- VE) / kr= (76+0.372-166)/0.9 = -76 kN
VRd2,red= 1.67 VRd2 (1 - cp,eff/fcd) VRd2
VRd2
422/
C16/20 10cm (C20/25, 418/, S500s) Rd= 1190 kNm,
.
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VRd2 d.bf wcd 902
1=
50060200
20700
200700 ...
f. ck ===
VRd2 ( ) kN20520501906051
2000060
2
1== ...
..
1
cp,eff
cp,eff( )
=
=
=
160
1511037255000003949 42
.
./..
A
/AfN
c
ssyksd
= -256.24 kPa
VRd2,red kN7034925120000
2425612052671 .
./
.. =
+=
VRd2,red VRd2, VRd2= 2052kN > Vsd= 234 kN.
2
cp,eff
cp,eff( )
=
=
=
160
1511037255000007524 42
.
./..
A
/AfN
c
ssyksd
= -963.91 kPa
VRd2,red kN5836745120000
9196312052671 .
./
.. =
+=
VRd2,red VRd2, VRd2= 2052kN > Vsd= 293 kN.
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3
cp,eff
cp,eff( )
=
=
=
160
1511037255000002429 42
.
./..
A
/AfN
c
ssyksd
= -1123.07 kPa
VRd2,red kN4837155120000
07112312052671 .
./
.. =
+=
VRd2,red VRd2, VRd2= 2052kN > V
sd= 76 kN
VRd3= Vcd+ Vwd
Nsd = -424.8 kN > 80051
200001601010 ==
...fA. cdc kN
Nsd = -329.2 kN> 800 kN
Nsd = -524.7 kN > 800 kNNsd = -429.2 kN > 800 kN
cdcsd fA.N 10> .
Vcd= 0.30VRd1*
VRd1
VRd1= ( ) dbk wcplRd 15.0402.1 ++
* 117.
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Rd = 0.26 MPa C20/25.
k= 1.6 - d= 1.6 - 0.95 = 0.65 < 1 k= 1
00409560
3725.
.
db
A
w
sll =
== 500.
ywdsw
wd fd.s
AV 90=
VRd3
= Vcd
+ Vwd
Vsd
= 293 kN
V
wd V
sd- V
cd= 293-74.54 =
218.46 kN
0590
151
50000095090
46218.
...
.
s
Asw =
cm
8 0170590
502
0590.
.
,
.
As sw =
= cm
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*
8337223131
mm8=
==
.// max,Lmm
smax 100
mm100
mm3006050
mm1441888
=
=
==
%min,L
mm
8/10.
8/7.5 (4.40).
uo
. asw
t
d
f
f. h
.ctk
ywd
sw
2
950
80
dh , fywd , fctk0.95
95% t . 8
578mm7676100
8
902151
50080
2
./...
.asw =
* q = 1.5 2000 18.4.4.1 .
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T 8/7.5 ()
. , .
4.40.: .
4.7.1.7 *
:
: C16/20, 822+616, S220, d1= 3 cm : C20/25, 818+814, S500s, d1= 5 cm : 8/7.5 S500s ( 2
):
(): sd 8424.= kN, Msd= 908.8 kNm(): sd 7524.= kN, Msd= 847.8 kNm
20, S500s. o c
c= min (7db,100 mm) = min (72.0=14.00 mm, 100 mm) = 10 cm
* 5.
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(
)
Vud kN4630151
500000
51
2000002001 22 .
...ffd ydcdbm ===
,
,
( 4.41).
,
*
(): Fcn= - 680 kN
Fs2n = - 195.52 k
(): Fs1n = 365.87 kN
Fcn, Fs1
n, Fs2n ,
, .
1.99,
1.07
+
-+
-1.2
2.47
() ()
1 1
1 1
4.41.: . ) .
) .
,
,
* 11
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F11 = Fcn+ Fs2
n= -680+(-195.52) = -875.52 kN
kN35526
151
500000101710
51
20000850060
151
50000010095
51
20000850040
52875
850850
4
4
1111
11
.F
..
...
..
...
.
fAf.fAf.FF
yd,Scd
yd,Scd
=+
+=
=++=
,
,
kN111831710
09587365
11
1 ..
..
A
AFF
,S
,Sn
s ===
Vsd= 183.11-(-526.35) = 709.46 k
n1 ===4630
46709
.
.
V
V
ud
EZ
sd 23.3 24
11
11 F11= -875.52k F11 = 365.87 kN.
11, ,
Vsd11= 365.87-(-875.52) = 1241.39 kN
11
.
(8, S500)
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Vuds kN874151
500000
51
2000000801 22 .
...ffd ydcdbm ===
10 cm 7.5 cm
nw 78157
102600=+
=
.
156
Vw= 1564.87 = 759.72
kN.
168154630
7275939124111
2 =
=
= ..
..
V
VVn
ud
wsd
11 n1 > n2. n = 24 . c = 10 cm
. s
s 225124
102600.=
= cm
27 20/22.5 ( 3 ).
( 5.4)
min = max(w,min, 0.12%)
cS AA= , w,min , As Ac .
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smax= min (6t., 80 cm)
C20/25, S500s w,min = 0.07%, min = 0.12%
%.bs
AA s
c
s 120=
.
smax= min (6t.,80 cm) = (610, 80) = 60 cm
s,11 6040120
14360min =
%.
., cm
1 1
. db=20 mm.
s1,1 73280120
14360min .
%.
., =
cm
1974181732
102600 =+ ..
n
s 232119
102600.=
= cm
o 21 20/30 ( 4 ).
,
d
)fAfA(.
Nv
cdccdc
sd
2211
d850 +
=
Ac1 , c2
, fcd1
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fcd2 .
1560
51
20000280
51
16000320850
3949.
..
...
.d =
+
= *
Nd= d(0.85fcd)Ac2 kN0449528051
200008501560 ..
... ==
VR = ntotVud= (221+227)30.46 = 2924.16 kN >Nd = 495.04 kN**
1. Ghobarah, A., Galal, K.E. (2004), Seismic rehabilitation of shortrectangular RC columns, Journal of Earthquake Engineering, 8, 1, pp. 45-68.2. Maheri, M.R., Kousari, R., Razazan, M. (2003), Pushover tests on steelX-braced and knee-braced RC frames, Engineering Structures, 25, 13, pp.1697-1705.3. Tremblay, R., Archambault, M.H., Filiatrault, A. (2003), Seismicresponse of concentrically braced steel frames made with rectangular hollowbracing members, ASCE Journal of Structural Engineering, 129, 12, pp.
1626-1636.4. Dogan, E., Krstulovic-Opara, N. (2003), Seismic retrofit with continuousslurry-infiltrated mat concrete jackets, ACI Structural Journal, 100, 6, pp.713-722.
*
, c=1.30.** 27 11( 4.41)
8/12/2019 enisxisi
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132
5. Tsonos, A.G. (2002), Seismic repair of reinforced concrete beam-column subassemblages of modern structures by epoxy injection technique,Structural Engineering and Mechanics,14, 5, pp. 543-563.
6. (2002), , -0, .7. Newman, A. (2001), Structural Renovation of Buildings: Methods,
Details, and Design Examples, McGraw-Hill, New York.8. (2001), ,
.
9. , .., , .., , .. (2001), , 2
, , . 71-79.10. , .., , .., , .. (2001), ,
2
, , . 81-90.11. Davaran, A. (2001), Effective length factor for discontinuous X-bracingsystems,ASCE Journal of Engineering Mechanics,127, 2, pp. 106-112.12. (2000), 2000, .
13. (2000), 2000, .14. Aboutaha, R.S., Engelhardt, M.D., Jirsa, J.O. (1999), Rehabilitation ofshear critical concrete columns by use of rectangular steel jackets, ACIStructural Journal,96, 1, pp. 68-78.15. CEN Technical Committee 250/SC8 (1996), Eurocode 8-Part 1.4.Design Provisions for Earthquake Resistance of Structures: Strengtheningand Repair of Buildings, prENV 1998-1-4, Brussels.16. Comit Eurointernational du Beton (1995), Fastenings for SeismicRetrofitting, State of Art Report on Design and Application, Tokyo.
17. Stoppenhagen, D.R., Jirsa, J.O., Wyllie, L.A. (1995), Seismic repair andstrengthening of a severely damaged concrete frame,ACI Structural Journal,92, 2, pp. 177-187.18. Carydis, P.G., Mouzakis, H.P., Taflambas, J.M. (1995), Shaking tabletests of composite steel-concrete, beam-column connections, Proceedings of10th European Conference on Earthquake Engineering, Vols 1-4, pp. 2435-2440.19. , .. (1991),
, , .
8/12/2019 enisxisi
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5
,
4.1.1 : ,
, , . , . , ,
. , , . .
. , . .
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134
.
( ) , . , ,
.
, l1 ( 5.1). . 5.1, l2, , .
l2, .
5.1.:
.
5.2
:
l1
l2
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, 135
.
.
, ( ) (). ( 5.2).
, , . ,
, , .
5.2.: .
. . , .
.
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136
, 250 C.
.
. :
1. . 2 ~ 6 mm
.2.
, . , ,
.3. . , , .
5.3 .
, , .
.
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, 137
.
5.3.: .
, ( 5.4), . , 5.5.* ,
.
5.4 .
* CEB.
db do= db+ (2 ~ 6) mm
lb 10db
5db
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5.5.: .
5.3
, .
5.3.1
, . 5.6, , .
min 100 mm
min 50 mm
min 100 mm
min 50 mm
min 100 mm
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, 139
. , :
1. : ( 5.7). . , VAud :
3=
fAV
ydsAud (5.1)
As fyd / 3 vonMises.
5.6.: .
2. : (5.7).
V
V
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VBud :
( ) ff..dV ydcdbmBud ][ 31-31+1= 22 (5.2):
f
f
d
e
yd
cd
b
3= (5.3)
db ,fcdfyd
, e . , m 1.30.
, , , m (5.2) .
o
, VBud
( ) ( )ff..dV ydcdbmBud
222 -131-31+1= ][ (5.4)
m = 1.30, = s / fyd s .
. m .
3. : ( 5.7). , , , .
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, 141
. : :
= 6db = 5db
: = 3db
. VCud
:
( ) cdlfdkV /pbb/
b cd
Cud
235121 1= [] (5.5)
db mm,fcd MPa,lb mm cp mm. k1 0.28 1/2 / mm. 1 2
:
( )c.t p /41= 321 1.0 (5.6)
( ) ][ c.cc,c.c..maxa pminnmaxnpminn 53+5170+30=2 1.0 (5.7)
t cn .
n s scr scr= 2 cp n= 2 scr= 3 cp n> 2, VC n,ud
VC n,ud = VCud (5.8)
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142
s < scr, VC n,ud n
VC n,ud = Vs
sn. Cud
cr
]1)-(
[ +1450 VCud (5.9)
, , VAud , V
Bud V
Cud .
, , . ,
. , , 7db 100 mm .
() () ()
5.7.: .
, , , . , , . , , .
V
VV
e
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, 143
5.3.2
, db= 16 mm,
t = 250 mm. S400 C16/20. lb= 200 mm. 5.8, Vsd e= 10 mm . cp = 200 mm, cn
max = 350 mm cnmin = 250 mm.
.
: H VAud
(5.1):
3=
fAV
ydsAud =
3
15.14001.2= 40.36 kN
5.8.: .
: VBud
(5.2) (5.3). m= 1.0. :
f
f
d
e
yd
cd
b
3= =15.1400
5.116
16
103 = 0.33
( ) ff..dV ydcdbmBud ][ 31-31+1=
22 =
t= 250 mm
cnmax = 350 mm cn
min = 250 mme= 10 mm
lb= 200 mm
cp= 200 mm
Vsd
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144
( )151
40
51
6133031-33031+16101=
22
..
....... ][ =
= 10.30 k : VCud
(5.5) 1 2 (5.6) (5.7), :
( )c.t p /41= 321 = ( )[ ]2004125032
. /
= 0.927 < 1.0
( ) ][ c.cc,c.c..maxa pminnmaxnpminn 53+5170+30=2 == ( ) ( ) ( ) ( )][ 20053250+3502005125070+30 .,...max =
= 0.857 < 1.0
( ) cdlfdkV /pbb/
b cd
Cud
235121 1= =
= ( ) 2001620051
161685709270280 23
51 //
.... =
= 13627 N = 13.63 kN
Vud :
Vud= min (VAud ,V
Bud ,V
Cud) =
= min (40.36 kN, 10.30 k, 13.63 kN) = 10.30 kN
, ( ). , ,
.5.3.3
5.3.3.1
() . , :
1. : ( 5.9).
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, 145
, , .
NRd,s :
fAN
s
yks
sRd =, (5.10)
As , fyk s
1.20. , As .
2. : ( 5.9) ( 5.9). NRd,c :
aa
lfkN yxc
N,ucr
/
ef,bckc,Rd
23
2= [] (5.11)
fck MPa lb,ef mm, . ucr,N
.
ucr,N = 1.0 . ucr,N = 1.4 . c :
c= 1 2 (5.12)
1 = 1.80 2
1.0, 1.2 1.4 ,
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146
, . k2 7.5 1/2/ mm1/2.
() ()
() ()
5.9.: .
. x y
(5.9) xy, . :
l.
c..
b
x
x51
70+30= 1.0 (5.13)
l.
c..
b
y
y51
70+30= 1.0 (5.14)
N N
NN
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, 147
cx cy xy, , lb
. , cx cy ccr= 1.5 lb, x y 1.0, . , .
nx ny
sx< 3 lb x sy< 3 lb y, :
Nl
sn
l
sn.N c,Rd
b
yy
b
xxnnc,Rdyx ]
1)-([]
1)-([
3+1
3+1450= (5.15)
N nn c,Rd yx nxnyNRd,c.3. :
( 5.9). NRd,b :
N
c
k
b,Rd =
(5.16)
k , , c , (5.12).
, , , ,.
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148
() . :
1. : V sRd,
3s
ykso
s,Rd
fAV = (5.17)
As fyk . ,
s : s = 1.20 fyk800 MPafyk/fuk0.80. s = 1.50 fyk> 800 MPafyk/fuk> 0.80.fuk .
2. B: . , , VRd,c
( )dl
dfckV nomf
.
c
V,ucrnomck
/
c,Rd
20123
3= [] (5.18)
fck
MPa, dnom mm, lf mm ( 8 dnom) c1 mm. k3 0.5
1/2/ mm. , ucr,V . ucr,V = 1.0. c (5.12).
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, 149
3. :
. VRd,cp :
NkV c,Rdcp,Rd 4= [] (5.19)
NRd,c (5.11) k4 : k4= 1.0 lb,ef< 60 mm. k
4= 2.0 lb,ef
60 mm.
VRd,s,VRd,c VRd,cp. , , . , , : := 0.80. := 0.70.
5.3.3.2
NSd VSd, :
V
V
N
N
M,Rd
Sd
M,Rd
Sd + 1.20 (5.20)
NRd,= max {NRd,s,NRd,c,NRd,b} VRd,= max {VRd,s,VRd,c,VRd,cp}. (5.20) NSdNRd, VSd VRd,. (5.20) :
( ) ( )VVNN m,RdSda
m,RdSda+ 1.00 (5.21)
NRd,m = min {NRd,s,NRd,c, NRd,b} VRd,m = min {VRd,s, VRd,c, VRd,cp}.: = 2.0 (NRd,m=NRd,s VRd,m= VRd,s). = 1.5 (NRd,m=NRd,cNRd,b VRd,m= VRd,c
VRd,cp).
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5.10, NSd/NRd VSd/VRd (5.20) (5.21), = 2.0.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.20 0.40 0.60 0.80 1.00 1.20
NSd/NRd
VSd/VRd
(20)
(21), = 1.5
(21), = 2.0
5.10.:
.
5.3.3.3
(
) . .
, .
() . :
1. : .
,
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. Nyd :
Nyd=Asfyd (5.22)
As fyd .
2. : .
bd (5.23)
dlf
Nb
bbbkbd = (5.23)
fbk , , lb , db b . b
1.50.
, , 8 MPa., 20 MPa, fbk 12 MPa.
(5.22) (5.23) , ,
. , , .
3. : . , Ncd
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dflkN
c
ockb
cd
5= [] (5.24)
fck MPa, lb mm,d mm c , 1.50. k5 4.5 1/2/ mm1/2.
() . ,
VRd 5.3.1, .
5.3.3.4
NSd VSd,
(5.21), NRd VRd ,
5.3.3.3 5.3.1, . ,
: = 2.0 . = 1.5 .
5.3.4
: ) ) .
1
: . 5.11 d= 16 mm, dnom= 20 mm, lb,ef=113 mm,
fyk = 640 MPa. C20/25 lb = 120 mm. NRk 40.95 . 11, xy cx=
250 mm cy = 300 mm, ,
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x. As= 1.57 cm
2.
() ()
5.11.:() .
() .
1.
: NRd,s (5.10)
fAN
s
yks
sRd =, =20.1
6401.2= 107.20 kN
: NRd,c (5.11).
ucr,N = 1.0. , (5.12) , c: c= 1 2 = 1.80x1.20 = 2.16. cx= 250 mm cy= 300 mm ccr=1.5lb= 1.5x120 = 180 mm, x y . (5.11)
d= 16 mm
lb,ef= 113 mm lb= 120 mm
Nsd
cy = 300 mm
Vsd
cx= 250 mm
dnom= 20 mm
x
y
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aa
lfkN yx
c
N,ucr/ef,bck
c,Rd
232
= =
=16.2
0.1113205.72/3
1.0 1.0 =
= 18653 = 18.65 k : (5.16),
NRd,b NRk c, (5.12)
NRd,b=NRk/ c= 40.95/2.16 = 18.96 k
, NRd
NRd= min (NRd,s,NRd,c,NRd,b) =
= min (107.20 kN, 18.65 k, 18.96 k) = 18.65 kN
.
2. : H
V sRd, (5.17). fyk= 640 MPa 800 MPa
fyk/fuk = 640 / 800 = 0.80 0.80 s = 1.