11 design flexural strengthening problema

8/3/2019 11 Design Flexural Strengthening Problema

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DESIGN EXAMPLE FLEXURAL STRENGTHENING

1

RC beam strengthened with CFRP composite for bending

.

410

370


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2. CROSS SECTION AND MATERIALS

RCbeam

h=40cm

FRPcomposite

bf =50mm

=

d=36.7cmAs1 =216=4.02cm

240

.

Efk =165000N/mm2

fku =1.7%

Concrete:

C30/37

fck =30N/mm2

Ec =33000N/mm2

fctm =2.9N/mm220

Steel:fyk =500N/mm

2

Es =210000N/mm2


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3. LOADS AND DESIGN VALUES

1.Selfweight G=

2.Liveloadbeforestrengthening q1 =

3.Liveloadafterstrengthening q1 +q2 =

,1 ,1

where c =1.5

=

s

f =1.2


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4. INITIAL SITUATION

ServicemomentMo selfweight+q1

Calculationoftheneutralaxisdepthx0:

2 2 2 1 Where

/


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1 1 1

Theconcretestrain co atthetopfibrecanbeexpressedas:

Where

3 12 22 1 2


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Basedonthestraincompatibility,thestrain o attheextremetensionfiber

canbederivedas


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5. ANALYSIS IN ULS

5.1. Full composite action Steelyieldingfollowedbyconcretecrushing

0.85 22 1 Where =0.8 and


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5. ANALYSIS IN ULS


Onlyiterativesolvingpossible:

1st proposal x=90mm =0.85

1 2nd ro osal x=.... cm

=.

1


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5. ANALYSIS IN ULS


)()()(2221dxEAxhEAxdfAM GsssGfffGydsRd

Where G =0.4


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5. ANALYSIS IN ULS

5.1. Full composite action SteelyieldingfollowedbyFRP fracture

istheoreticallypossibleifpropermechanicalanchorageareused

ISNOTTHECASE


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5. ANALYSIS IN ULS5.2. Loss composite action

a> +

aL


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5. ANALYSIS IN ULS5.2. Loss composite action

Endshearfailure

Where 1

1 2

34

0.15 3 3

1 200 1003

(designvalueofresistingshearstrengthofconcrete)


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5. ANALYSIS IN ULS5.3. Verification of peeling-off at the end anchorage and at flexural

Approach1: AnchorageverificationandFRP strainlimitation

cracks

Af

As1

lb

Ns1

z

NbNf


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Anchorageverification

cracks

ThemaximumFRP forcewhichcanbeanchored:, 1 Themaximumanchorable length:

, 2


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cracks

Where: =0.9or =1.0 forbeamswithsufficientinternalandexternalreinforcement

kc =1.0

2 geometry actor . 1 4001 = .c2 =2.0


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cracks

,

,


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cracks

Initialsituationatthepositionofz


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cracks

c

andx isunknownonlyiterativesolvingispossible


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cracks

Forceequilibriumcondition:

st

. 1 1 .... c .

1000 0.5 1000


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cracks

1st proposal x=....cm and c 0.002

8 1000

)()(11 xhEAxdEAM GGsssRd


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cracks

2nd proposal x=....cm and c 0.0021000 . 12

.


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cracks

2nd proposal x=....cm and c 0.002

8 1000

)()(11 xhEAxdEAM GGsssRd


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cracks

, , ,

Where cb =1.5

11 design flexural strengthening problema

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