Marian A. GIZEJOWSKI Leslaw KWASNIEWSKI Wael SALAH

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1 Robustness of continuous steel-concrete composite beams of slender plain webbed and cellular open webbed sections Marian A. GIZEJOWSKI Leslaw KWASNIEWSKI Wael SALAH Faculty of Civil Engineering Warsaw University i of ftechnology

2 Outline of the presentation Introductory remarks and objectives Slender section castellated composite beams Results of experimental investigations Proposed computer FE simulations with use of ABAQUS Comparison of results from simulations and experiments Final remarks

3 Basic restrained instability modes of composite beams in hogging moment regions Local buckling Lateral-torsional- torsional distortional buckling Lateral-distortional buckling Torsional- distortional buckling

4 Load-deflection deflection curves of slender section composite beams with different regions of the bending moment diagram Composite beam with the sagging moment region Composite beam with the hogging moment region

5 Continuous or semi-continuous castellated steel-concrete composite beams in multi-story buildings

6 Castellation process Castellation process for I-rolled section h 1.5 d Built-up up section with web openings

7 Advantages of using castellated sections in modern structures Steel castellated beams are lighter than conventional plain webbed shapes. Greater flexural stiffness of the castellated beams allows for creating flexible floor plans that tare free of interior i columns. The web openings are used to pass the services allowing to minimize the floor depth.

8 Disadvantages of using castellated sections in composite beams More severe conditions for restrained distortional instability of both the web and the bottom flange in the negative bending moment regions than in the case of plain webbed beams. Lower shear force resistance of the steel part of the composite section.

9 State-of-the-art t th tand research objective Previous conducted researches A review has been made of research work carried out to date on the effect of openings on the behaviour of thin-walled composite beams. Research was focused on simply supported composite beams with web openings. Current study objective This study aims to widen the knowledge of the behaviour of thin- walled composite beams for the behaviour in the negative moment region.

10 Arrangement of beams for testing and computer simulations R168 R168 R168 R168 long specimen with circular web openings long specimen with hexagonal web openings ,5

11 Arrangement of beams for testing and computer simulations long specimen with square web openings short specimen with circular web openings Reaction A Load A

12 Arrangement of beams for testing and computer simulations Reaction A Load A short specimen with hexagonal web openings short specimen with square web openings

13 Arrangement of beams for testing and computer simulations Section (A-A) A)

14 Experimental investigations Steel grades: S355 and S420

15 Test rig setup Composite beam with circular web openings Composite beam with hexagonal web openings Composite beam with Composite beam with rectangular web openings

16 Displacement control program designed for the experimental investigations Displacement control program for the tested long specimens Displacement control program for the tested short specimens

17 Beam deformation at the level of maximum load Long span specimen with circular web openings Vertical displacements Distortional df deformations Concrete slab cracks

18 Beam deformation at the end of the test Long span specimen with circular web openings Vertical displacements Distortional deformations Concrete slab Concrete slab cracks

19 Beam deformation at the level of maximum load Short span specimen with circular web openings Vertical displacements Distortional ti deformations Concrete slab cracks

20 Beam deformation at the end of the test Short span specimen with circular web openings Vertical displacements Distortional ti deformations Concrete slab cracks

21 Finite Element Analysis using ABAQUS

22 Finite Element modeling technique Materials Steel material Perfect and imperfect steel models with isotropic strain hardening Concrete material Smeared cracks model Shell elements S4R Shell elements S4R5 Beam element B31 Analysis types Perturbation elastic buckling analysis Elements used in the developed FE model Riks post-yielding, post-buckling and post-cracking analysis

23 Geometric imperfection pattern for long span beam First positive mode shape of the long specimen with circular web openings

24 Geometric imperfection patterns for short span beam First positive mode shape Second positive mode shape Third positive mode shape Combined mode shapes for the short beam specimen with circular web openings

25 FE calibration analysis 1. Nominal and measured web plate thickness. 2. Imperfection amplitude(s) for the first (the first several) buckling mode shape(s) () to be applied as initial geometric imperfection pattern. 3. Material imperfection parameter (n). 4. Concrete tension softening parameter ε cr

26 Effect of nominal vs. measured web thickness for idealized perfect material model test t w =3.8 mm 30 t w =4.0 mm Displacement (mm)

27 Effect of geometric imperfections for long span beam and for idealized perfect material model Long-span cellular composite beam

28 Material imperfections captured by using an equivalent stress-strain strain diagram σ = 1 Eε n + f y, R 1 + E st ε n 1/ n f E y, R st = = f f u u y E f ε ε y st st ε st J. MURZEWSKI, Random load carrying capacity of rod structures. PWN, Series: Engineering Studies, Warszawa 1976 [in Polish].

29 Calibration of material behavior parameters for the nominal web thickness

30 Calibration of material behavior parameters for the measured web thickness Appl lied load (k kn) n=2 n= 20 n= n=4 C4S355 t w =3.8mm, cr =0.001 test Displacement (mm)

31 Comparison between test data and FE results for long span beam Deformed shape of specimen C4S355 at the end of the test Deformed shape of specimen C4S355 at the end of the FE analysis

32 Long span beam final comparison for calibrated material behavior parameters load (kn) Applied l Comparison between test data and FE results for specimen C4S355 Comparison between test data and FE results for specimen C4S420

33 Comparison between test data and FE results for short span beam Deformed shape of specimen C2S355 at the end of the test Deformed shape of specimen C2S355 at the end of the FE analysis

34 Short span beam final comparison for calibrated material behavior parameters 100 Applie ed load (kn N) load (kn) Applied test FE Displacement (mm) Comparison between test data and FE results for specimen C2S355 Comparison between test data and FE results for specimen C2S420

35 Conclusions The behaviour of statically indeterminate castellated composite beams is more complex than thatt of simply supported beams. A castellated composite beam may be subjected to different instability effects in the negative moment regions where the bottom compression flange of the beam is unrestrained. The experimental tests indicate that the shape of the web opening has the significant effect on both, the ultimate load and the stiffness degradation up to and beyond the limit point on the equilibrium path.

36 Conclusions Within the same opening shape, there is no visible effect of steel grades S355 and S420 on the bh behavior of both, slender section long span and short span composite beam specimens. For slender welded steel sections, it is important to include the average value of measured web thickness and the effect of residual stresses, e.g. by using an equivalent stress-strain diagram dependent upon the material imperfection factor n, as it has been proposed herein.

37 Conclusions The calibration exercise shows that the maximum amplitude of geometric imperfections may be taken as equal to the nominal web thickness, material imperfection factor should be taken as n=2 2 and the concrete zero-tension strain ε cr as 0.1 and 0.01 for two different concrete properties used for long and short span beams, respectively. Both experimental investigations and the Finite Element modeling show that the unrestrained bottom flange of long span beams are forced to distort laterally whereas the short span beams become distorted only torsionally. Both distortional buckling modes, lateral and torsional for the long and short span beams respectively, are precisely captured in the numerical FE simulations with respect to the deformation patterns and the local values of the deformed shape amplitudes.

38 Future research FE calibration vs. hierarchical validation 1. Concrete tension softening parameter ε cr - experimental bending test on concrete beams/plates 2. Mt Material ilimperfection parameter (n). - laboratory coupon tension and bending tests (steel) 3. Nominal and measured web plate thickness (+ 2) - experimental bending test on rectangular steel plates 4. Geometrical imperfections (+ 2 and 3) - experimental bending test on castellated beams without concrete

39 Thank you for your kind attention ti

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