VE - velika ekscentrienost

-tf tI r--+E

MuE: Mu

'7ut

'7u;

Nu'Zr

kn=#;.Enojna a rmatu ra:

Ae = r".-u-u?,- + +i.Ekscentridni nategEkscentridni tlakCisti upogib

N>0N <0N=0

Pravokotni prerez enojna armatura Tabela 2

ts tx" l 1.00 1 "25 1.50-tr [?- ]

1 .7 5 2.00 2 .25 2.50 2.75 3.00 3.25 3.50

.400 .455 .500 .539 " 571 .600 .6251 .1 63 1 " 193 1.220 1 .247 1 .273 1 .2gg 1 .323.143 . 1gg .230 .26g .2gg .925 .346

kx1.5 kr

krr

.647 .667 ,684 .7001.347 1.370 1.391 1.411.364 .379 .391 .402

kx3.0 ks

krr

.250 .294 .3331"096 1.117 1.137.095 "130 .165

.369 .400 .4291"157 1.176 1.196

. 197 .227 .252

.455 .479 .500 .52A .5381.216 1.235 1.254 1.272 1.2g9.274 .293 .310 .325 .339

kx4.0 ks

kn

.200 "2391.075 1.092.078 . 108

"2731.109

. 138

.3041.126

. 168

.3331.143

. 194

.360 .3951.160 1,177.218 .24A

.407 .429 .448 .4671.194 1.210 1.226 1.241.259 .276 .291 .304

kx5.0 ks

krr

. 167 "200 .2311 " 062 1.076 1.091.065 .092 .119

.259 .296 .310 .333 .355 .375 .3g4 .4121.105 1 "120 1.135 1.150 1.165 1.179 1.193 1.2A7.145 .170 .192 .213 .231 .247 .262 .276,

kx6.0 ks

krr

.143 .172 .20A .226 "2501.053 1.065 1.079 1.091 1.103

.057 .090 .104 .12g .151

.273 .294 "314 .333 .351 .36S1.117 1.130 1.143 1.156 1.169 1.181.172 . 1 91 .208 .224 .239 .253

kx7.0 ks

kn

.125 .152 .1761 .046 1 .057 1 .069

. 050 .071 . 093

,200 .222 ,243 .263 "2g2 ,300 .g17 .3331.079 1.091 1.103 1.115 1.127 1.13g 1.150 1.161

. 1 15 .136 .155 .173 .190 .205 .21g .2g2

kxkskn

.111 .135 .1591 .040 1 .050 1 .060.044 .064 ,094

. 1 79 "200 .2201.071 1 ,091 1.092.104 .123 .141

.239 .256 .273 .2gg .3041.103 1 " 1 13 1.124 1. 135 1.145.159 .174 .1gg .202 .215.

kx9.0 ka

kn

.100 .122 .143 .1631.036 1.045 1 .054 1 .064.040 .059 .076 .095

" 192 .200 .2171"073 1.083 1.093.1 13 .130 .146

"234 .250 .265 .2801.103 1.1 13 1.122 1.132

" 161 .17 5 . 1gg .200

kx10. 0 ks

kn

.091 .111 .1301.033 1.041 1"049.037 .053 ,070

.200 .216 .231 .245 .2591.085 1.094 1.103 1.112 1.121.135 .149 .163 .175 ,197'

.149 .167 .1941.058 1.067 1 .076.087 .104 .120

Nu x

x

Ni'/ut

l,lu

l,lu r

kn

l4t'7ut

pf rtd,.-->l

I

l.{u Nu ' Zr

l,lu s-E;. ilTz

Ekscentrien'i nateg N > 0Ekscentrienitlak N<0Cisti upogib N=0

6=4h

6 s 0.076 > 0.07

k'

k'

1

1

Dvojna I rmat u ra :

Ar = k..+tr +

A'3 = k"k'r'+fu

NuE-

NI,

A,,

oTc

A.

Pravokotni prerez - dvojna armatura Tabela 3

-€r [x" ]ta tx" lkn kE

3.51.5k; kn

3-53.0ks k; kn

3.55-0ke kl kn

3"510- 0

kr kl

430 1.389450 1.375490 1.350520 1.334570 1.312

071115194245318

350360380390410

1

1

1

1

1

281 .036276 .065265 .1 19260 .143251 .1gg

290 1.200300 1.196310 1 . 192324 1.199330 1.195

340 1.192360 1.176380 1.171390 1.169410 1.164

430 1.160460 1.154490 1.149520 1.145550 1.141

051085117147175

242250294314351

384430469504535

, 190 'l .12a " 016,200 1"119 .069210 1.116 .117220 1,114 .160224 1.114 .160

230 1"112 .20024A 1. 1 1 1' .236250 1.109 "27A270 1. 107 .330280 1. 106 .356

290 1.105 .391310 1.103 .426330 1. 101 " 465350 1. 100 .500370 1.099 .531

400 1.097 .572430 1,095 .607470 1,093 .647

620680750850970

130350670210270

1

1

1

293 .379273 .440255 .499234 .567214 .630

195 .693175 .755156 .817136 .880116 .943

420 1,247440 1.239460 1.232480 1.226510 1 .217

209249285318362

1

1

1

2

3

1

1

1

1

1

5305603e06306T0

720780840

1

1

1

1

1

211 .389204 .426198.459190.499183 .532

176.570168.6091 61 .642Koefi c ient k'

1

1

1

590 1.137 "572630 1.133 " 604690 1.129 .645

6=a'/h krYlfrr lr IVt' r9l9

1 . 000 1 .147 .712r9u82A

I

1

llq n9f Y

120 .713c tu t.uvz . o6u560 1.091 .716

08 1.01 1

09 1 .02210 1.03312 1.05714 1 .09116 1.10718 1.13420 1.163

1

1

1

1

1

110250424650980

1

1

1

1

1

140.749133 .794126 .819119,955112 . gg2

1

1

1

1

910 1.115020 1.1 1 1

160 1.107350 1.102620 1.099

749784819855892

620 1 "0gg690 1.099790 1.096920 1.095100 1.093

751783820856892

370 1.092 .g2g810 1.090 "964

137

/.- ruz

Pr. P1-3. Velika ekscentriinost - enojna armatura: betoni obiiajne trdnosti

Mmr: Msa - I{u '2,M-,k,:-+ )k,ink," -f,u 'b'd

A, : k,y*!"-+Nuo ; x - kr.dd.6, Os

€t

[g] V K,/ )-

/,;J J Nuu/,:;:'''I

(.O.g

\8l-'*

ll

?)f.t

I

{-I

I

I

"ll

I

'\l

Armatura

4l%o1

Beton

< c50/60s 500-A s 500-8 s 500

os

tkN/cm2l

os,

lkN/cm2l

os

tkN/cm2l -0,50 -l,00Ql%ol

-1,50 -2,00 -2,50 -3,00 -3,50

30,00 30,00 30,00 l15kxktka

0,2541,093

0,052

0,4001,163

0,143

0,5001,2200.230

0,5711,213

0,299

0,6251,323

0,346

0,667 0,7001,370 l,4LL0,379 0,402

43,48 43,48 43,48 2,17kx

kka

0,1871,068

0,040

0,3 15

1,r240,117

0,4081,r730,196

0,4791,219

0,262

0,535

1,264

0,310

0,580 4,6171,301 .1,345

0,345 0,371

43,56 43,54 43,48 3

kx

l$kd

0,1431,051

0,031

0,2501,096

0.095

0,333

1,137

0,165

0,4001,176

0,227

0,455

1,216

0,274

0,500 0,5381,254 1,2890,310 0,339

43,65 43,61 43,48 4

k*ktka

0,111

1,039

0,024

0,2001,075

0,078

4,273

1,109

0,138

0

I

0

JJJ

143

194

0,385

T,I7]00244

0,429 0,4671,210 1,241

4,276 0,304

43,75 43,68 43,48 5

k.kt

0,091

1,0320.020

0,167

r,0620.065

0,2311,091

0,I19

0,2861,1200,170

0,333

I ,1500,213

0,375 0,4121,179 r,2070,247 0,276ka

43,84 43,16 43,48 6

lcx

ks

ka

4,0771,027

0,017

0,143

1,053

0,057

0,2001,078

0,104

0,2501 ,1030,151

0,2941,130

0,191

0,333 0,368

1,156 1,181

0,224 0,253

43,94 43,83 43,48 7

lL\

l{s

ka

0,4671,0230,015

0,1251,0460,050

a,ll61,068

0,093

0,2221,091

0"136

4,263l,l l5aJ73

0,300 0,333

1,138 l,16l0,205 0,,232

44,03 43,90 43,48 8

kx

ktkd

0,0591,021

0,013

0,lll1,040

0,044

0,1 58

1,060

0,084

0,2001,081

0.123

0,238

I ,1030,158

0,213 0,3041,124 1,145

0,199 0,215

44,13 43,97 43,48 9

lLt

ks

kd

0,053

1,018

0,0L2

0,1001,036

0,040

0,1431,054

0,076

0,1 82

1,073

0-l l3

0,217

1,093

0-146

0,250 0,280l,l 13 1,1320,175 0,200

44,22 44,05 43,48 10

kx

kt0,0481,017

0,01I

0,091

1,033

0,037

0,130T,049

0,070

0,1611,067

0.104

0,2001,085

0.135

0,231 0,259I , 103 1,121

0.163 0"187ka

44,70 44,41 43,48 l5k*kka

0,0321,011

0,007

0,0631,022

0,025

0,0911,034

0,049

0,1 l81,0460.075

0, i43I,0590.099

0,161 0,189I ,012 1,085

0.121 0.141

45,1 8 44,71 43,48 20

k*ks

ka

0,0241,009

0,006

0,048

1,011

0.019

0,0701,0260,038

0,091

1,035

0,059

0,lll1,045

0.078

0,1 30 0,149I ,056 1,066

0.096 0.113

45,41 44,96 43,48 22,5

kx

kt0,0221,008

0,005

0,043

1,015

0.017

0,063

1,023

0,034

0,0821,0320.053

0,100

|,4410.070

0,I l8 0,135

1,050 1,059

0.087 0.r03ktt

45,50 43"48 30

k,ktkd

0,0161,006

0,004

0,0321,01 I

0.013

0,0481,0r70,426

0,063

1,0240.041

0,077

1,031

0,055

0,091 0,1041,038 1,045

0,068 0,081

46,23 43,48 40

kx

l{s

ka

0,0121,004

0.003

0,0241,009

0.010

0,0361,013

0.020

0,04t3

1,018

0.03r

0,0591,024

4,042

0,070 0,0801,029 I ,0350,053 0,063

46.59 43,48 45

kx

ks

ka

0,011

1,004

0.002

0,022

1,008

0.009

0,0321,012

0.018

0,043

l,0ik0.028

0,053

l,a2l0.038

0,063 0,0721,026 1,031

0,047 0,057