application of ec2 to office buildings
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Design presentationTRANSCRIPT
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Paper: Albrecht
~~ ~~~ ~ ~ ~
Paper
Adica t ion of the structural Eurocode EC2 to
an office building
U. Albrecht, Professor Dr k g .
Fachhochschule Nordostniedersachsen, Buxtehude, Germany
Synopsis
EC2: ‘Design of concrete structures: Part I ’has been
published by CEN as an ENV.
This paper reports
on
the application of EC2: Part
I
to the
design of the major structural elements in an office building
which has also,
in
comparison, been designed to BS 81
I O .
The
exercise was undertaken in collaboration with Andrews, Kent
& Stone, consulting engineers, London. The purpose was to
provide an indication of the use of EC2 in the design of
‘everyday’ tructures.
Typical structural concrete elements ibbed slab, frat
slab, beam, column, raft foundation were analysed and
reinforced, and as far as relevant deflections and crack widths
were controlled. The paper identifies aspects where the use
of
EC2 may change current UK design practice. The EC2 design
was based on reinforcement with a yield stress of 500N/mm2
(as compared to 460N/mm2 forhe
BS
81
10
design) to
demonstrate the advantage for the ultimate limit states and the
limitation which may be required to control defections.
It is hoped this paper will encourage practising engineers to
use the ENV Eurocode EC2.
Introduction
In many discussionsabout the Eurocodes amongngineers in he Member
States of the EuropeanCommunity and EFTA oncern has been expressed
about the extent f changes from current national esign practice and the
complexity of the Eurocodes. This paper is intended to assist practising
engineers to become familiar with EC2.
An impression of the writing of EC2l has been given by Somerville2 nd
acomparison of the design requirements inEC2 and
BS
8110 by
Narayanan3.
Eurocode EC2: ‘Design ofconcrete structures: Part General rules and
rules for buildings’ has been published by CEN as an ENV. Its use by
engineers will then be optional for 3 years with a possible extension of 2
or perhaps more years before it becomes an EN, replacing the national
Codes such as
BS
8110.
During this time application to various structures is necessary in all
Member States to check and improve the resent ENV version. Practising
engineers have an opportunity during this time to influence the content
of the final version of EC2.
Only a few
of
the comparisons maden the separateMember States on
the use of EC2 have been published. The European Committee of the
Consulting Engineers of the Common Market (CEDIC) applied EC2 to
the design of three different structures which had also, in parallel, been
designed according to the respective national Code4.
This paper reports on another comparativeesign exercise,undertaken
during a 6-montheriod which he authorspent witha consulting engineer
in London. It describes the applicationof EC2: Part
1
(revised final draft,
December 1989)to the design of the major structural lements inan office
building (the EC2 design) which have also been designedo BS 81
lo5
(the
BS 8110design). In addition, a comparisonwith German design practice
and DIN
1045
was made and will be published in Germany. The exercise
was undertaken with the following questions in mind:
(1)
Will EC2 introduce a severe change in design practice compared to
BS 81lo?
(2) Is EC2 too complicated for the design of ‘everyday’ structures?
In addition, thebrief outline of the EC2design of the major structural
elements of the building given in his paper provides an indication of the
use of EC2 in design. Where alternative design methods aregiven in EC2
the more simple method was applied in this design exercise. The figures
in brackets
[
refer to the relevantclauseof EC2
- (
) indicating
‘principles’ for which there is no alternative, ) indicating ‘application rules’
for which alternative rules may be permit ted.
It should be noted that theanalysis and the calculationf reinforcement
described in this paper is only a part of the design of concrete structures.
Other important aspects, not reported here, relateo durability and detailing,
taking into account standards of workmanship.
General arrangement of the office building
The main part of the four-storey well-equipped office building, recently
built in the London area, haseen arranged arounda central atriumwith
stairs and lifts. In addition, he building has wing with a regular structural
system (Fig
1).
This
part
of the building contains typicalstructural concrete
elements:
-
ibbed slabs in the upper floors
-
hallow beams
-
olumns
-
lat slab in the ground floor
aft foundation
Fig 3 shows the cross-section of this part of the building: gridline D to
N and to
8;
Figs 1 and 2 how the spans and the arrangementf columns.
The structure contains everal shear walls,
so
that it can be assumed to
be fully braced. The foundation consists of a raft bearing onto clay.
Design information
Actions
ECl: ‘Basis of design and actions on structures’6 is at a draft stage of
development. Therefore the exercise was undertaken by reference to the
relevant British Standard Code, ut introducing he new CEN terminology.
12000 500
I
l
In
c-
In
CI
5:
r-
In
c-
In
550 dp
ribbed floor
-
l
Fig
1.
Office building: general arrangement,first hird floors
The
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TABLE
I Nominal cover to reinforcement
EC2 design
BS
8 110 design
Exposure
Nominal Nominal
Conditions
coverover
(mm)
Offices environment
.l
ry 20 mild 20 (C35)
262x874 600
x
6
Carpark, 2aumid
25
aft environment moderate 35
founda tion without frost
l
Column drop
45 x 45
I
NOTE: Nominal cover includes 5 mm allowance for tolerances
cube strengthf,,,,, is given in addition i3.1.2.41. The EC2 design exercise
was based on C30/37 which corresponds approximately to concrete grade
C35 used for the
BS
8110 design.
Specifications for reinforcement will eventually be included inN 10080.
A
provisional guide in EC2 specifies reinforcement with a yield stress
yk
=
500N/mm2. EC2 defines two classes of reinforcement ductility L3.2.4.21
which limit he redistribution of moments i2.5.3.4.2 (3)l. The EC2 design
was based on high ductility steel with
yk
=
500N/mm2 to demonstrate,
on the one hand, the advantage of high yield stress nd, on he other hand,
the limitations dueo serviceabilityequirements. The amount of
reinforcement cannot directly be compared in the two designs because he
BS
81 10 design was based on steel
f =
460N/mm2.
I
9 _
l
Fig
2.
Office building; general arrangement, ground floor
Considerationof durability
To enable design ofn adequately durable structure EC2ists the interrelated
factors affecting durability
12.41
and gives further provisions r4.11. The
concrete cover i4.1.3.31 is related to the environmental conditions [Table
4.11. To allow more direct comparisons ofhe EC2 design with he
BS
81 10
design the nominal covers given in Table 1 were used with a tolerance
allowance of only
h
=
5mm. It should be noted hat, in practice, a greater
tolerance allowance
Ah =
lOmm for
in situ
concrete structures is advisable
14.1.3.3
8)l.
Q
. 45 75
-
- 45
I I l
Fire protection
Provisions concerning fire protection re not included in EC2: ar t 1. They
will eventually be given in a separate Part. The provisions of
BS
81 10 or
a fire resistance of
l
h for all floors above ground and 4h for the lower
ground-floor used as a carpark were therefore applied to both the
BS
81
10
and the EC2 design.
3rd fr
2nd fir
Ribbed slab
Basis o design
The ribbed slab forminghe first, second and third floors covers two unequal
spans of 12.00m and 4.50m. Examination of the cross-section given in Fig
4 indicates the floor is rather slender.
1st flr
Grd
f
Ir
II
Lower grd
f
Ir
I I I I
W
Fig
3.
Office building; cross-section
l
125
Ribbed slab
The permanent action (EC2)
-
ead load (BS 81 10)
-
as not changed
for the EC2 design, althoughEC2 specifies the density of reinforced concrete
as 25 KN/m3 i4.2.1.21.
The variable action (EC2)
-
mposed load
(BS
81 10)
-
sed for the
design of the floors was the same for both designs:
5.0
kN/m2 third floor to ground loor, offices.
This valueexceeds the specifiedvalueof the national Code and he
Eurocode. For the column design a reduction in total mposed f loor load
was used as given in BS 6399:
Part
l and
AMD
4949.
l
12
Main beam
Material properties
EC2 relates the concrete strength class to the cylinder strengthf,, but the
Fig
4 .
Cross-section ribbed slab and main beam
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/ 7 July 1992
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TABLE 2 ibbed slab: design values
of
actions/loads
I EC2 design I BS
8
110esign
TABLE 3 - ibbed slab: design moments and tensile reinforcement
5
7
8
A A
A
12000500
Location
EC2 design
As
M
f y k= 500
(kNm) N/mm2edistr.
(mm2)
Support 7
176 0.9
829
Span 5-7
175 0.9
828
BS 8110 design
P
redistr.
As
f y = 460
N/mm2
(mm2)
847
193
I
0.8
I
1001
For the EC2 design, he basis is outlined in the following Eurocode clauses
ltimate limit states i2.3.21
-
artial safety factors for actions [2.3.3.11
-
artial safety factors for material properties i2.3.3.21
erviceability limit states 12.3.41
-
nalysis 12.51
The design values for actions are given in Table
2.
There are only small
differences between the EC2 and
BS
81 10 designs.
EC2 defines and EC l provides combination factors
g )
for additional
variable actions. Theyo not apply o the EC2 design of this office building.
The EC2 analysis for the ultimate limit states i2.5.3.2.21 may be linear
elastic with or without redistribution, non-linear or plastic. For the EC2
design the moments were calculated by linear analysis and redistributed
-
ee Table 3 .
An
explicit check on the rotation capacity may beomitted
i2.5.3.4.21 provided tha t
6
2 0.44 + 1.25 x/d), concrete grades not greater than C35145
6
2 0.7 , highuctilityteel
where
6
is the ratio of edistributedmoment to he moment before
redistribution and
x/d
is the ratio of neutral axis depth.
This limitation is more severe than the BS 81 10 requirements.
Reinforcement
The cross-sectiondesign sbased on stress-strain diagrams which are
parabolic-rectangular for concrete and bilinear for reinforcing teel
i4.2.2.3.21.
Although the EC2 partial safety factors for material properties are the
same as in
BS
81 10
y
= 1.5 for concrete
y =
1.15 for reinforcement
design charts are not yet available. For the present, the design aids in the
CEB manual* may be used. he resulting areas of reinforcementare given
in Table 3. The lower amount of steel in the EC2 design results mainly
from the higher yield stress used.
Limiting defections
Serviceability limit states include limitation of deflections. Generally, this
requirement may be met by limiting the span/depth ratio rather than on
the basis of an explicit calculation of deflection. EC2 gives in Table 4.13
basic ratios of span/depth for lightly and highly stressed concrete. These
ratios havebeen derived on he assumption that the steel stress under design
service load a t midspan is 250N/mm2, corresponding roughly t o
f y k
=
400N/mm2 k4.4.3.21. For sections with wide flanges he values should be
The Structural EngineerNolume 70/No.13 7 July 1992
multiplied by
0.8.
If there are partitions liable to be damaged by excessive
vertical deflections the values should also be reduced for spans exceeding
7m. Applying these actors in the EC2 design he spanldepth ratio amounts
to:
= 32 x
Om8 4 0 0 / f y k )
(As,prov/As,~eq)
For direct comparison with the
BS
81 10 design values
fyk =
460N/mm2,
As,prov As,req
ere taken giving:
I/d =
32
X 0.8
(400/460)
=
22.3
This result is reduced further when
fyk
=
500N/mm2, i.e.
l /d =
32
X
0.8
(400/500)=
20.5
These values are much lower than found in the BS 81 10 design where
combining Table 3.10 and 3.1 1 of BS 81 10 gave:
I/d =
20.8
X
1.46
=
30.4
without taking into account the reduction for spans exceeding 10m. In his
exercise, the 12m-long span ofhe 55Omm-deep ribbed slab could be justified
without further calculation
of
deflectionbecauseof the surplus of
reinforcement given by 2425 [982mm21bars.
The exercise illustrates that EC2 is rather conservative for elements such
as ribbed and solid slabs where
P
= AJbd < O S Yo.
For the range
0.5
Vo
< P < 1.5
Yo, the spanldepth atios of EC2 and BS 8110 correspond more
closely. However, the EC2 design ofhe shallow floor reinforced with high
yield steel shows tha t deflections may govern the design rather than the
ultimate limit states.
Main beam
Bending
To simplify analysis the beam in gridline 7 (Fig
1 )
was reduced to four
equal spans of 7.50m. EC2 provides no table for bending moments and
shear forces. They have o be calculated for different load cases i2.5.1.21:
(a) alternate spans carrying the design permanent and variable load
?G YQ Q,,
and other spans carrying only the design permanent load
Y G
(b) two adjacent spans carrying
yG G + yQ
Qk
nd all other spans
carrying only
yG
G,.
The calculated moments are given in Table 4. They are based on linear
analysis and have been redistributed. n addition EC2 offers simplifications
for beams and slabs i2.5.3.3 (4)l cast monolithically into their supports,
where the negative moment may be aken as that at theace of the support
(Fig
5 .
For the 600mm-wide columnadjacent to the pan of 7500mm the
reduction of the hogging moments is about 20%.
However, the design moment at the faces of the supports should not
be less than 65
Yo
of the support moment calculated assuming full fixity
at the faces of all continuous supports i2.5.3.4.2 (7)l as shown in Fig 5 .
The results derived from applying these rules are also given inTable 4.
Moments are about5-20
070
lower in the spans and about 30
070
lower over
the supports in the EC2 design compared to the
BS
81 10 design. The
redistribution was limited to
6 = 0,85
to provide minimum moments at
supports or to avoid increase of span moments.
Shear
The EC2 method for shear ssimilar to BS8110. Because of direct
transmission of loads close to supports the design shear force
V,
may be
calculated at a distance d from the face of the support i4.3.2.2 (lo)], at
the expense, however, of curtailment within
. 5d
from the support i4.3.2.2
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I
l I
I
I
I I In I I
Moments at
face
of
support
I
,
I
l
I
,
MI
I
l
M
nin
Mmin
Minimum
moments
I
1
Mmin=0.65 GdtQd)ln 2
I
Mmin=0.65GdtQd) n2
1
8 12
Fig 5 . Moments at face of support, minimum moments
(1 l)]. There are three values of design shear resistance l4.3.2.2 (l )]:
V,,,
is the shear resistance without shear reinforcement
V,,,
is the maximum shear force that can be carried by the notional
concrete struts
V,,,
is the shear force that can be carried with shear reinforcement.
Where
V,,
> VRdl i.e. shear einforcements required, twodesign
methods are given:
-
he standard method [4.3.2.4.31
-
he variable truss angle method l4.3.2.4.41.
TABLE 4 Main beam: design moments
L J
G E D
A
A
A
A
A
7500
Location
BS 81 10C2 design
MI, MII
(kNm)
(kNm)
support
edistr.
M
M min
ace of
M
Table 3.6
(kNm)
(kNm)
Support
J
811
.85
35
pan
J-G
1043
.85
89
pan L-J
927
19
08
*)
.85
39upport
G
1275 779
21
*)
.85 1069
NOTE:
*)
design moment
TABLE
5
Main beam: shear resistance and shear reinforcement
The first method assumes the notionalconcrete struts to be a t 45
,
similar
to
BS
81 10. The second method permits an inclination between 22 and
68 which reduces the shear reinforcement but affects the curtailment of
the tensile reinforcement.
The shear resistance without shear reinforcement depends on concrete
strength, effective depth, and reinforcement ratio 14.3.2.31.
Except for beams with low percentages of reinforcement, EC2 gives lower
values of shear resistance compared with BS 8110. When comparing the
values in Table
5 ,
it should be noted that the shear resistance is increased
because of the higher tensile reinforcement in the
BS
81 10 design.
For he EC2 design, the shear reinforcement required for he most
unfavourable section at the first interior support was calculated by the
standard method. The minimum shear reinforcement, which isbout 10
Yo
more compared with
BS
81 10, is almost sufficient for all other sections.
This suggests hat the simple standard method of EC2 will be suitableor
typical structural elements.
In general the design shear force
Vs,
will be less than the maximum
shear capacity V . The relative value V /
V,,,
governs the spacing of
links. In most cases the longitudinal and transverse spacing of links will
be limited to 300mm.
Flat
slab
Bending
An additional row of columns on gridline 5(a) could be provided in the
basement which is to be used for carparking (Fig 2). Thus the maximum
span is reduced to 7.50m which makes flat slab economical. The thickness
of 300mm is increased to 400mm by column drops.
The basic analysis for slabs in EC2 is the same as for beams. Different
load cases are considered as described above in oth directions. EC2 gives
no details about moment distribution for flat slabs. In the absence of
supporting documents providing more information, the divisionf moments
between column and middle strip as given in
BS
81 10 was applied or the
EC2 design.
Except fromhe interior span, EC2 ives ighermoments.The
reinforcement required in the EC2 design
to
resist the negative moment
over the first nterior support is illustrated n Fig 6. It hould be noted hat
P = As,,,/bd
in Fig 6 is almost constant within the column strip because
the higher amount of reinforcement in he central half of he column strip
is related t o the increased depth of the column drops.
However, EC2 requires that the tensile reinforcement over supports
should be greater han P
= 0.5
070 [4.3.4.1 (9)l to avoid punching. As shown
in Fig 6 this rule demands more tensile reinforcement within the critical
perimeter than that required to resist bending.
Punching
EC2 gives detailed principles nd rules for design against punching 4.3.41.
The critical perimeter for the EC2 design is at a distance 1.5d from both
the faceof the column and the column head. Because of rounded corners
the perimeter is less compared with the BS 81 10 design.
The method for punching shear design is characterised by
VR d l , V,,,,
VRd3 ,
f4.3.4.3. (l )] , as explained above, but related to the unit length. The
effects of eccentricity of loading are taken into account with the same facto
as
in
BS
8110, i.e. 1.15 for an internal column i4.3.4.3 4)l. The total design
shear force at the most unfavourable column J5(a) (Fig 2)
V = 1.15
X
982
=
1129kN
is almost identical with that for the BS 8110 design.
L J
G E
D
A iA
A
A
l 4 7500
)tc 7500
*
7500500
Location
EC2 design l BS 8 10esign
7q F
in. reinf.
Shear resistance
f y k
=
5yJ
without
N/mm
f
reinf.
( W
W
reinf.
335
41
1
2126
276
1320 258
min
06
A W
(mm2/m)
wd
764
532
Shear resistance
f,
=
460
without
( W
W
(mm2/m)
V
-
, bd
,
bd
reinf.
einf.
N/mm2
f
455
309 1559
325
207
min
236 1199
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methods. This difference may affecthe design of flat slabs without column
drops and, as shown later, the thickness of raft foundations.
Critical Derimeter
.
F
I
Tensile reinforcement
I
r p =0.5
Central cd strip
I
Middle stri p Column str ip
Middle strip
--
ly
=
4500
ly
=
7500
Fig 6. Flat slab, EC2 design: critical perimeter, tensile reinforcement
Limiting deflections
The valuesof spanldepth atio given in
EC214.4.3.21
and BS
8110
correspond for .5 To reinforcement, a enerally representative mount for
flat slabs:
EC2 : l /d = 30400/460)
=
26.1
fyk
=
460N/mm2
Column drop
<
U3
Table 3.1
1:f = 5/8 (460), M/bd = 1.25
BS8110 : l/d = 26 X 0.9 X 1 .13 = 26.4
However, the
EC2
design is based on a yield stress of 500N/mm2 which
consequently reduces
/d.
For the
EC2
design an increase of reinforcement
amount obtained simply by reducing the spacing in the critical endspan
avoids the need for a detailed calculation of deflection.
Control of cracking
The serviceability limit states in
EC2
require the control of cracking for
structural elements for exposure classes -4 r4.1.3.3Table 4.11.This control
of cracking is required in the carpark n the lower ground-floor where the
exposure is a humid environment,while the office floors, which are exposed
t o
a dry environment, need
no
consideration of control of cracking.
EC2 provides simple detailing rules i4.4.2.31for ensuring crack control
and does not require xplicit calculation of crack widths.he bardiameter
or the bar spacing has to be limited, depending on the steel stress under
the quasi-permanent combination of loads. The draft
ECl:
'Basis of design
and actions on structures' gives combination factor 2 = 0.3 for he
quasi-permanent combination for offices.
The design value is:
Gd
+
Q d = 1.35 X 8.7
+ 1.5
X 5.0 = 19.3kN/m2
and is associated with a quasi-permanent value:
Gk 2
Qk = 8.7
-l-
0.3
X
5.0 =
10.2kN/m2
A simplified approach for he steelstress under he quasi-permanent
combination, assuming
As prov As req
as used, giving
us
=
(10.2/19.3) (500/1.15) = 230 N/mm2
The maximum bar diameter and the maximum bar spacing are given in
Table 7; either requirement has to be met.
The bar spacing rules of BS
8110
are based on the service stress in the
The hear resistances without hear einforcement for both designs are
reinforcement which
may be assumed to be: = 5/8 (460) = 288
in
~ ~ b l ~
.
Because
of
the increased tensileeinforcement,he
Because Of
the advantages
for
'labs reinforced he
EC2 design gave hi.er
values
for the shear
stress.
But
when clear spacing is, in this ase,
320
mm for
0.5 To
reinforcement which
multiplied by
the shorter
perimeter the advantage
in
was reduced.
corresponds to acentre-to-centre spacing ofabout
340
mm
-
ee Table
7 .
However, shear reinforcement may be avoided in this case. The shear
Generally,
EC 2
design will be more conservative than BS
81 10
design
resistance at the
outside
the
drop
is
sufficientwithoutnelation to the maximumpacing of barss shownn the lastolumn
reinforcement for both the EC2 and BS 8110 designs.
of Table
7.
EC2 limits
the maximum shear resistance in flat slabs containing shear
reinforcement
14.3.4.5.2 (l)]
by
Interrelations
The design of flat slabs is characterised by the interrelation of
=
1.4
VRdl
-
ending, punching, deflections
This
procedure is ifferent to that required
in BS 81 10
where the shear stress
depending
on
at the face f the column s limited. The alues in the ast column of Table
-
epth
6 demonstrate the substantial difference resultingrom theEC2 and BS 81 10
-
mount and stress of reinforcement
TABLE
6
- lat slab: punching shear
Design Shear resistance
I . I I
Tensile
I
concrete
I
I
~~ ~ ~~~ ~ ~
EC2
design:
V, = 1129
kN
1570.64
.5
.2964.5d
from column drop
1572
123.59
.5
.23
64.5d from column face
Rd2
Rd 1
BS 8110 design: V,, = 1140kN
column
face of
VC
v, ud
1.5d
from column face
1290.49
.24
.97 264.5d
from column drop
3001
033.46.26.17
64
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TABLE 7- lat slab: control of cracking and detailing
Control of cracking General
e
=
0.5
070
rules
EC2
230 2o
200
<
1.5hesign
<
350
288
-
340
< 750
design
<
3d
The differentapproach of EC2 o assure shear resistance requiresn amount
of tensile reinforcementof 0.5
070
within the critical perimeter which may
be enough to avoid shear reinforcement in someases. On the other hand,
this surplus of reinforcement in flat slabs with column drops does not
produce an increase of the spanldepth ratio. The simple approach of
controlling deflections by the spanldepth ratio related to the steel stress
in the middle of the span may reduce the advantage of high yield steel.
Table8 demonstrates these interrelationsor the lat slab
of
300
mm
depth
with column drops and for alat slab without olumn drops butwith depth
increased to 350 mm. Though the atter requires shear reinforcement,his
different design may be an alternative with advantages for the provision
of formwork and services.
Columns
Classifcation of structure and slenderness
In compression members the influence f second-order effects should e
considered n EC2 design if the ncrease n bending moments due to
deflections exceeds 10 070. This may be assumed to be the case where the
slenderness of the st ructure or structural members exceeds certain limits
i4.3.5.1 (5)l.
The structure or members are classified 14.3.5.2 (4)l as
-
raced or unbraced and
-
way or non-sway
This office building contains substantial shearalls which are sufficiently
stiff to transmit at least 90
70
of all horizontal loads to the foundations.
It may be classified, therefore, as braced and non-sway.
The necessity to consider second-order effects dependsn the lenderness
ratio of the isolated column
X = / i
l,=
P x
l O l
where
l,
is the effective height
lcol
s the height measured
i
is the radius of gyration.
between centres of restraint
TABLE 8 - lat slab, EC2 design: interrelation of bending, punching and deflections
Isolated columns are considered slender if
X >
25 or 15/f
(N,/(A,
x
f,,))
which ever is the greater 14.3.5.3.5 (2)l.
But because of the advantage of restrained ends, isolated columns need
not be checked for second-order effects if
Xc t > 25 (2-eoJe02)
where eoland eO2re the eccentricities of the axial load at the endsf the
column. In this caseminimummoment should be considered i4.3.5.5.3 (2)l
The interior column gridline 7 and the erimeter column gridline
5
were
checked as described below.
Interior column:
M =
N
X
(h/20).
IC
=
3975mm
l, <
l ol ,
ake
l ,
=
3975mm
b
= h = 6 0 0 m m
X
=
3975/(0.289 X 600)
=
22.9 25
This column is not slender.
Perimeter column:
l ol 3975mm
h
=
262mm
,
b =
874 mm
Theeffective height
I
was determined by means of hemonogram
[4.3.5.3.5 (2)l based on the rigidity of restraints at the column ends:
P
=
0.67
X
= (0.67 X 3975) / (0.289 X 262) = 35.1
>25
The next step was to check the influence onuckling of bending moments
at the ends of the column. By subframe analysis, shown in Fig 7, the
eccentricity at the topf the column isopposite to that at the bottom,here
eo, = -0.5 eO2 I eo11 l eod
X
=
25
X
(2-
(-0.5)
/(l)
=
62.5
>
35
Thus no econd-order effect had to be taken intoaccount for theperimeter
column.
Compared with the BS 81 10design the range which omits second-order
effects is quite similar
EC2
:
Zo/0.289h
=
52 corresponds to
BS 81 10:Jh
=
15.
Axial forces and moments
EC2 allows the simplification that the loads transmittedo a column may
be calculated on the ssumption that beams and slabs are simply supported.
Continuity should, however, be taken into account at the first internal
support and a t other internal supports if the spans on either side of the
support differ by more than 30
070
i2.5.3.3 (6)l.
I Over support
Bending Punching
AS
reinforcement
070)
mm2/m)
070)
mm2/m)
Shear
s x = As,
With column drops
I
1250 0.34 1820
0.5
not
h
=
400mm
Without drops I 1570 0.5 I 1570 I 0.5 I
required
h = 350mm
I
atpan
I
Bending
I
Deflections
A s
I
I/d
s
k
(mm2/m)
7.42
0.0
(m)
mm2/m) (N/mm2)
h
=
300mm
d =
247 mm
[
11491
918
500
16
@
175
h
=
350mm
d
= 297 mm
10051
806
500
16 @ 200
29.9
8.89
234
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hcrit
t
+ l -1
Critlcal dQndQrnQSSatio A crit
02
JQ0’
I
Subframe, perimeter column bending moments
Q01
Q02
Fig 7 Column with restrained ends
This clear statement draws attention to the unfavourable conditions at
the first internal support which, in this case of two rather unequal spans,
increase the force by 46
070
compared with simple support .
The total imposed floor load for both designs was reduced according
to BS 6399 and AMD 5881.
EC 2 gives no rules concerning the moments to be considered for the
design of columns withhe exception of he above minimum moment. The
following assumptions were met:
-
eglect moments at interior columns
-
onsider moments at perimeter columns
This corresponds to the German practice for braced structures.
When comparing he
axial
forces for both designs
in
Table 9, the different
amount of redistribution should be remembered. The bending moments
were calculated by subframes, but M
=
143 kNm for column E7 in the
lower ground-floor designed by BS 81 10 corresponds to the minimum
moment. In theEC2 design the same provision of a minimum eccentricity
TABLE 9
- esign
of
columns
applies only to the slenderness ratio 25
<
h ,< hcrit. enerally, EC2 is less
rigorous inaccounting for bending of columns nbracednon-sway
structures.
Rein orcement
In columns, highly stressed by axial forces, the strength of the concrete
is a key figure for design. Small differences inhe design concretestrength
may result in large differences in the amount of reinforcement required.
The concrete strength class in the EC2 design C30137 may be stressed
under ultimate loads up to
d
=
0.85
(30A.5)
=
17 N/mm2
compared with the BS 81 10 design related to the concrete grade C35 the
stress may be up to
0.67f,,/yc
=
0.67 (35/1.5)
=
15.6N/mm2.
This difference, due to classification of concrete, increases the capacity
of an EC2 column by 9
70
or rather decreases the amount of reinforcement
required.
Furthermore, the bending moments due to subframe analysis require
additional reinforcement for the interior column E7 inhe
BS
8110 design.
Reinforcement for the perimetercolumnE5 sneeded to increase ts
compression strength in both the EC2 and BS 81 10 design.
For less stressed columnshe reinforcement in EC2 design ill not differ
that much f rom BS 8110 design.
In the EC2 design the minimum amount of longitudinal reinforcement
should be 15.4.1.2.1
(2)l
As i =
0.15 NSd/f,d 0.003
A .
This means hat the reinforcement of highly stressed columns has
o
carry
about 15
‘70
of the axial force. For concrete C30/37 and steel grade
500
the minimum reinforcement may be up to 0.6%.
The maximum amount of reinforcement is limited o
8 To,
even at lapped
joints 15.4.1.2.1 (3)1, which is slightly less than required in BS 81 10design.
The transverse reinforcement is similar inboth designs. However, EC2
reduces the spacing of links to 60 Yo on the top and at the bottom of the
column and at lapped joints L5.4.1.2.23.
Raft foundation
Scope
Part 1 of EC2 gives a general basis of the design of concrete structures
and provides general rules applicable mainly to buildings. Further parts
to be developed in the future will complement or adapt it for particular
aspects 1 l .31, one of which is
At present, however, EC2: Par t 1 covers punching shear in foundations
14.3.4.11, and these rules were applied. This was the only aspect of the
foundat ion design considered in the exercise.
The bending moments and the soil pressure were analysedby computer
for the BS 81 10 design. he EC2/BS81 10 omparison of the shear resistance
was based on the tensile reinforcement and forces as calculated in the
BS 81 10 design.
Part 3: ‘Concrete foundations and piling’.
Punching
Punching was checked for a column load of
V
= 5095 kN applied to the
600mm-thick raft, reinforced at the bottom in both directions by 432
Q250 mm. This force may be reduced byA
V
to allow for the soil reaction
of 171 kN/m2 within the critical perimeter f4.3.4.1 (5)l. The result
V,,,,
s
given in Table 10.
EC2 design BS
81 10 design
Location
C30/37,
fyk =
500N/mm2 C35,
f =
460 N/mm2
h x b
As
le
S
h
(mm)
(mm2)
kNm)kN)mm2)
kNm)kN)
-
Interior E7
gr flr
5400 143 7164.0
420*)
004
17
00
x 6
grflr
5760
75 6378.4
160*)
251
23
00
x
600
Perimeter E5
gr flr
3890 166515
2950 9.8
58 32755
62
x
874
NOTE:
*) min. reinforcement
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TABLE I O aft foundation: punching shear
Soil
(kN)
Shear resistance
(kW
(N/mm2) I (kN)
reinforcement
einforcement
V
d
Tensile
reinf.
reaction
max. with
ithout
,,
(mm)
Vo)
m)
EC2 design
‘Rd2
1.5d from column face
4323 3088
.47 3969
126 0.45 9.16 718
ncreased depth
2813 2009
.53 4390
05 0.62 7.28
18
BS 81 10 design
face of column
c ud
,
1 t perimeter
1 5d
from column face
518
5884
680
.60
302
93
.62 8.62
2nd perimeter
3646
.60626 1469 0.62 11.72
18
As described earlier for flat slabs, EC2 stipulates the perimeter with
rounded corners which allows less for the soil reaction and is shorter. In
addition, the basic shear given by EC2 is less for all but low percentages
of tensile reinforcement. Thus the concrete shearesistance is reduced by
about 25
Yo.
The main difference oncerns the maximum shear resistance with shear
reinforcement which is limited by EC2 i4.3.4.5.2 (l )]
to
= .4 ‘Rd
V =
2813 kN compared with
V,,, =
4390 kN in Table 10 for the EC2
design means that the thickness of the raft foundationhas to be increased
regardless of the amount of shear reinforcement. As shown in the last
column of Table 10, the maximum shear resistance given by BS 8110 at
the face of the column is more than twice the value given by EC2.
By an increase of thickness of 200 mm this severe requirement was met
in the EC2 design, though shear reinforcement was still required
-
ee
Table 10:
V,, > V .
However, the given tensile reinforcement now being
reduced to less than
p =
0.5 Vo does not any longer meet the requirement
of EC2 14.3.4.1 (9)l concerning punching, although there s an advantage
concerning bending. The question o be asked is whether the minimum of
0.5 9’0 tensile reinforcement is required for thick slabs like raft foundations
as well as for comparatively shallow floorslabs. The German Code,DIN
10459, for instance, makes this allowance for foundations to encourage
the designer to provide the shear capacity more by the thickness of concrete
than by shear reinforcement.
Conclusions
(1) At present several parts of the Eurocodes are still at a draft stage of
development. Therefore, reference to the relevant national Codes is
necessary to get all the information needed to complete a design.
(2) Because of its wide scope only parts of EC2 Par t
l
are required for
typical buildings. Once knowledge and familiaritywith the layoutof EC2
is gained, it wasound not to
be
too complicated for the design of ‘everyday’
structures. However, it took considerable time to learn the implications
of EC2 and to cope with the cross-references.
(3) A manualon the use ofEC2 for the design of ypical concrete buildings
comparable to the IStructE manual for the design of reinforced concrete
building struc tures” would assist ngineers to gain the necessary
knowledge more quickly. In addition, the publication of typical designs
to the new EC2 would greatly facilitate therocess and assist the build-up
of confidence.
4)
The basic analysis of EC2 does not distinguish between beams, ribbed
slabs, and flat labs. Depending on redistribution,which is more restrictive
in theEC2 design, the mgments calculated by linear analysis may be both
higher and lower than those based on BS 81 10.
( 5 )
The results concerninghe tensile reinforcement
can
hardly
be
generalised
except for the considerable reduction ver supports in theEC2 design for
beams and slabs cast monolithically into their supports.
(6) EC2 generally gives lower basic values for shear resistance but the
minimum shear reinforcement required will easily satisfy many cases.
(7) EC2 requires substantialchanges of design practice for flat slabs both
concerning the minimum tensile reinforcement and the shear capacity. EC2
may require an increased depth for hallow flat slabs and raft foundations.
(8)
The EC2 design was based on reinforcement with a yield stress of
500 N/mm2. The results cannot therefore be compared directly with the
BS
8110 design. The higher steel stresses result in higher deflections.
236
Generally, the span/depth ratios given in EC2 are similar to the BS 8110
values, but lightly reinforced members, such as ribbed or solid slabs, may
have to have an increase of depth.
(9) EC2 provides simple ruleso control cracking without urther calculation.
Generally, the EC2 design will require smaller maximum spacing of bars
for slabs.
(10) This paper refers to the final draf t of EC2, dated December 1989.
Alterations of some clauses in the ENV version may affect some findings
given in this paper.
Outlook
Many of the factors ha t affect the design of a building are traditional or
related to the different means provided locally in eachountry. For example,
in comparison to practice in the United Kingdom, mesh reinforcement is
common inGermany, where the steel manufacturers provide standard mesh
or curtailed mesh for slabs and mesh cages as links or beams and columns.
By means of partially prefabricated elements for slabs and beams German
consultants and contractors reduce formwork and expedite the construction
of
concrete buildings. The floors are completed with
in situ
concrete to
provide continuity and stiffness.
Standard details in design and simplified construction methods are means
to reduce costs and to assure quality. Although buildings will remain
individual products, many of their tructural elements could be tandardised.
Such standardisation is not a matter of Codes but one of he future
challenges for structural engineers in Europe. Albert Einstein expressed
it this way:
‘Everything should be made as simple as possible, but not simpler’.
Acknowledgements
The work described in the paper was carried out during the author’s
sabbatical with Andrews, Kent & Stone, London. The author would like
to thank Mr D.
W .
Lazenby, Dr J . B. Menzies and other Partners and staff
for assistance.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Eurocode EC2: ‘Design of concrete structures: Part 1 General rules
and rules for buildings’, revised final draft, December 1989
Somerville,
G:
‘The writing of Eurocode 2,
The Structural Engineer,
67 No. 11, 6 June, 1989, p216-218
Narayanan, R.
S.:
‘Comparison of design requirements in EC2 and
BS 8110’,
The StructuralEngineer, 7
No. 1 1,6 June, 1989, p218-227
CED1C:‘Comparative design Eurocodes
-
ational Codes: Eurocode
No. 2: Part 1: Design of concrete structures
-
eneral rules’, final
report, Part 1 Conclusions, revised draft, April 1990
BS81 10
Structuraluse of concrete,
London, British Standards
Institution, 1985
Eurocode EC1: ‘Basis of designnd actions on structures’,Task Group
document (1): draft: June 1990
BS
6399
Loading fo r buildings, Part : Code of practice for dead and
imposed loads,
London, British Standards Institution, 1984
CEBIFIP
Manual on bending and compression,
London,
Construction Press, 1982
DIN 1045:
Beton und Stahlbeton, Bemessung and Ausfuehrung,
uly
1988
Manual for the design of reinforced concrete building structures,
London, Institution
of
Structural Engineers, 1985
The
Structural
Engineer/Volume 70/No.
13
/ 7 July
1992