eurocode 2 presentation
DESCRIPTION
Eurocode 2 PresentationTRANSCRIPT
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1992 ( 2)
. .,
1/3
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EN1992 ( 2):
11 1: 2: 3: 4: 5: 6: 7: 8:
9:
10:
11: 12:
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:
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C : ( )
D :
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F :
G :
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I :
J :
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2.3.3 (3)2.4.2.1 (1)2.4.2.2 (1)2.4.2.2 (2)2.4.2.2 (3)2.4.2.3 (1)2.4.2.4 (1)2.4.2.4 (2)2.4.2.5 (2)3.1.2 (2)P3.1.2 (4)3.1.6 (1)P3.1.6 (2)P3.2.2 (3)P3.2.7 (2)3.3.4 (5)3.3.6 (7)4.4.1.2 (3)4.4.1.2 (5)4.4.1.2 (6)4.4.1.2 (7)4.4.1.2 (8)4.4.1.2 (13)
4.4.1.3 (2)4.4.1.3 (3)4.4.1.3 (4)5.1.2 (1)P5.2 (5)5.5 (4)5.6.3 (4)5.8.3.1 (1)5.8.3.3 (1)5.8.3.3 (2)5.8.5 (1)5.8.6 (3)5.10.1 (6)5.10.2.1 (1)P5.10.2.1 (2)5.10.2.2 (4)5.10.2.2 (5)5.10.3 (2)5.10.8 (2)5.10.8 (3)5.10.9 (1)P6.2.2 (1)6.2.2 (6)6.2.3 (2)6.2.3 (3)
6.2.4 (4)6.2.4 (6)6.4.3 (6)6.4.4 (1)6.5.2 (2)6.5.4 (4)6.5.4 (6)6.8.4 (1)6.8.4 (5)6.8.6 (1)6.8.6 (2)6.8.7 (1)7.2 (2)7.2 (3)7.2 (5)7.3.1 (5)7.3.2 (4)7.4.2 (2)8.2 (2)8.3 (2)8.6 (2)8.8 (1)9.2.1.1 (1)9.2.1.1 (3)9.2.1.2 (1)
9.2.1.4 (1)9.2.2 (4)9.2.2 (5)9.2.2 (6)9.2.2 (7)9.2.2 (8)9.3.1.1(3)9.4.3(1)9.5.2 (1)9.5.2 (2)9.5.2 (3)9.5.3 (3)9.6.2 (1)9.6.3 (1)9.7 (1)9.8.1 (3)9.8.2.1 (1)9.8.3 (1).8.3 (2)9.8.4 (1)9.8.5 (3)9.8.5 (4)9.10.2.2 (2)9.10.2.3 (3)9.10.2.3 (4)9.10.2.4 (2)
11.3.5 (1)P11.3.5 (2)P11.3.7 (1)11.6.1 (1)11.6.1 (2)11.6.2 (1)11.6.4.1 (1)12.3.1 (1)12.6.3 (2)A.2.1 (1)A.2.1 (2)A.2.2 (1)A.2.2 (2)A.2.3 (1)C.1 (1)C.1 (3)E.1 (2)J.1 (3)J.2.2 (2)J.3 (2)J.3 (3)
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library.tee.gr/digital/m2464/m2464_contents.htm
The Belgian Building Research Institute : www.bbri.be/antenne_norm/eurocodes/pdf/worked-examples-ec2-
def080723.pdf
www.bbri.be/antenne_norm/eurocodes/fr/pub_bbri.html#2
European Concrete Platform http://www.europeanconcrete.eu/publications/eurocodes/112-
worked-examples-for-eurocode-2 http://www.europeanconcrete.eu/publications/eurocodes/114-
commentarytoeurocode2
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: EN1992 1992 :
1998
/
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1
1.1 &
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1-1 1: 2:
3: 4: 5: 6: 7: 8: 9: 10:
11: 12:
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3 -
: , , , : -,
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:
fcm = fck + 8 (MPa)fcm(t) = cc(t) . fcm , =20C
s=0.2 CEM 42,5R, CEM53,5N, CEM53,5R s=0.25 CEM 32,5R, CEM42,5N s=0.3 CEM 32,5N
fcd = cc fck / c cc =1 , 0.85 (t>28.)c =1.5
=
5,0281exp)(t
stcc
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: /
:
fct = 0,9 fct,sp ()fctm(t) = (cc(t)) fctm
= 1 t < 28 = 2/3 t 28
fctm,fl=max{(1,6-h/1000)fctm; fctm}Ecm = 22 (fcm/10)0,3, fcm (MPa)Ecm(t) = (fcm(t) / fcm)0,3 Ecm
fct = 0,50fct,fl 0,90fct,spfctm = 0,3 fck2/3
Ecm = 9500(fc+8)1/3
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: -
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: (, , . , )
c2c1 c3
)2(1
2
+
=k
kfcm
c
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:
/
2=0.5 n s wd fcd
c2
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cc (,t0) = (, t0)(c/Ec0) , Ec0=1.05 Ecm (,t0): /, , , , k=c/fcm(to),
c>0.45fc(to).
< 0.45 fck(to) : :
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:
EC 2 cs = cd + ca
( )cd(t) = ds(t, ts) cd, =
ds(t, ts) kh cd,0
h0= 2Ac/u (
) : cd,a =as(t)ca() ,
as(t) =1exp(0,2 t 0,5 ) ca()=2,5 (fck10) 10-6
fck/fck,cube (MPa)
( 0/0)
20 40 60 80 90 100 20/25 0.62 0.58 0.49 0.30 0.17 0.00 40/50 0.48 0.46 0.38 0.24 0.13 0.00 60/75 0.38 0.36 0.30 0.19 0.10 0.00 80/95 0.30 0.28 0.24 0.15 0.08 0.00 90/105 0.27 0.25 0.21 0.13 0.07 0.00
h0 kh 100 1.0 200 0.85 300 0.75 500 0.70
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(,,C EN10080)
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1: 2: 3:
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1-1 1: 2: 3:
4:
5: 6: 7: 8: 9: 10:
11: 12:
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4:
: , , : /
( 206-1)
:XO XC (14)XD (13)XS (13)XF (14)XA (13)
() : cnom = cmin + cdev
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&
1992, 2cmin,b (= )
cmin = max 10mmcmin,dur + cdur, - cdur,st - cdur,add
cdev: 10mm 5mm c > 40mm c > 75mm
cmin,dur
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cmin,dur S4
50
. E . .1
4.3
4.4
cmin,dur
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25/50, XS1, C30/37, 314, 8/150mm, dg=20mm, 50 .
XS1 : .1 C30/37
50 S4 cmin,b = 14mm ( ) : 4.4 XS1 cmin,dur = 35mm cdur, = cdur,st = cdur,add = 0 Cmin = max (cmin,b , 10mm, cmin,dur ) = 35mm cdev= 10mm ():
cmin=35+15=50mm
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1-1 1: 2: 3: 4:
5: 6: 7: 8: 9: 10:
11: 12:
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5
/ /
: / (& -)
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:
20%
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/ 0.5 < li/li+1 < 2: C : 0.44 + 1,25 (0,6 + 0,0014/cu2) (xu/d) > 0.7
fck 50MPa() 0.44 + 1,25 (xu/d), cu2=0.0035
0.54 + 1,25 (0,6 + 0,0014/cu2) (xu/d) > 0.8
fck > 50MPa() 0.56 + 1,25 (xu/d)
allow>sallow= pl,d k: k=(/3)1/2, =MSd/ (VSd d)
allow k = 3,0
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!!
s=fyk
fyk
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8, 10 8m, , ( ) 50kN/m 35kN/m.
qsd=1.34 G + 1.5 Q = 120 kN/mLC_i
LC_ii
LC_iii
LC_iv
LC_v
:Concrete Design to EN1992
qsd
qsd gg
qsd g
qsd g
qsd g qsd
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gg g g g1062 kNm
502 kNm
743 kNm
624 kNm
616 kNm
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A(kNm) B(kNm) C(kNm) D(kNm)
(i) 0 357 -987 513 -987 357 0(ii) 0 90 -842 658 -842 90 0(iii) 0 502 -1062 616 -717 122 0(iv) 0 650 -681 128 -336 300 0(v) 0 681 -606 19 -606 681 0
30% [ (iii)](iii) 0 624 -743 770 -717 122 0
(iii) , (ii) 12%
(ii) 0 115 -743 757 -743 115 0
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( D)
.. ( ) ...
(. )
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/ (): :
Rd,max=fcd .:
Rd,max=0.6 fcd , =1-fck/250
C-T . :2Rd,max= 0.85 fcd
C-T > . :3Rd,max= 0.75 fcd
Rd,max
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:
CCC
C
CC
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3c16 a 0.25
3c16 a 0.25
832832
6c16 a 0.20
832
832
3c16 a 0.25
3c16 a 0.25
832
:fib Bul 61 : Design examples for strut-and-tie models
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:fib Bul 61 : Design examples for strut-and-tie models
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:fib Bul 61 : Design examples for strut-and-tie models
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:fib Bul 61 : Design examples for strut-and-tie models
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:fib Bul 61 : Design examples for strut-and-tie models
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( B - Bernoulii) - (
D Discontinuity)
: D / /
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: fyd : Rd,max=fcd :
Rd,max=0.6fcd, , =1-fck/250 :
Rd,max= fcd, -
Rd,max=0.85fcd -
Rd,max=0.85fcd
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5.40 x 3.0m, b = 250 mm), / 400 x 250 mm, 620.
C25/30, B500c
150 kN/m .
(..FEM), L/h=2, C2 0.67h2m .
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R = (150+150) 5.40/2 = 810kN, =arctan(2000/1300)=56.98 :
1: C1= q L/2 = 405 kN,
3: C3= R/sin= 966 kN
2: T1=C3 cos= 526 kN
4: 2 = qL/2= 405 kN 1:Asl 526kN/500MPa/1.15= 1210mm2,, 518 2:Asl 405kN/500MPa/1.15= 931mm2,, 320 :
3 C-C-T:2Rd,max=k2 fcd (1-fck/250)=12.75MPa (k2=0.85)c1=810kN/0.4m/0.25m=8.1MPa < Rd2,max
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/ (/, ).
: - & ,
: S-N
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2
2
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1-1 1: 2: 3: 4: 5:
6: 7: 8: 9: 10:
11: 12:
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6 :
. . (, ) = 0,8 fck50 MPa =0.80 =0.8[(fck50)/400 ] 50
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(.. )
( Bresler xa+ya=k)
: MRd (?)
CEB (Bul 141) BS8110 : Mx/dx > My/dy :
Mx=Mx + My (dx/dy) Mx/dx < My/dy :
My=My + Mx (dy/dx)
NEd/NRd 0.1 0.7 1.0
a 1 1.5 2
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VRd,c = [CRd,c k (100 l fck)1/3 + k1 cp] bwd ,
CRd,c = 0,18/c, k=1+(200/d)0.5, k1 =0.15
: VRd1=[Rd k (1.2+40l)+0.15 cp] bwd, Rd =0.052 fck2/3 / c
VRd,cmin = (vmin + k1 cp) bwd , vmin=0,035 k3/2 fck1/2
V < VRd,c ( min , 0.08fck /fyk): 30/55, C20/25,
: min=0.0022 VRd1 = 55.80kNEC2: min=0.0011 VRd,c = 41.75kN
min=0.0022 VRd,c = 51.91kN
1992
VRd,c VRd1VRd,s VwdVRd,max VRd2
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vRd,c (N/mm2) fck=25MPa fck = 20MPa x(0.87), 30MPa x(1.13), 35MPa x(1.23), 40MPa x(1.36)
: 30/55, C20/25,
: min=0.0022 VRd1 = 55.80kNEC2: min=0.0011 VRd,c = 41.75kN
min=0.0022 VRd,c = 51.91kN
100As/ bwd, mm
150 175 200 225 250 300 400 500 >600
0.15 0.55 0.54 0.53 0.52 0.51 0.49 0.45 0.42 0.38
0.25 0.57 0.56 0.55 0.54 0.53 0.51 0.47 0.43 0.39
0.50 0.61 0.60 0.59 0.58 0.57 0.55 0.50 0.46 0.42
0.75 0.65 0.64 0.63 0.62 0.61 0.59 0.54 0.50 0.45
1.00 0.70 0.68 0.67 0.66 0.65 0.62 0.58 0.53 0.48
1.50 0.78 0.77 0.76 0.74 0.73 0.70 0.65 0.59 0.54
2.00 0.87 0.86 0.84 0.83 0.81 0.78 0.72 0.66 0.60
3.00 1.04 1.03 1.01 0.99 0.97 0.94 0.86 0.79 0.72
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V > VRd,c , . . :
1 cot 2.5 (45 21.8) : VRd = min {VRd,max ,VRd,s }
VRd,max= bw z fcd/(cot+tan)
= 0,6 [1- fck /250]
45 21.8
VRd,s = (Asw/s) z fywd cot, Vcd =0
VRd =min {VRd3 ,VRd2}
VRd,2= fcdbwz
= 0,7 [1- fck /200]
=45, =0.9d
Vwd= (Asw/s) (0.9d) fywd
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VRd,c < VEd
=21.8
VRd,max
: VEd < VRd,max
oVs=Ved=(Asw/s) z fywd cot
21.8
-
cot = 2.5, =21.8 ( Asw )
Vd < VRd,max :
- - VEd= VRd,max
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20/80, C30/35, B500c, VEd=600kN
d=800-50=750mm, z=0.9d=675mm, =21.8
: VRd,c=60.72kN < VEd=600kN VRd,s = Ved = 600kN = (Asw/s) z fywd cot (=21.8 ) Asw/s = 817mm2/m : VRd,max=491.6kN < VEd VRd,max=VEd
= 0.5arcsin(VEd/ fcd bw z) = 29 (cot=1.8)
Asw/s=1135mm2/m
12 (): 2*113.1mm2/s=1135mm2/ms=0.19m w=Asw/bws = 0.03 > w,min=0.08(fck/fyk)=0.000876 sl,max=0.75d=0.56m , 12/190
Ftd=0.5VEd cot= 540kN (
)
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( ):
vEdi = VEd / (z bi) vRdivRdi = c fctd + n + fyd ( sin + cos) 0,5 fcd
vEdi f (sin + cos )yd
cf + ctd n
bi
bi
c
0,25 0,5
0,35 0,6
0,45 0,7
0,50 0,8
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: V+T:
(TEd /TRd,max) + (VEd /VRd,max) 1,0
(Tsd /TRd1)2 + (Vsd/VRd2)2 1,0 .
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(6.4, 9.4.3) : : 2d ( 1.5d - ) -
: : vEd < vRd,max=0.5fcd
u1 (2d)
vEd < VRd,c/bwd = vRd,c
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: rcont = 2d + lH + 0,5c : rcont = min [2d + 0.56(L1L2)1/2, 2d + 0.69 L1]
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1992 & : 45
-
,
W1 - u1
: =1.5, 1.40, 1.15 , ( ).
duVv
i
EdEd =
)/(,1Wu
VMk1 211 ccfk
1Ed
Ed =>+=
12
22121 dc2d16dc4cc2/cW ++++=1
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:vEd < vRd,c= CRd,c k (100 l fck)1/3 + 0.10cp
vRd,cmin = vmin + 0.10cp , vmin=0,035 k3/2 fck1/2
vRd,c < vEd < 1.6 vRd,c (=33.7):
( ), sw,min (1,5sin+cos)/(srst) 0,08(fc)/fyksr
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: uout,ef = VEd / (vRd,c d)
kd uout uout,ef (.: k=1.5)
2d
d
d
> 2d
kd
A B
kd
-
1
2
1
2d
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300x400mm 6m 225mm, 600kN, 45kNm.
20mm 12, d=225-20-12=193mm
2d: u1=2(300+400)+4193=3825mm {V+M},
:
W1=1512,6103 mm2, c1/c2=300/400=1.33 , k=0.63 ( 6.5).=1+063 (45kNm/600kN) (3825mm/1512,6 103 mm2)=1,12
duVv
i
EdEd = )/(,1W
uVMk1 211 ccfk
1Ed
Ed =>+=
12
22121 dc2d16dc4cc2/cW ++++=1
-
:
- 2d:
A . :
-: (5090-2(300+400))/2 =587mm ~ 3,04d.
(2d), st=1.5d:
d vVu
C,Rd
Edouter
=
-
0.5d 2dd