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DESIGN OF LYING STUDS WITH LONGITUDINAL SHEARFORCE

Ulrich BreuningerStructural Engineers Weischede, Herrmann und Partner, Germany

AbstractInnovative composite cross sections lead to an unusual positioning of the headed studshorizontally in the thin concrete slab. The behavior of this lying studs with longitudinalshear force has been investigated. The results of experimental and numericalinvestigations show that the failure characterized by splitting of the thin slab isinfluenced by different parameters compared to vertically positioned studs. Based on theinvestigations a design rule is presented.

1. Introduction

Composite sections of steel and concrete have a continuous connection between bothparts. In standard composite beams headed studs are welded vertical on the top flange ofthe steel girder as shear connector.

Fig. 1 Composite beam without topsteel flange

Fig. 2 Slim-floor composite beam (1)

The development of innovative composite cross sections for bridges and buildings leadsto modified and new sections of composite beams. The section of Fig. 1, for example,eliminates the less efficient steel top flange by welding the headed studs directly to theweb. For the final usage the concrete slabs serves as top flange. During erection

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sufficient resistance is provided by the precasted concrete web. As a second exampleFig. 2 shows a slim-floor structure. Again the function of the omitted top steel flange istaken over by the concrete slab. The horizontally lying studs allow a very thin slab whichis an advantage also from the architectural point of view.

A strong load transmission between arch and slab for tied arch bridges is achieved byconnecting the slab directly to the stiffening girder, see Fig. 3. Again studs arepositioned horizontally in the slab. Additional advantages of this construction are abetter corrosion protection of the transverse girders and the transverse girder acting ascomposite beam in its entire length.

Fig. 3 Section of a tied arch bridge with lying studs connecting the slab to the stiffeningsteel girder (2)

In contrast to the standard composite beam section the axis of the studs in the sections ofFig. 1, 2 and 3 is not vertical anymore but parallel to the plane of the slab. Thereforestuds arranged this way are called “lying studs”.

Fig. 4 Section through the shear connection oflying studs

cleavage crackscompression

The shear connection of composite beams is dominantly subjected to a longitudinal shearforce. So every lying stud mainly has to transfer a longitudinal shear load into the slab.The concentrated shear load of the stud has to spread across the thickness of the slab thusinitiating compression and tension forces vertical to the extension of the slab (Fig. 4).The tensile forces result in both a splitting action of the thin slab producing cleavage

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cracks parallel to the plate surface and an expansion of the concrete. The failure of theselying studs is mainly due to the splitting of the concrete. Vertical stirrups surround theexpanding concrete and prevent the extension of the cracks.

The design rule for headed studs in Eurocode 4 (3) is based on experimentalinvestigations for conventional vertical studs only and therefore it does not cover thesplitting failure of lying studs. To identify the major parameters for this special mode offailure and to quantify the carrying capacity of lying studs, a comprehensive researchprogram has been carried out(4) (5) (6). In this paper the results are presented.

In design practice the shear connection also can be used to transfer transverse shear loadfrom the slab into the steel girder. The content of a prosecuted research program ispresented in the next paper (7).

2. Experimental investigations

Two different situations of the shear connection with lying studs relative to the concreteslab can be distinguished. In composite girders without a top flange e.g., see Fig. 1 and2, the shear connection is situated in the middle of the concrete slab, whereas theexample of the tied arch bridge of Fig. 3 shows lying studs at the front side of theconcrete slab. Therefore two test series were carried out: series I with the shearconnection in the middle of the concrete slab corresponding to sections in buildings andseries II with the connection at the two edges of the concrete slab corresponding tobridge sections, see Fig. 5 and 6.

AA 800

Section A-A

80-1

30

lineare measure in mm

500

Fig. 5 Test specimen of series I with the shear connection in the middle of the concreteplate

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studs in one row

studs in two rows

300

1190

A

132800132

100

200

100

400

lineare measure in mm

300-

400A

Section A-A

Fig. 6 Test specimen of series II with the shear connection at the edges of the concrete slab

These two series comprising altogether 51 push-out specimens were designed asvariations of a so called basic sample. For a group of at least 3 specimens always onlyone main parameter was varied whereas the other parameters were kept constant. Thefollowing parameters were varied:� strength of concrete� thickness of concrete slab� distance, diameter and length of the studs� number, diameter and situation of the stirrups� tension or compression parallel to the shear force

According to Figure 7 three failure modes were observed in the tests:

a) splitting of the slab,tear off of the studs

If the reinforcement of the concrete is sufficiently strong,the carrying capacity is not reduced immediately aftersplitting and the lying studs suffer high deformations untilfinally the studs tear off.

b) splitting of the slab For low degrees of reinforcement or small distancesbetween stud and slab surface, the carrying capacity of theshear connection starts reducing just after the splitting ofthe slab has first occurred.

c) pull out of the studs In some rare cases, when the lying studs were situated atthe edge of the slab and the studs were too short, the shearconnection failed because of a pull-out of the studs.

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a) Splitting of the plate/tear off ofthe studs

b) Splitting of the plate c) Pull-out of the studs

Fig. 7 Failure modes of lying studs

0

50

100

150

200

0 5 10 15 20 25 30

load per stud [kN]

slip [mm]

Splitting of the slab, tear off of the studs

Splitting of the slab

Pull out of the studs

Fig. 8 Load-slip curves of different failure modes.

Typical load-slip curves of these three failure modes are given in Figure 8. If lying studsfail according to mode a) or b) the load slip curve shows a high carrying capacity a

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ductile deformation behavior beyond. If the failure is caused by pull-out of the studs(mode c), the carrying capacity decreases and the ductility is limited.

3. Variation of the parameters

Beside the experiments numerous numerical investigation were carried out. A non-linearFE program considering the size effect of concrete structures was used (8). Based on theexperimental and numerical investigations the influence of the parameters on thecarrying capacity can be determined

Concrete strengthThe splitting of the slab depending on the concrete tensile strength causes the collapse ofthe shear connection. Because of the well known relation between tensile andcompressive strength the carrying capacity can be described with an exponent functionof the concrete compressive strength that is more usual (Fig. 9).

Fig. 9 Carrying capacity Pe of lyingstuds dependent on theconcrete compressive strengthfc

Fig. 10 Relative carrying capacity P/Pv oflying studs dependent on theeffective edge distance of thestuds ar´ (for different distancesbetween the studs a)

Edge distance of the studsThe carrying capacity depends strong on the effective edge distance of the studs (ar´ =the edge distance of the studs without the concrete cover and a half of the stirrupdiameter) (Fig.10). The influence is big if the edge distance is small. With increasingedge distance (more than 100mm) the influence on the carrying capacity disappears.Also Fig. 11 shows with different FE models the strong influence of the edge distance onthe cleavage cracks in the structure.

0

30

60

90

120

150

180

0 10 20 30 40fc [N/mm2]

Pe [kN]

Test series I-6Test series II-1

K (fc/30N/mm2)0.4

0.7

0.8

0.9

1.0

1.1

1.2

20 40 60 80 100 120 140 160 180ar´ [mm]

Test series I-1Test series I-2Test series II-2FE

P/Pv [-]

K (ar´/80mm)0.4

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x

ar´ = 30 mm

ar´ = 75 mm

ar´ = 120 mm

Fig. 11 Cleavage cracks following main strains at maximum carrying capacity (black areasshow a strain ≥ 5 ‰)

Reinforcement of the slabFig. 11 shows the importance of the reinforcement in the slab. The stirrups andespecially the intersection between stirrups and longitudinal reinforcement is used asanchoring for the cracks. It can be concluded, that the carrying capacity increases withthe amount of stirrups per stud because this leads to more anchoring points. The effect ofstirrups with a greater diameter on the carrying capacity can be neglected.

The longitudinal distance between the studs and the stirrups has no decisive influence onthe carrying capacity. The support of the stirrups for the shear connection is still intact.This means that assembling inaccuracies are of less importance.

A minimum reinforcement is necessary for the cleavage tensile forces. According to (9)and to the magnitude of strains in the stirrups of the specimens, the reinforcement shouldbe dimensioned for the splitting force Zd

)´a

d(10.3PZr

dd �� [1]

Where Pd is the longitudinal shear design force.

deformation direction

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Length of the studsIf the studs are not long enough a premature pull-out failure occurs (compare Fig. 7c).This phenomena is explained very well in (10). To prevent this brittle failure the studshave to be anchored with an overlapping v behind the stirrups. The overlapping dependsif the concrete is cracked or not.

uncracked concrete: � ≤ 30°v ≥ 110 mm; v ≥ 1.7 ar´; v ≥ 1.7 s/2

cracked concrete: � ≤ 23°v ≥ 160 mm; v ≥ 2.4 ar´; v ≥ 2.4 s/2 [2]

Further parametersAlthough not shown by data presented here the following additional conclusions followfrom the investigations:� An increase of the diameter d of the stud leads to a higher carrying capacity of the shear

connection.� If the distance a between the studs and the distance s between the stirrups increases by

the same amount the carrying capacity stays on the same level.� For a concrete slab in tension, e.g. the slab of the tied arch bridges the carrying capacity

of the lying stud is insignificantly lower than for the slab in compression.

4. Design rule

Derived from the experimental (4), (5) and numerical (6) investigations the followingdesign rule for the carrying capacity of lying studs with failure because of cleavagecracks is proposed.

v

0.30.4

rckspRd,1A

sa´)ad(f42.1P

���

���

��� [3]

PRd,sp design resistance [kN] (index sp from german spalten)fck compressive strength of the concrete [N/mm2]19 mm ≤ d ≤ 25 mm diameter of stud [mm]50 mm ≤ ar´ distance between studs and stirrups vertical to the force

[mm]110 mm ≤ a ≤ 440 mm distance between studs parallel to the force [mm]s/ar´ ≤ 3 distance between stirrups / distance between studs and

stirrupsa/2 ≤ s ≤ a distance between stirrups [mm]A = 1.00 modification factor if the shear connection is situated at

the edge of the slab= 1.14 modification factor if the shear connection is situated in

the middle of the slabds ≥ 8 mm stirrup diameter [mm]�v = 1.25 partial safety factor according to Eurocode 4 (3)

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da

s

section A-A

headroom of the stud

concrete cover

concrete cover v

h

ar

sß d

a'r

+ d 2

s

+ d 2

s

Fig. 12 Designation of the geometrical parameters of the shear connection with lying studs

Formula [3] can be used under the following conditions:� The stirrups are able to bear the splitting forces according to formula [1].� The overlapping v of the studs fulfils formula [2].� The above limited parameters are checked.� The carrying capacity for standard studs in Eurocode 4 (3) is not exceeded.

Fig. 13 compares the carrying capacity of lying studs with standard studs according toEurocode (3) for one diameter.

0

30

60

90

120

150

15 20 25 30 35 40 45 50fck [N/mm2]

PRd [kN]

Eurocode 4 (3)Formula [3] with ar´ = 90 mmFormula [3] with ar´ = 70 mmFormula [3] with ar´ = 50 mm

d = 22 mmfuk = 500 N/mm2

a/s = 1A = 1.14

0

30

60

90

120

150

15 20 25 30 35 40 45 50fck [N/mm2]

PRd [kN]

Eurocode 4 (3)Formula [3] with ar´ = 130 mmFormula [3] with ar´ = 110 mmFormula [3] with ar´ = 90 mmFormula [3] with ar´ = 70 mmFormula [3] with ar´ = 50 mm

d = 22 mmfuk = 500 N/mm2

a/s = 1A = 1.00

a) shear connection in the middle of theconcrete plate

b) shear connection at the front side of theconcrete plate

Fig. 13 Design resistance of lying studs compared to studs in standard compositesections

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5. Conclusion

Stimulated from new composite cross sections and with the aim to support thedevelopment of further new composite constructions the carrying behavior of lying studsis investigated. First efforts are carried out to describe the carrying behaviour of lyingstuds for longitudinal shear. They lead to a practical design equation. Followinginvestigations will study lying studs under vertical and combined shear force and as wellas fatigue. At the moment the ”Institut für Konstruktion und Entwurf” of the Universityof Stuttgart is continuing the work in this field of research.

I would like to thank the “Bundesministerium für Verkehr” and the “Deutsches Institut fürBautechnik” for their support. They sponsored the experimental and numerical research.

6. References

1 Muess, H. (1996); ”Interessante Tragwerkslösungen im Verbund”; Stahlbau 65/10. S.349; Verlag Ernst & Sohn; Berlin.

2 Kuhlmann, U. (1996): “Design, Calculation and Details of Tied-Arch Bridges inComposite Construction”; Composite Construction in Steel and Concrete III,Proceedings of an Engineering Foundation Conference in Irsee, Germany, p. 359,published by ASCE 1997.

3 Eurocode 4 (1994): “Bemessung und Konstruktion von Verbundtragwerken aus Stahlund Beton, Teil 1-1: Allgemeine Bemessungsregeln und Bemessungsregeln für denHochbau“; Comité Européen de Normalisation.

4 Kuhlmann, U.; Breuninger, U. (1999): “Liegende Kopfbolzendübel unter Längsschubim Brückenbau“; Forschungsbericht; Bundesministerium für Verkehr; Bonn-BadGodesberg.

5 Kuhlmann, U.; Breuninger, U. (1999): “Liegende Kopfbolzendübel unter Längsschubim Hochbau“; Forschungsbericht; Deutsches Institut für Bautechnik; Berlin.

6 Breuninger, U. (Feb. 2000): ”Zum Tragverhalten von liegenden Kopfbolzendübeln unterLängsschubbeanspruchung”; Dissertation, Institut für Konstruktion und Entwurf I;Universität Stuttgart.

7 Kuhlmann, U.; Kürschner, K. (2001): “Behaviour of Lying Shear Studs in ReinforcedConcrete Slabs”; Symposium on Connections between Steel and Concrete, 55th RilemAnnual Week in Stuttgart, Germany.

8 Ožbolt, J.; Li, Y.; Kožar, I. (1999): “Mixed constrained microplane model for concrete“;to publish in: International Journal of Solids and Structures.

9 Leonhardt, F. (1962): “Spannbeton für die Praxis“; Verlag Ernst & Sohn; Berlin.10 Eligehausen, R.; Mallee, R.; Rehm, G. (1997): “Befestigungstechnik“ in: Betonkalender

Teil II; S. 609; Verlag Ernst & Sohn; Berlin.