Supplementary reinforcement for anchor
bolts according to EN 1992-4
LAB University of Applied Sciences
Bachelor of Engineering, Bachelor’s Degree in Construction Engineering
2022
Vsevolod Surkont
Abstract
Author(s)
Publication type
Completion year
Vsevolod Surkont
Bachelor’s thesis
2022
Number of pages
69
Title of the thesis
Supplementary reinforcement for anchor bolts according to EN 1992-4
Degree
Bachelor of Civil Engineering
Name, title, and organisation of the client
Ville Laine, chief technology officer, A-Insinöörit Suunnittelu Oy
Abstract
The thesis was written for A-Insinöörit Suunnittelu Oy. The purpose of the work was to
find better and more effective solutions for anchor bolts usage, study phenomena of
the supplementary reinforcement, and study how supplementary reinforcement can
affect headed and post-installed anchor bolts.
The theoretical part describes in general the types of anchor bolts that are applicable
for this work, failure modes of fasteners, phenomena of supplementary reinforcement,
and what conditions must be observed for its usage. This work is based on Eurocode
2. Design of concrete structures. Part 4: Design of fastenings for use in concrete (EN
1992-4).
A big part of this work is analyze of the calculations for supplementary reinforcement
and studies of the impact of each parameter of reinforcement on the design resistance of supplementary reinforcement along with requirements from the standard
EN 1992-4. The design resistance of a fastener and of a supplementary reinforcement was compared.
The supplementary reinforcement can be useful in the combination with anchor bolts
and can improve the strength of anchor bolts in case of concrete cone failure and
concrete edge failure. However, supplementary reinforcement is not always the solution for increasing the load-carrying capacity of an anchor.
Keywords
Supplementary reinforcement, fastenings, headed anchors, post-installed anchors,
EN 1992-4
Contents
List of symbols ...................................................................................................................1
1
Introduction .................................................................................................................5
2
General information ....................................................................................................6
2.1
Supplementary reinforcement ..............................................................................6
2.2
Fasteners.............................................................................................................7
2.2.1
Cast-in place headed anchors ......................................................................9
2.2.2
Post-installed anchors ................................................................................10
2.3
Failure modes of headed and post-installed fasteners .......................................11
2.3.1
Steel failure.................................................................................................12
2.3.2
Pull-out failure.............................................................................................12
2.3.3
Combined pull-out and concrete failure in case of post-installed bonded
fasteners ...................................................................................................................13
2.3.4
Concrete splitting failure .............................................................................14
2.3.5
Concrete blow-out failure ............................................................................15
2.3.6
Steel failure of fastener without lever arm ...................................................16
2.3.7
Steel failure of fastener with lever arm ........................................................17
2.3.8
Concrete pry-out failure ..............................................................................17
2.4
3
Detailing of supplementary reinforcement .................................................................20
3.1
Tension load ......................................................................................................20
3.1.1
Concrete cone failure..................................................................................20
3.1.2
General requirements .................................................................................24
3.2
4
Forces assigned to supplementary reinforcement ..............................................18
Shear load .........................................................................................................24
3.2.1
Concrete edge failure .................................................................................25
3.2.2
General requirements .................................................................................29
Failure of supplementary reinforcement ....................................................................30
4.1
Steel Failure ......................................................................................................30
4.1.1
Tension load ...............................................................................................30
4.1.2
Shear load ..................................................................................................41
4.2
Anchorage failure...............................................................................................42
4.2.1
Tension load ...............................................................................................42
4.2.2
Shear load ..................................................................................................54
5
Impact of supplementary reinforcement on anchor bolts strength .............................56
6
Summary ..................................................................................................................60
References ......................................................................................................................61
Appendixes
Appendix 1. Strength and deformation characteristics for concrete
Appendix 2. Settling details for HILTI HAS-U anchor bolts
Appendix 3. Concrete cone failure verification example
Appendix 4. Concrete edge failure verification example
1
List of symbols
𝐴𝑐,𝑁 – actual area of idealized concrete cone of a fixture
𝐴𝑐,𝑉 – actual projected area of idealized concrete break-out body of a fixture
𝐴0𝑐,𝑁 - area of idealized concrete cone of an individual fastener
𝐴0𝑐,𝑉 - area of idealized concrete break-out body of an individual fastener
𝐴ℎ - load bearing area of the head of the fastener
𝐴𝑠.𝑟𝑒 - cross section of the reinforcement
𝐴𝑠.𝑟𝑒.𝑖 - cross section of a reinforcing bar
𝑐1 - edge distance in direction 1
𝑐2 - edge distance in direction 2
𝑑 - diameter of fastener bolt or thread diameter, effective depth to supplementary reinforcement
𝑑𝑛𝑜𝑚 - outside diameter of a fastener
𝑒𝑠 - distance between the line of the shear load and the axis of the supplementary reinforcement for shear
𝑓𝑐𝑘 - nominal characteristic compressive cylinder strength (150 mm diameter by 300 mm
height)
𝑓𝑏𝑑 - design bond strength of supplementary reinforcement
𝑓𝑐𝑡𝑑 - design value of concrete tensile strength
𝑓𝑐𝑡𝑘.0.05 - characteristic axial tensile strength of concrete
𝑓𝑦𝑘.𝑟𝑒 - nominal characteristic steel yield strength of reinforcement
ℎ𝑒𝑓 - effective embedment depth
𝑘1 – factor taking into account cracks in the concrete in case of concrete cone failure
𝑘2 - factor taking into account cracks in the concrete in case of pull-out failure
𝑘9 - factor taking into account cracks in the concrete in case of concrete edge failure
𝑘10 - efficiency factor
2
𝑙𝑏𝑑 - design anchorage length of reinforcement
𝑙1 - anchorage length of the reinforcing bar in the assumed concrete break-out body
𝑁𝐸𝑑 - resultant design tension force of the tensioned fastener
ℎ
𝑁𝐸𝑑
- resultant design tension force of the tensioned fastener in group of fasteners
𝑁𝐸𝑑.𝑟𝑒 - design value of tension load acting on the supplementary reinforcement
𝑁𝐸𝑑.𝑠𝑢𝑚 - sum of the design tensile force of the fasteners in tension under the design value
of the actions
𝑁𝑅𝑑,𝑎 - design resistance of supplementary reinforcement associated with anchorage failure
𝑁𝑅𝑑,𝑐 - design resistance in case of concrete cone failure under tension load
𝑁𝑅𝑑,𝑐𝑏 - design resistance in case of concrete blow-out failure under tension load
𝑁𝑅𝑑,𝑐𝑝 - design resistance in case of concrete pry-out failure under tension load
𝑁𝑅𝑑,𝑝 - design resistance in case of pull-out failure of fastener
𝑁𝑅𝑑,𝑝𝑐 - design resistance in case of combined pull-out and concrete failure of fastener
𝑁𝑅𝑑.𝑟𝑒 - design resistance in case of steel failure of supplementary reinforcement
𝑁𝑅𝑑,𝑠 - design resistance in case of steel failure of fastener
𝑁𝑅𝑑,𝑠𝑀 - design resistance in case of steel failure with lever arm of fastener
𝑁𝑅𝑑,𝑠𝑝 - design resistance in case of concrete splitting failure under tension load
𝑁𝑅𝑘.𝑐 - characteristic resistance in case of concrete cone failure under tension load
𝑁𝑅𝑘,𝑐𝑏 - characteristic resistance in case of concrete blow-out failure under tension load
𝑁𝑅𝑘,𝑝 - characteristic resistance in case of pull-out failure under tension load
𝑁𝑅𝑘,𝑝𝑐 - characteristic resistance in case of pull-out and concrete failure under tension load
𝑁𝑅𝑘,𝑟𝑒 - characteristic resistance in case of steel failure under tension load
𝑁𝑅𝑘,𝑠 - characteristic resistance in case of steel failure under tension load
𝑁𝑅𝑘,𝑠𝑝 - characteristic resistance in case of concrete splitting failure under tension load
𝑛𝑟𝑒 - number of bars of supplementary reinforcement effective for one fastener
3
𝑁𝑅𝑑.𝑎 - design resistance of supplementary reinforcement associated with anchorage failure
in tension
𝑁0.𝑅𝑑.𝑎.𝑖 - design resistance of one rebar associated with anchorage failure in tension
𝑠 - centre to centre spacing of fasteners in a group
𝑠𝑐𝑟.𝑁 - characteristic spacing of fasteners or anchors of anchor channels to ensure the characteristic resistance of the individual fasteners or anchors of an anchor channel in case of
concrete cone failure under tension load (concrete edge failure under shear load)
𝑉𝐸𝑑 - design shear force
𝑉𝑅𝑑,𝑐 - design resistance in case of concrete edge failure under shear load
𝑉𝑅𝑑.𝑎 - design resistance of supplementary reinforcement associated with anchorage failure
in shear
𝑉𝑅𝑘,𝑐 - characteristic resistance in case of concrete edge failure under shear load
𝑉𝑅𝑘,𝑐𝑝 - characteristic resistance in case of concrete pry-out failure under shear load
𝑉𝑅𝑘,𝑠 - characteristic value of steel resistance of a fastener or a channel bolt under shear
load
𝑉𝑅𝑘,𝑠𝑀 - characteristic resistance in case of steel failure with lever arm under shear load
𝛼𝑐𝑡 - coefficient taking account of long-term effects on the tensile strength and of unfavorable effects, resulting from the way the load is applied
𝛼1 - influencing factor
𝛼2 - influencing factor
𝛾𝑐 - partial safety factor for concrete
𝛾𝑖𝑛𝑠𝑡 - factor accounting for the sensitivity to installation of post-installed fasteners
𝛾𝑀𝑐 - partial factor for concrete cone, concrete edge, concrete blow-out and concrete pryout failure modes
𝛾𝑀𝑠 - partial factor for steel failure of fastener
𝛾𝑀𝑠𝑝 - partial factor for concrete splitting failure
𝛾𝑀𝑠.𝑟𝑒 - partial factor for steel failure in reinforcement
𝜂1 - coefficient related to the quality of the bond condition and the position of the bar
4
during concreting
𝜂2 - coefficient related to the bar diameter
𝑧 - the height of the non-structural element above the level of application of the seismic
action
∅ - diameter
𝜓𝑒𝑐.𝑁 - factor taking into account the group effect when different tension loads are acting on
the individual fasteners of a group in case of concrete cone failure
𝜓𝑒𝑐.𝑉 - factor taking into account the group effect when different shear loads are acting on
the individual fasteners of a group in case of concrete edge failure
𝜓ℎ.𝑉 - actor taking into account the fact that concrete edge resistance does not increase
proportionally to the member thickness
𝜓𝑀.𝑁 - factor taking into account the effect of a compression force between the fixture and
concrete in case of bending moments with or without axial force
𝜓𝑟𝑒.𝑁 - shell spalling factor
𝜓𝑟𝑒.𝑉 - factor taking into account the effect of reinforcement located on the edge in case of
concrete edge failure
𝜓𝑠.𝑁 - factor taking into account the disturbance of the distribution of stresses in the concrete
due to the proximity of an edge in the concrete member in case of concrete cone failure
𝜓𝑠.𝑉 - factor taking into account the disturbance of the distribution of stresses in the concrete
due to the proximity of further edges in the concrete member in case of concrete edge failure
𝜓𝛼.𝑉 - factor taking into account the influence of a shear load inclined to the edge in case of
concrete edge failure
5
1
Introduction
Nowadays anchor bolts are one of the most popular fasteners in the world that are used in
modern buildings. Usually anchor bolts are used to attach steel structural elements to concrete structural elements (typically concrete foundation). With modern ways of structural
design, anchor bolts load-bearing capacity can be improved using supplementary reinforcement. Principles and requirements for usage of supplementary reinforcement are represented in the document “Eurocode 2. Design of concrete structures. Part 4: Design of fastenings for use in concrete” (EN-1992-4). This thesis is focused on how supplementary reinforcement can be calculated, what supplementary reinforcement depends on, and how
supplementary reinforcement impacts the anchor bolts. The purpose of the thesis was to
analyze and understand the phenomena, study how supplementary reinforcement can be
used with headed and post-installed anchor bolts according to SFS-EN-1992-4 and to study
how supplementary reinforcement effect load-bearing capacity of anchor bolts, in order to
find better and more effective solutions for usage of anchor bolts. The work was commissioned by A-Insinöörit Suunnittelu Oy.
To make calculations easier and to trace the causal relationship PTC Mathcad Prime was
used. Mathcad Prime is an engineering mathematic software, that is widely used in A-Insinöörit Suunnittelu Oy and other engineering companies. With this program calculations
with formulas can be done more easily, than by hand, and it is possible to trace how a
particular component of the formula affects the result of calculations.
This work covers the usage of supplementary reinforcement only for headed and post-installed fasteners, but not anchor channels. Supplementary reinforcement can be used to
resist shear forces, tension forces, or both. For shear and tension forces different conditions
should be met in accordance with SFS-EN-1992-4, this should be considered before supplementary reinforcement designing. In this work, anchor bolts can be also named fasteners, anchors, fastenings.
Initial data for calculations was considered by supervisors by A-Insinöörit Suunnittelu Oy
and is not related to the real project.
6
2
2.1
General information
Supplementary reinforcement
The supplementary reinforcement or anchor reinforcement can be described as reinforcement used with anchor bolts, that is binding a possible concrete breakout body to the concrete element. The supplementary reinforcement is used to improve the load-carrying capacity of anchors.
To describe how supplementary reinforcement interacts with fasteners, the strut-and-tie
model is often used. In this model, the forces that are applied to the anchorage are resisted
by a combination of concrete struts taking up the compression forces and tension ties
formed by the surface reinforcement or edge reinforcement and the stirrups. So there are
three most important components in the strut-and-tie model: the tension ties, the concrete
struts, and the nodes. Increasing the amount of anchor reinforcement leads to an increase
in the failure load of the tension ties. But important nuance is that increase of reinforcement
on a certain level lead to the limit of the failure load for the anchorage by the failure of
concrete struts. (Sharma et al. 2017, 1)
The load-bearing capacity of an anchorage with supplementary reinforcement results from
the anchorage in the concrete breakout body achieved by means of bond and bearing of a
hook or bend. When the anchorage is loaded in tension or shear close to and towards the
edge, first what is happening is that the concrete cracks form the breakout body, and then
the stirrups start to work to resist the load. The main problem is that if the anchorage length
of the stirrups within the concrete breakout body is small, they might reach bond failure prior
to yielding resulting in lower resistance than potentially achievable. For stirrups with relatively large anchorage lengths, as in the case of closely spaced stirrups, resistance equal
to the yield resistance of the stirrup can develop resulting in enhanced load and deformation
capacity of the anchorage. (Sharma et al. 2018, 2)
For tension load example of the strut and tie model is shown in Figure 1. For the shear load
example of the strut and tie model is shown in Figure 2.
7
Figure 1 Surface reinforcement to take up tension loads with simplified strut and tie model
(SFS-EN-1992-4 2008, 50)
Figure 2 Surface reinforcement to take up shear loads with simplified strut and tie model
(SFS-EN 1992-4 2018, 66)
2.2
Fasteners
Fastener design theory is used to describe the behavior of fasteners. According to this theory, the purpose of all fasteners is to join two or more components. In most cases, the
purpose of anchor bolts is to join steel elements (such as beams and columns) and concrete
elements (foundations, beams).
8
In fastener design theory the concrete tensile capacity is directly used to transfer loads into the concrete component. (SFS-EN 1992-4 2018, 9)
Figure 3 Fastener design theory on example (SFS-EN 1992-4 2018, 10)
It is important to understand with which type of fasteners supplementary reinforcement can
be used. This work covers a combination of supplementary reinforcement and:
•
cast-in fasteners (headed fasteners)
•
post-installed mechanical fasteners (expansion fasteners, undercut fasteners,
concrete screws)
•
post-installed bonded fasteners and bonded expansion fasteners.
If there is a need to use other fasteners, additional steps in the design provisions are necessary.
In Figure 3 are shown the configurations of anchors without hole clearance for all edge
distances and for all load directions and the configuration of fastenings with hole clearance
situated far from edges for all load directions and the configuration of fastenings with hole
clearance situated near an edge loaded in tension only, that are covered by this work.
9
Figure 4 Configuration of fastenings with headed and post-installed fasteners (SFS-EN
1992-4 2018, 11)
In Figure 4 are shown the configuration of fastenings with hole clearance situated near an
edge for all load directions, which are covered by this work.
Figure 5 Configuration of fastenings with cast-in and post-installed fasteners (SFS-EN
1992-4 2018, 11)
2.2.1 Cast-in place headed anchors
Headed anchors are cast-in fasteners with a head at the embedded end, which are placed
before pouring the concrete. An important fact about headed anchors and cast-in fasteners is that the head is installed inside the concrete. The standard SFS-EN 1992-4
(2018,18) provides that this type of anchor derives its tensile resistance from a mechanical interlock at the head of the fastener.
10
Figure 6 Types of headed fasteners: a) without anchor plate; b) with a large anchor plate at
least in one direction; c) with a small anchor plate in both directions (SFS-EN 1992-4 2018,
16)
2.2.2 Post-installed anchors
Post-installed anchors are fasteners, that are installed in concrete after the concrete hardens. There are several types of post-installed fasteners in the scope of this work and in
accordance with definitions from the standard SFS-EN 1992-4 (2018, 13-20) can be described as follows:
•
Torque-controlled fastener - post-installed expansion fastener that derives its tensile resistance from the expansion of one or more sleeves or other components
against the sides of the drilled hole through the application of torque, which pulls
the cone(s) into the expansion sleeve(s) during installation (Figure 6 – a; 6 – b);
•
Deformation-controlled expansion fastener - post-installed fastener that derives its
tensile resistance by expansion against the side of the drilled hole through movement of an internal plug in the sleeve or through movement of the sleeve over an
expansion element (plug), and with which, once set, no further expansion can occur (Figure 6 - c);
•
Undercut fastener - post-installed fastener that develops its tensile resistance from
the mechanical interlock provided by undercutting of the concrete at the embedded
end of the fastener (Figure 6 – d, 6 – e);
•
Concrete screw - threaded fastener screwed into a predrilled hole where threads
create a mechanical interlock with the concrete (Figure 6 – f);
11
•
Bonded fastener - fastener placed into a hole drilled in hardened concrete, which
derives its resistance from a bonding (Figure 6 – g);
•
Bonded expansion fastener - bonded fastener designed such that the fastener element can move relative to the hardened bonding compound resulting in follow-up
expansion (Figure 6 – h).
Figure 7 Types of post installed fasteners: a) torque-controlled fastener, sleeve type; b)
torque-controlled fastener, wedge type; c) deformation-controlled fastener; d) undercut fastener, type; 1 e) undercut fastener, type; 2 f) concrete screw; g) bonded fastener; h) bonded
expansion fastener (SFS-EN 1992-4 2018, 18)
2.3
Failure modes of headed and post-installed fasteners
On design stage post-installed and headed anchors should be verified for every possible
failure mode. Failure modes are divided into two groups depending on the type of load:
failure modes while the fastener is in tension and failure modes while the fastener is in
shear. Failure modes of fasteners under tension load: steel failure, concrete cone failure,
pull-out failure, combined pull-out failure and concrete failure, concrete splitting failure, and
concrete blow-out failure. Failure modes of fasteners under shear load: steel failure without
lever arm, steel failure with a lever arm, concrete pry-out failure, concrete edge failure.
For all the fasteners the main value to estimate strength capacity in each failure mode is
the corresponding characteristic resistance. Characteristic resistance should be divided by
partial factors to obtain design resistance, which is compared with design force. If the design
force is not bigger than the design resistance, the failure mode is verified, and configuration
can be used.
Detailed information about concrete cone failure and concrete edge failure can be found in
section 3 “Detailing of the supplementary reinforcement” in this work.
12
2.3.1 Steel failure
Steel failure of the fastener is a failure mode that should be verified for anchors in tension.
This failure mode happens when tensile strength is so big, that the fastener strength capacity can’t withstand the load, and the fastener starts to yield at first and then is torn apart.
The SFS-EN-1992-4 (2018, 51) provides that the characteristic resistance of a fastener in
case of steel failure is given in the relevant European Technical Product Specification. For
example, European Technical Product Specification can be Technical Datasheets or special magazines for customers, that can be found on websites of companies, that produce
fasteners.
Figure 8 Steel failure of a fastener (SFS-EN 1992-4 2018, 49)
For cast-in place and post-installed fasteners it should be verified that the resultant design
tension force of the tensioned fastener is not bigger, than the design resistance in case of
steel failure under tension load: (SFS-EN 1992-4 2018, 51)
𝑁𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑠 =
𝑁𝑅𝑘,𝑠
𝛾𝑀𝑠
(1)
To ensure that steel failure is prevented designer should choose a fastener from Technical
Product Specification with sufficient characteristic resistance.
2.3.2 Pull-out failure
According to SFS-EN-1992-4 (2018, 19) pull-out failure is a failure mode in which the fastener pulls out of the concrete without development of the full concrete resistance or in case
of post-installed mechanical fasteners a failure mode in which the fastener body pulls
through the expansion sleeve without development of the full concrete resistance.
13
Figure 9 Pull-out failure of a fastener (SFS-EN 1992-4 2018, 49)
For cast-in-place headed and post-installed fasteners it should be verified that the resultant
design tension force of the tensioned fastener is not bigger, than the design resistance in
case of pull-out failure of fastener with anchors under tension load: (SFS-EN 1992-4 2018,
51)
𝑁𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑝 =
𝑁𝑅𝑘,𝑝
𝛾𝑀𝑐
(2)
The characteristic resistance for fastenings in case of pull-out failure is given in according
to Technical Product specification, but for headed anchors, it is limited by the pressure of
concrete, that is placed under the head of the fastener. (SFS-EN 1992-4 2018, 56)
𝑁𝑅𝑘,𝑝 = 𝑘2 ∙ 𝐴ℎ ∙ 𝑓𝑐𝑘
(3)
To ensure that pull-out failure will not happen designer should choose a fastener from Technical Product Specification with sufficient characteristic resistance and calculate the limit for
headed anchors.
2.3.3 Combined pull-out and concrete failure in case of post-installed bonded fasteners
Сombined pull-out and concrete failure of post-installed bonded fasteners happen when the
connection between the bonding material and concrete base doesn’t have adequate
strength, and failure between them occurs. This can also happen to the anchor bolt and the
bonding material, and in addition concrete cone formed at the end of the fastener breaks
out with the fastener.
14
Figure 10 Combined pull-out and concrete failure of bonded fasteners (SFS-EN 1992-4
2018, 49)
For post-installed bonded anchors, it should be verified that the resultant design tension
force of the tensioned fastener is not bigger, than the design resistance in case of combined
pull-out and concrete failure of fastener with anchors under tension load: (SFS-EN 1992-4
2018, 51)
𝑁𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑝𝑐 =
𝑁𝑅𝑘,𝑝𝑐
𝛾𝑀𝑝
(4)
Provision of strength can be done by choosing enough diameter of the fastener, sufficient
effective embedment depth of a fastener, adequate concrete strength class, and increase
of distance between the fastener and edge of the concrete element.
2.3.4 Concrete splitting failure
Concrete splitting failure occurs when tension loads applied to a fastener are so high, that
concrete can’t withstand the load, and splitting cracks start to occur along a plane passing
through the axis of the fastener.
Figure 11 Concrete splitting failure (SFS-EN 1992-4 2018, 49)
15
For cast-in-place and post-installed fasteners, it should be verified that the resultant design
tension force of the tensioned fastener is not bigger, than the design resistance in case of
concrete splitting failure with anchors under tension load. (SFS-EN 1992-4 2018, 51)
𝑁𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑠𝑝 =
𝑁𝑅𝑘,𝑠𝑝
𝛾𝑀𝑠𝑝
(5)
Concrete splitting failure during installation (e.g., when applying the installation
torque on a fastener) is avoided by complying with minimum values for edge distances, spacing, member thickness and requirements for reinforcement as given in
the relevant European Technical Product Specification (SFS-EN 1992-4 2018, 59).
2.3.5 Concrete blow-out failure
Concrete blow-out failure is usually related to fasteners with a deep embedment and tiny
side covers. Also, it should be mentioned that verification in case of concrete blow-out failure applies to headed anchors, and if post-installed undercut fasteners are used as headed
anchors with edge distance not bigger than 50% of the effective embedment depth of the
fastener. The SFS-EN-1992-4:2018 (14) provides that concrete blow-out failure can be described as spalling of the concrete on the side face of the concrete element at the level of
the embedded head with no major breakout at the top concrete surface.
Figure 12 Concrete blow-out failure (SFS-EN 1992-4 2018, 49)
For headed and post-installed mechanical undercut fasteners designed as headed fasteners, it should be verified that the resultant design tension force of the tensioned fastener is
16
not bigger than design resistance in case of concrete blow-out failure with anchors under
tension load. (SFS-EN 1992-4 2018, 51)
𝑁𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑐𝑏 =
𝑁𝑅𝑘,𝑐𝑏
𝛾𝑀𝑐
(6)
If configuration with several fasteners acting as a group, verification should be done for the
anchor that is closest to the edge.
If at the design stage it is calculated that concrete blow-out failure will occur, it can be prevented by the usage of a higher concrete strength class and with an increase of edge distances.
2.3.6 Steel failure of fastener without lever arm
According to the SFS-EN 1992-4 (2018, 43) if the fixture is made out of steel and is in
contact with the fastener over a length of at least 50% of thickness of a fixture and the fixture
is fixed directly to the concrete without an intermediate layer or the fixture is fixed using a
levelling mortar with a thickness not larger than 50% of a diameter of a fastener under at
least the full dimensions of the fixture on a rough concrete surface as intermediate layer,
shear loads acting on fastenings may be assumed to act without a lever arm.
Steel failure of fastener without lever arm under shear load can happen because of the low
steel strength capacity of a certain fastener or because the diameter of the anchor is too
small.
The SFS-EN-1992-4 (2018, 66) provides that the characteristic resistance of a fastener in
case of steel failure is given in the relevant European Technical Product Specification.
Figure 13 Steel failure of fastener without lever arm (SFS-EN 1992-4 2018, 64)
For cast-in-place and post-installed fasteners it should be verified that the resultant design
shear force of the most loaded fastener is not bigger, than the design resistance in case of
steel failure without a lever arm with anchors under shear load. (SFS-EN 1992-4 2018, 65)
17
𝑉𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑠 =
𝑉𝑅𝑘,𝑠
𝛾𝑀𝑠
(7)
To prevent steel failure without a lever arm and to increase the resistance, a fastener with
bigger diameter and more resistant steel material should be chosen.
2.3.7 Steel failure of fastener with lever arm
In the case of steel failure of a fastener with a lever arm, a bending effect caused by a shear
load applied with a lever arm in relation to the surface of the concrete element is taken into
account.
Figure 14 Steel failure with lever arm (SFS-EN 1992-4 2018, 64)
For cast-in-place and post-installed fasteners, it should be verified that the resultant design
shear force of the most loaded fastener is not bigger than the design resistance in case of
steel failure with lever arm with anchors under shear load. (SFS-EN 1992-4 2018, 65)
𝑉𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑠𝑀 =
𝑉𝑅𝑘,𝑠𝑀
𝛾𝑀𝑠
(8)
To ensure that the steel failure of the fastener with the lever arm is verified, an anchor with
sufficient characteristic bending resistance should be used. The characteristic bending resistance of the fastener can be found in the relevant Technical Product Specification.
2.3.8 Concrete pry-out failure
The SFS-EN 1992-4 (2018, 14) provides concrete pry-out failure can be described as failure
that corresponds to the formation of a concrete spall opposite to the loading direction under
shear loading.
18
Figure 15 Concrete pry-out failure (SFS-EN 1992-4 2018, 64)
For cast-in-place and post-installed fasteners it should be verified that the resultant design
shear force of the most loaded fastener is not bigger, than the design resistance in case of
concrete pry out failure with anchors under shear load. (SFS-EN 1992-4 2018, 65)
𝑉𝐸𝑑 ≤ 𝑁𝑅𝑑,𝑐𝑝 =
𝑉𝑅𝑘,𝑐𝑝
𝛾𝑀𝑐
(9)
According to SFS-EN 1992-4 the value of the characteristic resistance in case of concrete
pry-out failure is less with supplementary reinforcement, rather than with supplementary
reinforcement. It is better to not use supplementary reinforcement in order to prevent concrete pry-out failure.
To increase the resistance in case of pry-out failure, designers can use anchors with bigger
diameters in configurations or increase the volume of engaged concrete
2.4
Forces assigned to supplementary reinforcement
Supplementary reinforcement can take up tension or shear loads and improve the loadbearing capacity of anchor bolts in cases of concrete cone failure and concrete edge failure.
In accordance with SFS-EN-1992-4 (2018, 47), the supplementary reinforcement shall be
designed for the resultant design tension force of the tensioned anchor (in case of the single
anchor is used) or design value of tensile load acting on the most stressed anchor of a
group (in case of a group of fasteners is used). Properties of suitable reinforcement are then
applied to all reinforcement designed for other anchors. Standardization of reinforcement
makes the process of design faster, makes processes of installation on site easier, and
minimizes the risk of making a mistake in the design stage.
The SFS-EN-1992-4 (2018, 47) provides that in case when supplementary reinforcement
is placed in the direction of the design shear force, the design tension force in the supplementary reinforcement caused by the design shear force acting on a fixture perpendicular
and towards the edge shall be calculated as follows:
19
𝑁𝐸𝑑,𝑟𝑒 = (
𝑒𝑠
+ 1) ∙ 𝑉𝐸𝑑
𝑧
(10)
After analyzing Formula (1) it can be concluded, that to minimize design tension force in the
supplementary reinforcement in the design stage, the distance between the axis of reinforcement and the line of shear force acting on the fixture should be as small as possible,
and effective depth to supplementary reinforcement should be as big as possible. Forces in
the reinforcement and concomitant distances are shown in Figure 7.
Figure 16 Fixture with supplementary reinforcement (SFS-EN 1992-4 2018, 48)
20
3
Detailing of supplementary reinforcement
Supplementary reinforcement can be designed to resist tension forces or shear forces. In
accordance with standard SFS-EN 1992-4 conditions for usage of supplementary reinforcement in tension and in shear should be met. If these requirements are not met, supplementary reinforcement cannot be used. Conditions for applying supplementary reinforcement to
take up shear loads, or tension loads differ depending on the type of load.
3.1
Tension load
At the design stage, it can be assumed that supplementary reinforcement will take up tension loads instead of relying this responsibility on concrete cone strength. This can be decided when high tension loads are applied to thin and small anchors or when anchors should
be placed near the corner or the edge of the element. When the design relies on supplementary reinforcement, concrete cone failure does not need to be verified. The values of
the design resistance of supplementary reinforcement will be used instead of design resistance of a fastener in case of concrete cone failure. This means, that supplementary
reinforcement should be assumed effective, if the design resistance of the supplementary
reinforcement will be bigger, than the design resistance of the anchor in case of concrete
cone failure. Sizing and placing of supplementary reinforcement should also be considered
following specific requirements.
3.1.1 Concrete cone failure
Concrete cone failure is one of the failure modes, that can occur when anchor bolts are
used. This failure mode applies both for headed and post-installed fasteners. Most of the
incident’s concrete in case of failure has a cone shape as shown in Figure 8.
Figure 17 Concrete cone failure diagram (SFS-EN 1992-4 2018, 49)
21
For cast-in-place and post-installed fasteners, it should be verified that the resultant design
tension force of the tensioned fastener is not bigger than design resistance in case of concrete cone failure under tension load. (SFS-EN 1992-4 2018, 51)
𝑁𝐸𝑑 < 𝑁𝑅𝑑,𝑐 =
𝑁𝑅𝑘,𝑐
𝛾𝑀𝑐
(11)
Partial factor for concrete cone failure mode should be defined before verification of concrete cone failure.
𝛾𝑀𝑐 = 𝛾𝑐 ∙ 𝛾𝑖𝑛𝑠𝑡
(12)
Values for corresponding partial factors are shown in Table 1.
Partial factor
Symbol
Value
factor accounting for
the sensitivity to installation of post-in-
=1,0 for headed fasteners
≥1,0 for post-installed fasteners in tension
𝛾𝑖𝑛𝑠𝑡
=1,0 for post-installed fasteners in shear
stalled fasteners
=1,5 for seismic repair and strengthening of
existing structures see the EN 1998 series
factor for concrete
𝛾𝑐
=1,2 for seismic repair and strengthening of
existing structures see the EN 1998 series
Table 1 Partial factors for concrete related failure (SFS-EN 1992-4 2018, 34)
The geometric effect of axial spacing and edge distance on the characteristic resistance is
considered by the division of actual area of the idealized concrete cone of a group of fasteners and reference projected area of the concrete cone of an individual fastener: (SFSEN-1992-4 2018, 52)
𝐴𝑐,𝑁
𝐴0𝑐,𝑁
(13)
22
Figure 18 Areas of the idealized concrete cone: a) reference projected area of the idealized
concrete cone of an individual fastener; b) actual area of the idealized concrete cone of a
group of four fasteners (SFS-EN-1992-4 2018, 52)
The algorithm for concrete cone failure verification is shown in Figure 19 and an example
of the calculation can be found in Appendix. The resistance can be greatly improved by
using high concrete strength class and by increasing the effective embedment depth of a
fastener. The placing of configuration is also important, it is better to place the configuration
far from edges and make edge distances as much as possible, which can be difficult in real
projects.
23
Figure 19 Algorithm of concrete cone failure verification
24
3.1.2 General requirements
According to EN-1992-4, the supplementary reinforcement to take up tension load should
be designed with following requirements: (SFS-EN-1992-4 2018, 49)
•
The shape of reinforcement shall be ribbed reinforcing bars with characteristic steel
yield strength less than 600 𝑁/𝑚𝑚 2. The diameter of the bars should be no larger
than 16 mm. Reinforcement shall be detailed as stirrups or loops with a mandrel
diameter according to EN-1992-1-1;
•
The supplementary reinforcement should be sized for the most loaded fastener in a
group, after that this certain type of reinforcement shall be placed for other fasteners;
•
In order to make effect of eccentricity as less as possible, supplementary reinforcement should be placed symmetrically and as close to the anchors as possible;
•
Only supplementary reinforcement with an anchorage length in the concrete failure
cone bigger than 4 diameters of a rebar (for anchorage with bends, hooks, or loops)
or bigger than 10 diameters of a rebar (for anchorage with straight bars with or without welded transverse bars) shall be assumed as effective;
•
The supplementary reinforcement bars with a distance less than 75 percent of effective embedment depth from the anchor should be assumed as effective;
•
The supplementary reinforcement should be anchored outside of the failure concrete cone with an anchorage length according to EN 1992-1-1. Anchoring of the
supplementary reinforcement is shown in Figure 2 – a;
•
Surface reinforcement should resist the forces arising from the assumed strut and
tie model and the splitting forces. Example of how surface reinforcement should be
provided is shown in Figure 1.
3.2
Shear load
When the design relies on supplementary reinforcement to take up shear loads, concrete
edge failure does not need to be verified. The values of the design resistance of supplementary reinforcement will be used instead of the design resistance of a fastener in case of
concrete edge failure. The supplementary reinforcement can be designed in the form of a
surface reinforcement as shown in Figure 2 or in the shape of stirrups or loops as shown in
Figure 20. Sizing and placing of supplementary reinforcement should also be considered
following specific requirements.
25
Figure 20 Reinforcement taking up shear forces acting on a fastening: a) supplementary
reinforcement in the shape of stirrups; b) supplementary reinforcement in the shape of loops
(SFS-EN 1992-4 2018, 66)
3.2.1 Concrete edge failure
Concrete edge failure is one of the failure modes, that can occur when anchor bolts are
used. This failure mode applies both for headed and post-installed fasteners. This failure
mode takes place when the concrete fails towards an edge under shear loading, as shown
in Figure 21.
Figure 21 Concrete edge failure diagram (SFS-EN-1992-4 2018, 64)
For cast-in-place and post-installed fasteners, it should be verified that the design shear
load of the most loaded fastener is not bigger than the design resistance in case of concrete
edge failure under shear load. (SFS-EN 1992-4 2018, 65)
𝑉𝐸𝑑 ≤ 𝑉𝑅𝑑,𝑐 =
𝑉𝑅𝑘,𝑐
𝛾𝑀𝑐
(14)
26
The partial factor for concrete edge failure mode should be defined before verification of
concrete edge failure. This can be done with Formula 3 and Table 1, the same as for concrete cone failure.
Only the fasteners located closest to the edge are used for the verification of concrete edge
failure. For fastenings with more than one edge, verification shall be carried out for all edges.
Where design checks are required, this should be for all suitable edges, as shown in Figure
13.
Figure 22 Verification for group of four fasteners at a corner: a) applied action; b) verification
for the left edge; c) verification for the bottom edge (SFS-EN-1992-4 2018, 70)
The geometrical effect of spacing as well as of further edge distances and the effect of
thickness of the concrete member on the characteristic resistance is taken into the account
by the division of actual area of the idealized concrete edge of a group of fasteners and
reference projected area of the concrete edge of an individual fastener: (SFS-EN-1992-4
2018, 71)
𝐴𝑐,𝑉
𝐴0𝑐,𝑉
(15)
27
Figure 23 Areas of the idealized concrete cone under shear loading: a) reference project
area for a single fastener; b) actual projected area for a single fastener at a corner; c) actual
projected area for group of fasteners at an edge in a thin concrete member (SFS-EN-19924 2018, 71)
The algorithm for concrete cone failure verification is shown in Figure 24 and an example
of the calculation can be found in Appendix. The general rule for concrete edge resistance
improvement is using a high concrete class and placing anchors as far as possible from the
edge.
28
Figure 24 Algorithm of concrete edge failure verification
29
3.2.2 General requirements
According to SFS-EN 1992-4 (2018, 65) , the supplementary reinforcement to take up shear
load shall be designed with following requirements:
•
Where supplementary reinforcement has been sized for the most loaded fastener,
the same reinforcement is provided around all fasteners considered effective for
concrete edge failure;
•
The supplementary reinforcement consists of ribbed bars with nominal characteristics steel yield strength not bigger than 600 𝑁/𝑚𝑚2 and the diameter is not larger
than 16 mm. The mandrel diameter complies with EN 1992-1-1;
•
Bars are within a distance of 75% of edge distance in direction perpendicular to the
edge from the fastener;
•
The anchorage length in the concrete breakout body equals at least 10 diameters
for straight bars with or without welded transverse bars and equals at least 4 diameters for bars with a hook, bend or loop;
•
The breakout body assumed should be the same as that for calculating the resistance for concrete edge failure;
•
Reinforcement along the edge of the member is provided and designed for the
forces according to an appropriate strut and tie model. As a simplification an angle
of the compression struts of 45 degrees may be assumed.
30
4
Failure of supplementary reinforcement
In order to increase the resistance of the fasteners against concrete cone failure and concrete edge failure, it is possible to use supplementary reinforcement around the fastening.
After the concrete cone crack surface is formed, the reinforcement acts on keeping the
concrete cone and member together. In such conditions not only the resistance of the anchorage is increased but also the ductility. So, the supplementary reinforcement delays and
prevents the formation of a concrete cone, and therefore two new failure modes may occur
- steel failure and anchorage failure.
A partial factor in supplementary reinforcement is used in calculations because of steel failure and negotiating the fact, that calculations are based on a simplified model and the fact
that steel properties are not uniform. A partial factor should be defined before verification of
supplementary reinforcement failure. This factor is changing depending on the design situation: permanent and transient design situation or accidental design situation. Partial factors
for steel failure in supplementary reinforcement are shown in Table 2.
Partial factor
Symbol
Situation
Permanent and
Steel failure in supplementary reinforcement
transient design
Value
1,15
𝛾𝑀𝑠,𝑟𝑒
Accidental design
situation
1,0
Table 2 Partial factors for supplementary reinforcement (SFS-EN-1992-4 2018, 33)
4.1
Steel Failure
When steel failure occurs reinforcement rebars are starting to yield at first and are then torn
apart, because of a lack of load-bearing capacity. The main property of reinforcement that
is responsible for load-bearing capacity regarding steel failure is the design resistance of
supplementary reinforcement in case of steel failure.
4.1.1 Tension load
For steel failure of supplementary reinforcement in tension, it should be verified, that the
design value of tension load acting on the supplementary reinforcement is not bigger than
the design resistance in case of steel failure of supplementary reinforcement: (SFS-EN
1992-4 2018, 51)
31
𝑁𝐸𝑑,𝑟𝑒 ≤ 𝑁𝑅𝑑,𝑟𝑒 =
𝑁𝑅𝑘,𝑟𝑒
𝛾𝑀𝑠,𝑟𝑒
(16)
The characteristic yield resistance of the supplementary reinforcement for one fastener is
calculated with the formula: (SFS-EN 1992-4 2018, 63)
𝑛𝑟𝑒
𝑁𝑅𝑘,𝑟𝑒 = ∑ 𝐴𝑠,𝑟𝑒,𝑖 ∙ 𝑓𝑦𝑘,𝑟𝑒
(17)
𝑖=1
Figure 25 Example of steel failure verification
As it can be seen from the formulas, the characteristic yield resistance of the supplementary
reinforcement depends directly proportional on:
•
nominal characteristic steel yield of reinforcement
•
number of the rebars of supplementary reinforcement effective for one fastener
•
cross section of a reinforcing bar
The bigger the characteristic yield resistance is, the bigger the design resistance of supplementary reinforcement gets. The bigger the design resistance is, the bigger loads reinforcement can withstand. To increase characteristic yield strength one of the components of the
formula should be increased. Cross section of a reinforcing bar can be increased by using
32
rebars with a bigger diameter, but according to requirements rebars with a diameter no
larger than 16 mm can be used.
One aspect of this work is to analyze how components of formulas can affect the result. In
order to trace the causal relationship between design resistance of supplementary reinforcement and changes in numbers of effective rebars, changes in yield strength, and
changes in the diameter of rebars, there should be a reference point. Other results will be
compared to a reference point, and it will be easier to compare other results between themselves. The configuration of reinforcement with properties as in Table 3 was used as a
reference point.
It is important to mention that in Finland rebars with a yield strength of 400 N/mm2 or with
a diameter of 14 mm are not used in real projects, but since this thesis work will be published
worldwide, rebars with a yield strength of 400 N/mm2 and a diameter of 14 mm will be used
in calculations.
Parameter
Symbol
Value
𝑓𝑦𝑘,𝑟𝑒
500 N/mm2
𝑑
6 mm
𝐴𝑠,𝑟𝑒,𝑖
28 mm2
𝑛𝑟𝑒
1
Partial factor
𝛾𝑀𝑠,𝑟𝑒
1,15
Design resistance
𝑁𝑅𝑑,𝑟𝑒
12 kN
Yield strength
Diameter of one rebar
Cross section of a rebar
Number of effective rebars
Table 3 Reference configuration in case of a steel failure in tension
After reference configuration has been obtained, components of the formula can be
changed one by one. This will show which of the effects of the components result in the
most. In the case of studying steel failure phenomena in this work, the diameter of one
rebar, the number of effective rebars, and yield strength have been increasing. The partial
factor value for all configurations was 1,15.
Configuration
Design resistance value, kN
1 rebar, 8 mm diameter, yield strength 500 N/mm2
22
1 rebar, 10 mm diameter, yield strength 500 N/mm2
34
33
1 rebar, 12 mm diameter, yield strength 500 N/mm2
49
1 rebar, 14 mm diameter, yield strength 500 N/mm2
67
1 rebar, 16 mm diameter, yield strength 500 N/mm2
87
Table 4 Design resistance in case of steel failure depending on changes in diameter of a
rebar
Figure 26 Design resistance in case of steel failure of the anchor reinforcement depending
on changes in diameter of a rebar
Configuration
Design resistance value kN
2 rebars, 6 mm diameter, yield strength 500 N/mm2
24
3 rebars, 6 mm diameter, yield strength 500 N/mm2
37
4 rebars, 6 mm diameter, yield strength 500 N/mm2
49
5 rebars, 6 mm diameter, yield strength 500 N/mm2
61
6 rebars, 6 mm diameter, yield strength 500 N/mm2
73
Table 5 Design resistance in case of steel failure depending on changes in number of effective rebars
34
Figure 27 Design resistance in case of steel failure of the anchor reinforcement depending
on changes in number of effective rebars
Configuration
1 rebar, 6 mm diameter, yield strength 600 N/mm2
Design resistance value, kN
17
Table 6 Design resistance in case of steel failure of the anchor reinforcement depending on
changes in yield strength
Figure 28 Design resistance in case of steel failure of the anchor reinforcement depending
on changes in yield strength
35
To compare the results between themselves the chars were combined in one chart.
Figure 29 Chart for the relationship between design resistance of supplementary reinforcement in case of steel failure and changes in numbers of rebars, yield strength, the diameter
of rebars
As it can be seen from the chart, an increase in yield strength affects design resistance
least out of all components, so in the design stage changes in yield strength can be done
last. At a short distance increase in effective rebars increase design resistance more, than
the increase in diameter of rebars. But on long-distance changes in the diameter of rebars
increase design resistance more, than changes in the amount of rebars. In a conclusion, it
can be said, that if a small increase in design resistance is needed, the number of rebars
can be increased in the first order, but if there is a need for a great improvement of design
resistance, changes in diameter can be done first.
Due to lack of space, it is sometimes impossible to increase the number of effective re-bars.
It is important to understand how design resistance is increasing without changing the number of effective rebars. In that case, only the yield strength and diameter of rebars can be
changed. To track how to design resistance is changing according to the increase of those
two parameters calculations were made.
Results showed that the peak value for design resistance that can be obtained with two
effective rebars is 210 kN. This peak value is achieved in configuration with a possibly
36
highest diameter of the rebar 16 mm and possibly highest yield strength of 600 N/mm2
according to requirements for supplementary reinforcement design.
After comparison of results for configurations with yield strengths of 400 N/mm2 and 500
N/mm2 as a conclusion, it can be said that design resistance growth is 25% for each possible diameter of the rebar. If the same comparison would be applied to configurations with
yield strengths of 500 N/mm2 and 600 N/mm2 , design resistance growth is 20%. In comparison for configurations with yield strengths of 400 N/mm2 and 600 N/mm2 design resistance growth is 50%.
Figure 30 Growth of design resistance depending on the yield strength
Partial factor Number of ef- Diameter of a Yield
fective rebars
1,15
1,15
1,15
1,15
2
2
2
2
rebar, mm
6
8
10
strength, Design resistance,
N/mm2
kN
400
19
500
24
600
29
400
35
500
43
600
52
400
55
500
69
600
82
400
79
500
98
12
37
1,15
1,15
2
2
14
16
600
118
400
107
500
134
600
161
400
140
500
175
600
210
Table 6 Design resistance depending on the different yield strengths and changes in diameter of a rebar
Figure 31 Chart for the relationship between design resistance of supplementary reinforcement in case of steel failure and supplementary reinforcement with different yield strength
and changes in the diameter of rebars
Design resistance of supplementary reinforcement grows if the diameter of reinforcement
is replaced with a bigger diameter. The track of the growth of the design resistance based
on changes in the diameter is shown in Figure 20.
38
The design resistance growth is almost the same for configurations with different yield
strengths. This can be explained by Figure 17 and among all the parameters yield strength
affects design resistance the least.
It can be seen that the bigger diameter gets, the lower the design resistance growth becomes. If the diameter of supplementary reinforcement will be changed from 6 mm to 8 mm,
design resistance will become almost two times bigger. But if in the same conditions diameter would be changed from 14 mm to 16 mm, design resistance growth will be 30%.
Figure 32 Growth of the design resistance depending on the diameter of the rebar
39
Last, but not least is a comparison of configurations of supplementary reinforcement with
different numbers of effective rebars. Fixtures with two, three, and four effective rebars were
chosen for the comparison. Results can be seen in Table 7 and Figure 21.
Partial factor
Yield strength, Diameter of a Number of effective Design resistance, kN
N/mm2
1,15
1,15
1,15
1,15
1,15
1,15
500
500
500
500
500
500
rebar, mm
rebars
6
8
10
12
14
16
2
24
3
37
4
49
2
43
3
65
4
87
2
69
3
103
4
137
2
98
3
147
4
197
2
134
3
201
4
268
2
175
3
262
4
350
Table 7 Design resistance depending on the number of the rebars and changes in diameter of a rebar
40
After a comparison of design resistances as a conclusion it can be said that in configurations
with 3 effective rebars design resistance 50% bigger, than with 2 effective rebars for all
applicable diameters of the rebar. If the same comparison would be applied to configurations with 3 effective rebars and 4 effective rebars, design resistance growth is 33%. Design
resistance in configurations with 4 effective rebars is twice as much as in configurations
with 2 effective rebars.
Figure 33 Chart for the relationship between design resistance of supplementary reinforcement in case of steel failure and supplementary reinforcement with different number of effective rebars and changes in the diameter of rebars
Figure 34 Growth of design resistance depending on number of the effective rebars
41
4.1.2 Shear load
For steel failure of supplementary reinforcement in shear it should be verified, that the design value of tension load acting on the supplementary reinforcement is not bigger than the
design resistance in case of steel failure of supplementary reinforcement. The design value
of the tension load should be calculated according to Formula 10. (SFS-EN 1992-4 2018,
65)
𝑁𝐸𝑑,𝑟𝑒 ≤ 𝑁𝑅𝑑,𝑟𝑒 =
𝑁𝑅𝑘,𝑟𝑒
𝛾𝑀𝑠,𝑟𝑒
(18)
The characteristic resistance of one fastener in use with supplementary reinforcement in
shear is calculated with the formula: (SFS-EN 1992-4 2018, 75)
𝑛𝑟𝑒
(19)
𝑁𝑅𝑘,𝑟𝑒 = 𝑘10 ∙ ∑ 𝐴𝑠,𝑟𝑒,𝑖 ∙ 𝑓𝑦𝑘,𝑟𝑒
𝑖=1
As it can be seen from the formulas, all calculations and conclusions in the case of tension
load can be applicable in the case of shear load, but the efficiency factor should be considered.
The efficiency factor takes into account the shape of the supplementary reinforcement: surface reinforcement as in Figure 2 or the shape of stirrups or loops enclosing the fastener as
in Figure 11 (SFS-EN-1992-4 2018, 75). Values for the efficiency factor are shown in Table
8.
Factor
Symbol
Shape of the supplementary reinforcement
Surface reinforcement
Efficiency
factor
𝑘10
Shape of stirrups or loops enclosing the
fastener
Value
1
0,5
Table 8 Values of efficiency factor
If supplementary reinforcement is placed in the shape of stirrups or loops enclosing the
fastener, it is twice less effective, than if supplementary reinforcement is designed in the
shape of surface reinforcement. The efficiency factor is affecting the characteristic resistance directly and the value of design resistance also will be half as much. For
42
supplementary reinforcement in the shape of surface reinforcement under shear load the
design resistance values are the same as under tension load.
4.2
Anchorage failure
Supplementary reinforcement used to resist either tensile or shear forces must be properly
anchored into the assumed concrete cone failure zone. The main property of reinforcement
that is responsible for load-bearing capacity regarding anchorage failure is the design resistance of supplementary reinforcement in case of anchorage failure.
4.2.1 Tension load
For anchorage failure of supplementary reinforcement in tension it should be verified, that
the design value of tension load acting on the supplementary reinforcement is not bigger
than the design resistance of supplementary reinforcement associated with anchorage failure. (SFS-EN 1992-4 2018, 51)
𝑁𝐸𝑑,𝑟𝑒 ≤ 𝑁𝑅𝑑,𝑎
(20)
The design resistance of the supplementary reinforcement provided for one fastener associated with anchorage failure in the concrete cone is: (SFS-EN 1992-4 2018, 63)
𝑛𝑟𝑒
0
𝑁𝑅𝑑,𝑎 = ∑ 𝑁𝑅𝑑,𝑎,𝑖
(21)
𝑖=1
In order to calculate the design resistance of the supplementary reinforcement, design resistance of one rebar should be calculated first: (SFS-EN 1992-4 2018, 64)
0
𝑁𝑅𝑑,𝑎
=
𝑙1 ∙ 𝜋 ∙ ∅ ∙ 𝑓𝑏𝑑
𝛼1 ∙ 𝛼2
(22)
To calculate the design resistance of one rebar, design bond strength should be calculated.
(SFS-EN 1992-1-1 2004, 133)
𝑓𝑏𝑑 = 2,25 ∙ 𝜂1 ∙ 𝜂2 ∙ 𝑓𝑐𝑡𝑑
(23)
In order to calculate design bond strength, the design tensile concrete strength should be
calculated. (SFS-EN 1992-1-1 2004, 34)
43
𝑓𝑐𝑡𝑑 =
𝛼𝑐𝑡 ∙ 𝑓𝑐𝑡𝑘,0,05
𝛾𝑐
(24)
According to the SFS-EN-1992-4, design resistance of one rebar should be no larger than
followed product of the parameters: (SFS-EN-1992-4 2018, 64)
0
𝑁𝑅𝑑,𝑎,𝑖
≤ 𝐴𝑠,𝑟𝑒 ∙ 𝑓𝑦𝑘,𝑟𝑒 ∙
Figure 35 Algorithm of anchorage failure verification
1
𝛾𝑀𝑠,𝑟𝑒
(25)
44
According to standard SFS-EN 1992-1-1 (2004, 133) due to the increasing brittleness of
higher strength concrete, the characteristic axial tensile strength of concrete should be limited to the value for C60/75, unless it can be verified that the average bond strength increases above this limit. Values for the characteristic axial tensile strength of concrete are
given in Appendix 1.
Long term coefficient is a coefficient taking account of long-term effects on the tensile
strength and unfavorable effects, resulting from the way the load is applied. (SFS-EN 19921-1 2004, 34)
Coefficient
Symbol
Recommended value
Long term coefficient
𝛼𝑐𝑡
1,0
Table 9 Long term coefficient
A partial safety factor for concrete is used to negotiate the fact, that calculations are based
on a simplified model and the possible heterogeneity of the material. Value for partial factor for concrete depends on the design situation: accidental or persistent and transient.
Values for partial factors for concrete are given in Table 10. (SFS-EN 1992-1-1 2004, 24)
Partial factor
Concrete
Symbol
Design situations
Value
Persistent & Transient
1,5
Accidental
1,2
𝛾𝑐
Table 10 Partial factor for concrete
The bond condition coefficient relates to the quality of the bond condition and the position
of the rebar during concreting. There can be good bond conditions and all other cases, or
situations when bars in structural elements build with slip-forms unless it can be shown that
good bond conditions exist. (SFS-EN 1992-1-1 2004, 133)
Coefficient
Bond condition coefficient
Symbol
𝜂1
Situation
Value
Good conditions
1,0
All other cases, bars in structural elements built with slip-forms
Table 11 Bond condition coefficient
0,7
45
Figure 36 Description of bond conditions (SFS-EN 1992-1-1 2004, 134)
The bar diameter coefficient is related to the bar diameter. Due to supplementary reinforcement design requirements, the rebar diameter cannot be bigger than 16 mm. If the rebar
diameter is no larger than 32 mm, the bar diameter coefficient value is 1,0. (SFS-EN 19921-1 2004, 134)
Coefficient
Symbol
Diameter, mm
Value
Bar diameter coefficient
𝜂2
< 32
1,0
Table 12 Bar diameter coefficient
Influence factors are considering the effect of the form of the bars assuming adequate
cover (See Figure 21) and the effect of concrete minimum cover (See Figure 22).
Table 13 Influencing factors (SFS-EN 1992-1-1 2004, 136)
46
Figure 37 Methods of anchorage other than by a straight bar (SFS-EN 1992-1-1 2004, 133)
Figure 38 Values of concrete minimum cover (SFS-EN 1992-1-1 2004, 135)
According to supplementary reinforcement requirements, the anchorage length in the concrete breakout body equals at least 10 diameters for straight bars with or without welded
transverse bars and equals at least 4 diameters for bars with a hook, bend, or loop. SFSEN-1992-4 2018, 66)
Parameter
Anchorage
length
Symbol
Type of a bar
Length, mm
Straight bar
min 10 diameters of a bar
Bars with a hook, bend or loop
min 4 diameters of a bar
𝑙1
Table 14 Anchorage length
47
As it can be seen from the formulas, the design resistance of the supplementary reinforcement depends on:
•
diameter of a rebar
•
anchorage length
•
strength class for concrete
•
shape of reinforcement
•
number of effective rebars
•
bond conditions
By increasing the strength class for concrete, the design tensile concrete strength will grow
in its turn. When design tensile concrete strength increases, design bond strength grows
too, which directly affects the design resistance of the supplementary reinforcement. If the
diameter of the rebar is changed with a bigger diameter, the anchorage length minimum
value will get bigger due to Table 14, which is also increasing the design resistance of the
supplementary reinforcement. Even so, in real projects, the values of minimum anchorage
length are not used, and the actual anchorage leg length is larger than the minimum. The
actual anchorage length is limited by the embedment length of the fastener, thus in the
actual case, it might be impossible to use bigger diameter rebars because bigger anchorage
lengths will be above the limit set by embedment length. However, in general, bond resistance is better with smaller diameter rebars.
In most cases, the anchorage length of the reinforcement is a crucial parameter out of all,
since it can be assumed as effective only if placed in a possible concrete cone break-out
body and have relatively small values. The anchorage length also is reducing because of
the concrete cover and because it cannot be placed right next to the anchor bolts. According
to the requirements for supplementary reinforcement placing, reinforcement should be
placed at a distance within 75% of the effective embedment depth of the anchor.
48
Figure 39 Placement of supplementary reinforcement under tension load (SFS-EN 1992-4
2018, 50)
To estimate the maximum length of anchorage reinforcement, anchor bolt HILTI HAS-U
M12 has been used in calculations. In a possible concrete cone to get the biggest values
for anchorage length, the reinforcement should be placed as close to the anchor as possible. The most important properties of the configuration for anchorage length estimation are
shown in Table 15.
Parameter
Symbol
Value
Anchor bolt
−
HILTI HAS-U M12
Diameter of anchor bolt
𝑑
12 mm
Embedment depth
ℎ𝑒𝑓
110 mm
Characteristic spacing
𝑠𝑐𝑟.𝑁
330 mm
Diameter of reinforcement
∅
12 mm
Concrete cover
-
20 mm
-
20 mm
𝑙1
72 mm
Minimum distance between fastener and rebar
Maximum anchorage length
Table 15 Properties of fixture
49
Figure 40 Supplementary reinforcement with diameter 12 mm with anchor bolt HILTI HASU M12 effective embedment depth 110 mm
As it can be seen from the calculations the anchorage length is 72 mm, which is low for
proper anchorage in general, but according to the SFS-EN 1992-4 requirements, this anchorage length is bigger than four diameters of reinforcement and is applicable for use.
If in the same configuration reinforcement with a lower diameter were used, the anchorage
length would get bigger. The use of reinforcement with a bigger diameter can be more complicated because rebars have minimum bending radius characteristics, which is depending
on the diameter of the rebar. In the case of applying a rebar with a bigger diameter, it might
need a bigger distance between the fastener and the rebar in order to make a curve for a
loop. A bigger distance between the fastener and rebar brings the reinforcement closer to
the surface of the concrete cone and at the same time makes the anchorage length value
lower.
50
Figure 40 Supplementary reinforcement with diameter 6 mm with anchor bolt HILTI HAUSU M12 effective embedment depth 110 mm
Another aspect is a consideration of how large rebar diameter can be used in order to fulfill
anchorage requirements with the use of fasteners with small effective embedment lengths.
With the assumption that the anchorage length value is about 70% of the embedment length
in Table 15, this relation is shown.
Table 15 Relation between diameter of a rebar and short effective embedment depths
After analyzing the relation between the diameter of rebar and effective embedment depths
as conclusion it can be said that it is almost impossible to use straight reinforcement with
short anchorages, which according to Formula 19 and Table 8 will lead to two times less
resistant reinforcement in the case of steel failure under shear.
51
The parameter that influences the anchorage length the most is effective embedment depth.
An increase of effective embedment depth will lead to the great improvement of anchor-age
length, but at the same time will lead to significant improvement of concrete cone failure,
which will cause doubts about the effectiveness of supplementary reinforcement in the current
design
situation.
Figure 41 Supplementary reinforcement with diameter 6 mm with anchor bolt HILTI HAUSU M12 effective embedment depth 220 mm
There are also other factors besides anchorage length that can help to increase the resistance of supplementary reinforcement. Also, due to element size restrictions, it is sometimes impossible to increase the number of effective rebars. The supplementary reinforcement design resistance can be improved by increasing concrete strength class and bigger
diameter instead. To track how design resistance is changing without changing the number
of rebars and anchorage length, the calculations were made using the reference configuration, with two effective rebars and using different concrete strength classes and with diameter changes. Results can be seen in Figure 42. However, it is important to understand that
there can be other ways of improving the design resistance of supplementary reinforcement,
for example in order to increase the resistance one rebar with a big diameter due to element
size restrictions can be changed to two rebars with less diameter, which will also lead to
increase of design resistance. There are no good and bad ways of design, they are dependent on the situation and all of them can lead to a positive result.
52
Parameter
Symbol
Value
Embedment length of a chosen
ℎ𝑒𝑓
100 mm
Maximum anchorage length
𝑙1.𝑚𝑎𝑥
70 mm
Partial factor for concrete
𝛾𝑐
1,5
Long-term coefficient
𝛼𝑐𝑡
1
Bond condition coefficient
𝜂1
1
Bar diameter coefficient
𝜂2
1
Anchorage length for all rebars
𝑙1
64 mm
∅
6 mm, 8 mm, 10 mm, 12 mm,
fastener
Diameter
Concrete strength class
14 mm, 16 mm
-
C12/15, C20/25, C30/37,
C40/50, C50/60, C60/75
First influence factor
𝛼1
1
Second influence factor
𝛼2
0,7
Number of effective rebars
𝑛𝑟𝑒
2
Shape of rebars
-
Loops
Table 16 Configurations for supplementary reinforcement
53
Figure 42 Chart for the relationship between design resistance of supplementary reinforcement in case of anchorage failure and supplementary reinforcement with same anchorage
length and different concrete strength classes and changes in the diameter of rebars
Track of design resistance growth depending on the concrete strength class is shown in
Figure 25. The bigger the concrete strength class gets the less is design resistance growth.
Figure 43 Growth track of design resistance of supplementary reinforcement associated
with anchorage failure based on increase of concrete strength class
Design resistance of supplementary reinforcement grows if the diameter of reinforcement
is replaced with a bigger diameter. The track of the growth of the design resistance based
54
on changes in the diameter is shown in Figure 26. The bigger diameter gets, the lower the
design resistance growth becomes. If the diameter of supplementary reinforcement will be
changed from 6 mm to 8 mm, the design resistance will become 80% bigger. But if in the
same conditions the diameter would be changed from 14 mm to 16 mm, design resistance
growth will be 30%.
Figure 44 Growth of the design resistance depending on the diameter of the rebar
4.2.2 Shear load
For supplementary reinforcement in shear in case of anchorage failure all the verifications
are the same as for tension load. For applications with supplementary reinforcement in the
shape of stirrups or loops in contact with the fastener (see Figure 20) no proof of the anchorage capacity of the supplementary reinforcement in the assumed concrete break-out
body is necessary. For applications in shear with supplementary reinforcement as a surface
reinforcement (See Figure 2) the design resistance is calculated as if the application would
have been in tension. (SFS-EN 1992-4 2018, 75)
55
Figure 45 Example for anchorage failure verification
56
5
Impact of supplementary reinforcement on anchor bolts strength
For fastenings with supplementary reinforcement design resistances for concrete cone failure and for a concrete edge failure are replaced with corresponding values for the failure of
supplementary reinforcement. (SFS-EN 1992-2-4 2018, 76)
Configuration of fastener for comparison of design resistances was proposed by supervisors from A-Insinöörit Suunnittelu Oy. An anchor bolt that is going to be used is HILTI HASU M12. All settling details have been taken from the HILTI technical datasheet, the table
with corresponding values is given in Appendix. In this example, tension load and shear
load are not acting at the same time on the fastener.
Parameter
Symbol
Value
Anchor bolt
−
HILTI HAS-U M12
Diameter of anchor bolt
𝑑
12 mm
Embedment depth
ℎ𝑒𝑓
70 mm
Factor for cracked concrete
𝑘1
7,7
Concrete strength class
-
C20/25
𝑓𝑐𝑘
20 N/mm2
Characteristic edge distance
𝑐𝑐𝑟.𝑁
105 mm
Characteristic spacing distance
𝑠𝑐𝑟.𝑁
210 mm
Edge distance
𝑐1
65 mm
Spacing distance
𝑠1
65 mm
Eccentricity
𝑒𝑛
0
Partial factor for concrete
𝛾𝑀𝑐
1
Factor for cracked concrete
𝑘9
1,7
Outside diameter of a fastener
𝑑𝑛𝑜𝑚
12 mm
Embedment length
𝑙𝑓 = ℎ𝑓
70 mm
Characteristic compressive cylinder strength of concrete
57
Stress distribution distance
ℎ
97.5 mm
Inclination angle
𝛼𝑣
0
Design tension force
𝑁𝐸𝑑
25 kN
Design shear force
𝑉𝐸𝑑
10 kN
𝑁𝑅𝑑,𝑐
12.4 kN
𝑉𝑅𝑑,𝑐
7 kN
Design resistance of a fastener
in case of concrete cone failure
Design resistance of a fastener
in case of concrete edge failure
Table 17 Configuration with anchor bolt HILTI HAUS-U M12 without supplementary reinforcement
Figure 46 Layout for configuration with anchor HILTI HAS-U M12
Design tension force and design shear forces are bigger than the design resistances of a
fastener, and this means that supplementary reinforcement is needed in both situations, for
tension load and for shear load too (or changes in configuration). After the design resistance
for the anchor bolt has been calculated, the supplementary reinforcement properties should
be selected. In given example supplementary reinforcement is designed taking up tension
loads only and taking up shear loads only, but have same properties for both situations. In
Figure 47 are shown drawings for supplementary reinforcement for tension load only and
for shear load only.
Parameter
Symbol
Value
Yield strength
𝑓𝑦𝑘,𝑟𝑒
500 N/mm2
58
Diameter of reinforcement
∅
12 mm
Cros-section area of rebar
𝐴𝑠,𝑟𝑒
113 mm2
Amount of effective rebars
𝑛𝑟𝑒
2
𝛾𝑀𝑠,𝑟𝑒
1,15
Shape of the reinforcement
-
Loops
Anchorage length
𝑙1
49 mm
Long-term coefficient
𝛼𝑐𝑡
1
Bond condition coefficient
𝜂1
1
Bar diameter coefficient
𝜂2
1
First influence factor
𝛼1
1
Second influence factor
𝛼2
0,7
Bond strength
𝑓𝑏𝑑
2,25 N/mm2
𝑁𝑅𝑑,𝑟𝑒
98.3 kN
𝑁𝑅𝑑,𝑟𝑒
49.15 kN
𝑁𝑅𝑑,𝑎
11.9 kN
Partial factor for reinforcement
Design resistance of supplementary reinforcement in
case of steel failure in tension
Design resistance of supplementary reinforcement in
case of steel failure in shear
Design resistance of supplementary reinforcement in
case of anchorage failure
(tension and shear)
Table 18 Supplementary reinforcement properties in combination with configuration with
anchor bolt HILTI HAUS-U M12
59
Figure 47 Supplementary reinforcement with anchor bolt HILTI HAS-U M12: a) to take up
tension loads only; b) to take up shear loads only
The supplementary reinforcement has bigger design resistances than the design resistances of a fastener, which means that selected reinforcement can improve the strength
of an anchor bolt HILTI HAS-U M12 with given design forces. However, because of low
embedment depth and strict limits for anchorage length it was difficult to choose appropriate
reinforcement.
The design resistance of supplementary reinforcement in case of steel failure under tension
is many times higher than other design resistances, which means that in most cases steel
failure is not a problem with supplementary reinforcement usage. With such high steel failure design resistance, the anchorage failure design resistance barely withstands the load.
It is important to understand, that if the design shear load was bigger, the anchor failure
would not be verified, and it would be impossible to somehow improve the anchor design
resistance due to the impracticability of anchoring the reinforcement with requirements
given in standard SFS-EN 1992-4. In that case, in order to improve the anchorage length
of the reinforcement, an increase in effective embedment depth and edge distances would
be needed. The effective embedment depth and edge distances are affecting concrete cone
design resistance and concrete edge resistance nearly the most out of all possible factors,
so the increase of those factors will greatly increase the design resistances of a fastener.
After the design resistances of an anchor bolt would be increased, the use of supplementary
reinforcement can be arguable. This means that supplementary reinforcement cannot be
used as a good solution in every design situation, the main principle of the anchor reinforcement usage is to apply it only when it is needed and design it according to the standard
restrictions.
60
6
Summary
The thesis demonstrates the full process of the supplementary reinforcement design for the
cast-in-place headed and post-installed anchor bolts. This work can be useful to familiarize
with supplementary reinforcement phenomena, and with failure modes for a fastener. All
the requirements and coefficients related to supplementary reinforcement design according
to standard EN 1992-4 have been collected in this work with examples for failure modes
verification.
In this thesis, the impact of different parameters of reinforcement on supplementary reinforcement strength has been analyzed, which can be useful for faster and better design of
anchor reinforcement. It is shown how each parameter affects the design resistance. Different ranges of values for supplementary reinforcement design resistances are collected
in analyzing part, which can help to understand the load-bearing abilities of anchor reinforcement.
An example of properly chosen reinforcement, which can increase the load-carrying capacity of anchor bolts is shown in this work. The supplementary reinforcement can improve
fastener resistance to concrete cone failure and concrete edge failure. However, this thesis
it is explained why the use of supplementary reinforcement in some cases can be arguable.
Due to strict limits of anchorage length of supplementary reinforcement, it sometimes can
be difficult to choose reinforcement with sufficient diameter, which leads to low strength
abilities. In order to increase the leg of anchorage, changes in the configuration of a fastening are needed, which in its turn increases the design resistance of a fastener and makes
applying supplementary reinforcement questionable.
61
References
HILTI HIT-HY 200 R V3 INJECTION MORTAR Technical Datasheet. Retrieved on 21 August 2022. Available at: https://www.hilti.fi/en/c/CLS_FASTENER_7135/CLS_ANCHOR_RODS_ELEMENTS_7135/r9864251#nav/close
SFS-EN 1992-4 (2018): Eurocode 2. Design of concrete structures. Part 4: Design of fastenings for use in concrete
SFS-EN 1992-1-1 (2004): Eurocode 2: Design of concrete structures. Part 1-1: General
rules and rules for buildings
Sharma, A.; Eligehausen, R.; Asmus, J. 2017. Comprehensive experimental investigations
on anchorages with supplementary reinforcement connections between steel and concrete.
Stuttgart. Retrieved on 12 August 2022. Available at: https://www.researchgate.net/publication/320165669_COMPREHENSIVE_EXPERIMENTAL_INVESTIGATIONS_ON_ANCHORAGES_WITH_SUPPLEMENTARY_REINFORCEMENT_Connections_between_Steel_and_Concrete
Sharma, A.; Eligehausen, R.; Asmus, J. & Bujnak, J. 2018. Behavior of Anchorages with
Supplementary Reinforcement Tension or Shear Forces. Stuttgart: Springer International
Publishing AG 2018. Retrieved on 12 August 2022. Available at: https://www.researchgate.net/publication/322168220_Behavior_of_Anchorages_with_Supplementary_Reinforcement_Under_Tension_or_Shear_Forces
Appendix 1. Strength and deformation characteristics for concrete (SFS-EN 1992-1-1 2004,
29)
Appendix 2. Settling details for HILTI HAS-U anchor bolts
Appendix 3. Concrete cone failure verification example
Appendix 4. Concrete edge failure verification example