EC2_Flowcharts3.pdf

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EC2 Flowcharts.cdr
prEN 1992-1 (3 draft)
rd
Slab Design Flowchart 2
for f <= 90 N/mm
ck
cd cc ck c
h = 1 - (f -50)/200 <= 1
ck
l = 0.8 - (f -50)/400 <= 0.8
ck
Concrete Stress Block
Design stress = h fcd
where f = a f / g
3.1.6 (1)
(3.21) & (3.22)
(3.19) & (3.20)
and
BENDING
Steel Design Stress
f = f / g
yd
Fig 3.8
yk
s
f
=
700
æ -
x
d
'
ø
£
f
yk
Design Formulae
sc
x
g
x
= d
-
0
) d
from (5.10)
M
s
max
K
=
bd
2
f
ck
K
'
=
x
max
l
è
d
-
l
x
max
ø
d
2
g
2
[
c
] d
d
z
=
1
+
1
-
2
g
(
min
K
,
K
'
)
£
0
95
2
c
(
) 0
M
'
=
bd
2
f
K
-
K
'
³
ck
As
'
=
M
'
(
)
f
sc -
d
d
'
As
=
M
-
M
' +
As
'
f
sc
f
z
f
yd
yd
As
>=
0.13%
>=
26%f /f
ctm yk
Primary s 3h 400
Secondary s 3.5h 450
<= <=
<= <=
9.3.1.1 (3) (4)
but not 1.5As
>
>=
9.2.1.1 9.3.1.1(1)
&
n
Dist
0.12%
>=
0.2As prov
&
(smaller near point loads)
9.3.1.1(2)
SHEAR
If V V no links,
Rd,ct Ed
otherwise see beams.
>=
V
=
0
18
b
w
d
k
100
r
f
)
1
3
³
0
f
b
d
(6.2)
Rd
ct
g
l
ck
ctd
w
c
Where
k
=
1
+
200
£
2
r
=
As
l
£
0
02
l
b
d
d
w
0
.
7
f
and
f
=
ct
ctm
(3.16)
ctd
g
c
DEFLECTION
CRACKING
Construction overload
or striking < 7 days?
Is h > 200 mm?
No
Yes
Yes
No
Use Table 7.3
for bar spacing
Check A , min to
s
L/d
7.4.2 (2)
See separate flowchart
Carry out check
to
Ca lculate
to 7.4.3
No cracking
check required
7.3.2 (2)
See separate flowchart
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ö
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æ
ö
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14255012.008.png 14255012.009.png
prEN 1992-1 (3 draft)
rd
Tee & Ell Beam Flowchart 2
for f <= 90 N/mm
ck
Concrete Stress Block
As for Slabs
BENDING
Steel Design Stress
As for Slabs
Compression & tension flange
widths to 5.3.2.1
Flange M OR
=
M
=
h
f
b
h
ç
d
-
h
f
÷
ORf
cd
f
f
2
è
ø
Yes
Is M > M ?
ORf
No
M
=
M
(
b
f
-
bw
)
As
>=
0.13%
>=
26%f /f
ctm yk
Treat as rectangular
section, substituting
b for b.
f
f
ORf
b
9.2.1.1
f
d
é
1
-
2
(
M
-
M
)
10
6
ù
As
>=
As crack
x
=
ê
ë
1
-
f
ú
û
£
x
7.3.2 (2)
max
l
ê
h
b
f
d
2
ú
Part of top steel at supports
must be spread across
the width of the flange
w
cd
(
)
z
=
M
f
ç
d
-
h
f
÷
+
M
-
M
f
è
d
-
l
x
ø
M
2
M
2
9.2.1.2 (2)
è
ø
SHEAR
z may be
taken as 0.9d
M
=
h
f
z
[
h
(
b
-
b
)
+
l
xb
]
OR
cd
f
f
w
w
For point load
near support, use
M
'
=
M
-
M
³
0
At support face
OR
6.2.2.5 6.2.3 (8)
or
As
'
=
(
M
'
)
w
=
cot
q
+
tan
q
=
b n
w
V
z
f
cd
(6.8)
f
sc -
d
d
'
Ed
As
=
M
-
M
' +
As
'
f
sc
where
n
=
0
è
1
-
f
ck
ø
(6.5)
f
z
f
250
yd
yd
w
+
w
2
-
4
1
£
cot
q
=
£
2
6.2.3 (2)
2
At d from support face
V
=
0
18
b
w
d
k
100
r
f
)
1
3
³
0
f
b
d
(6.2)
A
A
V
g
A
Rd
,
ct
g
l
ck
ctd
w
sw
min
£
sw
=
Ed
s
£
sw
max
(6.7)
c
s
s
s
As
zf
cot
q
200
ywk
r
=
l
£
0
02
where
k
=
1
+
£
2
l
b
d
d
A
0
08
b
f
w
w
ck
min =
where
(9.4) & (9.5)
sw
s
0
.
7
f
f
f
=
ct
ctm
(3.14)
and
yk
ctd
g
A
n
f
b
g
c
and
sw
max
=
cd
w
s
(6.9)
b
z
n
f
s
2
f
V
=
w
cd
³
V
(6.8)
(
)
ywk
Rd
max
cot
q
+
tan
q
Ed
s ,L = 0.75d
max
s ,T 0.75d 600
max
=
< =
(9.6)
(9.8)
CRACKING
DEFLECTION
Check main steel tensile
force due to shear) at zcot q /2
from support
T d
Use Table 7.3
for bar spacing
See separate flowchart
6.2.3 (7)
Fig 9.2
Process as Slabs
See separate flowchart
Or use Shift Rule
æ
ö
æ
ö
æ
ö
æ
ö
(
,
14255012.010.png 14255012.011.png
 
prEN 1992-1 (3 draft)
rd
Rectangular Columns
Design Flowchart
SLENDERNESS
Joint stiffnesses
At each end, k = relative column stiffness
ie. EI/l / S (EI/l ), but assume 50%
col beams
of beam stiffnesses to allow for cracking
simplification of 5.8.3.2 (3)
Yes
Is Column braced?
No
Effective length (5.15)
Effective length (5.16)
l
=
0
l
ç
1
+
k
1
÷
.
ç
1
+
k
2
÷
l
=
l
.
max
ì
1
+
10
k
k
2
;
ç
è
1
+
k
1
÷
ø
ç
è
1
+
k
2
÷
ø
ü
0
0
45
+
k
0
45
+
k
0
k
+
k
1
+
k
1
+
k
è
ø
è
ø
î
þ
1
2
1
2
1
2
Slenderness ratio
l = l /i
0
where i = radius of gyration of
section (including reinforcement)
(5.14)
No
Is l <= 25( w+0.9) (2 - M /M )?
01 02
where w =A f /(A f )>=0.05
syd ccd
(from 5.8.3.1)
Yes
Second order moment
M = 0
2
BUCKLING
MOMENTS
Axial load correction factor
K = (n - n)/(n - n ) <= 1
Second order moment
M = N e
2
(5.33)
E d
2
(5.36)
where e = (1/r) l /c
2
2
r
u u bal
where n = N /(A .f )
Ed
0
Imperfections
M = q N.l /2
imp
2
c normally p unless constant M 0E
c cd
n = 1 + w
u
M and M to
01 02
include any global
second order
effects
i
0
where
q =(2/3<=2/ l<=1)/200
i
n may be taken as 0.4
bal
Ö
Curvature
1/r = K . K .1/r
r f 0
where 1/r = f /(0.45d.E )
0
Creep correction
f = f M / M
ef
(5.34)
0Eqp 0Ed (5.19)
f from 3.1.3
k = 1
f
y d
Equivalent end moment
M = 0.6M + 0.4M >= 0.4M
0E
= f /103500d and
yk
K = 1 + bf >= 1
f
02
01
02
ef
(5.37)
where M >= M
02
01 (5.32)
Is f <= 2,
M/N >= h
and l < = 75?
Yes
Is eyb/exh<= 0.2
or exh/eyb < = 0.2?
First order moment
M = M + M
0Ed
No
0E
imp
No
No check
needed
b = 0.35 + f /200 - l /150
ck
Yes
BIAXIAL
BENDING
Final design moment
M = M + M
Ed
(5.33)
0Ed 2
M >= M
Ed
nd
Repeat all for 2 axis then check
02
N
Let , then
n
=
Ed
a
a
A
.
f
+
A
f
æ
M
ö
æ
M
ö
c
cd
s
yd
ç
è
Edx
÷
ø
+
ç
Edy
÷
£
1
Determine Rebar and M Rd
from N:M interaction charts
(5.39)
é
æ
10
n
+
11
ö
æ
5
n
+
1
ö
ù
a
=
If
n
p
0
Max
1
,
Min
2
M
M
è
ø
è
ø
ë
û
è
ø
12
3
Rdx
Rdy
æ
ö
æ
ö
æ
ö
æ
ö
1
.
í
ý
14255012.001.png 14255012.002.png
prEN 1992-1 (3 draft)
rd
Slab Punching Flowchart
(rectangular columns)
c = column dim in direction of M.
1
c = column width.
2
c = column dim parallel to edge.
Enhancement
factor b
x
c = column dim normal to edge.
y
u = full control perimeter ( 2d locus from
1
column face, allowing for holes as
Do adjacent spans
differ by <= 25%?
6.4.2 (3)
).
u * = reduced control perimeter.
1
d = (d x + d y )
may be taken as
for internal columns
for edge columns or
for corner columns
½
(6.33)
r
l
=
r
lx
. £
r
ly
0
02
No
1.5
6.4.3 (6)
Yes
Or
Internal Column
b = 1 + k M Ed u /(V Ed W)
1 1
where, if c / c< = 1,
(6.40)
12
k = 0.45 + 0.3( c / c - 0.5) >= 0.45
12
or if c / c > 1,
12
k = 0.6 + 0.1( c / c - 1) <= 0.8
Shear Stress
12
Table 6.1
(6.42)
c
2
and to
At Column Face
v Ed = b V Ed /(u .d)
0
0
Edge u min(c x +3d,c x +2c y )
Internal u = 2(c 1 +c 2 )
W
=
1
+
c
c
+
4
c
d
+
16
d
2
+
2
p
dc
1
2
1
2
2
1
0=
Corner u min(3d,c x +c y )
0=
6.4.5 (2)
(6.54)
where k is as internal column,
but replace c /c with c /2c
12
Edge Column
u
u
b
=
1
*
+
k
1
e
u
W
par
Is v Ed > 0.3f cd [1-f ck /250]?
1
1
(
) d
1 2
Yes
No
u
1
*
=
c
2
+
min
1
(6.46)
3
d
,
c
1
+
2
At Control Perimeter
v Ed = b V Ed /(u . d)
1
c
2
and to
(6.39)
0
18
W
=
1
+
c
c
+
4
c
d
+
8
d
2
+
p
dc
(
)
1
3
v
=
k
100
r
f
³
0
f
1
1
2
1
2
Increase h
4
Rd
,
c
g
l
ck
ctd
c
(6.48)
Corner Column
u
If e is towards
outside, treat as
internal column
b
=
1
No
Is v Ed > v Rd,c ?
u
*
(6.47) where
1
Yes
æ
c
ö
æ
c
ö
Links not required
u
*
=
min
è
1
d
,
1
ø
+
min
è
1
d
,
2
ø
+
p
d
1
2
2
Links
Min h = 200
A
sw
min
,
=
(9.11)
0
.
fck
S
r
1
.
S
t
.
f
yk
(
v
-
0
75
v
)
u
A
S <= 1.5d on 1
t,max
and <= 2d on last
perimeter
st
sw
=
Ed
Rd
c
1
S
1
.
5
f
r
ywd
,
ef
where
d
f
=
250
+
£
f
Outer control perimeter
u = V /(v d)
ywd
,
ef
4
ywd
Last link perimeter <= 1.5d
from u (polygonal shape)
out
A sw = total link area on 1st
perimeter (at >=0.3d &<=0.5d)
out
Ed
Rd,c
(6.55)
b
1.15
1.4
/
,
14255012.003.png 14255012.004.png
prEN 1992-1 (3 draft)
rd
Flexural Crack Width Calculation
Flowchart (rectangular sections)
M = full SLS moment
t = age at cracking in days
f s = maximum tension bar diameter
S = maximum tension bar spacing
s = cement type coefficient
0.20 for rapid hardening high strength
0.25 for normal & rapid hardening
0.38 for slow hardening
MATERIALS
Concrete modulus
Table 3.1
E cm = 22[(f ck +8)/10]
0.3
STRESSES
Modular ratio a e = E s /E cm
Time factor,
(3.2)
b
(
t
)
=
exp
ê
ë
s
ç
1
-
28
÷
ú
û
Neutral axis depth
cc
t
ê
è
ø
ú
é
ù
æ
d
ö
x
=
d
ê
ë
-
a
(
r
-
r
)
+
a
2
(
r
-
r
'
)
+
2
a
è
r
+
r
'
2
ø
ú
û
Mean concrete strength at cracking
f (t) = b (t) .f
e
e
e
d
ê
ú
cm
cc
cm
Concrete stress
Average concrete tensile strength
If f >50, f = 2.12ln(1+f /10)
ck
M
ct,eff
cm,t
s
=
otherwise, f 0.3(f - 8)
ct,eff =
2/3
c
é
bx
æ
x
ö
) (
x
-
d
) û
ù
cm,t
(
)(
ë
è
d
-
ø
+
As
a
-
1
d
-
d
2
2
3
2
e
2
x
Stress in tension steel
s
s
=
s
c a
æ -
d
x
ø
e
x
CRACKING
Effective tension area
7.3.4 (2)
( ) ( )
A eff
=
min
é
2
h
-
d
,
h
-
x
,
h
ù
ë
û
c
,
3
2
and
As
r
, =
p
eff
A
Average strain for crack width calculation
c
,
eff
(7.9)
(
s
-
0
f
ct
,
eff
1
+
a
r
)
Max final crack spacing, if spacing <=5c+2.5 f
s
r
e
p
eff
s
e
-
e
=
p
,
eff
³
0
s
sm
cm
E
E
0
2125
k
f
s
=
3
c
+
1
(7.11)
s
s
r
r
,
max
p
,
eff
otherwise, s = 1.3(h-x)
r,max
where k = 0.8 for high bond, otherwise 1.6
1
(7.12)
Crack width
W = s ( e - e )
k
(7.8)
and c = cover
max
sm
cm
æ
ö
é
ù
2
'
è
ö
,
14255012.005.png 14255012.006.png 14255012.007.png

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