[EMPA] Flexural Strengthening of Reinforced Concrete

7/27/2019 [EMPA] Flexural Strengthening of Reinforced Concrete

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Flexural strengthening of reinforced concreteSwiss Code 166 and other codes/guidelines

ETH Lecture 101-0167-01LFibre Composite Materials in Structural Engineering

Christoph Czaderski

7. November 2012


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2ETH Lecture Fibre Composite Materials in Structural Engineering, 7. November 2012

Literature

SIA166 (2004) Klebebewehrungen (Externally bonded reinforcement). Schweizerischer Ingenieur- undArchitektenverein SIA.

SIA (2004) D 0209, Dokumentation, Klebebewehrung, Einfhrung in die Norm SIA 166.

Ulaga T (2003) Dissertation ETH Nr. 15062, Betonbauteile mit Stab- und Lamellenbewehrung: Verbund- undZuggliedmodellierung, http://dx.doi.org/10.3929/ethz-a-004525392

Czaderski C (2012) Dissertation ETH No. 20504, Strengthening of reinforced concrete members by prestressed,externally bonded reinforcement with gradient anchorage, http://e-collection.library.ethz.ch/

ACI (2008) ACI440.2R-08, Guide for the design and construction of externally bonded FRP systems for

strengthening concrete structures. American Concrete Institute. CNR (2004) Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing

Structures, CNR-DT 200/2004. CNR - Advisory Committee on Technical Recommendations for Construction, Rome,Italy.

fib (2001) Externally bonded FRP reinforcement for RC structures - Bulletin 14. International Federation forStructural Concrete (fib), Switzerland.

TR55 (2004) Design guidance for strengthening concrete structures using fibre composite materials, SecondEdition. Technical Report No. 55 of the Concrete Society, UK.

Motavalli, M., C. Czaderski, A. Schumacher, and D. Gsell, Fibre reinforced polymer composite materials for buildingand construction, in Textiles, polymers and composites for buildings, G. Pohl, Editor. 2010, Woodhead PublishingLimited: Cambridge UK. p. 69-128.


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Overview

Introduction

Failure modes debonding according to SIA 166 End-anchorage

Debonding at shear cracks and/or discontinuities

Debonding at flexural cracks

Several additional topics according to SIA 166 e.g. Action effects M and V

Resistance factors

Cross-section analysis

etc. Summary, debonding failure modes treated in SIA 166


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Debonding failure modes


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End anchorage failure

Short beams

Cracks near the supports

Anchorage in free length

Small internal steel reinforcement cross-section


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Anchorage resistance

concrete

adhesive

strip

F

F


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Lap shear test (pull-off test, pull test on FRP-

to-concrete-bonded joint)

see: Czaderski, C., K. Soudki, et al. (2010). "Front and Side View Image Correlation Measurements on FRP to Concrete Pull-OffBond Tests." Journal of Composites for Construction, ASCE 14(4): 451-463.


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Lap shear test on the strong floor


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0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

StraininCFRP[]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 50 100 150 200 250

distance [mm ]

shearstres

s[MPa]

Longitudinal strain

Shear stress betweenstrip and concrete

hyperbolic shape

hyperbolic shape


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0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

S

traininCFRP[]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 50 100 150 200 250

distance [mm]

shearstress

[MPa]


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0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

S

traininCFRP[]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 50 100 150 200 250

distance [mm]

shearstress

[MPa]


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0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

S

traininCFRP[]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 50 100 150 200 250

distance [mm]

shearstress

[MPa]

trigonometric shape

trigonometric shape


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0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

S

traininCFRP[]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 50 100 150 200 250

distance [mm]

shearstress

[MPa]


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Bond behavior depends on

Elastic deformation

shear modulus of adhesive and concrete

thickness of adhesive plus a layer of concrete

Bond damage (Entfestigungsbereich, Verbundschdigung)

concrete quality

Additionally, the stiffness (Eltl)of the strip influences also thebond behaviour.

GFb

maximum slip

constant (~0.2 mm)


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Comparison with reinforcement

Internal steel reinforcement is surrounded

Deflection perpenticular to longitudinal direction is not possible

Normal (confinement) stresses due to interlocking and friction

the longer the anchor length, the higher the anchor force up toyielding of the steel reinforcement

Externally applied strip is free on one side

Deflection perpenticular to longitudinal direction is possible maximum anchorage force (anchorage resistance) withcorresponding length (active bond length)


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2/3l0 ct c4

= f =0.4 f 3

gl0 l0

g

ts = G

Ggtg1

l0 = 4.5 MPa

CFRP strip

according to Ulaga:

2/3s0 ctm ck=2f =0.6 f s0 = 5.8 MPa

s1 = 2.9 MPa

with fck = 30MPa (fc = 38MPa), tg=1mm, Gg=4GPa

sl0 = 0.001 mm

Reinforcement

according to Sigrist and Marti:

(Skript Stahlbeton Marti 2009)

sl1 0.225 mm

GFb = 0.51 N/mm

2/3

s1 ctm ck=f =0.3 f


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fl0 f,meanf,max

G= =

s

l0 = f,max = 4.1 MPa

CFRP strip

according to Czaderski(Diss ETH No. 20504):

with fck = 30MPa, dmax=32mm

slo = sf,el = 0.02 mm

sl1 = sf,max = 0.2 mm

2/3 1/4

f ck maxG =0.018 f d [N/mm]

GFb = Gf= 0.41 N/mm

ctHFb

fG =8

2/3

ctH ctm ckf f =0.3 f

CFRP strip

according to SIA 166

with

with fck = 30MPa, dmax=32mm

GFb = 0.36 N/mm

2/3l0 ctH ck4

= f 0.4 f 3

l0 = f,max = 3.9 MPa

2/3Fb ckG =0.0375 f [N/mm]

(fctH should better be

tested on site)


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l

f,mean

sl1

sl

Simplified bond shear stress-slip relation


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F = 5 kN

Ef= 165 GPa, bf= 50mm, tf= 1.2 mm, f,mean = 2.25 MPa

parabolic shape of slip


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F = 10 kN




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F = 15 kN




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F = 20 kN




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2

ll

l l

xs x =

E t 2

lll l

x = x

E t

l f,meanx =

b0,R

b0

f,mean l

Fl =

b

l b0 l1s x=l =s2

b0,R

l1 2

l l l f,max

Fs =

2Etb

with and we get from Eq. (1) and (3):

(1)

(2)

(3)

and withFb l1 f,maxG =s we get b0,R l Fb l lF =b 2G E t


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Equations for maximum anchorage resistance

ctHb0,R l Fb l l l l l l l l ctHf

F =b 2 G E t =b 2 E t =0.5b E t f 8

SIA 166

f i b Bulletin 14 ctmfffbc1maxfa, ftEbkkcN

ctmfffbmaxk, ftEbk0.5T TR55

1

400

b1

b

b2

1.06kf

f

b

please note: without safety factors!!

Italian CodectmckbFkFkffffdffk.;tE2bF 030

Take care to symbols. They depend on the reference. l in SIA: Lamelle, Gewebe or Gelege

see lecture of Prof. Motavalli, EBR flex. strength.


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Active bond length

(the length which is actively involved in the force transfer from the strip to the concrete)

b0,R l Fb l lF =b 2 G E t

b0,R

b0

l f,mean

F

l b

Fb l l Fb l lb0 2

f,mean f,mean

2 G E t G E tl

with


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Equations for active bond length(minimum necessary length for maximum anchor resistance Fb0,R)

SIA 166

f i b Bulletin 14

TR55


Italian Code

; ;Fb l l l lb0 l0 ctH b02l0 ctH

G E t E t4 3l 2 f l

2 3 16 f

ctm2

ffmaxb,

fc

tEl

ctm

ffmaxb,

f

tE0.7l

ctm

ffef2

tEl


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Units in equations in SIA 166

Equations for maximum anchorage resistance and active bond length

Please note, that the units are not conform!

2

0 5

1

ctHb0,R l Fb l l l l l l l l ctH

ctH

Fb

fF b 2 G E t b 2 E t . b E t f

8

N

fN mmG

mm8

mm

ctH

llb0ctHl02

l0

llFbb0

f

tE

16lf

tEG2

2l

3;

3

4;


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Example

mm

N

8

f

GctH

Fb

MPaf3

4ctHl0

18.9kN1.2165'0000.36250tEG2bF llFblRb0,

315MPaA

F

l

Rb0,Rb0, 1.91El

Rb0,

Rb0,

Concrete C30/37

Sika CarboDur S512 tensile strength > 2800 MPatensile strain > 17

for concreteC 20/25 to C 50/60

mm

N

0.368

2.9

GFb

MPa23

4l0 9.39.


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0

50

100

150

200

250

0

5

10

15

20

25

C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

activebond

lengthlb0[mm

]

AnchorageresistanceFb0[kN

]


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llFb

bl

llFblRb,

bb

tEG2

l

sintEG2bF

llif

22

0

0 :

0

5

10

15

20

25

0 50 100 150 200 250 300

Anchorage

resistanceF[kN

]

bond length l [mm]

C50/60

C45/55

C40/50

C35/45

C30/37

C25/30C20/25

C16/20

C12/15

i hil f i d


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Design philosopy of preventing end

anchorage failure

SIA166: anchorage in the uncracked zone

ACI:

If Vu > 0.67 Vc at strip end, then transverse reinforcement is necessary(they give a design equation for U-wrap reinforcement Af,anchor)

or (instead of detailed analysis)

for simply supported beams: length ldfafter last crack

Elastic solutions for calculating shear and normal stresses at stripend

E d h l t t t i d


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End anchorage, normal stresses at strip end

Sh d l t t t i d


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Shear and normal stresses at strip end

B4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40

Distance from plate end (mm)

Shearstress(MPa)

Closed-form solution

FEM2(nonlinear)

FEM2(linear)

FEM1

B4

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 10 20 30 40

Distance from plate end (mm)

Normalstress(MPa)

Closed-form solution

FEM2(nonlinear)

FEM2(linear)

see:

Aram, M.R., C. Czaderski, and M. Motavalli, Debonding failure modes of flexural FRP-strengthened RC beams. Composites Part B: Engineering, 2008. 39(5): pp. 826-841.

D b di f il d


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Debonding at shear cracks and/or


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Debonding at shear cracks and/ordiscontinuities

Large shear force, single loads, small distance between load andsupport

Discontinuities: internal stress state

cross-section

reinforcement (joint, ..)

Large compression zone so that no premature concrete crushing

Example


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Example

18.9kN1.2165'0000.36250tEG2bF llFblRb0,

,

,

b0 R

l0 R

l

F315MPa

A

,

, . l0 R

l0 R

l

1 91E

Concrete C30/37

Sika CarboDur S512 tensile strength > 2800 MPatensile strain > 17

According to SIA166,

the maximum allowed strain is 8!

??


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simple lap shear test

beam

Strain

Simple supported plate


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Simple supported plate

8


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-3

-2

-1

0

1

2

3

4

5

6

7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Length of beam / plate [m]

Str

aininconcreteandCFRP[]

10kN/m

10kN/m

8


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-3

-2

-1

0

1

2

3

4

5

6

7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


Str


10kN/m

20kN/m

10kN/m

20kN/m

8


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-3

-2

-1

0

1

2

3

4

5

6

7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


Str


10kN/m

20kN/m

25kN/m

10kN/m

20kN/m

25kN/m

8


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-3

-2

-1

0

1

2

3

4

5

6

7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


Str


10kN/m

20kN/m

25kN/m

26kN/m

10kN/m

20kN/m

25kN/m

26kN/m

8

10kN/m


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-3

-2

-1

0

1

2

3

4

5

6

7

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


StraininconcreteandCFRP[]

10kN/m

20kN/m

25kN/m

26kN/m

27kN/m

10kN/m

20kN/m

25kN/m

26kN/m

27kN/m


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90


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0

10

20

30

40

50

60

70

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


Tens

ileForceinoneCF

RPPlate[kN]

30kN/m

100


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-100

-80

-60

-40

-20

0

20

40

60

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


TensileForceCHANGEinone

CFRPplate[N/mm

']

30kN/m

Maximum Tensile Force CHANGE


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according to SIA 166

ckcliml,

lliml,

R

l

f0.32.52.5

bx

F

(c from SIA 262)

Example

Concrete C30/37

Sika CarboDur S512MPa300.32.52.5

mmNbx

F

climl,

lliml,

R

l

1.4

/205


6


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0

1

2

3

4

5

C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

Shearstressl,lim

[MPa]

300


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0

50

100

150

200

250

C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

Force

ChangeF

l0/x[N/mm]

Shear stress limitations, other guidelines


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3.7MPa2.90.71.8f1.8f ctkcb

f i b Bulletin 14 (approach 3)

TR55 PaM0.8b

f i b Bulletin 14 (approach 2) f (between cracks )


cbb f



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Debonding at flexural cracks


59/88


Less internal steel reinforcement cross-section, so that large strainsin EBR

Small shear load, large spans, continuous force development in thespan

Large compression zone so that no premature concrete crushing

Maximum strain in the strip according to SIA 166


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Local debonding due to compatibility problems between strip andconcrete at flexural cracks

8dlim,l,

supplier of the material

fullliml,llRl, EAEAF

fu

design value!(shall be used also for thecalculation in the exercise)

Maximum strain in strip, other guidelines


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8.56.5lim,f f i b Bulletin 14 (approach 1)

TR55

Italian Code

ACI

ff

ctmckb

crfddtE

ffk06.0k

With kcr = 3.0

8lim,f


fd

f f

0.41n E t

'

cf in SI units

(equation for DFM 2 and 3)

(equation for DFM 2 and 3)

Swiss Pre-Code 166 Externally bondedi f t


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reinforcement

Design philosophy


63/88


Ultimate limit state (ULS)

Serviceability (SLS) Stresses

Deflections

(Crack width)

Accidential situation

Check of deformation capacity

Ultimate limit state


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dd RE Design value of effects of action

Design value of ultimate resistance

Hazard Scenario (Gefhrdungsbild)


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ddki0ik1Q1kPkGd a,X,Q,Q,P,GEE

Ed effects of actions (Auswirkungen) E actions (Einwirkungen)

Gk permanent actions

Pk prestressing

Qk1 leading action (Leiteinwirkung)

Qki accompanying actions (Begleiteinwirkungen)

Xd material properties

ad geometry


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Accidential design situation: Hazard Scenario failure of EBR


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You have to prove, that the structure does not fail in the case of afailure of the EBR! remaining safety factor >1.0

Determination of action effects M and V(Schnittkrfte)


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(Schnittkrfte)

Plastic rotation capacity is reduced!

Elastic determination of action effects if FRP are used, e.g. two span

beam

Ultimate resistance


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d

M

kd a,

XRR

ddlim,d a,RR

Xk = characteristic value of material property

Depending on failure in strengthening material orbond failure:

= conversion factor

M = resistance factor

see Table 3 in SIA166

Table 3 in SIA 166


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Failure of EBR

Steel strip M = 1.05 = 1.0

FRP strip M = 1.30 = 0.8 FRP fabric M = 1.30 = 0.8

Bond failure

in adhesiv M = 1.50 = 0.8

in concrete M = 1.50 see SIA 262 in timber M, see SIA 265

in adhesiv M, see SIA 266

Characteristic values


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FRP:

l

l

ffd

fud

Ef1

specifications from seller company,

ask also for fraktile values

mixed fibers in strips can havenon-linear behavior

Cross-section analysis


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Bond factor according to SIA166: s=0.7, l=0.9

''

Compatibility with

Equilibrium with

Equations for cross-section analysis


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D Z

c l

x h x

c

sl

h

x

Equilibrium:

Compatibility:

one equation with unknowns c andx

s ls s l l

s l

Z E A E A

D next slides

d

c s

x d x

Concrete in compression by Hognestad


74/88


2

1

0.15

0.004 0.003

2

0.003

3

0.003

1

1

3

3

0.15

0.004

2

0.075

0.004


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13

12

1

3

1

5.1 0.004

0.024

3.925

10.2 0.9

0.016 0.048

0.003

Equations from:

An, W., H. Saadatmanesh, and M.R. Ehsani, RC beams strengthened with FRP plates. II: Analysis and parametric study.

Journal of Structural Engineering ASCE, 1991. 117(11): p. 3434-3455.

Proposal


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Make a table e.g. with Excel

c x s1 s2 l M F0

0.00005

0.00010

0.00015

0.00340

0.00345

0.00350

with this table you have l and can make the SIA verifications

Deformation capacity


77/88


SIA 166 and 262:

For mainly bending load: compression zone x/d 0.35 what limits

reinforcement ratio (If x/d > 0.35 but 0.5 then calculation of deformation capacity)

(on the basis of similar limitation, minimal values of strain in EBR andreinforcement at ultimate are given in fib Bulletin 14)

SLS and evenness


78/88


SIA 166: Serviceability (SLS)

Stresses in the internal reinforcement should not exceed 90% of yieldstrength.

Deflections should be checked

Evenness of concrete surface

for 2 m measurement length (Messlatte): max. 5 mm tolerance

for 0.3 m measurement length (Messlatte): max. 1 mm tolerance

Deflections


79/88


If the strains at top and bottom side along the beam is calculated,the curvature can be obtained.

By two times integrating, the deflection can be calculated. (consideralso boundary condition: (L/2)=0)

h

bottomtop

L

dx

0

681 22 mm Lw

Simplified calculation for 4-point beam(see e.g. Ulaga 2003): L

m = curvature between loadsL

L

dxw

0

Longitudinal force from shear force


80/88


Generally, longitudinal force due to shear force shall be carried frominternal steel

If it yields, see SIA 166

)(

2

1),('' VFEAVMF t

l

llll

cot)( VVFt = angle of compression struts

Assessment, some remarks


81/88


Consider existing stresses and deflections in the structure beforestrengthening

Internal reinforcement Good assessment: geometry, strength

Minimum value (brittle behaviour)

Risk of premature concrete crushing if steel is neglected in calculations

Concrete property (tensile strength good enough?)

Static system

See also SIA166 chapter 2.1

Normal design as usual


82/88


Concrete crushing

Bending resistance in the unstrengthened region

Shear resistance of cross-section etc.

Calculation procedure, first step


83/88


Cross-section analysis to determine the strain and forces along thestructure for an assumed maximum load

-3

-2

-1

0

1

2

3

4

5

6

7

8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


30kN/m

30kN/m

Check debonding failure mode 1:end strip failure


84/88


Determine the location of last crack and define anchorage zone

Compare the existing force in the strip at the last crack with anchorageresistance which can be anchored in the anchorage zone

I: uncracked cross-section

II: cracked cross-section, internal steel in elastic state

III: cracked cross-section, internal steel in yielding state

Check debonding failure mode 2:Debonding at strong strain increase in strip


85/88


Calculation of shear stress between strip and concrete(force change) and comparison with bond shear strength

l

l

bx

F

-100

-80

-60

-40

-20

0

20

40

60

80

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


TensileForceCHANGEinoneCFRPplate[N/mm']

30kN/m

Check debonding failure mode 3:at flexural cracks


86/88


Compare maximum existing strain with maximum admissible strain

0

1

2

3

4

5

6

7

8

0.0 0 .5 1.0 1.5 2 .0 2 .5 3 .0 3 .5 4 .0 4.5 5 .0

Length of beam / plate [m ]

StraininconcreteandCFRP[]

30kN/m

Calculation procedure for a four point beam

1. Calculation crackmoment Mcrand yieldmoment Mywith cross-section analysis (CSA)


87/88


- Strip strain at last crack and at the point of steel yielding

2. Assumption of a failure load Pult (larger as Py), then:- with CSA calculation of the maximum strain in the strip

- calculation of the location of the last crack lcrand the location ofMy(lyundx)

- with this l and l

3. The three SIA verifications and assumption of a new failure load Pultetc.

l,strip

M

P

l

crM

crl

yM

yl

M P

P

x

ly''

lcr

''

l,Load

''

l ll

l

E A

x b

'' ''

l l ,Load ly

Summary of the three SIA 166 verifications


88/88


1. End strip debonding failure at the last crack

2. Debonding at strong strain increase in strip

3. Debonding at flexural cracks

0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0


TensileForcein

oneCFRPPlate[kN]

30kN/m

12

3

''

b b,RF F

l

''

l,lim,d 8

l l

R

F F

x x

88

Documents

[EMPA] Flexural Strengthening of Reinforced Concrete