TO BASE PLATES OF HOLLOW SECTIONS COLUMNS

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1 TO BASE PLATES OF HOLLOW SECTIONS COLUMNS Kamila Horová, Jan Tomšů, František Wald Department of Steel and Civil Structures, Czech Technical University in Prague ABSTRACT This work describes the analytical prediction model of CHS and RHS column bases consisting of a base plate and anchor bolts under axial force and bending moment. An analytical model, which is based on the component method applied in EN :2005, allows determining axial force and bending moment resistance and the rotational stiffness. The analytical model consists of two components, base plate in bending and anchor bolts in tension, which is suitable for evaluation of hollow section base plates. The effective length of T-stub in tension was derived analytically using the yield line theory and checked by finite element simulation. The model is compared to the published experimental results in order to verify the resistance and the stiffness predictions. The comparison shows a good accuracy of the prediction of the moment-rotation curve. 1. INTRODUCTION Column bases are one of the least studied structural elements in the frame of European research. Contrarily to beam to column connections, the number of available tests is limited to about 200 with various complexity of data description. Classical approaches to design of base plates, see (Melchers, 1992), use an elastic analysis, based on the assumption that the section, consisting of anchor bolts and a base plate, remains plane in compression. By solving equilibrium equations, the maximum stress in the concrete can be determined, assuming a triangular stress distribution along the dimension of the stress block and tension in the holding down assemblies. Although this procedure proved to be satisfactory in service over many years, such approach ignores flexibility of the base plate in bending and behaviour of the holding down assemblies and of the concrete. The traditional elastic models for column base design give a safe, conservative solution with relatively thick base plates and expensive anchoring systems. The column base stiffness has an important effect on the calculated frame behaviour, particularly on frame sway. Traditionally, column bases are modelled as either pinned or as fixed, whilst the reality lies somewhere between these two extremes. In the European codes of practice (EN , 2005) the elastic design models were replaced by inelastic, and the model of foundation for crushing of the concrete under the flexible base plate was refined, see (Wald et al, 2008). The guidance for modelling the base by component method including stiffness prediction is available. In portal frames, the base stiffness has a major influence on the collapse mode in extreme situations caused by exceptional loading, such as fire, see (Song et al, 2009). The design of base plates is also crucial for seismic design, where the deformation capacity, see (Hsu and Liu, 2006) and detailing play important role and the base plate connections are tested during each earthquake loading, see (Di Sarno, 2007). Traditional design of base plates for hollow section columns is described in

2 (Wardenier et al, 1995). The elastic design was exchanged for an inelastic proposal, see (Liu, 2006), which focused on base plate uplift (Wikinson et al, 2009) and design or sign and lightening structures (Ansley et al, 2000). The anchor bolts, an important part of the column base, are evaluated as products according to ETAG (2002) or by developed prediction models, see (Eligehausen, 2006). Further research in the area of base plates is focused on innovative connections and on hollow sections. Between years 2007 and 2011, the development of design models of steel to concrete joints for the European standards and design rules were the objective of a project RFSR-CT InFaSo, led by Prof. Ulrike Kuhlman from the Institute of Structural Design at the University of Stuttgart, see (Kuhlmann, et al 2011). Within this project, a joint of steel beam to concrete wall and a base plate with steel plate using long header studs were developed. A design method for both connections and for the increase if resistance by stirrups were published, see (Henriques et al, 2011). Figure1. Force equilibrium for RHS column base with simplified effective area, both parts in compression. 2. COMPONENT METHOD Joints as well as the base plates are modelled using component method. This method is based on evaluation of resistance and stiffness, which are derived from the resistance and stiffness of each part of the joint. The first step of the component method is identification of individual connection parts - components. The base plate connection is disintegrated into two parts: base plate in bending plus concrete in compression, and base plate in bending plus anchor bolts in tension. There are also components of column web and flange in shear and compression, and bolts in shear, which should be checked during the design. The calculation of the column base bending resistance, based on the force equilibrium on the base plate, is given in (Wald et al, 2008). The connection is loaded by axial force N Ed and bending moment M Ed, as shown in Figures 1 and 2. The position of the neutral axis is calculated according to resistance of the tension part F T,Rd. The bending resistance M Rd is determined assuming plastic distribution of internal forces as it is shown in Figure 2. The effective area A eff under the base plate represents the equivalent rigid plate and is calculated from an equivalent T-stub, with

3 an effective width c. The compression force is assumed to act at the centre of the compressed part and the tensile force is located at the anchor bolts or in the middle when there are more rows or bolts. The calculation of stiffness of the base plate is compatible with beam to column stiffness calculation. The difference between these two procedures lies in the fact, that by the base plate connection the normal force has to be introduced. The detailed design procedure for based plates under columns of rectangular hollow section was described in (Wald et al, 2005) and of circular hollow section in (Horová et al, 2011). The failure mode derived by the yield line theory was evaluated by FEM simulation. Figure 2. The stiffness model of the base plate connection of RHS column. 3. EVALUATION ON EXPERIMENTS 3.1 Nakashima experiments Study performed by Shigetoshi Nakashima in Japan (Nakashima 1992) examined the mechanical characteristics of a column base, subjected to bending and shear forces, such as initial rigidity, hysteresis characteristics, ultimate strength and strain of main components. A life size steel column with a square base and a concrete block, as it is shown in Figure 3, was used as a specimen. Diameter and arrangement of the anchor bolts, thickness of the base plate, and cross-sectional dimensions of the column and concrete footing were the tested variables. The diameter of bolt hole in the base plate was 55 mm. As it is shown in Table 1, at anchoring of the base plate, the clearance at the bottom surface of the plate was 30 mm. Non-shrinking mortar was injected into the space under the base plate and into the clearance between anchor bolts and holes in the base plate. There was no initial tightening force in anchor bolts. Table 1 shows for tested specimens the characteristics of the column, the base plate, anchor bolts and the concrete foundation. In this paper, test results of fourteen specimens are described. For evaluation, only five set ups without stiffeners are chosen. Table 2 presents mechanical characteristics of the steel. The strength of the concrete used for manufacturing of specimens was 28,5 N/mm 2 and of grout 45,2 N/mm 2. The concrete block was reinforced with steel bars.

4 Figure 3. The test set up of base plates with four bolts and six bolts. Table 1. Selected specimens geometry. Specimens Steel column Base plates Anchor bolts Foundation Symbols A x B x t (mm) D (mm) b (mm) t (mm) Quantity Thread Shank b x D (mm) I x200x M36 D38 535x535 I x200x M36 D38 550x550 II x250x M33 D35 580x580 II x250x M36 D38 600x600 II x250x M36 D38 600x600 Steel columns Base plates Anchor bolts Table 2. Mechanical properties of steel. Steel σ y (N/mm 2 ) σ t (N/mm 2 ) El (%) 200x200x x200x x250x x250x x250x t = 32 mm t = 36 mm t = 40 mm t = 50 mm D D Behaviour of the column base from Nakashima s test is represented by moment-rotation curve. This curve describes the stiffness as well as bending resistance

5 of the joint. In Figure 4, there is a comparison of the two curves, the first obtained from the experiment and the second from the calculations worked out in (Horova, 2010). Figure 4. The comparison of presented model to test II Comparing the initial stiffness, the experimental and analytical results are close to each other with difference of about 4 % (0,24 knmrad -1 from the test and 0,23 knmrad -1 from the analytical model). The difference between resistances reflects the design model, which is focused on yielding of steel; there is also a good agreement between experimental and analytical results. The border of plasticizing of the first component as well as the maximum resistance of the column base is lower when using analytical component model. This is due to the use of nominal values of material properties in the analytical model, whereas the experiment results reflect the real behaviour of material. Summing up, it can be stated that the calculated values and measured values of the initial stiffness correlate well. The analytical component model can be used for design and prediction of the base plate resistance and stiffness. 3.2 Takamatsu and Tamai experiments After the earthquake in Hyogoken-nanbu, Japan, in 1995, during which many steel column bases were damaged, Takao Takmatsu and Hiroyuki Tamai from Hiroshima Institute of Technology performed their experimental study on RHS exposedtype column base, see (Takamatsu and Tamai, 2005). This study described force characteristics of an exposed-type column base with anchor bolts and thick base plate as well as a of a new exposed-type column base, improved by driving a wedge into the gap between the nut of the anchor bolt and the base plate, causing plastic elongation of the anchor bolt. Experiment was carried out on fixed column base using rolled threaded anchor bolts. The tested specimen is shown in Figures 5 and 6. The mechanical properties of the steel material and the dimensions of its parts are summarized in Table 4. A cold-formed square hollow section was used for the column and anchor bolts standardized by the Japanese Society of Steel Construction were used. In Fig-

6 ure 7 there is a comparison of the analytical component model to the experimental result. Figure 5. Measuring and loading system of tested specimen. Table 3. Geometry and material properties of tested specimen. Anchor bolt Column (mm) Base plate (mm) Ø (mm) A (mm 2 ) l eff (mm) 200x200x12 400x400x50 27, Material E (N/mm 2 ) σ y (N/mm 2 ) σ u (N/mm 2 ) σ y /σ u (%) ε u (%) Anchor bolt Base plate Column Figure 6. Base plate and anchor bolt of tested specimen.

7 Figure 7. Comparison of moment-rotation curves of prediction to tests results for zero axial force. Regarding the initial stiffness, the difference between the experimental and analytical value is about 12%, which is more than in case of comparison of the analytical model and Nakashima s experiment. However, discrepancy is limited and thus results obtained from analytical component model can be considered satisfactory. In the experimental study, the resistance was based on yielding of anchor bolts. The border of plasticizing of the first component in experimental moment-rotation diagram is represented by plasticizing of anchor bolt (125,40 knm). On the other hand, based on the analytical component calculation, the base plate resistance (104,24 knm) was proved as the lowest, thus failure of the column base is supposed to govern collapse. Nevertheless, values of the yield strength of anchor bolts in tension and of the base plate in bending are close to each other, so both the base plate and the anchor bolts can be the critical components. The fact that in performed calculation the base plate is the critical component is caused by calculation of the effective length of T-stub, which slightly differt in the analytical model from the real one. Despite these slight differences, the values calculated accordingly to the analytical component model and measured values obtained from this experimental study - especially the initial stiffness - correlate well. Also according to this comparison, it can be stated, that the analytical model, introduced in (Horova, 2010) can be used for design and prediction of the base plate resistance and stiffness. 5. CONCLUSIONS This paper is focused on comparison of predictions obtained using the analytical model of base plates of hollow sections columns with the real test results. Both in case of Nakashima s and Takamatsu s experiments, the values predicted by the analytical model show a good agreement with the test results, especially regarding the initial stiffness. In conclusion, the analytical model based on the component method allows a satisfactorily accurate prediction of resistance and stiffness for engineering purposes and thus can be used for design.

8 ACKNOWLEDGMENTS The work was supported by the research center of Ministry of education, youth and sports CIDEAS No. 1M0579. REFERENCES Ansley M.H., Cooc R.A. and Tia M., Use of grout pads for sign and lightening structures, Structural research report No. BB-512, University of Florida, Di Sarno L., Pecce M.R. and Fabbrocino G., Inelastic response of composite steel and concrete base column connections, Journal of Constructional Steel Research, 63, 2007, pp Mallée R. and Silva J. F., Anchorage in Concrete Construction, Ernst and Sohn Verlag, Darmstadt, 2006, ISBN EN , European Committee for Standardization CEN. Eurocode 3: Design of steel structures. Part 1.8: Design of joints, Brussels ETAG 001, Guideline for European technical approval of metal anchors for use in concrete, Parts1 to 5, Brussels, Henriques J., Ožbolt A., Kuhlmann U. et al, Behaviour of Steel-To-Concrete Joints - Moment Resisting Joint of a Composite Beam to Reinforced Concrete Wall, Steel Construction, 2011, vol. 4, no. 3, pp ISSN Horova K., Base plates of hollow sections, Diploma thesis, Czech Technical University in Prague, 73 p., Prague, Horová K., Wald F. and Sokol Z., Design of Circular Hollow Section Base Plates, Eurosteel 2011, 6th European Conference on Steel and Composite Structures, Budapest, 2011, vol. 1, pp ISBN Hsu H. L. and Lin H. W., Improving seismic performance of concrete-filled tube to base connections, Journal of Constructional Steel Research, 62, 2006, pp Kuhlmann et al, INFASO, Final report, RFSR-CT , Liu D., Design of circular base plates, ASCE, Practice Periodical on Structural Design and Construction, 11, 2006, pp Melchers R. E., Column-base response under applied moment, J. Construct. Steel Research, 23, 1992, pp Nakashima S., Experimental Behavior of Encased Steel Square Tubular Column-Base Connections, in Proceedings of the First Word Conference on Constructional Steel Design, Elsevier Applied Science, 1992, pp Song Y., Huang, Z. Burgess, I. W, Plank, R. J., The behaviour of single-storey industrial steel frames in fire, Advanced Steel Construction, 5 (3), 2009, pp Takamatsu T., Tamai H., Non-slip-type restoring force characteristics of an exposedtype column base, Journal of Constructional Steel Research, 61, 2005, pp Wald F., Bouguin V., Sokol Z. Muzeau J. P: Component Method for Base Plate of RHS, Proceedings of the Conference Connections in Steel Structures IV: Steel Connections in the New Millenium, October 22-25, Roanoke 2000, pp. IV/8- IV/816. Wald F., Sokol Z., Steenhouis M. and Jaspart, J.P., Component Method for Steel Column Bases, Heron, 2008, vol. 53, no. 1/2, pp. 3-20, ISSN Wardenier J., Dutta D., Yeomans N., Packer J.A. and Bucak O., Design guide for structural hollow section in mechanical applications, CIDECT, Construction with hollow section steel sections, Verlag TUV Rheinland Gmbh, Köln, Wilkinson T., Ranzi G., Williams P. and Edwards M., Bolt prying in hollow section base plate connections, Sixth International Conference on Advances in Steel Structures and Progress in Structural Stability and Dynamics, Hong Kong 2009, ISBN