How to Design Concrete Ltructures using Eurocode 2
Transkript
How to Design Concrete Ltructures using Eurocode 2
:cementZg]concretebg]nlmkrin[eb\Zmbhg Ahpmh=^lb`g<hg\k^m^ Lmkn\mnk^lnlbg`>nkh\h]^+ A J Bond F:FL\=B<Ia=FB<><>g` O Brooker ;>g`<>g`FB<>FBLmkn\m> A S Fraser ;>g`Ia=<>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 ;>g`Ia=<>g`?B<> R M Moss;L\Ia==B<<>g`FB<>FBLmkn\m> R S Narayanan?K>g` R Webster<>g`?BLmkn\m> Foreword Ma^bgmkh]n\mbhgh_>nkhi^ZglmZg]Zk]lmhND\hglmkn\mbhgblZlb`gbË\Zgm^o^gm'Ma^m^g]^lb`glmZg]Zk]l%dghpg Zlma^>nkh\h]^l%pbeeZ__^\mZee]^lb`gZg]\hglmkn\mbhgZ\mbobmb^lZl\nkk^gm;kbmblaLmZg]Zk]l_hk]^lb`gZk^]n^ mh[^pbma]kZpgbg+)*)Zmma^eZm^lm';L1**)%ahp^o^k%aZlZg^Zkeb^kpbma]kZpZe]Zm^h_FZk\a+))1'Ma^Zbf h_mablin[eb\ZmbhgblmhfZd^ma^mkZglbmbhgmh>nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^lZl^ZlrZlihllb[e^[r ]kZpbg`mh`^ma^kbghg^ieZ\^d^rbg_hkfZmbhgZg]\hff^gmZkrk^jnbk^]_hkma^]^lb`gZg]]^mZbebg`h_mrib\Ze \hg\k^m^^e^f^gml' Ma^\^f^gmZg]\hg\k^m^bg]nlmkrk^\h`gbl^]maZmZln[lmZgmbZe^__hkmpZlk^jnbk^]mh^glnk^maZmma^ND]^lb`g ikh_^llbhgphne][^Z[e^mhnl^>nkh\h]^+jnb\der%^__^\mbo^er%^_Ë\b^gmerZg]pbma\hgË]^g\^'Pbmalniihkm _khf`ho^kgf^gm%\hglnemZgmlZg]k^e^oZgmbg]nlmkr[h]b^l%ma^<hg\k^m^Bg]nlmkr>nkh\h]^+@khni!<B>@" pZl_hkf^]bg*222Zg]mabl@khniaZlikhob]^]ma^`nb]Zg\^_hkZ\h&hk]bgZm^]Zg]\heeZ[hkZmbo^ZiikhZ\amh ma^bgmkh]n\mbhgh_>nkh\h]^+'IZkmh_ma^hnminmh_ma^<B>@ikhc^\mpZlma^m^\agb\Ze\hgm^gm_hk0h_ma^** \aZim^klbgmablin[eb\Zmbhg'Ma^k^fZbgbg`\aZim^klaZo^[^^g]^o^ehi^][rMa^<hg\k^m^<^gmk^' Acknowledgements Ma^\hgm^gmh_<aZim^kl*Zg],mh1p^k^ikh]n\^]ZliZkmh_ma^ikhc^\m>nkh\h]^+3mkZglbmbhg_khfNDmh >nkhi^Zg\hg\k^m^]^lb`glmZg]Zk]l'Mablikhc^\mpZliZkm_ng]^][rma^=MBng]^kma^IZkmg^klbgBgghoZmbhg l\a^f^'Ma^e^Z]iZkmg^kpZl;kbmbla<^f^gm:llh\bZmbhg'Ma^phkdpZl\Zkkb^]hnmng]^kma^`nb]Zg\^h_ma^ <hg\k^m^Bg]nlmkr>nkh\h]^+@khniZg]ho^kl^^g[rZLm^^kbg`@khnih_ma^<B>@!f^f[^klZk^eblm^]hgbglb]^ [Z\d\ho^k"' IZkmb\neZkmaZgdlZk^]n^mhKh[bgPabmme^%m^\agb\Ze^]bmhkmhma^<>G(M<+.)(L<+\hffbmm^^!ma^\hffbmm^^ k^lihglb[e^_hklmkn\mnkZe>nkh\h]^l"%pahaZlk^ob^p^]Zg]\hff^gm^]hgma^\hgm^gml'MaZgdlZk^Zelh]n^mh ChagD^eerZg]<akbl<e^ZkpahaZo^\hgmkb[nm^]mhbg]bob]nZe\aZim^kl' @beebZg;hg]%BllrAZko^r%D^obgLfbmaZg]ma^]^lb`g^klZmF^]bZZg]=^lb`g:llh\bZm^lZg]Fb\aZ^e;nk[kb]`^Em] aZo^ZelhfZ]^^ll^gmbZe\hgmkb[nmbhglmhma^ikh]n\mbhgh_mablin[eb\Zmbhg' Published by The Concrete Centre Kbo^klb]^Ahnl^%-F^Z]hpl;nlbg^llIZkd%LmZmbhg:iikhZ\a%;eZ\dpZm^k%<Zf[^ke^r%Lnkk^r@N*02:; Tel:$--!)"*+0//)/1))Fax:$--!)"*+0//)/1)*www.concretecentre.com <<BI¾))/ In[ebla^]=^\^f[^k+))/%k^obl^]L^im^f[^k+))2 BL;G*&2)-1*1&-&* Ikb\^@khniI ¡FI:&Ma^<hg\k^m^<^gmk^' I^kfbllbhgmhk^ikh]n\^^qmkZ\ml_khf;kbmblaLmZg]Zk]lbl`kZgm^][r;kbmblaLmZg]Zk]lBglmbmnmbhg' ;kbmblaLmZg]Zk]l\Zg[^h[mZbg^]_khf;LB<nlmhf^kL^kob\^l%,12<ablpb\dAb`aKhZ]%Ehg]hgP--:E' Tel:$--!)"+)122/2))*email:\l^kob\^l9[lb&`eh[Ze'\hf <<BIin[eb\ZmbhglZk^ikh]n\^]hg[^aZe_h_ma^<^f^gmZg]<hg\k^m^Bg]nlmkrIn[eb\Zmbhgl?hknf¾Zgbg]nlmkr bgbmbZmbo^mhin[eblam^\agb\Ze`nb]Zg\^bglniihkmh_\hg\k^m^]^lb`gZg]\hglmkn\mbhg' <<BIin[eb\ZmbhglZk^ZoZbeZ[e^_khfma^<hg\k^m^;hhdlahiZmwww.concrete bookshop.com M^e3$--!)"0))-&/)0000 :eeZ]ob\^hkbg_hkfZmbhg_khfFI:&Ma^<hg\k^m^<^gmk^blbgm^g]^]hger_hknl^bgma^ND[r_hkmahl^pahpbee^oZenZm^ma^lb`gbË\Zg\^Zg]ebfbmZmbhgl h_bml\hgm^gmlZg]mZd^k^lihglb[bebmr_hkbmlnl^Zg]Ziieb\Zmbhg'GhebZ[bebmr!bg\en]bg`maZm_hkg^`eb`^g\^"_hkZgrehllk^lnembg`_khfln\aZ]ob\^hk bg_hkfZmbhgblZ\\^im^][rFI:&Ma^<hg\k^m^<^gmk^hkbmlln[\hgmkZ\mhkl%lniieb^klhkZ]oblhkl'K^Z]^kllahne]ghm^maZmin[eb\Zmbhgl_khfFI:&Ma^ <hg\k^m^<^gmk^ Zk^ ln[c^\m mh k^oblbhg _khf mbf^ mh mbf^ Zg] lahne] ma^k^_hk^ ^glnk^ maZm ma^r Zk^ bg ihll^llbhg h_ ma^ eZm^lm o^klbhg' IZkm h_ mabl in[eb\ZmbhgaZl[^^gikh]n\^]_heehpbg`Z\hgmkZ\mieZ\^][rma^=^iZkmf^gm_hkMkZ]^Zg]Bg]nlmkr!=MB"4ma^ob^pl^qik^ll^]Zk^ghmg^\^llZkbermahl^ h_ma^=MB' Ikbgm^][rFb\aZ^e;nk[kb]`^Em]%FZb]^ga^Z]' Ahpmh=^lb`g<hg\k^m^ Lmkn\mnk^lnlbg`>nkh\h]^+ <hgm^gml 1. 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' 21 A:KKBLHG%M:;KHHD>K%H'Ahpmhnl^;L1.))pbma;L1**)!M<<(),(**"'Ma^<hg\k^m^<^gmk^%+)).' 22 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L---23Li^\bË\Zmbhg_hk\Zk[hglm^^e[Zkl_hkma^k^bg_hk\^f^gmh_\hg\k^m^';LB%+)).' , 5 - ! 54/,3/53,1K, ' 23 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*))1)3Lm^^e_hkma^k^bg_hk\^f^gmh_\hg\k^m^¾P^e]Z[e^k^bg_hk\bg`lm^^e¾@^g^kZe';LB%+)).' 54/,3/53,1K, ,;:& #, 2(3 - ! 24 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*,/0)3>q^\nmbhgh_\hg\k^m^lmkn\mnk^l¾IZkm*3<hffhg';LB%]n^+)*)' 4*K,*5K*G *' $ ! 4 $! < 25 MA><HG<K>M>LH<B>MR'<L*.+3GZmbhgZelmkn\mnkZe\hg\k^m^li^\bË\Zmbhg_hk[nbe]bg`\hglmkn\mbhg%mabk]^]bmbhg'Ma^Lh\b^mr%+))-' 8 !BJGB78F<:A6BA6E8G8FGEH6GHE8FHF<A:HEB6B78 8GG<A:FG4EG87 O Brooker A: A: %" %"*GEH6G The design process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esign life +;878F<:A?<989BE4FGEH6GHE8<F:<I8A<AHEB6B78 .&.+#./-0 /0-( !".&$* 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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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inimum 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 KC 7HE45<?<GL 9<E8E8F<FG4A68 4A7D 78I <F4A4??BJ4A68J;<6;F;BH?758@478<AG;878F<:A9BE 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 F<:A<9<64AG?L@B7<9<8FG;84CCEB46;G4>8A<AHEB6B78 *J4F !G"!;L"h_ma^NDG:blghehg`^koZeb]' E8I<F87<A4A7+45?8 A*B9G;8,#&<FAB?BA:8EI4?<7 +))/ +;8I4E<BHF8KCBFHE86?4FF8F9EB@*4E8:<I8A<A+45?8 *8?86G87 E86B@@8A74G<BAF4E8:<I8A<A+45?8BAC4:89BEG;86BA6E8G8 FGE8A:G; @<A<@H@68@8AGE4G<B @<A<@H@6BA6E8G86BI8E4A7@4K<@H@ 68@8AG6BAG8AG9BEI4E<BHF8?8@8AGF<A4FGEH6GHE854F87BAG;88KCBFHE8 B9G;4G8?8@8AG +;<F<FG4>8A9EB@;4CG8E BE<:<A4??LCH5?<F;874F +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 4F * %<A<@H@54EF † %8G;B7<A7<64G8F9BE)4A7m 9< 4A7@4L58HF87 *88&QQ+45?8 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 9<E8E8F<FG4A68@4LFG<??5864EE<87BHG5LE898EE<A:GBG45?8FGB 78G8E@<A8G;8@<A<@H@6BI8E4A77<@8AF<BAF9BEI4E<BHF8?8@8AGF 4FF8GBHG58?BJ )4G;8EG;4A:<I<A:G;8@<A<@H@6BI8E G;8G45H?4E@8G;B7<F54F87 BAAB@<A4?4K<F7<FG4A68 F88<:HE8 +;<F<FG;87<FG4A689EB@G;8 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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able 10 Minimum dimensions and axis distances for reinforced concrete slabs Standard fire resistance )" )" )" %F %F %F Minimum dimensions (mm) 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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 X0 333 ?? )86B@@8A787G;4GG;<F8KCBFHE8<FABG4CC?<87GBE8<A9BE6876BA6E8G8 "AG8EA4?8?8@8AGF 8K68CG;H@<7 ?B64G<BAF XC1 333 ?? BE ) HE<876BA6E8G8 <A:EBHA7 6BA7<G<BAF 8 XC2 333 333 BE ) "AG8EA4?@4FF 6BA6E8G8 AC-1 ??8K68CG "-- 333 BE BE BE BE) ) ) ) XF1 ??8K68CG "-- 333 BE BE BE) ) ) XF3 ??8K68CG "-- 333 : BE )/: XF3 4<E 8AGE4<A87 ??8K68CG "-- 333 333 C?HF4<E :; C?HF4<E :; BE(- C?HF4<E : ; = BE(- ?? 333 333 ""- """ 333 333 333 333 333 333 333 333 333 333 *88 * """ "-- 333 333 333 333 333 ""- """ 333 333 333 333 333 %" "" ""* *)( 333 333 333 333 333 *88 * """ "-- 333 333 333 333 333 XF4 %" "" ""* *)( 333 333 333 333 333 *88 * : XF4 4<E 8AGE4<A87 ""- """ """ 333 333 333 333 333 : ; : ; : ; 333 333 333 *88 * ""- """ 333 333 333 *88 * - """ 333 333 333 XF3 or XF4 %" "" ""* *)( 333 333 333 *88 * : -8EG<64?FHE9468 CEBG86G879EB@ 7<E86GE4<A94?? KCBF87I8EG<64? FHE9468F 333 XC3 XC4 KCBF87;BE<MBAG4? FHE9468F ?8@8AGFFH5=86G GB4<E5BEA8 6;?BE<78F 333 XD19 4EC4E>786>F4A7 4E84FFH5=86GGB 78<6<A:FCE4L -8EG<64?8?8@8AGF FH5=86GGB78<6<A: FCE4L4A79E88M<A: 333 XD39 XF2 4EC4E>786>F E4@CF4A78KG8EA4? 4E84FFH5=86GGB 9E88M<A:4A7 78<6<A:F4?GF KCBF87I8EG<64? FHE9468FA84E6B4FG KCBF87;BE<MBAG4? FHE9468FA84E6B4FG ?? XF1 %" "" ""* *)( %" "" ""* *)( XS19 Key a +;<FG45?86B@CE<F8F4F8?86G<BAB96B@@BA8KCBFHE86?4FF6B@5<A4G<BAF )8DH<E8@8AGF9BEBG;8EF8GFB98KCBFHE86?4FF8F 8 : / /*4A7/*F;BH?7 5878E<I879EB@* AA8K b *88*+45?8 %"<F(BEG?4A768@8AG ""GB"-4E868@8AG6B@5<A4G<BAF c BECE8FGE8FF876BA6E8G8G;8@<A<@H@FGE8A:G;6?4FFF;BH?758 14 d e f g h j D 6 78I <F4A4??BJ4A689BE78I<4G<BAF BEF86G<BAF?8FFG;4A@@G;<6>E898EGB* ?FB478DH4G89BE8KCBFHE86?4FF/ E88M8G;4JE8F<FG<A:4::E8:4G8FF;BH?758FC86<9<87 <E8AGE4<A876BA6E8G8<FE8DH<E87 +;<FBCG<BA@4LABG58FH<G45?89BE4E84FFH5=86GGB F8I8E845E4F<BA 333 &BGE86B@@8A787 "A7<64G8FG;4G6BA6E8G8 DH4?<GL<A68??GBG;8?89G F;BH?7ABG58E87H687 +'@^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< 8 ABG4F4A4?G8EA4G<I8 ?B476B@5<A4G<BA BE:?B54?4A4?LF<F G;8<@C8E986G<BAF@4L58 E8CE8F8AG875L4A<A6?<A4G<BAy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y < Ka ; Ka @ J;8E8 a ; R( GB58G4>8A4FABG?8FFG;4AABE:E84G8EG;4A a @ 1 )20.5 ( <FG;8;8<:;GB9G;85H<?7<A:<A@8GE8F ) <FG;8AH@58EB9I8EG<64?@8@58EF6BAGE<5HG<A:GBG;8;BE<MBAG4? 9BE68<AG;85E46<A:FLFG8@ Figure 5 +;889986GB9G;8<A6?<A4G<BA@4L58E8CE8F8AG875LGE4AFI8EF89BE68F4G 846;?8I8?4A7<A6?H787<AG;84A4?LF<F4?BA:J<G;BG;8E46G<BAFF88 <: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 J;8E84 4A75 4E8?BA:<GH7<A4?9BE68F6BAGE<5HG<A:GB< "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 * GBG4??B479EB@,$*6B@5<A4G<BA FE8D 4E84B9E8<A9BE68@8AG4GG;8,$* FCEBI 4E84B9E8<A9BE68@8AGCEBI<787 d E4G<BB9E87<FGE<5HG87@B@8AGGB8?4FG<6@B@8AG To determine stress in the reinforcement (ss), calculate the ratio Gk/Qk, read up the graph to the appropriate curve and read across to determine ssu . As,req 1 ss can be calculated from the expression: ss = ssu As,prov d ( )( ) 15 +'@^mmbg`lmZkm^] References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C6=2E:@?D9:A@74@?4C6E6 @CD:>A=:4:EJ2?572>:=:2C:EJE96>6E9@5 AC6D6?E6596C6:DE96D:>A=:7:65C64E2?8F=2CDEC6DD3=@4< H9:49:D D:>:=2CE@E92E7@F?5:?*D66:8FC6 +96FC@4@568:G6DC64@>>6?52E:@?D7@CE9656D:8?@74@?4C6E6FAE@ 4=2DD !@H6G6C 7@C4@?4C6E68C62E6CE92?4=2DD E96DEC6DD 3=@4<:D>@5:7:65 "E:D:>A@CE2?EE@?@E6E92E4@?4C6E6DEC6?8E9:D32D65 @?E964J=:?56CDEC6?8E92?5?@EE964F36DEC6?8E9:6 7@C4=2DD E964J=:?56CDEC6?8E9:D%(2 H96C62DE964F36DEC6?8E9:D%(2 ,-2,*:054 FC@4@5692DEH@2=E6C?2E:G6>6E9@5D@756D:8?:?87@C567=64E:@? 6:E96C3J=:>:E:?8DA2?E@56AE9C2E:@@C3J2DD6DD:?8E96E96@C6E:42= 567=64E:@?FD:?8E96IAC6DD:@?D8:G6?:?E96FC@4@56 +96=2EE6C :D562=EH:E9:?56E2:=:?92AE6C @C:8:?2==JAF3=:D9652D "* %$ "+"* %$)7 +96DA2?E@56AE9C2E:@DD9@F=56?DFC6E92E567=64E:@?:D=:>:E65E@ DA2? 2?5E9:D:DE96AC@465FC6AC6D6?E65:?:8FC6 ,*85( !,03/,),('5(&7$1*8/$5675(66%/2&.)25&21&5(7(8372&/$66)520852&2'( ,*85( 52&('85()25$66(66,1*'()/(&7,21 (7(50,1$7,212)67((/675(66 Approximate steel stress at SLS for As,req, ,ssusu A s ,*85( #$"$ ,:,8304,)(90* -8530.;8, ,:,8304,(*:58 5880)),+58=(--2,92()9 D -=D CA - 09-2(4.,)8,(+:/(4+= 0980))8,(+:/ :/,8=09, ,:,8304,(*:58 &/,8,:/,92()96(4,>*,,+93(4+0:9;6658:9 )80::2,6(8:0:0549 ,-:/,8=09, ,:,8304,(*:58 s9 &/,8,s9 #:8,99048,04-58*,3,4:(:9,8<0*,()020:? 2030:9:(:,9,,0.;8, s9 3(?),(99;3,+:5), !(0, 5:, 9685< B 98,7E+ %(:054(244,> 4*8,(9, 9685< 9)(90* > >>C*:;(2 5 ',9 /,*1*5362,:, A $/,;85*5+,09(3)0.;5;98,.(8+04.204,(804:,8652(:054 :09;4+,89:55+:/(::/09 =(9:/,04:,4:0545-:/,+8(-:04.*5330::,,(4+0904204,=0:/*;88,4:%68(*:0*, 20 $5+,:,8304,9:8,9904:/,685<0+,+8,04-58*,3,4:s9 *(2*;2(:, :/,8(:0511 8,(+;6:/,.8(6/:5:/,(6685680(:,*;8<,(4+ 8,(+(*8599:5+,:,8304,s9; 98,7 s9 *(4),*(2*;2(:,+-853:/,,>68,99054 s9 s9; 9685< d ,'LeZ[l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v '& 5(6,67$1&(2)0(0%(56:,7+2876+($55(,1)25&(0(17 $ r ))(&7,9('(37+ d 00 A6 bd = > k +23=656C:G657C@> , )54 ! r I 4< N! 4< H96C6! 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GDA5A67 ,34>7?3K47GE76FA67F7D?;@747@6;@9?A?7@FE3@6 E:73D8AD57E8AD473?E BDAH;676F:7@AF7EFAF:7F34>73D7A4E7DH76 5D5B=9>5 6B?= G^Zkfb]]e^h_^g]liZg F8;DEF;@F7D;ADEGBBADF F?;66>7A8;@F7D;ADEB3@E A8EB3@?A?7@F !+($4 )'-.!@ $J]" ] )')2)@ )')2)"" ] e$)'*))J] e ¾)')2-!@ R ]$J ]""e )'/,!@] $J3]"Z !C L P .5C )'.)!@] $J]" %?3?=@B5CC9?>B59>6?B35=5>DB5AE9B54 (; ]?3K47GE7636<357@FFAF:7;@F7D;ADEB3@ $ )'..!@ $J]"fZr[^nl^]Z]cZ\^gmmhma^bgm^kbhkliZg 16(5 *76;EFD;4GF;A@A8EGBBADF?A?7@FE4K:3E477@;@5>G676 BB>;534>7FAAD?AD7EB3@EA@>K3@6I:7D7= O = %;@;?G?EB3@P>A@97EFEB3@ eblma^liZg%@ " ;EF:7EB3@ ]blma^]^lb`goZen^h_i^kfZg^gmZ\mbhgl!ZmNEL"Zg]J ;EF:7FAF3>A8F:7-$+B7D?3@7@F35F;A@E ;EF:7FAF3>]blma^]^lb`g A8F:7-$+H3D;34>735F;A@E oZen^h_oZkbZ[e^Z\mbhgl!ZmNEL"' &2D19><5F5B1B= 6B?=*12<5?BEC5 1 N 2 L Values for K ’ 1<3E<1D5<5F5B1B= 6B?= N P 1 1<3E<1D53?=@B5CC9?> B59>6?B35=5>DB5AE9B546B?= C ) *')) )'+)1Z *) )'2) )'*1+Z *. )'1. )'*/1 +) +. )'1) )'0. )'*., )'*,0 C3 )'0) 853;=9>9=E=B59>6?B35=5>D B5AE9B5=5>DCC55*12<5 3D= D C=9> G85B53; M I; )'*+) 1 HN4 H 2 I4 1<3E<1D5D5>C9?> B59>6?B35=5>DB5AE9B546B?= C Table 5 Table 6 z/d for singly reinforced rectangular sections Minimum percentage of required reinforcement z/d I4 C C3 I4 fck fctm Minimum percentage (0.26 fctm / fyka) ©)'). )' 2.) +. +'/ )'*, )')/ )'2-- )'*- )'1./ +1 +'1 )'*- )')0 )'2,- )'*. )'1-, ,) +'2 )'*. )')1 )'2+- )'*/ )'1,) ,+ ,') )'*/ )')2 )'2*, )'*0 )'1*/ ,. ,'+ )'*0 )'*) )'2)+ )'*1 )'1)+ -) ,'. )'*1 )'12* )'*2 )'010 -. ,'1 )'+) )'11) )'+) )'00* .) -'* )'+* Z P z/d )'1/1 K )'*, )'*+ C3N 853;=1H9=E=B59>6?B35=5>DB5AE9B5=5>DCC=1H 3 6?BD5>C9?>?B3?=@B5CC9?>B59>6?B35=5>D?EDC945<1@<?31D9?>C Key a Bmblh_m^gk^\hff^g]^]bgma^NDmaZmDÃlahne][^ebfbm^]mh)'*/1mh^glnk^]n\mbe^_Zbenk^' Bmblh_m^gk^\hf^g]^]bgma^NDmaZm D£lahne][^ebfbm^]mh)'*/1mh^glnk^]n\mbe^_Zbenk^' )'** N P d (redistribution ratio) K ’ % redistribution K 2 G85B5 1<3E<1D5D5>C9?>B59>6?B35=5>D B5AE9B546B?= C I4 Table 4 ,) ?=@B5CC9?>B59>6?B35=5>D B5AE9B54 )')//@ "" ] e$)')1/J] e ¾)')0.!@ R ]$J ]""e F;@F7D;ADEGBBADFE %? 3; 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ ,*74( GDA5A67A887DEH3D;AGE?7F:A6E8AD67F7D?;@;@9F:7EFD7EEEFD3;@ D7>3F;A@E:;BA85A@5D7F7 ADE;?B>;5;FK3@683?;>;3D;FKF:7?7F:A6 BD7E7@F76:7D7;EF:7E;?B>;8;76D75F3@9G>3DEFD7EE4>A5= I:;5:;E E;?;>3DFAF:3F8AG@6;@+E77;9GD7 !6476,0&.,0$6,10/(6+1' ?>3B5D5CDBED9>3?=@B5CC9?> GDA5A679;H7ED75A??7@63F;A@E8ADF:767E;9@A85A@5D7F7GBFA 5>3EE !AI7H7D 8AD5A@5D7F79D73F7DF:3@5>3EE F:7 EFD7EE4>A5=;E?A6;8;76 "F;E;?BADF3@FFA@AF7F:3F5A@5D7F7EFD7@9F: ;E43E76A@F:75K>;@67DEFD7@9F:3@6@AFF:75G47EFD7@9F:;7 8AD 5>3EE F:75K>;@67DEFD7@9F: 5= ;E%(3 I:7D73EF:75G47 EFD7@9F:;E%(3 y #?>79DE49>1< B59>6?B35=5>D9>D5>C9?> ,5BD931<C851B B59>6?B35=5>D ,5BD931<C851B ,*74( 41&('74()14'(6(4/,0,0*8(46,&$.5+($44(,0)14&(/(06 GDA5A67;@FDA6G57EF:7EFDGF;@5>;@3F;A@?7F:A68ADE:73D53B35;FK 5:75=E "@F:;E?7F:A6F:7E:73D;ED7E;EF764K5A@5D7F7EFDGFE35F;@9;@ 5A?BD7EE;A@3@6E:73DD7;@8AD57?7@F35F;@9;@F7@E;A@ START Determine vEd where vEd = design shear stress [ vEd = VEd /(bwz) = VEd /(0 9. bwd)] Determine the concrete strut capacity v Rd, max cot y = 2.5 from Table 7 Is vEd < vRd,max coty = 2.5? No Is v Ed < v Rd,max cot y = 1.0? (see Table 7) Yes (cot y = 2.5) No Redesign section Yes Determine y from: vEd y = 0.5 sin -1 0.20 fck (1 – fck /250) T V Calculate area of shear reinforcement: vEd bw Asw = s fywd cot y Check maximum spacing for vertical shear reinforcement: s l, max = 0.75 d ,:73@9>7A8F:75A@5D7F7EFDGFH3D;7E 67B7@6;@9A@F:7E:73D8AD57 3BB>;76E77;9GD7 ,:7BDA576GD78AD67F7D?;@;@9F:7E:73D53B35;FK A83E75F;A@;EE:AI@;@;9GD7I:;5:;@5>G67E-#&H3>G7E3@6;E ;@F7D?EA8E:73DEFD7EE;@F:7H7DF;53>B>3@7D3F:7DF:3@3H7DF;53>8AD57 3E9;H7@;@GDA5A67 /:7D7E:73DD7;@8AD57?7@F;ED7CG;D76 F:7@ F:73@9>7A8F:75A@5D7F7EFDGFE:AG>64753>5G>3F76 AD?3@KFKB;53> 473?EF:7?;@;?G?3@9>7A8EFDGFI;>>3BB>KI:7@5AFy ADy Q;7 8AD5>3EE 5A@5D7F7F:7EFDGF3@9>77J5776EQ A@>K I:7@F:7E:73DEFD7EE;E9D73F7DF:3@ & ??2 D787DFA,34>7 EI;F:+ F:7D7;E3?3J;?G?B7D?;FF76E:73D 53B35;FK +*6?3J I:7@5AFy AD y Q 4GFF:;E;E@AFD7EFD;5F76FA%(33E;@ + Deflection >nkh\h]^+aZlmphZem^kgZmbo^f^mah]l_hk\a^\dbg`]^_e^\mbhg% ^bma^kZebfbmbg`liZg&mh&]^imakZmbhfZr[^nl^]hkma^ma^hk^mb\Ze ]^_e^\mbhg\Zg[^Zll^ll^]nlbg`ma^^qik^llbhgl`bo^gbgma^<h]^' Ma^eZmm^kbl]^Zempbmabg]^mZbebg<aZim^k1%hkb`bgZeerin[ebla^]Zl '/ =^_e^\mbhg\Ze\neZmbhgl•' Ma^liZg&mh&]^imakZmbhllahne]^glnk^maZm]^_e^\mbhgblebfbm^]mh liZg(+.)Zg]mablblma^ikh\^]nk^ik^l^gm^]bg?b`nk^/' "$%.( ,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( ,*74( 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\Zgmbe^o^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 *+ rà 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ ,*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 G85B5 G 1DCE@@?BD 566 9>C@1> ,*74( .$&,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`^' Ma^ihlbmbhgh_ma^g^nmkZeZqbllahne] [^]^m^kfbg^]% Zg]ma^gma^ Zk^Zh_k^bg_hk\^f^gm\Zg[^\Ze\neZm^] ]^i^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&]^ima]^_e^\mbhg\a^\dlnlbg`kZmbhh_ m^glbhgk^bg_hk\^f^gmlahne][^[Zl^]hgZk^Zh_\hg\k^m^Z[ho^ \^gmk^h_m^glbhglm^^e' 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^llbgma^o^kmb\ZeieZg^[^mp^^gma^_eZg`^Zg]p^[lahne] [^Zll^ll^]Z\\hk]bg`mhl^\mbhg/'+'-Zg]?b`nk^/'0h_ma^>nkh\h]^ !k^ikh]n\^]a^k^Zl?b`nk^*,"' Ma^\aZg`^bg_hk\^bgma^_eZg`^\Zg [^Zll^ll^]_khfma^fhf^gmZg]e^o^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]ma^ihbgmpa^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[^ma^e^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`ma^ehg`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^k^iZkmb\neZkermabg_eZg`^lZk^nl^]ma^k^blZ]^jnZm^k^bg_hk\^f^gm' Ma^ehg`bmn]bgZela^Zk\ZiZ\bmrbl[Zl^]hgma^oZkbZ[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`ma^oZen^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^lbs^ienl.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^^e e(] LiZg&mh&]^imakZmbh :l+ :k^Zh_\hfik^llbhglm^^e F =^lb`gfhf^gmZmma^NEL :l% ikho :k^Zh_m^glbhglm^^eikhob]^] q =^imamhg^nmkZeZqbl !]&s"()'- :l% k^jÃ] :k^Zh_m^glbhglm^^ek^jnbk^] qfZq Ebfbmbg`oZen^_hk]^imamhg^nmkZeZqbl !d ¾)'-"] pa^k^d ©*') [^__ >__^\mbo^_eZg`^pb]ma s E^o^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^ ^eZlmb\[^g]bg`fhf^gm gf IZkmbZe_Z\mhk_hkfZm^kbZeikhi^kmb^l *'*._hkk^bg_hk\^f^gm!gl" *'._hk\hg\k^m^!g\" r) K^_^k^g\^k^bg_hk\^f^gmkZmbh R_\d (*))) r K^jnbk^]m^glbhgk^bg_hk\^f^gmZmfb]&liZg mhk^lblmma^fhf^gm]n^mhma^]^lb`g ehZ]l!hkZmlniihkm_hk\Zgmbe^o^kl" :l([] !_hkk^\mZg`neZk[^Zfl" rà K^jnbk^]\hfik^llbhgk^bg_hk\^f^gmZm fb]&liZgmhk^lblmma^fhf^gm]n^mhma^ ]^lb`gehZ]l!hkZmlniihkm_hk\Zgmbe^o^kl" :l+([] [p Pb]mah_l^\mbhg% hkpb]mah_p^[hg_eZg`^][^Zfl ] >__^\mbo^]^ima ]+ >__^\mbo^]^imamh\hfik^llbhgk^bg_hk\^f^gm _\] =^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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ .'<henfgl R Moss;L\%Ia=%=B<%<>g`%FB<>%FBLmkn\m>O Brooker;>g`%<>g`%FB<>%FBLmkn\m> 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^gmZkrhgma^ikhoblbhglpbmabgma^>nkh\h]^'Ma^eZrhnmZg]\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`bo^ikbg\bie^lZg]`^g^kZeZiieb\Zmbhgkne^lbgma^\h]^l Zg]_hk]^mZbe^]Ziieb\Zmbhgkne^lmh[^ik^l^gm^]bghma^klhnk\^lln\aZl m^qm[hhdlhk`nb]Zg\^]h\nf^gml' <aZim^k*%hkb`bgZeerin[ebla^]ZlBgmkh]n\mbhgmh>nkh\h]^l%ab`aeb`am^]ma^ 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^]makhn`ahnmmablin[eb\Zmbhg%bg\en]bg`oZen^lmaZmZk^^f[^]]^]bg ]^kbo^]_hkfneZ^'!=^kboZmbhgl\Zg[^_hng]Zmppp'^nkh\h]^+'bg_h'":_neeeblm h_lrf[helk^eZm^]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^glbhglaZo^ik^obhnler[^^g ]^m^kfbg^]]nkbg`\hg\^imnZe]^lb`ghk[rnlbg`jnb\d]^lb`gf^mah]l%_hk ^qZfie^mahl^ik^l^gm^]bg>\hghfb\\hg\k^m^_kZf^^e^f^gml '<henfglbs^l lahne]ghm[^lb`gb_b\Zgmer]b__^k^gm_khfmahl^h[mZbg^]nlbg`;L1**)'Lm^il *mh-h_MZ[e^*Zk^\ho^k^][r^Zkeb^k\aZim^klZg]ma^g^qmlm^iblma^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^%ahp^o^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](hkab`a_bk^k^lblmZg\^i^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`^,. Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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 , =^m^kfbg^pab\a\hf[bgZmbhglh_Z\mbhglZiier *3Bgmkh]n\mbhgmh>nkh\h]^l NDG:mh;L>G*22)MZ[e^lG:':*'*Zg]G:':*'+!;" - :ll^ll]nkZ[bebmrk^jnbk^f^gmlZg]]^m^kfbg^\hg\k^m^lmk^g`ma +3@^mmbg`lmZkm^] ;L1.))3+))/ . <a^\d\ho^kk^jnbk^f^gml_hkZiikhikbZm^_bk^k^lblmZg\^i^kbh] +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 Minimum dimensions (mm) 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^^__^\mbo^e^g`mah_Z[kZ\^]\henfgng]^k_bk^\hg]bmbhgleh%_b©,f'Ma^oZen^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]^eZieh\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^koZmbo^er[^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^kgZmbo^er Minimum dimensions (mm) 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^%Zemahn`a f^mah]:aZllfZee^kebfbmlhg^\\^gmkb\bmrmaZgf^mah];'F^mah]: blleb`amerlbfie^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\^^]ma^ebfbml_hk[hmaf^mah]l:Zg];'BgmabllbmnZmbhg :gg^q<h_>nkh\h]^+%IZkm*¾+fZr[^nl^]':em^kgZmbo^er% \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^mhma^ikh[e^f[^bg` \hglb]^k^]'Ma^_heehpbg`fZr[^nl^]3ebg^Zk^eZlmb\ZgZerlbl%ebg^Zk ^eZlmb\ZgZerlblpbmaebfbm^]k^]blmkb[nmbhg%ieZlmb\ZgZerlblZg] ghg&ebg^ZkZgZerlbl'Ebg^Zk^eZlmb\ZgZerlblfZr[^\Zkkb^]hnmZllnfbg` \khlll^\mbhglZk^ng\kZ\d^]!b'^'\hg\k^m^l^\mbhgikhi^kmb^l"% nlbg`ebg^Zklmk^ll&lmkZbgk^eZmbhglabilZg]Zllnfbg`f^ZgoZen^l h_ehg`&m^kf^eZlmb\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^^eZlmb\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^kgZmbo^ernl^ma^fhf^gmfZ`gb_b\Zmbhgf^mah] !<e.'1'0',"hkghfbgZe\nkoZmnk^f^mah]!<e.'1'1"ZlbeenlmkZm^]bg ?b`nk^,'Ma^eZmm^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][^ihlbmbo^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]blebd^ermh k^jnbk^lhf^bm^kZmbhgmh]^m^kfbg^ma^]^_e^\mbhgZmZiikhqbfZm^er fb]&a^b`am%^+'@nb]Zg\^bl`bo^gbg?b`nk^,' 35 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Figure 3 Effective length Flow chart for slender columns (nominal curvature method) ?b`nk^.`bo^l`nb]Zg\^hgma^^__^\mbo^e^g`mah_ma^\henfg' Ahp^o^k%_hkfhlmk^Zelmkn\mnk^l?b`nk^l._"Zg].`"hgerZk^ Ziieb\Z[e^%Zg]>nkh\h]^+ikhob]^lmph^qik^llbhglmh\Ze\neZm^ma^ ^__^\mbo^e^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^k^eZmbo^_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^kgZmbo^er% 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'Mablk^eZmbo^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_ma^ab`a^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^^__^\mbo^e^g`ma_Z\mhk%?%\Zg [^^lmZ[ebla^]_khfMZ[e^-_hk[kZ\^]\henfgl'Ma^^__^\mbo^e^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]%ma^oZen^h_d\hne][^)'**%Zg]ma^k^_hk^eh6)'.2e' Bgma^^]`^\hg]bmbhgdbl^__^\mbo^er]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\\^im^]maZmMZ[e^,'*2h_;L1**)fZr \hgl^koZmbo^er[^nl^]mh]^m^kfbg^ma^^__^\mbo^e^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 Zk^e^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^^[^ehp" 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^ma^eZk`^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"'Ahp^o^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^_khfma^ihbgmh_s^kh lmkZbgmakhn`ama^Âabg`^ihbgmÃh_)'))*0.lmkZbgZmfb]&]^imah_ma^ l^\mbhg'Pa^gma^g^nmkZeZqbleb^lwithinma^l^\mbhg]^imama^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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Ma^`^g^kZek^eZmbhglabibllahpgbg?b`nk^1]"'?hk\hg\k^m^\eZll^l Z[ho^<.)(/)ma^ikbg\bie^lZk^ma^lZf^[nmma^fZqbfnflmkZbg oZen^loZkr' Creep Mph^qik^llbhgl\Zg[^]^kbo^]_hkma^Zk^Zh_lm^^ek^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^]^imah_\hg\k^m^bg\hfik^llbhg6lq©a l6)'1_hk©<.)(/) q6=^imamhg^nmkZeZqbl a6A^b`amh_l^\mbhg =^i^g]bg`hgma^Zllnfimbhglnl^]bgma^]^lb`g%bmfZr[^g^\^llZkr mh]^m^kfbg^ma^^__^\mbo^\k^^ikZmbhh^_!k^_'<e','*'-.'1'-"': ghfh`kZfblikhob]^]bgma^>nkh\h]^!?b`nk^,'*"_hkpab\ama^ \^f^gmlmk^g`ma\eZllblk^jnbk^]4ahp^o^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^k^ineo^kbs^]_n^eZla!i_Z"^q\^^]l +)h_ma^\^f^gm\hf[bgZmbhg%<eZllGfZr[^Zllnf^]'Pa^k^ ``[l^q\^^]l/.hkpa^k^i_Z^q\^^]l,.%<eZllLfZr[^Zllnf^]' Biaxial bending Ma^^__^\mlh_[bZqbZe[^g]bg`fZr[^\a^\d^]nlbg`>qik^llbhg!.',2"% pab\apZl_bklm]^o^ehi^][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]^eebimb\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^kZmbo^erZg]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 Column design chart for rectangular columns d2 /h = 0.10 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 Column design chart for rectangular columns d2 /h = 0.15 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Figure 9d Column design chart for rectangular columns d2 /h = 0.20 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 Column design chart for rectangular columns d2 /h = 0.25 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]^+' Ahp^o^k%bm`bo^l`nb]Zg\^hgma^^__^\mbo^e^g`mah_Zgng[kZ\^] f^f[^kbg>qik^llbhg!.'*/"'Ma^oZen^_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\^]\henfgl4ahp^o^k k^_^k^g\^\Zg[^fZ]^mhma^<aZim^k*+ 2' Walls Pa^gma^l^\mbhge^g`mah_Zo^kmb\Ze^e^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\^im_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^^[^ehp"' Ma^k^blghli^\b_b\`nb]Zg\^`bo^g_hk[^g]bg`Z[hnmma^lmkhg`Zqbl _hklmZ[bebmr'Ahp^o^k%ma^ikbg\bie^lh_<BKB:K^ihkm*)1fZr[^ _heehp^]':em^kgZmbo^erma^lmknmZg]mb^f^mah]fZr[^nl^]!l^\mbhg /'.h_ma^>nkh\h]^"' : ?Z\mhk_hk]^m^kfbgbg`le^g]^kg^llebfbm *(!*$)'+h^_" :\ <khlll^\mbhgZeZk^Zh_\hg\k^m^ [a :l :k^Zh_mhmZe\henfgk^bg_hk\^f^gm ; ?Z\mhk_hk]^m^kfbgbg`le^g]^kg^llebfbm \ ?Z\mhk]^i^g]bg`hg\nkoZmnk^]blmkb[nmbhg *)!_hk\hglmZgm\khll&l^\mbhg" < ?Z\mhk_hk]^m^kfbgbg`le^g]^kg^llebfbm *'0¾kf ] >__^\mbo^]^ima ^+ 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^^e +))@IZ _\] =^lb`goZen^h_\hg\k^m^\hfik^llbo^lmk^g`ma α\\_\d(γ\ _\d <aZkZ\m^kblmb\\rebg]^klmk^g`mah_\hg\k^m^ e <e^Zka^b`amh_\hfik^llbhgf^f[^k[^mp^^g ^g]k^lmkZbgml e) >__^\mbo^e^g`ma Dk <hkk^\mbhg_Z\mhk]^i^g]bg`hgZqbZeehZ] Dh ?Z\mhkmZdbg`bgmhZ\\hngm\k^^i 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 K^eZmbo^ZqbZe_hk\^ G>](!:\_\]" g[Ze OZen^h_gZmfZqbfnffhf^gmh_k^lblmZg\^ )'- gn ?Z\mhkmhZeehp_hkk^bg_hk\^f^gmbgma^\henfg *$ω Rules for spacing and quantity of reinforcement G>] NembfZm^ZqbZeehZ] kf Fhf^gmkZmbh F)*(F)+ q =^imamhg^nmkZeZqbl !]¾s"()'- s E^o^kZkf Maximum areas of reinforcement α\\ <h^__b\b^gmmZdbg`Z\\hngmh_ehg`m^kf^__^\ml hg\hfik^llbo^lmk^g`maZg]h_ng_ZohnkZ[e^ ^__^\mlk^lnembg`_khfma^pZrehZ]blZiieb^] Bg>nkh\h]^+ma^fZqbfnfghfbgZek^bg_hk\^f^gmZk^Z_hk\henfgl Zg]pZeelhnmlb]^eZilbl-\hfiZk^]pbma/bg;L1**)'Ahp^o^k% mablZk^Z\Zg[^bg\k^Zl^]ikhob]^]maZmma^\hg\k^m^\Zg[^ieZ\^] Zg]\hfiZ\m^]ln__b\b^gmer'B_k^jnbk^]l^e_&\hfiZ\mbg`\hg\k^m^fZr [^nl^]_hkiZkmb\neZker\hg`^lm^]lbmnZmbhgl%pa^k^ma^k^bg_hk\bg`[Zkl lahne][^liZ\^]mh^glnk^maZmma^\hg\k^m^\Zg_ehpZkhng]ma^f' ?nkma^k`nb]Zg\^\Zg[^_hng]bgL^e_&\hfiZ\mbg`\hg\k^m^' Minimum reinforcement requirements Ma^k^\hff^g]^]fbgbfnf]bZf^m^kh_ehg`bmn]bgZek^bg_hk\^f^gmbg \henfglbl*+ff'Ma^fbgbfnfZk^Zh_ehg`bmn]bgZek^bg_hk\^f^gmbg \henfglbl`bo^g[r3:l%fbg6)'*)G>](_r]ª)'))+:\>qi'!2'*+G" Ma^]bZf^m^kh_ma^mkZglo^kl^k^bg_hk\^f^gmlahne]ghm[^e^llmaZg /ffhkhg^jnZkm^kh_ma^fZqbfnf]bZf^m^kh_ma^ehg`bmn]bgZe[Zkl' )'1._hk_e^qnk^Zg]ZqbZe ehZ]l'*')_hkhma^k ia^ghf^gZ!?khfNDG:" β ?Z\mhk )',.$_\d(+))¾λ(*.) εr] =^lb`goZen^h_lmkZbgbgk^bg_hk\^f^gm _r](>l γf IZkmbZe_Z\mhk_hkfZm^kbZeikhi^kmb^l *'*._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^^ikZmbh h!∞%mh"F>ji (F>] h !∞%m)" ?bgZe\k^^i\h&^__b\b^gmmh<e,'*'- ω F^\aZgb\Zek^bg_hk\^f^gmkZmbh uqu :[lhenm^oZen^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_ma^ehg`bmn]bgZe[Zkl' N/)h_ma^e^ll^k]bf^glbhgh_ma^\henfg' N+-)ff' :mZ]blmZg\^`k^Zm^kmaZgma^eZk`^k]bf^glbhgh_ma^\henfgZ[ho^ hk[^ehpZ[^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^lbs^ienl.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][^eh\Zm^]Zm^Z\a_Z\^'Ma^]blmZg\^[^mp^^g mphZ]cZ\^gmo^kmb\Ze[Zkllahne]ghm^q\^^]ma^e^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)'))*:\'Ahp^o^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^^e^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:'K^ihkm*)+3=^lb`gh_la^ZkpZee[nbe]bg`l'<BKB:%*21-' 11 MA><HG<K>M>LH<B>MR'M^\agb\ZeK^ihkmGh/+3L^e_&\hfiZ\mbg`\hg\k^m^':k^ob^p'Ma^Lh\b^mr%+)).' 42 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ /'?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_^erk^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]Zmbhgbml^e_'Ahp^o^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^]^ll^o^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`gbgmaZmebfbmlmZm^ikbg\bie^lZk^nl^]makhn`ahnmZg]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*k^eZmbg`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[^k^eb^]hg_hk`^g^kZe`nb]Zg\^hgmabl >nkh\h]^' Limit states Ma^_heehpbg`nembfZm^ebfbmlmZm^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_ma^ebfbmlmZm^lpbee`ho^kgma^]^lb`gZg] ma^k^_hk^bmpbeeghm[^g^\^llZkrmh\Zkkrhnm\a^\dl_hkZeeh_ma^f%Zemahn`a 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^*"' Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ mh[^Ziieb^]mhma^Z\mbhgl_hkma^l^\hf[bgZmbhglh_iZkmbZe_Z\mhkl Zk^`bo^gbgMZ[e^+Zg]ma^iZkmbZe_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' Ma^iZkmbZe_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]^i^g]hg bg]bob]nZe\bk\nflmZg\^l' Methods of design and combinations Ma^k^aZlghm[^^gZ\hgl^glnlZfhg`lm`^hm^\agb\Ze^g`bg^^kl ho^kma^Ziieb\Zmbhgh_ebfbmlmZm^ikbg\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]bg`ibe^Zg] Zg\ahkZ`^]^lb`g"ma^k^Zk^mphl^mlh_\hf[bgZmbhglmhnl^_hkma^ LMKZg]@>HnembfZm^ebfbmlmZm^l'Ma^oZen^l_hkma^iZkmbZe_Z\mhkl Ma^iZkmbZe_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^ma^ik^l\kbimbo^f^mah]blnl^]_hklik^Z]_hng]Zmbhgl !l^^iZ`^,"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]k^eZmbo^erlbfie^lmkn\mnk^l G^`eb`b[e^ Ghg^`bo^g + <hgo^gmbhgZemri^lh_lmkn\mnk^Zg]_hng]Zmbhg pbmagh]b__b\nem`khng]hkehZ]bg`\hg]bmbhgl Gh^q\^imbhgZekbld Lik^Z]_hng]Zmbhgl , :eehma^klmkn\mnk^l :[ghkfZekbldl EZk`^hkngnlnZelmkn\mnk^l >q\^imbhgZe`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^ma^oZkbZmbhgbgi^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]ma^oZkbZ[e^Z\mbhgllahne][^b`ghk^] c Ma^oZen^h_c h\Zg[^h[mZbg^]_khfMZ[e^G:':*'*h_ma^NDG:mh;L>G*22)!hkl^^MZ[e^,h_<aZim^k*" d Ma^oZen^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`gk^ihkmlahne][^ikh]n\^]_hk^Z\aikhc^\m% ^o^gb_bmblhgerZlbg`e^la^^m'Ma^k^ihkmlahne]\hgmZbg]^mZbelh_ ma^lbm^%bgm^kik^mZmbhgh_ma^`khng]bgo^lmb`Zmbhgk^ihkm%`^hm^\agb\Ze ]^lb`gk^\hff^g]ZmbhglZg]Z]ob\^hglni^koblbhg%fhgbmhkbg`Zg] fZbgm^gZg\^h_ma^phkdl'Bmblebd^ermaZmmablk^ihkmpbeek^jnbk^bginm _khffhk^maZghg^\hglnemZgm%]^i^g]bg`hgpa^ma^kma^ikhc^\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^kma^oZen^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^ma^oZkbZmbhgbgi^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]ma^oZkbZ[e^Z\mbhgllahne][^b`ghk^] c Ma^oZen^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[bebmrebfbmlmZm^iZkZf^m^klmaZmZelhlZmbl_rZeek^e^oZgm 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^[^Zkbg`ik^llnk^lÃaZo^[^^g nl^]mhebfbml^mme^f^gm'Mabl\hg\^imh_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\^imbhgbl_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^]nlbg`iZkmbZe_Z\mhklhgma^lhbeikhi^kmb^lZlp^eeZlhg ma^Z\mbhgl':mma^LELma^l^mme^f^gmh_ma^_hng]Zmbhgllahne][^ \Ze\neZm^]Zg]\a^\d^]Z`Zbglmi^kfbllb[e^ebfbml' Ma^ik^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^kfbg^ik^lnf^] !ZeehpZ[e^"[^Zkbg`ik^llnk^l_hk\Zm^`hkr*lmkn\mnk^lZg]ik^ebfbgZkr \Ze\neZmbhgl_hk\Zm^`hkr+lmkn\mnk^l':em^kgZmbo^er%ma^ik^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`gk^ihkm' 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^`kZo^e%hk]^gl^lZg]Zg]`kZo^e 7 /)) F^]bnf]^gl^`kZo^e%hkf^]bnf ]^gl^lZg]Zg]`kZo^e 5+))mh/)) Pb]mah__hng]Zmbhgghme^llmaZg*f' @khng]pZm^ke^o^eZllnf^]mh[^[^ehpma^[Zl^ h_ma^_hng]Zmbhg' <ha^lbo^ lhbel Ehhl^`kZo^e%hkehhl^lZg]Zg]`kZo^e 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\^imb[e^mhehg`&m^kf\hglheb]Zmbhgl^mme^f^gm Note Ma^l^oZen^lZk^_hkik^ebfbgZkr]^lb`ginkihl^lhger' 45 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ :_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`ma^ihm^gmbZeho^kmnkgbg`h_ ma^[Zl^bl]n^mhma^oZkbZ[e^Z\mbhg_khfma^pbg]%ma^_heehpbg` \hf[bgZmbhglahne][^nl^]!ma^oZkbZ[e^bfihl^]Z\mbhgblghm \hglb]^k^]mh\hgmkb[nm^mhma^lmZ[bebmrh_ma^lmkn\mnk^"3 Ma^ik^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`gk^ihkmZm[hma>JNZg]@>H nembfZm^ebfbmlmZm^l!l^^?b`nk^+"'B_ma^^\\^gmkb\bmrbl`k^Zm^kmaZg E(/ZmLEL%ma^gma^ik^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_rabfl^e_ 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$*'.Jd%p >JN\hf[bgZmbhg pa^k^3 @dblma^lmZ[beblbg`\aZkZ\m^kblmb\i^kfZg^gmZ\mbhg !Nl^*'*@d_hkZ]^lmZ[beblbg`i^kfZg^gmZ\mbhg" Jd%pblma^]^lmZ[beblbg`\aZkZ\m^kblmb\oZkbZ[e^pbg]Z\mbhg Reinforced concrete pads Figure 1 Pa^k^ma^iZ]_hng]Zmbhglk^jnbk^k^bg_hk\^f^gmma^_heehpbg`\a^\dl lahne][^\Zkkb^]hnmmh^glnk^3 N Ln__b\b^gmk^bg_hk\^f^gmmhk^lblm[^g]bg`fhf^gml' N Ing\abg`la^Zklmk^g`ma' N ;^Zfla^Zklmk^g`ma' Procedures for depth of spread foundations START Obtain soil parameters from Ground Investigation report Design using direct method? Yes No Ahp^o^k%ma^k^fZr[^^\hghfb^lmhfZ]^_khfnlbg`>qik^llbhgl !/'*)Z"hk!/'*)["_khfma^>nkh\h]^' Size foundation (geotechnical design) using the worst of Combinations 1 or 2 (ULS) for actions and geotechnical material properties. Combination 2 will usually govern. Use prescriptive method. Size foundation (geotechnical design) using SLS for actions and presumed bearing resistance Is there an overturning moment? Check overturning using EQU limit state for actions and GEO Combination 2 for material properties. Yes Ma^fhf^gmlZg]la^Zk_hk\^llahne][^Zll^ll^]nlbg`ma^LMK \hf[bgZmbhg3 *',.@d$*'.Jd LMK\hf[bgZmbhg*!>qi'!/'*)"" Ma^\kbmb\Ze[^g]bg`fhf^gml_hk]^lb`gh_[hmmhfk^bg_hk\^f^gm Zk^eh\Zm^]Zmma^\henfg_Z\^l';hma[^Zfla^ZkZg]ing\abg` la^Zklahne]ma^g[^\a^\d^]Zmma^eh\Zmbhgllahpgbg?b`nk^,'?hk ing\abg`la^Zkma^`khng]k^Z\mbhgpbmabgma^i^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^ ]^imah_ma^[Zl^':em^kgZmbo^er%ma^Zfhngmh_fZbgk^bg_hk\^f^gm \hne][^bg\k^Zl^]hk%e^ll]^lbkZ[er%la^Zkebgdl\hne][^ikhob]^]'!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^kZmbo^er%[nmbmbl `^g^kZeerZ\\^imZ[e^mh\a^\dZm]Zg]+]':em^kgZmbo^er%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]^+ "'Ma^ikh\^]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]^imal`k^Zm^kmaZg*)))\Ze\neZm^oK]%\]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[e^aZl[^^gik^iZk^]_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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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^ l^e^\mbhgh_ZgZiikhikbZm^f^mah]_hkZgZerlbg`ma^bgm^kZ\mbhg[^mp^^g ma^kZ_mZg]ma^`khng]lhZlmhZ\ab^o^Zk^ZlhgZ[e^k^ik^l^gmZmbhgh_ ma^bk[^aZobhnk'?hklmb__^kkZ_ml!b'^'liZg&mh&mab\dg^ll`k^Zm^kmaZg*)"pbma Z_Zbkerk^`neZkeZrhnm%lbfieb_b^]ZiikhZ\a^lln\aZlrb^e]ebg^hkma^_eZm leZ[^jnboZe^gm_kZf^f^mah]fZr[^^fiehr^]%hg\^Zg^lmbfZmbhgh_ ma^oZkbZmbhglbg[^Zkbg`ik^llnk^aZl[^^gh[mZbg^]_khfZ`^hm^\agb\Ze li^\bZeblm'PaZm^o^klbfieb_b\ZmbhglZk^fZ]^%bg]bob]nZe^eZlmb\kZ_m k^Z\mbhgllahne]^jnZm^mhma^Ziieb^]\henfgehZ]l' :em^kgZmbo^er%ZmknllZgZeh`rfZr[^nl^]4mablbl\ho^k^]bgL^\mbhgl.'/'- Zg]/'.h_>nkh\h]^+¾*¾*'Ma^lmknmZg`e^ylahne][^Zme^Zlm+*'1mh ma^ahkbshgmZe4ghm^maZmylahne][^f^Zlnk^]bgma^ieZg^h_ma^\henfg Zg]ibe^' Mabgg^k%fhk^_e^qb[e^kZ_mlhkmahl^pbmaZ\hfie^qeZrhnmfZrk^jnbk^ ma^Ziieb\Zmbhgh_Z_bgbm^^e^f^gmhk`kbeeZ`^ZgZerlbl'?hkkZ_ml[^Zkbg` hg`kZgneZkln[&`kZ]^lhkpa^g\hgmb`nhnl&ibe^]pZeelhk]bZiakZ`f i^kbf^m^kpZeelZk^ik^l^gm%ma^`khng]fZr[^fh]^ee^]ZlZl^kb^l h_Pbgde^klikbg`l'Ahp^o^k%_hk\ha^lbo^ln[&`kZ]^l%mablZiikhZ\abl ngebd^ermh[^oZeb]%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^]^imah_ma^ [Zl^':em^kgZmbo^er%ma^Zfhngmh_fZbgk^bg_hk\^f^gm\hne][^bg\k^Zl^]hk% e^ll]^lbkZ[er%la^Zkebgdl\hne][^ikhob]^]'<Zk^lahne][^mZd^gmaZmfZbg [ZklZk^_neerZg\ahk^]':lZfbgbfnf%Z_neeZg\ahkZ`^lahne][^ikhob]^] _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^^e 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 ?hkma^inkihl^h_mabl\aZim^kbmblZllnf^]maZmma^ibe^]^lb`gpbee[^ \Zkkb^]hnm[rZli^\bZeblmibebg`\hgmkZ\mhk'Ma^Z\mbhglhgma^ibe^lfnlm [^\e^Zker\hgo^r^]mhma^ibe^]^lb`g^k%Zg]ma^l^lahne][^[khd^g]hpg bgmhma^ng_Z\mhk^]i^kfZg^gmZ\mbhglZg]^Z\ah_ma^Ziieb\Z[e^oZkbZ[e^ Z\mbhgl!^'`'bfihl^]Zg]pbg]Z\mbhgl"'Ma^ibe^]^lb`g^k\Zgma^g\Zkkr hnmma^lmkn\mnkZeZg]`^hm^\agb\Ze]^lb`gh_ma^ibe^l' Pa^k^fhf^gmlZk^Ziieb^]mhma^ibe^\Zima^>JN\hf[bgZmbhg lahne]Zelh[^nl^]mh\a^\dma^ibe^l\Zgk^lblmma^ho^kmnkgbg`_hk\^l' Ma^l^>JNehZ]lfnlmZelh[^\e^Zker\hgo^r^]mhma^ibe^]^lb`g^k Zg]ikh\^]nk^linmbgieZ\^mh^glnk^ma^ibe^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%ma^oZen^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]^ima%a?%!l^^?b`nk^1"fZr[^ \Ze\neZm^]_khf3 ,) +'2 )'*. ,+ ,') )'*/ ,. ,'+ )'*0 -) ,'. )'*1 -. ,'1 )'+) .) -'* )'+* Key pa^k^3 s`]6ma^]^lb`goZen^h_ma^`khng][^Zkbg`ik^llnk^ _\m] 6ma^]^lb`g\hg\k^m^m^glbe^lmk^g`ma_khf>qi'!,'*/" 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)',)_\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_ma^ing\abg`la^Zk k^lblmZg\^pbmahnming\abg`la^Zkk^bg_hk\^f^gm oK]%\ =^lb`goZen^h_ma^ing\abg`la^Zklmk^ll k^lblmZg\^pbmahnming\abg`la^Zkk^bg_hk\^f^gm Maximum area of reinforcement oK]%fZq >q\^imZmeZieh\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 =^imamhg^nmkZeZqbl !]¾s"()'- qfZq Ebfbmbg`oZen^_hk]^imamhg^nmkZeZqbl !d¾)'-"]pa^k^d©*') s E^o^kZkf a\\ h^__b\b^gmmZdbg`Z\\hngmh_ehg`m^kf < ^__^\mlhg\hfik^llbo^lmk^g`maZg]h_ ng_ZohnkZ[e^^__^\mlk^lnembg`_khfma^pZr ehZ]blZiieb^]!?khfNDGZmbhgZe:gg^q" b ?Z\mhk_hk]^m^kfbgbg`ing\abg`la^Zklmk^ll d Zmbhh_ma^k^]blmkb[nm^]fhf^gmmhma^^eZlmb\ K [^g]bg`fhf^gm Deep elements gf IZkmbZe_Z\mhk_hkfZm^kbZeikhi^kmb^l ?hk]^^i^e^f^gmlma^Z]ob\^bg>nkh\h]^+_hkma^lb]^_Z\^lh_]^^i [^ZflfZr[^_heehp^]'Ma^NDGZmbhgZe:gg^qk^\hff^g]lmaZm)'+ blikhob]^]bg^Z\a_Z\^'Ma^]blmZg\^[^mp^^g[Zkllahne]ghm^q\^^] ma^e^ll^kh_mpb\^ma^[^Zf]^imahk,))ff'?hkibe^\Zilma^lb]^ _Z\^fZr[^ngk^bg_hk\^]b_ma^k^blghkbldh_m^glbhg]^o^ehibg`' r) K^_^k^g\^k^bg_hk\^f^gmkZmbh _\d(*))) r e K^jnbk^]m^glbhgk^bg_hk\^f^gmZmfb]&liZg mhk^lblmma^fhf^gm]n^mhma^]^lb`g ehZ]l!hkZmlniihkm_hk\Zgmbe^o^kl" :l e[] Minimum spacing of reinforcement Ma^fbgbfnfliZ\bg`h_[Zkllahne][^ma^`k^Zm^kh_3 N ;Zk]bZf^m^k% N :``k^`Zm^lbs^ienl.ff%hk N +)ff' 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 ; 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: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^llaZlik^obhnler[^^g]^m^kfbg^]]nkbg` \hg\^imnZe]^lb`g'<hg\^im]^lb`glik^iZk^]Zllnfbg`]^mZbe^]]^lb`gphne] [^mh;L1**)fZr[^\hgmbgn^]makhn`amh]^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^] ' Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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^%ahp^o^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 , =^m^kfbg^pab\a\hf[bgZmbhglh_Z\mbhglZiier *3Bgmkh]n\mbhgmh>nkh\h]^l G:mh;L>G*22)MZ[e^lG:':*'*Zg]G:':*'+!;" - =^m^kfbg^ehZ]bg`ZkkZg`^f^gml +3@^mmbg`lmZkm^] G:mh;L>G*22+¾*¾* . :ll^ll]nkZ[bebmrk^jnbk^f^gmlZg]]^m^kfbg^\hg\k^m^lmk^g`ma +3@^mmbg`lmZkm^] ;L1.))3+))/ / <a^\d\ho^kk^jnbk^f^gml_hkZiikhikbZm^_bk^k^lblmZg\^i^kbh] +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 Minimum dimensions (mm) 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][^ieZ\^]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_l^iZkZmbhg B BglneZmbhg a GhkfZeerma^k^jnbk^f^gmlh_;L>G*22+¾*¾*pbee]^m^kfbg^ma^\ho^k' 52 0'?eZmleZ[l Pab\a^o^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^^e^f^gmhkrb^e]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)(*).'Ahp^o^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][^eebfbm^]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 k^eZmbhglabih_\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`gnembfZm^ehZ]%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 Minimum percentage of reinforcement required fck +. +1 ,) ,+ ,. -) -. .) fctm +'/ +'1 +'2 ,') ,'+ ,'. ,'1 -'* Minimum % (0.26 fctm /fyka ) )'*, )'*- )'*. )'*/ )'*0 )'*1 )'+) )'+* Key a Pa^k^_rd 6.))FIZ 53 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Deflection >nkh\h]^+aZlmphZem^kgZmbo^f^mah]lh_]^lb`gbg`_hk]^_e^\mbhg4 ^bma^k[rebfbmbg`liZg&mh&]^imakZmbhhk[rZll^llbg`ma^ma^hk^mb\Ze ]^_e^\mbhgnlbg`ma^>qik^llbhgl`bo^gbgma^>nkh\h]^'Ma^eZmm^kbl ]^Zempbmabg]^mZbebg<aZim^k1%hkb`bgZeerin[ebla^]Zl=^_e^\mbhg \Ze\neZmbhgl ' ]^imakZmbhlZk^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&]^imakZmbhllahne]^glnk^maZm]^_e^\mbhgblebfbm^] mhliZg(+.)Zg]mablblma^ikh\^]nk^ik^l^gm^]bg?b`nk^,'Ma^ ;Z\d`khng]iZi^kmhma^NDGZmbhgZe:gg^q ;ghm^lmaZmma^liZg&mh& Ma^]^lb`goZen^h_ma^ing\abg`la^Zk_hk\^%O>]%pbeenlnZeer[^ma^ lniihkmk^Z\mbhgZmma^nembfZm^ebfbmlmZm^'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]^+'Ahp^o^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 Determine Factor 2 (F2) Where the slab span exceeds 8.5 m and it supports brittle partitions, F2 = 8.5/leff Otherwise F2 = 1.0 19 17 15 Determine Factor 3 (F3) 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 ] rà _\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]]^i^g]lhgma^\hg\k^m^lmk^g`manl^]' N Pbma>nkh\h]^+ma^i^kfbllb[e^la^Zkk^lblmZg\^pa^gnlbg`la^Zk ebgdlblab`a^k%Zemahn`aln\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[^eZb]hnm bgZkZ]bZehk\kn\b_hkfiZmm^kgZg]`bo^lliZ\bg`k^jnbk^f^gml_hk [hma'Hma^km^\agbjn^lZk^ZoZbeZ[e^_hkbg\k^Zlbg`ing\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^]ma^ikh\^]nk^bg>nkh\h]^+ bllbfie^k4ma^ihbgmZmpab\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' Ahp^o^k%ma^k^bg_hk\^f^gm\Zg[^eZb]hgZ`kb]ikhob]^]ma^ liZ\bg`kne^lZk^_heehp^]' Ma^ikh\^]nk^_hk]^m^kfbgbg`ma^ing\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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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[e^aZl[^^gik^iZk^]_hk_\d 6,)4 Pa^k^r I^q\^^]l)'-)ma^_heehpbg`_Z\mhklfZr[^nl^]3 Internal column b = 1.15 Rules for spacing and quantity of reinforcement 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_ma^ebgdlbgma^kZ]bZe]bk^\mbhg lm6ma^liZ\bg`h_ma^ebgdlbgma^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]^eZieh\Zmbhgl%ma^fZqbfnfZk^Zh_m^glbhghk\hfik^llbhg k^bg_hk\^f^gmlahne]ghm^q\^^]:l%fZq6)'-:\ Figure 8 Minimum spacing of reinforcement 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^lbs^ienl.ff N +)ff Maximum spacing of main reinforcement bz ?hkleZ[le^llmaZg+))ffmab\dma^_heehpbg`fZqbfnfliZ\bg`kne^lZiier3 N ?hkma^ikbg\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\^imbhgblbgZk^Zlpbma\hg\^gmkZm^]ehZ]lhkZk^Zlh_fZqbfnf 56 0'?eZmleZ[l fhf^gmpa^k^ma^_heehpbg`Ziieb^l3 N ?hkma^ikbg\biZek^bg_hk\^f^gm3+a[nmghmfhk^maZg+.)ff N ?hkma^l^\hg]Zkrk^bg_hk\^f^gm3,a[nmghmfhk^maZg-))ff Pa^k^ablma^]^imah_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^k^ing\abg`la^Zkk^bg_hk\^f^gmblk^jnbk^]ma^_heehpbg`kne^l lahne][^h[l^ko^]' N Bmlahne][^ikhob]^][^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^llma^i^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][^ieZ\^]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_ma^ebgdllahne]ghm^q\^^])'0.] !l^^?b`nk^2"' N Ma^mZg`^gmbZeliZ\bg`h_ma^ebgdllahne]ghm^q\^^]*'.]pbmabg +]h_ma^\henfg_Z\^' N Ma^mZg`^gmbZeliZ\bg`h_ma^ebgdllahne]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][^e^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 :\ <khlll^\mbhgZeZk^Zh_\hg\k^m^ [a :l :k^Zh_m^glbhglm^^e :l+ :k^Zh_\hfik^llbhglm^^e :l%ikho :k^Zh_m^glbhglm^^eikhob]^] :l%k^j :k^Zh_m^glbhglm^^ek^jnbk^] [ Pb]mah_leZ[ ] >__^\mbo^]^ima ]+ >__^\mbo^]^imamh\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 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^__ >__^\mbo^liZgh_f^f[^k L^^L^\mbhg.','+'+!*" e(] Ebfbmbg`liZg&mh&]^imakZmbh F =^lb`gfhf^gmZmma^NEL a\\_\d (g\ )',)_\d+(,_hk_\d©<.)(/) !_khfMZ[e^,'*%>nkh\h]^+" q =^imamhg^nmkZeZqbl !]¾s"()'- qfZq Ebfbmbg`oZen^_hk]^imamhg^nmkZeZqbl !d¾)'-"]pa^k^d©*') s E^o^kZkf a \\ <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^ ^eZlmb\[^g]bg`fhf^gm g f IZkmbZe_Z\mhk_hkfZm^kbZeikhi^kmb^l *'*._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 ) 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\Zgmbe^o^kl" :l([] rà K^jnbk^]\hfik^llbhgk^bg_hk\^f^gmZm fb]&liZgmhk^lblmma^fhf^gm]n^mhma^ ]^lb`gehZ]l!hkZmlniihkm_hk\Zgmbe^o^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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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^&]^imakZmbhl%pab\aZk^ ZiikhikbZm^Zg]^\hghfb\_hkma^oZlmfZchkbmrh_]^lb`gl'?nkma^k`nb]Zg\^ hgma^liZg&mh&^__^\mbo^&]^imaf^mah]bl`bo^gbg<aZim^kl,%-Zg]0% hkb`bgZeerin[ebla^]Zl;^Zfl%LeZ[lZg]?eZmleZ[l'Ahp^o^k%ma^k^Zk^ lbmnZmbhglpa^k^]bk^\m\Ze\neZmbhgh_]^_e^\mbhgblg^\^llZkr%Zleblm^][^ehp3 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]]bg`ehZ]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 Bgma^iZlmlmkn\mnk^lm^g]^]mh[^lmb__pbmak^eZmbo^erlahkmliZgl':l m^\agheh`rZg]ikZ\mb\^aZo^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^nembfZm^ebfbmlmZm^!NEL"Zg]k^lnembg`bgab`a^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]pbmaab`a^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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ N :`k^Zm^kng]^klmZg]bg`h_lmkn\mnkZe[^aZobhnkZg]ma^Z[bebmrmh ZgZerl^maZm[^aZobhnkjnb\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\ab^o^]b_ \hglb]^kZmbhgbl`bo^gmhma^_Z\mhklmaZmZ__^\mbm'Ma^fhk^bfihkmZgm _Z\mhklZk^]bl\nll^]bg]^mZbe[^ehp' 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'?hkab`ak^lmkZbgm _\mflahne][^nl^]' Creep <k^^iblma^mbf^&]^i^g]Zgmbg\k^Zl^bg\hfik^llbo^lmkZbgbgZ \hg\k^m^^e^f^gmng]^k\hglmZgm\hfik^llbo^lmk^ll'<k^^iblnlnZeer \hglb]^k^]bgma^]^lb`g[rfh]b_rbg`ma^^eZlmb\fh]nenlnlbg`Z \k^^i\h^__b\b^gm%h%pab\a]^i^g]lhgma^Z`^ZmehZ]bg`%lbs^h_ ma^f^f[^kZg]Zf[b^gm\hg]bmbhgl%bgiZkmb\neZkk^eZmbo^anfb]bmr' >nkh\h]^+`bo^lZ]ob\^hgma^\Ze\neZmbhgh_\k^^i\h^__b\b^gmlbg ]^mZbebg:gg^q;'BmZelhZ]obl^lhgma^ZiikhikbZm^k^eZmbo^anfb]bmr mhnl^bg?b`nk^,'*' Ma^\^f^gmlmk^g`ma\eZllblk^jnbk^]bgma^Zll^llf^gmh_\k^^i% ahp^o^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^k^i_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_pZeelpbmaab`a 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^^eZlmb\fh]nenlh_\hg\k^m^blbg_en^g\^][rZ``k^`Zm^mri^% phkdfZglabiZg]\nkbg`\hg]bmbhgl'Ma^^__^\mbo^^eZlmb\fh]nenl ng]^klnlmZbg^]ehZ]bg`pbee[^k^]n\^]ho^kmbf^]n^mhma^^__^\m h_\k^^i'Ma^l^_Z\mhklf^ZgmaZmlhf^cn]`^f^gmblk^jnbk^] mh]^m^kfbg^ZgZiikhikbZm^^eZlmb\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^l^oZen^lmh Z\\hngm_hk]b__^k^gmmri^lh_Z``k^`Zm^'Ma^ehg`&m^kf^eZlmb\fh]nenl lahne][^mZd^gZl3 1'=^_e^\mbhg\Ze\neZmbhgl >\%EM 6>\+1(!*$h" pa^k^ >\+1 6+1&]ZrmZg`^gmfh]nenl6*').>\f h 6<k^^i_Z\mhk'!Ghm^maZmpbma>nkh\h]^+%hk^eZm^lmhZ+1&]Zr lahkm&m^kf^eZlmb\fh]nenl%pa^k^ZlZÂmkn^Ã\k^^i_Z\mhkphne] [^Zllh\bZm^]pbmama^fh]nenlZmma^Z`^h_ehZ]bg`'" Ma^Zll^llf^gmh_ma^ehg`&m^kf>&oZen^\Zg[^\Zkkb^]hnmfhk^ Z\\nkZm^erZ_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 Ma^ehZ]bg`l^jn^g\^Zg]mbfbg`fZr[^\kbmb\Zebg]^m^kfbgbg` ma^]^_e^\mbhgh_Zlnli^g]^]leZ[[^\Znl^bmpbeebg_en^g\^ma^ihbgm Zmpab\ama^leZ[pbee\kZ\d!b_ZmZee"Zg]blnl^]mh\Ze\neZm^ma^\k^^i _Z\mhkl_hkma^leZ[':ehZ]bg`l^jn^g\^bllahpgbg?b`nk^+%pab\a lahplmaZmbgma^^ZkerlmZ`^lk^eZmbo^erab`aehZ]lZk^bfihl^]pabe^ \Zlmbg`ma^leZ[Z[ho^'Ma^ehZ]bg`l^jn^g\^fZroZkr%]^i^g]bg`hg ma^\hglmkn\mbhgf^mah]' LfZee^kehZ]lZk^bfihl^]pa^g_nkma^kleZ[lZk^\ZlmZ[ho^'Ma^ehZ]l Zk^ma^gbg\k^Zl^]i^kfZg^gmer[rma^Ziieb\Zmbhgh_ma^_ehhk_bgbla^l Zg]^k^\mbhgh_ma^iZkmbmbhgl'?bgZeer%ma^oZkbZ[e^Z\mbhglZk^Ziieb^] mhma^lmkn\mnk^Zg]%_hkma^inkihl^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'"Ahp^o^k%bmblebd^ermaZmma^ jnZlb&i^kfZg^gm\hf[bgZmbhgpbee[^^q\^^]^]]nkbg`ma^eb_^mbf^ h_ma^[nbe]bg`Zg]%_hkma^inkihl^h_]^m^kfbgbg`pa^ma^kma^leZ[ fb`amaZo^\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_ma^ehZ]l_khfZg^per\Zlm_ehhk!_hkfphkd%p^m\hg\k^m^%\hglmkn\mbhg ehZ]l"fZr[^\Zkkb^][rma^lnli^g]^]_ehhk[^ehp'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__^\mbg`iZkmbmbhglpbee[^lfZee^kb_ma^leZ[[^\hf^lÂ\kZ\d^]à [^_hk^%kZma^kmaZgZ_m^k%ma^bglmZeeZmbhgh_ma^\eZ]]bg`Zg](hkiZkmbmbhgl' Cracking =^_e^\mbhgh_\hg\k^m^l^\mbhglbl\ehl^erebgd^]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 ma^ehZ]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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Zgrh_ma^^Zkeb^kehZ]lmZ`^l'B_%ahp^o^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^ nembfZm^ebfbmlmZm^]^lb`g Shrinkage curvature LakbgdZ`^]^i^g]lhgma^pZm^k(\^f^gmkZmbh%k^eZmbo^ 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\neZm^ehg`&m^kf^eZlmb\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^^i\h^__b\b^gmZmk^e^oZgmehZ]bg`mbf^ Zg]]nkZmbhg 62 <hg\k^m^ikhi^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_ma^iZkmbmbhglZg](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^\mbhgZk^ik^l^gm^] [^ehp%Zg]ma^l^Zk^[Zl^]hgma^Z]ob\^bgMK.1 =^_e^\mbhglbg\hg\k^m^leZ[lZg][^Zfl' ?bgbm^^e^f^gmZgZerlblfZrZelh[^nl^]mhh[mZbg ^lmbfZm^lh_]^_e^\mbhg'Bgmabl\Zl^ma^ikbg\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 !hkk^i^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'Ahp^o^k%bmblhgerlnbmZ[e^_hk nl^pbma\hfinm^klh_mpZk^'Ma^<hg\k^m^<^gmk^aZl 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`^ehZ]bg`h_ma^ \hg\k^m^'?b`nk^,beenlmkZm^lma^ikbg\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^_heehpbg`ikhi^kmb^l3 <k^^i\h^__b\b^gml%h!:gg^q;h_>nkh\h]^+hk?b`nk^-" E hg`m^kf^eZlmb\fh]nenl%>EM!l^^IZg^e*" >__^\mbo^fh]nenlkZmbh%a^_khf3a^6>l (>EM G^nmkZeZqbl]^ima_hkng\kZ\d^]\hg]bmbhg%qn!l^^IZg^e+" L^\hg]fhf^gmh_Zk^Z_hkng\kZ\d^]\hg]bmbhg%Bn!l^^IZg^e+" <Ze\neZm^\kZ\dbg`fhf^gm%F\k_khf3 F\k6_\mf Bn(!a¾qn"%nlbg`ZiikhikbZm^oZen^_hk_\mf' N =h^lma^fhf^gmZmma^\kbmb\ZeehZ]lmZ`^^q\^^]ma^\kZ\dbg`fhf^gm8 B_r^l%ma^^e^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^^e^f^gmpbeeghm\kZ\dZmZgrlmZ`^' Determine the curvature of the slab N P a^gma^leZ[bl\kZ\d^]\Ze\neZm^ma^_heehpbg`ikhi^kmb^lZmma^ehZ]lmZ`^ [^bg`\hglb]^k^]%nlbg`ZiikhikbZm^oZen^l_hk_\mf%zZg]>EM3 G^nmkZeZqbl]^ima_hk\kZ\d^]l^\mbhg%q\!l^^IZg^e+" L^\hg]fhf^gmh_Zk^Z_hk\kZ\d^]\hg]bmbhg%B\!l^^IZg^e+" 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^^IZg^e+" N <Ze\neZm^ma^mhmZe\nkoZmnk^%*(km6*(k_e$*(k\l K^i^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^]%k^i^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__^\mbg`iZkmbmbhgl(\eZ]]bg`!?k^jn^gm\hf[bgZmbhg]^_e^\mbhg e^ll]^_e^\mbhgZmmbf^h_bglmZeeZmbhg" 1'=^_e^\mbhg\Ze\neZmbhgl 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^]^imamhm^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=^imamh\hfik^llbhgk^bg_hk\^f^gm a 6Ho^kZee]^imah_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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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^]mhkhn`aero^kb_r]^_e^\mbhgk^lneml_khf\hfinm^klh_mpZk^%hk nl^]pa^k^Z\hfinm^kblghmZoZbeZ[e^' Ma^fZchklbfieb_b\ZmbhgblmaZmma^^__^\mlh_^ZkerZ`^ehZ]bg`Zk^ghm \hglb]^k^]^qieb\bmer4kZma^kZgZeehpZg\^blfZ]^_hkma^bk^__^\mpa^g \Ze\neZmbg`ma^\kZ\dbg`fhf^gm'Lbfieb_b^]\k^^i_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 1'=^_e^\mbhg\Ze\neZmbhgl Precamber Table 2 Values for Kh h0 kh 7 *)) *') 7 +)) )'1. 7 ,)) )'0. 7 .)) )'0) :leZ[hk[^Zf\Zg[^ik^\Zf[^k^]mhk^]n\^ma^^__^\mh_]^_e^\mbhg [^ehpma^ahkbshgmZe!l^^?b`nk^1"'Ahp^o^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\\nkZm^er\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[lZk^o^krihineZkZg]^__b\b^gm_ehhklrlm^fl'Ahp^o^k% [^\Znl^ma^rliZgbgmph]bk^\mbhgl%bm\Zg[^]b__b\nemmh\Ze\neZm^ma^bk ]^_e^\mbhg'MK.1 `bo^ll^o^kZelnbmZ[e^f^mah]l_hkZll^llbg`_eZmleZ[ ]^_e^\mbhg'H_ma^l^%ZihineZkf^mah]blmhmZd^ma^Zo^kZ`^]^_e^\mbhg h_mphiZkZee^e\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\\^imZg\^\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 Ahp^o^k%ma^_heehpbg`bg_en^g\^lhg]^_e^\mbhgl\Zgghm[^Z\\nkZm^er 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"%ahp^o^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]^o^gma^ fhlmlhiablmb\Zm^]ZgZerlbl\Zglmbeek^lnembg$*.mh&,)^kkhk'Bmbl Z]oblZ[e^mh`bo^ZlnbmZ[e^\Zo^ZmpbmaZgr^lmbfZm^h_]^_e^\mbhgmaZm hma^klZk^k^erbg`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 B_fZqbfnfi^kfbmm^]d 6E(gZg] Qblma^ihlbmbhgh_fZqbfnfd pa^k^ E 6LiZg g 6Ebfbmbg`liZg&mh&]^imakZmbh% ^'`'+.) ma^gma^]^_e^\mbhgZmQlahne]ghm[^ `k^Zm^kmaZg+Z(g' !FZqbfnf]^_e^\mbhghg`kb]ebg^l fZr[^fhk^\kbmb\Ze'" 65 1'=^_e^\mbhg\Ze\neZmbhgl Cladding tolerances N FZgn_Z\mnk^klfZrlZrmaZmma^bk`eZs^]lrlm^fl\Zghger =^_e^\mbhgfZrZ__^\m\eZ]]bg`hk`eZsbg`bgma^_heehpbg`pZrl3 Ma^k^lahne][^hi^g]bl\nllbhgl[^mp^^gma^]^lb`g^kl_hkma^oZkbhnl ^e^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%ma^ehZ]hgma^\^gmkZe_bqbg`lpbee[^k^eb^o^] 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%+))-' 2 FHLL%KF;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3;^Zfl'Ma^<hg\k^m^<^gmk^%+))/' 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>LH<B>MR'M^\agb\Zek^ihkmGh'.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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 2'K^mZbgbg`pZeel A J BondF:%FL\%Ia=%=B<%FB<>%<>g`O 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,fab`aZg] ikhii^][Zl^f^gmpZeelnimhmphlmhk^rlab`a!0f"'Ma^l^ebfbmlaZo^[^^g \ahl^glhmaZmlbfieb_b\Zmbhgl\Zg[^fZ]^bgma^`^hm^\agb\Ze]^lb`g'Ma^ l^e_&p^b`amh_ma^l^pZeel%bg\en]bg`ma^l^e_&p^b`amh_[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\ak^erikbfZkberhg iZllbo^^Zkmaik^llnk^Zg]_e^qnkZek^lblmZg\^mhlniihkmma^k^mZbg^]fZm^kbZe' Ikbhkmhma^in[eb\Zmbhgh_ma^lmkn\mnkZe>nkh\h]^l%ma^`^hm^\agb\Ze]^lb`gh_ k^mZbgbg`pZeelpZl\ho^k^][r;L1))+':emahn`a\^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`gK^ihkm'Bmlahne][^k^Z]bg \hgcng\mbhgpbmamabl\aZim^k' >ll^gmbZe_^Zmnk^lh_>nkh\h]^0Zk^ik^l^gm^]%Zehg`pbmama^hk^mb\Zefh]^el _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^`ebZ[e^ kbld[^ehg`bg@^hm^\agb\Ze<Zm^`hkr*'PZeelmaZmk^mZbglhbehkpZm^kZg]]h ghmbgoheo^^q\^imbhgZekbldhk]b__b\nemlhbehkehZ]bg`\hg]bmbhgl[^ehg`bg @^hm^\agb\Ze<Zm^`hkr+%_hkpab\akhnmbg^ikh\^]nk^l_hk_b^e]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\^imbhgZeer ]b__b\nemlhbehkehZ]bg`\hg]bmbhgl[^ehg`bg@^hm^\agb\Ze<Zm^`hkr,%_hk pab\aZem^kgZmbo^ikhoblbhglZg]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^ Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ AEE EF?EF?? J,$ ■ 4I?EEA?EAB ? B?EE ■ ,?EAB?EE@KE ■ ,?EAB?EE@KGGE ?EEK EKEI? ?EE A D ■ )? A?EAB @ ?BB?EEBBF?K IEIEF ? ? AB?EE ■ 8?EA?EAB?EE 9B? ?I?E?@E A ? EB?E?K? E G ?EK BHDEKJG?G B G??AE? 9BEF??@IBA @BD@BABF ? @B?IAB ? AE F? @B?I Figure 1 (EBB!GIB+ (GG?BB:0 3 ? ?E( JGF EK+ (GG?B@ B :0. B?GG?B?EE? F@GAFBAA F@ ? AG??EA?AB897-4EF?9?@E . ?EE? A*F@ ? G??EA??B? ? ?GGE? ? ?EF??E EK$BEABA B?EE? @?DAEE??GF? ? %? KFG E?B??BGAB?EEGF? I??@E ? ??GGG?%? B?B? G?G ? B?EE@ ?KGF? ? . ?EE? A*F@ ? G??EA??B? ? ?GGEI??@E? EK? B BAB ? $BE ? B BF ? ? %? BE? EAB? ? ? AAIB E F? ? 9B I?E A? ? ? @JG?$ &g,c B g, &G??EA?AB? D &B??I?EAB? c &Bc cc*B?G? Ultimate limit states for reinforced concrete retaining walls D 8FE?EKB I?E/A? ? ? @JG?$ /& /Dg2 B g2&G??EA?AB? /D &B??I?EAB? a) Overall stability .FG? B?BG??EA?AhR?GGE? hR ? hR&? hRDgh Calculation models for strength limit states c) Toppling b) Sliding 9BFB? ?E@B?IA A ? EI?EE FF EK? ?EK A?F?EE? FE BB?JGE? @E d) Bearing .?FB?EB?I E@EAAIB BB ?EKFGEABF?BF? IEI9B??A?FG @ B A FKBAAAAAIB F?K@ E B e) Structural failure 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 gG,fav gQ gϕb gc gcu gγ Key ag-?GGE A?I?@EGF? ? bgh?GGE? hD 68 2 9B@ A?EAAAG?I?BG A AB?EE BG@E? @? @ ? A F?EEA A ?EE? EKF@EL ?A ?@EFIF AB?EE,BF! H?EE? @F?A GE? J?I? A A? ?EEBBABBAAAG?I ?BG . BJG BBEABAB?EEF ?EE@?? @?DAEE?favourable? B E ? GGE ? @?KG?EEKunfavourable? A @? @ BKB E ? ? KA 2'K^mZbgbg`pZeel B?E? BKF?K@A?I?@EO@B? BE @BD. B ?EE? A?I?@E? ? FEGE@KAA G??EA? A?I?@E? O 9?@E Calculation model A . BA?EE? FE,B?EE E @?DAEE @EDE ? GGE ?@KB ?BG? BI?E>I?EGE? 9B @ ?BB?EE@?F?E@ B?KB?EE EAB? ? K? I?EFG AA B I?EGE? ( ??IA?ABFEB?GIB?EEBE E? BB?BB)?,@ E ? ? ? EBBL ?EH?EB EG?BGA B?EEc = b GI?E?KB?c U h9BAB FE?GGE?@EK2BV3?? Oh BBAFF? B??7? D ?IL AFB B A A@ED ? B?BGAA ?EE?BB I @K7? D AFE? .A2BF?EEB B?EEF ABB7? D L ? cBE@cUhhO?EBBEK 7? D BK E ?GGE?@E? ?EE? FE) BE@ ? ,E ? GGE BF A?I?@EE? A? K FGB??B ,?BBAB B? BG . B?G ? A?I?@E?BG? BI?EGE? @ ?A?I?@EI?EA? B?EEBE ,@? BF A?I?@EE? ABB?B J B@?DAB?EEG Calculation model B . B ?EE? FE,B?EE E @?DAEE @EDE ? GGE ?@K?B Figure 2 Calculation model A a h Figure 3 Calculation model B h 69 3 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ G? Binclined>I?EGE? 9B?B B)?,@ E ?? ? EydBBL ?E 9B?FFE? ?EKGE? ?IK?EE9B @ ?BB?EE@?F?E@ B?K B?EEEAB? B ?FG AB?B B BI?EGE? (DKB?E?I? ?ABFEB?? @ EKA?EEA?EEB?G? LIF? ?I? ?B? IEI?AE ? A FK BB? EyGE?K ? A? EE? ?FGE? JG A%?? I?E? ?EK@? AF G@EBB?9GI BF?BF?@F IEI I?FGEA? ?@B?EEFK? B?AB E@?DAEE??EEKF? JGA? B2BIKF?EE? ?@E ?FB?B? EAA dF@EL?E BI?EGE? H?EB? EAB? ? ABEhM 9BF A?I?@EE? A? KFGB?KG?EEK B J B@?DAB?EEG ?B ,? I BB??EB E ? ? K AB?E? ? B? AFB?EEBE?E @ Figure 4 Overall design procedure Design procedure 9BI?EEGAB A A ? ?EEI ,? JGE? F?EIB J AG? 8 BL A A ?EEA EE@K E BG??EA?AF*F@ ? @E ?DB?IA? A9BBBDBE?E@ GAFA both combinations.)? ? ?E EB G B?EEFK? EGG Overall stability of the site ( ?EG?ABB ?E A? BD B?@EKAB?? I?EE? ?EA?E ,?? BAFAI?EE A?E-? BGAFB ?KIA? BGA BF @? @A EBA ! Initial sizing 9B@?BA? A ? EI? ?EE ?EEK@ ? !FI?EEBB83, 9B@?BAB?EEF2 F?EEK33? BBD AB?EE@?@9B@?BAB?EE2 KG?EEKH?E ,@?F ?EE FBBD EE F?EEK @F @KB?GA HF %A ?F FF BD AFF 8? *BDI?EE?@EKAB ,FGEK?FB??H?? ?KFEE@ ?EE@B B? ?EEB?G?G @ 8 B?G ?EEK ?A?FG B JG I B @?CAB B? *?K ?EL AB?EE +F B??F??EGG, Figure 5 Symbols for initial sizing *?EE?BB??I?EA? , 3 IFK *?EE?B I?EA? , *?KG??EKA@B *F@ ? ? + ?? E ,! + ?? GGE ,# 8AA ?G?K' + ?? @? A?E, = 8?E , 70 4 + FGE 2'K^mZbgbg`pZeel Panel 1 Material properties 9BB??I?EA?B ?EG??FA )83 ##!O*E5?N??F?ABI?E ?AA B ABEF?QF B @?AE?@?K? AEEFGEF @KEE ?@EBJG ? ?D ? ABL AE IEI *B??B ?EG??FBE@F @K? JG B ?E ? B-B ?E + 7G 9BGGB AB@?DAEE@B B? ?EE? ?EBB ?E AB?EE? BE@E ?AEEK, 9B EB Kg? EA B? ? h? ABI ? B. FF A? ?EE? BIAEE B? E?B A?BBBE@?I,B B B?EE??BGBB I?I,? E?@?DAEEBB??? EA B? ? F?EEK?D @ S? S 9BA ? @ ?BB?EE@??EB?EEE Figure 6 Procedure for determining material properties, geometry and actions From Figure 4 General expressions for geometry and actions .4&2"g4 .422gD 23&O2O2 2 &&2 &2& For calculation model A: 3&2"23? b 23? b .4&23"g 4 23 &&22 Wb &97 For calculation model B: 32&2" 23" .4&g 4 2 &22 3 y &? Determine characteristic material properties P<B KgDA? ? EAB? ? hDA A@?DAEE P<B KgDA ? BDA ? ? E AB? ? hDA AA ? E P<B KgD? KE BDA 23 32 Wy &97&&& & Panel 2 Determine initial geometry and actions (see Panel 1) 1 +F ?EFK, P ,?EE? FE)A E ? AI?EGE? (y 2 +F EI?F, 3 *?EE?A P *B??EAB.D.D@.DA P 9?EBΣ.D&.D.D@.DA P 9?EFF Σ.D&&.D&.D@&@.DA&A Carry out separately for both Combinations 1 and 2 General expressions for material properties and earth pressures For calculation model A: b OR h O b %1& b b R h O b g43 g*843 )1%1g! For calculation model B: Determine design material properties and earth pressures (see Panel 2) 1 (GGEKG??EF??EA?@? F??E GG P <B Kg&gDgg&gD gγ & P ( EAB? ? h&? ? hDgφ P : ? B&Dg 2 +F ?BG P ?BGAA %?&A AhA? b G ?EE? FE P ?BGA AI?EE?? %? To Figure 4 b 6 hOb h O h O6bOhOy ? h %& h 6=h %8%b %g%b b Oy g43 )1g!%g g %8843 * 71 5 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ ? @? ? ? GGBE@B ?AEEK 9B EB K? EAB? ? ? A BI ? B, ? AE B GGABE A?B??H E? B?DKGI,@? ? ? I?IF? ABGGABA ? EH 9BB KA F G?AB?EE EAB? BE@?D ?gD&D3 FA A ?? B# Design against sliding 9BGA A ? ?EE ?? E I ,! . BBF ? BBL ?E FG ABB BI?EGE? F@@K ?B B AB?EE@?"U"7? @KA BE F ? "U"7 Figure 7 Procedure for design against sliding 9BBG E?EK B BGGAB@?DAEE .A ?KF? ? @@K @?DAEEB? ?? EAB? ? 9B? G E?EK BGGABE A?@ B?EE@?? BA ? E.?E ?FAEE?B ?EE? AB ? @? ?EAEE? A ?EE? AB? @? AAI d>f, ??? E)83 ##!O *E FF df9>fBf9B ? IEF? EAB? ? ABA ? E ;?EAf9? G ABEE?I K? KG?EEK? AF!SSA? E?E,BIE B ? ? EE@?E .A ?K?B?DK? @FGIB?EE? E ,"9BDKB?B@ A$ From Figure 4 *?KG??EKA@B*F@ ? ? .A?? ?BB A?@ B@?? ?E?KA ? B B ? ? BE@EF"7U- O)83 ##!O*E 5.A? ??B A? ? F?K?GGEKI ABFE? +F BL ?EB I?EGE? 5? E P "&)?Ω .A?GGG?F ? E ? A?EE@? P "7&A +F ? E ? A?EE@? P *?EE?I?E? -&g?S<D P *?EE?I?E? AF)?5? E P *?EE?? E ? "75? E ■ .FIBA?EA???KAFB A?@ B ?EE? BA ? B?? FGII?EA d&fF?K@?F ■ .E B BA?EA?AF&R 2D@2 ■ .G ?EEK ?BG?I? A AB?EE BB B Design against toppling 9BGA A ? ?EE ?? GGE I ,#- ?EEKBBD EK B B? ?EEA DIKB?E ;AK"U"7A?GGG?? "U"7 9B?@E FF ?@B?EEG ,? ? ?? AFBB BI?EGE? F@ .A ?KG?B?@IB?B?DK 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 ?@E FF '?@G 5? E? '&)?W3 +F ?@E FF ?@G P <?EEF'&.& P <?EE@?'@&.@&@ P )?DAEE'A&.A&A P ,F?IB'IG&)? W&IG P '7&''@'A'IG ;AK'U'7 <B?B?DK$ R "+&g!19/ .4? h D 72 6 *?KG??EKA@B *F@ ? ? Panel 3 To Figure 4 2'K^mZbgbg`pZeel @KB?@E FF ?@B?FG ? AFB ?EEEAB'U'7 Figure 8 Effects of shear key 9B?@E FF G E?EK B BGG AB@?DAEE.A ?KF? ? @@K ? @?DAEEB??? EAB? ? 9B?@E FF G E?EK B?EEEAB E B@?DAEE 8FB? IEKB?@EKA? A ? ?EEGG E I @KEF?6: A !?NEA?@EKABB ??@KQ@?B BAB significant GI ? . ?GGE ?EEKI @KEF?-4 9KG?EEKAB? ?EEB?@ L?GGG?EKAE B GGE EE @?EB Design against bearing failure 9BGA A ? ?EE ?? @? A?EI , 9B@? G? @ ?BB?EE@?F@EB? @BBA ? BF ? @? ?G?K 8U87? E F? I?E8U87 9B@? GG B?EEEAB E @?DAEE? ? K ?? BI?EGE? 8 B A? ABE? @? A?EF I?@EK B AB?EE@?B@? GF@ ?EE?I? AAIB, 9B@? ?G?KG E?EK B BAB A ? E!IFGE? ?EK?EFBA @? ? ?EE? @? E??E@? ?G?K BK8 BE? @? A?EF I?@EK E F EA? B? ?@? ?G?KA? 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? (H? @@? AF, Figure 11 Bearing capacity factors, N, from ground properties From Figure 4 +F ? @? ?G?K87 A?GGG?5? E +F ? @? ?G?K875? E c Bearing capacity factor, N *?KG??EKA@B *F@ ? ? g +F @? G5? E? 8&-)? Ω ;AK8U87A?GGG?? 8U87 To Figure 4 Angle , 73 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ ? 9BAFE? AB? @? ?G?KI ,? 5? E?FB?B ?EIE?B AB@?AB? ?EE9BEE@ I?I A? B ?? @?? @?? V@EB?EE@?3 B?BI@ G BJG A@? ?G?KB?@?DAEE?@IB ?EE? EDEK@?F?EEI?E Structural design (? ?EEEDEK@FBAAB? B GG? BABFA? A ? EI ?EEF@ B? ?BG?B? B?IG?F B?EE? AE GGE ? @? ? +G BB?EE BEB@ A>FG? G10A>? G (BE GGE ? @? ? B? F@ ? AG??EA?BD?BEF?EF? 9BFBAFG? ?BG?EE? ?F B?BAEEGE? ?I@? EEB?GI AF F GBA?AB?EE.ABEE?EE?B B BGB<CEE@?B? B?I 5? E ?EEKE8 B?EE GAEKBH? I 5? E ? I?I At-rest earth pressures 2? K@?F ?EE? ? J % BKBE@ B? B??BG EE? , 9B?BGAA F BBL ?E G? B?EEI )83 ##!O*E# ? ?$%&O hR4*7 b B4*7B I E? ?AB? E? bB? EA Figure 13 Design procedure for structural design From Figure 4 Compaction earth pressures <?EEB?? @ABGE?F A@?DAEEBE@ B? BFG? ?BG, 9B?EEBE@ B?H?? ?B?? GEE @EG?? BF BE F? @ B 5? EIB?BGs 3? ?GB< B?EE F BB??FG? E E?)4, ?EEBE E?BE@?D ?BEEEAB ,I@? FG? HGF BFABEAB? B A?EI@?ABE@.AB A?EA D B A?I@? EEBEABF?K@ ?9BEABF@BE@B? ? ?GGG?ABI@? GE?FG?(EEA BE@ G E B?E B?EE+?EAKG?E FG? HGF ?I 9?@E *?KG??EKA@B *F@ ? ? 9B GI , *BDBFAB? ?EEAFG? G? ??GGG?$ P 2?JFF FF &'5? E P 2?JFF B?A&- P 7A*B?G ?EEKG@EB?,51211AB JG BD@ B?? AE *BDB? BEAB?EE @ ? B? BJG 5? EF ?GGE A? B JG AF*B?G BD@ B?? AE To Figure 4 Figure 14 Compaction earth pressures for structural design of cantilever retaining walls Figure 12 Effective base width, B’ zJ zK zD 74 8 2'K^mZbgbg`pZeel Panel 5 General expressions for designing walls for compaction pressures + E E? AD3 F)&g6)D b OR h O b ]%_ %1 & b Z] b R h O b ]%_ b R h O b ]%_ & %i] b 7 b OR h O b ]%_ R * - $C&%7 )] +GBAG $ ,< Di] pg D%_ % * +GBAG %<%D&%1 )] DZ] pg% d%_ R ) ? $BL ?E AD5? %i] gd%_ L s3 7 4 a] ) $? % R D%_ )]g% sa] 3 p ;^mp^^g ) %? %Z] gd%_ L sa] 3 1 4 Forces for stem design (see Figure 14) L < < OL OB0<+OL0 2F '& B/ / <+O / B/ + / B+ B/L/ 8B?-& B/<+O</B+OB0<+O<0 B A?9B4*7B?AF?JFFG?EIEA I?EB EIEAI?EAAI 4*7KG?EEK@? AF? F? D E ABE?EBKAB. I?I 2? K@?F IEI EIEAGGG ? IA? AE ? GGE ? ?K?E? AG ? OBKF?KEE@EI? BEB ?EE@ ;A? AB?E? A@?F ?EEAEE B?FG?B?A? EI?EE,B ?@E?EE? A? K?GB?F?K@EG B @?DAB?EEG?EEKA GI F?A? ? Table 2 Typical compaction equipment12 Description of compaction equipment Mass (kg) Centrifugal vibrator force (kN) Design force (kN) "DI@? GE?FG? " "DI@? GE?FG? " " "" DG? G? I@? EE !DI@? GE?FG? ! # G? G? I@? EE " ! "FBBEEE " 3 ( ! #@EI@? EE # " "! " FBBEEE " 3 ( " B/&B?$ 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 '& 8B?-&82 %&O hR4*7 b s9&g<8 ) ? . s3s3%s9 ) .? 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<< < < < O< < O< 8B?-& B( < B< < B< < B+ < 85? EAAA@? 75 9 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ <B B? $ ■ 8? ? ?IEBBGF?@EKEB?E?@E ? ?KF ?EE ■ 8E? E?KEGF?@EKE B )83 ##!O*E HB??@E@ ?D ?BNF?JFFG@EEIEBBF?K@B A? EB?H?KAB? ?KF? @ F ?? F? ? Q 9BEI? JG AB?E?BGs 3&AAI ?BGs3G?G? ?GB< B?EE?I 5? E A???@E?GB@E BGAB?EE9BJG ?FB?B?EE BGGG ? EA ?EE ?EE? )BAB?FG ? I?I Detailing Control of cracking .F?K@ ?K EB?D A? A ?EEA?B? F F? A? @?F ?EE,BE??E? B A? @?F I *.7.(7G#138EKBG B?@ A?E )8"? )8"!14@B G GE? @B)83 ##OO? )83 ##O3 * EA?D F?KB@?@K BF ?AKFBBBG B@K?EE? B?D BEKA*E!A)83 ##OO *?DF?K@EF?G?@EB@KBAEE F?$ ■ 5I?F FF?F A AF F %B?B AF KEFF?EKG AF? AB A?D ■ <BrestraintBF? ?A?D EFB@? ?FB?B 9?@E. B?? KEIEAE Figure 16 Earth and pore water pressures for structural design of retaining walls subject to 'at-rest' conditions F?K@B @BEI?EFB @ B?EE? AF ? BLAB@?BE@ EF?B ■ <BloadingBF? ?A?D EFB@? ?FB@?G? B?B 9?@E . B?@ AGAHF ?B B EF ?EE??DB:F?JF?K@FF ?EEJGE? H?GF? E?F@ ? *B?G 9BF FF??A AF EL E ?D BE@?EE?A?BG?ABFF@?AEE$ F &44AAs B 4& AG ? AG@ ?EEA B ?AB@ B B FF?EKG?D ? ABB? ABEI ?F??EA?D 4& BB?EEEB? FF? %& B J"FFBD, F? GE? F?K@,??EEABAAA AFEAHE@? BBE?? A? A AA& F? I?EAB E BA AAI ?BF?DF?K@AJG?B ?GGG??AA&F?@EA)83 ##1 & ??A B?G?AB BB ?EE?@ B L C@A BAF? ABA?D 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 O 9BEF?K@F?AFBJG @E ;46 H s& gF GId zW W B$ zD 76 10 ;4 &BB?? F KE gF &BG??EA?A AF E 6 &B?EE?AFH?GF? F@ ? &B?EE?AF:18F@ ? H&B??A AF ?B:18 GIB??A AF GI d &B?A@ FF E?FF 2'K^mZbgbg`pZeel s& ?@EI?EABF?JFFGF B AF FF?EK?ABAF? AB?D 9BI?EBE@B @? F BEF @? L? G? ? 9?@E ,?EEB?BB?J?EE?@?F ?EEBF? AF GE? ?B?EEA?BEB?I? I AF BAFAE DB?E?AGFA?EE ??<BEFB? @?A?FfU FF? BIE?B? f? I AF H Large radius bends .A ?KGIE??@ BF? AF ?B@?ABF@?ABBB E A B@?9BF FFF? E?FfFF BE@ ??AEE$ fFF V @1@f B E? ?@??B?A @& EAAFEF? B@ 1@ &B?EABGBAB@? F ?EIGEf f &@??F & I?EA FGI B 9B,116315 1515?GG J) ? FAE?@EB?EE? F B F FFF? EL Rules for spacing and quantity of reinforcement Vertical reinforcement <B?J?EAF ?BF FF??AI?E AF %B?EAB??BE@GE? ?B A?4BBF FFG ?A AF ? @@? AF9?@E A*B?G4E?GE? B F?JFF??AI?E AF %%BF?K@ @E?E?GE? 9B? @ ?C? I?E@?BE J BEABBFB?EEBD FF Figure 17 Typical drainage layout for a retaining wall Horizontal reinforcement 9BF FF??ABL ?E AF B?A BAI?E AF IB ?D EFG? ?EK?BF?E? B D?AA BE@ <BAEJ?EAF ?BHF F?K@E?J ABI?E AF ?? Practical issues Design for movement * B D?EKBF?EAAFF?EK?A ? 9B@?A?? ?EEK? @KB E BB@? BB ? B 9BAB AF ?E GL? H A BE@GE? EBE? ?D 9KG?EEKGL?G KBBEFBK? G AFD9B(115157116 FF GLB?F?JFF??AF2? F?JFFF FA? ?EE9B ? EEDBE?GLG@E? EE? B?BF FFIEFA A?G F3?AEE E?A??KFJ .?E??E ?@?K ??EEBAAA?EKB D?,B?I ?EE? ? ? ?DBA? ?EE? @A ?GG 1? 2A)83 ##O1 ,E E BA? ?EE ?EEK?GG? B?IJG? C IKOF%I B@?AB ?EEEEEE@? ,?FG?? AT*BC BE?EEAFFAFIF AIKFE BA?EE Drainage 300 mm wide granular backfill Weep hole Drainage pipe Large radius bend if required 9GI G?GAF@E GFG? GI? ?F??E@B ?? ?EE9BL FF?EK@B B?EEBE@A?A? ? E? 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G7?B1?@?K## 13 *.7.(7G#.1 216*.7.(## 14 )7.9.889(3 +(7+8.3 89.9:9.43 )8"!$71 1 1858)8.#"! 15 .3 89.9:9.43 4,897:*9:7(13 -.3 789*43 *7984*.9=,116315 15.89B* 8K 16 *43 897:*9(1151571B 9B* 8K 78 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ *)'=^mZbebg` O Brooker;>g`%<>g`%FB<>%FBLmkn\m> Introduction Mabl\aZim^kblbgm^g]^]_hknl^[r]^mZbe^klmhik^iZk^k^bg_hk\^f^gm]kZpbg`l _hkikhc^\mlmaZmaZo^[^^g]^lb`g^]nlbg`>nkh\h]^+'Bmikhob]^lZlnffZkr h_ma^k^jnbk^f^gmlh_ma^>nkh\h]^Zg]lbfieb_b^lma^fpa^k^ZiikhikbZm^' MhiZo^ma^pZr_hkma^bgmkh]n\mbhgh_>nkh\h]^+%hma^klniihkmbg` lmZg]Zk]laZo^[^^gbgmkh]n\^]hkk^obl^]%bg\en]bg`3 N ;L1.))3<hg\k^m^¾<hfie^f^gmZkrlmZg]Zk]mh;L>G+)/¾*pab\a k^ieZ\^];L.,+13<hg\k^m^hg*=^\^f[^k+)),Zg]lahne]Zek^Z]r[^ _ZfbebZk' N ;L---23Li^\b_b\Zmbhg_hk\Zk[hglm^^e[Zkl_hkma^k^bg_hk\^f^gmh_ \hg\k^m^pZlk^obl^]bg+)).lhmaZmbm[^\Zf^Z\hfie^f^gmZkr lmZg]Zk]mh;L>G*))1)3Lm^^e_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^^e k^bg_hk\^f^gm_hk\hg\k^m^¾li^\b_b\ZmbhgaZlZelh[^^gk^obl^]% 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^l^ebfbml% 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]ik^iZkZmbhgh_]kZpbg`l\Zg[^ _hng]bghma^k]h\nf^gml Type and grade of reinforcement Ma^+)).k^oblbhgh_;L---2bgmkh]n\^]Z\aZkZ\m^kblmb\rb^e]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[^ik^_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^]' Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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[ho^eblmaZobg` 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^^'`'ma^ebgdlbgZ[^Zf' :elh%ma^\ho^kmhma^fZbg[Zklahne][^Zme^Zlm^jnZemhma^lbs^h_ maZm[Zk%ienlma^ZeehpZg\^_hk]^obZmbhgl%D\]^o'Pa^k^ma^k^Zk^gh ebgdlma^ghfbgZe\ho^klahne][^Zme^Zlm^jnZemhma^lbs^h_ma^[Zk ienlD\]^o%mablfZr[^lb`gb_b\Zgm_hk[Zk]bZf^m^kl`k^Zm^kmaZg *+ff'D\]^ofZr[^.hk*)ff]^i^g]bg`hgma^jnZebmrZllnkZg\^ lrlm^fZllnf^]_hkma^ikhc^\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^^e' Figure 1 Description of bond conditions =bk^\mbhgh_\hg\k^mbg` Anchorage and lap lengths =bk^\mbhgh_\hg\k^mbg` 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[^]^o^ehi^]_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%Zemahn`amablblghm lmZm^]bgma^<h]^' +.) c) h > 250 mm a) 45º < a< 90º =bk^\mbhgh_\hg\k^mbg` =bk^\mbhgh_\hg\k^mbg` 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_^er 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^]bghg^eh\Zmbhg !a/6*'-" @hh] ,+) --) .0) 1,) *)2) *-+) *1*) +-/) .0f Ihhk -/) /,) 1+) **2) *./) +)+) +.2) ,.+) 1*f *))eZii^]bghg^eh\Zmbhg !a/6*'." @hh] ,-) -0) /*) 12) **0) *.+) *2-) +/-) /*f Ihhk -2) /1) 10) *+0) */0) +*0) +00) ,00) 10f LmkZb`am[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^[ZkZmma^ihlbmbhg_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_[ZklZk^eZii^]bghg^eh\Zmbhg%]^\k^Zl^ma^eZie^g`mal_hkÂ.)eZii^]bghg^eh\ZmbhgÃ[rZ_Z\mhkh_)'1+' 6 Ma^_b`nk^lbgmablmZ[e^aZo^[^^gik^iZk^]_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`^e^g`ma%e[]%!pab\a\Zg[^ h[mZbg^]_khfMZ[e^+"blf^Zlnk^]Zehg`ma^\^gmk^ebg^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][^ieZ\^]hnmlb]^^Z\a^g]h_ma^eZi e^g`mah_[Zklbg\hfik^llbhgZg]pbmabg-fh_ma^^g]lh_ma^eZi e^g`ma!l^^?b`nk^/["' Figure 2 Pa^k^ihllb[e^eZilbgZf^f[^klahne][^lmZ``^k^]!l^^?b`nk^-" Zg]ghmeh\Zm^]bgZk^Zlh_ab`almk^ll'Ma^ZkkZg`^f^gmh_eZii^][Zkl lahne]\hfierpbma?b`nk^.%Zll^mhnm[^ehp3 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^ma^eZie^g`malahne][^bg\k^Zl^][rZ e^g`ma^jnZemhma^\e^Zk]blmZg\^' 2. Ma^ehg`bmn]bgZe]blmZg\^[^mp^^gmphZ]cZ\^gmeZillahne]ghm[^ e^llmaZg)',mbf^lma^eZie^g`ma%e)'Pa^k^mablblghmma^\Zl^%ma^ [Zkllahne][^\hglb]^k^]Zl[^bg`eZii^]bghg^l^\mbhg' 3. Bg\Zl^h_Z]cZ\^gmeZil%ma^\e^Zk]blmZg\^[^mp^^gZ]cZ\^gm[Zkl lahne]ghm[^e^llmaZg+fhk+)ff' f lbd Figure 3 Anchorage of links *)f%[nm ª0)ff .f%[nm ª.)ff Pa^gma^ikhoblbhgl\hfierpbma*Zg],Z[ho^%ma^i^kfbllb[e^ i^k\^gmZ`^h_eZii^][Zklbgm^glbhgfZr[^*))pa^k^ma^[ZklZk^ Zeebghg^eZr^k'Bgmabl\Zl^ma^]^lb`geZie^g`ma%e)%_khfMZ[e^+%fnlm [^bg\k^Zl^]!l^^ghm^."'Pa^k^ma^[ZklZk^bgl^o^kZeeZr^klghfhk^ maZg.)lahne][^eZii^]bgZgrhg^eZr^k' :ee[Zklbg\hfik^llbhgZg]l^\hg]Zkr!]blmkb[nmbhg"k^bg_hk\^f^gmfZr [^eZii^]bgma^lZf^eh\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_ma^eZii^][Zklble^llmaZg+)ff%hkma^i^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_ma^eZii^][Zklbl`k^Zm^kmaZghk^jnZe mh+)ff%ma^mkZglo^kl^k^bg_hk\^f^gmlahne]aZo^ZmhmZeZk^Z%:lm !lnfh_Zeee^`liZkZee^emhma^eZr^kh_ma^lieb\^]k^bg_hk\^f^gm¾l^^ ?b`nk^/Z"h_ghme^llmaZgma^Zk^Z:lh_hg^eZii^][Zk!Σ:lmª*'):l"' Ma^mkZglo^kl^[Zklahne][^ieZ\^]i^ki^g]b\neZkmhma^]bk^\mbhgh_ ma^eZii^]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^ma^eZii^][ZklbgZleZ[Zk^eh\Zm^]bgZg Zk^Zh_ehplmk^ll%^'`'g^Zkma^ihbgmh_\hgmkZ_e^qnk^%bmbl`^g^kZeer Z\\^imZ[e^mhZllnf^maZmmkZglo^kl^k^bg_hk\^f^gmblghmk^jnbk^]' B_fhk^maZg.)h_ma^[ZklZk^eZii^]bghg^eh\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^_hk^a/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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Beams Figure 7 Illustration of curtailment of longitudinal reinforcement Curtailment Ah``bg`k^bg_hk\^f^gm Nge^llma^Z]]bmbhgZem^glbe^_hk\^bgma^ehg`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]ma^ihbgmZm pab\abmblk^jnbk^]_hk_e^qnkZelmk^g`ma!mablbldghpgZlma^Âlab_m kne^Ã"nlbg`ma^_heehpbg`^qik^llbhg!l^^Zelh?b`nk^0"3 >go^ehi^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^ s6e^o^kZkf y 6Zg`e^h_\hfik^llbhglmknm Ze e[] Mabl\Zg\hgl^koZmbo^er[^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^]'Ahp^o^k%ma^lbfieb_b\ZmbhglZk^\hgl^koZmbo^Zg]^\hghfb^l \Zg[^Z\ab^o^][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^^__^\mbo^e^g`ma' 2 Zeblma^]blmZg\^mhZeehp_hkm^glbe^_hk\^]n^mhla^Zk_hk\^' 3 e[]blma^]^lb`gZg\ahkZ`^e^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^lma^ehg`^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*$e)(!,l"pa^k^l6liZ\bg`h_ma^mkZglo^kl^[Zkl' c) Simple support, bottom reinforcement *)'=^mZbebg` Reinforcement in end supports Minimum spacing of reinforcement Bgfhghebmab\\hglmkn\mbhg%^o^gpa^glbfie^lniihkmlaZo^[^^g Zllnf^]bg]^lb`g%ma^l^\mbhgZmlniihkml!mhik^bg_hk\^f^gm"lahne] [^]^lb`g^]_hkZ[^g]bg`fhf^gmZkblbg`_khfiZkmbZe_bqbmrh_Zm e^Zlm+.h_ma^fZqbfnf[^g]bg`fhf^gmbgma^liZg!b'^'ikhob]^ +.h_fb]&liZg[hmmhfk^bg_hk\^f^gm"' Ma^fbgbfnf\e^Zk]blmZg\^[^mp^^g[Zkllahne][^ma^`k^Zm^kh_3 N ;Zk]bZf^m^k N :``k^`Zm^lbs^ienl.ff N +)ff Shear reinforcement Ma^Zk^Zh_[hmmhfk^bg_hk\^f^gmikhob]^]Zmlniihkmlpbmaebmme^hkgh ^g]_bqbmrZllnf^]bg]^lb`g%lahne][^Zme^Zlm+.h_ma^Zk^Zh_lm^^e ikhob]^]bgma^liZg'Ma^[Zkllahne][^Zg\ahk^]mhk^lblmZ_hk\^%?>' ?>6!uO>]uZe(s"$G>] pa^k^ uO>]u 6Z[lhenm^oZen^h_la^Zk_hk\^ G>] 6ma^ZqbZe_hk\^b_ik^l^gm Ma^ehg`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^gmZmeZilbgma^ehg`bmn]bgZe[Zkl'Ma^mkZglo^kl^liZ\bg` h_ma^e^`lbgZl^kb^lh_la^Zkebgdllahne]ghm^q\^^]3 lm%fZq6)'0.]©/))ff Ma^Zg\ahkZ`^%e[]%lahne][^f^Zlnk^][^rhg]ma^ebg^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\^immaZmZ 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`ma^oZen^ h_[m' Maximum area of longitudinal reinforcement Hnmlb]^eZieh\Zmbhgl%ma^fZqbfnfZk^Zh_m^glbhghk\hfik^llbhg 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][^ikhob]^]!l^^?b`nk^*)\"'Ma^ [Zkllahne][^Zg\ahk^]mhk^lblmZ_hk\^%?>%Zl`bo^gbgma^l^\mbhg hg[^Zfl' Minimum percentage of reinforcement required 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Minimum spacing requirements Minimum areas of reinforcement Ma^fbgbfnf\e^Zk]blmZg\^[^mp^^g[Zkl!ahkbshgmZehko^kmb\Ze" lahne]ghm[^e^llmaZgma^[Zklbs^%[%!]`$.ff"%hk+)ff%pa^k^ ]`blma^fZqbfnflbs^h_Z``k^`Zm^' Ma^fbgbfnfZk^Zh_k^bg_hk\^f^gmmh[^ikhob]^]oZkb^lpbmama^ \hg\k^m^lmk^g`ma!l^^MZ[e^-"' Maximum area of longitudinal reinforcement Maximum spacing of reinforcement ?hkleZ[le^llmaZg+))ffmab\dma^_heehpbg`fZqbfnfliZ\bg` kne^lZiier!ablma^]^imah_ma^leZ["3 N ?hkma^ikbg\biZek^bg_hk\^f^gm3,a[nmghmfhk^maZg-))ff' N ?hkma^l^\hg]Zkrk^bg_hk\^f^gm3,'.a[nmghmfhk^maZg-.)ff' Ma^^q\^imbhgblbgZk^Zlpbma\hg\^gmkZm^]ehZ]lhkZk^Zlh_ fZqbfnffhf^gmpa^k^ma^_heehpbg`Ziieb^l3 N ?hkma^ikbg\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^^elmk^ll%sl%bm\Zg`^g^kZeer[^Zllnf^]maZmslpbee ghm^q\^^],+)FIZ_hkZmrib\ZeleZ['Pa^k^ma^leZ[lniihkmlh__b\^ hkk^lb]^gmbZeZk^Zlbmblngebd^ermaZmslpbee^q\^^]+1)FIZ' Hnmlb]^eZieh\Zmbhgl%ma^fZqbfnfZk^Zh_m^glbhghk\hfik^llbhg 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^^__^\mbo^e^g`ma' e[]blma^]^lb`gZg\ahkZ`^e^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^lma^ehg`^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]^Zg^o^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^\mZg`enZki^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_ma^ebgdlbgma^kZ]bZe]bk^\mbhg l m 6ma^liZ\bg`h_ma^ebgdlbgma^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][^ieZ\^]bgZ pb]ma^jnZemhma^lnfh_)'*+.mbf^lma^iZg^epb]mahg^bma^klb]^ h_ma^\henfg':mk^ik^l^gmlma^Zk^Zh_k^bg_hk\^f^gmk^jnbk^]mh k^lblmma^_neeg^`Zmbo^fhf^gm_khfma^lnfh_ma^mphaZe_iZg^el ^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][^ikhob]^]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[Zklknggbg`iZkZee^emhma^ 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] [^ieZ\^]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^k^ing\abg`la^Zkk^bg_hk\^f^gmblk^jnbk^]ma^_heehpbg`kne^l lahne][^h[l^ko^]' N Bmlahne][^ikhob]^][^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^llma^i^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][^ieZ\^]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_ma^ebgdl%lklahne]ghm^q\^^])'0.]!l^^?b`nk^*-"' N Ma^mZg`^gmbZeliZ\bg`h_ma^ebgdl%l]lahne]ghm^q\^^]*'.] pbmabg+]h_ma^\henfg_Z\^' N Ma^mZg`^gmbZeliZ\bg`h_ma^ebgdllahne]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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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]^eZilbl-\hfiZk^]pbma/bg;L1**)'Ahp^o^k% mablZk^Z\Zg[^bg\k^Zl^]ikhob]^]maZmma^\hg\k^m^\Zg[^ieZ\^] Zg]\hfiZ\m^]ln__b\b^gmer'L^e_&\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]bgL^e_&\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[^e^llmaZg/ff hkhg^jnZkm^kh_ma^fZqbfnf]bZf^m^kh_ma^ehg`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][^ikhob]^]bg ^Z\a_Z\^' Ma^]blmZg\^[^mp^^gmphZ]cZ\^gmo^kmb\Ze[Zkllahne]ghm^q\^^] ma^e^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)'))*:\' Ahp^o^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[^ikhob]^] 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[^eZii^]Zmma^lZf^eh\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^lpbmabgma^eZi 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]^obZmbhglbgma^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]^obZmbhgl' 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_lmkZb`ame^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*) $.%¾+. Table 11 16 20 25 32 40 *2+[ /\ +-)[ /\ +-)[ 1 +-)[ 1 +-)[ *) Key a : mZ]blmZg\^`k^Zm^kmaZgma^eZk`^k]bf^glbhgh_ma^\henfgZ[ho^hk[^ehpZ [^ZfhkleZ[%]bf^glbhgl\Zg[^bg\k^Zl^][rZ_Z\mhkh_*'/0' b ;nmghm`k^Zm^kmaZgfbgbfnf]bf^glbhgh_ma^\henfg' c /ff[ZklZk^ghmk^Z]berZoZbeZ[e^bgma^ND' 86 N I^kfbllb[e^i^k\^gmZ`^h__Z[kb\fZbgk^bg_hk\^f^gmmaZmfZr[^ Deductions to bar dimensions to allow for deviations between two concrete faces Distance between concrete faces (mm) )¾*))) *)))¾+))) Ho^k+))) :gre^g`ma Type of bar EbgdlZg]hma^k[^gm[Zkl EbgdlZg]hma^k[^gm[Zkl EbgdlZg]hma^k[^gm[Zkl LmkZb`am[Zkl Total deduction (mm) *) *. +) -) *)'=^mZbebg` Figure 15 ek 6ma^`k^Zm^kh_ma^]blmZg\^l!bgf"[^mp^^gma^\^gmk^lh_ma^ \henfgl%_kZf^lhkpZeellniihkmbg`ZgrmphZ]cZ\^gm_ehhk liZglbgma^]bk^\mbhgh_ma^mb^ng]^k\hglb]^kZmbhg ?m 6!+)$-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_e^o^eZg^__^\mbo^er\hgmbgnhnli^kbia^kZemb^ lahne][^ikhob]^]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][^ikhob]^]Zm^Z\a_ehhkZg]khh_e^o^ebgmph ]bk^\mbhglZiikhqbfZm^erZmkb`amZg`e^l'Ma^rlahne][^^__^\mbo^er \hgmbgnhnlmakhn`ahnmma^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]^o^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`^i^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^][rma^ikZ\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^^e[Zkl_hkma^k^bg_hk\^f^gmh_\hg\k^m^';LB%+)).' 4 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*))1)3Lm^^e_hkma^k^bg_hk\^f^gmh_\hg\k^m^¾P^e]Z[e^k^bg_hk\bg`lm^^e¾@^g^kZe';LB%+)).' 5 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1///3L\a^]nebg`%]bf^glbhgbg`%[^g]bg`Zg]\nmmbg`h_lm^^ek^bg_hk\^f^gm_hk\hg\k^m^¾Li^\b_b\Zmbhg';LB%+)).' 6 BGLMBMNMBHGH?LMKN<MNK:E>G@BG>>KL(<HG<K>M>LH<B>MR'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^%+))/' 10 FHLL%KF;KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+3;^Zfl'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>LH<B>MR'M^\agb\Zek^ihkm/+3L^e_&\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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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) *1*) +,.) ,))) -)1) 2-f @hh] -)) ..) 0*) *),) *,/) *0/) ++.) ,)/) 0)f Ihhk .*) 02) *)*) *-1) *2-) +,+) ,++) -,0) *))f @hh] +,) ,+) -*) /)) 01) *)*) *,)) *0/) -)f Ihhk ,,) -.) .1) 1.) **+) *-.) *1.) +.*) .1f @hh] ,+) -*) -2) /.) 1*) *)*) *,)) *0/) -)f Reinforcement in compression Concrete class C20/25 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl .)eZii^]bghg^ eh\Zmbhg!a/6*'-" EZie^g`ma% l) *))eZii^] bghg^eh\Zmbhg!a/6*'." Concrete class C25/30 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl EZie^g`ma% l) Ihhk -/) .1) 0)) 2,) **/) *-.) *1.) +.*) .1f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] ,+) --) .0) 1,) *)2) *-+) *1*) +-/) .0f Ihhk -/) /,) 1+) **2) *./) +)+) +.2) ,.+) 1*f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] ,-) -0) /*) 12) **0) *.+) *2-) +/-) /*f Ihhk -2) /1) 10) *+0) */0) +*0) +00) ,00) 10f @hh] +*) ,)) ,1) ..) 0,) 2-) *+)) */,) ,0f Ihhk ,)) -+) .-) 02) *),) *,-) *0+) +,,) .,f @hh] ,)) ,1) -.) /)) 0.) 2-) *+)) */,) ,0f Concrete class C28/35 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl EZie^g`ma% l) Ihhk -+) .-) /.) 1/) *)0) *,-) *0+) +,,) .,f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] ,)) -*) .,) 00) *)*) *,+) */1) ++1) .+f Ihhk -+) .2) 0/) **)) *-.) *11) +-)) ,+/) 0.f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] ,+) --) .0) 1,) *)2) *-*) *1)) +-.) ./f Ihhk -.) /,) 1*) **1) *..) +)*) +.0) ,-0) 1)f @hh] +*) +1) ,/) .,) /2) 2)) **.) *./) ,/f Ihhk +2) -)) .+) 0.) 22) *+1) */-) ++,) .*f @hh] +2) ,/) -,) .1) 0+) 2)) **.) *./) ,/f Ihhk -*) .+) /+) 1+) *),) *+1) */-) ++,) .*f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] +2) ,2) .*) 0-) 20) *+/) */*) +*1) .)f Ihhk -*) ./) 0+) *).) *,1) *02) ++2) ,**) 0+f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] ,*) -+) .-) 02) *)-) *,.) *0+) +,-) .-f Ihhk -,) /)) 01) **,) *-1) *2+) +-/) ,,-) 00f @hh] +)) +0) ,.) .*) //) 1/) **)) *-2) ,-f Ihhk +1) ,1) .)) 0+) 2.) *+,) *.0) +*,) -2f @hh] +0) ,.) -+) ..) /2) 1/) **)) *-2) ,-f Ihhk ,2) -2) .2) 02) 21) *+,) *.0) +*,) -2f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] +0) ,1) -2) 0*) 2,) *+)) *.-) +)2) -1f Ihhk ,2) .-) /2) *)*) *,+) *0+) ++)) +21) /2f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] +2) -)) .+) 0/) 22) *+2) */.) ++-) .*f Ihhk -+) .0) 0-) *)1) *-+) *1-) +,.) ,+)) 0,f Concrete class C30/37 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl EZie^g`ma% l) Concrete class C32/40 LmkZb`am[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 @hh] +/) ,,) ,2) .+) /.) 1*) *)-) *-*) ,+f Ihhk ,0) -0) ./) 0-) 2,) **/) *-1) +)*) -/f @hh] +/) ,/) -/) /0) 10) **,) *-.) *20) -.f Ihhk ,0) .*) /.) 2.) *+.) */+) +)0) +1*) /.f @hh] +1) ,1) -2) 0*) 2-) *+*) *..) +**) -1f Ihhk ,2) .-) 0)) *)+) *,-) *0,) +++) ,)*) /2f @hh] *0) +,) ,)) --) .0) 0-) 2.) *+2) ,)f Ihhk +-) ,,) -,) /+) 1+) *)/) *,.) *1-) -+f @hh] +-) ,)) ,/) -1) /)) 0-) 2.) *+2) ,)f Reinforcement in compression Concrete class C35/45 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl .)eZii^]bghg^ eh\Zmbhg!a/6*'-" EZie^g`ma% l) *))eZii^] bghg^eh\Zmbhg!a/6*'." Concrete class C40/50 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl EZie^g`ma% l) Ihhk ,-) -,) .*) /1) 1.) *)/) *,.) *1-) -+f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] +-) ,,) -+) /*) 1)) *)-) *,,) *1)) -*f Ihhk ,-) -/) /)) 10) **-) *-1) *12) +.0) .2f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] +.) ,.) -.) /.) 1/) ***) *-+) *2,) --f Ihhk ,/) .)) /-) 2,) *++) *.2) +),) +0/) /,f @hh] */) ++) +1) -)) .,) /2) 11) **2) +0f Ihhk ++) ,*) -)) .1) 0/) 21) *+.) *0)) ,2f @hh] ++) +1) ,,) --) ..) /2) 11) **2) +0f Concrete class C45/55 LmkZb`am[Zklhger :g\ahkZ`^ e^g`ma%l[] Hma^k[Zkl EZie^g`ma% l) Ihhk ,*) ,2) -0) /,) 01) 21) *+.) *0)) ,2f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] ++) ,)) ,2) ./) 0-) 2/) *+,) */0) ,1f Ihhk ,*) -,) ..) 1)) *)/) *,0) *0.) +,1) ..f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] +,) ,+) -+) /)) 02) *),) *,*) *01) -*f Ihhk ,,) -/) .2) 1/) **,) *-0) *11) +..) .1f @hh] *.) +)) +/) ,1) -2) /-) 1+) ***) +.f Ihhk +*) +2) ,0) .-) 0)) 2*) **0) *.1) ,/f @hh] ++) +1) ,,) --) ..) /2) 11) **2) +0f Ihhk ,*) ,2) -0) /,) 01) 21) *+.) *0)) ,2f .)eZii^]bghg^ eh\Zmbhg!a/6*'-" @hh] ++) ,)) ,2) ./) 0-) 2/) *+,) */0) ,1f Ihhk ,*) -,) ..) 1)) *)/) *,0) *0.) +,1) ..f *))eZii^] bghg^eh\Zmbhg!a/6*'." @hh] +,) ,+) -+) /)) 02) *),) *,*) *01) -*f Ihhk ,,) -/) .2) 1/) **,) *-0) *11) +..) .1f Concrete class C50/60 LmkZb`am[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^[ZkZmma^ihlbmbhg_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_[ZklZk^eZii^]bghg^eh\Zmbhg%]^\k^Zl^ma^eZie^g`mal_hk .)eZii^]bghg^eh\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, -0* ..) /+1 0)0 01. ++/ ,,2 -.+ ./. /02 02+ 2). *)+) **,) */ +)* -)+ /), 1)- *)*) *+*) *-*) */*) *1*) +)*) +) ,*- /+1 2-+ *+/) *.0) *11) ++)) +.*) +1,) ,*-) +. -2* 21+ *-0) *2/) +-.) +2.) ,--) ,2,) --+) -2*) ,+ 1)- */*) +-*) ,++) -)+) -1,) ./,) /-,) 0+-) 1)-) -) *+/) +.*) ,00) .),) /+1) 0.-) 11)) *)*)) **,)) *+/)) 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 +.* ++, +)* *1, */1 *) *).) 01. /+1 .+- --2 ,2, ,-2 ,*- +1/ +/+ *+ *.*) **,) 2). 0.- /-/ ./. .), -.+ -** ,00 */ +/1) +)*) */*) *,-) **.) *)*) 12- 1)- 0,* /0) +) -*2) ,*-) +.*) +)2) *1)) *.0) *-)) *+/) **-) *).) +. /.-) -2*) ,2,) ,+0) +1)) +-.) +*1) *2/) *01) */-) ,+ *)0)) 1)-) /-,) .,/) -/)) -)+) ,.0) ,++) +2+) +/1) -) */1)) *+/)) *)*)) 1,1) 0*1) /+1) ..2) .),) -.0) -*2) 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-/ *) )'/*0 *'+,, *'1.) +'-// ,')1, ,'/22 -',*/ -'2,+ .'.-2 /'*/. *+ )'111 *'00/ +'//, ,'..* -'-,2 .',+0 /'+*. 0'*), 0'22) 1'101 */ *'.01 ,'*.0 -'0,. /',*, 0'12+ 2'-0) **')-1 *+'/+0 *-'+). *.'01, +) +'-// -'2,+ 0',21 2'1/. *+',,* *-'020 *0'+/, *2'0+2 ++'*2. +-'//+ +. ,'1., 0'0)0 **'./) *.'-*, *2'+/0 +,'*+) +/'20- ,)'1+0 ,-'/1) ,1'.,- ,+ /',*, *+'/+0 *1'2-) +.'+., ,*'./0 ,0'11) --'*2, .)'.)0 ./'1+) /,'*,, -) 2'1/. *2'0+2 +2'.2- ,2'-.1 -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-/ ,'*.0 +'/,* +'+.. *'20, *'0.- *'.01 *'-,. *',*. *) 1'++* /'*/. -'2,+ -'**) ,'.+, ,')1, +'0-) +'-// +'+-+ +').. *+ **'1,1 1'101 0'*), .'2*2 .')0, -'-,2 ,'2-/ ,'..* ,'++1 +'2.2 */ +*')-- *.'01, *+'/+0 *)'.++ 2')*2 0'12+ 0')*. /',*, .'0,2 .'+/* +) ,+'11+ +-'//+ *2'0+2 */'--* *-')2+ *+',,* *)'2/* 2'1/. 1'2/1 1'++* +. .*',01 ,1'.,- ,)'1+0 +.'/12 ++')*2 *2'+/0 *0'*+/ *.'-*, *-')*+ *+'1-. ,+ 1-'*01 /,'*,, .)'.)0 -+')12 ,/')0/ ,*'./0 +1').2 +.'+., ++'2.1 +*')-- -) *,*'.+1 21'/-/ 01'2*0 /.'0/- ./',/2 -2',+, -,'1-, ,2'-.1 ,.'10* ,+'11+ 90 $ 5"$ / $ 6'/$ 7'/# $ / $ 6'/$ 6' !" 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"$ #" "D "" "" ! $ " " " "*" #" $ " $ "" " " 0!"0 ? <'#'#,>,<'>#'#:#'O> D /F $ " :'H'>N<,</#,H'6># ( ) (4) <$ # <'#'#,>,<'>#'#:#'O> 4D $ ' (9"!'4) $ <'#'#,>,<'>#'#:#'O> >II$ D # '(@ ) 4 <'#'#,>,<'>#'#:#'O> -D * # +, # # '$ IIB = <'#'#,>,<'>#'#:#'O> @-, $ -.#$ +, /# # '$ III > #/O>/<#O/'#P #" 4@D # #"/!$ 4 9 L:,<<P 5<O:/#,O/',#'O> ="9 0 % A A /O>#<:/# # #- /$ @ ! <'#'#,>,<'>#'#:#'O> @BD # ##+ '$ II 98 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+' *+'Lmkn\mnkZe_bk^]^lb`g A S Fraser;>g`Ia=<>g`FB<>FBLmkn\m>A E K Jones ;>g`Ia=<>g`?B<> Introduction Mabl\aZim^k\ho^klma^lmkn\mnkZe_bk^]^lb`gh_\hg\k^m^lmkn\mnk^lmh >nkh\h]^+%IZkm*+3Lmkn\mnkZe_bk^]^lb`g*%pab\apbee[^k^_^kk^]mhZlIZkm *+makhn`ahnm'Bml^mlhnmmak^^]^lb`gf^mah]lmhZeehpma^^g`bg^^kmh lZmbl_rma^i^k_hkfZg\^k^jnbk^f^gmlh_Zlmkn\mnk^bg_bk^3 N MZ[neZkf^mah]l N Lbfieb_b^]\Ze\neZmbhgf^mah]l N :]oZg\^]\Ze\neZmbhgf^mah]l Mabl\aZim^k`bo^l`nb]Zg\^hgma^mZ[neZkZg]lbfieb_b^]f^mah]l'Ma^ Z]oZg\^]f^mah]l%pab\ak^jnbk^li^\bZeblmdghpe^]`^Zg]mhhel%Zk^hnmlb]^ ma^l\hi^h_mablin[eb\Zmbhg'?nkma^kbg_hkfZmbhg\Zg[^_hng]bg@nb]^mh ma^Z]oZg\^]_bk^lZ_^mr^g`bg^^kbg`h_lmkn\mnk^l+':`nb]^mhl^e^\mbg`ma^ ZiikhikbZm^f^mah]_hkma^]^lb`gh_^e^f^gmlbgma^_bk^\hg]bmbhgbl`bo^gbg ?b`nk^*[^ehp' Bmlahne][^ghm^]maZmma^NDGZmbhgZe:gg^q,!G:"oZen^laZo^[^^g nl^]makhn`ahnm%bg\en]bg`pbmabgma^_hkfneZ^Zg]mZ[e^l'BgZ]]bmbhg%mabl in[eb\Zmbhg]h^lghm\ho^kma^nl^h_\hg\k^m^\eZll^l`k^Zm^kmaZg<.)(/)% _hkpab\ama^k^blZ]]bmbhgZe`nb]Zg\^bgIZkm*+' <_]kh[' <bemY^Whji^em_d]m^_Y^\_h[h[i_ijWdY[Z[i_]dc[j^eZjeWZefj 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: ?djheZkYj_edje Eurocodes =[jj_d]ijWhj[Z IbWXi 8[Wci 9ebkcdi <ekdZWj_edi <bWjibWXi :[\b[Yj_edi H[jW_d_d]mWbbi :[jW_b_d] 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ <_]kh[( Coefficient kc(y Wbbem_d]\ehZ[Yh[Wi[e\Y^WhWYj[h_ij_Yijh[d]j^ (fck) of concrete Basic concepts Ma^k^Zk^lhf^[Zlb\\hg\^imlpbmabgIZkm*¾+maZmZk^bgmkh]n\^] a^k^mhZb]ng]^klmZg]bg`%iZkmb\neZker_hkma^lbfieb_b^]\Ze\neZmbhg f^mah]l'Ma^k^bl\hglb]^kZ[erfhk^]^mZbebgMa^<hg\k^m^<^gmk^ in[eb\Zmbhg@nb]^mhma^_bk^k^lblmZg\^h_\hg\k^m^lmkn\mnk^l-' Level of protection Ma^k^Zk^mak^^lmZg]Zk]_bk^^qihlnk^\hg]bmbhglmaZmfZrg^^]mh[^ lZmbl_b^]!_hkbglmZg\^mh\hfierpbma[nbe]bg`k^`neZmbhgl"3 R F^\aZgb\Zek^lblmZg\^_hkehZ][^Zkbg` E Bgm^`kbmrh_l^iZkZmbhg I BglneZmbhg Ma^k^jnbk^]i^k_hkfZg\^\kbm^kbZpbee]^i^g]hgma^_ng\mbhgh_ ma^^e^f^gm%pbmaleZ[l`^g^kZeerk^jnbkbg`ehZ]k^lblmZg\^Zg]_bk^ l^iZkZmbhg\ZiZ[bebmrpa^k^Zl\henfglfZrhgerg^^]ehZ]k^lblmZg\^' Coefficient, k c (y ) >nkh\h]^*%IZkm*+.ikhob]^lZ\ahb\^[^mp^^gghfbgZeZg]gZmnkZe _bk^^qihlnk^\hg]bmbhgl'GhfbgZe_bk^lZk^k^ik^l^gm^][r`^g^kZebl^] _bk^\nko^l_hkma^inkihl^lh_\eZllb_b\ZmbhgZg]\hfiZkblhg[nm ma^r[^Zkghk^eZmbhglabimhma^iZkmb\neZk\aZkZ\m^kblmb\lh_ma^ [nbe]bg`ng]^k\hglb]^kZmbhg'GZmnkZe!iZkZf^mkb\"_bk^lZk^]^Zempbma [r\Ze\neZmbhgm^\agbjn^l[Zl^]hgZ\hglb]^kZmbhgh_ma^iarlb\Ze iZkZf^m^klli^\b_b\mhZiZkmb\neZk[nbe]bg`hk_bk^\hfiZkmf^gm'Ma^ fhlm\hffhgghfbgZe_bk^^qihlnk^nl^]bg]^lb`gblma^lmZg]Zk] _bk^\nko^4mablblma^Zllnf^]_bk^^qihlnk^bgmabl\aZim^k' 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 Pa^k^bmblk^jnbk^]%ma^k^lblmZg\^h_Zl^\mbhglahne][^\Ze\neZm^]% mZdbg`ma^fZm^kbZe_Z\mhkgF%_bZl*')pbmak^li^\mmh[hmama^ ma^kfZeZg]f^\aZgb\Zeikhi^kmb^lh_ma^\hg\k^m^%k^bg_hk\^f^gmhk ik^lmk^llbg`lm^^e' 0.2 0 0 200 400 600 800 1000 1200 o Temperature, y ( C) Ma^lmk^g`mah_\hg\k^m^%k^bg_hk\^f^gmZg]ik^lmk^llbg`lm^^ek^]n\^l pbmabg\k^Zlbg`m^fi^kZmnk^'?hk_bk^]^lb`gmablblZ\\hngm^]_hk[r ma^nl^h_lmk^g`mak^]n\mbhg_Z\mhkl' Bgma^\Zl^h_\hg\k^m^%ma^k^]n\mbhg_Z\mhk%d\!y "%blZ_ng\mbhgh_ ma^Z``k^`Zm^mri^Zllahpghg?b`nk^+'Lbeb\^hnlZ``k^`Zm^lln\a ZllZg]lmhg^lZk^\hfihl^]fZbgerh_lbeb\hg]bhqb]^Zg]jnZkmsbm^l% pabe^\Ze\Zk^hnlZ``k^`Zm^lln\aZlebf^lmhg^lZk^\hfihl^]fZbger h_\Ze\bnf\Zk[hgZm^'Ma^k^]n\mbhg_Z\mhkl_hkk^bg_hk\bg`Zg] ik^lmk^llbg`lm^^el%dl!y "Zg]di!y "%Zk^lahpgbg?b`nk^l,Zg]-' <_]kh[* 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 Pa^k^bmblk^jnbk^]_hkf^f[^kZgZerlbl%ma^^__^\mh__bk^hgZ\mbhgl blZ\\hngm^]_hk[rZiierbg`Zk^]n\mbhg_Z\mhk%n_b%mhma^Zf[b^gm ]^lb`goZen^'Pa^k^>qik^llbhg!/'*)"h_>nkh\h]^aZl[^^gnl^]%n_b bl]^_bg^]Zl3 n_b6!@d$c_bJd%*"(!*',.@d$*'.Jd%*" 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 *+'Lmkn\mnkZe_bk^]^lb`g :llnfbg`ma^NDGZmbhgZe:gg^qoZen^lZiikhikbZm^mh>qik^llbhg !/'*)"bg>nkh\h]^aZo^[^^gnl^]%ma^gc_b6c*%*'?b`nk^.\Zgnl^] mhehhdnima^oZen^h_n_b B_>qik^llbhgl/'*)!Z"Zg]/'*)!["aZo^[^^gnl^]%ma^gma^lfZee^k oZen^]^m^kfbg^]_khfma^_heehpbg`lahne][^nl^]_hkn_b3 n_b6!@d$c_bJd%*"(!*',.@d$*'.c)%*Jd%*" TIZkm*+>qi'!+'.Z"V n_b6!@d$c_bJd%*"(!*'+.@d$*'.Jd%*" TIZkm*+>qi'!+'.["V pa^k^c)%*blZ_ng\mbhgh_nl^]^m^kfbg^]_khf;L>G*22)3+))+/% l^^<aZim^k*hkb`bgZeerin[ebla^]ZlBgmkh]n\mbhgmh>nkh\h]^l0_hk _nkma^k]^mZbel'c_bZelhoZkb^lbg^Z\ah_ma^Z[ho^^qik^llbhglZg]bl \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 Mablblngebd^ermhh\\nkpa^gma^fhblmnk^\hgm^gmh_ma^\hg\k^m^ ble^llmaZg,[rp^b`am'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`blngebd^ermhh\\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^b`am\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\^immaZmIZkm*+ 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^Zk^ikhob]^]_hkZgnf[^kh_ f^f[^kmri^lnimhZ_bk^^qihlnk^i^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^\mbhge^o^elfZr[^Z\ab^o^][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[^aZobhnkbg_bk^\hg]bmbhgl blZ\\hngm^]_hk[rma^k^eZqZmbhgmaZm%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\^imbhgmhmablbl_hk\henfglZg]ehZ]& [^Zkbg`pZeelpa^k^mableZmm^kiZkZf^m^kblk^ieZ\^][rZnmbeblZmbhg _Z\mhkbgma^_bk^lbmnZmbhg%m_b'Ahp^o^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($+WWdZXe\FWhj'( 0.90 0.80 0.70 Reduction factor, n fi Concrete falling off the section Mrib\Zeer^qi^kb^g\^]bgma^eZmm^klmZ`^lh__bk^^qihlnk^%mablfZr[^ ik^o^gm^][r`hh]]^mZbebg`'Bg\Zl^lpa^k^ma^Zqbl]blmZg\^mhma^ fZbgk^bg_hk\^f^gmbl^jnZemhhk`k^Zm^kmaZg0)ff%Zg]bgma^ Z[l^g\^h_m^lmbg`%lnk_Z\^k^bg_hk\^f^gmpbmaZ]bZf^m^kh_Zme^Zlm -fflahne][^nl^]%liZ\^]Zm*))ff\^gmk^lhke^ll' c 0, 1 = 1.0 ; c 1, 1 = 0.9 0.60 c 0, 1 = 0.7 ; c 1, 1 = 0.7 0.50 c 0, 1 = 0.7 ; c 1, 1 = 0.5 c 0, 1 = 0. 5 ; c 1, 1 = 0. 2 0.40 <_]kh[+ :[j[hc_dWj_ede\nfiki_d];nfh[ii_ed($+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[hi^em_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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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]ma^ehZ] k^]n\mbhg_Z\mhk_hk_bk^ehZ]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^]!nlnZeermakhn`a_bk^^g`bg^^kbg`"maZm ma^ik^lmk^llbg`lm^^e]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]hglZk^eZr^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[^oZeb]%manlk^jnbkbg`ma^^g`bg^^k mhnl^Zlbfieb_b^]\Ze\neZmbhgf^mah]mh]^fhglmkZm^Z\\^imZ[bebmr' Ahp^o^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\^oZen^l_hk oZkbhnlk^lblmZg\^mbf^lZg]nmbeblZmbhgkZmbhl!m_b"'Ma^k^lmkb\mbhglhg ma^nl^h_F^mah]:Zk^3 N Ma^^__^\mbo^e^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%Ãbà 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^koZmbo^er%bm\Zg[^mZd^gmaZmm_b6n_b6)'0% b'^'bmblZllnf^]maZmma^\henfgk^lblmZg\^bl^jnZemhbml\ZiZ\bmrZm Zf[b^gmnembfZm^ehZ]l' Columns IZkm*¾+ik^l^gmlmphf^mah]l%:Zg];%pab\aZk^[hmaZ\\^imZ[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]^__^\mbo^e^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 Ma^oZen^lbgma^mZ[e^Zk^\Ze\neZm^]mZdbg`a\\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"'Ahp^o^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[j^eZ7 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 Minimum dimensions (mm) 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.(,. *+'Lmkn\mnkZe_bk^]^lb`g Method B MZ[e^+`bo^lfbgbfnfl^\mbhglbs^lZg]Zqbl]blmZg\^oZen^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 ma^ebfbm3 ^6F)>]%_b(G)>]%_b©^fZq pa^k^ ^fZq6*))ff ^([ ©)'+. [ 6fbgbfnf\henfg]bf^glbhg Ma^ehZ]e^o^eZmghkfZem^fi^kZmnk^\hg]bmbhgl%g%blnl^]bgma^ ]^m^kfbgZmbhgh_ma^fbgbfnfoZen^l'<hgl^koZmbo^er%bmfZr[^ Zllnf^]maZmg6)'0'PabelmmablZllnfimbhgfZr[^h_nl^bgbgbmbZe \hg\^im]^lb`g%lb`gb_b\Zgmk^]n\mbhglbgma^fbgbfnfl^\mbhglbs^ Zg]Zqbl]blmZg\^_hkZ`bo^g_bk^k^lblmZg\^i^kbh]fZr[^Z\ab^o^][r \Ze\neZmbg`g^qieb\bmer_khf3 g6G)>]%_b(T)'0!:\_\]$:l_r]"V' Ghm^maZmbgma^mZ[e^ma^f^\aZgb\Zek^bg_hk\^f^gmkZmbh%w%blhg^ h_ma^k^jnbk^]iZkZf^m^kl'Bg>nkh\h]^+%IZkm**1%Z\hgl^koZmbo^ oZen^bgma^]^m^kfbgZmbhgh_ebfbmbg`le^g]^kg^ll_hkma^\henfgbl )'*'?hkZ\eZll<,)(,0\hg\k^m^mablk^ik^l^gml)'-k^bg_hk\^f^gm% pa^k^Zlpa^gw6*')%ma^\henfgphne]k^jnbk^-k^bg_hk\^f^gm' ?hkZeemri^l%ZebfbmZmbhgblieZ\^]hgma^kZmbhh_\e^Zka^b`ammh mab\dg^ll%e)(m©-)%mhZohb]^q\^llbo^ma^kfZe]^_hkfZmbhge^Z]bg`mh _Zbenk^h_bgm^`kbmr[^mp^^gpZeeZg]leZ['Ahp^o^k%_hkZee[nmma^mabgg^lm h_pZeel%mablebfbmblngebd^ermh[^k^Z\a^]bgmrib\ZeZiieb\Zmbhgl' ?hkghg&ehZ][^Zkbg`pZeel hgerma^kfZeZg](hkbgm^`kbmr\kbm^kbZ !BZg]>"g^^]mh[^f^mZg]fbgbfnfmab\dg^llZehg^`ho^kglma^ Z]^jnZ\rbgma^_bk^ebfbmlmZm^%b'^'gh\a^\dblk^jnbk^]hgma^Zqbl ]blmZg\^'?hkehZ][^Zkbg`pZeelZfbgbfnfpZeemab\dg^ll%Zg]Zqbl ]blmZg\^mhma^k^bg_hk\^f^gm%fnlm[^ikhob]^]'Ma^fbgbfnfoZen^l _hk[hmamri^lZk^`bo^gbgMZ[e^,'Ghm^maZmmablmZ[e^fZrZelh[^ nl^]_hkieZbg\hg\k^m^pZeel' 8[Wci Fbgbfnfl^\mbhglbs^lZg]Zqbl]blmZg\^lmhk^bg_hk\^f^gm_hk[^Zfl Zk^lahpgbgMZ[e^-'Bgnlbg`ma^mZ[neZkf^mah]%ma^_heehpbg` Zllnfimbhgl(k^lmkb\mbhglZk^fZ]^3 N Ma^l^\mbhgbl^qihl^]hgmak^^lb]^lpbmama^nii^klnk_Z\^ Zllnf^]mh[^bglneZm^]'Ahp^o^k%pa^k^Zeelnk_Z\^lZk^^qihl^] mh_bk^%ma^mZ[e^lfZrlmbee[^nl^][nmpbmaZ]]bmbhgZek^lmkb\mbhgl ieZ\^]hgma^fbgbfnfl^\mbhglbs^' Table 2 C_d_ckcYebkcdZ_c[di_ediWdZWn_iZ_ijWdY[\ehYebkcdim_j^h[YjWd]kbWhehY_hYkbWhi[Yj_edi¸C[j^eZ8 Standard fire resistance K,) K/) K2) K*+) K*1) K+-) Mechanical reinforcement ratio, w Minimum dimensions (mm). Column width bmin%Wn_iZ_ijWdY["a n3&$'+ 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 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ N Ma^ikh_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&[^Zflk^eZmbg`mhihllb[e^_Zbenk^f^\aZgblflZm_bk^ k^lblmZg\^i^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][^iZb] mhma^fh]b_b\Zmbhgk^jnbk^]mhma^Zqbl]blmZg\^h_ma^ik^lmk^ll^] ^e^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^ \^gmk^ebg^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 Minimum dimensions (mm) 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^\^gmk^ebg^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 ^__^\mbo^e^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_[^Zflpbmahgerhg^eZr^kh_k^bg_hk\^f^gm'al]6a$*)ff%nge^llma^oZen^lh_[fbgZk^`k^Zm^k maZgmaZm`bo^gbg\henfg,_hklbfierlniihkm^][^Zflhk\henfg1_hk\hgmbgnhnl[^Zfl%pa^gghbg\k^Zl^blk^jnbk^]' 104 *+'Lmkn\mnkZe_bk^]^lb`g 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[^e^llmaZg+[fbg+ pa^k^[fbgblma^fbgbfnfZeehpZ[e^l^\mbhgpb]mamZd^g_khfma^ mZ[neZm^]]ZmZ' N Pa^k^ma^ehZ][^Zkbg`\ZiZ\bmrblk^]n\^][r^q\^llbo^^ehg`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^lZk^ikhob]^]_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[^][^ehp' 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][^ikhob]^]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^NDma^ikh\nk^f^gmh_k^bg_hk\^f^gm]h^lghmghkfZeer Zeehpma^ikh]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[^ikhob]^]' Ma^]^mZbebg`blln^lk^eZmbg`mhah``bg`k^bg_hk\^f^gmbg\hgmbgnhnl leZ[lZk^ma^lZf^Zlmahl^]^l\kb[^]ik^obhnler_hk\hgmbgnhnl[^Zfl' Two-way slabs Ma^mph&pZr\hg\^imZiieb^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^ k^eZmbhglabi_hkliZglerªeqblma^hiihlbm^h_maZmbg>nkh\h]^+% IZkm**_hk_eZmleZ[lpa^k^eqªer' 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+-) Minimum dimensions (mm) 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[lk^eZm^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^\mbhglZmkb`amZg`e^l"pa^k^erblma^ ehg`^kliZg' 2 ?hkik^lmk^ll^]\henfglZqbl]blmZg\^lahne][^bg\k^Zl^]¾l^^m^qm' 105 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ 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][^ieZ\^]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^ ^oZenZmbhgh_hg^&pZrkb[[^]leZ[l'?hkmph&pZrliZggbg`kb[[^]leZ[l% ma^bg_hkfZmbhgbgMZ[e^/blikhob]^]pbmama^ebfbmZmbhgmhma^bknl^ [^bg`maZmma^ehZ]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][^iZb]mhma^fh]b_b\Zmbhgk^jnbk^]mhma^Zqbl ]blmZg\^h_ma^ik^lmk^ll^]^e^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;', Ahp^o^k%[^_hk^l^e^\mbg`Zgrh_ma^Z[ho^f^mah]l%bmblbfihkmZgm mhghm^maZmma^rZ]]k^ll_e^qnk^hgerpbmala^ZkZg]mhklbhg[^bg` \ho^k^]l^iZkZm^ereZm^kbgmabl<aZim^k' mZ[neZkf^mah]Zg]fZr[^nl^]bgma^]^lb`gh_[^ZflZg]leZ[l pa^k^ma^ehZ]blik^]hfbgZgmerngb_hkfer]blmkb[nm^]Zg]%_hk \hgmbgnhnlf^f[^kl%ma^e^o^eh_k^]blmkb[nmbhg]h^lghm^q\^^] *.'?hkab`a^ke^o^elh_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 Minimum dimensions (mm) 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' Ahp^o^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]lZk^ik^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 ^__^\mbo^e^g`mah_[^ZfhkleZ[ /) .) Z 6,) =^m^kfbgZmbhgh_ma^]^lb`gk^lblmZg\^Zg]hma^k\a^\dl]^i^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_bk^ehZ]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_[^Zflpbmahgerhg^eZr^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" *+'Lmkn\mnkZe_bk^]^lb`g pa^k^ iZkmbZefZm^kbZe_Z\mhk_hklm^^eZmZf[b^gmm^fi^kZmnk^l iZkmbZefZm^kbZe_Z\mhk_hklm^^eng]^k_bk^\hg]bmbhgl lmk^g`mak^]n\mbhgZiieb^]mhlm^^e_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^go^ehi^' 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^]^imah_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 maZgma^e^g`ma]^m^kfbg^]bg>nkh\h]^+%IZkm**Zg]lahne][^\a^\d^]' +&&9_iej^[hcc[j^eZ Bgma^blhma^kff^mah]%\hg\k^m^ZmZm^fi^kZmnk^Z[ho^.))<bl g^`e^\m^]bgma^\Ze\neZmbhgh_l^\mbhgk^lblmZg\^%pabelm\hg\k^m^Zmhk[^ehp .))<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^gmmakhn`aZl^\mbhg]^ghm^][r blhma^kflfZr[^]^m^kfbg^]_khfm^lmbg`%IZkm*¾+ikhob]^l m^fi^kZmnk^ikh_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^\mZg`e^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[\[h[dY[Ykhl[i\ehYh_j_YWbj[cf[hWjkh[e\h[_d\ehY_d]WdZfh[ijh[ii_d] ij[[b\ehki[m_j^jWXkbWhc[j^eZWdZ7dd[n; Start Calculate MEd, fi. 1.0 Determine y, using temperature profiles in Annex A of Part 1-2. Determine ks(y) from Figure 12 0.8 Calculate MRd, fi Is the element a simply supported? No Calculate the support design moment of resistance, MRd, fi, support ‘Fit’ the ‘free’ bending moment so that MEd,fi = MRd,fi Yes Is MEd, fi. ≤ MRd, fi? No Redesign section or use alternative methods Yes Yes Coefficient, ks (ycr) or kp (ycr) gl 6 gl%_b 6 dl!y " 6 F>] 6 :l%ikho6 :l%k^j 6 :l[^_hk^%bgZee\Zl^lpa^k^ma^l^\mbhgblik^lmk^ll^]%iZkmb\neZk Zmm^gmbhglahne][^iZb]mhma^fh]b_b\Zmbhgk^jnbk^]mhma^Zqbl ]blmZg\^h_ma^ik^lmk^ll^]^e^f^gml%ZlZek^Z]r]bl\nll^]bgma^ bgmkh]n\mbhgmhma^mZ[neZkf^mah]' Reinforcing steel 0.6 Prestressing steel (bars) 0.4 Prestressing steel (wires and strands) 0.2 Are the support moments exceeded? 0 No Finish 0 200 400 600 800 1000 12 o Temperature, y ( C) 107 Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lnlbg`>nkh\h]^+ Hg\^ma^k^]n\^]\khll&l^\mbhgbl]^m^kfbg^]%ma^m^fi^kZmnk^h_ ^Z\ak^bg_hk\bg`[Zkbl_hng]nlbg`m^fi^kZmnk^ikh_be^lZg]_khf mabl%ma^k^]n\^]lmk^g`mah_ma^k^bg_hk\^f^gm]n^mhm^fi^kZmnk^ fZr[^]^m^kfbg^]bgZ\\hk]Zg\^pbma?b`nk^l,Zg]-'Ghm^maZm% bglhf^bglmZg\^l%ma^k^bg_hk\^f^gmfZr_Zeehnmlb]^h_ma^k^lb]nZe \khll&l^\mbhg'Bgln\a\Zl^l%ma^l^[ZklfZrlmbee[^\hngm^]pa^g ]^m^kfbgbg`ma^l^\mbhg\ZiZ\bmr' Ma^l^\mbhgk^lblmZg\^fZrma^g[^]^m^kfbg^]nlbg`\hgo^gmbhgZe \Ze\neZmbhgf^mah]l%Zlbg]b\Zm^]bg?b`nk^*.Zg]\hfiZk^]Z`Zbglm ma^]^lb`gehZ]bgma^_bk^lbmnZmbhgbgmabl_b`nk^pa^k^3 [_b 6 pb]mah_k^]n\^]\khll&l^\mbhg ]_b 6 ^__^\mbo^]^imah_ma^k^]n\^]\khll&l^\mbhg s 6 e^o^kZkf[^mp^^gma^m^glbhgk^bg_hk\^f^gm Zg]\hg\k^m^ sà 6 e^o^kZkf[^mp^^gma^m^glbhgZg]\hfik^llbhg k^bg_hk\^f^gm :l 6 Zk^Zh_m^glbhgk^bg_hk\^f^gm :l* 6 iZkmh_m^glbhgk^bg_hk\^f^gmbg^jnbeb[kbnf pbmama^\hg\k^m^\hfik^llbhg[eh\d Fn*6 :l* _l]%_b!yf"s Fn+6 :l+ _l\]%_b!yf"sà :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 ^__^\mbo^a^b`amh_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^^IZkm*+% <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_\] ]^lb`goZen^h_ma^m^glbhgk^bg_hk\^f^gmlmk^g`mabg 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^maZghg^eZr^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\mbhgZmmable^o^e' <_]kh[') Reduced cross-section of reinforced concrete beam and column Compression :l+ 6 :là 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 *+'Lmkn\mnkZe_bk^]^lb`g Pa^gma^fhf^gm\hgmkb[nmbhglZk^Zll^ll^]ZllahpgZ[ho^%ma^ mhmZefhf^gm\ZiZ\bmrblh[mZbg^]_khf3 Fn6Fn*$Fn+ Ma^]^lb`gikh\^llbllnffZkbl^]bg?b`nk^*/' @bo^gma^\hfie^qbmrh_ma^ZiikhZ\a%ma^mZ[e^lbg:gg^q<h_ IZkm*+aZo^[^^g]^kbo^]_khfmablf^mah]Zg]fZr[^nl^]mh \a^\dmaZmma^l^\mbhglbs^Zg]Zqbl]blmZg\^lZk^Z]^jnZm^_hkZ `bo^g\Zl^' Calculation methods for shear and torsion 9heii#i[Yj_edi[nfei[ZjeX[dZ_d]WdZWn_WbbeWZ :gg^q;',ikhob]^lZ\Ze\neZmbhgf^mah]_hkf^f[^kl!ikbfZkber \henfgl"pa^k^ma^lmkn\mnkZe[^aZobhnkbllb`gb_b\Zgmerbg_en^g\^] [rl^\hg]hk]^k^__^\mlng]^k_bk^\hg]bmbhgl'Ahp^o^k%Zlpbmama^ mZ[neZkf^mah]%ma^ZiikhZ\ablebfbm^]mhf^f[^klmaZm\Zg[^ \hglb]^k^]Zl[^bg`[kZ\^]' <_]kh[', <bemY^Whj\eh+&&9_iej^[hcc[j^eZ Start Pa^gnlbg`ma^mZ[neZkf^mah]%b_ma^fbgbfnfl^\mbhg]bf^glbhgl Zk^ikhob]^]%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_bk^ehZ]bg`blng\hffhgZg] pabelmghm[^bg`_neeroZeb]Zm^]%pa^gnlbg`ma^\Ze\neZmbhgf^mah] ik^l^gm^]%ma^ikbg\bie^lbg>nkh\h]^+%IZkm**fZr[^Ziieb^]mhZ k^]n\^]\khll&l^\mbhgZl]^m^kfbg^]_khfZgrh_ma^\Ze\neZmbhgf^mah]l eblm^]Z[ho^'Ahp^o^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^ ebgdlZk^ikhob]^]%pa^ma^k_hkla^ZkZehg^hkZelh_hkmhklbhg%ma^ lmk^g`mah_ma^ebgdlblk^]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 *+'Lmkn\mnkZe_bk^]^lb`g 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' ?hkbgbmbZe]^lb`g%ma^[Z\d`khng]iZi^kmhma^NDGZmbhgZe:gg^q^l 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 \a^\d^]bgZ\\hk]Zg\^pbma^bma^kma^.))<blhma^kff^mah]hkma^ shg^f^mah]' Bg\Zl^lpa^k^ma^lmkn\mnk^blng[kZ\^]%hkmaZmihkmbhgh_ma^ lmkn\mnk^[^bg`\hglb]^k^]\Zgghm[^\hglb]^k^]Zl[kZ\^][rmaZm iZkmh_ma^lmkn\mnk^k^fhm^_khfma^_bk^ma^gma^_heehpbg`himbhgbl ZoZbeZ[e^mhma^^g`bg^^k' Ln\aZgZiikhZ\aphne][^nglZ_^pa^k^ma^f^f[^klbgma^_bk^ shg^ikhob]^ma^ik^]hfbgZgmf^Zglh_lmkn\mnkZelmZ[bebmrZg]bg ln\a\Zl^lZ]oZg\^]\Ze\neZmbhgf^mah]lZg]li^\bZeblmZ]ob\^fZr[^ k^jnbk^]' <_]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 pi^ekbZX[[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 ' ;KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+*+%=^lb`gh_\hg\k^m^lmkn\mnk^l'@^g^kZekne^llmkn\mnkZe_bk^]^lb`g';LB%+))-' 2 BGLMBMNMBHGH?LMKN<MNK:E>G@BG>>KL'@nb]^mhma^Z]oZg\^]_bk^lZ_^mr^g`bg^^kbg`h_lmkn\mnk^l'BLmkn\m>%+))0' ) ;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]^mhma^i^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 ;KBMBLALM:G=:K=LBGLMBMNMBHG';L1**)%Ma^lmkn\mnkZenl^h_\hg\k^m^';LB%*220' '& 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>%+))/' '' ; KHHD>K%H'Ahpmh]^lb`g\hg\k^m^lmkn\mnk^lmh>nkh\h]^+3=^mZbebg`'Ma^<hg\k^m^<^gmk^%+))/' '( ;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 ChagFZlhg LmnZkm:e^qZg]^k IZe<aZgZ <aZke^l@hh]\abe] MhgrChg^l :g]rEre^ Kb\aZk]Fhll GZkrGZkZrZgZg Kb\aZk]LabifZg Kh[^kmOheenf KnllPhelm^gahef^ Kh]P^[lm^k :eZg;Zqm^k:llh\bZm^l!<aZbkfZg" PLI@khniie\ ;kbmbla<^f^gm:llh\bZmbhg Ma^<hg\k^m^<^gmk^ :kni GKF<hglnemZgml ?hkf^kerh_Ihp^eeMheg^k:llh\bZm^l <eZkdLfbmaIZkmg^klabi =<E@ Bfi^kbZe<hee^`^%Ngbo^klbmrh_Ehg]hg PL:mdbgl=MBIkhc^\mH_Ë\^k <hg\k^m^BgghoZmbhgZg]=^lb`g Members of the Concrete Industry Eurocode 2 Group (CIEG) ChagFhhk^ <ebo^;n]`^ IZe<aZgZ Chag<eZkd^ <hebg<e^o^ker <aZke^l@hh]\abe] AZb`@neoZg^llbZg @^h__AZk]bg` MhfAZkkblhg MhgrChg^l ChagFZlhg Kb\aZk]Fhll GZkrGZkZrZgZg Kb\aZk]LabifZg FZkmbgLhnma\hmm KnllPhelm^gahef^ Kh]P^[lm^k <hglnemZgm!<aZbkfZg" ;kbmblaIk^\Zlm<hg\k^m^?^]^kZmbhg ;kbmbla<^f^gm:llh\bZmbhg Ma^<hg\k^m^Lh\b^mr <hglmkn\m Ma^<hg\k^m^<^gmk^ ;K> =<E@ JnZkkrIkh]n\ml:llh\bZmbhg :kni :eZg;Zqm^k:llh\bZm^l ?hkf^kerh_Ihp^eeMheg^k:llh\bZm^l <eZkdLfbmaIZkmg^klabi =<E@ <hglnemZgm PL:mdbgl <hg\k^m^BgghoZmbhgZg]=^lb`g <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. Mablin[eb\ZmbhgmZd^ma^ikZ\mblbg`^g`bg^^kmakhn`ama^ikh\^llh_ ]^lb`gbg`mh>nkh\h]^+Zg]bg\en]^l\hff^gmZkr%Ìhp\aZkml%]ZmZ mZ[e^lZg]]^lb`gZb]lmh^gZ[e^]^lb`g^klmhZiier>nkh\h]^+jnb\der Zg]\hgË]^gmermhma^]^lb`gh_\hg\k^m^lmkn\mnk^l' Dr Andrew BondblZND]^e^`Zm^hgma^<>G(M<+.)(L<0 \hffbmm^^k^lihglb[e^_hk>nkh\h]^0%ma^`^hm^\agb\Ze>nkh\h]^% Zg]blma^B<>Ãlk^ik^l^gmZmbo^hgma^GZmbhgZeLmkZm^`r<hffbmm^^ _hkbfie^f^gmZmbhgh_>nkh\h]^l' Owen BrookerblL^gbhkLmkn\mnkZe>g`bg^^k_hkMa^<hg\k^m^<^gmk^ pa^k^a^ikhfhm^l^_Ë\b^gm\hg\k^m^]^lb`gmakhn`a`nb]Zg\^ ]h\nf^gml%ik^l^gmZmbhglZg]ma^gZmbhgZea^eiebg^' Dr Andrew FraserblZL^gbhk>g`bg^^kpbma:kni:]oZg\^] M^\agheh`rZg]K^l^Zk\apa^k^a^ikhob]^lli^\bZeblmZ]ob\^hgma^ ZgZerlbl%]^lb`gZg]]^mZbebg`h_\hg\k^m^lmkn\mnk^l' Andrew HarrisblZ_hkf^k:llh\bZm^=^Zgh_Dbg`lmhgNgbo^klbmr Zg]aZlik^iZk^]in[eb\ZmbhglZg]`bo^lik^l^gmZmbhglhg>nkh\h]^0% ma^`^hm^\agb\Ze>nkh\h]^' Prof Tom Harrisonbl\aZbkfZgh_ma^;LB\hg\k^m^\hffbmm^^'A^ blm^\agb\Ze\hglnemZgmmhma^JI:¾;KF<:Zg]Zoblbmbg`bg]nlmkbZe ikh_^llhkZmma^Ngbo^klbmrh_=ng]^^' Dr Tony Jonesbl:llh\bZm^=bk^\mhkh_:]oZg\^]M^\agheh`rZg] K^l^Zk\aZm:kni'A^lbmlhgma^;LB<hffbmm^^k^lihglb[e^_hkma^ fZbgm^gZg\^h_^qblmbg`;kbmblaLmZg]Zk]lZg]ma^<>G\hffbmm^^ k^lihglb[e^_hkma^]^o^ehif^gmh_>nkhi^Zg<h]^l' <<BI&))/ In[ebla^]=^\^f[^k+))/%k^obl^]L^im^f[^k+))2 BL;G*&21-1*1&-0&* Ikb\^@khniI ¡FI:&Ma^Concrete<^gmk^ Kbo^klb]^Ahnl^%-F^Z]hpl;nlbg^llIZkd% LmZmbhg:iikhZ\a%;eZ\dpZm^k%<Zf[^ke^r%Lnkk^r%@N*02:; Tel: $--!)"*+0//)/1))Fax:$--!)"*+0//)/1)* ppp'concretecentre'\hf Dr Richard Mossbl_hkf^kerh_;nbe]bg`K^l^Zk\a>lmZ[eblaf^gmZg] blZnmahkh_Zgnf[^kh_ma^bkm^\agb\Zein[eb\Zmbhgl' Prof R S NarayananbliZlm<aZbkfZgh_<>G(M<+.)(L<+%ma^ \hffbmm^^k^lihglb[e^_hklmkn\mnkZe>nkh\h]^lhg\hg\k^m^'A^bl \hglnemZgmmh<eZkdLfbmaIZkmg^klabi' Rod Websterh_<hg\k^m^BgghoZmbhgZg]=^lb`gblZg^qi^kmbgma^ ]^lb`gh_mZee\hg\k^m^[nbe]bg`lZg]bgZ]oZg\^]ZgZermb\Zef^mah]l'
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