euro code flat_slabs
Post on 04-Apr-2018
219 Views
Preview:
TRANSCRIPT
-
7/30/2019 Euro Code Flat_slabs
1/17
HHOOWW TTOO DDEESSIIGGNN
CCOONNCCRREETTEESSTTRRUUCCTTUURREESS
Flat Slabs
-
7/30/2019 Euro Code Flat_slabs
2/17
I nst ruct ions fo r t he Members o f BI BM, CEMBUREAU, EFCA and ERMCO:
"All or part of the information contained herein may be used, translated and adapted at nationallevel with reference and credit to the original publication issued by the European ConcretePlatf orm" . (See guidelines)I t is t he responsibili t y of the Member s (nat ional associat ions) of BI BM, CEMBUREAU, EFCA andERMCO to tr anslate and/ or adapt t his publication w it hin th eir national framew ork, to publish it
under th eir own name and logo and to disseminate it t o their contacts at nati onal level. The logo ofth e European Concrete Platf orm cannot be used at national level.
I t is t he responsibili t y of the Member s (nat ional associat ions) of BI BM, CEMBUREAU, EFCA and
ERMCO to submit for authorisation th e national version of th e Concise Eurocode 2 and t he "How toleaflets" to t heir respective nati onal standardisation comm it tee responsible for t he Eurocodes.
Copyright: Name of national concrete platf orm or nat ional MemberAcknowledgements to the European Concrete Platform ASBL
To be adapted at nat ional level:
Copyright: Name of national concrete platform or National member, date
Acknow ledgement s to t he European Concrete Platfor m ASBL
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means,electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of (Name of national concrete platform or
National member).
Published by Name of national concrete platform or National memberEditor:
address
country
Layout & Printing by Name of national concrete platform or National member
All information in this document is deemed to be accurate by (Name of national concrete platform or National member)at the time of goinginto press. It is given in good faith.
Information on (Name of national concrete platform or National member)document does not create any liability for its Members. While the
goal is to keep this information timely and accurate, (Name of national concrete platform or National member)cannot guarantee either. Iferrors are brought to its attention, they will be corrected.
The opinions reflected in this document are those of the authors and (Name of national concrete platform or National member)cannot beheld liable for any view expressed therein.
All advice or information from (Name of national concrete platform or National member) is intended for those who will evaluate thesignificance and limitations of its contents and take responsibility for its use and application. No liability (including for negligence) for any lossresulting from such advice or information is accepted.
Readers should note that all (Name of national concrete platform or National member)publications are subject to revision from time to timeand therefore ensure that they are in possession of the latest version.
-
7/30/2019 Euro Code Flat_slabs
3/17
How to design concrete structures using Eurocode 2
7. Flat slabs
IntroductionThis should be redrafted as appropriate
in a country
Designing to Eurocode 2
This guide covers the analysis and design of concrete flat slabs to
Eurocode 21. Eurocode 2 does not contain the derived formulae or
specific guidance on determining moments and shear forces. This has
arisen because it has been European practice to give principles in the
codes and for the detailed application to be presented in other sources
such as textbooks.
The first guide in this series, How to design concrete structures using
Eurocode 2: Introduction to Eurocodes2
, provides an overview ofEurocodes including terminology.
Where NDPs occur in the text in this publication, recommended valuesin EN 1992 are used and highlighted in yellow. The UK values havebeen used for NDPs embedded in figures and charts and the relevantNDPs are scheduled separately to assist other users in adapting thefigures and charts.(derivations can be found at www.eurocode2.info). A
list of symbols related to flat slab design is given at the end of this guide.
Analysis
The following methods may be used: Equivalent frame method
Finite element analysis
Yield line analysis
Grillage analogy
The Eurocode gives further advice on the equivalent frame method in
Annex I. Once the bending moments and shear forces have been
determined, the following guidance can be used for the design of flat
slabs.
Design procedure
A procedure for carrying out the detailed design of flat slabs is shown in
Table 1. This assumes that the slab thickness has previously been
determined during conceptual design. More detailed advice on
determining design life, loading, material properties, methods of
analysis, minimum concrete cover for durability and bond, and control of
crack widths can be found in another guide in this series, How to designconcrete structures using Eurocode 2: Getting started
3.
-
7/30/2019 Euro Code Flat_slabs
4/17
Fire resistance
Eurocode 2, Part 12: Structural fire design4, gives a
choice of advanced, simplified or tabular methods for
determining the fire resistance. Using tables is the
fastest method for determining the minimum
dimensions and cover for flat slabs. There are,
however, some restrictions and if these apply furtherguidance can be obtained from specialist literature.
Rather than giving a minimum cover, the tabular
method is based on nominal axis distance, a. This is
the distance from the centre of the reinforcing bar to
the surface of the member.
It is a nominal (not minimum) dimension, so the
designer should ensure that a cnom + link + bar/2
The requirements for flat slabs are given in Table 2
Flexure
The design procedure for flexural design is given inFigure 1; this includes derived formulae based on the
simplified rectangular stress block from Eurocode 2.
Where appropriate Table 3 may be used to determine
bending moments for flat slabs.
-
7/30/2019 Euro Code Flat_slabs
5/17
Whichever method of analysis is used, Cl. 9.4.1 requires
the designer to concentrate the reinforcement over the
columns. Annex I of the Eurocode gives
recommendations for the equivalent frame method on
how to apportion the total bending moment across a bay
width into column and middle strips to comply with Cl.
9.4.1. Designers using grillage, finite element or yield
line methods may also choose to follow the advice in
Annex I to meet this requirement.
Eurocode 2 offers various methods for determining the
stress-strain relationship of concrete. For simplicity the
method presented here is the simplified rectangular
stress block (see Figure 2).
The Eurocode gives recommendations for the design of
concrete up to class C90/105. However, for concrete
strength greater than class C50/60, the stress block is
modified. It is important to note that concrete strength is
based on the cylinder strength and not the cube strength
(i.e. for class C28/35 the cylinder strength is 28 MPa,
whereas the cube strength is 35 MPa).
-
7/30/2019 Euro Code Flat_slabs
6/17
Deflection
Eurocode 2 has two alternative methods of designing for
deflection; either by limiting span-to-depth ratio or by
assessing the theoretical deflection using the
Expressions given in the Eurocode. The latter is dealtwith in detail in another guide in this series, How todesign concrete structures using Eurocode 2: Deflection
calculations5.
The span-to-depth ratios should ensure that deflection is
limited to span/250 and this is the procedure presented
in Figure 3. The span-to-depth ratios are
appropriate where the structure remains propped during
construction or until the concrete attains sufficient strength
to support the construction loads. It can generally be
assumed that early striking of formwork will not significantly
affect the deflection after installing the cladding and/or
partitions6.
Punching shear
The design value of the punching shear force, VEd, will
usually be the support reaction at the ultimate limit state.
Standard factors for edge and corner columns that allow
for moment transfer () are greater in Eurocode 2.
However,can be calculated directly from Expressions
(6.38) to (6.46) of the Eurocode to give more efficient
designs.
Corrected Fig 3 at end of file
-
7/30/2019 Euro Code Flat_slabs
7/17
In Eurocode 2 the maximum value of shear at the
column face depends on the concrete strength
used.
The control perimeters for rectangular columns in
Eurocode 2 have rounded corners.
Where shear reinforcement is required the
procedure in Eurocode 2 is simple; the point at
which no shear reinforcement is required can be
calculated directly and then used to determine theextent of the area over which shear reinforcement is
required.
It is assumed that the reinforcement will be in a
radial arrangement. However, the reinforcement
can be laid on a grid provided the spacing rules are
followed.
The procedure for determining the punching shear
requirements is shown in Figure 6.
As an alternative to using shear links, proprietary shear studrails may be used. Eurocode 2 (Figure 6.22) allows them tobe laid out in a radial or cruciform pattern and gives spacingrequirements for both. Other techniques are available forincreasing punching shear resistance and these arecovered in a best practice guide.
Figure 6Procedure for determining punching shear capacity
-
7/30/2019 Euro Code Flat_slabs
8/17
Rules for spacing and quantity ofreinforcement
Minimum area of reinforcement
The minimum area of longitudinal reinforcement in the main
direction is As,min = 0.26 fctmbtd/fyk but not less than0.0013bd(see Table 6).
The minimum area of a link leg for vertical punching shear
reinforcement is1.5Asw,min /(sr.st) 0.08(fck
)/fyk.
which can be rearranged asAsw,min (sr.st)/F
wheresr = the spacing of the links in the radial directionst = the spacing of the links in the tangential directionFcan be obtained from Table 10
Maximum area of reinforcement
Outside lap locations, the maximum area of tension or
compression reinforcement should not exceedAs,max = 0.4 Ac
Minimum spacing of reinforcementThe minimum spacing of bars should be the greater of:
1 x Bar diameter
Aggregate size plus 5 mm
20 mm
Maximum spacing of main reinforcementFor slabs less than 200 mm thick the following maximum
spacing rules apply:
For the principal reinforcement: 3h but not more than
400 mm
For the secondary reinforcement: 3.5h but not more
than 450 mm
3.68
4.50
4.97
5.28
5.58
6.02
6.72
7.38
8.00
Corrected Table 7 at end of file
-
7/30/2019 Euro Code Flat_slabs
9/17
The exception is in areas with concentrated loads or areas of
maximum moment where the following applies: For the principal reinforcement: 2hbut not more than
250 mm For the secondary reinforcement: 3hbut not more than
400 mm, where his the depth of the slab.
For slabs 200 mm thick or greater reference should be made
to Section 7.3.3 of the Eurocode orHow to design concretestructures using Eurocode 2: Getting started3.
Spacing of punching shear reinforcementWhere punching shear reinforcement is required the
following rules should be observed.
It should be provided between the face of the column
and kdinside the outer perimeter where shearreinforcement is no longer required. kis 1.5, unless the
perimeter at which reinforcement is no longer requiredis less than 3dfrom the face of the column. In this casethe reinforcement should be placed in the zone 0.3dto1.5dfrom the face of the column.
There should be at least two perimeters of shear links. The radial spacing of the links should not exceed 0.75d
(see Figure 9).
The tangential spacing of the links should not exceed1.5dwithin 2dof the column face.
The tangential spacing of the links should not exceed2dfor any other perimeter.
The distance between the face of the column and thenearest shear reinforcement should be less than 0.5d.
Note
-
7/30/2019 Euro Code Flat_slabs
10/17
References1 EN 199211, Eurocode 2: Design of concrete structures General rules and rules for buildings.2 NARAYANAN, R S & BROOKER, O. How to design concrete structures using Eurocode 2: Introduction to
Eurocodes. The Concrete Centre, 2005.3 BROOKER, O. How to design concrete structures using Eurocode 2: Getting started. The Concrete Centre, 2005.4 EN 199212, Eurocode 2: Design of concrete structures. General rules structural fire design.5 WEBSTER, R & BROOKER, O. How to design concrete structures using Eurocode 2: Deflection calculations. The
Concrete Centre, 2006.
6 PALLETT, P. Guide to flat slab formwork and falsework. Construct, 2003.
Additional references for precast construction1. EN 13224 - Ribbed floor elements2. EN 13747 - Floor plates for floor systems3. EN 15037-1 - Beam-and-block floor systems - Beams4. prEN 15037[-2 to -5] - Beam-and-block floor systems - Blocks5. EN 1168 - Hollow core slabs6. EN 13369-Common rules for precast concrete products
AcknowledgementsThis guide was originally published by BCA and The Concrete Centre in the UK. The authors of the original publication
were R MossBSc, PhD, DIC, CEng, MICE, MIStructE and O BrookerBEng, CEng, MICE, MIStructE
Europeanised versions of Concise EC2 and How To LeafletsConvention used in the text
1. Nationally determined parameters that occur in the text have been highlighted yellow
2. Text is highlighted in pink indicates that some action is required on the part of thecountry adapting the documents for its use
-
7/30/2019 Euro Code Flat_slabs
11/17
Tables & Charts: Word versions (corrected text highlighted in green)
T a b l e 1 F l a t sl a b d e s i gn p r o c e d u r e
Further guidanceStep TaskChapter in thispublication
Standard
1 Determine design life 2: Ge t t i n g st a r t e d NA to EN 1990
2 Assess actions on the slab 2: Ge t t i n g st a r t e d EN 1991 (10 parts) andNational Annexes
3 Determine which combinations ofactions apply
1: In t r o d uc t i o n t o E u r o c o d e s
NA to EN 1990
4 Determine loading arrangements 2: Ge t t i n g st a r t e d NA to EN 1992115 Assess durability requirements and
determine concrete strength2: Ge t t i n g st a r t e d
6 Check cover requirements forappropriate fire resistance period
2: G e t t i n g st a r t e d and Table 2
EN 199212: Section 5
7 Calculate min. cover for durability, fireand bond requirements
2: Ge t t i n g st a r t e d EN 199211 Cl 4.4.1
8 Analyse structure to obtain criticalmoments and shear forces
2: G e t t i n g st a r t e d and Table 3
EN 199211 Section 5
9 Design flexural reinforcement See Figure 1 EN 199211 Section 6.110 Check deflection See Figure 3 EN 199211 Section 7.4
11 Check punching shear capacity See Figure 6 EN 199211 Section 6.4
12 Check spacing of bars 2: Ge t t i n g st a r t e d EN 199211 Section 7.3
13Check resistance to moment transferfrom column to slab
EN 199211 Annex I 1.2(5)
N o t e NA = National Annex
T a b l e 2 : M i n i m u m d i m e n si o n s a n d a x i s d i s t a n c e s f o r r e i n f o r c e d c o nc r e t e sl a b s
Minimum dimensions (mm)Standard fire resistance
Slab thickness, hs Axis distance, aREI 60 180 15a
REI 90 200 25
REI 120 200 35
REI 240 200 50
Notes1 This table is taken from EN 199212 Table 5.9.2 The axis distance is to the outer layer of reinforcement3 The table is valid only if the detailing requirements (see note 4) are observed and, in the normal temperature
design, redistribution of bending moments does not exceed 15%.4 For fire resistance of R90 and above, at least 20% of the total top reinforcement in each direction over
intermediate supports required by EN 199211 should be continuous over the full span. This reinforcement
should be placed in the column strip.
5 There are three standard fire exposure conditions that may need to be satisfied:
R Mechanical resistance for load bearing
E Integrity of separation
I InsulationKeya Normally the requirements of EN 199211 will determine the cover
-
7/30/2019 Euro Code Flat_slabs
12/17
F i g u r e 1 P r o c e d u r e f o r d e t e r m i n i n g f l e x u r a l r e i n f o r c e m e n t ( a s s u m i n g t h e r e c o m m e n d e d e x p r e s s i o n f o r , cc
( = 1 . 0 ) a n d c ( = 1 . 5 )
Determine K from Table 4 or 214.0137.0547.0'2 = K where
Is K K ?
Compression reinforcementrequired not recommended
for typical slabs
No compression reinforcement required
Yes
No
Obtain lever arm z from Table 5 or
[ ] dKdz 95.00.3112
+=
Calculate tension reinforcement required from
A s= M/fyd.z
Check minimum reinforcement requirements(see Table 6)
A s,min = 0.26 fctmbt d/fyk where fck 25
Check maximum reinforcement requirements A s,max = 0.04 Ac for
tension or compression reinforcement outside lap locations
Concrete class
C50/60? Outside scope of this publication
Yes
No
START
Determine K from:ckfbd
M
K 2=
Carry out analysis of slab todetermine design moments
(M) (Where appropriate usecoefficients from Table 3)
Arranged with horizontaldividing line in final printedcopy (x2)
-
7/30/2019 Euro Code Flat_slabs
13/17
T a b l e 3 Be n d i n g m o m e n t c o e f f i c i e n t s f o r f l a t s l a b s ( Su b st i t u t e d a t a c o m m o n l y u se d i n t h e c o u nt r y )
End support/slab connectionPinned ContinuousEndsupport
End span Endsupport
End span
Firstinteriorsupport
Interiorspans
Interiorsupports
Moment 0 0.086Fl 0.04Fl 0.075Fl 0.086Fl 0.063Fl 0.063Fl
Notes1 Applicable to slabs where the area of each bay exceds 30 m2,
Qk 1.25 Gk and qk 5 kN/m22 F is the total design ultimate load, l is the effective span3 Minimum span > 0.85 longest span, minimum 3 spans4 Based on 20% redistribution at supports and no decrease in span moments
T a b l e 4 V a l u e s f o r K (a ssu m i n g t h e r e c o m m e n d e d e x p r e ssi o n f o r a n d t h e r e c o m m e n d e d v al u e f o r c)
% redistribution (redistribution ratio) K
0 1.00 0.196a10 0.90 0.182a
15 0.85 0.16820 0.80 0.153
25 0.75 0.13730 0.70 0.102Keya It is often recommended that K should be limited to 0.168 to ensure ductile failure
T a b l e 5 z/d f o r s in g l y r e i n f o r c e d r e c t a n g u l a r s e ct i o n s ( a s s u m i n g t h e r e c o m m e n d e d v a l u e f o r c)
K z/d K z/d
0.07 0.944 0.15 0.871
0.08 0.936 0.16 0.861
0.09 0.927 0.17 0.85
0.10 0.918 0.18 0.839
0.11 0.909 0.19 0.828
0.12 0.900 0.196 0.821
0.13 0.891
0.14 0.881
T a b l e 6 Mi n i m u m p e r c e n t a g e o f r e i n f o r c e m e n t r e q u i r e d
fck fctm Minimum % (0.26fctm/fyka)
25 2.6 0.13%
28 2.8 0.14%
30 2.9 0.15%32 3.0 0.16%35 3.2 0.17%40 3.5 0.18%
45 3.8 0.20%50 4.1 0.21%
Keya Where fyk = 500 MPa
-
7/30/2019 Euro Code Flat_slabs
14/17
F i g u r e 3 P r o c e d u r e f o r a s se s si n g d e f l e c t i o n
The Eurocode is ambiguous regarding linear interpolation. It is understood that this was the intention of the drafting committee.
Is basic l/d F1 F2 F3 Actual l/d?
Determine Factor 1 (F1)For ribbed or waffle slabs
F1 = 1.1 0.1 ((bf/bw) 1) 0.8
(bf is flange breadth and bw is rib breadth)
Otherwise F1 = 1
Yes
Increase
A s,prov
Determine Factor 3 (F3)
F3 = 310/s
Where s = Stress in reinforcement at serviceabilitylimit state (see Figure 5)
s can be assumed to be 310 MPa (i.e. F3 = 1.0)
Check complete
Determine basic l/d from Figure 4
Determine Factor 2 (F2)Where the slab span exceeds 8.5 m and it supports
brittle partitions, F2 = 8.5/leffOtherwise F2 = 1.0
START
No
-
7/30/2019 Euro Code Flat_slabs
15/17
F i g ur e 6 P r o c e d u r e f o r d e t e r m i n i n g p u n ch i n g sh e a r c a p a c i t y
Determine concrete punching shear capacity (without shearreinforcement), vRd,c from Table 8where l = ( ly lz)
0.5
( ly lz are the reinforcement ratios in two orthogonal directions forfully bondedtension steel, taken over a width equal to column width
plus 3d each side)
Punching shearreinforcement not
required
Determine value of factor (refer to Figure 7 or Expressions (6.38) to
(6.46) of the Euroode)
Is vEd,max < vRd,max? Redesign slab
No
Yes
Is vEd > vRd,c?
No
Yes
START
Determine value ofvEd, (design shear stress) from:vEd,max = VEd/(u1deff)
where u1 is length of control perimeter(see Figure 8)
Determine value ofvRd,max from Table 7
Determine value ofvEd,max (design shear stress at face of column) from:vEd,max = VEd/(uideff)where: ui is perimeter of column
deff= (dy + dz)/2 (dy and dz are the effective depths in orthogonal directions)
Determine area of punching shear reinforcement per perimeter from:A sw = (vEd 0.75vRd,c)sru1/(1.5 fywd,ef)where sr is the radial spacing of shear reinforcement (see Figure 9)
fywd,ef= 250 + 0.25 defffywd (see Table 9)
Determine the length of the outer perimeter where shearreinforcement not required from:
uout,ef= VEd/(vRd,cd)
Determine layout of punching shear reinforcement (see Spacing of
punching shear reinforcement section and Figure 9)
Greek beta
-
7/30/2019 Euro Code Flat_slabs
16/17
T a b l e 7 V a l u e s f o r vR d , m a x a ssu m i n g t h e r e c o m m e n d e d v a l u e s f o r , cc a n d c)
fck vRd,max
20 3.68
25 4.50
28 4.97
30 5.28
32 5.58
35 6.0240 6.72
45 7.38
50 8.00
T a b l e 8 vR d , c r e si s t a n c e o f m e m b e r s w i t h o u t s h ea r r e i n f o r c e m e n t , M P a
Effective depth, d (mm)I
200 225 250 275 300 350 400 450 500 600 750
0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.43 0.41 0.40 0.38 0.36
0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.45
0.75% 0.68 0.66 0.64 0.63 0.62 0.59 0.58 0.56 0.55 0.53 0.511.00% 0.75 0.72 0.71 0.69 0.68 0.65 0.64 0.62 0.61 0.59 0.57
1.25% 0.80 0.78 0.76 0.74 0.73 0.71 0.69 0.67 0.66 0.63 0.61
1.50% 0.85 0.83 0.81 0.79 0.78 0.75 0.73 0.71 0.70 0.67 0.65
1.75% 0.90 0.87 0.85 0.83 0.82 0.79 0.77 0.75 0.73 0.71 0.68
2.00% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71
k 2.000 1.943 1.894 1.853 1.816 1.756 1.707 1.667 1.632 1.577 1.516Notes
1 Table derived from: vRd,c = (0.18/c) k (100 Ifck)1/3 0.035 k1.5fck
0.5 where
k = 1 + (200/d) 2 and I = ( ly lz) 0.02, ly = A sy/(b d) and lz = A sz/(b d) and c =1.52 This table has been prepared for fck = 30;Where I exceeds 0.40% the following factors may be used:
fck 25 28 32 35 40 45 50
Factor 0.94 0.98 1.02 1.05 1.10 1.14 1.19
T a b l e 9 V a l u e s f o r fy w d , e f
deff fywd,ef
150 288
175 294
200 300
225 306
250 313
275 319300 325
325 331
350 338
Greek rho
-
7/30/2019 Euro Code Flat_slabs
17/17
T a b l e 1 0 Fa c t o r , F, f o r d e t e r m i n i n g As w , m i n
fck Factor, F
25 1875
28 1772
30 1712
32 1657
35 158540 1482
45 1398
50 1326
Notefck has been taken as 500 MPa
Se l e c t e d s y m b o l s
Symbol Definition Value
A c Cross sectional area of concrete b hA s Area of tension steel
A s2 Area of compression steel
A s, prov Area of tension steel provided
A s, reqd Area of tension steel required
b Width of slab
d Effective depth
d2 Effective depth to compression reinforcement
fcd Design value of concrete compressive strength cc fck/c
fck Characteristic cylinder strength of concrete
fctm Mean value of axial tensile strength 0.30 fck2/3 for fck C50/60 (fromTable 3.1, Eurocode 2)
hs Slab thickness
K Factor to take account of the differentstructural systems
See NA
leff Effective span of member See Section 5.3.2.2 (1)
l/d Limiting span-to-depth ratio
M Design moment at the ULS
x Depth to neutral axis (d z)/0.4
xmax Limiting value for depth to neutral axis 0.8( 0.44)d where 1.0
z Lever armcc Coefficient taking account of long term effects
on compressive strength and of unfavourableeffects resulting from the way load is applied
1.0
Ratio of the redistributed moment to the elasticbending moment
m Partial factor for material properties 1.15 for reinforcement (s)
1.5 for concrete (c)
0 Reference reinforcement ratio fck/1000
Required tension reinforcement at mid-span toresist the moment due to the design loads (or atsupport for cantilevers)
A s/b d
Required compression reinforcement at mid-span to resist the moment due to the designloads (or at support for cantilevers)
A s2/b d
top related