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DESIGN EXAMPLE FLEXURAL STRENGTHENING

410

370

P/2 P/2

RC beam strengthened with CFRP composite for bending

1. SYSTEM

1

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RC beamh = 40 cm

b = 20 cm

d = 36.7 cm

As1 = 216 = 4.02 cm2

Concrete:C30/37

fck = 30 N/mm2

Ec = 33000 N/mm2

fctm = 2.9 N/mm2

Steel:

fyk = 500 N/mm2

Es = 210000 N/mm2

2. CROSS SECTION AND MATERIALS

20

40

FRP compositebf= 50 mm

tf= 1.2 mm

Efk = 165000N/mm2

fku = 1.7%

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1. Self-weight G =

2. Live load before strengthening q1 =

3. Live load after strengthening q1 + q2 =

where c = 1.5

s = 1.15

f = 1.2

3. LOADS AND DESIGN VALUES

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Service moment Mo self-weight + q1

Calculation of the neutral axis depth x0:

Where

4. INITIAL SITUATION

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The concrete strain co at the top fibre can be expressed as:

Where

4. INITIAL SITUATION

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Based on the strain compatibility, the strain o at the extreme tension fibercan be derived as

4. INITIAL SITUATION

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Steel yielding followed by concrete crushing

Where =0.8 and

5. ANALYSIS IN ULS

5.1. Full composite action

0.85

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Steel yielding followed by concrete crushing

Only iterative solving possible:

1st proposal x = 90 mm

2nd proposal x = .... cm

=

0.85

=0.85

5. ANALYSIS IN ULS

5.1. Full composite action

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Steel yielding followed by concrete crushing

Where G

= 0.4

)()()( 2221 dxEAxhEAxdfAM GsssGfffGydsRd ! HIHIH

5. ANALYSIS IN ULS

5.1. Full composite action

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Steel yielding followed by FRP fracture

is theoretically possible if proper mechanical anchorage are used

IS NOTTHE CASE

5. ANALYSIS IN ULS

5.1. Full composite action

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5. ANALYSIS IN ULS

5.2. Loss composite action

a > L + d

aL

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End shear failure

Where

(design value of resisting shear strength of concrete)

5. ANALYSIS IN ULS

5.2. Loss composite action

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Approach 1: Anchorage verification and FRP strain limitation

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

lb

Af

As1

Nb

Ns1

Nf

z

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Anchorage verification

The maximum FRP force which can be anchored:

The maximum anchorable length:

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

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Anchorage verification

Where: = 0.9 or = 1.0 for beams with sufficient internaland external reinforcement

kc = 1.0

geometry factor

c1 = 0.64

c2 = 2.0

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

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Anchorage verification

z =

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

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Anchorage verification

Initial situation at the position of z

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

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Anchorage verification

candx is unknownonlyiterative solving is possible

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

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Anchorage verification

Force equilibrium condition:

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

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

0.85

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Anchorage verification

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

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

0.

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Anchorage verification

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

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks

)()(11 xhEAxdEAM GfffGsssRd ! HIHI

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Anchorage verification

Where cb = 1.5

5. ANALYSIS IN ULS

5.3. Verification of peeling-off at the end anchorage and at flexural

cracks