Dowel Action

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Dowel Action in High Performance

Lightweight Aggregate Concrete

Frank Dehn1, Thomas He2

SUMMARY

Previous investigations showed that a shear force applied to a longitudinally

reinforced beam can be divided up in several components.

In former times the influence of the reinforcement on the total shear force was

underestimated. But several reports indicate that the reinforcing bars are partici-

pating in bearing the shear force applied to beams.

The previously conducted experiments analyze this problem only for Normal

Aggregate Concrete. To evaluate the magnitude of the force borne by the rein-

forcement in Lightweight Aggregate Concrete (LWAC), test series with several

strengths of Lightweight Concrete were carried out.

In the following report various test arrangements, the most important analytical

studies to describe the above mentioned fact for normal concrete, the experimen-

tal results and the conclusions for LWAC are shown.

1 INTRODUCTIONIf the longitudinal reinforcement of a beam is loaded by a component of a force

acting perpendicular to the reinforcement bars this is called dowel action.

1 Dipl.-Ing., Institut fr Massivbau und Baustofftechnologie, Universitt Leipzig2 Dipl.-Ing.(FH), Institut fr Massivbau und Baustofftechnologie, Universitt Leipzig


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There are two possible failure modes of the dowel mechanism:

(1) yield of the bar and concrete crushing under the dowel

(2) concrete splitting lateral or below the reinforcement bars.

The underside concrete cover is the main parameter on which the mode of the

dowel mechanism depends. The more frequent case is failure mode (2) if consid-

ering reinforced beams because of their small concrete cover in comparison with

the bar diameter.

The comparison of the concrete cover with the net width bct at the side of the bars

determine if the splitting cracks open either at the bottom or at the side of a cross

section. In beams with usual dimensions the opening of the crack at the side of

the reinforcement is the more usual case of failure.

Therefore the following test programmes to determine the dowel-splitting load

were carried out, that is the force at which the concrete splits.

2 TEST PROGRAMME

Dowel tests were carried out and reported by several investigators. All of themdeveloped a test arrangement that makes it possible to isolate the dowel effect

from the other components of shear capacity. Because of this they produced sepa-

rated specimens.

Fenwick [6] carried out tests on two separate specimens, with short dowel and

long dowel (fig. 1). The short dowel was intended to model the conditions in a

beam between cracks and the long one to model the conditions at the end of the

beam beyond the last crack.

Fig. 1: Fenwick short dowel and long dowel [6]


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Such test arrangement has the disadvantage, that the steel is not under tension and

cannot exactly model the behaviour of dowels in beams. These tests therefore

obtained lower values for the dowel-splitting load as in reality.

Lorentsen [5] carried out tests with a divided beam. The vertical division was

formed by a 1 mm wide oiled plate, removed after casting. In the compression

zone of the beams the concrete was cut out leaving either two 25 mm bars or one

32 mm bar acting over 300 mm length of the compression zone.

This scarely modified the load-displacement relation in comparison with the

reality because of the fact that the bars in the compression zone are constrained at

both ends.

Houde and Mirza [8] developed a test arrangement applying the dowel-splittingload to a halved beam specimen which was fixed in a test rig. Simultaneously the

longitudinal reinforcement could be loaded by a tensile stress.

This arrangement has the advantage of controlling tensile force when applying

dowel load. The real behaviour of dowels in beams can be simulated well. The

disadvantage is the expensive test rig, in which the beam has to be tested.

Fig. 2: Lorentsen [5]

Fig. 3: Houde and Mirza [8]


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Krefeld and Thurston [1] carried out nine tests on divided beams in which the

tension zone was casted separately from the compressive zone and was fixed to it

only by the main steel. The dowel was tested by pulling the centre section of the

beam downwards until the dowel splits. This arrangement has the advantages that

it is beam-like in layout, the main steel being in tension throughout the test and

that the test has a simple arrangement. The dowel shear force and the tensile steel

stress are related to each other by the geometry of the test specimen.

Fig. 4: Test specimen for the LWAC investigation

Because of the beam-like behaviour of the load-displacement relation and the

simple arrangement, Taylor [4] and Baumann/Rsch [2] chose a modification of

the Krefeld/Thurston [1] test arrangement.

Taylor [4] tested smaller beams with scaled dimensions and aggregates for the

concrete mix.

For the experiments of the presented research work with Lightweight Concrete

the layout of beams of the Baumann/Rsch [2] test series was used (fig. 4). It was


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intended to have a comparison of beams made of Normal Aggregate Concrete

with some made of LWAC.

The test beam has two cross sections. The section B-B of the beam consists onlyof the compression zone which is more narrow than as the section A-A because of

the device for applying shear loads.

To prevent shear friction in the defined inclined crack a plastic foil was placed

between test beam and separated beam. For the longitudinal reinforcement two 20

mm bars and four 8 mm stirrups where used. The only variable parameter of the

test was the compressive strength of the Lightweight Concrete. The centre section

was casted with Normal Concrete. For the beams a series with the following

concrete strengths were planned:

LC 16/18, LC 20/22, LC 40/44, LC 45/50, LC 60/66

At the place of the stirrups (in the middle section) at each side of the beam the

dowel displacement was measured to find out whether the separated beam cocked

during the test and to determine the load-displacement relation.

3 EXPERIMENTAL RESULTS3.1 Load-displacement relationDiagram 1 (fig. 5) shows the load-displacement relation of the beams made out of

the mentioned several strengths of the LWAC. In the diagram the lower axis

describes the load-displacement relation at a displacement of 0 2 mm and the

upper the values of the displacement of 0 14 mm.

It shows that after the dowel splitting load is reached up to a displacement of 2

mm the load keeps nearly constant. By increasing further the dowel load the

mechanism is able to bear higher loads up to displacements of 14 16 mm. This

can be explained by the fact that if the dowel splitting load is reached, the hori-

zontal crack spreads out to the support and the dowel load keeps constant. When

the crack reaches the stirrup at a distance of 15 mm from the flexural crack the

dowel load increases.

Further, the lower curves show that specimens with the higher strengths are able

to bear higher loads at the same values of displacement. This is connected with

the relation of the compressive and tensile strengths of concrete.


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4 CONCLUSIONS4.1 Analytical studies of the previous test results to determine the dowel

force

Here only the models are treated whose test results are coming from a modifica-

tion of the Krefeld/Thurston [1] test arrangement. Further the mathematicalmodel of Vintzeleou/Tassios [7] will be considered.

4.1.1 Several equations for the prediction of dowel force

Krefeld/Thurston [1] determined the force at which the dowel consisting out of

two bars splits as follows:

Fig. 5: Load-displacement relation for LWAC beams

GFI

GD

IE+ EE

F NE

F N

F U

+

+

=

0

5

10

15

20

25

30

35

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

Vertical displacement [mm]

= 0,0 - 2,0 mm

DowelForceH[

kN]

0 2 4 6 8 10 12 14

Vertical displacement [mm]

= 0,0 - 14,0 mm

LC 60/66

LC 45/50

LC 40/44

LC 20/22

LC 16/18


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In contrast to the equations of Taylor [4] or Baumann/Rsch [2] the dowel split-

ting strength depends on the distance of the flexural crack to the support.

The dowel force up to a displacement of 0,17 mm estimated by Taylor [4] is of

the form:

in which the dowel splitting force is

After the displacement reached the value 0,17 mm the dowel load drops to 0,5 H crand keeps constant.

Baumann/Rsch [2] developed the following formula to determine the dowel

force:

In this equation, only the bar diameter, the net width bct and the concrete strength

are variables. Despite of the simplicity of this equation, in comparison with the

test results the determined dowel force fits the experimental values reasonably

well.

The investigations of Vintzeleou/Tassios [7] are based on a mathematical model

in which the bar is considered as a beam on an elastic foundation. By determining

the compressive force under the bar, a tensile force lateral the bars has to be

equilibrated (4.1.3). So for the dowel splitting force the equation:

is given in which the variable takes a possible bending moment into account.Because of the fact, that the bending moment results from the flexural crack

width (about 1,0 2,0 mm), the moment has low magnitudes. Therefore values of

1,95 1,98 are describing the influence of the bending moment sufficientlyexact.

4.1.2 Comparison of the calculated values of dowel force with the test results forNormal Concrete

In this investigations several models where analyzed and compared with the ex-

perimental results found in the literature. Diagram 2 and 3 (fig. 6, 7) show the

calculated dowel forces in comparison with the test results of Baumann/Rsch [2]

and Krefeld/Thurston [1].

[ ] IFF+F W

LVF U

++=

F U

++ =

IEG+ F NF WEF U

=

IGE+F WEF WF U


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How expected, the calculated values of Krefeld/Thurston [1] and Baumann/Rsch

[2] correspond best with the test results of their own models.

0,00

3,00

6,00

9,00

12,00

15,00

0,00 3,00 6,00 9,00 12,00 15,00

Hcr experimental [kN]

H

crcalculated[kN]

Krefeld, Thurston

Taylor

Baumann/Rsch

Vintzeleou, Tassios

Hcr calc/Hcr exp = 1,0

Fig. 7: Comparison of the calculated with the experimentallly determinedvalues of Krefeld/Thurstons test series [1]

0,00

3,00

6,00

9,00

12,00

15,00

18,00

0,00 3,00 6,00 9,00 12,00 15,00 18,00

Hcr experimental [kN]

Hcrcalculated[kN] Krefeld, Thurston

Taylor

Baumann/Rsch

Vintzeleou, Tassios

Hcr calc/Hcr exp = 1,0

Fig. 6: Comparison of the calculated with the experimentally determinedvalues of Baumann/Rsch [2]


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Although the dowel forces calculated by Baumann/Rsch [2] in the Kre-

feld/Thurston [1] test series are unsafe it was shown, that Baumanns formula fits

the real values of dowel splitting force reasonably well.

The Krefeld/Thurston model [1] describes the real behaviour of the dowel force

also well with the difference, that his equation has not such a simple form like

those of Baumann/Rsch [2].

In diagram 2 (fig. 6) and in comparison with other models, it was shown that

Taylors [4] investigations are too empirical. The term 9,1 in his equation (4.1.1)

is too high in comparison with the remaining term, which describes the influence

of the net width bct and the concrete tensile strength fct.

Despite of the fact, that Vintzeleou/Tassios [7] did not carry out tests to support

their theoretical investigations, their model fits well the test results of several

series. It is astonishing that the models of Vintzeleou/Tassios [7] and Bau-

mann/Rsch [2] have the same parameters. That is why the model of

Vintzeleou/Tassios [7] was chosen for the consideration of dowels in Lightweight

Aggregate Concrete.

4.1.3 Mathematical model for dowel action in Lightweight Concrete

By considering the plane which goes through the center of gravity of the rein-

forcing bars the dowel load causes compressive stresses under the bar and tensile

stresses lateral the reinforcement (fig. 8).

To determine the dowel splitting load, it is necessary to find out the magnitude of

compressive forces under the bars up to the point where the stresses along the bar

Fig. 8: Distribution of compressive and tensile stresses


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are zero. The bars can be considered as beams on an elastic foundation. The dis-

tribution of stresses along the bar can be described as a function [9]. If the con-

crete would not be able to bear tensile stresses, the bars and the cover below

would separate and the beam splits. From the distribution of tensile stresses along

the bar up to the point where the compressive stresses are zero (fig. 8, left) the

resulting tensile force has to be determined. In contrast to the model of

Vintzeleou/Tassios [7] which compares the concrete tensile strength fct with the

tensile stresses from the loaded reinforcement to estimate the dowel force, it can

be determined more exactly by attaching the fracture mechanic behaviour of

concrete under tensile stresses [10].

The further investigations will analyze how far these assumptions are corre-

sponding with the real behaviour of perpendicular loaded reinforcements in

beams.

4.2 NotationH dowel force across one flexural crack

Hcr dowel force across one flexural crack, at which the dowel splits

cs side cover to bars in dowel test specimen

ci distance between bars in dowel test specimen

cb bottom cover to bars in dowel test specimen

b width of concrete cross section

bct net width of concrete cross section [bct = b (cs + ci)]db bar diameter

fct concrete tensile strength

fck concrete compressive strength (150 x 300 mm cylinder)

a shear span

shear displacement across flexural crack percentage of reinforcement

REFERENCES

[1] Krefeld/Thurston: Contribution of longitudinal steel to shear resistance of

reinforced concrete beams, ACI-Journal, Vol. 63, 1966, pp.325-344

[2] Baumann/Rsch: Versuche zum Studium der Verdbelungswirkung der

Biegezugbewehrung eines Stahlbetonbalkens DAfStb, Heft 210, 1970


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[3] Soroushian, Obaseki, Rojas, Sim: Analysis of dowel bars acting against

concrete cover ACI-Journal, Vol.84, 1987, pp.170-176

[4] Taylor: Investigation of the dowel shear forces carried by the tensile steel

in reinforced concrete beams Cement and Concrete Association, Techni-

cal Report, No. 431, Nov 1969

[5] Lorentsen: Shear and bond in prestressed concrete beams without shear

reinforcement Stockholm, svenska Forskningstitutet fr Cement och Be-

tong, 1964. pp. 195

[6] Fenwick: The shear strength of reinforced concrete beams PhD thesis,

University of Canterbury, Christchurch, 1966, 172pp

[7] Vintzeleou/Tassios: Mathematical models for dowel action under mono-

tonic and cyclic conditions Thesis submitted to the department of civil

engineering, National technical university of Athens

[8] Houde/Mirza: A finite element Analysis of shear strength of reinforced

concrete beams Detroit, American Concrete Institute 1974 ACI Special

Publication SP 42-5. Vol. 1. pp. 103-128

[9] Beyer: Die Statik im Stahlbetonbau Springer Verlag Berlin Heidelberg

New York pp. 141-150

[10] Brameshuber: Bruchmechanische Eigenschaften von jungem Beton,

Dissertation Karlsruhe 1988, Schriftenreihe Institut fr Massivbau und

Baustofftechnologie Heft 5


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