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Workshop on Cracking and Durability of Reinforced Concrete
Concerning the Serviceability Limit State
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Starting points of structural analysis
• Analysis in ULS and SLS:- main concern safety; - durability of minor concern.
• According to code VBB 1995:- dead weight = 1,5;- traffic loading = 1,5.
• According to code NAD ENV 1991-3:- dead weight = 1,35;- traffic loading = 1,42;- with the actual traffic lane subdivision;- with reduction of structure service life.
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Requirements SLS - NEN 6720
• For all structures important crack width!• Maximum permissible crack width depends on
environmental exposure conditions: - humid (outside): wmax = 0,3 mm;
- aggressive (outside&salt): wmax = 0,2 mm;
- in case of pre-stressing: wmax = 0,1 mm.
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J.M. Zwarthoed 4Possible locations with regard to exceeding maximum crack width (1)
1
3
2 4
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5
6
7
8
9 10
11 12 13
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Analyses crack width calculations reinforced concrete slab
• five different calculation methods• concrete slab: K300 (C20/B25), CEM I
• rebars: 16-200 QR40 fs = 329 N/mm2
(FeB 400) hot rolled steel
• cracked section• crack width during and after completion of
crack development phase
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Comparison result calculations
Crackwidth calculation reinforced slab
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
100 150 200 250 300 350 400 450
steelstress [N/mm2]
crac
kwid
th [
mm
]
method A method B
former national code NEN 3880 Noakowski static
Noakowski dynamic
appr. region of steelstresses SLS
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Crack width calculation pre-stressed concrete slab
• concrete bridge deck: B37,5 (C30/37) CEM I• rebars: 12-250 FeB 400 hot rolled steek• pre-stressing: 35·1182 mm2 FeP 1860
• Md/Mu = 21988/23145= 0,95 [kNm/kNm]
• Mrep = 14659 kNm
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Result calculations
• bridge deck meets all requirements ULS except fatigue, meets none with regard to SLS
• assumption: no imposed deformations• during stage of development crack pattern
wmax = 0,4 mm
• in case of fully developed crack pattern wmax = 0,32 mm
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Conclusions (1)
The first main problem is:• insufficient transversal rebar reinforcement in
decks causing cracks according to model 1, 2, 5 and 13 with wmax 0,2-0,4 mm.
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Conclusions (2)
The second main problem is:• insufficient longitudinal rebar reinforcement in
combination with main pre-stressing reinforcement causing cracks according to model 6, and 7 with wmax 0,5 mm;
• insufficient longitudinal rebar reinforcement causing cracks according to model 11 and 12 with wmax 0,2-0,4 mm.
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Note!
One has to keep in mind the following aspects:
• We assume the calculated crack width according to NEN 3880 as an upper limit.
• Calculations bases on the 28th-day concrete strength.
• Did the actual SLS loading occur?