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J.M. Zwarthoed

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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J.M. Zwarthoed 5Possible locations with regard to exceeding maximum crack width (2)

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?