DESIGN OF LYING STUDS WITH LONGITUDINAL SHEAR FORCE

Transcription

1 DESIGN OF LYING STUDS WITH LONGITUDINAL SHEAR FORCE Ulrich Breuninger Structural Engineers Weischede, Herrmann und Partner, Germany Abstract Innovative composite cross sections lead to an unusual positioning of the headed studs horizontally in the thin concrete slab. The behavior of this lying studs with longitudinal shear force has been investigated. The results of experimental and numerical investigations show that the failure characterized by splitting of the thin slab is influenced by different parameters compared to vertically positioned studs. Based on the investigations a design rule is presented. 1. Introduction Composite sections of steel and concrete have a continuous connection between both parts. In standard composite beams headed studs are welded vertical on the top flange of the steel girder as shear connector. Fig. 1 Composite beam without top steel flange Fig. 2 Slim-floor composite beam (1) The development of innovative composite cross sections for bridges and buildings leads to 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 the web. For the final usage the concrete slabs serves as top flange. During erection 1015

2 sufficient resistance is provided by the precasted concrete web. As a second example Fig. 2 shows a slim-floor structure. Again the function of the omitted top steel flange is taken over by the concrete slab. The horizontally lying studs allow a very thin slab which is an advantage also from the architectural point of view. A strong load transmission between arch and slab for tied arch bridges is achieved by connecting the slab directly to the stiffening girder, see Fig. 3. Again studs are positioned horizontally in the slab. Additional advantages of this construction are a better corrosion protection of the transverse girders and the transverse girder acting as composite beam in its entire length. Fig. 3 Section of a tied arch bridge with lying studs connecting the slab to the stiffening steel girder (2) In contrast to the standard composite beam section the axis of the studs in the sections of Fig. 1, 2 and 3 is not vertical anymore but parallel to the plane of the slab. Therefore studs arranged this way are called lying studs. compression cleavage cracks Fig. 4 Section through the shear connection of lying studs The shear connection of composite beams is dominantly subjected to a longitudinal shear force. 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 thus initiating 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 1016

3 cracks parallel to the plate surface and an expansion of the concrete. The failure of these lying studs is mainly due to the splitting of the concrete. Vertical stirrups surround the expanding concrete and prevent the extension of the cracks. The design rule for headed studs in Eurocode 4 (3) is based on experimental investigations for conventional vertical studs only and therefore it does not cover the splitting failure of lying studs. To identify the major parameters for this special mode of failure and to quantify the carrying capacity of lying studs, a comprehensive research program 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 load from the slab into the steel girder. The content of a prosecuted research program is presented in the next paper (7). 2. Experimental investigations Two different situations of the shear connection with lying studs relative to the concrete slab can be distinguished. In composite girders without a top flange e.g., see Fig. 1 and 2, the shear connection is situated in the middle of the concrete slab, whereas the example of the tied arch bridge of Fig. 3 shows lying studs at the front side of the concrete slab. Therefore two test series were carried out: series I with the shear connection in the middle of the concrete slab corresponding to sections in buildings and series II with the connection at the two edges of the concrete slab corresponding to bridge sections, see Fig. 5 and 6. A 800 A lineare measure in mm Section A-A Fig. 5 Test specimen of series I with the shear connection in the middle of the concrete plate 1017

4 300 A A studs in one row studs in two rows lineare measure in mm 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 as variations of a so called basic sample. For a group of at least 3 specimens always only one main parameter was varied whereas the other parameters were kept constant. The following 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 after splitting and the lying studs suffer high deformations until finally the studs tear off. b) splitting of the slab For low degrees of reinforcement or small distances between stud and slab surface, the carrying capacity of the shear connection starts reducing just after the splitting of the slab has first occurred. c) pull out of the studs In some rare cases, when the lying studs were situated at the edge of the slab and the studs were too short, the shear connection failed because of a pull-out of the studs. 1018

5 a) Splitting of the plate/tear off of the studs b) Splitting of the plate c) Pull-out of the studs Fig. 7 Failure modes of lying studs load per stud [kn] 200 Splitting of the slab, tear off of the studs 150 Splitting of the slab Pull out of the studs slip [mm] 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 studs fail according to mode a) or b) the load slip curve shows a high carrying capacity a 1019

6 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-linear FE program considering the size effect of concrete structures was used (8). Based on the experimental and numerical investigations the influence of the parameters on the carrying capacity can be determined Concrete strength The splitting of the slab depending on the concrete tensile strength causes the collapse of the shear connection. Because of the well known relation between tensile and compressive strength the carrying capacity can be described with an exponent function of the concrete compressive strength that is more usual (Fig. 9). P e [kn] Fig. 9 K (f c/30n/mm 2 ) 0.4 Test series I-6 Test series II f c [N/mm 2 ] Carrying capacity P e of lying studs dependent on the concrete compressive strength f c P/P v [-] 1.2 K (a r /80mm) Fig. 10 Test series I-1 Test series I-2 Test series II-2 FE a r [mm] Relative carrying capacity P/Pv of lying studs dependent on the effective edge distance of the studs a r (for different distances between the studs a) Edge distance of the studs The carrying capacity depends strong on the effective edge distance of the studs (a r = the edge distance of the studs without the concrete cover and a half of the stirrup diameter) (Fig.10). The influence is big if the edge distance is small. With increasing edge 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 on the cleavage cracks in the structure. 1020

7 x deformation direction a r = 30 mm a r = 75 mm Fig. 11 a r = 120 mm Cleavage cracks following main strains at maximum carrying capacity (black areas show a strain 5 ) Reinforcement of the slab Fig. 11 shows the importance of the reinforcement in the slab. The stirrups and especially the intersection between stirrups and longitudinal reinforcement is used as anchoring for the cracks. It can be concluded, that the carrying capacity increases with the amount of stirrups per stud because this leads to more anchoring points. The effect of stirrups with a greater diameter on the carrying capacity can be neglected. The longitudinal distance between the studs and the stirrups has no decisive influence on the 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 should be dimensioned for the splitting force Z d d Zd Pd 0.3 (1 ) [1] a r Where P d is the longitudinal shear design force. 1021

8 Length of the studs If 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 studs have to be anchored with an overlapping v behind the stirrups. The overlapping depends if the concrete is cracked or not. uncracked concrete: > 30 v 110 mm; v 1.7 a r ; v 1.7 s/2 cracked concrete: > 23 v 160 mm; v 2.4 a r ; v 2.4 s/2 [2] Further parameters Although not shown by data presented here the following additional conclusions follow from 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 following design rule for the carrying capacity of lying studs with failure because of cleavage cracks is proposed. PRd,sp 1.42 (f ck a 1 d a r ) A s C v [3] P Rd,sp design resistance [kn] (index sp from german spalten) f ck compressive strength of the concrete [N/mm 2 ] 19 mm d 25 mm diameter of stud [mm] 50 mm a r distance between studs and stirrups vertical to the force [mm] 110 mm a 440 mm distance between studs parallel to the force [mm] s/a r 3 distance between stirrups / distance between studs and stirrups a/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 slab d s 8 mm stirrup diameter [mm] C v = 1.25 partial safety factor according to Eurocode 4 (3) 1022

9 h a concrete cover d + d s 2 v headroom of the stud ß d s s section A-A a r a' r concrete cover + d s 2 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 to Eurocode (3) for one diameter. P Rd [kn] 150 d = 22 mm f uk = 500 N/mm a/s = 1 A = 1.14 P Rd [kn] 150 d = 22 mm f uk = 500 N/mm a/s = 1 A = Eurocode 4 (3) Formula [3] with a r = 90 mm Formula [3] with a r = 70 mm Formula [3] with a r = 50 mm f ck [N/mm 2 ] a) shear connection in the middle of the concrete plate Eurocode 4 (3) Formula [3] with a r = 130 mm Formula [3] with a r = 110 mm Formula [3] with a r = 90 mm Formula [3] with a r = 70 mm Formula [3] with a r = 50 mm f ck [N/mm 2 ] b) shear connection at the front side of the concrete plate Fig. 13 Design resistance of lying studs compared to studs in standard composite sections 1023

10 5. Conclusion Stimulated from new composite cross sections and with the aim to support the development of further new composite constructions the carrying behavior of lying studs is investigated. First efforts are carried out to describe the carrying behaviour of lying studs for longitudinal shear. They lead to a practical design equation. Following investigations will study lying studs under vertical and combined shear force and as well as fatigue. At the moment the Institut für Konstruktion und Entwurf of the University of Stuttgart is continuing the work in this field of research. I would like to thank the Bundesministerium für Verkehr and the Deutsches Institut für Bautechnik 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 in Composite Construction ; Composite Construction in Steel and Concrete III, Proceedings of an Engineering Foundation Conference in Irsee, Germany, p. 359, published by ASCE Eurocode 4 (1994): Bemessung und Konstruktion von Verbundtragwerken aus Stahl und Beton, Teil 1-1: Allgemeine Bemessungsregeln und Bemessungsregeln für den Hochbau ; Comité Européen de Normalisation. 4 Kuhlmann, U.; Breuninger, U. (1999): Liegende Kopfbolzendübel unter Längsschub im Brückenbau ; Forschungsbericht; Bundesministerium für Verkehr; Bonn-Bad Godesberg. 5 Kuhlmann, U.; Breuninger, U. (1999): Liegende Kopfbolzendübel unter Längsschub im Hochbau ; Forschungsbericht; Deutsches Institut für Bautechnik; Berlin. 6 Breuninger, U. (Feb. 2000): Zum Tragverhalten von liegenden Kopfbolzendübeln unter Längsschubbeanspruchung ; Dissertation, Institut für Konstruktion und Entwurf I; Universität Stuttgart. 7 Kuhlmann, U.; Kürschner, K. (2001): Behaviour of Lying Shear Studs in Reinforced Concrete Slabs ; Symposium on Connections between Steel and Concrete, 55 th Rilem Annual 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. 1024