Translation of the reviewed German paper published in 5. …€¦ · · 2017-11-11Translation of the reviewed German paper published in 5. Jahrestagung des DAfStb in Kaiserslautern,

Translation of the reviewed German paper published in 5. Jahrestagung des DAfStb in Kaiserslautern, September 2017

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Design of Anchor Fastenings with Elastic Base Plates

Subjected to Tension and Bending

Longfei Li 1)

1 Dr. Li Anchor Profi GmbH

Abstract

For the design of anchor fastenings with base plates under the combined loadings of tension and

bending, FprEN 1992-4 (EC2, part 4) [1] dictates that the anchor tension forces are distributed in a linear

fashion assuming that the base plate remains flat. To fulfill this condition, the base plate must be

sufficiently stiff or rigid so that relative deformation caused by bending is negligibly small. The condition

for a rigid base plate has been studied and discussed for decades without a satisfactory solution. The

latest investigations show that the required thickness for the rigid base plate can be so great in many

application cases that it cannot be used in practice. This is confirmed by Schneider's statements of 1999

and 2014 [10, 11] that the assumption of rigid base plates seems to be useless for the calculation of

anchor tension forces for plates with normal thicknesses. That means, for base plates of normal

thicknesses, the bending deformations of the base plate must be considered in the design and an elastic

base plate model must be used in practice.

In this paper, the regulations in FprEN 1992-4 for the calculation of anchor tension force are analyzed.

The special features for the design of anchor fastenings with elastic base plates are explained and

discussed by calculation examples using a third-party design software for headed studs and post-

installed anchors [2].

Keywords: Base plate stiffness, beam theory, rigid base plate, elastic base plate

1. Introduction

The derivation of action loads in anchors is generally regulated by section 6.1 of FprEN 1992-4 [1]

as follows:

6.1 (2) The actions acting on a base plate shall be transferred to the anchors as statically equivalent

tension and shear forces.

6.1 (4) … prying effects shall be explicitly considered in the design of the anchor (see Figure 1.1).

Prying forces Cpr arise with deformation of the base plate and displacement of the anchors.

6.1 (5) In general, elastic analysis may be used for establishing the loads on individual anchors both at

ultimate and serviceability limit states.

Section 6.2.1 of FprEN 1992-4 [1], however, allows the calculation of the anchor tension forces as

if it follows the “beam theory” (Fig. 1.2), or analogous to Bernoulli's hypothesis assuming a linear

distribution along the base plate and a linear stress- strain relationship assuming the base plate is

sufficiently stiff. The condition of sufficient base plate rigidity is defined by FprEN 1992-4 in 6.2.1 (2) as

follows:

a) the base plate remains elastic under design actions (σEd ≤ σRd) and

b) its deformation remains negligible in comparison with the axial displacement of the fasteners.

If this requirement for the deformation is not fulfilled, the elastic deformation behavior of the base plate

has to be taken into account to determine the design value of tension forces acting on each fastener.

From the above-mentioned regulations, the following questions arise:

1) How accurate must the calculation model or calculation assumption be, with which the calculated

anchor tension forces can be treated as equivalent in comparison to the real anchor tension forces in

base plates according to section 6.1 (2) of FprEN 1992-4 [1]?

2) How can the prying effects be considered in the anchor design?

3) Does the beam theory in section 6.2.1 of [1] correspond to the prescribed elastic analysis of section

6.1?


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4) What is the sufficient level of base plate stiffness, according to [1], to justify the use of the beam

theory assumption for the calculation of anchor tension forces?

5) If the sufficient level of base plate rigidity according to section 6.2.1 (2) of [1] cannot be verified or

cannot be achieved, how can the elastic bending deformation of base plate be considered when

calculating the anchor tension forces?

6) If the anchor tension forces are determined taking account of the elastic deformations of the base

plates, can the anchor resistances be calculated according to the existing clauses of [1]? That means,

are the design methods in [1] suitable for elastic base plates?

These questions are to be examined, discussed and potential answers to be put forward in the following

sections with design examples from [2].

Definition:

The rigid base plate is defined as a fictitious base plate with infinite bending stiffness so that its

plane surface remains planar under the combined actions of tension and bending loadings. As a result,

the tensile force distribution of anchors is linear, much like that in the beam theory (Fig. 1.2).

An elastic base plate, on the other hand, takes into account the plate’s flexural deflection in the

determination of anchor tension force distribution. Such a model can provide more precise anchor

tension force distribution that matches more closely the actual behavior of anchor fastening with base

plate.

Fig. 1.1 Example for prying force [1]

Fig. 1.2 Fastening with a rigid base plate in

which the anchor tension forces are calculated

by beam theory [1]

2. Current situation about base plate thickness design

2.1 General information

In Europe, there have been directives or specifications [3, 4, 5, 6] for the design of anchor fastenings

with base plate since 1997. These are yet to be transferred to a European standard [1]. For calculating

the anchor tension forces on base plates, the beam theory is prescribed, provided that the base plates

must be sufficiently rigid. For the proof of the adequate base plate stiffness, experts have been

researching and discussing for decades without consensus [7, 8, 9, 10, 11]. This has led to the currently

very different base plate thickness design methods. These are reviewed in the following 2 calculation

examples.


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2.2 Calculation example 1 for base plate thickness design

Fig. 2.1 shows an anchor group with four anchors. The actions of tension load and bending moments

about the x- and y-axis are transferred into the concrete by means of a connection profile HE 160 B on

a base plate via 4 anchors. The profile is welded onto the base plate.

Fig. 2.1 Calculation example 1 for an anchor group with 4 anchors

Two anchor systems were investigated. A system with anchor stiffness of 50.6 kN/mm under SLS

simulates a mechanical anchor M12. Another system with anchor stiffness of 147.5 kN/mm under SLS

simulates a bonded anchor M12 with a continuous metric thread rod. With this example, 6 anchor design

programs currently used widely in the industry were tested and results from the tests were compared.

The required thicknesses for an equivalent rigid base plate from the tested programs are shown in figure

2.2. These vary from 13 mm to 48 mm.

Fig. 2.2 Recommended base plate thicknesses for a rigid base plate produced by different

programs widely adopted in the industry, calculation example 1

Figure 2.3 shows the highest anchor tension forces (anchor No.3, Fig. 2.1) as a function of the base

plate thickness. In case of beam theory, the base plate is assumed to be rigid and the calculated highest

anchor tension force is therefore independent on the base plate thickness.

When using the elastic base plate model [2], the highest anchor tension force decreases with

increasing base plate thickness which suggests a more linear distribution as base plate thickness

increases. In fact, the decisive parameter in determining the anchor tension force distribution is the plate

flexural stiffness relative to the axial stiffness of the anchors. For example, with the base plate thickness


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fixed, anchor with lower stiffness will also lead to more linearly distributed anchor tension forces. With a

base plate thickness of 34 mm, the anchors with the axial stiffness of 50.6 kN/mm results in

approximately the same highest anchor tension force from the elastic base plate as that from the rigid

base plate. As the axial stiffness of the anchors increase to 147.5 kN/mm, to achieve the same

comparable highest anchor tension force between the rigid and elastic base plate, the required plate

thickness is about 49mm. At a (practical) base plate thickness of 15 mm, the differences in the highest

anchor tension forces between the elastic and rigid base plate are respectively in the region of 30% for

an anchor stiffness of 50.6 kN/mm and (increased to) 35% for an anchor stiffness of 147.5 kN/mm.

Fig. 2.3 Calculated highest anchor tension force at anchor No. 3 in the group as a function of

base plate thickness and anchor stiffness (rigid base plate from all programs

No. 1-6, and elastic base plate from program No. 6 [2])

Figure 2.4 compares the distribution of the tension and compression forces between the elastic base

plate (tfix = 15mm) and the rigid base plate (beam theory). In the case of the elastic base plate, the inner

lever arm is significantly smaller than in the rigid base plate. This results in the difference between the

determined highest anchor tension forces.

a) Elastic base plate (tfix=15mm) b) Rigid base plate (beam theory)

Fig. 2.4 Comparison of anchor tension and concrete compression forces between elastic base plate

(tfix = 15mm, anchor stiffness 147.5 kN / mm) and rigid base plate (beam theory) [2]


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To clarify why the calculated base plate thicknesses (Fig. 2.2) are so different, the used different

calculation methods are analyzed as follows.

The base plate thickness calculated by the software programs No 1 - 5 is using the stress condition

(Fig. 2.5 b)) as follows:

1) The tension forces in anchors and the compression forces onto the concrete are first calculated with

the assumption of a linear strain distribution along the base plate according to the beam theory (Fig.

1.2).

2) These calculated forces, together with the applied force from the steel profile are then treated as

external loads to the base plate to determine the plate thickness. The base plate is assumed to be a

free body and is analyzed by means of a finite element method. The base plate itself is made sure to

remain in the elastic range

3) With the condition that the maximum stress in the base plate of 2) does not exceed the yield stress

of the base plate, the base plate thickness is determined.

In this calculation, the anchor displacement, the concrete and base plate deformations and the

compatibility of their deformations (between the calculation steps 1 and 2) are not considered. Therefore,

this approach contradicts clearly with the elastic analysis of the investigated total system with concrete,

anchors, base plate and steel profile acting together. The base plate thickness tfix thus determined is

found to be relatively thin. From this analysis, it can be stated that an accurate anchor tension force

distribution cannot be in general generated base on the beam theory. The beam theory approach may

only give adequate anchor tension force distribution when the base plate has sufficiently large

thicknesses such as a beam section with a constant cross section over a certain length tfix, for example,

with a load propagation angle α up to a maximum of 45 ° (Fig. 2.5 b) above).

a) Elastic base plate b) Rigid base plate

Fig. 2.5 Comparison of behaviors between elastic and rigid base plate

For software No. 6 [2], the base plate thickness is determined with the stiffness condition according

to [8]. It is determined in such a way that the difference between the highest anchor tension forces

calculated with the beam theory and the elastic base plate model is within a tolerance of 3% (see Figure

2.3).

In the case of the elastic base plate model (Fig. 2.5 a)) [2], it is assumed that the base plate is

elastically bedded onto the concrete in the compressive regions of the base plate. This is similar to the

plate on elastic foundation problem. The anchors are simulated using elastic springs supporting the


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base plate in the tension region. The forces from the steel profile are calculated using the beam theory

and applied to the base plate as external loads. With the following parameters of the partial components

of base plate, anchors and concrete, the entire fastening system is calculated by Kirchhoff's plate theory:

1) Base plate thickness tfix and associated modulus of elasticity.

2) Anchor spring constant or anchor stiffness under SLS.

3) Concrete bedding factor to simulate elastic foundation.

The calculation takes several iterative steps to make sure that the system is in equilibrium and no

components violate the rules that concrete only takes compressive forces and anchors take tensile

forces. The investigations in [8] showed that this elastic base plate model can very accurately simulate

the anchor tension force distribution. This model corresponds to the elastic analysis prescribed in [1]

better than the beam theory approach.

2.3 Calculation example 2 for base plate thickness design

Figure 2.6 shows an anchor group with 8 anchors. The actions of tension load and bending moments

about the x- and y-axis are transferred to the concrete by means of a connection profile HE 400 A welded

onto a base plate via 8 anchors.

Fig. 2.6 Calculation example 2 with 8 anchors

The system shown above has an anchor stiffness of 50.8 kN/mm at SLS and simulates the head

studs M12 with the anchorage depth of hef = 72 mm. With this example, 5 design software programs

that are widely used in the industry were investigated. The thicknesses required for a rigid base plate

obtained from these programs are shown in Fig. 2.7. They vary from 11 mm to 87 mm.

The majority of tested programs recommended a design base plate thickness of 20 mm for this

example (Fig. 2.7 No. 1-3). Using this plate thickness, the anchor tension and concrete compression

force distribution with the elastic base plate model [2] is reproduced. Comparing the anchor tension


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force distribution between the elastic base plate with the plate thickness of 20 mm (Fig. 2.8) and the

assumed rigid base plate (Fig. 2.9), the differences are observed as follows:

- The highest anchor tension force is not at anchor No.6, but at No. 4 (Fig. 2.8, using the elastic plate

model).

- The assumption of the rigid base plate underestimates the highest anchor tension force by 73.6% (=

100 x (15.1-8.7) / 8.7)

This difference shows that the assumption of the beam theory approach for the recommended base

plate thickness of 20 mm does not provide an equivalent anchor tension force distribution.

If the base plate thickness is increased to 87 mm, the results from [2] are as follows:

- The highest anchor tension force is now also at anchor No. 6 (Fig. 2.10).

- The difference between the highest anchor tension forces between the rigid base plate (Fig. 2.9)

and the elastic base plate is -0.15% <3% (= 100x (8.696-8.709) / 8.709).

Thus, the stiffness condition of [8] is satisfied.

Fig. 2.7 Recommended base plate thickness for a rigid base plate from different software of current

practice, calculation example 2

Fig. 2.8 Calculated distribution of anchor and concrete forces for a plate thickness of 20 mm [2]

From the calculation examples 1 and 2 the following points become clear.

- The base plate thicknesses currently determined with the stress condition are clearly unconservative

(see the determined base plate thicknesses of programs No. 1-5 in Fig. 2.2 and Program No. 1-4 in Fig.

2.7). The reason for this is that the distribution of the tension and compression forces calculated with

the beam theory approach does not match the base plate thickness recommended by the programs; i.e.

No compatibility of deformations from base plate, anchors and concrete is considered.


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- To achieve an equivalent distribution of the tension and compression forces as in the case of the beam

theory approach, the base plate thicknesses are unrealistically large for these common application

examples (see the determined base plate thicknesses of program No. 6 [2] in Fig. 2.2 and 2.7).

The investigation with the calculation examples shows that the beam theory approach cannot

generally be used for the determination of the anchor tension force distribution. To use the normal base

plate thickness, the flexural deformation of the base plate must be considered in the calculation (see

next section).

Fig. 2.9 Calculated distribution of anchor tension and concrete compression forces according to

beam theory approach [2]

Fig. 2.10 Calculated distribution of anchor tension and concrete compression forces at a base plate

thickness of 87 mm using elastic base plate model [2]

3. Design with elastic base plate

As shown in the calculation example 2 of section 2, the anchor tension forces are generally not evenly

distributed in the anchor group with 8 anchors with a normal base plate thickness depending on the

profile arrangement. For this, the design model in FprEN 1992-4 [1] cannot be used for the calculation

of the resistance at concrete cone failure of the anchor group because the factor ψec, N (see [1], section

7.2.1.4, (6), eq (7.6)) is not applicable for considering the load eccentricity of the unevenly distributed

anchor tension forces [12].

Figure 3.1 shows a recalculation of test results from [8]. The anchor group with 9 headed studs [13]

was tested with a base plate (tfix = 15mm) subjected to a centric tension load until failure. The calculated

concrete cone failure load using rigid base plate is approximately 136 kN. In the test, however, the group

failed at a much lower tension load of approximately 94 kN, since the anchor in the middle failed due to

a higher load than that from a rigid base plate calculation (see Fig. 3.1, right).

If the tested group is designed according to [1], a design resistance of 90.7 kN results in the concrete

cone failure of the group. The available partial safety factor is γMc = 94 / 90.7 = 1.04. This is substantially

less than the minimum required of γMc = 1.5. The reason for this is that the anchor tension forces which

are not evenly distributed result from the reduction factor ψec,N for the load eccentricity due to the double

symmetry of the anchor forces to ψec,N = 1.0 (according to [1]).


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For this reason, in [8] an additional proof for concrete cone failure or combined pullout and concrete

cone failure of the anchor group was proposed as follows for the elastic base plates (Fig. 3.2)

ψec,N =1,0 (3.1)

NEd h ≤ NRd,c /n (3.2)

with NEd h: Highest anchor tension force in the Group

NRd,c: Design anchor resistance of anchor group at concrete cone failure with ψec,N =1,0

n: Number of anchors subjected to tension load in the group

The comparison of the calculated results with tests show that the proposed additional proof is

conservative [8].

The design with elastic base plates with this additional proof is explained in detail in the next section

with several design examples.

fc,150 = 43.4 N/mm², hef =65 mm, tfix=15mm,

Fig. 3.1 Calculated anchor tension force distribution in the anchor group with 9 anchors [8]

Fig. 3.2 Illustrative representation of the additional proof for elastic base plates [8]


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4. Design examples with elastic base plates illustrating the proposed additional proof

4.1 Anchor group with 8 anchors under tension load

The anchor group with anchor layout shown in Figure 2.6 (section 2.3) is loaded under a tension load

NEd of 120 kN through the connection profile (Fig. 4.1). For most current software, the design is

performed as follows:

- The anchor force is calculated on the assumption of rigid base plates with NEd, i = 120/8 = 15 kN per

anchor without load eccentricity in the group.

- The resistance of the group is calculated with these anchor tension forces.

- The base plate thickness is then determined with the anchor tension forces of 15 kN per anchor and

the forces from the steel profile on the base plate with FEM under the stress condition that the max.

stress in the base plate does not exceed its yield point. This results in a required thickness of

approximately 19 mm.

This example was calculated with elastic base plate (tfix = 20 mm) and with headed studs d16 x 175

(Fig. 4.1) [2]. The anchor stiffness of 119.4 kN/mm was calculated with the anchor length, the shaft cross

section, the shoulder area of the headed stud and the concrete bedding factor according to [8].

The calculated anchor tension force distribution is shown in Fig. 4.2. It is obvious that the anchor

tension force is distributed in the base plate by the stiffness of the anchor position in the base plate. The

anchors No. 4 and 5 are located closest to the flange of the connecting profile and thus receive the

highest tension force in the group. This anchor tension force of 30.5 kN is more than twice as high as

that according to the beam theory approach (i.e., rigid base plate).

Fig. 4.1 Boundary condition of the design example 4.1

The detailed calculation of the group resistance for concrete cone failure is given in Tables 4.1 and

4.2. The anchor group with the rigid base plate has the resistance utilization of 100x120/253.7 = 47%

(table 4.1, with Nsd = 142.141 kN minus the plying force of 22.141 kN). With the elastic base plate, the

resistance utilization is 56% without considering the load eccentricity (Table 4.1) and 96% with additional

proof (Table 4.2).


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For the anchor layout of the design example 4.1, one current design software from an anchor

manufacturer recommends a bonded anchor of M12 with ETA (European Technical Assessment) in

cracked concrete C30/37 using the following parameters at resistance utilization of 97% (<100%):

- anchorage depth hef of 70 mm

- Required minimum base plate thickness of 19 mm

A comparative calculation based on an elastic base plate with hef = 70 mm and tfix = 19 mm [2] with

the same product, however, yields the anchor tension force distribution shown in Fig 4.3. The highest

anchor tension force thus determined is more than twice as high as in the case of a rigid base plate.

Since the available anchor spacing is s = 220mm (> 3hef = 210mm), the resistance utilization for the

elastic base plate is 31.7 / 15 x 97 = 205% >> 100%. For a safe fastening with the base plate thickness

of 20 mm, an anchorage depth hef of 180 mm would be required instead with the above-mentioned

product [2].

Fig. 4.2 Calculated anchor tension force

distribution of the anchor group in Fig. 4.1 [2]

4.3 Calculated anchor tension force distribution

with hef =70 mm and tfix =19 mm [2]

Table 4.1 Calculation of the group resistance in the case of concrete cone failure with an elastic

base plate without consideration of load eccentricity [2]

Table 4.2 Additional proof for elastic anchor plate [2]


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In design example 4.1, a safety gap with a factor of 2 in the current design of the base plate thickness

with stress condition (program No. 1-5, Fig. 2.2 and 2.7) can be observed. Reasons for this are as

follows:

- The anchor tension force distribution from the rigid base plate is not correct for the recommended base

plate thickness of 20 mm. At this base plate thickness, the prying force is already more than 22 kN.

- The factor that the anchor tension forces are not evenly distributed in the elastic base plate with tfix =

20 mm were not taken into account.

4.2 Anchor group with 8 anchors under bending moment

In ACI 355.3R-11 [14], there is a design example with a fastening with 8 headed studs under bending

moment and shear loading. This example is investigated here with the bending moment alone (Fig. 4.4).

From one current design software from an anchor manufacturer, this fastening would be realized with

the following parameters at the resistance utilization of 100%.

- Bonded anchor M12 with ETA and an optimized anchorage depth hef of 105 mm

- Required base plate thickness of at least 28 mm.

The maximum anchor tension force calculated with the rigid base plate approach is 21.1 kN.

However, the comparison calculation with [2] produces the anchor tension force distribution shown

in Fig. 4.5. The highest anchor tension force thus determined is more than twice as high as that from

the rigid base plate approach. The utilization of design resistance for the elastic base plate is 283% >>

100%. For a safe fastening at the resistance utilization of 96%, the bonded anchor M20 from the same

ETA as the size M12 above with the anchorage depth of 280 mm would instead be required.

Fig. 4.4 Boundary condition of design example 4.2


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Fig. 4.5 Calculated anchor tension force distribution with hef =105 mm and tfix =28 mm [2]

Table 4.3 Calculation of group resistance at combined pullout and concrete cone failure with elastic

base plate [2]

4.3 Anchor group with 6 anchors and circular base plate under bending moment

For this example, the boundary conditions are given in Figure 4.6. From one current design software

of an anchor manufacturer, this fastening would be realized with the following parameters at a resistance

utilization of 100%.

- Bonded anchor M12 with ETA and the optimized anchorage depth hef of 139 mm

- Required base plate thickness of at least 13 mm.

The maximum anchor tension force calculated by means of a rigid base plate is 12.2 kN (Fig. 4.7).

However, a comparison calculation with the elastic base plate model [2] yields the anchor tension

force distribution as shown in Fig. 4.8. The highest anchor tension force thus determined is 21 kN. The

resistance utilization for the elastic base plate is much higher at 197% >> 100% (Table 4.4).


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Fig. 4.6 Boundary condition of design example 4.3

Fig. 4.7 Calculated anchor tension force distribution with M12 and rigid base plate [2]

Fig. 4.8 Calculated anchor tension forces with M12 and elastic base plate (tfix =13 mm) [2]


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Table 4.4 Calculation of group resistance at combined pullout and concrete cone failure with

elastic base plate [2]

5. Conclusions

The design of fastenings with base plates is generally regulated by FprEN 1992-4 [1]. For this,

various questions arise during the application. These questions were investigated and discussed in the

present paper. The investigations yield the following results and conclusions.

The assumption of the linear strain distribution along the base plate (the beam theory approach) in

[1] section 6.2.1 (1) for the calculation of the anchor tension force distribution is not generally applicable

because an almost unrealistic base plate thickness would be required to obtain an equivalent anchor

tension force distribution as from the beam theory approach. At the practical range of base plate

thicknesses, the real highest anchor tension force can be much higher than that from the beam theory

approach. This is clearly unsafe. These results agree with the advice of ACI 355 [15].

The assumption of the beam theory in [1] section 6.2.1 (1) is in contradiction with the elastic analysis

in [1] section 6.1 (5) because the deformations of base plates and anchors and their compatibility are

not considered.

The plying effects cannot be detected with the beam theory approach. The elastic base plate model

considers the plying force on the base plate naturally.

The stiffness condition in [1] section 6.2.1 (2) is technically questionable and currently not applicable

with ETA conformation because the bending deformations of the base plate and the axial anchor

displacement can only be determined by their deformation compatibility and for that the anchor stiffness

at SLS is required. This anchor stiffness is currently not specified in ETAs.

From the above reasons, a sufficiently stiff or rigid base plate according to [1] section 6.2.1 (2) cannot

be verified. This means that the elastic base plate bending deformations must be considered during the

design. However, this is currently not possible according to [1], because the anchor stiffness required

for the calculation is not specified. In addition, the design model in [1] is not suitable for the elastic base

plate design model [12].

The above situation shows that the rules for the base plates in [1] are contradictory and cannot be

put into practical use. This situation will lead to the fact that no stiffness condition for the base plates

according to [1] can be introduced into the anchor design practice and the base plate thickness is


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determined as before according to the stress condition. As a result, safety gaps exist in the practice of

anchor designs. The following provisions are necessarily recommended to close these safety gaps.

- Add the anchor stiffness at SLS in the anchor specification ETA, e.g. Analogous to ACI 355.2 [16]

- Add the design method for elastic base plates in [1]

Thus, the anchor tension force distribution can be calculated with the elastic analysis and the design

of fastenings can be carried out generally with elastic base plates.

6. Acknowledgments

The research on elastic base plates was promoted by the State of Baden-Württemberg with

Innovationsgutschein B Hightech 2015. At this point, we would like to thank very much!

References

[1] Draft FprEN 1992-4 Eurocode 2 — Design of concrete structures — Part 4 Design of fastenings for

use in concrete, CEN/TC 250 N 1454, 2016-03-17

[2] Dr. Li Anchor Profi GmbH: Third-party anchor design software Anchor Profi 3.1.0, Mai 2017

[3] ETAG 001, Annex C: DESIGN METHODS FOR ANCHORAGES, EOTA, 1040 Brussels, Amended October 2001

[4] EOTA TR029 Design of Bonded Anchors, Edition June 2007, EOTA, 1040 Brussels, Amended

September 2010

[5] Technical specification CEN/TS 1992-4: Design of Fastenings for Use in Concrete, European

Committee for Standardization, 2009

[6] fib bulletin 58: Design of anchorages in concrete, ISSN 1562-3610, July 2011

[7] Fichtner, S.: Untersuchungen zum Tragverhalten von Gruppenbefestigungen unter Berücksich-

tigung der Ankerplattendicke und einer Mörtelschicht, Dissertation Universität Stuttgart 2011

[8] Li, L.: Required Thickness of Flexurally Rigid Baseplate for Anchor Fastenings, proceedings of fib Symposium Maastricht 2017, High Tech Concrete: Where Technology and Engineering Meet, DOI 10.1007/978-3-319-59471-2 109, © Springer International Publishing AG 2018

[9] Li, L.: Erforderliche Dicke für die biegesteife Ankerplatte, Stellungnahme zu CEN/TC 250 N 1454,

Abschnitt 6.2.1 Tension loads, an DIN, NA 005-07-01-01 AK, March 2016

[10] Schneider, H.: Zum Einfluss der Ankerplattensteifigkeit auf die Ermittlung der Dübelkräfte bei

Mehrfachbefestigungen, August 1999 (nicht veröffentlicht)

[11] Schneider H.: Ich glaube mit der Annahme, dass man die Ankerplatten nur ausreichend steif machen muss, um die postulierte lineare Pressungsverteilung (… diese Annahme hat im Übrigen nicht im Entferntesten etwas mit „Elastizitätstheorie“ zu tun!) zu bekommen, wird man keinen Erfolg haben. Ministerium für Umwelt, Klima und Energiewirtschaft Referat 45 Bautechnik, Bauökologie, Kernerplatz 9, 70182 Stuttgart, E-Mail 05 Juni 2014 (nicht veröffentlicht)

[12] DRAFT MINUTES of fib TG 2.9 meeting “Fastenings to structural concrete and masonry” (formerly

SAG 4) TU Dresden (Dresden, Germany) 26-27 October 2015 (not published)

[13] FMPA Stuttgart: Bericht über Belastungsversuche an einbetonierten Kopfbolzengruppen, Bericht

II.4-14 151, 16. Mai 1983 (not published)

[14] ACI 355.3R-11: Guide for Design of Anchorage to Concrete: Examples Using ACI 318 Appendix D,

ISBN 978-0-87031-425-4, ACI May 2011

[15] ACI 355: Seminar “Anchorage to Concrete”, page 163, Email Annex of Ronald A. Cook, Ph.D., P.E., F.ACI, F. ASCE, F.SEI, Professor Emeritus, Department of Civil Engineering University of Florida, 06 April 2017

[16] ACI 355.2: Qualification of Post-Installed Mechanical Anchors in Concrete and Commentary, ISBN

978-0-87031-247-2, ACI 355.2-07

Documents

Translation of the reviewed German paper published in 5. …€¦ · · 2017-11-11Translation of the reviewed German paper published in 5. Jahrestagung des DAfStb in Kaiserslautern,