Civil Engineering Reference
In-Depth Information
Deflection check
3
2
l
d
ρ
ρ
ρ
ρ
=
K
11+1.5
f
ck
f
ck
+3.2
f
ck
f
ck
1
if
ρ
0
≤
ρ
0
Determine basic
l
/
d
ratio (See Figure 17.8 or
d
ratio (See Figure 17.8 or
d
panel)
1
12
l
d
ρ
0
ρ−ρ
′
ρ
′
ρ
0
=
K
11+1.5
f
ck
f
ck
f
ck
f
ck
if
ρ
>
ρ
+
If the section is flanged, apply a factor
(F1) of 0.8
where:
l/d
= span/depth ratio
K
= factor for different structural systems
= 1.0 for simply supported spans
= 1.2 for flat slabs
= 1.3 for end span condition
= 1.5 for interior spans
Where the floor supports partitions that are
liable to be damaged by excessive deflections
apply the following factor (F2):
For flat slabs where
l
eff
f
c
f
×
10
-3
ρ
= required tension reinforcement ratio to
resist the moment due to the design loads
ρ
′
= required compression reinforcement ratio
to resist the moment due to design
The stress in the reinforcement can be estimated
from:
= reference reinforcement ratio =
f
ck
l
ef
l
≥
8.5 m: 8.5/
l
eff
l
eff
ρ
0
For other elements where
l
eff
l
ef
l
≥
7.0 m: 7.0/
l
eff
l
eff
To take account of the stress in the
reinforcement, the following factor (F3)
can be applied: 310/
σσσ
f
yk
f
yk
ΨΨΨ
Q
k
+
G
k
A
s,req
1
σ
s
σ
s
σ
=
γγγ
A
s,prov
δ
1.5
Q
k
+ 1.35
k
+ 1.35
G
k
Increase
A
s,prov
or
f
ck
f
ck
No
Is basic
l
/
d
×
F1
×
F2
×
F3
≥
actual
l
/
d
?
Ye s
Carry out reinforcement detailing
Figure 17.7 Design process checking defl ection
alternatively the following can be used to give a reasonable
estimate of the stress at the quasi-permanent limit state:
limit the cracking. The limits in Eurocode 2 are presented in
Table 17.9
.
Cracking is generally reduced by providing bars at a closer
spacing. There are two approaches to the control of cracking:
either direct calculation can be undertaken, or simple rules
can be applied. Direct calculations should give more accurate
results, but just as with defl ection there are a number of factors
=
fA
y
fA
yk
Q
k k
QG
k
QG
QG
ψ
yk sreq
ψψ
k
+
QG
QG
k
k
sr
sr
σ
s
γ
δ
1
.
5
A
Q
13
5
G
G
+
k
k
k
+
13
5
G
G
G
k
k
k
γ
ss
γ
ss
ss
A
δ
prov
δ
1
.
Q
k
+
13
.
.
,
,
prov
Designers in the UK should note that the UK National Annex
to Eurocode 2 applies restrictions on the use of Expression
(7.17) in the form of note 5 to Table NA.5. This notes that
σ
s
should be calculated for the characteristic action, not quasi-
permanent actions (i.e. in the equation above
ψ
2
= 1.0). In prac-
tice, this means that
σ
s
will always be greater than 310 MPa
and only by providing more reinforcement than is required
for the ULS will the stress in the reinforcement be reduced
suffi ciently to reduce defl ection. Some would argue that in
Eurocode 2 Expression (7.17) is not a Nationally Determined
Parameter and therefore the UK National Annex should apply
these restrictions in this way.
RC and unbounded
pre-stressed members
Bonded pre-stressed
members
Exposure
class
Quasi-permanent
combinations of actions
Frequent combinations
of actions
X0, XC1
0.4
1
0.2
XC2, XC3, XC4
0.3
0.2
2
XD1, XD2,
XS1, XS2, XS3
Decompression
3
Notes:
1. For X0 and XC1 exposure conditions, crack wdith does not affect durability and
this limit is set for acceptable appearance.
2. Decompression should be checked under quasi-permanent combination of actions.
3. Decompression requires that all parts of the bonded tendons or duct lie at least
25 mm within concrete in compression.
17.5.7 Cracking
All reinforced concrete will crack; however, the extent of the
cracking should be controlled. Limits are usually placed on the
size of the crack width, and then reinforcement is designed to
Table 17.9 Crack width limits (mm) (data taken from BSI, 2004)
