Worked Examples to Eurocode 2.pdf

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Worked Examples to Eurocode 2 25 February 2010 Amended 18 January 2012

Revisions required to Worked Examples to Eurocode 2 due to Amendment 1 to NA to BS EN 1992-1-1:2004 dated Dec 2009.

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Amended 18/1/2012 to illustrate 40K limit on l/d according to Table NA.5 Note 6

Page Where Old text 37/38 3.1.6 Allowable l/d = N u K u F1 u F2 u F3 where N = 25.6 (U = 0.41%, fck = 30) K = 1.0 (simply supported) F1 = 1.0 (beff/bw = 1.0) F2 = 1.0 (span < 7.0 m) F3 = 310/Vs 1.5 where Vs = Vsn (As,req/As,prov) 1/G where Vsn | 242 MPa (From Concise Figure 15.3 and gk/qk = 1.79, \2 = 0.3, Jg = 1.25) G = redistribution ratio = 1.0 ? Vs | 242 u 594/645 = 222 ? F3 = 310/222 = 1.40 ? Allowable l/d = 25.6 u 1.40 = 35.8 Actual l/d = 4800/144 = 33.3 ? OK Use H12 @ 175 B1 (645 mm2/m) 38

3.1.7

By inspection, OK However, if considered critical: V = 29.5 kN/m as before VEd = 29.5 ȭ 0.14 u 12.3 = 27.8 kN/m vEd = 27.8 u 103/144 u 103 = 0.19 MPa vRd,c = 0.53 MPa

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Revised text Allowable l/d = N u K u F1 u F2 u F3 where N = 25.6 (U = 0.41%, fck = 30) K = 1.0 (simply supported) F1 = 1.0 (beff/bw = 1.0) F2 = 1.0 (span < 7.0 m) F3 = As,prov /As,req 1.50 = 645/ 594 = 1.09 ? Allowable l/d = 25.6 u 1.09 = 27.9 Actual l/d = 4800/144 = 33.3 ? no good Try 33.3/27.9 x 654 = 784 mm2/m i.e. H12@140 (807 mm2/m) F3 = 807/ 594 = 1.36

? Allowable l/d = 25.6 u 1.36 = 34.8 (which is < 40K = 40) [Table NA.5 Note 6] i.e. > 33.3? OK Use H12 @ 140 B1 (807 mm2/m) By inspection, OK However, if considered critical: V = 29.5 kN/m as before VEd = 29.5 ȭ 0.14 u 12.3 = 27.8 kN/m vEd = 27.8 u 103/144 u 103 = 0.19 MPa U = 804/1000 x 144 =0.56% say 50% curtailed use 0.28% vRd,c = 0.54 MPa

Page 1 of 13

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42

3.2.6

F3 = As,prov /As,req 1.50 F3 = 310/Vs 1.5 = 645/ 639 = 1.01 where Allowable l/d = N u K u F1 u F2 u F3 Vs = (fyk/JS) (As,req/As,prov) (SLS = 23.5 u 1.3 u 1.0 u 1.01 loads/ULS loads) (1/G) = 30.8 = fyd u (As,req/As,prov) u (gk + \2 Max. span = 30.8 u 144 = 4435 mm, qk)/(JGgk + JQqk) (1/G) i.e. < 5795 mm = (500/1.15) u (639/645) u [(5.9 ? No good + 0.3 u 3.3)/12.3] u 1.081 = 434.8 u 0.99 u 0.56 u 1.08 = 260 MPa F3 = 310/260 = 1.19 Note: As,prov/As,req d 1.50 Allowable l/d = N u K u F1 u F2 u F3 = 23.5 u 1.3 u 1.0 u 1.19 = 36.4 Max. span = 36.4 u 144 = 5675 mm, i.e. < 5795 mm ? No good Try H12 @ 150 B1 (754 mm2/m) Try H12 @ 125 B1 (904 mm2/m) Vs = 434.8 u 639/754 u 0.56 u 1.08 = 223 F3 = 310/223 = 1.39 Allowable l/d = 23.5 u 1.3 u 1.0 u 1.39 F3 = 904/639 = 1.41 = 42.5 Allowable l/d = 23.5 u 1.3 u 1.0 u 1.41 Max. span = 42.5 u 144 = 6120 mm, = 43.1 i.e. > 5795 mm OK Max. span = 43.1 u 144 = 6206 mm, ? H12 @ 150 B1 (754 mm2/m) OK i.e. > 5795 mm OK ? H12 @ 125 B1 (904 mm2/m) OK

43

3.2.7

F3 = As,req/As,prov 1.5 F3 = 310/Vs 1.5 = 502/ 465 = 1.08 where Vs = fyd u (As,req/As,prov) u (gk + \2 qk)/(JGgk + JQqk) (1/G) = (500/1.15) u (465/502) u [ (5.9 + 0.3 u 3.3)/12.3] u 1.03 = 434.8 u 0.93 u 0.56 u 1.03 = 233 MPa F3 = 310/233 = 1.33 Allowable l/d = N u K u F1 u F2 u F3 = 35.8 u 1.5 u 1.0 u 1.33 Allowable l/d = N u K u F1 u F2 u F3 = 71.4 = 35.8 u 1.5 u 1.0 u 1.08 Max. span = 71.4 u 144 = 10280 mm i.e. > = 58.0 5795 mm OK (which is < 40K = 40 x 1.5 =60) [Table NA.5 Note 6] Max. span = 58.0 u 144 = 8352 mm i.e. > 5795 mm OK

44

3.2.9

In Figure 3.4 H12@150

46

3.2.10a) Crack control As slab < 200 mm, measures to control cracking are unnecessary.

In Figure 3.4 H12@125 Crack control As slab < 200 mm, measures to control cracking are unnecessary.

1

The use of Table 15.2 from Concise Eurocode 2implies certain amounts of redistribution, which are defined in Concise Eurocode 2 Table 15.14. Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Page 2 of 13

However, as a check on end span: However, as a check on end span: Loading is the main cause of cracking, Loading is the main cause of cracking, ? use Table 7.2N or Table 7.3N for wmax = 0.4 ? use Table 7.2N or Table 7.3N for wmax = 0.4 mm and V = 241 MPa (see deflection check). mm and V = 241 MPa (see deflection check). Max. bar size = 20 mm Max. bar size = 20 mm or max. spacing = 250 mm or max. spacing = 250 mm ? H12 @ 150 B1 OK. ? H12 @ 125 B1 OK

46

End supports: effects of partial fixity

End supports: effects of partial fixity

Try H12 @ 450 (251 mm2/m) U-bars at supports

Try H12 @ 500 (226 mm2/m) U-bars at supports

3.2.10b) End span, bottom reinforcement Try H12 @ 300 (376 mm2/m) at supports

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49

51

End span, bottom reinforcement Try H12 @ 250 (452 mm2/m) at supports

3.2.10b) Supporrt B bottom steel at support iii For convenience use H12 @ 300 B1 (376 mm2/m)

Support B bottom steel at support

3.2.11

See A below

Figure 3.6

57/58 3.3.5b) Span A®®B: Deflection

For convenience use H12 @250 B1 (452 mm2/m) Span A® ®B: Deflection

F3 = 310/Vs 1.5 F3 = 310/Vs 1.5 where where Vs = (fyk/JS) (As,req/As,prov) (SLS Vs = (fyk/JS) (As,req/As,prov) (SLS loads/ULS loads) (1/G) loads/ULS loads) (1/G) = 434.8(523/628) [ (4.30 + = 434.8(523/628) [ (4.30 + 0.3 u 5.0)/13.38] (65.3/61.7$) 5.0)/13.38] (65.3/61.7$) = 434.8 u 0.83 u 0.70 u 1.06 = 434.8 u 0.83 u 0.43 u 1.06 = 267 MPa = 164 MPa F3 = 310/Vs F3 = 310/Vs = 310/267 = 1.16 = 310/164 = 1.89# but 1.50 therefore say 1.50 ? Permissible l/d = 22.8 u 1.3 u 0.8 u 0.93 u ? Permissible l/d = 22.8 u 1.3 u 0.8 u 0.93 u 1.16 = 25.6 1.50 = 33.0 Actual l/d = 7500/257 = 29.2 Actual l/d = 7500/257 = 29.2 ?no good ? OK Use 2 no. H20/rib (628 mm2/rib) Try 1H25 + 1H20/rib (805 mm2/rib) d = 254 mm; K = 0.028; z = 241 mm Asreq = 529 mm2 ? Vs = 434.8(529/805) [ (4.30 + 5.0)/13.38] (65.3/61.7$) = 434.8 u 0.66 u 0.70 u 1.06 = 213 MPa F3 = 310/213 = 1.45 Permissible l/d = 22.8 u 1.3 u 0.8 u 0.93 u 1.45 = 32.0 Actual l/d = 7500/254 = 29.5 ? OK Use 1H25 + 1H20/rib (805 mm2/rib)

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

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61

3.3.6b) Span B®C C ® : Deflection

Span B®C C ® : Deflection

F3 = 310/VS 1.5 F3 = 310/VS 1.5 where where Vs = (fyk/Js) (As,req/As,prov) (SLS loads/ULS Vs = (fyk/Js) (As,req/As,prov) (SLS loads/ULS loads) (1/G) loads) (1/G) = 434.8 u (474/628) [(4.30 + 0.3 u = 434.8 u (474/628) [(4.30 + 5.0) 5.0)/13.38](61.1/55.9) /13.38](61.1/55.9) = 434.8 u 0.75 u 0.43 u 1.09 = 434.8 u 0.75 u 0.70 u 1.09 = 153 MPa = 249 MPa F3 = 310/Vs F3 = 310/Vs = 310/153 = 2.03, say = 1.502 = 310/249 = 1.24 ? Permissible l/d = 26.8 u 1.5 u 0.8 u 0.77 ? Permissible l/d = 26.8 u 1.5 u 0.8 u 0.77 u 1.50 = 37.1 u 1.24 = 30.7 Actual l/d = 9000/257 = 35 Actual l/d = 9000/257 = 35 ? ? no good OK ?Use 2 H20/rib (628 mm2/rib) Try 1H25 + 1H20/rib (805 mm2/rib) d = 254 mm; K = 0.025; z = 241 mm Asreq = 480 mm2 ? Vs = 434.8(480/805) [ (4.30 + 5.0)/13.38] (61.1/55.9) = 434.8 u 0.60 u 0.70 u 1.09 = 199 MPa F3 = 310/199 = 1.56 but 1.50 Permissible l/d = 26.8 u 1.5 u 0.8 u 0.77 u 1.50 = 37.1 Actual l/d = 9000/254 = 35.4 ? OK Use 1H25 + 1H20/rib (805 mm2/rib) 65

3.3.10

69

3.3.10b) Support B (and C): bottom steel curtailment viii BA and BC To suit prefabrication 2 no. H20/rib will be curtailed at solid/rib interface, 1000 mm from BA (B towards A) and BC.

Support B (and C): bottom steel curtailment BA and BC To suit prefabrication 1 H20 + 1H25 /rib will be curtailed at solid/rib interface, 1000 mm from BA (B towards A) and BC.

69

3.3.10c) Laps At AB, check lap 1 no. H20 B to 2 no. H20 B in rib full tension lap: l0 = D1 D6 lb,rqd > l0,min where D1 = 1.0 (cd = 45 mm, i.e. < 3M) D6 = 1.5 (as > 50% being lapped) lb,rqd = (M/4) (Vsd/fbd) where M = 20 Vsd = 434.8 = 3.0 MPa as before fbd

Laps At AB, check lap 1 no. H20 B to 1 H20 B + 1H25 B in rib full tension lap: l0 = D1 D6 lb,rqd > l0,min where D1 = 1.0 (cd = 45 mm, i.e. < 3M) D6 = 1.5 (as > 50% being lapped) lb,rqd = (M/4) (Vsd/fbd) where M = 20 Vsd = 434.8 (bar assumed to be fully stressed) fbd = 3.0 MPa as before

65

3.3.10d) Figure 3.17

See C below

74

3.4.5b) F3 = 310/Vs 1.5 where

F3 = 310/Vs 1.5 where

Figure 3.15

See B below

2

Both As,prov/As,req and any adjustment to N obtained from Expression (7.16a) or Expression (7.16b) is restricted to 1.5 by Note 5 to Table NA.5 in the UK NA. Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

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Vs = Vsn (As,req/As,prov) 1/G

Vs = Vsn (As,req/As,prov) 1/G where where Vsn = (500/1.15) u (8.5 + 0.3 u 4.0) Vsn = (500/1.15) u (8.5 + 4.0) /16.6 = /16.6 = 254 MPa 327 MPa (or | 253 MPa (From Concise Figure 15.3 for Gk/Qk = 2.1, \2 = 0.3 and Jg = 1.25) G = redistribution ratio = 1.03 G = redistribution ratio = 1.03 Vs | 327 u (1324/1570)/1.03 = 267 ? ? Vs | 253 u (1324/1570)/1.03 = 207 ? F3 = 310/267 = 1.16 ? F3 = 310/207 = 1.50 ? Allowable l/d = 20.3 u 1.2 u 1.16 = 28.2 ? Allowable l/d = 20.3 u 1.2 u 1.50 = 36.5 Actual l/d = 9500/260 = 36.5 ?no good Actual l/d = 9500/260 = 36.5 ? OK Try H16 @100 (2010 mm2/m) and Use H20 @ 200 B1 (1570) F3 = As,prov /As,req 1.50 = 2010/ 1340 = 1.50 1.50 ? Allowable l/d = 20.3 u 1.2 u 1.50 = 36.5 Actual l/d = 36.5 ? OK Use H16@100B1 (2093 mm2/m) 78

3.4.7b) Allowable l/d = N u K u F1 u F2 u F3 Allowable l/d = N u K u F1 u F2 u F3 where where N = 26.2 (U = 0.40%, fck = 30) N = 26.2 (U = 0.40%, fck = 30) K = 1.2 (flat slab) K = 1.2 (flat slab) F1 = 1.0 (beff/bw = 1.0) F1 = 1.0 (beff/bw = 1.0) F2 = 1.0 (no brittle partitions) F2 = 1.0 (no brittle partitions) F3 = As,prov /As,req 1.50 F3 = 310/Vs = 1005/ 959 = 1.05 1.50 where Vs = Vsn (As,req/As,prov) 1/G where Vsn | 283 MPa (from Concise Figure 15.3 and Gk/Qk = 3.6, \2 = 0.3, Jg = 1.25) G = redistribution ratio = 1.08 ? Vs | 283 u (959/1005)/1.08 = 250 ? F3 = 310/250 = 1.24 ?Allowable l/d = 26.2 u 1.2 u 1.24 = 39.0 ?Allowable l/d = 26.2 u 1.2 u 1.05 = 33.0 Actual l/d = 5900/240 = 24.5 ? OK Actual l/d = 5900/240 = 24.5 ? OK Use H16 @ 200 B2 (1005 mm2/m) Use H16 @ 200 B2 (1005 mm2/m)

90

3.4.13

Spans 1®2 and 2®3: Column strip and middle strip: H20 @ 200 B

Spans 1®2 and 2®3: Column strip and middle strip: H16 @ 100 B1

92

3.4.13

Figure 3.26

See D below

112

4.2.6

F3 = 310/Vs 1.5 where

F3 = As,prov /As,req 1.50 = 4824/4158 = 1.16

Vs in simple situations = (fyk/JS) (As,req/As,prov) (SLS loads/ULS loads) (1/G). However in this case separate analysis at SLS would be required to determine Vs. Therefore as a simplification use the conservative assumption: 310/Vs = (500/fyk) (As,req/As,prov) = (500/500)u(4824/4158) = 1.16

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

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123

4.3.5b) F3 = 310/Vs 1.5 where Vs=(fyk/JS)(As,req/As,prov)(SLS loads/ULS loads)(1/G) =434.8u(5835/5892) [(47.8+0.3u45.8)/(1.25 u 47.8 + 1.5 u 45.8)] u (1/0.945) = 434.8 u 0.99 u 0.48 u 1.06 = 219 MPa

124

4.3.5b)

F3 = As,prov /As,req 1.50 = 5892/5835= 1.01

F3 = 310/Vs 1.5 = 310/219 = 1.41 ? Permissible l/d= 17.8u1.3 u0.90u0.95 u1.41 = 27.9 ?Permissible l/d= 17.8u1.3 u0.90u0.95 u1.01 = 20.0 Actual l/d = 7500/252 = 29.8 ? no good Actual l/d = 7500/252 = 29.8 ? no good Try 12 no. H32 B (9648 mm2) Try 13 no. H25 B (6383 mm2) F3 = As,prov /As,req 1.50 F3 = 310/Vs 3 = 9648 /5835 = 1.654 = say 1.50 = 310/219 u 13/12 = 1.53 = say 1.50 ? Permissible l/d = 17.8u1.3u0.90u0.95u1.50 = 29.7 ? Permissible l/d = 17.8u1.3u0.90u0.95u1.50 = 29.7 Actual leff/d = 7400/252 = 29.8 Actual leff/d = 7400/252 = 29.8 Say OK Say OK 2 Use 13 no. H25 B (6383 mm2) Use 13 no. H25 B (6383 mm )

124

4.3.6

127

4.3.7d) F3 = 310/Vs 1.5 F3 = As,prov /As,req 1.50 = 3828/3783= 1.01 where Vs=(fyk/JS)(As,req/As,prov)(SLS loads/ULS loads)(1/G) =434.8u (3783/3828)[(47.8+0.3u 45.8)/(1.25 u 47.8 + 1.5 u 45.8)] u (1/0.908) = 434.8 u 0.99 u 0.48 u 1.10 = 227 MPa F3 = 310/Vs = 310/227 = 1.37 ? Permissible l/d = 44.7 u 1.37 u 0.88 u 0.95 ? Permissible l/d u 1.37 = 70.1 = 44.7 u 1.50 u 0.88 u 0.95 u 1.01 = 56.6 Actual l/d = 7500/252 = 29.8 ? OK Use 8 no. H25 B (3928 mm2) (which is < 40K = 40 x 1.5 =60) [Table NA.5 Note 6]

Figure 4.20

See E below

Actual l/d = 7500/252 = 29.8 ? OK Use 8 no. H25 B (3928 mm2 133

4.3.10

Figures 4.22 and 4.23

See F below

146

5.3

Figure 5.6 300 mm flat slabs All columns 400 mm sq

300 mm flat slabs All columns 500 mm sq

153

5.3.8

2WP]VTa`TÓ³S

183

References

183

References

1a National Annex to Eurocode 2- Part 1- 1a National Annex to Eurocode 2- Part 11. BSI 2005 1. Incorporating Amendment No.1 BSI 2009 5 R S NARAYANAN & C H GOODCHILD. 5 R S NARAYANAN & C H GOODCHILD. The Concrete Centre. Concise Eurocode The Concrete Centre. Concise Eurocode 2, CCIP-005. TCC 2006 2, CCIP-005. TCC 2006 As Amended

3

Both As,prov/As,req and any adjustment to N obtained from Expression (7.16a) or Expression (7.16b) is restricted to 1.5 by Note 5 to Table NA.5 in the UK NA. 4 Both As,prov/As,req and any adjustment to N obtained from Expression (7.16a) or Expression (7.16b) is restricted to 1.5 by Note 5 to Table NA.5 in the UK NA. Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Page 6 of 13

190

B1.1

Delete existing text. See G below

2010 New text: According to Note 5 of Table NA.5 the NA [1a] to BS EN 1992-1-1 the modification factor for service stress used with the l/d method of checking the SLS state of deformation (designated factor F3 in TCC publications) may be determined as either x

310/Vs using characteristic load combinations to determine the service stress, Vs

or

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x

(500/fyk)(As,prov /As,req)

In either case the modification factor is restricted to a maximum of 1.50. In the UK fyk = 500 MPa. Assuming Vs is proportional to Vu, and using characteristic load combinations to determine Vs produces values of 310/Vs = 1.00 +3% - 6%. and so is not as attractive to using As,prov /As,req. The use of F3 = As,prov /As,req 1.5 is therefore advocated in checking deformation using the l/d method. 190 191 191 201 204

B1.2 B1.4 B1.5 C7 C8

See H below See J below See K below See L below See M below

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Page 7 of 13

A Amends to p 51 Figure 3.7

300 250 150 125

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300 250

B Amends to p 65 Figure 3.15

2H20/rib 1H25 + 1H20/rib x3

C Amends to p 70 Figure 3.17

2H20/rib 1H25 + 1H20/rib x2 Note curtailed bat

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Page 8 of 13

D Amends to p 92 Figure 3.26

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H20@200 H16@100

E Amends to p 124 Figure 4.20

25 bar 32 bar

20 bar 20/25 bar

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Page 9 of 13

F Amends to p133 Figures 4.22 and 4.23

13H25 12H32

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x2 T25 in section x2

G Amends to p190 B1.1 NewText According to Note 5 of Table NA.5 the NA to BS EN 1992-1-1[1a] the modification factor for service stress used with the l/d method of checking the SLS state of deformation (designated factor F3 in TCC publications) may be determined as either x

310/Vs using characteristic load combinations to determine the service stress, Vs

x

(500/fyk)(As,prov /As,req)

or

In either case the modification factor is restricted to a maximum of 1.50. In the UK fyk = 500 MPa. Assuming Vs is simply proportional to the ultimate stress, Vu, produces values of 310/Vs = 1.00 +/- 5% and so for hand calculations is not as attractive as using As,prov /As,req. The use of F3 = As,prov /As,req 1.5 is therefore advocated in checking deformation using the l/d method by hand.

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

Page 10 of 13

H Amends to p190 B1.2 combination values of actions combination values of actions taking account of SLS moments, compression reinforcement, As,prov /As,req, etc.

[1]

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310/Vs

NewText

[1a]

an accurate

J Amends to p191 B1.4

were

Add new text

using the quasi permanent values of actions (see B.4)

New para

In the light of the above disparity and pending clarification, the UK NA was revised and published in December 2009 as detailed in B1.1 above.

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

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K Amends to p191 B1.4

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New paras

Prior to the publication of the revised UK NA[1a] it was allowable to calculate the moderation factor using in l/d verifications of deformation(F3) by using quasi permanent loads. Assuming Vs due to quasi permanent actions is proportional to Vu, the method as outlined in C8 may be used to determine Vs in verifications of crack widths, etc.

L Amends to p201 C7

New text: either x

310/Vs using characteristic load combinations to determine the service stress, Vs

x

(500/fyk)(As,prov /As,req)

or

In either case the modification factor is restricted to a maximum of 1.50.

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

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M Amends to p204 C8

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below

New text ex p 201:

chg 25 Feb 2010

Amends to Worked Examples to Eurocode 2 - Jan 2012.doc

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WORKED EXAMPLES

STANDARDS

CONCRETE INDUSTRY PUBLICATIONS

PUBLICATIONS BY OTHERS

NA CONCISE EUROCODE 2

BS EN 1990 BASIS OF DESIGN

MANUALS

VOL 2 NA BS EN 1991–2 NA BS EN 1991–1–1 –2 NA NA –3 NA ACTIONS –4 NA –6

WORKED EXAMPLES TO EUROCODE 2 VOL 1

HOW TO DESIGN CONCRETE STRUCTURES DETAILERS HANDBOOK

Densities and imposed loads Fire Snow Wind Execution

www. Eurocode2 .info DESIGN GUIDES

PD6687 NA

NA BS EN 1992–1–1 1–2 NA NA DESIGN OF –2 CONCRETE –3 STRUCTURES General Fire Bridges Liquid retaining

RC SPREAD SHEETS

BS EN 13670 EXECUTION OF CONCRETE STRUCTURES

PRECAST DESIGN MANUAL

PRECAST WORKED EXAMPLES

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2

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Bg ma^ >nkh\h]^ lrlm^f ;L >G *22)% >nkh\h]^3 ;Zlbl h_ lmkn\mnkZe ]^lb`gT*)V ho^kZk\a^l Zee ma^ hma^k>nkh\h]^l%;L>G*22*mh;L>G*222';L>G*22)]^Ëg^lma^^__^\mlh_Z\mbhgl%bg\en]bg` `^hm^\agb\Ze Zg] l^blfb\ Z\mbhgl% Zg] Ziieb^l mh Zee lmkn\mnk^l bkk^li^\mbo^ h_ ma^ fZm^kbZe h_ \hglmkn\mbhg'Ma^fZm^kbZe>nkh\h]^l]^Ëgâhpma^^__^\mlh_Z\mbhglZk^k^lblm^][r`bobg`kne^l_hk ]^lb`gZg]]^mZbebg`h_\hg\k^m^%lm^ê%\hfihlbm^%mbf[^k%fZlhgkrZg]Zenfbgbnf'!l^^?b`nk^*',"' BS EN 1990, Eurocode: Basis of structural design

Structural safety, serviceability and durability

BS EN 1991, Eurocode 1: Actions on structures

Actions on structures

BS EN 1992, Eurocode 2: Concrete BS EN 1993, Eurocode 3: Steel BS EN 1994, Eurocode 4: Composite BS EN 1995, Eurocode 5: Timber BS EN 1996, Eurocode 6: Masonry BS EN 1999, Eurocode 9: Aluminium BS EN 1997, Eurocode 7: Geotechnical design

Design and detailing

BS EN 1998, Eurocode 8: Seismic design

Geotechnical and seismic design

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l^kob\^k^jnbk^f^gmlZk^ghehg`^kf^m' :eeZ\mbhglZk^Zllnf^]mhoZkrbgmbf^Zg]liZ\^'LmZmblmb\Zeikbg\bie^lZk^Ziieb^]mhZkkbo^Zmma^ fZ`gbmn]^h_maîZkmbZeehZ]_Z\mhklmh[^nl^]bg]^lb`gmhZ\abô^ma^k^jnbk^]kêbZ[bebmrbg]^q !eôêh_lZ_^mr"'Ma^k^blZgng]^kerbg`ZllnfimbhgmaZmma^Z\mbhglma^flêo^lZk^]^l\kb[^]bg lmZmblmb\Zem^kfl' 3

*', Eurocode 1: Actions on structures

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

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*'- Eurocode 2: Design of concrete structures >nkh\h]^+3=^lb`gh_\hg\k^m^lmkn\mnk^lT*¾-Vhi^kZm^lpbmabgZg^gobkhgf^gmh_hma^k>nkhi^Zg Zg];kbmblalmZg]Zk]l!l^^?b`nk^*',"'Bmbl`ho^kg^][r;L>G*22)T*)VZg]ln[c^\mmhma^Z\mbhgl ]^Ëg^]bg>nkh\h]^l*T**V%0T*+VZg]1T*,V'Bm]î^g]lhgoZkbhnlfZm^kbZelZg]^q^\nmbhglmZg]Zk]l Zg] bl nl^] Zl ma^ [Zlbl h_ hma^k lmZg]Zk]l' IZkm +% ;kb]`^lT,V% Zg] IZkm ,% Ebjnb]k^mZbgbg`Zg] \hgmZbgf^gmlmkn\mnk^lT-V%phkd[r^q\îmbhgmhIZkm*¾*Zg]*¾+%maZmbl%\eZnl^lbgIZkml+Zg], \hgËkf%fh]b_rhkkîeZ\^\eZnl^lbgIZkm*¾*'

BS EN 1990 EUROCODE Basis of Structural Design BS EN 1997 EUROCODE 7 Geotechnical Design

BS EN 1998 EUROCODE 8 Seismic Design BS EN 1991 EUROCODE 1 Basis of Structural Design

BS 4449 Reinforcing Steels

BS 8500 Specifying Concrete

BS EN 206 Concrete

BS EN 13670 Execution of Structures

BS EN 1995 EUROCODE 5 Design of Composite Structures

BS EN 1992 EUROCODE 2 Design of concrete structures Part 1–1: General Rules for Structures Part 1–2: Structural Fire Design

BS EN 1992 EUROCODE 2 Part 2: Bridges

BS EN 1992 EUROCODE 2 Part 3: Liquid Retaining Structures

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EC1-1-3: 5.2(7) &Table 5.1

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EC1-1-4: Figs NA.7, NA.8

EC1-1-4: Fig. NA.1

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13

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EC1-1-4: 4.2(1) Note 2 & NA 2.4, 2.5

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EC1-1-4: 4.2(2) Note 3 & NA 2.7: Fig. NA.2

EC1-1-4: 4.2(1) Notes 4 & 5 & NA 2.8

EC1-1-4: 4.2(1) Note 2 & NA 2.4: Fig. NA.1

EC1-1-4: 4.2(2) Note 1 & NA 2.5

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EC1-1-4: 7.2.2(2) Note 1 & NA.2.27, Table NA.4

Cladding loads ?hkZk^ZlZ[ho^*f+%\i^%*)lahne][^nl^]'\i^%*)fZr[^]^m^kfbg^]_khf MZ[e^0'*h_;L>G*22*¾*¾-'L^^MZ[e^+'*)'

EC1-1-4: 7.2.2(2) Note 1 & NA.2.27

15

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EC1-1-4: NA.2.28 & NA advisory note

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EC1-1-4: 7.2.9(6) Note 2

EC1-1-4: NA 2.27, Table NA.4

MZ[e^+'2 G^mik^llnk^\h^__b\b^gm%\i^%*)%_hkpZeelh_k^\mZg`neZkieZg[nbe]bg`l#

EC1-1-4: 7.2.3, NA.2.28 & NA advisory note

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

BS 6399: Table 8 & Fig. 18

\ib 6 bgm^kgZeik^llnk^\h^_Ë\b^gm' ?hkgh]hfbgZgmhi^gbg`l\ibfZr[^mZd^gZlma^fhk^hg^khnlh_$)'+Zg]¾)',

a(] 5 1 ª 0.25

G^mik^llnk^\h^__b\b^gm%\i^%*) *', *'* )'1

Ghm^l *#bg^__^\mma^lôZen^lZk^_hk\^\h^__b\b^gml_hk]^m^kfbgbg`ho^kZeeehZ]lhg[nbe]bg`l' +a6a^bàmh_[nbe]bg`' ,[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"' -]6]îmah_[nbe]bg`!iZkZeeêmhpbg]"' .OZen^lfZr[^bgm^kiheZm^]' />q\en]^l_nggêebg`'

EC1-1-4: 7.2.2(2) Table 7.1, Note 1 & NA 2.27: Tables NA.4a , NA.4b

MZ[e^+'*) >qm^kgZeik^llnk^\h^__b\b^gm%\i^%*)%_hkpZeelh_k^\mZg`neZk&ieZg[nbe]bg`l =^l\kbimbhg

Zone A

?hkpZeeliZkZeeêmhma^pbg]]bk^\mbhg%Zk^Zlpbmabg )'+fbgT[4+aVh_pbg]pZk]^]`^

¾*'+

Zone B

?hkpZeeliZkZeeêmhma^pbg]]bk^\mbhg%Zk^Zlpbmabg )'+fbgT[4+aVh_pbg]pZk]^]`^

¾)'1

Zone C

?hkpZeeliZkZeeêmhma^pbg]]bk^\mbhg%Zk^Zl_khf )'+fbgT[4+aVmhfbgT[4+aVh_pbg]pZk]^]`^

Zone D

Pbg]pZk]pZee

$)'1

Zone E

E^^pZk]pZee

FZq'

Zones D G^m and E Ghm^l *a6a^bàmh_[nbe]bg`' +[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"' EC1-1-4: 7.2, Table 7.2 & NA

\i^%*)

Shg^

¾)'.

¾)'0 $*',

MZ[e^+'** >qm^kgZeik^llnk^\h^__b\b^gm%\i^%*)_hk_eZmkhh_l# Shg^

=^l\kbimbhg

\i^%*) LaZki^]`^ Zm^Zo^l

16

Fbg'

PbmaiZkZi^m

Zone F

Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]pbmabg ¾*'1 )'+fbgT[4+aVh_k^mnkg^]`^!iZkZeeêmhpbg]]bk^\mbhg"

¾*'/

Zone G

Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]hnmpbma ¾*'+ )'+fbgT[4+aVh_k^mnkg^]`^!iZkZeeêmhpbg]]bk^\mbhg"

¾*'*

Zone H

Khh_[^mp^^g)'*fbgT[4+aVZg])'.fbgT[4+aV_khf pbg]pZk]^]`^

¾)'0

¾)'0

Zone I K^fZbg]^k[^mp^^g)'.fbgT[4+aVZg]e^^pZk]^]`^ ¨)'+ ¨)'+ Ghm^l *#:\\hk]bg`mhG:mh;L>G*22*&*&-%mablmZ[e^blghmk^\hff^g]^]_hknl^bgma^ND' +a6a^bàmh_[nbe]bg`' ,[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"'

:gZerlbl%Z\mbhglZg]ehZ]ZkkZg`^f^gml MZ[e^+'*+ >qm^kgZeik^llnk^\h^__b\b^gm%\i^%_hk_eZmkhh_l

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

Shg^

=^l\kbimbhg

EC1-1-4: 7.2.3, NA.2.28 & NA advisory note.

\i^ LaZki^]`^ Zm^Zo^l

PbmaiZkZi^m

Zone A

Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]pbmabg )'+.fbgT[4+aVh_k^mnkg^]`^!iZkZeeêmhpbg]]bk^\mbhg"

¾+')

¾*'2

Zone B

Pbmabg)'*fbgT[4+aVh_pbg]pZk]^]`^Zg]hnmpbma )'+.fbgT[4+aVh_k^mnkg^]`^!iZkZeeêmhpbg]]bk^\mbhg"

¾*'-

¾*',

Zone C

Khh_[^mp^^g)'*fbgT[4+aVZg])'.fbgT[4+aV_khf pbg]pZk]^]`^

¾)'0

¾)'0

Zone D

K^fZbg]^k[^mp^^g)'.fbgT[4+aVZg]e^^pZk]^]`^

¨)'+

¨)'+

BS 6399: Table 8 & Fig. 18

Ghm^l *a6a^bàmh_[nbe]bg`' +[6[k^Z]mah_[nbe]bg`!i^ki^g]b\neZkmhpbg]"'

+'/'. Calculate the overall wind force, Fw ?p6\l\]Spd :k^_ pa^k^

EC1-1-4: 5.3.2, Exp. (5.4) & NA

pd 6 ZlZ[ho^

EC1-1-4: 6.2(1) a), 6.2(1) c)

\l\] 6 lmkn\mnkZe_Z\mhk%\hgl^koZmboêr 6 *') hkfZr[^]^kbo^] pa^k^ \l 6 lbs^_Z\mhk \lfZr[^]^kbo^]_khf>qi'!/'+"hkmZ[e^G:','=î^g]bg`hgoZen^lh_ ![$a"Zg]!s¾a]bl"Zg]]bob]bg`bgmhShg^:%;hkqi'!/',"hkË`nk^G:'2'=î^g]bg`hgoZen^lh_dl !eh`Zkbmafb\]^\k^f^gmh_lmkn\mnkZe]Zfibg`"Zg]a([%ZoZen^h_\]!Z_Z\mhk7 *'))"fZr[^_hng]'

\ ]fZr[^mZd^gZl*')_hk_kZf^][nbe]bg`lpbmalmkn\mnkZepZeelZg]fZlhgkr bgm^kgZepZeel%Zg]_hk\eZ]]bgìZgêlZg]ê^f^gml

:k^_6k^_^k^g\^Zk^Zh_ma^lmkn\mnk^hklmkn\mnkZeê^f^gm

+'0 Variable actions: others :\mbhgl]n^mh\hglmkn\mbhg%mkZ_Ë\%Ëk^%ma^kfZeZ\mbhgl%nl^Zllbehlhk_khf\kZg^lZk^hnmlb]^ ma^l\hi^h_mablin[eb\ZmbhgZg]k^_^k^g\^lahne][^fZ]^mhli^\bZeblmebm^kZmnk^'

EC1-1-4: 6.2(1) e) & NA.2.20

EC1-1-4: 6.3(1), Exp. (6.2) & NA.2.20, Table NA3

EC1-1-4: 6.3(1), Exp. (6.3) & NA.2.20: Fig. NA9 EC1-1-4: 5.3.2, Exp. (5.4) & NA

EC1-1-6, EC1-2, EC1-1-2, EC1-1-5, EC1-3 & EC1-4

17

+'1 Permanent actions Ma^ ]^glbmb^l Zg] Zk^Z ehZ]l h_ \hffhger nl^] fZm^kbZel% la^^m fZm^kbZel Zg] _hkfl h_ \hglmkn\mbhgZk^`bo^gbgMZ[e^l+'*,mh+'*.' :\mbhglZkblbg`_khfl^mme^f^gm%]^_hkfZmbhgZg]\k^îZk^hnmlb]^ma^l\hi^h_mabl]h\nf^gm [nm `^g^kZeer Zk^ mh [^ \hglb]^k^] Zl i^kfZg^gm Z\mbhgl' Pa^k^ \kbmb\Ze% k^_^k mh li^\bZeblm ebm^kZmnk^' MZ[e^+'*, ;ned]^glbmb^l_hklhbelZg]fZm^kbZelT**%+/V dG(f,

;ned]^glbmb^l

H"ghmbgoheobg``^hm^\agb\ZeZ\mbhgl Either >qi'!/'*)"

*',.!*')"Z

*'.

c)*'.

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c)*'.

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*'+.!*')"Z

*'.

c)*'.

or the worst case of >qi'!/'*)Z" and >qi'!/'*)["

\"Lmk^g`maZmNEL!LMK(@>H"pbma`^hm^\agb\ZeZ\mbhgl Worst case of L^m;

*',.!*')"Z

*'.!)')"Z

*')

*',

and L^mqi'!/'**Z" _"L^blfb\ >qi'!/'*+Z(["

D^r Z OZen^b__ZohnkZ[e^!lahpgbg[kZ\d^ml" [ E^Z]bg`Z\\b]^gmZeZ\mbhg%:]%blng_Z\mhk^] \ L^blfb\Z\mbhg%:>] ] K^_^kmh;L>G*22)3:*'+'+G:

Ghm^l * MaôZen^lh_cZk^`bo^gbgMZ[e^+'*0' + @^hm^\agb\ZeZ\mbhgl`bo^gbgma^mZ[e^ Zk^[Zl^]hg=^lb`g:iikhZ\a*bg qik^llbhg!/'*)"hkma^ phklm\Zl^h_>qik^llbhg!/'*)Z"hk>qik^llbhg!/'*)["'

EC0: 6.4.3.2(3)

Single variable action :mNEL%ma^]^lb`goZen^h_Z\mbhglbl ^bma^k

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

>qi'!/'*)" *',.@d$*'.Jd%* hkma^phklm\Zl^h_3 >qi'!/'*)Z" *',.@d$c)%**'.Jd%* Zg] >qi'!/'*)[" *'+.@d$*'.Jd%* pa^k^ @d 6 i^kfZg^gmZ\mbhg Jd%*6 lbgèôZkbZ[e^Z\mbhg c)%*6 \hf[bgZmbhg_Z\mhk_hkZlbgèôZkbZ[eêhZ]!l^^MZ[e^+'*0" MZ[e^+'*0 OZen^lh_c_Z\mhkl EC0: A1.2.2 & NA

EC1-1-1: 3.3.2

:\mbhg

c)

c*

c+

Bfihl^]ehZ]lbg[nbe]bg`l

Category A: domestic, residential areas

)'0

)'.

)',

Category B: office areas

)'0

)'.

)',

Category C: congregation areas

)'0

)'0

)'/

Category D: shopping areas

)'0

)'0

)'/

Category E: storage areas

*')

)'2

)'1

Category F: traffic area (vehicle weight © 30 kN)

)'0

)'0

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Category G: traffic area (30 kN < vehicle weight © 160 kN)

)'0

)'.

)',

Category H: roofsZ

)'0

)')

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Snow loads where altitude © 1000 m a.m.s.l.Z

)'.

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Wind loadsZ

)'.

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Temperature effects (non-fire)Z

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D^r a Hgkhh_l%bfihl^]ehZ]l%lghpehZ]lZg]pbg]ehZ]llahne]ghm[^Ziieb^]mh`^ma^k' Ghm^l 1 Ma^gnf^kb\ZeoZen^l`bo^gZ[ho^Zk^bgZ\\hk]Zg\^pbma;L>G*22)Zg]bmlNDGZmbhgZe:gg^q' 2 qik^llbhg!/'*)"blZepZrl^jnZemhhkfhk^\hgl^koZmbo^maZgmaê^ll_ZohnkZ[e^h_>qik^llbhgl !/'*)Z"Zg]!/'*)["'>qik^llbhg!/'*)["pbeeghkfZeerZiierpa^gmaî^kfZg^gmZ\mbhglZk^ghm `k^Zm^kmaZg-'.mbf^lmaôZkbZ[e^Z\mbhgl!^q\îm_hklmhkZ`êhZ]l%\Zm^`hkr>bgMZ[e^+'*0% pa^k^>qik^llbhg!/'*)Z"ZepZrlZiieb^l"' Ma^k^_hk^%^q\îmbgma^\Zl^h_\hg\k^m^lmkn\mnk^llniihkmbg`lmhkZ`êhZ]lpa^k^c)6*')% hk_hkfbq^]nl^%>qik^llbhg!/'*)["pbeenlnZeerZiier'Manl%_hkf^f[^kllniihkmbgò^kmb\Ze Z\mbhglZmNEL%*'+.@d$*'.Jdpbee[^ZiikhikbZm^_hkfhlmlbmnZmbhglZg]Ziieb\Z[e^mhfhlm \hg\k^m^lmkn\mnk^l!l^^?b`nk^+'."' qik^llbhg!/'*)"%ma^nl^h_^bma^k>qik^llbhg!/'*)Z"hk!/'*)["e^Z]l mh Z fhk^ \hglblm^gm kêbZ[bebmr bg]^q Z\khll ebàmp^bàm Zg] a^Zorp^bàm fZm^kbZel'

22

:gZerlbl%Z\mbhglZg]ehZ]ZkkZg`^f^gml 50

gk kN/m (or kN/m2)

40

Use Exp. (6.10a)

30

Use Exp. (6.10b)

10 0

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

Ghm^ :llnfbg`c)6)'0 b'^'Ziieb\Z[e^mhZeeZk^Zl ^q\îmlmhkZ`^'

20

1

2

3

4

5

6

7

8

9

10

q k kN/m (or kN/m2) ?b`nk^+'. Pa^gmhnl^>qi'!/'*)Z"hk>qi'!/'*)["

Accompanying variable actions :`Zbg ma^ ]^lb`g^k fZr \ahhl^ [^mp^^g nlbg` >qik^llbhg !/'*)" hk ma^ e^ll _ZohnkZ[e^ h_ >qik^llbhgl!/'*)Z"hk!/'*)["'

EC0: 6.4.3.2(3)

>bma^k >qi'!/'*)" *',.@d$*'.Jd%*$S!c)%b*'.Jd%b " hkma^phklm\Zl^h_3 >qi'!/'*)Z" *',.@d$c)%**'.Jd%*$S!c)%b*'.Jd%b" Zg] >qi'!/'*)[" *'+.@d$*'.Jd%*$S!c)%b*'.Jd%b" pa^k^ @d 6 i^kfZg^gmZ\mbhg Jd%*6 *lmoZkbZ[e^Z\mbhg Jd%b 6 bmaoZkbZ[e^Z\mbhg c)%*6 \aZkZ\m^kblmb\\hf[bgZmbhg_Z\mhk_hk*lmoZkbZ[eêhZ]!l^^MZ[e^+'*0" c)%b 6 \aZkZ\m^kblmb\\hf[bgZmbhg_Z\mhk_hkbmaoZkbZ[eêhZ]!l^^MZ[e^+'*0" Bgma^Z[ho^%Jd%*!Zg]c)%b "k^_^klmhmaê^Z]bgòZkbZ[e^Z\mbhgZg]Jd%b!Zg]c)%b "k^_^klmh Z\\hfiZgrbg`bg]î^g]^gmoZkbZ[e^Z\mbhgl'Bg`^g^kZe%ma^]blmbg\mbhg[^mp^^gma^mphmri^lh_ Z\mbhglpbee[^h[obhnl!l^^?b`nk^+'/"4pa^k^bmblghm%^Z\aehZ]lahne]bgmnkg[^mk^Zm^]Zlma^ e^Z]bg`Z\mbhg':elh%ma^gnf^kb\ZeoZen^l_hkiZkmbZe_Z\mhkl`bo^gbgma^NDGZmbhgZe:gg^qT*)ZV Zk^nl^]bgma^^jnZmbhglZ[ho^'MaôZen^h_c)]î^g]lhgma^nl^h_ma^[nbe]bg`Zg]lahne] [^h[mZbg^]_khfma^NDGZmbhgZe:gg^q_hk;L>G*22)!l^^MZ[e^+'*0"'

EC0: A1.2.2, A1.3.1 & NA

qk2 gk2 qk1 gk1 qk1 gk1

qk3 = wk

qk1 gk1 qk1 gk1 A ?b`nk^+'/ Bg]î^g]^gmoZkbZ[e^Z\mbhgl

B

C

Ghm^ @^g^kZeermaôZkbZ[e^ Z\mbhglhgZmrib\Zeh__b\^ [eh\dphne][^\hglb]^k^] Zl[^bg`mak^^l^mlh_ bg]î^g]^gmoZkbZ[e^ Z\mbhgl3 *' Bfihl^]h__b\êhZ]l hgma^h__b\^_ehhkl' +' Khh_bfihl^]ehZ]' ,' Pbg]ehZ]'

23

Ma^^qik^llbhglmZd^bgmhZ\\hngmmaîkh[Z[bebmrh_chbgmh\\nkk^g\^h_ehZ]l[rZiierbg`ma^ c)%b_Z\mhkmhma^Z\\hfiZgrbgòZkbZ[e^Z\mbhg'Maîkh[Z[bebmrmaZmma^l^\hf[bg^]Z\mbhglpbee [^^q\^^]^]bl]^^f^]mh[^lbfbeZkmhmaîkh[Z[bebmrh_Zlbgè^Z\mbhg[^bg`^q\^^]^]' B_ma^mphbg]î^g]^gmoZkbZ[e^Z\mbhglJd%*Zg]Jd%+Zk^Zllh\bZm^]pbma]b__^k^gmliZglZg]ma^ nl^h_>qik^llbhg!/'*)["blZiikhikbZm^%ma^gbghg^l^mh_ZgZerl^lZiier *'+.@d$*'.Jd%*mhma^Jd%*liZgl Zg]*'+.@d$c)'b*'.Jd%*mhma^Jd%+liZgl' BgZllh\bZm^]ZgZerl^lZiier *'+.@d$c)%b*'.Jd%*mhma^Jd%*liZgl Zg]*'+.@d$*'+.Jd%+mhma^Jd%+liZgl'

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

L^^>qZfie^+'**'+!mphoZkbZ[e^Z\mbhgl"'

+'2', Design values at SLS EC0: 6.5 & Table A1.4

Ma^k^Zk^mak^^\hf[bgZmbhglh_Z\mbhglZmLEL!hkehZ]\hf[bgZmbhgZmLEL"'Ma^l^Zk^`bo^gbg MZ[e^+'*1'Ma^\hf[bgZmbhgZg]oZen^mh[^nl^]]î^g]lhgma^gZmnk^h_maêbfbmlmZm^[^bg` \a^\d^]' JnZlb&i^kfZg^gm \hf[bgZmbhgl Zk^ Zllh\bZm^] pbma ]^_hkfZmbhg% \kZ\d pb]mal Zg] \kZ\d\hgmkhe'?k^jn^gm\hf[bgZmbhglfZr[^nl^]mh]^m^kfbg^pa^ma^kZl^\mbhgbl\kZ\d^]hk ghm'Ma^gnf^kb\oZen^lh_c)%c*Zg]c+Zk^`bo^gbgMZ[e^+'*0' 0.3d but < 0.5d from face of column. Say 0.4d = 100 mm from face of column.

Cl. 9.4.3

Cl. 9.4.3(1)

Fig. 9.10, Cl. 9.4.3(4)

By inspection of Figure 3.23 the equivalent of 10 locations are available at 0.4d from column therefore try 2 × 10 no. H10 = 1570 mm2. By inspection of Figure 3.23 the equivalent of 18 locations are available at 1.15d from column therefore try 18 no. H10 = 1413 mm2. By inspection of Figure 3.23 the equivalent of 20 locations are available at 1.90d from column therefore try 20 no. H10 = 1570 mm2. By inspection of Figure 3.23 beyond u1 to uout grid of H10 at 175 x 175 OK. ‡ Clause 6.4.5 provides Exp. (6.52), which by substituting v for v Ed Rd,c, allows calculation of the area of required shear reinforcement, Asw, for the basic control perimeter, u1. § The same area of shear reinforcement is required for all perimeters inside or outside perimeter u1. See Commentary on design, Section 3.4.14. Punching shear reinforcement is also subject to requirements for minimum reinforcement and spacing of shear reinforcement (see Cl. 9.4.3).

84

Cl. 6.4.5 Exp. 6.5.2

Cl. 9.4.3

,'-3?eZmleZ[

e) Summary of punching shear refreshment required at column C2 uout

C

S = 112 H10 legs of links u1 at 2d from column

175 175 175 175 200 200 200 175 175 175 175

100 400 100 716

2

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

716

Punching shear reinforcement no longer required 1.5d = 375

uout

175 175 175 175 200 200 200 175 175 175 175 375

716

100

400

100

716

Figure 3.23 Punching shear links at column C2 (112 no. links) (column D2 similar)

3.4.11 Punching shear, edge column Assuming penultimate support, VEd = 1.18 × 516.5 = 609.5 kN a) Check at perimeter of column vEd = b VEd/uid < vRd,max where b = factor dealing with eccentricity; recommended value 1.4 VEd = applied shear force ui = control perimeter under consideration. For punching shear adjacent to edge columns u0 = c2 + 3d < c2 + 2c1 = 400 + 750 < 3 × 400 mm = 1150 mm d = as before 250 mm vEd = 1.4 × 609.5 × 103/1150 × 250 = 2.97 MPa vRd,max, as before = 5.28 MPa = OK

Table C3 Cl. 6.4.3(2), 6.4.5(3) Fig. 6.21N & NA Cl. 6.4.5(3)

Exp. (6.32) Cl. 6.4.5(3) Note 85

Cl. 6.4.2

Fig. 6.15

Exp. (6.47) & NA

where gC = 1.5 k = as before = 1 +(200/250)0.5 = 1.89 rl = (r lyr lz )0.5 where rer, rlz = Reinforcement ratio of bonded steel in the y and z direction in a width of the column plus 3d each side of column. r ly: (perpendicular to edge) 10 no. H20 T2 + 6 no. H12 T2 in 2 × 750 + 400, i.e. 3818 mm2 in 1900 mm =r ly = 3818/(250 × 1900) = 0.0080 r lz : (parallel to edge) 6 no. H20 T1 + 1 no. T12 T1 in 400 + 750 i.e. 1997 mm2 in 1150 mm. =r lz = 1997/(250 × 1150) = 0.0069 r l = (0.0080 × 0.0069)0.5 = 0.0074 fck = 30 vRd,c = 0.18/1.5 × 1.89 × (100 × 0.0074 × 30)0.333 = 0.64 MPa = Punching shear reinforcement required C

3d = 750

6H20T1 @175

3d = 750 10H20 U-bars in pairs @ 200 cc 400

H12 @ 200 U-bars

400

1

3d = 750

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

b) Check shear stress at basic perimeter u1 (2.0d from face of column) vEd = bVEd/u1d < vRd,c where b, VEd and d as before u1 = control perimeter under consideration. For punching shear at 2d from edge column columns u1 = c2 + 2c1+ Q × 2d = 2771 mm vEd = 1.4 × 609.5 × 103/2771 × 250 = 1.23 MPa vRd,c = 0.18/ gC × k × (100 rlfck)0.333

H12 @ 175T1

Figure 3.24 Flexural tensile reinforcement adjacent to columns C1 (and C3) ‡

86

vRd,c for various values of d and rl is available from Table C6.

Cl. 6.4.4.1(1)

Table C6‡

,'-3?eZmleZ[

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

c) Perimeter at which punching shear links no longer required uout = 609.5 × 1.4 × 103/(250 × 0.64) = 5333 mm Length attributable to column faces = 3 × 400 = 1200 mm = radius to uout from face of column = say (5333 − 1200)/Q = 1315 mm from face of column Perimeters of shear reinforcement may stop 1370 – 1.5 × 250 = 940 mm from face of column. d) Shear reinforcement As before, sr,max = 175 mm; st,max = 350 mm and fywd,ef = 312 MPa For perimeter u1 Asw ≥ (vEd – 0.75vRd,c) sr u1/1.5fywd,ef = (1.23 – 0.75 × 0.64) × 175 × 2771/(1.5 × 312) = 777 mm2 per perimeter Asw,min ≥ 0.08 × 300.5 (175 × 350)/(1.5 × 500) = 36 mm2 Asw/u1 ≥ 777/2771 = 0.28 mm2/mm Using H8 max. spacing = 50/0.28 = 178 mm cc =Use min. H8 (50 mm2) legs of links at 175 mm cc around perimeters: perimeters at 175 mm centres e) Check area of reinforcement > 777 mm2 in perimeters inside u1§ 1st perimeter to be > 0.3d but < 0.5d from face of column. Say 0.4d = 100 mm from face of column By inspection of Figure 3.27 the equivalent of 6 locations are available at 0.4d from column therefore try 2 × 6 no. H10 = 942 mm2

Exp. (6.54)

Cl. 6.4.5(4) & NA

Cl. 9.4.3(1), 9.4.3(2) Exp. (6.52)

Exp. (9.11)

Fig. 9.10, Cl. 9.4.3(4)

By inspection of Figure 3.27 the equivalent of 12 locations are available at 1.15d from column therefore try 12 no. H10 = 942 mm2 By inspection of Figure 3.27 the equivalent of 14 locations are available at 1.90d from column therefore try 14 no. H10 = 1099 mm2 By inspection of Figure 3.27 beyond u1 to uout grid of H10 at 175 x 175 OK.

3.4.12 Punching shear, edge column with hole Check columns D1 and D3 for 200 × 200 mm hole adjacent to column. As previously described use 4 no. H20 U-bars each side of column for transfer moment. Assuming internal support, VEd = 516.5 kN § See Commentary on design Section 3.4.14. Punching shear reinforcement is also subject to requirements for minimum reinforcement and spacing of shear reinforcement (see Cl. 9.4.3).

Cl. 9.4.3

87

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a) Check at perimeter of column vEd = bVEd/uid < vRd,max where b = factor dealing with eccentricity; recommended value 1.4 VEd = applied shear force ui = control perimeter under consideration. For punching shear adjacent to edge columns u0 = c2 + 3d < c2 + 2c1 = 400 + 750 < 3 × 400 mm = 1150 mm Allowing for hole, u0 = 1150 – 200 = 950 mm d = 250 mm as before vEd = 1.4 × 516.5 × 103/950 × 250 = 3.06 MPa = OK vRd,max as before = 5.28 MPa b) Check shear stress at basic perimeter u1 (2.0d from face of column) vEd = bVEd/u1d < vRd,c where b, VEd and d as before u1 = control perimeter under consideration. For punching shear at 2d from edge column columns u1 = c2 + 2c1+ Q × 2d = 2771 mm Allowing for hole 200/(c1/2): x/(c1/2 + 2d) 200/200: x/( 200 + 500) = x = 700 mm u1 = 2771 – 700 = 2071 mm vEd = 1.4 × 516.5 × 103/2071 × 250 = 1.40 MPa vRd,c = 0.18/gC × k × (100 rlfck)0.333

Cl. 6.4.3(2), 6.4.5(3) Fig. 6.21N & NA

Cl. 6.4.5(3)

Exp. (6.32) Cl. 6.4.5(3) Note Cl. 6.4.2

Fig. 6.15

Fig. 6.14

Exp. (6.47) & NA

where gC = 1.5 k = as before = 1 + (200/250)0.5 = 1.89 rl = (r ly r lz )0.5 where rer, rlz = Reinforcement ratio of bonded steel in the y and z direction in a width of the column plus 3d each side of column rly: (perpendicular to edge) 8 no. H20 T2 + 6 no. H12 T2 in 2 × 720 + 400 − 200, i.e. 3190 mm2 in 1640 mm. =r ly = 3190/(240 × 1640) = 0.0081 rlz: (parallel to edge) 6 no. H20 T1 (5 no. are effective) + 1 no. T12 T1 in 400 + 750 – 200, i.e. 1683 mm2 in 950 mm. =r lz = 1683/(260 × 950) = 0.0068 88

Cl. 6.4.4.1(1)

,'-3?eZmleZ[

rl = (0.0081 × 0.0068)0.5 = 0.0074 = 30 fck vRd,c = 0.18/1.5 × 1.89 × (100 × 0.0074 × 30)0.33 = 0.64 MPa = punching shear reinforcement required

Table C6‡

D

3d = 750 400

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H12 @ 175T1

H12 @ 200 U-bars

6H20T @ 175 3d = 750

400

3

8H20 U-bars in pairs @ 200 cc 3d = 750

Figure 3.25 Flexural tensile reinforcement adjacent to columns D1 and D3 c) Perimeter at which punching shear links no longer required uout = 516.5 × 1.4 × 103/(250 × 0.64) = 4519 mm Length attributable to column faces = 3 × 400 = 1200 mm Angle subtended by hole from centre of column D1 (See Figures 3.25 & 3.27) = 2 tan−1(100/200) = 2 × 26.5° = 0.927 rads. = radius to uout from face of column = say (4519 − 1200)/(Q − 0.927) = 1498 mm from face of column Perimeters of shear reinforcement may stop 1498 – 1.5 × 250 = 1123 mm from face of column d) Shear reinforcement As before, sr,max = 175 mm; st,max = 350 mm and fywd,ef = 312 MPa For perimeter u1 Asw ≥ (vEd – 0.75vRd,c) sr u1/1.5fywd,ef) per perimeter = (1.40 – 0.75 × 0.64) × 175 × 2071/(1.5 × 312) = 712 mm2 per perimeter

Exp. (6.54)

Cl. 6.4.5(4) & NA

Cl. 9.4.3(1) 9.4.3(2) Exp. (6.52)

Asw,min ≥ 0.08 × 300.5 (175 × 350)/(1.5 × 500) = 36 mm2 Asw/u1 ≥ 712/2071 = 0.34 mm2/mm ‡v Rd,c for various values of d and rl is available from Table C6.

89

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Using H8 (50 mm2) max. spacing = min[50/0.3; 1.5d] = min[147; 375] = 147 mm cc No good Try using H10, max. spacing = 78.5/0.34 = 231 mm cc, say 175 cc = Use min. H10 (78.5 mm2) legs of links at 175 mm cc around perimeters: perimeters at 175 mm centres Check min. 9 no. H10 legs of links (712 mm2) in perimeter u1, 2d from column face. e) Check area of reinforcement > 712 mm2 in perimeters inside u1‡ 1st perimeter to be 100 mm from face of column as before. By inspection of Figure 3.27 the equivalent of 6 locations are available at 0.4d from column therefore try 2 × 6 no. H10 = 942 mm2.

Fig. 9.10, Cl. 9.4.3(4)

By inspection of Figure 3.27 the equivalent of 10 locations are available at 1.15d from column therefore try 10 H10 = 785 mm2. By inspection of Figure 3.27 beyond 1.15d to uout grid: H10 at 175 x 175 OK.

3.4.13 Summary of design Grid C flexure End supports: Column strip: (max. 200 mm from column) 10 no. H20 U-bars in pairs (where 200 × 200 hole use 8 no. H20 T1 in U-bars in pairs) Middle strip: H12 @ 200 T1 Spans 1–2 and 2–3: Column strip and middle strip:

H20 @ 200 B

Central support: Column strip centre: for 750 mm either side of support: Column strip outer: Middle strip:

H20 @ 100 T1 H20 @ 250 T1 H16 @ 200 T1

Grid 1 (and 3) flexure Spans: Column strip: Middle strip:

H16 @ 200 B2 H12 @ 300 B2

‡ See Commentary on design Section 3.4.14. Punching shear reinforcement is also subject to requirements for minimum reinforcement and spacing of shear reinforcement.

90

Cl. 9.4.3

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,'-3?eZmleZ[

Interior support: Column strip centre: Column strip outer: Middle strip:

6 no. H20 @ 175 T2 H12 @ 175 T2 H12 @ 300 T2

Grid 2 flexure Spans: Column strip: Middle strip:

H16 @ 250 B2 H10 @ 200 B2

Interior support: Column strip centre: Column strip outer: Middle strip:

H20 @ 200 T2 H16 @ 250 T2 H12 @ 300 T2 See Figure 3.26

Punching shear Internal (e.g. at C2): Generally, use H10 legs of links in perimeters at max. 175 mm centres, but double up on 1st perimeter Max. tangential spacing of legs of links, st,max = 270 mm Last perimeter, from column face, min. 767 mm See Figure 3.26 Edge (e.g. at C1, C3 assuming no holes): Generally, use H10 legs of links in perimeters at max. 175 mm centres but double up on 1st perimeter Max. tangential spacing of legs of links, st,max = 175 mm Last perimeter, from column face, min. 940 mm Edge (e.g. at D1, D3 assuming 200 × 200 hole on face of column): Generally, use H10 legs of links in perimeters at max. 175 mm centres but double up on 1st perimeter Max. tangential spacing of legs of links, st,max = 175 mm Last perimeter, from column face, min. 1123 mm See Figure 3.27

91

C

D

10H20 T1 U-bars in pairs @ 200 H12 @ 200 T1 U-bars

6H20 - 175 T2 8H20 T1 U-bars in pairs @ 200

H12 - 200 T1 U-bars

1

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H20 @ 200 B1

H16 @ 175 B2* 5H12 @ 175 T2

H12 @ 300 B2 H10 @ 200 T2

4H16 @ 250 T2 3H20 @ 250 T1

H16 @ 175 B2* 2

16H20 @ 100 T1

9H20 @ 175 T2* 3H20 @ 250 T1 16H20 @ 100 T1

3H20 @ 250 T1 H16 @ 200 T1 Note:* Spacing rationalised to suit punching shear links

Figure 3.26 Reinforcement details bay C–D, 1–2

3.4.14 Commentary on design a) Method of analysis The use of coefficients in the analysis would not usually be advocated in the design of such a slab. Nonetheless, coefficients may be used and, unsurprisingly, their use leads to higher design moments and shears, as shown below.

92

Method

Moment in Centre support Centre support 9.6 m span per moment per reaction VEd (kN) 6 m bay (kNm) 6 m bay (kNm)

Coefficients

842.7

952.8

1205

Continuous beam

747.0

885.6

1103

Plane frame columns 664.8 below

834.0

1060

Plane frame columns 616.8 above and below

798.0

1031

,'-3?eZmleZ[

D 375

1123

6H20 @ 175 T2 6H16 @ 175 B2

8H20 T1 U-bars in pairs uout

H10 @ 200 T1 U-bars

H10 @ 200 T1 U-bars

1

175 175

1 u1

500

175 175

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175

1.5d uout

175 175 175 175 175 Ineffective area S = 152 H10 legs of links CL @ 175 mm centres 175 175 175 175 175 175 200 200 175 175 175 175 175 175 100

100

Note: For internal column see Figure 3.23

Figure 3.27 Punching shear links at column D1 (and D3) (penultimate support without hole similar) These higher moments and shears result in rather more reinforcement than when using other more refined methods. For instance, the finite element analysis used in Guide to the design and construction of reinforced concrete flat slabs[27] for this bay, leads to: t H16 @ 200 B1 in spans 1–2 (cf. H20 @ 200 B1 using coefficients) t H20 @ 125 T1 at support 2 (cf. H20 @ 100 T1 using coefficients) t 3 perimeters of shear links at C2 for VEd = 1065 kN (cf. 5 perimeters using coefficients) t 2 perimeters of shear links at C3 (cf. 7 perimeters using coefficients) b)

Effective spans and face of support In the analysis using coefficients, advantage was taken of using effective spans to calculate design moments. This had the effect of reducing span moments. At supports, one may base the design on the moment at the face of support. This is borne out by Guide to the design and construction of reinforced concrete flat slabs[27] that states that hogging moments greater than those at a distance hc/3 may be ignored (where hc is the effective diameter of a column or column head). This is in line with BS 8110[7] and could have been used to reduce support moments.

Cl. 5.3.2.2(1)

Cl. 5.3.2.2(3)

93

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c)

Punching shear reinforcement Arrangement of punching shear links According to the literal definition of :lp in Exp. (6.52), the same area of shear reinforcement is required for all perimeters inside or outside perimeter n* (rather than (:lp/n*)/sr being considered as the required density of shear reinforcement on and within perimeter n*). For perimeters inside n*, it might be argued that Exp. (6.50) (enhancement close to supports) should apply. However, at the time of writing, this expression is deemed applicable only to foundation bases. Therefore, large concentrations of shear reinforcement are required close to the columns – in this example, this included doubling up shear links at the 1st perimeter.

Exp. 6.50

Similar to BS 8110[7] figure 3.17, it is apparent that the requirement for punching shear reinforcement is for a punching shear zone 1.5d wide. However, in Eurocode 2, the requirement has been ‘simplified’ in Exp. (6.52) to make the requirement for a perimeter (up to 0.75d wide). It might appear reasonable to apply the same 40%:60% rule (BS 8110 Cl. 3.7.7.6) to the first two perimeters to make doubling of punching shear reinforcement at the first perimeter unnecessary: in terms of Eurocode 2 this would mean 80% Asw on the first perimeter and 120% Asw on the second. Using this arrangement it would be possible to replace the designed H10 links in the first two perimeters with single H12 links.

BS 8110: Fig. 3.17

Outside u1, the numbers of links could have been reduced to maintain provision of the designed amount of reinforcement Asw. A rectangular arrangement of H12 links would have been possible (within perimeter u1, 350 × 175; outside u1, 500 × 175). However, as the grid would need to change orientation around each column (to maintain the 0.75d radial spacing) and as the reinforcement in B2 and T2 is essentially at 175 centres, it is considered better to leave the arrangement as a regular square grid.

Cl. 9.4.3(1)

Use of shear reinforcement in a radial arrangement, e.g. using stud rails, would have simplified the shear reinforcement requirements. VEd/VRd,c In late 2008, a proposal was made for the UK National Annex to include a limit of 2.0 or 2.5 on VEd/VRd,c (or vEd/vRd,c) within punching shear requirements. It is apparent that this limitation could have major effects on flat slabs supported on relatively small columns. For instance in Section 3.4.12, edge column with hole, VEd/VRd,c = 2.18. Curtailment of reinforcement In this design, the reinforcement would be curtailed and this would be done either in line with previous examples or, more practically, in line with other guidance[20, 21].

94

Exp. 6.52

BS 8110: Cl. 3.7.7.6

,'.3LmZbk_ebàm 3.5 Stair flight

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Mabl^qZfie^bl_hkZmrib\ZelmZbk_ebàm' Ikhc^\m]^mZbel

0.02 × 1129.6 = 89.6 + 8.9 > 22.6 = 98.5 kNm Load case 2: MEdy = 68.7 kNm MEdz = 6.0 + (l0/400) × 1072.1 × 10−3 > 0.02 × 1072.1 where l0 = 0.9 × 3000 = 13.2 > 21.4 = 21.4 kNm

Table C16

5.2.5 Design using iteration of x For axial load: AsN/2 = (NEd – accnfckbdc /gC)/(ssc – sst)

142

Concise: Section 6.2.2, Appendix A3

For moment: [MEd – accnfckbdc (h/2 – dc/2)/ gC] AsM/2 = (h/2 – d2) (ssc – sst) where MEd = 98.5 × 106 NEd = 1129.6 × 103 acc = 0.85 n = 1.0 for fck ≤ 50 MPa

Cl. 3.1.6(1) & NA Exp. (3.21)

‡The effects of imperfections need only be taken into account in the most unfavourable direction.

Cl. 5.8.9(2)

Appendices A3, C9.2,

.'+3I^kbf^m^k\henfg

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fck b h dc

= 30 = 300 = 300 = depth of compression zone = lx = 0.8x < h where x = depth to neutral axis d2 = 35 + 8 + 25/2 = 55 mm assuming H25 = 1.5 gC ssc, (sst) = stress in reinforcement in compression (tension) o

fcd = accnfck/gC o

ecu2

Table 2.1N

d2 ssc

As2

esc

Exp. (3.19)

dc

x h

n. axis ey o a) Strain diagram

As1

sst

d2 o

b) Stress diagram

Figure 5.4 Section in axial compression and bending

Fig. 6.1

Try x = 200 mm = ecu2 = 0.0035 ecu 0.0035 × (x – d2) 0.0035 × (200 – 55) esc = = x 200 = 0.0025 ssc = 0.0025 × 200000 ≤ fyk/gS = 500 ≤ 500/1.15 = 434.8 MPa = 0.0035(h – x – d2)/x = 0.0035(300 – 200 – 55)/200 est = 0.0008 sst = 0.0008 × 200000 ≤ 500/1.15 = 160 MPa 1129.6 × 103 – 0.85 × 1.0 × 30 × 300 × 200 × 0.8/(1.5 × 103) AsN/2 = 434.8 – 160 = (1129.6 – 816.0) × 103 = 1141 mm2 274.8 143

98.5 × 106 – 0.85 × 1.0 × 30 × 300 × 200 × 0.8 (300/2 – 200 × 0.8/2)/(1.5 × 103) (300/2 – 55) (434.8 + 160) 6 (98.5 – 57.1) × 10 = = 733 mm2 95 × 594.8

AsM/2 =

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Similarly for x = 210 mm ecu = 0.0035 esc = 0.0026 = ssc = 434.8 est = 0.0006 = sst = 120 MPa AsN/2 =

(1129.6 – 856.8) × 103 = 866 mm2 434.8 – 120

AsM/2 =

(98.5 – 56.5) × 106 = 796 mm2 95 × 554.8

Similarly for x = 212 mm ssc = 434.8 = 0.00054 =est = 109 MPa est AsN/2 =

(1129.6 – 865.0) × 103 = 812 mm2 434.8 – 109

AsM/2 =

(98.5 – 56.3) × 106 = 816 mm2 95 × 543.8

= as AsN/2 ≈ AsM/2, x = 212 mm is approximately correct and AsN ≈ AsM, ≈ 1628 mm2 = Try 4 no. H25 (1964 mm2)

5.2.6 Check for biaxial bending By inspection, not critical. [Proof: Section is symmetrical and MRdz > 98.5 kNm. Assuming ey/ez > 0.2 and biaxial bending is critical, and assuming exponent a = 1 as a worst case for load case 2: (MEdz/MRdz)a + (MEdy/MRdy)a = (21.4/98.5)1 + (68.7/98.5)1 = 0.91 i.e. < 1.0 = OK.]

Cl. 5.8.9(3)

Exp. (5.39)

5.2.7 Links Minimum size links = 25/4 = 6.25, say 8 mm Spacing: minimum of a) 0.6 × 20 × 25 = 300 mm, b) 0.6 × 300 = 180 mm or c) 0.6 × 400 = 240 mm

Cl. 9.5.3(3), 9.5.3(4) Use H8 @ 175 mm cc

144

.'+3I^kbf^m^k\henfg

5.2.8 Design summary 4 H25 H8 links @ 175 cc cnom = 35 mm to links

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Figure 5.5 Design summary: perimeter column

145

.', Internal column

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Ma^ÌZmleZ[lahpgbg>qZfie^,'-!kîkh]n\^]Zl?b`nk^.'/"bliZkmh_Zg1&lmhk^rlmkn\mnk^ Z[ho^`khng]pbmaZ[Zl^f^gm[êhp`khng]'Maîkh[e^fblmh]^lb`g\henfg 0.2 and < 5 = Design for biaxial bending.

Cl. 5.8.9(3)

Cl. 5.9.3(3), Exp. (5.38b)

C z ey

MEdy

*

b

Centre of reaction

ez y 2

MEdz

h

Figure 5.10 Eccentricities

5.3.12 Design for biaxial bending Check (MEdz/MRdz)a + (MEdy/MRdy)a ≤ 1.0 For load case 2 where MEdz = 178.7 kNm MEdy = 95.7 kNm MRdz = MRdy = moment resistance. Using charts: From Figure C4d), for d2/h = 0.20 and Asfyk/bhfck = 9648 × 500/500 × 500 × 50 = 0.39 NEd/bhfck = 9000 x 103/(5002 x 50) = 0.72 2 MRd/bh fck = 0.057

Cl. 5.9.3(4), Exp. (5.39)

Fig. C5d)

= MRd ≈ 0.057 × 5003 × 50 = 356.3 kNm

155

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a = exponent dependent upon NEd/NRd where = Acfcd + Asfyd NRd = 500 × 500 × 0.85 × 50/1.5 + 9648 × 500/1.15 = 7083 + 3216 = 10299 kN NEd/NRd = 9000/10299 = 0.87. Interpolating between values given for NEd/NRd = 0.7 (1.5) and for NEd/NRd = 1.0 (2.0) = a = 1.67

Cl. 5.8.3(4)

Notes to Exp. (5.39)

Check (MEdz/MRdz)a + (MEdy/MRdy)a ≤ 1.0 (178.7/356.3)1.67 + (95.7/356.3)1.67

= 0.32 + 0.11 = 0.43 i.e. < 1.0 = OK Use 12 no. H32

5.3.13 Links Minimum diameter of links: = f/4 = 32/4 = 8 mm Spacing, either: a) 0.6 × 20 × f = 12 × 32 = 384 mm, b) 0.6 × h = 0.6 × 500 = 300 mm or c) 0.6 × 400 = 240 mm. = Use H8 links at 225 mm cc Number of legs: Bars at 127 mm cc i.e. < 150 mm = no need to restrain bars in face but good practice suggests alternate bars should be restrained. = Use single leg on face bars both ways @ 225 mm cc

5.3.14 Design summary 12 H32 H8 links @ 225 cc 35 mm to link 500 mm sq fck = 50 MPa

Figure 5.11 Design summary: internal column

156

Cl. 9.5.3 & NA

Cl. 9.5.3(3), 9.5.3(4)

Cl. 9.5.3(6) SMDSC: 6.4.2

.'-3LfZeei^kbf^m^k\henfg .'- Small perimeter column subject to two-hour fire resistance Mabl \Ze\neZmbhg bl bgm^g]^] mh lahp Z lfZee le^g]^k \henfg ln[c^\m mh Z k^jnbk^f^gm _hk +&ahnkËk^k^lblmZg\^'Bmbl[Zl^]hgma^^qZfie^lahpgbgL^\mbhg-'+' Ikhc^\m]^mZbel

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Small perimeter column subject to two-hour fire resistance

36.5 = 159.5 kNm

Cl. 5.8.8.2 Cl. 5.8.8.2(1), 6.1.4

Cl. 5.2.7

M0Ed = equivalent 1st order moment at about z axis at about mid-height may be taken as M0ez where M0ez = (0.6M02 + 0.4M01) ≥ 0.4M02 = 0.6 × 159.5 + 0.4 × 0 ≥ 0.4 × 159.5 = 95.7 kNm = nominal 2nd order moment = N>]e2 M2 where e2 = (1/r) l02/10 where 1/r = curvature = KvKh[fyd/(Es × 0.45d)] where Kv = a correction factor for axial load = (nu – n)/(nu – nbal)

Cl. 5.8.8.2(2) Cl. 5.8.8.2(3) Cl. 5.8.8. 3 Exp. (5.34)

161

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where nu = 1 + w where w = mechanical ratio = Asfyd/Acfd = 1.08 as before nu = 2.08 n = NEd/Acfcd = 1824.1/2082 = 0.88 nbal = the value of n at maximum moment resistance = 0.40 (default) (2.08 – 0.88)/(2.08 – 0.40) 1.20/1.68 = 0.71 a correction factor for creep 1 + bhef

Kv = = Kh = = where b = = = = hef = =

0.35 + (fck/200) – (l/150) 0.35 + 30/200 – 29.3/150 0.35 + 0.15 – 0.195 0.305 effective creep coefficient‡ h(∞,t0) M0,Eqp/M0Ed

where h(∞,t0) = final creep coefficient = from Figure 3.1 for inside conditions h = 350 mm, C30/37, t0 = 15 ƺ 2.4 M0,Eqp = 1st order moment due to quasipermanent loads Gk + h2 Qk × Mz + eiNEd ≈ jgGGk + h0gQQk = =

M0Ed

Cl. 5.8.4(2)

Cl. 3.1.4(2) Fig. 3.1a

63.3 + 0.8 × 46.0 × Mz + eiNEd 1.35 × 63.3 + 1.5 × 46.0 100.1 × 146.1 + 13.4 154.5

= 108.1 kNm = M02

= 159.5 kNm

‡

With reference to Exp. (5.13N), hef may be taken as equal to 2.0. However, for the purpose of illustration the full derivation is shown here.

162

Exp. (5.1.3N)

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.'-3LfZeei^kbf^m^k\henfg

Kh = 1 + 0.305 × 2.4 × 108.1/159.5 = 1.50 fyd = 500/1.15 = 434.8 MPa Es = 200000 MPa d = effective depth = 350 – 35 – 8 – 16 = 291 mm 1/r = 0.71 × 1.50 × 434.8/(200000 × 0.45 × 291) = 0.0000177 l0 = 2965 mm as before e2 = (1/r) l02/10 = 15.6 mm = 0.0000177 × 29652/10 =M2 = NEde2 = 1824.1 × 103 × 15.6 = 28.4 kNm =0 M01 = MEdz = max[M02z; M0Edz + M2; M01 + 0.5M2] = max[159.5; 95.7 + 28.4; 0 + 28.4/2] = 159.5 kNm

Mz = 146.1 kNm

+

Mz = 0

M2/2 = 14.2 kNm

a) 1st order moments from analysis

MEdz = 159.5 kNm

eiNEd = 13.4 kNm

M2 = 28.4 kNm

Cl. 3.2.7(3)

MOEdz = 95.8 kNm

=

Mz = 0

c) Design moments: MEdz b) Including 2nd order moments: about z axis MEdz = max [M02, MOEd + M2, M01 = 0.5M2]

Figure 5.13 Design moments MEdz

5.4.6 Design moments: MEdy about y axis

MEdy = max[ M02y ; M0Edy + M2 ; M01 + 0.5M2]

where M02y = = = M0Edy = =

§

My + eiNEd ≥ e0NEd 114.5 + 13.4§ ≥ 36.7 kNm 127.9 kNm (0.6M02y + 0.4 M01y) ≥ 0.4M02y 0.6 × 114.5 + 0.4 × 0

Imperfections need to be taken into account in one direction only.

Cl. 5.8.9(2) 163

M2

= 68.7 kNm = 0 (as column is not slender not slender about y axis). = MEdy = 127.9 kNm

5.4.7 Design in each direction using charts = 1824.1 × 103/(3502 × 30) = 0.50 2 MEd/bh fck = 159.5 × 106/(3503 × 30) = 0.124 Assuming 8 bar arrangement, centroid of bars in half section: d2 ≥ 35 + 8 + 16 + (350/2 – 35 –8 – 16) × 1/4 ƽ 59 + 29 = 88 mm d2/h = 0.25

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In z direction: NEd/bhfck

From Figure C4e) Asfyk/bhfck = 0.50 = 0.50 × 3502 × 30/500 = 3675 mm2 As = 4 no. H32 + 4 no. T25 (5180 mm2) OK.

Fig. C4e)

Fig. C4e)

In y direction: MEd/bh2fck = 127.9 × 106/(3503 × 30) = 0.10 NEd/bhfck = 0.50 From Figure C4e) Asfyk/bhfck = 0.34 = 0.34 × 3502 × 30/500 = 2499 mm2 As = 4 no. H32 + 4 no. T25 (5180 mm2) OK.

5.4.8 Check biaxial bending ly ≈ lz = OK. ez = MEdy/NEd ey = MEdz/NEd MEdz 159.5 ey/heq = = = 1.25 MEdy 127.9 ez/beq = need to check biaxial bending (MEdz/MRdz)a + (MEdy/MRdy)a ≤ 1.0 where MRdz = MRdy = moment resistance= Using Figure C4e) Asfyk/bhfck = 5180 × 500/(3502 × 30) = 0.70 for NEd/bhfck = 0.50 MEd/bh2fck = 0.160 = MRd = 0.160 × 3503 × 30 164

Exp. (5.38a)

Exp. (5.38b)

Exp. (5.39)

Fig. C4e)

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

.'-3LfZeei^kbf^m^k\henfg

= 205.8 kNm a depends on NEd/NRd where = Acfcd + Asfyd NRd = 3502 × 0.85 × 30/1.5 + 5180 × 500/1.15 = 2082.5 + 2252.2 = 4332.7 kN NEd/NRd = 1824.1/4332.7 = 0.42 = a = 1.27 (159.5/205.8)1.27 + (114.5/205.8)1.27 = 0.72 + 0.47 = 1.19 = No good = Try 8 no. T32 (6432 mm2) For Asfyk/bhfck = = for NEd/bhfck = = MEd/bh2fck = MRd =

6432 × 500/(3502 × 30) 0.88 0.50 0.187 240.5 kNm

Check biaxial bending (159.5/245.7)1.27 + (114.5/245.7)1.27

= 0.59 + 0.39

Cl. 5.8.9(4)

Fig. C4e)

= 0.98 OK

5.4.9 Check maximum area of reinforcement As/bd = 6432/3502 = 5.2% > 4% However, if laps can be avoided in this single lift column then the integrity of the concrete is unlikely to be affected and 5.2% is considered OK. OK

Cl. 9.5.2(3) & NA

PD 6687: 2.19

5.4.10 Design of links Diameter min. = 32/4 = 8 mm Spacing max. = 0.6 × 350 = 210 mm

Cl. 9.5.3 & NA Cl. 9.5.3(3), 9.5.3(4) = Use H8 @ 200 mm cc

5.4.11 Design summary 8 H32 H8 links @ 200 cc 35 mm cover to link No laps in column section Note The beam should be checked for torsion.

Figure 5.14 Design summary: small perimeter column 165

/ Walls /') General PZeel Zk^ ]^Ëg^] Zl [^bg` o^kmb\Ze ê^f^gml pahl^ e^g`mal Zk^ _hnk mbf^l `k^Zm^k maZg ma^bk mab\dg^ll^l'Ma^bk]^lb`g]h^lghm]b__^klb`gbË\Zgmer_khfma^]^lb`gh_\henfglbgmaZmZqbZe ehZ]lZg]fhf^gmlZ[hnm^Z\aZqblZk^Zll^ll^]Zg]]^lb`g^]_hk' Ma^\Ze\neZmbhglbgmabll^\mbhgbeenlmkZm^ma^]^lb`gh_Zlbgè^la^ZkpZee'

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

@^g^kZeer%ma^f^mah]h_]^lb`gbg`pZeelblZl_heehpl'BgikZ\mb\^%lô^kZeh_ma^l^lmîlfZr[^ \hf[bg^]' N =^m^kfbg^]^lb`geb_^'

EC0 & NA Table NA 2.1

N :ll^llZ\mbhglhgma^pZee'

EC1 (10 parts) & UK NAs

N =^m^kfbg^pab\a\hf[bgZmbhglh_Z\mbhglZiier'

EC0 & NA: Tables NA A1.1 & NA: A1.2(B)

N :ll^ll]nkZ[bebmrk^jnbk^f^gmlZg]]^m^kfbg^\hg\k^m^

BS 8500–1

lmk^g`ma' N ]% bg ma^ ieZg^ i^ki^g]b\neZk mh ma^ pZee'Ma^ ^__^\ml h_ Zeehpbg`_hkbfi^k_^\mbhglZk^ZelhbeenlmkZm^]' Ikhc^\m]^mZbel

G*22+¾*¾*%>nkh\h]^+¾IZkm*¾*3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾@^g^kZekne^lZg]kne^l_hk[nbe]bg`l';LB%+))-' 1a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm*¾*';LB%+)).' 2 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾*¾+%>nkh\h]^+¾IZkm*¾+3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾@^g^kZekne^l¾Lmkn\mnkZe_bk^]^lb`g';LB%+))-' 2a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm*¾+';LB%+)).'

3 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾+%>nkh\h]^+¾IZkm+3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾;kb]`^l';LB%+)).' 3a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm+';LB%+))0'

4 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22+¾,%>nkh\h]^+¾IZkm,3=^lb`gh_ \hg\k^m^lmkn\mnk^l¾Ebjnb]&k^mZbgbg`Zg]\hgmZbgf^gmlmkn\mnk^l';LB%+))/' 4a GZmbhgZe:gg^qmh>nkh\h]^+¾IZkm,';LB%+))0'

5 K LG:K:R:G:GKL(MA>LHMR(=MB'LmZg]Zk] f^mah]h_]^mZbebg`lmkn\mnkZe\hg\k^m^%Mabk]>]bmbhg'BLmkn\m>%+))/'

10 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22)%>nkh\h]^3;Zlblh_lmkn\mnkZe]^lb`g' ;LB%+))+' 10a GZmbhgZe:gg^qmh>nkh\h]^';LB%+))-' 11 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*22*%>nkh\h]^*3:\mbhglhglmkn\mnk^l !*)iZkml"';LB%+))+¾+))/' 11a GZmbhgZe:gg^q^lmh>nkh\h]^*';LB%+)).¾+))1Zg]bgikîZkZmbhg' 12 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*220¾*%>nkh\h]^0'@^hm^\agb\Ze]^lb`g' @^g^kZekne^l';LB%+))-' 12a GZmbhgZe:gg^qmh>nkh\h]^0;L>G*220¾*';LB%+))0' 13 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L>G*221¾*%>nkh\h]^1'=^lb`gh_lmkn\mnk^l_hk ^ZkmajnZd^k^lblmZg\^'@^g^kZekne^l'L^blfb\Z\mbhgl_hk[nbe]bg`l';LB%+))-' 13a GZmbhgZe:gg^qmh>nkh\h]^1;L>G*221¾*';LB%+))1'

14 ; KBMBLALM:G=:K=LBGLMBMNMBHG';L1.))¾*3]bmbhg%JN>>G LIKBGM>KH?:GM%Ma^;nbe]bg`K^`neZmbhgl+)))'Ma^ LmZmbhg^krH__b\Êbfbm^]%+)))'

21 M A>LM:MBHG>KRH??BEBFBM>=!MLH"%;nbe]bg`!:f^g]f^gm"!Gh+"K^`neZmbhgl+))+ Zg]ma^;nbe]bg`!:iikho^]Bgli^\mhkl^m\'"!:f^g]f^gm"K^`neZmbhgl+))+'MLH%+))+'

22 ; KBMBLALM:G=:K=LBGLMBMNMBHG'==>GO*,/0)¾*3+)))3>q^\nmbhgh_\hg\k^m^ lmkn\mnk^l3nkh\h]^*¾IZkm*¾-';LB%+))1'

26 ; KHHD>K%H']phne][^nl^]'

185

Lheobg`ma^jnZ]kZmb\^jnZmbhg3 s(]6T*$!*¾,'.+2D")'.V(+ s6]T*$T*¾,'.+2D")'.V(+

Table C5

Bmbl\hglb]^k^]`hh]ikZ\mb\^bgma^NDmhebfbms(]mhZfZqbfnfh_)'2.]'!Mabl`nZk]lZ`Zbglm kêrbg` hg o^kr mabg l^\mbhgl h_ \hg\k^m^ pab\a Zm ma^ ^qmk^f^ mhi h_ Z l^\mbhg fZr [^ h_ jn^lmbhgZ[e^lmk^g`ma'"MZ[e^l`bobgòZen^lh_s(]Zg]q(]_hkoZen^lh_DfZr[^nl^]' Area of reinforcement, As MZdbg`fhf^gmlZ[hnmma^\^gmk^h_ma^\hfik^llbhg_hk\^3 F6)'10:l _rds

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

:l6F(!)'10_rd s" Limiting value of relative flexural compressive stress, K' :llnfbg` gh k^]blmkb[nmbhg mZd^l ieZ\^% Z ebfbmbg` oZen^ !hg ma^ lmk^g`ma h_ \hg\k^m^ bg \hfik^llbhg"_hkD\Zg[^\Ze\neZm^]!]^ghm^]D "Zl_heehpl' Table 3.1

e\n, 6 \hg\k^m^lmkZbg6)')),. 6 k^bg_hk\^f^gmlmkZbg el 6 .))(!*'*.+))*),"6)'))++ ?khflmkZbg]bZ`kZf%?b`nk^:* q 6 )')),.](!)')),.$)'))++" 6 )'/] ?khf^jnZmbhglZ[ho^3 F 6 )'-.,_\d[qs F 6 )'-.,_\d[)'/]!]¾)'-)'/]" 6 )'+)0_\d[]+ =D 6)'+)0 Bm bl h_m^g \hglb]^k^] `hh] ikZ\mb\^ mh ebfbm ma^ ]îma h_ ma^ g^nmkZe Zqbl mh Zohb] Âho^k& k^bg_hk\^f^gmÃ!b'^'mh^glnk^maZmma^k^bg_hk\^f^gmblrbê]bg`Zm_Zbenk^%manlZohb]bg`[kbmme^ _Zbenk^h_ma^\hg\k^m^"'H_m^gq(]blebfbm^]mh)'-.'Mablblk^_^kk^]mhZlma^[ZeZg\^]l^\mbhg [^\Znl^Zmma^nembfZmêbfbmlmZm^ma^\hg\k^m^Zg]lm^êk^Z\ama^bknembfZm^lmkZbglZmma^ lZf^mbf^T,*V'MablblghmZ>nkh\h]^+k^jnbk^f^gmZg]blghmZ\\îm^][rZee^g`bg^^kl' Ghg^maê^ll_hkq6)'-.] ?khf^jnZmbhglZ[ho^3 F 6 )'-.,_\d[qs F 6 )'-.,_\d[)'-.]!]¾)'-)'-.]" 6 )'*/0_\d[]+ =D 6 )'*/0

Cl. 5.5(4)

q(]blZelhk^lmkb\m^][rma^Zfhngmh_k^]blmkb[nmbhg\Zkkb^]hnm'?hk_\d©.)FIZ dª)'-$!)'/$)'))*-e\n"qn(] pa^k^ ] 6 k^]blmkb[nm^]fhf^gm(êZlmb\[^g]bg`fhf^gm[^_hk^k^]blmkb[nmbhg qn 6 ]îmah_ma^g^nmkZeZqblZmNELZ_m^kk^]blmkb[nmbhg e\n 6 \hfik^llbo^lmkZbgbgma^\hg\k^m^ZmNEL Mabl`bo^lmaôZen^lbgMZ[e^:*'

186

:ii^g]bq:3=^kbo^]_hkfneZ^ Table A1 Limits on D with respect to redistribution ratio, d d

1

0.95

0.9

0.85

0.8

0.75

0.7

% redistribution

)

.

*)

*.

+)

+.

,)

K'

)'+)1

)'*2.

)'*1+

)'*/1

)'*.,

)'*,0

)'*+)

B_D7D ma^l^\mbhglahne][^k^lbs^]hk\hfik^llbhgk^bg_hk\^f^gmblk^jnbk^]'Bgebg^pbma \hglb]^kZmbhg h_ `hh] ikZ\mb\^ hnmebg^] Z[ho^% this publication adopts a maximum value of K'= 0.167'

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

A1.2 Compression reinforcement, As2 Ma^fZchkbmrh_[^Zflnl^]bgikZ\mb\^Zk^lbgèrk^bg_hk\^]%Zg]ma^l^[^Zfl\Zg[^]^lb`g^]nlbg` ma^_hkfneZ]^kbo^]Z[ho^'Bglhf^\Zl^l%\hfik^llbhgk^bg_hk\^f^gmblZ]]^]bghk]^kmh3 N Bg\k^Zl^l^\mbhglmk^g`mapa^k^l^\mbhg]bf^glbhglZk^k^lmkb\m^]%b'^'pa^k^D7D N Mhk^]n\êhg`m^kf]^_e^\mbhg N Mh]^\k^Zl^\nkoZmnk^(]^_hkfZmbhgZmnembfZmêbfbmlmZm^

As2

As Figure A3 Beam with compression reinforcement

Pbmak^_^k^g\^mh?b`nk^:*%ma^k^blghpZg^qmkZ_hk\^ ?l\6)'10:l+ _rd Ma^Zk^Zh_m^glbhgk^bg_hk\^f^gm\Zgghp[^\hglb]^k^]bgmphiZkml%ma^_bklmiZkmmh[ZeZg\^ ma^\hfik^llbo^_hk\^bgma^\hg\k^m^%ma^l^\hg]iZkmmh[ZeZg\^ma^_hk\^bgma^\hfik^llbhg lm^ê'Ma^Zk^Zh_m^glbhgk^bg_hk\^f^gmk^jnbk^]blma^k^_hk^3 :l6D _\n[] +(!)'10_rds"$:l+ pa^k^ sbl\Ze\neZm^]nlbg`D'bglm^Z]h_D :l+\Zg[^\Ze\neZm^][rmZdbg`fhf^gmlZ[hnmma^\^gmk^h_ma^m^glbhg_hk\^3 F6F $)'10_rd:l+!]¾]+" F6D _\n[] +$)'10_rd:l+!]¾]+" K^ZkkZg`bg`3 :l+6!D¾D " _\d[] +(T)'10_rd!]¾]+"V

A2 Shear A2.1 Shear resistance (without shear reinforcement), VRd,c OK]%\6T] ([s6O>] (![)'2]" Bgfhlm\Zl^l%pa^k^\hmy6+'.%y6+*'1 oK]%fZq%\hmy6+'.6)'*,1[ps_\dT*¾_\d (+.)V hk oK]%fZq%\hmy6+'.6)'*,1_\dT*¾_\d (+.)V pa^k^ oK]%fZq%\hmy6+'. 6OK]%fZq%\hmy6+'.(![s" 6OK]%fZq%\hmy6+'.(!)'2[]" Pa^k^\hmy7+'.%ma^Zgè^h_ma^lmknmZg]oK]%fZqlahne][^\Ze\neZm^]%hkoK]%fZqfZr[^ ehhd^]nibgmZ[e^lhk\aZkml!^'`'MZ[e^] (s_rp]\hmy hk :lp(lªo>]%s[p(_rp]\hmy

Exp. (9.5N) & NA

FbgbfnfZk^Zh_la^Zkk^bg_hk\^f^gm :lp%fbg (!l[plbga"ª)')1_\d)'.(_rd pa^k^ l 6 ehg`bmn]bgZeliZ\bg`h_ma^la^Zkk^bg_hk\^f^gm [p 6 [k^Z]mah_ma^p^[

188

:ii^g]bq:3=^kbo^]_hkfneZ^ a 6 Zgè^h_ma^la^Zkk^bg_hk\^f^gmmhmaêhg`bmn]bgZeZqblh_ma^f^f[^k'?hko^kmb\Ze ebgdllbga6*')' K^ZkkZg`bg`_hko^kmb\Zeebgdl3 Alp%fbg (lª)')1[plbga_\d)'.(_rd

A3 Columns

Licensed copy from CIS: kierg, Kier Group, 12/02/2015, Uncontrolled Copy.

el\

_\]6a\\n_\d(g< sl\ ] + :

e\n+

l+

]\

q a

g'Zqbl er

:l*

slm

e\ a) Strain diagram

Fig. 6.1

]+

b) Stress diagram

Figure A4 Section in axial compression and bending

?hkZqbZeehZ] G>]6_\] []\$:l+sl\¾:l*slm ;nmZl:l+6:l*6:lG(+ G>]6_\] []\$:lG!sl\¾slm"(+ G>]¾_\] []\6:lG!sl\¾slm"(+ !G>]¾_\] []\"(!sl\¾slm"6:lG(+ :lG(+6!G>]¾_\] []\"(!sl\¾slm" =:lG(+6!G>]¾a\\n_\d[]\ (g]6_\] []\!a(+¾]\ (+"$:l+sl\!a(+¾]+"$:l*slm!a(+¾]+" ;nmZl:l+6:l*6:lF(+ F>]6_\] []\!a(+¾]\ (+"$:lF!sl\$slm"!a(+¾]+"(+ F>]¾_\] []\!a(+¾]\ (+"6:lF!sl\$slm"!a(+¾]+"(+ TF>]¾_\] []\!a(+¾]\ (+"V(!sl\$slm"!a(+¾]+"6:lF(+ =:lF(+6TF>]¾a\\n_\d []\!a(+¾]\ (+"(gG*22+¾*¾+lmbineZm^lmaZm+.h_^g]liZg fhf^gmlahne][^nl^]mh]^m^kfbg^^g]lniihkmk^bg_hk\^f^gm'MablblnlnZeerZ\\hffh]Zm^] [rikhob]bg`+.h_^g]liZg[hmmhflm^êZlmhilm^êZm^g]lniihkml'Bmblhgmabl[ZlblmaZm ma^\Ze\neZmbhglbgmablin[eb\ZmbhgZk^\hglb]^k^]Zl[^bg`_nkma^kln[lmZgmbZm^]'

B1.5 Note regarding factor 310/ss (factor F3) :mma^mbf^h_in[eb\Zmbhg!=^\^f[^k+))2"ma^Znmahklp^k^ZpZk^h_Zikh[Z[e^\aZg`^mh NDG:T+ZVMZ[e^G:'.pab\a%bg^__^\m%phne]f^ZgmaZmma^_Z\mhk,*)(sl!?,"6:l%ikho(:l%k^j ≤ *'.% manl ]blZeehpbg` ma^ Z\\nkZm^ f^mah] hnmebg^] bg L^\mbhgl ,'*% ,'+% ,',% ,'-% -', Zg] :ii^g]b\^l;*'*%;*'+Zg]qi' !/'*)[" pbee [^ ZiikhikbZm^% ^q\îm _hk lmhkZ`^ pa^k^ ma^ nl^ h_ >qi' !/'*)Z" blebdêrmh[^fhk^hg^khnl' ?hkma^LELh_]^_hkfZmbhg%jnZlb&i^kfZg^gmehZ]llahne][^Ziieb^]'Ma^l^Zk^*')@d$c+Jd pa^k^c+bl]î^g]^gmhgnl^%^'`')',_hkh__b\^lZg]k^lb]^gmbZeZg])'0_hklmhkZ`^'

C2 Values of actions MaôZen^lh_Z\mbhgl!b'^'ehZ]l"Zk^]^_bg^]bg>nkh\h]^*T**V'MaîZkmlh_>nkh\h]^*Zk^`bo^g bgMZ[e^G*22*¾*¾*lmZm^lmaZmma^]^glbmrh_\hg\k^m^bl+-dG(f,%k^bg_hk\^]\hg\k^m^%+.dG(f, Zg]p^mk^bg_hk\^]\hg\k^m^%+/dG(f,' Table C1 The parts of Eurocode 1[11]

194

Reference

Title

BS EN 1991-1-1

=^glbmb^l%lê_&p^bàmZg]bfihl^]ehZ]l

BS EN 1991-1-2

:\mbhglhglmkn\mnk^l^qihl^]mh_bk^

BS EN 1991-1-3

LghpehZ]l

BS EN 1991-1-4

Pbg]Z\mbhgl

BS EN 1991-1-5

Ma^kfZeZ\mbhgl

BS EN 1991-1-6

:\mbhgl]nkbg`^q^\nmbhg

BS EN 1991-1-7

:\\b]^gmZeZ\mbhgl]n^mhbfiZ\mZg]^qiehlbhgl

BS EN 1991-2

MkZ__b\ehZ]lhg[kb]`^l

BS EN 1991-3

:\mbhglbg]n\^][r\kZg^lZg]fZ\abg^kr

BS EN 1991-4

:\mbhglbglbehlZg]mZgdl

:ii^g]bq]6 ]^lb`gfhf^gm _r] 6 _rd (gL6.))(*'*.6-,-'1FIZ s 6 ]T)'.$)'.!*¾,'.,D")'.V©)'2.] OZen^lh_s(]!Zg]q(]"fZr[^mZd^g_khfMZ[e^nkh\h]^+Zg]NDGZmbhgZe:gg^q' 2MZ[e^\k^Zm^]_hk_\d6,)FIZZllnfbgò^kmb\Zeebgdl' 3?hkr eª)'-Zg] _\d6+.FIZ%Ziier_Z\mhkh_)'2-

_\d6-)FIZ%Ziier_Z\mhkh_*'*)

_\d6.)FIZ%Ziier_Z\mhkh_*'*2

_\d6,.FIZ%Ziier_Z\mhkh_*').

_\d6-.FIZ%Ziier_Z\mhkh_*'*-

GhmZiieb\Z[e^_hk_\d7.)FIZ

C5.2 Section capacity check B_o>]%s7oK]%fZqma^gl^\mbhglbs^blbgZ]^jnZm^ pa^k^ o>]%s 6 O>] ([ps6O>] ([p)'2]%_hkl^\mbhglpbmala^Zkk^bg_hk\^f^gm oK]%fZq6 \ZiZ\bmrh_\hg\k^m^lmknml^qik^ll^]ZlZlmk^llbgmaô^kmb\ZeieZg^ 6 OK]%fZq ([ps 6 OK]%fZq ([p)'2] oK]%fZq\Zg[^]^m^kfbg^]_khfMZ[e^nkh\h]^+Zg]NDGZmbhgZe:gg^qZllnfbgò^kmb\Zeebgdl%b'^'\hma6) 2v6)'/T*¾!_\d (+.)"V 3oK]%fZq6v_\]!\hmy$\hma"(!*$\hm+y"

198

Strength reduction factor, v

:ii^g]bq]%s[p(_rp]\hmy pa^k^ :lp 6 Zk^Zh_la^Zkk^bg_hk\^f^gm!o^kmb\ZeebgdlZllnf^]" l 6 liZ\bg`h_la^Zkk^bg_hk\^f^gm o>]%s 6 O>] ([ps%Zl[^_hk^ [p 6 [k^Z]mah_ma^p^[ _rp] 6 _rpd (gL6]^lb`grbê]lmk^g`mah_la^Zkk^bg_hk\^f^gm

:em^kgZmboêr% :lp(l i^k f^mk^ pb]ma h_ [p fZr [^ ]^m^kfbg^] _khf ?b`nk^ ]7oK]%\ma^ging\abg`la^Zkk^bg_hk\^f^gmblk^jnbk^] pa^k^ o>] 6 bO>] (nb]

pa^k^ b 6 _Z\mhk]^Zebg`pbma^\\^gmkb\bmr O>] 6 Ziieb^]la^Zk_hk\^ nb 6 e^g`mah_maî^kbf^m^kng]^k\hglb]^kZmbhg ] 6 f^Zg^__^\mbo^]îma oK]%\ 6 la^Zkk^lblmZg\^pbmahnmla^Zkk^bg_hk\^f^gm!l^^MZ[e^]¾)'0.oK]%\"(!*'._rp]%^_" pa^k^ :lp 6 Zk^Zh_la^Zkk^bg_hk\^f^gmbghgî^kbf^m^kZkhng]ma^\henfg' ?hk:lp%fbgl^^nkh\h]^+%L^\mbhg*)'-'+Zg]_hkeZrhnml^^L^\mbhg*+'-', lk 6 kZ]bZeliZ\bg`h_i^kbf^m^klh_la^Zkk^bg_hk\^f^gm Concise: 10.4.2, 12.4.3

_rp]%^_

n* 6 [Zlb\\hgmkhei^kbf^m^k+]_khf\henfg_Z\^ 6 ^__^\mbo^]^lb`glmk^g`mah_k^bg_hk\^f^gm6!+.)$)'+.]"©_rp]'?hk@kZ]^ .))la^Zkk^bg_hk\^f^gml^^MZ[e^]≤OK]fZq_hk\hmy6*')`bo^gbgMZ[e^

Worked Examples to Eurocode 2.pdf

Short Description

Description

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