IStructE Manual To Prelim Design in EC2 in Chp4n7-2006 (Extract)
December 1, 2022 | Author: Anonymous | Category: N/A
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Th e In sti titu tu ti tio o n o f Str tru u c tu ra l En g in e e rs
Ma n u a l fo r t h e d e sig n o f c o nc re t e b ui uilld ing st ruc t ur uree s t o Eu ro ro c o d e 2
Se p t e m b e r 2 0 0 6
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
i
C ont onte ents
Notation Foreword 1 Int Intr rod oduc ucttion
x xiii 1
1.1 1.2 1. 2
Aim s o f the M Aim Ma a nua l Eur uro o c o d e sys yste te m
1 1
1 .3 .3 1.4 1. 4 1.5 1. 5
Sc o p e o f t h e M Ma a nua nuall C o nt e nt s of t he M Ma a nua l Not a t ion ion a nd t e rmi mino no log y
3
2 General pr princ inciples iples 2.1 2.1 2.2 2.3 2.4 2. 4 2.5 2.6
G e ne ra l Sta b ility Ro b ustne ss Move m e nt jo ints Fire re sista nc e Dura b ility
3 Des Design ign pr princ inciples iples - reinf einfor orc c ed c onc oncr ret ete e 3.1 3.1 3.2
Lo a d ing Lim it sta te s 3.2.1 Ulti tim m a te lim it sta te (U (UL LS) 3.2.2 Se rvi vicc e a b ility lim it sta te s (S (SL LS)
4 Initia iall de des sign - reinfor einforc c ed c onc oncr rete 4.1 4.1 4.2 4.3 4. 3 4.4 4. 4 4.5 4.6
Intr ntro o d uc ti tio on Lo a d s Ma te ria l p ro p e rti tiee s Str truc uc tur turaa l fo rm a nd fra m ing Fire re sista nc e Dura b ility
4.7 4.8
Sti tiff ffn n e ss Sizi zin ng 4.8.1 4.8.2 4.8.3 4.8.4 4.8.5 4.8.6 4.8.7
4
5 5 5 6 6 7 7
8 8 9 9 10
11 11 11 12 12 13 14
14 15 Intr ntro o d uc ti tio on 15 Lo a d ing 15 Wid t h of b e a ms a nd rib s 15 Size s a nd re inf nfo o rc e m e nt o f c o lum ns 15 Wa lls (h H 4 b) 17 Punc hi hing ng she a r in fla t sla b s a t c o lum ns 17 Ad e q u a c y o f c h o se se n se c t io io n s t o a c c o m m o d a t e t h e re in fo fo rc rc e m e n t 1 8 4.8.7.1 Be n d in g m o m e n t a n d sh e a r fo rc rc e s 18 4.8.7.2 4.8. 7.2 Pro Pr o vi visi sio o n o f re inforc e m e nt 20 The ne xt ste p s 21
4.9 4. 9
4
4.10 4. 10 Re inf nfo o rc e m e nt e sti tim m a te s
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
21
iii
5 Final de des sign - reinfor einforc c ed c onc oncr rete 5.1 5. 1
5.2
Intr ntro o d uc ti tio on 5.1. 5. 1.1 1 C he c king o f a ll informa ti tio on 5.1. 5. 1.2 2 Pree p a ra ti Pr tio o n o f a list o f d e sig n d a ta 5.1. 5. 1.3 3 Am e nd m e nt o f d ra wi wing ng s a s a b a sis fo r fina l c a lc ul ulaa ti tio o ns 5.1. 5. 1.4 4 Fina l d e sig n c a lc ul ulaa ti tio o ns Sla b s 5.2.1 5.2. 1 Introd uc ti tio on
23 23 24 24 25 25 25
5.2. 5. 2.2 2
26 26 26 28 28 28 29 31 35 35 38 43
5.2. 5. 2.3 3
5.2.4 5.2. 4
Fire re sista nc e a nd d ur uraa b ility 5.2.2.1 5.2. 2.1 Fire re sista nc e 5.2.2.2 Dura b ility Be nd ing m om e nt s a nd she a r fo rc e s 5.2.3 5. 2.3.1 .1 Ge ne ra l 5.2. 5. 2.3. 3.2 2 On e -wa y sp a nni nning ng sla b s 5.2.3 5. 2.3.3 .3 Two -wa y sp a nn ing sla b s o n line a r sup p o rts 5.2.3.4 Fla t sl slaa b s Se c ti tio o n d e sig n - so lid sl slaa b s 5.2.4.1 5.2. 4.1 Be nd ing 5.2.4.2 5.2. 4.2 She a r 5.2.4 5. 2.4.3 .3 Op e ni ning ng s
5.2.5 5.2. 5 5.2. 5. 2.6 6
5.3
5.4 5. 4
Sp a n/ e ffe c t ive ive d e p t h ra t ios ios Se c t ion ion d e sig n - rib b e d a nd c of fe fe re d sla b s 5.2.6.1 5.2. 6.1 Be nd ing 5.2. 5. 2.6. 6.2 2 Sp a n/ e ffe c ti tive ve d e p th ra ti tio os 5.2.6.3 5.2. 6.3 She a r 5.2. 5. 2.6. 6.4 4 Be a m str triip s in rib b e d a nd c o ffe re d sla b s 5.2. 5. 2.7 7 No te s o n the use o f p re c a st flo o rs Str truc uc tura l fra m e s 5.3.1 Divi Di visi sio o n int o sub fra m e s 5.3.2 Ela sti sticc a n a lys ysiis 5.3. 5. 3.3 3 Re d istr triib uti utio o n o f m o m e nts 5.3. 5. 3.4 4 De sig n she a r fo rc e s
43 43 44 44 44 45 45 46 46 47 47 48
Be a m s 5.4.1 5.4. 1 5.4. 5. 4.2 2
48 48 49 49 50 51 52 52 54 56 57
5.4.3 5.4. 3 5.4. 5. 4.4 4
5.4. 5. 4.5 5
iv
23
Introd uc ti tio on Fire re sista nc e a nd d ur uraa b ility 5.4.2.1 5.4. 2.1 Fire re sista nc e 5.4.2.2 Dura b ility Be nd ing m om e nt s a nd she a r fo rc e s Se c ti tio o n d e sig n 5.4.4.1 5.4. 4.1 Be nd ing 5.4. 5. 4.4. 4.2 2 Mini nim m um a nd m a xim um a m o unts o f re inf nfo o rc e m e nt 5.4.4.3 5.4. 4.3 She a r Sp a n/ e ffe c t ive ive d e p t h ra t ios ios
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
5.5 5. 5
5.6
Co lum ns (h G 4 b) 5.5.1 5.5. 1 Introd uc ti tio on 5.5. 5. 5.2 2 Sle nd e rne ss, fire re sista nc e a nd d ur uraa b ility 5.5.2.1 5.5. 2.1 Sle nd e rne ss 5.5.2.2 5.5. 2.2 Fire re si sissta nc e 5.5.2.3 Dura b ility 5.5. 5. 5.3 3 Axia l lo a d s a nd m o m e nts - c o lum ns 5.5. 5. 5.4 4 Axia l lo a d s a nd m o m e nts - sle nd e r c o lum ns Ax 5.5. 5. 5.4.1 4.1 G e ne ra l
5.5.5 5.5. 5 5.5. 5. 5.6 6 Wa lls 5.6.1 5.6. 1 5.6. 5. 6.2 2
5.6. 5. 6.3 3
5.7 5. 7
5.8 5. 8
5.5.4. 5.5. 4.2 2 Ca lc ul ulaa ti tio o n o f firstt-o o rd e r m o m e nts a ro und m id he ig ht 5.5. 5. 5.4. 4.3 3 Ca lc ul ulaa ti tio o n o f the ul ulti tim m a te d e fle c ti tio on Se c ti tio o n d e sig n Re infor nforcc e m e nt Introd uc ti tio on Sle nd e rne ss, fire re sista nc e a nd d ur uraa b ility 5.6.2.1 5.6. 2.1 Sle nd e rne ss 5.6.2.2 5.6. 2.2 Fire re si sissta nc e 5.6.2.3 Dura b ility Axia l lo a d s a nd m o m e nts 5.6. 5. 6.3. 3.1 1 Inn-p p la ne b e nd ing
57 57 58 58 60 60 61 62 62 64 64 65 66 66 66 67 67 68 68 68 68
5.6.3.2 5.6. 3.2 Be nd ing a t rig ht-a ng le s to the wa lls Be 5.6.3.3 Sle nd e r wa lls 5.6. 5. 6.4 4 Se c ti tio o n d e sig n 5.6. 5. 6.4.1 4.1 Wa lls no t sub je c t to sig ni niffic a nt b e nd ing a t rig htht-aa ng le s to the wa ll 5.6.4.2 5.6. 4.2 Inte rse c ti ting ng wa lls 5.6. 5. 6.5 5 Re infor nforcc e m e nt 5.6. 5. 6.6 6 Op e ni ning ng s in she a r a nd c o re wa lls Sta irc a se s 5.7.1 5.7. 1 Introd uc ti tio on 5.7. 5. 7.2 2 Fire re sista nc e a nd d ur uraa b ility 5.7.2.1 5.7. 2.1 Fire re si sissta nc e
70 70 70 70 71 71 71 71
5.7.2.2 Dura b ility 5.7. 5. 7.3 3 Be nd ing mo m e nt s a nd she a r for orcc e s 5.7.4 5.7. 4 Effe c ti tive ve sp a ns 5.7. 5. 7.4. 4.1 1 Sta irs sp a nni nning ng b e twe e n b e a m s o r wa lls 5.7. 5. 7.4. 4.2 2 Sta irs sp a nni Sta nning ng b e twe e n la nd ing sla b s 5.7.4.3 Sta irs wi with th o p e n we lls 5.7. 5. 7.5 5 Sp a n/ e ffe c t ive ive d e p t h ra t io io s 5.7. 5. 7.6 6 Se c ti tio o n d e sig n De sig n o f no n-s n-sus usp p e nd e d g ro und flo o r sla b s
71 71 71 71 72 72 72 73 73
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
69 69 69
v
5.9 5. 9
5.10 5. 10
G uid uid a nc e fo r t he d e sig n of b a se m e nt w a lls 5.9. 5. 9.1 1 Ge ne ra l 5.9. 5. 9.2 2 Be nd ing m om e nt s a nd she a r fo rc e s 5.9. 5. 9.3 3 Se c ti tio o n d e sig n 5.9. 5. 9.4 4 Fo un d a ti tio on 5.9. 5. 9.5 5 Re infor nforcc e m e nt Fo un d a ti tio o ns 5.10.1 5.10. 1 Introd uc ti tio on 5.10. 5. 10.2 2 Duraa b ility a nd c o ve r Dur
74 74 74 74 74 74 74 74 75
5.10.3 5.10. 3 5.10. 5. 10.4 4 5.10. 5. 10.5 5
75 76 76 76 76 77 78 78 78 78 78 79
5.10. 5. 10.6 6
5.10.7 5.10. 7 5.10.8 5.10. 8 5.10. 5. 10.9 9
Typ e s o f fo un d a ti tio on Plaa n a re a o f fo und a ti Pl tio o ns De sig n o f sp re a d fo o ti ting ng s 5.10. 5. 10.5. 5.1 1 Axia lly lo a d e d unr Axi unree inf nfo o rc e d sp re a d fo o ti ting ng s 5.10. 5. 10.5. 5.2 2 Axia lly lo a d e d re infor nforcc e d sp re a d fo o ti ting ng s 5.10. 5. 10.5. 5.3 3 Ec c e ntr ntriic a lly lo a d e d fo o ti ting ng s De sig n o f o the r fo o ti ting ng s 5.10.6.1 Str triip fo o ti ting ng s 5.10 5. 10..6. 6.2 2 C o m b ine d foo t ing ing s a nd b a la nc e d foo t ing ing s Re infor nforcc e m e nt in fo o ti ting ng s De sig n o f ra fts De sig n o f p ile c a p s
5.10.10 5.10. 10 Re inf nfo o rc e m e nt in p ile c a p s 5.11 Ro b ustne ss 5.11. 5. 11.1 1 Ge ne ra l 5.11. 5. 11.2 2 Tie fo rc e s a nd a rra ng e m e nts 5.12 De ta iling 5.12. 5. 12.1 1 Ge ne ra l 5.12. 5. 12.2 2 Bo nd c o nd iti tio o ns 5 .1 .1 2. 2.3 An c h o ra ra g e a n d la p le n g t h s 5.12. 5. 12.4 4 Tra nsve rse re infor nforcc e m e nt 5.12. 5. 12.5 5 Add iti tio o na l rul ulee s fo r la rg e d ia m e te r b a rs 5.12. 5. 12.6 6 C ur urta ta ilm e nt o f b a rs in fle xur uraa l m e m b e rs 5.12. 5. 12.7 7 C o rb e ls a nd ni nib bs
6 Des Design ign pri princ nciple iples s - pres presttress essed ed c onc oncr rete 6.1 6.1 6.2 6.3 6. 3
6.4 6. 4
vi
Intr ntro o d uc ti tio on De si sig g n p rinc ip le s Lo a d ing 6.3.1 Se rvi vicc e a b ility lim it sta te (S (SL LS) 6.3.2 Ulti tim m a te lim it sta te (U (UL LS) Ma te ria ls, p re str tree ssing c o m p o ne nts
81 81 81 83 84 84 84 85 88 89 90 90
95 95 95 97 98 100 100
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
7 Prelimina liminar ry de des sign - prestressed c onc oncr rete 7.1 7. 1
7.2 7.3 7. 3 7.4 7.4 7.5 7. 5 7.6
7.7
104 10 4
Intr ntro o d uc ti tio on 7.1. 7. 1.1 1 Ge ne ra l 7.1.2 7.1. 2 Effe c ti tive ve le ng ths 7.1.3 7.1. 3 La te ra l b uc kl kliing 7.1.4 To rs rsiio n Lo a d s Ma te ria l p ro p e rti tiee s
104 104 104 104 104 105 106
Str truc uc tur turaa l fo rm a nd fra m ing Fire re sista nc e a nd d ur uraa b ility Sti tiff ffn n e ss 7.6.1 Sla b s 7.6. 7. 6.2 2 Iso la te d b e a m s Sizi zin ng 7.7.1 7.7. 1 Introd uc ti tio on 7.7. 7. 7.2 2 Lo a d ing 7.7. 7. 7.3 3 Wid th o f b e a m s a nd rib s 7.7.4 7.7. 4 She a r 7.7. 7. 7.4.1 4.1 G e ne ra l 7.7. 7. 7.4. 4.2 2 Be a m s a nd sla b s (s (siing le a nd two wa y)
106 108 109 109 112 112 112 112 113 113 113 113
7.7.4.3 Fla t sl slaa b s Ad e q u a c y o f c h o se se n se c t io io n s t o a c c o m m o d a t e t h e t e n d o n s a n d re in fo fo rc rc e m e n t 7.7. 7. 7.5. 5.1 1 Be nd ing m om e nt s a nd she a r for orcc e s 7.7. 7. 7.5. 5.2 2 Pro Pr o vi vissio n o f te nd o ns a nd re inf nfo o rc e m e nt Ini niti tiaa l d e si sig gn 7.8.1 7.8. 1 Introd uc ti tio on 7.8.1.1 7.8. 1.1 Te nd o n p ro file 7.8.1.2 7.8. 1.2 Te nd o n fo rc e p ro file – Ini niti tiaa l fo rc e (Po) 7.8.1.3 7.8. 1.3 Te nd o n fo rc e p ro file – Fina l fo rc e (Pm, ) 7.8. 7. 8.1. 1.4 4 Te nd o n sp a c ing 7.8. 7. 8.2 2 Postt -t Pos -t e ns nsiion e d a nc ho ra g e s
114
7 .7 .5
7.8
∞
7.8.2. 7.8. 2.1 1 Anc ho ra g e zo ne s 7.8.2.2 Bu rsti stin ng 7.8.2.3 O ve ra ll e q ui uillib rium 7.8.2.4 Sp a llin g 7.8. 7. 8.3 3 Post-te Postte nsi nsio o ne d Co up le rs 7.9 7. 9 The ne xt ste p s 7.10 7. 10 Re inf nfo o rc e m e nt e sti tim m a te s
Refe efer renc nce es Appendix Ap pendix A App ppe endix B Appendix Ap pendix C Appe Ap pendix ndix D
Desi esign gn da datta Durability C olumn design c har hartts Strength and de defform orma ation prope proper rties of c onc oncr rete
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
1 14 14 114 11 4 115 116 116 116 116 119 120 121 12 1 121 121 122 124 124 125 125
127 127 129 130 13 0 137 141 14 1
vii
Tables Ta b le 3. 3.1 1
No ti tio o na l inc lina ti tio o n o f a str truc uc tur turee
8
Ta b le 3.2 3.2
Pa rti tiaa l fa c to rs fo r lo a d s cf a t the ul ulti tim m a te lim it sta te
9
Ta b le 3. 3.3 3
Se rvi vicc e a b ility lo a d c a se s
10
Ta b le 3.4
} fa c to rs fo r b ui uilld ing s
10
Ta b le 4. 4.1 1
Fire re sista nc e re q ui uirre m e nts fo r the ini niti tiaa l d e sig n o f c o nti ntinu nu o us m e m b e rs
13
Ta b le 4.2
Ba sic ra ra ti tio o s o f sp a n/ e ffe c ti tive ve d e p th fo fo r ini niti tiaa l d e sig n f ( yk = 500MP 500MPaa )
14
Ta b le 4.3 Ta b le 4. 4.4 4
Eq ui uiva va le nt ‘s ‘str tree ss’ va lue s Ult ima ima t e b e nd ing mo m e nt s a nd she a r for orcc e s
16 18
Ta b le 5. 5.1 1
Fire re sista nc e re q ui uirre m e nts fo r sla b s
27
Ta b le 5. 5.2 2
Be nd ing m om e nt s a nd she a r for orcc e s for o ne -w a y sla b s
28
Ta b le 5.3 5.3
Be nd ing m o m e nt c o e ffic ie nts fo r two-wa y sp a nni nning ng re c t a ng ul ulaa r sla b s
30
Be nd ing m o m e nt a nd she she a r fo rc e c o e ffic ie nts fo r fla t sla b p a n e ls o f t h re re e o r m o re e q u a l sp a n s
32
Ta b le 5. 5.5 5
Disstr Di triib uti utio o n o f d e sig n m o m e nts o f fla t sla b s
32
Ta b le 5.6
Alte rna ti tive ve re re q ui uirre m e nts to c o ntr ntro o l c ra c k wi wid d ths
Ta b le 5.7 5.7
t o 0. 0.3mm 3mm for m e m b e rs re inf nfor orcc e d w it it h hi hig g h b on d b a rs Ulti tim m a te she she a r str tree ss vRd,c
38 41
Ta b le 5. 5.8 8
Sp a n/ e ffe c ti tive ve d e p th ra ti tio o s fo r sla b s
44
Ta b le 5. 5.9 9
Effe c ti tive ve wi wid d ths o f fla ng e d b e a m s
46
Ta b le 5.4 5.4
Ta b le 5. 5.10 10 Fire re sista nc e re q ui uirre m e nts fo r sim p ly sup p o rte d b e a m s
50
Ta b le 5. 5.11 11 Fire re sista nc e re q ui uirre m e nts fo r c o nti ntinuo nuo us b e a m s
51
Ta b le 5. 12 12 Be nd ing m om e nt s a nd she a r for orcc e s for b e a m s a t ulti ul tim m a te lim it sta te
52
Ta b le 5. 5.13 13 Sp a n/ e ffe c t ive ive d e p t h ra t ios ios for b e a ms
58
Ta b le 5.14 Ef Effe c ti tive ve h e ig ht, l0, fa c to rs fo r c o lum ns
60
Ta b le 5. 5.15 15 Fire re sista nc e re q ui uirre m e nts fo fo r c o lum ns with with re c ta ng ul ulaa r o r c irc ul ulaa r se c ti tio on
61
Ta b le 5. 5.16 16 Be nd ing m o m e nts a t a ro und m id -he ig ht in sle nd e r c o lum ns
63
Ta b le 5. 5.17 17 De sig n m o m e nts fo r b ia xia l b e nd ing
65
Ta b le 5. 5.18 18 C o e ffic ie nts fo r b ia xia l b e nd ing
66
Ta b le 5.19 Effe c ti tive ve he ig ht fa c to rs fo r wa lls
67
Ta b le 5.20 Fire re sista nc e re q ui uirre m e nts fo r wa lls
68
Ta b le 5. 5.21 21 Sp a n/ e ffe c ti tive ve d e p th ra ti tio o s fo r sta irs
73
Ta b le 5. 5.22 22 De p th/ p ro je c ti tio o n ra ti tio o s fo r unr unree inf nfo o rc e d fo o ti ting ng s
76
viii
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Ta b le 5 .2 .2 3 Re in fo fo rc rc e m e n t p e rc e n t a g e s, d e p t h / p ro je je c t io io n ra ra t io io s a n d u n fa fa c t o re re d g ro ro u n d p re ssu ssure re s fo r re in fo rc e d fo o tin ting g s fo r f ck = 25M 25MPa Pa 77 Ta b le 5. 5.24 24 Typi ypicc a l va lue s o f a nc ho ra g e a nd la p le ng ths fo r sla b s
86
Ta b le 5. 5.25 25 Typi ypicc a l va lue s of a nc ho ra g e a nd la p le ng t hs for b e a ms
86
Ta b le 5. 5.26 26 Typi ypicc a l va lue s of a nc ho ra g e a nd la p le ng t hs for c ol olum um ns
87
Ta b le 5. 5.27 27 Typi ypicc a l va lue s o f a nc ho ra g e a nd la p le ng ths fo r wa lls
87
Ta b le 6 .1 .1
Ad v a n t a g e s a n d d isa d v a n t a g e s o f p re - a n d p o st s t -t -t e n s io io n in in g
96
Ta b le 6. 6. 2
Ad v a n t a g e s a n d d is isa d v a n ta ta g e s o f b o n d e d a n d u n b o n d e d c o n s tr tru c t io io n
96
Ta b le 6. 6.3 3
Typi ypicc a l d im e ns nsiio na l d a ta fo r c o m m o n p o stt-te te nsi nsio o ni ning ng sys yste te m s fo r sla b s
101
Ta b le 6.4
Typi ypicc a l d im e ns nsiio na l d a ta for c o m m o n po stt-te te nsi nsio o ni ning ng sys syste m s (1 to 19 str traa nd s)
102
Ta b le 7. 7.1 1
Str traa nd lo a d s (a fte r lo sse s) to b e use d fo r ini niti tiaa l d e sig n
106
Ta b le 7.2
Mini Mi nim m um m e m b e r size s a nd a xis d ista nc e s fo r p re str tree sse d m e m b e rs in fi fire
108
Ta b le 7. 7.3 3
Mini Mi nim m um c o ve r to c ur urve ve d d uc ts
109
Ta b le 7. 7.4 4
Typ ic a l sp a n/ d e p th ra ra ti tio o s fo r a va rie ty o f se c ti tio o n typ typ e s fo r m ul ulti ti--sp a n fl flo o rs 110
Ta b le 7. 7.5 5
Sp a n/ e ffe c ti Sp tive ve d e p th ra ti tio o s fo r ini niti tiaa l sizing o f iso la te d b e a m s
112
Ta b le 7. 7.6 6 Ta b le 7.7
Mom e nt c o e ffic ie nts fo r two -wa y so lid sla b s o n line a r sup p o rts Alllo wa b le str Al stree sse s fo r ini niti tiaa l d e sig n
114 115
Ta b le 7. 7.8 8
Ma xim um ja c king lo a d s p e r str traa nd
118
Ta b le 7. 7.9 9
Ela sti ticc m o d ul ulus us o f c o nc re te
119
Ta b le 7.10 Shri hrinka nka g e str straa ins fo r str tree ng th c la ss C 35/ 45
119
Ta b le 7. 7.11 11 Cr Cree e p c o e ffic ie nts
119
Ta b le 7. 7.12 12 Mini Minim m um d ista nc e b e twe e n c e ntr ntree -line s o f d uc ts in p la n e o f c u rva tu re
12 0
Ta b le 7. 7.13 13 De sig n b ur urssti ting ng te ns nsiile fo rc e s in a nc ho ra g e zo ne s
121 12 1
Ta b le B.1 Ta b le B. B.2
Ta b le B. B.3
Exp os ure ure c la sse s re la t e d t o e nvi nvirron m e nt a l c on d it ion ion s in a c c or ord d a nc e w ith BS EN 20 206-1 6-1 Re c o mm e nd a t ion ion s for no rma l-w e ig ht c on c re t e q ua lit y fo r se se le c t e d e xp o s u re re c la sse s a n d c o v e r t o re re in fo fo rc rc e m e n t for a 50 ye ye a r int e nd e d w o rking life a nd 20 20m mm m a xim u m a g g re re g a t e size Re c o mm e nd a t ion ion s for no rma l-w e ig ht c on c re t e q ua lit y for se le c t e d e xp o su s u re re c la sse s a n d c o v e r t o re re in fo fo rc rc e m e n t fo fo r a 1 00 00 ye ye a r in t e n d e d w o rking life a nd 20 20m m m ma xim um a g g re g a t e size
Ta b le D.1 St re re ng t h a nd d e for ma t ion ion p rop e rt ie ie s of c on c re t e
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130 13 0
1 33 33
135 13 5 141 14 1
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Notation
Latin upper case letters A A Ac A p As As,min Asw D DEd E E c, E E c(28)
E c,eff E cd E cm E c(t )
E p E s
x
Accidental action Cross sectional area Cross sectional area of concrete Area of a prestressing tendon or tendons Cross sectional area of reinforcement minimum cross sectional area of reinforcement Cross sectional area of shear reinforcement Diameter of mandrel Fatigue damage factor Effect of action Tangent modulus of elasticity of normal weight concrete at a stress of vc = 0 and at 28 days Effective modulus of elasticity of concrete Design value of modulus of elasticity of concrete Secant modulus of elasticity of concrete Tangent modulus of elasticity of normal weight concrete at a stress of vc = 0 and at time t Design value of modulus of elasticity of prestressing steel Design value of modulus of elasticity of reinforcing steel
EI EQU F F d F k Gk I L M M Ed N N Ed P P0 Qk Qfat R S S SLS T T Ed
ULS V V Ed
Bending stiffness Static equilibrium Action Design value of an action Characteristic value of an action Characteristic permanent action Second moment of area of concrete section Length Bending moment Design value of the applied internal bending moment Axial force Design value of the applied axial force (tension or compression) Prestressing force Initial force at the active end of the tendon immediately after stressing Characteristic variable action Characteristic fatigue load Resistance Internal forces and moments First moment of area Serviceability limit state Torsion orsional al moment Design value of the applied torsional moment Ultimate limit state Shear force Design value of the applied shear force
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La ti tin n low lowe e r c a se le tt tte e rs a a Δa
b bw d d d g e f c f cd f ck f cm f ctk f ctm f cu f p f pk f p0,1 f p0,1k
Distance Geometrical data Deviation for geometrical data Overall width of a cross-section, or actual flange width in a T or L beam Width of the web on T, I or L beams Diameter; Depth Effective depth of a cross-section Largest nominal maximum aggregate size Eccentricity Compressive strength of concrete Design value of concrete compressive strength Characteristic compressive cylinder strength of concrete at 28 days Mean value of concrete cylinder compressive strength Characteristic axial tensile strength of concrete Mean value of axial tensile strength of concrete Characteristic compressive cube strength of concrete at 28 days Tensile strength of prestressing steel Characteristic tensile strength of prestressing steel 0,1% proof-stress of prestressing steel Characteristic 0,1% proof-stress of prestressing steel
f 0,2k
Characteristic 0,2% proof-stress of reinforcement Tensile strength of reinforcement f t Characteristic tensile strength of f tk reinforcement Yield strength of reinforcement f y f yd Design yield strength of reinforcement f yk Characteristic yield strength of reinforcement f ywd Design yield of shear reinforcement Height h h Overall depth of a cross-section Radius of gyration i Coefficient; Factor k (or L) Length; Span l effective length or lap length l0 Mass m Radius r 1/r Curvature at a particular section Thickness t t Time being considered The age of concrete at the time of t 0 loading Perimeter of concrete cross-section, u having area Ac u,v,w Components of the displacement of a point Neutral axis depth x Coordinates x,y,z x,y,z Lever arm of internal forces z
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G ree k lowe lowe r case c ase lett letters ers a b c cA cC cF cF,fat cC,fat cG cM
cP cQ cS cS,fat
cf cg
cm
d g fc fc1 fcu fu
xii
Angle ; ratio Angle ; ratio; coefficient Partial factor Partial factor for accidental actions A Partial factor for concrete Partial factor for actions, F Partial factor for fatigue actions Partial factor for fatigue of concrete Partial factor for permanent actions, G Partial factor for a material property property,, taking account of uncertainties in the material property itself, in geometric deviation and in the design model used Partial factor for actions associated with prestressing, P Partial factor for variable actions, Q Partial factor for reinforcing or prestressing steel Partial factor for reinforcing or prestressing steel under fatigue loading Partial factor for actions without taking account of model uncertainties Partial factor for permanent actions without taking account of model uncertainties Partial factors for a material property property,, taking account only of uncertainties in the material property Increment/redistribution ratio Reduction factor/distribution coefficient Compressive strain in the concrete Compressive strain in the concrete at the peak stress f c Ultimate compressive strain in the concrete Strain of reinforcement or prestressing steel at maximum load
fuk
Characteristic strain of reinforcement or prestressing steel at maximum load i Angle m Slenderness ratio n Coefficient of friction between the tendons and their ducts o Poisson’ss ratio Poisson’ Strength reduction factor for concrete o cracked in shear g Ratio of bond strength of prestressing and reinforcing steel t Oven-dry density of concrete in kg/m3 t1000 Value of relaxation loss (in %), at 1000 hours after tensioning and at a mean temperature of 20°C tl Reinforcement ratio for longitudinal reinforcement tw Reinforcement ratio for shear reinforcement vc Compressive stress in the concrete Compressive stress in the concrete vcp from axial load or prestressing Compressive stress in the concrete at vcu the ultimate compressive strain fcu x Torsional shear stress z Diameter of a reinforcing bar or of a prestressing duct zn Equivalent diameter of a bundle of reinforcing bars {(t ,t 0) Creep coefficient, defining creep between times t and and t 0, related to elastic deformation at 28 days {(3,t 0) Final value of creep coefficient } Factors defining representative values of variable actions: }0 for combination values }1 for frequent values }2 for quasi-permanent values
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Foreword The Eurocode for the Design of Concrete Structures (Eurocode 2) comprising BS EN 1992-11:2004 and BS EN 1992-1-2:2004 was published at the end of 2004 by The British Standards Institution. The UK National Annexes (NA) setting out the Nationally Determined Parameters (NDPs) have also been published. These documents, together with previously published documents BS EN 1990:2002: Eurocode - Basis of Structural Design and BS EN 1991: 2002: Eurocode 1 – Actions on Structures and their respective NAs, provide a suite of information for the design of most types of reinforced and pre-stressed concrete building structures in the UK. After a period of co-existence, the current National Standards will be withdrawn and replaced by the Eurocodes. This Manu Manual al is a complete revision to the Manu Manual al for the desi design gn of re reinfo inforc rced ed conc concre rete te previously usly published published jointly jointly by by the Institutio Institution n of Structural Structural building structures to EC2 March 2000 previo Engineers and the Institution of Civil Engineers, but follows the same basic format. It provides guidance on the design of reinforced and pre-stressed concrete building structures that do not rely on bending in the columns for their resistance to horizontal forces and are also non-sway. The limit state design of foundations is included but the final design of pre-stressed concrete structures has been exclude excluded. d. Struct Structures ures design designed ed in accord accordance ance with this Manu Manual al will normally comply with Eurocode 2. However it is not intended to be a substitute for the greater range of Eurocode 2. The NDPs from fro m the UKshould NA have been taken into account account in the design design formulae formulae that are are presented. presented. Designers find thistaken Manual concise and useful in practical design. It is laid out for hand calculation, but the procedures are equally suitable for spread sheet and/or computer application. The preparation of this Manu Manual al was partly funded by The Concrete Centre and BCA. This funding allowed the appointment of a Consultant to assist the Task Group with the drafting and editing of the document. Special thanks are due to all of the members of the Task Group and to their organisations, who have given their time voluntarily. In addition, I would like to single out Tony Jones and his colleagues at Arup who acted as the Consultant to the Group, researching and drafting the final document whilst ensuring that the original programme was achieved. I am also grateful to Berenice Chan for acting as secretary to the Group and for fulfilling this considerable task with tolerance and skill. During the review process, members of the Institution provided invaluable comment on the draft Manu Manual al that has contributed to its improvement. I join with all of the other members of the Task Group in commending this Manua Manuall to the industry.
D PIKE Chairman
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1 Int Introduc ducttio ion n
1.1
Aims of the M Man anua uall
This Manual provides guidance on the design of reinforced and prestressed concrete building structures. Structures designed in accordance with this Manual will normally comply with BS EN 1992-1-1: 20041 and BS EN 1992-1-2: 2004 2. It is primarily related to those carrying out hand calculations and not necessarily relevant to computer analysis. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
1.2
Eur uroc ocod ode e sys systtem
The structural Eurocodes were initiated by the European Commission but are now produced by the Comité Européen de Normalisation (CEN) which is the European standards organisation, its members being the national standards bodies of the EU and EFTA countries, e.g. BSI. CEN is publishing the design standards as full European Standards EN (Euronorms): BS EN 1990: Eurocode: Basis of design (EC0) BS EN 1991: Eurocode 1: Actions on structures (EC1) Part 1-1: General actions – Densities, self-weight and imposed loads Part 1-2: General actions on structures exposed to fire Part 1-3: General actions – Snow loads Part 1-4: General actions – Wind loads Part 1-6: Actions during execution Part 1-7: Accidental actions from impact and explosions Part 2: Traffic loads on bridges Part 3: Actions induced by cranes and machinery Part 4: Actions in silos and tanks BS EN 1992: Eurocode 2: Design of concrete structures (EC2) Part 1-1: General rules and rules for buildings (EC2 Part 1-1) Part 1-2: General rules - Structural fire design (EC2 Part 1-2) Part 2: Reinforced and prestressed concrete bridges (EC2 Part 2) Part 3: Liquid retaining and containing structures (EC2 Part 3) BS EN 1993: Eurocode 3: Design of steel structures (EC3) BS EN 1994: Eurocode 4: Design of composite steel and concrete structures (EC4) BS EN 1995: Eurocode 5: Design of timber structures (EC5) BS EN 1996: Eurocode 6: Design of masonry structures (EC6) BS EN 1997: Eurocode 7: Geotechnical design (EC7) BS EN 1998: Eurocode 8: Earthquake resistant design of structures (EC8) BS EN 1999: Eurocode 9: Design of aluminium alloy structures (EC9) The European and British Standards relating to EC2 are shown in Figure 1.1.
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
1
BS EN 1990 (EC 0) Basis of structural st ructural design design
BS EN 1991 (EC1): Action Actions s on structures 1991-1-1: General actions Densities, self weight, imposed loads for buildings 1991-1-2: General actions Actions on structures ex expose posed d to fire f ire 1991-1-3: General actions Snow loads
BS ENV 13670-1 Execution of concrete structures
1991-1-4: General actions W ind loads 1991-1-5: General actions Thermal actions 1991-1-6: General actions Construc Construction tion loads 1991-1-7: General actions Accidental loads
BS EN 1992-1-1 (EC2) General rules and rules for buildings
1992-1-2 (EC2 Part 1-2) Structural fire design 1992-2 (EC2 Part 2) Reinforced and prestressed concrete bridges 1992-3 (EC2 Part 3) Liquid retaining and containing structures
Precast Concrete Products BS ENs 13369: Common rules for Precast Products 13225: Precast Concrete Products - Linear Linear Structural Elements 14843: Precast Concrete Stairs 1168:
Precast Concrete Products - Hollow core slabs
13224: Precast Concrete Products - Ribbed Ribbed floor elements 13693: Precast Concrete Products - Special roof elements 14844: Precast Concrete - Box Box Culverts
BS EN 206-1 Concrete: Specification, performance, production and conformity BS EN 10080 BS 8500 Complementary Concrete. British Standard to BS EN 206-1
Steel for the reinforcement of concrete BS 4449 Steel for the reinforcement of concrete Weldable reinforcing steel - Bar, coil and decoiled product BS 4483 Steel fabric for the reinforcement of concrete
BS EN 10138: Prestressing steels Part 1: General requirements Part Pa rt 2: W ire Part 3: Strand Part 4: Bars
BS 8666 Specification for scheduling, dimensioning, bending and cutting of steel reinforcement for concrete
Fllo w c ha rt of st a nd a rd s fo r Eur uro oc ode 2 Fig 1 F
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All Eurocodes follow a common editorial style. The codes contain ‘Principles’ and ‘Application rules’. Principles are identified by the letter P following the paragraph number. Principles are general statements and definitions for which there is no alternative, as well as, requirements and analytical models for which no alternative is permitted unless specifically stated. Application rules are generally recognised rules which comply with the Principles and satisfy their requirements. Alternative rules may be used provided that compliance with the Principles can be demonstrated, however the resulting design cannot be claimed to be wholly in accordance with the Eurocode although it will remain in accordance with Principles. Each Eurocode gives values with notes indicating where national choice may have to be made. These are recorded in the National Annex for each Member State as Nationally Determined Parameters (NDPs).
1.3 1. 3
Scop ope e of the Ma Manual nual
The range of structures and structural elements covered by the Ma Manu nual al is limited to building structures that do not rely on bending in columns for their resistance to horizontal forces and are also non-sway. This will be found to cover the vast majority of all reinforced and prestressed concrete building structures. In using the Ma Manu nual al the following should be noted: • The Manual has been drafted to comply with BS EN 1992-1-11 (EC2 Part 1-1) and BS EN 1992-1-22 (EC2 Part 1-2) together with the UK National Annexes. • The assumed design working life of the structure is 50 years (see BS 8500 3). • The structures are braced and non-sway. • The concrete is of normal weight concrete (see Appendix D for properties). • The structure is predominantly in-situ. For precast concrete, reference should be made to the EC2 manual for precast concrete4. • Norma Nor mall st struc ructu ture re/c /cla laddi dding ng an and d fi fini nish shes es in inte terf rfac aces es are as assu sume med. d. Fo Forr se sens nsit itiv ivee cl cladd addin ing g or fi fini nish shes es reference should be made to the deflection assessment methods in EC2 1. • Only initial design information is given with regard to prestressed concrete. • Prestressed concrete members have bonded or unbonded internal tendons. • Only tabular methods of fire design are covered. • The use of mild steel reinforcement is not included. Refer to other standards if its use is required. • Structures requiring seismic resistant design are not covered. Refer to BS EN 19985 (Eurocode 8). • For elements of foundation and substructure the Manual assumes that appropriate section sizes and loads have been obtained from BS EN 19976. • The Manual can be used in conjunction with all commonly used materials in construction; however the data given assumes the following: – concrete up to characteristic cylinder strength of 50MPa (cube strength 60MPa) – high-tensile reinforcement with characteristic strength of 500MPa with Class B ductility – ribbed wire fabric reinforcement with characteristic strength of 500MPa with Class A ductility ductility.. Moment redistribution is limited to 20% and yield y ield line design is excluded, except where noted – prestressing tendons with 7-wire 7 -wire low-relaxation (Class 2) strands. For structures or elements outside this scope EC21,2,7 should be used.
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Ma a nua l 1.4 1.4 Co nt e nt s o f t he M The Manual covers the following design stages: i) general principles that govern the design of the layout of the structure ii) initial sizing of members iii) estimating of quantities of reinforcement and prestressing tendons iv) final design of members (except for prestressed concrete members). 1.5 1.5 No t a t io io n a nd t e rm ino lo g y The notation and terminology follow the Eurocode system.
A xe xess The definitions of the axes are as shown in Figure 1.2.
A c tions Actions include both loads (permanent or variable) and imposed deformations (e.g. temperature, shrinkage etc.).
C ombinat ombination ion of ac tion ionss •
•
Quasi-permanent combination of actions: The combination of permanent and variable loads which is most likely to be present most of the time during the design working life of the structure. Frequent combination of actions: The most likely highest combination of permanent and variable loads which is likely to occur during the design working life of the structure.
x z
y
z x
y
Plan view with global axes
io n fo r g e o m e t ri ric a xe s Fig 1.2 No t a t io
View of element local axes
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2 Gene ener ral pr prin inc c iples
This section outlines the general principles that apply to the design of both reinforced and prestressed concrete building structures, and states the design parameters that govern all design stages.
2.1
General
One engineer should be responsible for the overall design, including stability, and should ensure the compatibility of the design and details of parts and components even where some or all of the design and details of those parts and components are not made by the same engineer. The structure should be so arranged that it can transmit permanent (dead) and variable (wind and imposed) loads in a direct manner to the foundations. The general arrangement should ensure a robust and stable structure that will not collapse progressively under the effects of misuse or accidental damage to any one element. The permanent and variable load factors to be used for the proportioning of foundations should be obtained from EC08 and EC76 (see also Section 3.2.1). The factored loads are, however, required for determining the size of foundation members and for the design of any reinforcement. The engineer should consider site constraints, buildability9, maintainability and decommissioning. The engineer should take account of their responsibilities as a ‘Designer’ under the Construction (Design & Management) Regulations10.
2.2
Stab tabili ility ty
Unbraced structures (‘sway frames’) are not covered by this Manual and reference should be made to EC21 for their design. Lateral stability in two orthogonal directions should be provided by a system of strongpoints within the structure so as to produce a braced non-sway structure, which is stiff enough that the columns will not be subject to significant sway moments, nor the building subject to significant global second order effects (see Section 4.8.5). Strongpoints can generally be provided by the core walls enclosing the stairs, lifts and service ducts. Additional stiffness can be provided by shear walls formed from a gable end or from some other external or internal subdividing wall. The core and shear walls should preferably be distributed throughout the structure and so arranged that their combined shear centre is located approximately on the line of the resultant in plan of the applied overturning forces. Where this is not possible, the resulting twisting moments must be considered when calculating the load carried by each strongpoint. These walls should generally be of reinforced concrete not less than 150mm thick to facilitate concreting. For low rise buildings they may be of 215mm brickwork or 190mm solid blockwork properly tied and pinned up to the framing. Strongpoints should be effective throughout the full height of the building. If it is essential for strongpoints to be discontinuous at one level, provision must be made to transfer the forces to other vertical components.
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It is essential that floors be designed to act as horizontal diaphragms, particularly if precast units are used. Where a structure is divided by movement joints each part should be b e structurally independent and designed to be stable and robust without relying on the stability of adjacent sections.
2.3
Robustne ness ss
All members of the structure should be effectively tied together in the longitudinal, transverse and vertical directions. A well-designed and well-detailed cast-in-situ structure will normally satisfy the detailed tying requirements set out in Section 5.11. Elements whose failure would cause collapse of more than a limited part of the structure adjacent to them should be avoided. Where this is not possible, alternative load paths should be identified or the element in question strengthened.
2.4
Movement Move ment jo joint ints s
Movement joints may need to be provided to reduce the effects of movements caused by, for example, early age shrinkage, temperature variations, creep and settlement. The effectiveness of movement joints depends on their location. Movement joints should divide the structure into a number of individual sections, and should pass through the whole structure above ground level in one plane. The structure should be framed on both sides of the joint. Some examples of positioning movement mov ement joints in plan are given in Figure 2.1. Movement joints may also be required where there is a significant change in the type of foundation, or the height or plan form of the structure. For reinforced concrete frame structures in UK conditions, movement joints at least 25mm wide should normally be provided at approximately 50m centres both longitudinally and transversely. In the top storey with an exposed slab and for open buildings joints should normally be provided to give approximately 25m spacing. Where any joints are placed at over 30m centres the effects of movement (see above) should be included in the global analysis (which is outside the scope of this Manual). Joint spacing in exposed parapets should be approximately 12m. Joints should be incorporated in the finishes and in the cladding at the movement joint locations.
Alternative positions
lo c a t io io n o f m o v e m e n t jo in t s Fig 2.1 Su g g e st e d lo
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2.5
Fire resis sisttanc nce e
For the required period of fire resistance (prescribed in the Building Regulations 11), the structure should: • have adequate loadbearing capacity • limit the temperature rise on the far face by sufficient insulation, and • have sufficient integrity to prevent the formation of cracks that will allow the passage of fire and gases. This Manual uses the tabular method given in EC2 Part 1-2 2. However, there may be benefits if the more advanced methods given in that code are used. The above requirements for fire resistance may dictate sizes for members greater than those required for structural strength alone.
2.6
Durability
The design should take into account the likely deterioration of the structure and its components in their environment having due regard to the anticipated level of maintenance. The following inter-related factors should be considered: • the required performance criteria • the expected environmental conditions and possible failure mechanism • the composition, properties and performance of materials • the shape of members and detailing • the quality of workmanship/execution • any protective measure • the accessibility and location of elements together with likely maintenance during the intended life. Concrete of appropriate quality with adequate cover to the reinforcement should be specified. The above requirements for durability may dictate sizes for members greater than those required for structural strength alone.
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3 Des Design ign pr prin inc c iples – reinf einfor orc c ed c onc oncr ret ete e
3.1
Loading
The loads to be used in calculations are: • Characteristic permanent action (dead load), Gk : the weight of the structure complete with finishes, fixtures and fixed partitions. • The characteristic variable actions (live loads) Qki; where variable actions act simultaneously a leading variable action is chosen Qk1, and the other actions are reduced by the appropriate combination factor factor.. Where it is not obvious which should be the leading variable action, each action should be checked in turn and the worse case taken. For typical buildings these loads are found in: • BS EN 1991: Eurocode 1: Actions on structures (EC1) – Part 1-1: General actions – Densities, self -weight and imposed loads12 – Part 1-3: General actions – Snow loads13 – Part 1-4: General actions – Wind loads14 • BS EN 1997: Eurocode 7: Geotechnical design (EC76) At the ultimate limit state the horizontal forces to be resisted at any level should be the sum of: i) The horizontal load due to the vertical load being applied to a structure with a notional inclination. This inclination can be taken from Table 3.1. This notional inclination leads to all vertical actions having a corresponding horizontal action. This horizontal action should have the same load factor and combination factor as the vertical load it is associated with. ii) The wind load derived from BS EN 1991-1- 414 multiplied by the appropriate partial safety factor f actor.. The horizontal forces should be distributed between the strongpoints according to their stiffness and plan location.
Table 3.1 Notiona Notionall inc inc lina linattion of a struc ucttur ure e Building height Number of columns columns stabilis bilised ed by brac bracing ing syst system (m) 1 5 10 H 20 H10
1/ 300
1/ 390
1/ 410
1/ 410
7
1/ 270
1/ 340
1/ 360
1/ 370
4
1/ 200
1/ 260
1/ 270
1/ 280
Note The se va lue s a re d e rive d fro m Exp re ssi sio o n (5.1) (5.1) o f EC 2 1.
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3.2
Limi imitt states
This Manual adopts the limit-state principle and the partial factor format common to all Eurocodes and as defined in BS EN 1990 8 (EC0). 3.2.1 Ulti tim m a te lim it sta te (U (UL LS) The design loads are obtained by multiplying the characteristic loads by the appropriate partial factor cf from Table 3.2. When more than one live load (variable action) is present the secondary live load may be reduced by the application of a combination factor }0 (see Table 3.4). The basic load combination for a typical building becomes:
cG Gk + cQQk1 + RcQ }0 Qki Where: Qk1, Qk2 and Qk3 etc. are the actions due to vertical imposed loads, wind loads and snow etc., Qk1 being the leading action for the situation considered. EC08 allows alternative combinations which, whilst more complex, may allow for greater economy. The ‘unfavourable’ and ‘favourable’ factors should be used so as to produce the most onerous condition. Generally permanent actions from a single load source may be multiplied by either the ‘unfavourable’ or the ‘favourable’ factor. factor. For example, all actions originating from the self weight of the structure may be considered as coming from one source and there is no requirement to consider different factors on different spans. Exceptions to this are where overall equilibrium is being checked checked and the the structure structure is very sensiti sensitive ve to variations variations in permanent permanent loads loads (see EC0 EC0 8).
Table 3.2 Partia iall fa fac tors for loa loads ds cf a att the ult ultima imatte limit state Variable Variab le Act Ac tions (Imposed, wind and snow load) Qki
Permanent Act Ac tion (Dead load) Gk
c G,sup
1 .3 5
c G,inf
1 .0 0
c (u n fa fa v ) Q
c (f (faa v)
Earthb and waterd (thes (t hese e can c an gener generally ally be c onsi onside der red as as pe per rmane manent nt actions and factored accordingly)
Q
1 .5 0
0 .0 0
1 .3 5
Notes a Alte rn a ti tiv v e v a lu e s m a y b e re q u ir ire d to c h e c k o v e ra ll e q u il ilib riu m o f str tru u c tu re re s se n si siti tiv v e to v a ria ti tio o n in in d e a d we ig h t (se (se e EC0 8).
b Th is is a ssu m e s th a t c o m b in a ti tio o n 1 o f Ca se 1 (s (see e E EC7 C7 6) is is c riti ticc a l fo r the str struc uc tura l d e sig n. Thi hiss is no rm a l fo r typ ic a l fo un d a ti tio o ns whe n siz size d to EC EC 7 6. Fo Fo r c e rta in str tru u c tu re re s, su c h a s re ta in in in g wa lls, c o m b in a ti tio o n 2 ma y b e m o re re o n e ro u s fo r th e str truc uc tur turaa l d e sig n. In In this this c o m b ina ti tio o n cG = 1.0, cQ = 1. 1.3 , a n d re d u c t io io n fa c t o rs rs a re a p p lie d t o t h e so il il st re re n g t h . Re fe re n c e sh o u ld ld b e m a d e t o EC EC 7 6.
c Fo r t h e d e sig n o f p ile s a n d a n c h o rs rs re fe re n c e sh o u ld ld b e m a d e t o EC EC 7 6. re c a lc u la la t e d is is t h e m o s t u n fa fa v o u ra ra b le v a lu e t h a t c o u ld ld d If t h e w a t e r p re ssu re o c c u r d u ri rin g t h e life o f th th e st ru ru c t u re re a p a rt ia ia l fa c t o r o f 1. 1.0 m a y b e u se se d .
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Further guidance on the use of the use of load combinations is given in Worked Examples for the design of concrete buildings buildings to Eurocode 219 being prepared by The Concrete Centre. 3.2.2 Se rvi vicc e a b ility lim it sta te s (S (SL LS) The appropriate serviceability serviceability limit state should be considered for each specific case. EC21 provides specific checks under characteristic, characteristic, frequent and quasi-permane quasi-permanent nt loads; the check required varies depending on the effect considered. The corresponding load cases are given in Table 3.3 and are obtained by multiplying the characteristic variable actions by appropriate reduction factors (} or I }2). The values of }1 and }2 are given in Table 3.4. The effects of these factors have been included, where appropriate, in the formulae and tables presented in the Manua Manuall.
Table 3. 3.3 3 Servic ervicea eabilit bility y loa load d c ases Permanent Ac tions Combination
Variable Ac tions
Gk,sup
Le a d in g Qk1
C h a ra c t e rist ic
1 .0
1 .0
}0
Fre q u e n t
1 .0
}1
}2
Q u a si-p e rm a n e n t
1 .0
}2
}2
Oth e rs Qki
Table 3.4 } fac facttors for build buildings ings Action
}0
}1
}2
Do m e st ic , re sid e n t ia l a re a
0 .7
0 .5
0 .3
O ffic e a re a
0 .7
0 .5
0 .3
C o n g re g a t io n a re a s
0 .7
0 .7
0 .6
Sh o p p in g a re a s
0 .7
0 .7
0 .6
St o ra g e a re a s
1 .0
0 .9
0 .8
Tra ffic a re a
0 .7
0 .7
0 .6
0 .7
0 .5
0 .3
Ro o fs
0 .7
0 .0
0 .0
Sn o w lo lo a d s
0 .7
0 .5
0 .2
0 .5
0 .2
0 .0
Win d lo a d s
0 .5
0 .2
0 .0
Te m p e ra t u re ( n o n fire )
0 .6
0 .5
0 .0
Ve hi hicc le
G30kN
Tra ffic a re a 30kN G V Vee hi hicc le
G 160kN
H H1 00 00 0m 0m a b o v e se a le v e l (a .s.l .l)) Sn o w lo lo a d s H G 100 1000m 0m a .s .s.l .l
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4 Ini Inittial de des sign – reinf einfor orc c ed conc concr rete
4.1
Introd oduc ucttion
In the initial stages of the design of building structures it is necessary, often at short notice, to produce alternative schemes that can be assessed for architectural and functional suitability and which can be compared for cost. They will usually be based on vague and limited information on matters affecting the structure such as imposed loads and nature of finishes, and without dimensions, but it is nevertheless expected that viable schemes be produced on which reliable cost estimates can be based. It follows that initial design methods should be simple, quick, conservative and reliable. Lengthy analytical methods should be avoided. This section offers some advice on the general principles to be applied when preparing a scheme for a structure, followed by methods for sizing members of superstructures. Foundation design is best deferred to later stages when site investigation results can be evaluated. The aim should be to establish a structural scheme that is suitable for f or its purpose, sensibly economical, and not unduly sensitive to the various changes that are likely to be imposed as the overall design develops. Sizing of structural members should be based on the longest spans of slabs and beams and largest areas of roof and/or floors carried by beams, columns, walls and foundations. The same sizes should be assumed for similar but less onerous cases- this saves design and costing time at this stage and is of actual benefit in producing visual and constructional repetition and hence, ultimately,, cost benefits. ultimately Simple structural schemes are quick to design and easy to build. They may be complicated later by other members of the design team trying to achieve their optimum conditions, but a simple scheme provides a good ‘benchmark’ at the initial stage. Loads should be carried to the foundation by the shortest and most direct paths. In constructional terms, simplicity implies (among other matters) repetition, avoidance of congested, awkward or structurally sensitive details and straightforward temporary works with minimal requirements for unorthodox sequencing to achieve the intended behaviour of the completed structure. The health and safety aspects of the scheme need to be assessed and any hazards identified and designed out wherever possible10.
4.2
Loads
Loads should be based on BS EN 1991 12-18 (see also Section 3.1). Imposed loading should initially be taken as the highest statutory figures where options exist. The imposed load reduction allowed in the loading code should not be taken advantage of in the initial design stage except when assessing the load on the foundations. Loading should be generous and not less than the following in the initial stages: • floor finish (screed) 1.8kN/m2 • ceiling and service load 0.5kN/m2
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• •
Allowance for: demountable lightweight partitions 1.0kN/m2 – to be treated as imposed loads. blockwork partitions 2.5kN/m2 – to be treated as dead loads when the layout is fixed.
Loading from reinforced concrete should be taken as 25kN/m 3.
4.3
Matteria Ma iall prope proper rtie ies s
Design stresses are given in the appropriate sections of the Manu Manual al. It should be noted that EC2 1 specifies concrete strength class by both the cylinder strength and cube strength (for example C25/30 is a concrete with a characteristic cylinder strength of 25MPa and cube strength of 30MPa at 28 days). Standard strength classes given in EC21 are C20/25, C25/30, C30/37, C35/45, C40/50, C45/55 and C50/60. BS 85003 gives the following additional classes C28/35 and C32/40 which are not included in either EC21 or Appendix D; however interpolation of values is generally applicable. All design equations which include concrete compressive strength use the 28 day characteristic cylinder strength, f ck . Appendix D gives the strength and deformation properties for concrete. The partial factor, cc, for concrete is 1.5 for ultimate limit state and 1.0 for serviceability limit state. It should also be noted that, for the ultimate limit state f should also be multiplied ck by acc, hence the design strength, f cd = acc f ck / cc. The coefficient acc takes account of long term effects on the compressive strength and unfavourable effects resulting from the way the load is applied. In the UK the value of acc is generally taken as 0.85, except for shear resistance, where it is taken as 1.0. The strength properties of reinforcement are expressed in terms of the characteristic yield strength, f yk . Partial factors for reinforcement steel are 1.15 for ultimate limit state and 1.0 for serviceability limit state. For normal construction in the UK, a concrete strength C30/37MPa should normally be assumed for the initial design. For UK steels a characteristic strength f of 500MPa should be used. yk
4.4
Struc ucttur ura al form and framing
The following measures are recommended for braced structures: • provide stability against lateral forces and ensure braced construction by arranging suitable shear walls deployed symmetrically wherever possible • adopt a simple arrangement of slabs, beams and columns so that the load path to the foundations is the shortest and most direct route • allow for movement joints (see Section 2.4) • choose a regular grid arrangement that will limit the maximum span of slabs (including flat slabs) to between 6m and 9m and beam spans to between 8m and l2m • adopt a minimum column size of 300mm x 300mm or equivalent area or as required by fire considerations • provide a robust rob ust structure.
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The arrangement should take account of possible large openings for services and problems with foundations, e.g. columns immediately adjacent to site boundaries may require balanced or other special foundations.
4.5
Fire resis sisttanc nce e
The size of structural members may be governed by b y the requirements of fire resistance. Table Table 4.1 shows the minimum practical member sizes for different periods of fire resistance and the axis distance, a, from the surface of the concrete to the centre of the main reinforcing bars, required for fo r continuous members (where the moment redistribution is limited to 15%). For simply supported members (and greater redistribution of moments), sizes and axis distance should be increased (see Section 5 and Appendix B).
Table 4.1 Fir ire e resistanc nce e req equir uireme ement nts s for for the the init initia iall design design of contin c ontinuous uous members members Critical dimension
Member
Minimum dimension (mm) R 30
R 60
R 90
200
250
300
450
500
500
200
350
500
500
600
>60 0b
w id t h
155
155
155
175
230
293
Wa lls e xp o se d o n t w o sid e s w id t h
120
140
170
220
270
350
Wa lls e xp o se d o n o n e sid e
w id t h
120
130
140
160
210
270
width
80
15 0
20 0
20 0
24 0
28 0
a xis d ista n c e
20 d
25 d
35 d
50
60
75
C o nti ntinuo nuo us sl sla b s with with
thicc kne ss thi
60
80
10 0
12 0
15 0
17 5
p la in so ffi ffitt
a xis d ista nc e
15 d
15 d
20 d
20 d
30 d
40
C o nti ntinuo nuo us sl sla b s with with
thicc kne ssc thi
80
80
10 0
12 0
15 0
17 5
rib b e d o p e n so so ff f fit a n d n o stirrrup s sti
wid th o f rib s wid a xis d ista nc e
80 15 d
10 0d 25
12 0d 35
16 0 45
31 0 60
45 0 70
thicc kne ss thi
15 0
18 0
20 0
20 0
20 0
20 0
a xis d ista nc e
15 d
15 d
25 d
35 d
45
50
Columns fully
nfia G 0 .5
e xp o se d to fire
nfia G 0 .7
C o lum ns pa rtl tly y e xp o se d to fire
nfia G 0 .7
Be a m s
Fla t sla sla b s
R 120 R 180
R 240
width
Notes a nfi i iss ‘t ‘the he d e sig n a xia l lo a d in the fire situa ti tio o n’ divi divid d e d b y ‘t ‘the he d e sig n re re sista nc e o f th t h e c o lu lu m n a t n o r m a l t e m p e ra t u re re c o n d it io io n s’. A v a lu e o f 0. 0. 5 sh sh o u ld o n ly ly b e a ss ssum um e d if it is is lig ht ly lo lo a d e d . ItIt is is un like ly tha t it it wil will e xc e e d 0.7.
b Pa rti ticc ul ulaa r a sse ssm e nt fo r b uc kling re re q ui uirre d . c Th ic ic kn e ss o f str tru u c tu ra ra l to p p in g p lu s a n y n o n -c -c o m b u sti stib b le sc re e d . d Fo r p ra c t ic ic a l p u rp rp o s e s t h e a xis d ist a n c e sh o u ld b e su c h th t h a t t h e m in im im u m c o v e r is 2 0m 0m m .
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4.6
Durability
The size of structural members may be affected by the cover necessary to ensure durability (see Appendix B).
4.7
Stiffne iffness ss
To provide adequate stiffness, the effective depths of beams, slabs and the waist of stairs should not be less than those derived from Table 4.2. Beams should be of sufficient depth to avoid the necessity for excessive compression reinforcement and to ensure that economical amounts of tension and shear reinforcement are provided. This will also facilitate the placing of concrete.
Table 4.2 Basic ratios of spa span/ n/e effec fecttive dep deptth for for init initia iall design design ( f 500MPa)) f yk = 500MPa Struc ructur tural system
Spa pan/ n/E Effec fecttive Dept Depth Ratio
Sim p ly su p p o rt e d b e a m
Be a m
Sla b
14
O n e -w a y o r t w o -w a y sp a n n in g sim p ly su p p o rt e d sla b
20
En d sp a n o f:
C o n t in in u o u s b e a m
O n e -w a y c o n t in in u o u s sla b ; o r t w o -w - w a y sp a n n in in g
18 26
sla b c o n ti tin n u o u s o v e r o n e lo n g sid e Inte rio r sp a n o f:
Be a m Be
O n e -w a y o r t w o -w -w a y sp a n n in in g sla b
20 30
Sla b su p p o rte d o n c o lu m n s wi with th o u t b e a m s (f (flla t sl sla b ),
24
b a se d o n lo n g e r sp a n C a n t ile v e r
6
8
Notes a Fo r t w o -w - w a y sp a n n in in g sl sla b s ( su su p p o rt rt e d o n b e a m s) , t h e c h e c k o n t h e ra ra t io io o f sp a n / e ffe c t iv iv e d e p t h sh sh o u ld ld b e c a rrie d o u t o n t h e sh o rt rt e r sp a n . Fo Fo r fl fla t sl sla b s, t h e lo lo n g e r sp a n sh sh o u ld ld b e t a ke n .
b Fo r fla n g e d se c ti tio o n s wi with th th th e ra ti tio o o f th e fla n g e to th e rib rib w id th g re re a te r th a n 3, 3, th e Ta b le v a lu e fo r b e a m s sh o u ld ld b e m u lti ltip p lie d b y 0. 0. 8 .
c Fo r m e m b e rs, o th e r th a n fl fla t sla b p a n e ls, wh ic ic h su su p p o rt p a rti titi tio o n s lia b le to b e d a m a g e d b y e xc e ssi ssive ve d e fl flee c t io n o f t h e m e m b e r, a n d w h e re t h e sp a n e xc e e d s 7 m , th th e Ta b le v a lu e sh o u ld ld b e m u lt lt ip ip lie d b y 7/ 7/ sp a n .
d Fo r fla t sla b s w h e re t h e g re a t e r sp a n e xc e e d s 8 .5 .5 m , t h e Ta b le v a lu e sh o u ld ld b e m ul ulti tip p lie d b y 8. 8.5/sp 5/sp a n.
e Th e v a lu e s m a y n o t b e a p p ro p ria t e w h e n th t h e fo r m w o rk is st ru ru c k a t a n e a rly a g e o r w h e n th t h e c o n st s t ru ru c t io io n lo lo a d s e xc e e d t h e d e sig n lo lo a d . In th t h e se c a se s t h e d e fle c t io io n m a y n e e d t o b e c a lc u la la t e d u si sin g a d v ic ic e in sp sp e c ia list lilit e ra t u re re .
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4.8
Sizi izing ng
4.8.1 Intr ntro o d uc ti tio on When the depths of slabs and beams have been obtained it is necessary to check the following: • width of beams and ribs • column sizes and reinforcement • shear in flat slabs at columns • practicality practicali ty of reinforce reinforcement ment arrangem arrangements ents in beams, slabs and at beam-colu beam-column mn junctions. 4.8.2 Lo a d ing Ultimate loads, i.e. characteristic loads multiplied by the appropriate partial factors, should be used throughout. At this stage it may be assumed that all spans are fully loaded, unless the members (e.g. overhanging cantilevers) concerned are sensitive to unbalanced loading (see Section 4.8.7.1). For purposes of assessing the self-weight of beams, the width of the downstand can be taken as half the overall depth but usually not less than 300mm. 4.8.3 W id t h o f b e a m s a n d rib s The width should be determined by limiting the shear stress in beams to 2.0MPa and in ribs to 0.6MPa for concrete of characteristic strength f / f f H 25/30MPa: ck cu • width of beam (in mm) = 1000V / 2d • width of rib (in mm) = 1000V / 0.6d Where: V is the maximum shear force (in kN) on the beam or rib, considered as simply supported is the effective depth in mm. d 4.8.4 Size s a nd re inf nfo o rc e m e nt o f c o lum ns Where possible it will generally be best to use ‘stocky columns’ (i.e. generally for typical columns for which the ratio of the effective height to the least lateral dimension does not exceed 15) as this will avoid the necessity of designing for the effects of slenderness. Slenderness effects can normally be neglected in non-sway structures where the ratio of the effective height to the least lateral dimension of the column is less than 15. For the purpose of initial design, the effective height of a braced column may be taken as 0.85 times the storey height. The columns should be designed as axially loaded, but to compensate for the effect of eccentricities, the ultimate load from the floor immediately above the column being considered should be multiplied by the factors listed below: • For columns loaded by beams and/or slabs of similar stiffness on both sides 1.25 of the column in two directions at right-angles to each other, e.g. some internal columns. • For columns loaded in two directions at right-angles to each other by 2.00 unbalanced beams and/or slabs, e.g. corner columns. • In all other cases, e.g. façade columns. 1.50 It is recommended that the columns are made the same size through at least the two
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topmost storeys, as the above factors may lead to inadequate sizes if applied to top storey columns for which the moments tend to be large in relation to the axial loads. For the initial design of columns, the required cross-sectional area may be calculated by dividing the ultimate load by the selected equivalent ‘stress’ given in Table 4.3. Alternatively, for a known column size the ultimate load capacity may be found by using the selected equivalent ‘stress’. When choosing the column dimensions, care should be taken to see that the column remains stocky, as defined above.
Tabl ble e 4.3 Equiva Equivale lent nt ‘stress’ va value lues s
Equivalent stresses (MPa) for c onc oncr rete strength class classes es
Reinf inforc orce ement (500MP (500MPa a) percentage t
C 25/ 30
C 30/ 37
C 35/ 45
t = 1%
14
17
19
t = 2%
18
20
22
t = 3%
21
23
25
t = 4%
24
27
29
The equivalent ‘stresses’ given in Table 4.3 are derived from the expression:
t stress = 0.44 fck + 100 (0.67 fyk - 0.44 fck)
Where: f ck f y t
is the characteristic concrete strength in MPa the characteristic strength of reinforcement in MPa the percentage of reinforcement.
Where slender columns (i.e. the ratio of the effective height l0, to the least lateral dimension, b, exceeds 15) are used, the ultimate load capacity of the column or equivalent ‘stress’ should be reduced by the appropriate factor from Figure 4.1. In braced frames l0 may be taken as the clear floor to soffit height.
1.0 0.9 0.8 0.7 Capacity 0.6 reduction factor 0.5 0.4 0.3 0.2 10
15
25
20
30
l0
least lateral dimen dimension sion
io n fa c t ors ors fo r sle nd e r c o lum ns Fig 4.1 Re d uc t io
35
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4.8.5 Wa lls ( h H 4 b ) Walls carrying vertical loads can initially be designed as columns. column s. Shear walls should be designed as vertical cantilevers, and the reinforcement arrangement should be checked as for a beam. Where the shear walls have returns at the compression end, they should be treated as flanged beams. This Manual assumes that shear walls are sufficiently stiff that global second order effects do not need to be considered. The walls should be sized such that: F V, Ed G 0.517
ns
(ns + 1.6 )
/ E
I
cm c 2
L
Where: F V,Ed is the total vertical load (on the whole structure stabilised by the wall) is the number of storeys ns L is the total height of building above level of moment restraint is the mean modulus of elasticity E cm I c is the second moment of area (uncracked concrete section) of the wall(s). This assumes that: • torsional instability is not governing, i.e. structure is reasonably symmetrical • global shear deformations are negligible (as in a bracing system mainly consisting of shear walls without large openings) • base rotations are negligible • the stiffness of the wall is reasonably constant throughout the height • the total vertical load increases by approximately the same amount per storey. In the above equation for F V,Ed it should be noted that the value 0.517 should be halved if the wall is likely to be cracked. 4.8.6 P unc hi hing ng she a r in fl f la t sl sla b s a t c o lum ns Check that: i) where shear reinforcement is to be avoided or slabs are less than 200mm thick 1250w (A sup p) G 0.6MPa 6 MPa (uc + 12h) h ii)
where shear reinforcement may be provided 1250w (A sup p) G 1.0MPa 0 MPa (uc + 12h) h
iii)
Check also that in the above verification 1250w (A sup p) G 0.15 f ck (uc) h
Where: w h Asupp u
is is is is
the total design ultimate load per unit area in kN/m2 the thickness of the slab at the column in mm. the area supported by the column in m2 column perimeter in mm.
c
It should be noted that for slabs less than 200mm thick shear reinforcement is not effective.
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4.8.7 Ad e q u a c y o f c h o se se n se se c t io n s t o a c c o m m o d a t e t h e re in fo fo rc rc e m e n t The actual bar arrangement should be considered at an early stage particularly where the design is close to reinforcement limits.
4.8.7.1
Bending moment and shea shea r for forcc es
In the initial stage the reinforcement needs to be checked only at midspan and at the supports of critical spans.
Bea ms and one one-wa -wayy sol solid id slab slab s Bending moments and shear forces in continuous structures can be obtained from Table 4.4 when: • the imposed load does not exceed the dead load • there are at least three spans, and • the spans do not differ in length by more than 15% of the longest span.
Table 4.4 Ult ltima imatte bending bending moment moments s and shea shear r forc orces es Uniformly distributed loads C ent entr ral point load loads s to ta l d e sig n u lti ltim m a te ltim m a te p o in t F = to W = d e sig n u lti lo a d o n sp sp a n
Be n d in g m o m e n t s
lo a d
a t su p p o rt rt
– 0.100 FL
– 0.150 WL
a t m id id sp sp a n
0.080 FL
0.175 WL
0 .6 5 F
0.65 W
Sh e a r fo rc e s
Note iss t h e sp a n . L i
Alternatively, bending moments and shear forces may be obtained by elastic analysis.
Two wo-wa -wa y solid solid sla sla b s on line linea a r sup supp p orts If the longer span l does not exceed 1.5 times the shorter span l , the average moment per metre y x width may be taken as: lx ly kN w kNm m per per me metr tree 18 Where: w is the design ultimate load in kN/m2, and lx and ly are in metres. If ly > 1.5 lx the slab should be treated as acting one-way.
Solid Sol id flat sla sla b s Determine the moments per unit width in the column strips (see Figure 4.2) in each direction as 1.5 times those for one-way slabs.
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O ne-way ribb ribb ed slab s Assess the bending moments at midspan on a width equal to the rib spacing, assuming simple supports throughout.
Two wo-wa -wa y rib rib b e d sla bs on linea linearr supp supp ort ortss If the longer span does not exceed 1.5 times the shorter span, estimate the average rib moment in both directions as: w
lx ly kNm m per per rib c kN 18
Where: c is the rib spacing in metres. If ly > 1.5lx the slab should be treated as acting one-way.
C offered slab s on c ol olumn umn supp supp ort ortss Assess the average bending moment at midspan on a width equal to the rib spacing using Table 4.4. For the column strips increase this by 15%.
Column strip
Middle strip
lx
4 p i r t s e l d d i M
p i r t s n m u l o C
x
l
lx
2
ly -
lx
lx
2
4
ly
Longer span
Divi vissio n of p a ne l wi witho tho ut d ro p s into stri strip s Fig 4.2 Di
n a p s r e t r o h S
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4.8.7.2
Provision Provis ion of reinfor reinforcc e me ment nt
Using the bending moments above reinforcement may be calculated as follows:
Tension reinforcement Reinforcement can now be calculated by the following formula: As =
M 0.87 fyk 0.8d
Where: M d
is the design ultimate bending moment at the critical section is the effective depth.
C ompres ompresssion reinfor reinforcc eme nt If, for a rectangular section, M > > 0.167 f ck bd 2, assuming no redistribution, compression reinforcement is required: As2 =
Where: As2 d 2 b d
M - 0.167 fck bd 2 0.87 fyk (d - d 2)
is the area of the compression steel is the depth to its centroid is the width of the section is its effective depth.
If, for flanged sections, M > > 0.567 f ck bf hf (d - 0.5hf ) the section should be redesigned. bf and hf are the width and the thickness of the flange. hf should not be taken as more than 0.36 d . It should be noted that where compression reinforcement is required transverse reinforcement should be provided to restrain the main reinforcement from buckling.
Shea She a r re re info inforc rc e me nt Asw
V
s
=
f ywd
Where: V s d f ywd
cot i 0.9d
b
(for initial sizing cot i
=
1)
l
is the design ultimate shear force at the critical section is the spacing of shear reinforcement is the effective depth is the design yield strength of the shear reinforcement.
Bar arr arrang ang eme nt ntss When the areas of the main reinforcement in the members have been calculated, check that the bars can be arranged with the required cover in a practicable manner avoiding congested areas. In beams, this area should generally be provided by not less than 2 nor more than 8 bars. In slabs, the bar spacing should not be less than 150mm nor more than 300mm; the bars should not be less than 10mm nor normally more than 20mm in diameter.
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4.9
The ne next xt steps
At this stage general arrangement drawings, including sections through the entire structure, should be prepared and sent to other members of the design team for comment, together with a brief statement of the principal design assumptions, e.g. imposed loadings, weights of finishes, fire ratings and durability. The scheme may have to be amended following receipt of comments. The amended design should form the basis for the architect’s drawings and may also be used for preparing reinforcement estimates for budget costings.
4.10 4.1 0
Reinf inforc orce ement estima imattes
In order for the cost of the structure to be estimated it is necessary for the quantities of the materials, including those of the reinforcement, to be available. Fairly accurate quantities of the concrete and brickwork can be calculated from the layout drawings. If working drawings and schedules for the reinforcement are not available it is necessary to provide an estimate of the anticipated quantities. In the case of reinforcement quantities the basic requirements are, briefly: • for bar reinforcement to be described separately by: steel type, diameter and weight and divided up according to: a) element of structure, e.g. foundations, slabs, walls, columns, etc. b) bar ‘shape’, e.g. straight, bent or hooked; curved; links, stirrups and spacers. • for fabric (mesh) reinforcement to be described separately by: steel type, fabric type and area, divided up according to a) and b) above. There are different methods for estimating the quantities of reinforcement; three methods of varying accuracy are given below.
Me M e thod 1 The simplest method is based on the type of structure and the volume of the reinforced concrete elements. Typical values are, for example: • warehouses and similarly loaded and proportioned structures: 1 tonne of reinforcement per 10m 3 • offices, shops, hotels: 1 tonne per 13.5m3 • residential, schools: 1 tonne per l5m3. However, while this method is a useful check on the total estimated quantity it is the least accurate, and it requires considerable experience to break the tonnage down.
Me M e thod 2 Another method is to use factors that convert the steel areas obtained from the initial design calculations to weights, e.g. kg/m2 or kg/m as appropriate to the element.
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If the weights are divided into practical bar diameters and shapes, this method can give a reasonably accurate assessment. The factors, however, do assume a degree of standardisation both of structural form and detailing. This method is likely to be the most flexible and relatively precise in practice, as it is based on reinforcement requirements indicated by the initial design calculations. Reference should be made to standard tables and spreadsheets available from suitable organisations (e.g. The Concrete Centre).
Me M e thod 3 For this method sketches are made for the ‘typical’ cases of elements and then weighted. This method has the advantages that: • the sketches are representative of the actual structure • the sketches include the intended form of detailing and distribution of main and secondary reinforcement • an allowance of additional steel for variations and holes may be made by inspection. This method can also be used to calibrate or check the factors described in method 2 as it takes account of individual detailing methods. When preparing the reinforcement estimate, the following items should be considered: • Laps and starter bars – A reasonable allowance should be made for normal laps in both main and distribution bars, and for starter bars. This should be checked if special lapping arrangements are used. • Architectural features – The drawings should be looked at and sufficient allowance made for the reinforcement required for such ‘non-structural’ features. • Contingency – A contingency of between 10% and 15% should be b e added to cater for fo r some changes and for possible omissions.
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5 Fin ina al de des sign - reinf einfor orc c ed c onc oncr rete
5.1
Introd oduc ucttion
Section 4 describes how the initial design of a reinforced concrete structure can be developed to the stage where preliminary plans and reinforcement estimates may be prepared. Now the approximate cost of the structure can be estimated. Before starting the final design it is necessary to obtain approval of the preliminary drawings from the other members of the design team. The drawings may require further amendment, and it may be necessary to repeat this process until approval is given by all parties. When all the comments have been received it is then important to marshal all the information received into a logical format ready for use in the final design. This may be carried out in the following sequence: i) checking of all information ii) preparation of a list of design data iii) amendment of drawings as a basis for final calculations. 5.1.1 5.1. 1 C he c king o f a ll informa ti tio on To ensure that the initial design assumptions are still valid, the comments and any other information received from the client and the members of the design team, and the results of the ground investigation, should be checked.
Stabilility Stab ity Ensure that no amendments have been made to the sizes and to the disposition of the core and shear walls. Check that any openings in these can be accommodated in the final design.
Mo M o ve me nt joints joints Ensure that no amendments have been made to the disposition of the movement joints.
Loading Check that the loading assumptions are still correct. This applies to dead and imposed loading such as floor finishes, ceilings, services, partitions and external wall thicknesses, materials and finishes thereto. Make a final check on the design wind loading and consider whether or not loadings such as earthquake, accidental, constructional or other temporary loadings should be taken into account. In general the load case including permanent, imposed, and wind load will be most onerous for all elements, however it is not normally considered necessary to include wind load for members that do not form part of the direct wind resistance system as the wind load effects will be small and can be neglected. However local effects do need to be b e checked.
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Fir ire e resi resist stanc anc e , d urab urabil ilit ityy a nd sound ins insul ula a ti tion on Establish with other members of the design team the fire resistance required for each part of the structure, the durability classifications that apply to each part and the mass of floors and walls (including finishes) required for sound insulation.
Foundations Examine the information from the ground investigation and decide on the type of foundation to be used in the final design. Consider especially any existing or future structure adjacent to the perimeter of the structure that may influence not only the location of the foundations but also any possible effect on the superstructure and on adjacent buildings.
Performanc Perfor manc e c rit ite e ria Establish which codes of practice and other design criteria are to be used in the final design.
Ma M a te terial rialss Decide on the concrete mixes and grade of reinforcement to be used in the final design for each or all parts of the structure, taking into account the fire-resistance and durability requirements, the availability of the constituents of concrete mixes and any other specific requirements such as water resisting construction for basements.
Hazards Identify any hazard resulting from development of the scheme design. Explore options to mitigate10. 5.1.2 5.1. 2 Pr Pree p a ra ti tio o n of a list o f d e sig n da ta The information obtained from the above check and that resulting from any discussions with parties such as the client, design team members, building control and material suppliers should be entered into a design information data list. A suitable format for such a list is included in Appendix A. This list should be sent to the design team leader for approval before the final design is commenced. 5.1.3 5.1. 3 Am e nd m e nt o f d ra wi wing ng s a s a b a sis fo r fina l c a lc ul ulaa ti tio o ns The preliminary drawings should be brought up to date incorporating any amendments arising out of the final check of the information previously accumulated and finally approved. In addition the following details should be added to all the preliminary drawings as an aid to the final calculations: • Gridlines – Establish gridlines in two directions, mutually at right-angles for orthogonal building layouts, consistent with that adopted by the rest of the design design team: identify these on the plans. • Members – Give all walls, columns, beams and slabs unique reference numbers or a combination of letters numbers if possible to the grid, so that they can be readily identified on theand drawings andrelated in the calculations.
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•
Loading – Prepare drawings showing the loads that are to be carried by each element, clearly indicating whether the loads are factored or unfactored. It is also desirable to mark on the plans the width and location of any walls or other special loads to be carried by the slabs or beams.
5.1.4 5.1. 4 Fina l d e sig n c a lc ul ulaa ti tio o ns When all the above checks, design information, data lists and preparation of the preliminary drawings have been carried out the final design calculations for the structure can be commenced. It is important that these should be carried out in a logical sequence. The remainder of this section has been laid out in the following order: • slabs (Section 5.2) • structural frames (Section 5.3) • beams (Section 5.4) • columns (Section 5.5) • walls (Section 5.6) • staircases (Section 5.7) • non-suspended ground floor slabs (Section 5.8) • retaining walls, basements (Section 5.9) •• •
foundations (Section5.11) 5.10) robustness (Section detailing (Section 5.12).
5.2
Slabs
5.2.1 Introd 5.2.1 Introd uc ti tio on The first step in preparing the final design is to complete the design of the slabs. This is necessary in order that the final loading is determined for the design of the frame. The initial design should be checked, using the methods described in this subsection, to obtain the final sizes of the slabs and to calculate the amount and dimensions of the reinforcement. Thiscoefficients subsection gives the requirements for firetwo-way resistance and durability, bending and shear force for one-way spanning slabs, spanning slabs onand linear supports, and flat slabs using solid, ribbed and coffered construction. The coefficients apply to slabs complying with certain limitations which are stated for each type. For those cases where no coefficients are provided the bending moments and shear forces for one-way spanning slabs may be obtained by elastic analysis. These moments may then be redistributed, maintaining equilibrium with applied loads, up to a maximum of 30%, although normally 15% is considered a reasonable limit. The treatment of shear around columns for flat slabs and the check for deflection for all types of slab are given, together with some notes on the use of precast slabs. The general procedure to be adopted is as follows: i) ii)
Check that the cross section and cover comply with requirements for fire resistance. Check that cover and concrete grade comply with requirements for durability.
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iii) iv) v) vi)
Calculate bending moments and shear forces. Calculate reinforcement. Make final check on span/depth ratios. For flat slabs check shear around columns and calculate shear reinforcement as necessary.
The effective span of a simply supported slab should normally be taken as the clear distance
between of supports plusthe theeffective slab thickness. However, where bearing padbetween is provided pr ovided between the the faces slab and the support, span should be taken asathe distance the centres of the bearing pads. The effective span of a slab continuous over its supports should normally be taken as the distance between the centres of the supports. The effective length of a cantilever slab where this forms the end of a continuous slab is the length of the cantilever from the centre of the support. 5.2. 5. 2.2 2
5.2.2.1 5.2. 2.1
Fire re re sista nc e a nd d ur uraa b ility
Fire Fi re resis re sista tanc nc e
The member size and reinforcement cover required to provide fire resistance are given in Table When using this table, the redistribution slabs shouldmay be limited5.1. to 15% although the bending moments given inofTables Tmoments ables 5.2, in 5.3continuous and 5.4 of o f this manual be used. The cover in the Table may need to be increased for durability (see Section 5.2.2.2).
5.2.2.2 5.2. 2.2
D ura urab b ilility ity
The requirements for achieving durability in any given environment are: • an upper limit to the water/cement ratio • a lower limit to the cement content • a lower limit to the nominal cover to the reinforcement • good compaction • adequate curing •
good detailing.
For a given value of nominal cover (expressed as minimum cover plus an allowance for deviation, Dcdev) Table B.2 (50 years) and Table B.3 (100 years) of Appendix B give values of concrete class, an upper limit to the water cement ratio and cement content which, in combination, will be adequate to ensure durability for various environments. Where it is specified that only a contractor with a recognised quality system shall do the work (e.g. member of SpeCC, the Specialist Concrete Contractors certification scheme) Dcdev = 5mm, otherwise Dcdev = 10mm.
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ble e 5.1 5.1 Fire resis sisttanc nce e re requi quir reme ment nts s for slab slabs s Tabl Standard fire resis esisttanc nce e (R) in minutes
Plain soffit solid slab (including (inc luding joist + bloc k) Minimum Minim um overall overall depth (mm)
Ribb ibbed ed soffit soffit (inc (including luding T-sec ecttion + c hannel sect sec tion) Non-combustible finish t
Flat slabs Minimum overall depth (mm)
b
Minimum thic hickness/ kness/widt width, h, (mm// mm (mm mm)) Sim p ly Supported
R 60 R 90 R 120 R 180
80 100 120 150
t/b 80/ 120 100/ 160 120/ 190 150/ 260
R 240
175
175/ 350
Continuous
t/b 80/ 100 100/ 120 120/ 160 150/ 310
175/ 450 Axis distanc nce e to reinf einforc orceme ement nt, a (mm)
180 200 200 200 200
Simply supported
C ont ontinuous inuous
Simply supported
Conttinuou Con ous s
Flat slab abs s
R 60
20a
10 a
25 a
25 a
15 a
R 90
30a
15 a
40
35a
25 a
R 120
40
20a
55
45
35a
R 180
55
30a
70
60
45
R 240
65
40
75
70
50
Notes a Fo r p ra c t ic ic a l p u rp rp o s e s t h e
a xis d ist a n c e sh o u ld b e su c h th t h a t t h e m in im im u m
c o v e r is 2 0m 0m m . iss m e a su re re d fro m t h e s ur u rfa c e o f t h e c o n c re t e t o t h e c e n t re re b The a xis d ista nc e , a i o f th e m a in re re in fo fo rc in g b a rs.
c The a xis d ista nc e , a s sh h o u ld ld b e in c re a se d b y 10 10 m m fo r p re re st re re ssin g b a rs a n d 15mm fo r p re st strre ssing wi wirre s o r str traa nd s.
d Fo r o th e r c o m b in a ti tio o n s o f rib w id th a n d a xis d ista n c e se e EC2 , P a rt 1 -2 -2 2. e W h e r e a i iss 70mm o r m o re re fe r to EC 2, Pa Pa rt 1-2 1-2 2 f fo o r a d d iti tio o n a l re q u ir ire m e n ts. ts.
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Amendment - May 2010
Load Slab
l
x
Effective width
Unsupported edge
x 1.2 x (1 - l )
l
3 . 0
Load width
l
ive w id id t h o f so lid sl sla b c a rryi ying ng a c o nc e nt ra ra t e d lo lo a d ne a r a n Fig 5.1 Effe c t ive u n su su p p o rt rt e d e d g e
5.2. 5.2.3.3 3.3 moments Tw o -w -wa a ytwo-way spa nning sla sl amay b s on lcalculated inea a r sup supp p orts Bending in slabs be line by any valid method provided the ratio between support and span moments are similar to those obtained by the use of elastic theory with appropriate redistribution. In slabs where the corners are prevented from lifting, the coefficients in Table 5.3 may be used to obtain bending moments per unit width ( msx and msy) in the two directions for various edge conditions, i.e.: msx = bsxnlx2 msy = bsynlx2
Where: bsx and bsy
are the coefficients given in Table 5.3
is the total design ultimate load per unit area (1.35 Gk + 1.5 Qk ) is the shorter span.
n l x
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5.3 3 Bending Bending moment coe coefffic icient ients s for for twotwo-way way spanning rect rec tangular slab slabs s Table 5. Short spa span n coe c oeff ffic icients ients bsx
Type of panel and moments moment s consi conside der red
1
Inte rio r p a ne ls:
Ne g a t iv e m o m e n t a t
Values of
l y l x
Long-span c oe oefffic icient ients s bsy for all values l of y l x
1.00
1.25
1.50
1.75
2.00
0 .0 3 1
0 .0 4 4
0 .0 5 3
0 .0 5 9
0 .0 6 3
0 .0 3 2
0 .0 2 4
0 .0 3 4
0 .0 4 0
0 .0 4 4
0 .0 4 8
0 .0 2 4
c o n t in in u o u s e d g e
P o s itit iv iv e m o m e n t a t m id id s p a n
2
O n e sh o rt rt e d g e d isc o nti ntinuo nuo us:
Ne g a t iv e m o m e n t a t c o n t in in u o u s e d g e
0 .0 3 9
0 .0 5 0
0 .0 5 8
0 .0 6 3
0 .0 6 7
0 .0 3 7
P o s itit iv iv e m o m e n t a t
0 .0 2 9
0 .0 3 8
0 .0 4 3
0 .0 4 7
0 .0 5 0
0 .0 2 8
0 .0 3 9
0 .0 5 9
0 .0 7 3
0 .0 8 2
0 .0 8 9
0 .0 3 7
0 .0 3 0
0 .0 4 5
0 .0 5 5
0 .0 6 2
0 .0 6 7
0 .0 2 8
0 .0 4 7
0 .0 6 6
0 .0 7 8
0 .0 8 7
0 .0 9 3
0 .0 4 5
0 .0 3 6
0 .0 4 9
0 .0 5 9
0 .0 6 5
0 .0 7 0
0 .0 3 4
m id id s p a n 3
O n e lo n g e d g e d isc o nti ntinuo nuo us:
Ne g a t iv e m o m e n t a t c o n t in in u o u s e d g e
P o s itit iv iv e m o m e n t a t m id id s p a n
4
Tw o a d ja ja c e n t e d g e s d isc o nti ntinuo nuo us:
Ne g a t iv e m o m e n t a t c o n t in in u o u s e d g e
P o s itit iv iv e m o m e n t a t m id id s p a n
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The distribution of the reactions of two-way slabs on to their supports can be derived from Figure 5.2. It should be noted that reinforcement is required in the panel corners to resist the torsion forces (see Section 5.2.4.1 (i)). Class A reinforcement is assumed to have sufficient ductility for use with this simplified design method or yield line analysis of two way slabs.
5.2.3.4 5.2. 3.4
Fla Fl a t sl sla b s
If a flat slab has at least three spans or bays in each direction and the ratio of the longest span to the shortest does not exceed 1.2, the maximum values of the bending moments and shear forces in each direction may be obtained from Table 5.4. This assumes 20% redistribution of bending moments. Where the conditions above do not apply, bending moments in flat slabs should be obtained by frame analysis (see Section 5.3). The structure should then be considered as being divided longitudinally and transversely into frames consisting of columns and strips of slab. The width of slab contributing to the effective stiffness should be the full width of the panel. The stiffening effects of drops and column heads may be ignored for the analysis but need to be taken into account when considering the distribution of reinforcement.
ly
B
A
Load on AB Load
lx
on AD
45º 45º D
C
Notes
a
The re re a c t ion ion s show n a p p ly w he n a ll e d g e s a re c on t inuo inuo us ( or d isc on t inuo inuo us us)) .
b
Whe n o ne e d g e is is d isc on t inuo inuo us us,, t he re re a c t ion ion s on a ll c on t inuo inuo us e d g e s sho ul uld d b e in c re a se d b y 1 0% a n d th e re a c tio n o n th e d isc o n tin tinu uo us e d g e m a y b e re d u c e d b y 2 0% 0%.
c
Wh e n a d ja c e n t e d g e s a re d isc o n t in in u o u s, s, t h e re re a c t io io n s sh o u ld ld b e a d ju st st e d fo fo r e la st ic ic sh e a r c o n si s id e rin g e a c h sp sp a n se se p a ra t e ly ly .
Fig 5.2 Di Disstr triib uti utio o n o f re a c ti tio o ns fro m two -wa y sla b s o nto sup sup p o rts
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ending ing moment moment and shea shear r for forc c e coe c oeff ffic icients ients for fla latt slab pa panels of three Table 5.4 Bend or more equal spans
Moment
Outer support
Near middle of end span
At first interior support
- 0.040 Flb
0.086 Flc
- 0.086 Fl
At middle At internal of interior supports span(s) 0.063 Fl
- 0.063 Fl
Sh e a r
0 . 4 6 0 F
–
0.60 0. 60 0 F
–
0.50 0. 50 0 F
To t a l c o lu lu m n m o m e n t sd
0.040 Fl
–
0.02 0. 02 2 Fl
–
0.02 0. 02 2 Fl
Notes a F is is th e to ta l d e sig n u lti ltim m a te lo a d (1 (1..3 5Gk + 1.5 Qk ). b Th e se m o m e n ts t s m a y h a v e t o b e re d u c e d t o b e c o n si sist e n t w it it h th th e c a p a c it y t o t ra ra n sf sfe r m o m e n t s t o t h e c o lu lu m n s; s; t h e m id id sp a n m o m e n t s c m u st s t th th e n b e in c re a se d c o rr rre sp o n d in g ly .
d Th e t o t a l c o lu lu m n m o m e n t sh o u ld ld b e d ist ri rib u t e d e q u a lly b e t w e e n t h e c o lu lu m n s a b o ve v e a n d b e lo w .
e M o m e n t s a t su p p o rt rt s m a y b e re re d u c e d b y 0 . 1 5 Fhc w h e re hc i iss th th e e ffe c ti tiv ve d ia m e t e r o f t he h e c o lu lu m n o r c o lu lu m n h e a d .
Divission of pa nel Divi nelss (e xc ep t in in the the reg ion of ed g e and c or orner ner c ol olumn umnss) Flat slab panels should be assumed to be divided into column strips and middle strips (see Figure 4.2). In the assessment of the widths of the column and middle strips, drops should be ignored if their smaller dimension is less than one-third of the smaller dimension of the panel.
D ivi ivission of moment mome ntss bet be twe e n c ol olumn umn and middl middle e strips The design moments obtained from analysis of the frames or from Table 5.4 should be divided between the column and middle strips in the proportions propo rtions given in Table 5.5. Tabl ble e 5.5 Distrib ibut utio ion n of design moment moments s of fla flatt slab slabs s
Design moment
C olumn strip %
Middle strip %
Ne g a tive
75
25
Po sit iv e
55
45
Note Fo r t h e c a se w h e re t h e w id id t h o f c o lu lu m n st ri rip is t a ke n a s e q u a l t o t h a t o f t h e d ro p a n d t h e m id d le st ri rip is t h e re b y in c re a se d in w id id t h , t h e d e sig n m o m e n t s t o b e re si sist stee d b y th e m id d le st stri rip p sh o u ld b e in c re a se d in p ro p o rtio n t o its in c re a se d w id id t h . Th e d e sig n m o m e n t s t o b e re sist e d b y th th e c o lu lu m n st ri rip m a y b e d e c re a se d b y a n a m o u n t su c h t h a t t h e t o t a l p o si sitt ive a n d t h e t o t a l n e g a t ive d e si sig g n m o m e n ts re sist e d b y t h e c o lu lu m n st st ri rip a n d m id id d le st ri rip t o g e t h e r a re u n c h a n g e d .
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In general, moments will be able to be transferred only between a slab and an edge or corner column by a column strip considerably narrower than that appropriate for an internal panel. The breadth of this strip, be, for various typical cases is shown in Figure 5.3. be should not be taken as greater than the column strip width appropriate for an interior panel.
Cx
Cy y
be
be = Cx
= C x + y
y
be
be = Cx + y
= Cx + Cy
$ Column strip as
defined in figure 4.2
y
y
x
be = Cx +
y 2
be y = +x 2
Note
y is the distance from the face of the slab to the innermost face of the column.
niti tio o n o f wi wid d th of e ffe c ti tive ve m o m e nt tra tra nsf nsfee r str triip , be o n p la n Fig 5.3 De fini
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The maximum design moment that can be transferred to a column by this strip is given by: Mmax = 0.17 fck be d 2
Where: d is is the effective depth for the top reinforcement in the column strip, and f ck G 35MPa.
Where the transfer moment at an edge column obtained from Table 5.4 is greater than M max a further moment redistribution G 10% may be carried out. Where the elastic transfer moment at an edge column obtained from a frame analysis is greater than M max moment redistribution G 50% may be carried out. Where the slab is supported by a wall, or an edge beam with a depth greater than 1.5 times the thickness of the slab then: • the total design load to be carried by the beam or wall should include those loads directly on the wall or beam plus a uniformly distributed load equal to one-quarter of the total design load on the panel; and • the design moments of the half-column strip adjacent to the beam or wall should be onequarter of the design moments obtained from analysis.
Effec ti tive ve she hear ar forc e s in fl fla t sl slab s Generally the critical consideration for shear in flat slab structures is that of punching shear around the columns. This should be checked in accordance with Section 5.2.4.2 except that the shear forces should be increased to allow for the effects of moment transfer as indicated below. The design effective shear force V eff at the perimeter of the column should be taken as: V eff
Where: V Ed
= 1.15 V Ed for internal columns with approximately equal spans = 1.4 V Ed for edge columns = 1.5 V Ed for corner columns
is the design shear transferred to the column and is calculated on the assumption that the maximum design load is applied to all panels adjacent to the column considered. Where the adjacent spans differ by more than 25% or the lateral stability depends on frame action V eff should be calculated in accordance with EC21, Clause 6.4.3.
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5.2. 5. 2.4 4
Se c ti tio o n d e sig n – so lid sl sla b s
5.2 .4.1 5.2.4. 1 Bend Be nding ing (i) Reinforcement To avoid compression reinforcement in slabs check that the applied moment is less than the limiting moment of resistance M u = K lim f f ck bd 2, which is based on Figure 5.4. The values of K lim should be obtained from Figure 5.5 for the amount of redistribution carried out. The area of tension reinforcement is then given by: As =
M
0.87 f y z
Where: z is obtained from Figure 5.5 for different values of K =
M bd 2 f ck
For two-way spanning slabs, care should be taken to use the value of d appropriate appropriate to the direction of the reinforcement.
(ii) Detailing Two -wa y sl sla b s o n li line a r sup p o rts
The reinforcement calculated from the bending moments obtained from Section 5.2.3.3 should be provided for the full width in both directions. In the corner area shown in Figure 5.6: i) provide top and bottom reinforcement ii) in each layer provide bars parallel to the slab edges iii) in each of the four layers the area of reinforcement per unit u nit length should be equal to 75% of the reinforcement required for the maximum moment in the span per unit length iv) the area of reinforcement in iii) can be halved if one edge of the slab in the corner is continuous.
0.57 f ck Stress block depth = 0.8x
C
d
A
N
Lever arm
Neutral axis depth x = n d
z = a 1d
0.87 f yk As
Fig 5.4 Str tree ss d ia g ra m
T
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IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
0 5 . 7 0 1 . 0
5 4 . 0
0 4 . 0
5 3 . 0
0 3 . 0
5 2 . 0
0 2 . 0
5 1 . 0
0 1 . 0
5 0 . 0
0 0 . 0 7 1 . 8 0
6 1 . 0 =
x d
6 1 . 0
K
5 1 . 0
3 5 1 . 0 = K
4 1 . 0
7 3 1 . 0 = K
3 1 . 0 2 1 . 0
0 2 1 . 0 = K
6 1 . 0 5 1 . 0 4 1 . 0 3 1 . 0 2 1 . 0
1 1 . 0
1 1 . 0
1 . 0
0 1 . 0 k c
9 0 . 0
2 f M d = b K
8 0 . 0
9 0 . 0 8 0 . 0
7 0 . 0
7 0 . 0
6 0 . 0
6 0 . 0
5 0 . 0
5 0 . 0
4 0 . 0 3 0 . 0
4 0 . 0 3 0 . 0
z d
2 0 . 0
2 0 . 0
x d
1 0 . 0
z d
0
1 0 . 0 0
0 0 . 1
8 9 . 0
6 9 . 0
4 9 . 0
2 9 . 0
0 9 . 0
8 8 . 0
6 8 . 0
4 8 . 0
ra l a xis d e p t h Fig 5.5 Va lue s o f le ve r a rm a nd n e ut ra
2 8 . 0
0 8 . 0
% 5 1
G
% 0 2
h t e h t i w , 2 e d o c o r u % E 0 3 o t x e n n A l a n o t i a N K U e h t n i s e l u r n o i t u b i r t s i d e r e s n o h u i t o t i u r b g a n v i t r i s r s u o i f d d e h e r r . p t a 5 a p 4 r n e e . g r 0 f m p o o n = t i m e x d e f m i o L % b s t i a m h i l e r l u a n g i o i f t i e s t d o i h d N T a % 5 2
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IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Simply supported
0.2 l
x
Simply supported 0.2 l
x
Note lx
is the shorter span.
Fig 5.6 C o rne r re inf nfo o rc e m e nt : t w o-w o- w a y sp a nni nning ng sl sla b s
sla b s Fla t sl
Column and middle strips should be reinforced to withstand the design moments obtained from Section 5.2.3.4. In general two-thirds of the amount of reinforcement required to resist the negative design moment in the column strip should be placed in a width equal to half that of the column strip symmetrically positioned about the centreline of the column. Min im im u m a n d m a xim u m re in fo fo rc rc e m e n t 2/3
The area of reinforcement in each direction should not be less than 0.00014 f f ck bh or 0.0015bh Where: h is the overall depth of the slab (taken as d /0.87) /0.87) is the width for which the reinforcement is calculated. b If control of shrinkage and temperature cracking is critical, the area of reinforcement should not be less than 0.0065bh or 20% of the area of main reinforcement. The area of tension or compression reinforcement in either direction should not exceed 4% of the area of concrete. Main bars should not be less than 10mm in diameter. To control flexural cracking the maximum bar b ar spacing or maximum bar diameter of high bond bars should not exceed the values given in Table 5.6, corresponding to the stress in the bar. In any case bar spacings should not exceed the lesser of 3 h or 500mm.
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IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
5.6.. Alt Alternative ernative requir requireme ement nts s to c ontrol c rac k widths to 0.3 0.3mm mm for me membe mber rs Table 5.6 reinf einforc orced ed with high bond bond ba bars Maximum bar Maximum bar Stress range Stress range (MPa) diameter (mm) spacing (mm) (MPa) 40
150 – 165
300
G 1 60
32
165 – 190
275
160 – 180
25
190 – 210
250
180 – 200
20
210 – 230
225
200 – 220
16
230 – 260
200
220 – 240
12
260 – 290
175
240 – 260
10
290 – 320
150
260 – 280
8
320 - 360
125
280 – 300
100
300 – 320
75
320 – 340
50
340 – 360
OR
Note Th e str tree ss in th e re in fo fo rc e m e n t ma y b e e sti tim m a te d fro m th e re la ti tio o n sh sh ip ip :
f yk
vs =
}2 Qk + G k
As,req
1 .
c c shmo(u1ldl.d5Qb e+o1b.3 ta5G in e2 dd Afro mnTca dbmle 3 .4.4 fo r th e p a rtiticc u lala r tytypp e o f
ms
Wh e re :
}2
f yk yk c ms As,req
k
k
s,prov
lo a d in g c o n si s id e re d . m a y b e t a ke n a s 4 35 35 fo r 5 00 00 MP MP a re re in fo fo rc rc e m e n t . is t h e a re a o f t e n si sio n re in fo fo rc rc e m e n t re q u ir ire d a t t h e se se c t io io n c o n si sid e re d fo r th e u lti ltim m a te lim it sta sta te .
As,prov
is t h e a re a o f re in fo fo rc rc e m e n t a c t u a lly p ro v id id e d .
d
is th e ra ti tio o o f th e re d istr triib u te d u lti ltim m a te m o m e n t to th e e la sti ticc u lt lt im im a t e m o m e n t a t th th e se c t io io n c o n si s id e re d ( G 1 ).
5.2.4.2 5.2. 4.2
Shea She a r
It should be noted that for slabs less than 200mm thick shear reinforcement is not effective.
Solid Sol id sing le -w -wa a y and a nd two two-w -wa a y sla sla b s Shear reinforcement is not normally required provided the design ultimate shear force V Ed does not exceed V Rd,c. 1/3
V Rd,c = 0.12k (100t f ck ) bwd but not less than: V Rd,c =
3/2
0.035√ f ck k bw d
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IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Where: k =1 + Where: Asl
200 d
G2
and
t=
Asl G 0.02 b w d
is the area of tensile reinforcement, which extends beyond the section considered taking account of the ‘shift rule’ (see Section 5.12.6).
For heavy point loads the punching shear stress should be checked using the method for shear around columns in flat slabs. Flat slabs
The shear stress at the column perimeter should be checked first: v Ed =
Where: V eff
d
u0
1000V eff MPa u0 d
G
f m m f c c 250
0.2 1 -
ck
ck
is the effective shear force in kN (the shear force magnified by the effect of moment transfer, see Section 5.2.3.4) is the average of the effective depth of the tension reinforcement in both directions is the column perimeter in mm. For an interior column u0 = length of the column perimeter For an edge column u0 = c2 + 3d G c2 + 2c1 For a corner column u0 = 3 d G c2 + c1.
The shear stresses should then be checked at the basic control perimeter, 2d from from the column perimeter: v Ed =
Where: u1
1000V eff MPa u1 d is the length of the basic control perimeter in mm as defined in Figure 5.7 (columns close to a free edge), Figure 5.8 or Figure 5.9 (openings close to columns).
c2
2 d
2 d
c1 c2
c2 u1 c1
c1
2 d
2
u1
u1
2 d
2 d
d
ro l p e rim e t e rs fo r lo a d e d a re a s c lo s e t o o r a t a n e d g e Fig 5.7 Ba sic c o n t ro
IStr truc uc tE Ma nua l for the the d e sig n o f c o nc re te b ui uilld ing str truc uc tur turee s to Eur Euro ocode 2 Am e n d m e n t – Ma rc h 2 00 00 8
Section
i
d
i
2d
h
basic control perimeter
1 arctan n ( 2 ) i = arcta c
= 26.6°
loaded area
2d
further control perimeter
basic control perimeter
Plan
Fig 5.8 She a r p e rim e te rs fo r inte rna l c o lum ns
2d
G6d
l1G l2
l2
Opening
ro l p e rim e t e r n e a r a n o p e n in in g Fig 5.9 C o n t ro
l1>l2
39
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IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
If the applied shear stress at the basic control perimeter is less than the permissible ultimate shear stress vRd1 (see Table Table 5.7) no further checks are required. If vEd > vRd,c, the outer control perimeter, uout, at which vEd G vRd,c is then determined.
Table 5.7 5.7 Ultima imatte she hea ar stress vRd,c M MP Pa Effec tive de depth (mm)
100 As bw d G0.25
150 0 .5 4
175 0 .5 4
200 0 .5 4
225 0 .5 2
250 0 .5 0
275 0 .4 8
300 0 .4 7
400 0 .4 3
500 0 .4 0
750 1000 2000 0 .3 6 0 .3 4 0 .3 1
0 .5
0 .5 9
0 .5 9
0 .5 9
0 .5 7
0 .5 6
0 .5 5
0 .5 4
0 .5 1
0 .4 8
0 .4 5
0 .4 3
0 .3 9
0 .7 5
0 .6 8
0 .6 8
0 .6 8
0 .6 6
0 .6 4
0 .6 3
0 .6 2
0 .5 8
0 .5 5
0 .5 1
0 .4 9
0 .4 5
1 .0 0
0 .7 5
0 .7 5
0 .7 5
0 .7 2
0 .7 1
0 .6 9
0 .6 8
0 .6 4
0 .6 1
0 .5 7
0 .5 4
0 .4 9
1 .2 5
0 .8 0
0 .8 0
0 .8 0
0 .7 8
0 .7 6
0 .7 4
0 .7 3
0 .6 9
0 .6 6
0 .6 1
0 .5 8
0 .5 3
1 .5
0 .8 5
0 .8 5
0 .8 5
0 .8 3
0 .8 1
0 .7 9
0 .7 8
0 .7 3
0 .7 0
0 .6 5
0 .6 2
0 .5 6
H2.00
0 .9 4
0 .9 4
0 .9 4
0 .9 1
0 .8 9
0 .8 7
0 .8 5
0 .8 0
0 .7 7
0 .7 1
0 .6 8
0 .6 2
Notes la t e d va va lu e s a p p ly fo r f ck = 3 0MP 0MPaa . Ap Ap p ro x im im a te v a lu e s fo fo r o th e r a Th e t a b u la c o n c re t e st s t re re n g t h s m a y b e u se se d :
Fo r f ck = 2 5M Fo 5MP a th e ta b u la la te d v a lu e s sh o u ld ld b e m u lti ltip p lie d b y 0 .9 .9 5
Fo r f ck = 3 5M Fo 5MP a th e ta b u la la te d v a lu e s sh o u ld ld b e m u lti ltip p lie d b y 1 .0 .0 5
Fo r f ck = 4 0M Fo 0MP a th e ta b u la la te d v a lu e s sh o u ld ld b e m u lti ltip p lie d b y 1 .1 .1
Fo r f ck = 4 5M Fo 5MP a th e ta b u la la te d v a lu e s sh o u ld ld b e m u lti ltip p lie d b y 1 .1 .1 5. 5.
b The Ta b le d o e s no t a llo w fo fo r a ny c o ntr ntriib uti utio o n fr fro m a xia l lo a d s. Fo r a n a xia l c o m p re ssio n wh e re str tree ss o f vcp = ( N/Ac) MP MP a , th e Ta b le v a lu e s sh o u ld ld b e in c re a se d b y 0 .1 .1 vcp, w h e re N is is t h e d e sig n a xia l lo a d a n d Ac i iss t h e a re a o f c o n c re t e se se c t io io n .
Shear reinforcement should be provided within the area between the column face and 1.5 d inside inside the outer control perimeter (see Figure 5.10) such that:
b d s l A f c u1d m sin a
vRd, cs = 0.75vRd, c + 1.5
Where: Asw sr f ywd,ef
r
sw ywd, eeff
1
is the area of one perimeter of shear reinforcement around the column is the radial spacing perimeters of shear reinforcement is the effective design strength of the punching shear reinforcement, according to:
f ywd,ef = 250 + 0.25d
G
f y 1.15
d
is the mean of the effective depths in the orthogonal directions
a
is the angle between the reinforcement and the plane of the slab.
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
The reinforcement should be provided in at least two perimeters of links. The spacing of link perimeters (see Figure 5.10) should not exceed 0.75d. The spacing of link legs around a perimeter should not exceed 1.5 d within the basic control perimeter (2d from the column face) and should not exceed 2 d for perimeters outside the basic control perimeter where that part of the perimeter is assumed to contribute to the shear capacity (see Figure 5.10). Outer control perimeter
Outer perimeter of shear reinforcement G0.75d
kd
(2dd if if>>22dd G1.5d (2
from column)
from A column)
A
0.5d
Outer control perimeter G0.5d G0.75d kd
Section A - A
Note k = =
1.5, unless the perimeter at which w hich reinforcement is no longer required is less than 3d from the face of the loaded area/column. In this case the reinforcement should be placed in the zone 0.3 d and 1.5d from the face of the column.
Laa yout o f fla t sl sla b she a r re inf nfo o rc e m e nt Fig 5.10 L
41
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The area of a link leg (or equivalent), Asw,min, is given by:
Asw,min
Where: sr st
1.5 sr st
H 0.08
f ck f yk
is the spacing of shear links in the radial direction is the spacing of shear links in the tangential direction.
The distance between the face of a support, or the circumference of a loaded area, and the nearest shear reinforcement taken into account in the design should not exceed d /2. /2. This distance should be taken at the level of the tensile reinforcement. Where proprietary products are used as shear reinforcement, V Rd,cs should be determined by testing in accordance with the relevant European Technical Approval.
5.2.4.3 5.2. 4.3
O p e ning s
When openings in floors or roofs are required such openings should be trimmed where necessary by special beams or reinforcement so that the designed strength of the surrounding floor is not unduly impaired by the opening. Due regard should be paid to the possibility of diagonal cracks developing at the corners of openings. The area of reinforcement interrupted by such openings should be replaced by an equivalent amount, half of which should be placed along each edge of the opening. For flat slabs, openings in the column strips should be avoided. 5.2.5 5.2. 5 Sp a n/ e ffe c t ive ive d e p t h ra t io io s The span/effective depth ratio should not normally exceed the appropriate value in Table Table 5.8. The depth of slab may be further optimised by reference to EC2 1. 5.2.6 5.2. 6 Se c t io io n d e sig n - rib b e d a nd c o ffe re d sl sla b s Ribbed or waffle slabs need not be treated as discrete elements for the purposes of analysis, provided that the flange or structural topping and transverse ribs have sufficient torsional stiffness. This may be assumed provided that: • the rib spacing does not exceed 1500mm • the depth of the rib below the flange does not exceed 4 times its width • the depth of the flange is at least 1/10 of the clear distance between ribs or 50mm, whichever is the greater • transverse ribs are provided at a clear spacing not exceeding 10 times the overall depth of the slab.
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pan/ n/eff effe ec tive depth depth ratios for slab slabs s Table 5.8 Spa Loc ocati ation on
As,req bd
H 1.5 %
As,req = 0.5 % bd
As,req bd
G 0.35 %
- w a y sp a n n in in g sla b : O n e -o r t w o -w
Sim p ly sup p o rte d
14
20
30
En d sp a n
18
26
39
Inte rio r sp a n Fla t sla b
20 17
30 24
45 36
6
8
12
C a n t ile v e r
Notes in t e rp rp o la la t e d . a Va lu e s m a y b e in
b Fo r fla n g e d s e c t io io n s w h e re t h e ra r a t io io o f t h e fla n g e t o t h e ri rib w id t h e xc e e d s 3 , th e v a lu e s sh o u ld ld b e m u lti ltip p lie d b y 0. 0. 8 .
c Fo r sp a n s e xc e e d in g 7 m, o th e r th a n fo fo r fla t sl sla b s, su p p o rti rtin g p a rti titi tio o n s lia b le to b e d a m a g e d b y e xc e ssi ssive ve d e fl flee c t io n s, t h e va lu e sh o u ld b e m u lt ip lie d b y 7 /sp a n (in (in m e tr tree s). 500MPaa . If If o the r va lue s o f f yk a re u se se d th e n m u lti ltip p ly d Th e a b o v e a ssu m e s f yk = 500MP t he h e a b o v e b y 50 50 0 / f yk .
e As,req / bd is is c a lc u la la t e d a t t h e lo c a t io io n o f m a xim u m ssp p a n m o m e n t . Th e v a lu e s g iv e n in t h e Ta b le m a y b e in c re a se d b y t h e ra t io io o f As,prov / As,req . f Fo r fla t sla b s, su p p o rti tin n g b rittl ttlee p a rti titi tio o n s, s, wh e re th e g re a te r sp a n e xc e e d s 8 .5 .5 m, t h e v a lu e sh o u ld b e m u lt ip ip lie d b y 8. 8.5 / sp sp a n .
5.2.6.1 5.2. 6.1
Bend Be nding ing
The bending moments per metre width obtained for solid slabs from Section 5.2.3 should be multiplied by the spacing of the ribs to obtain the bending moments per rib. The rib section should be checked to ensure that the moment of resistance is not exceeded by using the methods for beams described in Section 5.4. The area of tension reinforcement should be obtained from the same subsection. Structural topping should contain the minimum reinforcement indicated for solid slabs.
5.2.6.2 5.2. 6.2
Spa n/e ffe ffecc tive d e p th ratios
The span/effective depth ratio should not exceed the appropriate value from Table 5.8.
5.2.6.3 5.2. 6.3
Shea She a r
The shear force per metre width obtained from Section 5.2.3 should be multiplied by the spacing of the ribs to obtain the shear force per rib. The shear stress should be calculated from: vEd = 1000V Ed MPa bw d
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IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Where: V Ed bw d
is the design shear force arising from design ultimate loads per rib in kN is the average width of the rib in mm is the effective depth in mm.
If the shear stress vSd exceeds the permissible shear stress vRd1 in Table 5.7 then one of the following should be adopted: • increase width of rib • • •
reduce spacing of ribs provide solid concrete at supports provide shear reinforcement r einforcement only if none of the above is possible.
For ribbed and coffered flat slabs, solid areas should be provided at columns, and the punching shear stress should be checked in a similar manner to the shear around columns for solid flat slabs.
5.2.6.4 5.2. 6.4
Bea Be a m strip stripss in in ribb e d a nd c offe re red d sl sla abs
Beam strips may be used to support ribbed and coffered slabs. The slabs should be designed as continuous, and the beam strips should be designed as beams spanning between the columns. column s. The shear around the columns should be checked in a similar manner to the shear around columns in solid flat slabs. The shear in the ribs should be checked at the interface between the solid areas and the ribbed areas. If shear reinforcement is required in the ribs, these should be extended into the solid areas for a minimum distance equal to the effective depth. 5.2.7 5.2. 7 No te s o n the use o f p re c a st flo o rs Use of precast or semi-precast construction in an otherwise in-situ reinforced concrete building is not uncommon. There are various proprietary precast and prestressed concrete floors on the market. Precast floors can be designed to act compositely with an in-situ structural topping, although the precastt element can precas can carry loads without without reliance reliance on the topping. topping. Design Design using proprietary proprietary products products should be carried out closely in conjunction with the particular manufacturer and in accordance with EC2, Section 101. The following points may be helpful to the designer: • The use of a structural topping should be considered, particularly to reduce the risk of cracking in the screed and finishes: – when floors are required to resist heavy concentrated loads such as those due to storage racking and heavy machinery – when resistance to moving loads such as forklift trucks is required or to provide diaphragm action when a floor is used which would otherwise have insufficient capacity for transmitting in-plane shear. When used, a structural topping should always incorporate light fabric reinforcement. • In selecting a floor, fire rating, durability and acoustic insulation need to be considered as well as structural strength.
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•
•
Precast components should be detailed to give a minimum bearing (after allowing for tolerances) of 75mm on concrete beams and walls, but in cases where this bearing cannot be achieved reference should be made to EC2, Section 101 for more detailed guidance. Mechanical anchorage at the ends should be considered. The design should cater for the tying requirements for accidental loading (see Section 5.11). Precast floor units, particularly those that are prestressed, have cambers that should be allowed for in the thickness of finishes. When two adjoining units have different spans, any differential camber could also be critical, and this has to be allowed for in the applied finishes (both top and bottom). A ceiling to mask steps between adjoining units may be necessary. Holes required for services need to be planned. An in-situ make-up strip should be provided to take up the tolerances between precast units and in-situ construction.
• • •
5.3
Struc ucttur ura al frame mes s
5.3.1 Di Divi visi sio o n in to su b fra m e s The moments, loads and shear forces to be used in the design of individual columns and beams of a frame supporting vertical loads only may be derived from an elastic analysis of a series of subframes. Each subframe may be taken to consist of the beams at one level, together with the columns above and below. The ends of the columns remote from the beams may generally be assumed to be fixed unless the assumption of a pinned end is clearly more reasonable. Normally a maximum of only five beam spans need be considered at a time. For larger buildings, several overlapping subframes should be used. Other than for end spans of a frame, subframes should be arranged so that there is at least one beam span beyond that beam for which bending moments and shear forces are sought. The relative stiffness of members may be based on the gross concrete section ignoring reinforcement. For the purpose of calculating the stiffness of flanged beams the flange width of T- and L-beams may be taken from Table 5.9, in which l = length of the span or cantilever and bw = width of the web.
Table 5.9 Effec tive widt widths of fla flange nged d bea beams ms T-beam
L-beam
En d sp a n
bw + 0.170 l
bw + 0.085 l
Inte rio r sp a ns
bw + 0.140 l
bw + 0.070 l
C a n t ilile v e r
bw + 0.200 l
bw + 0.100 l
Notes a Th e ra ra t io io o f t h e a d ja c e n t sp a n s sh o u ld ld b e b e t w e e n 1 a n d 1 .5 .5 . b Th e le n g t h o f t h e c a n t ilile v e r sh o u ld b e le le ss t h a n h a lf t h e a d ja c e n t sp a n . c Th e a c t u a l fla n g e w id id t h sh o u ld ld b e u se se d w h e re it it is le ss t h a n th th e v a lu e o b t a in e d fro m the Ta b le .
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IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
sticc a n a lys ysiis 5.3.2 Ela sti Frames should be analysed for the most unfavourable arrangements of design loads. For frames subjected to predominantly uniformly distributed loads it will be sufficient to consider one the following arrangements of loads only for ultimate limit state verification: i) a) Alternate spans carrying the maximum design permanent and variable load, i.e. (1.35Gk + 1.5Qk ), other spans carrying the maximum design permanent load, i.e. 1.35Gk and
iii)
Any two adjacent spans carrying the maximum design permanent and variable load, i.e. (1.35Gk + 1.5Qk ), other spans carrying the maximum design permanent load, i.e. 1.35Gk . a) All spans carrying the design permanent and variable load, i.e. (1.35Gk + 1.5Qk ) and b) Alternate spans carrying the design permanent and variable load, i.e. (1.35Gk + 1.5Qk ), other spans carrying only the design permanent load, i.e. 1.35Gk . For slabs only: All spans loaded condition, i.e. (1.35Gk + 1.5Qk ), provided that: a) In a one-way spanning slab the area of each bay exceeds 30m2 and b) Qk / Gk G 1.25 and
c)
ii)
b)
Qk G 5kN/m2.
Where analysis is carried out for the single load case of all spans loaded, the resulting support moments except those at the supports of cantilevers should be reduced by 20% with a consequential increase in the span moments. In this context a bay means a strip across the full width of a structure bounded on the other two sides by lines of support. The above simplifications may be applied using Expression 6.10 or 6.10a and 6.10b of BS EN 19908. 5.3.3 5.3. 3 Re d istr triib uti utio o n o f m o m e nts The moments obtained from elastic analysis may be redistributed up to a maximum of 30% to produce members that are convenient to detail and construct, noting that: • the resulting distribution of moments remains in equilibrium with the applied load • the design redistribution moment at any section should not be less than 70% of the elastic moment • there are limitations on the depth of the neutral axis of the section depending on the percentage of redistribution (see Section 5.4.4.1), and • the design moment for the columns should be the greater of the redistributed moment or the elastic moment prior to redistribution.
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A simple procedure may be adopted that will satisfy the above criteria: i) Adjacent spans loaded – Reduce the common support moment to not less than the support moment obtained from the alternate spans loaded case. ii) Alternate spans loaded – Move the moment diagram of the loaded span up or down by the percentage redistribution required; do not move moment diagram of the unloaded span (see Figure 5.11). 5.3.4 5.3. 4 De sig n she a r fo rc e s Shear calculations at the ultimate limit state may be based on the shear forces compatible with the bending moments arising from the higher of the load load combinations noted in Section Section 5.3.2 and any redistribution carried out in accordance with Section 5.3.3.
5.4
Beams
5.4.1 Introd 5.4.1 Introd uc ti tio on This subsection describes the final design of beams of normal proportions and spans. Deep beams with a clear span less than twice the effective depth are not considered. The general procedure to be adopted is as follows: i) check that the section complies with the requirements for fire resistance ii) iii) iv) v)
check that cover and concrete quality comply with durability requirements calculate bending moments and shear forces according to Section 5.4.3. calculate reinforcement required for bending and shear check span/depth ratio.
Elastic diagram Design for this
Design support moment for beam (redistributed)
column moment
Redistributed diagram
Do not move this diagram
Note
It is not recommended to redistribute the span moment upwards.
triib uti utio o n p ro c e d ur uree s fo r fra m e s Fig 5.11 Re d istr
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The effective span of a simply supported beam should normally be taken as the clear distance between the faces of supports plus one-third of the beam seating width at each end. However, where a bearing pad is provided between the slab and the support, the effective span should be taken as the distance between the centres of the bearing pads. The effective span of a beam continuous over its supports should normally be taken as the distance between the centres of the supports. The effective length of a cantilever beam where this forms the end of a continuous beam
is the length of the cantilever from the centre of the support. To prevent lateral buckling, the length of the compression flange measured between adequate lateral restraints to the beam should not exceed 50b, where b is the width of the compression flange, and the overall depth of the beam should not exceed 4 b. In normal slab-and-beam or framed construction specific calculations for torsion are not usually necessary, torsional cracking being adequately controlled by shear reinforcement. Where torsion is essential for the equilibrium of the structure, e.g. the arrangement of the structure is such that loads are imposed mainly on one face of a beam without corresponding rotational restraints being provided, EC21 should be consulted. 5.4. 5. 4.2 2
5.4.2.1 5.4. 2.1
Fire re re sista nc e a nd d ur uraa b ility
Fire Fi re resis re sista tanc nc e
The member sizes and reinforcement axis distances required to provide fire resistance are shown in Table 5.10 and 5.11. When using these tables, continuous beams should be treated as simply supported if the redistribution of bending moments for normal temperature design exceeds 15%.
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Table 5.1 5.10 0 Fir ire e resistanc nce e req equir uireme ement nts s for for simply support supported be bea ams Standard fire resistanc nce e (R (R)) in minutes R30 R60 R90 R120 R180 R240
Poss ossible ible c ombina ombinattions of a the average axis distance and bmin the width of beam
Web thic hickness kness bw
Mini Mi nim m um d im e nsi nsio o ns (m (m m )
bmin = 80 a = 25
12 0
16 0
20 0
20 a
15 a
15 a
bmin = a = bmin = a = bmin = a = bmin = a = bmin = a =
120 40 150
16 0 35 a 20 0
20 0 30 a 30 0
30 0 25 a 40 0
55 200
45 24 0
40 30 0
35 a 50 0
65 240
60 30 0
55 40 0
50 60 0
80 280
70 35 0
65 50 0
60 70 0
80
75
70
90
80 10 0 11 0 13 0 15 0 17 0
Notes ic a l p u rp rp o s e s t h e a xis d ist a n c e sh o u ld b e su c h th th a t t h e m in im im u m a Fo r p ra c t ic c o v e r is 2 0m 0m m .
b The a xis d ista nc e , a, is m e a su re re d fro m t h e su s u rf rfa c e o f t h e c o n c re t e t o t h e c e n t re re o f th e m a in re re in fo fo rc in g b a rs.
c The a xis d ista nc e , a, sh sh o u ld ld b e in c re a se d b y 10 10 m m fo r p re re st re re ssin g b a rs a n d 15m m fo r p re str stree ssi sing ng wi wirre s o r st strra nd s.
d Fo r o th e r c o m b in a ti tio o n s o f rib w id th a n d a xis d ista n c e se e EC2 , Pa rt 11-2 2. e W h e r e a is 70m m o r m o re re fe r to EC 2, Pa rt 1-2 1-2 2 f fo o r a d d iti tio o n a l re q u ir ire m e n ts. ts. asd i iss t h e a xis d ist a n c e t o t h e sid e o f b e a m fo r t h e c o r n e r b a rs ( o r t e n d o n o r f wirre ) o f b e a m s wi wi with th o n ly o n e la y e r o f re in fo fo rc rc e m e n t (asd = a + 10m 10m m ). Fo r va lue s o f bmin g re a t e r t h a n t h a t g iv iv e n in in t h e h ig ig h li lig h t e d c o lu lu m n n o in in c re a se o f asd is re q u ir ire d .
5.4.2.2 5.4. 2.2
D ura urab b ilility ity
The requirements for durability in any given environment are: i) an upper limit to the water/cement ratio ii) a lower limit to the cement content iii) a lower limit to the thickness of the cover to the reinforcement iv) good compaction v) adequate curing vi) good detailing. Values for i), ii) and iii) which, in combination, will give adequate durability are given in Appendix B for various environments.
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5.11 1 Fir ire e resistanc nce e req equir uireme ement nts s for for contin c ontinuous uous bea beams Table 5.1 Standard fire resistanc nce e (R (R) in minutes R60 R90 R120 R180 R240
Poss ossible ible c ombina ombinattions of a t the he aver averag age e axis a xis dis disttanc ance e and bmin the width width of be bea am
Web thic hickness kness bw
Mini Mi nim m um d im e nsi nsio o ns (m (m m )
bmin = 120 a = 25 a
20 0
bmin = a = bmin = a = bmin = a = bmin = a =
150 35 a
25 0 25 a
200
30 0
45 0
50 0
45
35 a
35 a
30 a
240
40 0
55 0
60 0
60
50
50
40
280
50 0
65 0
70 0
75
60
60
50
10 0
12 a
11 0 13 0 15 0 17 0
Notes a Fo r p ra c t ic ic a l p u rp rp o s e s t h e a xis d ist a n c e sh o u ld b e su c h th t h a t t h e m in im im u m c o v e r is 2 0m 0m m . re d fro m t h e su s u rf rfa c e o f t h e c o n c re t e t o t h e c e n t re re b The a xis d ista nc e , a, is m e a su re o f th e m a in re re in fo fo rc in g b a rs. sh o u ld ld b e in c re a se d b y 10 10 m m fo r p re st re re ssin g b a rs a n d c The a xis d ista nc e , a, sh 15mm fo r p re st strre ssing wi wirre s o r str traa nd s.
d Fo r o th e r c o m b in a ti tio o n s o f rib w id th a n d a xis d ista n c e se e EC2 , P a rt 1 -2 -2 2. e W h e r e a i iss 70m m o r m o re re fe r to EC 2, Pa rt 1-2 1-2 2 f fo o r a d d iti tio o n a l re q u ir ire m e n ts. ts. f asd i iss t h e a xis d ist a n c e t o t h e sid e o f b e a m fo r t h e c o r n e r b a rs ( o r t e n d o n o r wirre ) o f b e a m s wi wi with th o n ly o n e la y e r o f re in fo fo rc e m e n t ( asd = a + 10m 10m m ). Fo r va lue s o f bmin g re re a t e r t h a n t h a t g iv iv e n in in t h e h ig ig h li lig h t e d c o lu lu m n n o in c re a se o f asd is required.
5 .4 .4 .3 .3 Be n d in g m o m e n t s a n d sh sh e a r fo rc rc e s The maximum values of the bending moments and shear forces at any section of a continuous beam may be obtained by either: i) consideration of the beam as part of a structural frame as described in Section 5.3, or ii) as a beam that is continuous over its supports and capable of free rotation about them. For beams with a) substantially uniform loading, b) one type of imposed load, and c) three or more spans that do not differ by more than 15%, the bending moments and shear forces may be calculated using the coefficients given in Table 5.12 for ultimate limit state verification. No redistribution of moments should be made when using values obtained from this Table.
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5.12 2 Bend Bending ing moments moments and shear shear forc orce es for for bea beams at ultima imatte limit state Table 5.1 At outer support Mo m e n t
0a
Sh e a r
0 . 4 5 F
Near middle of At first inte interio rior r At middle of end span support interior spans 0.09 Fl
- 0.11 Fl
–
0.07 Fl
0.60 0. 60 F
At interior supports - 0.10 Fl
–
0.55 0. 55 F
Notes tio o n 5. 5.4. 4.4. 4.2. 2. a Se e Se c ti b F is is th e to ta l d e sig n u lti ltim m a te lo a d (1 (1..3 5Gk + 1.5 Qk ) fo r e a c h sp sp a n , a n d l i iss the le n g t h o f t h e s p a n .
c No re re d ist ri rib u t io io n o f t h e m o m e n t s c a lc u la la t e d f ro ro m t h is is Ta b le s h o u ld ld b e m a d e . 5.4. 5. 4.4 4
Se c ti tio o n d e sig n
5.4.4.1 5.4. 4.1
Bend Be nding ing
The most common beams have flanges at the top. At the supports they are designed as rectangular beams and in the spans as flanged beams. For upstand beams, the reverse applies. The effective width of flange should be based on the distance l between points of zero 0 moment, which may be obtained from Figure 5.12. If the applied moment M is is less than the limiting moment M u for the concrete, compression steel will not be needed. The resistance moments of concrete sections that are required to resist flexure only can be determined from the formulae that are based on the stress diagram in Figure 5.4. The effect of any small axial compressive load on the beam can be ignored if the design ultimate axial force is less than 0.08f ck bh, where h is the overall depth of the section.
Rec tang ul ular ar be ams The procedure for the design of rectangular beams is as follows: i) Calculate M u = K lim f as obtained from f ck bd 2 where K lim is the limiting value of K as Figure 5.5 for the amount of redistribution carried out. ii)
If M < < M u , the area of tension reinforcement As is calculated from: M As = 0.87 z f yk l1
l0 =
0.85
l1
l0 =
0.15 ( l1+ l2 )
l2
l0 =
0.7
l2
l3
l0 =
0.15 l2 + l3
tio o n o f lo f fo o r c a lc ul ulaa ti tio o n o f e ffe c ti tive ve fla ng e wi wid d th Fig 5.12 De fin iti
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Where: z
is obtained from Figure 5.5 for different values of K K =
iii)
M bd2 f ck
If M > > M u then compression reinforcement is needed. The area of compression reinforcement As2 is calculated from: M - M u 0.87 fyk (d - d 2) Where: d 2 is the depth to to the centre of the compression reinforcement from the compression face. f yk d If d 2 > 1 x, use 700 l - 2 in lieu of 0. 87 f yk x 800 As2 =
c
m
b
l
The area of tension reinforcement As is calculated from: As =
M u + As2 0.87 fyk z
Flang ed b ea ms For section design, provided that the ratio of adjacent spans is between 1 and 1.5, the effective width of a flanged beam (see Figure 5.13) may be derived as: beff =
/b
eff, i
+ bw G b
Where: beff, i = 0.2bi + 0.1l0 G 0.2l0 and
beff, i
G
bi (bi is either b1 or b2).
It should be noted that the flange width at the support will be different from that at midspan. The length of the cantilever should be less than half the adjacent span. b eff b eff ,1 ,1
b eff ,2 ,2
bw
bw b1
b1
b
Efffe c t ive ive fl f la ng e w id id t h pa ra m e t e rs Fig 5.13 E
b2
b2
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The procedure for the design of flanged beams is as follows: i) Check the position of the neutral axis by determining M K = beff d 2 f ck using effective flange width beff and selecting values of x and z from Figure 5.5. ii)
If 0.8 x < hf then As is determined as for a rectangular beam of breadth beff , i.e. As =
iii)
M 0.87 z f yk
If 0.8 x > hf then the stress block lies outside the flange. Calculate the resistance moment of the flange M uf from: M uf = 0.57 f ck (beff - bw)hf ( d - 0.5hf )
iv)
Calculate
K f =
- M uf M fck bw d 2
If K f G K lim, obtained from Figure 5.5 for the amount of redistribution carried out, then select value of z/d and and hence z. Calculate As from: - M uf M uf M + As = 0.87 fyk z 0.87 fyk d - 0.5hf
]
g
If K f > K lim, redesign the section.
5.4.4.2 5.4. 4.2
M inimum a nd ma ximum a mo mounts unts of reinforc re inforc e me nt
The areas of reinforcement derived from the previous calculations may have to be modified or supplemented in accordance with the requirements below in order to prevent brittle failure (without warning) and/or excessive cracking. Main bars in beams should normally not be less than 16mm in diameter.
Tension reinforcement The area of reinforcement should not be less than 0.00016 f ck 2/3 b td or 0.0013 b td , where bt is the mean width of the tension zone. In monolithic construction, even when simple supports have been assumed in design (e.g. the end support of a continuous beam), the section should be designed for a support moment of at least 25% of the maximum bending moment in the span. At intermediate supports of continuous beams, the total amount of tensile reinforcement As of a flanged cross-section may be distributed uniformly over the effective width, beff , as shown in Figure 5.14.
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beff As hf beff,1
beff, 2
bw
Disstr triib uti utio o n o f re inf nfo o rc e m e nt in in fl fla ng e d b e a m s Fig 5.14 Di
C ompres ompresssion reinf einfor orcc eme nt The minimum areas of compression reinforcement where required should be: rectangular beam 0.002bh flanged beam web in compression 0.002bwh
Ma M a ximum a rea of reinforc re inforc e me nt Neither the area of the tension reinforcement, nor the area of compression reinforcement should exceed 0.04 Ac.
Bars al along ong th the e side side of be ams (to c ontr ontrol ol cracking) Where the overall depth of the beam is 750mm or more, 16mm diameter bars should be placed along the sides, below any flange, at a maximum pitch of 250mm.
Ma M a ximum spa sp a c ing fo forr te te nsion ba b a rs To control flexural cracking at serviceability the maximum bar spacing or maximum bar diameters of high-bond bars should not exceed the values in Table 5.6, corresponding to the stress in the bar.
Minimum M inimum spa sp a c ing The horizontal or vertical distance between bars should not be less than the bar diameter or 20mm or aggregate size + 5mm, whichever is the greatest. Where there are two or more rows the gaps between corresponding bars in each row should be in line vertically, and the space between the resulting columns of bars should permit the passage of an internal vibrator.
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5.4. 4.3 5.4.4.3
Shea She a r
Shear reinforcement is not required where the design ultimate shear force V Ed does not exceed V Rd,c. VRd, c = 0.12k (100tfck) 1/3 bw d
but not less than: VRd, c = 0.035 f ck k3/2 bw d
Where: k = = 1 + 200/d G 2 t = Asl /bwd G 0.02 where Asl is the area of flexural tensile reinforcement provided, which extends beyond the section. Where V Ed exceeds V Rd,c shear reinforcement is required. This is assessed by the variable strut inclination method as shown in Figure 5.15. coti =
y/ z z (where z may be taken as 0.9d ) and 1 G coti G 2.5 VRd,min = 0.16 d bw Asw /s = 0.08 bw
V Rd,sy =
fck
fck /f ywk
Asw z f f ywd coti/s
(shear reinforcement control)
V Rd,max = 0.18 d bw f f ck (1- f f ck /250)sin 2i (concrete strut control) for strut at (coti = 2.5): V Rd,max = 0.13 d bw (1- f ck /250) f f ck for strut at (coti = 1): V Rd,max = 0.18 d bw (1- f ck /250) f ck
Proc Pr oc ed ur ure e for de sig n i)
Calculate shear capacity for minimum reinforcement. Vmin = 0.15d bw fck (assuming coti = 2.5)
Asw
Asw V Ed
s
z
V Ed
d
z
θ
edge support
y
Vaa ria b le str trut ut inc inc lina ti tio o n m e tho d Fig 5.15 V
edge support
y
d
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iii) iv)
Calculate angle i, of strut for full shear force at end of beam (assuming acc =1 and z = 0.9d ). ). 5.56V Ed i = 0. 5 sin- 1 bw d ^1 - f ck /250h f ck If there is no solution then this implies that the strut has failed. If coti 1.5 (cx + 3d ), ), at least two-thirds of the reinforcement parallel to ly should be concentrated in a band width (cx + 3d ) centred at the column, where d is the effective depth, lx and cx are the footing and column dimensions in the x-direction and ly and cy are the footing and column dimensions in the y-direction (see Figure 5.22). The same applies in the transverse direction with suffixes x and y transposed. Reinforcement should be anchored each side of all critical sections for bending. It is usually possible to achieve this with straight bars. The spacing between centres of reinforcement should not exceed 200mm for bars with f y = 500MPa. Reinforcement need normally not be provided in the side face nor in the top face, except for balanced or combined foundations. Starter bars should terminate in a 90º bend tied to the bottom reinforcement, or in the case of an unreinforced footing spaced 75mm off the blinding. 5.10.8 De sig n o f ra fts 5.10.8 The design of a raft is analogous to that of an inverted flat slab (or beam-and-slab) system, with the important difference that the column loads are known but the distribution of ground bearing pressure is not.
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1.5d
1.5d
cx 2 3
of desig design n reinfo reinforceme rcement nt within with in this widt width h lx (>1.5 ( cx
+ 3d ))
Laa y o ut of re inf nfo o rc e m e nt in in a p a d fo o t ing ing Fig 5.22 L
A distribution of ground bearing pressure has to be determined that: • satisfies equilibrium by matching the column loads • satisfies compatibility by matching the relative stiffness of raft and soil • allows for the concentration of loads by slabs or beams continuous over supports, and • stays within the allowable bearing pressure determined from geotechnical considerations of strength and settlement. Provided that such a distribution can be determined or estimated realistically by simple methods, design as a flat slab or beam-and-slab may be carried out. In many cases, however, a realistic distribution cannot be determined by simple methods, and a more complex analysis is required. 5.10.9 5.10. 9 De sig n o f p ile c a p s The design of pile caps should be carried out in accordance with the following general principles: • The spacing of piles should generally be three times the pile diameter. • The piles should be grouped symmetrically under the loads. • The load carried by each pile is equal to N /(no. /(no. of piles). When a moment is transmitted to the pile cap the loads on the piles should be calculated to satisfy equilibrium. • Pile caps should extend at least 150mm beyond the theoretical circumference of the piles. •
For pile caps supported on one or two piles only, a moment arising from a column eccentricity of 75mm should be resisted either by ground beams or by the piles.
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The general procedure to be adopted is as follows: i) Using the unfactored loads and moments calculate the number of piles required under Using each column. ii) Proportion the pile caps on plan in accordance with the above general principles. Typical Proportion arrangements are shown in Figure 5.23 where s is the spacing of the piles. iii) Determine the initial depth of the pile cap as equal to the horizontal distance from the Determine centreline of the column to the centreline of the pile furthest away. iv)
Check C heck the face shear as for reinforced spread footings, using factored loads, and modify the depth if necessary. v) Calculate the bending moments and the reinforcement in the pile caps using the factored loads. As an alternative to iv) and v) use the ‘strut and tie’ methods to determine capacity and As reinforcement for the pile cap.
0.5s
0.5s 0.5s
0.5s
0.5s
2 Piles
0.58s
0.29s
0.5s
4 Piles 0.5s
0.5s Note s
3 Piles
is the spacing of piles.
Ty y p ic a l a rra n g e m e n t o f p ile c a p s Fig 5.23 T
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5. 5.10. 10.10 10 Re inf nfo o rc e m e nt in p ile c a p s All pile caps should generally be reinforced in two orthogonal directions on the top and bottom faces. Where bars with f y = 500MPa are used the amount of reinforcement should not be less than 0.0015bh in each direction. The bending moments and the reinforcement should be calculated on critical sections at the column faces, assuming that the pile loads are concentrated at the pile centres. This reinforcement should be continued past the piles and bent up vertically to provide full anchorage past the centreline of each pile. In addition, fully lapped, circumferential horizontal reinforcement consisting of bars not less than 12mm in diameter at a spacing not more than 250mm, should be provided.
5.11
Robustne ness ss
5.11..1 G e ne ra l 5.11 If the recommendations of this Manual for an in-situ structure have been followed, a robust structure will have been designed, subject to the reinforcement being properly detailed. However the requirements of the Building Regulations (Approved Document A) 24 should be checked. In order to demonstrate that the requirements for robustness have been met, the reinforcement already designed should be checked to ensure that it is sufficient to act as: i) ii) iii) iv)
peripheral ties internal ties external column or wall ties vertical ties.
The arrangement of these (notional) ties and the forces they should be capable of resisting are stated in Section 5.11.2. Reinforcement considered as part of the above ties should have full tension laps throughout so as to be effectively continuous. For the purpos purposee of checki checking ng the adequa adequacy cy of the ties, this reinforcement may be assumed to be acting at its characteristic strength when resisting the forces stated below, and no other forces need to be considered in this check. The minimum dimension of any in-situ concrete section in which tie bars are provided should not be less than the sum of the bar size (or twice the bar size at laps) plus twice the maximum aggregate size plus 10mm. Horizontal ties, i.e. i), ii) and iii) above, should be present at each floor level and at roof level. In precast concrete construction ties may be provided wholly within in-situ concrete toppings or connections partly within in-situ concrete and partly within precast members or wholly within precast members but they should be effectively continuous. In addition the tie should also satisfy one of the following conditions: • A bar or tendon in a precast member lapped with a bar in in-situ connecting concrete bounded on two opposite sides by rough faces of the same precast member (see Figure 5.24). •
A bar or tendon in a precast concrete member lapped with a bar in in-situ topping or connecting concrete anchored to the precast member by enclosing links. The ultimate
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•
•
tensile resistance of the links should be not less than the ultimate tension in the tie (see Figure 5.25). Bars projecting from the ends of precast members joined by one of the following methods provided that the full strength of the bar can be shown to exist through the joint: – lapping of bars – grouting into an aperture – overlapping reinforcement loops – sleeving – threaded reinforcement. Bars lapped within in-situ topping or connecting concrete to form a continuous reinforcement with projecting links from the support of the precast floor or roof members to anchor such support to the topping or connecting concrete (see Figure 5.26).
Tie
ntinui nuity ty o f ti tiee s: b a rs in p re c a st me m b e r la p p e d wi with th b a r in inin-ssitu Fig 5.24 C o nti concrete Tie
Tie
Tie
Fig 5.25 C o nti ntinui nuity ty of ti tiee s: a nc ho ra g e b y e nc lo sing links
Tie
ntinu nu ity o f ti tiee s: b a rs la p p e d wi withi thin n in-situ c o n c re t e Fig 5.26 C o nti
Tie
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In addition precast roof, floor and stair members not containing ties should be anchored back to the parts of the structure containing the ties. The capacity of this anchorage should be capable of carrying the dead weight of the member. 5.11..2 Ti 5.11 Tie fo rc e s a nd a rra ng e m e nt s Forces to be resisted by horizontal ties are derived from a ‘tie force coefficient’: F t = (20 + 4 n) kN for n G 10, or for n > 10 F t = 60 kN
Where: n is the number of storeys.
Peri Pe rip p he heral ral ti tie es Peripheral ties should be located in zones within 1.2m from the edges; they should be capable of resisting a tie force of 1.0F t per storey and should be fully anchored at all corners.
Internall ti Interna tie es Internal ties should be present in two directions approximately at right-angles to each other. Provided that the floor spans do not exceed 5m and the total characteristic dead and imposed load does not exceed 7.5kN/m 2, the ties in each direction should be capable of resisting a tie force of 1.0F t kN per metre width at each storey level. If the spans exceed 5m and/or the total load exceeds 7.5kN/m 2, the tie force to be resisted should be increased pro rata. Internal ties may be spread evenly in the slabs or may be concentrated at beams or other locations, spaced at not more than 1.5 times the span. They should be anchored to the peripheral ties at each end. In spine or crosswall construction the length of the loadbearing wall between lateral supports should be considered in lieu of the spans when determining the force to be resisted by the internal ties in the direction of the wall.
Externall c ol Externa olumn umn or o r wa ll ti tie es External columns and loadbearing walls should be tied to the floor structure. Corner columns should be tied in both directions. Provided that the clear floor-to-ceiling height does not exceed 2.5m, the tie force for each column and for each metre length of wall is 1.0 F t per story. For floorto-ceiling heights greater than 2.5m, the tie forces should be increased pro pro rata, up to a maximum of 2.0F t. The tie force should in no case be assumed less than 3% of the total design ultimate load carried by the column or wall. This reinforcement should be fully anchored in both vertical and horizontal elements.
V ert ertic ical al ties ties Vertical ties should be present in each column and loadbearing wall. They should be capable of resisting a tensile force equal to the maximum total design ultimate load received by the column or wall from any one floor or roof.
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Where effectively continuous vertical ties cannot be provided (e.g. in some precast construction), the effect of each column or loadbearing wall being removed in turn should be considered, and alternative load paths should be provided if necessary. In this context: cG = 1.0 cQ = 0.33 cc = 1.3, and cs = 1.0.
5.12
Detailing
5.12.. 1 G e ne ra l 5.12 Certain aspects of reinforcement detailing may influence the design. The most common of these are outlined below. Additional rules for bars exceeding 40mm in diameter are given in Section 5.12.5. 5.12.2 5.12. 2 Bo Bo nd c o nd iti tio o ns The bond conditions affect the anchorage and lap lengths. Good and poor bond conditions are illustrated in Figure 5.27.
A
A
h
250mm
h G
45º G G 90º for all values of h (e.g. columns) A
A 300
250 h
h
> 250mm
h
> 600mm
Notes
a unhatched zone – 'good' bond conditions. b hatched zone – 'poor' bond conditions. c
A Direction of concreting.
niti tio o n o f b o nd c o nd iti tio o ns in in se c ti tio o na l e le va ti tio o ns Fig 5.27 De fini
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5 ..1 1 2. 2.3 An An c h o ra g e a n d la la p le le n g t h s Anchorage and lap lengths should be obtained from Table 5.24 to Table Table 5.27 for bars and welded mesh fabric (see Figure 5.28). The values apply to reinforcing steel as specified in BS 444925 and BS 448326. The clear spacing between two lapped bars should be in accordance with Figure 5.29 (see also Section 5.12.5). It should be noted that where the distance between lapped bars is greater than 50mm or 4 z the lap length should be increased by the amount by which the clear space exceeds 50mm or 4 z.
l bd
l b
Note l b
is the basic anchorage length.
ra g e le n g t h , l bd Fig 5.28 De sig n a n c h o ra
H 0.3 l0
l0 G
F s
F s
F s
50mm,
G
φ4φ
F s
a
F s H 20mm, H 2φ
F s
Ad d ja c e n t la p s Fig 5.29 A
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Table 5.24 Typic ypica al values values of anc nchor hora age and lap lap lengt lengths hs for slab labs s Length in bar diameters
Bond c ondit onditions ions
f ck / f cu =
f ck / f cu =
f ck / f cu =
f ck / f cu =
25/30
28/35
30/37
32/40
good
40
37
36
34
p o o r
58
53
51
49
good
46
43
42
39
p o o r
66
61
59
56
Ful ulll te nsi nsio o n a nd c o m p re re ssio n a n c h o ra ra g e le n g th , l bd Ful ulll te nsi nsio o n a nd c o m p re ssio n la p le n g t h , l0
Notes a The fo fo llo wi wing ng is is a ssum e d :
- b a r size is is n o t g re re a t e r t h a n 3 2m 2m m . If > 32 32 t h e n t h e a n c h o ra ra g e a n d la la p le le n g t h s sh o u ld ld b e d iv id id e d b y a fa c to r (1 (13 3 2 - b a r size )/1 0 0
- no rm a l c o ve r e xists
- n o c o n fi fin e m e n t b y tr traa n sv sv e rse p re ssu re re
- n o c o n f in in e m e n t b y t ra ra n sv sv e rse re in fo fo rc rc e m e n t - n o t m o re t ha h a n 3 3 % o f t he h e b a rs a re la la p p e d a t o n e p la c e .
b La p le le n g th s p ro v id id e d (fo (fo r n o m in a l b a rs, e tc .) sh o u ld ld n o t b e le ss th a n 15 15 ti tim mes th e b a r size o r 2 00 00 mm , wh ic ic h e v e r is g re a te r.
Table 5.25 5.25 Typic ypica al values values of anchor anc hora age and lap length lengths s for beams beams
Ful ulll te nsi nsio o n a nd
Length in bar diameters
Bond c ondit onditions ions
f ck / f cu =
f ck / f cu =
f ck / f cu =
f ck / f cu =
25/30
28/35
30/37
32/40
good
36
34
32
31
p o o r
48
45
43
41
good
42
39
37
35
p o o r
56
52
49
47
c o m p re re ssio n a n c h o ra ra g e le n g th , l b,rqd Ful ulll te nsi nsio o n a nd c o m p re ssio n la p le n g t h , l0
Note The fo llo wi wing ng is a ssum e d : - b a r size is n o t g re re a t e r t h a n 3 2m 2m m . If > 32 32 th th e n t h e a n c h o ra ra g e a n d la p le n g t h s sh o u ld ld b e d iv id id e d b y a fa c to r (1 (13 3 2 - b a r size )/1 0 0 - no rm a l c o ve r e xists - n o c o n fi fin e m e n t b y tr traa n sv sv e rse p re ssu re re - c o nf nfiine m e nt b y lilinks – fa fa c to r = 0.9 0.9 - n o t m o re re t ha h a n 33 3 3 % o f t he h e b a rs a re la p p e d a t o n e p la la c e .
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Table 5.26 5.26 Typic ypica al values values of anchor anc hora age and lap length lengths s for columns columns Length in bar diameters
Bond c ondit onditions ions
f ck / f cu =
f ck / f cu =
f ck / f cu =
f ck / f cu =
25/30
28/35
30/37
32/40
good
36
34
32
31
p o o r
48
45
43
41
good
54
51
48
46
p o o r
73
67
64
62
Ful ulll te nsi nsio o n a nd c o m p re re ssio n a n c h o ra ra g e le n g th , l b,rqd Ful ulll te nsi nsio o n a nd c o m p re ssio n la p le n g t h , l0
Note The fo llo wi wing ng is a ssum e d : - b a r size is n o t g re a t e r t h a n 3 2m 2m m . If > 32 32 th th e n t h e a n c h o ra ra g e a n d la p le n g t h s sh o u ld ld b e d iv id id e d b y a fa c to r (1 (13 3 2 - b a r size )/1 0 0 - no rm a l c o ve r e xists - n o c o n fi fin e m e n t b y tr traa n sv sv e rse p re ssu re re - c o nf nfiine m e nt b y lilinks – fa c to r = 0.9 0.9 - m o re t h a n 5 0% 0% o f t h e b a rs a re la p p e d a t o n e p la c e – fa c t o r = 1. 1.5 .
Table 5.27 Typic ypica al values values of anc nchor hora age and lap lap lengt lengths hs for wa walls Length in bar diameters
Bond c ondit onditions ions
f ck / f cu =
f ck / f cu =
f ck / f cu =
f ck / f cu =
25/30
28/35
30/37
32/40
good
40
37
36
34
p o o r
54
50
48
46
good
61
56
54
51
p o o r
81
75
71
68
Ful ulll te nsi nsio o n a nd c o m p re re ssio n a n c h o ra ra g e le n g th , l bd Ful ulll te nsi nsio o n a nd c o m p re ssio n la p le n g t h , l0
Notes a The foll follo wi wing ng is is a ss ssum um e d : - b a r size is n o t g re a t e r t h a n 3 2m 2m m . If If > 32 32 th th e n t h e a n c h o ra ra g e a n d la p le n g t h s sh o u ld ld b e d iv id id e d b y a fa c to r (1 (13 3 2 - b a r size )/1 0 0 - no rm a l c o ve r e xists - n o c o n f in in e m e n t b y t ra ra n sv sv e rse p re ssu re re - m o re t h a n 50 5 0 % o f t h e b a rs a re la p p e d a t o n e p la c e – fa c t o r = 1 .5 .5 . a p le le n g th s p ro v id id e d (fo (fo r n o m in a l b a rs, e tc .) sh o u ld ld n o t b e le ss th a n 15 15 ti tim me s b L th e b a r size o r 2 00 00 mm , wh ic ic h e v e r is g re a te r.
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5. 5.12. 12.4 4 Tr Tra nsv nsvee rse re infor nforcc e m e nt
A nc ho horag rag e zon one es Links should be provided and placed in the anchorage zones of beams with a minimum area of 25% of the area of a single anchored bar. Transverse reinforcement should be evenly distributed in tension anchorages and concentrated at the ends of compression anchorages.
Laps Transverse reinforcement is required in the lap zone to resist transverse tension forces. Where the diameter of bars lapped is less than 20mm or the area of bars lapped is less than 25% of the total area of tension reinforcement then any transverse reinforcement or links necessary for other reasons may be assumed sufficient. Otherwise the area of total transverse reinforcement, Ast, should be equal to or greater than the area of one lapped bar. The transverse bars should be placed perpendicular to the direction of the lapped reinforcement and between that and the surface of the concrete. The transverse reinforcement should be placed as shown in Figure 5.30.
A nc ho horag rag e of links links Links should be anchored using one of the methods shown in Figure 5.31.
Σ Ast/2
l0 / 3
Σ Ast/2
l0 / 3 G
F s
150mm
F s
l0
bars in tension
Σ Ast/2
Σ Ast/2
G
150mm F s
F s
l0
4φ
l0 / 3
l0 / 3
bars in compression
nsve ve rse re inf nfo o rc e m e nt fo fo r la p p e d sp lic e s Fig 5.30 Tra ns
4φ
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5. 5.12. 12.5 5 Ad d iti tio o na l rul ulee s fo r la rg e d ia m e te r b a rs Bars exceeding 40mm in diameter should be used only in elements with a depth not less than 15 times the bar diameter. Such bars should not be anchored in tension zones. Lapped joints in tension or compression are not permitted, and mechanical devices (e.g. couplers) should be used instead. Transverse reinforcement, additional to that for shear, is required in the anchorage zone where transverse pressure is not present as shown in Figure 5.32. The reinforcement should not be less than the following: • in the direction parallel to the tension face: Ast = n1 x 0.25 As • in the direction perpendicular to the tension face: Ast = n2 x 0.25 As Where: n1 is the number of layers with bars anchored at the same point in the member n2 is the number of bars anchored in each layer.
5z, but H 50mm
z H 2 2z
10z, but 10z H 70mm
H 20mm G 50mm H 10mm
H 10mm
H
1.4z 1.4z
z H 0.7 0.7z
z
z
a)
b)
z c)
z d)
Note
For c) and d) the cover should not be less than either 3z 3 z or 50mm.
Fig 5.31 Anc ho ra g e o f links / Asv H 0.5As1
/ Asv H 0.5As1
Note
As1 As1
/ Ash H 0.25As1
/ Ash H 0.5As1
Example: In the left hand case n 1 = 1, n 2 = 2 and in the right hand case n 1 = 2,
n2
= 2.
io n a l re in fo fo rc rc e m e n t in in a n a n c h o ra g e zo n e fo r la rg e d ia m e t e r b a rs Fig 5.32 Ad d it io
w he re t he re is no t ra ra ns nsve ve rse c o m p re ssio n
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5. 5.12. 12.6 6 C ur urta ta ilm e nt o f b a rs in fl fle xur uraa l m e m b e rs i) When a bar is curtailed in a flexural member, it should be anchored beyond the point when it is no longer required, for a length of l b,net or d , whichever is the greater. In determining the location where a bar is no longer required, the force in the bar should be calculated taking into account: a) the bending moment and b) the effect of a truss model for resisting shear, (‘shift rule’).
ii)
This may be assessed by the ‘shift rule’, i.e. by shifting the bending moment diagram in the direction of reducing moment by an amount al, where al = 0.45d cot coti for beams and 1.0d for for slabs, where i is the angle of the concrete truss assumed in shear design. A practical method is: a) determine where the bar can be curtailed based on bending moment alone, and b) anchor this bar beyond this location for a distance l bd + a1. This procedure is illustrated in Figure 5.33. At simply supported ends, the bar should be anchored beyond the line of contact between the member and its support by: • Direct support for slabs: 0.7 times the value given in Table 5.24 • Direct support for beams: 0.8 times the value given in Table 5.25. • All indirect supports: 1.0 times the values given in Tables 5.24 and 5.25 A ‘direct’ support is one where the reaction provides compression across the bar being anchored. All other supports are considered ‘indirect’ (see Figure 5.34).
5.12.7 5.12. 7 C o rb e ls a nd ni nib bs Corbels and nibs should be designed using strut and tie models when 0.4hc G ac G hc or as cantilevers when ac > hc where ac is the shear span and hc is the overall depth. Unless special provision is made to limit the horizontal forces on the support, the corbel (or nib) should be designed for the combined effects of the vertical force F Ed and a minimum horizontal force of 0.2 F Ed . The minimum effective depth of corbel is determined by the maximum resistance of the concrete compressive strut (see Figure 5.35(a)). This may be calculated as follows: Limiting
z0 F Ed + ac to 1.0 gives d H ac 0.34v b f ck l
l
l
Where: v = 1 - f ck 250 l
Limiting
b l
z0 z to 0 d d
min
gives d H
ac
l
l l
cb l - b zd l m - b zd l
0.68ac v b bffck z0 F d Ed
0
min
2
min
The value of ( z0/d ) min should not normally be taken less than 0.75.
0
2 min
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IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Envelope of
: D
MEd + NEd z
l bd l bd
Acting tensile force Resisting tensile force
l bd
al
l bd
F td
al F td l bd
l bd l bd
l bd
fo r the d e sig n o f fle xur uraa l m e m b e rs - c ur urta ta ilm e nt le le ng ths Fig 5.33 Enve lo p e d e sig n fo
l bd
l bd
b
Direct support Beam Bea m su suppo pporte rted d by wal alll or col colum umn n
Indirect supp Indirect support ort Beam Beam int intersect ersecting ing another anoth er su suppor pporti ting ng beam
ra g e a t e n d su su p p o rt rt s Fig 5.34 An c h o ra
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
The bearing stress in the corbels should be limited to 0.48(1- f ck /250) f f ck The tie force, F td = F td ' + HEd where F td ' and the value of z0/d may may be determined from Figure 5.36(a) and Figure 5.36(b) respectively. The value of ( z0/d ) min is assumed to be 0.75. In addition to the reinforcement required to resist F td , horizontal stirrups with a total area of 0.5 As should be provided as shown in Figure 5.35(b). F Ed
ac
H Ed F td
aH ac' z0
d
hc
σ
x
a) Strut and and tie layout for corbels
As,main
Anchorage device or loops
Σ As,link H 0.5 As,main
b) Link requirement for corbels
91
Fig 5.35 Co rb e ls a nd n ib s
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Ftd
l
bd v Rd ,max 0.25
0.2
0. 0.6 6
0.5
0.15 l
ac d
=
0.8
0.45 0.4
0.1
l
ac d
0.05
=
0.35
0 0
0.05
0.1
0.15
0.2
l
a) Corbels: Values of F td (assuming ( z0/d )min = 0.75)
FEd
0.25
bd v Rd ,max
z0 d 1
0.95
0.9 l
ac d
=
l
ac
0.35
d
=
0.8
0.85
0.8
0. 0.4 4 0.45
0.6 0.5
0.75 0
0.05
0.1
0.15
b) Corbels: Values of z0/ d (assuming ( z0/d )min = 0.75) Notes
a v Rd, max b
c c 250 mm
is taken as 0.34 f ck 1
f ck
-
.
The curves on these these figures should not be extrapolated. extrapolated.
0.2
FEd
0.25
bd v Rd ,max
Fig 5.36 De sig n c ha rt fo r c o rb e ls
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
The arrangement of strut and ties for nibs should take account of the position of the bar in the main beam where the strut forces are picked up (see Figure 5.37). It should also be noted that the force in the leg of the beam links close to the nib is increased by a value more than the force on the nib.
Balancing force
F Ed
]a1 + a2gF Ed a2 a2
F td
a1 H Ed
σ
trut ut a nd ti tiee la you t fo fo r ni nib bs Fig 5.37 Str
93
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6 Desi Design gn pri princ nciple iples s - prest prestr ress essed ed c onc oncr rete
6.1
Introd oduc ucttion
This section outlines the general principles which apply to both the initial and final design of prestressed concrete members and sets out the design parameters that govern all design stages. The general recommendations given in Section 2 are applicable to all concrete con crete building structures and are not repeated here. Detail design is often carried out by specialists using automated software. For further information reference should be made, for example, to the Concrete Society Technical Report Post-tensioned Concrete Floors - Design Handbook 27.
6.2 6. 2
Design Des ign pri princ nciples iples
Prestressed concrete is different from ordinary (non-prestressed) reinforced concrete because the tendons apply loads to the concrete as a result of their prestress force, whilst in reinforced concrete the stresses in the reinforcement result from the loads applied to the structure. A proportion of the external loads is therefore resisted by applying a load in the opposite sense through the prestressing whilst the balance has to be resisted by ordinary reinforcement. Prestressed tendons may be internal, i.e. within the concrete, either bonded to the concrete or unbonded (single strand in a plastic tube filled with grease), or external, i.e. outside the concrete but inside the envelope of the member, see Figure 6.1. This Manual deals only with prestressed concrete members with internal tendons. Prestressed members can be either pretensioned, i.e. the tendons are stressed before the concrete is cast around them and the force transferred to the concrete when it has obtained sufficient strength, or post-tensioned, i.e. ducts are cast into the concrete through which the tendons are threaded and then stressed after the concrete has gained sufficient strength. This Table 6.1 compares the advantages and Manual deals with both pre- and post-tensioned members. Table disadvantages of pre- and post-tensioning. Precast members will generally be pretensioned with the tendons bonded to the concrete whilst in-situ members will be post-tensioned with the tendons either bonded or unbonded. Table 6.2 lists factors affecting the choice of bonded or unbonded tendons.
Internal tendon (bonded or unbonded) External tendon
x t e rn rn a l t e n d o n s Fig 6.1 In t e rn a l a n d e xt
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
Table 6.1 Ad Adva vant ntage ges s and disa disadva dvant ntage ges s of pre- and and post-tensionin ensioning g Type of c onstruc ucttion Pre t e n si sio ne ne d
Advantages
Disadvantages
• n o n e e d fo fo r a n c h o ra g e s
• h e a v y st re re ssin g b e d re q u ir ire d
• t e n d o n s p ro ro t e c t e d b y
• m o re d iffic u lt lt to in in c o rp o ra te
c o n c re t e w it it h o u t t h e n e e d fo fo r
d e fle c t e d t e n d o n s
g ro u tin tin g o r o th e r p ro te c ti tio on • p re str tree ss is is g e n e ra lly b e tte r d istr striib ute d in tra tra nsm iss ssiio n zones • fa c t o ry ry p ro ro d u c e d p re re c a st units Po st s t -t -t e n si sio n e d
• n o e xt e rn rn a l st re re ssin g b e d re q ui uirre d
• t e n d o n s re q u ir ire a p ro t e c t iv iv e sys yste te m
• m o re fle xib ility in in te nd o n la yout a nd p ro file
• la rg e c o n c e n tr t ra t e d fo rc rc e s in e n d b lo c ks
• d ra ra p e d t e n d o n s c a n b e u se se d • in-situ o n si site te
Tab able le 6.2 6.2 Adva Advant ntages and disadvant disadvantag ages es of bonde bonded d and and unbonde unbonded d cons c onsttruc ucttion Type of c onstruc ucttion Bo n d e d
Advantages • te t e nd n d o n s a re re m o re e ff ffe c t iv e a t ULS • d o e s n o t d e p e n d o n th th e a n c h o ra ra g e a ft e r g ro ro u t in in g
Disadvantages • t e n d o n c a n no n o t b e in sp sp e c t e d o r re p la la c e d • t e n d o n s c a n n o t b e re -st re re sse d o n c e g ro ro u te te d
• lo c a lise s th e e ffe c ts o f damage • t h e p re st re re ssin g t e n d o n s c a n c o n t ri rib u t e t o t he h e c o n c re t e sh e a r c a p a c it y Un b o n d e d
• te t e nd n d o n s c a n b e re re m o v e d fo r in sp sp e c t io io n a n d a re re p la c e a b le if c o rr rro d e d • re d u c e d fric ti tio o n lo lo sse s
• le ss e ffic ie nt a t UL ULS • re lie s o n the inte g rity o f the a n c h o ra ra g e s a n d d e v ia t o rs rs • a b ro ro ke ke n te te n d o n c a u se se s
• g e n e ra lly fa ste r c o n str stru u c ti tio on
p re st stre re ss t o b e lo st fo r th t h e fu ll
• t e n d o n s c a n b e re -st re re sse d
le n g t h o f t h a t te te n d o n
• t h in in n e r w e b s a n d la rg e r le v e r a rm
• le ss e ffic ie nt in in c o ntr ntro o lling c ra c kin g • c a re fu l a tte n tio tio n is is re q u ir ire d in d e sig n t o e n su su re re a g a in st st
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p ro g re ssi ssive ve c o lla p se
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Strand
Duct Sheath Concrete Wire
Construction joint Anchorage
Coupling assembly
Anchorage
Tendon profile
Coupler
Direction of construction
Fig 6.2 No m e n c la t u re re a sso c ia t e d w it it h p re st re sse d c o n c re t e m e m b e rs
Figure 6.2 shows some common features and nomenclature associated with prestressed concrete.
6.3
Loading
The loads and load combinations to be used in calculations are given in Section 3. In this Manual prestressing forces are considered as variable loads for serviceability limit states and as resistances for the ultimate limit state.
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6.3.1 Se rvi vicc e a b ility lim it sta te (SL (SLS) The effects of prestressing at SLS are normally taken into account by equivalent loads (see Figure 6.3). The analysis using equivalent loads automatically takes account of secondary effects (‘parasitic effects’) (see Figure 6.4). For SLS the dead load and post-tensioning effects, including the effect of losses due to creep, long term shrinkage and relaxation of the prestressing steel, should be considered acting with those combinations of variable loads which result in the maximum stresses. Unless there are specific abnormal loads present, it will generally be sufficient to consider the post-tensioning effects in combination with the variable loads as given in Section 3. For flat slabs it is normally satisfactory to apply the combinations of loading to alternate full width strips of the slab in each direction. However it will normally be satisfactory to obtain the moments and forces under the single load case using the frequent load values.
Pe
Centroid of section
e
P
P
P
sin
Anchorage
P
P
8P
l
l2
Parabolic drape
Pe
P
Centroid of shallow section e
Centroid of deep section
Change in centroid position
P
cos
uiva va le nt lo a d s Fig 6.3 Eq ui
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D e fl fle e c ti tion on limit limit st sta a te – Where the analysis is used to determine deflections, span/500 after finishes have been added is normally an appropriate limit using the quasi-permanent load combination (Gk + PBL + }2 Qk , where PBL is the prestress equivalent load). It may be necessary to consider other limits and loads depending on the requirements for the slab.
C rac k width limi limitt state state – For analysis to determine crack widths the frequent load combination (Gk + PBL + }1 Qk ) should be used for bonded tendons and the quasi-permanent load combination (Gk + PBL + }2 Qk ) for unbonded tendons. Unless otherwise agreed with the client the crack width limit should be 0.2mm, except for water retaining structures where the limit should be 0.1mm.
Unstressed element in structure
Unstressed isolated element
Stressed isolated element
Reactions applied to make beam pass through support positions
Reactions applied to make beam have compatible rotations
Total secondary forces and moments for element
Fig 6.4 Se c o nd a ry e ffe c ts fro m p re str tree ssing in in a sta ti ticc a lly ind e te rm ina te
str truc uc ture
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At transfer of prestress the permanent loads present during stressing, together with the posttensioning effects and the effects of early thermal shrinkage, should be considered in obtaining stresses. Where the applied loads change significantly during construction or phased stressing is employed, the various stages should each be checked for transfer stress limits. 6.3.2 Ulti tim m a te lim it sta te (U (UL LS) At the ULS the following load combinations should be used to arrive at the maximum moments and shears at any section (see also Section 3): 1.35Gk + 1.5Qk1 + /1.05Qki + c p P Where: Gk Qk1 Qki P c p
is the permanent load is the primary variable action (load) any other variable action is the prestressing force. should be taken as c p,fav = 0.9 when beneficial or c p,unfav = 1.1 when unfavourable.
When checking flexural stresses, secondary effects of prestressing should be included in the applied loads with a load factor of 1.0.
6.4
Matteria Ma ials, ls, prestressing c omp ompone onent nts s
In the UK the most common prestressing tendons are comprised of 7-wire low relaxation (T (Type ype 2) strands to BS 589628 (this standard will be replaced by EN 1013829) which are generally available in three different types: standard, super and dyform (or drawn); and two nominal diameters: 12.9mm and 15.7mm (18mm is also available). In post-tensioned normal building construction these are used singly with unbonded tendons and in groups with bonded tendons. Unbonded tendons – Unbonded tendons are protected by a layer of grease inside a plastic sheath. Under normal conditions, the strand is supplied direct from the manufacturer already greased and sheathed. In no circumstances should PVC be used for the plastic sheath, as it is suspected that chloride ions can be released in certain conditions. Bonde d tendons tend ons – Bonded tendons are placed in metal or plastic ducts, which can be either circular or oval in form. Metal ducts are made from either spirally wound or seam folded galvanised metal strip. The use of plastic ducts should be considered when designing car parks. The oval duct is used in conjunction with an anchorage, which ensures that up to four strands are retained in the same plane in order to achieve maximum eccentricity. For beams, up to 19 strands may be used in a tendon. This should normally be considered the limit. Table 6.3 (slabs) and Table 6.4 (beams) give typical dimensional data for ducts, anchorages, anchorage pockets and jacks for the more commonly used prestressing systems in the UK. For more precise information and when other prestressing systems are used, the engineer should refer to the manufacturer’s literature.
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Table 6.3 Typ ypic ica al dimens dimensiona ionall dat data for commo common n postpost-tens nsioning ioning systems for for sla labs bs Strand Poc ocket ket diameter dimensions - number of strands (mm)
Anchorage dimensions (mm)
Duct Duct external dimensionsb (mm)
Anchorage spacing
J ack clearances
(mm)
(mm)
1a
1b
2
3a
3b
4
5
xe
ye
xs
ys
12.9 - 1
130
130
110
70
110
70
3 0 d ia .
125
80
150
12.9 - 4
144
310
103
96
250
13 0
75 × 20
220
14 0
15.7 - 1
150
150
115
130
130
95
3 5 d ia .
145
15.7 - 4
168
335
127
115
280
24 0
75 × 20
235
C
E
F
100 1390
100
-
370
220 1200
90
280
10 0
175
125 1450
100
-
16 0
400
230 1450
70
327
Notes a Th e d im e n si sio n s a n d c le a ra n c e s a re illu str straa te d in in Fi Fig u re re 6 .5 .5 . rru g a t e d s te te e l sh e a t h s w it it h a t h ic ic kn e ss o f 1 .5 .5 m m . b Da t a a re fo r c o rr c Th e v a lu e s in th t h e Ta b le a re b a se d o n a n e n ve v e lo p e o f t h e re re q u ir ire m e n t s o f a n u m b e r o f m a n u fa fa c t u re re rs’ sy sy st e m s . Wh e re c le a ra n c e s a re c rit ic ic a l it is re c o m m e n d e d t h a t re re fe re n c e is m a d e t o t h e sp s p e c ific m a n u fa fa c t u re re rs’ c a t a lo g u e s.
x e
x s
y e y s
1b 3b
5
y s
End view of anchorage
C 1a 3a
5 F E
2
Sectional views
4
4-strand anchor Jack clearances
Note
The dimensions shown in this figure are given in Table 6.3 for different tendon sizes.
nsiio ns o f c o m m o n p o stt-te te nsi nsio o ni ning ng sys yste te m s (1 - 9 str traa nd s) Fig 6.5 Dim e ns
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Table 6.4 Typic ypica al dimensiona dimensionall data for for c ommon postpost-tensionin ensioning g syste syst ems (1 to 19 strand rands) s) Strand diameter - number of strands
Poc ocket ket dimensions
Anchorage dimensions
Duct Duct diameter intt/ extc in
Anchorage spacing
J ack di diam amet eter and clearances
(mm)
(mm)
(mm)
(mm)
(mm)
1
2 a
3
4
5
6
7
C
D
E
1 2 .9 - 1
130 110
30°
70
85
25/ 30
80
90
1200
140
100
1 2 .9 - 3
180 115
30°
120
210
40/ 45
115
155
1100
200
150
1 2 .9 - 4
240 115
30°
135
210
45/ 50
125
180
1100
248
175
1 2 .9 - 7
240 120
30°
175
215
55/ 60
155
235
1200
342
220
1 2 .9 - 1 2
330 125
30°
230
405
75/ 82
195
305
1300
405
250
1 2 .9 - 1 9
390 140
30°
290
510
80/ 87
230
385
2100
490
295
1 5 .7 - 1
135 115
30°
75
85
30/ 35
95
105
1200
140
100
1 5 .7 - 3
200 115
30°
150
210
45/ 50
130
185
1100
210
140
1 5 .7 - 4
240 120
30°
157
215
50/ 55
140
210
1200
342
220
1 5 .7 - 7
305 125
30°
191
325
60/ 67
175
280
1300
405
250
1 5 .7 - 1 2
350 140
30°
270
510
80/ 87
220
365
1500
490
295
1 5 .7 - 1 9
470 160
30°
340
640
100/ 107
265
460
2000
585
300
Notes a Th e d im e n si sio n s a n d c le a ra n c e s a re illu str straa te d in in Fi Fig u re re 6 .6 .6 . b Th e v a lu e s in th t h e Ta b le a re b a se d o n a n e n ve v e lo p e o f t h e re re q u ir ire m e n t s o f a n u m b e r o f m a n u fa fa c t u re re rs’ syst e m s . Wh e re c le a ra n c e s a re c rit ic ic a l it is re c o m m e n d e d t h a t re re fe re n c e is m a d e t o t he h e sp e c ific m a n u fa fa c t u re re rs’ c a t a lo g u e s. fo r c o rr rru g a t e d st s t e e l sh e a t h s w it it h b o n d e d te t e n d o n s. s. c Da t a a re fo
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1 3
2
5
4
Sectional view
6
7
End view of anchorage
D
E C
Jack clearances Note
The dimensions shown in this figure are given in i n Table Table 6.4 for different tendon sizes.
Fig 6.6 Dim e ns nsiio ns o f c o m m o n p o stt-te te nsi nsio o ni ning ng sys yste te m s fo r sla b s
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7 Preliminary de des sign - pre prestressed c onc oncr rete
7.1
Introd oduc ucttion
7 .1 .1 .1 .1 G e n e ra l The following information should enable engineers to do the initial sizing of members. It is assumed that the final design is carried out by a specialist. Sizing of structural members should be based on the longest spans (slabs and beams) and on the largest areas of roof and/or floors carried (beams). The same sizes should be assumed for similar but less onerous cases - this saves design and costing time at this stage and is of actual benefit in producing produ cing visual and constructional repetition and hence, ultimately, cost benefits. Loads should be carried to the foundations by the shortest and most direct routes. In constructional terms, simplicity implies (among other matters) repetition; avoidance of congested, cong ested, awkward or structurally sensitive details and straightforward temporary works with minimal requirements for unorthodox sequencing to achieve the intended behaviour of the completed structure. Standardised construction items will usually be cheaper and more readily available than purpose-made items. 7.1.2 Effe c ti 7.1.2 tive ve le ng ths The effective span of a simply supported member should normally be taken as the clear distance between the faces of the supports plus one third of their widths. However, where a bearing pad is provided between the member and the support, the effective span should be b e taken as the distance between the centres of the bearing pads. The effective span of a member continuous over its supports should normally be taken as the distance between centres of supports. The effective length of a cantilever where this forms the end of a continuous member is the length of the cantilever from the centre of the support. Where the member is an isolated cantilever the effective length is the length of the cantilever from the face of the support. 7.1.3 La te ra l b uc kling 7.1.3 To prevent lateral buckling of beams, the length of the compression flange measured between adequate lateral restraints to the beam should not exceed 50b, where b is the width of the compression flange, and the overall depth of the beam should not exceed 4 b. 7.1 .4 To rs rsiio n In normal slab-and-beam or framed construction specific calculations for torsion are not usually necessary, torsional cracking being adequately controlled by shear reinforcement. Where torsion is essential for the equilibrium of the structure, e.g. the arrangement of the structure is such that loads are imposed mainly on one face of a beam without corresponding rotational r otational restraints being provided, EC2 1 should be consulted.
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7.2
Loads
The loads and load combinations to be used in calculations are given in Section 3. In this Manual prestressing forces are considered as variable loads for serviceability limit states and as resistances for the ultimate limit state. Imposed loading should initially be taken as the highest statutory figures where options exist. The imposed load reduction allowed in the loading code should not be taken advantage of in the initial design stage except when assessing the load on the foundations. Loading should be generous and not less than the following in the initial stages: • floor finish (screed) 1.8kN/m2 • ceiling and service load 0.5kN/m2 Allowance for: • demountable lightweight partitions 1.0kN/m2 – treat these as variable actions. • blockwork blockwor k partitions partitions 2.5kN/m2 – treat these as permanent actions when the layout is fixed. Loading of concrete should be taken as 25kN/m 3. The initial design of prestressed concrete members should be carried out at the serviceability limit state using the following simplified load combinations i) to iv): i)
ii)
iii)
iv)
permanent action + variable action: 1.0 # characteristic permanent load + 1.0
# characteristic
variable load
permanent action + wind action: 1.0 # characteristic permanent load + 1.0
# characteristic
wind load
permanent action + snow action: 1.0 # characteristic permanent load + 1.0
# characteristic
snow load
permanent action + variable action + wind action + snow action: 1.0 # characteristic permanent load + 1.0 # characteristic variable load + 0.7 # characteristic wind load + 0.7 # characteristic snow load Where appropriate the other combinations should be checked: 1.0 characteristic permanent load + 1.0 # characteristic wind load + 0.7 # characteristic variable load + 0.7 # characteristic snow load and 1.0 # characteristic permanent load + 1.0 # characteristic snow load + 0.7 # characteristic wind load + 0.7 # characteristic variable load.
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7.3
Matteria Ma iall prope proper rtie ies s
It is recommended that the minimum concrete grade for post-tensioned construction is C30/37. A higher grade concrete may need to be used in order to allow higher compressive stresses to be carried by the concrete and to meet durability requirements. For initial design, concrete grades greater than C40/50 should not be considered. For initial design, prestress forces after losses should be taken from Table 7.1.
Table 7.1 Strand loa loads (af (after losses) to to be be used for init initia iall design design Strand load (kN) Strand type 12.9mm dia. 15.7mm dia. St a n d a rd
88
125
Su p e r
100
143
When UK steels are used for reinforcement a characteristic strength, f yk , of 500MPa should be adopted.
7.4
Struc ucttur ura al form and framing
In choosing column and wall layouts and spans for a prestressed floor the designer should provide stabili stability ty against against lateral lateral forces forces and ensure ensure braced braced construction. construction. Several Several possibilities may be considered to optimise the design, which include: • Reducing the length of the end spans or, if the architectural considerations permit, inset the columns from the building perimeter to provide small cantilevers (see Figure 7.1). Consequently, end span bending moments will be reduced and a more equitable bending moment configuration obtained. It also moves the anchorages away from the columns. • Reducing, if necessary, the stiffness of the columns or walls in the direction of the prestressing to minimise the prestress lost and resulting cracking in overcoming the restraint offered to floor shortening. Figure 7.2 shows some typical floor layouts. Favourable layouts (see Figure 7.2a)) allow the floors to shorten towards the stiff walls. Unfavourable layouts (see Figure 7.2b)) restrain the floors from shortening. • Where span lengths vary, adjust the tendon profiles and the number of tendons to provide the uplift required for each span. Generally this will be a similar percentage of the dead load for each span. Once the layout of columns and walls has been determined, the next consideration is the type of floor to be used. This again is determined by a number of factors such as span lengths, magnitude of loading, architectural form and use of the building, special requirements such as services, location of building, and the cost of materials available. The slab thickness must meet two primary functional requirements – structural strength and deflection. Vibration should also be considered where there are only a few panels. The selection of thickness or type (e.g. flat slabs with or without drops, coffered or waffle, ribbed or even beam and slab) is also influenced by concrete strength and loading and architectural intent. There are likely to be several alternative solutions to the same problem and a preliminary costing
exercise may be necessary in order to choose the most economical. More information can be found in the Concrete Society Technical report TR4327.
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Fig 7.1 Typ ic a l flo o r la you t to m a xim ise p re str tree ssing e ffe c ts
a) Favourable layout of restraining walls
b) Unfav Unfavourabl ourable e layout of restra restraining ining walls
re d uc e lo ss o f p re st re re ss a nd c ra c king e ffe c t s Fig 7.2 La yo ut of she a r w a lls t o re Allowance for sufficient topping should be made to accommodate cambers induced by prestressing, including any differential cambers between adjoining members. The arrangement should take account of possible large openings for services. Tendon positions should be chosen to avoid locations of any possible future holes. holes. Sufficient space should
be provided to allow for jacking and for the possible replacement of unbonded tendons.
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7.5
Fir ire e resistanc nce e and durab durabilit ility y
The size of structural members may be governed by the requirement of fire resistance. Table 7.2 gives the minimum practical member sizes and cover to the prestressing tendons required for different periods of fire resistance. For beams and ribbed slabs, width can be traded against axis distance to give the necessary fire resistance. Thus Table Table 7.2 gives two sets of data for each hourly rating, one based on minimum width and the other based on minimum axis distance.
Table 7.2 Minimum member member siz sizes es and axis dist dista anc nces es for for prest prestr ressed memb membe ers in fir fire e Member
Minimum dimension (mm) for standa ndar rd fir ire e resistanc nce e (mins) of:
Beams
Wid Wi d th
280 700 200 500 120 300
Plain soffit slabs:
Axiis d ista nc e , a: Ax Sim p ly su p p o rt e d C o n t i n u o u sa De p th (in (in c lu d in g
105 85 90 65 175
80 65 60 45 120
Axiis d ista nc e , a: Ax Sim p ly su p p o rt e d C o n t i n u o u sb
80 55
55 35
35 25
Sim p ly su p p o rt e d C o n t i n u o u sb
65 55
40 35
30 25
R240
R120
R60
55 40
40 27c 80
no n-c o m b usti ustib b le fini nisshe s)
Sin g le w a y
Tw o -w a y
Ribbed slabs: Sim p ly su p p o rt e d Axiis dis Ax dista nc e to si sid d e o f rib
asd = a + 10
Wid t h o f rib , br Axiis d ista nc e b, a Ax De p t h o f fla n g e , hs Axiis d ista nc e o f fla ng e , af Ax
C o n t in u o u s
Wid t h o f rib , br
Axiis dis Ax dista nc e to si sid d e o f rib
asd = a + 10
Axis d ista nc e , a: Axi De p t h o f fla n g e , hs
Flat slabs
280 500 160 300 100 200 105 85 85 55 50 30 175 17 120 95 55
35
25
450 700 160 300 100 200 85 75 175
60 45 120
40 25 80
Axis d ista nc e o f fla ng e , af Axi De p th (in (in c lu d in g
55 200
35 200
25 180
no n-c o m b usti ustib b le fini nisshe s) Axiis d ista nc e b, a Ax
65
50
30
Notes a Wh e re m o re re t h a n 15 15 % m o m e n t re d ist ri rib u t io io n h a s b e e n a ssu m e d t h e v a lu e s fo r sim p ly su su p p o rt rt e d b e a m s sh sh o u ld ld b e u se se d .
b Wh e re m o re re t h a n 15 15 % m o m e n t re d ist ri rib u t io io n h a s b e e n a ssu m e d t h e v a lu e s fo r sin g le wa y sim p ly su p p o rte d sla b s sh o u ld ld b e u se se d .
c No rma lly th e c o v e r re q u ir ire d fo fo r b o n d a n d d u ra ra b ility a t n o rm a l te m p e ra tu re re w ill
c o ntr ntro o l.
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The values given in Table 7.2 will also ensure that there will be sufficient cover for exposure condition XC1. For other exposure conditions reference should be made to Appendix B. Unless otherwise stated grouting of ducts should be carried out in accordance with the National Structural Concrete Specification30. Reference should also be made to the Concrete Society Technical Report No. TR4731 with regard to grouting of ducts and protection of anchorages. Where tendons are curved, the cover perpendicular to the plane of curvature should be increased to prevent bursting of the cover concrete in accordance with Table 7.3.
Table 7. 7.3 3 Minimum Minimum cove cover r to c urved duc ductts (mm) (mm) Radius of c urva vattur ure e of duct (m)
Ductt int Duc internal ernal dia diameter meter (mm)
159
229
477
636
2
30
35
70
95
45
50
25
30
40
45
50
55
60
75
80
100
1603
1908
2748
4351
Tendo endon n forc force e (kN)
4 6
916
1113
Ra d ii n o t n o rm a lly u se d 70
80
120
140
55
60
80
95
135
215
65
80
105
160
90 85
130 115
85
105
8 10 12 14
30
35
45
50
55
60
65
80
Notes a Th e Ta b le is is b a se d o n re fe re n c e 3 2. 2. b Th e te n d o n fo fo rrcc e sh o wn is is th e m a xim u m n o rma lly a v a ila b le fo r th e g iv e n si size o f duct.
c Wh e re t e n d o n p ro fi f ile rs o r sp a c e rs a re p ro v id id e d in in th th e d u c t s, s, a n d t h e se a re o f a ty typ p e wh ic ic h wil will c o n c e n tra tra te th e ra d ia l fo rc e , th th e v a lu e s g iv e n in in th e Ta b le wi willl n e e d t o b e in c re re a se d .
d Th e c o v e r fo r a g iv e n c o m b in a t io io n o f d u c t in t e rn a l d ia m e t e r a n d ra ra d iu s o f c u rv rv a t u re re sh o w n in in t h e Ta b le , m a y b e re d u c e d in p ro p o rt rt io io n t o t h e sq u a re ro o t o f t h e t e n d o n f o rc rc e w h e n t h is is is le ss t h a n t h e v a lu e t a b u la la t e d .
7.6
Stiffne iffness ss
7.6.1 Sla b s To provide adequate stiffness, the effective depths of slabs and the waist of stairs should not be less than those derived from Table 7.4. It should be noted that Table 7.4 is applicable for multi-span floors only. For single-span floors the depth should be increased by approximately 15%.
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Table 7.4 Typ ypic ica al spa pan/ n/de depth pth ratios for a var variety of sec secttion typ ype es for multi-span floors Total Spa pan/ n/de dept pth h Additional imposed ratios Sec tion typ type e requirements load 6m G L G 1 13 3m for vibration (kN/ (k N/m) m) (kN// m) (kN 1
2
So lid fla t sl slaa b
H ¾ h
5
5.0 5. 0
36
10.0
30
2.5 2. 5
44
5.0 5. 0
40
10.0
36
A
A
H span/3
Ba n d e d fla t sla b
span/5
4
40
So li lid fl fla t sla b with with d ro p p a n e l
h
3
2.5 2. 5
Sla b
Be a m
2.5 2. 5
45
25
5.0 5. 0
40
22
10.0
35
18
A
C o ffe re d fla t sla b
2. 5 2.5 5.0 5. 0
25 23
10.0
20
2.5 2. 5
28
5.0 5. 0
26
10.0
23
B
C o ffe re d fl fla t sla b with with so lid p a ne ls
H
span/3
B
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ypic ica al spa pan/ n/de depth pth ratios for a var variety of sec secttion typ ypes es for Table 7.4 Typ (cont ont.) .) multi-span floors(c Total Spa pan/ n/de dept pth h Additional imposed ratios Sec tion typ type e requirements load 6m G L G 1 13 3m for vibration (kN// m) (kN (kN/ (k N/m) m) 6
C o ff f fe re d sla b w it it h b a n d b e a m d
H
7
8
2.5 2. 5
28
5.0 5. 0
26
10.0
23
2.5 2. 5
30
5.0 5. 0
27
10.0
24
B
span/6
Rib b e d sla b e
B
O n e -w a y sla b w it it h n a rro w b e a m Sla b
Be a m
2.5 2. 5
42
18
5.0 5. 0
38
16
10.0
34
13
A
span/15
Notes tio o n . Th e fo llo wi win n g a d d iti tio o n a l c h e c k sh o u ld ld b e m a d e fo r n o rm a l o ffic e a Vib ra ti c o n d iti tio o n s if if n o fu rth rth e r v ib ib ra ti tio o n c h e c ks a re c a rrie d o u t: A
e ith e r th e flo o r h a s a t le le a st fo u r p a n e ls a n d is a t le a st 25 25 0m 0m m th ic ic k o r th e flo o r h a s a t le le a st e ig h t p a n e ls a n d is a t le le a st 20 20 0m 0m m th ic ic k.
B
e ith e r th e flo o r h a s a t le a st fo u r p a n e ls a n d is is a t le a st 4 00 00 mm th ic ic k o r th e flo o r h a s a t le le a st e ig h t p a n e ls a n d is a t le le a st 30 30 0m 0m m th ic ic k.
b All p a n e ls a ssu m e d to t o b e sq sq u a re . c Sp a n / d e p t h ra t io io s n o t a ffe c t e d b y c o lu lu m n h e a d . d It m a y b e p o s si sib le t h a t p re st re re sse d t e n d o n s w il ill n o t b e re q u ir ire d in in th th e b a n d e d se c ti tio o ns a nd tha t unte nsi nsio o ne d re inf nfo o rc e m e nt wil will suff uffiic e in the rib s, o r vi vicc e v e rsa . io c a n v a ry a c c o rd rd in g t o t h e w id id t h o f t h e b e a m . e Th e v a lu e s o f sp a n / d e p t h ra t io
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7. 7.6. 6.2 2 Iso la t e d b e a m s For initial sizing the effective depth of isolated beams should be determined from Table 7.5. For further refinement reference should be made to a specialist contractor or EC2 1.
Table 7.5 Spa pan/ n/eff effec ec tive dep deptth ratios for for init initia iall sizing sizing of isola olatted be bea ams C a n t ile v e r Sim p ly su p p o rt e d C o n t in u o u s
7.7
8 18 22
Sizi izing ng
7.7.1 Introd 7.7.1 Introd uc ti tio on When the depths of the slabs and beams have been obtained it is necessary to check the following: • width of beams and ribs • column sizes and reinforcement (see Section 4.8.4) • shear in flat slabs at columns • practicality of tendon and reinforcement arrangements in beams, slabs and at beamcolumn junctions. 7.7.2 Lo 7.7.2 Lo a d ing Serviceability loads should be used throughout for initial design (see Section 7.2). For prestressed concrete members it is necessary to calculate the maximum shear force and both the maximum and minimum bending moments at the critical sections. A critical condition may occur at transfer (when the prestressing force is initially applied to the concrete member) as the prestressing force is at its highest value and the applied loading may be significantly less than the maximum load which the member will eventually have to carry. Secondary effects of prestress are taken into account using equivalent loads (see Section 6.3.1). The loading arrangements to be considered for continuous members may follow either of the following methods: i) Alternate spans carrying the design variable and permanent load, other spans carrying the design permanent load and Any two adjacent adjacent spans carrying the design variable and permanent load, other spans carrying design permanent load. ii) All spans carrying the design variable and permanent load and Alternate spans carrying the design variable and permanent load, other spans carrying design permanent load.
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7. 7.7. 7.3 3 Wid t h o f b e a m s a nd rriib s The width may be determined by limiting the shear stress in beams to 2.0MPa and in ribs to 0.8MPa. 1000V SLS width of beam (in mm) = 2d width o off rib (in mm) =
Where: V SLS
d
7.7. 7. 7.4 4
She a r She
7.7.4. 7.7 .4.1 1
1000V SLS 0.8d
is the maximum shear shear force at the serviceability serviceability limit state (in kN) on the beam or rib, considered as simply supported, and is the effective depth in mm.
G ene ral
Shear checks for prestressed concrete members are carried out at the ultimate limit state. The shear capacity of prestressed elements is made up from three components: i) The concrete shear component (or in the case of shear reinforced concrete the combined concrete and shear steel component): V Rd,c, V Rd,cs, V Rd,s. ii) The part of the shear that is carried by arch (vault for flat slabs) action not dependent on bonded reinforcement. iii) The part of the load which does not act on the failure surface as it is carried to the columns by the vertical component of the tendons: V p. When calculating the contribution of the prestressing force at ULS, both the direct stress, vcp, and the beneficial effects due to the vertical component of the prestress force, the mean value of prestress calculated should be multiplied by an appropriate safety factor c p. The value of c p, given in UK National Annex, is 0.9 when the prestress effect is favourable, and 1.1 when it is unfavourable. In the case of linear elements requiring shear reinforcement the contribution of the concrete to the shear strength is ignored and calculation is based on the variable strut method. The effective depth, d , used in checking the shear capacity should be calculated ignoring any inclined tendons.
7.7.4.2 7.7 .4.2 Be Be ams and slab s (si (sing ng le and two wa y) For slabs not requiring shear reinforcement reference should be made to Section 5.2.4.2. Where beams (or slabs) require shear reinforcement the contribution of the concrete to the shear strength is ignored and calculation is based on the variable strut method (see Section 5.4.4.3). The effect of levels of prestress up to 25% of the design compressive strength is to increase the value of V (the maximum strut force) that can be used. This allows higher values Rd,max of Coti (the strut angle) to be used which in turn reduces the number of links required to take a
given shear force. The result of this approach is that to obtain benefits from fro m the axial compression
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the designer will need to maximise the value of Coti. The contribution of the tendon inclination can be included with the term V td which is the design value of the shear component in an inclined tensile chord.
7.7.4.3 Flat slabs For the preliminary design it is considered reasonable to neglect any prestressing effects and treat the slab as a reinforced concrete slab (see Section 4.8). 4.8 ). For more information reference should be made to the Concrete Society Technical Report No. 4327. 7 . 7 .5
Ad e q u a c y o f c h o se se n se c t io n s t o a c c o m m o d a t e t he he t e n d o n s a n d reinforcement In the initial stage the number of prestressing tendons needs to be checked only at midspan and at the supports of critical spans.
7.7.5.1 7.7. 5.1
Bendin Bend ingg mome moment ntss and shea r for forcc es
Bea ms and one one-wa -wayy sol solid id slab slab s Bending moments and shear forces may be obtained by elastic analysis.
Two wo-wa -wa y solid solid sla sla b s on line linea a r sup supp p orts If the longer span ly does not exceed 1.5 times the shorter span lx, the average moment per metre width may be taken as that shown in Table 7.6.
Table 7.6 Mome Moment nt c oe oefffic icients ients for twowo-way way solid slabs slabs on linea linear su supp pport orts
a t m id id s p a n
in u o u s a t a c o n t in support
Short span (kNm per metre)
Long span (kNm per metre)
wSLS lx ly 20
wSLS l 2x 20
- wSLS lx ly 17
- wSLS l 2x 17
Notes a wSLS i iss the d e sig n lo lo a d a t the se rvi vicc e a b ility lilim it sta sta te in kN/ kN/ m 2 , a n d lx a n d ly a re in m e tr tree s.
b If ly > 1.5 lx t h e sl s la b sh o u ld ld b e t re re a t e d a s a c t in in g o n e -w a y .
Solid Sol id flat sla sla b s Determine the moments per unit width in each direction as for one-way slabs.
Ribb Ri bb ed slab s Determine the bending moments per rib by multiplying the moments for solid slabs by the rib
spacing.
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7.7 7.7.5.2 .5.2 Provis Pr ovision ion of tendo tendons ns and re in infor forcc eme nt D ete eterrmi mine ne the numbe r of tend tend ons An estimate of the size and number of tendons required can be made using ‘equivalent loads’ to represent the effects of prestressing (see Section 6.3.1). In this approach the concrete section is considered loaded by the applied dead and imposed loads which are partially supported (or balanced) by the forces from the prestressing tendons. Any out-of-balance forces have to be resisted by the concrete section and ordinary reinforcement. The exact degree of load balancing required is a matter of experience, judgement and the degree of cracking that is considered acceptable. When draped tendons are used and cracking is acceptable an economical design will generally be obtained when the prestressing tendons balance approximately 50% of the total dead and imposed loading. The bending moments, axial forces and corresponding stresses in the concrete member under dead, imposed and the equivalent loads are calculated as described in Section 7.7.5.1, assuming a homogeneous section. The prestressing force and tendon profile are adjusted until the stresses obtained comply with the limits given in Table 7.7. When checking the stresses at transfer, the prestressing force required for the in-service condition should be increased by 60%, as the long-term (time-dependent) losses will not have occurred, and no tension should be allowed in the concrete.
Table 7.7 Allo Allowab wable le stresses for init initia iall design Ma xim u m c o m p re ssiv e str tree ss
0.6 f ck
M a xi xim u m t e ns n sile st re ss ss: n o t e ns n sio n a ll llo w e d
0
5 MPa
o t h e rw ise
Note iss th e c o n c re te c y lilin d e r str tree n g th . f ck i
When the prestressing force has been determined, calculate the size and number of tendons using Table 7.1. When tension in concrete has been taken into account, ordinary reinforcement should be provided in order to control crack widths and to give adequate ultimate capacity capacity.. The area of reinforcement provided should be sufficient to resist the total net tensile force on the section when acting at a stress of 0.63 f yk (see Figure 7.3) when bonded tendons are used. When unbonded tendons are employed, increase this area by 20%.
Tend endon on a nd reinf einfor orcc eme nt arr arrang eme nt ntss When the number and size of the prestressing tendons, ordinary reinforcement and the areas of the main reinforcement in any non-prestressed elements (see Section 4.8.7) have been determined, check that the tendons and bars can be arranged with the required cover in a practicable manner avoiding congested areas. In post-tensioned construction, check that there is sufficient space for the cable anchorages and their associated reinforcement and that the stressing jacks can be located on the ends of the
tendons and extended (see Section 6.4).
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115
cc
x h
Note Tensile force = b( h-x )ct 2 where b h ct
ct
= width of tension zone = depth of tension zone = max. tensile stress in concrete
nsille fo fo rc e Fig 7.3 To ta l ne t te nsi
7.8
Initia Init iall de design sign
7.8.1 Introd 7.8.1 Introd uc ti tio on The following clauses are intended for initial design only.
7.8.1.1
Te nd ndon on p rofil rofile e
A tendon profile is chosen which satisfies the cover requirements and reflects the bending moment diagram for the applied loads (i.e. high over the supports and low at midspan). For slabs it is common practice to choose the points of contraflexure of the tendon profile so that 90% of the drape occurs over 90% of the half span (see Figure 7.4). The tendon profile should be sketched at this stage and the leading dimensions indicated.
7.8.1.2
Te nd ndon on forc e p rofi rofille - Init Initial ial forc force e ( P0 )
The force in the tendon reduces with distance from the jacking point because of friction which arises due to both intentional and unintentional deviations of the tendon. For most building structures with draped tendons it is sufficiently accurate to assume that the unintentional angular deviation is uniform along the member so that the force in the tendon, Px, becomes
6
Px = P0 1 - (na + K) x
Where: P0 n a K
is is is is
@
the initial jacking force the coefficient of friction of the duct the angular deviation per unit length in rad/m the wobble factor (which allows for unintentional deviation) in m-1, and
x
is the distance from the point at which the tendon is jacked in metres.
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Point of contraflexure
Total drape = D
0.9D
L
20
L
2 Support
Span
Fig 7.4 G e o m e t ry ry o f t e nd o n p ro file
Values of n and K depend depend on the surface characteristics of the tendon and duct, on the presence of rust, on the elongation of the tendon and on the tendon profile. Information on appropriate values are provided by the manufacturers of prestressing systems, but in the absence of more exact data values of n = 0.25 and K = = 0.003 m-1 may be used. With wedge-anchored tendon systems the tendon force profile must be adjusted to allow for the wedge draw-in or anchorage set. This depends on the wedge set movement which can be obtained from the prestressing system manufacturer and is typically 6mm. The loss due to anchorage draw-in, DP is given by:
DP =
Where: L = d A ps E p m n a k
E p Aps d + mL L
d A ps E p G le leng ngth th of te tend ndon on m is the wedge draw-in is the area of a tendon is the elastic modulus of the tendon which may be taken as 190kN/mm2 is the rate of change of prestressing force due to friction, i.e. P0 n(a + k ) is the coefficient of friction is the angular deviation per unit length is the unintentional angular deviation per unit length.
The tendon force profile is shown in Figure 7.5. The maximum force in the tendon after lock-off is Pmax = P0 – m ld . The initial jacking force should be chosen so that P0 and Pmax do not exceed
the values given in Table 7.8, which gives values for commonly used strands.
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Tendon force
Jacking force profile
Po
l Pmax
m
Initial force profile
Final force profile ld
Distance from jack
Fig 7.5 Te nd o n fo rc e p ro file
Table 7.8 Maximum jac jac king loads loads per per strand Strand type
Diameter
Area
(mm)
(mm2)
1 5 .2
1 4 0 .0
1 6 .0
1 5 0 .0
1 2 .5
f pk
f p0.1k
(MPa)
(MPa)
1770
1520
P0
Pmax
(kN)
(kN)
192
181
205
194
9 3 .0
134
126
1 3 .0
1 0 0 .0
144
136
1 5 .2
1 4 0 .0
202
190
1 6 .0
1 5 0 .0
216
204
Y1 8 6 0 S7 G
1 2 .7
1 1 2 .0
1860
1610
162
153
Y1 8 2 0 S7 G
1 5 .2
1 6 5 .0
1820
1560
232
219
Y1 7 0 0 S7 G
1 8 .0
2 2 3 .0
1700
1470
294
278
Y1770S7
Y1860S7
1860
1600
When the force from pretensioned tendons is transferred to the concrete, the concrete and tendons tendon s shorten, reducing the prestress force. The tendon force should be calculated prior to transfer of prestress. In a post-tensioned member the tendons are normally stressed sequentially and the average loss due to elastic shortening is only 50% of the value for a pretensioned member. Calculate the initial prestressing force, Pm,0, by multiplying the force profile for one
tendon (see Figure 7.5) by the number of tendons and subtracting the elastic loss.
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7.8.1.3
Te nd ndon on forc e p rofi rofille – Final forc force e ( Pm, ) ∞
The tendon force will reduce with time due to relaxation of the tendon and creep and shrinkage of the concrete. The loss due to relaxation depends on the tendon type and the initial stress in the tendon. For low relaxation strands this loss may be taken as 5% of the jacking force. The loss of force in the tendon due to creep and shrinkage is calculated by multiplying together the strain due to these effects, the elastic modulus of the tendon and the total area of the tendons. Creep and shrinkage strains depend on the type of concrete and its environment. In the absence of more specific data, the shrinkage strain may be obtained from Tables 7.9 and 7.10. The strain due to creep is proportional to the stress in the concrete and is calculated by dividing a creep coefficient by the 28-day elastic modulus of the concrete, i.e. Creep strain = (Creep coefficient / E c) x (stress in the concrete at transfer at the level of the tendons).
Table 7. 7.9 9 Elast Elastic ic modulus of conc concr rete Strength c lass C 30/ 37 C 35/ 45 3 0 .0 3 5 .0 f ck ( MP a ) 3 2 .0 3 3 .5 E c ( G P a )
C 40/ 50
C 50/ 60
4 0 .0
5 0 .0
3 5 .0
3 7 .0
Tabl ble e 7.10 Shr hrinka inkage ge strains for strength cla class ss C 35/ 35/45 45 Loc ocati ation on of Relative humidity Notional size 2 Ac/ u ( m m ) the member (%) G 1 50 H 6 00 In d o o rs
50
4 6 5 × 1 0 -6
360 × 10 -6
O u t d o o rs
80
2 8 5 × 1 0 -6
220 × 10 -6
Notes s-se c t io io n a l a re a o f c o n c re t e . a Ac is t h e c ro s sb u is t h e p e rim e t e r o f t h e c ro s ss-se c t io io n a l a re a o f c o n c re t e .
In the absence of more specific data, the creep coefficient can be obtained from Table 7.11. For unbonded tendons the creep strain should be the mean value averaged over the length of the tendon. Add together the losses due to relaxation, shrinkage and creep to give the long-term (timedependent) losses and subtract them from the initial force, P m,0 , to give the final prestressing force, Pm, . 3
Table 7.11 7.11 C ree eep p coe c oefffic icient ients s Age at loading (days)
Notional size 2 Ac/ u ( (m mm ) Indoors (RH = 50%) Outdoors (RH = 80%) 50 150 600 50 150 600
1
5 .5
4 .6
3 .7
3 .6
3 .2
2 .9
7
3 .9
3 .1
2 .6
2 .6
2 .3
2 .0
28
3 .0
2 .5
2 .0
1 .9
1 .7
1 .5
90
2 .4
2 .0
1 .6
1 .5
1 .4
1 .2
Notes
a Ac b u
is t h e c ro s s se c t io io n a l a re a o f c o n c re t e . is t h e p e rim e t e r o f t h e c ro s ss-se c t io io n a l a re a o f c o n c re t e .
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7.8. 7.8.1.4 1.4
Tend on spa c in ingg
The minimum clear horizontal distance between pretensioned tendons should not be less than twice the diameter of the tendon or the maximum size of the aggregate plus 5mm, nor less than 20mm. In post-tensioned construction, the minimum clear horizontal distance between ducts should not be less than the outside diameter of the sheath or 50mm. Where there are two or more rows the gaps between corresponding tendons or ducts in each row should be vertically in line. In members where internal vibration is being used the horizontal gaps should be wide enough to allow the passage of a poker vibrator. In pretensioned members, the clear vertical distance between tendons should not be less than twice the diameter of the tendon or the maximum size of the aggregate 10mm. In post-tensioned construction, the clear vertical distance should not be less than the outside diameter of the sheath or 40mm, nor less than the maximum size of the aggregate plus 5mm. When tendons are curved, the minimum clear spacing between tendons in the plane of curvature should be increased to prevent local failure of the concrete in accordance with Table 7.12.
Table 7.1 7.12 2 Minimum Minimum dist distanc nce e be bettween c ent entr ree-lines lines of duct ducts in pla plane ne of of c ur urva vattur ure e (mm) Radius of c ur urva vattur ure e of duct duct (m)
159
229
477
636
2
80
95
180
240
85
100
125
175
215
300
355
95
100
125
145
205
245
345
535
110
125
160
190
265
420
120
140
170
215
330
130
160
185
280
14
180
245
16 18
170
230 220
170
215
25
30
40
Ductt int Duc internal ernal dia diameter meter (mm) 45
50
55
60
75
80
100
1603
1908
2748
4351
Tendo endon n forc force e (kN)
4 6 8
916
1113
Ra d ii n o t n o rm a lly u se d
10 12
20
80
85
95
100
110
120
130
160
Notes a Th e Ta b le is is b a se d o n re re fe re n c e 3 2. 2. b Th e te n d o n fo fo rc e sh o wn is is th e m a xim u m n o rm a lly a v a ila b le fo r th e g iv e n si size o f duct.
c Wh e re t e n d o n p ro f ilile rs o r sp a c e rs a re p ro v id id e d in in th th e d u c t s, s, a n d t h e se a re o f a ty typ p e wh ic ic h wil will c o n c e n tra tra te th e ra d ia l fo rc e , th th e v a lu e s g iv e n in in th e Ta b le wi willl n e e d t o b e in c re a se d . If n e c e ssa ry re in fo fo rc rc e m e n t sh sh o u ld ld b e p ro v id id e d b e t w e e n t he h e d u c t s. s. fo r a g iv e n c o m b in a t io io n o f d u c t in t e rn a l d ia m e t e r a n d ra ra d iu s d Th e d ist a n c e fo
o f c u rv rv a t u re re sh o w n in in t h e Ta b le m a y b e re d u c e d in p ro p o rt rt io io n t o t h e t e n d o n
fo rc rc e w h e n t h is is is le ss t h a n t h e v a lu e t a b u la la t e d .
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7. 7.8. 8.2 2
P o st -t -t e ns nsiio ne d a nc ho ra g e s
7.8. 7. 8.2. 2.1 1
A nc hor horag ag e zones
In post-tensioned members the prestress force is transferred from the tendons to the concrete through anchorage assemblies. The anchorages are supplied as part of the prestressing system and will have been designed designed by the manufacturer manufacturer to limit the bearing bearing stress stress on the concrete to acceptable acceptable values, values, providing providi ng the requirement requirementss on concrete concrete strength, strength, spacing spacing and the length length of straight straight tendon tendon adjacent adjacent to the anchorage specified by the manufacturer are satisfied, see Section 6.4. The concentrated loads from the anchorages can induce the following tensile forces in the concrete member: i) Bursting forces behind the anchorages. These forces act normally to the line of the prestress force in all lateral planes. ii) Forces required to maintain overall equilibrium of the anchorage zone. iii) Spalling forces on the end face of the anchorage zone. Reinforcement to resist these forces should be designed at the ultimate limit state as described below.. At each point in the anchorage zone the area of reinforcement provided should be that below required for the most critical effect, i.e. i) or ii) or iii). The design force from each tendon, Pd , should be taken as equal to 1.2 x the jacking force. The resulting tensile forces should be resisted by reinforcement working at a stress G 300MPa in order to obviate the need to check crack widths. As well as tensile forces, significant compressive forces occur in anchorage zones and it is essential that the reinforcement is detailed to allow sufficient room for the concrete to be placed and properly compacted.
7.8.2.2
Bursting
The design bursting tensile force, F bst, can be derived from Table Table 7.13. For rectangular anchorages and/or rectangular end blocks, the bursting bu rsting force should be calculated in each of the two principal directions using the appropriate value of y / y y for each direction (see Figure 7.6), where y is p0 0 0 the half the side of the end block, y p0 is the half the side of the loaded area, and Pd is the design force in the tendon. Circular bearing plates should be treated as square plates of equivalent area.
Table 7.1 7.13 3 Design Design bursting tensile tensile forc forc es in anc nchorag horage e zones zones y p0/ y0
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
F bst/ Pd
0 .2 0
0 .1 8
0 .1 5
0 .1 3
0 .1 0
0 .0 8
Reinforcement to resist this force should be distributed in a region extending from 0.2 y0 to 2 y0 from the loaded face. The reinforcement should be provided in the form of closed hoops or spirals and be positi pos itione oned d as nea nearr as pos possib sible le to the oute outerr edg edgee of the lar larges gestt pris prism m whos whosee cros crosss sec sectio tion n is sim simila ilarr to and concentric with that of the anchor plate, having regard to the direction in which the load is spreading, and at least 50mm outside the edge of the anchor plate. Where spirals are provided as part of the
anchorage system additional reinforcement may still be required to resist the bursting forces.
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Anchorages y p0
*
y 0
y p0
y p0 y p0
*
y 0
=
*
y 0
=
*
y 0
Note
*Use the smaller of the two values for
y 0.
fin n iti tio o n o f y p0 a n d y0 f fo o r e n d b lo c ks Fig 7.6 De fi
7.8.2.3
O ve ral ralll e q uil uilibrium ibrium
Determine the tensile forces required to maintain overall equilibrium of the anchorage zone using strut-and-tie models. Separate models can be used when considering equilibrium in the horizontal and vertical directions, or a three dimensional model may be used. Construct the models by sketching the flow of forces within the anchorage zone and providing notional concrete struts to carry the compressive forces and ties to carry the tensile forces. Calculate the forces in the resulting truss by considering equilibrium. The model should be chosen to minimise the length of the ties and with the angles between the struts and ties not less than 45º and preferably approximately equal to 60º. Models for some common anchorage zone arrangements are shown in Figure 7.7. For more detailed information the engineer should refer to specialist texts. Reinforcement to resist the tensile forces should be distributed over a length of z/2 where it is adjacent to a free edge, see Figure 7.7(a), (c), (d) and (e). Where the tensile force occurs within the body of the member, as in Figure 7.7(b), the reinforcement should be distributed over a length equal to z, where z is defined in Figure 7.7. When tendons are to be stressed sequentially, overall equilibrium should be checked at
each stage as the tendons are stressed.
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P
~60º
P
P
~60º
h P
P
P
P
P
z
z
a)
b)
P1
45º
P1
P
~60º
Equal areas
P P
P P1
>45º
P
P
P
z
c)
z
d)
P1 P1 P P
2P P
2 z
e)
Notes
x depth of section ( h ).
a
Generally z
b
Similar principles can be applied to anchorage zones with inclined tendons.
8
Fig 7.7 S Stt ru ru t a n d t ie ie m o d e ls fo r t h e d e sig n o f a n c h o ra g e zo n e s
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7.8.2.4
Spalling 33
Effectively bonded reinforcement should be placed as close to the loaded face of the anchorage zone as cover requirements allow to resist a force of 0.04Pd in either direction. The reinforcement should be distributed as uniformly as possible over the end face. When the configuration of the anchorages is such that the prestressing force acts on an unsymmetrical prism see Figure 7.8 and d 1 > 2d 2, additional spalling stresses are set up and additional reinforcement should be provided close to the loaded face to carry a force equal to:
c m
d1 - d 2 3 0.2 P d1 + d 2 d
This reinforcement need only be provided in the plane of the unsymmetrical prism and not at right angles to it. 7.8.3 7.8. 3 Pos Postt-te te nsi nsio o ne d C o up le rs A coupler is an anchorage assembly which allows a tendon to be extended. It consists of two parts – an anchorage anchor age and the coupling assembly. The spacing and alignment of tendons at coupler locations should be in accordance with the prestressing system manufacturer’s recommendations. The zone behind the anchorage-side of the coupler should be designed in accordance with Section 7.8.2. The placing of couplers on more than 50% of the tendons at any cross-section should be avoided. Tendons which are not coupled at a section should not be coupled within 1.5m of that section.
Symmetrical prism d 2 Pd
Unsymmetrical prism d 1
Dim m e ns nsiio ns use use d in c a lc ul ulaa ti ting ng sp a lling fo rc e s Fig 7.8 Di
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7.9
The ne next xt steps
At this stage general arrangement drawings, including sections through the entire structure, should be prepared and sent to other members of the design team for comment, together with a brief statement of the principal design assumptions, e.g. imposed loading, weights of finishes, fire ratings and durability durability.. The scheme may have to be amended following receipt of comments. The amended design should form the basis for the architect’s drawings and may also be used for preparing material estimates for budget costing.
7.10 7.1 0
Reinf inforc orce ement estima imattes
In order for the cost of the structure to be estimated it is necessary for the quantities of the materials, including those of the prestressing tendons and reinforcement, to be available. Fairly accurate quantities of the concrete, brickwork, prestressing tendon size and length, and number of o f prestressing anchorages can be calculated from the layout drawings. If working drawings and schedules for the reinforcement are not available it is necessary to provide an estimate of the anticipated quantities. The quantities of ordinary reinforcement associated with prestressed concrete members can be estimated using the following methods.
Sla Sl a b s – Po Post st-te -tensione nsione d The area calculated in section 7.7.5.2, but not less than 0.15% of cross-sectional area longitudinally, and (h + b) A p f pk # 10 -5 kg per end block Where: h b A p f pk
is the depth of the end block in metres is the width of the end block in metres is the total area of prestressing tendons anchored within the end block in mm2, and is the characteristic strength of the tendons in MPa.
Bea Be a ms – Shea r links links Treat as unprestressed beam (refer to Section 4.10).
Bea ms – Post-t Post-te e ns nsione ioned d The area calculated in Section 7.7.5.2, but bu t not less than 0.15% (high yield) of cross-sectional area longitudinally,, and longitudinally (h + b) A A p f pk # 10 -5 kg per end block Where: h b A p f pk
is the depth of the end block in metres is the width of the end block in metres is the total area of prestressing tendons anchored within the end block in mm2, and is the characteristic strength of the tendons in MPa.
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When preparing the reinforcement estimate, the following items should be considered: • Laps and starter bars – A reasonable allowance for normal laps has been made in the previous paragraphs. It should however be checked if special lapping arrangements are used. • Architectural features – The drawings should be looked at and sufficient allowance made for the reinforcement required for such ‘non-structural’ features. • Contingency – A contingency of between 10% and 15% should be added to cater for some changes and for possible omissions.
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Referenc eference es
1 2 3 4 5 6 7
8 9 10 11
12
13 14 15 16 17
BS EN 1992-1-1: 2004: Eurocode Eurocode 2: Design of concr concrete ete structur structures, es, Part 1-1: General rules and rules for buildings. London: British Standards Institution, 2004 BS EN 1992-1-2: 2004: Eurocode Eurocode 2: Design of concr concrete ete structur structures, es, Part 1-2: General rules – Structural fire design. London: British Standards Institution, 2005 BS 8500 (2 parts): Concrete. Complementary British Standard to BS EN 206-1. London: British Standards Institution, 2002 British Precast. Euro European pean manual for preca precast st concr concrete ete. Leicester: British Precast (due for publication 2006) BS EN 1998 (6 parts): Eur Eurocod ocodee 8: Desig Design n of struc structur tures es for earth earthquak quakee re resista sistance nce. London: British Standards Institution, 2005/2006 (parts 2, 3, 4 and 6 not yet published) BS EN 1997-1: 2004: Eurocode Eurocode 7: Geotechnical design – general rules. London: British Standards Institution, 2004 BS EN 1992-3: 2006: Euroco Eurocode de 2: Design of concr concrete ete structur structures, es, Part 3: Liquid retaining and containment structures. London: British Standards Institution, 2006 (not yet published) BS EN 1990: 2002: Euroc Eurocode: ode: Basis of structural design. London: British Standards Institution, 2002 Adams, S. Practical buildability. London: CIRIA; Butterworths, 1989 (CIRIA Building Design Report) Construction (Design and Management) Regulations 1994. SI 1994/3140 (amended by Construction (Design and Management) (Amendment) Regulations 2000. SI 2000/2380) Great Britain. Office of the Deputy Prime Minister Minister.. The Building Regulations 2000: Approved Appr oved document B – Fire safety. 2000 edition consolidated with 2000 and 2002 amendments. London: The Stationery Office, 2002 BS EN 1991-1-1: 2002: Eurocode Eurocode 1: Actions on structur structures es, Part 1-1: General actions – Densities, self-weight, imposed loads for buildings. London: British Standards Institution, 2002 BS EN 1991-1-3: 2003: Eurocode Eurocode 1: Actions on structur structures, es, Part 1-3: General actions – Snow loads. London: British Standards Institution, 2003 BS EN 1991-1-4: 2005: Eurocode Eurocode 1: Actions on structur structures es, Part 1-4: General actions – Wind loads. loads. London: British Standards Institution, 2005 BS EN 1991-1-2: 2002: Eurocode Eurocode 1: Actions on structur structures es, Part 1-2: General actions – Actions Actions on structures structures exposed to fire. London: British Standards Institution, 2002 BS EN 1991-1-5: 2003: Eurocode Eurocode 1: Actions on structur structures es, Part 1-5: General actions – Thermal actions. London: British Standards Institution, 2004 BS EN 1991-1-6: 2005: Eurocode Eurocode 1: Actions on structur structures es, Part 1-6: General actions – Actions during execution. London: British Standards Institution, 2005 (not yet published)
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18 19 20
21 22 23
24 25 26 27 28 29 30 31 32 33 34
BS EN 1991-1-7: 2006: Eurocode Eurocode 1: Actions on structur structures, es, Part 1-7: General actions – Accidental Accidental actions. London: British Standards Institution, 2006 (not yet published) Concrete Centre. Worked examples for the design of concrete buildings to Eurocode 2. Camberley: Concrete Centre, 2006 (not yet published). Concrete Society Society.. Concrete industrial ground floors: a guide to their design and construction. 3rd ed. Crowthorne: Concrete Society, 2003 (Concrete Society Technical Report 34) Construction Industry Research and Information Association. Water-resisting basement construction:: a guide. London: CIRIA, 1995 (CIRIA Report 139) construction BS 8102: 1990: Code of Practice for prot protection ection of structur structures es against water from the ground. London: British Standards Institution, 1990 Building Research Establishment. Sulfate and acid resistance of concrete in the ground . Watford: Construction Research Communication, 1996 (BRE Digest 363; superseded by BRE Special Digest 1, Concrete in aggressive ground , 1st ed 2001, 2 nd ed 2003, 3 rd ed 2005) Great Britain. Office of the Deputy Prime Minister Minister.. The Building Regulations 2000: Approved Appro ved document A – Structure. Structure. 2004 ed. London: The Stationery Office, 2004 BS 4449: 4449: 2005 2005:: Steel for the reinf reinfor orcemen cementt of conc concre rete te – Welda eldable ble re reinfo inforc rcing ing steel – Bar Bar, coil and decoiled pro product. duct. Specification. London: British Standards Institution, 2005 BS 4483: 2005: Steel fabric for the reinf reinforcemen orcementt of concrete. Specification. London: British Standards Institution, 2005 Concrete Society Society.. Post-tensioned concrete floors: design handbook . 2nd ed. Camberley: Concrete Society, 2005 (Concrete Society Technical Report 43) BS 5896: 1980: Specification for high tensile tensile steel wire and strand strand for the prestressing prestressing of concrete. London: British Standards Institution, 1980 BS EN 10138: Prestressing steels , British Standards Institution, London (publication anticipated in 2007) CONSTRUCT. National Structural Concr Concrete ete Specification Specification for building building construction. 3rd ed. Camberley: Concrete Society, 2004 Concrete Society Society.. Durable bonded bonded post-tensioned post-tensioned concr concrete ete bridges bridges. 2nd ed. Crowthorne: Concrete Society, 2002 (Concrete Society Technical Report 47) McLeish, A. Bursting stresses due to pres prestressin tressing g tendons in curved ducts, Proc. ICE , Part 2, 79, Sept 1985, pp605-615 Clarke, J.L. A guide to the design of anchor blocks for post-tensione post-tensioned d pres prestressed tressed concrete. London: CIRIA, 1976 (CIRIA Guide 1) BS EN 206-1: 2000: Concrete. Concrete. Specification, performance, production production and conformity. London: British Standards Institution, 2000
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Ap Appe pendix ndix A Des Design ign da datta
Design data should include: • General description, intended use, unusual environmental conditions • Site constraints • Design assumptions • Stability provisions • Movement joints • Loading • Fire resistance • Durability • Soil conditions and foundation design • Performance criteria • Materials • Ground slab construction • Method statement assumed in design • Quality plan • Method of analysis • Computer programs used • Responsible designer • Responsible approver • Health and safety plan • Risk analyses • Other data.
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App ppe endix B Du Dur rabilit bility y
Environmental conditions are classified according to Table B.1, based on BS EN 206-1 34.
Table B.1 B.1 Expo xpos sure class c lasses es rela elatted to envir environment onmenta al condit conditions ions in ac c ordanc ordance e with BS EN 206-1 206-1 Class Des esc c ription of the envi envir ron onm men entt designation
Infor Inf orm mat atiive exam exampl ples es wher ere e exposure classes may occur
1 No ris risk k of c orrosion or attac k X0
Fo r c o n c re t e w it h o u t
C o nc re te insi nsid d e b ui uilld ing s with with ve ry
re in fo fo rc rc e m e n t o r e m b e d d e d
lo w a ir hu m id ity
m e t a l: a ll e xp o s u re re s e xc e p t w h e re t h e re is fre e ze / t h a w , a b ra r a sio n o r c h e m ic ic a l a t t a c k Fo r c o n c re te wi with th re in fo fo rc rc e m e n t o r e m b e d d e d m e ta l: v e ry d ry ry
2 C or orr rosi osion on indu induc c ed by carbonat carbonation ion XC 1
Dry o r p e rm a n e n t ly w e t
C o n c re re te t e in in sid e b ui u ild in in g s w it h lo w a ir ir hu m id ity C o n c re t e p e rm a n e n tl t ly su b m e rg e d in w a t e r
XC 2
We t , ra re ly d ry
C o n c re t e su rfa c e s su b je c t t o lo n g t e rm w a t e r c o n ta ta c t Ma n y fo u n d a t io io n s
XC 3
M o d e ra t e h u m id it y
C o n c re t e in sid e b u ild in g s w it h m o d e ra te o r h ig ig h a ir h u m id ity Exte rn a l c o n c re te sh e lte re d fro m ra in
XC 4
C y c lic w e t a n d d ry
C o n c re t e su rfa c e s su b je c t t o w a t e r c o nta c t, no t withi within n e xp o sur uree c la ss XC2
3 C or orr rosi osion on indu induc c ed by chlor chlorides XD1
M o d e ra t e h u m id it y
C o n c re t e su rfa c e s e xp o se d t o a irb o rn e c h lo lo rid rid e s
XD2
We t , ra re ly d ry
Sw im m in g p o o ls C o n c re t e c o m p o n e n ts t s e xp o se d t o ind ust ustrria l wa te rs c o nta ini ning ng c hl hlo o rid e s
XD3
C y c lic w e t a n d d ry
P a rt s o f b rid g e s e xp o se d t o sp ra y c o n t a in in in g c h lo lo ri rid e s Pavements
C a r p a rk sla b s
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B.1 Expo xposu sur re class c lasses es rela elatted to envir environment onmenta al condit conditions ions in ac c ordanc ordance e Table B.1 with BS EN 206-1 206-1 Class Des esc c ription of the envi envir ron onm men entt Infformat In atiive exam exampl ples es wher ere e designation exposur exposu re c las lass ses may may oc occ c ur 4 C orrosion induc induced ed by chlor c hloride ides s from sea sea wat water XS1
Exp o se d to to a ir irb o rn e sa sa lt lt b ut u t n o t St ru ru c t u re re s n e a r t o o r o n t h e c o a st in d ir ire c t c o n t a c t w itit h se a w a t e r
XS2
P e rm a ne n e n t ly su b m e rg rg e d
P a rt rt s o f m a ri rin e st ru c t u re s
XS3
Tid a l,l, sp la la sh s h a n d sp sp ra ra y zo ne ne s
P a rt rt s o f m a ri rin e st s t ru c tu t u re s
5 Free eeze/ ze/ thaw attac k XF1 XF2
M o d e ra ra te t e w a te t e r sa tu t u ra ti t io n ,
Ve rt ic ic a l c o n c re t e su su rf rfa c e s e xp o s e d
w it it h o u t d e -ic in g a g e n t
to ra ra in a n d fre e zin g
M o d e ra ra te t e w a te t e r sa tu t u ra ti t io n ,
Ve rt ic ic a l c o n c re t e su rf rfa c e s o f ro a d
w it it h d e -ic in g a g e n t
st ru ru c t u re re s e xp o s e d t o fr fre e zin g a n d a irb o rn r n e d e -ic in g a g e n t s
XF3 XF4
Hig h w a t e r sa t u ra t io n, n , w it h o u t
Ho riz rizo n ta l c o n c re te su rf rfa c e s
d e -ic in g a g e n ts ts
e xp o s e d t o ra ra in a n d fre e zin g
Hig h w a te t e r sa tu t u ra ti t io n w it h d e -
Ro a d a n d b rid g e d e c ks e xp o se d t o
ic in g a g e n ts t s o r se a w a t e r
d e -ic in g a g e n ts ts C o n c re t e su s u rf rfa c e s e xp o se s e d t o d ire c t sp ra y c o n t a in in in g d e -ic in g a g e n t s a n d fre e zin g Sp la sh zo zo ne o f m a rine str truc uc tur turee s e xp o s e d t o fr f re e zin g
6 C hemi hemic c al at atttac k XA1
Slig ht h t ly a g g re re ss ssiv e c h e m ic ic a l
Na t u ra l so ils a n d g ro u n d w a t e r
e n vi v iro n m e n t a c c o rd rd in g to BS EN 20 6-1 34, Ta b le 2 XA2
Mo d e ra te t e ly ly a g g re ss ssiv e c he h e m ic a l Na t u ra l so ils a n d g ro u n d w a t e r e n v iriro n m e n t a c c o rd rd in g to BS EN 206-1 34, Ta b le 2
XA3
Hig hl h ly a g g re ss ssiv e c h e m ic a l
Na t u ra l so ils a n d g ro u n d w a t e r
e n vi v iro n m e n t a c c o rd rd in g t o BS EN 206-1 34, Ta b le 2
The requirements for durability in any given environment are: i) an upper limit to the water/cement ratio ii) a lower limit to the cement content iii) a lower limit to the nominal cover to the reinforcement iv) v)
good compaction adequate curing, and
vi)
good detailing.
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For a given value of nominal cover (expressed as minimum cover plus an allowance for deviation, Dcdev , see 5.2.2.2) Table B.2 (50 years) and Table B.3 (100 years) give values of concrete class, the maximum water cement ratio i) and the minimum cement content ii), which, in combination, will be adequate to ensure durability for various environments. As i) and ii) at present cannot be checked by methods that are practical for use during construction, the concrete class strengths given are those that have to be specified in the UK so that requirements i) and ii) are satisfied. For frost resistance the use of air entrainment of the concrete should be considered; however the effects of air entrainment on the concrete properties should be taken into account. The concrete class strengths quoted in Tables B.2 and B.3 will often require cement contents that are higher than those in the Table. The potential problems of increased shrinkage arising from high cement and water contents should be considered in the design. For situations not covered by Table B.1 reference should be made to BS 8500 3 and associated guidance.
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The notes below apply to Tables B2 and B3. The Tables give recommendations for normal weight concrete quality for selected exposure classes and cover to reinforcement for a given working life and maximum aggregate size.
N otes to Ta Ta b le s B.2 B.2 and a nd B.3 a
Where W here it is specified that only a contractor with a recognised quality system shall do the work (e.g. member of SpeCC, the Specialist Concrete Contractors certification scheme) ∆cdev = 5mm, otherwise ∆cdev = 10mm.
b
The cover to the main reinforcement should not be less than the bar size. The
c
For F or exposure conditions XF1 a minimum concrete grade C28/35 C28 /35 (w/c ratio 0.6, minimum cement content 280kg/m3) should be used. For exposure conditions XF2 a minimum concrete grade C32/40 (w/c ratio 0.55, min cement content 300kg/m 3) should be used. Minimum concrete grades may be reduced if air entrained.
d For specified. For exposure The conditions and obliged XF4 freeze/thaw aggregates should be producerXF3 is then to conformresisting to the requirements given in BS 8500-13 (Clause 4.3).
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t n e m e c r o f n i e r o t r e v o c d n a s e s s a l c e r u s o p x e d e t c
v e d
c ∆ + 0 5
< < < <
< < < <
) 3 m e t / e g r K c ( n t c o < < n ∆ c < < e t < < e + d l < < n 5 b 4 e o c a c r c o n o i l p c f i n < i t < p a a b ∆ e < < r < < n t + i < o < b e r n 0 t e 4 e m h m d o e i l c w e c r t r c p < < o e ∆ p < < o f e t r n + a < < < < n c i 5 t e n e o 3 n o r m o s e c t i c d r c e < < . e e ∆ r < < t v n u < i < a o + s < < m n c 0 o < , i g l 3 p x o a i e t s n e i , 0 0 a s < 0 6 3 r d c i 3 / , C m ∆ o h < t c t n N 5 2 l e e / R z 5 + t < s i 2 e r 6 l s < a . w 5 r C o 0 a h . 2 t o e v x f t i a u d y a t q e < g i m l e , e c d < a r s r ∆ – < u g s o + n e < a q g l < 0 m a c 2 e t m h t e o r m g , 0 5 c 5 u c n 4 2 e 2 n m c R / 2 C e i r , – o x t ∆ 0 0 R 2 c a S r 7 + . v e d
v e d
v e d
v e d
v e d
v e d
< < < <
< < < <
< < < <
< < < <
< < < <
, 0 5 6 4 / 3 , 5 5 3 4 . C 0
, 0 5 4 3 / 3 , 8 0 2 5 . C 0
, 0 0 4 3 / 3 , 5 0 2 5 . C 0
< < < <
< < < <
< < < <
< < < <
< < < <
, 0 0 8 5 / 3 , 0 0 4 4 . C 0
, 0 0 6 4 / 3 , 2 5 3 4 . C 0
, 0 5 6 3 / 3 , 8 5 2 4 . C 0
< < < <
< < < <
, 0 5 2 3 / 3 , 8 5 2 5 . C 0
, 0 0 2 3 / 3 , 5 5 2 5 . C 0
, 0 5 2 2 / 3 , 0 5 2 5 . C 0
, 0 5 8 5 / 3 , 5 5 4 3 . C 0
, 0 5 8 4 / 3 , 5 0 3 4 . C 0
, 0 0 8 4 / 3 , 2 0 3 4 . C 0
, 0 0 6 0 3 3 / 2 , 5 5 C R 2 6 r . C 0 o
, 0 5 0 3 / 3 , 8 0 2 6 . C 0
, 0 0 4 4 / 3 , 2 0 3 5 . C 0
, 0 5 4 3 / 3 , 8 0 2 5 . C 0
, 0 0 4 3 / 3 , 5 0 2 5 . C 0
–
–
–
, 0 5 8 5 3 3 / 2 C , 8 0 R 2 6 r . o C 0
, 0 0 2 4 / 3 , 2 5 3 5 . C 0
, 0 0 8 5 / 3 , 0 0 4 4 . C 0
, 0 5 8 4 / 3 , 5 0 3 4 . C 0
, 0 0 8 4 / 3 , 2 0 3 4 . C 0
–
–
–
, 0 0 0 0 4 4 / 3 , 2 5 C R 3 5 r . C 0 o
, 0 0 6 5 / , 0 3 4 5 4 . C 0
–
–
–
–
–
–
, 0 0 4 0 5 5 / 3 C , 0 5 R 4 4 r . o C 0
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
v e d
t C 0 o 5 h m 1 g i t . b a e m n s l l m e m w e l l 0 m l o A A e c p y / a 2 d C t m r n o a t s n e e n r f y i r l w o o i f d t y i l s g t y d l n i n n n e k t e o o r i t o e n c l a w a r p e d o r m y m r n u d o r e s e e o C D p d m p n x m 0 1 E e t X C o n X c i e r n R a o e i t y a d i n o n B 2 . 0
l l A
t l p l e B A c V x I e
, , C l I S l A A I B P I , I S R
d y n r a d t y l e e e t e y y r t w t t a a i i r r a r c d i d e i e i , d m l d m t c o u y y e r o u W M h C d M h 2 3 4 1 C C C D X X X X
e d e d i n i n o i g e n s
A B , , I I I I C S A , V - P I I , V B B - I B I , I S R I I
y r d y l e r a r , t e W 2 D X r t e
A B I I I I , V V , B - I B I I
d n a t e w c i l c y y r C d 3 D X
5 e a l b r a o T f
d e s d d i r c o u i r a l o r u o m w l r l a h d o c x h o r n C i c e c f e s
k s o e s b i r r c r u o r o a d o n c N C i
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t n e m e c r o f n i e r o t r e v o c d n a s e s s a l c e r u s o p x e d e t c
v e d
c ∆ + 0 5
) 3 m / g K ( t c n ∆ e t l e + n b 5 o 4 c a c n o i l p c i t ∆ a p n a b t + i b e r n 0 e e 4 m h m o c w e c r t r c o e o ∆ f t e r n + n c i 5 e n e r 3 o m o e c t c d r c . e e ∆ t v n i a o + m n c 0 , i g l 3 o s a i t e i n a r d c m ∆ c t n o l e e z / + s i N e l 5 r s w . a 2 o e v f t x i a u y a t q g i l e m c , a r s e ∆ r s u g o + a q g l 0 a c 2 e t h t e r m u c g n m n c e i r o x t ∆ c a S +
v e d
v e d
v e d
v e d
< < < <
< < < <
< < < <
< < < <
< < < <
< < < <
, 0 0 8 5 / 3 , 0 0 4 4 . C 0
, 0 5 4 3 / 3 , 8 0 2 5 . C 0
, 0 0 4 3 / 3 , 5 0 2 5 . C 0
< < < <
< < < <
< < < <
< < < <
< < < <
< < < <
, 0 5 8 5 / 3 , 5 5 4 3 . C 0
, 0 0 6 4 / 3 , 2 5 3 4 . C 0
, 0 5 6 3 / 3 , 8 5 2 4 . C 0
, 0 5 4 4 / 3 , 5 0 3 5 . C 0
, 0 0 4 4 / 3 , 2 0 3 5 . C 0
, 0 0 2 3 / 3 , 5 5 2 5 . C 0
, 0 5 2 3 / 3 , 8 5 2 5 . C 0
, 0 0 2 3 / 3 , 5 5 2 5 . C 0
, 0 5 2 2 / 3 , 0 5 2 5 . C 0
–
, 0 5 8 4 / 3 , 5 0 3 4 . C 0
, 0 0 8 4 / 3 , 2 0 3 4 . C 0
, 0 0 6 5 / 3 , 0 5 4 4 . C 0
, 0 5 6 4 / 3 , 5 5 3 4 . C 0
, 0 5 4 3 / 3 , 8 0 2 5 . C 0
, 0 0 4 4 / 3 , 2 0 3 5 . C 0
, 0 5 4 3 / 3 , 8 0 2 5 . C 0
, 0 0 4 3 / 3 , 5 0 2 5 . C 0
–
–
–
, 0 0 8 6 / 3 , 0 5 5 3 . C 0
, 0 5 8 5 / 3 , 5 5 4 3 . C 0
, 0 5 8 4 / 3 , 5 0 3 4 . C 0
, 0 0 8 5 / 3 , 0 0 4 4 . C 0
, 0 5 8 4 / 3 , 5 0 3 4 . C 0
, 0 0 8 4 / 3 , 2 0 3 4 . C 0
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
B V I , B I
, , C A I S I B P I , I S R
A I I I , V B I I
B V I , B I
, , C A I S I B P I , I S R
A I I I , V B I I
B V I , B I
v e d
v e d
v e d
t 5 h m 1 g i . t b a I e m n , , C A I s I e m S w A m e , I P 0 I m l o B V , I S R I B e c p I y a 2 / d C t I m r n o a t t s n e u c n r f a i b t l o o i s f t t i l n o s g d n a c i n s n t k o o r i e c t o c n e a w r i r e o d d r n u b d r o s i e e o A n d m p n x 1 m E e S t o n X c i e r R a e r y t e d i n o B 2 . 0
y r d y l e r a r , t e W 2 S X
d n a h s s e a n l o p s z , y l a a r d i T p s 3 S X
5 e a l b r a o T f
a e s w c r u o r a d e n o S i c
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
) 3 t n c m ∆ / e g + m K 0 ( e 5 t c r n o e f t e c n i n l ∆ b e o r + c a 5 c o t n i 4 l r o p i e v t a p b n a o t c i ∆ e c b r n + e e 0 d m n m 4 o h a c w e s r t r e c e o o c s f t e s r n ∆ n i + c a l e e n 5 r c m o o 3 e e c t r c d r u s . e e c n o v ∆ i t a o + p m n c 0 x , i e g l 3 o a i d t s n e i e a t r d m c c t + o ∆ l e i e z / c n e N s w e l 5 s e . a 2 r t x i v o a a u f y g c m q e t i ∆ r , e l g s + a g s r o 0 u a 2 q a l c e m h t u t e c r m g ∆ c i n + n x e r 5 o a t 1 c m S t . t h m n b a e m s g i m m o e e 0 p e c t y w 2 l a d n C / s m r a n o f e o i n i t l i r d o g f n n i o s k n r c o o i e t w r a u s d d o n e p e d x n m e E t m n o i c r e a R e y v e d
v e d
v e d
v e d
v e d
v e d
v e d
v e d
3 . 0 B
e t e r c n o c d e c r o f n i e r o t d e i l p p a t o n s i e r u s o p x e s i h t a h t d e d n e m m , o 5 c 2 / e 0 R 2
< < < <
< < < <
< < < <
< < < <
< < < <
, 0 5 8 3 / 2 , 8 0 2 6 . C 0
5 3 C R r o
< < < <
< < < <
0 4 C R r o
< < < <
< < < <
< < < < <
< < < <
0 , 0 4 / 3 , 2 5 3 5 . C 0 r , o 5 0 4 / 2 5 3 , 3 0 C 5 . 0 , 0 0 4 5 / 3 , 0 5 4 4 . C 0
< < < <
, 0 0 6 3 2 / 5 , 2 5 6 . C 0
< < < < <
–
–
–
–
l l A
t p l l e B A c V x I
0 4 2 , 0 7 . C 0
l l A
5 2 C R r o
l l A
t e y r w d y l t y l n e t e e n l p r a m m o r o y r e C D p 1 0 C X X n o i t a d i n n o
5 4 C R 0 5 C R r o
0 3 C R r o
–
e y r d y l e r a r , t e W 2 C X
d n a t e e t y a i w r t c e d i i d m l o u c y y r M h C d 3 4 C C X X
s l t t e e a e e y l t , s t t m e d s a u s o n ‘ b e f r l e i m s d n s o i l e i n i u d i e a e f t i o s l m n s s s h s o f e g e s n h t i r c o c e o k t a e e u s p r o r h a y b t w o e e s 0 l h 5 a h t a d t e r r f e t o d o v s f l o i u e g g e d o t n o g i e e h r s r d t g e y c n y u s v t r n s a a i l o t o i t s c a r s i , t u c e s s e d e a q h c e h v e i e t n t t l u n d n e s g n e i a r n c h t i h k t n a t a r r o e t h a t o e c d i t r h r w a o l o t e e e v h h r t t c n g a c a o c u s c n h i e r e t f i r e d t o l f n e e e i r e g h w c t n t t s i y e k a r o b e n o s v o m t r c i t w e u g c s e s e a h a n t t t r a n d s r i r o h o n f o f a f C c s h s a . e . g s m s s r n s i n c o i s i m a a c a t a , 5 l r a c b u e s 1 d e d e v e r e y r s e r n e u s t , m e c m w d o b o o a - n f r H e p y e m s x b . a a o s e - m t e e a c r e S e e s r r c c X a r d u n s f e i o d c f s o o i n a i e n p b a n e d c x e r e s D o r a e o r p S r X d t X a e t p r s s c d e e i y s e s s v e u 0 e r e d n o h 5 a s T o s c r o r t a g t . p D f o X s d n n o i n n i n n e t o a s e i a m e ’ s v i i t s e r v d o e c r r e u c a a s g r
135
k s i r o N
1 e a l b r a f o T
136
o e c b r u a d n C i
t i n o q e y . f e n 0 g . i d 0 e e r a 1
s o r r o c
e p c t e e l o h e N T s
r e v o c
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
Ap Appe pendi ndix xC
C olu olumn mn desi design gn c har hartts
This Appendix contains design charts for circular columns with d/h = 0.6, 0.7, 0.8 and 0.9, and rectangular columns with d/h = 0.8, 0.85, 0.9 and 0.95. 1.4 M=Nh /20
Ratio d/h = 0.6 1.2 A s
h
d
1.0
ρ
f
y k / f c k
0.8 N/h2f ck 0.6
0.4
ρ
= 1 . 0
0 . 9 0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 0 2
= 4 As / π h2
As = total steel area
0 1 . 0 . 1 0.2
0 0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
M/h3f ck 1.4 M=Nh /20
Ratio d/h = 0.7
1.2 A s
h 1.0 ρ f
0.8 N/h2f ck 0.6
0.4
0.2
y k / f c k
0 . 9 0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 0 . 0
= 1 . 0
ρ
= 4 As / π h2
As = total steel area
d
0.28
0 0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
M/h3f fck
137
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
1.4 M=Nh /20
Ratio d/h = 0.8
1.2 A s
h
d
1.0 ρ
f
y k f / c k =
0 . 9 0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1
0.8 N/h2f ck 0.6
0.4
1 . 0
= 4 As / π h2
ρ
As = total steel area
0 . 0 0.2
0 0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
M/h3f ck
1.4 M=Nh /20
Ratio d/h = 0.9
1.2 A s
h
d
ρ
f
1.0
y k / f c k =
0 . 9 9 0 . 8 0.8
1 .0 ρ
0 . 7
As = total steel area
0 . 6
N/h2f ck
= 4 As / π h2
0 . 5
0 . 4
0.6
0 . 3 0 . 2
0 . 1
0.4
0 . 0 0.2
0 0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
M/h3f ck
138
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
1.4 M=Nh /20 M=Nh /20
Ratio d/h = 0.8 1.2 A s /2 h 1.0
A s f y k / b h f c k = 0 . 9 1 0 . 0 . 8 0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 0 . 0
0.8 N/bhf ck
0.6
0.4
d
A s /2
b
0.2
0 0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
M/bh2f ck
1.4 M=Nh /20 M=Nh /20
Ratio d/h = 0.85 1.2 A s /2 h 1.0
0.8 N/bhf ck
0.6
0.4
0.2
0
A s f y k / b h c f 0 . 9 k = 1 . 0 . 8 0
0 . 7 0 . 6 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 0 . 0
A s /2
b
d
0.50
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
M/bh2f ck
139
IStr truc uc tE Ma nua l for the d e sig n o f c on c re te b ui uilld ing st strruc tur turee s to to Eur uroc oc o d e 2
1.4 M=Nh /20 M=Nh /20
Ratio d/h = 0.9 1.2 A s /2 h
A s f y k / b h f c
1.0
d
A s /2
k
0 . 9 0 . 8 0 . 7 0 . 6
0.8 N/bhf ck
= 1 . 0
b
0 . 5 0 . 4
0 . 3 0 . 2 0 . 1
0.6
0 . 0 0.4
0.2
0 0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
M/bh2f ck
1.4 M=Nh /20 M=Nh /20
Ratio d/h = 0.95 1.2 A s /2
A s f f y k / b h f c k = 0 . 0 1 . 0 0 . 8 9 0 . 7 0 . 6 0 . 5 0 . 4
1.0
0.8 N/bhf ck
0 . 3 0 . 2
0.6
0 . 1
0 . 0 0.4
0.2
0
h
A s /2
b
d
0.50
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
M/bh2f ck
140
IStr truc uc tE Ma nua l fo r the d e sig n o f c on c re te b ui uilld ing str truc uc tur turee s to to Eur uroc oc od e 2
App ppe endix D Streng engtth and de defform orma ation prope proper rties of c onc oncr rete Table D.1 Strength and de deformation propert properties ies of conc c oncr rete Analytic Analyt ica al rela elattion/ explanation
Streng engtth cla c lass sses for c onc oncr rete f ck (MP (M Pa )
12
16
20
25
30
35
40
45
50
f ck,cube (MP (M Pa )
15
20
25
30
37
45
50
55
60
f cm (MP (M Pa )
20
24
28
33
38
43
48
53
58
fcm = f ck + 8
f ctm (MP (M Pa )
1 .6
1 .9
2 .2
2 .6
2 .9
3 .2
3 .5
3 .8
4 .1
fctm = 0.30fck (2 /3) G C 50/60
f ctk, 0.05 (MP (M Pa )
1 .1
1 .3
1 .5
1 .8
2 .0
2 .2
2 .5
2 .7
2 .9
ctk, 0.95 f ctk, (MP (M Pa )
2 .0
E cm ( G Pa Pa )
(MPA)
fctk, 0.05 = 0.7f ctm
5% fr fraa c ti tille
27
2 .5
29
2 .9
30
3 .3
31
3 .8
33
4 .2
34
4 .6
35
4 .9
36
5 .3
fctk, 0.95 = 1.3f ctm 95% fr fraa c ti tille
37
f cm E cm = 22 10
; E
0.3
( f cm in MPA) MPA )
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