Flexural strengthening of reinforced concrete Swiss Code

Flexural strengthening of reinforced concrete

Swiss Code 166 and other codes/guidelines

ETH Lecture 101-0167-01L

Fibre Composite Materials in Structural Engineering

Christoph Czaderski

3. November 2021

2ETH Lecture «Fibre Composite Materials in Structural Engineering», C. Czaderski, 3. November 2021

Overview

Program overview of my lectures and laboratory work

Laboratory competition

Second written intermediate exam

Introduction

Bond between CFRP strip and concrete

Lap-shear test

Slip, Bond shear stress and Bond shear stress-Slip-Relation

Simplified modeling

Debonding failure modes according to SIA 166

End-anchorage

Debonding at shear cracks

Debonding at flexural cracks

Summary, debonding failure modes treated in SIA 166

Example

Several additional topics according to SIA 166


Program overview of my lectures and laboratory work

Wednesday 03.11.2021, 15:45-17:30 (ETH Hönggerberg)

Lecture on Flexural Strengthening

Preparations for laboratory experiments and intermediate exam

Wednesday 01.12.2021, 15:45 - ca.18:30 (Empa Dübendorf)

Meeting point at Busstation ETH Hönggerberg ETH Link 15:30!!

Application of Externally Bonded FRP Reinforcement

Second written interim exam

Wednesday 15.12.2021, 15:45 – 17:30 (Empa Dübendorf)

Meeting point at Busstation ETH Hönggerberg ETH Link 15:30!!

Laboratory experiments and awarding of lab competition

Empa structural laboratory tour



Laboratory Competition


Concrete

Casting on 24.9.2021

fc,cube28 = 65.5 N/mm2

Steel

fs = 487 N/mm2

ft = 566 N/mm2

CFRP

Ef = 150’000 N/mm2

Test Beam


Laboratory competition

Lap experiments will be performed on 15.12.2021

Who makes the best prediction ?

Predictions (in kN):

Failure load of Beam

Failure load of Cylinder2

Failure load of Cylinder3

→Submission of the three numbers by email latest by 13.12.2021 to:

[email protected]

mailto:[email protected]


Content of the second exam on

01.12.2021, 15:45 - ca. 18:30!!! at Empa Dübendorf

Topics:

Design of FRP profiles and all FRP structures

Lecture from 20.10.2021, Teacher Dr. M. Shahverdi

Flexural strengthening of RC according to SIA166

Lecture from 03.11.2021, Teacher Dr. C. Czaderski

Column confinement of RC

Lecture from 10.11.2020, Teacher Prof. Dr. M. Motavalli

Externally bonded FRP reinforcement for metallic structures

Lecture from 17.11.2021, Teacher Dr. E. Ghafoori

Conceptual questions on the topics which were presented in the mentioned lectures. Furthermore, some calculations

have to be performed.

Time: 60 Minutes

No laptops, tablets, smart phones etc.

Only a calculator

One A4 – Summary (both sides or two pages one side)


Introduction







Bond between CFRP strip and concrete


Lap-shear test

Fl

Bond length lb Fl

strip

adhesive

concrete




Concrete block

CFRP-strip

Image Correlation Measurement System







Active Bond length lb0

slipshifting by

calculation

Active bond length: the length which is actively involved in the force transfer from the strip to the concrete.


Slip

sf

xx

Slip

sf

sfsf

F

Slip

sf

x

x

Str

aine

Str

aine

x

without connection connection in one point Connection

in several points

x

Fo

rce

pe

r P

oin

t

sf

F

sf

F


x

Fo

rce

pe

r C

on

ne

ctio

n P

oin

t

F

Connection Point

Picture taken from http://www.seilziehclub-gonten.ch/images/diverse/Comic1.JPG (displayed mirrored)

rope pulling

http://www.seilziehclub-gonten.ch/images/diverse/Comic1.JPG


x

Fo

rce

pe

r C

on

ne

ctio

n P

oin

t

x

Slip

sf

Force F’

per Point

Slip sf

Behavior of the

Connection Point:

sf

F’

F’

F

Connection Point


x

Fo

rce

pe

r C

on

ne

ctio

n P

oin

t

x

sf

F’

F’

F

Connection Point S

lip s

fBehavior of the

Connection Point:

Force F’

per Point

Slip sf


x

Fo

rce

pe

r C

on

ne

ctio

n P

oin

t

x

sf

F’

F’

F

Connection PointS

lip s

fBehavior of the

Connection Point:

Force F’

per Point

Slip sf


x

Fo

rce

pe

r C

on

ne

ctio

n P

oin

t

x

sf

F’

F’

F

Connection PointS

lip s

fBehavior of the

Connection Point:

Force F’

per Point

Slip sf


F

F f

Force N

unit area mm2

f

Bond s

he

ar

str

ess

f

Slip sf

Bond shear stress – Slip – Relation

f Bond shear stress

This relation characterizes the bond behavior.

GFb

The area under the bond shear stress – slip – relation

corresponds to the specific fracture energy GFb.

f

sf



Parabolic


Trigonometric


Hyperbolic

Trigonometric


Comparison Modelling - Measurement


Lap-shear test with strain gauges (SG)

ICS measures slip

SG’s measure strain


0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

Str

ain

in

CF

RP

[‰

]

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]

sh

ear

str

ess [

MP

a]

Longitudinal strain

Shear stress between

strip and concrete

hyperbolic shape

hyperbolic shape


0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

Str

ain

in

CF

RP

[‰

]

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]

sh

ear

str

ess [

MP

a]


0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

Str

ain

in

CF

RP

[‰

]

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]

sh

ear

str

ess [

MP

a]


0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

Str

ain

in

CF

RP

[‰

]

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]

sh

ear

str

ess [

MP

a]

trigonometric shape

trigonometric shape


0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250

distance [mm]

Str

ain

in

CF

RP

[‰

]

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]

sh

ear

str

ess [

MP

a]


f

f,mean

sf1

sf

Simplified bond shear stress-slip relation

GFb =f,meansf1


F = 5 kN

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

parabolic shape of slip


F = 10 kN




F = 15 kN




F = 20 kN




2

ff

f f

xs x =

E t 2

ff

f f

x = xE t

e

f f,meanx =

b0,R

b0

f,mean f

Fl =

b f b0 f1s x=l =s

2

b0,R

f1 2

f f f f,mean

Fs =

2E t b with and we get from Eq. (1) and (3):

(1)

(2)

(3)

and withFb f1 f,meanG =s we get

b0,R f Fb f fF =b 2G E t

(slide 44)


Bond behavior depends on

Elastic deformation

shear modulus of adhesive and concrete

thickness of adhesive plus a layer of concrete

Bond damage (Entfestigungsbereich, Verbundschädigung)

concrete quality

Additionally, the stiffness (Eftf)

of the strip influences also the

bond behaviour.

GFb

maximum slip

constant (~0.2 mm)


Comparison with reinforcement

Internal steel reinforcement is surrounded Deflection perpendicular 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 to yielding of the steel reinforcement

Externally applied strip is free on one side Deflection perpendicular to longitudinal direction is possible

→ maximum anchorage force (anchorage resistance) with corresponding length (active bond length)


2/3

f0 ct c

4= f =0.4 f

3

g

f0 f0

g

ts =

G

Gg

tg1

f0 = 4.5 MPa

CFRP strip

according to Ulaga:

2/3

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

s1 = 2.9 MPa

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

sf0 = 0.001 mm

Internal steel reinforcement

according to Sigrist and Marti:

(Skript Stahlbeton Marti 2009)

sf1 ≈ 0.225 mm

GFb = 0.51 N/mm

2/3

s1 ctm ck=f =0.3 f

In SIA262 (2013): fb=1.4fctm


ff,max f,mean

f,max

2G=2 =

s

f0 = f,max = 4.1 MPa

CFRP strip

according to Czaderski(Diss ETH No. 20504):

with fck = 30MPa, dmax=32mm

sfo = sf,el = 0.02 mm

sf1 = 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 ctH

fG = 0.125f

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

2/3

f0 ctH ck

4= f 0.4 f

3

f0 = 3.9 MPa

2/3

Fb ckG =0.0375 f [N/mm]

(fctH should better be

tested on site)

(SIA D0182)





concrete

Concept of

SIA166

lb

Fb,R


Equations for maximum anchorage resistance

ctHb0,R f Fb f f f f f f f f ctH

fF =b 2 G E t =b 2 E t =0.5b E t f

8 SIA 166

fib Bulletin 14 ctmfffbc1maxfa, ftEbkkcαN

k,max b f fd f ctkT =0.5 k b E t f TR55

1

f

bf

b2

bk 1.06b

1400

please note: without safety factors!! See example on slide 66 for the safety concept!!

Italian CodectmckbFkFkffffd ffk.;tE2bF 030

Take care to symbols. They depend on the reference.


Active bond length

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

b0,R f Fb f fF =b 2 G E t

b0,R

b0

f f,mean

Fl

b

Fb f f

b0

f,mean

2 G E tl

with

If we assume a constant bond shear stress:

Fb f f

2

f,mean

G E t

proportional to


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

SIA 166

fib Bulletin 14

TR55

please note: without safety factors!!

Italian Code

; ;Fb f f f fb0 f0 ctH b02

f0 ctH

G E t E t4 3l 2 f l

2 3 16 f

ctm2

ffmaxb,

fc

tEl

fd ft,max

ctk

E tl =0.7

f

ctm

ffe

f2

tEl


Units in equations in SIA 166

Equations for maximum anchorage resistance and active bond length

Please note, that the units are not conform!

ctHb0,R f Fb f f f f f f f f ctH

ctH 2

Fb

fF =b 2 G E t =b 2 E t =0.5 b E t f

8

Nf

N mmG =

1mm8

mm


f0 ctH

G E t E t4 3l 2 f l

2 3 16 f


Example

ctHFb

f NG

8 mm

f0 ctH

4f MPa

3

b0,R f Fb f fF b 2 G E t 50 2 0.36 165'000 1.2 18.9kN

b0,R

b0,R

f

F315MPa

A

b0,R

b0,R

f

1.91‰E

e

Concrete C30/37

Sika CarboDur S512 tensile strength > 2800 MPa

tensile strain > 17‰

for concrete

C 20/25 to C 50/60

Fb

2.9 NG 0.36

8 mm

f0

42.9 3.9MPa

3


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

ac

tive

bo

nd

le

ng

th l

b0

[mm

]

An

ch

ora

ge

re

sis

tan

ce

Fb

0[k

N]


0

5

10

15

20

25

0 50 100 150 200 250 300

An

ch

ora

ge r

esis

tan

ce F

[kN

]

bond length l [mm]

C50/60

C45/55

C40/50

C35/45

C30/37

C25/30

C20/25

C16/20

C12/15

b b0

2 2

f0 bb,R f Fb f f

Fb f f

if l l :

lF b 2 G E t sin

2 G E t

use radiant in the calculator for sin()


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 ldf after last crack

Elastic solutions for calculating shear and normal stresses at strip end


End anchorage, normal stresses at strip end


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)

Sh

ear

stre

ss (

MP

a)

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)

No

rmal

str

ess

(MP

a)

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.


Safety concept

Example: concrete tensile strength at the concrete surface

Mean value from tests fctH = 4.0 GPa

Characteristic value (5% fractile) fctH,k = 3.2 GPa

Design value:

𝑓𝑐𝑡𝐻,𝑑 =𝑓𝑐𝑡𝐻,𝑘𝛾𝑀

=3.2

1.5= 2.1𝑀𝑃𝑎 gM = 1.5 (Tabelle 3 in SIA166, see slide 114)

𝐺𝑓𝑏𝑑 =𝑓𝑐𝑡𝐻,𝑑8

=2.1

8= 0.26𝑁/𝑚𝑚

Design value of fracture energy:


Debonding failure modes


b0,R

b0,R

f

1.91‰E

e

Example

b0,R f Fb f fF b 2 G E t 50 2 0.36 165'000 1.2 18.9kN

Concrete C30/37

Sika CarboDur S512 tensile strength > 2800 MPa

tensile strain > 17‰

According to SIA166,

the maximum allowed strain is 8‰!

??

b0,R

b0,R

f

F315MPa

A


Figure 38 of PhD Thesis of C.Czaderski (Diss ETH No. 20504):

Global bond shear stress Local bond shear stress

→ bond length constant,

bond shear stress increases

→ bond length increases,

bond shear stress constant


Figure 38 of PhD Thesis of C.Czaderski (Diss ETH No. 20504):

Global bond shear stress Local bond shear stress

→ bond length constant,

bond shear stress increases

→ bond length increases,

bond shear stress constant


Simple supported plate


-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

Length of beam / plate [m]

Str

ain

in

co

nc

rete

an

d C

FR

P [

‰]

10kN/m

10kN/m


-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


Str

ain

in

co

nc

rete

an

d C

FR

P [

‰]

10kN/m

20kN/m

10kN/m

20kN/m


-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


Str

ain

in

co

nc

rete

an

d C

FR

P [

‰]

10kN/m

20kN/m

25kN/m

10kN/m

20kN/m

25kN/m


-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


Str

ain

in

co

nc

rete

an

d C

FR

P [

‰]

10kN/m

20kN/m

25kN/m

26kN/m

10kN/m

20kN/m

25kN/m

26kN/m


-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


Str

ain

in

co

nc

rete

an

d C

FR

P [

‰]

10kN/m

20kN/m

25kN/m

26kN/m

27kN/m

10kN/m

20kN/m

25kN/m

26kN/m

27kN/m


-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


Str

ain

in

co

nc

rete

an

d C

FR

P [

‰]

10kN/m

20kN/m

25kN/m

26kN/m

27kN/m

30kN/m

10kN/m

20kN/m

25kN/m

26kN/m

27kN/m

30kN/m


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


Te

ns

ile

Fo

rce

in

on

e C

FR

P P

late

[k

N]

30kN/m


-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


Te

ns

ile

Fo

rce

CH

AN

GE

in

on

e C

FR

P p

late

[N

/mm

']

30kN/m


Maximum Tensile Force CHANGE

according to SIA 166

ff,lim l

R

f,lim c ck

Fb

x

2.5 2.5 0.3 f

(c from SIA 262)

Example

Concrete C30/37

Sika CarboDur S512

ff,lim f

R

f,lim c

Fb 205N mm

x

2.5 2.5 0.3 30 4.1MPa

/


f0

42.9 3.9MPa

3 In comparison, the local maximum bond shear stress (Slide 53):


0

1

2

3

4

5

6

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

Sh

ea

r s

tre

ss

l,

lim

[M

Pa

]


Shear stress limitations, other guidelines

3.7MPa2.90.71.8f1.8f ctkcb

fib Bulletin 14 (approach 3)

TR55

fib Bulletin 14 (approach 2) f (between cracks …)


cbb f

lim,c ctk0.8f outside yield zone

lim,y ctk4.5f

fmax fy y

t f ctk

ed

Mt 7.8 1.1- f

x M

in the yield zonem= mean shear stress sc=additional shear stress

due to stress concentration

at flexural cracks

add f f

cs a

h-xV α A

I b


Debonding failure modes


Maximum strain in the strip according to SIA 166

Local debonding due to compatibility problems between strip and

concrete at flexural cracks

f,lim,d 8‰e

supplier of the material

f,R f f f,lim f f fuF A E A Ee e

fue

design value!


Maximum strain in strip, other guidelines

8.5‰6.5lim,f efib Bulletin 14 (approach 1)

TR55

Italian Code

ACI

b ck ctm

fdd cr

f f

0.06k f fk

E te

With kcr = 3.0

scfmax fd

fd f

0.114E t

e e


'

cfd

f f

f0.41

n E te

in SI units

(equation for DFM 2 and 3)

(equation for DFM 2 and 3)

sc=localised strain increase at flexural cracks


Cross-section analysis

Cross-section analysis to determine the strains in the CFRP strips

so that the debonding failure modes 1, 2 and 3 according to

SIA 166 can be verified.

Bond factor according to SIA166: ks=0.7, kf=0.9

''e

ek

Equilibrium with e’’

Compatibility with e


es’

Equations for cross-section analysis

'' ''

c s' s fC=T F +F =F F

c f

c c

=x h-x

e eec

es

ef

h

xc

Equilibrium:

Compatibility:

→ one equation with unknowns ec and xc

'' '' s fs f s s f f

s f

T=F F = E A + E Ae e

k k

cF = next slides

d

c s

c c

=x d-x

e e

s' s' s s'F = E Ae

Tensile force:

Compression force:

ds’

c s'

c s' c

=x d -x

e e


Cross-section analysis

Excel

Mathlab

Software programs e.g. FAGUS

…


Summary of calculation procedure: first step

Cross-section analysis to determine the strain and forces along the

structure 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

Str

ain

in

co

ncre

te a

nd

CF

RP

[‰

]


30kN/m

30kN/m


Check debonding failure mode 1:

end strip failure

Determine the location of last crack and define anchorage zone

Compare the existing force in the strip at the last crack with anchorage

resistance 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


Calculation of shear stress between strip and concrete

(force change) and comparison with bond shear strength

ff

f

F

x b


Debonding at strong strain increase in strip

-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


Ten

sile F

orc

e C

HA

NG

E in

on

e C

FR

P p

late

[N

/mm

']

30kN/m



at flexural cracks

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


Str

ain

in

co

ncre

te a

nd

CF

RP

[‰

]

30kN/m


Calculation procedure for a four point beam

1. Calculation crackmoment Mcr and yieldmoment My with cross-section analysis (CSA)- 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 lcr and the location of My (ly und x)

- with this ef and f

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

fe

M

P

crM

crl

yl

P

x

fyefcre

f,Loade

f ff

f

E A

x b

e

f f,Load fye e e

yM

M P

f


Summary of the Equations from SIA

ctHFb

f NG

8 mm

f0 ctH

4f MPa

3

2/3

ctH ctm ckf f =0.3 f

b0,R f Fb f fF =b 2G E t

b b0

2 2

f0 bb,R f Fb f f

Fb f f

if l l :

lF b 2 G E t sin

2 G E t



f0 ctH

G E t E t4 3l 2 f l

2 3 16 f

𝜏𝑓,𝑙𝑖𝑚 = 2.5 ⋅ 𝜏𝑐 = 2.5 ⋅ 0.3 ⋅ 𝑓𝑐𝑘

Δ𝐹𝑓

Δ𝑥𝑅

= 𝜏𝑓,𝑙𝑖𝑚 ⋅ 𝑏𝑓


Summary of the three SIA 166 verifications

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


Te

ns

ile

Fo

rce i

n o

ne C

FR

P P

late

[kN

]

30kN/m

12

3

𝐹𝑓𝑐𝑟 ≤ 𝐹𝑏,𝑅

Δ𝐹𝑓

Δ𝑥≤

Δ𝐹𝑓

Δ𝑥𝑅

= 𝜏𝑓,𝑙𝑖𝑚 ∙ 𝑏𝑓

𝜀𝑓 ≤ 𝜀𝑓,𝑙𝑖𝑚,𝑑 = 8‰


Note: SIA166 is under revision, a new approach for

debonding mode verifications

Combination of debonding

failure modes 2 and 3

with one verification:


Example


Concrete C30/37

Cylinder compressive strength fck = 30 MPa

Tensile strength fctm=2.9 MPa

CFRP

Elastic modulus Ef= 170 GPa

Tensile strength ff = 3000 MPa

Reinforcing steel B500

fsk=500 MPa

Es =205 GPa


Mcr = 11.8 kNm

εf,cr=1.49‰

Crack

Moment

Calculation with FAGUS from Company Cubus


My = 24.0 kNm

εf,y=3.14‰

Yielding

Moment


Mmax = 42.9 kNm

εf,max=8.00‰

Maximum

Moment


1. Step: evaluation of the end anchorage force capacity with

the SIA equations (see slide 94)

ctHFb

f NG

8 mm

f0 ctH

4f MPa

3

b0,R f Fb f fF =b 2G E tTensile strength fctm=2.9 MPa

b b0

2 2

f0 bb,R f Fb f f

Fb f f

if l l :

lF b 2 G E t sin

2 G E t



f0 ctH

G E t E t4 3l 2 f l

2 3 16 f


Mcr =11.8 kNm

εf,cr=1.49‰

My = 24.0 kNm

εf,y=3.14‰

Mmax =42.9 kNm

(with F=28.6kN)

εf,max=8.0‰

from QSA:

2. Step:

F=28.6kN


Notes


Notes


Several additional topics according to

Swiss Code 166 “Externally bonded reinforcement”


Design philosophy

Ultimate limit state (ULS)

Serviceability (SLS)

Stresses

Deflections

Accidential situation

Check of deformation capacity


Ultimate limit state

dd RE

Design value of effects of action ≤ Design value of ultimate resistance


Hazard Scenario (Gefährdungsbild)

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

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

→ see Swiss Code 166


Accidential design situation:

Hazard Scenario → failure of EBR

Vandalism

High temperature

Impact

Chemical exposure

Fire

…

ddki2idkkd a,X,Q,A,P,GEE

Failure of strip: Ad=0 but reduced resistance of cross-section

Ad: accidential load

→ see Swiss Code 166


Accidential design situation:

Hazard Scenario → failure of EBR

You have to prove, that the structure does not fail in the case of a

failure of the EBR!

→ remaining safety factor >1.0


Determination of action effects M and V (Schnittkräfte)

Plastic rotation capacity is reduced!

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


Ultimate resistance

g

d

M

kd a,

XRR ddlim,d a,RR e

Xk = characteristic value of material property

Depending on failure in strengthening material or

bond failure:

= conversion factor

gM = resistance factor

→ see Table 3 in SIA166


Table 3 in SIA 166

Failure of EBR

Steel strip gM = 1.05 = 1.0

FRP strip gM = 1.30 = 0.8

FRP fabric gM = 1.30 = 0.8

Bond failure

in adhesive gM = 1.50 = 0.8

in concrete gM = 1.50 : see SIA 262

in timber gM, : see SIA 265

in masonry gM, : see SIA 266


Characteristic values

FRP:

el

f

ffd

efud

Ef

1

→specifications from seller

company, ask also for fractile

values

→CFRP (carbon fibers) might

have an increase of elastic

modulus with loading


SLS and evenness

SIA 166: Serviceability (SLS)

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

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

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. (consider

also boundary condition: j(L/2)=0)

top bottom

h

e e

0

dxL

22

m m

1w =L -

8 6

Simplified calculation for 4-point beam

(see e.g. Ulaga 2003): L

m = curvature between loads

L

0

dxL

w


Glass transition temperature Tg

a) b)

Loading Specimen

Supports

Data aquisition

RSA III

Nitrogen supply

Testing chamber


Glass transition temperature Tg

The Tg of the used epoxies defines the maximum allowable service temperature of the

structure.

fib Bulletin 90:

maximum allowable service temperature Tser ≤ Tg – (10°C to 20°C)

Tg should be larger as 40°C

Tg should be determined according to EN12614

Consider that age, temperature and moisture can influence Tg

SIA 166: the feasibility of the adhesive has to be demonstrated. Beside many other points,

the maximum service temperature has to be declared.


Deformation capacity

SIA 166 and 262:

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

on the basis of similar limitation, minimal values of strain in EBR and reinforcement at

ultimate are given in fib Bulletin 14


Assessment, some remarks

Consider existing stresses and deflections in the structure before strengthening

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


Longitudinal force from shear force

Generally, longitudinal force due to shear force shall be carried from

internal steel

If it yields, see SIA 166

and do not forget:

‘Normal’ design as usual

Concrete crushing

Bending resistance in the unstrengthened region

Shear resistance of cross-section

etc.


Recommendations for durability

For a good long-term behavior of EBR:

No direct UV radiation (also not indirect from snow or water)

No water wetting (exposition classes X0, XC1(dry) and XC3)

For other exposition classes: special measures such as coatings

Moderate sustained loading (prestressing, load)

Service temperatures ≤ ca. 20° lower as Tg

→ new durability concept in the new SIA166, which is currently under revision.


Literature: Codes/Guidelines

fib (2001) Externally bonded FRP reinforcement for RC structures - Bulletin 14. International Federation for Structural

Concrete (fib), Switzerland.

fib (2019) Externally applied FRP reinforcement for concrete structures - Bulletin 90. International Federation for

Structural Concrete (fib), Switzerland.

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

Architektenverein SIA.

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

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.

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

concrete structures. American Concrete Institute.

TR55 (2012) Design guidance for strengthening concrete structures using fibre composite materials, Third Edition.

Technical Report No. 55 of the Concrete Society, UK.


Literature

PhD Theses (can freely be downloaded from www.research-collection.ethz.ch )

Ulaga T (2003) Dissertation ETH Nr. 15062, Betonbauteile mit Stab- und Lamellenbewehrung: Verbund- und

Zuggliedmodellierung, 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://dx.doi.org/10.3929/ethz-a-007569614

Book chapters

Motavalli, M., C. Czaderski, A. Schumacher, and D. Gsell, Fibre reinforced polymer composite materials for building

and construction, in Textiles, polymers and composites for buildings, G. Pohl, Editor. 2010, Woodhead Publishing

Limited: Cambridge UK. p. 69-128.

Czaderski C., Flexural and Shear Strengthening of Reinforced Concrete Structures, in The International Handbook of

FRP Composites in Civil Engineering, CRC Press, 2013.

p. 235-252

http://www.research-collection.ethz.ch/

http://dx.doi.org/10.3929/ethz-a-004525392

http://dx.doi.org/10.3929/ethz-a-007569614

Documents

Flexural strengthening of reinforced concrete Swiss Code