Ccip Worked Examples Ec2
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Download Ccip Worked Examples Ec2...
Description
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WORKED EXAMPLES
STANDARDS
CONCRETE INDUSTRY PUBLICATIONS
PUBLICATIONS BY OTHERS
NA CONCISE EUROCODE 2
BS EN 1990 BASIS OF DESIGN
MANUALS
VOL 2 NA BS EN 1991–2 NA BS EN 1991–1–1 –2 NA NA –3 NA ACTIONS –4 NA –6
WORKED EXAMPLES TO EUROCODE 2 VOL 1
HOW TO DESIGN CONCRETE STRUCTURES DETAILERS HANDBOOK
Densities and imposed loads Fire Snow Wind Execution
www. Eurocode2 .info DESIGN GUIDES
PD6687 NA
NA BS EN 1992–1–1 1–2 NA NA DESIGN OF –2 CONCRETE –3 STRUCTURES General Fire Bridges Liquid retaining
RC SPREAD SHEETS
BS EN 13670 EXECUTION OF CONCRETE STRUCTURES
PRECAST DESIGN MANUAL
PRECAST WORKED EXAMPLES
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@^g^kZeer% ma^ \Ze\neZmbhgl Zk^ \khll&k^_^k^g\^] mh ma^ k^e^oZgm \eZnl^l bg Zee _hnk iZkml h_ >nkh\h]^ +T*¾-V Zg]% pa^k^ ZiikhikbZm^% mh hma^k ]h\nf^gml' L^^ ?b`nk^ *'+ _hk Z `nb]^ mh ik^l^gmZmbhg'K^_^k^g\^lmh;L1**)T0Vk^_^kmhIZkm*nge^llhma^kpbl^lmZm^]' @^g^kZeer%ma^Âlbfie^Ã^qZfie^l]^i^g]hg^jnZmbhglZg]]^lb`gZb]l]^kbo^]_khf>nkh\h]^+' Ma^]^kbo^]^jnZmbhglZk^`bo^gbg:ii^g]bq:Zg]ma^]^lb`gZb]l_khfL^\mbhg*.h_nkh\h]^+T.VZk^k^i^Zm^]bg:ii^g]bq;' Ma^^qZfie^lZk^bgm^g]^]mh[^ZiikhikbZm^_hkma^bkinkihl^%pab\ablmhbeenlmkZm^ma^nl^h_ >nkh\h]^+_hkbg&lbmn\hg\k^m^[nbe]bg`lmkn\mnk^l'Ma^k^Zk^lbfie^^qZfie^lmhbeenlmkZm^ahp mrib\ZeaZg]\Ze\neZmbhglfb`am[^]hg^nlbg`ZoZbeZ[e^\aZkmlZg]mZ[e^l]^kbo^]_khfma^nkh\h]^+%l^o^kZeh_ma^\Ze\neZmbhglZk^ik^l^gm^]bg]^mZbe_Zk bg^q\^llh_maZmg^\^llZkrbg]^lb`g\Ze\neZmbhglhg\^nl^klZk^_ZfbebZkpbmama^nkh\h]^+Zk^`^g^kZeerfhk^bgoheo^]maZgmahl^mh;L1**)% lhf^ h_ ma^ ]^lb`gl ik^l^gm^] bg mabl in[eb\Zmbhg aZo^ [^^g ^qm^g]^] bgmh Zk^Zl maZm aZo^ mkZ]bmbhgZeer[^^gma^k^lihglb[bebmrh_]^mZbe^kl'Ma^l^^qm^g]^]\Ze\neZmbhglZk^ghmg^\^llZkber iZkm h_ÂghkfZeà ]^lb`g [nm Zk^ bg\en]^] Zm ma^ ^g] h_ lhf^ \Ze\neZmbhgl' Bm bl Zllnf^] maZm ma^]^lb`g^kpbee]bl\nllZg]Z`k^^pbmama^]^mZbe^kZk^Zlh_k^lihglb[bebmrZg]ma^]^`k^^h_ kZmbhgZeblZmbhg% ma^ ^qm^gm h_ ]^lb`gbg` ]^mZbel% Zll^llf^gm h_ \nkmZbef^gm Zg] hma^k Zli^\ml maZmma^]^mZbe^klahne]ng]^kmZd^'Bmblk^\h`gbl^]maZmbgma^oZlmfZchkbmrh_\Zl^l%ma^kne^l `bo^gbg]^mZbebg`fZgnZelT1%2Vpbee[^nl^]'Ahp^o^k%ma^^qZfie^lZk^bgm^g]^]mha^eipa^g \nkmZbef^gm%Zg\ahkZ`^Zg]eZie^g`malg^^]mh[^]^m^kfbg^]'
2
Bgmkh]n\mbhg *'+ Eurocode: Basis of structural design Bg ma^ >nkh\h]^ lrlm^f ;L >G *22)% >nkh\h]^3 ;Zlbl h_ lmkn\mnkZe ]^lb`gT*)V ho^kZk\a^l Zee ma^ hma^k>nkh\h]^l%;L>G*22*mh;L>G*222';L>G*22)]^Ëg^lma^^__^\mlh_Z\mbhgl%bg\en]bg` `^hm^\agb\Ze Zg] l^blfb\ Z\mbhgl% Zg] Ziieb^l mh Zee lmkn\mnk^l bkk^li^\mbo^ h_ ma^ fZm^kbZe h_ \hglmkn\mbhg'Ma^fZm^kbZe>nkh\h]^l]^Ëg^ahpma^^__^\mlh_Z\mbhglZk^k^lblm^][r`bobg`kne^l_hk ]^lb`gZg]]^mZbebg`h_\hg\k^m^%lm^^e%\hfihlbm^%mbf[^k%fZlhgkrZg]Zenfbgbnf'!l^^?b`nk^*',"' BS EN 1990, Eurocode: Basis of structural design
Structural safety, serviceability and durability
BS EN 1991, Eurocode 1: Actions on structures
Actions on structures
BS EN 1992, Eurocode 2: Concrete BS EN 1993, Eurocode 3: Steel BS EN 1994, Eurocode 4: Composite BS EN 1995, Eurocode 5: Timber BS EN 1996, Eurocode 6: Masonry BS EN 1999, Eurocode 9: Aluminium BS EN 1997, Eurocode 7: Geotechnical design
Design and detailing
BS EN 1998, Eurocode 8: Seismic design
Geotechnical and seismic design
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EC0: 2.1
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*', Eurocode 1: Actions on structures :\mbhglZk^]^Ëg^]bgma^*)iZkmlh_;L>G*22*>nkh\h]^*3:\mbhglhglmkn\mnk^lT**V3 ;L>G*22*¾*¾*3+))+3=^glbmb^l%l^e_&p^b`am%bfihl^]ehZ]l_hk[nbe]bg`l ;L>G*22*¾*¾+3+))+3:\mbhglhglmkn\mnk^l^qihl^]mhËk^ ;L>G*22*¾*¾,3+)),3LghpehZ]l ;L>G*22*¾*¾-3+)).3Pbg]Z\mbhgl ;L>G*22*¾*¾.3+)),3Ma^kfZeZ\mbhgl ;L>G*22*¾*¾/3+)).3:\mbhgl]nkbg`^q^\nmbhg ;L>G*22*¾*¾03+))/3:\\b]^gmZeZ\mbhgl ;L>G*22*¾+3+)),3:\mbhglhglmkn\mnk^l'MkZ_Ë\ehZ]lhg[kb]`^l ;L>G*22*¾,3+))/3G*22*¾-3+))/3LbehlZg]mZgdl Mabl in[eb\Zmbhg bl fZbger \hg\^kg^] pbma ]^lb`gbg` _hk ma^ Z\mbhgl ]^Ëg^] [r IZkm¾*¾*3 =^glbmb^l%l^e_&p^b`am%bfihl^]ehZ]l_hk[nbe]bg`l' =^lb`goZen^lh_Z\mbhglZg]ehZ]ZkkZg`^f^gmlZk^\ho^k^]bgL^\mbhg+'
*'- Eurocode 2: Design of concrete structures >nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^lT*¾-Vhi^kZm^lpbmabgZg^gobkhgf^gmh_hma^k>nkhi^Zg Zg];kbmblalmZg]Zk]l!l^^?b`nk^*',"'Bmbl`ho^kg^][r;L>G*22)T*)VZg]ln[c^\mmhma^Z\mbhgl ]^Ëg^]bg>nkh\h]^l*T**V%0T*+VZg]1T*,V'Bm]^i^g]lhgoZkbhnlfZm^kbZelZg]^q^\nmbhglmZg]Zk]l Zg] bl nl^] Zl ma^ [Zlbl h_ hma^k lmZg]Zk]l' IZkm +% ;kb]`^lT,V% Zg] IZkm ,% Ebjnb]k^mZbgbg`Zg] \hgmZbgf^gmlmkn\mnk^lT-V%phkd[r^q\^imbhgmhIZkm*¾*Zg]*¾+%maZmbl%\eZnl^lbgIZkml+Zg], \hgËkf%fh]b_rhkk^ieZ\^\eZnl^lbgIZkm*¾*'
BS EN 1990 EUROCODE Basis of Structural Design BS EN 1997 EUROCODE 7 Geotechnical Design
BS EN 1998 EUROCODE 8 Seismic Design BS EN 1991 EUROCODE 1 Basis of Structural Design
BS 4449 Reinforcing Steels
BS 8500 Specifying Concrete
BS EN 206 Concrete
BS EN 13670 Execution of Structures
BS EN 1995 EUROCODE 5 Design of Composite Structures
BS EN 1992 EUROCODE 2 Design of concrete structures Part 1–1: General Rules for Structures Part 1–2: Structural Fire Design
BS EN 1992 EUROCODE 2 Part 2: Bridges
BS EN 1992 EUROCODE 2 Part 3: Liquid Retaining Structures
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pa^k^ \^!s" 6 ^qihlnk^_Z\mhk_khf?b`nk^+', \^M 6 mhpgm^kkZbg_Z\mhk_khf?b`nk^+'- j[ 6 )'))/o[+dG(f+ pa^k^ o[ 6 o[%fZi\Zem pa^k^ o[%fZi6 _ng]Zf^gmZe[Zlb\pbg]o^eh\bmr_khf?b`nk^+'+ \Zem 6 Z embmn]^_Z\mhk%\hgl^koZmbo^er%\Zem6*$)'))*: pa^k^ :6Zembmn]^Z'f'l'e
EC1-1-4: Figs NA.7, NA.8
EC1-1-4: Fig. NA.1
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13
+'/'* Determine basic wind velocity, vb o[6\]bk\l^Zlhg\ikh[o[%) EC1-1-4: 4.2(1) Note 2 & NA 2.4, 2.5
pa^k^ \]bk
EC1-1-4: 4.2(2) Note 3 & NA 2.7: Fig. NA.2
EC1-1-4: 4.2(1) Notes 4 & 5 & NA 2.8
EC1-1-4: 4.2(1) Note 2 & NA 2.4: Fig. NA.1
EC1-1-4: 4.2(2) Note 1 & NA 2.5
6 ]bk^\mbhgZe_Z\mhk G*22*¾*¾-'
EC1-1-4: 7.2.2(2) Note 1 & NA.2.27
hp^o^k%_hkma^]^m^kfbgZmbhgh_ho^kZeeehZ]lhg[nbe]bg`l%ma^g^mik^llnk^ A \h^_Ë\b^gml`bo^gbgMZ[e^+'2fZr[^nl^]'Bgmabl\Zl^bmpbee[^ngg^\^llZkr mh]^m^kfbg^bgm^kgZepbg]ik^llnk^\h^_Ë\b^gml'
EC1-1-4: 7.2.2(2) Note 1 & NA.2.27, Table NA.4
Cladding loads ?hkZk^ZlZ[ho^*f+%\i^%*)lahne][^nl^]'\i^%*)fZr[^]^m^kfbg^]_khf MZ[e^0'*h_;L>G*22*¾*¾-'L^^MZ[e^+'*)'
EC1-1-4: 7.2.2(2) Note 1 & NA.2.27
15
Flat roofs ?hkÌZmkhh_l%Z\\hk]bg`mhma^:]oblhkrGhm^bgma^G:lhf^h_ma^oZen^l h_\i^%*)bgMZ[e^0'+h_;L>G*22*¾*¾-!l^^MZ[e^+'**"Zk^lb`gbË\Zgmer ]b__^k^gm_khf\nkk^gmikZ\mb\^bgma^ND'Bmk^\hff^g]lmaZm]^lb`g^kllahne] \hglb]^knlbg`ma^oZen^lbg;L/,223+mhfZbgmZbgma^\nkk^gme^o^elh_lZ_^mr Zg]^\hghfr'L^^MZ[e^+'*+'
EC1-1-4: NA.2.28 & NA advisory note
? hkhma^k_hkflh_khh_k^_^kmh;L>G*22*¾*¾-Zg]ma^NDG:' BmpbeeZelh[^g^\^llZkrmh]^m^kfbg^bgm^kgZepbg]ik^llnk^\h^_Ë\b^gml_hk ma^]^lb`gh_\eZ]]bg`'
EC1-1-4: 7.2.9(6) Note 2
EC1-1-4: NA 2.27, Table NA.4
MZ[e^+'2 G^mik^llnk^\h^__b\b^gm%\i^%*)%_hkpZeelh_k^\mZg`neZkieZg[nbe]bg`l#
EC1-1-4: 7.2.3, NA.2.28 & NA advisory note BS 6399: Table 8 & Fig. 18
\ib 6 bgm^kgZeik^llnk^\h^_Ë\b^gm' ?hkgh]hfbgZgmhi^gbg`l\ibfZr[^mZd^gZlma^fhk^hg^khnlh_$)'+Zg]¾)',
a(] 5 1 ª 0.25
G^mik^llnk^\h^__b\b^gm%\i^%*) *', *'* )'1
Ghm^l *#bg^__^\mma^l^oZen^lZk^_hk\^\h^__b\b^gml_hk]^m^kfbgbg`ho^kZeeehZ]lhg[nbe]bg`l' +a6a^b`amh_[nbe]bg`' ,[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"' -]6]^imah_[nbe]bg`!iZkZee^emhpbg]"' .OZen^lfZr[^bgm^kiheZm^]' />q\en]^l_ngg^eebg`'
EC1-1-4: 7.2.2(2) Table 7.1, Note 1 & NA 2.27: Tables NA.4a , NA.4b
MZ[e^+'*) >qm^kgZeik^llnk^\h^__b\b^gm%\i^%*)%_hkpZeelh_k^\mZg`neZk&ieZg[nbe]bg`l Shg^
=^l\kbimbhg ?hkpZeeliZkZee^emhma^pbg]]bk^\mbhg%Zk^Zlpbmabg )'+fbgT[4+aVh_pbg]pZk]^]`^
¾*'+
Zone B
?hkpZeeliZkZee^emhma^pbg]]bk^\mbhg%Zk^Zlpbmabg )'+fbgT[4+aVh_pbg]pZk]^]`^
¾)'1
Zone C
?hkpZeeliZkZee^emhma^pbg]]bk^\mbhg%Zk^Zl_khf )'+fbgT[4+aVmhfbgT[4+aVh_pbg]pZk]^]`^
Zone D
Pbg]pZk]pZee
$)'1
Zone E
E^^pZk]pZee
¾)'.
¾)'0 $*',
MZ[e^+'** >qm^kgZeik^llnk^\h^__b\b^gm%\i^%*)_hk_eZmkhh_l# Shg^
=^l\kbimbhg
\i^%*) LaZki^]`^ Zm^Zo^l
16
Fbg'
Zone A
Zones D G^m and E Ghm^l *a6a^b`amh_[nbe]bg`' +[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"' EC1-1-4: 7.2, Table 7.2 & NA
\i^%*) FZq'
PbmaiZkZi^m
Zone F
Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]pbmabg ¾*'1 )'+fbgT[4+aVh_k^mnkg^]`^!iZkZee^emhpbg]]bk^\mbhg"
¾*'/
Zone G
Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]hnmpbma ¾*'+ )'+fbgT[4+aVh_k^mnkg^]`^!iZkZee^emhpbg]]bk^\mbhg"
¾*'*
Zone H
Khh_[^mp^^g)'*fbgT[4+aVZg])'.fbgT[4+aV_khf pbg]pZk]^]`^
¾)'0
¾)'0
Zone I K^fZbg]^k[^mp^^g)'.fbgT[4+aVZg]e^^pZk]^]`^ ¨)'+ ¨)'+ Ghm^l *#:\\hk]bg`mhG:mh;L>G*22*&*&-%mablmZ[e^blghmk^\hff^g]^]_hknl^bgma^ND' +a6a^b`amh_[nbe]bg`' ,[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"'
:gZerlbl%Z\mbhglZg]ehZ]ZkkZg`^f^gml MZ[e^+'*+ >qm^kgZeik^llnk^\h^__b\b^gm%\i^%_hk_eZmkhh_l Shg^
=^l\kbimbhg
EC1-1-4: 7.2.3, NA.2.28 & NA advisory note.
\i^ LaZki^]`^ Zm^Zo^l
PbmaiZkZi^m
Zone A
Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]pbmabg )'+.fbgT[4+aVh_k^mnkg^]`^!iZkZee^emhpbg]]bk^\mbhg"
¾+')
¾*'2
Zone B
Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]hnmpbma )'+.fbgT[4+aVh_k^mnkg^]`^!iZkZee^emhpbg]]bk^\mbhg"
¾*'-
¾*',
Zone C
Khh_[^mp^^g)'*fbgT[4+aVZg])'.fbgT[4+aV_khf pbg]pZk]^]`^
¾)'0
¾)'0
Zone D
K^fZbg]^k[^mp^^g)'.fbgT[4+aVZg]e^^pZk]^]`^
¨)'+
¨)'+
BS 6399: Table 8 & Fig. 18
Ghm^l *a6a^b`amh_[nbe]bg`' +[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"'
+'/'. Calculate the overall wind force, Fw ?p6\l\]Spd :k^_ pa^k^
EC1-1-4: 5.3.2, Exp. (5.4) & NA
pd 6 ZlZ[ho^
EC1-1-4: 6.2(1) a), 6.2(1) c)
\l\] 6 lmkn\mnkZe_Z\mhk%\hgl^koZmbo^er 6 *') hkfZr[^]^kbo^] pa^k^ \l 6 lbs^_Z\mhk \lfZr[^]^kbo^]_khf>qi'!/'+"hkmZ[e^G:','=^i^g]bg`hgoZen^lh_ ![$a"Zg]!s¾a]bl"Zg]]bob]bg`bgmhShg^:%;hkqi'!/',"hkË`nk^G:'2'=^i^g]bg`hgoZen^lh_dl !eh`Zkbmafb\]^\k^f^gmh_lmkn\mnkZe]Zfibg`"Zg]a([%ZoZen^h_\]!Z_Z\mhk7 *'))"fZr[^_hng]'
\ ]fZr[^mZd^gZl*')_hk_kZf^][nbe]bg`lpbmalmkn\mnkZepZeelZg]fZlhgkr bgm^kgZepZeel%Zg]_hk\eZ]]bg`iZg^elZg]^e^f^gml
:k^_6k^_^k^g\^Zk^Zh_ma^lmkn\mnk^hklmkn\mnkZe^e^f^gm
+'0 Variable actions: others :\mbhgl]n^mh\hglmkn\mbhg%mkZ_Ë\%Ëk^%ma^kfZeZ\mbhgl%nl^Zllbehlhk_khf\kZg^lZk^hnmlb]^ ma^l\hi^h_mablin[eb\ZmbhgZg]k^_^k^g\^lahne][^fZ]^mhli^\bZeblmebm^kZmnk^'
EC1-1-4: 6.2(1) e) & NA.2.20
EC1-1-4: 6.3(1), Exp. (6.2) & NA.2.20, Table NA3
EC1-1-4: 6.3(1), Exp. (6.3) & NA.2.20: Fig. NA9 EC1-1-4: 5.3.2, Exp. (5.4) & NA
EC1-1-6, EC1-2, EC1-1-2, EC1-1-5, EC1-3 & EC1-4
17
+'1 Permanent actions Ma^ ]^glbmb^l Zg] Zk^Z ehZ]l h_ \hffhger nl^] fZm^kbZel% la^^m fZm^kbZel Zg] _hkfl h_ \hglmkn\mbhgZk^`bo^gbgMZ[e^l+'*,mh+'*.' :\mbhglZkblbg`_khfl^mme^f^gm%]^_hkfZmbhgZg]\k^^iZk^hnmlb]^ma^l\hi^h_mabl]h\nf^gm [nm `^g^kZeer Zk^ mh [^ \hglb]^k^] Zl i^kfZg^gm Z\mbhgl' Pa^k^ \kbmb\Ze% k^_^k mh li^\bZeblm ebm^kZmnk^' MZ[e^+'*, ;ned]^glbmb^l_hklhbelZg]fZm^kbZelT**%+/V dG(f,
;ned]^glbmb^l
]\
c+%b
^":\\b]^gmZe]^lb`glbmnZmbhgl >qi'!/'**Z" _"L^blfb\ >qi'!/'*+Z(["
D^r Z OZen^b__ZohnkZ[e^!lahpgbg[kZ\d^ml" [ E^Z]bg`Z\\b]^gmZeZ\mbhg%:]%blng_Z\mhk^] \ L^blfb\Z\mbhg%:>] ] K^_^kmh;L>G*22)3:*'+'+ G:
Ghm^l * Ma^oZen^lh_cZk^`bo^gbgMZ[e^+'*0' + @^hm^\agb\ZeZ\mbhgl`bo^gbgma^mZ[e^ Zk^[Zl^]hg=^lb`g:iikhZ\a*bg qik^llbhg!/'*)"hkma^ phklm\Zl^h_>qik^llbhg!/'*)Z"hk>qik^llbhg!/'*)["'
EC0: 6.4.3.2(3)
Single variable action :mNEL%ma^]^lb`goZen^h_Z\mbhglbl ^bma^k >qi'!/'*)" *',.@d$*'.Jd%* hkma^phklm\Zl^h_3 >qi'!/'*)Z" *',.@d$c)%**'.Jd%* Zg] >qi'!/'*)[" *'+.@d$*'.Jd%* pa^k^ @d 6 i^kfZg^gmZ\mbhg Jd%*6 lbg`e^oZkbZ[e^Z\mbhg c)%*6 \hf[bgZmbhg_Z\mhk_hkZlbg`e^oZkbZ[e^ehZ]!l^^MZ[e^+'*0" MZ[e^+'*0 OZen^lh_c_Z\mhkl EC0: A1.2.2 & NA
EC1-1-1: 3.3.2
:\mbhg
c)
c*
c+
Bfihl^]ehZ]lbg[nbe]bg`l
Category A: domestic, residential areas
)'0
)'.
)',
Category B: office areas
)'0
)'.
)',
Category C: congregation areas
)'0
)'0
)'/
Category D: shopping areas
)'0
)'0
)'/
Category E: storage areas
*')
)'2
)'1
Category F: traffic area (vehicle weight © 30 kN)
)'0
)'0
)'/
Category G: traffic area (30 kN < vehicle weight © 160 kN)
)'0
)'.
)',
Category H: roofsZ
)'0
)')
)')
Snow loads where altitude © 1000 m a.m.s.l.Z
)'.
)'+
)')
Wind loadsZ
)'.
)'+
)')
Temperature effects (non-fire)Z
)'/
)'.
)')
D^r a Hgkhh_l%bfihl^]ehZ]l%lghpehZ]lZg]pbg]ehZ]llahne]ghm[^Ziieb^]mh`^ma^k' Ghm^l 1 Ma^gnf^kb\ZeoZen^l`bo^gZ[ho^Zk^bgZ\\hk]Zg\^pbma;L>G*22)Zg]bmlNDGZmbhgZe:gg^q' 2 qik^llbhg!/'*)"blZepZrl^jnZemhhkfhk^\hgl^koZmbo^maZgma^e^ll_ZohnkZ[e^h_>qik^llbhgl !/'*)Z"Zg]!/'*)["'>qik^llbhg!/'*)["pbeeghkfZeerZiierpa^gma^i^kfZg^gmZ\mbhglZk^ghm `k^Zm^kmaZg-'.mbf^lma^oZkbZ[e^Z\mbhgl!^q\^im_hklmhkZ`^ehZ]l%\Zm^`hkr>bgMZ[e^+'*0% pa^k^>qik^llbhg!/'*)Z"ZepZrlZiieb^l"' Ma^k^_hk^%^q\^imbgma^\Zl^h_\hg\k^m^lmkn\mnk^llniihkmbg`lmhkZ`^ehZ]lpa^k^c)6*')% hk_hkfbq^]nl^%>qik^llbhg!/'*)["pbeenlnZeerZiier'Manl%_hkf^f[^kllniihkmbg`o^kmb\Ze Z\mbhglZmNEL%*'+.@d$*'.Jdpbee[^ZiikhikbZm^_hkfhlmlbmnZmbhglZg]Ziieb\Z[e^mhfhlm \hg\k^m^lmkn\mnk^l!l^^?b`nk^+'."' qik^llbhg!/'*)"%ma^nl^h_^bma^k>qik^llbhg!/'*)Z"hk!/'*)["e^Z]l mh Z fhk^ \hglblm^gm k^ebZ[bebmr bg]^q Z\khll eb`amp^b`am Zg] a^Zorp^b`am fZm^kbZel'
22
:gZerlbl%Z\mbhglZg]ehZ]ZkkZg`^f^gml 50
gk kN/m (or kN/m2)
40
Use Exp. (6.10a)
30 Ghm^ :llnfbg`c)6)'0 b'^'Ziieb\Z[e^mhZeeZk^Zl ^q\^imlmhkZ`^'
20 Use Exp. (6.10b)
10 0
1
2
3
4
5
6
7
8
9
10
q k kN/m (or kN/m2) ?b`nk^+'. Pa^gmhnl^>qi'!/'*)Z"hk>qi'!/'*)["
Accompanying variable actions :`Zbg ma^ ]^lb`g^k fZr \ahhl^ [^mp^^g nlbg` >qik^llbhg !/'*)" hk ma^ e^ll _ZohnkZ[e^ h_ >qik^llbhgl!/'*)Z"hk!/'*)["'
EC0: 6.4.3.2(3)
>bma^k >qi'!/'*)" *',.@d$*'.Jd%*$S!c)%b*'.Jd%b " hkma^phklm\Zl^h_3 >qi'!/'*)Z" *',.@d$c)%**'.Jd%*$S!c)%b*'.Jd%b" Zg] >qi'!/'*)[" *'+.@d$*'.Jd%*$S!c)%b*'.Jd%b" pa^k^ @d 6 i^kfZg^gmZ\mbhg Jd%*6 *lmoZkbZ[e^Z\mbhg Jd%b 6 bmaoZkbZ[e^Z\mbhg c)%*6 \aZkZ\m^kblmb\\hf[bgZmbhg_Z\mhk_hk*lmoZkbZ[e^ehZ]!l^^MZ[e^+'*0" c)%b 6 \aZkZ\m^kblmb\\hf[bgZmbhg_Z\mhk_hkbmaoZkbZ[e^ehZ]!l^^MZ[e^+'*0" Bgma^Z[ho^%Jd%*!Zg]c)%b "k^_^klmhma^e^Z]bg`oZkbZ[e^Z\mbhgZg]Jd%b!Zg]c)%b "k^_^klmh Z\\hfiZgrbg`bg]^i^g]^gmoZkbZ[e^Z\mbhgl'Bg`^g^kZe%ma^]blmbg\mbhg[^mp^^gma^mphmri^lh_ Z\mbhglpbee[^h[obhnl!l^^?b`nk^+'/"4pa^k^bmblghm%^Z\aehZ]lahne]bgmnkg[^mk^Zm^]Zlma^ e^Z]bg`Z\mbhg':elh%ma^gnf^kb\ZeoZen^l_hkiZkmbZe_Z\mhkl`bo^gbgma^NDGZmbhgZe:gg^qT*)ZV Zk^nl^]bgma^^jnZmbhglZ[ho^'Ma^oZen^h_c)]^i^g]lhgma^nl^h_ma^[nbe]bg`Zg]lahne] [^h[mZbg^]_khfma^NDGZmbhgZe:gg^q_hk;L>G*22)!l^^MZ[e^+'*0"'
EC0: A1.2.2, A1.3.1 & NA
qk2 gk2 qk1 gk1 qk1 gk1
qk3 = wk
qk1 gk1 qk1 gk1 A ?b`nk^+'/ Bg]^i^g]^gmoZkbZ[e^Z\mbhgl
B
C
Ghm^ @^g^kZeerma^oZkbZ[e^ Z\mbhglhgZmrib\Zeh__b\^ [eh\dphne][^\hglb]^k^] Zl[^bg`mak^^l^mlh_ bg]^i^g]^gmoZkbZ[e^ Z\mbhgl3 *' Bfihl^]h__b\^ehZ]l hgma^h__b\^_ehhkl' +' Khh_bfihl^]ehZ]' ,' Pbg]ehZ]'
23
Ma^^qik^llbhglmZd^bgmhZ\\hngmma^ikh[Z[bebmrh_chbgmh\\nkk^g\^h_ehZ]l[rZiierbg`ma^ c)%b_Z\mhkmhma^Z\\hfiZgrbg`oZkbZ[e^Z\mbhg'Ma^ikh[Z[bebmrmaZmma^l^\hf[bg^]Z\mbhglpbee [^^q\^^]^]bl]^^f^]mh[^lbfbeZkmhma^ikh[Z[bebmrh_Zlbg`e^Z\mbhg[^bg`^q\^^]^]' B_ma^mphbg]^i^g]^gmoZkbZ[e^Z\mbhglJd%*Zg]Jd%+Zk^Zllh\bZm^]pbma]b__^k^gmliZglZg]ma^ nl^h_>qik^llbhg!/'*)["blZiikhikbZm^%ma^gbghg^l^mh_ZgZerl^lZiier *'+.@d$*'.Jd%*mhma^Jd%*liZgl Zg]*'+.@d$c)'b*'.Jd%*mhma^Jd%+liZgl' BgZllh\bZm^]ZgZerl^lZiier *'+.@d$c)%b*'.Jd%*mhma^Jd%*liZgl Zg]*'+.@d$*'+.Jd%+mhma^Jd%+liZgl' L^^>qZfie^+'**'+!mphoZkbZ[e^Z\mbhgl"'
+'2', Design values at SLS EC0: 6.5 & Table A1.4
Ma^k^Zk^mak^^\hf[bgZmbhglh_Z\mbhglZmLEL!hkehZ]\hf[bgZmbhgZmLEL"'Ma^l^Zk^`bo^gbg MZ[e^+'*1'Ma^\hf[bgZmbhgZg]oZen^mh[^nl^]]^i^g]lhgma^gZmnk^h_ma^ebfbmlmZm^[^bg` \a^\d^]' JnZlb&i^kfZg^gm \hf[bgZmbhgl Zk^ Zllh\bZm^] pbma ]^_hkfZmbhg% \kZ\d pb]mal Zg] \kZ\d\hgmkhe'?k^jn^gm\hf[bgZmbhglfZr[^nl^]mh]^m^kfbg^pa^ma^kZl^\mbhgbl\kZ\d^]hk ghm'Ma^gnf^kb\oZen^lh_c)%c*Zg]c+Zk^`bo^gbgMZ[e^+'*0' 0.3d but < 0.5d from face of column. Say 0.4d = 100 mm from face of column.
Cl. 9.4.3
Cl. 9.4.3(1)
Fig. 9.10, Cl. 9.4.3(4)
By inspection of Figure 3.23 the equivalent of 10 locations are available at 0.4d from column therefore try 2 × 10 no. H10 = 1570 mm2. By inspection of Figure 3.23 the equivalent of 18 locations are available at 1.15d from column therefore try 18 no. H10 = 1413 mm2. By inspection of Figure 3.23 the equivalent of 20 locations are available at 1.90d from column therefore try 20 no. H10 = 1570 mm2. By inspection of Figure 3.23 beyond u1 to uout grid of H10 at 175 x 175 OK. ‡ Clause 6.4.5 provides Exp. (6.52), which by substituting v for v Ed Rd,c, allows calculation of the area of required shear reinforcement, Asw, for the basic control perimeter, u1. § The same area of shear reinforcement is required for all perimeters inside or outside perimeter u1. See Commentary on design, Section 3.4.14. Punching shear reinforcement is also subject to requirements for minimum reinforcement and spacing of shear reinforcement (see Cl. 9.4.3).
84
Cl. 6.4.5 Exp. 6.5.2
Cl. 9.4.3
,'-3?eZmleZ[
e) Summary of punching shear refreshment required at column C2 uout
C
S = 112 H10 legs of links u1 at 2d from column
175 175 175 175 200 200 200 175 175 175 175
2
716
100 400 100
716
Punching shear reinforcement no longer required 1.5d = 375
uout
175 175 175 175 200 200 200 175 175 175 175 375
716
100
400
100
716
Figure 3.23 Punching shear links at column C2 (112 no. links) (column D2 similar)
3.4.11 Punching shear, edge column Assuming penultimate support, VEd = 1.18 × 516.5 = 609.5 kN a) Check at perimeter of column vEd = b VEd/uid < vRd,max where b = factor dealing with eccentricity; recommended value 1.4 VEd = applied shear force ui = control perimeter under consideration. For punching shear adjacent to edge columns u0 = c2 + 3d < c2 + 2c1 = 400 + 750 < 3 × 400 mm = 1150 mm d = as before 250 mm vEd = 1.4 × 609.5 × 103/1150 × 250 = 2.97 MPa vRd,max, as before = 5.28 MPa = OK
Table C3 Cl. 6.4.3(2), 6.4.5(3) Fig. 6.21N & NA Cl. 6.4.5(3)
Exp. (6.32) Cl. 6.4.5(3) Note 85
b) Check shear stress at basic perimeter u1 (2.0d from face of column) vEd = bVEd/u1d < vRd,c where b, VEd and d as before u1 = control perimeter under consideration. For punching shear at 2d from edge column columns u1 = c2 + 2c1+ Q × 2d = 2771 mm vEd = 1.4 × 609.5 × 103/2771 × 250 = 1.23 MPa vRd,c = 0.18/ gC × k × (100 rlfck)0.333
Cl. 6.4.2
Fig. 6.15
Exp. (6.47) & NA
where gC = 1.5 k = as before = 1 +(200/250)0.5 = 1.89 rl = (r lyr lz )0.5 where rer, rlz = Reinforcement ratio of bonded steel in the y and z direction in a width of the column plus 3d each side of column. r ly: (perpendicular to edge) 10 no. H20 T2 + 6 no. H12 T2 in 2 × 750 + 400, i.e. 3818 mm2 in 1900 mm =r ly = 3818/(250 × 1900) = 0.0080 r lz : (parallel to edge) 6 no. H20 T1 + 1 no. T12 T1 in 400 + 750 i.e. 1997 mm2 in 1150 mm. =r lz = 1997/(250 × 1150) = 0.0069 r l = (0.0080 × 0.0069)0.5 = 0.0074 fck = 30 vRd,c = 0.18/1.5 × 1.89 × (100 × 0.0074 × 30)0.333 = 0.64 MPa = Punching shear reinforcement required C
3d = 750
6H20T1 @175
3d = 750 10H20 U-bars in pairs @ 200 cc 1
3d = 750
400
H12 @ 200 U-bars
400
H12 @ 175T1
Figure 3.24 Flexural tensile reinforcement adjacent to columns C1 (and C3) ‡
86
vRd,c for various values of d and rl is available from Table C6.
Cl. 6.4.4.1(1)
Table C6‡
,'-3?eZmleZ[
c) Perimeter at which punching shear links no longer required uout = 609.5 × 1.4 × 103/(250 × 0.64) = 5333 mm Length attributable to column faces = 3 × 400 = 1200 mm = radius to uout from face of column = say (5333 − 1200)/Q = 1315 mm from face of column Perimeters of shear reinforcement may stop 1370 – 1.5 × 250 = 940 mm from face of column. d) Shear reinforcement As before, sr,max = 175 mm; st,max = 350 mm and fywd,ef = 312 MPa For perimeter u1 Asw ≥ (vEd – 0.75vRd,c) sr u1/1.5fywd,ef = (1.23 – 0.75 × 0.64) × 175 × 2771/(1.5 × 312) = 777 mm2 per perimeter Asw,min ≥ 0.08 × 300.5 (175 × 350)/(1.5 × 500) = 36 mm2 Asw/u1 ≥ 777/2771 = 0.28 mm2/mm Using H8 max. spacing = 50/0.28 = 178 mm cc =Use min. H8 (50 mm2) legs of links at 175 mm cc around perimeters: perimeters at 175 mm centres e) Check area of reinforcement > 777 mm2 in perimeters inside u1§ 1st perimeter to be > 0.3d but < 0.5d from face of column. Say 0.4d = 100 mm from face of column By inspection of Figure 3.27 the equivalent of 6 locations are available at 0.4d from column therefore try 2 × 6 no. H10 = 942 mm2
Exp. (6.54)
Cl. 6.4.5(4) & NA
Cl. 9.4.3(1), 9.4.3(2) Exp. (6.52)
Exp. (9.11)
Fig. 9.10, Cl. 9.4.3(4)
By inspection of Figure 3.27 the equivalent of 12 locations are available at 1.15d from column therefore try 12 no. H10 = 942 mm2 By inspection of Figure 3.27 the equivalent of 14 locations are available at 1.90d from column therefore try 14 no. H10 = 1099 mm2 By inspection of Figure 3.27 beyond u1 to uout grid of H10 at 175 x 175 OK.
3.4.12 Punching shear, edge column with hole Check columns D1 and D3 for 200 × 200 mm hole adjacent to column. As previously described use 4 no. H20 U-bars each side of column for transfer moment. Assuming internal support, VEd = 516.5 kN § See Commentary on design Section 3.4.14. Punching shear reinforcement is also subject to requirements for minimum reinforcement and spacing of shear reinforcement (see Cl. 9.4.3).
Cl. 9.4.3
87
a) Check at perimeter of column vEd = bVEd/uid < vRd,max where b = factor dealing with eccentricity; recommended value 1.4 VEd = applied shear force ui = control perimeter under consideration. For punching shear adjacent to edge columns u0 = c2 + 3d < c2 + 2c1 = 400 + 750 < 3 × 400 mm = 1150 mm Allowing for hole, u0 = 1150 – 200 = 950 mm d = 250 mm as before vEd = 1.4 × 516.5 × 103/950 × 250 = 3.06 MPa = OK vRd,max as before = 5.28 MPa b) Check shear stress at basic perimeter u1 (2.0d from face of column) vEd = bVEd/u1d < vRd,c where b, VEd and d as before u1 = control perimeter under consideration. For punching shear at 2d from edge column columns u1 = c2 + 2c1+ Q × 2d = 2771 mm Allowing for hole 200/(c1/2): x/(c1/2 + 2d) 200/200: x/( 200 + 500) = x = 700 mm u1 = 2771 – 700 = 2071 mm vEd = 1.4 × 516.5 × 103/2071 × 250 = 1.40 MPa vRd,c = 0.18/gC × k × (100 rlfck)0.333
Cl. 6.4.3(2), 6.4.5(3) Fig. 6.21N & NA
Cl. 6.4.5(3)
Exp. (6.32) Cl. 6.4.5(3) Note Cl. 6.4.2
Fig. 6.15
Fig. 6.14
Exp. (6.47) & NA
where gC = 1.5 k = as before = 1 + (200/250)0.5 = 1.89 rl = (r ly r lz )0.5 where rer, rlz = Reinforcement ratio of bonded steel in the y and z direction in a width of the column plus 3d each side of column rly: (perpendicular to edge) 8 no. H20 T2 + 6 no. H12 T2 in 2 × 720 + 400 − 200, i.e. 3190 mm2 in 1640 mm. =r ly = 3190/(240 × 1640) = 0.0081 rlz: (parallel to edge) 6 no. H20 T1 (5 no. are effective) + 1 no. T12 T1 in 400 + 750 – 200, i.e. 1683 mm2 in 950 mm. =r lz = 1683/(260 × 950) = 0.0068 88
Cl. 6.4.4.1(1)
,'-3?eZmleZ[
rl = (0.0081 × 0.0068)0.5 = 0.0074 = 30 fck vRd,c = 0.18/1.5 × 1.89 × (100 × 0.0074 × 30)0.33 = 0.64 MPa = punching shear reinforcement required
Table C6‡
D
400
3d = 750
H12 @ 175T1
H12 @ 200 U-bars
6H20T @ 175 3d = 750
400
3
8H20 U-bars in pairs @ 200 cc 3d = 750
Figure 3.25 Flexural tensile reinforcement adjacent to columns D1 and D3 c) Perimeter at which punching shear links no longer required uout = 516.5 × 1.4 × 103/(250 × 0.64) = 4519 mm Length attributable to column faces = 3 × 400 = 1200 mm Angle subtended by hole from centre of column D1 (See Figures 3.25 & 3.27) = 2 tan−1(100/200) = 2 × 26.5° = 0.927 rads. = radius to uout from face of column = say (4519 − 1200)/(Q − 0.927) = 1498 mm from face of column Perimeters of shear reinforcement may stop 1498 – 1.5 × 250 = 1123 mm from face of column d) Shear reinforcement As before, sr,max = 175 mm; st,max = 350 mm and fywd,ef = 312 MPa For perimeter u1 Asw ≥ (vEd – 0.75vRd,c) sr u1/1.5fywd,ef) per perimeter = (1.40 – 0.75 × 0.64) × 175 × 2071/(1.5 × 312) = 712 mm2 per perimeter
Exp. (6.54)
Cl. 6.4.5(4) & NA
Cl. 9.4.3(1) 9.4.3(2) Exp. (6.52)
Asw,min ≥ 0.08 × 300.5 (175 × 350)/(1.5 × 500) = 36 mm2 Asw/u1 ≥ 712/2071 = 0.34 mm2/mm ‡v Rd,c for various values of d and rl is available from Table C6.
89
Using H8 (50 mm2) max. spacing = min[50/0.3; 1.5d] = min[147; 375] = 147 mm cc No good Try using H10, max. spacing = 78.5/0.34 = 231 mm cc, say 175 cc = Use min. H10 (78.5 mm2) legs of links at 175 mm cc around perimeters: perimeters at 175 mm centres Check min. 9 no. H10 legs of links (712 mm2) in perimeter u1, 2d from column face. e) Check area of reinforcement > 712 mm2 in perimeters inside u1‡ 1st perimeter to be 100 mm from face of column as before. By inspection of Figure 3.27 the equivalent of 6 locations are available at 0.4d from column therefore try 2 × 6 no. H10 = 942 mm2.
Fig. 9.10, Cl. 9.4.3(4)
By inspection of Figure 3.27 the equivalent of 10 locations are available at 1.15d from column therefore try 10 H10 = 785 mm2. By inspection of Figure 3.27 beyond 1.15d to uout grid: H10 at 175 x 175 OK.
3.4.13 Summary of design Grid C flexure End supports: Column strip: (max. 200 mm from column) 10 no. H20 U-bars in pairs (where 200 × 200 hole use 8 no. H20 T1 in U-bars in pairs) Middle strip: H12 @ 200 T1 Spans 1–2 and 2–3: Column strip and middle strip:
H20 @ 200 B
Central support: Column strip centre: for 750 mm either side of support: Column strip outer: Middle strip:
H20 @ 100 T1 H20 @ 250 T1 H16 @ 200 T1
Grid 1 (and 3) flexure Spans: Column strip: Middle strip:
H16 @ 200 B2 H12 @ 300 B2
‡ See Commentary on design Section 3.4.14. Punching shear reinforcement is also subject to requirements for minimum reinforcement and spacing of shear reinforcement.
90
Cl. 9.4.3
,'-3?eZmleZ[
Interior support: Column strip centre: Column strip outer: Middle strip:
6 no. H20 @ 175 T2 H12 @ 175 T2 H12 @ 300 T2
Grid 2 flexure Spans: Column strip: Middle strip:
H16 @ 250 B2 H10 @ 200 B2
Interior support: Column strip centre: Column strip outer: Middle strip:
H20 @ 200 T2 H16 @ 250 T2 H12 @ 300 T2 See Figure 3.26
Punching shear Internal (e.g. at C2): Generally, use H10 legs of links in perimeters at max. 175 mm centres, but double up on 1st perimeter Max. tangential spacing of legs of links, st,max = 270 mm Last perimeter, from column face, min. 767 mm See Figure 3.26 Edge (e.g. at C1, C3 assuming no holes): Generally, use H10 legs of links in perimeters at max. 175 mm centres but double up on 1st perimeter Max. tangential spacing of legs of links, st,max = 175 mm Last perimeter, from column face, min. 940 mm Edge (e.g. at D1, D3 assuming 200 × 200 hole on face of column): Generally, use H10 legs of links in perimeters at max. 175 mm centres but double up on 1st perimeter Max. tangential spacing of legs of links, st,max = 175 mm Last perimeter, from column face, min. 1123 mm See Figure 3.27
91
C
D
10H20 T1 U-bars in pairs @ 200 H12 @ 200 T1 U-bars
6H20 - 175 T2 8H20 T1 U-bars in pairs @ 200
H12 - 200 T1 U-bars
1 H20 @ 200 B1
H16 @ 175 B2* 5H12 @ 175 T2
H12 @ 300 B2 H10 @ 200 T2
4H16 @ 250 T2 3H20 @ 250 T1
H16 @ 175 B2* 2
16H20 @ 100 T1
9H20 @ 175 T2* 3H20 @ 250 T1 16H20 @ 100 T1
3H20 @ 250 T1 H16 @ 200 T1 Note:* Spacing rationalised to suit punching shear links
Figure 3.26 Reinforcement details bay C–D, 1–2
3.4.14 Commentary on design a) Method of analysis The use of coefficients in the analysis would not usually be advocated in the design of such a slab. Nonetheless, coefficients may be used and, unsurprisingly, their use leads to higher design moments and shears, as shown below.
92
Method
Moment in Centre support Centre support 9.6 m span per moment per reaction VEd (kN) 6 m bay (kNm) 6 m bay (kNm)
Coefficients
842.7
952.8
1205
Continuous beam
747.0
885.6
1103
Plane frame columns 664.8 below
834.0
1060
Plane frame columns 616.8 above and below
798.0
1031
,'-3?eZmleZ[
D 375
1123
6H20 @ 175 T2 6H16 @ 175 B2
8H20 T1 U-bars in pairs uout
H10 @ 200 T1 U-bars
H10 @ 200 T1 U-bars
1
175 175
1 u1
500
175 175 175
1.5d uout
175 175 175 175 175 Ineffective area S = 152 H10 legs of links CL @ 175 mm centres 175 175 175 175 175 175 200 200 175 175 175 175 175 175 100
100
Note: For internal column see Figure 3.23
Figure 3.27 Punching shear links at column D1 (and D3) (penultimate support without hole similar) These higher moments and shears result in rather more reinforcement than when using other more refined methods. For instance, the finite element analysis used in Guide to the design and construction of reinforced concrete flat slabs[27] for this bay, leads to: t H16 @ 200 B1 in spans 1–2 (cf. H20 @ 200 B1 using coefficients) t H20 @ 125 T1 at support 2 (cf. H20 @ 100 T1 using coefficients) t 3 perimeters of shear links at C2 for VEd = 1065 kN (cf. 5 perimeters using coefficients) t 2 perimeters of shear links at C3 (cf. 7 perimeters using coefficients) b)
Effective spans and face of support In the analysis using coefficients, advantage was taken of using effective spans to calculate design moments. This had the effect of reducing span moments. At supports, one may base the design on the moment at the face of support. This is borne out by Guide to the design and construction of reinforced concrete flat slabs[27] that states that hogging moments greater than those at a distance hc/3 may be ignored (where hc is the effective diameter of a column or column head). This is in line with BS 8110[7] and could have been used to reduce support moments.
Cl. 5.3.2.2(1)
Cl. 5.3.2.2(3)
93
c)
Punching shear reinforcement Arrangement of punching shear links According to the literal definition of :lp in Exp. (6.52), the same area of shear reinforcement is required for all perimeters inside or outside perimeter n* (rather than (:lp/n*)/sr being considered as the required density of shear reinforcement on and within perimeter n*). For perimeters inside n*, it might be argued that Exp. (6.50) (enhancement close to supports) should apply. However, at the time of writing, this expression is deemed applicable only to foundation bases. Therefore, large concentrations of shear reinforcement are required close to the columns – in this example, this included doubling up shear links at the 1st perimeter.
Exp. 6.50
Similar to BS 8110[7] figure 3.17, it is apparent that the requirement for punching shear reinforcement is for a punching shear zone 1.5d wide. However, in Eurocode 2, the requirement has been ‘simplified’ in Exp. (6.52) to make the requirement for a perimeter (up to 0.75d wide). It might appear reasonable to apply the same 40%:60% rule (BS 8110 Cl. 3.7.7.6) to the first two perimeters to make doubling of punching shear reinforcement at the first perimeter unnecessary: in terms of Eurocode 2 this would mean 80% Asw on the first perimeter and 120% Asw on the second. Using this arrangement it would be possible to replace the designed H10 links in the first two perimeters with single H12 links.
BS 8110: Fig. 3.17
Outside u1, the numbers of links could have been reduced to maintain provision of the designed amount of reinforcement Asw. A rectangular arrangement of H12 links would have been possible (within perimeter u1, 350 × 175; outside u1, 500 × 175). However, as the grid would need to change orientation around each column (to maintain the 0.75d radial spacing) and as the reinforcement in B2 and T2 is essentially at 175 centres, it is considered better to leave the arrangement as a regular square grid.
Cl. 9.4.3(1)
Use of shear reinforcement in a radial arrangement, e.g. using stud rails, would have simplified the shear reinforcement requirements. VEd/VRd,c In late 2008, a proposal was made for the UK National Annex to include a limit of 2.0 or 2.5 on VEd/VRd,c (or vEd/vRd,c) within punching shear requirements. It is apparent that this limitation could have major effects on flat slabs supported on relatively small columns. For instance in Section 3.4.12, edge column with hole, VEd/VRd,c = 2.18. Curtailment of reinforcement In this design, the reinforcement would be curtailed and this would be done either in line with previous examples or, more practically, in line with other guidance[20, 21].
94
Exp. 6.52
BS 8110: Cl. 3.7.7.6
,'.3LmZbk_eb`am 3.5 Stair flight Mabl^qZfie^bl_hkZmrib\ZelmZbk_eb`am' Ikhc^\m]^mZbel
0.02 × 1129.6 = 89.6 + 8.9 > 22.6 = 98.5 kNm Load case 2: MEdy = 68.7 kNm MEdz = 6.0 + (l0/400) × 1072.1 × 10−3 > 0.02 × 1072.1 where l0 = 0.9 × 3000 = 13.2 > 21.4 = 21.4 kNm
Table C16
5.2.5 Design using iteration of x For axial load: AsN/2 = (NEd – accnfckbdc /gC)/(ssc – sst)
142
Concise: Section 6.2.2, Appendix A3
For moment: [MEd – accnfckbdc (h/2 – dc/2)/ gC] AsM/2 = (h/2 – d2) (ssc – sst) where MEd = 98.5 × 106 NEd = 1129.6 × 103 acc = 0.85 n = 1.0 for fck ≤ 50 MPa
Cl. 3.1.6(1) & NA Exp. (3.21)
‡The effects of imperfections need only be taken into account in the most unfavourable direction.
Cl. 5.8.9(2)
Appendices A3, C9.2,
.'+3I^kbf^m^k\henfg
fck b h dc
= 30 = 300 = 300 = depth of compression zone = lx = 0.8x < h where x = depth to neutral axis d2 = 35 + 8 + 25/2 = 55 mm assuming H25 = 1.5 gC ssc, (sst) = stress in reinforcement in compression (tension) o
fcd = accnfck/gC o
ecu2
Table 2.1N
d2 ssc
As2
esc
Exp. (3.19)
dc
x h
n. axis ey o a) Strain diagram
As1
sst
d2 o
b) Stress diagram
Figure 5.4 Section in axial compression and bending
Fig. 6.1
Try x = 200 mm = ecu2 = 0.0035 ecu 0.0035 × (x – d2) 0.0035 × (200 – 55) esc = = x 200 = 0.0025 ssc = 0.0025 × 200000 ≤ fyk/gS = 500 ≤ 500/1.15 = 434.8 MPa = 0.0035(h – x – d2)/x = 0.0035(300 – 200 – 55)/200 est = 0.0008 sst = 0.0008 × 200000 ≤ 500/1.15 = 160 MPa 1129.6 × 103 – 0.85 × 1.0 × 30 × 300 × 200 × 0.8/(1.5 × 103) AsN/2 = 434.8 – 160 = (1129.6 – 816.0) × 103 = 1141 mm2 274.8 143
98.5 × 106 – 0.85 × 1.0 × 30 × 300 × 200 × 0.8 (300/2 – 200 × 0.8/2)/(1.5 × 103) (300/2 – 55) (434.8 + 160) 6 (98.5 – 57.1) × 10 = 733 mm2 = 95 × 594.8
AsM/2 =
Similarly for x = 210 mm ecu = 0.0035 esc = 0.0026 = ssc = 434.8 est = 0.0006 = sst = 120 MPa AsN/2 =
(1129.6 – 856.8) × 103 = 866 mm2 434.8 – 120
AsM/2 =
(98.5 – 56.5) × 106 = 796 mm2 95 × 554.8
Similarly for x = 212 mm ssc = 434.8 = 0.00054 =est = 109 MPa est AsN/2 =
(1129.6 – 865.0) × 103 = 812 mm2 434.8 – 109
AsM/2 =
(98.5 – 56.3) × 106 = 816 mm2 95 × 543.8
= as AsN/2 ≈ AsM/2, x = 212 mm is approximately correct and AsN ≈ AsM, ≈ 1628 mm2 = Try 4 no. H25 (1964 mm2)
5.2.6 Check for biaxial bending By inspection, not critical. [Proof: Section is symmetrical and MRdz > 98.5 kNm. Assuming ey/ez > 0.2 and biaxial bending is critical, and assuming exponent a = 1 as a worst case for load case 2: (MEdz/MRdz)a + (MEdy/MRdy)a = (21.4/98.5)1 + (68.7/98.5)1 = 0.91 i.e. < 1.0 = OK.]
Cl. 5.8.9(3)
Exp. (5.39)
5.2.7 Links Minimum size links = 25/4 = 6.25, say 8 mm Spacing: minimum of a) 0.6 × 20 × 25 = 300 mm, b) 0.6 × 300 = 180 mm or c) 0.6 × 400 = 240 mm
Cl. 9.5.3(3), 9.5.3(4) Use H8 @ 175 mm cc
144
.'+3I^kbf^m^k\henfg
5.2.8 Design summary 4 H25 H8 links @ 175 cc cnom = 35 mm to links
Figure 5.5 Design summary: perimeter column
145
.', Internal column Ma^ÌZmleZ[lahpgbg>qZfie^,'-!k^ikh]n\^]Zl?b`nk^.'/"bliZkmh_Zg1&lmhk^rlmkn\mnk^ Z[ho^`khng]pbmaZ[Zl^f^gm[^ehp`khng]'Ma^ikh[e^fblmh]^lb`g\henfg 0.2 and < 5 = Design for biaxial bending.
Cl. 5.8.9(3)
Cl. 5.9.3(3), Exp. (5.38b)
C z ey
MEdy
*
b
Centre of reaction
ez y 2
MEdz
h
Figure 5.10 Eccentricities
5.3.12 Design for biaxial bending Check (MEdz/MRdz)a + (MEdy/MRdy)a ≤ 1.0 For load case 2 where MEdz = 178.7 kNm MEdy = 95.7 kNm MRdz = MRdy = moment resistance. Using charts: From Figure C4d), for d2/h = 0.20 and Asfyk/bhfck = 9648 × 500/500 × 500 × 50 = 0.39 NEd/bhfck = 9000 x 103/(5002 x 50) = 0.72 2 MRd/bh fck = 0.057
Cl. 5.9.3(4), Exp. (5.39)
Fig. C5d)
= MRd ≈ 0.057 × 5003 × 50 = 356.3 kNm
155
a = exponent dependent upon NEd/NRd where = Acfcd + Asfyd NRd = 500 × 500 × 0.85 × 50/1.5 + 9648 × 500/1.15 = 7083 + 3216 = 10299 kN NEd/NRd = 9000/10299 = 0.87. Interpolating between values given for NEd/NRd = 0.7 (1.5) and for NEd/NRd = 1.0 (2.0) = a = 1.67
Cl. 5.8.3(4)
Notes to Exp. (5.39)
Check (MEdz/MRdz)a + (MEdy/MRdy)a ≤ 1.0 (178.7/356.3)1.67 + (95.7/356.3)1.67
= 0.32 + 0.11 = 0.43 i.e. < 1.0 = OK Use 12 no. H32
5.3.13 Links Minimum diameter of links: = f/4 = 32/4 = 8 mm Spacing, either: a) 0.6 × 20 × f = 12 × 32 = 384 mm, b) 0.6 × h = 0.6 × 500 = 300 mm or c) 0.6 × 400 = 240 mm. = Use H8 links at 225 mm cc Number of legs: Bars at 127 mm cc i.e. < 150 mm = no need to restrain bars in face but good practice suggests alternate bars should be restrained. = Use single leg on face bars both ways @ 225 mm cc
5.3.14 Design summary 12 H32 H8 links @ 225 cc 35 mm to link 500 mm sq fck = 50 MPa
Figure 5.11 Design summary: internal column
156
Cl. 9.5.3 & NA
Cl. 9.5.3(3), 9.5.3(4)
Cl. 9.5.3(6) SMDSC: 6.4.2
.'-3LfZeei^kbf^m^k\henfg .'- Small perimeter column subject to two-hour fire resistance Mabl \Ze\neZmbhg bl bgm^g]^] mh lahp Z lfZee le^g]^k \henfg ln[c^\m mh Z k^jnbk^f^gm _hk +&ahnkËk^k^lblmZg\^'Bmbl[Zl^]hgma^^qZfie^lahpgbgL^\mbhg-'+' Ikhc^\m]^mZbel
Small perimeter column subject to two-hour fire resistance
36.5 = 159.5 kNm
Cl. 5.8.8.2 Cl. 5.8.8.2(1), 6.1.4
Cl. 5.2.7
M0Ed = equivalent 1st order moment at about z axis at about mid-height may be taken as M0ez where M0ez = (0.6M02 + 0.4M01) ≥ 0.4M02 = 0.6 × 159.5 + 0.4 × 0 ≥ 0.4 × 159.5 = 95.7 kNm = nominal 2nd order moment = N>]e2 M2 where e2 = (1/r) l02/10 where 1/r = curvature = KvKh[fyd/(Es × 0.45d)] where Kv = a correction factor for axial load = (nu – n)/(nu – nbal)
Cl. 5.8.8.2(2) Cl. 5.8.8.2(3) Cl. 5.8.8. 3 Exp. (5.34)
161
where nu = 1 + w where w = mechanical ratio = Asfyd/Acfd = 1.08 as before nu = 2.08 n = NEd/Acfcd = 1824.1/2082 = 0.88 nbal = the value of n at maximum moment resistance = 0.40 (default) (2.08 – 0.88)/(2.08 – 0.40) 1.20/1.68 = 0.71 a correction factor for creep 1 + bhef
Kv = = Kh = = where b = = = = hef = =
0.35 + (fck/200) – (l/150) 0.35 + 30/200 – 29.3/150 0.35 + 0.15 – 0.195 0.305 effective creep coefficient‡ h(∞,t0) M0,Eqp/M0Ed
where h(∞,t0) = final creep coefficient = from Figure 3.1 for inside conditions h = 350 mm, C30/37, t0 = 15 ƺ 2.4 M0,Eqp = 1st order moment due to quasipermanent loads Gk + h2 Qk × Mz + eiNEd ≈ jgGGk + h0gQQk = =
Cl. 5.8.4(2)
Cl. 3.1.4(2) Fig. 3.1a
63.3 + 0.8 × 46.0 × Mz + eiNEd 1.35 × 63.3 + 1.5 × 46.0 100.1 × 146.1 + 13.4 154.5
= 108.1 kNm M0Ed = M02
= 159.5 kNm
‡
With reference to Exp. (5.13N), hef may be taken as equal to 2.0. However, for the purpose of illustration the full derivation is shown here.
162
Exp. (5.1.3N)
.'-3LfZeei^kbf^m^k\henfg
Kh = 1 + 0.305 × 2.4 × 108.1/159.5 = 1.50 fyd = 500/1.15 = 434.8 MPa Es = 200000 MPa d = effective depth = 350 – 35 – 8 – 16 = 291 mm 1/r = 0.71 × 1.50 × 434.8/(200000 × 0.45 × 291) = 0.0000177 l0 = 2965 mm as before e2 = (1/r) l02/10 = 15.6 mm = 0.0000177 × 29652/10 =M2 = NEde2 = 1824.1 × 103 × 15.6 = 28.4 kNm =0 M01 = MEdz = max[M02z; M0Edz + M2; M01 + 0.5M2] = max[159.5; 95.7 + 28.4; 0 + 28.4/2] = 159.5 kNm
Mz = 146.1 kNm
+
Mz = 0
M2/2 = 14.2 kNm
a) 1st order moments from analysis
MEdz = 159.5 kNm
eiNEd = 13.4 kNm
M2 = 28.4 kNm
Cl. 3.2.7(3)
MOEdz = 95.8 kNm
=
Mz = 0
c) Design moments: MEdz b) Including 2nd order moments: about z axis MEdz = max [M02, MOEd + M2, M01 = 0.5M2]
Figure 5.13 Design moments MEdz
5.4.6 Design moments: MEdy about y axis
MEdy = max[ M02y ; M0Edy + M2 ; M01 + 0.5M2]
where M02y = = = M0Edy = =
§
My + eiNEd ≥ e0NEd 114.5 + 13.4§ ≥ 36.7 kNm 127.9 kNm (0.6M02y + 0.4 M01y) ≥ 0.4M02y 0.6 × 114.5 + 0.4 × 0
Imperfections need to be taken into account in one direction only.
Cl. 5.8.9(2) 163
M2
= 68.7 kNm = 0 (as column is not slender not slender about y axis). = MEdy = 127.9 kNm
5.4.7 Design in each direction using charts = 1824.1 × 103/(3502 × 30) = 0.50 MEd/bh2fck = 159.5 × 106/(3503 × 30) = 0.124 Assuming 8 bar arrangement, centroid of bars in half section: d2 ≥ 35 + 8 + 16 + (350/2 – 35 –8 – 16) × 1/4 ƽ 59 + 29 = 88 mm d2/h = 0.25
In z direction: NEd/bhfck
From Figure C4e) Asfyk/bhfck = 0.50 = 0.50 × 3502 × 30/500 = 3675 mm2 As = 4 no. H32 + 4 no. T25 (5180 mm2) OK.
Fig. C4e)
Fig. C4e)
In y direction: MEd/bh2fck = 127.9 × 106/(3503 × 30) = 0.10 NEd/bhfck = 0.50 From Figure C4e) Asfyk/bhfck = 0.34 = 0.34 × 3502 × 30/500 = 2499 mm2 As = 4 no. H32 + 4 no. T25 (5180 mm2) OK.
5.4.8 Check biaxial bending ly ≈ lz = OK. ez = MEdy/NEd ey = MEdz/NEd MEdz 159.5 ey/heq = = = 1.25 MEdy 127.9 ez/beq = need to check biaxial bending (MEdz/MRdz)a + (MEdy/MRdy)a ≤ 1.0 where MRdz = MRdy = moment resistance= Using Figure C4e) Asfyk/bhfck = 5180 × 500/(3502 × 30) = 0.70 for NEd/bhfck = 0.50 MEd/bh2fck = 0.160 = MRd = 0.160 × 3503 × 30 164
Exp. (5.38a)
Exp. (5.38b)
Exp. (5.39)
Fig. C4e)
.'-3LfZeei^kbf^m^k\henfg
= 205.8 kNm a depends on NEd/NRd where = Acfcd + Asfyd NRd = 3502 × 0.85 × 30/1.5 + 5180 × 500/1.15 = 2082.5 + 2252.2 = 4332.7 kN NEd/NRd = 1824.1/4332.7 = 0.42 = a = 1.27 (159.5/205.8)1.27 + (114.5/205.8)1.27 = 0.72 + 0.47 = 1.19 = No good = Try 8 no. T32 (6432 mm2) For Asfyk/bhfck = = for NEd/bhfck = = MEd/bh2fck = MRd =
6432 × 500/(3502 × 30) 0.88 0.50 0.187 240.5 kNm
Check biaxial bending (159.5/245.7)1.27 + (114.5/245.7)1.27
= 0.59 + 0.39
Cl. 5.8.9(4)
Fig. C4e)
= 0.98 OK
5.4.9 Check maximum area of reinforcement As/bd = 6432/3502 = 5.2% > 4% However, if laps can be avoided in this single lift column then the integrity of the concrete is unlikely to be affected and 5.2% is considered OK. OK
Cl. 9.5.2(3) & NA
PD 6687: 2.19
5.4.10 Design of links Diameter min. = 32/4 = 8 mm Spacing max. = 0.6 × 350 = 210 mm
Cl. 9.5.3 & NA Cl. 9.5.3(3), 9.5.3(4) = Use H8 @ 200 mm cc
5.4.11 Design summary 8 H32 H8 links @ 200 cc 35 mm cover to link No laps in column section Note The beam should be checked for torsion.
Figure 5.14 Design summary: small perimeter column 165
/ Walls /') General PZeel Zk^ ]^Ëg^] Zl [^bg` o^kmb\Ze ^e^f^gml pahl^ e^g`mal Zk^ _hnk mbf^l `k^Zm^k maZg ma^bk mab\dg^ll^l'Ma^bk]^lb`g]h^lghm]b__^klb`gbË\Zgmer_khfma^]^lb`gh_\henfglbgmaZmZqbZe ehZ]lZg]fhf^gmlZ[hnm^Z\aZqblZk^Zll^ll^]Zg]]^lb`g^]_hk' Ma^\Ze\neZmbhglbgmabll^\mbhgbeenlmkZm^ma^]^lb`gh_Zlbg`e^la^ZkpZee' @^g^kZeer%ma^f^mah]h_]^lb`gbg`pZeelblZl_heehpl'BgikZ\mb\^%l^o^kZeh_ma^l^lm^ilfZr[^ \hf[bg^]' N =^m^kfbg^]^lb`geb_^'
EC0 & NA Table NA 2.1
N :ll^llZ\mbhglhgma^pZee'
EC1 (10 parts) & UK NAs
N =^m^kfbg^pab\a\hf[bgZmbhglh_Z\mbhglZiier'
EC0 & NA: Tables NA A1.1 & NA: A1.2(B)
N :ll^ll]nkZ[bebmrk^jnbk^f^gmlZg]]^m^kfbg^\hg\k^m^
BS 8500–1
lmk^g`ma' N ]% bg ma^ ieZg^ i^ki^g]b\neZk mh ma^ pZee'Ma^ ^__^\ml h_ Zeehpbg`_hkbfi^k_^\mbhglZk^ZelhbeenlmkZm^]' Ikhc^\m]^mZbel
G*22+¾*¾*%>nkh\h]^+¾IZkm*¾*3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾@^g^kZekne^lZg]kne^l_hk[nbe]bg`l';LB%+))-' 1a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm*¾*';LB%+)).' 2 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾+%>nkh\h]^+¾IZkm*¾+3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾@^g^kZekne^l¾Lmkn\mnkZe_bk^]^lb`g';LB%+))-' 2a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm*¾+';LB%+)).'
3 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾+%>nkh\h]^+¾IZkm+3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾;kb]`^l';LB%+)).' 3a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm+';LB%+))0'
4 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾,%>nkh\h]^+¾IZkm,3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾Ebjnb]&k^mZbgbg`Zg]\hgmZbgf^gmlmkn\mnk^l';LB%+))/' 4a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm,';LB%+))0'
5 K LG:K:R:G:G KL(MA>LHMR(=MB'LmZg]Zk] f^mah]h_]^mZbebg`lmkn\mnkZe\hg\k^m^%Mabk]>]bmbhg'BLmkn\m>%+))/'
10 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22)%>nkh\h]^3;Zlblh_lmkn\mnkZe]^lb`g' ;LB%+))+' 10a GZmbhgZe:gg^qmh>nkh\h]^';LB%+))-' 11 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22*%>nkh\h]^*3:\mbhglhglmkn\mnk^l !*)iZkml"';LB%+))+¾+))/' 11a GZmbhgZe:gg^q^lmh>nkh\h]^*';LB%+)).¾+))1Zg]bgik^iZkZmbhg' 12 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*220¾*%>nkh\h]^0'@^hm^\agb\Ze]^lb`g' @^g^kZekne^l';LB%+))-' 12a GZmbhgZe:gg^qmh>nkh\h]^0;L>G*220¾*';LB%+))0' 13 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*221¾*%>nkh\h]^1'=^lb`gh_lmkn\mnk^l_hk ^ZkmajnZd^k^lblmZg\^'@^g^kZekne^l'L^blfb\Z\mbhgl_hk[nbe]bg`l';LB%+))-' 13a GZmbhgZe:gg^qmh>nkh\h]^1;L>G*221¾*';LB%+))1'
14 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L1.))¾*3]bmbhg%JN>>G LIKBGM>KH?:GM%Ma^;nbe]bg`K^`neZmbhgl+)))'Ma^ LmZmbhg^krH__b\^Ebfbm^]%+)))'
21 M A>LM:MBHG>KRH??BEBFBM>=!MLH"%;nbe]bg`!:f^g]f^gm"!Gh+"K^`neZmbhgl+))+ Zg]ma^;nbe]bg`!:iikho^]Bgli^\mhkl^m\'"!:f^g]f^gm"K^`neZmbhgl+))+'MLH%+))+'
22 ; KBMBLALM:G=:K=LBGLMBMNMBHG'==>GO*,/0)¾*3+)))3>q^\nmbhgh_\hg\k^m^ lmkn\mnk^l3nkh\h]^*¾IZkm*¾-';LB%+))1'
26 ; KHHD>K%H']phne][^nl^]'
185
Lheobg`ma^jnZ]kZmb\^jnZmbhg3 s(]6T*$!*¾,'.+2D")'.V(+ s6]T*$T*¾,'.+2D")'.V(+
Table C5
Bmbl\hglb]^k^]`hh]ikZ\mb\^bgma^NDmhebfbms(]mhZfZqbfnfh_)'2.]'!Mabl`nZk]lZ`Zbglm k^erbg` hg o^kr mabg l^\mbhgl h_ \hg\k^m^ pab\a Zm ma^ ^qmk^f^ mhi h_ Z l^\mbhg fZr [^ h_ jn^lmbhgZ[e^lmk^g`ma'"MZ[e^l`bobg`oZen^lh_s(]Zg]q(]_hkoZen^lh_DfZr[^nl^]' Area of reinforcement, As MZdbg`fhf^gmlZ[hnmma^\^gmk^h_ma^\hfik^llbhg_hk\^3 F6)'10:l _rds :l6F(!)'10_rd s" Limiting value of relative flexural compressive stress, K' :llnfbg` gh k^]blmkb[nmbhg mZd^l ieZ\^% Z ebfbmbg` oZen^ !hg ma^ lmk^g`ma h_ \hg\k^m^ bg \hfik^llbhg"_hkD\Zg[^\Ze\neZm^]!]^ghm^]D "Zl_heehpl'
Table 3.1
e\n, 6 \hg\k^m^lmkZbg6)')),. el 6 k^bg_hk\^f^gmlmkZbg 6 .))(!*'*.+))*),"6)'))++ ?khflmkZbg]bZ`kZf%?b`nk^:* q 6 )')),.](!)')),.$)'))++" 6 )'/] ?khf^jnZmbhglZ[ho^3 F 6 )'-.,_\d[qs F 6 )'-.,_\d[)'/]!]¾)'-)'/]" 6 )'+)0_\d[]+ =D 6)'+)0 Bm bl h_m^g \hglb]^k^] `hh] ikZ\mb\^ mh ebfbm ma^ ]^ima h_ ma^ g^nmkZe Zqbl mh Zohb] Âho^k& k^bg_hk\^f^gmÃ!b'^'mh^glnk^maZmma^k^bg_hk\^f^gmblrb^e]bg`Zm_Zbenk^%manlZohb]bg`[kbmme^ _Zbenk^h_ma^\hg\k^m^"'H_m^gq(]blebfbm^]mh)'-.'Mablblk^_^kk^]mhZlma^[ZeZg\^]l^\mbhg [^\Znl^Zmma^nembfZm^ebfbmlmZm^ma^\hg\k^m^Zg]lm^^ek^Z\ama^bknembfZm^lmkZbglZmma^ lZf^mbf^T,*V'MablblghmZ>nkh\h]^+k^jnbk^f^gmZg]blghmZ\\^im^][rZee^g`bg^^kl' Ghg^ma^e^ll_hkq6)'-.] ?khf^jnZmbhglZ[ho^3 F 6 )'-.,_\d[qs F 6 )'-.,_\d[)'-.]!]¾)'-)'-.]" 6 )'*/0_\d[]+ =D 6 )'*/0
Cl. 5.5(4)
q(]blZelhk^lmkb\m^][rma^Zfhngmh_k^]blmkb[nmbhg\Zkkb^]hnm'?hk_\d©.)FIZ dª)'-$!)'/$)'))*-e\n"qn(] pa^k^ ] 6 k^]blmkb[nm^]fhf^gm(^eZlmb\[^g]bg`fhf^gm[^_hk^k^]blmkb[nmbhg qn 6 ]^imah_ma^g^nmkZeZqblZmNELZ_m^kk^]blmkb[nmbhg e\n 6 \hfik^llbo^lmkZbgbgma^\hg\k^m^ZmNEL Mabl`bo^lma^oZen^lbgMZ[e^:*'
186
:ii^g]bq:3=^kbo^]_hkfneZ^ Table A1 Limits on D with respect to redistribution ratio, d d
1
0.95
0.9
0.85
0.8
0.75
0.7
% redistribution
)
.
*)
*.
+)
+.
,)
K'
)'+)1
)'*2.
)'*1+
)'*/1
)'*.,
)'*,0
)'*+)
B_D7D ma^l^\mbhglahne][^k^lbs^]hk\hfik^llbhgk^bg_hk\^f^gmblk^jnbk^]'Bgebg^pbma \hglb]^kZmbhg h_ `hh] ikZ\mb\^ hnmebg^] Z[ho^% this publication adopts a maximum value of K'= 0.167'
A1.2 Compression reinforcement, As2 Ma^fZchkbmrh_[^Zflnl^]bgikZ\mb\^Zk^lbg`erk^bg_hk\^]%Zg]ma^l^[^Zfl\Zg[^]^lb`g^]nlbg` ma^_hkfneZ]^kbo^]Z[ho^'Bglhf^\Zl^l%\hfik^llbhgk^bg_hk\^f^gmblZ]]^]bghk]^kmh3 N Bg\k^Zl^l^\mbhglmk^g`mapa^k^l^\mbhg]bf^glbhglZk^k^lmkb\m^]%b'^'pa^k^D7D N Mhk^]n\^ehg`m^kf]^_e^\mbhg N Mh]^\k^Zl^\nkoZmnk^(]^_hkfZmbhgZmnembfZm^ebfbmlmZm^
As2
As Figure A3 Beam with compression reinforcement
Pbmak^_^k^g\^mh?b`nk^:*%ma^k^blghpZg^qmkZ_hk\^ ?l\6)'10:l+ _rd Ma^Zk^Zh_m^glbhgk^bg_hk\^f^gm\Zgghp[^\hglb]^k^]bgmphiZkml%ma^_bklmiZkmmh[ZeZg\^ ma^\hfik^llbo^_hk\^bgma^\hg\k^m^%ma^l^\hg]iZkmmh[ZeZg\^ma^_hk\^bgma^\hfik^llbhg lm^^e'Ma^Zk^Zh_m^glbhgk^bg_hk\^f^gmk^jnbk^]blma^k^_hk^3 :l6D _\n[] +(!)'10_rds"$:l+ pa^k^ sbl\Ze\neZm^]nlbg`D'bglm^Z]h_D :l+\Zg[^\Ze\neZm^][rmZdbg`fhf^gmlZ[hnmma^\^gmk^h_ma^m^glbhg_hk\^3 F6F $)'10_rd:l+!]¾]+" F6D _\n[] +$)'10_rd:l+!]¾]+" K^ZkkZg`bg`3 :l+6!D¾D "_\d[] +(T)'10_rd!]¾]+"V
A2 Shear A2.1 Shear resistance (without shear reinforcement), VRd,c OK]%\6T] ([s6O>] (![)'2]" Bgfhlm\Zl^l%pa^k^\hmy6+'.%y6+*'1 oK]%fZq%\hmy6+'.6)'*,1[ps_\dT*¾_\d (+.)V hk oK]%fZq%\hmy6+'.6)'*,1_\dT*¾_\d (+.)V pa^k^ oK]%fZq%\hmy6+'. 6OK]%fZq%\hmy6+'.(![s" 6OK]%fZq%\hmy6+'.(!)'2[]" Pa^k^\hmy7+'.%ma^Zg`e^h_ma^lmknmZg]oK]%fZqlahne][^\Ze\neZm^]%hkoK]%fZqfZr[^ ehhd^]nibgmZ[e^lhk\aZkml!^'`'MZ[e^] (s_rp]\hmy hk :lp(lªo>]%s[p(_rp]\hmy
Exp. (9.5N) & NA
FbgbfnfZk^Zh_la^Zkk^bg_hk\^f^gm :lp%fbg (!l[plbga"ª)')1_\d)'.(_rd pa^k^ l 6 ehg`bmn]bgZeliZ\bg`h_ma^la^Zkk^bg_hk\^f^gm [p 6 [k^Z]mah_ma^p^[
188
:ii^g]bq:3=^kbo^]_hkfneZ^ a 6 Zg`e^h_ma^la^Zkk^bg_hk\^f^gmmhma^ehg`bmn]bgZeZqblh_ma^f^f[^k'?hko^kmb\Ze ebgdllbga6*')' K^ZkkZg`bg`_hko^kmb\Zeebgdl3 Alp%fbg (lª)')1[plbga_\d)'.(_rd
A3 Columns
el\
_\]6a\\n_\d(g< sl\ ] + :
e\n+
l+
]\
q a
g'Zqbl er
:l*
slm
e\ a) Strain diagram
Fig. 6.1
]+
b) Stress diagram
Figure A4 Section in axial compression and bending
?hkZqbZeehZ] G>]6_\] []\$:l+sl\¾:l*slm ;nmZl:l+6:l*6:lG(+ G>]6_\] []\$:lG!sl\¾slm"(+ G>]¾_\] []\6:lG!sl\¾slm"(+ !G>]¾_\] []\"(!sl\¾slm"6:lG(+ :lG(+6!G>]¾_\] []\"(!sl\¾slm" =:lG(+6!G>]¾a\\n_\d[]\ (g]6_\] []\!a(+¾]\ (+"$:l+sl\!a(+¾]+"$:l*slm!a(+¾]+" ;nmZl:l+6:l*6:lF(+ F>]6_\] []\!a(+¾]\ (+"$:lF!sl\$slm"!a(+¾]+"(+ F>]¾_\] []\!a(+¾]\ (+"6:lF!sl\$slm"!a(+¾]+"(+ TF>]¾_\] []\!a(+¾]\ (+"V(!sl\$slm"!a(+¾]+"6:lF(+ =:lF(+6TF>]¾a\\n_\d []\!a(+¾]\ (+"(gG*22+¾*¾+lmbineZm^lmaZm+. h_^g]liZg fhf^gmlahne][^nl^]mh]^m^kfbg^^g]lniihkmk^bg_hk\^f^gm'MablblnlnZeerZ\\hffh]Zm^] [rikhob]bg`+. h_^g]liZg[hmmhflm^^eZlmhilm^^eZm^g]lniihkml'Bmblhgmabl[ZlblmaZm ma^\Ze\neZmbhglbgmablin[eb\ZmbhgZk^\hglb]^k^]Zl[^bg`_nkma^kln[lmZgmbZm^]'
B1.5 Note regarding factor 310/ss (factor F3) :mma^mbf^h_in[eb\Zmbhg!=^\^f[^k+))2"ma^Znmahklp^k^ZpZk^h_Zikh[Z[e^\aZg`^mh NDG:T+ZVMZ[e^G:'.pab\a%bg^__^\m%phne]f^ZgmaZmma^_Z\mhk,*)(sl!?,"6:l%ikho(:l%k^j ≤ *'.% manl ]blZeehpbg` ma^ Z\\nkZm^ f^mah] hnmebg^] bg L^\mbhgl ,'*% ,'+% ,',% ,'-% -', Zg] :ii^g]b\^l;*'*%;*'+Zg]qi' !/'*)[" pbee [^ ZiikhikbZm^% ^q\^im _hk lmhkZ`^ pa^k^ ma^ nl^ h_ >qi' !/'*)Z" blebd^ermh[^fhk^hg^khnl' ?hkma^LELh_]^_hkfZmbhg%jnZlb&i^kfZg^gmehZ]llahne][^Ziieb^]'Ma^l^Zk^*')@d$c+Jd pa^k^c+bl]^i^g]^gmhgnl^%^'`')',_hkh__b\^lZg]k^lb]^gmbZeZg])'0_hklmhkZ`^'
C2 Values of actions Ma^oZen^lh_Z\mbhgl!b'^'ehZ]l"Zk^]^_bg^]bg>nkh\h]^*T**V'Ma^iZkmlh_>nkh\h]^*Zk^`bo^g bgMZ[e^G*22*¾*¾*lmZm^lmaZmma^]^glbmrh_\hg\k^m^bl+-dG(f,%k^bg_hk\^]\hg\k^m^%+.dG(f, Zg]p^mk^bg_hk\^]\hg\k^m^%+/dG(f,' Table C1 The parts of Eurocode 1[11]
194
Reference
Title
BS EN 1991-1-1
=^glbmb^l%l^e_&p^b`amZg]bfihl^]ehZ]l
BS EN 1991-1-2
:\mbhglhglmkn\mnk^l^qihl^]mh_bk^
BS EN 1991-1-3
LghpehZ]l
BS EN 1991-1-4
Pbg]Z\mbhgl
BS EN 1991-1-5
Ma^kfZeZ\mbhgl
BS EN 1991-1-6
:\mbhgl]nkbg`^q^\nmbhg
BS EN 1991-1-7
:\\b]^gmZeZ\mbhgl]n^mhbfiZ\mZg]^qiehlbhgl
BS EN 1991-2
MkZ__b\ehZ]lhg[kb]`^l
BS EN 1991-3
:\mbhglbg]n\^][r\kZg^lZg]fZ\abg^kr
BS EN 1991-4
:\mbhglbglbehlZg]mZgdl
:ii^g]bq]6 ]^lb`gfhf^gm _r] 6 _rd (gL6.))(*'*.6-,-'1FIZ s 6 ]T)'.$)'.!*¾,'.,D")'.V©)'2.] OZen^lh_s(]!Zg]q(]"fZr[^mZd^g_khfMZ[e^nkh\h]^+Zg]NDGZmbhgZe:gg^q' 2MZ[e^\k^Zm^]_hk_\d6,)FIZZllnfbg`o^kmb\Zeebgdl' 3?hkr eª)'- Zg] _\d6+.FIZ%Ziier_Z\mhkh_)'2-
_\d6-)FIZ%Ziier_Z\mhkh_*'*)
_\d6.)FIZ%Ziier_Z\mhkh_*'*2
_\d6,.FIZ%Ziier_Z\mhkh_*').
_\d6-.FIZ%Ziier_Z\mhkh_*'*-
GhmZiieb\Z[e^_hk_\d7.)FIZ
C5.2 Section capacity check B_o>]%s7oK]%fZqma^gl^\mbhglbs^blbgZ]^jnZm^ pa^k^ o>]%s 6 O>] ([ps6O>] ([p)'2]%_hkl^\mbhglpbmala^Zkk^bg_hk\^f^gm oK]%fZq6 \ZiZ\bmrh_\hg\k^m^lmknml^qik^ll^]ZlZlmk^llbgma^o^kmb\ZeieZg^ 6 OK]%fZq ([ps 6 OK]%fZq ([p)'2] oK]%fZq\Zg[^]^m^kfbg^]_khfMZ[e^nkh\h]^+Zg]NDGZmbhgZe:gg^qZllnfbg`o^kmb\Zeebgdl%b'^'\hma6) 2v6)'/T*¾!_\d (+.)"V 3oK]%fZq6v_\]!\hmy$\hma"(!*$\hm+y"
198
Strength reduction factor, v
:ii^g]bq]%s[p(_rp]\hmy pa^k^ :lp 6 Zk^Zh_la^Zkk^bg_hk\^f^gm!o^kmb\ZeebgdlZllnf^]" l 6 liZ\bg`h_la^Zkk^bg_hk\^f^gm o>]%s6 O>] ([ps%Zl[^_hk^ [p 6 [k^Z]mah_ma^p^[ _rp] 6 _rpd (gL6]^lb`grb^e]lmk^g`mah_la^Zkk^bg_hk\^f^gm @^g^kZeer:lp(lªo>]%s[p(*)10 pa^k^_rpd6.))FIZ%gL6*'*.Zg]\hmy6+'. :em^kgZmbo^er% :lp(l i^k f^mk^ pb]ma h_ [p fZr [^ ]^m^kfbg^] _khf ?b`nk^ ] 6 bO>] (nb]
pa^k^ b 6 _Z\mhk]^Zebg`pbma^\\^gmkb\bmr O>] 6 Ziieb^]la^Zk_hk\^ nb 6 e^g`mah_ma^i^kbf^m^kng]^k\hglb]^kZmbhg ] 6 f^Zg^__^\mbo^]^ima oK]%\ 6 la^Zkk^lblmZg\^pbmahnmla^Zkk^bg_hk\^f^gm!l^^MZ[e^]¾)'0.oK]%\"(!*'._rp]%^_" pa^k^ :lp 6 Zk^Zh_la^Zkk^bg_hk\^f^gmbghg^i^kbf^m^kZkhng]ma^\henfg' ?hk:lp%fbgl^^nkh\h]^+%L^\mbhg*)'-'+Zg]_hkeZrhnml^^L^\mbhg*+'-', lk 6 kZ]bZeliZ\bg`h_i^kbf^m^klh_la^Zkk^bg_hk\^f^gm Concise: 10.4.2, 12.4.3
_rp]%^_
n* 6 [Zlb\\hgmkhei^kbf^m^k+]_khf\henfg_Z\^ 6 ^__^\mbo^]^lb`glmk^g`mah_k^bg_hk\^f^gm6!+.)$)'+.]"©_rp]'?hk@kZ]^ .))la^Zkk^bg_hk\^f^gml^^MZ[e^]≤OK]fZq_hk\hmy6*')`bo^gbgMZ[e^
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