How to Design Concrete Ltructures using Eurocode 2

Transkript

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A J Bond F:FL\=B<Ia=FB<><>g`
O Brooker ;>g`<>g`FB<>FBLmkn\m>
A S Fraser ;>gÌa=<>g`FB<>FBLmkn\m>
A J Harris ;L\FL\=B<FB<><>g`?@L
T Harrison ;L\Ia=<>g`FB<>?B<M
A E K Jones ;>gÌa=<>g`?B<>
R M Moss;L\Ia==B<<>g`FB<>FBLmkn\m>
R S Narayanan?K>g`
R Webster<>g`?BLmkn\m>
Foreword
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Acknowledgements
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Published by The Concrete Centre
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1.
Introduction to Eurocodes
*
2.
Getting started
2
3.
Slabs
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4.
Beams
+.
5.
Columns
,,
6.
Foundations
-,
7.
Flat slabs
.*
8.
Deflection calculations
.2
9.
Retaining walls
/0
10. Detailing
02
11. BS 8500 for building structures
2*
12. Structural fire design
22
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9 54/,3/53,1K,
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6K!
56A 5KK25! K )
#
%3 "**> ;>%#- *
*
! :
10
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54/,3/53,1K,
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11
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5KK25!
K
)
#
%3
"**> ;>&#- *
*
! '
12 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾+%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'Lmkn\mnkZeËk^]^lb`g';LB%+))-'
54/,3/53,1K,
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13
;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3@^mmbg`lmZkm^]!M<<(),(*0"'Ma^<hg\k^m^<^gmk^%+)).'
54/,3/53,1K,
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:
15 !
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16
54/,3/53,1K,
& !
- ! %&
;LB%+))/'
54/,3/53,1K,
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& - "#
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/
=5!
5A
5KK25!
K
)
#
%3
"**> ;>#- *
*
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17 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*220%>nkh\h]^03@^hm^\agb\Ze]^lb`g';LB!+iZkml"'
. 54/,3/53,1K,
,%%! - ":#
18
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0
19
20
54/,3/53,1K,
' !"#$%&' (4 "#
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4/55K,!
/A
5KK25!
K
)
*+&&*((&"**>
;># *
*
! '
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54/,3/53,1K,
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21
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22
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, 5 - ! 54/,3/53,1K,
'
23
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54/,3/53,1K,
,;:& #,
2(3 - ! 24
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4*K,*5K*G *' $
!
4 $! <
25 MA><HG<K>M>LHMR'<L*.+3GZmbhgZelmkn\mnkZe\hg\k^m^li^\bË\Zmbhg_hk[nbe]bg`\hglmkn\mbhg%mabk]^]bmbhg'Ma^Lh\b^mr%+))-'
8
!BJGB78F<:A6BA6E8G8FGEH6GHE8FHF<A:HEB6B78
8GG<A:FG4EG87
O Brooker A: A: %" %"*GEH6G
The design process
+;<F6;4CG8E<F<AG8A787GB4FF<FGG;878F<:A8E78G8E@<A84??G;878F<:A
<A9BE@4G<BAE8DH<E87CE<BEGB8@54E><A:BA78G4<?878?8@8AG78F<:A
"G
6BI8EF78F<:A?<98 46G<BAFBAFGEH6GHE8F ?B474EE4A:8@8AGF 6B@5<A4G<BAF
B946G<BAF @8G;B7B94A4?LF<F @4G8E<4?CEBC8EG<8F FG45<?<GL4A7
<@C8E986G<BAF @<A<@H@6BA6E8G86BI8E4A7@4K<@H@6E46>J<7G;F
+;8CEB68FFB978F<:A<A:8?8@8AGFJ<??ABG58E8IB?HG<BA<F874F4E8FH?G
B9HF<A:HEB6B781 4?G;BH:;@H6;B9G;878G4<?@4L6;4A:8Q4F
78F6E<587<AFH5F8DH8AG6;4CG8EF
*<@<?4E?L G;8CEB68FFB978G4<?<A:J<??ABGI4ELF<:A<9<64AG?L9EB@6HEE8AG
CE46G<68
H<74A6864A589BHA7<A;4CG8EBE<A/*!-!)"/%+!+#
!"/&(&*$ 2
.<G;E8:4E7GBFC86<9<64G<BA 47I<6864A589BHA7<A;4CG8E
BE<:<A4??LCH5?<F;874F*/-+!0 /&+*/+0-+ +!".3
BA68CG78F<:AF
CE8C4E874FFH@<A:G;4G78G4<?8778F<:AJBH?758GB*@4L58
6BAG<AH87G;EBH:;GB78G4<?8778F<:AHF<A:HEB6B78
"AG;8?BA:G8E@<G<F4AG<6<C4G87G;4GHEB6B78J<???847GB@BE8
86BAB@<6FGEH6GHE8F
Design life
+;878F<:A?<989BE4FGEH6GHE8<F:<I8A<AHEB6B78 .&.+#./-0 /0-(
!".&$* 4
+;8,#&4G<BA4?AA8K&GBHEB6B78CE8F8AGF,#I4?H8F
9BE78F<:A?<98 G;8F84E8:<I8A<A+45?8BI8E?849
+;8F8F;BH?758HF87
GB78G8E@<A8G;87HE45<?<GLE8DH<E8@8AGF9BEG;878F<:AB9E8<A9BE687
6BA6E8G8FGEH6GHE8F
Actions on structures
HEB6B78 /&+*.+*./-0 /0-".5 6BAF<FGFB9C4EGF:<I<A:78G4<?FB9
4J<78I4E<8GLB946G<BAF
HEG;8E<A9BE@4G<BABAG;8<A7<I<7H4?6B78F
64A589BHA7<A;4CG8E
HEB6B78 (4EGQ "*"-( /&+*.5
"*.&/&".."(#2"&$%/&),+."!(+!.#+-0&(!&*$.6 :<I8FG;878AF<G<8F4A7
F8?9J8<:;GFB95H<?7<A:@4G8E<4?FF88+45?8BI8E?849
+;8>8L6;4A:8GB6HEE8AGCE46G<68<FG;4GG;85H?>78AF<GLB9E8<A9BE687
6BA6E8G8;4F588A<A6E84F87GB>&@3
+;87E49G&4G<BA4?AA8KGB
G;<FHEB6B78:<I8FG;8<@CBF87?B47F9BE,#5H<?7<A:F4A74F8?86G<BA<F
Table 1
Indicative design working life (from UK National Annex to Eurocode)
Design life (years)
Examples
+8@CBE4ELFGEH6GHE8F
Q
)8C?46845?8FGEH6GHE4?C4EGF
Q
:E<6H?GHE4?4A7F<@<?4EFGEH6GHE8F
H<?7<A:F4A7BG;8E6B@@BAFGEH6GHE8F
%BAH@8AG4?5H<?7<A:F 5E<7:8F4A7BG;8E6<I<?
8A:<A88E<A:FGEH6GHE8F
Table 2
Selected bulk density of materials (from Eurocode 1, Part 1–1)
Material
Bulk density (kN/m3)
&BE@4?J8<:;G6BA6E8G8
)8<A9BE687ABE@4?J8<:;G6BA6E8G8
.8GABE@4?J8<:;GE8<A9BE6876BA6E8G8
E8CEB7H687<A+45?8
"GF;BH?758ABG87G;4GG;8E8<FAB47I<68:<I8A
9BEC?4AGEBB@F
GG;8G<@8B9JE<G<A:ABG4??G;8C4EGFB9HEB6B784A7G;8<E&4G<BA4?
AA8K8F4E84I4<?45?8 <G<F47I<F87G;4G8K<FG<A:FG4A74E7F4E86BAF<78E87
9BEHF8J;8E8HEBC84AFG4A74E7F;4I8ABGL8G588A<FFH87
Load arrangements
+;8G8E@?B474EE4A:8@8AGFE898EFGBG;84EE4A:<A:B9I4E<45?846G<BAF
8
:
<@CBF874A7J<A7?B47FGB:<I8G;8@BFGBA8EBHF9BE68F<A4
@8@58EBEFGEH6GHE84A74E8:<I8A<AHEB6B784A7<GF,#&
BE5H<?7<A:FGEH6GHE8F G;8,#&GBHEB6B78 (4EGQ4??BJF4AL
B9G;89B??BJ<A:F8GFB9?B474EE4A:8@8AGFGB58HF879BE5BG;G;8
H?G<@4G8?<@<GFG4G84A7F8EI<6845<?<GL?<@<GFG4G8
Figure 1
Alternate spans loaded
Load set 1. Alternate or adjacent spans loaded
+;878F<:AI4?H8FF;BH?758B5G4<A879EB@G;8@BE86E<G<64?B9
?G8EA4G8FC4AF64EEL<A:G;878F<:AI4E<45?84A7C8E@4A8AG?B47F
J<G;BG;8EFC4AF?B4787J<G; BA?LG;878F<:AC8E@4A8AG?B47F88
<:HE8
+;8I4?H8B9 g F;BH?758G;8F4@8G;EBH:;BHG
ALGJB47=468AGFC4AF64EEL<A:G;878F<:AI4E<45?84A7
C8E@4A8AG?B47FJ<G;BG;8EFC4AF?B4787J<G;BA?LG;878F<:A
C8E@4A8AG?B47F88<:HE8
+;8I4?H8B9 g F;BH?758G;8
F4@8G;EBH:;BHG
Load set 2. All or alternate spans loaded
Figure 2
Adjacent spans loaded
+;878F<:AI4?H8FF;BH?758B5G4<A879EB@G;8@BE86E<G<64?B9
??FC4AF64EEL<A:G;878F<:AI4E<45?84A7C8E@4A8AG?B47F
F88<:HE8
?G8EA4G8FC4AF64EEL<A:G;878F<:AI4E<45?84A7C8E@4A8AG?B47F
J<G;BG;8EFC4AF?B4787J<G;BA?LG;878F<:AC8E@4A8AG?B47F88
<:HE8
+;8I4?H8B9g F;BH?758G;8F4@8G;EBH:;BHG
8A8E4??L ?B47F8GJ<??58HF879BE584@F4A7F?45F<AG;8,#4F<G
E8DH<E8FG;E88?B474EE4A:8@8AGFGB586BAF<78E87 J;<?8?B47F8G
J<??B9G8AE8DH<E8@BE8G;4AG;E884EE4A:8@8AGFGB584FF8FF87
?G8EA4G<I8?L G;8,#&@4>8FG;89B??BJ<A:CEBI<F<BA9BEF?45F
Load set 3. Simplified arrangements for slabs
Figure 3
All spans loaded
10
+;8?B474EE4A:8@8AGF64A58F<@C?<9<879BEF?45FJ;8E8<G<FBA?L
A868FF4ELGB6BAF<78EG;84??FC4AF?B47874EE4A:8@8AGF88<:HE8
CEBI<787G;89B??BJ<A:6BA7<G<BAF4E8@8G
"A4BA8J4LFC4AA<A:F?45G;84E84B9846;54L8K6887F@2
454L@84AF4FGE<C46EBFFG;89H??J<7G;B94FGEH6GHE85BHA787
BAG;8BG;8EF<78F5L?<A8FB9FHCCBEG
+;8E4G<BB9G;8I4E<45?846G<BAF>GBG;8C8E@4A8AG46G<BAF>
7B8FABG8K6887
+;8@4:A<GH78B9G;8I4E<45?846G<BAF8K6?H7<A:C4EG<G<BAF7B8FABG
8K6887>&@2
+'@^mmbg`lmZkm^]
Combination of actions
+;8G8E@6B@5<A4G<BAB946G<BAFE898EFGBG;8I4?H8B946G<BAFGB58
HF87J;8A4?<@<GFG4G8<FHA78EG;8<A9?H8A68B97<998E8AG46G<BAF
+;8AH@8E<64?I4?H8FB9G;8C4EG<4?946GBEF9BEG;8,$*6B@5<A4G<BA64A
58B5G4<A875LE898EE<A:GBHEB6B78 .&.+#./-0 /0-(!".&$*BEGB
;4CG8E
For members supporting one variable action the ULS combination
1.25 Gk + 1.5 Qk (derived from Exp. (6.10b), Eurocode)
can be used provided the permanent actions are not greater than
4.5 times the variable actions (except for storage loads).
+;8E84E8G;E88*$*6B@5<A4G<BAFB946G<BAFQ6;4E46G8E<FG<6 9E8DH8AG
4A7DH4F<C8E@4A8AG
+;8AH@8E<64?I4?H8F4E8:<I8A<AHEB6B78 .&.
+#./-0 /0-(!".&$*
Material properties
Concrete
"AHEB6B78G;878F<:AB9E8<A9BE6876BA6E8G8<F54F87BAG;8
6;4E46G8E<FG<66L?<A78EFGE8A:G;E4G;8EG;4A6H58FGE8A:G;4A7F;BH?7
58FC86<9<87466BE7<A:GB* +* -"/"5 +),(")"*/-4-&/&.%
/*!-!/+57 8
:
9BE6?4FF6BA6E8G8G;86L?<A78E
FGE8A:G;<F%(4 J;8E84FG;86H58FGE8A:G;<F%(4
+LC<64?
6BA6E8G8CEBC8EG<8F4E8:<I8A<A+45?8
BA6E8G8HCGB6?4FF64A5878F<:A87HF<A:HEB6B78
BE6?4FF8F45BI8 ;BJ8I8E G;8E84E8477<G<BA4?EH?8F4A7
I4E<4G<BAF
BEG;<FE84FBA G;878F<:AB9G;8F8;<:;8E6?4FF8F<FABG
6BAF<78E87<AG;<FCH5?<64G<BA
Reinforcing steel
Reinforcing steel
HEB6B7864A58HF87J<G;E8<A9BE68@8AGB96;4E46G8E<FG<6
HEB6B7864A58HF87J<G;E8<A9BE68@8AGB96;4E46G8E<FG<6
FGE8A:G;FE4A:<A:9EB@GB%(4
+;8CEBC8EG<8FB9FG88?
FGE8A:G;FE4A:<A:9EB@GB%(4
+;8CEBC8EG<8FB9FG88?
E8<A9BE68@8AG<AG;8,#9BEHF8J<G;HEB6B784E8:<I8A<A
E8<A9BE68@8AG<AG;8,#9BEHF8J<G;HEB6B784E8:<I8A<A
*
," &#& /&+*#+- -+*./""(-.#+-/%"
8 4A74E8FH@@4E<F87<A+45?8BAC4:8
*
&#& /&+*#+-
-+*./""(-.#+-/%"
-"&*#+")"*/+# ,"
+* -"/"
8
-"&*#+- ")"*/+# +* -"/" 4A74E8FH@@4E<F87<A+45?8BAC4:8
6;4E46G8E<FG<6L<8?7FGE8A:G;B9%(4;4F588A47BCG875LG;8
6;4E46G8E<FG<6L<8?7FGE8A:G;B9%(4;4F588A47BCG875LG;8
,#E8<A9BE68@8AG<A7HFGEL
,#E8<A9BE68@8AG<A7HFGEL
+;8E84E8G;E886?4FF8FB9E8<A9BE68@8AG 4A7 J;<6;CEBI<78
+;8E84E8G;E886?4FF8FB9E8<A9BE68@8AG
4A7 J;<6;CEBI<78
<A6E84F<A:7H6G<?<GL
?4FF<FABGFH<G45?8J;8E8E87<FGE<5HG<BAB9
<A6E84F<A:7H6G<?<GL
?4FF<FABGFH<G45?8J;8E8E87<FGE<5HG<BAB9
4A745BI8;4F588A4FFH@87<AG;878F<:A
+;8E8<FAB
4A745BI8;4F588A4FFH@87<AG;878F<:A
+;8E8<FAB 5HG
CEBI<F<BA9BEG;8HF8B9C?4<A54EBE@<?7FG88?E8<A9BE68@8AG
CEBI<F<BA9BEG;8HF8B9C?4<A54EBE@<?7FG88?E8<A9BE68@8AG 5HG9
:H<74A68<F:<I8A<AG;8546>:EBHA7C4C8EGBG;8&4G<BA4?AA8K
:H<74A68<F:<I8A<AG;8546>:EBHA7C4C8EGBG;8&4G<BA4?AA8K9
Table 3
Selected imposed loads for buildings (from draft UK National Annex to Eurocode 1, Part 1–1)
Category
Example use
qk (kN/m2)
??HF8FJ<G;<AF8?96BAG4<A877J8??<A:HA<GF
87EBB@F4A77BE@<GBE<8F
87EBB@F<A;BG8?F4A7@BG8?F ;BFC<G4?J4E7F4A7GB<?8GF
4?6BA<8F<AF<A:?894@<?L7J8??<A:HA<GF
4?6BA<8F<A;BG8?F4A7@BG8?F
@<A
4GBHG8E87:8
'99<68F9BE:8A8E4?HF8
FF8@5?L4E84J<G;BHG9<K87F84G<A: 6BA68EG;4??F 54EF C?468FB9JBEF;<C
*;BCC<A:4E84F
8A8E4?FGBE4:8
8AF8@B5<?8FG46><A:<AJ4E8;BHF8F
Qk (kN)
C8E@;8<:;G
C8E@;8<:;G@<A
EBFFI8;<6?8J8<:;GO>&
Table 4
Selected concrete properties based on Table 3.1 of Eurocode 2, Part 1–1
Symbol
Description
Properties
#6> %(4
;4E46G8E<FG<66L?<A78EFGE8A:G;
4
4
#6>6H58 %(4
;4E46G8E<FG<66H58FGE8A:G;
#6@ %(4
%84A6L?<A78EFGE8A:G;
#6G@ %(4
%84AG8AF<?8FGE8A:G;
*864AG@B7H?HFB98?4FG<6<GL
5
6@ (4
Key
a BA6E8G86?4FFABG6<G87<A+45?8
HEB6B78 (4EGQ
b %84AF864AG@B7H?HFB98?4FG<6<GL4G74LF9BE6BA6E8G8J<G;DH4EGM<G84::E8:4G8F
BE6BA6E8G8FJ<G;BG;8E4::E8:4G8FE898EGB?
11
Table 5
Structural analysis
Characteristic tensile properties of reinforcement
Class (BS 4449) and designation (BS 8666)
A
B
C
;4E46G8E<FG<6L<8?7FGE8A:G;#L> BE# > %(4
%<A<@H@I4?H8B9' #G #L >
P
P
P
;4E46G8E<FG<6FGE4<A4G@4K<@H@9BE68 e H> P
P
P
Notes
1 +45?878E<I879EB@*&QQAA8K * 4A7*& 2 +;8AB@8A6?4GHE8HF87<A* 7<998EF9EB@G;4GHF87<A*&QQ
AA8K4A7HF87;8E8
3 "A466BE74A68J<G;* \eZllAfZr[^li^\bË^]%bgpab\a\Zl^\eZll:%;hk<
6?4FF!58FC86<9<87 <AJ;<6;64F86?4FF BE
*+ff%hma^kpbl^\eZll^l;hk<fnlm[^lniieb^]'
@4L58FHCC?<87J;8A54E7<4@8G8EO@@
BG;8EJ<F86?4FF8FBE@HFG58FHCC?<87
Table 6
Bending moment and shear co-efficients for beams
'HG8EFHCCBEG
Moment
Shear
B9FC4A@B@8AG
)'-.!@
]$J
]"
¾)')2-!@
$J
Q ]
]( "e
)'/,!@
$J
]
]4"Z
)')//@
e$)')1/J
(]
( ] e
G@<77?8B9<AG8E<BEFC4AF
G<AG8E<BEFHCCBEGF
¾)')0.!@
$J
Q ]
]("e
)'.)!@
$J
]
]"
Key
a )'..!@
]$J
@4L58HF8747=468AGGBG;8<AG8E<BEFC4A
]"fZr[^nl^]Z]cZ\^gmmhma^bgm^kbhkliZg
Notes
1 )87<FGE<5HG<BAB9FHCCBEG@B@8AGF5L;4F588A<A6?H787
2 CC?<645?8GBBE@BE8FC4AFBA?L4A7J;8E8> O >
3 %<A<@H@FC4AP
?BA:8FGFC4A
4 eblma^liZg%@
( <FG;889986G<I8?8A:G;
<FG;8GBG4?B9G;8,$*C8E@4A8AG46G<BAF <FG;8GBG4?
]blma^]^lb`goZen^h_i^kfZg^gmZ\mbhgl!ZmNEL"Zg]J
]blma^]^lb`g
B9G;8,$*I4E<45?846G<BAF
oZen^h_oZkbZ[e^Z\mbhgl!ZmNEL"'
Table 7
Exposure classes
Class
Description
No risk of corrosion or attack
/
+;8GLC8B94A4?LF<FF;BH?7584CCEBCE<4G8GBG;8CEB5?8@58<A:
6BAF<78E87
+;89B??BJ<A:@4L58HF87 ?<A84E8?4FG<64A4?LF<F ?<A84E
8?4FG<64A4?LF<FJ<G;?<@<G87E87<FGE<5HG<BA 4A7C?4FG<64A4?LF<F
$<A84E
8?4FG<64A4?LF<F@4L5864EE<87BHG4FFH@<A:6EBFFF86G<BAF4E8
HA6E46>87<
8
6BA6E8G8F86G<BACEBC8EG<8F HF<A:?<A84EFGE8FFFGE4<A
E8?4G<BAF;<CF 4A74FFH@<A:@84AI4?H8FB98?4FG<6@B7H?HF
)')2)@
e$)'*))J
(] ( ] e
&84E@<77?8B98A7FC4A
G9<EFG<AG8E<BEFHCCBEG
+;8CE<@4ELCHECBF8B9FGEH6GHE4?4A4?LF<F<A5H<?7<A:FGEH6GHE8F<FGB
8FG45?<F;G;87<FGE<5HG<BAB9<AG8EA4?9BE68F4A7@B@8AGFBI8EG;8
J;B?8BEC4EGB94FGEH6GHE84A7GB<78AG<9LG;86E<G<64?78F<:A
6BA7<G<BAF4G4??F86G<BAF
+;8:8B@8GEL<F6B@@BA?L<784?<F875L
6BAF<78E<A:G;8FGEH6GHE8GB58@478HCB9?<A84E8?8@8AGF4A7C?4A8
GJB7<@8AF<BA4?8?8@8AGF
BE6BA6E8G8J<G;BHGE8<A9BE68@8AGBE8@587787@8G4?J;8E8G;8E8
<FABF<:A<9<64AG9E88M8G;4J 45E4F<BABE6;8@<64?4GG46>
Corrosion induced by carbonation
/
ELBEC8E@4A8AG?LJ8G
/
.8G E4E8?L7EL
/
%B78E4G8;H@<7<GLBE6L6?<6J8G4A77EL
Corrosion induced by chlorides other than from seawater
/
%B78E4G8;H@<7<GL
/
.8G E4E8?L7EL
/
L6?<6J8G4A77EL
Corrosion induced by chlorides from seawater
/*
KCBF87GB4<E5BEA8F4?G5HGABG<A7<E86G6BAG46GJ<G;F84J4G8E
/*
(8E@4A8AG?LFH5@8E:87
/*
+<74? FC?4F;4A7FCE4LMBA8F
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4A4?LF<F@4L58E87<FGE<5HG87HCGB4@4K<@H@B9CEBI<787
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G;84CC?<87?B47F4A7FH5=86GGB68EG4<A?<@<GF4A778F<:A6E<G8E<48
:
?<@<G4G<BAFB978CG;GBA8HGE4?4K<F
)8:4E7?8FFB9G;8@8G;B7B94A4?LF<FHF87 G;89B??BJ<A:CE<A6<C?8F4CC?L
.;8E84584@BEF?45<F@BAB?<G;<6J<G;<GFFHCCBEGF G;86E<G<64?
78F<:A;B::<A:@B@8AG@4L58G4>8A4FG;4G4GG;89468B9G;8
FHCCBEG 5HGF;BH?7ABG58G4>8A4F?8FFG;4A
G<@8FG;89H??
9<K878A7@B@8AG
.;8E84584@BEF?45<F6BAG<AHBHFBI8E4FHCCBEGG;4G@4L58
6BAF<78E87ABGGBCEBI<78EBG4G<BA4?E8FGE4<AG G;8@B@8AG
64?6H?4G874GG;868AGE8?<A8B9G;8FHCCBEG@4L58E87H6875L
7FHC / J;8E87FHC <FG;8FHCCBEGE846G<BA4A7/ <FG;85E847G;
B9G;8FHCCBEG
BEG;878F<:AB96B?H@AFG;88?4FG<6@B@8AGF9EB@G;89E4@8
46G<BAF;BH?758HF87J<G;BHG4ALE87<FGE<5HG<BA
8A7<A:@B@8AG4A7F;84E9BE686B899<6<8AGF9BE584@F4E8:<I8A<A
+45?8 G;8F84E8FH<G45?8J;8E8FC4AF4E8B9F<@<?4E?8A:G;4A7G;8
BG;8EABG8FGBG;8G45?84E8B5F8EI87
Minimum concrete cover
+;8AB@<A4?6BI8E64A584FF8FF874F9B??BJF
@<A
D
Freeze/thaw with or without de-icing agents
.;8E8
@<A
F;BH?758F8GGBF4G<F9LG;8E8DH<E8@8AGF58?BJ
/
%B78E4G8J4G8EF4GHE4G<BAJ<G;BHG78<6<A:4:8AG
F498GE4AF@<FF<BAB95BA79BE68F
/
%B78E4G8J4G8EF4GHE4G<BAJ<G;78<6<A:4:8AG
/
!<:;J4G8EF4GHE4G<BAJ<G;BHG78<6<A:4:8AG
/
!<:;J4G8EF4GHE4G<BAJ<G;78<6<A:4:8AGBEF84J4G8E
Chemical attack (ACEC classes)
)898EGB*Q4A7*C86<4?<:8FG
12
AB@
78I
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7HE45<?<GL
9<E8E8F<FG4A68
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78I<4G<BAF9EB@G;8@<A<@H@6BI8E
"GF;BH?758G4>8A4F@@
HA?8FF945E<64G<BA<
8
6BAFGEH6G<BA<FFH5=86G87GB4DH4?<GL4FFHE4A68
FLFG8@ <AJ;<6;64F8<G<FC8E@<GG87GBE87H68D 78I GB@@
+'@^mmbg`lmZkm^]
Figure 4
Sections through structural members, showing nominal axis distance, a
4CC?<87G;EBH:;G;86B@C?8@8AG4ELFG4A74E7*
+;<F
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+2/+0."
2&/%
13
Design for fire resistance
Table 9
Minimum column dimensions and axis distances for columns with
rectangular or circular section – method A
Standard fire
resistance
Minimum dimensions (mm)
Column width ( bmin)/axis distance (a) of the main bars
Column exposed on more
than one side ( m f i = 0.7)
Exposed on one side
( m f i = 0.7)
)
)
)
N
Notes
1 )898EGB*&QQ9BE78F<:A?<@<G4G<BAF
2 m 9< <FG;8E4G<BB9G;878F<:A4K<4??B47HA78E9<E86BA7<G<BAFGBG;878F<:AE8F<FG4A68
B9G;86B?H@A4GABE@4?G8@C8E4GHE86BA7<G<BAF
BAF8EI4G<I8?Lm 9< @4L58G4>8A
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* %<A<@H@54EF
† %8G;B7<A7<64G8F9BE)4A7m 9< 4A7@4L58HF87
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5
Minimum cover for bond
+;8@<A<@H@6BI8EGB8AFHE8478DH4G85BA7F;BH?7ABG58?8FFG;4A
G;854E7<4@8G8E BE8DH<I4?8AG54E7<4@8G8E9BE5HA7?8754EF HA?8FF
G;84::E8:4G8F<M8<FBI8E@@
Minimum cover for durability
HEB6B78(4EGQ /-0 /0-(#&-"!".&$*14 :<I8FF8I8E4?@8G;B7F
9BE78G8E@<A<A:G;89<E8E8F<FG4A68B96BA6E8G88?8@8AGF 9HEG;8E
:H<74A6864A58B5G4<A879EB@FC86<4?<FG?<G8E4GHE8
8F<:A9BE
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4FF8GBHG58?BJ
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BAAB@<A4?4K<F7<FG4A68 F88<:HE8
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68AGE8B9G;8@4<AE8<A9BE6<A:54EGBG;8FHE9468B9G;8@8@58E
"G<F
4AB@<A4?ABG@<A<@H@7<@8AF<BA
+;878F<:A8EF;BH?78AFHE8G;4G
≥ AB@ f ?<A> f 54E
+;8E84E8G;E88FG4A74E79<E88KCBFHE86BA7<G<BAFG;4G@4L58F4G<F9<87
R %86;4A<64?E8F<FG4A689BE?B47584E<A:
E "AG8:E<GLB9F8C4E4G<BA
I "AFH?4G<BA
+45?8F4A7:<I8G;8@<A<@H@7<@8AF<BAF9BE6B?H@AF4A7F?45F
GB@88GG;845BI86BA7<G<BAF
+;8G45?8FB998E@BE89?8K<5<?<GLG;4A
*<AG;4GG;8E84E8BCG<BAF4I4<?45?8GBG;878F<:A8E8
:
F86G<BA
F<M8F64A58E87H6875L<A6E84F<A:G;84K<F7<FG4A68
HEG;8E<A9BE@4G<BA
<F:<I8A<AHEB6B784A7FH5F8DH8AG6;4CG8EF <A6?H7<A:78F<:A
?<@<G4G<BAF4A774G49BEJ4??F4A7584@F
+;8E86B@@8A74G<BAF9BE7HE45<?<GL<AHEB6B784E854F87BA
*&Q12
"AG;8,#G;8E8DH<E8@8AGFB9*&Q4E8
Table 10
Minimum dimensions and axis distances for reinforced concrete slabs
Standard
fire
resistance
)"
)"
)"
%F
%F
%F
One-way
Two-way spanning slab
spanning slab l y /l x ≤ 1.5
1.5 < l y /l x ≤ 2
Flat slab
Ribs in a two-way spanning ribbed slab
(bmin is the width of the rib)
@<A @<A @<A P
P
QQQ
Notes
1 )898EGB*&QQ9BE78F<:A?<@<G4G<BAF
2 <FG;84K<F7<FG4A68F88<:HE8
3 % F <FG;8F?45G;<6>A8FF <A6?H7<A:4ALABA6B@5HFG<5?89?BBE<A:
13
Table 8
Selected 4 recommendations for normal-weight reinforced concrete quality for combined exposure classes and cover to reinforcement for at least a 50year intended working life and 20 mm maximum aggregate size
Cement/
Strength classc, maximum w/c ratio, minimum cement or combination
combination
combination content (kg/m3), and equivalent designated concrete (where applicable)
designationsb
Exposure conditions
Typical example
Nominal cover to reinforcementd
Primary Secondary
15 + D c dev 20 + D c dev 25 + D c dev 30 + D c dev 35 + D c dev 40 + D c dev 45 + D c dev 50 + D c dev
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Key
a +;<FG45?86B@CE<F8F4F8?86G<BAB96B@@BA8KCBFHE86?4FF6B@5<A4G<BAF
)8DH<E8@8AGF9BEBG;8EF8GFB98KCBFHE86?4FF8F 8
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b *88*+45?8
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c BECE8FGE8FF876BA6E8G8G;8@<A<@H@FGE8A:G;6?4FFF;BH?758
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+'@^mmbg`lmZkm^]
Stability and imperfections
Crack control
+;889986GFB9:8B@8GE<6<@C8E986G<BAFF;BH?7586BAF<78E87<A
6B@5<A4G<BAJ<G;G;889986GFB9J<A7?B47F<
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9BE68<AG;85E46<A:FLFG8@
Figure 5
+;889986GB9G;8<A6?<A4G<BA@4L58E8CE8F8AG875LGE4AFI8EF89BE68F4G
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<:HE8
Examples of the effect of geometric imperfections
9986GBA5E46<A:FLFG8@
< y < 5 Q 4
9986GBA9?BBE7<4C;E4:@
< y < 5 4
9986GBAEBB97<4C;E4:@
< y < 4
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"A@BFG64F8F 4A4??BJ4A689BE<@C8E986G<BAF<F@478<AG;8C4EG<4?
946GBEFHF87<AG;878F<:AB98?8@8AGF
!BJ8I8E9BE6B?H@AF G;889986G
B9<@C8E986G<BAF J;<6;<FF<@<?4E<ACE<A6<C?8GBG;845BI8 @HFG58
6BAF<78E87F88;4CG8E BE<:<A4??LCH5?<F;874F +(0)*.15
a) Bracing system
b) Floor diaphragm
c) Roof diaphragm
Figure 6
Determination of steel stress for crack width control
Maximum bar size or spacing to limit crack width
wmax = 0.3 mm
Steel
wmax = 0.4 mm
stress
Maximum
Maximum
(s s)MPa bar
bar
size (mm)
spacing (mm)
Maximum
bar
size (mm)
OR OR Maximum
bar
spacing (mm)
Note
Approximate steel stress at SLS for As, req, ssu
Table 11
+;8FG88?FGE8FF@4L588FG<@4G879EB@G;88KCE8FF<BA58?BJBEF88<:HE8
sF #L> )FE8D
gF * FCEBI d
J;8E8
#L>
6;4E46G8E<FG<6E8<A9BE68@8AGL<8?7FGE8FF
gF
C4EG<4?946GBE9BEE8<A9BE6<A:FG88?
)
GBG4??B479EB@DH4F<C8E@4A8AG6B@5<A4G<BA
*
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FE8D 4E84B9E8<A9BE68@8AG4GG;8,$*
FCEBI 4E84B9E8<A9BE68@8AGCEBI<787
d
E4G<BB9E87<FGE<5HG87@B@8AGGB8?4FG<6@B@8AG
To determine stress in the reinforcement (ss), calculate the ratio Gk/Qk,
read up the graph to the appropriate curve and read across to determine ssu .
As,req
1
ss can be calculated from the expression: ss = ssu
As,prov d
(
)( )
15
+'@^mmbg`lmZkm^]
References
1 )"+"*!*+&)*"&*+"+,+"'&
*& HEB6B78 ".&$*+# +* -"/"./-0 /0-".
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3 &)0&& )*)''#) '
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+;8BA6E8G88AGE8 4 )"+"*!*+&)*"&*+"+,+"'&
*& HEB6B78 .&.+#./-0 /0-(!".&$*
*" 5 )"+"*!*+&)*"&*+"+,+"'&
*& HEB6B78 /&+*.+*./-0 /0-".
*"C4EGF
6 )"+"*!*+&)*"&*+"+,+"'&
*& HEB6B78 /&+*.+*./-0 /0-". -/5 "*"-( /&+*.5"*.&/&". ."(#2"&$%/ &),+."!(+!.
#+-0&(!&*$.
*" 7 )"+"*!*+&)*"&*+"+,+"'&
*Q +* -"/"5+),(")"*/-4-&/&.%/*!-!/+55-/ "/%+!+#.," &#4&*$*!
$0&!* "#+-/%".," &#&"-
*" 8 )"+"*!*+&)*"&*+"+,+"'&
* ," &#& /&+*#+- -+*./""(-.#+-/%"-"&*#+- ")"*/+# +* -"/" *" 9 )"+"*!*+&)*"&*+"+,+"'&
'$-+0*!,,"-/+/%"/&+*(**"3/+55 *" 10 )"+"*!*+&)*"&*+"+,+"'&
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1 N 2 L
Values for K ’
1<3E<1D5<5F5B1B= 6B?=
N P
1
1<3E<1D53?=@B5CC9?>
B59>6?B35=5>DB5AE9B546B?=
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1
HN4
H
2
I4
1<3E<1D5D5>C9?>
B59>6?B35=5>DB5AE9B546B?=
C Table 5
Table 6
z/d for singly reinforced rectangular sections
Minimum percentage of required reinforcement
z/d
I4 C
C3
I4
fck
fctm
Minimum percentage (0.26 fctm / fyka)
©)').
)' 2.)
+.
+'/
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+1
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.)
-'*
)'+*
Z
P z/d
)'1/1
K
)'*,
)'*+
C3N 853;=1H9=E=B59>6?B35=5>DB5AE9B5=5>DCC=1H 3
6?BD5>C9?>?B3?=@B5CC9?>B59>6?B35=5>D?EDC945<1@<?31D9?>C
Key
a Bmblh_m^gk^\hff^g]^]bgma^NDmaZmDÃlahne][êbfbm^]mh)'*/1mh^glnk^]n\mbe^_Zbenk^'
Bmblh_m^gk^\hf^g]^]bgma^NDmaZm D£lahne][êbfbm^]mh)'*/1mh^glnk^]n\mbe^_Zbenk^'
)'**
N P d (redistribution ratio) K ’
% redistribution
K
2
G85B5
1<3E<1D5D5>C9?>B59>6?B35=5>D
B5AE9B546B?=
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B5AE9B54
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5D5B=9>5P 6B?=*12<5?B
P d N
d N
G85B5d L
(0',0*/1/(06$0'5+($4&1()),&,(065)14%($/5
1/(06
Outside scope of this
publication
.5C
"$%.(
'GF7DEGBBADF
%?
Key
Key
a Ebfbmbg`s mh)'2.] blghmZk^jnbk^f^gmh_>nkh\h]^+% [nmbl\hglb]^k^]mh[^`hh]ikZ\mb\^'
a :llnfbg`_rd 6 .))FIZ
27
,*74(
GDA5A67A887DEH3D;AGE?7F:A6E8AD67F7D?;@;@9F:7EFD7EEEFD3;@
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BD7E7@F76:7D7;EF:7E;?B>;8;76D75F3@9G>3DEFD7EE4>A5= I:;5:;E
E;?;>3DFAF:3F8AG@6;@+E77;9GD7
!6476,0&.,0$6,10/(6+1'
?>3B5D5CDBED9>3?=@B5CC9?>
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5>3EE
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F:7
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;E43E76A@F:75K>;@67DEFD7@9F:3@6@AFF:75G47EFD7@9F:;7 8AD
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GDA5A67;@FDA6G57EF:7EFDGF;@5>;@3F;A@?7F:A68ADE:73D53B35;FK
5:75=E "@F:;E?7F:A6F:7E:73D;ED7E;EF764K5A@5D7F7EFDGFE35F;@9;@
5A?BD7EE;A@3@6E:73DD7;@8AD57?7@F35F;@9;@F7@E;A@
START
Determine vEd where
vEd = design shear stress [ vEd = VEd /(bwz) = VEd /(0 9. bwd)]
Determine the concrete strut capacity v Rd, max cot y = 2.5
from Table 7
Is
vEd < vRd,max coty = 2.5?
No
Is
v Ed < v Rd,max cot y = 1.0?
(see Table 7)
Yes
(cot y = 2.5)
No Redesign
section
Yes
Determine y from:
vEd
y = 0.5 sin -1
0.20 fck (1 – fck /250)
T
V
Calculate area of shear reinforcement:
vEd bw
Asw
=
s
fywd cot y
Check maximum spacing for vertical shear reinforcement:
s l, max = 0.75 d
,:73@9>7A8F:75A@5D7F7EFDGFH3D;7E 67B7@6;@9A@F:7E:73D8AD57
3BB>;76E77;9GD7 ,:7BDA576GD78AD67F7D?;@;@9F:7E:73D53B35;FK
A83E75F;A@;EE:AI@;@;9GD7I:;5:;@5>G67E-#&H3>G7E3@6;E
;@F7D?EA8E:73DEFD7EE;@F:7H7DF;53>B>3@7D3F:7DF:3@3H7DF;53>8AD57
3E9;H7@;@GDA5A67 /:7D7E:73DD7;@8AD57?7@F;ED7CG;D76 F:7@
F:73@9>7A8F:75A@5D7F7EFDGFE:AG>64753>5G>3F76 AD?3@KFKB;53>
473?EF:7?;@;?G?3@9>7A8EFDGFI;>>3BB>KI:7@5AFy ADy Q;7 8AD5>3EE
5A@5D7F7F:7EFDGF3@9>77J5776EQ A@>K
I:7@F:7E:73DEFD7EE;E9D73F7DF:3@ &
??2 D787DFA,34>7
EI;F:+ F:7D7;E3?3J;?G?B7D?;FF76E:73D 53B35;FK +*6?3J I:7@5AFy AD y Q 4GFF:;E;E@AFD7EFD;5F76FA%(33E;@
+
Deflection
>nkh\h]^+aZlmphZem^kgZmbo^f^mah]l_hk\a^\dbg`]^_e^\mbhg%
^bma^kZebfbmbg`liZg&mh&]îmakZmbhfZr[^nl^]hkma^ma^hk^mb\Ze
]^_e^\mbhg\Zg[^Zll^ll^]nlbg`ma^^qik^llbhgl`bo^gbgma^<h]^'
MaêZmm^kbl]^Zempbmabg]^mZbebg<aZim^k1%hkb`bgZeerin[ebla^]Zl
'/
=^_e^\mbhg\Ze\neZmbhgl•'
Ma^liZg&mh&]îmakZmbhllahne]^glnk^maZm]^_e^\mbhgblebfbm^]mh
liZg(+.)Zg]mablblmaîkh\^]nkîk^l^gm^]bg?b`nk^/'
"$%.(
,0,/7/$0'/$:,/7/&10&4(6(56476&$2$&,6;,06(4/51)564(55
f&
28
v '/$: &16 y v '/$: &16 y Flanged beams
?eZg`^][^Zfl\Zg[^mk^Zm^]bgfn\ama^lZf^pZrZlbg;L1**)'
Ma^fZbg]b__^k^g\^l\hfiZk^]pbma;L1**)Zk^maZmma^Zll^llf^gm
h_ma^_eZg`^pb]mablfhk^lhiablmb\Zm^]!l^^?b`nk^l2Zg]*)"Zg]
maZm>nkh\h]^+\hgmZbglZ\a^\dmh\hg_bkfmaZmma^la^Zklmk^llZm
<hgmbgn^liZ`^,*
-';^Zfl
,*74(
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41&('74()14$55(55,0*'().(&6,10
(6(4/,0$6,101)56((.564(55
)*(*
Approximate
steel stress at SLS for A
+>=?496954CD55<CDB5CCs
CEs,req,ssu
5D5B=9>521C93 1>4 6B?=97EB5
5D5B=9>513D?B
For flanged sections
?BB92254?BG166<5C<12C
N
6GNM
K
6 9C6<1>752B514D81>4G 9CB922B514D8
&D85BG9C5
5D5B=9>513D?B
Where
the beam span exceeds 7 m and it supports
-85B5D85C<12C@1>5H3554C=1>49DCE@@?BDC
2B9DD<5@1BD9D9?>C 566 L &D85BG9C5
5D5B=9>513D?B
sC
-85B5sC )DB5CC9>B59>6?B35=5>D1DC5BF935129<9DI
<9=9DCD1D5C5597EB5
sC =1I1CCE=54D?25
$'195 (1D9?; ;
%?D5 C@B?F LCB5AP4 +"%1D9?>1<>>5H
!>3B51C5
C@B?F
!C21C93 H HHHM3DE1< c
g
c
g
c
g
c
g
c
g
c
g
c
g
%?
.5C
To determine stress in the provided reinforcement
(ss), calculate the ratio
*?45D5B=9>5CDB5CC9>D85B59>6?B35=5>Ds
C 31<3E<1D5D85B1D9?
;; B514E@D857B1@8D?D851@@B?@B91D53EBF51>4B51413B?CC
D?45D5B=9>5sCE CB5A
sC 31>2531<3E<1D546B?=D855H@B5CC9?> sC sCE
C@B?F d
853;3?=@<5D5
K *85EB?3?459C1=297E?ECB571B49>7<9>51B9>D5B@?<1D9?> !D9CE>45BCD??4D81D
9DG1CD859>D5>D9?>?6D854B16D9>73?==9DD55D81D<9>51B9>D5B@?<1D9?>25EC54
1>4D89C9C9><9>5G9D83EBB5>D+"@B13D935
Figure 7
Basic span-to-effective-depth ratios
36
Notes
34
fck = 50
fck = 45
fck = 40
fck = 35
fck = 32
fck = 30
fck = 28
fck = 25
fck = 20
32
Span to depth ratio (l/d)
30
28
26
24
1 Mabl`kZiaZllnf^llbfierlniihkm^]liZg\hg]bmbhg
!D 6*')"'
D 6*'._hkbgm^kbhkliZg\hg]bmbhg
D 6*',_hk^g]liZg\hg]bmbhg
D 6)'-_hk\Zgmbeô^kl'
2 <hfik^llbhgk^bg_hk\^f^gm% rÃ% aZl[^^gmZd^gZl)'
3 <nko^l[Zl^]hgma^_heehpbg`^qik^llbhgl3
T
*'. _\d r )
e
$ ,'+
6D ** $
r
]
_\d
*'.
r)
¾*
r
! "V
pa^k^r ©r )
22
Zg]
20
T
*'. _\d r )
e
$
6D ** $
]
! r ¾ r Ã"
18
_\d
*+
rÃ
r)
V
pa^k^r 7r ) '
16
14
12
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
2.00%
Percentageof
oftension
tensionreinforcement
reinforcement (A
(As,req’d
Percentage
/bd)
s,req/bd)
29
,*74(
,*74(
41&('74()14'(6(4/,0,0*).(:74$.&$2$&,6;1)).$0*('%($/5
(),0,6,101)l1 )14&$.&7.$6,101)())(&6,8().$0*(9,'6+
)*(*
5D5B=9>5
C5597EB51>4566 6B?=
566 566 566G85B5
566 L
L
566 L
L
,*74(
))(&6,8().$0*(9,'6+2$4$/(6(45
%?D5 *856<1>75G94D81DD85CE@@?BDG9<<25
49665B5>D6B?=D81D1D=94C@1>
?BCI=2?<CB565BD?97EB5C1>4
5D5B=9>5 6B?= 1BBI?ED1>1<IC9C?6251=D?45D5B=9>545C97>
=?=5>DC C55*12<5
566
566
G
3;
566
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566 9>C@1>
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.$&,0*1)6(05,104(,0)14&(/(06,0).$0*('&41555(&6,10
5D5B=9>5P 6B?=*12<5?B
P d N
d N
G85B5d L
566
C
1<3E<1D5<5F5B1B=J6B?=
N L
1
2
6
566
1<3E<1D545@D8D?>5EDB1<1H9C 6B?=
566
G
N
.5C
!C 6 %?
%5EDB1<1H9C9>
6<1>75 5C97>
1CB53D1>7E<1B
C53D9?>97EB5
1>4D85>3853;
<?>79DE49>1<C851B
97EB5
,*74(
%5EDB1<1H9C9>G52
1<3E<1D5=?=5>D31@139DI?66<1>756B?=
16$6,105)146+(&100(&6,10%(69((0).$0*($0'9(%
(6 3; 566 NG6 4N
6
1>4
6 N(6
4
3; G 4
30
?=@B5CC9F5CDBEDC
D
C6
6
(545C97>C53D9?>
6
#?>79DE49>1<21B
1>38?B5425I?>4
D89C@B?:53D54@?9>D
.5C
1<3E<1D51B51?6B59>6?B35=5>DB5AE9B546B?=
(6
N(6
C IG4
–N
fIG4
fyd (d
0.5 hf6)
ydzz
566
%?
!C6 L P
y6
853;<?>79DE49>1<
C851B
C5597EB5
4 D 4
4 D 4
G
-';^Zfl
ma^bgm^k_Z\^h_ma^_eZg`^Zg]p^[\Zg[^k^lblm^][rma^mkZglo^kl^
k^bg_hk\^f^gmbgma^_eZg`^' Maîhlbmbhgh_ma^g^nmkZeZqbllahne]
[^]^m^kfbg^]% Zg]ma^gma^ Zk^Zh_k^bg_hk\^f^gm\Zg[^\Ze\neZm^]
]î^g]bg`pa^ma^kbmeb^lbgma^_eZg`^hkp^[!l^^?b`nk^**"'
Minimum area of shear reinforcement
:mlniihkmlma^m^glbhgk^bg_hk\^f^gmmhk^lblmah``bg`fhf^gml
lahne][^]blmkb[nm^]Z\khllma^_neepb]mah_ma^^__^\mbo^_eZg`^Zl
lahpgbg?b`nk^*+' Ma^liZg&mh&]îma]^_e^\mbhg\a^\dlnlbg`kZmbhh_
m^glbhgk^bg_hk\^f^gmlahne][^[Zl^]hgZk^Zh_\hg\k^m^Z[ho^
\^gmk^h_m^glbhglm^ê'
pa^k^r p%fbg \Zg[^h[mZbg^]_khfMZ[e^2'
Ma^fbgbfnfZk^Zh_la^Zkk^bg_hk\^f^gmbg[^Zfl%:lp%fbglahne]
[^\Ze\neZm^]_khf
:lp
4 r p%fbg
l[p
Figure 14
Procedure for determining longitudinal shear capacity of flanged beams
Calculate the longitudinal shear stress
from: vEd = D Fd/(hf D x)
(see Figure 13)
Longitudinal shear
Ma^la^Zklmk^llbgmaô^kmb\ZeieZg^[^mp^^gma^_eZg`^Zg]p^[lahne]
[^Zll^ll^]Z\\hk]bg`mhl^\mbhg/'+'-Zg]?b`nk^/'0h_ma^>nkh\h]^
!kîkh]n\^]a^k^Zl?b`nk^*,"' Ma^\aZg`^bg_hk\^bgma^_eZg`^\Zg
[^Zll^ll^]_khfma^fhf^gmZg]eô^kZkfZmZiZkmb\neZkeh\Zmbhg'
Ma^>nkh\h]^lmZm^lmaZmma^fZqbfnfe^g`mamaZm\Zg[^\hglb]^k^]
_hkma^\aZg`^bg_hk\^blaZe_ma^]blmZg\^[^mp^^gma^fZqbfnf
fhf^gmZg]maîhbgmpa^k^ma^fhf^gmbls^kh' <e^Zker% ma^fZqbfnf
ehg`bmn]bgZe_hk\^pbeeh\\nkpa^k^ma^\aZg`^bgfhf^gm% Zg]
ma^k^_hk^_hk\^% blma^`k^Zm^lm4 _hkZngb_hkfer]blmkb[nm^]ehZ]hgZ
\hgmbgnhnl[^Zfmablpbee[^maê^g`mah_[^Zf\ehl^lmmhma^lniihkm'
No
Determine the concrete strut capacity
from Table 8 or from:
vRd = 0.160 fck (1 – fck/250)
?b`nk^*-lahplZ_ehp\aZkm_hkZll^llbg`maêhg`bmn]bgZela^Zk
\ZiZ\bmr4 bgfZgr\Zl^lma^mkZglo^kl^k^bg_hk\^f^gmbgma^leZ[pbee[^
ln__b\b^gmmhk^lblmma^la^Zk_hk\^' Mabl\a^\dblbg\en]^]mh^glnk^maZm
pa^kîZkmb\neZkermabg_eZg`^lZk^nl^]ma^k^blZ]^jnZm^k^bg_hk\^f^gm'
Maêhg`bmn]bgZela^Zk\ZiZ\bmrbl[Zl^]hgmaôZkbZ[e^lmknmbg\ebgZmbhg
f^mah]% pab\apZl]^l\kb[^]bgma^l^\mbhghgo^kmb\Zela^Zk'
Rules for spacing and
quantity of reinforcement
Determine the concrete
strut capacity from Table 8
or from:
vRd = 0.195 fck (1 – fck/250)
Yes
Is length of
flange under consideration
in tension?
Determine y f from:
No
Is v RD > vEd ?
Yes
yf = 0.5 sin-1
T
vEd
0.2 fck (1 – fck /250)
V
No
Is v RD > vEd ?
(cot y f = 2.0)
Yes
(cot y f
= 1.25)
Calculate area of transverse reinforcement from:
vEd hf
Asf
=
s
fyd cot y f
Table 8
Concrete strut capacity for longitudinal shear in flanged beams
Minimum area of longitudinal reinforcement
Ma^fbgbfnfZk^Zh_k^bg_hk\^f^gmbl:l%fbg 6)'+/_\ mf [ m ](_r d [nm
ghme^llmaZg)'))*,[ m]% pa^k^[ m blma^f^Zgpb]mah_ma^m^glbhg
shg^!l^^MZ[e^/"' ?hkZM&[^Zfpbmama^_eZg`^bg\hfik^llbhg% hger
ma^pb]mah_ma^p^[blmZd^gbgmhZ\\hngmbg\Ze\neZmbg`maôZen^h_[
Maximum area of longitudinal reinforcement
Ma^fZqbfnfZk^Zh_m^glbhghk\hfik^llbhgk^bg_hk\^f^gm% hnmlb]^
eZieh\Zmbhgllahne]ghm^q\^^]:l%fZq 6)')-:\
fck
v Rd,max
Flange in compression
Flange in tension
+)
+.
+1
,)
,+
,.
-)
-.
.)
+'2,'/)
,'21
-'++
-'-/
-'1+
.',1
.'2)
/'-)
,'.2
-',2
-'1.
.'*.
.'-.'10
/'..
0'+)
0'1)
Minimum spacing of reinforcement
Ma^fbgbfnf\e^Zk]blmZg\^[^mp^^g[Zkllahne][^ma^`k^Zm^kh_3
;Zk]bZf^m^k
:``k^`Zm^lbsîenl.ff
+)ff
Table 9
Values for r w,min
fck
20
25
28
30
32
35
40
45
50
r p%fbgq*) &, )'0+ )'1) )'1. )'11 )'2* )'2. *')* *')0 *'*,
31
-';^Zfl
Selected symbols
Symbol
Definition
:\
:l
Value
Symbol
Definition
<khlll^\mbhgZeZk^Zh_\hg\k^m^
eh
=blmZg\^[^mp^^gihbgmlh_s^khfhf^gm
:k^Zh_m^glbhglm^ê
e(]
LiZg&mh&]îmakZmbh
:l+
:k^Zh_\hfik^llbhglm^ê
F
=^lb`gfhf^gmZmma^NEL
:l% ikho
:k^Zh_m^glbhglm^êikhob]^]
q
=îmamhg^nmkZeZqbl
!]&s"()'-
:l% k^jÃ]
:k^Zh_m^glbhglm^êk^jnbk^]
qfZq
EbfbmbgòZen^_hk]îmamhg^nmkZeZqbl
!d ¾)'-"] pa^k^d ©*')
[^__
>__^\mbo^_eZg`^pb]ma
s
Eô^kZkf
[m
F^Zgpb]mah_ma^m^glbhgshg^
a \\
[fbg
Pb]mah_[^Zfhkkb[
<h^__b\b^gmmZdbg`Z\\hngmh_ehg`m^kf
^__^\mlhg\hfik^llbo^lmk^g`maZg]h_
ng_ZohnkZ[e^^__^\mlk^lnembg`_khfma^
pZrehZ]blZiieb^]
d
KZmbhh_ma^k^]blmkb[nm^]fhf^gmmhma^
êZlmb\[^g]bg`fhf^gm
gf
IZkmbZe_Z\mhk_hkfZm^kbZeikhi^kmb^l
*'*._hkk^bg_hk\^f^gm!gl"
*'._hk\hg\k^m^!g\"
r)
K^_^k^g\^k^bg_hk\^f^gmkZmbh
R_\d (*)))
r
K^jnbk^]m^glbhgk^bg_hk\^f^gmZmfb]&liZg
mhk^lblmma^fhf^gm]n^mhma^]^lb`g
ehZ]l!hkZmlniihkm_hk\Zgmbeô^kl"
:l([] !_hkk^\mZg`neZk[^Zfl"
rÃ
K^jnbk^]\hfik^llbhgk^bg_hk\^f^gmZm
fb]&liZgmhk^lblmma^fhf^gm]n^mhma^
]^lb`gehZ]l!hkZmlniihkm_hk\Zgmbeô^kl"
:l+([]
[p
Pb]mah_l^\mbhg% hkpb]mah_p^[hg_eZg`^][^Zfl
]
>__^\mbo^]îma
]+
>__^\mbo^]îmamh\hfik^llbhgk^bg_hk\^f^gm
_\]
=^lb`goZen^h_\hg\k^m^\hfik^llbo^lmk^g`ma
_\d
<aZkZ\m^kblmb\\rebg]^klmk^g`mah_\hg\k^m^
_\mf
F^ZgoZen^h_ZqbZem^glbe^lmk^g`ma
a_
?eZg`^mab\dg^ll
D
?Z\mhkmhmZd^Z\\hngmh_ma^]b__^k^gm
lmkn\mnkZelrlm^fl
L^^mZ[e^G:'-bg
NDGZmbhgZe:gg^q
e^__
>__^\mbo^liZgh_f^f[^k
L^^L^\mbhg.','+'+!*"
a\\ _\d (g\ _hk_\d ©<.)(/)
)',)_\d!+(," _hk_\d ©<.)(/)
!_khfMZ[e^,'*% >nkh\h]^+"
Value
)'1._hk_e^qnk^Zg]
ZqbZeehZ]l
*')_hkhma^kia^ghf^gZ
!?khfNDGZmbhgZe:gg^q"
References
1 ;KBMBLALM:G=:K=LBGLMBMNMBHG' ;L>G*22+¾*¾*% >nkh\h]^+3 =^lb`gh_\hg\k^m^lmkn\mnk^l¾IZkm*¾*@^g^kZekne^lZg]kne^l_hk
[nbe]bg`l' ;LB% +))-'
2 ;KBMBLALM:G=:K=LBGLMBMNMBHG' ;L1**)¾*3 Ma^lmkn\mnkZenl^h_\hg\k^m^¾IZkm*% <h]^h_ikZ\mb\^_hk]^lb`gZg]\hglmkn\mbhg' ;LB% *220'
3 G:K:R:G:G% KL;KHHD>K% H' Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3 Bgmkh]n\mbhgmh>nkh\h]^l' Ma^<hg\k^m^<^gmk^% +)).'
4 ;KHHD>K% H' Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3 @^mmbg`lmZkm^]' Ma^<hg\k^m^<^gmk^% +)).'
5 ;KBMBLALM:G=:K=LBGLMBMNMBHG' ;L>G*22+¾*¾+% >nkh\h]^+3 =^lb`gh_\hg\k^m^lmkn\mnk^l' @^g^kZekne^l¾lmkn\mnkZe_bk^]^lb`g' ;LB% +))6
P>;LM>K%K;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3=^Ì^\mbhg\Ze\neZmbhgl'Ma^<hg\k^m^<^gmk^%+))/'
6 =>I:KMF>GMH?<HFFNGBMB>L:G=EH<:E@HO>KGF>GM'
AZg][hhdmh>G&*22+&*&+ ' =<E@%]n^+))/'
7 P>;LM>K% K;KHHD>K% H' Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3 =^_e^\mbhg\Ze\neZmbhgl' Ma^<hg\k^m^<^gmk^% +))/'
32
.'<henfgl
Designing to Eurocode 2
Mabl\aZim^kblbgm^g]^]mhZllblm^g`bg^^klpbmama^]^lb`gh_\henfglZg]
pZeelmh>nkh\h]^+'Bml^mlhnmZ]^lb`gikh\^]nk^mh_heehpZg]`bo^lnl^_ne
\hff^gmZkrhgmaîkhoblbhglpbmabgma^>nkh\h]^'MaêZrhnmZg]\hgm^gm
h_>nkh\h]^+fZrZii^ZkngnlnZemh]^lb`g^kl_ZfbebZkpbma;L1**)'
>nkh\h]^+]h^lghm\hgmZbgma^]^kbo^]_hkfneZ^4mablbl[^\Znl^bmaZl[^^g
>nkhi^ZgikZ\mb\^mh`boîkbg\bie^lZg]`^g^kZeZiieb\Zmbhgkne^lbgma^\h]^l
Zg]_hk]^mZbe^]Ziieb\Zmbhgkne^lmh[îk^l^gm^]bghma^klhnk\^lln\aZl
m^qm[hhdlhk`nb]Zg\^]h\nf^gml'
d^r]b__^k^g\^l[^mp^^g>nkh\h]^+Zg];L1**)%bg\en]bg`m^kfbgheh`r'
Bmlahne]Zelh[^ghm^]maZmoZen^l_khfma^NDGZmbhgZe:gg^q!G:"aZo^
[^^gnl^]makhnàhnmmablin[eb\Zmbhg%bg\en]bgòZen^lmaZmZk^^f[^]]^]bg
]^kbo^]_hkfneZ^'!=^kboZmbhgl\Zg[^_hng]Zmppp'^nkh\h]^+'bg_h'":_neeeblm
h_lrf[helkêZm^]mh\henfg]^lb`gbl`bo^gZmma^^g]h_mabl\aZim^k'
Design procedure
:ikh\^]nk^_hk\Zkkrbg`hnmma^]^mZbe^]]^lb`gh_[kZ\^]\henfgl!b'^'
\henfglmaZm]hghm\hgmkb[nm^mhk^lblmZg\^h_ahkbshgmZeZ\mbhgl"bllahpg
bgMZ[e^*'MablZllnf^lmaZmma^\henfg]bf^glbhglaZoîkôbhnler[^^g
]^m^kfbg^]]nkbg`\hg\îmnZe]^lb`ghk[rnlbg`jnb\d]^lb`gf^mah]l%_hk
^qZfie^mahlîk^l^gm^]bg>\hghfb\\hg\k^m^_kZf^ê^f^gml '<henfglbs^l
lahne]ghm[^lb`gb_b\Zgmer]b__^k^gm_khfmahl^h[mZbg^]nlbg`;L1**)'Lmîl
*mh-h_MZ[e^*Zk^\ho^k^][r^Zkeb^k\aZim^klZg]ma^g^qmlmîblma^k^_hk^
mh\hglb]^k_bk^k^lblmZg\^'
Fire resistance
>nkh\h]^+%IZkm*¾+3Lmkn\mnkZe_bk^]^lb`g%`bo^lZ\ahb\^h_Z]oZg\^]%lbfieb_b^]
hkmZ[neZkf^mah]l_hk]^m^kfbgbg`_bk^k^lblmZg\^h_\henfgl'Nlbg`mZ[e^lblma^
_Zlm^lmf^mah]_hk]^m^kfbgbg`ma^fbgbfnf]bf^glbhglZg]\ho^k_hk\henfgl'
Ma^k^Zk^%ahpô^k%lhf^k^lmkb\mbhglZg]b_ma^l^Ziier_nkma^k`nb]Zg\^\Zg[^
h[mZbg^]_khfli^\bZeblmebm^kZmnk^'Ma^lbfieb_b^]f^mah]fZr`bo^fhk^^\hghfb\
\henfgl%^li^\bZeer_hklfZee\henfglZg](hkabà_bk^k^lblmZg\î^kbh]l'
KZma^kmaZg`bobg`Zfbgbfnf\ho^k%ma^mZ[neZkf^mah]bl[Zl^]hgghfbgZe
Zqbl]blmZg\^%Z!l^^?b`nk^*"'Mablblma^]blmZg\^_khfma^\^gmk^h_ma^fZbg
<hgmbgn^liZ`^,.
Table 1
Column design procedure
Step
Task
Further guidance
Chapter in the publication
Standard
*
=^m^kfbg^]^lb`geb_^
+3@^mmbg`lmZkm^]
NDG:mh;L>G*22)MZ[e^G:'+'*
+
:ll^llZ\mbhglhgma^\henfg
+3@^mmbg`lmZkm^]
;L>G*22*!*)iZkml"Zg]NDGZmbhgZe:gg^q^l
,
NDG:mh;L>G*22)MZ[e^lG:':*'*Zg]G:':*'+!;"
-
+3@^mmbg`lmZkm^]
;L1.))3+))/
.
+3@^mmbg`lmZkm^]Zg]MZ[e^+
:iikho^]=h\nf^gm;';L>G*22+¾*¾+
/
<Ze\neZm^fbg'\ho^k_hk]nkZ[bebmr%_bk^Zg][hg]k^jnbk^f^gml
+3@^mmbg`lmZkm^]
;L>G*22+¾*¾*<e'-'-'*
0
:gZerl^lmkn\mnk^mhh[mZbg\kbmb\Zefhf^gmlZg]ZqbZe
_hk\^l
+3@^mmbg`lmZkm^]Zg]ÂLmkn\mnkZe
ZgZerlblÃl^\mbhg
;L>G*22+¾*¾*l^\mbhg.
1
<a^\dle^g]^kg^ll
L^^?b`nk^l+Zg],
;L>G*22+¾*¾*l^\mbhg.'1
2
=^m^kfbg^Zk^Zh_k^bg_hk\^f^gmk^jnbk^]
L^^?b`nk^l+Zg],
;L>G*22+¾*¾*l^\mbhg/'*
*)
<a^\dliZ\bg`h_[Zkl
ÂKne^l_hkliZ\bg`Ãl^\mbhg
;L>G*22+¾*¾*l^\mbhgl1Zg]2
Note
G:6GZmbhgZe:gg^q'
Table 2
Figure 1
Minimum column dimensions and axis distances for fire resistance
Section through structural member, showing nominal axis distance a
Standard fire
resistance
Column width bmin/axis distance, a, of the main
bars
Column exposed on more than
one side
K/)
μfi = 0.5
μfi = 0.7
Column
exposed on
one side
(μfi = 0.7)
+))(,/
+.)(-/
*..(+.
,))(,*
,.)(-)
,))(-.
,.)(.,
-))(,1 Z
-.)(-) Z
,.)(-. Z
,.)(.0 Z
-.)(-) Z
-.)(.*Z
-.)(0.Z
[
h≥b
a
K2)
K*+)
K+-)
*..(+.
b
*0.(,.
+2.(0)
Table 3
Minimum reinforced concrete wall dimensions and axis distances for
load-bearing for fire resistance
Note
Ma^mZ[e^blmZd^g_khf;L>G*22+¾*¾+MZ[e^.'+Z!f^mah]:"Zg]bloZeb]ng]^kma^
_heehpbg`\hg]bmbhgl3
1 Ma^^__^\mboê^g`mah_Z[kZ\^]\henfgng]^k_bk^\hg]bmbhgleh%_b©,f'MaôZen^h_eh%_b
Standard
fire
resistance
nl^f^mah];!l^^>nkh\h]^+%IZkm*¾+%MZ[e^.'+["'Ma^^\\^gmkb\bmrng]^k_bk^
\hg]bmbhglfZr[^mZd^gZlmaZmnl^]bgghkfZem^fi^kZmnk^]^lb`g'
3 Ma^k^bg_hk\^f^gmZk^Zhnmlb]êZieh\Zmbhgl]h^lghm^q\^^]-h_ma^\hg\k^m^
\khlll^\mbhg'
4 ¬
_bblma^kZmbhh_ma^]^lb`gZqbZeehZ]ng]^k_bk^\hg]bmbhglmhma^]^lb`gk^lblmZg\^h_
ma^\henfgZmghkfZem^fi^kZmnk^\hg]bmbhgl'¬_bfZr\hgl^koZmboêr[^mZd^gZl)'0'
Key
Wall thickness/axis distance, a, of the main bars
Wall exposed on one side
( μfi = 0.7)
Wall exposed on two
sides ( μfi = 0.7)
K>B/)
*,)(*) Z
*-)(*) Z
K>B2)
*-)(+.
*0)(+.
K>B*+)
*/)(,.
++)(,.
K>B+-)
+0)(/)
,.)(/)
fZr[^mZd^gZl.)h_ma^Z\mnZee^g`ma_hkbgm^kf^]bZm^_ehhklZg][^mp^^g.)
Zg]0)h_ma^Z\mnZee^g`ma_hkma^nii^k_ehhk\henfg'
2 Ma^_bklmhk]^k^\\^gmkb\bmrng]^k_bk^\hg]bmbhgllahne][^©)'*.[!hka"':em^kgZmboêr
Notes
1 Ma^mZ[e^blmZd^g_khf;L>G*22+¾*¾+MZ[e^.'-'
bgbfnf1[Zkl
a F
2 L^^ghm^-h_MZ[e^+'
b F^mah];fZr[^nl^]pab\abg]b\Zm^l/))(0)_hkK+-)Zg]¬_b6)'0'
L^^;L>G*22+¾*¾+MZ[e^.'+[
Key
34
a GhkfZeerma^k^jnbk^f^gmlh_;L>G*22+¾*¾*pbee]^m^kfbg^ma^\ho^k'
.'<henfgl
k^bg_hk\bg`[Zkmhma^lnk_Z\^h_ma^f^f[^k'BmblZghfbgZe!ghm
fbgbfnf"]bf^glbhg%Zg]ma^]^lb`g^klahne]^glnk^maZm3
Zª\ghf$f ebgd$f [Zk(+'
?hk\henfglma^k^Zk^mphmZ[e^l`bo^gbg>nkh\h]^+IZkm*¾+maZm
ik^l^gmf^mah]l:Zg];';hmaZk^^jnZeerZiieb\Z[e^%Zemahnà
f^mah]:aZllfZee^kebfbmlhg^\\^gmkb\bmrmaZgf^mah];'F^mah]:
bllebàmerlbfie^kZg]blik^l^gm^]bgMZ[e^+4ebfbmlh_Ziieb\Z[bebmr
Zk^`bo^gbgma^ghm^l'LbfbeZk]ZmZ_hkehZ]&[^Zkbg`pZeelbl`bo^gbg
MZ[e^,'
?hk\henfgllniihkmbg`ma^nii^kfhlmlmhk^r%ma^^\\^gmkb\bmrpbee
h_m^g^q\^^]maêbfbml_hk[hmaf^mah]l:Zg];'BgmabllbmnZmbhg
:gg^q<h_>nkh\h]^+%IZkm*¾+fZr[^nl^]':em^kgZmboêr%
\hglb]^kZmbhg\Zg[^`bo^gmhmk^Zmbg`ma^\henfgZlZ[^Zf_hk
]^m^kfbgbg`ma^]^lb`g_bk^k^lblmZg\^'
Figure 2
Flow chart for braced column design
START
Initial column size may be determined using quick design
methods or through iteration.
Column design
:_ehp\aZkm_hkma^]^lb`gh_[kZ\^]\henfglbllahpgbg?b`nk^+'?hk
le^g]^k\henfgl%?b`nk^,pbeeZelh[^k^jnbk^]'
Determine the actions on the column
using an appropriate analysis method.
The ultimate axial load is NEd and the ultimate moments
are Mtop and Mbottom (Moments from analysis)
Structural analysis
Ma^mri^h_ZgZerlbllahne][^ZiikhikbZm^mhmaîkh[e^f[^bg`
\hglb]^k^]'Ma^_heehpbg`fZr[^nl^]3ebg^ZkêZlmb\ZgZerlbl%ebg^Zk
êZlmb\ZgZerlblpbmaebfbm^]k^]blmkb[nmbhg%ieZlmb\ZgZerlblZg]
ghg&ebg^ZkZgZerlbl'Ebg^ZkêZlmb\ZgZerlblfZr[^\Zkkb^]hnmZllnfbg`
\khlll^\mbhglZk^ng\kZ\d^]!b'^'\hg\k^m^l^\mbhgikhi^kmb^l"%
nlbgèbg^Zklmk^ll&lmkZbgkêZmbhglabilZg]Zllnfbg`f^ZgoZen^l
h_ehg`&m^kfêZlmb\fh]nenl'
Determine the effective length, l0, using either:
1. Figure 5
2. Table 4
3. Expression (5.15) from BS EN 1992–1–1
Determine first order moments (see Figure 4)
M01 = Min {|Mtop|, |Mbottom|} + ei NEd
M02 = Max {|Mtop|, |Mbottom|} + ei NEd
Where ei = Max {l0/400, h/30, 20} (units to be in millimetres).
M01 and M02 should have the same sign
if they give tension on the same side.
?hkma^]^lb`gh_\henfglma^êZlmb\fhf^gml_khfma^_kZf^Z\mbhg
lahne][^nl^]pbmahnmZgrk^]blmkb[nmbhg'?hkle^g]^k\henfglZ
ghg&ebg^ZkZgZerlblfZr[^\Zkkb^]hnmmh]^m^kfbg^ma^l^\hg]hk]^k
fhf^gml4Zem^kgZmboêrnl^ma^fhf^gmfZ`gb_b\Zmbhgf^mah]
!<e.'1'0',"hkghfbgZe\nkoZmnk^f^mah]!<e.'1'1"ZlbeenlmkZm^]bg
?b`nk^,'MaêZmm^kbl^qi^\m^]mh[^Z]him^]bgma^ND'
Determine slenderness, l, from either:
l = l0/i where i = radius of gyration or
l = 3.46 l0/h for rectangular sections (h = overall depth) or
l = 4.0 l0/d for circular sections (d = column diameter)
Design moments
Ma^]^lb`g[^g]bg`fhf^gmblbeenlmkZm^]bg?b`nk^-Zg]]^_bg^]Zl3
Determine slenderness limit, λlim, from:
l
15.4C
lim =
√n
(See ‘Slenderness’ section on page 5 for explanation.)
Yes
Is l ≥ l lim?
No
Column is not slender. MEd = M02
Use column chart (see Figure 9) to find As required for NEd
and MEd. Alternatively, solve by iteration or by using RC
Spreadsheet TCC53 from Spreadsheets for concrete design to
BS 8110 and Eurocode 2 6
Check rules for spacing and quantity of reinforcement
(see page 7)
Column is slender
(refer to Figure 3).
F>]6FZqtF)+%F)^$F+%F)*$)'.F+v
pa^k^
F)*6FbgtuFmhiu%uF[hmmhfuv$^bG>]
F)+6FZqtuFmhiu%uF[hmmhfuv$^bG>]
^b6FZqteh(-))%a(,)%+)v!ngbmlmh[^bgfbeebf^mk^l"'
Fmhi%F[hmmhf6Fhf^gmlZmma^mhiZg][hmmhfh_ma^\henfg
F)^6)'/F)+$)'-F)*ª)'-F)+
F+6G>]^+pa^k^G>]blma^]^lb`gZqbZeehZ]Zg]^+
bl]^_e^\mbhg]n^mhl^\hg]hk]^k^__^\ml
F)*Zg]F)+lahne][îhlbmbo^b_ma^r`bo^m^glbhghgma^lZf^lb]^'
:ghg&le^g]^k\henfg\Zg[^]^lb`g^]b`ghkbg`l^\hg]hk]^k^__^\ml
Zg]ma^k^_hk^ma^nembfZm^]^lb`gfhf^gm%F>]6F)+'
Ma^\Ze\neZmbhgh_ma^^\\^gmkb\bmr%^+%blghmlbfie^Zg]blebdêrmh
k^jnbk^lhf^bm^kZmbhgmh]^m^kfbg^ma^]^_e^\mbhgZmZiikhqbfZmêr
fb]&a^bàm%^+'@nb]Zg\^bl`bo^gbg?b`nk^,'
35
Figure 3
Effective length
Flow chart for slender columns (nominal curvature method)
?b`nk^.`bo^l`nb]Zg\^hgma^^__^\mboê^g`mah_ma^\henfg'
Ahpô^k%_hkfhlmk^Zelmkn\mnk^l?b`nk^l._"Zg].`"hgerZk^
Ziieb\Z[e^%Zg]>nkh\h]^+ikhob]^lmph^qik^llbhglmh\Ze\neZm^ma^
^__^\mboê^g`ma_hkma^l^lbmnZmbhgl'>qik^llbhg!.'*."bl_hk[kZ\^]
f^f[^klZg]>qik^llbhg!.'*/"bl_hkng[kZ\^]f^f[^kl'
From Figure 2
Determine Kr from Figure 9 or from
Kr = (nu - n) / (nu - nbal) ≤ 1
where
n = NEd / (Ac fcd), relative axial force
NEd = the design value of axial force
nu = 1 + w
nbal = 0.4
w = As,est fyd / (Ac fcd)
As,est = the estimated total area of steel
Ac = the area of concrete
Bg[hma^qik^llbhgl%ma^kêZmbo^_e^qb[bebmb^lZm^bma^k^g]%d*Zg]d+%
lahne][^\Ze\neZm^]'Ma^^qik^llbhg_hkd`bo^gbgma^>nkh\h]^
bgoheo^l\Ze\neZmbg`ma^khmZmbhgh_ma^k^lmkZbgbg`f^f[^kl%pab\abg
ikZ\mb\^k^jnbk^lma^nl^h__kZf^phkdZgZerlbllh_mpZk^':em^kgZmboêr%
I=//103;Z\d`khng]iZi^kmhma^NDGZmbhgZeZgg^q ikhob]^lZ
lbfieb_b\Zmbhg%[Zl^]hgma^lmb__g^llh_ma^[^ZflZmmZ\a^]mh^bma^k
lb]^h_ma^\henfg'MablkêZmbo^lmb__g^ll%d%\Zgma^k^_hk^[^\Ze\neZm^]
Zl_heehpl!ikhob]^]ma^lmb__g^llh_Z]cZ\^gm\henfgl]h^lghmoZkr[r
fhk^maZg*.h_maâbà^klmb__g^ll"3
Calculate Kh from Kh = 1 + b hef ≥ 1
where
hef = the effective creep ratio
b = 0.35 + fck/200 – λ/150
l = the slenderness ratio.
See section on creep (page 6)
Σ
EI k= c
lc
!
"
Kh fyd
2
l0
0.45d Es
where
Es = elastic modulus of reinforcing steel
(200 GPa)
Kr
2EIb
≥ 0.1
lb
pa^k^
B\%B[Zk^ma^\henfgZg][^Zfng\kZ\d^]l^\hg]fhf^gmlh_Zk^Z
e\%e[Zk^ma^\henfgZg][^Zfe^g`mal
Calculate e2 from
e2 = 0.1
Revise value
of As,est
Hg\^d*Zg]d+aZo^[^^g\Ze\neZm^]%ma^^__^\mboê^g`ma_Z\mhk%?%\Zg
[^^lmZ[ebla^]_khfMZ[e^-_hk[kZ\^]\henfgl'Ma^^__^\mboê^g`mabl
ma^geh6?e'
M0e = 0.6 M02 + 0.4 M01 ≥ 0.4 M02
M2 = NEd e2
MEd = Max {M02, M0e + M2, M01 + 0.5 M2}
?hkZ-))ffljnZk^bgm^kgZe\henfglniihkmbg`Z+.)ffmab\d_eZm
leZ[hgZ0'.f`kb]%maôZen^h_d\hne][^)'**%Zg]ma^k^_hkêh6)'.2e'
Bgma^^]`^\hg]bmbhgdbl^__^\mboêr]hn[e^]Zg]eh6)'/0e'B_ma^bgm^kgZe
\henfgaZ]ZghmbhgZeerÂibgg^]ÃlniihkmZmbml[Zl^ma^geh6)'00e'
Use column chart to find As,req’d for NEd and MEd
Alternatively, solve by iteration or by using
RC Spreadsheet6
BmblZelh`^g^kZeerZ\\îm^]maZmMZ[e^,'*2h_;L1**)fZr
\hgl^koZmboêr[^nl^]mh]^m^kfbg^ma^^__^\mboê^g`ma_Z\mhk'Bgma^
ehg`m^kf%>qik^llbhgl!.'*."Zg]!.'*/"pbee[^[^g^_b\bZeZlma^rZk^
iZkmb\neZkerlnbmZ[e^_hkbg\hkihkZmbhgbgmh]^lb`glh_mpZk^'
No
Is As req’d & As, est?
Figure 4
Yes
Design bending moments
Check detailing requirements
M02
M
Figure 5
ei NEd
M02
Effective lengths for isolated members
M0e
y
l
y
M01
M
36
b) l0 = 2l
c) l0 = 0.7l
d) l0 = l /2
e) l0 = l
f) l/2 < l0 < l
M0e + M2
=
+
y
a) l0 = l
M2 = NEd e2
g) l0 > 2l
First order
moments for
‘stocky’ columns
0.5 M2
Additional second
order moments for
‘slender’ columns
M01 + 0.5 M2
Total moment
diagram for
‘slender’ columns
.'<henfgl
Table 4
Slenderness
Effective length factor, F, for braced columns
k2
>nkh\h]^+lmZm^lmaZml^\hg]hk]^k^__^\mlfZr[^b`ghk^]b_ma^r
Zkê^llmaZg*)h_ma^_bklmhk]^k^__^\ml':lZgZem^kgZmbo^%b_ma^
le^g]^kg^ll!l"ble^llmaZgma^le^g]^kg^llebfbm!l ebf"%ma^gl^\hg]
hk]^k^__^\mlfZr[^b`ghk^]'
k1
0.10 0.20 0.30 0.40 0.50 0.70 1.00 2.00 5.00 9.00 Pinned
0.10
0.59 0.62 0.64 0.66 0.67 0.69 0.71 0.73 0.75 0.76 0.77
0.20
0.62 0.65 0.68 0.69 0.71 0.73 0.74 0.77 0.79 0.80 0.81
0.30
0.64 0.68 0.70 0.72 0.73 0.75 0.77 0.80 0.82 0.83 0.84
0.40
0.66 0.69 0.72 0.74 0.75 0.77 0.79 0.82 0.84 0.85 0.86
0.50
0.67 0.71 0.73 0.75 0.76 0.78 0.80 0.83 0.86 0.86 0.87
0.70
0.69 0.73 0.75 0.77 0.78 0.80 0.82 0.85 0.88 0.89 0.90
1.00
0.71 0.74 0.77 0.79 0.80 0.82 0.84 0.88 0.90 0.91 0.92
2.00
0.73 0.77 0.80 0.82 0.83 0.85 0.88 0.91 0.93 0.94 0.95
5.00
0.75 0.79 0.82 0.84 0.86 0.88 0.90 0.93 0.96 0.97 0.98
9.00
0.76 0.80 0.83 0.85 0.86 0.89 0.91 0.94 0.97 0.98 0.99
Le^g]^kg^ll%l6eh(bpa^k^b6kZ]bnlh_`rkZmbhgZg]le^g]^kg^llebfbm'
20ABC
15.4C
≤
l lim =
n n
pa^k^
:6*(!*$)'+h^_"!b_h^_blghmdghpg%:6)'0fZr[^nl^]"
;6
!b_ω% k^bg_hk\^f^gmkZmbh%blghmdghpg%
;6*'*fZr[^nl^]"
<6*'0¾kf!b_kfblghmdghpg%<6)'0fZr[^nl^]¾l^^[êhp"
g6G>](!:\_\]"
kf6F)*(F)+
F)*%F)+Zk^ma^_bklmhk]^k^g]fhf^gml%uF)+uªuF)*u
Pinned 0.77 0.81 0.84 0.86 0.87 0.90 0.92 0.95 0.98 0.99 1.00
Figure 6
Calculating factor C
B_ma^^g]fhf^gmlF)*Zg]F)+`bo^m^glbhghgma^lZf^lb]^%
kflahne][^mZd^gihlbmbo^'
105 kNm
105 kNm
105 kNm
105 kNm
0
105 kNm
rm = 1.0
rm = 0
rm = -1.0
a) C = 1.7 - 1 = 0.7
b) C = 1.7 - 0 = 1.7
H_ma^mak^^_Z\mhkl:%;Zg]<%<pbeeaZo^maêZk`^lmbfiZ\mhg
l ebfZg]blma^lbfie^lmmh\Ze\neZm^':gbgbmbZeZll^llf^gmh_l ebf\Zg
ma^k^_hk^[^fZ]^nlbg`ma^]^_ZnemoZen^l_hk:Zg];%[nmbg\en]bg`
Z\Ze\neZmbhg_hk<!l^^?b`nk^/"'<Zk^lahne][^mZd^gbg]^m^kfbgbg`
<[^\Znl^ma^lb`gh_ma^fhf^gmlfZd^lZlb`gb_b\Zgm]b__^k^g\^'?hk
ng[kZ\^]f^f[^kl<lahne]ZepZrl[^mZd^gZl)'0'
c) C = 1.7 + 1.0 = 2.7
Column design resistance
?hkikZ\mb\Zeinkihl^lma^k^\mZg`neZklmk^ll[eh\dnl^]_hkma^]^lb`g
h_[^Zfl!l^^<aZim^k-%hkb`bgZeerin[ebla^]Zl;^Zfl "fZrZelh[^
nl^]_hkma^]^lb`gh_\henfgl!l^^?b`nk^0"'Ahpô^k%ma^fZqbfnf
\hfik^llbo^lmkZbg_hk\hg\k^m^\eZll^lnimhZg]bg\en]bg`<.)(/)%
pa^gma^pahe^l^\mbhgblbgink^\hfik^llbhg%bl)'))*0.!l^^?b`nk^
1Z"'Pa^gma^g^nmkZeZqbl_Zeeloutsidema^l^\mbhg!?b`nk^1["%ma^
fZqbfnfZeehpZ[e^lmkZbgblZllnf^]mheb^[^mp^^g)'))*0.Zg]
)')),.%Zg]fZr[^h[mZbg^][r]kZpbg`Zebg^_khfmaîhbgmh_s^kh
lmkZbgmakhnàma^Âabg`îhbgmÃh_)'))*0.lmkZbgZmfb]&]îmah_ma^
l^\mbhg'Pa^gma^g^nmkZeZqbleb^lwithinma^l^\mbhg]îmama^gma^
fZqbfnf\hfik^llbo^lmkZbgbl)')),.!l^^?b`nk^1\"'
Figure 7
Stress block diagram for columns
esc
d2
f cd
ecu 2
s sc
As2
dc
x
h
n. axis
ey
a) Strain diagram
As
d2
s st
b) Stress diagram
Figure 8
Strain diagrams for columns
0.00175
0.0035 max
0.00175 x / ( x – h /2)
0.0035 max
x
hinge
point
h
h/ 2
x
hinge
point
h d
x
ex
ex
0.00175 min
0.00175
a) Pure compression
b) When x > h
c) When x < h
d) General relationship
37
Ma^`^g^kZekêZmbhglabibllahpgbg?b`nk^1]"'?hk\hg\k^m^\eZll^l
Z[ho^<.)(/)maîkbg\bie^lZk^ma^lZf^[nmma^fZqbfnflmkZbg
oZen^loZkr'
Creep
Mph^qik^llbhgl\Zg[^]^kbo^]_hkma^Zk^Zh_lm^êk^jnbk^]%![Zl^]hg
Zk^\mZg`neZklmk^ll[eh\d%l^^?b`nk^0"hg^_hkma^ZqbZeehZ]lZg]ma^
hma^k_hkma^fhf^gml3
:lG (+6!G>]¾_\][]\"(!σl\¾σlm"
pa^k^
:lG6:k^Zh_k^bg_hk\^f^gmk^jnbk^]mhk^lblmZqbZeehZ]
G>]6:qbZeehZ]
_\]6=^lb`goZen^h_\hg\k^m^\hfik^llbo^lmk^g`ma
σl\!σlm"6Lmk^llbg\hfik^llbhg!Zg]m^glbhg"k^bg_hk\^f^gm
[6;k^Z]mah_l^\mbhg
]\6>__^\mbo^]îmah_\hg\k^m^bg\hfik^llbhg6lq©a
l6)'1_hk©<.)(/)
q6=îmamhg^nmkZeZqbl
a6A^bàmh_l^\mbhg
=î^g]bg`hgma^Zllnfimbhglnl^]bgma^]^lb`g%bmfZr[^g^\^llZkr
mh]^m^kfbg^ma^^__^\mbo^\k^îkZmbhh^_!k^_'<e','*'-.'1'-"':
ghfh`kZfblikhob]^]bgma^>nkh\h]^!?b`nk^,'*"_hkpab\ama^
\^f^gmlmk^g`ma\eZllblk^jnbk^]4ahpô^k%Zmma^]^lb`glmZ`^bmh_m^g
ghm\^kmZbgpab\a\eZllZiieb^l'@^g^kZeer%<eZllKlahne][^Zllnf^]'
Pa^k^ma^`khng]`kZgneZm^][eZlm_nkgZ\^leZ`!``[l"^q\^^]l,.
h_ma^\^f^gm\hf[bgZmbhghkpa^kîneo^kbs^]_nêZla!i_Z"^q\^^]l
+)h_ma^\^f^gm\hf[bgZmbhg%<eZllGfZr[^Zllnf^]'Pa^k^
``[l^q\^^]l/.hkpa^kî_Z^q\^^]l,.%<eZllLfZr[^Zllnf^]'
Biaxial bending
Ma^^__^\mlh_[bZqbZe[^g]bg`fZr[^\a^\d^]nlbg`>qik^llbhg!.',2"%
pab\apZl_bklm]ôêhi^][r;k^leZ^k'
a
a
! " +! " ≤ 1.0
MEdz
MRdz
MEdy
MRdy
pa^k^
F>]s%r6=^lb`gfhf^gmbgma^k^li^\mbo^]bk^\mbhgbg\en]bg`l^\hg]
hk]^k^__^\mlbgZle^g]^k\henfg
FK]s%r6Fhf^gmh_k^lblmZg\^bgma^k^li^\mbo^]bk^\mbhg
Z6+_hk\bk\neZkZg]êebimb\Zel^\mbhgl4k^_^kmhMZ[e^._hkk^\mZg`neZk
l^\mbhgl
GK]6:\_\]$:l_r]
:lF (+6TF¾_\][]\!a(+¾]\(+"V(T!a(+¾]+"!σl\$σlm"V
pa^k^
:lF 6MhmZeZk^Zh_k^bg_hk\^f^gmk^jnbk^]mhk^lblmfhf^gm
K^Zeblmb\Zeer%ma^l^\Zghger[^lheo^]bm^kZmboêrZg]ma^k^_hk^^bma^k
\hfinm^klh_mpZk^!^'`'K<Lik^Z]la^^mM<<.,_khfLik^Z]la^^ml_hk
\hg\k^m^]^lb`gmh;L1**)Zg]><+"hk\henfg]^lb`g\aZkml!l^^
?b`nk^l2Zmh2^"fZr[^nl^]'
<hgmbgn^liZ`^-*
Figure 9a
Column design chart for rectangular columns d2 /h = 0.05
1.3
Kr = 0.2
1.2
d2/h = 0.05
0.3 Asfyk/bhfck
1.1
1.0
0.9
1.0
0.8
0.9
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.8
N/bhfck
0.4
0.7
0.6
0.5
0.5
0.6
0.7
0
0.8
0.4
0.9
0.3
1.0
0.2
0.1
0
0
0.05
0.10
0.15
0.20
0.25
2
M/bh fck
38
0.30
0.35
0.40
0.45
.'<henfgl
Figure 9b
1.3
0.2
1.2
0.3
d2/h = 0.10
Asfyk/bhfck
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.0
0.9
N/bhfck
0.8
0.7
0.6
0.5
0.4
0.5
0.6
0.7
0
0.8
0.4
0.9
0.3
Kr =1
0.2
0.1
0
0
0.05
0.10
0.15
0.25
0.20
0.30
0.35
0.40
0.45
2
M/bh fck
Figure 9c
1.3
0.2
d2/h = 0.15
1.2
0.3
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.0
0.9
N/bhfck
0.8
0.7
0.6
0.5
Asfyk/bhfck
0.4
0.5
0.6
0.7
0
0.8
0.4
0.9
0.3
Kr =1
0.2
0.1
0
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
2
M/bh fck
39
Figure 9d
1.3
0.2
1.2
d2/h = 0.20
1.1
1.0
0.9
1.0
0.4
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.9
0.8
N/bhfck
Asfyk/bhfck
0.3
0.7
0.6
0.5
0.5
0.6
0.7
0
0.8
0.4
0.9
0.3
0.2
Kr = 1
0.1
0
0
0.05
0.15
0.10
0.20
0.25
0.30
0.35
2
M/bh f ck
Figure 9e
1.3
0.2
1.2
d2/h = 0.25
0.3
1.1
Asfyk/bhfck
1.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.9
N/bhfck
0.8
0.7
0.6
0.5
0.4
0.5
0.6
0.7
0
0.4
0.8
0.3
0.9
0.2
0.1
Kr = 1
0
0
0.05
0.10
0.15
2
M/bh fck
40
0.20
0.25
0.30
.'<henfgl
Table 5
Selected symbols
Value of a for rectangular sections
Symbol
Definition
Value
*(k)
K^_^k^g\^\nkoZmnk^
εr](!)'-.]"
*(k
<nkoZmnk^
DkDh*(k)
Z
:qbl]blmZg\^_hk_bk^k^lblmZg\^
NEd /NRd
0.1
0.7
1.0
Z
*')
*'.
+')
Note
Ebg^Zkbgm^kiheZmbhgfZr[^nl^]'
Unbraced columns
Ma^k^blgh\hff^gmfZ]^hgma^]^lb`gh_lpZr_kZf^lbg>nkh\h]^+'
Ahpô^k%bm`bo^l`nb]Zg\^hgma^^__^\mboê^g`mah_Zgng[kZ\^]
f^f[^kbg>qik^llbhg!.'*/"'MaôZen^_hk<h_)'0lahne]ZepZrl[^
nl^]bg>qik^llbhg!.'*,G"'Ma^]^lb`gfhf^gmllahne][^Zll^ll^]
bg\en]bg`l^\hg]hk]^k^__^\ml'Ma^mZ[neZkf^mah]_hk_bk^k^lblmZg\^
]^lb`g!IZkm*¾+"]h^lghm^qieb\bmer\ho^kng[kZ\^]\henfgl4ahpô^k
k^_^k^g\^\Zg[^fZ]^mhma^<aZim^k*+ 2'
Walls
Pa^gma^l^\mbhge^g`mah_Zo^kmb\Zeê^f^gmbl_hnkmbf^l`k^Zm^k
maZgbmlmab\dg^llbmbl]^_bg^]ZlZpZee'Ma^]^lb`gh_pZeel]h^lghm
]b__^klb`gb_b\Zgmer_khfmaZm_hk\henfgl^q\îm_hkma^_heehpbg`3
NMa^k^jnbk^f^gml_hk_bk^k^lblmZg\^!l^^MZ[e^,"'
N;^g]bg`pbee[^\kbmb\ZeZ[hnmma^p^ZdZqbl'
NMa^k^Zk^]b__^k^gmkne^l_hkliZ\bg`Zg]jnZgmbmrh_k^bg_hk\^f^gm
!l^^[êhp"'
Ma^k^blghli^\b_b\`nb]Zg\^`bo^g_hk[^g]bg`Z[hnmma^lmkhg`Zqbl
_hklmZ[bebmr'Ahpô^k%maîkbg\bie^lh_<BKB:Kîhkm*)1fZr[^
_heehp^]':em^kgZmboêrma^lmknmZg]mb^f^mah]fZr[^nl^]!l^\mbhg
/'.h_ma^>nkh\h]^"'
:
?Z\mhk_hk]^m^kfbgbg`le^g]^kg^llebfbm
*(!*$)'+h^_"
:\
[a
:l
:k^Zh_mhmZe\henfgk^bg_hk\^f^gm
;
\
?Z\mhk]î^g]bg`hg\nkoZmnk^]blmkb[nmbhg
*)!_hk\hglmZgm\khll&l^\mbhg"
<
*'0¾kf
]
>__^\mbo^]îma
^+
L^\hg]hk]^k^\\^gmkb\bmr
^b
>\\^gmkb\bmr]n^mh`^hf^mkb\bfi^k_^\mbhgl
!*(k"e)(\
>l
>eZlmb\fh]nenlh_k^bg_hk\bg`lm^ê
+))@IZ
_\]
α\\_\d(γ\
_\d
e
<e^Zka^bàmh_\hfik^llbhgf^f[^k[^mp^^g
^g]k^lmkZbgml
e)
>__^\mboê^g`ma
Dk
<hkk^\mbhg_Z\mhk]î^g]bg`hgZqbZeehZ]
Dh
?Z\mhkmZdbg`bgmhZ\\hngm\k^î
F)*%F)+
? bklmhk]^kfhf^gmlbg\en]bg`ma^^__^\mh_
`^hf^mkb\bfi^k_^\mbhgluF)+uªuF)*u
F+
GhfbgZel^\hg]hk]^kfhf^gm
G>]^+
F)^
>jnboZe^gm_bklmhk]^kfhf^gm
)'/F)+$)'-F)*ª)'-F)+
F>]
NembfZm^]^lb`gfhf^gm
F>ji
? bklmhk]^k[^g]bg`fhf^gmng]^k
jnZlb&i^kfZg^gmehZ]bg`
g
KêZmbo^ZqbZe_hk\^
G>](!:\_\]"
g[Ze
OZen^h_gZmfZqbfnffhf^gmh_k^lblmZg\^
)'-
gn
?Z\mhkmhZeehp_hkk^bg_hk\^f^gmbgma^\henfg
*$ω
G>]
NembfZm^ZqbZeehZ]
kf
Fhf^gmkZmbh
F)*(F)+
q
=îmamhg^nmkZeZqbl
!]¾s"()'-
s
Eô^kZkf
Maximum areas of reinforcement
α\\
<h^__b\b^gmmZdbg`Z\\hngmh_ehg`m^kf^__^\ml
hg\hfik^llbo^lmk^g`maZg]h_ng_ZohnkZ[e^
^__^\mlk^lnembg`_khfma^pZrehZ]blZiieb^]
Bg>nkh\h]^+ma^fZqbfnfghfbgZek^bg_hk\^f^gmZk^Z_hk\henfgl
Zg]pZeelhnmlb]êZilbl-\hfiZk^]pbma/bg;L1**)'Ahpô^k%
mablZk^Z\Zg[^bg\k^Zl^]ikhob]^]maZmma^\hg\k^m^\Zg[îeZ\^]
Zg]\hfiZ\m^]ln__b\b^gmer'B_k^jnbk^]lê_&\hfiZ\mbg`\hg\k^m^fZr
[^nl^]_hkiZkmb\neZker\hg`^lm^]lbmnZmbhgl%pa^k^ma^k^bg_hk\bg`[Zkl
lahne][^liZ\^]mh^glnk^maZmma^\hg\k^m^\Zg_ehpZkhng]ma^f'
?nkma^k`nb]Zg\^\Zg[^_hng]bgLê_&\hfiZ\mbg`\hg\k^m^'
Minimum reinforcement requirements
Ma^k^\hff^g]^]fbgbfnf]bZf^m^kh_ehg`bmn]bgZek^bg_hk\^f^gmbg
\henfglbl*+ff'Ma^fbgbfnfZk^Zh_ehg`bmn]bgZek^bg_hk\^f^gmbg
\henfglbl`bo^g[r3:l%fbg6)'*)G>](_r]ª)'))+:\>qi'!2'*+G"
Ma^]bZf^m^kh_ma^mkZglo^kl^k^bg_hk\^f^gmlahne]ghm[ê^llmaZg
/ffhkhg^jnZkm^kh_ma^fZqbfnf]bZf^m^kh_maêhg`bmn]bgZe[Zkl'
)'1._hk_e^qnk^Zg]ZqbZe
ehZ]l'*')_hkhma^k
ia^ghf^gZ!?khfNDG:"
β
?Z\mhk
)',.$_\d(+))¾λ(*.)
εr]
=^lb`goZen^h_lmkZbgbgk^bg_hk\^f^gm
_r](>l
γf
*'*._hkk^bg_hk\^f^gm!γl"
*'._hk\hg\k^m^!γ\"
l
Le^g]^kg^ll
e)(b
l ebf
Le^g]^kg^llebfbm
¬_b
=^`k^^h_nmbeblZmbhgbgZ_bk^
G>]%_b (GK]
h^_
>__^\mbo^\k^îkZmbh
h!∞%mh"F>ji (F>]
h !∞%m)"
?bgZe\k^î\h&^__b\b^gmmh<e,'*'-
ω
F^\aZgb\Zek^bg_hk\^f^gmkZmbh
uqu
:[lhenmôZen^h_q
:l_r](!:\_\]"
FZq'tq%r$svMa^fZqbfnfh_oZen^lqhkr$s
41
.'<henfgl
Spacing requirements for columns
Particular requirements for walls
Ma^fZqbfnfliZ\bg`h_mkZglo^kl^k^bg_hk\^f^gm!b'^'ebgdl"bg
\henfgl!<eZnl^2'.',!*""lahne]ghm^q\^^]3
N*+mbf^lma^fbgbfnf]bZf^m^kh_maêhg`bmn]bgZe[Zkl'
N/)h_maê^ll^k]bf^glbhgh_ma^\henfg'
N+-)ff'
:mZ]blmZg\^`k^Zm^kmaZgmaêZk`^k]bf^glbhgh_ma^\henfgZ[ho^
hk[êhpZ[^ZfhkleZ[ma^l^liZ\bg`l\Zg[^bg\k^Zl^][rZ_Z\mhk
h_*'/0'Ma^fbgbfnf\e^Zk]blmZg\^[^mp^^gma^[Zkllahne][^ma^
`k^Zm^kh_ma^[Zk]bZf^m^k%Z``k^`Zm^lbsîenl.ffhk+)ff'
Ghehg`bmn]bgZe[Zklahne][^_nkma^kmaZg*.)ff_khfmkZglo^kl^
k^bg_hk\^f^gm!ebgdl"bgma^\hfik^llbhgshg^'
Ma^fbgbfnfZk^Zh_o^kmb\Zek^bg_hk\^f^gmbgpZeelbl`bo^g[r3
:l%fbg6)'))+:\
AZe_h_mablZk^Zlahne][êh\Zm^]Zm^Z\a_Z\^'Ma^]blmZg\^[^mp^^g
mphZ]cZ\^gmo^kmb\Ze[Zkllahne]ghm^q\^^]maê^ll^kh_^bma^kmak^^
mbf^lma^pZeemab\dg^llhk-))ff'
Ma^fbgbfnfZk^Zh_ahkbshgmZek^bg_hk\^f^gmbgpZeelblma^`k^Zm^k
h_^bma^k+.h_o^kmb\Zek^bg_hk\^f^gmhk)'))*:\'Ahpô^k%pa^k^
\kZ\d\hgmkheblbfihkmZgm%^ZkerZ`^ma^kfZeZg]lakbgdZ`^^__^\ml
lahne][^\hglb]^k^]^qieb\bmer'
References
1 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾*%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^lZg]kne^l_hk[nbe]bg`l';LB%+))-'
2 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1**)¾*%Lmkn\mnkZenl^h_\hg\k^m^¾IZkm*%<h]^h_ikZ\mb\^_hk]^lb`gZg]\hglmkn\mbhg';LB%+))-'
3 G:K:R:G:G%KL;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3Bgmkh]n\mbhg'Ma^<hg\k^m^<^gmk^%+)).'
4 @HH=<ABE=%<A%>EBHMM%DLP>;LM>K%KF'>\hghfb\\hg\k^m^_kZf^ê^f^gml'Ma^<hg\k^m^<^gmk^%+))2'
5 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾+'>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^l¾lmkn\mnkZe_bk^]^lb`g';LB%+))-'
6 @HH=<ABE=%<AP>;LM>K%KF'Lik^Z]la^^ml_hk\hg\k^m^]^lb`gmh;L1**)Zg]>nkh\h]^+%o^klbhg,'Ma^<hg\k^m^<^gmk^%+))/'
7 ;
KBMBLALM:G=:K=LBGLMBMNMBHG'I=//10%;Z\d`khng]iZi^kmhma^NDGZmbhgZe:gg^qmh;L>G*22+¾*¾*Zg];L>G*22+¾*¾+';LB%+))/'
8 FHLL%KF;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3;^Zfl'Ma^<hg\k^m^<^gmk^%+))/'
9 ?K:L>K%:LCHG>L:>D'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3Lmkn\mnkZe_bk^]^lb`g'Ma^<hg\k^m^<^gmk^%+))2'
10 <BKB:'Kîhkm*)+3=^lb`gh_la^ZkpZee[nbe]bg`l'<BKB:%*21-'
11 MA><HG<K>M>LHMR'M^\agb\ZeKîhkmGh/+3Lê_&\hfiZ\mbg`\hg\k^m^':kôb^p'Ma^Lh\b^mr%+)).'
42
/'?hng]Zmbhgl
R Webster<>g`%?BLmkn\m>O Brooker;>g`%<>g`%FB<>%FBLmkn\m>
Eurocode 7: Geotechnical design
Scope
:ee_hng]Zmbhgllahne][^]^lb`g^]lhmaZmma^lhbelZ_êrk^lblmlma^
Z\mbhglZiieb^]mhma^lmkn\mnk^'Ma^]^lb`gh_Zgr_hng]Zmbhg\hglblmlh_
mph\hfihg^gml4ma^`^hm^\agb\Ze]^lb`gZg]ma^lmkn\mnkZe]^lb`gh_ma^
_hng]Zmbhgbmlê_'Ahpô^k%_hklhf^_hng]Zmbhgl!^'`'_e^qb[e^kZ_ml"ma^^__^\m
h_ma^bgm^kZ\mbhg[^mp^^gma^lhbeZg]lmkn\mnk^fZr[^\kbmb\ZeZg]fnlm
Zelh[^\hglb]^k^]'@^hm^\agb\Ze]^lb`gbl\ho^k^][r>nkh\h]^0%pab\a
lni^kl^]^llô^kZe\nkk^gm;kbmblaLmZg]Zk]lbg\en]bg`;L.2,)%;L1))+
Zg];L1))-'Ma^g^p>nkh\h]^fZkdlZlb`gb_b\Zgm\aZg`^bg`^hm^\agb\Ze
]^lb`gbgmaZmebfbmlmZmîkbg\bie^lZk^nl^]makhnàhnmZg]mabllahne]
^glnk^\hglblm^g\r[^mp^^gma^>nkh\h]^l'Ma^k^Zk^mphiZkmlmh>nkh\h]^0%
IZkm*3@^g^kZekne^lZg]IZkm+3@khng]bgo^lmb`ZmbhgZg]m^lmbg`'@nb]Zg\^hg
ma^]^lb`gh_k^mZbgbg`pZeel\Zg[^_hng]bg<aZim^k2'
Ma^^ll^gmbZe_^Zmnk^lh_>nkh\h]^0%IZkm*kêZmbg`mh_hng]Zmbhg]^lb`gZk^
]bl\nll^]bgmabl\aZim^k'Bmlahne][^^fiaZlbl^]maZmmablin[eb\Zmbhg\ho^kl
hgerma^]^lb`gh_lbfie^_hng]Zmbhgl%pab\aZk^ZlfZeeiZkmh_ma^l\hi^h_
>nkh\h]^0'Ma^k^_hk^bmlahne]ghm[^kêb^]hg_hk`^g^kZe`nb]Zg\^hgmabl
>nkh\h]^'
Limit states
Ma^_heehpbg`nembfZmêbfbmlmZm^l!NEL"lahne][^lZmbl_b^]_hk`^hm^\agb\Ze
]^lb`g4ma^r^Z\aaZo^ma^bkhpg\hf[bgZmbhglh_Z\mbhgl'!?hkZg^qieZgZmbhg
h_>nkh\h]^m^kfbgheh`rie^Zl^k^_^kmh<aZim^k*%hkb`bgZeerin[ebla^]Zl
Bgmkh]n\mbhgmh>nkh\h]^l'"
EQU Ehllh_^jnbeb[kbnfh_ma^lmkn\mnk^'
STR Bgm^kgZe_Zbenk^hk^q\^llbo^]^_hkfZmbhgh_ma^lmkn\mnk^hklmkn\mnkZe
f^f[^k'
GEO ?Zbenk^]n^mh^q\^llbo^]^_hkfZmbhgh_ma^`khng]'
UPL Ehllh_^jnbeb[kbnf]n^mhnieb_m[rpZm^kik^llnk^'
HYD ?Zbenk^\Znl^][rar]kZneb\`kZ]b^gml'
BgZ]]bmbhg%ma^l^kob\^Z[bebmrebfbmlmZm^l!LEL"lahne][^lZmbl_b^]'Bmpbee
nlnZeer[^\e^ZkmaZmhg^h_maêbfbmlmZm^lpbee`ho^kgma^]^lb`gZg]
ma^k^_hk^bmpbeeghm[^g^\^llZkrmh\Zkkrhnm\a^\dl_hkZeeh_ma^f%Zemahnà
bmbl\hglb]^k^]`hh]ikZ\mb\^mhk^\hk]maZmma^raZo^Zee[^^g\hglb]^k^]'
Geotechnical Categories
>nkh\h]^0k^\hff^g]lmak^^@^hm^\agb\Ze<Zm^`hkb^lmhZllblmbg^lmZ[eblabg`
ma^`^hm^\agb\Ze]^lb`gk^jnbk^f^gml_hkZlmkn\mnk^!l^^MZ[e^*"'
mh[^Ziieb^]mhma^Z\mbhgl_hkma^l^\hf[bgZmbhglh_iZkmbZe_Z\mhkl
Zk^`bo^gbgMZ[e^+Zg]maîZkmbZe_Z\mhkl_hkma^`^hm^\agb\Ze
fZm^kbZeikhi^kmb^lZk^`bo^gbgMZ[e^,'<hf[bgZmbhg*pbee`^g^kZeer
`ho^kgma^lmkn\mnkZek^lblmZg\^%Zg]<hf[bgZmbhg+pbee`^g^kZeer
`ho^kgma^lbsbg`h_ma^_hng]Zmbhgl'
MaîZkmbZe_Z\mhkl_hklhbek^lblmZg\^mhleb]bg`Zg][^Zkbg`lahne][^
mZd^gZl*')_hk[hma\hf[bgZmbhgl'
BmblZgmb\biZm^]maZmlmkn\mnkZe^g`bg^^klpbeemZd^k^lihglb[bebmr_hkma^
`^hm^\agb\Ze]^lb`gh_\Zm^`hkr*lmkn\mnk^l%Zg]maZm`^hm^\agb\Ze
^g`bg^^klpbeemZd^k^lihglb[bebmr_hk\Zm^`hkr,lmkn\mnk^l'Ma^
`^hm^\agb\Ze]^lb`gh_\Zm^`hkr+lmkn\mnk^lfZr[^ng]^kmZd^g[r
f^f[^klh_^bma^kikh_^llbhg'Mabl]^\blbhgpbeeo^krfn\a]î^g]hg
bg]bob]nZe\bk\nflmZg\^l'
Methods of design and combinations
Ma^kâZlghm[^^gZ\hgl^glnlZfhg`lm`^hm^\agb\Ze^g`bg^^kl
ho^kma^Ziieb\Zmbhgh_ebfbmlmZmîkbg\bie^lmh`^hm^\agb\Ze]^lb`g'
Ma^k^_hk^%mhZeehp_hkma^l^]b__^k^g\^lh_hibgbhg%>nkh\h]^0
ikhob]^l_hkmak^^=^lb`g:iikhZ\a^lmh[^nl^]_hkma^NEL'Ma^
]^\blbhghgpab\aZiikhZ\amhnl^_hkZiZkmb\neZk\hngmkrbl`bo^g
bgbmlGZmbhgZe:gg^q'Bgma^ND=^lb`g:iikhZ\a*pbee[^li^\b_b^]
bgma^GZmbhgZe:gg^q'?hkmabl=^lb`g:iikhZ\a!^q\en]bgìbe^Zg]
Zg\ahkZ`^]^lb`g"ma^k^Zk^mphl^mlh_\hf[bgZmbhglmhnl^_hkma^
LMKZg]@>HnembfZmêbfbmlmZm^l'MaôZen^l_hkmaîZkmbZe_Z\mhkl
MaîZkmbZe_Z\mhklmh[^Ziieb^]mhma^Z\mbhglZmma^>JNebfbmlmZm^
Zk^`bo^gbgMZ[e^-4ma^`^hm^\agb\ZefZm^kbZeiZkmbZe_Z\mhklZk^`bo^g
bgMZ[e^,'
?hkma^LEL%>nkh\h]^0]h^lghm`bo^ZgrZ]ob\^hgpa^ma^kma^
\aZkZ\m^kblmb\%_k^jn^gmhkjnZlb&i^kfZg^gm\hf[bgZmbhglahne][^
nl^]'Pa^k^maîk^l\kbimbo^f^mah]blnl^]_hklik^Z]_hng]Zmbhgl
!l^îZ`^,"ma^gma^\aZkZ\m^kblmb\oZen^llahne][^Z]him^]'?hk
Table 1
Geotechnical categories of structures
Category
Description
Risk of geotechnical failure
Examples from Eurocode 7
*
LfZeeZg]kêZmboêrlbfie^lmkn\mnk^l
G^èb`b[e^
Ghg^`bo^g
+
<hgo^gmbhgZemri^lh_lmkn\mnk^Zg]_hng]Zmbhg
pbmagh]b__b\nem`khng]hkehZ]bg`\hg]bmbhgl
Gh^q\îmbhgZekbld
Lik^Z]_hng]Zmbhgl
,
:eehma^klmkn\mnk^l
:[ghkfZekbldl
EZk`^hkngnlnZelmkn\mnk^l
>q\îmbhgZe`khng]\hg]bmbhgl
Table 2
Design values of actions derived for UK design, STR/GEO ultimate limit state – persistent and transient design situations
Combination
Expression reference
from BS EN 1990
Permanent actions
Unfavourable
Leading variable
action
Favourable
Accompanying variable actions
Main (if any)
Others
Combination 1 (Application of combination 1 (BS EN 1997) to set B (BS EN 1990))
>qi'!/'*)"
*',.@dZ
*')@dZ
*'.[Jd
¾
*'.[ch%b\Jd%b
>qi'!/'*)Z"
*',.@dZ
*')@dZ
¾
*'.ch%*\Jd
*'.[ch%b\Jd%b
>qi'!/'*)["
)'2+.]q*',.@dZ
*')@dZ
*'.[Jd
¾
*'.[ch%b\Jd%b
¾
*',[ch%b \Jd%b
Combination 2 (Application of combination 2 (BS EN 1997) to set C (BS EN 1990))
>qi'!/'*)"
*')@dZ
*')@dZ
*',[Jd%*
Key
a Pa^k^maôZkbZmbhgbgi^kfZg^gmZ\mbhgblghm\hglb]^k^]lb`gb_b\Zgm@d%c%lniZg]@d%c%bg_fZr[^mZd^gZl@d
b Pa^k^ma^Z\mbhgbl_ZohnkZ[e^%gJ%b6)Zg]maôZkbZ[e^Z\mbhgllahne][^b`ghk^]
c MaôZen^h_c h\Zg[^h[mZbg^]_khfMZ[e^G:':*'*h_ma^NDG:mh;L>G*22)!hkl^^MZ[e^,h_<aZim^k*"
d MaôZen^h_jbgma^NDG:mh;L>G*22)bl)'2+.
Table 3
Partial factors for geotechnical material properties
Angle of shearing resistance
(apply to tan h)
Effective cohesion
Undrained shear
strength
Unconfined
strength
Bulk density
Symbol
gh
gc’
gcu
gqu
gg
<hf[bgZmbhg*
*')
*')
*')
*')
*')
<hf[bgZmbhg+
*'+.
*'+.
*'-
*'-
*')
>JN
*'*
*'*
*'+
*'+
*')
44
/'?hng]Zmbhgl
]bk^\mf^mah]lh_\Ze\neZmbhgma^_k^jn^gm\hf[bgZmbhg\Zg[^nl^]
_hklbsbg`h__hng]ZmbhglZg]ma^jnZlb&i^kfZg^gm\hf[bgZmbhg\Zg[^
nl^]_hkl^mme^f^gm\Ze\neZmbhgl'
?nkma^kbg_hkfZmbhghg]^lb`g\hf[bgZmbhgl\Zg[^_hng]bg<aZim^k*%
hkb`bgZeerin[ebla^]ZlBgmkh]n\mbhgmh>nkh\h]^l'
Geotechnical design report
:`^hm^\agb\Ze]^lb`gkîhkmlahne][îkh]n\^]_hk^Z\aikhc^\m%
ô^gb_bmblhgerZlbgè^la^^m'Ma^kîhkmlahne]\hgmZbg]^mZbelh_
ma^lbm^%bgm^kik^mZmbhgh_ma^`khng]bgo^lmb`Zmbhgkîhkm%`^hm^\agb\Ze
]^lb`gk^\hff^g]ZmbhglZg]Z]ob\^hglni^koblbhg%fhgbmhkbg`Zg]
fZbgm^gZg\^h_ma^phkdl'BmblebdêrmaZmmablkîhkmpbeek^jnbk^bginm
_khffhk^maZghg^\hglnemZgm%]î^g]bg`hgpa^ma^kmaîkhc^\mblbg
@^hm^\agb\Ze<Zm^`hkr*%+hk,'
Ma^_hng]Zmbhg]^lb`gk^\hff^g]Zmbhgllahne]bg\en]^[^Zkbg`
k^lblmZg\^lZg]\aZkZ\m^kblmb\oZen^l_hklhbeiZkZf^m^kl'Bmlahne]
Zelh\e^ZkerlmZm^pa^ma^kmaôZen^lZk^Ziieb\Z[e^mhLELhkNELZg]
pa^ma^kma^rZk^_hk<hf[bgZmbhg*hk<hf[bgZmbhg+'
Table 4
Design values of actions derived for UK design, EQU ultimate limit
state – persistent and transient design situations
Combination Permanent actions
Expression
reference
Unfavourable Favourable
Leading Accompanying variable
variable actions
action
Main
Others
(if any)
>qi'!/'*)"
*'.[Jd
*'*@dZ
)'2)@dZ
*'.[ch%b\Jd%b
¾
Key
a P
a^k^maôZkbZmbhgbgi^kfZg^gmZ\mbhgblghm\hglb]^k^]lb`gb_b\Zgm@d%c%lni
Zg]@d%c%bg_fZr[^mZd^gZl@d
b Pa^k^ma^Z\mbhgbl_ZohnkZ[e^%gJ%b6)Zg]maôZkbZ[e^Z\mbhgllahne][^b`ghk^]
c MaôZen^h_ch\Zg[^h[mZbg^]_khfMZ[e^G:':*'*h_ma^NDG:mh;L>G*22)
Spread foundations
Ma^`^hm^\agb\Ze]^lb`gh_lik^Z]_hng]Zmbhgl!^'`'lmkbiZg]iZ]
_hng]Zmbhgl"bl\ho^k^][rl^\mbhg/h_>nkh\h]^0%IZkm*Zg]mabl
`bo^lmak^^f^mah]l_hk]^lb`g3
N =bk^\mf^mah]¾\Ze\neZmbhgbl\Zkkb^]hnm_hk^Z\aebfbmlmZm^'
N Bg]bk^\mf^mah]¾^qi^kb^g\^Zg]m^lmbg`nl^]mh]^m^kfbg^
l^kob\^Z[bebmrebfbmlmZmîZkZf^m^klmaZmZelhlZmbl_rZeekêôZgm
ebfbmlmZm^l!bg\en]^]bg>nkh\h]^0fZbgermhlnbm?k^g\a]^lb`g
f^mah]l%Zg]blghm]bl\nll^]_nkma^ka^k^"'
N Ik^l\kbimbo^f^mah]bgpab\aZik^lnf^][^Zkbg`k^lblmZg\^blnl^]'
?hkfhlmlik^Z]_hng]Zmbhglbgma^ND%l^mme^f^gmpbee[^ma^
`ho^kgbg`\kbm^kbhg4mkZ]bmbhgZeerÂZeehpZ[e^[^Zkbgìk^llnk^lÃaZo^[^^g
nl^]mhebfbml^mme^f^gm'Mabl\hg\îmh_bg\k^Zlbg`ma^_Z\mhkh_lZ_^mr
hg[^Zkbg`k^lblmZg\^lmh\hgmkhel^mme^f^gmfZrlmbee[^nl^]pbmama^
ik^l\kbimbo^f^mah]'Ma^^q\îmbhgbl_hklh_m\eZrlpa^k^>nkh\h]^0
k^jnbk^ll^mme^f^gm\Ze\neZmbhglmh[^ng]^kmZd^g'
Pa^gnlbg`ma^]bk^\mf^mah]%\Ze\neZmbhglZk^\Zkkb^]hnm_hk^Z\a
ebfbmlmZm^':mma^NEL%ma^[^Zkbg`k^lblmZg\^h_ma^lhbelahne][^
\a^\d^]nlbgìZkmbZe_Z\mhklhgma^lhbeikhi^kmb^lZlpêeZlhg
ma^Z\mbhgl':mma^LELma^l^mme^f^gmh_ma^_hng]Zmbhgllahne][^
\Ze\neZm^]Zg]\a^\d^]Z`Zbglmi^kfbllb[eêbfbml'
Maîk^l\kbimbo^f^mah]fZr[^nl^]pa^k^\Ze\neZmbhgh_ma^lhbe
ikhi^kmb^lblghmihllb[e^hkg^\^llZkrZg]\Zg[^nl^]ikhob]^]maZm
\hgl^koZmbo^kne^lh_]^lb`gZk^nl^]'Ma^k^_hk^k^_^k^g\^\Zg\hgmbgn^
mh[^fZ]^mhMZ[e^*h_;L1))-!l^^MZ[e^."mh]^m^kfbgîk^lnf^]
!ZeehpZ[e^"[^Zkbgìk^llnk^l_hk\Zm^`hkr*lmkn\mnk^lZg]ikêbfbgZkr
\Ze\neZmbhgl_hk\Zm^`hkr+lmkn\mnk^l':em^kgZmboêr%maîk^lnf^]
[^Zkbg`k^lblmZg\^mhZeehp_hkl^mme^f^gm\Zg[^\Ze\neZm^][rma^
`^hm^\agb\Ze]^lb`g^kZg]bg\en]^]bgma^`^hm^\agb\Ze]^lb`gkîhkm'
Table 5
Presumed allowable bearing values under static loading (from BS 8004)
Category
Type of soil
Presumed allowable bearing value (kN/m2)
Remarks
Ghg&
\ha^lbo^
lhbel
=^gl^`kZoê%hk]^gl^lZg]Zg]`kZoê
7 /))
F^]bnf]^gl^`kZoê%hkf^]bnf
]^gl^lZg]Zg]`kZoê
5+))mh/))
Pb]mah__hng]Zmbhgghme^llmaZg*f'
@khng]pZm^keôêZllnf^]mh[^[êhpma^[Zl^
h_ma^_hng]Zmbhg'
<ha^lbo^
lhbel
Ehhl^`kZoê%hkehhl^lZg]Zg]`kZoê
5+))
<hfiZ\mlZg]
7 ,))
F^]bnf]^gl^lZg]
*))mh,))
Ehhl^lZg]
5*))
O^krlmb__[hne]^k\eZrZg]aZk]\eZr
,))mh/))
Lmb__\eZr
*.)mh,))
?bkf\eZr
0.mh*.)
Lh_m\eZrZg]lbem
50.
O^krlh_m\eZrZg]lbem
GhmZiieb\Z[e^
Lnl\îmb[e^mhehg`&m^kf\hglheb]Zmbhgl^mme^f^gm
Note
Ma^lôZen^lZk^_hkikêbfbgZkr]^lb`ginkihl^lhger'
45
:_ehp\aZkmlahpbg`ma^]^lb`gikh\^ll_hklaZeehp_hng]Zmbhglbl
`bo^gbg?b`nk^*'
IZkmbZe_Z\mhkl_hkma^lhbeiZkZf^m^klnl^]mh]^m^kfbg^ma^k^lblmZg\^l
\Zg[^h[mZbg^]_khfMZ[e^,Z[ho^!<hf[bgZmbhg+"'
Pa^k^ma^k^blZfhf^gmZiieb^]mhma^_hng]Zmbhg%ma^>JNebfbm
lmZm^lahne]Zelh[^\a^\d^]':llnfbg`maîhm^gmbZeho^kmnkgbg`h_
ma^[Zl^bl]n^mhmaôZkbZ[e^Z\mbhg_khfma^pbg]%ma^_heehpbg`
\hf[bgZmbhglahne][^nl^]!maôZkbZ[e^bfihl^]Z\mbhgblghm
\hglb]^k^]mh\hgmkb[nm^mhma^lmZ[bebmrh_ma^lmkn\mnk^"3
Maîk^llnk^]blmkb[nmbhgng]^kma^[Zl^lahne][^Zll^ll^]mh^glnk^
maZmma^fZqbfnfik^llnk^]h^lghm^q\^^]ma^[^Zkbg`k^lblmZg\^l
h[mZbg^]_khfma^`^hm^\agb\Ze]^lb`gkîhkmZm[hma>JNZg]@>H
nembfZmêbfbmlmZm^l!l^^?b`nk^+"'B_ma^^\\^gmkb\bmrbl`k^Zm^kmaZg
E(/ZmLEL%ma^gmaîk^llnk^]blmkb[nmbhgnl^]mh]^m^kfbg^ma^
l^mme^f^gmlahne][^fh]b_b^][^\Znl^m^glbhg\Zgghmh\\nk[^mp^^g
ma^[Zl^Zg]ma^lhbe'Bgmabl\Zl^ma^]^lb`g^klahne]lZmbl_rabflê_
maZmma^k^pbee[^ghZ]o^kl^\hgl^jn^g\^l!^'`'^q\^llbo^khmZmbhgh_
ma^[Zl^"'Bmlahne]Zelh[^ghm^]maZmma^NELik^llnk^]blmkb[nmbhg
]bZ`kZfpbee[^k^\mZg`neZkZg]ghmmkZi^shb]Ze'
)'2@d$*'.Jd%p >JN\hf[bgZmbhg
pa^k^3
@dblma^lmZ[beblbg`\aZkZ\m^kblmb\i^kfZg^gmZ\mbhg
!Nl^*'*@d_hkZ]^lmZ[beblbgì^kfZg^gmZ\mbhg"
Jd%pblma^]^lmZ[beblbg`\aZkZ\m^kblmb\oZkbZ[e^pbg]Z\mbhg
Reinforced concrete pads
Figure 1
Pa^k^maîZ]_hng]Zmbhglk^jnbk^k^bg_hk\^f^gmma^_heehpbg`\a^\dl
lahne][^\Zkkb^]hnmmh^glnk^3
N Ln__b\b^gmk^bg_hk\^f^gmmhk^lblm[^g]bg`fhf^gml'
N Ing\abg`la^Zklmk^g`ma'
N ;^Zfla^Zklmk^g`ma'
Procedures for depth of spread foundations
START
Obtain soil parameters from Ground Investigation report
Design using
direct method?
Yes
No
Ahpô^k%ma^k^fZr[^^\hghfb^lmhfZ]^_khfnlbg`>qik^llbhgl
!/'*)Z"hk!/'*)["_khfma^>nkh\h]^'
Size foundation
(geotechnical design) using
the worst of Combinations
1 or 2 (ULS) for actions
and geotechnical material
properties. Combination 2
will usually govern.
Use prescriptive method.
Size foundation
(geotechnical design)
using SLS for actions
and presumed
bearing resistance
Is there an
overturning moment?
Check overturning using EQU
limit state for actions and
GEO Combination 2
for material properties.
Yes
Ma^fhf^gmlZg]la^Zk_hk\^llahne][^Zll^ll^]nlbg`ma^LMK
\hf[bgZmbhg3
*',.@d$*'.Jd LMK\hf[bgZmbhg*!>qi'!/'*)""
Ma^\kbmb\Ze[^g]bg`fhf^gml_hk]^lb`gh_[hmmhfk^bg_hk\^f^gm
Zkêh\Zm^]Zmma^\henfg_Z\^l';hma[^Zfla^ZkZg]ing\abg`
la^Zklahne]ma^g[^\a^\d^]Zmmaêh\Zmbhgllahpgbg?b`nk^,'?hk
ing\abg`la^Zkma^`khng]k^Z\mbhgpbmabgmaî^kbf^m^kfZr[^
]^]n\m^]_khfma^\henfgehZ]!>qik^llbhg!/'-1"%>nkh\h]^+¾*¾*"'
BmblghmnlnZe_hkZiZ]_hng]Zmbhgmh\hgmZbgla^Zkk^bg_hk\^f^gm%
ma^k^_hk^bmblhgerg^\^llZkrmh^glnk^maZmma^\hg\k^m^la^Zklmk^ll
\ZiZ\bmrpbmahnmla^Zkk^bg_hk\^f^gm!oK]%\¾l^^MZ[e^/"bl`k^Zm^kmaZg
Ziieb^]la^Zklmk^ll!o>]6O>](![]""'
No
B_ma^[Zlb\la^Zklmk^llbl^q\^^]^]%ma^]^lb`g^kfZrbg\k^Zl^ma^
]îmah_ma^[Zl^':em^kgZmboêr%ma^Zfhngmh_fZbgk^bg_hk\^f^gm
\hne][^bg\k^Zl^]hk%e^ll]^lbkZ[er%la^Zkebgdl\hne][îkhob]^]'!L^^
<aZim^k-%hkb`bgZeerin[ebla^]Zl;^Zfl_hkZg^qieZgZmbhgh_ahpmh
]^lb`gla^Zkk^bg_hk\^f^gm'"
Design foundation (structural design) using the worst of
Combinations 1 and 2 (ULS) for actions and geotechnical
material properties.
Figure 2
Pressure distributions for pad foundations
M
M
P
1
L
P
P
or
P
e
e = M/ P
L = width of base
SLS pressure distributions
46
P
P
L 2e
2P
1.5 L 3 e
P
6e
1+
L
L
M
6e
L
P
e
P
e
ULS pressure distribution
/'?hng]Zmbhgl
Figure 4
Design for punching shear
>nkh\h]^+ikhob]^lli^\b_b\`nb]Zg\^hgma^]^lb`gh__hng]Zmbhgl_hk
ing\abg`la^Zk%Zg]mabloZkb^l_khfmaZm`bo^g_hkleZ[l'Bg>nkh\h]^+ma^
la^Zki^kbf^m^kaZlkhng]^]\hkg^klZg]ma^_hk\^l]bk^\merk^lblm^][r
ma^`khng]lahne][^]^]n\m^]!mhZohb]ngg^\^llZkber\hgl^koZmbo^
]^lb`gl"'Ma^\kbmb\Zei^kbf^m^klahne][^_hng]bm^kZmboêr%[nmbmbl
`^g^kZeerZ\\îmZ[e^mh\a^\dZm]Zg]+]':em^kgZmboêr%Zlik^Z]la^^m
\hne][^nl^]!^'`'lik^Z]la^^mM<<1*_khfLik^Z]la^^ml_hk\hg\k^m^
]^lb`gmh;L1**)Zg]>nkh\h]^+ "'Maîkh\^]nk^_hk]^m^kfbgbg`ma^
ing\abg`la^Zkk^jnbk^f^gmlbllahpgbg?b`nk^-'
Procedure for determining punching shear capacity for pad foundations
START
Determine value of factor β
(β =1.0 when applied moment is zero; refer to Expressions
(6.38) to (6.42) from BS EN 1992–1–1 for other cases)
Determine value of vEd,max
(design shear stress at face of column) from:
vEd,max = β(VEd – DVEd) (from Exp. (6.38))
(u0deff)
Table 6
vRd,c resistance of members without shear reinforcement, MPa
rl
where u0 is perimeter of column
(see Clause 6.4.5 for columns at base edges)
deff = (dy + dz)/2 where dy and dz
are the effective depths in orthogonal directions
Effective depth, d (mm)
0.25%
300
400
500
600
700
800
900
0.47
0.43
0.40
0.38
0.36
0.35
0.35
1000a
0.34
0.50%
0.54
0.51
0.48
0.47
0.45
0.44
0.44
0.43
0.75%
0.62
0.58
0.55
0.53
0.52
0.51
0.50
0.49
1.00%
0.68
0.64
0.61
0.59
0.57
0.56
0.55
0.54
1.25%
0.73
0.69
0.66
0.63
0.62
0.60
0.59
0.58
1.50%
0.78
0.73
0.70
0.67
0.65
0.64
0.63
0.62
1.75%
0.82
0.77
0.73
0.71
0.69
0.67
0.66
0.65
≥2.00%
0.85
0.80
0.77
0.74
0.72
0.70
0.69
0.68
1.816
1.707
1.632
1.577
1.535
1.500
1.471
1.447
k
Key
a?hk]îmal`k^Zm^kmaZg*)))\Ze\neZmôK]%\]bk^\mer'
Notes
1MZ[e^]^kbo^]_khf3oK]%\6)'*+d!*))r B_\d"!*(,"ª)'),.d*'._\d)'.
pa^k^d6*$√!+))(]"©+Zg]r B6√!rBr$r Bs"©)')+%
r Br6:lr(![]"Zg]r Bs6:ls(![]"
2MablmZ[eâZl[^^gikîZk^]_hk_\d6,)4
pa^k^r e^q\^^])'-)ma^_heehpbg`_Z\mhklfZr[^nl^]3
Determine value of vRd,max (refer to Table 7)
No
Redesign foundation
Is vEd,max < vRd,max?
Yes
Determine value of vEd, (design shear stress) from:
vEd = (VEd – DVEd)
(u1deff)
where u1 is length of control perimeter (refer to Figure 5). For
eccentrically loaded bases, refer to Exp. (6.51).
The control perimeter will have to be found through iteration;
it will usually be between d and 2d
Determine concrete punching shear capacity vRd (without
shear reinforcement) from 2dvRd,c/a (Refer to Table 6 for vRd,c)
f\d
25
28
32
35
40
45
50
Factor
)'2-
)'21
*')+
*').
*'*)
*'*-
*'*2
No
Is vEd < vRd at
critical perimeter?
Figure 3
Yes
Shear checks for pad foundations
Either increase main
steel, or provide
punching shear
reinforcement required.
(Not recommended
for foundations.)
No shear reinforcement required. Check complete.
Punching shear perimeters,
(load within deducted from V Ed)
Beam shear
faces
Figure 5
Typical basic control perimeters around loaded areas
2d
u1
2d
2d
u1
bz
d
h
Bends may be
required
d
by
47
Raft foundations
_e^qnk^k^_^k^g\^lahne][^fZ]^mh<aZim^k-%hkb`bgZeerin[ebla^]Zl
;^Zfl '
Ma^[Zlb\]^lb`gikh\^ll^l_hkkZ_mlZk^lbfbeZkmhmahl^_hkblheZm^]
iZ]_hng]Zmbhglhkibe^\Zil'Ma^hger]b__^k^g\^bgZiikhZ\aeb^lbgma^
lê^\mbhgh_ZgZiikhikbZm^f^mah]_hkZgZerlbg`ma^bgm^kZ\mbhg[^mp^^g
ma^kZ_mZg]ma^`khng]lhZlmhZ\abô^Zk^ZlhgZ[e^kîk^l^gmZmbhgh_
ma^bk[âZobhnk'?hklmb__^kkZ_ml!b'^'liZg&mh&mab\dg^ll`k^Zm^kmaZg*)"pbma
Z_Zbkerk^`neZkeZrhnm%lbfieb_b^]ZiikhZ\a^lln\aZlrbê]ebg^hkma^_eZm
leZ[^jnboZe^gm_kZf^f^mah]fZr[^^fiehr^]%hg\^Zg^lmbfZmbhgh_
maôZkbZmbhglbg[^Zkbgìk^llnkâZl[^^gh[mZbg^]_khfZ`^hm^\agb\Ze
li^\bZeblm'PaZmô^klbfieb_b\ZmbhglZk^fZ]^%bg]bob]nZeêZlmb\kZ_m
k^Z\mbhgllahne]^jnZm^mhma^Ziieb^]\henfgehZ]l'
:em^kgZmboêr%ZmknllZgZeh`rfZr[^nl^]4mablbl\ho^k^]bgL^\mbhgl.'/'-
Zg]/'.h_>nkh\h]^+¾*¾*'Ma^lmknmZgè^ylahne][^Zme^Zlm+*'1mh
maâhkbshgmZe4ghm^maZmylahne][^f^Zlnk^]bgmaîeZg^h_ma^\henfg
Zg]ibe^'
Mabgg^k%fhk^_e^qb[e^kZ_mlhkmahl^pbmaZ\hfie^qeZrhnmfZrk^jnbk^
ma^Ziieb\Zmbhgh_Z_bgbm^ê^f^gmhk`kbeeZ`^ZgZerlbl'?hkkZ_ml[^Zkbg`
hg`kZgneZkln[&`kZ]^lhkpa^g\hgmb`nhnl&ibe^]pZeelhk]bZiakZ`f
i^kbf^m^kpZeelZkîk^l^gm%ma^`khng]fZr[^fh]êe^]ZlZl^kb^l
h_Pbgde^klikbg`l'Ahpô^k%_hk\ha^lbo^ln[&`kZ]^l%mablZiikhZ\abl
ngebdêrmh[ôZeb]%Zg]li^\bZeblmlh_mpZk^pbee[^k^jnbk^]'
;hma[^Zfla^ZkZg]ing\abg`la^Zklahne]ma^g[^\a^\d^]Zllahpgbg
?b`nk^/'?hk[^Zfla^Zk%ma^]^lb`gk^lblmZg\^lbgMZ[e^/fZr[^nl^]'B_ma^
[Zlb\la^Zklmk^llbl^q\^^]^]%ma^]^lb`g^klahne]bg\k^Zl^ma^]îmah_ma^
[Zl^':em^kgZmboêr%ma^Zfhngmh_fZbgk^bg_hk\^f^gm\hne][^bg\k^Zl^]hk%
e^ll]^lbkZ[er%la^Zkebgdl\hne][îkhob]^]'<Zk^lahne][^mZd^gmaZmfZbg
[ZklZk^_neerZg\ahk^]':lZfbgbfnf%Z_neeZg\ahkZ`^lahne][îkhob]^]
_khfma^bgg^k_Z\^h_ibe^l'EZk`^kZ]bnl[^g]lfZr[^k^jnbk^]'
Pa^gZll^llbg`ma^la^Zk\ZiZ\bmrbgZibe^\Zi%hgerma^m^glbhglm^ê
ieZ\^]pbmabgma^lmk^llshg^lahne][^\hglb]^k^]Zl\hgmkb[nmbg`mhma^
la^Zk\ZiZ\bmr!l^^?b`nk^0"'
Figure 6
Critical shear perimeters for piles
Piled foundations
Beam shear 5 d from column face
f /5
?hkmaînkihl^h_mabl\aZim^kbmblZllnf^]maZmmaîbe^]^lb`gpbee[^
\Zkkb^]hnm[rZli^\bZeblmibebg`\hgmkZ\mhk'Ma^Z\mbhglhgmaîbe^lfnlm
[^\e^Zker\hgo^r^]mhmaîbe^]^lb`g^k%Zg]ma^l^lahne][^[khd^g]hpg
bgmhma^ng_Z\mhk^]i^kfZg^gmZ\mbhglZg]^Z\ah_ma^Ziieb\Z[eôZkbZ[e^
Z\mbhgl!^'`'bfihl^]Zg]pbg]Z\mbhgl"'Maîbe^]^lb`g^k\Zgma^g\Zkkr
hnmma^lmkn\mnkZeZg]`^hm^\agb\Ze]^lb`gh_maîbe^l'
Pa^k^fhf^gmlZk^Ziieb^]mhmaîbe^\Zima^>JN\hf[bgZmbhg
lahne]Zelh[^nl^]mh\a^\dmaîbe^l\Zgk^lblmma^ho^kmnkgbg`_hk\^l'
Ma^l^>JNehZ]lfnlmZelh[^\e^Zker\hgo^r^]mhmaîbe^]^lb`g^k
Zg]ikh\^]nk^linmbgieZ\^mh^glnk^maîbe^lZk^]^lb`g^]_hkma^
\hkk^\m_hk\^l'
f /5
Punching shear 5 2d from column face
f
Figure 7
Shear reinforcement for pilecaps
A s contributing to shear capacity
:ibe^\ZifZr[^mk^Zm^]ZlZ[^Zfbg[^g]bg`%pa^k^ma^\kbmb\Ze
[^g]bg`fhf^gml_hkma^]^lb`gh_ma^[hmmhfk^bg_hk\^f^gmZk^
eh\Zm^]Zmma^\henfg_Z\^l'?hk_nkma^k`nb]Zg\^hg]^lb`gbg`_hk
Stress zone
45
Table 7
Values for vRd, max
fck
vRd,max
Figure 8
+)
,'/1
Dimensions for plain foundations
+.
-'.)
+1
-'20
,)
.'+1
,+
.'.1
,.
/')+
-)
/'0+
-.
0',1
.)
1'))
48
a
a
hF
bF
o
/'?hng]Zmbhgl
Plain concrete foundations
Table 8
Minimum percentage of reinforcement required
LmkbiZg]iZ]_hhmbg`lfZr[^\hglmkn\m^]_khfieZbg\hg\k^m^
ikhob]^]ma^_heehpbg`kne^lZk^Z]a^k^]mh'
fck
fctm
Minimum % (0.26 fctm /fyka )
+.
+'/
)'*,
N Bg\hfik^llbhg%maôZen^h_a\\%ma^\h^__b\b^gmmZdbg`Z\\hngmh_
+1
+'1
)'*-
ehg`&m^kf^__^\mlZiieb^]mh]^lb`g\hfik^llbo^lmk^g`ma
!l^^<e','*'/"%lahne][^mZd^gZl)'/Zlhiihl^]mh)'1._hk
k^bg_hk\^]\hg\k^m^'
N Ma^fbgbfnf_hng]Zmbhg]îma%a?%!l^^?b`nk^1"fZr[^
\Ze\neZm^]_khf3
,)
+'2
)'*.
,+
,')
)'*/
,.
,'+
)'*0
-)
,'.
)'*1
-.
,'1
)'+)
.)
-'*
)'+*
Key
pa^k^3
s`]6ma^]^lb`goZen^h_ma^`khng][^Zkbgìk^llnk^
_\m] 6ma^]^lb`g\hg\k^m^m^glbe^lmk^g`ma_khf>qi'!,'*/"
?hkfZgrlbmnZmbhglmablblngebdêrmhh__^kZgrlZobg`lho^kma^\nkk^gm
ikZ\mb\^h_]^lb`gbg`_hka_ªZ'
Maîhllb[bebmrh_liebmmbg`_hk\^l%ZlZ]obl^]bg<eZnl^2'1'-h_>nkh\h]^
+¾*¾*%fZrg^^]mh[^\hglb]^k^]'
>nkh\h]^+ZeehplieZbg\hg\k^m^_hng]Zmbhglmh\hgmZbgk^bg_hk\^f^gm
_hk\hgmkheh_\kZ\dbg`'
a Pa^k^_rd 6.))FIZ'
Selected symbols
Symbol
Definition
Value
:\
[a
:l :k^Zh_m^glbhglm^ê
:l%ikho
:l%k^j
]
>__^\mbo^]îma
]^__
:o^kZ`^^__^\mbo^]îma
!]r$]s"(+
_\]
a\\_\d (g\
_\d
_\mf
@d
<aZkZ\m^kblmb\oZen^h_i^kfZg^gmZ\mbhg
a
Ho^kZee]îmah_ma^l^\mbhg
e^__
F
Crack control
Jd
<aZkZ\m^kblmb\oZen^h_ZoZkbZ[e^Z\mbhg
K^_^kmh<aZim^k+%hkb`bgZeerin[ebla^]Zl@^mmbg`lmZkm^]'
Jd%p
<aZkZ\m^kblmb\oZen^h_ZoZkbZ[e^pbg]Z\mbhg
O>]
=^lb`goZen^h_Ziieb^]la^Zk_hk\^
)',)_\d+(,_hk_\d©<.)(/)
!_khfMZ[e^,'*%>nkh\h]^+"
L^^L^\mbhg.','+'+!*"
Minimum area of principal reinforcement
o>]
=^lb`goZen^h_Ziieb^]la^Zklmk^ll
Ma^fbgbfnfZk^Zh_k^bg_hk\^f^gmbl:l%fbg6)'+/_\mf[m](_rd[nmghm
e^llmaZg)'))*,[m]!l^^MZ[e^1"'
OK]%\
=^lb`goZen^h_maîng\abg`la^Zk
k^lblmZg\^pbmahnming\abg`la^Zkk^bg_hk\^f^gm
oK]%\
=^lb`goZen^h_maîng\abg`la^Zklmk^ll
k^lblmZg\^pbmahnming\abg`la^Zkk^bg_hk\^f^gm
Maximum area of reinforcement
oK]%fZq
>q\îmZmeZieh\Zmbhgl%ma^fZqbfnfZk^Zh_m^glbhghk\hfik^llbhg
k^bg_hk\^f^gm%lahne]ghm^q\^^]:l%fZq6)')-:\
^lb`goZen^h_ma^fZqbfnfing\abg`la^Zk
=
k^lblmZg\^Zehg`ma^\hgmkhel^\mbhg\hglb]^k^]
q
=îmamhg^nmkZeZqbl
!]¾s"()'-
qfZq
!d¾)'-"]pa^k^d©*')
s
Eô^kZkf
a\\
h^__b\b^gmmZdbg`Z\\hngmh_ehg`m^kf
<
ng_ZohnkZ[e^^__^\mlk^lnembg`_khfma^pZr
ehZ]blZiieb^]!?khfNDGZmbhgZe:gg^q"
b
?Z\mhk_hk]^m^kfbgbgìng\abg`la^Zklmk^ll
d
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K
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Deep elements
gf
?hk]^îê^f^gmlma^Z]ob\^bg>nkh\h]^+_hkma^lb]^_Z\^lh_]^î
[^ZflfZr[^_heehp^]'Ma^NDGZmbhgZe:gg^qk^\hff^g]lmaZm)'+
blikhob]^]bg^Z\a_Z\^'Ma^]blmZg\^[^mp^^g[Zkllahne]ghm^q\^^]
maê^ll^kh_mpb\^ma^[^Zf]îmahk,))ff'?hkibe^\Zilma^lb]^
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r e
:l e[]
Ma^fbgbfnfliZ\bg`h_[Zkllahne][^ma^`k^Zm^kh_3
N ;Zk]bZf^m^k%
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c )
?Z\mhk_hk\hf[bgZmbhgoZen^h_ZoZkbZ[e^Z\mbhg
c* ?Z\mhk_hk_k^jn^gmoZen^h_ZoZkbZ[e^Z\mbhg
c+ ?Z\mhk_hkjnZlb&i^kfZg^gmoZen^h_ZoZkbZ[e^Z\mbhg
)'1._hk_e^qnk^Zg]
ZqbZeehZ]l%*')_hk
hma^kia^ghf^gZ
49
/'?hng]Zmbhgl
References
1 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*2203>nkh\h]^03@^hm^\agb\Ze]^lb`g';LB!+iZkml"'
2 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L.2,)3<h]^h_ikZ\mb\^_hklbm^bgo^lmb`Zmbhg';LB%*222'
3 ;
KBMBLALM:G=:K=LBGLMBMNMBHG';L1))+3<h]^h_ikZ\mb\^_hk^Zkmak^mZbgbg`lmkn\mnk^l';LB%*22-'
4 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1))-3<h]^h_ikZ\mb\^_hk_hng]Zmbhgl';LB%*21/'
5 G:K:R:G:G%KL;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3Bgmkh]n\mbhgmh>nkh\h]^l'Ma^<hg\k^m^<^gmk^%+)).'
6 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾*%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^lZg]kne^l_hk[nbe]bg`l';LB%+))-'
7 @HH=<ABE=%<AP>;LM>KKF'Lik^Z]la^^ml_hk\hg\k^m^]^lb`gmh;L1**)Zg]>nkh\h]^+%o^klbhg,'Ma^<hg\k^m^<^gmk^%+))/'
9 ;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3@^mmbg`lmZkm^]'Ma^<hg\k^m^<^gmk^%+)).'
50
0'?eZmleZ[l
Designing to Eurocode 2
Mabl\aZim^k\ho^klma^ZgZerlblZg]]^lb`gh_\hg\k^m^_eZmleZ[lmh>nkh\h]^
+%Zikh\^llpab\abl^ll^gmbZeerma^lZf^Zlpa^gnlbg`;L1**)'Ahpô^k%
maêZrhnmZg]\hgm^gmh_>nkh\h]^+fZrZii^ZkngnlnZemh]^lb`g^kl
_ZfbebZkpbma;L1**)'>nkh\h]^+]h^lghm\hgmZbgma^]^kbo^]_hkfneZ^hk
li^\b_b\`nb]Zg\^hg]^m^kfbgbg`fhf^gmlZg]la^Zk_hk\^l'MablaZlZkbl^g
[^\Znl^bmaZl[^^g>nkhi^ZgikZ\mb\^mh`boîkbg\bie^lbgma^\h]^lZg]_hk
ma^]^mZbe^]Ziieb\Zmbhgmh[îk^l^gm^]bghma^klhnk\^lln\aZlm^qm[hhdl'
d^r]b__^k^g\^l[^mp^^g>nkh\h]^+Zg];L1**)%bg\en]bg`m^kfbgheh`r'
Bmlahne][^ghm^]maZmoZen^l_khfma^NDGZmbhgZe:gg^q!G:"aZo^[^^g
nl^]makhnàhnmmablin[eb\Zmbhg%bg\en]bgòZen^lmaZmZk^^f[^]]^]bg
]^kbo^]_hkfneZ^!]^kboZmbhgl\Zg[^_hng]Zmppp'^nkh\h]^+'bg_h"':eblmh_
lrf[helkêZm^]mh_eZmleZ[]^lb`gbl`bo^gZmma^^g]h_mabl\aZim^k'
Analysis
Nlbg`>nkh\h]^+_hkma^ZgZerlblh__eZmleZ[lbllbfbeZkmhnlbg`;L1**)'Ma^
_heehpbg`f^mah]lfZr[^nl^]3
N >jnboZe^gm_kZf^f^mah]
N ?bgbm^ê^f^gmZgZerlbl
N Rbê]ebg^ZgZerlbl
N @kbeeZ`^ZgZeh`r
Ma^>nkh\h]^`bo^l_nkma^kZ]ob\^hgma^^jnboZe^gm_kZf^f^mah]bg
:gg^qBZg]]^lb`g^klnl^]mh;L1**)pbee_bg]mablo^kr_ZfbebZk'Hg\^ma^
[^g]bg`fhf^gmlZg]la^Zk_hk\^laZo^[^^g]^m^kfbg^]%ma^_heehpbg`
`nb]Zg\^\Zg[^nl^]_hkma^]^lb`gh__eZmleZ[l'
Design procedure
:ikh\^]nk^_hk\Zkkrbg`hnmma^]^mZbe^]]^lb`gh__eZmleZ[lbllahpgbgMZ[e^*'
MablZllnf^lmaZmma^leZ[mab\dg^llaZlikôbhnler[^^g]^m^kfbg^]]nkbg`
\hg\îmnZe]^lb`g'<hg\îm]^lb`glikîZk^]Zllnfbg`]^mZbe^]]^lb`gphne]
[^mh;L1**)fZr[^\hgmbgn^]makhnàmh]^mZbe^]]^lb`gnlbg`>nkh\h]^+'
Fhk^]^mZbe^]Z]ob\^hg]^m^kfbgbg`]^lb`geb_^%ehZ]bg`%fZm^kbZeikhi^kmb^l%
f^mah]lh_ZgZerlbl%fbgbfnf\hg\k^m^\ho^k_hk]nkZ[bebmrZg][hg]%Zg]
\hgmkheh_\kZ\dpb]mal\Zg[^_hng]bg<aZim^k+%hkb`bgZeerin[ebla^]Zl
@^mmbg`lmZkm^] '
Fire resistance
!ghmfbgbfnf"]bf^glbhg%lhma^]^lb`g^klahne]^glnk^maZm
Zª\ghf$f ebgd$f [Zk (+
>nkh\h]^+%IZkm*¾+3Lmkn\mnkZe_bk^]^lb`g%`bo^lZ\ahb\^h_Z]oZg\^]%
lbfieb_b^]hkmZ[neZkf^mah]l_hk]^m^kfbgbg`ma^_bk^k^lblmZg\^'Nlbg`
mZ[e^lblma^_Zlm^lmf^mah]_hk]^m^kfbgbg`ma^fbgbfnf]bf^glbhgl
Zg]\ho^k_hk_eZmleZ[l'Ma^k^Zk^%ahpô^k%lhf^k^lmkb\mbhglZg]b_ma^l^
Ziier_nkma^k`nb]Zg\^\Zg[^h[mZbg^]_khfli^\bZeblmebm^kZmnk^'
Ma^k^jnbk^f^gml_hk_eZmleZ[lZk^`bo^gbgMZ[e^+'
KZma^kmaZg`bobg`Zfbgbfnf\ho^k%ma^mZ[neZkf^mah]bl[Zl^]
hgghfbgZeZqbl]blmZg\^%Z'Mablblma^]blmZg\^_khfma^\^gmk^h_
ma^k^bg_hk\bg`[Zkmhma^lnk_Z\^h_ma^f^f[^k'BmblZghfbgZe
Flexure
Ma^]^lb`gikh\^]nk^_hk_e^qnkZe]^lb`gbl`bo^gbg?b`nk^*4mabl
bg\en]^l]^kbo^]_hkfneZ^[Zl^]hgma^lbfieb_b^]k^\mZg`neZklmk^ll
[eh\d_khf>nkh\h]^+'Pa^k^ZiikhikbZm^MZ[e^,fZr[^nl^]mh
]^m^kfbg^[^g]bg`fhf^gml_hk_eZmleZ[l'
Table 1
Flat slab design procedure
Step
Task
Further guidance
Chapter in this publication
Standard
*
=^m^kfbg^]^lb`geb_^
+3@^mmbg`lmZkm^]
G:mh;L>G*22)MZ[e^G:'+'*
+
:ll^llZ\mbhglhgma^leZ[
+3@^mmbg`lmZkm^]
;L>G*22*!*)iZkml"Zg]GZmbhgZe:gg^q^l
,
G:mh;L>G*22)MZ[e^lG:':*'*Zg]G:':*'+!;"
-
=^m^kfbgêhZ]bg`ZkkZg`^f^gml
+3@^mmbg`lmZkm^]
G:mh;L>G*22+¾*¾*
.
+3@^mmbg`lmZkm^]
;L1.))3+))/
/
+3@^mmbg`lmZkm^]Zg]MZ[e^+
:iikho^]=h\nf^gm;';L>G*22+¾*¾*3L^\mbhg.
0
<Ze\neZm^fbg'\ho^k_hk]nkZ[bebmr%_bk^Zg][hg]k^jnbk^f^gml
+3@^mmbg`lmZkm^]
;L>G*22+¾*¾*<e-'-'*
1
:gZerl^lmkn\mnk^mhh[mZbg\kbmb\Zefhf^gmlZg]la^Zk_hk\^l
+3@^mmbg`lmZkm^]Zg]MZ[e^,
;L>G*22+¾*¾*L^\mbhg.
2
=^lb`g_e^qnkZek^bg_hk\^f^gm
L^^?b`nk^*
;L>G*22+¾*¾*L^\mbhg/'*
*)
<a^\d]^_e^\mbhg
L^^?b`nk^,
;L>G*22+¾*¾*L^\mbhg0'-
**
<a^\ding\abg`la^Zk\ZiZ\bmr
L^^?b`nk^/
;L>G*22+¾*¾*L^\mbhg/'-
*+
<a^\dliZ\bg`h_[Zkl
+3@^mmbg`lmZkm^]
;L>G*22+¾*¾*L^\mbhg0',
*,
<a^\dk^lblmZg\^mhfhf^gmmkZgl_^k_khf\henfgmhleZ[
¾
;L>G*22+¾*¾*:gg^qB*'+!."
Note
G:6GZmbhgZe:gg^q
Table 2
Minimum dimensions and axis distances for reinforced concrete slabs
Standard fire resistance
Slab thickness, hs
Axis distance, a
K>B/)
*1)
*.Z
K>B2)
+))
+.
K>B*+)
+))
,.
K>B+-)
+))
.)
Notes
1 MablmZ[e^blmZd^g_khf;L>G*22+¾*¾+MZ[e^.'2'
2 Ma^Zqbl]blmZg\^blmhma^\^gmk^h_ma^hnm^keZr^kh_k^bg_hk\^f^gm'
3 Ma^mZ[e^bloZeb]hgerb_ma^]^mZbebg`k^jnbk^f^gml!l^^ghm^-"Zk^h[l^ko^]Zg]%bgma^ghkfZem^fi^kZmnk^]^lb`g%k^]blmkb[nmbhgh_[^g]bg`fhf^gml]h^lghm^q\^^]*.'
4 ? hk_bk^k^lblmZg\^h_K2)Zg]Z[ho^%Zme^Zlm+)h_ma^mhmZemhik^bg_hk\^f^gmbg^Z\a]bk^\mbhgho^kbgm^kf^]bZm^lniihkmlk^jnbk^][r;L>G*22+¾*¾*lahne][^\hgmbgnhnlho^k
ma^_neeliZg'Mablk^bg_hk\^f^gmlahne][îeZ\^]bgma^\henfglmkbi'
5 Ma^k^Zk^mak^^lmZg]Zk]_bk^^qihlnk^\hg]bmbhglmaZmfZrg^^]mh[^lZmbl_b^]3
Key
K F^\aZgb\Zek^lblmZg\^_hkehZ][^Zkbg`
> Bgm^`kbmrh_lîZkZmbhg
B BglneZmbhg
a GhkfZeerma^k^jnbk^f^gmlh_;L>G*22+¾*¾*pbee]^m^kfbg^ma^\ho^k'
52
0'?eZmleZ[l
Pab\aô^kf^mah]h_ZgZerlblblnl^]%<e'2'-'*k^jnbk^lma^]^lb`g^k
mh\hg\^gmkZm^ma^k^bg_hk\^f^gmho^kma^\henfgl':gg^qBh_ma^
>nkh\h]^`bo^lk^\hff^g]Zmbhgl_hkma^^jnboZe^gm_kZf^f^mah]hg
ahpmhZiihkmbhgma^mhmZe[^g]bg`fhf^gmZ\khllZ[Zrpb]mabgmh
\henfgZg]fb]]e^lmkbilmh\hfierpbma<e'2'-'*'=^lb`g^klnlbg`
`kbeeZ`^%_bgbm^ê^f^gmhkrbê]ebg^f^mah]lfZrZelh\ahhl^mh_heehp
ma^Z]ob\^bg:gg^qBmhf^^mmablk^jnbk^f^gm'
Figure 1
Procedure for determining flexural reinforcement
START
Carry out analysis of slab to determine design moments
(M) (Where appropriate use coefficients from Table 3).
No
Concrete class
≤C50/60?
Outside scope of
this publication
Yes
Determine KK from:
from: K =
Determine
Ma^>nkh\h]^`bo^lk^\hff^g]Zmbhgl_hkma^]^lb`gh_\hg\k^m^ni
mh\eZll<2)(*).'Ahpô^k%_hk\hg\k^m^lmk^g`ma`k^Zm^kmaZg\eZll
<.)(/)%ma^lmk^ll[eh\dblfh]b_b^]'BmblbfihkmZgmmhghm^maZm
\hg\k^m^lmk^g`mabl[Zl^]hgma^\rebg]^klmk^g`maZg]ghmma^\n[^
lmk^g`ma!b'^'_hk\eZll<+1(,.ma^\rebg]^klmk^g`mabl+1FIZ%pa^k^Zl
ma^\n[^lmk^g`mabl,.FIZ"'
M
bd 2 fck
Determine K’ from Table 4 or
K’ = 0.60d – 0.18 d 2 – 0.21 where d ≤ 1.0
Compression
reinforcement
required – not
recommended for
typical slabs
No
Is K ≤ K ’ ?
Yes
No compression reinforcement required
Obtain lever arm z from Table 5 or
d
1 + 1 – 3.53 K ≤ 0.95d
2
z=
[
]
Table 4
Values for K ’
d (redistribution ratio)
*'))
)'2)
)'1.
)'1)
)'0.
)'0)
% redistribution
)
*)
*.
+)
+.
,)
K’
)'+)1Z
)'*1+Z
)'*/1
)'*.,
)'*,0
)'*+)
Key
a Bmblh_m^gk^\hff^g]^]bgma^NDmaZmD£lahne][êebfbm^]mh)'*/1mh^glnk^
]n\mbe^_Zbenk^
Calculate tension reinforcement required from
M
As =
fyd z
Table 5
z/d for singly reinforced rectangular sections
K
©)').
)')/
)')0
)')1
)')2
)'*)
)'**
)'*+
Check minimum reinforcement requirements (see Table 6)
0.26 fctm bt d
As,min =
where fyk ≥ 25
fyk
Check maximum reinforcement requirements.
As,max = 0.04 Ac for tension or compression
reinforcement outside lap locations
z/d
)'2.)Z
)'2-)'2,)'2+)'2*,
)'2)+
)'12*
)'11)
K
)'*,
)'*)'*.
)'*/
)'*0
)'*1
)'*2
)'+)
z/d
)'1/1
)'1./
)'1-,
)'1,)
)'1*/
)'1)+
)'010
)'00*
Key
a Ebfbmbg`smh)'2.]blghmZk^jnbk^f^gmh_>nkh\h]^+%[nmbl\hglb]^k^]mh[^`hh]ikZ\mb\^
Table 3
Bending moment coefficients for flat slabs
End support/slab connection
Fhf^gm
>nkh\h]^+h__^kloZkbhnlf^mah]l_hk]^m^kfbgbg`ma^lmk^ll&lmkZbg
kêZmbhglabih_\hg\k^m^'?hklbfieb\bmrZg]_ZfbebZkbmrma^f^mah]
ik^l^gm^]a^k^blma^lbfieb_b^]k^\mZg`neZklmk^ll[eh\d!l^^?b`nk^+"%
pab\abllbfbeZkmhmaZm_hng]bg;L1**)'
Pinned
Continuous
End
End
support span
End
End
support span
)
Table 6
First
Interior
interior spans
support
)')1/?e ¾ )')-?e )')0.?e ¾)')1/?e )')/,?e
Notes
1 :
iieb\Z[e^mhleZ[lpa^k^ma^Zk^Zh_^Z\a[Zr^q\^^]l,)f+%
Jd%©*'+.@dZg]jd©.dG(f+
2 ?blma^mhmZe]^lb`gnembfZmêhZ]%eblma^^__^\mbo^liZg
3 FbgbfnfliZg7 )'1.ehg`^lmliZg%fbgbfnf,liZgl
4 ;Zl^]hg+)k^]blmkb[nmbhgZmlniihkmlZg]gh]^\k^Zl^bgliZgfhf^gml
Interior
supports
¾)')/,?e
fck
+.
+1
,)
,+
,.
-)
-.
.)
fctm
+'/
+'1
+'2
,')
,'+
,'.
,'1
-'*
Minimum % (0.26 fctm /fyka )
)'*,
)'*-
)'*.
)'*/
)'*0
)'*1
)'+)
)'+*
Key
a Pa^k^_rd 6.))FIZ
53
Deflection
>nkh\h]^+aZlmphZem^kgZmbo^f^mah]lh_]^lb`gbg`_hk]^_e^\mbhg4
^bma^k[rebfbmbg`liZg&mh&]îmakZmbhhk[rZll^llbg`ma^ma^hk^mb\Ze
]^_e^\mbhgnlbg`ma^>qik^llbhgl`bo^gbgma^>nkh\h]^'MaêZmm^kbl
]^Zempbmabg]^mZbebg<aZim^k1%hkb`bgZeerin[ebla^]Zl=^_e^\mbhg
\Ze\neZmbhgl '
]îmakZmbhlZk^ZiikhikbZm^pa^k^ma^lmkn\mnk^k^fZbglikhii^]
]nkbg`\hglmkn\mbhghkngmbema^\hg\k^m^ZmmZbglln__b\b^gmlmk^g`mamh
lniihkmma^\hglmkn\mbhgehZ]l'Bm\Zg`^g^kZeer[^Zllnf^]maZm^Zker
lmkbdbg`h__hkfphkdpbeeghmlb`gb_b\ZgmerZ__^\mma^]^_e^\mbhgZ_m^k
bglmZeebg`ma^\eZ]]bg`Zg](hkiZkmbmbhgl'
Punching shear
Ma^liZg&mh&]îmakZmbhllahne]^glnk^maZm]^_e^\mbhgblebfbm^]
mhliZg(+.)Zg]mablblmaîkh\^]nkîk^l^gm^]bg?b`nk^,'Ma^
;Z\d`khng]iZi^kmhma^NDGZmbhgZe:gg^q ;ghm^lmaZmma^liZg&mh&
Ma^]^lb`goZen^h_maîng\abg`la^Zk_hk\^%O>]%pbeenlnZeer[^ma^
lniihkmk^Z\mbhgZmma^nembfZmêbfbmlmZm^'Bgikbg\bie^ma^]^lb`g
_hking\abg`la^Zkbg>nkh\h]^+Zg];L1**)bllbfbeZk'Ma^fZbg
]b__^k^g\^lZk^Zl_heehpl'
Figure 2
N LmZg]Zk]_Z\mhkl_hk^]`^Zg]\hkg^k\henfglmaZmZeehp_hk
Simplified rectangular stress block for concrete up to class C50/60
from Eurocode 2
fhf^gmmkZgl_^k!b"Zk^`k^Zm^kbg>nkh\h]^+'Ahpô^k%b\Zg
[^\Ze\neZm^]]bk^\mer_khf>qik^llbhgl!/',1"mh!/'-/"h_ma^
>nkh\h]^mh`bo^fhk^^__b\b^gm]^lb`gl'
Figure 4
Basic span-to-effective-depth ratios for flat slabs
39
fck
fck
fck
fck
fck
fck
fck
fck
fck
37
Figure 3
Procedure for assessing deflection
Span-to-effective-depth ratio (l/d)
35
START
Determine basic l/d from Figure 4
Determine Factor 1 (F1)
For ribbed or waffle slabs
F1 = 1 – 0.1 ((bf/bw) – 1) ≥ 0.8†
(bf is flange breadth and bw is rib breadth)
Otherwise F1 = 1.0
33
31
29
=
=
=
=
=
=
=
=
=
50
45
40
35
32
30
28
25
20
27
25
23
21
Where the slab span exceeds 8.5 m and it supports
brittle partitions, F2 = 8.5/leff
Otherwise F2 = 1.0
19
17
15
F3 = 310/ss
Where ss = Stress in reinforcement at serviceability
limit state (see Figure 5)
ss may be assumed to be 310 MPa (i.e. F3 = 1.0)
0.40% 0.60% 0.80% 1.00% 1.20% 1.40% 1.60% 1.80% 2.00%
Percentage of tension reinforcement (A s ,req/bd)
Notes
Note: As,prov ≤ 1.5 As,req’d (UK National Annex)
Increase
As,prov
1 Mabl`kZiaZllnf^lZlbfierlniihkm^]_eZmleZ[!D6*'+"'
2 <hfik^llbhgk^bg_hk\^f^gm%rÃ%aZl[^^gmZd^gZl)'
3 <nko^l[Zl^]hgma^_heehpbg`^qik^llbhgl3
Is basic l/d x F1 x F2 x F3 ≥ Actual l/d ?
No
Yes
Check complete
† The Eurocode is ambiguous regarding linear interpolation. It is understood that this
was the intention of the drafting committee and is in line with current UK practice.
54
[
[
( ) ]
]
*'.
e
r)
*'. _\dr )
$ ,'+ _\d
¾*
6D ** $
pa^k^r©r
) Zg]
r
r
]
rÃ
_\d
*'. _\dr )
e
pa^k^r7 r ) '
$
6D ** $
r)
*+
]
! r ¾ r Ã"
0'?eZmleZ[l
N Bg>nkh\h]^+ma^fZqbfnfoZen^h_la^ZkZmma^\henfg_Z\^bl
ghmebfbm^]mh.FIZ%Zg]]î^g]lhgma^\hg\k^m^lmk^g`manl^]'
N Pbma>nkh\h]^+maî^kfbllb[e^la^Zkk^lblmZg\^pa^gnlbg`la^Zk
ebgdlblabà^k%Zemahnàln\a]^lb`glfZrghm[^^\hghfb\hk
]^lbkZ[e^'
N Ma^\hgmkhei^kbf^m^kl_hkk^\mZg`neZk\henfglbg>nkh\h]^+aZo^
khng]^]\hkg^kl'
:lZgZem^kgZmbo^mhnlbg`la^Zkebgdl%ikhikb^mZkrla^Zklmn]kZbel
fZr[^nl^]'>nkh\h]^+!?b`nk^/'++"Zeehplma^fmh[êZb]hnm
bgZkZ]bZehk\kn\b_hkfiZmm^kgZg]`bo^lliZ\bg`k^jnbk^f^gml_hk
[hma'Hma^km^\agbjn^lZk^ZoZbeZ[e^_hkbg\k^Zlbgìng\abg`la^Zk
k^lblmZg\^Zg]ma^l^Zk^\ho^k^]bgZ[^lmikZ\mb\^`nb]^'
Figure 6
Procedure for determining punching shear capacity
N Pa^k^la^Zkk^bg_hk\^f^gmblk^jnbk^]maîkh\^]nk^bg>nkh\h]^+
bllbfie^k4maîhbgmZmpab\aghla^Zkk^bg_hk\^f^gmblk^jnbk^]\Zg
[^\Ze\neZm^]]bk^\merZg]ma^gnl^]mh]^m^kfbg^ma^^qm^gmh_ma^
Zk^Zho^kpab\ala^Zkk^bg_hk\^f^gmblk^jnbk^]'
N BmblZllnf^]maZmma^k^bg_hk\^f^gmpbee[^bgZkZ]bZeZkkZg`^f^gm'
Ahpô^k%ma^k^bg_hk\^f^gm\Zg[êZb]hgZ`kb]ikhob]^]ma^
liZ\bg`kne^lZk^_heehp^]'
Maîkh\^]nk^_hk]^m^kfbgbg`maîng\abg`la^Zkk^jnbk^f^gmlbl
lahpgbg?b`nk^/'
START
Determine value of factor β
(refer to Figure 7 or Expressions (6.38) to (6.46)
of the Eurocode)
Determine value of vEd
(design shear stress at face of column) from:
vEd = β VEd /(ui deff)
where ui is perimeter of column
deff = (dy + dz)/2 (dy and dz
are the effective depths in orthogonal directions)
Figure 5
Appromximate
,s
Approximatesteel
steelstress
stressat
atSLS
SLSfor
forAAs,req
s,req su
Determination of steel stress
Determine value of vRd,max from Table 7
No
320
Redesign slab
Is vEd,4 vRd?
300
Yes
280
Determine value of vEd, (design shear stress) from:
vEd = β VEd /(ui deff)
where u1 is length of control perimeter (see Figure 8)
260
240
Determine concrete punching shear capacity
(without shear reinforcement), vRD,c from Table 8
where r l = (r ly r lz)0.5
(r ly, r lz are the reinforcement ratios in two orthogonal
directions for fully bonded tension steel, taken over a
width equal to column width plus 3d each side.)
220
200
180
1.0
2.0
4.0
3.0
Ratio Gk/Qk
Is vEd > vRd,c?
c2 = 0.8, gG = 1.35
c2 = 0.6, gG = 1.25
c2 = 0.6, gG = 1.35
c2 = 0.3, gG = 1.25
c2 = 0.3, gG = 1.35
c2 = 0.2, gG = 1.25
c2 = 0.2, gG = 1.35
To determine stress in the provided reinforcement (ss), calculate the ratio
Gk/Qk , read up the graph to the appropriate curve and read across to
determine ssu .
ss can be calculated from the expression: ss = ssu
(
As,req
As,prov
)( )
1
d
c2 is the factor for quasi-permanent value of a variable action. For further
explanation refer to How to design concrete structures using Eurocode 2:
Introduction to Eurocodes3.
No
Punching shear
reinforcement not
required
Yes
Determine area of punching shear reinforcement per perimeter
from:
Asw = (vEd – 0.75vRd,c)sr u1/(1.5 fywd,ef)
where
sr is the radial spacing of shear reinforcement (see Figure 9)
fywd,ef = 250 + 0.25 deff ≤ fywd (see Table 9)
Determine the length of the outer perimeter where shear
reinforcement not required from:
uout,ef = b VEd/(vRd,c d)
Determine layout of punching shear reinforcement
(see ‘Spacing of punching shear reinforcement’
Section and Figure 9).
55
Table 7
Table 9
Values for vRd,max
Figure 7
Values for fywd,ef
Recommended standard values for b
fck
vRd, max
deff
fywd,ef
+)
,'/1
*.)
+11
+.
-'.)
*0.
+2-
+1
-'21
+))
,))
,)
.'+1
++.
,)/
,+
.'.1
+.)
,*,
,.
/')+
+0.
,*2
-)
/'0+
,))
,+.
-.
0',1
,+.
,,*
.)
1'))
,.)
,,1
Corner column
b = 1.5
Edge column
b = 1.4
Table 8
vRd,c resistance of members without shear reinforcement, MPa
rI
Effective depth, d (mm)
≤200 225 250 275 300 350 400 450 500 600 750
0.25%
)'.- )'.+ )'.) )'-1 )'-0 )'-. )'-, )'-* )'-) )',1 )',/
0.50%
)'.2 )'.0 )'./ )'.. )'.- )'.+ )'.* )'-2 )'-1 )'-0 )'-.
0.75%
)'/1 )'// )'/- )'/, )'/+ )'.2 )'.1 )'./ )'.. )'., )'.*
1.00%
)'0. )'0+ )'0* )'/2 )'/1 )'/. )'/- )'/+ )'/* )'.2 )'.0
1.25%
)'1) )'01 )'0/ )'0- )'0, )'0* )'/2 )'/0 )'// )'/, )'/*
1.50%
)'1. )'1, )'1* )'02 )'01 )'0. )'0, )'0* )'0) )'/0 )'/.
1.75%
)'2) )'10 )'1. )'1, )'1+ )'02 )'00 )'0. )'0, )'0* )'/1
≥ 2.00% )'2- )'2* )'12 )'10 )'1. )'1+ )'1) )'01 )'00 )'0- )'0*
k
+'))) *'2-, *'12- *'1., *'1*/ *'0./ *'0)0 *'//0 *'/,+ *'.00 *'.*/
Notes
1MZ[e^]^kbo^]_khf3o K]%\6)'*+d!*))r I_\d"*(,ª)'),.d*'._\d )'.pa^k^
d6*$R!+))(]"©+Zg]r I6R!r er$r es"©)')+%r er 6:lr(![]"Zg]r es 6:ls(![]"
2 M ablmZ[eâZl[^^gikîZk^]_hk_\d 6,)4
Pa^k^r I^q\^^]l)'-)ma^_heehpbg`_Z\mhklfZr[^nl^]3
Internal column
b = 1.15
Minimum area of reinforcement
Ma^fbgbfnfZk^Zh_ehg`bmn]bgZek^bg_hk\^f^gmbgma^fZbg]bk^\mbhg
bl:l%fbg6)'+/_\mf[m](_rd[nmghme^llmaZg)'))*,[]!l^^MZ[e^/"'
Ma^fbgbfnfZk^Zh_Zebgde^`_hko^kmb\Zeing\abg`la^Zk
k^bg_hk\^f^gmbl
*'.:lp%fbg(!lk'lm"ª)')1_\d(_rd
pab\a\Zg[^k^ZkkZg`^]Zl
:lp%fbgª!lk'lm"(?
pa^k^
lk6ma^liZ\bg`h_maêbgdlbgma^kZ]bZe]bk^\mbhg
lm6ma^liZ\bg`h_maêbgdlbgma^mZg`^gmbZe]bk^\mbhg
f\d
25
28
32
35
40
45
50
Factor
)'2-
)'21
*')+
*').
*'*)
*'*-
*'*2
?\Zg[^h[mZbg^]_khfMZ[e^*)
Maximum area of reinforcement
Hnmlb]êZieh\Zmbhgl%ma^fZqbfnfZk^Zh_m^glbhghk\hfik^llbhg
k^bg_hk\^f^gmlahne]ghm^q\^^]:l%fZq6)'-:\
Figure 8
Typical basic control perimeters around loaded areas
u1
2d
2d
u1
Ma^fbgbfnfliZ\bg`h_[Zkllahne][^ma^`k^Zm^kh_3
N ;Zk]bZf^m^k
N :``k^`Zm^lbsîenl.ff
N +)ff
Maximum spacing of main reinforcement
bz
?hkleZ[le^llmaZg+))ffmab\dma^_heehpbg`fZqbfnfliZ\bg`kne^lZiier3
N ?hkmaîkbg\biZek^bg_hk\^f^gm3,a[nmghmfhk^maZg-))ff
N ?hkma^l^\hg]Zkrk^bg_hk\^f^gm3,'.a[nmghmfhk^maZg-.)ff
by
Ma^^q\îmbhgblbgZk^Zlpbma\hg\^gmkZm^]ehZ]lhkZk^Zlh_fZqbfnf
56
0'?eZmleZ[l
fhf^gmpa^k^ma^_heehpbg`Ziieb^l3
N ?hkmaîkbg\biZek^bg_hk\^f^gm3+a[nmghmfhk^maZg+.)ff
N ?hkma^l^\hg]Zkrk^bg_hk\^f^gm3,a[nmghmfhk^maZg-))ff
Pa^kâblma^]îmah_ma^leZ['
Table 10
Factor, F, for determining Asw, min
fck
Factor, F
+.
*10.
+1
*00+
,)
*0*+
,+
*/.0
,.
*.1.
-)
*-1+
-.
*,21
.)
*,+/
?hkleZ[l+))ffmab\dhk`k^Zm^k%ma^[Zklbs^Zg]liZ\bg`lahne][^
ebfbm^]mh\hgmkhema^\kZ\dpb]maZg]k^_^k^g\^lahne][^fZ]^mh
L^\mbhg0',',h_ma^>nkh\h]^hk<aZim^k+%hkb`bgZeerin[ebla^]Zl
@^mmbg`lmZkm^]'
Spacing of punching shear reinforcement
Pa^kîng\abg`la^Zkk^bg_hk\^f^gmblk^jnbk^]ma^_heehpbg`kne^l
lahne][^h[l^ko^]'
N Bmlahne][îkhob]^][^mp^^gma^_Z\^h_ma^\henfgZg]d]
bglb]^ma^hnm^ki^kbf^m^kpa^k^la^Zkk^bg_hk\^f^gmblghehg`^k
k^jnbk^]'dbl*'.%nge^llmaî^kbf^m^kZmpab\ak^bg_hk\^f^gmblgh
ehg`^kk^jnbk^]ble^llmaZg,]_khfma^_Z\^h_ma^\henfg'Bgmabl
\Zl^ma^k^bg_hk\^f^gmlahne][îeZ\^]bgma^shg^)',]mh*'.]
_khfma^_Z\^h_ma^\henfg'
N Ma^k^lahne][^Zme^Zlmmphi^kbf^m^klh_la^Zkebgdl'
N Ma^kZ]bZeliZ\bg`h_maêbgdllahne]ghm^q\^^])'0.]
!l^^?b`nk^2"'
N Ma^mZg`^gmbZeliZ\bg`h_maêbgdllahne]ghm^q\^^]*'.]pbmabg
+]h_ma^\henfg_Z\^'
N Ma^mZg`^gmbZeliZ\bg`h_maêbgdllahne]ghm^q\^^]+]_hkZgr
hma^ki^kbf^m^k'
N Ma^]blmZg\^[^mp^^gma^_Z\^h_ma^\henfgZg]ma^g^Zk^lmla^Zk
k^bg_hk\^f^gmlahne][ê^llmaZg)'.]'
Figure 9
Punching shear layout
Outer perimeter of shear
reinforcement
Outer control
perimeter
u out
≤ 0.75d
A
A
≤1.5d
0.5 d
≤1.5 d
(2 d if > 2d
from column)
sr
st
sr ≤ 0.75 d
≤ 0.5 d
Outer control
perimeter
kd
Section A - A
Note
_\d aZl[^^gmZd^gZl.))FIZ
Selected symbols
Symbol
Definition
Value
:\
[a
:l :k^Zh_m^glbhglm^ê
:l+
:k^Zh_\hfik^llbhglm^ê
:l%ikho
:l%k^j
[
Pb]mah_leZ[
]
>__^\mbo^]îma
]+ >__^\mbo^]îmamh\hfik^llbhgk^bg_hk\^f^gm
_\]
_\d
_\mf
al
LeZ[mab\dg^ll
D
?Z\mhkmhmZd^Z\\hngmh_ma^]b__^k^gm
lmkn\mnkZelrlm^fl
L^^MZ[e^G0'-bg
NDGZmbhgZe:gg^q
e^__
L^^L^\mbhg.','+'+!*"
e(]
Ebfbmbg`liZg&mh&]îmakZmbh
F
a\\_\d (g\
)',)_\d+(,_hk_\d©<.)(/)
!_khfMZ[e^,'*%>nkh\h]^+"
q
=îmamhg^nmkZeZqbl
!]¾s"()'-
qfZq
!d¾)'-"]pa^k^d©*')
s
Eô^kZkf
a \\
<h^__b\b^gmmZdbg`Z\\hngmh_ehg`m^kf
ng_ZohnkZ[e^^__^\mlk^lnembg`_khfma^
pZrehZ]blZiieb^]
d
KZmbhh_ma^k^]blmkb[nm^]fhf^gmmhma^
êZlmb\[^g]bg`fhf^gm
g f
*'*._hkk^bg_hk\^f^gm!gl "
*'._hk\hg\k^m^!g\ "
)'1._hk_e^qnk^Zg]
ZqbZeehZ]l'
*')_hkhma^kia^ghf^gZ
!?khfNDGZmbhgZe:gg^q"
r )
R_\d (*)))
r
:l([]
rÃ
K^jnbk^]\hfik^llbhgk^bg_hk\^f^gmZm
fb]&liZgmhk^lblmma^fhf^gm]n^mhma^
]^lb`gehZ]l!hkZmlniihkm_hk\Zgmbeô^kl"
:l+([]
57
0'?eZmleZ[l
References
1 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾*%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l¾@^g^kZekne^lZg]kne^l_hk[nbe]bg`l';LB%+))-'
2 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1**)¾*3Ma^lmkn\mnkZenl^h_\hg\k^m^¾IZkm*%<h]^h_ikZ\mb\^_hk]^lb`gZg]\hglmkn\mbhg';LB%*220'
3 G:K:R:G:G%KL;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3Bgmkh]n\mbhgmh>nkh\h]^l'Ma^<hg\k^m^<^gmk^%+)).'
4 ;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3@^mmbg`lmZkm^]'Ma^<hg\k^m^<^gmk^%+)).'
5 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾+%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^l¾lmkn\mnkZe_bk^]^lb`g';LB%+))-'
6 P>;LM>K%K;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3=^_e^\mbhg\Ze\neZmbhgl'Ma^<hg\k^m^<^gmk^%+))/'
7 ;KBMBLALM:G=:K=LBGLMBMNMBHG'I=//10%;Z\d`khng]iZi^kmhma^NDGZmbhgZe:gg^qmh;L>G*22+¾*¾*Zg];L>G*22+¾*¾+';LB%+))/'
8 I:EE>MM%I'@nb]^mh_eZmleZ[_hkfphkdZg]_Zel^phkd'<hglmkn\m%+)),'
9 ;KBMBLA<>F>GM:LLH<B:MBHG'Ik^_Z[kb\Zm^]ing\abg`la^Zkk^bg_hk\^f^gm_hkk^bg_hk\^]\hg\k^m^_eZmleZ[l';<:%+))*'
58
1'=^_e^\mbhg\Ze\neZmbhgl
R Webster<>g`%?BLmkn\m>O Brooker;>g`%<>g`%FB<>%FBLmkn\m>
Methods for checking deflection
Mabl\aZim^k]^l\kb[^lma^nl^h_>nkh\h]^+mh\a^\d]^_e^\mbhg[r
\Ze\neZmbhg'Ma^Zem^kgZmbo^f^mah]_hk\hfierbg`pbmama^\h]^k^jnbk^f^gml
blmhnl^ma^]^^f^]&mh&lZmbl_rliZg&mh&^__^\mbo^&]îmakZmbhl%pab\aZk^
ZiikhikbZm^Zg]^\hghfb\_hkmaôZlmfZchkbmrh_]^lb`gl'?nkma^k`nb]Zg\^
hgma^liZg&mh&^__^\mbo^&]îmaf^mah]bl`bo^gbg<aZim^kl,%-Zg]0%
hkb`bgZeerin[ebla^]Zl;^Zfl%LeZ[lZg]?eZmleZ[l'Ahpô^k%ma^k^Zk^
lbmnZmbhglpa^k^]bk^\m\Ze\neZmbhgh_]^_e^\mbhgblg^\^llZkr%Zleblm^][êhp3
N Pa^gZg^lmbfZm^h_ma^]^_e^\mbhgblk^jnbk^]'
N Pa^g]^_e^\mbhgebfbmlh_liZg(+.)_hkjnZlb&i^kfZg^gmZ\mbhgl!l^^
k^_^k^g\^._hk>nkh\h]^m^kfbgheh`r"hkliZg(.))_hkiZkmbmbhgZg](hk
\eZ]]bgèhZ]lZk^ghmZiikhikbZm^'
N Pa^gma^]^lb`gk^jnbk^lZiZkmb\neZkerlaZeehpf^f[^k%]bk^\m\Ze\neZmbhg
h_]^_e^\mbhgfZrikhob]^Zfhk^^\hghfb\lhenmbhg'
N Mh]^m^kfbg^ma^^__^\mhg]^_e^\mbhgh_^Zkerlmkbdbg`h__hkfphkdhkh_
m^fihkZkrehZ]bg`]nkbg`\hglmkn\mbhg'
Overview
BgmaîZlmlmkn\mnk^lm^g]^]mh[^lmb__pbmakêZmboêrlahkmliZgl':l
m^\agheh`rZg]ikZ\mb\âZo^Z]oZg\^]%fhk^_e^qb[e^lmkn\mnk^laZo^k^lnem^]'
Ma^k^Zk^Zgnf[^kh_k^Zlhgl_hkmabl%bg\en]bg`3
N Ma^bg\k^Zl^bgk^bg_hk\^f^gmlmk^g`mae^Z]bg`mhe^llk^bg_hk\^f^gm[^bg`
k^jnbk^]_hkma^nembfZmêbfbmlmZm^!NEL"Zg]k^lnembg`bgabà^kl^kob\^
lmk^ll^lbgma^k^bg_hk\^f^gm'
N Bg\k^Zl^lbg\hg\k^m^lmk^g`mak^lnembg`_khfma^g^^]mhbfikho^[hma
]nkZ[bebmrZg]\hglmkn\mbhgmbf^%Zg]e^Z]bg`mh\hg\k^m^maZmblfhk^lmb__
Zg]pbmaabà^kl^kob\^lmk^ll^l'
What affects deflection?
There are numerous factors
that affect deflection. These
factors are also often timerelated and interdependent,
which makes the prediction
of deflection difficult.
The main factors are:
Concrete tensile strength
Creep
Elastic modulus
Other factors include:
Degree of restraint
Magnitude of loading
Time of loading
Duration of loading
Cracking of the concrete
Shrinkage
Ambient conditions
Secondary load-paths
Stiffening by other elements
N :`k^Zm^kng]^klmZg]bg`h_lmkn\mnkZe[âZobhnkZg]ma^Z[bebmrmh
ZgZerl^maZm[âZobhnkjnb\der[r\hfinm^k'
N Ma^k^jnbk^f^gmmhikh]n\^^\hghfb\]^lb`gl_hkleZ[lpahl^
mab\dg^ll^lZk^mrib\Zeer]^m^kfbg^][rma^l^kob\^Z[bebmrebfbmlmZm^
!LEL"Zg]pab\a\hglmbmnm^1)mh2)h_ma^lni^klmkn\mnk^\hlml'
N <eb^gmk^jnbk^f^gml_hkehg`^kliZglZg]`k^Zm^khi^kZmbhgZe
_e^qb[bebmr_khfma^bklmkn\mnk^l'
Factors affecting deflection
:gZ\\nkZm^Zll^llf^gmh_]^_e^\mbhg\Zghger[^Z\abô^]b_
\hglb]^kZmbhgbl`bo^gmhma^_Z\mhklmaZmZ__^\mbm'Ma^fhk^bfihkmZgm
_Z\mhklZk^]bl\nll^]bg]^mZbe[êhp'
Tensile strength
Ma^m^glbe^lmk^g`mah_\hg\k^m^blZgbfihkmZgmikhi^kmr[^\Znl^
ma^leZ[pbee\kZ\dpa^gma^m^glbe^lmk^llbgma^^qmk^f^_b[k^bl
^q\^^]^]'Bg>nkh\h]^+ma^\hg\k^m^m^glbe^lmk^g`ma%_\mf%blZf^Zg
oZen^!pab\ablZiikhikbZm^_hk]^_e^\mbhg\Ze\neZmbhgl"Zg]bg\k^Zl^l
Zlma^\hfik^llbo^lmk^g`mabg\k^Zl^l'MablblZgZ]oZg\^f^gmpa^g
\hfiZk^]pbma;L1**)pa^k^ma^m^glbe^lmk^g`mabl_bq^]_hkZee
\hg\k^m^lmk^g`mal'
Bmblh_m^gk^\hff^g]^]maZmma^]^lb`goZen^h_ma^\hg\k^m^
m^glbe^lmk^g`ma_hkZehpk^lmkZbgmeZrhnmblmZd^gZlma^Zo^kZ`^
h__\mf%_eZg]_\mf%mhZeehp_hkngbgm^gmbhgZek^lmkZbgm'?hkabàk^lmkZbgm
_\mflahne][^nl^]'
Creep
<k^îblma^mbf^&]î^g]Zgmbg\k^Zl^bg\hfik^llbo^lmkZbgbgZ
\hg\k^m^ê^f^gmng]^k\hglmZgm\hfik^llbo^lmk^ll'<k^îblnlnZeer
\hglb]^k^]bgma^]^lb`g[rfh]b_rbg`ma^êZlmb\fh]nenlnlbg`Z
\k^î\h^__b\b^gm%h%pab\a]î^g]lhgma^Z`^ZmehZ]bg`%lbs^h_
ma^f^f[^kZg]Zf[b^gm\hg]bmbhgl%bgiZkmb\neZkkêZmboânfb]bmr'
>nkh\h]^+`bo^lZ]ob\^hgma^\Ze\neZmbhgh_\k^î\h^__b\b^gmlbg
]^mZbebg:gg^q;'BmZelhZ]obl^lhgma^ZiikhikbZm^kêZmboânfb]bmr
mhnl^bg?b`nk^,'*'
Ma^\^f^gmlmk^g`ma\eZllblk^jnbk^]bgma^Zll^llf^gmh_\k^î%
ahpô^k%Zmma^]^lb`glmZ`^bmblh_m^gghm\e^Zkpab\a\eZlllahne]
[^nl^]'@^g^kZeer%<eZllKlahne][^Zllnf^]'Pa^k^ma^`khng]
`kZgneZm^][eZlm_nkgZ\^leZ`!``[l"\hgm^gm^q\^^]l,.h_ma^
\^f^gm\hf[bgZmbhghkpa^k^_erZla!i_Z"^q\^^]l+)h_ma^
\^f^gm\hf[bgZmbhg%<eZllGfZr[^Zllnf^]'Pa^k^``[l^q\^^]l
/.hkpa^kî_Z^q\^^]l,.<eZllLfZr[^Zllnf^]'
Elastic modulus
Ma^]^`k^^h_k^lmkZbgmmhlakbgdZ`^fho^f^gmlpbeebg_en^g\^ma^
^__^\mbo^m^glbe^lmk^g`mah_ma^\hg\k^m^':eZrhnmh_pZeelpbmaabà
k^lmkZbgmpbee]^\k^Zl^ma^^__^\mbo^m^glbe^lmk^g`ma'Mrib\Ze^qZfie^l
h_pZeeeZrhnmlZk^`bo^gbg?b`nk^*'?hkZehpk^lmkZbgmeZrhnmma^
_heehpbg`^qik^llbhgfZr[^nl^]_hkma^\hg\k^m^m^glbe^lmk^g`ma3
_\mf%_e 6!*'/¾a(*)))"_\mf7 _\mf
pa^k^
_\mf%_e 6F^Zg_e^qnkZem^glbe^lmk^g`mah_k^bg_hk\^]\hg\k^m^
_\mf 6F^Zgm^glbe^lmk^g`mah_\hg\k^m^
Figure 1
Typical floor layouts
a) Favourable layout of restraining walls (low restraint)
b) Unfavourable layout of restraining walls (high restraint)
60
Ma^êZlmb\fh]nenlh_\hg\k^m^blbg_en^g\^][rZ``k^`Zm^mri^%
phkdfZglabiZg]\nkbg`\hg]bmbhgl'Ma^^__^\mbo^êZlmb\fh]nenl
ng]^klnlmZbg^]ehZ]bg`pbee[^k^]n\^]ho^kmbf^]n^mhma^^__^\m
h_\k^î'Ma^l^_Z\mhklf^ZgmaZmlhf^cn]`^f^gmblk^jnbk^]
mh]^m^kfbg^ZgZiikhikbZm^êZlmb\fh]nenl'>nkh\h]^+`bo^l
k^\hff^g]^]oZen^l_hkma^+1&]Zrl^\Zgmfh]nenl%>\f%!bgMZ[e^,'*"
Zg]fZd^lk^\hff^g]Zmbhgl_hkZ]cnlmf^gmlmhma^lôZen^lmh
Z\\hngm_hk]b__^k^gmmri^lh_Z``k^`Zm^'Maêhg`&m^kfêZlmb\fh]nenl
lahne][^mZd^gZl3
>\%EM 6>\+1(!*$h"
pa^k^
>\+1 6+1&]ZrmZg`^gmfh]nenl6*').>\f
h 6<k^î_Z\mhk'!Ghm^maZmpbma>nkh\h]^+%hkêZm^lmhZ+1&]Zr
lahkm&m^kfêZlmb\fh]nenl%pa^k^ZlZÂmkn^Ã\k^î_Z\mhkphne]
[^Zllh\bZm^]pbmama^fh]nenlZmma^Z`^h_ehZ]bg`'"
Ma^Zll^llf^gmh_maêhg`&m^kf>&oZen^\Zg[^\Zkkb^]hnmfhk^
Z\\nkZmêrZ_m^kma^\hgmkZ\mhkaZl[^^gZiihbgm^][^\Znl^ma^rlahne][^
Z[e^mhb]^gmb_rma^\hg\k^m^lniieb^k!Zg]a^g\^ma^mri^h_Z``k^`Zm^l"
Zg]Zelhma^\hglmkn\mbhgl^jn^g\^!Zg]a^g\^ma^Z`^Zm_bklmehZ]bg`"'
Loading sequence
MaêhZ]bg`l^jn^g\^Zg]mbfbg`fZr[^\kbmb\Zebg]^m^kfbgbg`
ma^]^_e^\mbhgh_Zlnli^g]^]leZ[[^\Znl^bmpbeebg_en^g\^maîhbgm
Zmpab\ama^leZ[pbee\kZ\d!b_ZmZee"Zg]blnl^]mh\Ze\neZm^ma^\k^î
_Z\mhkl_hkma^leZ[':ehZ]bg`l^jn^g\^bllahpgbg?b`nk^+%pab\a
lahplmaZmbgma^^ZkerlmZ`^lkêZmboêrabàehZ]lZk^bfihl^]pabe^
\Zlmbg`ma^leZ[Z[ho^'MaêhZ]bg`l^jn^g\^fZroZkr%]î^g]bg`hg
ma^\hglmkn\mbhgf^mah]'
LfZee^kehZ]lZk^bfihl^]pa^g_nkma^kleZ[lZk^\ZlmZ[ho^'MaêhZ]l
Zk^ma^gbg\k^Zl^]i^kfZg^gmer[rma^Ziieb\Zmbhgh_ma^_ehhk_bgbla^l
Zg]^k^\mbhgh_maîZkmbmbhgl'?bgZeer%maôZkbZ[e^Z\mbhglZk^Ziieb^]
mhma^lmkn\mnk^Zg]%_hkmaînkihl^h_]^_e^\mbhg\Ze\neZmbhg%ma^
jnZlb&i^kfZg^gm\hf[bgZmbhglahne][^nl^]'!L^^<aZim^k*%
hkb`bgZeerin[ebla^]ZlBgmkh]n\mbhgmh>nkh\h]^l_hk_nkma^k
bg_hkfZmbhghg\hf[bgZmbhglh_Z\mbhgl'"Ahpô^k%bmblebdêrmaZmma^
jnZlb&i^kfZg^gm\hf[bgZmbhgpbee[^^q\^^]^]]nkbg`maêb_^mbf^
h_ma^[nbe]bg`Zg]%_hkmaînkihl^h_]^m^kfbgbg`pa^ma^kma^leZ[
fbàmaZo^\kZ\d^]%ma^_k^jn^gm\hf[bgZmbhgfZr[^\kbmb\Ze'
<hff^k\bZeik^llnk^lh_m^ge^Z]mhZk^jnbk^f^gmmhlmkbd^ma^_hkfphkd
ZllhhgZlihllb[e^Zg]fho^hgmhln[l^jn^gm_ehhkl%pbmama^fbgbfnf
h_ikhiibg`'M^lmlhg_eZmleZ[laZo^]^fhglmkZm^]maZmZlfn\aZl0)
h_maêhZ]l_khfZg^per\Zlm_ehhk!_hkfphkd%p^m\hg\k^m^%\hglmkn\mbhg
ehZ]l"fZr[^\Zkkb^][rma^lnli^g]^]_ehhk[êhp'Bm\Zg`^g^kZeer
[^Zllnf^]maZm^Zkerlmkbdbg`h__hkfphkdpbeeghm`k^ZmerZ__^\mma^
]^_e^\mbhgZ_m^kbglmZeebg`ma^\eZ]]bg`Zg](hkiZkmbmbhgl'Mablbl[^\Znl^ma^
]^_e^\mbhgZ__^\mbgìZkmbmbhglpbee[^lfZee^kb_ma^leZ[[^\hf^lÂ\kZ\d^]Ã
[^_hk^%kZma^kmaZgZ_m^k%ma^bglmZeeZmbhgh_ma^\eZ]]bg`Zg](hkiZkmbmbhgl'
Cracking
=^_e^\mbhgh_\hg\k^m^l^\mbhglbl\ehlêrebgd^]mhma^^qm^gmh_
\kZ\dbg`Zg]ma^]^`k^^mhpab\a\kZ\dbg`\ZiZ\bmrbl^q\^^]^]'Ma^
ihbgmZmpab\a\kZ\dbg`h\\nklbl]^m^kfbg^][rma^fhf^gmlbg]n\^]
bgma^leZ[Zg]ma^m^glbe^lmk^g`mah_ma^\hg\k^m^%pab\abg\k^Zl^l
pbmaZ`^'H_m^gma^\kbmb\ZelbmnZmbhgblpa^gma^leZ[bllmkn\d%hkpa^g
maêhZ]h_ma^leZ[Z[ho^blZiieb^]'Hg\^ma^leZ[aZl\kZ\d^]bml
lmb__g^llbli^kfZg^gmerk^]n\^]'
Bmblma^k^_hk^g^\^llZkrmh_bg]ma^\kbmb\ZeehZ]bg`lmZ`^Zmpab\a
\kZ\dbg`_bklmh\\nkl'Mabl\kbmb\ZeehZ]bg`lmZ`^\hkk^lihg]lpbmama^
fbgbfnfoZen^h_D%pa^k^3
K = fctm
^W
0.5h
pa^k^
P 6Ma^l^kob\^Z[bebmrehZ]bg`Ziieb^]nimhmaZmlmZ`^
_\mf6Ma^\hg\k^m^m^glbe^lmk^g`maZmmaZmlmZ`^
Pa^k^ma^_k^jn^gm\hf[bgZmbhgblma^\kbmb\ZeehZ]lmZ`^%ma^g
ma^]^`k^^h_\kZ\dbg`!z"\Ze\neZm^]_hkma^_k^jn^gm\hf[bgZmbhg
lahne]Zelh[^nl^]_hkma^jnZlb&i^kfZg^gm\hf[bgZmbhg%[nmghm_hk
Figure 2
Loading history for a slab – an example
14
h
12
10
Load (kN/m)
g
b
f
c
8
a
e
d
6
Loading sequence
Slab struck
a
1st slab above cast
b
2nd slab above cast
c
3rd slab above cast
d
4
2
e
f
g
h
Floor finishes applied
Partitions erected
Quasi-permanent variable actions
Frequent variable actions
0
0
50
100
150
200
250
300
Duration (days)
61
Zgrh_ma^^Zkeb^kehZ]lmZ`^l'B_%ahpô^k%Zg^Zkeb^klmZ`^
ikho^l\kbmb\Ze%ma^zoZen^ZmmaZmlmZ`^lahne][^\Zkkb^]
_hkpZk]mhZeeln[l^jn^gmlmZ`^l'
Figure 3
Outline of rigorous method for calculating deflection
Collate input data
?nkma^kbg_hkfZmbhg\Zg[^_hng]bgma^[^lmikZ\mb\^
`nb]^>Zkerlmkbdbg`Zg]bfikho^][Z\dikhiibg`
N >e^f^gm]bf^glbhglZg]k^bg_hk\^f^gm]^mZbelZg]ZkkZg`^f^gml_khfma^
nembfZmêbfbmlmZm^]^lb`g
Shrinkage curvature
LakbgdZ`^]î^g]lhgma^pZm^k(\^f^gmkZmbh%kêZmbo^
anfb]bmrZg]ma^lbs^Zg]laZi^h_ma^f^f[^k'Ma^^__^\m
h_lakbgdZ`^bgZgZlrff^mkb\Zeerk^bg_hk\^]l^\mbhgblmh
bg]n\^Z\nkoZmnk^maZm\Zge^Z]mhlb`gb_b\Zgm]^_e^\mbhgbg
laZeehpf^f[^kl'Mabl^__^\mlahne][^\hglb]^k^]bgma^
]^_e^\mbhg\Ze\neZmbhgl'
Determining long term elastic modulus of elasticity
<Ze\neZmêhg`&m^kfêZlmb\fh]nenl%>EM_khf3
E LT = RW
c
W1
W2
W3
W4
W5
+
+
+
+
Eeff,1 Eeff, 2 Eeff, 3
Eeff, 4 Eeff, 5
m
pa^k^
>^__ 6>\+1(!*$h"
Pg 6L^kob\^Z[bebmrehZ]ZmlmZ`^g
h 6<k^î\h^__b\b^gmZmkêôZgmehZ]bg`mbf^
Zg]]nkZmbhg
62
<hg\k^mîkhi^kmb^l!l^^MZ[e^*"
F^Zg\hfik^llbo^lmk^g`ma!_\f"
F^Zgm^glbe^lmk^g`ma!_\mfhk_\mf%_e"
>eZlmb\fh]nenl!>\+1"6*').>\f
N =
^m^kfbg^ma^\kbmb\ZeehZ]lmZ`^Zmpab\a\kZ\dbg`_bklmh\\nkl'
!L^^Â<kZ\dbg`ÃhgiZ`^,"
Repeat at 1/20 points for all three loading stages
Rigorous method
Panel 1
N
Lmkbdbg`ma^_hkfphkd
<Zlmbg`ma^_ehhkZ[ho^
>k^\mbhgh_maîZkmbmbhglZg](hk\eZ]]bg`
:iieb\Zmbhgh__bgbla^l
Ma^l^jn^g\^pbeeoZkr_khfikhc^\mmhikhc^\m
Assess whether the element has flexural cracking
Mphf^mah]l_hk\Ze\neZmbg`]^_e^\mbhgZkîk^l^gm^]
[êhp%Zg]ma^l^Zk^[Zl^]hgma^Z]ob\^bgMK.1
=^_e^\mbhglbg\hg\k^m^leZ[lZg][^Zfl'
?bgbm^ê^f^gmZgZerlblfZrZelh[^nl^]mhh[mZbg
^lmbfZm^lh_]^_e^\mbhg'Bgmabl\Zl^maîkbg\bie^l
bg?b`nk^,lahne][^Ziieb^]b_\k^]b[e^k^lnemlZk^mh
[^h[mZbg^]'
E hZ]bg`l^jn^g\^^'`'
N <kbmb\ZeZkkZg`^f^gmh_Z\mbhgl
!hkkî^Zmma^\Ze\neZmbhgl_hk^Z\aZkkZg`^f^gmmh]^m^kfbg^ma^\kbmb\Ze\Zl^"
Methods for
calculating deflections
Ma^kb`hkhnlf^mah]_hk\Ze\neZmbg`]^_e^\mbhglblma^
fhlmZiikhikbZm^f^mah]_hk]^m^kfbgbg`Zk^Zeblmb\
^lmbfZm^h_]^_e^\mbhg'Ahpô^k%bmblhgerlnbmZ[e^_hk
nl^pbma\hfinm^klh_mpZk^'Ma^<hg\k^m^<^gmkâZl
ikh]n\^]Zgnf[^kh_lik^Z]la^^mlmaZmnl^mablf^mah]
mh\Zkkrhnm]^_e^\mbhg\Ze\neZmbhgl_hkZoZkb^mrh_leZ[l
Zg][^Zfl'Ma^l^h__^kZ\hlm&^__^\mbo^pZrmh\Zkkr
hnm]^mZbe^]]^_e^\mbhg\Ze\neZmbhgl%Zg]ma^rbg\en]^ma^
Z[bebmrmh\hglb]^kma^^__^\mh_^ZkerZ`êhZ]bg`h_ma^
\hg\k^m^'?b`nk^,beenlmkZm^lmaîkbg\bie^lh_ma^f^mah]
Zg]lahplahpma^_Z\mhklZ__^\mbg`]^_e^\mbhgZk^
\hglb]^k^]bgma^kb`hkhnl]^_e^\mbhg\Ze\neZmbhgl'
N
N
<Ze\neZm^ma^_heehpbgìkhi^kmb^l3
<k^î\h^__b\b^gml%h!:gg^q;h_>nkh\h]^+hk?b`nk^-"
E hg`m^kfêZlmb\fh]nenl%>EM!l^ÎZgê*"
>__^\mbo^fh]nenlkZmbh%a^_khf3a^6>l (>EM
G^nmkZeZqbl]îma_hkng\kZ\d^]\hg]bmbhg%qn!l^ÎZgê+"
L^\hg]fhf^gmh_Zk^Z_hkng\kZ\d^]\hg]bmbhg%Bn!l^ÎZgê+"
<Ze\neZm^\kZ\dbg`fhf^gm%F\k_khf3
F\k6_\mf Bn(!a¾qn"%nlbg`ZiikhikbZmôZen^_hk_\mf'
N
=h^lma^fhf^gmZmma^\kbmb\ZeehZ]lmZ`^^q\^^]ma^\kZ\dbg`fhf^gm8
B_r^l%ma^ê^f^gmbl\kZ\d^]ZmZeeln[l^jn^gmlmZ`^l'
z
6*¾)'.!F\k(F"+Tz6)_hkng\kZ\d^]lbmnZmbhgV
Nl^ma^l^\kbmb\ZeoZen^lh__\mfZg]z_hkln[l^jn^gmlmZ`^l'
B_gh%ma^ê^f^gmpbeeghm\kZ\dZmZgrlmZ`^'
Determine the curvature of the slab
N P
a^gma^leZ[bl\kZ\d^]\Ze\neZm^ma^_heehpbgìkhi^kmb^lZmmaêhZ]lmZ`^
[^bg`\hglb]^k^]%nlbg`ZiikhikbZmôZen^l_hk_\mf%zZg]>EM3
G^nmkZeZqbl]îma_hk\kZ\d^]l^\mbhg%q\!l^ÎZgê+"
L^\hg]fhf^gmh_Zk^Z_hk\kZ\d^]\hg]bmbhg%B\!l^ÎZgê+"
N <Ze\neZm^ma^_e^qnkZe\nkoZmnk^3
MQP
MQP
1
rfl = g E e Ic + ]1 – g g E e Iu
N <Ze\neZm^ma^\nkoZmnk^]n^mhlakbgdZ`^lmkZbg*(k\l!l^ÎZgê+"
N <Ze\neZm^ma^mhmZe\nkoZmnk^%*(km6*(k_e$*(k\l
Kî^Zmma^\Ze\neZmbhglZm_k^jn^gmbgm^koZel!lZrZm*(+)ihbgml"Zg]bgm^`kZm^
mpb\^mhh[mZbgma^ho^kZee]^_e^\mbhg'
B_]^_e^\mbhgZ__^\mbg`\eZ]]bg`Zg](hkiZkmbmbhglblk^jnbk^]%kî^Zm\Ze\neZmbhgl
_hk_k^jn^gm\hf[bgZmbhgZg]_hkehZ]bg`Zmmbf^h_bglmZeeZmbhgh_iZkmbmbhgl
Zg](hk\eZ]]bg`'
>lmbfZm^]^_e^\mbhgl3
N Ho^kZee]^_e^\mbhg!jnZlb&i^kfZg^gm\hf[bgZmbhg"
N =^_e^\mbhgZ__^\mbgìZkmbmbhgl(\eZ]]bg`!?k^jn^gm\hf[bgZmbhg]^_e^\mbhg
e^ll]^_e^\mbhgZmmbf^h_bglmZeeZmbhg"
Table 1
Concrete properties
fck
MPa
_\f
6!_\d$1"
320
325
328
330
332
335
340
350
FIZ
,+1
,,,
,,/
,,1
,-)
,-,
,-1
,.1
_\mf 6!)',_\d!+(,"©<.)(/)hk+'*+eg!*$!_\f(*)""7 <.)(/)"
FIZ
,,+'+*
,,+'./
,,+'00
,,+'2)
,,,')+
,,,'+*
,,,'.*
,,-')0
_\mf#6!)',_\f!+(,"©<.)(/)hk*')1eg!_\f"$)'*7 <.)(/)"Z
FIZ
,,+'00
,,,')2
,,,'+0
,,,',2
,,,'.*
,,,'/1
,,,'2/
,,-'.)
>\f 6!++T!_\f"(*)V)',
@IZ
,,)')
,,*'.
,,+',
,,+'1
,,,',
,,-'*
,,.'+
,,0',
>\+1 6!*').>\f"
@IZ
,,*'.
,,,')
,,,'2
,,-'.
,,.')
,,.'1
,,0')
,,2'*
e\]%)<>F\eZllK%KA 6.)
fb\khlmkZbg
0-/
0)/
/1,
//1
/.,
/,+
.21
.,/
e\]%)<>F\eZllK%KA 61)
fb\khlmkZbg
-*/
,2-
,1*
,0+
,/-
,.,
,,-
+22
e\]%)<>F\eZllG%KA 6.)
fb\khlmkZbg
.--
.*+
-2-
-1+
-0*
-.-
-+1
,02
e\]%)<>F\eZllG%KA 61)
fb\khlmkZbg
,),
+1/
+0.
+/2
+/,
+.,
+,2
+*+
e\]%)<>F\eZllL%KA 6.)
fb\khlmkZbg
--*
-*,
,20
,10
,00
,/,
,-)
+21
e\]%)<>F\eZllL%KA 61)
fb\khlmkZbg
+-/
+,)
++*
+*/
+*)
+)+
*12
*//
e\Z!∞"
fb\khlmkZbg
,+.
,,1
,-.
,.)
,..
,/,
,0.
*))
Key
a _\mf#fZr[^nl^]pa^glmkbdbg`Zme^llmaZg0]Zrlhkpa^k^\hglmkn\mbhgho^kehZ]blmZd^gbgmhZ\\hngm'
Panel 2
Useful Expressions for a rectangular section
bh 2
2 + ] ae - 1 g ] Asd + As2 d2 g
xu =
bh + ] ae - 1 g ] As + As2 g
pa^k^
2
2
2
bh 3
h
I u = 12 + bh a 2 - xuk + ] ae - 1 g 6 As ]d - xu g + As2 ] x u - d 2 g @
[ 6;k^Z]mah_l^\mbhg
:l 6:k^Zh_m^glbhgk^bg_hk\^f^gm
:l+6:k^Zh_\hfik^llbhgk^bg_hk\^f^gm
] 6>__^\mbo^]îmamhm^glbhg
k^bg_hk\^f^gm
# 7 ^ As ae + A s2 ] ae - 1 g h 2+ 2 b ^ As d ae + A s2d2 ] ae - 1 g h A 0.5- ^ As ae + As2 ] ae - 1 g h -
xc =
b
bx c3
2
2
I c = 3 + ae As ^ d - x c g + ^ ae - 1 g As2 ^ d2 - x c g
]+ 6=îmamh\hfik^llbhgk^bg_hk\^f^gm
a 6Ho^kZee]îmah_l^\mbhg
a^ 6Fh]neZkkZmbh
Ln 6:l!]¾qn"¾:l+!qn¾]+"
SLu\
SLnc
1
rcs = g f cs a e BI\u +^1 - g h fcs ae IBnc
L\ 6:l!]¾q\"¾:l+!q\¾]+"
Figure 4
Method for determining creep coefficient h(∞,t0)
1
S
N
1
R
2
3
2
3
5
5
t 0 10
t 0 10
20
30
20
30
50
50
100
7.0 6.0 5.0 4.0 3.0 2.0 1.0
h (?, t 0 )
a) Inside conditions - RH = 50%
Ke y
C20/25
C25/30
C30/37
C35/45
C40/50
C45/55
C50/60
0 100 300 500 700 900 1100 1300
h 0 (mm)
S
N
R
100
7.0 6.0 5.0 4.0 3.0 2.0 1.0
h (?, t 0)
0
100 300 500 700 900 1100 1300
h o (mm)
b) Outside conditions - RH = 80%
Notes
1 t0 = age of concrete at time of loading
2 h0 = 2A c /u
3 Intersection point between lines D & E can also be above point A
4 For t0 > 100 it is sufficiently accurate to assume t = 100
How to use Nonogram
D
A
E
B
C
63
Figure 5
Simplified method
:lbfieb_b^]f^mah]_hk\Ze\neZmbg`]^_e^\mbhgblik^l^gm^]bg?b`nk^.'
Bmbl_^Zlb[e^mh\Zkkrhnmma^l^\Ze\neZmbhgl[raZg]%Zg]ma^r\hne][^
nl^]mhkhnàero^kb_r]^_e^\mbhgk^lneml_khf\hfinm^klh_mpZk^%hk
nl^]pa^k^Z\hfinm^kblghmZoZbeZ[e^'
Ma^fZchklbfieb_b\ZmbhgblmaZmma^^__^\mlh_^ZkerZ`êhZ]bg`Zk^ghm
\hglb]^k^]^qieb\bmer4kZma^kZgZeehpZg\^blfZ]^_hkma^bk^__^\mpa^g
\Ze\neZmbg`ma^\kZ\dbg`fhf^gm'Lbfieb_b^]\k^î_Z\mhklZk^nl^]Zg]
]^_e^\mbhg_khfma^\nkoZmnk^h_ma^leZ[blZiikhqbfZm^]nlbg`Z_Z\mhk'
Values for K for various bending moment diagrams
Bending moment diagram
M
M
al
W
l
M = Wa (1-a ) l
0.9 fctm I u
=
3 4a 2
48 (1-a)
If a = 1 , K = 1
12
2
No
Yes
Is Mcr > MQP?
Section is uncracked
z=0
Section is cracked
z = 1 – 0.5(Mcr/MQP)2
Calculate depth to neutral axis for cracked
condition, xc and calculate second moment of area
for cracked condition, Ic
W/2
al
0.125
Wal
2
q
a2
6
Calculate flexural curvature
q
1
rn
=
g
MQP
Eeff Ic
MQP
+ ^1 – g h E
eff Iu
Calculate total shrinkage strain ecs from ecs = ecd + eca where:
ecd = kh ecd,0 = Drying shrinkage strain
kh = Coefficient based on notional size, see Table 2
ecd,0 = Nominal unrestrained drying shrinkage, see Table 1
eca = bas(t) eca(∞) = eca(∞) for long-term deflection, see Table 1
0.104
ql 2
8
0.102
ql
Calculate curvature due to shrinkage strain 1/rcs (see Panel 2)
2
15.6
q
MA
MC
MB
K = 0.104 (1
b=
al
W
1
Calculate total curvature r
t,QP
=
1
rn
1
rcs
1
KL 2 rt,QP
where K can be obtained from Figure 6 and L is the span.
Calculate quasi-permanent deflection from dQP
MA + MB
MC
+
Do you need
to calculate deflection
due to cladding and
partitions?
=
No
Finish
Yes
2 2
a (4 a )
12
if a = l , K = 0.25
qa l
2
MA
MB
K = 0.083 (1
b=
MC
al
b
)
10
End deflection
a (3 a )
=
6
load at end K = 0.333
Wal
al
q
al
2
Wl (3 4a 2)
24
64
Calculate creep coefficient, h(∞,t0), using either Figure 4
or Annex B (in which case look-up fcm in Table 1)
h – xu
(Note the factor 0.9 has been introduced into this method
because the loading sequence is not considered)
M
M=
Obtain concrete properties, fctm, and Ec28 from Table 1
Calculate cracking moment, Mcr from: Mcr
0.0625
W/2
al
Calculate the moment, MQP, due to quasi-permanent actions at
the critical section (i.e. mid-span or at support for cantilever)
K
0.125
M
START
1 Calculate long term elastic modulus, Eeff from: Eeff = Ec28/[1+h (∞,t0)]
2 Calculate effective modulus ratio, ae from ae = Es/Eeff, where Es is
elastic modulus for reinforcement (200 GPa)
3 Calculate depth to neutral axis for uncracked condition, xu
4 Calculate second moment of area for uncracked condition, Iu
Figure 6
Loading
Simplified method for calculating deflection
MA + MB
MC
1 (5 4a 2 )
80 3 4a
2
b
)
4
Calculate the deflection that will occur at the time of application of
the load due to partitions and/or cladding.
1 Calculate the creep coefficient h(t,t0), where t is the age when
partition/cladding loads are applied and t0 is the age of striking.
h(t,t0) ≈ h(∞,t0) bc(t,t0). For bc(t,t0) refer to Figure 7, alternatively
refer to Annex B of Eurocode 2.
2 Calculate the moment due to self-weight, partitions/cladding and any
other loads which have been applied prior to the installation of the
cladding/partition, Mpar and use in place of MQP
3 Recalculate the section properties, curvature and hence deflection,
dpar, using h(t,t0) or equivalent instead of h(∞,t0)
4 The approximate deflection affecting cladding and partitions is
d = dQP – dpar
Precamber
Table 2
Values for Kh
h0
kh
7 *))
*')
7 +))
)'1.
7 ,))
)'0.
7 .))
)'0)
:leZ[hk[^Zf\Zg[îk^\Zf[^k^]mhk^]n\^ma^^__^\mh_]^_e^\mbhg
[êhpmaâhkbshgmZe!l^^?b`nk^1"'Ahpô^k%bgikZ\mb\^mhhfn\a
ik^\Zf[^kbl`^g^kZeernl^]Zg]ma^leZ[k^fZbgli^kfZg^gmer
\Zf[^k^]'Mablbl[^\Znl^h_ma^]b__b\nemrbgZ\\nkZmêr\Ze\neZmbg`
]^_e^\mbhg':ik^\Zf[^kh_nimhaZe_ma^jnZlb&i^kfZg^gm
\hf[bgZmbhg]^_e^\mbhg\hne][^nl^]%[nmZehp^k_b`nk^bl
k^\hff^g]^]'Ik^\Zf[^k]h^lghmk^]n\^ma^]^_e^\mbhglZ__^\mbg`
iZkmbmbhglhk\eZ]]bg`'
Notes
a)blma^ghmbhgZelbs^!ff"h_ma^\khll&l^\mbhg6+:\(n
pa^k^
:\6<hg\k^m^\khll&l^\mbhgZeZk^Z
n6I^kbf^m^kh_maZmiZkmh_ma^\khlll^\mbhgpab\abl^qihl^]mh]krbg`
Flat slabs
Figure 7
Coefficient for development of creep with time after loading
0.60
0.55
Coefficient, bc (t, t0)
0.50
?eZmleZ[lZkô^krihineZkZg]^__b\b^gm_ehhklrlm^fl'Ahpô^k%
[^\Znl^ma^rliZgbgmph]bk^\mbhgl%bm\Zg[^]b__b\nemmh\Ze\neZm^ma^bk
]^_e^\mbhg'MK.1 `bo^llô^kZelnbmZ[e^f^mah]l_hkZll^llbg`_eZmleZ[
]^_e^\mbhg'H_ma^l^%ZihineZkf^mah]blmhmZd^ma^Zo^kZ`^]^_e^\mbhg
h_mphiZkZeeê\henfglmkbilZg]mhZ]]ma^]^_e^\mbhgh_ma^fb]]e^
lmkbiliZggbg`hkmah`hgZeermh`^mZgZiikhqbfZmbhgh_ma^fZqbfnf
]^_e^\mbhgbgma^\^gmk^h_ma^leZ['
Ma^k^\hff^g]^]Z\\îmZg\^\kbm^kbZ_hkZ_eZmleZ[Zk^lahpgbg?b`nk^2'
0.45
Accuracy
0.40
Ma^\Ze\neZmbhgh_]^_e^\mbhgbg>nkh\h]^+nlbg`ma^kb`hkhnlf^mah]
ik^l^gm^]a^k^blfhk^Z]oZg\^]maZgmaZmbg;L1**)'Bm\Zg[^
nl^]mhmZd^Z\\hngmh_^Zker&Z`^\hglmkn\mbhgehZ]bg`[r\hglb]^kbg`
k^]n\^]^Zker\hg\k^m^m^glbe^lmk^g`mal'
0.35
Ahpô^k%ma^_heehpbg`bg_en^g\^lhg]^_e^\mbhgl\Zgghm[^Z\\nkZmêr
Zll^ll^]3
0.30
0.25
100
300
500
h 0 (mm)
700
900
N M^glbe^lmk^g`ma%pab\a]^m^kfbg^lma^\kZ\dbg`fhf^gm'
N <hglmkn\mbhgehZ]bg`'
t = 90, t0 = 3
t = 90, t0 = 7
t = 60, t0 = 3
t = 60, t0 = 7
t = 28, t0 = 3
t = 28, t0 = 7
Notes
m 6:`^h_\hg\k^m^pa^giZkmbmbhgl(\eZ]]bg`Ziieb^]
m) 6:`^h_\hg\k^m^pa^glmkn\d
_\d 6,)!_\f6,1"%ahpô^kma^\h^__b\b^gmblghmiZkmb\neZkerl^glbmbo^mh\hg\k^m^\eZll
N >eZlmb\fh]nenl'
Ma^k^_hk^Zgr\Ze\neZmbhgh_]^_e^\mbhgblhgerZg^lmbfZm^%Zg]ô^gma^
fhlmlhiablmb\Zm^]ZgZerlbl\Zglmbeek^lnembg$*.mh&,)^kkhk'Bmbl
Z]oblZ[e^mh`bo^ZlnbmZ[e^\Zo^ZmpbmaZgr^lmbfZm^h_]^_e^\mbhgmaZm
hma^klZk^kêrbg`hg'
Figure 8
Figure 9
Precambering of slabs
Recommended acceptance criteria for flat slabs
Precamber
Just before installation
of partitions
Notes
a
X
Deflection due to
quasi-permanent
combination
Deflection due to
frequent combination
Deflection affecting partitions
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65
Cladding tolerances
N FZgn_Z\mnk^klfZrlZrmaZmma^bkèZs^]lrlm^fl\Zghger
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Ma^k^lahne][^hi^g]bl\nllbhgl[^mp^^gma^]^lb`g^kl_hkmaôZkbhnl
ê^f^gmlmh]^m^kfbg^ma^fhlm\hlm&^__^\mbo^pZrh_]^Zebg`pbmama^
bgm^kZ\mbhgh_ma^lmkn\mnk^Zg]\eZ]]bg`'
N Pa^gZleZ[]^_e^\ml%maêhZ]hgma^\^gmkZe_bqbg`lpbee[^kêbô^]
Zg]la^]mhhnm^k_bqbg`l'
Z\\hffh]Zm^]^_e^\mbhgZlehpZl.ff'
References
1 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾*%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^lZg]kne^l_hk[nbe]bg`';LB%+))-'
3 FHLL%KF;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3LeZ[l'Ma^<hg\k^m^<^gmk^%+))/'
4 FHLL%KF;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3?eZmleZ[l'Ma^<hg\k^m^<^gmk^%+))/'
5 G:K:R:G:G%KL;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3Bgmkh]n\mbhgmh>nkh\h]^l'Ma^<hg\k^m^<^gmk^%+)).
6 ;KBMBLA<>F>GM:LLH<B:MBHG'>Zkerlmkbdbg`Zg]bfikho^][Z\dikhiibg`';<:%+))*'!:oZbeZ[e^_khfppp'\hg\k^m^\^gmk^'\hf"
7 I:EE>MM%I'@nb]^mh_eZmleZ[_hkfphkdZg]_Zel^phkd'<hglmkn\m%+)),
8 MA><HG<K>M>LHMR'M^\agb\ZekîhkmGh'.1=^_e^\mbhglbg\hg\k^m^leZ[lZg][^Zfl'Ma^<hg\k^m^Lh\b^mr%+)).'
9 @HH=<ABE=%<AP>;LM>K%KF'Lik^Z]la^^ml_hk\hg\k^m^]^lb`gmh;L1**)Zg]><+%o^klbhg,'Ma^<hg\k^m^<^gmk^%+))/'
10 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1**)¾*'Lmkn\mnkZenl^h_\hg\k^m^¾<h]^h_ikZ\mb\^_hk]^lb`gZg]\hglmkn\mbhg';LB%*220'
66
2'K^mZbgbg`pZeel
A J BondF:%FL\%Ia=%=B<%FB<>%<>gÒ Brooker;>g`%<>g`%FB<>%FBLmkn\m>A J Harris;L\%FL\%=B<%FB<>%<>g`%?@L
Introduction
Mabl\aZim^k\ho^klma^ZgZerlblZg]]^lb`gh_k^bg_hk\^]\hg\k^m^k^mZbgbg`
pZeelmh>nkh\h]^l+Zg]0'Bm\hglb]^klk^mZbgbg`pZeelnimh,fabàZg]
ikhii^][Zl^f^gmpZeelnimhmphlmhk^rlabà!0f"'Ma^lêbfbmlaZo^[^^g
\ahl^glhmaZmlbfieb_b\Zmbhgl\Zg[^fZ]^bgma^`^hm^\agb\Ze]^lb`g'Ma^
lê_&p^bàmh_ma^l^pZeel%bg\en]bg`ma^lê_&p^bàmh_[Z\d_beehgma^f%ieZrlZ
lb`gb_b\Zgmkhe^bglniihkmbg`ma^k^mZbg^]fZm^kbZe'Ma^\aZim^k]h^lghm\ho^k
ma^ZgZerlblZg]]^lb`gh_^f[^]]^]k^mZbgbg`pZeel%pab\akêrikbfZkberhg
iZllbo^^Zkmaik^llnk^Zg]_e^qnkZek^lblmZg\^mhlniihkmma^k^mZbg^]fZm^kbZe'
Ikbhkmhmaîn[eb\Zmbhgh_ma^lmkn\mnkZe>nkh\h]^l%ma^`^hm^\agb\Ze]^lb`gh_
k^mZbgbg`pZeelpZl\ho^k^][r;L1))+':emahnà\^kmZbgikhoblbhglh_mabl
\h]^Zk^lni^kl^]^][r>nkh\h]^0%ma^_hkf^klmbee\hgmZbglnl^_nejnZebmZmbo^
bg_hkfZmbhgk^`Zk]bg`ma^]^lb`gh_k^bg_hk\^]\hg\k^m^pZeel'
:fhk^`^g^kZebgmkh]n\mbhgmhma^>nkh\h]^lbl`bo^gbg<aZim^kl*Zg]+
hkb`bgZeerin[ebla^]ZlBgmkh]n\mbhgmh>nkh\h]^lZg]@^mmbg`lmZkm^]'Ma^
^ll^gmbZe_^Zmnk^lh_>nkh\h]^0IZkm*Zk^\ho^k^]bg<aZim^k/%?hng]Zmbhgl%
pab\abg\en]^lZ]bl\nllbhgh_ebfbmlmZm^l%@^hm^\agb\Ze<Zm^`hkb^l%
f^mah]lh_]^lb`g%Zg]ma^@^hm^\agb\Ze=^lb`gKîhkm'Bmlahne][^k^Z]bg
\hgcng\mbhgpbmamabl\aZim^k'
>ll^gmbZe_^Zmnk^lh_>nkh\h]^0Zkîk^l^gm^]%Zehg`pbmama^hk^mb\Zefh]êl
_hkma^ZgZerlblh_k^mZbgbg`pZeel':ikh\^]nk^_hkZgZerlblZg]]^lb`gbl`bo^g
hgiZ`^0)'
Geotechnical Categories
>nkh\h]^0IZkm*]^_bg^lmak^^@^hm^\agb\Ze<Zm^`hkb^lmaZm\Zg[^nl^]mh
^lmZ[ebla`^hm^\agb\Ze]^lb`gk^jnbk^f^gml'Lbfie^lmkn\mnk^lpbmag^èbZ[e^
kbld[êhg`bg@^hm^\agb\Ze<Zm^`hkr*'PZeelmaZmk^mZbglhbehkpZm^kZg]]h
ghmbgoheo^^q\îmbhgZekbldhk]b__b\nemlhbehkehZ]bg`\hg]bmbhgl[êhg`bg
@^hm^\agb\Ze<Zm^`hkr+%_hkpab\akhnmbgîkh\^]nk^l_hk_bê]Zg]eZ[hkZmhkr
m^lmbg`Zg]_hk]^lb`gZg]^q^\nmbhgfZr[^nl^]'Ma^]^lb`gh_ln\a
lmkn\mnk^lk^jnbk^ljnZgmbmZmbo^`^hm^\agb\Ze]ZmZZg]ZgZerlbl'
PZeelmaZmbgoheo^Z[ghkfZekbldhkpa^k^ma^k^blngnlnZehk^q\îmbhgZeer
]b__b\nemlhbehkehZ]bg`\hg]bmbhgl[êhg`bg@^hm^\agb\Ze<Zm^`hkr,%_hk
pab\aZem^kgZmboîkhoblbhglZg]kne^lmhmahl^`bo^gbg>nkh\h]^0fZr[^
g^^]^]4ma^rZk^hnmlb]^ma^l\hi^h_mablin[eb\Zmbhg'
Limit states
Ma^]^lb`gh_k^bg_hk\^]\hg\k^m^k^mZbgbg`pZeelk^jnbk^lo^kb_b\ZmbhgmaZmma^
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Table 1
Partial factors to be used for retaining wall design according to
design approach 1 (UK National Annex)
Combination
Partial factors on
actions
Partial factors on material
properties of soil
gGa
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Material properties
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Procedure for determining material properties, geometry and actions
From Figure 4
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Determine characteristic material properties
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General expressions for material properties and earth pressures
For calculation model A:
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Figure 9
Procedure for design against toppling
To Figure 4
From Figure 4
Expressions for drained sliding resistance
Undrained sliding resistance:
"+&
Drained sliding resistance:
d&h9
"+&-?
d&g!19/ .4?
h9
+F
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Panel 3
To Figure 4
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Figure 8
Effects of shear key
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Figure 10
Procedure for design against bearing failure
0
Panel 4
Expressions for bearing resistance
3
g-/.D&)?
W &IG=)?W
&O
-)?
W
&O
Undrained bearing resistance:
87&A
(8
B(&p &
R O)
W
A
?
Drained bearing resistance:
878(HHgA
=g(g g
)?W
8&O
g-/.D)?
W
g
H
;?EA((g?
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Figure 11
Bearing capacity factors, N, from ground properties
From Figure 4
+F
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E
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c
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,
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Figure 13
Design procedure for structural design
From Figure 4
Compaction earth pressures
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Figure 14
Compaction earth pressures for structural design of cantilever
retaining walls
Figure 12
Effective base width, B’
zJ
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74
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Panel 5
General expressions for designing walls for compaction pressures
+
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1 4
Forces for stem design (see Figure 14)
L < < OL OB0<+OL0
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Table 2
Typical compaction equipment12
Description of compaction
equipment
Mass (kg)
Centrifugal
vibrator
force (kN)
Design
force (kN)
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Forces for heel design (see Figure 15b)
Panel 6
. 2 8 2 O
2F
'B& - 0A B O B
Expressions for the structural design of basement walls for ‘at-rest’
pressures
8B?-B&-.0AO82BO
Forces for toe design (see Figure 15a)
8 2 2F
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b s9&g<8
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Figure 15
g:<=<:
Pressure diagram for design of reinforced concrete base
s3%s9O
Soil pressure above
toe ignored
s3s3
Forces for stem design
< < 0
< 2F
'& B( : <O < B< <<O < B<<O<< B+ <O<<
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Figure 16
Earth and pore water pressures for structural design of retaining
walls subject to 'at-rest' conditions
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Table 3
Maximum bar size or spacing to lmit crack width (mm)
Steel
stress
(ss)
MPa
"
Note
Wmax = 0.3
Wmax = 0.2
Maximum
Maximum
bar size
bar spacing
(mm)
(mm)
47 "
Maximum
Maximum
bar size
bar spacing
(mm)
(mm)
47
"
O
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Rules for spacing and quantity of
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Vertical reinforcement
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Figure 17
Typical drainage layout for a retaining wall
Horizontal reinforcement
9BF
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Practical issues
Design for movement
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Drainage
300 mm wide
granular backfill
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if required
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References
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kîeZ\^];L.,+13<hg\k^m^hg*=^\^f[^k+)),Zg]lahne]Zek^Z]r[^
_ZfbebZk'
N ;L---23Li^\b_b\Zmbhg_hk\Zk[hglm^ê[Zkl_hkma^k^bg_hk\^f^gmh_
\hg\k^m^pZlkôbl^]bg+)).lhmaZmbm[^\Zf^Z\hfie^f^gmZkr
lmZg]Zk]mh;L>G*))1)3Lm^ê_hkma^k^bg_hk\^f^gmh_\hg\k^m^Zg]
GhkfZmbo^:gg^q<h_>nkh\h]^+'
N ;L1///3+)).%L\a^]nebg`%]bf^glbhgbg`%[^g]bg`Zg]\nmmbg`h_lm^ê
k^bg_hk\^f^gm_hk\hg\k^m^¾li^\b_b\ZmbhgaZlZelh[^^gkôbl^]%
bgmkh]n\bg`>nkh\h]^+k^jnbk^f^gmlZg]Z`k^Zm^kkZg`^h_laZi^\h]^l'
Bgmablin[eb\ZmbhgZgnf[^kh_ZllnfimbhglaZo^[^^gfZ]^'FZgrh_ma^
]^kbo^]^qik^llbhglZg]_b`nk^lZllnf^NDoZen^l_hkma^GZmbhgZe=^m^kfbg^]
IZkZf^m^kl!G=Il"'BmblZllnf^]maZm[Zkllbs^lZk^-)ffhke^llZg]maZm
ma^[Zklpbeeghm[^[ng]e^]mh`^ma^k'BmblZelhZllnf^]maZmma^\hg\k^m^
\eZllpbeeghm^q\^^]<.)(/)'?hkZ]]bmbhgZek^jnbk^f^gmlhnmlb]^ma^lêbfbml%
k^_^k^g\^lahne][^fZ]^mh>nkh\h]^+'
Mabl\aZim^k_h\nl^lhg]^mZbebg`ma^k^bg_hk\^f^gmmh\hfierpbma>nkh\h]^+4
`nb]Zg\^hgikh\^]nk^l%k^lihglb[bebmb^lZg]ikîZkZmbhgh_]kZpbg`l\Zg[^
_hng]bghma^k]h\nf^gml
Type and grade of reinforcement
Ma^+)).kôblbhgh_;L---2bgmkh]n\^]Z\aZkZ\m^kblmb\rbê]lmk^g`ma
h_.))FIZ'Ma^k^Zk^ghpmak^^`kZ]^lh_k^bg_hk\^f^gm%:%;Zg]<!l^^
MZ[e^*"%pab\ah__^kbg\k^Zlbg`]n\mbebmr'Bmbl^qi^\m^]maZm_hkma^]^lb`gh_
ND[nbe]bg`lZeemak^^`kZ]^l:%;hk<pbee[^ZiikhikbZm^Zg]bgmabl\Zl^ma^
[Zklbs^\Zg[îk^_bq^]pbmaZgA!^'`'A*+"'@kZ]^:blghmlnbmZ[e^_hknl^
pa^k^k^]blmkb[nmbhgZ[ho^+)aZl[^^gZllnf^]bgma^]^lb`gZg]Z
`kZ]^;[Zklahne][^li^\b_b^]bgma^l^\bk\nflmZg\^l!^'`';*+"'@kZ]^<bl
_hkl^blfb\\hg]bmbhglhkpa^k^Z]]bmbhgZe]n\mbebmrblk^jnbk^]'
Cover
Table 1
Notation for steel reinforcement
Type of steel reinforcement
Notation
@kZ]^;.)):%@kZ]^;.));hk@kZ]^;.))<\hg_hkfbg`mh
;L---23+)).
A
@kZ]^;.)):\hg_hkfbg`mh;L---23+)).
:
@kZ]^;.));hk@kZ]^;.))<\hg_hkfbg`mh;L---23+)).
;
@kZ]^;.))<\hg_hkfbg`mh;L---23+)).
<
K^bg_hk\^f^gmh_Zmri^ghmbg\en]^]bgma^Z[hoêblmaZobg`
fZm^kbZeikhi^kmb^lmaZmZk^]^_bg^]bgma^]^lb`ghk\hgmkZ\m
li^\b_b\Zmbhg'
Q
Ma^ghfbgZe\ho^klahne]`^g^kZeer[^li^\b_b^][rma^]^lb`g^kZg]
_nee]^mZbelh_ahpmh]^m^kfbg^mablZk^`bo^gbg<aZim^k+%hkb`bgZeer
in[ebla^]Zl%@^mmbg`lmZkm^]'Ma^ghfbgZe\ho^klahne][^lahpg
hgma^]kZpbg`lZg]lahne]k^_^kmhma^k^bg_hk\^f^gmg^Zk^lmmhma^
lnk_Z\^h_ma^\hg\k^m^^'`'maêbgdlbgZ[^Zf'
:elh%ma^\ho^kmhma^fZbg[Zklahne][^Zme^Zlm^jnZemhma^lbs^h_
maZm[Zk%ienlma^ZeehpZg\^_hk]ôbZmbhgl%D\]ô'Pa^k^ma^k^Zk^gh
ebgdlma^ghfbgZe\ho^klahne][^Zme^Zlm^jnZemhma^lbs^h_ma^[Zk
ienlD\]ô%mablfZr[^lb`gb_b\Zgm_hk[Zk]bZf^m^kl`k^Zm^kmaZg
*+ff'D\]ôfZr[^.hk*)ff]î^g]bg`hgma^jnZebmrZllnkZg\^
lrlm^fZllnf^]_hkmaîkhc^\m'B_ma^\ho^kg^^]lmh[^bg\k^Zl^]mh
f^^mma^l^k^jnbk^f^gml%ma^]^mZbe^klahne]\hglnempbmama^]^lb`g^k'
Note
Bgma^@kZ]^]^l\kbimbhg;.)):%^m\'%Ã;Ãbg]b\Zm^lk^bg_hk\bg`lm^ê'
Figure 1
Description of bond conditions
=bk^\mbhgh_\hg\k^mbg`
Anchorage and lap lengths
a
>nkh\h]^+bgmkh]n\^lZkZg`^h__Z\mhkl!a*mha/"_hknl^pa^g
\Ze\neZmbg`ma^ZiikhikbZm^Zg\ahkZ`^Zg]eZie^g`mal':gnf[^kh_
Zllnfimbhgl\Zg[^fZ]^maZm^gZ[e^MZ[e^+mh[^]ôêhi^]_hk
Zg\ahkZ`^Zg]eZie^g`mal'B_ma^\hg]bmbhglghm^]bgma^mZ[e^Zk^ghm
f^mma^gk^_^k^g\^lahne][^fZ]^mh>nkh\h]^+'EZie^g`mal_hk
ng^jnZelbs^[ZklfZr[^[Zl^]hgma^lfZee^k[Zk%Zemahnàmablblghm
lmZm^]bgma^<h]^'
+.)
c) h > 250 mm
a) 45º < a< 90º
ª,))
a
a
d) h > 600 mm
b) h < 250 mm
Anchorage of bars and links
Key
Â@hh]Ã[hg]\hg]bmbhgl
ÂIhhkÃ[hg]\hg]bmbhgl
:eek^bg_hk\^f^gmlahne][^Zg\ahk^]lhmaZmma^_hk\^lbgbmZk^lZ_êr
mkZglfbmm^]mhma^lnkkhng]bg`\hg\k^m^[r[hg]pbmahnm\Znlbg`
Table 2
Anchorage and lap lengths for concrete class C25/30 (mm)
Bond
condition,
(see Figure 1)
Reinforcement
in
compression
8
10
12
16
20
25
32
40
@hh]
+,)
,+)
-*)
/))
01)
*)*)
*,))
*0/)
-)f
Ihhk
,,)
-.)
.1)
1.)
**+)
*-.)
*1.)
+.*)
.1f
@hh]
,+)
-*)
-2)
/.)
1*)
*)*)
*,))
*0/)
-)f
Ihhk
-/)
.1)
0))
2,)
**/)
*-.)
*1.)
+.*)
.1f
.)eZii^]bghgêh\Zmbhg
!a/6*'-"
@hh]
,+)
--)
.0)
1,)
*)2)
*-+)
*1*)
+-/)
.0f
Ihhk
-/)
/,)
1+)
**2)
*./)
+)+)
+.2)
,.+)
1*f
*))eZii^]bghgêh\Zmbhg
!a/6*'."
@hh]
,-)
-0)
/*)
12)
**0)
*.+)
*2-)
+/-)
/*f
Ihhk
-2)
/1)
10)
*+0)
*/0)
+*0)
+00)
,00)
10f
LmkZbàm[Zklhger
:g\ahkZ`^
e^g`ma%e[]
Hma^k[Zkl
EZie^g`ma%
e)
Reinforcement in tension, bar diameter, f (mm)
Notes
1 GhfbgZe\ho^kmhZeelb]^lZg]]blmZg\^[^mp^^g[Zklª+.ff!b'^'a+5*"'
2 a*6a,6a-6a.6*')'
3 =
^lb`glmk^llaZl[^^gmZd^gZl-,.FIZ'Pa^k^ma^]^lb`glmk^llbgma^[ZkZmmaîhlbmbhg_khfpa^k^ma^Zg\ahkZ`^blf^Zlnk^]%sl]%ble^llmaZg-,.FIZma^_b`nk^lbgmabl
mZ[e^\Zg[^_Z\mhk^][rsl](-,.'Ma^fbgbfnfeZie^g`mabl`bo^gbg\e1'0',h_>nkh\h]^+'
4 Ma^Zg\ahkZ`^Zg]eZie^g`malaZo^[^^gkhng]^]nimhma^g^Zk^lm*)ff'
5 Pa^k^,,h_[ZklZkêZii^]bghgêh\Zmbhg%]^\k^Zl^maêZie^g`mal_hkÂ.)eZii^]bghgêh\ZmbhgÃ[rZ_Z\mhkh_)'1+'
6 Ma^_b`nk^lbgmablmZ[eâZo^[^^gikîZk^]_hk\hg\k^m^\eZll<+.(,)4k^_^kmhMZ[e^*,_hkhma^k\eZll^lhknl^ma^_heehpbg`_Z\mhkl_hkhma^k\hg\k^m^\eZll^l'
Concrete class
C20/25
C28/35
C30/37
C32/40
C35/45
C40/50
C45/55
C50/60
?Z\mhk
*'*/
)'2,
)'12
)'1.
)'1)
)'0,
)'/1
)'/,
80
*)'=^mZbebg`
\kZ\dbg`hkliZeebg`'Ma^]^lb`gZg\ahkZ`ê^g`ma%e[]%!pab\a\Zg[^
h[mZbg^]_khfMZ[e^+"blf^Zlnk^]Zehg`ma^\^gmkêbg^h_ma^[Zk
!l^^?b`nk^+"'Ma^Zg\ahkZ`^h_ebgdlbllahpgbg?b`nk^,'
Arrangement of laps
Bars in compression
BgZ]]bmbhgmhma^kne^l_hk[Zklbgm^glbhg!?b`nk^/Z"%hg^[Zkh_ma^
mkZglo^kl^k^bg_hk\^f^gmlahne][îeZ\^]hnmlb]^^Z\a^g]h_maêZi
e^g`mah_[Zklbg\hfik^llbhgZg]pbmabg-fh_ma^^g]lh_maêZi
e^g`ma!l^^?b`nk^/["'
Figure 2
Pa^kîhllb[eêZilbgZf^f[^klahne][^lmZ``^k^]!l^^?b`nk^-"
Zg]ghmeh\Zm^]bgZk^Zlh_abàlmk^ll'Ma^ZkkZg`^f^gmh_eZii^][Zkl
lahne]\hfierpbma?b`nk^.%Zll^mhnm[êhp3
Design anchorage length lbd, for any shape measured along the
centreline
1. Ma^\e^Zk]blmZg\^[^mp^^geZii^][Zkllahne]ghm[^`k^Zm^kmaZg
-fhk.)ff%hma^kpbl^maêZie^g`malahne][^bg\k^Zl^][rZ
e^g`ma^jnZemhma^\e^Zk]blmZg\^'
2. Maêhg`bmn]bgZe]blmZg\^[^mp^^gmphZ]cZ\^gmeZillahne]ghm[^
e^llmaZg)',mbf^lmaêZie^g`ma%e)'Pa^k^mablblghmma^\Zl^%ma^
[Zkllahne][^\hglb]^k^]Zl[^bgèZii^]bghg^l^\mbhg'
3. Bg\Zl^h_Z]cZ\^gmeZil%ma^\e^Zk]blmZg\^[^mp^^gZ]cZ\^gm[Zkl
lahne]ghm[ê^llmaZg+fhk+)ff'
f
lbd
Figure 3
Anchorage of links
*)f%[nm
ª0)ff
.f%[nm
ª.)ff
Pa^gmaîkhoblbhgl\hfierpbma*Zg],Z[ho^%maî^kfbllb[e^
i^k\^gmZ`^h_eZii^][Zklbgm^glbhgfZr[^*))pa^k^ma^[ZklZk^
ZeebghgêZr^k'Bgmabl\Zl^ma^]^lb`geZie^g`ma%e)%_khfMZ[e^+%fnlm
[^bg\k^Zl^]!l^^ghm^."'Pa^k^ma^[ZklZk^bglô^kZeeZr^klghfhk^
maZg.)lahne][êZii^]bgZgrhgêZr^k'
:ee[Zklbg\hfik^llbhgZg]l^\hg]Zkr!]blmkb[nmbhg"k^bg_hk\^f^gmfZr
[êZii^]bgma^lZfêh\Zmbhg'
f
f
a) Bend angle > 150º
b) Bend angle © 150º
Figure 4
Transverse reinforcement
Percentage of lapped bars in one lapped section
e)
Bars in tension
[Zk*
MkZglo^kl^m^glbe^lmk^ll^lh\\nkZmma^^g]lh_eZii^][Zkl'Pa^k^ma^
]bZf^m^k%f%h_maêZii^][Zklble^llmaZg+)ff%hkmaî^k\^gmZ`^
h_eZii^][ZklbgZgrl^\mbhgble^llmaZg+.%ma^gZgrmkZglo^kl^
k^bg_hk\^f^gmhkebgdlg^\^llZkr_hkhma^kk^ZlhglfZr[^Zllnf^]
ln__b\b^gm_hkma^mkZglo^kl^m^glbe^_hk\^lpbmahnm_nkma^kcnlmb_b\Zmbhg'
Pa^k^ma^]bZf^m^k%f%h_maêZii^][Zklbl`k^Zm^kmaZghk^jnZe
mh+)ff%ma^mkZglo^kl^k^bg_hk\^f^gmlahne]aZo^ZmhmZeZk^Z%:lm
!lnfh_Zeee^`liZkZeeêmhmaêZr^kh_ma^lieb\^]k^bg_hk\^f^gm¾l^^
?b`nk^/Z"h_ghme^llmaZgma^Zk^Z:lh_hgêZii^][Zk!Σ:lmª*'):l"'
Ma^mkZglo^kl^[Zklahne][îeZ\^]i^ki^g]b\neZkmhma^]bk^\mbhgh_
maêZii^]k^bg_hk\^f^gmZg][^mp^^gmaZmZg]ma^lnk_Z\^h_ma^
\hg\k^m^'MZ[e^,`bo^lk^\hff^g]^]fbgbfnfZk^Zl_hkmkZglo^kl^
k^bg_hk\^f^gm'Pa^k^maêZii^][ZklbgZleZ[Zkêh\Zm^]bgZg
Zk^Zh_ehplmk^ll%^'`'g^Zkmaîhbgmh_\hgmkZ_e^qnk^%bmbl`^g^kZeer
Z\\îmZ[e^mhZllnf^maZmmkZglo^kl^k^bg_hk\^f^gmblghmk^jnbk^]'
B_fhk^maZg.)h_ma^[ZklZkêZii^]bghgêh\ZmbhgZg]ma^
]blmZg\^%Z%[^mp^^gZ]cZ\^gmeZilZmZl^\mbhgbl©*)f!l^^?b`nk^."
mkZglo^kl^k^bg_hk\^f^gmlahne][^_hkf^][rebgdlhkN&[ZklZg\ahk^]
bgmhma^[h]rh_ma^l^\mbhg'
[Zk+
[Zk,
[Zk-
)'/.e)
>qZfie^3[Zkl+Zg],Zk^
hnmlb]^ma^l^\mbhg[^bg`
\hglb]^k^]'
Ma^k^_hkâ/6*'-
)'/.e)
L^\mbhg\hglb]^k^]
Figure 5
Arranging adjacent lapping bars
ª)',e)
e)
?l
?l
?l
Z
©.)ff
©-f
ª+f
ª+)ff
f
?l
?l
?l
81
Beams
Figure 7
Illustration of curtailment of longitudinal reinforcement
Curtailment
Ah``bg`k^bg_hk\^f^gm
Nge^llma^Z]]bmbhgZem^glbe^_hk\^bgmaêhg`bmn]bgZek^bg_hk\^f^gm
]n^mhla^ZkaZl[^^g\Ze\neZm^]%ma^\nkmZbef^gme^g`mah_ma^
ehg`bmn]bgZek^bg_hk\^f^gmlahne][^^qm^g]^][^rhg]maîhbgmZm
pab\abmblk^jnbk^]_hk_e^qnkZelmk^g`ma!mablbldghpgZlma^Âlab_m
kne^Ã"nlbg`ma^_heehpbg`^qik^llbhg!l^^Zelh?b`nk^0"3
>goêhi^h_F>](s$G>]
e[]
e[]
:\mbg`m^glbe^_hk\^?l
K^lblmbg`m^glbe^_hk\^?Kl
e[]
Ze6s\hmy(+_hko^kmb\Zela^Zkk^bg_hk\^f^gm'
Ze
pa^k^
s6eô^kZkf
y 6Zgè^h_\hfik^llbhglmknm
Ze
e[]
Mabl\Zg\hgl^koZmboêr[^mZd^gZl3
D ?m]
e[]
e[]
Ze6*'*+.]
D ?m]
e[]
e[]
?hk[^Zfl]^lb`g^]nlbg`ma^\h&^__b\b^gml`bo^gbgMZ[e^,h_<aZim^k-%
hkb`bgZeerin[ebla^]Zl;^Zfl%ma^lbfieb_b^]kne^llahpgbg?b`nk^1
fZr[^nl^]'Ahpô^k%ma^lbfieb_b\ZmbhglZk^\hgl^koZmbo^Zg]^\hghfb^l
\Zg[^Z\abô^][r\nkmZbebg`[Zklmhlnbmma^Z\mnZefhf^gml'
LZ``bg`k^bg_hk\^f^gm
Figure 8
Figure 6
Simplified detailing rules for beams
Transverse reinforcement for lapped splices
:lm(+
e)(,
:lm(+
e)(,
©*.)ff
l a"l
?l
?l
! l a
a) Bars in tension
e)
a) Continuous member, top reinforcement
:lm(+
:lm(+
©*.)ff
?l
?l
l &a
$
%
! e)
b) Bars in compression
-f
e)(,
-f
e)(,
b) Continuous member, bottom reinforcement
Table 3
Bar sizes for transverse reinforcement
Lap length
(mm), for
transverse
bars at 150
mm centresa
Number
of bars
at each
lap
l
Bar size (mm)
20
25
32
40
As = 314
As = 491
As = 804
As = 1260
#l
$
% ©-.)
+
*)
*/
*/
+.
-.* ¾2))
,
*)
*+
*/
+)
2)*¾*,.)
-
1
*)
*+
*/
Notes
*,.*¾*1))
.
1
1
*+
*/
*1)*¾++.)
/
1
1
*)
*+
++.*¾+0))
0
G(:
1
*)
*+
1 eblma^^__^\mboê^g`ma'
2 Zeblma^]blmZg\^mhZeehp_hkm^glbe^_hk\^]n^mhla^Zk_hk\^'
3 e[]blma^]^lb`gZg\ahkZ`ê^g`ma'
4Jd©@d'
5 Fbgbfnfh_mphliZglk^jnbk^]'
6 :iieb^lmhngb_hkfer]blmkb[nm^]ehZ]lhger'
7 Ma^lahkm^lmliZgfnlm[^`k^Zm^kmaZghk^jnZemh)'1.mbf^lmaêhg`^lmliZg'
8 :iieb^lpa^k^*.k^]blmkb[nmbhgaZl[^^gnl^]'
Key
a ? hkmkZglo^kl^[ZklZme^llmaZg*.)ff\^gmk^lnl^ma^_heehpbg`^qik^llbhgmh
\Ze\neZm^ma^k^jnbk^]gnf[^kh_[ZklZg]a^g\^ma^k^jnbk^]mkZglo^kl^[Zk]bZf^m^k3
82
Gnf[^kh_[Zklk^jnbk^]6*$e)(!,l"pa^k^l6liZ\bg`h_ma^mkZglo^kl^[Zkl'
c) Simple support, bottom reinforcement
*)'=^mZbebg`
Reinforcement in end supports
Bgfhghebmab\\hglmkn\mbhg%ô^gpa^glbfie^lniihkmlaZo^[^^g
Zllnf^]bg]^lb`g%ma^l^\mbhgZmlniihkml!mhik^bg_hk\^f^gm"lahne]
[^]^lb`g^]_hkZ[^g]bg`fhf^gmZkblbg`_khfiZkmbZe_bqbmrh_Zm
e^Zlm+.h_ma^fZqbfnf[^g]bg`fhf^gmbgma^liZg!b'^'ikhob]^
+.h_fb]&liZg[hmmhfk^bg_hk\^f^gm"'
Ma^fbgbfnf\e^Zk]blmZg\^[^mp^^g[Zkllahne][^ma^`k^Zm^kh_3
N ;Zk]bZf^m^k
N :``k^`Zm^lbsîenl.ff
N +)ff
Shear reinforcement
Ma^Zk^Zh_[hmmhfk^bg_hk\^f^gmikhob]^]Zmlniihkmlpbmaebmme^hkgh
^g]_bqbmrZllnf^]bg]^lb`g%lahne][^Zme^Zlm+.h_ma^Zk^Zh_lm^ê
ikhob]^]bgma^liZg'Ma^[Zkllahne][^Zg\ahk^]mhk^lblmZ_hk\^%?>'
?>6!uO>]uZe(s"$G>]
pa^k^
uO>]u 6Z[lhenmôZen^h_la^Zk_hk\^
G>] 6ma^ZqbZe_hk\^b_ik^l^gm
Maêhg`bmn]bgZeliZ\bg`h_o^kmb\Zela^Zkk^bg_hk\^f^gmlahne]ghm
^q\^^])'0.]'Ghm^ma^k^jnbk^f^gm_hkZfZqbfnfliZ\bg`h_
*.)ffpa^k^ma^la^Zkk^bg_hk\^f^gmZ\mlZlZmkZglo^kl^
k^bg_hk\^f^gmZmeZilbgmaêhg`bmn]bgZe[Zkl'Ma^mkZglo^kl^liZ\bg`
h_maê^`lbgZl^kb^lh_la^Zkebgdllahne]ghm^q\^^]3
lm%fZq6)'0.]©/))ff
Ma^Zg\ahkZ`^%e[]%lahne][^f^Zlnk^][^rhg]maêbg^h_\hgmZ\m
[^mp^^gma^[^ZfZg]lniihkm'
Ma^fbgbfnfZk^Zh_la^Zkk^bg_hk\^f^gmbg[^Zfl%:lp%fbglahne][^
\Ze\neZm^]_khf3
:lp
ªrp%fbg
pa^k^rp%fbg\Zg[^h[mZbg^]_khfMZ[e^-'
l[p
Ikhob]^]sl]blmZd^gZl-,.FIZbgma^\Ze\neZmbhgh_ma^Zg\ahkZ`^
e^g`ma!pab\ablZllnf^]bgMZ[e^l+Zg]*,"ma^gbmlahne]ghm[^
g^\^lZkrmh\Ze\neZm^?>'
Slabs
Flanged beams
Curtailment
:mlniihkmlma^m^glbhgk^bg_hk\^f^gmmhk^lblmah``bg`fhf^gml
lahne][^]blmkb[nm^]Z\khllma^_neepb]mah_ma^^__^\mbo^_eZg`^Zl
lahpgbg?b`nk^24iZkmh_bmfZr[^\hg\^gmkZm^]ho^kma^p^['
Ma^\nkmZbef^gmkne^l_hk[^Zfllahne][^_heehp^]%^q\îmmaZmZ
oZen^h_Ze6]fZr[^nl^]'
Minimum area of longitudinal reinforcement
Ma^fbgbfnfZk^Zh_k^bg_hk\^f^gmbl:l%fbg6)'+/_\mf[m](_rd[nm
ghme^llmaZg)'))*,[m]%pa^k^[mblma^f^Zgpb]mah_ma^m^glbhg
shg^!l^^MZ[e^-"'?hkZM&[^Zfpbmama^_eZg`^bg\hfik^llbhg%hger
ma^pb]mah_ma^p^[blmZd^gbgmhZ\\hngmbg\Ze\neZmbg`maôZen^
h_[m'
k^bg_hk\^f^gmlahne]ghm^q\^^]:l%fZq6)')-:\'
Figure 9
As
hf
beff2
Bglbfierlniihkm^]leZ[l%ma^Zk^Zh_k^bg_hk\^f^gmfZr[^k^]n\^]
mhaZe_ma^\Ze\neZm^]liZgk^bg_hk\^f^gmZg]\hgmbgn^]nimhma^
lniihkm%hma^kpbl^*))h_ma^k^bg_hk\^f^gmfZr[^\hgmbgn^]
mhma^lniihkm';^rhg]ma^_Z\^h_ma^lniihkm*.h_ma^Zk^Zh_
fZqbfnfk^bg_hk\^f^gmlahne][îkhob]^]!l^^?b`nk^*)\"'Ma^
[Zkllahne][^Zg\ahk^]mhk^lblmZ_hk\^%?>%Zl`bo^gbgma^l^\mbhg
hg[^Zfl'
beff
bw
Reinforcement in end supports
Table 4
Placing of tension reinforcement in flanged cross section
beff1
?hkleZ[l]^lb`g^]nlbg`ma^\h&^__b\b^gml`bo^gbgMZ[e^,h_<aZim^k,%
hkb`bgZeerin[ebla^]ZlLeZ[l%ma^lbfieb_b^]kne^llahpgbg?b`nk^*)
fZr[^nl^]'
fck
fctm
Minimim percentage
(0.26 fctm / fyka)
rw, min x 10-3
+.
+'/
)'*,
)'1)
+1
+'1
)'*-
)'1.
,)
+'2
)'*.
)'11
,+
,')
)'*/
)'2*
,.
,'+
)'*0
)'2.
-)
,'.
)'*1
*')*
-.
,'1
)'+)
*')0
.)
-'*
)'+*
*'*,
Key
a
:llnfbg`_rd6.))FIZ
83
Minimum spacing requirements
Minimum areas of reinforcement
Ma^fbgbfnf\e^Zk]blmZg\^[^mp^^g[Zkl!ahkbshgmZehko^kmb\Ze"
lahne]ghm[ê^llmaZgma^[Zklbs^%[%!]`$.ff"%hk+)ff%pa^k^
]`blma^fZqbfnflbs^h_Z``k^`Zm^'
Ma^fbgbfnfZk^Zh_k^bg_hk\^f^gmmh[îkhob]^]oZkb^lpbmama^
\hg\k^m^lmk^g`ma!l^^MZ[e^-"'
Maximum spacing of reinforcement
?hkleZ[le^llmaZg+))ffmab\dma^_heehpbg`fZqbfnfliZ\bg`
kne^lZiier!ablma^]îmah_ma^leZ["3
N ?hkmaîkbg\biZek^bg_hk\^f^gm3,a[nmghmfhk^maZg-))ff'
N ?hkma^l^\hg]Zkrk^bg_hk\^f^gm3,'.a[nmghmfhk^maZg-.)ff'
Ma^^q\îmbhgblbgZk^Zlpbma\hg\^gmkZm^]ehZ]lhkZk^Zlh_
fZqbfnffhf^gmpa^k^ma^_heehpbg`Ziieb^l3
N ?hkmaîkbg\biZek^bg_hk\^f^gm3+a[nmghmfhk^maZg+.)ff'
N ?hkma^l^\hg]Zkrk^bg_hk\^f^gm3,a[nmghmfhk^maZg-))ff'
?hkleZ[l+))ffmab\dhk`k^Zm^k%ma^liZ\bg`k^jnbk^f^gmlZk^`bo^g
bgMZ[e^.'Pa^k^ma^]^lb`g^kaZlghmli^\b_b^]ma^k^jnbk^]liZ\bg`
hkikhob]^]ma^lm^êlmk^ll%sl%bm\Zg`^g^kZeer[^Zllnf^]maZmslpbee
ghm^q\^^],+)FIZ_hkZmrib\ZeleZ['Pa^k^ma^leZ[lniihkmlh__b\^
hkk^lb]^gmbZeZk^ZlbmblngebdêrmaZmslpbee^q\^^]+1)FIZ'
k^bg_hk\^f^gm%lahne]ghm^q\^^]:l%fZq6)')-:\':meZieh\Zmbhgl
:l%fZq6)')1:\'
Edge reinforcement
:ehg`Z_k^^!nglniihkm^]"^]`^%ZleZ[lahne]ghkfZeer\hgmZbgehg`bmn]bgZe
Zg]mkZglo^kl^k^bg_hk\^f^gm%`^g^kZeerZkkZg`^]Zllahpgbg?b`nk^**'
Flat slabs
:_eZmleZ[lahne][^]bob]^]bgmh\henfgZg]fb]]e^lmkbil!l^^
?b`nk^*+"4ma^]boblbhgh_ma^fhf^gml[^mp^^gma^\henfgZg]
fb]]e^lmkbilbl`bo^gbgMZ[e^/'
Figure 11
Figure 10
Edge reinforcement for slab
Simplified detailing rules for slabs
l l
h
l
≥ 2h
a) Continuous member, top reinforcement
Table 5
Values for rw,min
Steel
stress
l
b) Continuous member, bottom reinforcement
l
c) Simple support, bottom reinforcement
Notes
1
2
3
4
5
6
7
84
eblma^^__^\mboê^g`ma'
e[]blma^]^lb`gZg\ahkZ`ê^g`ma'
Jd©*'+.@d Zg]jd©.dG(f+'
Fbgbfnfh_mphliZglk^jnbk^]'
:iieb^lmhngb_hkfer]blmkb[nm^]ehZ]lhger'
Ma^lahkm^lmliZgfnlm[^`k^Zm^kmaZghk^jnZemh)'1.mbf^lmaêhg`^lmliZg'
:iieb^lpa^k^+)k^]blmkb[nmbhgaZl[^^gnl^]'
(es) MPa
wmax = 0.3 mm
wmax = 0.4 mm
Maximum
bar size
(mm)
Maximum
bar spacing
(mm)
Maximum
bar size
(mm)
Maximum
bar spacing
(mm)
*/)
-)
,))
,+
,))
+))
,+
,))
+.
+.)
+-)
+)
+.)
*/
+))
+1)
*/
+))
*+
*.)
OR
OR
,+)
*+
*.)
*)
*))
,/)
*)
*))
1
.)
Table 6
Apportionment of bending moments in flat slabs – equivalent frame method
Location
Negative moments
Positive moments
<henfglmkbi
/)¾1)
.)¾0)
Fb]]e^lmkbi
-)¾+)
.)¾,)
Notes
Ma^mhmZeg^`Zmbo^Zg]ihlbmbo^fhf^gmlmh[^k^lblm^][rma^\henfgZg]fb]]e^
lmkbilmh`^ma^klahne]ZepZrlZ]]nimh*))
*)'=^mZbebg`
Ma^bgm^gmbhgblmhikhob]^Zgô^g]blmkb[nmbhg(]^glbmrh_ing\abg`
la^Zkk^bg_hk\^f^gmpbmabgma^shg^pa^k^bmblk^jnbk^]'Hg^
lbfieb\Zmbhgmh^gZ[e^k^\mZg`neZki^kbf^m^klh_la^^kk^bg_hk\^f^gmbl
mhnl^Zgbgm^glbmrh_:lp(n*Zkhng]k^\mZgènZki^kbf^m^kl'
Figure 12
Division of panels in flat slabs
lx > ly
ly /4
ly /4
Middle strip = lx – ly /2
Ma^fbgbfnfZk^Zh_Zebgde^`_hko^kmb\Zeing\abg`la^Zkk^bg_hk\^f^gmbl
ly /4
*'.:lp%fbg(!lk l m "ª)')1√ _ \d _rd
ly /4
pab\a\Zg[^k^ZkkZg`^]Zl3
:lp%fbgª!l k l m "(?
Middle strip = ly /2
ly
Column strip = ly /2
pa^k^
lk 6ma^liZ\bg`h_maêbgdlbgma^kZ]bZe]bk^\mbhg
l m 6ma^liZ\bg`h_maêbgdlbgma^mZg`^gmbZe]bk^\mbhg
? 6_Z\mhkh[mZbg^]_khfMZ[e^0
Figure 13
Effective width, be of a flat slab
:mbgm^kgZe\henfgl%nge^llkb`hkhnll^kob\^Z[bebmr\Ze\neZmbhglZk^
\Zkkb^]hnm%mhik^bg_hk\^f^gmh_Zk^Z)'.:mlahne][îeZ\^]bgZ
pb]ma^jnZemhma^lnfh_)'*+.mbf^lmaîZgêpb]mahg^bma^klb]^
h_ma^\henfg':mkîk^l^gmlma^Zk^Zh_k^bg_hk\^f^gmk^jnbk^]mh
k^lblmma^_neeg^`Zmbo^fhf^gm_khfma^lnfh_ma^mphaZe_iZgêl
^Z\alb]^h_ma^\henfg'BmblZelhZ]oblZ[e^mhZiiermablk^jnbk^f^gm
mhi^kbf^m^k\henfglZl_ZkZlblihllb[e^'
\q
\q
LeZ[^]`^
LeZ[^]`^
\r
\r
r
r
s
[^6\q$r
:mbgm^kgZe\henfglZme^Zlmmph[Zklh_[hmmhfk^bg_hk\^f^gmbg^Z\a
hkmah`hgZe]bk^\mbhglahne][îkhob]^]Zg]ma^rlahne]iZll[^mp^^g
ma^\henfgk^bg_hk\^f^gm'PabelmbmblghmZ\h]^k^jnbk^f^gmbmbl
\hglb]^k^]`hh]ikZ\mb\^mhikhob]^mph[ZklknggbgìZkZeeêmhma^
leZ[^]`^[^mp^^gma^k^bg_hk\^f^gmh_Zg^qm^kgZe\henfg'
K^bg_hk\^f^gmi^ki^g]b\neZkmhZ_k^^^]`^k^jnbk^]mhmkZglfbm
[^g]bg`fhf^gml_khfma^leZ[mhZg^]`^hk\hkg^k\henfglahne]
[îeZ\^]pbmabgma^^__^\mbo^pb]ma%[^%lahpgbg?b`nk^*,'
[^6s$r(+
LeZ[^]`^
s\Zg[^7 \qZg]r\Zg[^7 \r
r\Zg[^7 \r
a) Edge column
b) Corner column
Note
rblma^]blmZg\^_khfma^^]`^h_ma^leZ[mhma^bgg^kfhlm_Z\^h_ma^\henfg
Figure 14
Punching shear layout
u Punching shear reinforcement
Pa^kîng\abg`la^Zkk^bg_hk\^f^gmblk^jnbk^]ma^_heehpbg`kne^l
lahne][^h[l^ko^]'
N Bmlahne][îkhob]^][^mp^^gma^_Z\^h_ma^\henfgZg]d]
bglb]^ma^hnm^ki^kbf^m^kpa^k^la^Zkk^bg_hk\^f^gmblghehg`^k
k^jnbk^]'dbl*'.%nge^llmaî^kbf^m^kZmpab\ak^bg_hk\^f^gmblgh
ehg`^kk^jnbk^]ble^llmaZg,]_khfma^_Z\^h_ma^\henfg'Bgmabl
\Zl^ma^k^bg_hk\^f^gmlahne][îeZ\^]bgma^shg^)',]mh*'.]
_khfma^_Z\^h_ma^\henfg'
N Ma^k^lahne][^Zme^Zlmmphi^kbf^m^klh_la^Zkebgdl'
N Ma^kZ]bZeliZ\bg`h_maêbgdl%lklahne]ghm^q\^^])'0.]!l^^?b`nk^*-"'
N Ma^mZg`^gmbZeliZ\bg`h_maêbgdl%l]lahne]ghm^q\^^]*'.]
pbmabg+]h_ma^\henfg_Z\^'
N Ma^mZg`^gmbZeliZ\bg`h_maêbgdllahne]ghm^q\^^]+]_hkZgr
hma^ki^kbf^m^k'
N Ma^]blmZg\^[^mp^^gma^_Z\^h_ma^\henfgZg]ma^g^Zk^lmla^Zk
k^bg_hk\^f^gmlahne][^[^mp^^g)',]Zg])'.]
d
d
d
s d
d
d
"d&"d
!
kd
85
Columns and walls
Lapping fabric
Maximum areas of reinforcement
Nge^llÂ_erbg`^g]Ã_Z[kb\bl[^bg`li^\b_b^]%eZilh__Z[kb\lahne][^
ZkkZg`^]Zllahpgbg?b`nk^*.'Pa^g_Z[kb\k^bg_hk\^f^gmbleZii^]
[reZr^kbg`%ma^_heehpbg`lahne][^ghm^]3
Bg>nkh\h]^+ma^fZqbfnfghfbgZek^bg_hk\^f^gmZk^Z_hk\henfgl
Zg]pZeelhnmlb]êZilbl-\hfiZk^]pbma/bg;L1**)'Ahpô^k%
mablZk^Z\Zg[^bg\k^Zl^]ikhob]^]maZmma^\hg\k^m^\Zg[îeZ\^]
Zg]\hfiZ\m^]ln__b\b^gmer'Lê_&\hfiZ\mbg`\hg\k^m^fZr[^nl^]
_hkiZkmb\neZker\hg`^lm^]lbmnZmbhgl%pa^k^ma^k^bg_hk\bg`[Zkllahne]
[^liZ\^]mh^glnk^maZmma^\hg\k^m^\Zg_ehpZkhng]ma^f'?nkma^k
`nb]Zg\^\Zg[^_hng]bgLê_&\hfiZ\mbg`\hg\k^m^'
Minimum reinforcement requirements
Ma^k^\hff^g]^]fbgbfnf]bZf^m^kh_ehg`bmn]bgZek^bg_hk\^f^gm
bg\henfglbl*+ff'Ma^fbgbfnfZk^Zh_ehg`bmn]bgZek^bg_hk\^f^gm
bg\henfglbl`bo^g[r3:l%fbg6)'*)G>](_r]ª)'))+:\'Ma^]bZf^m^k
h_ma^mkZglo^kl^k^bg_hk\^f^gm!ebgd"lahne]ghm[ê^llmaZg/ff
hkhg^jnZkm^kh_ma^fZqbfnf]bZf^m^kh_maêhg`bmn]bgZe[Zkl!l^^
MZ[e^1"'Ghehg`bmn]bgZe[Zklahne][^fhk^maZg*.)ff_khfZ
mkZglo^kl^[Zk'
Particular requirements for walls
Ma^fbgbfnfZk^Zh_o^kmb\Zek^bg_hk\^f^gmbgpZeelbl`bo^g[r3
:l%ofbg6)'))+:\!l^^ZelhMZ[e^2"'AZe_ma^Zk^Zlahne][îkhob]^]bg
^Z\a_Z\^'
Ma^]blmZg\^[^mp^^gmphZ]cZ\^gmo^kmb\Ze[Zkllahne]ghm^q\^^]
maê^ll^kh_^bma^kmak^^mbf^lma^pZeemab\dg^llhk-))ff'
Ma^fbgbfnfZk^Zh_ahkbshgmZek^bg_hk\^f^gmbg^Z\a_Z\^h_ZpZee
blma^`k^Zm^kh_^bma^k+.h_o^kmb\Zek^bg_hk\^f^gmhk)'))*:\'
Ahpô^k%pa^k^\kZ\d\hgmkheblbfihkmZgm%^ZkerZ`^ma^kfZeZg]
lakbgdZ`^^__^\mllahne][^\hglb]^k^]'
Ma^k^blghZ]ob\^`bo^gbgma^<h]^hgikhoblbhgh_k^bg_hk\^f^gm
mh\hgmkhe\kZ\dbg`bgieZbgpZeel%[nmk^bg_hk\^f^gmfZr[îkhob]^]
b_k^jnbk^]'
eZii^]bgZgrl^\mbhgbl*))b_!:l(l"©*+))ff+(f!pa^k^lbl
ma^liZ\bg`h_[Zkl"Zg]/)b_:l(l7 *+))ff+(f'
N :eel^\hg]Zkrk^bg_hk\^f^gmfZr[êZii^]Zmma^lZfêh\Zmbhg
Zg]ma^fbgbfnfeZie^g`mae)%fbg_hkeZr^k^]_Z[kb\blZl_heehpl3
ª*.)ff_hkf©/ff
ª+.)ff_hk/ff5f©1'.ff
ª,.)ff_hk1'.ff5f©*+ff
Ma^k^lahne]`^g^kZeer[^Zme^Zlmmph[Zkibm\a^lpbmabgmaêZi
e^g`ma'Mabl\hne][^k^]n\^]mhhg^[Zkibm\a_hkf©/ff'
Tolerances
Ma^mhe^kZg\^l_hk\nmmbg`Zg](hk[^g]bg`]bf^glbhglZk^`bo^gbgMZ[e^*)
Zg]lahne][^mZd^gbgmhZ\\hngmpa^g\hfie^mbg`ma^[Zkl\a^]ne^'
Pa^k^ma^k^bg_hk\^f^gmblk^jnbk^]mh_bm[^mp^^gmph\hg\k^m^_Z\^l
!^'`'ebgdl"ma^gZgZeehpZg\^lahne][^fZ]^_hk]ôbZmbhglbgma^f^f[^k
lbs^Zg][^g]bg`mhe^kZg\^l'Ma^k^blgh`nb]Zg\^`bo^gbg>nkh\h]^+%[nm
MZ[e^**`bo^l`nb]Zg\^hgma^]^]n\mbhglmh[^fZ]^_hk]ôbZmbhgl'
Table 9
Minimum area of vertical reinforcement in walls (half in each face)
As,min /m length of wall (mm2)
-))
.))
/))
0))
1))
Wall thickness (mm)
+))
+.)
,))
,.)
-))
Table 10
Tolerance
Table 7
Factor, F, for determining Asw, min
fck
+.
+1
,)
,+
,.
-)
-.
.)
Factor, F
*10.
*00+
*0*+
*/.0
*.1.
*-1+
*,21
*,+/
Note
_rd aZl[^^gmZd^gZl.))FIZ
Table 8
Requirements for column reinforcement
Bar dia. (mm)
12
FZqliZ\bg`Z!ff" *--[
Fbgebgd]bZ'!ff" / \
Cutting and bending processes
<nmmbg`h_lmkZbàme^g`mal
!bg\en]bg`k^bg_hk\^f^gm_hk
ln[l^jn^gm[^g]bg`"
Bending:
©*)))ff
7 *)))ffmh©+)))ff
7 +)))ff
Tolerance (mm)
$+.%¾+.
$.%¾.
$.%¾*)
$.%¾+.
Table 11
16
20
25
32
40
*2+[
/\
+-)[
/\
+-)[
1
+-)[
1
+-)[
*)
Key
a :
mZ]blmZg\^`k^Zm^kmaZgmaêZk`^k]bf^glbhgh_ma^\henfgZ[ho^hk[êhpZ
[^ZfhkleZ[%]bf^glbhgl\Zg[^bg\k^Zl^][rZ_Z\mhkh_*'/0'
b ;nmghm`k^Zm^kmaZgfbgbfnf]bf^glbhgh_ma^\henfg'
c /ff[ZklZk^ghmk^Z]berZoZbeZ[e^bgma^ND'
86
N I^kfbllb[eî^k\^gmZ`^h__Z[kb\fZbgk^bg_hk\^f^gmmaZmfZr[^
Deductions to bar dimensions to allow for deviations between two
concrete faces
Distance between
concrete faces (mm)
)¾*)))
*)))¾+)))
Ho^k+)))
:gre^g`ma
Type of bar
EbgdlZg]hma^k[^gm[Zkl
LmkZbàm[Zkl
Total deduction
(mm)
*)
*.
+)
-)
*)'=^mZbebg`
Figure 15
ek 6ma^`k^Zm^kh_ma^]blmZg\^l!bgf"[^mp^^gma^\^gmk^lh_ma^
\henfgl%_kZf^lhkpZeellniihkmbg`ZgrmphZ]cZ\^gm_ehhk
liZglbgma^]bk^\mbhgh_ma^mb^ng]^k\hglb]^kZmbhg
?m 6!+)$-g)"©/)dG!g)blma^gnf[^kh_lmhk^rl"
Lapping of welded fabric
?l
?l
e)
Ma^fZqbfnfliZ\bg`h_bgm^kgZemb^lbl*'.ek'
a) Intermeshed fabric (longitudinal section)
?l
?l
e)
Minimum radii and end
projections
b) Layered fabric (longitudinal section)
Tying requirements
:m^Z\a_ehhkZg]khh_eôêZg^__^\mboêr\hgmbgnhnli^kbia^kZemb^
lahne][îkhob]^]pbmabg*'+f_khfma^^]`^4mablg^^]ghm[^
Z]]bmbhgZek^bg_hk\^f^gm'BgikZ\mb\^%_hkfhlm[nbe]bg`lma^mb^lahne]
k^lblmZm^glbe^_hk\^h_/)dG':gZk^Zh_k^bg_hk\^f^gmh_*,1ff+bl
ln__b\b^gmmhk^lblmmabl_hk\^'
Bgm^kgZemb^llahne][îkhob]^]Zm^Z\a_ehhkZg]khh_eôêbgmph
]bk^\mbhglZiikhqbfZmêrZmkbàmZgè^l'Ma^rlahne][^^__^\mboêr
\hgmbgnhnlmakhnàhnmma^bke^g`maZg]lahne][^Zg\ahk^]mhma^
i^kbia^kZemb^lZm^Z\a^g]%nge^ll\hgmbgnbg`ZlahkbshgmZemb^lmh\henfgl
hkpZeel'Ma^bgm^kgZemb^lfZr%bgpahe^hkbgiZkm%[^lik^Z]ô^gerbg
ma^leZ[lhkfZr[^`khni^]Zmhkbg[^Zfl%pZeelhkhma^kZiikhikbZm^
ihlbmbhgl'BgpZeelma^rlahne][^pbmabg)'.f_khfma^mhihk[hmmhfh_
_ehhkleZ[l'Bg^Z\a]bk^\mbhg%bgm^kgZemb^llahne][^\ZiZ[e^h_k^lblmbg`Z
]^lb`goZen^h_m^glbe^_hk\^?mb^%bgm!bgdGi^kf^mk^pb]ma"3
?mb^%bgm6T!jd$`d"(0'.V!ek(."!?m"ª?mdG(f
pa^k^
!jd$`d" 6lnfh_ma^Zo^kZ`î^kfZg^gmZg]oZkbZ[e^_ehhkehZ]l
!bgdG(f+"
Ma^fbgbfnfkZ]bb_hk[^g]lZg]e^g`mah_^g]ikhc^\mbhglZk^`bo^g
bgMZ[e^*+'
Table 12
Minimum scheduling radii and bend allowances
≥ 5d
r
Nominal
size of bar,
d (mm)
1
*)
*+
*/
+)
+.
,+
-)
Minimum
radius for
scheduling,
r (mm)
*/
+)
+,+
0)
10
**+
*-)
P
Mimimum end projection, P
General (min 5d
straight), including
links where bend >
150° (mm)
**.Z
*+)Z
*+.Z
*,)
*2)
+-)
,).
Links where bend
< 150° (min 10d
straight) (mm)
**.Z
*,)
*/)
+*)
+2)
,/.
-/.
.1)
Key
a M a^fbgbfnf^g]ikhc^\mbhgl_hklfZee^k[Zklbl`ho^kg^][rmaîkZ\mb\Zebmb^lh_
[^g]bg`[Zkl'
References
1 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l';LB!-iZkml"'
2 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1.))3<hg\k^m^¾<hfie^f^gmZkrlmZg]Zk]mh;L>G+)/¾*';L*%+))+'
3 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L---23Li^\b_b\Zmbhg_hk\Zk[hglm^ê[Zkl_hkma^k^bg_hk\^f^gmh_\hg\k^m^';LB%+)).'
4 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*))1)3Lm^ê_hkma^k^bg_hk\^f^gmh_\hg\k^m^¾Pê]Z[e^k^bg_hk\bg`lm^ê¾@^g^kZe';LB%+)).'
5 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1///3L\a^]nebg`%]bf^glbhgbg`%[^g]bg`Zg]\nmmbg`h_lm^êk^bg_hk\^f^gm_hk\hg\k^m^¾Li^\b_b\Zmbhg';LB%+)).'
6 BGLMBMNMBHGH?LMKN<MNK:E>G@BG>>KL(<HG<K>M>LHMR'LmZg]Zk]f^mah]h_]^mZbebg`lmkn\mnkZe\hg\k^m^'BL>(<L%+))/'
7 <HGLMKN<M'GZmbhgZelmkn\mnkZe\hg\k^m^li^\b_b\Zmbhg!mabk]^]bmbhg"';<:%+))-'
8 <HGLMKN<M':`nb]^mh\hgmkZ\mhk]^mZbebg`h_k^bg_hk\^f^gmbg\hg\k^m^';<:%*220'
9 ;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3@^mmbg`lmZkm^]'Ma^<hg\k^m^<^gmk^%+))/'
11 FHLL%KF;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3LeZ[l'Ma^<hg\k^m^<^gmk^%+))/'
12 MA><HG<K>M>LHMR'M^\agb\Zekîhkm/+3Lê_&\hfiZ\mbg`\hg\k^m^'<<BI¾))*'Ma^<hg\k^m^Lh\b^mr%+)).'
13 JN>>GLIKBGM>KH?:<MLH?I:KEB:F>GM'Ma^<hglmkn\mbhg!=^lb`gZg]FZgZ`^f^gm"K^`neZmbhgl'*22-'JIH:I%*22-'
87
Table 13
Anchorage and lap lengths
Bond condition Reinforcement in tension, bar diameter, f (mm)
(see Figure 1)
8
10
12
16
20
25
32
40
@hh]
+0)
,0)
-1)
/2)
2*)
**1)
*.))
+)-)
-0f
Ihhk
,1)
.+)
/1)
22)
*+2)
*/1)
+*.)
+2+)
/0f
@hh]
,0)
-0)
.0)
0.)
2-)
**1)
*.))
+)-)
-0f
Ihhk
.,)
/0)
1*)
*)1)
*,-)
*/1)
+*.)
+2+)
/0f
@hh]
,0)
.*)
//)
20)
*+0)
*/-)
+*))
+1/)
//f
Ihhk
.,)
0,)
2.)
*,1)
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+,.)
,)))
-)1)
2-f
@hh]
-))
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*),)
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++.)
,)/)
0)f
Ihhk
.*)
02)
*)*)
*-1)
*2-)
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-,0)
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+,)
,+)
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/))
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*,))
*0/)
-)f
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*1.)
+.*)
.1f
@hh]
,+)
-*)
-2)
/.)
1*)
*)*)
*,))
*0/)
-)f
Reinforcement
in compression
Concrete class C20/25
LmkZbàm[Zklhger
:g\ahkZ`^
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EZie^g`ma%
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bghgêh\Zmbhg!a/6*'."
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/,)
1+)
**2)
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+)+)
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LmkZbàm[Zklhger
:g\ahkZ`^
e^g`ma%l[]
Hma^k[Zkl
EZie^g`ma%
l)
LmkZbàm[Zklhger
:g\ahkZ`^
e^g`ma%l[]
Hma^k[Zkl
EZie^g`ma%
l)
88
*)'=^mZbebg`
Bond condition Reinforcement in tension, bar diameter, f (mm)
(see Figure 1)
8
10
12
16
20
25
32
40
@hh]
*2)
+/)
,,)
-1)
/,)
1*)
*)-)
*-*)
,+f
Ihhk
+/)
,/)
-0)
/1)
12)
**/)
*-1)
+)*)
-/f
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,,)
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.+)
/.)
1*)
*)-)
*-*)
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Ihhk
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+)*)
-/f
@hh]
+/)
,/)
-/)
/0)
10)
**,)
*-.)
*20)
-.f
Ihhk
,0)
.*)
/.)
2.)
*+.)
*/+)
+)0)
+1*)
/.f
@hh]
+1)
,1)
-2)
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2-)
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0))
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2.)
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-+f
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Reinforcement
in compression
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EZie^g`ma%
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e^g`ma%l[]
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1.)
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1))
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-/)
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10)
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LmkZbàm[Zklhger
:g\ahkZ`^
e^g`ma%l[]
Hma^k[Zkl
EZie^g`ma%
l)
Notes
1 <ho^kmhZeelb]^lZg]]blmZg\^[^mp^^g[Zklª+.ff!b'^'a+5*"'
2 a*6a,6a-6a.6*')'
3 =
^lb`glmk^llaZl[^^gmZd^gZm-,.FIZ'Pa^k^ma^]^lb`glmk^llbgma^[ZkZmmaîhlbmbhg_khfpa^k^ma^Zg\ahkZ`^blf^Zlnk^]%sl]%ble^llmaZg-,.FIZma^_b`nk^lbgmabl
mZ[e^\Zg[^_Z\mhk^][rsl](-,.'Ma^fbfbfnfeZie^g`mab]`bo^gbg\e1'0',h_>nkh\h]^+'
4 Ma^Zg\ahkZ`^Zg]eZie^g`malaZo^[^^gkhng]^]nimhma^g^Zk^lm*)ff'
5 Pa^k^,,h_[ZklZkêZii^]bghgêh\Zmbhg%]^\k^Zl^maêZie^g`mal_hk .)eZii^]bghgêh\Zmbhg [rZ_Z\mhkh_)'1+'
89
*)'=^mZbebg`
Table 14
Sectional areas of groups of bars (mm2)
Bar size
(mm)
Number of bars
1
1
*)
*+
2
.)',
01'.
**,
3
*)*
4
*.*
+)*
5
+.*
6
,)+
7
8
,.+
9
-)+
10
-.+
.),
*.0
+,/
,*-
,2,
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..)
/+1
0)0
01.
++/
,,2
-.+
./.
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02+
2).
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*/
+)*
-)+
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1)-
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*-*)
*/*)
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+)*)
+)
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/+1
2-+
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*11)
++))
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+1,)
,*-)
+.
-2*
21+
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+2.)
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,2,)
--+)
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1)-
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,++)
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-)
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,00)
.),)
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0.-)
11))
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*+/))
175
200
225
250
275
300
Table 15
Sectional areas per metre width for various spacings of bars (mm2)
Bar size
(mm)
Spacing of bars (mm)
75
100
125
150
1
/0)
.),
-)+
,,.
+10
+.*
++,
+)*
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*/1
*)
*).)
01.
/+1
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,-2
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/-/
./.
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-/))
-)+)
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+/1)
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*)*))
1,1)
0*1)
/+1)
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4
5
6
7
8
9
10
Table 16
Mass of groups of bars (kg per metre run)
Bar size
(mm)
Number of bars
1
2
3
1
)',2.
)'012
*'*1-
*'.01
*'20,
+',/1
+'0/+
,'*.0
,'..*
,'2-/
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+'//,
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+2'.2-
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-2',+,
.2'*11
/2').+
01'2*0
11'01*
21'/-/
175
200
225
250
275
300
Table 17
Mass in kg per square metre for various spacings of bars (kg per m2)
Bar size
(mm)
Spacing of bars (mm)
75
100
125
150
1
.'+/*
,'2-/
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21'/-/
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90
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A S Fraser;>gÌa=<>g`FB<>FBLmkn\m>A E K Jones ;>gÌa=<>g`?B<>
Introduction
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<bemY^Whjiêm_d]m^_Y^\_h[h[i_ijWdY[Z[i_]dc[jêZjeWZefj
Start
This chapter is an addendum to The Concrete Centre's
publication, How to design concrete structures using
Eurocode 2 (Ref. CCIP–006), which includes chapters on:
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Eurocodes
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8I.+&&
Can the
tabular method conditions
be met?
No
Use simplified methods
Is the element a
braced column?
Yes
Use tabular method
No
Is there an
acceptable solution?
Yes
Use Annex C of Part 1–2:
Buckling of columns under fire
Yes
Use Annex E of Part 1–2:
Simplified calculation method
for beams and slabs
No
Is there an
acceptable solution?
Yes
No
Is the element a
slab or beam?
No
Use
500oc
isotherm method
or zone method
Finish
Yes
99
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Coefficient kc(y Wbbem_d]\ehZ[Yh[Wi[e\Y^WhWYj[h_ij_Yijh[d]j^
(fck) of concrete
Basic concepts
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Coefficient, k c (y )
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fhlm\hffhgghfbgZe_bk^^qihlnk^nl^]bg]^lb`gblma^lmZg]Zk]
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0.8
Calcareous
aggregates
Siliceous
aggregates
0.6
0.4
0.2
0
0
200
600
400
800
1000
1200
o
Temperature, y ( C)
<_]kh[)
Coefficient ks(y Wbbem_d]\ehZ[Yh[Wi[e\Y^WhWYj[h_ij_Yijh[d]j^fck)
of tension and compression reinforcement (class N)
1. 0
Hot-rolled tension
reinforcement, e s,fi 2%
0.8
Coefficient, k s (y )
Fire types
1.0
Cold-worked tension
reinforcement, e s,fi 2%
0.6
Compression
reinforcement and
tension reinforcement,
where es,fi < 2%
0.4
Material factors
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0.2
0
0
200
400
600
800
1000
1200
o
Temperature, y ( C)
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Coefficient kp(y Wbbem_d]\ehZ[Yh[Wi[e\Y^WhWYj[h_ij_Yijh[d]j^
(b fpke\fh[ijh[ii_d]ij[[b
1.0
Quenched and tempered
prestressing steel (bars)
0.8
Coefficient, k p (y )
Ijh[d]j^h[ZkYj_ed
0.6
0.4
Combinations of actions
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100
TIZkm*+>qi'!+'."V
Cold-worked prestressing
steel (wires and strands)
Class A
Cold-worked
prestressing
steel (wires and
strands) Class B
0.2
0
0
200
400
600
o
800
Temperature, y ( C)
1000
1200
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\aZkm^]bg?b`nk^/_hkoZkbhnloZen^lh_c)%*'
IfWbb_d]
Mphmri^lh_liZeebg`Zk^\hglb]^k^]bgIZkm*+3^qiehlbo^liZeebg`Zg]
\hg\k^m^_Zeebg`h__ma^l^\mbhg'
Explosive spalling
Mablblngebdêrmhh\\nkpa^gma^fhblmnk^\hgm^gmh_ma^\hg\k^m^
ble^llmaZg,[rp^bàm'Pa^k^mabloZen^bl^q\^^]^]%^qieb\bm\a^\dl
!IZkm*+<e'-'.'*!.""Zk^k^jnbk^]'BmblZllnf^]maZmpa^k^Zf^f[^k
aZl[^^g]^lb`g^]mhaZo^Zg^qihlnk^\eZllh_Q)hkQ<*bgZ\\hk]Zg\^
pbma>nkh\h]^+%IZkm**1%^qiehlbo^liZeebg`blngebdêrmhh\\nk%Zg]
mablpbeemrib\Zeer[^ma^\Zl^_hkbgm^kgZe\hg\k^m^'Bgma^mZ[neZkf^mah]%
pa^gma^Zqbl]blmZg\^mhma^fZbgk^bg_hk\^f^gmble^llmaZg0)ff
ma^ggh_nkma^k\a^\dlZk^k^jnbk^]_hkghkfZep^bàm\hg\k^m^'
Tabular method
Mabl]^^f^]&mh&lZmbl_r]^mZbebg`f^mah]bgL^\mbhg.h_IZkm*+fhlm
k^l^f[e^lma^_ZfbebZk;L1**)2%IZkm*ZiikhZ\a%^q\îmmaZmIZkm*+
nl^lma^ghfbgZe]blmZg\^_khfma^_Z\^h_ma^l^\mbhgmhma^Zqblh_
ma^k^bg_hk\^f^gm!l^^?b`nk^0"Zg]ghmma^\ho^k]blmZg\^'Ma^mZ[e^l
h_Zqbl]blmZg\^Zg]fbgbfnfl^\mbhglbs^Zkîkhob]^]_hkZgnf[^kh_
f^f[^kmri^lnimhZ_bk^^qihlnkî^kbh]h_+-)fbgnm^l'
Ma^fbgbfnfk^jnbk^]Zqbl]blmZg\^%Z%]^m^kfbg^]_khfma^mZ[e^lblZ
ghfbgZeoZen^%b'^'ZgZeehpZg\^_hkmhe^kZg\^l]h^lghmg^^]mh[^Z]]^]
mhmabloZen^'Pabelm\kbm^kbZ>Zg]Bikhm^\mbhgeôêlfZr[^Z\abô^][r
lZmbl_rbg`ma^fbgbfnfl^\mbhgk^jnbk^f^gml%\kbm^kbhgKk^jnbk^lmaZmma^
fbgbfnfZqbl]blmZg\^k^jnbk^f^gmllahne]Zelh[^lZmbl_b^]'
Ma^bg_en^g\^h_Z``k^`Zm^mri^hgl^\mbhg[âZobhnkbg_bk^\hg]bmbhgl
blZ\\hngm^]_hk[rma^kêZqZmbhgmaZm%pa^k^\Ze\Zk^hnlZ``k^`Zm^lZk^
nl^]%ma^fbgbfnfmab\dg^llfZr[^k^]n\^][r*)'
Ma^mZ[neZm^]]ZmZaZl[^^g[Zl^]hgZ\kbmb\Zem^fi^kZmnk^h_.))<
Zg]ZoZen^h_n_b6)'0'Ma^^q\îmbhgmhmablbl_hk\henfglZg]ehZ]&
[^Zkbg`pZeelpa^k^mableZmm^kiZkZf^m^kblkîeZ\^][rZnmbeblZmbhg
_Z\mhkbgma^_bk^lbmnZmbhg%m_b'Ahpô^k%n_bfZr[^nl^]bglm^Z]h_m_b
ZlZ\hgl^koZmbo^lbfieb_b\Zmbhg'
<_]kh[,
:[j[hc_dWj_ede\nfiki_d];nfh[ii_edi($+WWdZXe\FWhj'(
0.90
0.80
0.70
Reduction factor, n fi
Concrete falling off the section
Mrib\Zeer^qi^kb^g\^]bgmaêZmm^klmZ`^lh__bk^^qihlnk^%mablfZr[^
ikô^gm^][r`hh]]^mZbebg`'Bg\Zl^lpa^k^ma^Zqbl]blmZg\^mhma^
fZbgk^bg_hk\^f^gmbl^jnZemhhk`k^Zm^kmaZg0)ff%Zg]bgma^
Z[l^g\^h_m^lmbg`%lnk_Z\^k^bg_hk\^f^gmpbmaZ]bZf^m^kh_Zme^Zlm
-fflahne][^nl^]%liZ\^]Zm*))ff\^gmk^lhke^ll'
c 0, 1 = 1.0 ; c 1, 1 = 0.9
0.60
c
0, 1
= 0.7 ; c 1, 1 = 0.7
0.50
c
0, 1
= 0.7 ; c 1, 1 = 0.5
c
0, 1
= 0. 5 ; c 1, 1 = 0. 2
0.40
<_]kh[+
:[j[hc_dWj_ede\nfiki_d];nfh[ii_ed($+e\FWhj'(
0.30
0.20
0.90
0
0.5
1.0
1.5
Ratio,
2.0
2.5
3.0
0.80
Reduction factor, n fi
0.70
c 1, 1 = 0.9
0.60
<_]kh[I[Yj_edj^hek]^c[cX[hiêm_d]dec_dWbWn_iZ_ijWdY["a
c 1, 1 = 0.7
0.50
c 1, 1 = 0.5
0.40
h
b
b
c 1, 1 = 0.2
0.30
a
0.20
0
0.5
1.0
1.5
Ratio,
2.0
2.5
3.0
a
a sd
b
101
Pa^k^ma^\kbmb\Zem^fi^kZmnk^blghm.))<%Zf^mah]blikhob]^]
mhfh]b_rma^Zqbl]blmZg\^`bo^g[rma^mZ[neZkf^mah]_hkm^glbhg
f^f[^klZg]lbfierlniihkm^]f^f[^klbg[^g]bg`'Ma^fh]b_b\Zmbhg
blZ_ng\mbhgh_ma^Zk^Zh_k^bg_hk\^f^gmikhob]^]Zg]maêhZ]
k^]n\mbhg_Z\mhk_hk_bkêhZ]bg`'Ma^k^]n\mbhgbl\aZkm^]bg?b`nk^1_hk
k^bg_hk\bg`[Zklpbmabgma^kZg`^,.)<©y\k©0))<'Bmlahne]Zelh[^
ghm^]maZmmablikhoblbhg]h^lghmZeehpma^fbgbfnf\ho^kk^jnbk^f^gml
h_>nkh\h]^+%IZkm**mh[^k^]n\^]'
?hkik^lmk^ll^]f^f[^kl%ma^\kbmb\Zem^fi^kZmnk^blZllnf^]mh
[^-))<_hk[ZklZg],.)<_hkm^g]hgl'Ma^k^_hk^%bgik^lmk^ll^]
f^f[^kl%ma^k^jnbk^]Zqbl]blmZg\^_khfma^mZ[e^llahne][^bg\k^Zl^]
[r*)ff_hkik^lmk^llbg`[ZklZg]*.ff_hkik^lmk^llbg`pbk^lZg]
lmkZg]l'B_bm\Zg[^]^fhglmkZm^]!nlnZeermakhnà_bk^^g`bg^^kbg`"maZm
maîk^lmk^llbg`lm^ê]h^lghmk^Z\ama^\kbmb\Zem^fi^kZmnk^ma^gma^
Z]]bmbhgZeZqbl]blmZg\^blghmk^jnbk^]'
Pa^k^k^bg_hk\^f^gmhkik^lmk^llbg`m^g]hglZkêZr^k^]%Z_nkma^k
\a^\dblk^jnbk^]mhlahpmaZmma^mZ[neZm^]Zqbl]blmZg\^blghme^ll
maZgma^Zo^kZ`^Zqbl]blmZg\^%Zf%]^m^kfbg^]_khfma^_heehpbg`3
ma^\Zl^maZmg^bma^kf^mah]pbee[ôZeb]%manlk^jnbkbg`ma^^g`bg^^k
mhnl^Zlbfieb_b^]\Ze\neZmbhgf^mah]mh]^fhglmkZm^Z\\îmZ[bebmr'
Ahpô^k%ZlZgZem^kgZmbo^%bgln\abglmZg\^lpa^k^ma^]^lb`gZqbZe
_hk\^blghm`k^Zm^kmaZg)'*_\dmbf^lma^`khll\khll&l^\mbhgZeZk^Z%ma^
f^f[^kfZr[^]^lb`g^]ZlZ[^Zf'
Method A
MZ[e^*`bo^lfbgbfnfl^\mbhglbs^lZg]Zqbl]blmZg\ôZen^l_hk
oZkbhnlk^lblmZg\^mbf^lZg]nmbeblZmbhgkZmbhl!m_b"'Ma^k^lmkb\mbhglhg
ma^nl^h_F^mah]:Zk^3
N Ma^^__^\mboê^g`mah_ma^[kZ\^]\henfgbgma^_bk^\hg]bmbhg%e)%_b
lahne][^©,f
N Ma^_bklmhk]^k^\\^gmkb\bmrng]^k_bk^\hg]bmbhgllahne]lZmbl_rma^
ebfbm3
^6F)>]%_b(G>]%_b©^fZq
pa^k^
F)>]%_b 6 _bklmhk]^k]^lb`gfhf^gm
G>]%_b 6 ZqbZe_hk\^ng]^k_bk^\hg]bmbhgl
^fZq 6 )'*.a!hk)'*.[_hk\bk\neZkl^\mbhgl"
Zf6S :lbZb(S:lb
N Ma^k^bg_hk\^f^gmhnmlb]^h_eZillahne]lZmbl_r3:l©)')-:\
pa^k^
:lb6 ma^Zk^Zh_[Zkhkm^g]hg%ÃbÃ
Zb 6 ma^Zqbl]blmZg\^mh[Zkhkm^g]hgÂbÃ_khfma^g^Zk^lm
^qihl^]lnk_Z\^'
Ma^]^`k^^h_nmbeblZmbhgbgma^_bk^lbmnZmbhgbl]^_bg^][r
m_b6G>]%_b(GK]Zg]blnl^]mh]^m^kfbg^ma^\hkk^\mmZ[neZm^]oZen^'
?hklbfieb\bmr%Zg]\hgl^koZmboêr%bm\Zg[^mZd^gmaZmm_b6n_b6)'0%
b'^'bmblZllnf^]maZmma^\henfgk^lblmZg\^bl^jnZemhbml\ZiZ\bmrZm
Zf[b^gmnembfZmêhZ]l'
Columns
IZkm*¾+ik^l^gmlmphf^mah]l%:Zg];%pab\aZk^[hmaZ\\îmZ[e^_hk
nl^bgma^ND'Ma^rZiiermh[kZ\^]lmkn\mnk^l4ng[kZ\^]lbmnZmbhglZk^
Z]]k^ll^]eZm^kbgmabl<aZim^k'F^mah]:blma^lbfie^lmmhnl^%[nmbl
Zelhfhk^k^lmkb\mbo^'
Bg[hmaf^mah]l%nl^h_ma^mZ[e^lblk^lmkb\m^][rma^ZeehpZ[e^
^\\^gmkb\bmrZg]^__^\mboê^g`malh_ma^\henfgl'Bglhf^bglmZg\^l%
_hk^qZfie^ma^\henfgllniihkmbg`ma^nii^kfhlm_ehhk%bmfZr[^
<_]kh[.
H[ZkYj_ed_dWn_iZ_ijWdY["a"Z[f[dZ_d]edWh[We\ij[[bfhel_Z[Z
MaôZen^lbgma^mZ[e^Zk^\Ze\neZm^]mZdbgà\\6*')'Ma^NDGZmbhgZe
:gg^qmZd^la\\6)'1.Zg]mablfZr[^Z\\hngm^]_hk[r_Z\mhkbg`ma^
\Ze\neZm^]oZen^h_m_b[r)'1.¾*%hk[rnlbg`>qik^llbhg!.'0"'Ahpô^k%bm
pbee[^\hgl^koZmbo^mhnl^ma^mZ[neZm^]oZen^lpbmahnmln\afh]b_b\Zmbhg'
JWXb['
C_d_ckcYebkcdZ_c[di_ediWdZWn_iZ_ijWdY[\ehYebkcdim_j^
h[YjWd]kbWhehY_hYkbWhi[Yj_edi¸C[jêZ7
Standard
fire
resistance
0
Reduction in axis distance D a (mm)
2
n fi = 0.7
4
K,)
+))(+.
+))(+.
+))(,+
,))(+0
*..(+.
K/)
+))(+.
+))(,*
+.)(-/
,.)(-)
,.)(.,
*..(+.
K2)
+))(,/
,))(,*
,))(-.
,))(+.
-))(,1
-.)(-)a
+.)(-)
,.)(-.a
,.)(.0a
,.)(,.
-.)(-)
-.)(.*a
K*1)
,.)(-.a
,.)(/,a
-.)(0)a
+,)(..
K+-)
Key
,.)(/*a
-.)(0.a
-
+2.(0)
6
n fi = 0.5
8
10
K*+)
12
14
16
n fi = 0.2
18
20
0.5
0.6
0.7
Ratio, As,req / A
102
Column width bmin%Wn_iZ_ijWdY["a, of the
main bars
9ebkcd[nfei[Zedceh[j^Wded[i_Z[
;nfei[Z
on one side
mfi = 0.2
mfi3&$+
mfi3&$mfi3&$-
0.8
0.9
1.0
aFbgbfnf1[Zkl'
Note
?hkik^lmk^ll^]\henfglZqbl]blmZg\^lahne][^bg\k^Zl^]¾l^^m^qm'
*..(+.
*0.(,.
Method B
MZ[e^+`bo^lfbgbfnfl^\mbhglbs^lZg]Zqbl]blmZg\ôZen^l_hk
oZkbhnlk^lblmZg\^mbf^lZg]nmbeblZmbhgZg]k^lblmZg\^kZmbhl'Ma^
k^lmkb\mbhglhgma^nl^h_F^mah];Zk^3
N Ma^le^g]^kg^llh_ma^\henfgng]^k_bk^\hg]bmbhgllahne][^
Walls
PZeelZk^\Zm^`hkbl^]bgmhghg&ehZ][^Zkbg`%ehZ][^Zkbg`%Zg]_bk^
pZeel'?bk^pZeelaZo^mh\hfierpbmabfiZ\mk^lblmZg\^\kbm^kbZ':l
mabl\Zm^`hkblZmbhgblmrib\Zeerghmnl^]bgma^ND%_bk^pZeelZk^ghm
\hglb]^k^]Zgr_nkma^ka^k^'
l_b6e)%_b(b©,)pa^k^bblma^fbgbfnfkZ]bnlh_bg^kmbZ'
N Ma^_bklmhk]^k^\\^gmkb\bmrng]^k_bk^\hg]bmbhgllahne]lZmbl_r
maêbfbm3
^6F)>]%_b(G)>]%_b©^fZq
pa^k^
^fZq6*))ff
^([ ©)'+.
[ 6fbgbfnf\henfg]bf^glbhg
MaêhZ]eôêZmghkfZem^fi^kZmnk^\hg]bmbhgl%g%blnl^]bgma^
]^m^kfbgZmbhgh_ma^fbgbfnfoZen^l'<hgl^koZmboêr%bmfZr[^
Zllnf^]maZmg6)'0'PabelmmablZllnfimbhgfZr[^h_nl^bgbgbmbZe
\hg\îm]^lb`g%lb`gb_b\Zgmk^]n\mbhglbgma^fbgbfnfl^\mbhglbs^
Zg]Zqbl]blmZg\^_hkZ`bo^g_bk^k^lblmZg\î^kbh]fZr[^Z\abô^][r
\Ze\neZmbg`g^qieb\bmer_khf3
g6G)>]%_b(T)'0!:\_\]$:l_r]"V'
Ghm^maZmbgma^mZ[e^ma^f^\aZgb\Zek^bg_hk\^f^gmkZmbh%w%blhg^
h_ma^k^jnbk^]iZkZf^m^kl'Bg>nkh\h]^+%IZkm**1%Z\hgl^koZmbo^
oZen^bgma^]^m^kfbgZmbhgh_ebfbmbg`le^g]^kg^ll_hkma^\henfgbl
)'*'?hkZ\eZll<,)(,0\hg\k^m^mablkîk^l^gml)'-k^bg_hk\^f^gm%
pa^k^Zlpa^gw6*')%ma^\henfgphne]k^jnbk^-k^bg_hk\^f^gm'
?hkZeemri^l%ZebfbmZmbhgblieZ\^]hgma^kZmbhh_\e^Zka^bàmmh
mab\dg^ll%e)(m©-)%mhZohb]^q\^llbo^ma^kfZe]^_hkfZmbhge^Z]bg`mh
_Zbenk^h_bgm^`kbmr[^mp^^gpZeeZg]leZ['Ahpô^k%_hkZee[nmma^mabgg^lm
h_pZeel%mablebfbmblngebdêrmh[^k^Z\a^]bgmrib\ZeZiieb\Zmbhgl'
?hkghg&ehZ][^Zkbg`pZeel hgerma^kfZeZg](hkbgm^`kbmr\kbm^kbZ
!BZg]>"g^^]mh[^f^mZg]fbgbfnfmab\dg^llZehg^`ho^kglma^
Z]^jnZ\rbgma^_bkêbfbmlmZm^%b'^'gh\a^\dblk^jnbk^]hgma^Zqbl
]blmZg\^'?hkehZ][^Zkbg`pZeelZfbgbfnfpZeemab\dg^ll%Zg]Zqbl
]blmZg\^mhma^k^bg_hk\^f^gm%fnlm[îkhob]^]'Ma^fbgbfnfoZen^l
_hk[hmamri^lZk^`bo^gbgMZ[e^,'Ghm^maZmmablmZ[e^fZrZelh[^
nl^]_hkieZbg\hg\k^m^pZeel'
8[Wci
Fbgbfnfl^\mbhglbs^lZg]Zqbl]blmZg\^lmhk^bg_hk\^f^gm_hk[^Zfl
Zk^lahpgbgMZ[e^-'Bgnlbg`ma^mZ[neZkf^mah]%ma^_heehpbg`
Zllnfimbhgl(k^lmkb\mbhglZk^fZ]^3
N Ma^l^\mbhgbl^qihl^]hgmak^^lb]^lpbmama^nii^klnk_Z\^
Zllnf^]mh[^bglneZm^]'Ahpô^k%pa^k^Zeelnk_Z\^lZk^^qihl^]
mh_bk^%ma^mZ[e^lfZrlmbee[^nl^][nmpbmaZ]]bmbhgZek^lmkb\mbhgl
ieZ\^]hgma^fbgbfnfl^\mbhglbs^'
Table 2
C_d_ckcYebkcdZ_c[di_ediWdZWn_iZ_ijWdY[\ehYebkcdim_j^h[YjWd]kbWhehY_hYkbWhi[Yj_edi¸C[jêZ8
Standard fire resistance
K,)
K/)
K2)
K*+)
K*1)
K+-)
Mechanical
reinforcement ratio, w
Minimum dimensions (mm). Column width bmin%Wn_iZ_ijWdY["a
n3&$'+
n3&$)
n3&$+
n3&$-
)'*))
*.)(+.a
*.)(+.a
+))(,)3+.)(+.a
,))(,)3,.)(+.a
)'.))
*.)(+.a
*.)(+.a
*.)(+.a
+))(,)3+.)(+.a
*')))
*.)(+.a
*.)(+.a
*.)(+.a
+))(,)3,))(+.a
)'*))
*.)(,)3+))(+.a
+))(-)3,))(+.a
,))(-)3.))(+.a
.))(+.a
)'.))
*.)(+.a
*.)(,.3+))(+.a
+.)(,.3,.)(+.a
,.)(-)3..)(+.a
*')))
*.)(+.a
*.)(,)3+))(+.a
+))(-)3-))(+.a
,))(.)3/))(,)
)'*))
+))(-)3+.)(+.a
,))(-)3-))(+.a
.))(.)3..)(+.a
..)(-)3/))(+.a
)'.))
*.)(,.3+))(+.a
+))(-.3,))(+.a
,))(-.3..)(+.a
.))(.)3/))(-)
*')))
+))(+.a
+))(-)3,))(+.a
+.)(-)3..)(+.a
.))(.)3/))(-.
)'*))
+.)(.)3,.)(+.a
-))(.)3..)(+.a
..)(+.a
..)(/)3/))(-.
)'.))
+))(-.3,))(+.a
,))(-.3..)(+.a
-.)(.)3/))(+.a
.))(/)3/))(.)
*')))
+))(-)3+.)(+.a
+.)(.)3-))(+.a
-.)(-.3/))(,)
/))(/)
)'*))
-))(.)3.))(+.a
.))(/)3..)(+.a
..)(/)3/))(,)
b
)'.))
,))(-.3-.)(+.a
-.)(.)3/))(+.a
.))(/)3/))(.)
/))(0.
*')))
,))(,.3-))(+.a
-.)(.)3..)(+.a
.))(/)3/))(-.
b
)'*))
.))(/)3..)(+.a
..)(-)3/))(+.a
/))(0.
b
)'.))
-.)(-.3.))(+.a
..)(..3/))(+.a
/))(0)
b
*')))
-))(-.3.))(+.a
.))(-)3/))(,)
/))(/)
b
Key
aGhkfZeerma^\ho^kk^jnbk^][r;L>G*22+¾*¾*pbee\hgmkhe'
bK^jnbk^lpb]ma`k^Zm^kmaZg/))ff'IZkmb\neZkZll^llf^gm_hk[n\debg`blk^jnbk^]'
103
N Maîkh_be^lbg?b`nk^2Zk^k^_^k^g\^]bgIZkm*+_hkma^mZ[neZk
+)k^]blmkb[nmbhgZg]%b_nl^]%phne]k^jnbk^ma^lbfierlniihkm^]
Zllnfimbhgmh[^Z]him^]'
f^mah]'Bghma^kbglmZg\^lln\aZlE&[^Zflhk_hkghg&lmZg]Zk]
l^\mbhglaZi^l%^g`bg^^kbg`cn]`^f^gmlahne][^nl^]bg
]^m^kfbgbg`ma^Ziieb\Z[bebmrh_ma^mZ[e^l'
N :]]bmbhgZe\a^\dlZk^k^jnbk^]_hkma^_bklmbgm^kgZelniihkmlh_
\hgmbgnhnlB&[^ZflkêZmbg`mhihllb[e^_Zbenk^f^\aZgblflZm_bk^
k^lblmZg\î^kbh]lh_*+)fbgnm^lZg]Z[ho^'
N :]]bmbhgZeebfbmlZk^Ziieb^]mhma^fbgbfnfZqbl]blmZg\^_hk
\hkg^k[Zkl'
N ?hk\hgmbgnhnl[^Zfl%b_k^]blmkb[nmbhg^q\^^]l*.bgma^
Zf[b^gm\hg]bmbhg%ma^mZ[e^l_hklbfierlniihkm^]l^\mbhgllahne]
[^nl^]nge^llma^fhf^gm\ZiZ\bmrbl^qieb\bmer\a^\d^]':l^\hg]
bfieb\Zmbhgh_mablebfbmblmaZmlmZg]Zk]mZ[e^lh_[^g]bg`fhf^gm
Zg]la^Zk\h^__b\b^gml%ln\aZlmahl^bgma^FZgnZe_hkma^]^lb`gh_
\hg\k^m^[nbe]bg`lmkn\mnk^lmh>nkh\h]^+*)%Zk^mrib\Zeer[Zl^]hg
JWXb[)
Minimum wall thicknesses for walls
Standard
fire
resistance
K>B,)
K>B/)
K>B2)
K>B*+)
K>B*1)
K>B+-)
Key
NonbeWZX[Wh_d]
wall
thickness
(mm)
/)b
1)b
*))b
*+)b
*.)b
*0.b
Pa^k^ma^l^\mbhgblik^lmk^ll^]%iZkmb\neZkZmm^gmbhglahne][îZb]
mhma^fh]b_b\Zmbhgk^jnbk^]mhma^Zqbl]blmZg\^h_maîk^lmk^ll^]
ê^f^gml%Zl]bl\nll^]bgma^bgmkh]n\mbhgmhma^mZ[neZkf^mah]'
?hk\hgmbgnhnl[^Zfl%\nkmZbef^gmkne^lZk^`bo^g_hkma^mhik^bg_hk\^f^gm
h_l^\mbhglbg_bk^'Ma^mhik^bg_hk\^f^gmlahne]^qm^g])',e^___khfma^
\^gmkêbg^h_ma^lniihkmpbmama^k^jnbk^]Zk^Z[^bg`Zeehp^]mhoZkrbg
Z\\hk]Zg\^pbmama^^qik^llbhg%Zg]ZlbeenlmkZm^]bg?b`nk^*)'
:l%k^j!q"6:l%k^j!)"!*+'.q(e^__"
BeWZX[Wh_d]h[_d\ehY[ZYedYh[j[mWbbi
MWbbj^_Yad[ii%Wn_iZ_ijWdY["a
mfi3&$mfi3&$)+
Number of sides of
mWbb[nfei[Z
One
Two
*))(*)b
*+)(*)b
**)(*)b
*+)(*)b
*+)(+)b
*-)(*)b
*.)(+.
*/)(+.
*1)(-)
+))(-.
+,)(..
+.)(..
pa^k^
q
6
:l%k^j!q" 6
:l%k^j!)" 6
e^__
6
Number of sides of
mWbb[nfei[Z
One
Two
*+)(*)b
*+)(*)b
*,)(*)b
*-)(*)b
*-)(+.
*0)(+.
*/)(,.
++)(,.
+*)(.)
+0)(..
+0)(/)
,.)(/)
]blmZg\^_khfma^\^gmkêbg^h_ma^lniihkm
fbgbfnfZk^Zh_mhik^bg_hk\^f^gmk^jnbk^]Zm
]blmZg\^q_khfma^lniihkm[nmghme^llmaZgma^
fbgbfnfZeehp^]_khf>nkh\h]^+%IZkm**
ma^Zk^Zh_mhik^bg_hk\^f^gmk^jnbk^]ho^kma^
lniihkmbgZf[b^gm]^lb`g
^__^\mboê^g`mah_ma^liZg
B_)',e^__blln[lmbmnm^]bgmhma^Z[ho^%ma^Zk^Zh_k^bg_hk\^f^gmpa^k^
k^jnbk^]]khilmh+.h_maZmk^jnbk^]Zmma^lniihkm'Bglhf^\Zl^l%
mabl\nkmZbef^gme^g`mafZr[^fhk^hg^khnlmaZgmaZm]^m^kfbg^]_khf
lhf^lbfie^]^mZbebg`kne^lpabelmma^lbfieb_b^]]^mZbebg`kne^lik^l^gm^]
bg<aZim^k*)%=^mZbebg`**pbeek^lnembgZlZ_^]^mZbe_hklmZg]Zk]\Zl^l'
aÂKÃ^qihlnk^\hg]bmbhgghmZiieb\Z[e^mhghg&ehZ][^Zkbg`pZeel
bGhkfZeerma^\ho^kk^jnbk^][r;L>G*22+¾*¾*pbee\hgmkhe'
JWXb[*
C_d_ckcZ_c[di_edWdZWn_iZ_ijWdY[i\ehYedj_dkekiX[WcicWZ[m_j^h[_d\ehY[ZWdZfh[ijh[ii[ZYedYh[j[
Standard fire Minimum dimensions (mm)
resistance
Simply supported beams
Continuous beams
Possible combinations of a and bmin where a is the Web
Possible combinations of a and bmin where a is the Web
Wl[hW][Wn_iZ_ijWdY[WdZbmin is the width of beam thickness bw Wl[hW][Wn_iZ_ijWdY[WdZbmin is the width of beam thickness bw
K,) [fbg
Z
K/) [fbg
Z
K2) [fbg
Z
K*+) [fbg
Z
K*1) [fbg
Z
K+-) [fbg
Z
'
2
)
*
1)
+.
*+)
-)
*.)
..
+))
/.
+-)
1)
+1)
2)
*+)
+)
*/)
,.
+))
-.
+-)
/)
,))
0)
,.)
1)
*/)
*.a
+))
,)
,))
-)
,))
..
-))
/.
.))
0.
+))
*.a
,))
+.
-))
,.
.))
.)
/))
/)
0))
0)
+
1)
*))
**)
*,)
*.)
*0)
6
-
1)
*.a
*+)
+.
*.)
,.
+))
-.
+-)
/)
+1)
0.
*/)
*+a
+))
*+a
+.)
+.
,))
,.
-))
.)
.))
/)
.
9
'&
1)
*))
110
-.)
,.
..)
.)
/.)
/)
.))
,)
/))
-)
0))
.)
130
150
170
Key
aGhkfZeerma^\ho^kk^jnbk^][r;L>G*22+¾*¾*pbee\hgmkhe
Notes
'?hkik^lmk^ll^]\henfglZqbl]blmZg\^lahne][^bg\k^Zl^]¾l^^m^qm'
2al]blma^Zqbl]blmZg\^mhma^lb]^h_[^Zf_hkma^\hkg^k[Zkl!hkm^g]hghkpbk^"h_[^ZflpbmahgerhgêZr^kh_k^bg_hk\^f^gm'al]6a$*)ff%nge^llmaôZen^lh_[fbgZk^`k^Zm^k
maZgmaZm`bo^gbg\henfg,_hklbfierlniihkm^][^Zflhk\henfg1_hk\hgmbgnhnl[^Zfl%pa^gghbg\k^Zl^blk^jnbk^]'
104
N Fbgbfnfg^`Zmbo^k^bg_hk\^f^gm^jnZemh)'.h_ma^`khll
Tensile members
Ma^mZ[neZm^]]ZmZ_hk[^ZflfZr[^nl^]_hkm^glbe^f^f[^klpbma
ma^_heehpbg`k^lmkb\mbhgl3
N Ma^`khll\khll&l^\mbhgZeZk^Zlahne]ghm[ê^llmaZg+[fbg+
pa^k^[fbgblma^fbgbfnfZeehpZ[e^l^\mbhgpb]mamZd^g_khfma^
mZ[neZm^]]ZmZ'
N Pa^k^maêhZ][^Zkbg`\ZiZ\bmrblk^]n\^][r^q\^llbo^êhg`Zmbhg%
IZkm*+`bo^l`nb]Zg\^mhZ]]k^llmabl'
Slabs
OZkbhnl_hkflh_leZ[Zk^\hglb]^k^]3lbfierlniihkm^]%\hgmbgnhnl%
mph&pZr%_eZm%Zg]kb[[^]%Zg]mZ[e^lZkîkhob]^]_hk^Z\a':lpbma
hma^kf^f[^kmri^l%Zgnf[^kh_k^lmkb\mbhglZk^Ziieb^]bg^Z\a\Zl^4
ma^l^Zk^]^l\kb[^][êhp'
Simply supported slabs
MZ[e^.blikhob]^]_hklbfierlniihkm^]f^f[^klpbmaghli^\bZe
ikhoblbhgl(k^lmkb\mbhgl'
Continuous slabs
<hgmbgnhnlleZ[lfZr[^mk^Zm^]Zlmph&pZrliZggbg`leZ[lpa^k^
er(eq©*'.Zl`bo^gbgMZ[e^.'Ma^_heehpbg`\hg]bmbhgllahne][^f^m3
N ?hk\hgmbgnhnlleZ[l%b_k^]blmkb[nmbhg^q\^^]l*.bgma^Zf[b^gm
\hg]bmbhg%ma^mZ[e^l_hklbfierlniihkm^]l^\mbhgllahne][^nl^]
nge^llfhf^gm\ZiZ\bmrbl^qieb\bmer\a^\d^]'
<_]kh[/
:[\_d_j_ede\Z_c[di_edi\ehZ_\\[h[djjof[ie\X[Wci[Yj_ed
bw
b
b
(a) Constant width
(b) Variable width
b
l^\mbhgZk^Zlahne][îkhob]^]nge^llahm&khee^]k^bg_hk\^f^gm
aZl[^^gnl^]%k^lmkZbgmblikhob]^]Zmma^^g]lniihkmlh_mph&
liZgleZ[l%Zg]mkZglo^kl^]blmkb[nmbhgh_ehZ]blZ\\hngm^]_hk'
Bgma^NDmaîkh\nk^f^gmh_k^bg_hk\^f^gm]h^lghmghkfZeer
Zeehpmaîkh]n\mbhgf^mah]mh[^li^\b_b^]'@^g^kZeer%<eZll:
k^bg_hk\^f^gmbl\he]phkd^]Zg]<eZll;k^bg_hk\^f^gmblahmkhee^]%
[nmbmblihllb[e^mh_hkf<eZll;k^bg_hk\^f^gm[r\he]phkdbg`'
:mik^l^gm<eZll<k^bg_hk\^f^gmlniieb^]bgma^NDblahmkhee^]
Zg]ma^k^_hk^\Zg[^li^\b_b^]lhmaZmma^fbgbfnfk^bg_hk\^f^gm
k^jnbk^]Z[ho^g^^]ghm[îkhob]^]'
Ma^]^mZbebg`blln^lkêZmbg`mhah``bg`k^bg_hk\^f^gmbg\hgmbgnhnl
leZ[lZk^ma^lZf^Zlmahl^]^l\kb[^]ikôbhnler_hk\hgmbgnhnl[^Zfl'
Two-way slabs
Ma^mph&pZr\hg\îmZiieb^lmh[hmalbfierlniihkm^]Zg]
\hgmbgnhnlleZ[mri^l'BgZ]]bmbhgmhma^\hff^gml_hk\hgmbgnhnl
leZ[lfZ]^Z[ho^%Zqbl]blmZg\^mhma^k^bg_hk\^f^gm%a%blmZd^gZl
ma^]blmZg\^_khfma^lnk_Z\^mhma^Zqblh_ma^hnm^kfhlmeZr^kh_
k^bg_hk\^f^gm'
Ma^^g`bg^^klahne]ghm^maZmma^\hgo^gmbhgbgMZ[e^.%pa^k^ma^
kêZmbhglabi_hkliZglerªeqblma^hiihlbm^h_maZmbg>nkh\h]^+%
IZkm**_hk_eZmleZ[lpa^kêqªer'
JWXb[+
C_d_ckcZ_c[di_ediWdZWn_iZ_ijWdY[i\ehh[_d\ehY[ZWdZ
prestressed solid slabs
Standard fire
resistance
K>B,)
(c) I -Section
K>B/)
<_]kh['&
;dl[bef[e\h[i_ij_d]X[dZ_d]cec[djiel[hikffehji\eh\_h[YedZ_j_edi
0.3 l eff
0.4 l eff
0.3 l eff
K>B2)
K>B*+)
BM from Exp. (5.11)
K>B*1)
K>B+-)
One-way Jme#mWoifWdd_d]ibWXa Flat slab
ifWdd_d]
ly/ln ≤'$+ '$+2ly/ln ≤ 2 d ≤'+c d4'+c
slab
al
/)
/)
/)
Z
*)b
*)b
*)b
al
1)
1)
1)
*)b
*.b
*.)
*)b
*1)
*.b
*.)
*)b
*1)
+)
Z
+)
al
*))
Z
,)
+)
+.
,)
al
*+)
*+)
*+)
+))
+))
Z
-)
+)
+.
,.
-)
*))
*.b
*))
+))
+))
al
*.)
*.)
*.)
+))
+))
Z
..
,)
-)
-.
..
al
*0.
*0.
*0.
+))
+))
Z
/.
-)
.)
.)
/.
Key
BM in fire location
aMa^m^kfmphpZrleZ[lkêZm^lmhleZ[llniihkm^]ZmZee_hnk^]`^l'B_mablblghmma^\Zl^
ma^rlahne][^mk^Zm^]Zlhg^&pZrliZggbg`leZ[l'
bGhkfZeerma^\ho^kk^jnbk^][r;L>G*22+¾*¾*pbee\hgmkhe'
BM when
t =0
cdblma^k^]blmkb[nmbhgkZmbh'
Design BM
according to
BS EN 1992–1–1
Notes
'eqZg]erZk^ma^liZglh_Zmph&pZrleZ[!mph]bk^\mbhglZmkbàmZgè^l"pa^kêrblma^
ehg`^kliZg'
2 ?hkik^lmk^ll^]\henfglZqbl]blmZg\^lahne][^bg\k^Zl^]¾l^^m^qm'
105
Flat slabs
?hk_eZmleZ[l%MZ[e^.fZr[^nl^]':me^Zlm+)h_ma^mhmZemhi
k^bg_hk\^f^gmbg^Z\a]bk^\mbhg!:m"lahne][îeZ\^]ho^kma^
lniihkmlbgma^\henfglmkbiZg][^\hgmbgnhnlho^kma^_neeliZg'
Ma^\h]b_b^]\Ze\neZmbhgf^mah]lZg]ma^bkZllh\bZm^]Zgg^q^lbg
IZkm*+Zk^3
Ribbed slabs
Ma^kne^l_hk[^ZflZg]\hgmbgnhnlleZ[llahne][^nl^]bgma^
ôZenZmbhgh_hg^&pZrkb[[^]leZ[l'?hkmph&pZrliZggbg`kb[[^]leZ[l%
ma^bg_hkfZmbhgbgMZ[e^/blikhob]^]pbmamaêbfbmZmbhgmhma^bknl^
[^bg`maZmmaêhZ]bg`blik^]hfbgZgmerngb_hkfer]blmkb[nm^]'
N Shg^f^mah]!lmZg]Zk]_bk^lhger"3IZkm*+k^\hff^g]lmabl
:lpbma[^Zfl%bgZee\Zl^lpa^k^ma^l^\mbhgblik^lmk^ll^]%iZkmb\neZk
Zmm^gmbhglahne][îZb]mhma^fh]b_b\Zmbhgk^jnbk^]mhma^Zqbl
]blmZg\^h_maîk^lmk^ll^]ê^f^gml%ZlZek^Z]r]bl\nll^]bgma^
bgmkh]n\mbhgmhma^mZ[neZkf^mah]'
\hglb]^k^]:gg^q;'+'!Mablf^mah]blghmbg\en]^]bgmabl\aZim^k"
N F^mah]_hkma^ZgZerlblh_\henfglpbmalb`gb_b\Zgml^\hg]hk]^k
^__^\ml:gg^q;',
Ahpô^k%[^_hk^lê^\mbg`Zgrh_ma^Z[ho^f^mah]l%bmblbfihkmZgm
mhghm^maZmma^rZ]]k^ll_e^qnk^hgerpbmala^ZkZg]mhklbhg[^bg`
\ho^k^]lîZkZmêreZm^kbgmabl<aZim^k'
mZ[neZkf^mah]Zg]fZr[^nl^]bgma^]^lb`gh_[^ZflZg]leZ[l
pa^k^maêhZ]blik^]hfbgZgmerngb_hkfer]blmkb[nm^]Zg]%_hk
\hgmbgnhnlf^f[^kl%maêôêh_k^]blmkb[nmbhg]h^lghm^q\^^]
*.'?hkabà^keôêlh_k^]blmkb[nmbhg%ma^fhf^gm\ZiZ\bmrZmma^
lniihkmlfnlm[^\a^\d^][^_hk^mablZiikhZ\afZr[^Ziieb^]'
Mablf^mah]ikhob]^lZf^Zglh_\a^\dbg`pa^ma^kZk^]n\^]Zqbl
]blmZg\^_khfmaZm]^m^kfbg^]bgma^mZ[neZkf^mah]\Zg[^cnlmb_b^]
Table 6
C_d_ckcZ_c[di_ediWdZWn_iZ_ijWdY[\ehjme#mWoifWdd_d]"i_cfbo
supported ribbed slabs in reinforced or prestressed concrete
Standard fire
resistance
Slab thickness
hsWdZWn_i
distance a in
7jb[Wijed[[Z][ \bWd][
restrained
[fbg
1)
1)
al61)
Z
*.a
*)a
Z 6*)a
[fbg
Z
[fbg
Z
K>B*+) [fbg
Z
K>B*1) [fbg
Z
K>B+-) [fbg
Z
*))
*+)
,.
+.
*+)
*/)
-.
-)
*/)
*2)
/)
..
++)
+/)
0.
0)
+1)
,.)
2)
0.
ª+)) *))
*.a
+.
ª+.) *+)
*+)
ª+)) al61)
*.a
*)a Z 6*)a
*/)
ª+.) al6*))
,.
+.
*.a Z 6*.a
ª,)) */)
*2)
ª,)) al6*+)
,)
-.
-)
ª-*) ,*)
-)
/))
/)
[rZfhk^]^mZbe^]^qZfbgZmbhgh_ma^_e^qnkZe\ZiZ\bmrh_ma^l^\mbhg'
Ahpô^k%ghk^]n\mbhgfZr[^fZ]^mhma^l^\mbhglbs^]^m^kfbg^]
_khfma^mZ[neZkf^mah]'
Possible combinations of width of
ribs bminWdZWn_iZ_ijWdY[a
Simply supported
K>B2)
blik^_^kk^]pa^k^lfZeel^\mbhglhkle^g]^k\henfglZk^[^bg`
Mablf^mah]%`bo^gbg:gg^q>h_IZkm*¾+%blZg^qm^glbhgmhma^
?hnklbfieb_b^]\Ze\neZmbhgf^mah]lZkîk^l^gm^]bgIZkm*&+'Ma^_bklm
h_ma^l^blZlbfieb_b^]\Ze\neZmbhgf^mah]li^\b_b\Zeer_hk[^ZflZg]
leZ[l'Bgma^hma^kf^mah]l%Zlbfieb_b^]\khll&l^\mbhg\Ze\neZmbhgblnl^]
mh]^m^kfbg^ma^_e^qnkZek^lblmZg\^h_ma^l^\mbhgbgma^_bk^\hg]bmbhg%
Zg]mablbl\hfiZk^]pbmama^^__^\mh_Z\mbhglbgma^_bk^lbmnZmbhg'
K>B/)
N .))<blhma^kff^mah]!lmZg]Zk]hkiZkZf^mkb\_bk^l":gg^q;'*
Simplified calculation method for beams
and slabs
Simplified calculation
methods
K>B,)
N Lbfieb_b^]\Ze\neZmbhgf^mah]_hk[^ZflZg]leZ[l:gg^q>
,) Z 6+)
al6*.)
Ma^ZiikhZ\ablmh\a^\dmaZmma^]^lb`gfhf^gmbg_bk^bl^jnZemhhk
e^llmaZgma^]^lb`gk^lblmZg\^bg_bk^%b'^'F>]%_b©FK]%_b'Ma^m^kfF>]%_b
bl]^_bg^]Zl3
F>]%_b6p>]%_be^__+(1
pa^k^
p>]%_b6 ngb_hkfer]blmkb[nm^]ehZ]!dG(f"ng]^k_bk^\hg]bmbhgl'
6 n_bp>]
n_b 6 k^]n\mbhg_Z\mhk!l^^Â\hf[bgZmbhglh_Z\mbhglÃl^\mbhg
hgiZ`^+"
p>] 6 ngb_hkfer]blmkb[nm^]ehZ]!dG(f"ng]^kZf[b^gm
\hg]bmbhgl
e^__ 6 ^__^\mboê^g`mah_[^ZfhkleZ[
/)
.)
Z 6,)
=^m^kfbgZmbhgh_ma^]^lb`gk^lblmZg\^Zg]hma^k\a^\dl]î^g]hg
ª.)) -.)
0))
al6*0.
pa^ma^kma^f^f[^kbllbfierlniihkm^]hk\hgmbgnhnl':_ehp\aZkm
/)
Z 6-)
h_ma^]^lb`gikh\^llblik^l^gm^]bg?b`nk^**'
0)
0)
Key
aGhkfZeerma^\ho^kk^jnbk^][r;L>G*22+**pbee\hgmkhe'
Simply supported members
Notes
Ma^]^lb`gk^lblmZg\^ng]^k_bkêhZ]bg`bl]^m^kfbg^]_khfma^
'?hkik^lmk^ll^]\henfglZqbl]blmZg\^lahne][^bg\k^Zl^]¾l^^m^qm'
2 Zl]blma^Zqbl]blmZg\^mhma^lb]^h_[^Zf_hkma^\hkg^k[Zkl!hkm^g]hghkpbk^"
h_[^ZflpbmahgerhgêZr^kh_k^bg_hk\^f^gm'Zl]6Z$*)ff'
106
_heehpbg`^qik^llbhg3
FK]%_b6!gl(gl%_b"dl!y"F>]!:l%ikho(:l%k^j"
pa^k^
iZkmbZefZm^kbZe_Z\mhk_hklm^êZmZf[b^gmm^fi^kZmnk^l
iZkmbZefZm^kbZe_Z\mhk_hklm^êng]^k_bk^\hg]bmbhgl
lmk^g`mak^]n\mbhgZiieb^]mhlm^ê_hkZ`bo^g
m^fi^kZmnk^!y "ng]^kma^k^jnbk^]_bk^k^lblmZg\^
]^lb`gfhf^gm_hkZf[b^gm]^lb`g
\khll&l^\mbhgZeZk^Zh_m^glbhgk^bg_hk\^f^gmikhob]^]
\khll&l^\mbhgZeZk^Zh_m^glbhgk^bg_hk\^f^gmk^jnbk^]
Ma^kZmbh:l%ikho(:l%k^jlahne]ghm[^mZd^g`k^Zm^kmaZg*','Ma^
\h^__b\b^gmdl!y"fZr[^]^m^kfbg^]_khf?b`nk^*+'Ghm^mablblZ
lbfieb_b\Zmbhgh_?b`nk^,%_hknl^pbmama^mZ[neZkf^mah]Zg]:gg^q>'
Continuous members
Bgma^_bk^\hg]bmbhg%IZkm*+Zeehplfhf^gmk^]blmkb[nmbhg_khf
ma^liZg[Z\dmhma^lniihkmlb_ln__b\b^gmk^bg_hk\^f^gmblikhob]^]
ho^kma^lniihkmZg]maZmmablk^bg_hk\^f^gmbllnbmZ[er\nkmZbe^]mh
Z\\hffh]Zm^ma^[^g]bg`fhf^gm^goêhi^'
Ma^fb]&liZgfhf^gmk^lblmZg\^\Zg[^\Ze\neZm^]_khfma^
^qik^llbhg_hkFK]%_bZ[ho^'Ma^Â_k^^Ã[^g]bg`fhf^gm_hkma^_bk^
lbmnZmbhgblma^g]^m^kfbg^]Zg]Â_bmm^]Ãmhma^fhf^gmh_k^lblmZg\^
h_ma^liZg'Ma^fhf^gmh_k^lblmZg\^Zmma^lniihkm_hkma^_bk^\Zl^
fZrma^g[^\Ze\neZm^]Zl_heehpl3
FK]%_b%Lniihkm6!gl (gl%_b"F>]!:l%ikho(:l%k^j"!]Z"(]
pa^k^
] 6 ^__^\mbo^]îmah_ma^l^\mbhg
Z 6 k^jnbk^]Zo^kZ`^[hmmhfZqbl]blmZg\^mZd^g_khfMZ[e^-%
\henfg-%_hk[^Zfl%Zg]_khfMZ[e^._hkhg^&pZrleZ[l
Ma^\nkmZbef^gme^g`mak^jnbk^]ng]^k_bk^\hg]bmbhglfZr[^`k^Zm^k
maZgmaê^g`ma]^m^kfbg^]bg>nkh\h]^+%IZkm**Zg]lahne][^\a^\d^]'
+&&9_iej^[hcc[jêZ
Bgma^blhma^kff^mah]%\hg\k^m^ZmZm^fi^kZmnk^Z[ho^.))<bl
g^è^\m^]bgma^\Ze\neZmbhgh_l^\mbhgk^lblmZg\^%pabelm\hg\k^m^Zmhk[êhp
.))<blZllnf^]mhk^mZbgbml_nee%Zf[b^gmm^fi^kZmnk^lmk^g`ma'Bg
IZkm*¾+ma^f^mah]blbeenlmkZm^]pbmak^_^k^g\^mhk^\mZg`neZkl^\mbhgl'
Manl%ma^\Ze\neZmbhgikh\^llblmh_bklm\a^\dmaZmma^l^\mbhgf^^ml
ma^fbgbfnf\khll&l^\mbhgZepb]mak^jnbk^f^gmlbgMZ[e^0'
B_ma^fbgbfnfk^jnbk^f^gmlZk^f^m%ma^Zk^Zghm]ZfZ`^][r
a^Zm%b'^'pbmabgma^.))<blhma^kf%bl]^m^kfbg^]mh`bo^Zk^]n\^]
l^\mbhglbs^![_b%]_b"pa^k^ma^\hg\k^m^k^mZbglbmlhkb`bgZeikhi^kmb^l'
Pabelmma^m^fi^kZmnk^`kZ]b^gmmakhnàZl^\mbhg]^ghm^][r
blhma^kflfZr[^]^m^kfbg^]_khfm^lmbg`%IZkm*¾+ikhob]^l
m^fi^kZmnkîkh_be^l_hkZgnf[^kh_mrib\Zef^f[^kmri^lZg]
\khll&l^\mbhgl'!L^^^qZfie^bg?b`nk^*,"'
Ma^khng]^]\hkg^klh_ma^k^lb]nZel^\mbhgk^_e^\mma^k^Zeikh_be^h_
ma^blhma^kfZg]fZr[^ZiikhqbfZm^]mhZk^\mZgè^Zllahpgbg
?b`nk^*-4lhf^bgm^kik^mZmbhgfZr[^k^jnbk^]'
JWXb[Minimum width of cross-section as function of fire resistance
:l%ikho(:l%k^jlahne]ghm[^mZd^g`k^Zm^kmaZg*','
<_]kh[''
Flow chart for simplified calculation method for beams and slabs
Fire resistance
K/)
K2)
K*+) K*1) K+-)
Minimum width of
cross-section (mm)
2)
*+)
*/)
+))
+1)
<_]kh['(
H[\[h[dY[Ykhl[i\ehYh_j_YWbj[cf[hWjkh[e\h[_d\ehY_d]WdZfh[ijh[ii_d]
ij[[b\ehki[m_j^jWXkbWhc[jêZWdZ7dd[n;
Start
Calculate MEd, fi.
1.0
Determine y, using temperature profiles in Annex A of Part 1-2.
Determine ks(y) from Figure 12
0.8
Calculate MRd, fi
Is the element a
simply supported?
No
Calculate the support design
moment of resistance,
MRd, fi, support
‘Fit’ the ‘free’ bending
moment so that MEd,fi = MRd,fi
Yes
Is MEd, fi. ≤ MRd, fi?
No
Redesign section or use
alternative methods
Yes
Yes
Coefficient, ks (ycr) or kp (ycr)
gl 6
gl%_b 6
dl!y " 6
F>] 6
:l%ikho6
:l%k^j 6
:l[^_hk^%bgZee\Zl^lpa^k^ma^l^\mbhgblik^lmk^ll^]%iZkmb\neZk
Zmm^gmbhglahne][îZb]mhma^fh]b_b\Zmbhgk^jnbk^]mhma^Zqbl
]blmZg\^h_maîk^lmk^ll^]ê^f^gml%ZlZek^Z]r]bl\nll^]bgma^
bgmkh]n\mbhgmhma^mZ[neZkf^mah]'
Reinforcing steel
0.6
Prestressing steel (bars)
0.4
Prestressing steel
(wires and strands)
0.2
Are the support
moments exceeded?
0
No
Finish
0
200
400
600
800
1000
12
o
Temperature, y ( C)
107
Hg\^ma^k^]n\^]\khll&l^\mbhgbl]^m^kfbg^]%ma^m^fi^kZmnk^h_
^Z\ak^bg_hk\bg`[Zkbl_hng]nlbg`m^fi^kZmnkîkh_be^lZg]_khf
mabl%ma^k^]n\^]lmk^g`mah_ma^k^bg_hk\^f^gm]n^mhm^fi^kZmnk^
fZr[^]^m^kfbg^]bgZ\\hk]Zg\^pbma?b`nk^l,Zg]-'Ghm^maZm%
bglhf^bglmZg\^l%ma^k^bg_hk\^f^gmfZr_Zeehnmlb]^h_ma^k^lb]nZe
\khll&l^\mbhg'Bgln\a\Zl^l%ma^l^[ZklfZrlmbee[^\hngm^]pa^g
]^m^kfbgbg`ma^l^\mbhg\ZiZ\bmr'
Ma^l^\mbhgk^lblmZg\^fZrma^g[^]^m^kfbg^]nlbg`\hgo^gmbhgZe
\Ze\neZmbhgf^mah]l%Zlbg]b\Zm^]bg?b`nk^*.Zg]\hfiZk^]Z`Zbglm
ma^]^lb`gehZ]bgma^_bk^lbmnZmbhgbgmabl_b`nk^pa^k^3
[_b 6 pb]mah_k^]n\^]\khll&l^\mbhg
]_b 6 ^__^\mbo^]îmah_ma^k^]n\^]\khll&l^\mbhg
s 6 eô^kZkf[^mp^^gma^m^glbhgk^bg_hk\^f^gm
Zg]\hg\k^m^
sÃ 6 eô^kZkf[^mp^^gma^m^glbhgZg]\hfik^llbhg
k^bg_hk\^f^gm
:l 6 Zk^Zh_m^glbhgk^bg_hk\^f^gm
:l* 6 iZkmh_m^glbhgk^bg_hk\^f^gmbg^jnbeb[kbnf
pbmama^\hg\k^m^\hfik^llbhg[eh\d
Fn*6 :l* _l]%_b!yf"s
Fn+6 :l+ _l\]%_b!yf"sÃ
:l 6 :l*$:l+
500oC
d fi = d
d fi
Compression
Tension
b fi
bfi
b
b
b) Fire exposure on three sides with
the compression zone exposed
a) Fire exposure on three sides
with tension zone exposed
500oC
h fi
h
b fi
b
c) Fire exposure on four sides (beam or column)
<_]kh['+
Ijh[iiZ_ijh_Xkj_edWjkbj_cWj[b_c_jijWj[\ehWh[YjWd]kbWhYedYh[j[
cross-section with compression reinforcement.
n f cd, 1(20)
lx
x
l xb n fcd, 1(20)
Fs = As1f scd,fi (ym)
As
d1
z Mu1
As1 fsd,fi (ym)
<_]kh['*
;nWcfb[j[cf[hWjkh[fhe\_b[
240
220
200
180
100
160
140
200
120
100
300
80
400
500
60
A s1
z’
pa^k^
:l 6 mhmZem^glbhgk^bg_hk\^f^gmZk^Z
_l]%_b 6 ]^lb`gm^glbe^lmk^g`mah_k^bg_hk\^f^gm
_l\]%_b 6 ]^lb`glmk^g`ma_hk\hfik^llbo^k^bg_hk\^f^gm
[_b 6 pb]mah_ma^_bk^^qihl^]\khll&l^\mbhg
]_b 6 ^__^\mboâ^bàmh_ma^_bk^^qihl^]\khll&l^\mbhg
Distance from bottom left corner of element (mm)
o
Note: _l]%_b!yf"Zg]_l\]%_b!yf"fZraZo^]b__^k^gmoZen^l!l^ÎZkm*+%
<e-'+'-',"
?l 6 mhmZe_hk\^bg\hfik^llbhgk^bg_hk\^f^gmbgma^
_bk^lbmnZmbhg%Zg]bl^jnZemhiZkmh_ma^mhmZe_hk\^bg
ma^m^glbhgk^bg_hk\^f^gm
l%nZg]qZk^]^_bg^]bg>nkh\h]^+%IZkm**
Ma^[^g]bg`fhf^gm\Ze\neZmbhgh_ma^\khll&l^\mbhgbl3
Tension
500 C
iZkmh_m^glbhgk^bg_hk\^f^gmbg^jnbeb[kbnf
pbmama^\hfik^llbhgk^bg_hk\^f^gm
Zk^Zh_\hfik^llbhgk^bg_hk\^f^gm
]^lb`goZen^h_\hfik^llbhglmk^g`ma\hg\k^m^bg
ma^_bk^lbmnZmbhgZmghkfZem^fi^kZmnk^
_\d (g\%_b6_\]
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ma^_bk^lbmnZmbhgZmf^Zgm^fi^kZmnk^yfbgmaZmeZr^k
]^lb`goZen^h_ma^\hfik^llbhgk^bg_hk\^f^gmlmk^g`ma
bgma^_bk^lbmnZmbhgZmf^Zgm^fi^kZmnk^yfbgmaZmeZr^k
Pa^gma^k^bg_hk\^f^gmbl]blmkb[nm^]bgfhk^maZghgêZr^k%IZkm*¾+
h__^kllbfieb_rbg`f^mah]lmh]^m^kfbg^ma^Zqbl]blmZg\^mhma^\^gmk^
h_ma^k^bg_hk\^f^gmeZr^klZg]ma^m^fi^kZmnk^k^]n\mbhgZmmableôê'
<_]kh[')
Reduced cross-section of reinforced concrete beam and column
Compression
:l+ 6
:lÃ 6
_\]%_b!+)" 6
6
_l]%_b!yf" 6
_l\]%_b!yf"6
z’ Mu2
600
700
40
800
900
20
0
b1
108
0
60
20
40
80
100
120
Distance from bottom left corner of element (mm)
140
Pa^gma^fhf^gm\hgmkb[nmbhglZk^Zll^ll^]ZllahpgZ[ho^%ma^
mhmZefhf^gm\ZiZ\bmrblh[mZbg^]_khf3
Fn6Fn*$Fn+
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`bo^g\Zl^'
Calculation methods for shear and torsion
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[rl^\hg]hk]^k^__^\mlng]^k_bk^\hg]bmbhgl'Ahpô^k%Zlpbmama^
mZ[neZkf^mah]%ma^ZiikhZ\ablebfbm^]mhf^f[^klmaZm\Zg[^
\hglb]^k^]Zl[^bg`[kZ\^]'
<_]kh[',
<bemY^Whj\eh+&&9_iej^[hcc[jêZ
Start
Pa^gnlbg`ma^mZ[neZkf^mah]%b_ma^fbgbfnfl^\mbhg]bf^glbhgl
Zkîkhob]^]%gh\a^\dl[^rhg]mahl^\Zkkb^]hnm_hkZf[b^gm
m^fi^kZmnk^]^lb`gZk^k^jnbk^]'Bghma^k\Zl^l%f^f[^kk^lblmZg\^
lahne][^]^m^kfbg^][r\Ze\neZmbhgZg]`nb]Zg\^bl`bo^gbg:gg^q=
h_IZkm*+'
?hkmrib\Zel^\mbhgl%la^Zk_Zbenk^]n^mh_bkêhZ]bg`blng\hffhgZg]
pabelmghm[^bg`_neeroZeb]Zm^]%pa^gnlbg`ma^\Ze\neZmbhgf^mah]
ik^l^gm^]%maîkbg\bie^lbg>nkh\h]^+%IZkm**fZr[^Ziieb^]mhZ
k^]n\^]\khll&l^\mbhgZl]^m^kfbg^]_khfZgrh_ma^\Ze\neZmbhgf^mah]l
eblm^]Z[ho^'Ahpô^k%_hkZmrib\Zel^\mbhgl%ln\aZlmahl^pbmamabgp^[l
pa^k^p^[_Zbenk^fZr`ho^kg%ma^l^f^mah]llahne][^nl^]pbma\Zk^'
Calculate MEd, fi (see simplified calculation method for beams and slabs)
Bg\Zl^lpa^k^la^Zkk^bg_hk\^f^gmblghmikhob]^]%ma^l^\mbhg
k^lblmZg\^mhla^Zkblikhob]^][rma^\hg\k^m^'Bgln\a\Zl^lmabl
k^lblmZg\^fnlm[^k^]n\^]mhZ\\hngm_hkm^fi^kZmnk^^__^\ml[rZ
_Z\mhkh_d\m!y"%pab\afZr[^mZd^g_khf?b`nk^*0'Bg\Zl^lpa^k^
ebgdlZkîkhob]^]%pa^ma^k_hkla^ZkZehg^hkZelh_hkmhklbhg%ma^
lmk^g`mah_maêbgdlblk^]n\^]]n^mhma^m^fi^kZmnk^^__^\mlZg]ma^
l^\mbhgk^lblmZg\^ma^g]^m^kfbg^]%[Zl^]hgma^k^]n\^]l^\mbhg'Ma^
\Ze\neZmbhgikh\^llbllahpgbg?b`nk^*1'
Check the minimum dimensions exceed the values in Table 7
Determine reduced section size (bfi dfi) using Figure 13 and
temperature profiles in Annex A of Part 1–2
Determine y, using temperature profiles in Annex A of Part 1–2
Determine ks (y ), from Figure 3 or Figure 4
Calculate Mu, using stress distribution shown in Figure 15. Mu = Mu1 + Mu2
No
Is MEd,fi ≤ MRd,fi?
<_]kh['.
:[i_]d\bemY^Whj\ehi^[WhWdZjehi_edZ[i_]d
Redesign section or use
alternative methods
Start
Yes
Finish
Determine the reduced cross-section using either 500°C
isotherm or zone methods
<_]kh['Coefficient kc,t(yWbbem_d]\ehZ[Yh[Wi[e\j[di_b[ijh[d]j^fck,t) of
concrete at elevated temperatures
Determine position P, the point at which the reference temperature,
y p is calculated. P is located along section A–A, which is
determined from hc,ef (see Figure 19)
1.0
Determine y p using temperature profiles in Annex A of Part 1–2
0.8
Coefficient, k c, t (y )
Calculate the compressive and tensile concrete strengths:
For isotherm method, fcd,fi = fcd,fi(20) = fck and fctd,fi = fctd,fi(20) = fctk
For zone method, fcd,fi = kc(ym) fcd,fi(20) and fctd,fi = kct(ym) fctd,fi(20),
where kc(ym) and kct(ym) may be taken as kc(y) and can be determined
from Figure 2
0.6
Calculate the reduced design strength of the shear reinforcement, fsd,fi,
from: fsd,fi = ks(y) fsd(20) = ks(y) fywd
where ks(y) can be determined from Figure 3 or Figure 4
0.4
Calculate the shear resistance using the methods given for ambient
temperature design, see Chapter 4 Beams11
Does the section
also resist torsion?
0.2
0
0
100
200
300
400
o
Temperature, y ( C)
500
600
No
Finish
Yes
Calculate the reference
temperature at points P along
the line A–A − see Figure 20
Calculate the torsion resistance
and interaction with shear using
section 6.3 of Eurocode 2, Part 1–1
109
Unbraced structures
BmaZl[^^gghm^]maZm_hk\henfglZg]pZeel%pa^gnlbg`ma^mZ[neZk
f^mah]%[kZ\^]lmkn\mnk^lhgerZk^\hglb]^k^]bgIZkm*+'MablblZelh
mkn^_hkma^lbfieb_b^]\Ze\neZmbhgf^mah]ik^l^gm^]bg:gg^q;',%
pab\abl]^l\kb[^]ZlZshg^f^mah]_hkma^ZgZerlblh_\henfglpbma
lb`gb_b\Zgml^\hg]hk]^k^__^\ml'
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mh;L>G*22+*lmZm^lmaZm%Zmma^]bl\k^mbhgh_ma^]^lb`g^k%ma^
mZ[neZkf^mah]fZr[^nl^]_hk`^g^kZe]^lb`gZg]\kbmb\Ze\henfgl
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shg^f^mah]'
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ZoZbeZ[e^mhma^^g`bg^^k'
Ln\aZgZiikhZ\aphne][^nglZ_^pa^k^ma^f^f[^klbgma^_bk^
shgîkhob]^maîk^]hfbgZgmf^Zglh_lmkn\mnkZelmZ[bebmrZg]bg
ln\a\Zl^lZ]oZg\^]\Ze\neZmbhgf^mah]lZg]li^\bZeblmZ]ob\^fZr[^
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<_]kh['/
:[j[hc_dWj_ede\b_d[7¸7je[dWXb[[lWbkWj_ede\h[\[h[dY[
temperature y p at point P
<_]kh[(&
The reference temperature y piêkbZX[[lWbkWj[ZWbed]j^[b_d[7¸7\eh
the calculation of torsion resistance
x
e2 = 0
d
y p in links
A
h
A
A
A
A
h c,ef
e1
A c,eff
c,ef
= MIN {2.5 (
A
A
A
A
A
); (
References
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2
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) ;KBMBLALM:G=:K=LBGLMBMNMBHG'G:mh;L>G*22+*+%NDGZmbhgZe:gg^qmh>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^llmkn\mnkZe_bk^
]^lb`g';LB%+)).'
* ;:BE>R%<'DAHNKR%@'@nb]^mhmaî^k_hkfZg\^h_\hg\k^m^lmkn\mnk^lbg_bk^'Ma^<hg\k^m^<^gmk^%]n^+))2'
+ ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22**+%>nkh\h]^*3:\mbhglhglmkn\mnk^l'@^g^kZeZ\mbhgl:\mbhglhglmkn\mnk^l^qihl^]mh_bk^'
;LB%+))+'
6
;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22)%>nkh\h]^3;Zlblh_lmkn\mnkZe]^lb`g';LB%+))+'
- G:K:R:G:G%KL;KHHD>K%HAhpmh]^lb`g\hg\k^m^lmkn\mnk^lmh>nkh\h]^+3Bgmkh]n\mbhgmh>nkh\h]^l'Ma^<hg\k^m^<^gmk^%+)).'
. ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+**%>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^lZg]kne^l_hk[nbe]bg`l';LB%+))-'
9
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'& M A>BGLMBMNMBHGH?LMKN<MNK:E>G@BG>>KL'FZgnZe_hkma^]^lb`gh_\hg\k^m^[nbe]bg`lmkn\mnk^lmh>nkh\h]^+'BLmkn\m>%+))/'
'' ;
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'( ;KBMBLALM:G=:K=LBGLMBMNMBHG'I=//10%;Z\d`khng]iZi^kmhma^NDGZmbhgZe:gg^qmh;L>G*22+**';LB%+))/
') ;
KHHD>K%HFHLL%K'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lmh>nkh\h]^+3;^Zfl'Ma^<hg\k^m^<^gmk^%+))/'
110
Members of the Steering Group
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PL:mdbgl=MBIkhc^\mH_Ë\^k
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Members of the Concrete Industry Eurocode 2 Group (CIEG)
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<B(L_[
N=<
/+-')*+'-'))*'/,
How to Design Concrete Structures using Eurocode 2
This publication brings together in one place “How to...”
guidance for the design, specification and detailing of a broad
range of concrete elements.
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Zg]\hgË]^gmermhma^]^lb`gh_\hg\k^m^lmkn\mnk^l'
Dr Andrew BondblZND]ê^`Zm^hgma^<>G(M<+.)(L<0
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How to Design Concrete Ltructures using Eurocode 2

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