2018 Concrete Overlay Theory

STRENGTHENING AND
REHABILITATION WITH CONCRETE

OVERLAYS FOR BRIDGES, TUNNELS
AND CIVIL STRUCTURES
Structural principles and design
for redundant systems
Foreword
Placing fresh concrete against existing, hardened concrete is a routine
task in building construction. In fact, it is a condition which occurs at every
joint in concrete construction work. For some time now, the placement of
concrete overlays has been gaining in importance as a result of the
increasing need for rehabilitation and strengthening of existing
structures. For the design of these composite concrete structures, the
transfer of internal stresses across the bond interface between new and
old concrete is a critical aspect. A design method has been developed
based on shear tests specially carried out for this purpose by Hilti
Corporate Research for a variety of surface treatments.
The Institute for Concrete Structures of the University of Innsbruck,

Austria, provided scientific support during the development of the
connectors and the associated design method. At the same time, test
results given in the literature were incorporated. Among other things it
was found that, contrary to the usual design approach, the full tensile
yield strength of the connectors cannot be equated to the tension
clamping force across the interface.
In contrast to design methods described in the literature, this new design Former Professor Dr. techn. Manfred Wicke,
Institure for Concrete Structures
approach considers all three mechanisms: cohesion, friction, and shear University of Innsbruck, Austria
resistance (dowel action) of the shear reinforcement positioned across
the interface, in determining the effective shear transfer. The
compressive stress required at the interface for shear transfer by friction
is set up by activating tensile forces in the connectors. The design
method is based on a single equation to calculate the resistance of the
bond interface for each different surface treatment from the three above
components.
With increasing surface roughness, shear resistance and shear stiffness

are significantly increased. Furthermore, the distribution of total
resistance shared by the three components changes considerably. At
the extremes, if the surfaces are very rough, the connectors across the
bond interface are primarily stressed in tension, whereas, if the surfaces
are smooth, the shear resistance of the connectors themselves (dowel
action) predominates. For roughened surfaces, the interlocking effect is
sufficient to transfer small shear forces without connectors. It is often
adequate for concrete overlays to be anchored only at their perimeter.
The very user-friendly Hilti design method is based on the Eurocode

safety concept (prEN 1992-4) and is particularly notable for its
transparency. The use of design diagrams makes the method
straightforward for designers to apply.
Manfred Wicke
For comments and questions, contact our engineers
2
Contents
1 HILTI CONNECTORS FOR OVERLAYS ..................................................................................................................... 6
1.1 RANGE OF APPLICATIONS............................................................................................................................................. 6

1.2 ADVANTAGES OF THE STRENGTHENING WITH CONCRETE OVERLAY ................................................................................ 6
1.3 EXAMPLE OF APPLICATIONS ......................................................................................................................................... 6
2 PRODUCTS OVERVIEW .............................................................................................................................................. 8
2.1 HIT-RE 500 V3 INJECTION MORTAR ............................................................................................................................. 9

2.2 HUS3 SCREW ANCHOR .............................................................................................................................................. 10
2.3 HCC-B SHEAR CONNECTOR ...................................................................................................................................... 11
2.4 HCC-K SHEAR CONNECTOR ...................................................................................................................................... 12
2.5 HCC-HIT-V ............................................................................................................................................................... 13
2.6 REBAR ...................................................................................................................... ERROR! BOOKMARK NOT DEFINED.
3 DESIGN OF INTERFACE ........................................................................................................................................... 15
3.1 BASIC CONSIDERATIONS ............................................................................................................................................ 15

3.2 PRINCIPLE AND SET-UP OF THE ANALYTICAL MODEL .................................................................................................... 15
3.3 DESIGN SHEAR RESISTANCE AT THE INTERFACE, 𝒗𝑹𝒅 ............................................................................................... 15
3.4 DESIGN SHEAR STRENGTH AT THE INTERFACE, EOTA TR066 ..................................................................................... 16
3.5 DESIGN SHEAR STRENGTH AT THE INTERFACE, HILTI METHOD .................................................................................... 17
3.6 DESIGN SHEAR FORCE ACTING LONGITUDINALLY AT INTERFACE, 𝒗𝑬𝒅 ....................................................................... 19
3.7 SHEAR FORCE TO BE TRANSFERRED AT OVERLAY PERIMETER ..................................................................................... 20
3.7.1 VERIFICATION ACCORDING TO EOTA TR066 INDICATIONS ..................................................................... 20
3.7.2 VERIFICATION ACCORDING TO HILTI METHOD INDICATIONS .................................................................... 20
3.8 CENTRAL REGIONS WITHOUT SHEAR CONNECTORS ..................................................................................................... 21
3.8.1 VERIFICATION OF AN INTERFACE WITHOUT SHEAR CONNECTORS ACCORDING TO EOTA TR066 .. 21
3.8.2 VERIFICATION OF AN INTERFACE WITHOUT SHEAR CONNECTORS ACCORDING TO HILTI METHOD... 21
3.9 REDUNDANT LOAD TRANSFER .................................................................................................................................... 21
3.10 FATIGUE LOADING ................................................................................................................................................... 21
3.10.1 GENERAL OBSERVATIONS ............................................................................................................................. 21
3.10.2 PROOF FOR FATIGUE ...................................................................................................................................... 21
3.11 SEISMIC LOADING .................................................................................................................................................... 22
3.12 SERVICEABILITY LIMIT STATE ................................................................................................................................... 22
3.13 ADDITIONAL RULES AND DESIGN DETAILS ................................................................................................................. 22
3.13.1 MIXED SURFACE TREATMENT ....................................................................................................................... 22
3.13.2 MINIMUM AMOUNT OF REINFORCEMENT AT THE INTERFACE .................................................................. 22
3.13.3 LAYOUT OF CONNECTORS ........................................................................................................................... 23
3.13.4 RECOMMENDATION FOR OVERLAY PLACEMENT ..................................................................................... 23
3.13.5 RECOMMENDATION FOR SURFACE TREATMENT ..................................................................................... 23
3.14 ANCHORAGE OF THE SHEAR CONNECTORS IN THE EXISTING AND NEW CONCRETE ...................................................... 23
3.14.1 GENERAL OBSERVATIONS ........................................................................................................................... 23
3.14.2 INSTALLATION GEOMETRY ........................................................................................................................... 23
3.14.3 DESIGN PROOFS FOR THE CONNECTOR ................................................................................................... 24
3.14.4 GEOMETRICAL BOUNDARY CONDITIONS FOR EXISTING CONCRETE AND CONCRETE OVERLAYS.. 25
4 EXAMPLES ................................................................................................................................................................ 27
4.1 DESCRIPTION OF THE DESIGN CASE, STRUCTURAL ANALYSIS ...................................................................................... 27
4.2 DATA FOR DESIGN OF THE CONNECTION AT EXTERNAL SUPPORTS .............................................................................. 28
4.3 DETERMINATION OF LONGITUDINAL SHEAR................................................................................................................. 30
4.4 VERIFICATION OF CONNECTORS: CENTRAL PART, EXISTING SLAB................................................................................ 30
4.4.1 STEEL FAILURE ................................................................................................................................................ 30
4.4.2 COMBINED CONCRETE CONE/PULL-OUT VERIFICATION .......................................................................... 30
4.4.3 CONCRETE CONE BREAKOUT VERIFICATION ............................................................................................. 31
4.4.4 SPLITTING VERIFICATION............................................................................................................................... 32
4.4.5 SUMMARY ......................................................................................................................................................... 32
4.5 VERIFICATION OF CONNECTORS: CENTRAL PART, NEW SLAB ...................................................................................... 32
4.5.1 PULL-OUT VERIFICATION ............................................................................................................................... 32
4.5.4 SUMMARY ......................................................................................................................................................... 33
4.6 VERIFICATION OF CONNECTORS: LATERAL PART, EXISTING SLAB ................................................................................ 33
4.6.1 STEEL FAILURE ................................................................................................................................................ 33
4.6.2 COMBINED CONCRETE CONE/PULL-OUT VERIFICATION .......................................................................... 33
4.6.5 SUMMARY ......................................................................................................................................................... 34
4.7 VERIFICATION OF CONNECTORS: LATERAL PART, NEW SLAB ....................................................................................... 34
4.7.1 PULL-OUT VERIFICATION ............................................................................................................................... 34
4.7.4 SUMMARY ......................................................................................................................................................... 35
4.8 VERIFICATION OF THE INTERFACE IN THE CENTRAL PART OF THE SLAB ........................................................................ 36
4.9 VERIFICATION OF THE CONNECTION CLOSE TO THE EDGES.......................................................................................... 36
4.10 VERIFICATION OF THE CONNECTION FOR A ROUGH INTERFACE .................................................................................. 38
4.11 ALTERNATIVE DESIGN SOLUTION USING THE HILTI METHOD ...................................................................................... 40
4.12 VERIFICATION OF CONNECTORS: CENTRAL PART, EXISTING SLAB.............................................................................. 41
4.12.1 STEEL FAILURE: ............................................................................................................................................ 41
4.12.2 COMBINED CONCRETE CONE/PULL-OUT VERIFICATION ........................................................................ 41
4.12.3 CONCRETE CONE BREAKOUT VERIFICATION........................................................................................... 42
4.12.4 SPLITTING VERIFICATION ............................................................................................................................ 43
4.12.5 SUMMARY ...................................................................................................................................................... 43
4.13 VERIFICATION OF CONNECTORS: CENTRAL PART, NEW SLAB .................................................................................... 43
4.13.1 PULL-OUT VERIFICATION ............................................................................................................................. 43
4.13.4 SUMMARY ...................................................................................................................................................... 44
4.14 VERIFICATION OF CONNECTORS: LATERAL PART, EXISTING SLAB .............................................................................. 44
4.14.1 STEEL FAILURE ............................................................................................................................................. 44
4.14.2 COMBINED CONCRETE CONE/PULL-OUT VERIFICATION ........................................................................ 44
4.14.5 SUMMARY ...................................................................................................................................................... 45
4.15 VERIFICATION OF CONNECTORS: LATERAL PART, NEW SLAB ..................................................................................... 45
4.15.1 PULL-OUT VERIFICATION ............................................................................................................................. 45
4.15.4 SUMMARY ...................................................................................................................................................... 46
4.16 VERIFICATION OF THE INTERFACE IN THE CENTRAL PART OF THE SLAB ...................................................................... 46
4.17 VERIFICATION OF THE CONNECTION CLOSE TO THE EDGES........................................................................................ 47
5 NOTATIONS .............................................................................................................................................................. 49
4
6 LITERATURE ............................................................................................................................................................. 52
5
1 Hilti connectors for overlays
1.1 Range of applications
When a new layer of concrete is applied to existing concrete with the aim of strengthening or repairing a
structure, the result is referred to as a composite concrete structure. The overlay is usually cast directly or
applied as shotcrete. Its function is to augment the flexural compression or flexural tension zones, depending
on the position of placement. Prior to placement of the overlay, the surface of the old concrete member is
prepared by suitable means, and pre-wetted.
Shrinkage of the new concrete overlay can be reduced by careful selection of the concrete mix. However, the
constraint forces caused by differential shrinkage and, in certain cases, by differential temperature gradients,
cannot be avoided. Initially, stresses in the bond interface result from a combination of peripheral loads and
internal constraint forces. It must be borne in mind that stresses due to shrinkage and temperature gradients
in the new concrete typically reach their maximum at the perimeter (peeling forces). The combination of
peripheral and internal stresses often exceeds the capacity of the initial bond, thus requiring the designer to
allow for a de-bonded interface. This is particularly true in the case of bridge overlays, which are subject to
fatigue stresses resulting from traffic loads.
Furthermore, these stresses vary with time, and bond failure can take place years after installing the overlay.
When this happens, the tensile forces set up must be taken up by connectors positioned across the interface.
Typical examples are shown schematically in the following table
Strengthening of bridges by means of concrete Strengthening of buildings, decks and slabs

overlays
Fig. 1: Examples of overlay applications
1.2 Advantages of the strengthening with concrete overlay
 Simple and reliable application to a variety of cases

 Monolithic structural component behaviour assured
 Shear forces are reliably transferred even if the interface is cracked
 Wide range of applications
 Suitable for use with the most common methods of surface roughening
 Reduced requirements for anchor embedment
1.3 Example of applications

Rehabilitation of a bridge deck
• Removal of damaged concrete layer using
high-pressure water jetting
• Anchoring of additional reinforcement using
Hilti injection mortar
• Installation of shear connectors using Hilti
injection mortar
• Placement of new concrete overlay
✓ Monolithic load-bearing behaviour
✓ Reliable shear transfer
✓ Stiff connection
✓ Reduced connector embedment
Strengthening the floor of an industrial building

• Removal of covering and any loose overlay
• Roughening of surface by shot-blasting
• Installation of connectors using Hilti injection
mortar according to engineer's instructions
• Inspections, if necessary, of concrete surface
for roughness and pull-away strength, and of
connectors for pull-out strength.
• Placement of reinforcement and overlay
concrete
✓ Reliable and verifiable shear transfer
✓ Adequate connection stiffness
✓ Small anchorage depth
Strengthening an industrial building foundation

• exposure of foundation
• Installation of connectors using Hilti injection
mortar as per design specifications (smooth
surface)
• Placement of reinforcement and overlay
concrete
✓ Reduced labour
✓ Reduced anchor embedment
✓ Ductile connection
Repairing and strengthening a pier

• Roughening of concrete surface
• Installation of shear connectors using Hilti injection
mortar as per design specifications
• Placement of reinforcement and overlay concrete
✓ Stiff connection
✓ Reduced anchor embedment
7
2 Products overview
The following table summarizes the considered products:
Anchor type HCC-B +

HUS 3
HIT-V + HCC-K + REBAR +
RE500 V3 RE500 V3 RE500 V3 RE500 V3
Anchor size 14 8 - 10 - 14 10 - 12 - 16 10 - 16 8… - … 20
material
Cracked concrete Ѵ Ѵ Ѵ Ѵ Ѵ
Base
Non-cracked concrete Ѵ Ѵ Ѵ Ѵ Ѵ
European Technical approval

(ETA) for Ѵ Ѵ X X X
Approvals
concrete overlay static
European Technical approval

(ETA) for Ѵ X X X X
concrete overlay fatigue
TR066 Ѵ Ѵ X X X
method
Design
Hilti method static X X Ѵ* Ѵ* Ѵ
Hilti method seismic X X X X Ѵ

High productivity Ѵ Ѵ X X X
Setting
Flexible length X X Ѵ X Ѵ
Symmetric shape Ѵ Ѵ Ѵ Ѵ X
* Based on TR066
8
HIT-RE 500 V3 injection mortar
In the following tables are schematically illustrated the products for shear connection provided by Hilti
company and considered in this work.
Injection mortar system Benefits

- SafeSet technology: Simplified
method of borehole preparation
using either Hilti hollow drill bit for
hammer drilling or Roughening tool
for diamond cored applications
- Suitable for cracked/non-cracked
concrete C 20/25 to C 50/60
- High loading capacity
- Suitable for dry and water saturated
Foil pack: HIT-RE 500 V3 concrete
(available in 330, 500 and 1400 ml cartridges) - Hilti Technical Data for under water
application
- Long working time at elevated
temperatures
- Cures down to -5°C
- Odourless epoxy
Base material Installation conditions
Concrete Concrete Hammer Diamond Hilti SafeSet

(non- (cracked) drilled holes drilled technology
cracked) holes
Load conditions Other information
Static/ Seismic, ETA- European CE PROFIS

quasi-static C1, C2 Technical conformity Anchor design
Assessment Software
Approvals / certificates
Description Authority / Laboratory No. / date of issue
European Technical Assessment CSTB ETA-16/0143 / 2017-07-12
a)
Shockproof fastenings in civil Federal Office for Civil Protection,
BZS D 16-601/ 2016-08-31
defence installations Bern
Fire test report b) MFPA Leipzig GS 3.2/15-361-4 / 2016-08-04
9
HUS3 Screw anchor
Anchor version Benefits
- High productivity - less drilling and fewer operations
than with conventional anchors
- ETA approval for concrete overlays
HUS3-H - Small edge and spacing distance
M8, M10, M14 - Three embedment depths for maximum design
flexibility
- Immediate placement of the reinforcement
Base material Load conditions
Concrete Concrete Static / quasi-

(non-cracked) (cracked) static
Installation conditions Other information Design Method
EOTA
TR 066
Small edge European CE

distance and Technical conformity
spacing Assessment

European Technical Assessment DIBt ETA-xx/xxxx / 2018-xx-xx
10
HCC-B Shear connector
- ETA approval for shear connection
- Available data according to EOTA TR066
- High shear loads
- Small edge and spacing distance
- User selection of embedment depths for maximum
design flexibility
- Anchor head designed to allow the easy placement
of the overlay reinforcements
HCC-B
Ø 14 - Immediate placement of the reinforcement before
the curing time of the resin
- fatigue loads
- high productivity
Concrete (non- Concrete Small edge

cracked) (cracked) distance and
spacing
Load conditions Other information Design Method
EOTA
TR 066
Static/ fatigue European CE conformity

quasi-static Technical
Assessment

European Technical Assessment DIBt ETA-xx/xxxx / 2018-xx-xx
11
HCC-K Shear connector

- User selection of embedment depths for
maximum design flexibility
HCC-K
Ø 10, 12, 14, 16
Concrete (non- Concrete Small edge Variable

cracked) (cracked) distance and embedment
spacing depth
Load conditions Design Method
Hilti
Design
Method*
Static/ d
quasi-static
*Design method : EOTA TR066 with parameters based on Hilti’s internal testing
12
HCC-HIT-V
- flexible length
HCC-HIT-V
M8, M10, M12, M16 - stainless steel available for highly
aggressive environments
- head position in new concrete can be
adjusted after anchor installation
Concrete (non- Concrete Small edge Variable embedment depth

cracked) (cracked) distance and
spacing
Static/ Hilti
quasi-static Design *Design method : EOTA TR066 with
Method* parameters based on Hilti’s internal testing
d
13
REBAR
- High shear loads
- User selection of embedment depths
for maximum design flexibility
- Seismic loads
- flexible length
REBAR
Ø 8, 10, 12, 14, 16, 20
Concrete (non- Concrete Small edge Variable

cracked) (cracked) distance and embedment
spacing depth
Hilti
Design
Method
Static/ Seismic d
quasi-static
14
3 Design of interface
3.1 Basic considerations
Structures made of reinforced concrete or prestressed concrete which have a concrete overlay at least 40 mm
in thickness (prEN 1992-4), or at least 60 mm on bridge structures, may be designed as monolithic building
components if the shear forces at the interface between the new and the existing concrete are restrained
3.2 Principle and set-up of the analytical model
Forces at the interface between the new and existing concrete are determined from the external forces acting
on the building component. In designing the interface, it must normally be assumed that the interface is de-
bonded. The shear connectors crossing the interface must be placed in such a way that shear forces (“shear
flow”) at the interface are transmitted at design level.
Fig. 8: Load contribution of the different components
Because of separation at the interface, the shear connectors are subject to a tensile force and simultaneously
to a bending moment, both of which depend on the roughness of the interface surfaces. If the surfaces are
roughened, additional interlocking effects and cohesion can take up part of the shear force at the interface.
3.3 Design shear resistance at the interface, 𝒗𝑹𝒅
The transmission of shear forces at the interface between the new and existing concrete is determined by
the roughness and surface finish of the joint as well as of the transverse reinforcement perpendicular to the
interface. In general, the following equation applies:
𝑣𝑅𝑑 ≥ 𝑣𝐸𝑑
Where:
𝑣𝑅𝑑 = Design resistance of the allowable shear force per meter ("shear flow") in [kN/m] at
the interface
𝑣𝐸𝑑 = Design value of the shear flow acting at the interface in [kN/m]
Two different models are available for the computation of the longitudinal shear resistance of the interface: the
method proposed by the EOTA TR066 and the HILTI method, also indicated as Palieraki method.
15
3.4 Design shear strength at the interface, EOTA TR066
According to TR066 the following equation define the resistance of the interface:
1
𝑓𝑦𝑘 0,85∙𝑓𝑐𝑘 0,85∙𝑓𝑐𝑘
3
𝑣𝑅𝑑 = {𝑐𝑟 ∙ 𝑓𝑐𝑘 + 𝜇 ∙ 𝜎𝑛 + 𝜇𝑒 ∙ 𝜅1𝑒 ∙ 𝛼𝑘1 ∙ 𝜌 ∙ 𝜎𝐴 + 𝜅2𝑒 ∙ 𝛼𝑘2 ∙ 𝜌 ∙ √ ∙ } 𝑏𝑗 ≤ (𝛽𝑐 ∙ 𝜈𝑒 ∙ ) 𝑏𝑗 (TR066,2.31,2.9)
𝛾𝑠 𝛾𝑐 𝛾𝑐
Interlock pull-out dowel concrete strut
Where:
cr = Coefficient for adhesive bond resistance in a reinforced interface

fck = minimum value of concrete compressive strength of the two concrete layers,
measured on cylinders
fyk = Characteristic yield strength of the shear connector
µe = Friction coefficient
n = Lowest expected compressive stress resulting from an eventual normal force acting
on the interface (compression has a positive sign)
1e = Interaction coefficient for tensile force activated in the shear connector
2e = Interaction coefficient for flexural resistance in the shear connector
k1 = Modification factor for material properties of the connector
k2 = Modification factor for geometry of the connector
 = Reinforcement ratio of the steel of the shear connector crossing the interface
 = Steel stress associated to the relevant failure mode, (see section 3.14)
c = Safety factor for concrete; 1,50 as given in EN 1992-4 for strengthening of existing
structures
s = Safety factor for steel; 1,15 as given in EN 1992-4 for supplementary reinforcement
bi = Width of the interface of the composed section
e = Coefficient for reduction of concrete strength
c = Coefficient for the strength of the compression strut
Coefficients and parameters for different surface roughness

Surface characteristics of e
ca cr 1e 2e c
interface fck ≥ 20 fck ≥ 35
Very rough,
(including shear keys 1)) 0,5 0,2 0,5 0,9 0,5 0,8 1,0
Rt ≥ 3,0 mm
Rough,
0,4 0,1 0,5 0,9 0,5 0,7
Rt ≥ 1,5 mm
Smooth
(concrete surface without
treatment after vibration or 0,2 0 0,5 1,1 0,4 0,6
slightly roughened when
cast against formwork)
Very smooth
(steel, plastic, timber 0,025 0 0 1,5 0,3 0,5
formwork)
1) Shear keys should satisfy the geometrical requirements given in Fig.9
1⁄
e = 0,55 ∙ (
30
)
3
< 0,55
𝑓𝑐𝑘
k1 = given in the European Technical Assessment of the connector
k2 = given in the European Technical Assessment of the connector
16
Product specific coefficients according to TR066
Anchor 𝜶𝒌𝟏 𝜶𝒌𝟐
HCC-B 0.8 1.3
HUS3 0.8 1.0
HCC-K N.A N.A
HCC-HIT-V N.A N.A
REBAR N.A N.A
≤ 30° h2 ≤ 10*dk
dk ≥ 5 mm
3∙dk ≤ h1 ≤ 10∙dk
Fig. 9: Geometry of shear keys
3.5 Design shear strength at the interface, HILTI method
According to the Hilti method the governing equation for interface resistance is:
𝑣𝑅𝑑 = {𝜇ℎ (𝜎𝑛 + 𝜌 min( 𝜎𝐴 , 𝜅1ℎ 𝜎𝑠 ) + 𝜅2ℎ 𝜌 √𝑓𝑦𝑑 𝑓𝑐𝑑 }𝑏𝑗 ≤ 𝛽𝑐 𝜈ℎ 𝑓𝑐𝑑 𝑏𝑗
Pull-out dowel concrete strut
Where:
fcd = minimum value of concrete design compressive strength of the two concrete layers,
fyd = design yield strength of the shear connector
µh = Friction coefficient
n = Lowest expected compressive stress resulting from an eventual normal force acting
on the interface (compression has a positive sign)
1h = contribution factor for the friction mechanism
2h = contribution factor for the dowel mechanism
 = Reinforcement ratio of the steel of the shear connector crossing the interface
A = Steel stress associated to the relevant failure mode (see section 3.14)
bi = Width of the interface of the composed section
h = Effectiveness factor for the concrete according to fib MC2010, Eq. (7.3-51)
c = Coefficient for the strength of the compression strut
s = Effective steel stress in the connector
The following definitions are valid for the considered method:
3
𝑓𝑐𝑑 2
𝜇ℎ = 0.3 √(𝜎 +𝜎 )
𝑐 𝑛
𝜎𝑐 = 𝜌 𝜎𝑠
17
𝜎
𝐴
𝜎𝑠 = 0.80
1
30 3
𝜈ℎ = 0.55 (𝑓 ) < 0.55 (Fib MC2010 7.3-51)
𝑐𝑘
In the following are reported the tables with the parameters needed for the application of the Hilti method
Parameter 1h for different interface characteristics: monotonic loading

𝟔𝒅 < 𝒍𝒆𝒎𝒃 < 𝟐𝟎 𝒅
Mechanically roughened (1/4-in. amplitude), normal strength concrete 0.60
Mechanically roughened (1/4-in. amplitude), lightweight or high strength concrete 0.40
Smooth Interface 0.40
Very Smooth Interface, steel formed 0.20
Smooth Interface, lightweight concrete 0.20
Smooth Interface, no cohesion 0.10
Rough Interface, external compressive stress 0.70
Smooth Interface, external compressive stress 0.50
Interface with Shear Keys 0.80
Parameter 1h for different interface characteristics: cyclic loading, maximum resistance
𝒍𝒆𝒎𝒃 > 𝟐𝟎𝒅 𝟏𝟎𝒅 < 𝒍𝒆𝒎𝒃 < 𝟐𝟎𝒅
Mechanically roughened (1/4-in. amplitude), normal strength 0.60 𝑙𝑒𝑚𝑏
concrete 0.02 + 0.2
𝑑
Mechanically roughened (1/4-in. amplitude), lightweight or high 0.40 𝑙𝑒𝑚𝑏
strength concrete 0.02
𝑑
Smooth Interface 0.20
Very Smooth Interface, steel formed N/A
Smooth Interface, lightweight concrete N/A
Smooth Interface, no cohesion N/A
Rough Interface, external compressive stress 0.70
Smooth Interface, external compressive stress 0.50
Interface with Shear Keys 0.40 N/A
Parameter 1h for different interface characteristics: cyclic loading, resistance after three cycles
𝟏𝟎𝒅 ≤ 𝒍𝒆𝒎𝒃 ≤ 𝟏𝟐𝒅
Cyclic Loading: Resistance of Mechanically roughened interface, without
external compressive stress, after three loading cycles: 0.10
Applied displacement smax≥1.00mm
Cyclic Loading: Resistance of Mechanically roughened interface, with external
compressive stress, after three loading cycles: 0.20
Applied displacement 0.20mm<smax<1.00mm
Cyclic Loading: Resistance of Mechanically roughened interface, with external
compressive stress, after three loading cycles: 0.10
Applied displacement smax<0.20mm, or smax>1.00mm
Parameter 2h for different normalized embedment depth

ℎ𝑒𝑓 0.70
𝑑
>8
6≤
ℎ𝑒𝑓
≤8 𝑙𝑒𝑚𝑏
𝑑 0.1 − 0.1
𝑑
ℎ𝑒𝑓 0.5
𝑑
=6
Residual interface resistance 0.5 𝜅2
18
3.6 Design shear force acting longitudinally at interface, 𝒗𝑬𝒅
Normally, the design shear force 𝑣𝑒𝑑 is calculated from the bending resistance of the cross-section (shear
failure of the member should not be the governing factor). The design shear force 𝑣𝑒𝑑 can also be calculated
from the change of the compression and/or tension (shear load 𝑣𝑒𝑑 ) force in the concrete overlay.
In this case, the definition of the acting longitudinal shear is made starting from the value of shear defined
with the structural analysis. It is possible to account for both for the case of positive and negative bending
moments. The formulas used are the following:
Computation of the longitudinal shear on the interface

Positive bending moment, compressed part of the slab all contained in the overlay depth
𝑉
𝑣𝐸𝐷,𝑖 =
𝑧
𝑧 = 0,9 𝑑
Positive bending moment, compressed part of the slab not fully contained in the overlay depth
𝑉 ℎ𝑛
𝑣𝐸𝐷,𝑖 =
𝑧 𝑥
𝑧 = 0,9 𝑑
Negative bending moment:
𝑉 𝐴𝑠,𝑛
𝑣𝐸𝐷,𝑖 =
𝑧′ 𝐴𝑠,𝑛 + 𝐴𝑠,𝑒𝑥
𝑧 ′ = 0,9 𝑑′
Where:
𝑣𝐸𝐷,𝑖 = longitudinal shear

𝑉 = shear acting on the considered section
𝑥 = depth of the compressed part of the composite slab
𝐴𝑠,𝑛 = area of the reinforcements in the new slab
𝐴𝑠,𝑒𝑥 = area of the reinforcements on top of the existing slab
𝑧 = internal lever harm of the composite slab
d = effective depth of the slab, positive bending moment
d‘ = effective depth of the slab, negative bending moment
19
3.7 Shear force to be transferred at overlay perimeter
At the perimeter of a new concrete overlay, the maximum tensile force Fcr must be taken into account in the
design. In fact, here the most severe action on the interface can be related to the effect of shrinkage.
Considering the cracking force for the design of the interface it is conservatively defined the maximum possible
action on the connection. Particular attention must be paid to constraining the moment arising from F cr:
Fig. 10: Equilibrium condition at the edges of the slab
3.7.1 Verification according to EOTA TR066 indications

∗
𝐹𝑐𝑟 = 𝑉𝐸𝑑 = ℎ𝑁 ∙ 𝑏𝑗 ∙ 𝑓𝑐𝑡𝑑 (TR066 2.3)
∗ ℎ𝑁 ∙𝑏𝑗 ∙𝑓𝑐𝑡𝑑
∗ 𝑉𝑒𝑑
𝑁𝑒𝑑 = = (TR066 2.5)
6 6
𝑙𝑒 = 3 ∙ ℎ𝑁 𝑓𝑜𝑟 𝑣𝑒𝑟𝑦 𝑟𝑜𝑢𝑔ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠

{ 𝑙𝑒 = 6 ∙ ℎ𝑁 𝑓𝑜𝑟 𝑟𝑜𝑢𝑔ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠 (TR066 2.1)
𝑙𝑒 = 9 ∙ ℎ𝑁 𝑓𝑜𝑟 𝑠𝑚𝑜𝑜𝑡ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
Where:
𝑙𝑒 = Width of the lateral strip considered as subjected to the highest shrinkage forces
ℎ𝑁 = Thickness of the overlay
𝑓𝑐𝑡𝑑 = Design tension resistance of concrete
3.7.2 Verification according to HILTI method indications

∗
𝐹𝑐𝑟 = 𝑉𝐸𝑑 = ℎ𝑁 ∙ 𝑏𝑗 ∙ 𝑘 ∗ 𝑓𝑐𝑡,𝑒𝑓𝑓
∗
∗ 𝑉𝑒𝑑
𝑁𝑒𝑑 = 6
𝑙 = 3 ℎ𝑁 𝑓𝑜𝑟 𝑟𝑜𝑢𝑔ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠

{ 𝑒
𝑙𝑒 = 6 ℎ𝑁 𝑓𝑜𝑟 𝑠𝑎𝑛𝑑 𝑏𝑙𝑎𝑠𝑡𝑒𝑑 𝑎𝑛𝑑 𝑠𝑚𝑜𝑜𝑡ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
Where:
𝑙𝑒 = Width of the lateral strip considered as subjected to the highest shrinkage forces
ℎ𝑁 = Thickness of the overlay
𝑘 = Coefficient to allow for non-uniform self-equilibrating stresses = 0.8 for hN=30 cm
𝑓𝑐𝑡,𝑒𝑓𝑓 = Tensile strength of overlay effective at the time when the cracks may first be expected
to occur as per [1], Section 7.3.2 (for general cases: f ct,eff = 3 N/mm2)
20
3.8 Central regions without shear connectors
Where the shear stresses are low, shear connectors need not be used in the central region (area) of the
overlay if the load is predominantly static and if connectors are positioned around the perimeter. The
resistance of the interface without shear connectors can be computed with two different methods: the one
proposed by EOTA TR066 or the Hilti method.
3.8.1 Verification of an interface without shear connectors according to EOTA TR066
𝜏𝑅𝑑,𝑐𝑡 = 𝑐𝑎 ∙ 𝑓𝑐𝑡𝑑 + 𝜇𝑒 ∙ 𝜎𝑛 ≤ 0,5 ∙ 𝜈𝑒 ∙ 𝑓𝑐𝑑 (TR066 2.9)
The coefficients and the parameters present in the equation are defined in section 3.4
3.8.2 Verification of an interface without shear connectors according to Hilti method
𝜏𝑅𝑑,𝑐𝑡 = 𝜇ℎ 𝜎𝑛 ≤ 𝛽𝑐 𝜈ℎ 𝑓𝑐𝑑
The coefficients and the parameters present in the equation are defined in section 3.5
3.9 Redundant load transfer
The design applies to redundant load transfer; which means that a local load must be transferred by at least
3 shear connectors.
3.10 Fatigue loading
3.10.1 General observations
(1) Bond interfaces subject to substantial changes in stress, i.e. not to predominantly static forces, must
be designed to withstand fatigue.
(2) Bonds subject to fatigue must always be roughened.
(3) The effect of the superposition of fatigue loading and static loading is not addressed in this work
3.10.2 Proof for fatigue
Fatigue loadings are accounted differently according to the method considered:
- According to Hilti method the effect of fatigue loading is taken into account by means of the use of the
relevant parameters (Section 3.5) in the formula for the definition of longitudinal shear resistance
- According to EOTA TR066 fatigue is taken into account by means of a reduction coefficient ηsc
Δ𝜏𝐸𝑑 ≤ 𝜂𝑠𝑐 ∙ 𝜏𝑅𝑑 (TR066 2.13)
Without the effect of static loadings:
Δ𝜏𝐸𝑑 = 𝜏𝐸𝑑,max (TR066 2.14)
𝜂𝑠𝑐 = 0,4 Or otherwise given in the European Technical Assessment of the shear connector for
interfaces with use of shear connectors
Where:
Ed = Shear stress acting as fatigue relevant loading
sc = Factor for fatigue loading
Ed,max = Upper shear stress acting as fatigue relevant loading
𝜏𝑅𝑑 = Resisting shear stress
21
3.11 Seismic loading
Seismic loadings are verified only according to the Hilti method. In this case, the verification of the interface
is made using the parameters related to the case of “cycling loading maximum resistance” (see section 3.5).
The anchor verification is made with reference to the C1 category bond strength as defined in the ETA of the
product. For the failure mechanism considered in the proofs (See section 3.14) the following reduction
coefficients are considered:
Reduction coefficient of the design resistances of the anchors

Steel failure 1,00
Combined concrete cone/pull-out failure 0,85
Pull-out failure 1,00
Concrete cone failure 0,75
Concrete cone failure for cast-in headed anchors 0,85
Splitting failure 0,85
3.12 Serviceability limit state
As an approximation in normal cases, the additional deformation of a strengthened bending element may be
determined using the monolithic cross-section, and then increased as follows:
𝑊𝑒𝑓𝑓 = 𝛾 𝑊𝑐𝑎𝑙𝑐
𝑊𝑒𝑓𝑓 = additional deformation calculated for the reinforced section considering the
elasticity of the shear connectors
𝑊𝑐𝑎𝑙𝑐 = additional deformation calculated for the reinforced section assuming a
perfect bond
γ = factor reported in the following table
sd = displacement of connectors under the mean permanently acting load
Fp  0.5 Fuk
The displacements reported in the table can be used for more precise calculations:
Surface treatment Mean roughness Rt [mm] γ sd [mm]

High-pressure water jets / scoring > 3.0 1.0 ≈ 0,005 ∅
Sand-blasting / chipping hammer > 0.5 1.1 ≈ 0,015 ∅
 =diameter of shear connectors
3.13 Additional rules and design details
3.13.1 Mixed surface treatment
The surface treatments used for a building component may differ only if the non-uniform stiffness arising in the
bond is taken into account (also see Error! Reference source not found., displacement sd). Note that a non-
cracked interface, i.e., rigid bond, is assumed for interfaces with low shear stress that do not require connectors
in the central region
3.13.2 Minimum amount of reinforcement at the interface
If shear connectors cannot be omitted, the following minimum reinforcement ratio must be provided in the
interface:
𝑓𝑐𝑡𝑚
𝜌min. = 0.12 𝑓𝑦𝑘
≥ 0.0005 (FIB MC2010)
22
3.13.3 Layout of connectors
(1) The connectors must be positioned in the load-bearing direction of the building component with respect
to the distribution of the applied shear force in such a way that the shear force at the interface can be
constrained, and de-bonding of the new concrete overlay prevented.
(2) If the new concrete overlay is on the tension side of the load-bearing component, the connectors must be
distributed to accord with the grid spacing of the longitudinal reinforcement without any allowance being
made for anchorage length
(3) The connector spacing in the load-bearing direction may not be larger than 6 times the thickness of the
new concrete overlay, or 800 mm.
3.13.4 Recommendation for overlay placement
Pre-treatment:
A primer consisting of thick cement mortar is recommended.
Before the cement mortar primer is applied, the old concrete should be adequately wetted 24 hours in advance,
and thereafter at suitable intervals. Before applying the primer, the concrete surface should be allowed to dry
to such an extent that it has only a dull moist appearance.
The mortar used as a primer should consist of water and equal parts by weight of Portland cement and sand
of 0/2 mm particle size. This is applied to the prepared concrete surface and brushed in.
Overlay:
The concrete mix for the overlay should normally be such as to ensure low-shrinkage (W/C  0.40). The overlay
must be placed on the still fresh primer, i.e. wet on wet.
Curing:
Careful follow-up is necessary to ensure an overlay of adequate durability. Immediately after placement, the
concrete overlay must be protected for a sufficiently long period (at least five days) against drying out and
excessive cooling.
3.13.5 Recommendation for surface treatment
The roughness of the interface has a decisive influence on the shear force that can be transferred. For design
purposes, the characteristic dimension is the mean depth of roughness, R t, measured according to the sand-
patch method [9]. It must be borne in mind that Rt is a mean value, and thus the difference between the peaks
and valleys is about 2 Rt.
It is recommended that a mean roughness, Rt, be stipulated when specifying the surface treatment. Prior to
approving the treatment, a sample surface must be made up and this checked using the sand-patch method.
3.14 Anchorage of the shear connectors in the existing and new concrete
3.14.1 General observations
The anchorage of the shear connectors must be verified both in the existing slab and in the overlay according
to the prescriptions of prEN 1992-4. The shear connectors are considered alternatively as post installed
anchors in the existing concrete slab and as cast-in anchors in the overlay. The minimum resistance between
the two is considered for the definition of the ultimate load carrying capacity of the connectors. From the
ultimate load carrying capacity, considering the effective cross section of the connectors, it is defined the stress
𝜎𝐴 used for interface verifications
3.14.2 Installation geometry
To guarantee the efficiency of the connection, the shear connectors are to be anchored sufficiently in the
existing concrete and in the overlay. In the following, it is reported the description of the geometrical
parameters involved in the proofs needed for the verification of the anchors.
Setting details for shear connectors
Lcon Length of shear connector [mm]
hef,e Embedment depth in the existing slab [mm]
hef,n Embedment depth in the overlay [mm]
hE Thickness of the existing slab [mm]
hN Thickness of the overlay [mm]
d0 Drill bit diameter [mm]
d Anchor stud diameter [mm]
As Effective steel area of the anchor [mm]
Ah Area of the anchor head [mm]
c Anchor edge distance [mm]

s Anchors spacing [mm]
3.14.3 Design proofs for the connector
The design proofs considered for the connectors are the ones defined by the prEN 1992-4.
Due to the characteristic of the design problem, it was chosen to neglect the possibility of concrete blowout
failure. This decision is justified by the geometry of the problem.
The following table summarizes the design proofs that are carried out.
Design proofs considered for connectors verification:
Steel failure resistance
Resistance depending on the connector properties, independent from the

embedment in the concrete element.
Notation: 𝑁𝑅𝑑,𝑠
Combined concrete cone failure/pull-out resistance
Resistance depending on the connector properties and on concrete element

properties, verified for the anchorage in the existing slab
Notation: 𝑁𝑅𝑑,𝑐𝑝
24
Splitting failure

properties, verified independently for both overlay and existing slab
Notation: 𝑁𝑅𝑑,𝑠𝑝
Concrete cone failure

properties, verified independently for both overlay and existing slab
Notation: 𝑁𝑅𝑑,𝑐
Pull-out failure

properties, verified for the embedment in the overlay
Notation: 𝑁𝑅𝑑,𝑝
3.14.4 Geometrical boundary conditions for existing concrete and concrete overlays
The connectors layout is organized in two different regions, the central part of the slab and the lateral one. In
the central part it is considered that the connectors are installed following a regular square grid. In the lateral
region it is assumed that the connectors are organized in rows. The width of the lateral region is assumed as
equal to 𝑙𝑒 (see section 3.7).
In the following it is reported a general scheme of the connectors layout.
25
Fig. 11: Connector layout
According to the described geometry
2(𝑙𝑒−𝑐)
𝑠2 = 2𝑟−1
𝑟 = Number of the lateral rows of anchors

𝑐 = Distance of the first row of anchors from the free edge
26
4 Examples
4.1 Description of the design case, structural analysis
In the following, it is presented an example about the design of the connection between an existing concrete
slab and an overlay. We consider the case of a continuous beam with two equal spans.
Fig. 12: Static scheme of the beam for the design example
It is assumed that the value of the shear at the central and lateral supports are already available from
structural analysis:
𝑉𝐴 = 79,9 𝑘𝑁
𝑉𝐵 = 133,1 𝑘𝑁
The geometry of the composite section made with the concrete overlay is the following:
Geometrical details:
Thickness of new slab (overlay) hN = [mm] 100
Thickness of existing slab hE = [mm] 200
Net cover on top of existing slab Cs = [mm] 45
Effective depth of existing slab d= [mm] 155
Width of the slab bj = [mm] 5000
It is assumed that the reinforcements in the existing slab are known while the presence of reinforcements in
the overlay is neglected. The reinforcements that are present at the bottom of the existing slab are Φ16 with
spacing 250 mm while the top reinforcements are made with Φ20 with the same spacing.
The concrete class is C20/25 for the existing slab and C25/30 for the overlay. The reinforcements are made
with steel B450C
From the analysis of the section at ultimate limit state, considering the stress block approximation for the
description of the concrete in compression and the elastic perfectly plastic constitutive model for steel, it is
possible to evaluate the ultimate bending moment resistance and the position of the neutral axis in the
section.
The steel areas on top and bottom of the existing slab are respectively:
𝐴𝑠𝑒,− = 7853,98 𝑚𝑚2
𝐴𝑠𝑒,+ = 5026,55 𝑚𝑚2
Under the hypothesis of planarity of the sections and perfect bond concrete-steel, imposing the translational
equilibrium, it is possible to find the depth of the neutral axis X and the strains in the reinforcements.
Considering the case of positive bending moment resistance, we get:
27
Neutral axis position and steel bars strains:
Positive bending moment
Depth of the neutral axis X= [mm] 75.5
Top steel strains εs Ase- = [%] 0.32 Steel
90 yielded in tension
Bottom steel strains εs Ase+ = [%] 0.83 Steel yielded in tension
These values have been obtained under the conservative hypothesis (for the interface shear verification) of
having the same class of concrete both for the overlay and for the existing slab. The class of concrete
considered was the higher one in order to maximize the longitudinal shear.
Fig. 13: Details of the beam for the design example
4.2 Data for design of the connection at external supports
After the preliminary definition of the quantities of interest, it is now possible to try to get the best solution for
the design problem related to the longitudinal shear connection of new and existing slab. First, it is
necessary to define the situation that we want to analyse. Since we consider that the compressed part of the
composite slab is in the upper portion of the structure, we chose the case of positive bending moment.
Then it is necessary to define the depth of the compressed part of the slab, as defined in the previous
computations X=75.5 mm. It was chosen to neglect the beneficial compression on the interface due to the
external load so 𝜎𝑁 = 0. As already stated the shear is 𝑉 = 79,9 𝑘𝑁
The geometrical data describing the problem are:
Geometrical details:
Thickness of new slab (overlay) hN = [mm] 100
Thickness of existing slab hE = [mm] 200
Slab width bj = [mm] 5000
Reinforcements diameter on top of the existing slab Φex = [mm] 20
Reinforcements spacing on top of the existing slab ss,ex = [mm] 200
Embedment depth in the new slab hef,n = [mm] 55
Furthermore, it is assumed not to have sufficient reinforcements in order to limit the crack width to 0.3 mm,
both in existing and new slab.
It is also necessary to define the state of concrete (cracked or un-cracked), the concrete class for both new
and existing slab and the properties of the interface. In this example:
28
Concrete element properties:
Concrete state cracked
Existing slab concrete class C20/25
New slab concrete class C25/30
Surface treatment Very smooth
Than it is needed to define the parameters of our design: first of all the choice of the connector and of the
resin and then the geometrical parameters describing the positioning of the connectors:
type of connector HCC-B 14-180
type of resin HIT-RE 500-V3
Anchor spacing s= [mm] 300

Spacing between anchors close to the edge s1 = [mm] 100
Anchors edge distance c= [mm] 100
Number of rows of anchors close to the edge r= [-] 3
Finally it is required the selection of the method to be used for carrying out the verification of the interface.
This method must be available for the chosen type of connectors and for the considered loading conditions.
In this example, it was chosen to use the FIB model.
From the choice of connector and of the resin, it is possible to find all the needed data from the
documentation of the product. These data are reported in the table below:
Data from the relevant documentation:

Hole diameter d0 = [mm] 16
Anchor diameter d= [mm] 14
Anchor head diameter dh = [mm] 42
Anchorage cross section area As = [mm2] 83,00
Safety coefficient for concrete cone γMc = [-] 1.5
Safety coefficient for splitting γMsp = [-] 1.8
Safety coefficient for pull-out γMp = [-] 1.5
Safety coefficient for steel failure γMS = [-] 1.2
Steel resistance of the anchorage f uk = [MPa] 400,00
Design resistance of the anchor steel fyd = [MPa] 333,33
Minimum existing slab thickness for splitting h min E = [mm] 157
Minimum new slab thickness for splitting h min N = [mm] 87
Critical spacing for splitting in new slab scr,spN = [mm] 70
Critical edge distance for splitting in new slab ccr,spN = [mm] 70
Critical spacing for splitting in existing slab scr,spE = [mm] 70
Critical edge distance for splitting in existing slab ccr,spE = [mm] 70
Bond strength in existing cracked concrete τe = [MPa] 8.50
Bond strength in new cracked concrete τn = [MPa] 8.67
Bond strength in uncracked concrete C20/25 τRk,ucr = [MPa] 14.00
29
4.3 Determination of longitudinal shear
In this case, since ℎ𝑁 > 𝑋 the compressed part of the slab is totally contained into the new slab. The
longitudinal shear is computed as:
𝑉 79,9 𝑘𝑁
𝑣𝐸𝐷,𝑖 = = = 348,15 𝑘𝑁/𝑚 (𝐵2.5 5.1.2)
𝑧 0,2295 𝑚
With:
𝑧 = 0,9 𝑑 = 229,50 𝑚𝑚
4.4 Verification of connectors: central part, existing slab
The load carrying capacity of the connector is defined taking into account separately the geometry of the
installation in the central part of the slab and in the external part close to the edge.
First, the central part of the slab is considered, taking into account that the tensile resistance of the
connector is the minimum one between the values obtained considering the anchorage in the existing and in
the new slab.
In the existing slab the connector is a post installed bonded anchor, the computation of the load carrying
capacity requires to consider different failure modes:
4.4.1 Steel failure
The steel failure resistance of the connector is taken directly from the values given in the relevant
documentation
𝑁𝑅𝑘,𝑠 = 33,20 𝑘𝑁
From this, the design values is obtained as:

𝑁𝑅𝑘,𝑠 33,20 𝑘𝑁
𝑁𝑅𝑑,𝑠 = = = 27,67 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑠 1,2
4.4.2 Combined concrete cone/pull-out verification
0
𝑁𝑅𝑘,𝑝 = 𝜋 𝑑 ℎ𝑒𝑓,𝑒 𝜏𝑅𝑘 = 𝜋 14𝑚𝑚 ∗ 125𝑚𝑚 ∗ 8,5𝑀𝑃𝑎 = 46,73 𝑘𝑁 (EN1992-4 7.3.1)
𝑠𝑐𝑟,𝑁𝑝 = 7.3 𝑑 √𝜏𝑅𝑘,𝑢𝑐𝑟 = 7.3 ∗ 14𝑚𝑚 √14 𝑀𝑃𝑎 = 382.39 𝑚𝑚 (EN1992-4 7.5)
𝑠𝑐𝑟,𝑁𝑝 ≤ 3 ℎ𝑒𝑓 = 375 𝑚𝑚 (EN1992-4 7.5)
𝑠𝑐𝑟,𝑁𝑝 = 375 𝑚𝑚
𝑠𝑐𝑟,𝑁𝑝 375 𝑚𝑚
𝑐𝑐𝑟,𝑁𝑝 = = = 187.5 𝑚𝑚 (EN1992-4 5.6)
2 2
𝐴0𝑝,𝑁 = (𝑠𝑐𝑟,𝑁𝑝 )(𝑠𝑐𝑟,𝑁𝑝 ) = (375 𝑚𝑚)2 = 140625 𝑚𝑚2 (EN1992-4 7.3.2)

2
𝐴𝑝,𝑁 = (min(𝑠, 𝑠𝑐𝑟,𝑁𝑝 )) = (min(300 𝑚𝑚; 375 𝑚𝑚))2 = 90000 𝑚𝑚2
𝑐
𝜓𝑠,𝑁𝑝 = 0.7 + 0.3 ≤1 = 𝑠𝑖𝑛𝑐𝑒 𝑐 = ∞ 1 (EN1992-4 7.10)
𝑐𝑐𝑟,𝑁𝑝
30
1
𝜓𝑒𝑐,𝑁𝑝 = 𝑒𝑛 = 𝑠𝑖𝑛𝑐𝑒 𝑒𝑛 = 0 1 (EN1992-4 7.12)
1+2
𝑠𝑐𝑟,𝑁𝑝
Assuming conservatively n=8 for the maximum number of anchors:

1.5
0
𝑑 𝜋 𝜏𝑅𝑘
𝜓𝑔,𝑁𝑝 = √𝑛 − (√𝑛 − 1) ( ) ≥1 =
𝑘8 √ℎ𝑒𝑓 𝑓𝑐𝑘
𝜋∗14 𝑚𝑚∗8.5 𝑀𝑃𝑎 1.5

= √8 − (√8 − 1) ( ) ≥1 = 1.079 (EN1992-4 7.8-7.9)
7.7 √125 𝑚𝑚∗20𝑀𝑃𝑎
0.5
0
𝑆 0
𝜓𝑔,𝑁𝑝 = 𝜓𝑔,𝑁𝑝 −( ) (𝜓𝑔,𝑁𝑝 − 1) ≥ 1 =
𝑆𝑐𝑟,𝑁𝑝
300𝑚𝑚 0.5
= 1.079 − ( ) (1.079 − 1) ≥ 1 = 1.008 (EN1992-4 7.7)
375𝑚𝑚
ℎ𝑒𝑓
𝜓𝑟𝑒,𝑁𝑝 = 0.5 + ≤1= 1 (EN1992-4 7.11)
200
It is then possible to define the characteristic and the design resistances:
0
𝐴𝑝,𝑁
𝑁𝑅𝑘,𝑝 = 𝑁𝑅𝑘,𝑝 𝜓𝑠,𝑁𝑝 𝜓𝑔,𝑁𝑝 𝜓𝑒𝑐,𝑁𝑝 𝜓𝑟𝑒,𝑁𝑝 =
𝐴0𝑝,𝑁
90000 𝑚𝑚2
= 46,73 𝑘𝑁 ∗ ∗1∗1∗1∗1= 30.16 𝑘𝑁 (EN1992-4 7.3)
140625 𝑚𝑚2
𝑁𝑅𝑘,𝑝 30.16 𝑘𝑁
𝑁𝑅𝑑,𝑝 = = = 20.10 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑝 1.5
4.4.3 Concrete cone breakout verification
0
𝑁𝑅𝑘,𝑐 = 𝑘𝑔 √𝑓𝑐𝑘 ℎ1.5
𝑒𝑓 = 7.7 √20 𝑀𝑃𝑎 (125 𝑚𝑚)
1.5
= 48,13 𝑘𝑁 (EN1992-4 7.14)
𝑠𝑐𝑟,𝑁 = 3 ℎ𝑒𝑓 = 3 ∗ 125 𝑚𝑚 = 375 𝑚𝑚 (EN1992-4 7.14)
𝑠𝑐𝑟,𝑁 375 𝑚𝑚
𝑐𝑐𝑟,𝑁 = = = 187,5 𝑚𝑚
2 2
2 2
𝐴𝑐,𝑁 = (min(𝑠, 𝑠𝑐𝑟,𝑁 )) = (min(300 𝑚𝑚; 375 𝑚𝑚)) = 90000 𝑚𝑚2
𝐴0𝑐,𝑁 = (𝑠𝑐𝑟,𝑁 )(𝑠𝑐𝑟,𝑁 ) = (375 𝑚𝑚)2 = 140625 𝑚𝑚2 (EN1992-4 7.15)

𝑐
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1 = 1 (EN1992-4 7.16)
𝑐𝑐𝑟,𝑁
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
ℎ𝑒𝑓
𝜓𝑟𝑒,𝑁 = 0.5 + ≤1 = 1 (EN1992-4 7.11)
200
0
𝐴𝑐,𝑁
𝑁𝑅𝑘,𝑐 = 𝑁𝑅𝑘,𝑐 𝜓𝑠,𝑁 𝜓𝑒𝑐,𝑁 𝜓𝑟𝑒,𝑁 =
𝐴0𝑐,𝑁
90000 𝑚𝑚2
= 48,13 𝑘𝑁 ∗ ∗1∗1∗1∗1 = 30.80 𝑘𝑁 (EN1992-4 7.13)
140625 𝑚𝑚2
𝑁𝑅𝑘,𝑐 30.80 𝑘𝑁
𝑁𝑅𝑑,𝑐 = = = 20.53 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑐 1,5
31
4.4.4 Splitting verification
The concrete is assumed to be cracked, so the splitting failure verification is not needed
4.4.5 Summary
The lowest resistance of the anchorage in the existing slab is associated to the steel failure 𝑁𝑅𝑑,𝑠 =
27,67 𝑘𝑁
4.5 Verification of connectors: central part, new slab
It is now necessary to evaluate also the anchorage in the new slab. In this case, the connector can be seen
as a cast-in headed stud.
4.5.1 Pull-out verification

𝜋 𝜋
𝐴ℎ = (𝑑ℎ2 − 𝑑 2 ) = ((42 𝑚𝑚)2 − (14 𝑚𝑚)2 ) = 1231.54 𝑚𝑚2 (EN1992-4 7.2)
4 4
𝑁𝑅𝐾,𝑝 = 𝑘1 𝐴ℎ 𝑓𝑐𝑘 = 7.5 ∗ 1231.54 𝑚𝑚2 ∗ 25 𝑀𝑃𝑎 = 230,91 𝑘𝑁 (EN1992-4 7.1)

𝑁𝑅𝑘,𝑝 230,91 𝑘𝑁
𝑁𝑅𝑑,𝑝 = = = 153,94 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑝 1.5

0
𝑒𝑓 = 7.7 √25 𝑀𝑃𝑎 (55 𝑚𝑚)
1.5
= 18,15 𝑘𝑁 (EN1992-4 7.14)
𝑠𝑐𝑟,𝑁 = 3 ℎ𝑒𝑓 = 3 ∗ 55 𝑚𝑚 = 165 𝑚𝑚 (EN1992-4 7.14)
𝑐𝑐𝑟,𝑁 = = = 82,5 𝑚𝑚
2 2
2 2

𝑐
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1 = 1 (EN1992-4 7.16)
𝑐𝑐𝑟,𝑁
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
ℎ𝑒𝑓
𝜓𝑟𝑒,𝑁 = 0.5 + ≤1 = 1 (EN1992-4 7.11)
200
0 𝐴𝑐,𝑁
𝐴0
𝑐,𝑁
27225 𝑚𝑚2
= 18,15 𝑘𝑁 ∗ ∗1∗1∗1∗1= 18,15 𝑘𝑁 (EN1992-4 7.13)
27225 𝑚𝑚2
𝑁𝑅𝑘,𝑐 18,15 𝑘𝑁
𝑁𝑅𝑑,𝑐 = = = 12,10 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑐 1,5
Since the concrete is assumed to be cracked, the splitting failure verification is not needed.
32
4.5.4 Summary
The lower resistance of the anchorage in the new slab is related to the concrete cone breakout, this value is
also smaller than the minimum one coming from the verification of the connection with the existing slab. In
conclusion, we can consider that the failure mode of the connector is associated to concrete cone breakout
in the new slab and the tension design resistance is 𝑁𝑅𝑑,𝑐 = 12,10 𝑘𝑁
4.6 Verification of connectors: lateral part, existing slab
A similar procedure is than followed for the verification of the connectors of the external rows, close to the
edges of the concrete slab. Only the parameters that differs from the ones computed for the central part
need to be recomputed. In this case the verification is carried out considering a strip of anchors
perpendicular to the free edge of the slab. We start considering the existing slab:
4.6.1 Steel failure
Since the connectors are assumed to be the same both for lateral and central part of the plate the steel
failure resistance is obviously the same
First, it is needed to define the spacing of the anchors. We compute the width of the lateral strip subjected to
higher shrinkage stresses as:
3ℎ 𝑟𝑜𝑢𝑔ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
𝑙𝑒 = { 𝑁
6 ℎ𝑁 𝑠𝑚𝑜𝑜𝑡ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
For this example:
𝑙𝑒 = 6 ∗ 100𝑚𝑚 = 600𝑚𝑚 (B2.5, 3.3.1)

2(𝑙𝑒 −𝑐) 2(600 𝑚𝑚−100 𝑚𝑚)
𝑆2 = = = 200 𝑚𝑚
2𝑟−1 2∗3−1
Then it is possible to define the idealized failure area:

𝑠𝑐𝑟,𝑁𝑝 𝑠
𝐴𝑝,𝑁 = {min(𝑐, 𝑐𝑐𝑟,𝑁𝑝 ) + (𝑟 − 1) min(𝑠2 , 𝑠𝑐𝑟,𝑁𝑝 ) + min ( , 2)} ∗ min(𝑠1 , 𝑠𝑐𝑟,𝑁𝑝 )
2 2
375 200
𝐴𝑝,𝑁 = {min(100; 187,5) + (3 − 1) min(200; 375) + min ( , )} ∗ min(100; 375)
2 2
= 60000 𝑚𝑚2
𝑐 100 𝑚𝑚
𝜓𝑠,𝑁𝑝 = 0.7 + 0.3 ≤ 1 = 0.7 + 0.3 = 0.86 (EN1992-4 7.10)
𝑐𝑐𝑟,𝑁𝑝 187,5 𝑚𝑚
1
𝜓𝑒𝑐,𝑁𝑝 = 𝑒𝑛 = (𝑠𝑖𝑛𝑐𝑒 𝑒𝑛 = 0) 1 (EN1992-4 7.12)
1+2
We can now define the characteristic and the design resistances:

0 𝐴𝑝,𝑁
𝐴0
𝑝,𝑁
60000 𝑚𝑚2
= 46,73 𝑘𝑁 ∗ ∗ 0,86 ∗ 1 ∗ 1 ∗ 1 = 17,29 𝑘𝑁 (EN1992-4 7.3)
140625 𝑚𝑚2
𝑁𝑅𝑑,𝑝 = = = 11,52 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑝 1.5
33
𝑠𝑐𝑟,𝑁 𝑠
𝐴𝑐,𝑁 = {min(𝑐, 𝑐𝑐𝑟,𝑁 ) + (𝑟 − 1) min(𝑠2 , 𝑠𝑐𝑟,𝑁 ) + min ( , 2)} ∗ min(𝑠1 , 𝑠𝑐𝑟,𝑁 )
2 2
375 200
𝐴𝑐,𝑁 = {min(100; 187,5) + (3 − 1) min(200; 375) + min ( , )} ∗ min(100; 375)
2 2
= 60000 𝑚𝑚2
100
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1 = 0,86 (EN1992-4 7.16)
187,5
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
0 𝐴𝑐,𝑁
𝐴0
𝑐,𝑁
60000 𝑚𝑚2
= 48,13 𝑘𝑁 ∗ ∗ 0,86 ∗ 1 ∗ 1 ∗ 1 = 17,66 𝑘𝑁 (EN1992-4 7.13)
140625 𝑚𝑚2
𝑁𝑅𝑑,𝑐 = = = 11,77 𝑘𝑁 (EN1992-4 Table7.1)
𝛾𝑀𝑐 1,5
4.6.5 Summary
The lower resistance of the anchorage to the existing slab is associated to the combined pull-out/concrete
cone failure. 𝑁𝑅𝑑,𝑝 = 11,52 𝑘𝑁.
4.7 Verification of connectors: lateral part, new slab
It is now necessary to evaluate also the anchorage in the new slab. In this case, the connector can be seen
as a cast in headed stud
The verification for pull-out of a cast in headed stud is referred to the single anchor, so in this case the
resistance is the same as in the central part of the slab.
2 2
165 200
𝐴𝑐,𝑁 = {min(100; 82,5) + (3 − 1) min(200; 165) + min ( , )} ∗ min(100; 165)
2 2
= 49500 𝑚𝑚2
100 𝑚𝑚
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤ 1 1 (EN1992-4 7.16)
82,5 𝑚𝑚
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
0 𝐴𝑐,𝑁
𝐴0
𝑐,𝑁
34
49500 𝑚𝑚2
= 18,15 𝑘𝑁 ∗ ∗1∗1∗1∗1= 33,00 𝑘𝑁 (EN1992-4 7.13)
27225 𝑚𝑚2
𝑁𝑅𝑑,𝑐 = = = 22,00 𝑘𝑁 (EN1992-4 Table7.1)
𝛾𝑀𝑐 1,5
4.7.4 Summary
The resistance of the connectors placed close to the edges is governed by the combined concrete cone/pull-
out failure in the existing slab. The ultimate resistance is 𝑁𝑅𝑑,𝑝 = 11,52 𝑘𝑁
The following tables summarize the resistance of the connectors:
Design resistance, central part of the slab
Steel failure resistance 𝑁𝑅𝑑,𝑠 = 27,67 kN
Existing slab
Combined concrete cone/pull-out resistance 𝑁𝑅𝑑,𝑝 = 20,10 kN
Concrete cone breakout resistance 𝑁𝑅𝑑,𝑐 = 20,53 kN
New slab
Pull-out resistance 𝑁𝑅𝑑,𝑝 = 153,94 kN
Failure mode: Concrete cone breakout in the new slab
Resistance: 𝑁𝑟𝑑 = 12,10 𝑘𝑁
Design resistance, lateral part of the slab
Steel failure resistance 𝑁𝑅𝑑,𝑠 = 27,67 kN
Existing slab
Combined concrete cone/pull-out resistance 𝑁𝑅𝑑,𝑝 = 11,53 kN
New slab
Pull-out resistance 𝑁𝑅𝑑,𝑝 = 153,94 kN
Failure mode: Combined concrete cone/pull-out in the existing slab
Resistance: 𝑁𝑟𝑑 = 11,53 𝑘𝑁
35
4.8 Verification of the interface in the central part of the slab
The method of verification chosen for this example is the one proposed by FIB in model code 2010.
First, it is computed the longitudinal shear resistance of the interface without shear connectors:
𝑣𝑅𝐷,𝑐𝑡 = (𝑐𝑎 𝑓𝑐𝑡𝑑 + 𝜇𝑒 𝜎𝑛 ) 𝑏𝑗 ≤ (0.5 𝜈𝑒 𝑓𝑐𝑑 )𝑏𝑗
= (0,025 ∗ min(1.20 𝑀𝑃𝑎; 1,03 𝑀𝑃𝑎) + 0.5 ∗ 0) ∗ 5000 𝑚𝑚

≤ (0.5 ∗ 0,55 ∗ min(13,3 𝑀𝑃𝑎; 16,7 𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
𝑘𝑁
= 128.94 (MC 2010, 7.3-50)
𝑚
Since:
𝑘𝑁 𝑘𝑁
𝑣𝐸𝐷,𝑖 = 348,15 ≥ 𝑣𝑅𝐷,𝑐𝑡 = 128.94
𝑚 𝑚
The shear connectors are needed in the central part of the slab. The resistance of the interface is
recomputed taking into account the presence of the connectors. The geometry considered for the connectors
installation is the one already defined (see section 4.2).
From the verification of the connectors in the central part of the slab we have 𝑁𝑅𝑑,𝑐 = 12,10 𝑘𝑁
𝑁𝑟𝑑 12,10 𝑘𝑁
𝜎𝐴 = = = 146 𝑀𝑃𝑎
𝐴𝑆 83 𝑚𝑚2
𝐴𝑠 83 𝑚𝑚2
𝜌= 2
= = 0,0912 %
𝑠 (300 𝑚𝑚)2
It is now possible to use the formula for the computation of the interface shear resistance according to FIB:
1
3
𝑣𝑅𝐷 = (𝑐𝑟 𝑓𝑐𝑘 + 𝜇𝑒 𝜎𝑛 + 𝜌 𝜇min(𝜎𝐴 , 𝑘1𝑒 𝑓𝑦𝑑 ) + 𝑘2𝑒 𝜌 √𝑓𝑦𝑑 𝑓𝑐𝑑 ) 𝑏𝑗 ≤ (𝛽𝑐 𝜈 𝑓𝑐𝑑 )𝑏𝑗
1 0.091
= (0 ∗ min(20𝑀𝑃𝑎; 25𝑀𝑃𝑎)3 + 0.5 ∗ 0 + ∗ 0.5 ∗ min(146 𝑀𝑃𝑎; 0 ∗ 333,3 𝑀𝑃𝑎) + 1.5
100
0.091
∗ √333,3 𝑀𝑃𝑎 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎) ) ∗ 5000 𝑚𝑚
100
≤ (0,3 ∗ 0,55 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
𝑘𝑁
= 460.53 (MC 2010, 7.3-51)
𝑚
𝑘𝑁
In this case 𝑣𝐸𝐷,𝑖 = 348,15 ≤ 𝑉𝑅𝐷 = 460.53 𝑘𝑁/𝑚 so the selected design option for the shear connection
𝑚
can be effectively used.
4.9 Verification of the connection close to the edges
It is necessary to define the actions on the interface close to the edge. In this position the most relevant
source of longitudinal shear load is the effect of shrinkage. It is assumed as maximum shear due to
shrinkage a force equal to the cracking force in the new slab. This assumption is conservative since the
design of the interface for this force is equivalent to impose that the connection cannot experience shear
failure since for higher actions the cracking happens before reaching the shear resistance.
36
2 2
3
𝑓𝑐𝑡,𝑒𝑓𝑓 = 𝑓𝑐𝑡𝑚 = 0.3𝑓𝑐𝑘 = 0.3 ∙ 253 = 2.6 MPa (MC 2010, 7.2.3.1.1)
𝑙𝑒 = 6ℎ𝑁 = 600 mm (B2.5, 3.3.1)
𝐹𝑐𝑟 = ℎ𝑁 𝑏𝑗 𝑘 𝑓𝑐𝑡,𝑒𝑓𝑓 = 100 𝑚𝑚 ∗ 5000 𝑚𝑚 ∗ 0,8 ∗ 2,6 𝑀𝑝𝑎 = 1026 kN (B2.5, 3.3.1)
𝑉𝑒𝑑 = 𝐹𝑐𝑟 = 1026 kN (B2.5, 3.3.1)

𝑉𝑒𝑑 1026 𝑘𝑁
𝑣𝑒𝑑 = = = 1709.98 kN/m (B2.5, 3.3.1)
𝑙𝑒 600𝑚𝑚
Considering the rotational equilibrium of the end portion of the upper slab close to the edge, it is possible to
approximate conservatively the tension load acting on the connectors as:
𝐹𝑐𝑟 1026 𝑘𝑁
𝑁𝑇,𝑒𝑑 = = = 171.00 𝑘𝑁 (B2.5, 3.3.1)
6 6
As in the previous computations, also in this case the longitudinal shear resistance of the interface without
connectors is considered:
𝑘𝑁 𝑘𝑁
𝑣𝐸𝐷 = 1709.98 ≥ 𝑣𝑅𝐷,𝑐𝑡 = 128.94
𝑚 𝑚
So the shear connectors are needed also to sustain the shear at the edges.
In this case 𝑁𝑅𝑑,𝑝 = 11,52 𝑘𝑁:

𝜎𝐴 = = = 46.29 𝑀𝑃𝑎
𝐴𝑆 𝑟 83 𝑚𝑚2 ∗3
𝐴𝑆 𝑟 83 𝑚𝑚2 ∗3
𝜌= = = 0,42 %
𝑙𝑒 𝑠1 600 𝑚𝑚∗100 𝑚𝑚
1
3
𝑣𝑅𝐷 = (𝑐𝑟 𝑓𝑐𝑘 + 𝜇 𝜎𝑛 + 𝜌𝜇𝑒 min(𝜎𝐴 , 𝑘1𝑒 𝑓𝑦𝑑 ) + 𝑘2𝑒 𝜌 √𝑓𝑦𝑑 𝑓𝑐𝑑 ) 𝑏𝑗 ≤ (𝛽𝑐 𝜈𝑒 𝑓𝑐𝑑 )
1 0.42
= (0 ∗ min(20𝑀𝑃𝑎; 25𝑀𝑃𝑎)3 + 0.5 ∗ 0 + ∗ 0.5 ∗ min(37,13 𝑀𝑃𝑎; 0 ∗ 333,3 𝑀𝑃𝑎) + 1.5
100
0.42
∗ √333,3 𝑀𝑃𝑎 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎) ) ∗ 5000 𝑚𝑚
100
≤ (0,3 ∗ 0,55 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
= 2072.40 𝑘𝑁/𝑚 (MC 2010, 7.3-51)
𝑘𝑁
In this case 𝑣𝐸𝐷 = 1709.98 ≤ 𝑣𝑅𝐷 = 2072.40 𝑘𝑁/𝑚 so the connection is verified for shear.
𝑚
At the edges, also the tensile resistance of the connectors must be considered:
𝑏𝑗 5000 𝑚𝑚
𝑁𝑇,𝑅𝐷 = 𝑁𝑟𝑑 = 11,52 𝑘𝑁 ∗ = 576.33 𝑘𝑁
𝑠1 100 𝑚𝑚
Since 𝑁𝑇,𝑒𝑑 = 171.00 𝑘𝑁 ≤ 𝑁𝑇,𝑅𝐷 = 576.33 𝑘𝑁 the connection is verified also for tension
37
The obtained results are reported in the figure below:
Fig. 14: Layout of the connectors (measurements in millimetres)
4.10 Verification of the connection for a rough interface
It is now of interest the design of a connection similar to the one already designed in the previous
paragraphs but, in this case, assuming a very rough surface. The verifications are still carried out according
to FIB Model Code 2010. All the data used in the computations remains the same as for the previous design.
As already done, first it is computed the longitudinal shear resistance of the interface without shear
connectors:
𝑣𝑅𝐷,𝑐𝑡 = (𝑐𝑎 𝑓𝑐𝑡𝑑 + 𝜇𝑒 𝜎𝑛 ) 𝑏𝑗 ≤ (0.5 𝜈𝑒 𝑓𝑐𝑑 )𝑏𝑗
= (0,5 ∗ min(1.20 𝑀𝑃𝑎; 1,03 𝑀𝑃𝑎) + 0.8 ∗ 0) ∗ 5000 𝑚𝑚

≤ (0.5 ∗ 0,55 ∗ min(13,3 𝑀𝑃𝑎; 16,7 𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
𝑘𝑁
= 2578,8 (MC 2010, 7.3-50)
𝑚
Since:
𝑘𝑁 𝑘𝑁
𝑣𝐸𝐷,𝑖 = 348,15 < 𝑣𝑅𝐷,𝑐𝑡 = 2578.8
𝑚 𝑚
It is possible to avoid the installation of the connectors in the central part of the plate. Even if they are not
needed for static reasons, it is recommended to insert at least two connectors for square meter, for
constructive reasons.
Close to the edges of the concrete slab the connectors are always needed since it is necessary to sustain
the tension normal to the interface, coming from the effect of the restrained shrinkage of the new layer of
concrete
38
It was chosen for the design of the connectors close to the edge to make reference to a configuration with
only one row of edge anchors with spacing 𝑠1 = 300 𝑚𝑚. For the distance from the edge c it was chosen the
maximum one allowed, equal to 150 mm.
Also in this case it is necessary to define the actions on the interface:
𝑉𝑒𝑑 = 𝐹𝑐𝑟 = 1026 kN (B2.5, 3.3.1)
𝑙𝑒 = 3ℎ𝑁 = 300 mm (B2.5, 3.3.1)

𝑉𝑒𝑑 1026 𝑘𝑁
𝑣𝑒𝑑 = = = 3419.95 kN/m (B2.5, 3.3.1)
𝑙𝑒 300𝑚𝑚
It is possible to approximate conservatively the tension load acting on the connectors as:
𝐹𝑐𝑟 1026 𝑘𝑁
𝑁𝑇,𝑒𝑑 = = = 171.00 𝑘𝑁 (B2.5, 3.3.1)
6 6
connectors is considered:
𝑘𝑁 𝑘𝑁
𝑣𝐸𝐷 = 3419.95 ≥ 𝑣𝑅𝐷,𝑐𝑡 = 2578.8
𝑚 𝑚
So the shear connectors are needed to sustain the shear at the edges.
In this case 𝑁𝑅𝑑,𝑁 = 12.10 𝑘𝑁:

𝑁𝑟𝑑 12.10 𝑘𝑁
𝜎𝐴 = = = 145.79 𝑀𝑃𝑎
𝐴𝑆 𝑟 83 𝑚𝑚2 ∗3
𝐴𝑆 𝑟 83 𝑚𝑚2 ∗1
𝜌= = = 0,09 %
𝑙𝑒 𝑠1 300 𝑚𝑚∗300 𝑚𝑚
1
3
𝑣𝑅𝐷 = (𝑐𝑟 𝑓𝑐𝑘 + 𝜇𝑒 𝜎𝑛 + 𝜌𝜇 min(𝜎𝐴 , 𝑘1𝑒 𝑓𝑦𝑑 ) + 𝑘2𝑒 𝜌 √𝑓𝑦𝑑 𝑓𝑐𝑑 ) 𝑏𝑗 ≤ (𝛽𝑐 𝜈𝑒 𝑓𝑐𝑑 )
1 0.09
= (0.2 ∗ min(20𝑀𝑃𝑎; 25𝑀𝑃𝑎)3 + 0.8 ∗ 0 + ∗ 0.8 ∗ min(37,13 𝑀𝑃𝑎; 0.5 ∗ 333,3 𝑀𝑃𝑎) + 0.9
100
0.09
∗ √333,3 𝑀𝑃𝑎 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎) ) ∗ 5000 𝑚𝑚
100
≤ (0,5 ∗ 0,55 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
= 3528.55 𝑘𝑁/𝑚 (MC 2010, 7.3-51)
𝑘𝑁
In this case, 𝑣𝐸𝐷 = 3419.95 ≤ 𝑣𝑅𝐷 = 3528.55 𝑘𝑁/𝑚 so the connection is verified for shear.
𝑚
At the edges, the tensile resistance of the connectors must be considered:
𝑁𝑇,𝑅𝐷 = 𝑁𝑟𝑑 = 12.10 𝑘𝑁 ∗ = 201.68 𝑘𝑁
𝑠1 300 𝑚𝑚
Since 𝑁𝑇,𝑒𝑑 = 171.00 𝑘𝑁 ≤ 𝑁𝑇,𝑅𝐷 = 201.68 𝑘𝑁 the connection is verified also for tension
39
4.11 Alternative design solution using the Hilti method
In the following, an alternative solution is proposed based on the use of hooked rebar connectors verified by
means of the Hilti method for interface verification. The design problem considered is the same as the one
solved in the previous part, considering a very smooth interface between the existing concrete and the
concrete overlay.
The data regarding this new design solution are reported below:
type of connector Rebar Φ10
type of resin HIT-RE 500-V3
Anchor spacing s= [mm] 300

Spacing between anchors close to the edge s1 = [mm] 120
Anchors edge distance c= [mm] 100
Number of rows of anchors close to the edge r= [-] 3
Embedment depth in the new slab hef,n = [mm] 60
Length of the connector L= [mm] 120
From the choice of connector and of the resin, it is possible to find all the needed data from the
documentation of the product. These data are displayed in the table below:
40
Data from the relevant documentation:
Hole diameter d0 = [mm] 12
Anchor diameter d= [mm] 10
Anchorage cross section area As = [mm2] 78,54
Safety coefficient for concrete cone γMc = [-] 1.5
Safety coefficient for splitting γMsp = [-] 1.5
Safety coefficient for pull-out γMp = [-] 1.5
Safety coefficient for steel failure γMS = [-] 1.4
Steel resistance of the anchorage fuk = [MPa] 540,00
Design resistance of the anchor steel f yd = [MPa] 357,14
Minimum existing slab thickness for splitting hmin E = [mm] 90
Minimum new slab thickness for splitting h min N = [mm] 90
Critical spacing for splitting in new slab scr,spN = [mm] 192
Critical edge distance for splitting in new slab ccr,spN = [mm] 96
Bond strength in existing cracked concrete τe = [MPa] 8.50
Bond strength in new cracked concrete τn = [MPa] 8.67
Bond strength in uncracked concrete C20/25 τRk,ucr = [MPa] 14.00
4.12 Verification of connectors: central part, existing slab
As already computed, the longitudinal shear is: 348,15 𝑘𝑁/𝑚
The load carrying capacity of the connector is defined taking into account separately the geometry of the
installation in the central part of the slab and in the external part close to the edge.
First, the central part of the slab is considered, taking into account that the tensile resistance of the
connector is the minimum one between the values obtained considering the anchorage in the existing and in
the new slab.
In the existing slab the connector is a post installed bonded anchor, the computation of the load carrying
capacity requires to consider different failure modes:
4.12.1 Steel failure:
The steel failure resistance of the connector is taken directly from the values given in the relevant
documentation
𝑁𝑅𝑘,𝑠 = 43,00 𝑘𝑁
From this, the design values is obtained as:

𝑁𝑅𝑘,𝑠 43,00 𝑘𝑁
𝑁𝑅𝑑,𝑠 = = = 30,71 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑠 1,4
0
𝑁𝑅𝑘,𝑝 = 𝜋 𝑑 ℎ𝑒𝑓,𝑒 𝜏𝑅𝑘 = 𝜋 10𝑚𝑚 ∗ 60𝑚𝑚 ∗ 8,5𝑀𝑃𝑎 = 16,02 𝑘𝑁 (EN1992-4 7.3.1)
41
𝑠𝑐𝑟,𝑁𝑝 = 7.3 𝑑 √𝜏𝑅𝑘,𝑢𝑐𝑟 = 7.3 ∗ 10𝑚𝑚 √14 𝑀𝑃𝑎 = 273,14 𝑚𝑚 (EN1992-4 7.5)
𝑠𝑐𝑟,𝑁𝑝 ≤ 3 ℎ𝑒𝑓 = 180 𝑚𝑚 (EN1992-4 7.5)
𝑠𝑐𝑟,𝑁𝑝 = 180 𝑚𝑚
𝑠𝑐𝑟,𝑁𝑝 180 𝑚𝑚
𝑐𝑐𝑟,𝑁𝑝 = = = 90 𝑚𝑚 (EN1992-4 5.6)
2 2
𝐴0𝑝,𝑁 = (𝑠𝑐𝑟,𝑁𝑝 )(𝑠𝑐𝑟,𝑁𝑝 ) = (180 𝑚𝑚)2 = 32400 𝑚𝑚2 (EN1992-4 7.3.2)

2
𝐴𝑝,𝑁 = (min(𝑠, 𝑠𝑐𝑟,𝑁𝑝 )) = (min(300 𝑚𝑚; 180 𝑚𝑚))2 = 32400 𝑚𝑚2
𝑐
𝜓𝑠,𝑁𝑝 = 0.7 + 0.3 ≤1= 𝑠𝑖𝑛𝑐𝑒 𝑐 = ∞ 1 (EN1992-4 7.10)
𝑐𝑐𝑟,𝑁𝑝
1
𝜓𝑒𝑐,𝑁𝑝 = 𝑒𝑛 = 𝑠𝑖𝑛𝑐𝑒 𝑒𝑛 = 0 1 (EN1992-4 7.12)
1+2
Assuming conservatively n=8 for the maximum number of anchors:

1.5
0
𝑑 𝜋 𝜏𝑅𝑘
𝜓𝑔,𝑁𝑝 = √𝑛 − (√𝑛 − 1) ( ) ≥1=
𝑘8 √ℎ𝑒𝑓 𝑓𝑐𝑘
𝜋∗10 𝑚𝑚∗8.5 𝑀𝑃𝑎 1.5

= √8 − (√8 − 1) ( ) ≥1= 1 (EN1992-4 7.8-7.9)
7.7 √60 𝑚𝑚∗20𝑀𝑃𝑎
0.5
0
𝑆 0
𝜓𝑔,𝑁𝑝 = 𝜓𝑔,𝑁𝑝 −( ) (𝜓𝑔,𝑁𝑝 − 1) ≥ 1 =
𝑆𝑐𝑟,𝑁𝑝
300𝑚𝑚 0.5
= 1.00 − ( ) (1 − 1) ≥ 1 = 1 (EN1992-4 7.7)
180𝑚𝑚
ℎ𝑒𝑓
𝜓𝑟𝑒,𝑁𝑝 = 0.5 + ≤1 = 1 (EN1992-4 7.11)
200
It is then possible to define the characteristic and the design resistances:
0
𝐴𝑝,𝑁
𝐴0𝑝,𝑁
32400 𝑚𝑚2
16,02 𝑘𝑁 ∗ ∗1∗1∗1∗1= 16,02 𝑘𝑁 (EN1992-4 7.3)
32400 𝑚𝑚2
𝑁𝑅𝑑,𝑝 = = = 10,68 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑝 1.5
0
𝑒𝑓 = 7.7 √20 𝑀𝑃𝑎 (60 𝑚𝑚)
1.5
= 16,00 𝑘𝑁 (EN1992-4 7.14)
𝑠𝑐𝑟,𝑁 = 3 ℎ𝑒𝑓 = 3 ∗ 60 𝑚𝑚 = 180 𝑚𝑚 (EN1992-4 7.14)
𝑐𝑐𝑟,𝑁 = = = 90 𝑚𝑚
2 2
2 2
42
𝑐
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1 = 1 (EN1992-4 7.16)
𝑐𝑐𝑟,𝑁
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
ℎ𝑒𝑓
𝜓𝑟𝑒,𝑁 = 0.5 + ≤1 = 1 (EN1992-4 7.11)
200
0
𝐴𝑐,𝑁
𝐴0𝑐,𝑁
32400 𝑚𝑚2
= 16,00 𝑘𝑁 ∗ ∗1∗1∗1∗1= 16,00 𝑘𝑁 (EN1992-4 7.13)
32400 𝑚𝑚2
𝑁𝑅𝑑,𝑐 = = = 10,67 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑐 1,5
The concrete is assumed to be cracked, so the splitting failure verification is not needed
4.12.5 Summary
The lowest resistance of the anchorage in the existing slab is associated to concrete cone breakout. 𝑁𝑅𝑑,𝑐 =
10,67 𝑘𝑁
4.13 Verification of connectors: central part, new slab
It is now necessary to evaluate also the anchorage in the new slab. In this case, the connector is a cast-in
hooked rebar.
𝑒ℎ = min(𝑚𝑎𝑥(ℎ𝑒𝑓,𝑛 − 𝑑, 3𝑑), 4,5𝑑) = 45 𝑚𝑚 (ACI code)
𝑁𝑅𝑘,𝑝 = 0,9 𝑓𝑐𝑘 𝑒ℎ 𝑑 = 10,13 𝑘𝑁 (ACI code)

𝑁𝑅𝑑,𝑝 = = = 6,75 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑐 1,5

0
𝑒𝑓 = 7.7 √25 𝑀𝑃𝑎 ( 60 𝑚𝑚)
1.5
= 20,68 𝑘𝑁 (EN1992-4 7.14)
𝑠𝑐𝑟,𝑁 = 3 ℎ𝑒𝑓 = 3 ∗ 60 𝑚𝑚 = 180 𝑚𝑚 (EN1992-4 7.14)
𝑐𝑐𝑟,𝑁 = = = 90 𝑚𝑚
2 2
2 2

𝑐
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1 = 1 (EN1992-4 7.16)
𝑐𝑐𝑟,𝑁
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
ℎ𝑒𝑓
𝜓𝑟𝑒,𝑁 = 0.5 + ≤1 = 1 (EN1992-4 7.11)
200
43
0 𝐴𝑐,𝑁
𝐴0
𝑐,𝑁
32400 𝑚𝑚2
= 20,68 𝑘𝑁 ∗ ∗1∗1∗1∗1= 20,68 𝑘𝑁 (EN1992-4 7.13)
32400 𝑚𝑚2
𝑁𝑅𝑑,𝑐 = = = 13,79 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑐 1,5
4.13.4 Summary
The lower resistance of the anchorage in the new slab is related to the pull-out, this value is also smaller
than the minimum one coming from the verification of the connection with the existing slab. In conclusion, we
can consider that the failure mode of the connector is associated to pull-out in the new slab and the tension
design resistance is 𝑁𝑅𝑑,𝑐 = 6,75 𝑘𝑁
4.14 Verification of connectors: lateral part, existing slab
A similar procedure is than followed for the verification of the connectors of the external rows, close to the
edges of the concrete slab. Only the parameters that differs from the ones computed for the central part
need to be recomputed. In this case the verification is carried out considering a strip of anchors
perpendicular to the free edge of the slab. We start considering the existing slab:
4.14.1 Steel failure
Since the connectors are assumed to be the same both for lateral and central part of the plate the steel
failure resistance is obviously the same
First, it is needed to define the spacing of the anchors. We compute the width of the lateral strip subjected to
higher shrinkage stresses as:
3 ℎ𝑁 𝑟𝑜𝑢𝑔ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
𝑙𝑒 = {
6 ℎ𝑁 𝑠𝑚𝑜𝑜𝑡ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
For this example:
𝑙𝑒 = 6 ∗ 100𝑚𝑚 = 600𝑚𝑚 (B2.5, 3.3.1)

2(𝑙𝑒 −𝑐) 2(600 𝑚𝑚−100 𝑚𝑚)
𝑆2 = = = 200 𝑚𝑚
2𝑟−1 2∗3−1
Then it is possible to define the idealized failure area:

𝑠𝑐𝑟,𝑁𝑝 𝑠
𝐴𝑝,𝑁 = {min(𝑐, 𝑐𝑐𝑟,𝑁𝑝 ) + (𝑟 − 1) min(𝑠2 , 𝑠𝑐𝑟,𝑁𝑝 ) + min ( , 2)} ∗ min(𝑠1 , 𝑠𝑐𝑟,𝑁𝑝 )
2 2
180 200
𝐴𝑝,𝑁 = {min(100; 90) + (3 − 1) min(200; 180) + min ( , )} ∗ min(120; 180)
2 2
= 64800 𝑚𝑚2
𝑐 100 𝑚𝑚
𝜓𝑠,𝑁𝑝 = 0.7 + 0.3 ≤ 1 = 0.7 + 0.3 ≤1= 1 (EN1992-4 7.10)
𝑐𝑐𝑟,𝑁𝑝 90 𝑚𝑚
1
𝜓𝑒𝑐,𝑁𝑝 = 𝑒𝑛 = (𝑠𝑖𝑛𝑐𝑒 𝑒𝑛 = 0) 1 (EN1992-4 7.12)
1+2
44
We can now define the characteristic and the design resistances:
0 𝐴𝑝,𝑁
𝐴0
𝑝,𝑁
64800 𝑚𝑚2
= 16,02 𝑘𝑁 ∗ ∗1∗1∗1∗1 = 32,04 𝑘𝑁 (EN1992-4 7.3)
32400 𝑚𝑚2
𝑁𝑅𝑑,𝑝 = = = 21,36 𝑘𝑁 (EN1992-4 Table 7.1)
𝛾𝑀𝑝 1.5

𝑠𝑐𝑟,𝑁 𝑠2
𝐴𝑐,𝑁 = {min(𝑐, 𝑐𝑐𝑟,𝑁 ) + (𝑟 − 1) min(𝑠2 , 𝑠𝑐𝑟,𝑁 ) + min ( ; )} ∗ min(𝑠1 , 𝑠𝑐𝑟,𝑁 )
2 2
180 200
𝐴𝑐,𝑁 = {min(100; 90) + (3 − 1) min(200; 180) + min ( ; )} ∗ min(120; 180)
2 2
= 64800 𝑚𝑚2
100
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1= 1 (EN1992-4 7.16)
90
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
0 𝐴𝑐,𝑁
𝐴0
𝑐,𝑁
64800 𝑚𝑚2
= 16,00 𝑘𝑁 ∗ ∗1∗1∗1∗1= 32,00 𝑘𝑁 (EN1992-4 7.13)
32400 𝑚𝑚2
𝑁𝑅𝑑,𝑐 = = = 21,34 𝑘𝑁 (EN1992-4 Table7.1)
𝛾𝑀𝑐 1,5
4.14.5 Summary
The lower resistance of the anchorage to the existing slab is associated to the concrete cone breakout
failure. It is now necessary to evaluate also the anchorage in the new slab. In this case the connector can be
seen as a cast in hooked rebar.
4.15 Verification of connectors: lateral part, new slab
The verification for pull-out of a cast in headed stud is referred to the single anchor, so in this case the
resistance is the same as in the central part of the slab.

2 2
180 200
𝐴𝑐,𝑁 = {min(100; 90) + (3 − 1) min(200; 180) + min ( , )} ∗ min(120; 180)
2 2
= 64800 𝑚𝑚2
45
100 𝑚𝑚
𝜓𝑠,𝑁 = 0.7 + 0.3 ≤1 1 (EN1992-4 7.16)
90 𝑚𝑚
1
𝜓𝑒𝑐,𝑁 = 𝑒𝑛 = 1 (EN1992-4 7.17)
1+2
𝑠𝑐𝑟,𝑁
0 𝐴𝑐,𝑁
𝐴0
𝑐,𝑁
64800 𝑚𝑚2
= 20,68 𝑘𝑁 ∗ ∗1∗1∗1∗1= 41,36 𝑘𝑁 (EN1992-4 7.13)
32400 𝑚𝑚2
𝑁𝑅𝑑,𝑐 = = = 27,58 𝑘𝑁 (EN1992-4 Table7.1)
𝛾𝑀𝑐 1,5
4.15.4 Summary
The resistance of the connectors placed close to the edges is governed by the pull-out failure in the new
slab. The ultimate resistance is 𝑁𝑅𝑑,𝑝 = 20,25 𝑘𝑁
4.16 Verification of the interface in the central part of the slab
The method of verification chosen for this example is the Hilti method (also known as Palieraki method).
First, it is computed the longitudinal shear resistance of the interface without shear connectors: in this case,
since the external stress acting normal to the interface can be assumed equal to zero, the shear resistance
without connectors, according to Hilti method is null.
𝑘𝑁
𝑣𝑅𝑑,𝑐𝑡 = 𝜇ℎ 𝜎𝑛 𝑏𝑗 ≤ 𝛽𝑐 𝜈ℎ 𝑓𝑐𝑑 𝑏𝑗 = 0
𝑚
The shear connectors are needed in the central part of the slab. The resistance of the interface is
recomputed taking into account the presence of the connectors. The geometry considered for the connectors
installation is the one already defined (see section 4.11).
From the verification of the connectors in the central part of the slab we have 𝑁𝑅𝑑,𝑝 = 6,75 𝑘𝑁
𝜎𝐴 = = = 85,94 𝑀𝑃𝑎
𝐴𝑆 78,54 𝑚𝑚2
𝐴𝑠 78,54 𝑚𝑚2
𝜌= = = 0,09 %
𝑠 2 (300 𝑚𝑚)2
It is now possible to use the formula for the computation of the interface shear resistance according to Hilti
method:
Where we assume, considering the selected surface condition (Very smooth) and the type of loading (static
monotonic):
𝑘1ℎ = 0,2
𝑘2ℎ = 0,5
46
2 2
3 3
𝑓 13,3 𝑀𝑃𝑎
𝜇ℎ = 0,3 √(𝜌 𝜎𝐴𝑐𝑑 ) = 0,3 √(0,09 85,94 ) = 8,16
+𝜎𝑛 ∗ +0
0,8 100 0,8
0,09 85,94 𝑀𝑃𝑎

𝑣𝑅𝑑 = {8,16 ∗ (0 + min (85,94 𝑀𝑃𝑎; 0,2 ∗ )) + 0.5
100 0,8
0,09
∗ √357,14 𝑀𝑃𝑎 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)} ∗ 5000 𝑚𝑚
100
≤ (0,3 ∗ 0,55 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
𝑘𝑁
= 915,39
𝑚
𝑘𝑁
In this case 𝑣𝐸𝐷,𝑖 = 348,15 ≤ 𝑉𝑅𝐷 = 915,39 𝑘𝑁/𝑚 so the selected design option for the shear connection
𝑚
can be effectively used.
4.17 Verification of the connection close to the edges
It is necessary to define the actions on the interface close to the edge. As for the previous example:
𝑉𝑒𝑑
𝑣𝑒𝑑 = = 1709.98 kN/m (B2.5, 3.3.1)
𝑙𝑒
𝐹𝑐𝑟
𝑁𝑇,𝑒𝑑 = = 171.00 𝑘𝑁 (B2.5, 3.3.1)
6
connectors is null.
So the shear connectors are needed also to sustain the shear at the edges. In this case 𝑁𝑅𝑑,𝑝 = 20,25 𝑘𝑁:
𝜎𝐴 = = = 85,94 𝑀𝑃𝑎
𝑟 𝐴𝑆 3∗78,54 𝑚𝑚2
𝐴𝑆 𝑟 78,54 𝑚𝑚2 ∗3
𝜌= = = 0,33 %
𝑙𝑒 𝑠1 600 𝑚𝑚∗120 𝑚𝑚
𝑘1 = 0,2
𝑘2 = 0,5
2 2
3 3
𝑓 13,3 𝑀𝑃𝑎
𝜇ℎ = 0,3 √(𝜌 𝜎𝐴𝑐𝑑 ) = 0,3 √(0,33 85,94 ) = 3,38
+𝜎𝑛 ∗ +0
0,8 100 0,8
0,33 85,94 𝑀𝑃𝑎

𝑣𝑅𝑑 = {3,38 ∗ (0 + min (85,94 𝑀𝑃𝑎; 0,2 ∗ )) + 0.5
100 0,8
0,33
∗ √357,14 𝑀𝑃𝑎 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)} ∗ 5000 𝑚𝑚
100
≤ (0,3 ∗ 0,55 ∗ min(13,3𝑀𝑃𝑎; 16,7𝑀𝑃𝑎)) ∗ 5000 𝑚𝑚
𝑘𝑁
= 1752,42
𝑚
𝑘𝑁 𝑘𝑁
In this case 𝑣𝐸𝐷 = 1709.98 ≤ 𝑣𝑅𝐷 = 1752,42 so the connection is verified for shear.
𝑚 𝑚
47
At the edges, also the tensile resistance of the connectors must be considered:
𝑁𝑇,𝑅𝐷 = 𝑁𝑟𝑑 = 20,25 𝑘𝑁 ∗ = 843,75 𝑘𝑁
𝑠1 120 𝑚𝑚
Since 𝑁𝑇,𝑒𝑑 = 171.00 𝑘𝑁 ≤ 𝑁𝑇,𝑅𝐷 = 843,75 𝑘𝑁 the connection is verified also for tension
48
5 Notations
Design and characteristic resistances:
fck = minimum value of concrete compressive strength of the two concrete layers,
fyk = characteristic yield strength of the shear connector
fcd = minimum value of concrete design compressive strength of the two concrete layers,
fyd = design yield strength of the shear connector
fctd = design tension resistance of concrete
fct,eff = tensile strength of overlay effective at the time when the cracks may first be expected
to occur as per [1], Section 7.3.2 (for general cases: fct,eff = 3 N/mm2)
fuk = ultimate characteristic steel resistance of the anchorage
Safety coefficients:
γMc = safety coefficient for concrete cone

γMsp = safety coefficient for splitting
γMp = safety coefficient for pull-out
γMS = safety coefficient for steel failure
c = safety factor for concrete; 1,50 as given in EN 1992-4 for strengthening of existing
structures
s = safety factor for steel; 1,15 as given in EN 1992-4 for supplementary reinforcement
Stresses:
n = lowest expected compressive stress resulting from an eventual normal force acting on
the interface (compression has a positive sign)
A = steel stress associated to the relevant failure mode, (see section 3.14)
s = effective steel stress in the connector
Ed = shear stress acting as fatigue relevant loading
Ed,max = upper shear stress acting as fatigue relevant loading
𝜏𝑅𝑑 = resisting shear stress
τe = bond strength in existing concrete
τn = bond strength in new concrete
τRk,ucr = bond strength in non-cracked concrete C20/25
Forces:
Fcr = cracking force for the overlay

𝑁𝑅𝑑,𝑠 = steel failure resistance of the connector
𝑁𝑅𝑑,𝑐𝑝 = combined concrete cone failure/pull-out resistance of the connector
𝑁𝑅𝑑,𝑠𝑝 = splitting failure resistance of the connector
𝑁𝑅𝑑,𝑐 = concrete cone failure resistance of the connector
𝑁𝑅𝑑,𝑝 = pull-out failure resistance of the connector
V = shear acting on the considered section
𝑣𝐸𝐷 = acting longitudinal shear
𝑣𝑅𝐷 = resisting longitudinal shear
49
Deformations, displacements and strains:
𝑊𝑒𝑓𝑓 = additional deformation calculated for the reinforced section considering the
elasticity of the shear connectors
𝑊𝑐𝑎𝑙𝑐 = additional deformation calculated for the reinforced section assuming a
perfect bond
sd = displacement of connectors under the mean permanently acting load
Fp  0.5 Fuk
εs Ase- = top steel strains [%]
εs Ase+ = bottom steel strains [%]
Areas:
𝐴𝑠,𝑛 = area of the reinforcements in the new slab

𝐴𝑠,𝑒𝑥 = area of the reinforcements on top of the existing slab
As = effective steel area of the anchor
Ah = area of the anchor head
Length:
bi = width of the interface of the composed section

𝑥 = depth of the compressed part of the composite slab
𝑧 = internal lever harm of the composite slab
d = effective depth of the slab, positive bending moment
d‘ = effective depth of the slab, negative bending moment
𝑙𝑒 = width of the lateral strip considered as subjected to the highest shrinkage forces
ℎ𝑁 = thickness of the overlay
hE = thickness of the existing slab
hef,e = embedment depth in the existing slab
hef,n = embedment depth in the overlay
Lcon = length of shear connector
d0 = drill bit diameter
d = anchor stud diameter
dh = anchor head diameter
c = anchor edge distance
s = central anchors spacing
s2 = anchor rows spacing at the edges
s1 = anchor in-row spacing at the edges
hmin E = minimum existing slab thickness for splitting
hmin N = minimum new slab thickness for splitting
scr,spN = critical spacing for splitting in new slab
ccr,spN = critical edge distance for splitting in new slab
scr,spE = critical spacing for splitting in existing slab
ccr,spE = critical edge distance for splitting in existing slab
ss,ex = reinforcements spacing on top of the existing slab
X = depth of the neutral axis
Φex = reinforcements diameter on top of the existing slab
cs = Net cover
50
Coefficients and ratios:
cr = coefficient for adhesive bond resistance in a reinforced interface

µe = friction coefficient according to Eota Method
1e = interaction coefficient for tensile force activated in the shear connector
2e = interaction coefficient for flexural resistance in the shear connector
k1 = modification factor for material properties of the connector
k2 = modification factor for geometry of the connector
 = reinforcement ratio of the steel of the shear connector crossing the interface
e = coefficient for reduction of concrete strength
c = coefficient for the strength of the compression strut
µh = friction coefficient according to Hilti method
1h = contribution factor for the friction mechanism
2h = contribution factor for the dowel mechanism
h = effectiveness factor for the concrete according to fib MC2010, Eq. (7.3-51)
𝑘 = coefficient to allow for non-uniform self-equilibrating stresses = 0.8 for hN=30 cm
sc = factor for fatigue loading
γ = factor for displacements
r = number of the lateral rows of anchors
𝜌𝑚𝑖𝑛 = minimum reinforcement ratio for the interface
51
6 Literature
[1] EC 2; Design of concrete structures: ENV 1992-1-1: 2004;
[2] Technisches Handbuch der Befestigungstechnik für Hoch- und Ingenieurbau, HILTI
[3] FIB model code 2010
[4] ACI 318-11 - Building Code Requirements (Imperial)
[5] EOTA etag-001-annex-c-10-08-01
[6] Elizabeth Vintzileou and Vasiliki Palieraki, Giovacchino Genesio, Roberto Piccinin: Shear behaviour of interfaces
within repaired/strengthened RC elements subjected to cyclic actions, fib International Workshop on Advanced Materials
and Innovative Systems in Structural Engineering: Seismic Practices (IWAMISSE), November 16, 2018; Istanbul, Turkey
[7] EOTA TR066 design concrete shear connection
Hilti Corporation
FL-9494 Schaan
Principality of Liechtenstein Hilti Fastening Technology Manual
www.hilti.com
52

2018 Concrete Overlay Theory

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STRENGTHENING AND

REHABILITATION WITH CONCRETE

The Institute for Concrete Structures of the University of Innsbruck,

With increasing surface roughness, shear resistance and shear stiffness

The very user-friendly Hilti design method is based on the Eurocode

For comments and questions, contact our engineers

1.1 RANGE OF APPLICATIONS............................................................................................................................................. 6

2 PRODUCTS OVERVIEW .............................................................................................................................................. 8

2.1 HIT-RE 500 V3 INJECTION MORTAR ............................................................................................................................. 9

3 DESIGN OF INTERFACE ........................................................................................................................................... 15

3.1 BASIC CONSIDERATIONS ............................................................................................................................................ 15

Strengthening of bridges by means of concrete Strengthening of buildings, decks and slabs

1.2 Advantages of the strengthening with concrete overlay

 Simple and reliable application to a variety of cases

1.3 Example of applications

Strengthening the floor of an industrial building

Strengthening an industrial building foundation

Repairing and strengthening a pier

The following table summarizes the considered products:

Anchor type HCC-B +

European Technical approval

concrete overlay static

European Technical approval

Hilti method static X X Ѵ* Ѵ* Ѵ

Hilti method seismic X X X X Ѵ

Injection mortar system Benefits

Base material Installation conditions

Concrete Concrete Hammer Diamond Hilti SafeSet

Load conditions Other information

Static/ Seismic, ETA- European CE PROFIS

Base material Load conditions

Concrete Concrete Static / quasi-

Installation conditions Other information Design Method

Small edge European CE

Description Authority / Laboratory No. / date of issue

Base material Installation conditions

Concrete (non- Concrete Small edge

Load conditions Other information Design Method

Static/ fatigue European CE conformity

Description Authority / Laboratory No. / date of issue

- Small edge and spacing distance

Base material Installation conditions

Concrete (non- Concrete Small edge Variable

Load conditions Design Method

Concrete (non- Concrete Small edge Variable embedment depth

Load conditions Design Method

Base material Installation conditions

Concrete (non- Concrete Small edge Variable

Load conditions Design Method

Fig. 8: Load contribution of the different components

3.3 Design shear resistance at the interface, 𝒗𝑹𝒅

Interlock pull-out dowel concrete strut

cr = Coefficient for adhesive bond resistance in a reinforced interface

Coefficients and parameters for different surface roughness

Fig. 9: Geometry of shear keys

3.5 Design shear strength at the interface, HILTI method

The following definitions are valid for the considered method:

Parameter 1h for different interface characteristics: monotonic loading

Parameter 2h for different normalized embedment depth

Computation of the longitudinal shear on the interface