Experimental and theoretical study of composite trusses

Experimental and theoretical study of composite trusses

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Transportation Research Procedia 40 (2019) 815–822 www.elsevier.com/locate/procedia

13th International Scientific Conference on Sustainable, Modern and Safe Transport 13th International 2019), Scientific Conference on Sustainable, and Safe Transport (TRANSCOM High Tatras, Novy Smokovec –Modern Grand Hotel Bellevue, (TRANSCOM 2019),Slovak High Tatras, Novy Smokovec – Grand Hotel Bellevue, Republic, May 29-31, 2019 Slovak Republic, May 29-31, 2019

Experimental and theoretical study of composite trusses Experimental and theoreticala study of acomposite trusses Peter Michálek , Ján Bujňák * Peter Micháleka, Ján Bujňáka*

University of Zilina, Faculty of Civil Engineering, Univerzitna 8215/1, 010 26 Zilina, Slovakia University of Zilina, Faculty of Civil Engineering, Univerzitna 8215/1, 010 26 Zilina, Slovakia

a a

Abstract Abstract The optimal use of the properties of steel and concrete is the advantage of composite constructions made of these materials. Especially, section works of efficiently tension and theadvantage concrete part may transfer loads in compression. In composite The optimalthe usesteel of the properties steel andinconcrete is the of composite constructions made of these materials. element, they in works common to resistinaxial forces bending moments. This structural behaviour is rather Especially, theare steelacting section efficiently tension andand the concrete part may transfer loads in system compression. In composite complicate, mainly in the in case of steel to trusses withand a concrete Experimental researchsystem and numerical simulations element, they are acting common resistcombined axial forces bendingdeck. moments. This structural behaviour is rather based on finite element method aresteel usedtrusses to analyse the mechanical behaviour of Experimental these modern research structuraland members. complicate, mainly in the case of combined with a concrete deck. numerical simulations based on finite element method are used to analyse the mechanical behaviour of these modern structural members. © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility the scientific of the 13th International Scientific Conference on Sustainable, © 2019 The Authors. Published byof Elsevier B.V. committee Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). Modern and Safe Transport (TRANSCOM 2019). Keywords: truss beam, shear contact, numerical modeling Keywords: truss beam, shear contact, numerical modeling

1. Introduction 1. Introduction The typical cross-section of the composite beam normally consists of a reinforced concrete deck joined by shear The typical cross-section the generally compositerepresents beam normally offlange a reinforced concrete deck joined by in shear connectors to steel truss. Theofslab a largeconsists concrete with non-uniform distribution the connectors to steel truss. The slab generally represents a large concrete flange with non-uniform distribution in the transverse direction of normal bending stresses due to shear longitudinal displacement. The currently applied design transverse direction stresses width due tobshear longitudinalaccording displacement. currently design to theThe standard STNapplied EN 1994-1-1 of composite systemsofisnormal based bending on the effective eff consideration, of composite systems basedEN on 1994-2 the effective width 4b eff consideration, to the standardthe STN EN shear 1994-1-1 (Eurocode 4 1992) andis STN (Eurocode 1996), practicallyaccording sufficiently describing above lag (Eurocode 4 1992) connection and STN EN (Eurocode 4 1996),slab, practically describing the are above shear lag effect. For assuring of 1994-2 steel beams and a concrete varioussufficiently types of shear connectors used. effect. For assuring connection of steel and a concrete types of shear connectors are used. Composite steel-concrete trusses canbeams be considered as one slab, of thevarious most economical systems for building, especially steel-concrete trusses be considered as one of the most columns. economical especially for Composite greater spans allowing better usecan of internal space without restricting Thesystems trussesfor arebuilding, appropriate also to for greater spans allowing better use of internal space without restricting columns. The trusses are appropriate also to

* Corresponding author. Tel.: +421 41 513 56 50; fax: +421 41 513 56 90. E-mail address:author. [email protected] * Corresponding Tel.: +421 41 513 56 50; fax: +421 41 513 56 90. E-mail address: [email protected] 2352-1465 © 2018 The Authors. Published by Elsevier B.V. Peer-review©under responsibility of the scientific committee 2352-1465 2018 The Authors. Published by Elsevier B.V. of the 13th International Scientific Conference on Sustainable, Moder n and Safe Transport (TRANSCOM 2019). Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Moder n and Safe Transport (TRANSCOM 2019). 2352-1465  2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). 10.1016/j.trpro.2019.07.115

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Peter Michálek et al. / Transportation Research Procedia 40 (2019) 815–822 Michalek, Bujnak / Transportation Research Procedia 00 (2019) 000–000

meet the requirements for building height limitation as well as the need to run complex electrical, heating, ventilation, and communication systems. Also composite steel bridges, whose carriageway deck is supported on a filigree steel truss structure and slim piers, are particularly preferable especially to ordinary concrete superstructures. To create an interaction between steel parts and concrete, it is necessary to prevent relative slips at the steel-concrete interface using connectors. In the case of truss beam, they are typically located essentially in the nodes of upper chords. This discrete connector distribution can result to the different load transfer in special way and usually may represent a critical design task. Appropriate solution requires to identify corresponding shear resistance as well as load and slipping relationship as the key design characteristics. Our developed potential procedures are based on the results of recently completed experimental research. The outputs of these studies are presented in the paper. 2. Composite truss beam experimental testing To analyse the global behaviour of steel-concrete composite trusses, experimental program was executed (Bujňak J., Perkowski Z. 2016). In the frame of this investigation, four similar steel-concrete composite truss beam specimens of span 3.75 m were completed and equipped. Steel truss components were made from the steel grade S235. The upper chord of the beam specimens was prepared from parallel flange IPE 160 sections, bottom ones somewhat differently from two UPE 120 channels welded jointly to the form of box component. The edge web members at side parts consisted of square hollow section SHS 70x70x6.3 and the middle diagonals of the rectangular hollow unit SHS 40x40x3. Concrete slab of size 800x100 mm was made with demand on concrete class C25/30. Transversal and longitudinal reinforcement was formed from the bars ϕ10. Shear connection has comprised mainly headed studs of diameter 10 mm and height 50 mm located only above the nodes as shown in Fig. 1. Data received from the strain gauge packages were digitized and sent to the notebook. This computer was used to communicate with the measurement system for commands regarding data acquisition, calibration, initialization, downloading and display.

T9

P18

T10

P16

Fig. 1. Components of composite truss specimen with device locations

Progressively growing static loading applied in the thirds of span above nodes can be seen in Fig.2 in the case of experimental testing of the third truss specimen. Strains were recorded in both chords and web members of the girders as well as concrete slab by system of sixteen strain gauges. The deflection transducers were situated at the girders ends as well as in the middle and near the quarter part of span. The respective locations of the devices are indicated also in Fig.1. The recorded deflections have been initially developing proportionally till the loading level of 325 kN. Even the stress distribution in strut sections has been initially rather uniform and progress proportionally. However, with increasing loading, the resulting stress patterns have proved different faster development, as illustrated in Fig.5. However, with increasing loading, the resulting stress patterns have proved different faster development. Especially the upper chord yielded rapidly in the mid-span sections due to combination of bending and compression as a result of significant beam deflections. Finally, the chord failed by local instability. The experimental limit load carrying



Peter Michálek et al. / Transportation Research Procedia 40 (2019) 815–822 Michalek & Bujnak / Transportation Research Procedia 00 (2019) 000–000

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capacity of the specimen was 530 kN. This value is in good agreement with the numerical result (Bujňák J., Furtak K. 2014).

Fig. 2. Loading and general view of measurement system

3. Numerical study of truss shear connection behavior 3.1. Connection numerical models of truss beam tests The finite element analyses can be used to investigate numerically shear connection of the truss structural system, exploiting several computer procedures. The software CAD of Scia system was used to evaluate the structural behavior of the reference composite truss, taken from the above experimental investigation. Serious considerations had to be given to proper representation of the geometric characteristics. To simulate the actual composite action of the tested truss, beside real shear headed studs connectors ϕ 10/50 mm used at the key positions shown in Fig. 3a, the others connection models were developed. The alternative model 1 takes into account influence of surrounding concrete by tube-shaped envelope under stud head of 19 mm in diameter, as illustrated in Fig. 3b. Considering second moment of steel shank area IS,St = π. DS,St4/64 = 491 mm4, the concrete tube can contribute to the resulting sectional characteristic by the value IC,C = 5 910 mm4. Consequent effective composite connector second moment of area would be Ieff = 1 360 mm4. Introducing this modified sectional parameter in the computation model, the deflections might be more exactly theoretically reproduced, as illustrated by dot-dash line in Fig. 5. But in the case of normal stresses the accuracy seems inferior.

a)

b) Fig. 3. a) real steel connectors, b) model 1 of composite studs

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a)

b)

Fig. 4. a) different cylinder-shaped model 2, b) conic model 3 of composite studs

For this reason, the next stud connector model 2 according to Fig. 4a may consider slight larger concrete cylindrical stud cover entirely of 33 mm in diameter. The second moment of its area would increase at I C,C = 57 700 mm4. Thus effective value of this parameter will be greater and equal to Ieff = (EI)eff / Es = 1,89 .10-3 / 210 000 = 9010 mm4. From dash line in Fig. 5, it is evident improved agreement in stress development, but inferior accordance of deflections progress. The in-between shape model 3 might simulate composite stud as a tapered concrete cone, surrounding steel shank with its diameter of 20 mm at its top and 80 mm in bottom base, as it is shown in Fig. 4b. Due to limit mutual pitch, a cone intersection usually can arrive. The approximation to the cylinder should be generally imposed using equality of volume of both connection bodies. In this example, the real cone-shaped connector volume is Vc = 91 300mm3. The equivalent diameter of cylinder-shaped composite stud would be 50 mm with the second moment of area IC,C = 327 000 mm4 and the effective value of this sectional characteristic Ieff = (EI)eff / Es = 1,03 .10-2 / 210000 = 48 800 mm4. The dotted lines in Fig. 5 indicate even stronger conformity of stresses results. But inversely, it is seen a significant drop of accuracy between theoretical and experimental deflection values.

Fig. 5. Composite truss deflections (P16) and normal stresses (T9 and T10) in the mid-span

3.2. Numerical models of push-out tests Connection using steel studs is actually the most common mode of the concrete slab joining to the upper chord of a truss. A real behavior of this connection type has been initially investigated experimentally. The standard push-out test specimens according to STN EN 1994-1-1 (Eurocode 4 1992) were prepared, since this testing can provide necessary input data by simple and rather straightforward way. As shown in Fig. 6, the specimens consisted of a steel profile HEB 260 and two identic adjacent slabs 650 mm long and 600 mm wide of concrete class C 25/30. The round studs of the structural steel grade S 235J2 with 10 mm in diameter and 50 mm height were used as shear connectors.



Peter Michálek et al. / Transportation Research Procedia 40 (2019) 815–822 Michalek & Bujnak / Transportation Research Procedia 00 (2019) 000–000 SP 2 560 600

100

260

460 100

600

100

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250

SP 4

600

100

460 100

100

650

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100

600

32

315

100

260

6060 215 100

260

335 40 40 235 100

650

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SP 5 460

100

260

315

650

250

250

100

250

650

SP 3 460

150

150 100

260

150 100

150

6060 215 100

SP 1

819 5

Fig. 6. Push-out specimen arrangement

450

[kN]

Five similar specimen groups as SP1 to SP5 were tested. The first two sets SP1 and SP2 had only four headed studs on each of both steel-concrete interfaces, 100 mm horizontally and 250 mm vertically spaced. But the slab thickness varied. It was 150 mm thick for SP1 specimen and only 100 mm in the case of SP2. The next three specimen groups SP3 to SP5 had concrete slabs 100 mm thick connected by six shear studs of different spacing values. Three pieces from each specimen series were tested. Thus, there were totally 15 push-out specimens, experimentally studied and corresponding registered load-slip relationships, as shown in Fig. 7b. force_slip - specimen SP5-1

450 Shear force F [kN]

400 350 300 250 200

experiment

150 100

FEM_model

50

0

1

2

3

400 350 300 250 200 150 100

[mm] 0

SP1-2 SP1-1 SP1-3 SP2-2 SP2-3 SP3-1 SP3-2 SP3-3 SP4-1 SP4-2 SP4-3 SP5-1 SP5-2 SP5-3 Slip  [mm]

test results

4

5

50 0

0

1

2

3

4

a)

5

6

7

8

9

10

11

12

b)

Fig. 7. Example of numerical and experimental load-slip relationship of specimen SP5-1 and outline of additional experimental testing

Magnitudes of representative experimental parameters for all specimens are given in the table 1. Table 1. Representative load and slip values Specimen

Ultimate strength

Characteristic strength

Slip

Pu[kN]

PRk [kN]

δuk [mm]

SP1

255.28

229.68

4.5

SP2

235.84

212.24

4.4

SP3

399.48

359.52

4.7

SP4

355.68

320.04

4.1

SP5

409.08

368.16

5.9

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But the push-out testing proved to be rather challenging and time-consuming. Therefore, the developments of a numerical model based on experimental data simulating connection behavior succeed as the next theoretical part of our research. Theoretical model of connection behavior in push-out experimental tests has been created using nonlinear analysis provided by ADINA software. This computational system offers numerous possibilities for more correct simulation of particularities of the concrete and steel properties of composite specimens, including headed studs. Even though, shear connection modelling has required some modification to simulate more appropriately real interaction at the interface of the concrete slab and steel part as the main problem of nonlinear analysis. Beside the composite action of both constitutive parts and headed studs modelling, it was necessary to include effect of the contact shear surface contribution. This influence has been taken into account in analyses by an equivalent shear modulus representing action of an equivalent connector surrounding area. The input in the model was calibrated particularly using the test output of the push-out specimen SP5 from Fig.7a.

Fig. 8. Shear stud effectively cooperating composite body

An action of the real group of six stud connectors surrounded by concrete might be simulated as a tapered concrete pyramid with its base length of 200 mm and 100 mm in width, as it is shown in Fig. 8. As illustrated in Fig.9, the web of the steel part of a specimen could be discredited in shell-like elements. The solid space 3D isoparametric four-node elements were used to substitute numerically the steel flanges and adjacent concrete slabs. Shell 3D Solid

Shear surface

Fig. 9. Final elements in the numerical model



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The corresponding shearing surface would be A = 100 . 200 = 20 000 mm2. Considering a steel connector shank of 10 mm in diameter, its area is A = π. D2/4 = 78.54 mm2.The entirely six studs shear surface amounts As = 6A = 471.2 mm2. With the shear steel modulus Gs = 81 000 N/mm2, shear resistance would be GsAs = 38 167 kN. The equality of the above six-stud group shear resistance gives corresponding value of the shear modulus of the active surface in the form Gs,N = GsAs /A = 1 908 N/mm2. Finally Young’s modulus can be calculated from evident relationship Es,N = Gs,N [2(1 + ν)] = 49 621 N/mm2 with Poisson’s number ν = 0.3. Stress-strain diagram

[MPa]

12.5 10.0

9.80

8.70 8.50

7.5

10.25

9.20

5.0 2.5 0.0

[ε] 0

0.005

0.01

0.015

0.02

0.025

Fig. 10. Stress-strain diagram of alternative surface

More significant nonlinear connection behavior due to cracking propagation in the concrete slab together with steel studs bending started evidently at the value of loading force 205 kN. Thus, the corresponding stress on the hypothetical contact surface amounts fu,N = 205/20 = 10.25 N/mm2. More accurate stress values were also calculated in the similar way for some immediately precedent loading stages, allowing construction of the multi-linear working diagram of the shear connection in Fig. 10. This slip-load relationship of the specimen SP5 was determined using developed analytical model for the following gradually increasing loading up to the maximum final failure force of 409 kN. Sufficiently good agreement of experimental results with the theoretically declared values can be seen in Fig. a. It confirms the suitability of modeling of the shear connection of concrete and steel with an alternative shear surface. The displacements of the SP5 sample under different load ratios obtained by analytical modelling are shown in Fig.11. The test results, especially the maximum vertical displacements recorded by gauges placed at opposite slab surfaces reveal the symmetrical distribution. Moreover, the theoretical modelling assessed accurately even horizontal deformations, because all prediction errors fall within a very restrain interval. Another important finding relates to the real distribution of deformations correlated to the experimental form within the load-band.

(a)

(b)

(c)

Fig. 11. Progressive deformation of specimen SP5 at different load ratio: (a) dominantly vertical displacement at level 25% (b); even horizontal translation at level 75% (c) final deformation at final load level 100%

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Peter Michálek et al. / Transportation Research Procedia 40 (2019) 815–822 Michalek, Bujnak / Transportation Research Procedia 00 (2019) 000–000

4. Concluding remarks In this study, connection behavior in composite trusses is investigated. For this purpose, fifteen push-out laboratory standard push-out tests and three similar tests of composite truss specimens were carried out. In the proposed procedure, the four different stud connectors models were developed and exanimated. They were additionally verified by the results of measurements. The calculation models can reflect more correctly trusses behavior in comparison to the previous procedure in the paper. For a push-out test the steel beam and concrete slabs were modeled by appropriate elements, as a result of special examination in ADINA software system. Load-slip relationships are drawn and numerical results compared. Generally, the comparisons are in good agreement with the numerical result, if the extremely complex character of composite truss is considered. Acknowledgements The paper presents results of the research activities supported by the Slovak Science Grant Agency, grant No. 1/0343/18 and the Research and Development Agency, grant No. SK-PL-18-0005. References Eurocode 4, Design of composite steel and concrete structures, Part 1-1, General rules and rules for buildings, March 1992. Eurocode 4, Design of composite steel and concrete structures, Part 2, Bridges, July 1996. Bujňak J., Perkowski Z. Performance study of composite truss, Conference Proceedings of the 4th International Conference on contemporary Achievements in Civil Engineering, Subotica, Serbia, 22 April 2016, p. 165-172, http://www.gf.uns.ac.rs/, (last visited 10 November 2017). Bujňák J., Furtak K. Connection slip in composite elements under quasi-long-term actions, Pollack Periodica, No. 2, 2014, pp. 29‒34.