Strengthening under Load: Numerical Study of Flexural Buckling of Columns

Procedia Engineering 190 ( 2017 ) 118 – 125 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SPACE 2016 doi: 10.1016/j.proeng.2017.05.316 ScienceDirect Available online at www.sciencedirect.com Structural and Physical Aspects of Construction Engineering Strengthening under Load: Numerical Study of Flexural Buckling of Columns Martin Vilda, * , Miroslav Bajera aBrno University of Technology, Faculty of Civil Engineering, Veveří 95, Brno 602 00, Czech Republic Abstract The paper refers to the strengthening of doubly symmetric columns under load by welded plates. A validated numerical study containing more than 500 models was performed to question the currently used design procedures. These procedures are not unified but vary greatly in different countries. The overly conservative design approach used in the Czech Republic contrasts with the approach completely neglecting the effect of preload commonly used in the USA. The effect of various parameters on the flexural buckling resistance of columns strengthened under load was investigated. The selected parameters were the thickness of the strengthening flange, the column length, the initial bow imperfection, the preload magnitude and the direction of the axis which is pinned while the other axis is fixed. Several conclusions were reached from provided results and a simple analytical method is proposed. The load under which the column is strengthened weakens the column but only slightly. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the issue editors. Keywords: Column; experiment; finite element analysis; parametric study; steel; strengthening under load 1. Introduction This paper investigates strengthening of steel members under load using welded plates. It focuses on flexural buckling of doubly symmetrical axially loaded columns. The paper contains a description and results of experimental research performed in years 2015 and 2016 which served to study the feasibility of column strengthening under high magnitudes of preload (the load under which the column is strengthened), the temperature changes raised by welding * Corresponding author. Tel.: +420 54114 7329. E-mail address: [email protected] © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SPACE 2016 119 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 process and the size of affected area, and to validate the numerical models used for parametric study. The results are compared with two vastly different analytical approaches. The first, used in the USA [1], presumes that the strength of columns strengthened under preload and under no load is identical. This claim is supported by various researchers, e.g. O’Sullivan [2], Nagaraja Rao and Tall [3], Tide [4], Wu and Grondin [5]. The second approach does not allow the steel of the base section to yield in the case of members susceptible to buckling. It was introduced by Spal [6] and later adopted by Czech technical recommendations [7] and other authors, e.g. Vašek [8]. This safe approach is supported by e.g. Brown [9] and Ricker [10]. The design of a member under high preload magnitude according to the first or second approach leads to completely different crosssection and use of material. This big discrepancy may be caused by only several experimental studies in this area. To author’s knowledge, experiments of strengthening steel compressed members under load are very scarce and were conducted by O’Sullivan [2] (2 specimens strengthened under compressive load, bolted plates, very low effect of buckling), Kolesnikov [11] (3 specimens, high preload magnitudes, no comparison with member strengthened under no load), Nagaraja Rao and Tall [3] (1 specimen, complemented with stub column tests), Marzouk and Mohan [12] (7 specimens, high preload magnitudes, no comparison with member strengthened under no load) and authors [13, 14] (6 specimens, torsional-flexural buckling and local buckling). The authors believe that the load resistance of steel members strengthened under load is decreased by the effect of preload but only slightly. There are two factors that should be accounted for in the structural design: x Increased initial deflection caused by lower stiffness of the base section compared to the strengthened section as suggested by Unterweger [15]; distortion caused by asymmetric welds [16] added to this increased bow imperfection. x Residual stress caused by welding (hardly predictable) and preload. The exact solution is difficult and contains some hardly predictable variables for practical design. Therefore, a simple solution with a coefficient k is introduced. Nomenclature A0 area of a base cross-section Az gross area of a strengthened cross-section L column length N1 preload magnitude Nb,0,Rk load resistance of a base member Nb,z,Rk load resistance of a strengthened member Ns,R load resistance of a member strengthened under preload fy yield strength of used material k coefficient adjusting the effect of preload magnitude χ0 buckling reduction factor of the base section χz buckling reduction factor of the strengthened section 2. Methods 2.1. Experimental research Experimental research took place at the laboratory of the Institute of Metal and Timber Structures at Brno University of Technology in years 2015 and 2016. Hot rolled steel section HEA 100 was selected as the base section and strengthening plates with cross-section dimensions 120×10 mm were used. The cross-sections along with strain gauges and draw-wire sensor positions are shown in Fig. 1. All columns were 3 m long and all steel was grade S235 (yield strength from coupon tests: 309 ± 4 MPa – base section, 294 ± 6 MPa – strengthening plates; modulus of elasticity was not measured and was estimated 210 GPa). The boundary conditions were determined by knife-edge 120 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 bearings along axis z; the column was therefore pinned perpendicular to axis z and fixed perpendicular to axis y. The strengthening plates were welded using intermittent welds with throat thickness 4 mm. The experimental procedure, boundary conditions and measuring devices are described in greater detail in previous article by authors [17]. Two strengthening patterns were selected: (O) with strengthening plates perpendicular to the flanges of the base section and (H) with strengthening plates parallel to the flanges. Each set with the distinguished pattern contained six specimens. Two columns from each set were welded on a bench without preload and loaded to failure, other four columns were strengthened under load using following procedure: 1. Strengthening plates were welded to the base section with one short weld at mid-height and then strain gauges were glued. 2. A column was inserted into the loading frame, all measuring devices were activated and the column was loaded to desired preload (see Table 2). 3. The strengthening plates were fastened into position using C-clamps and then welded to the base section using intermittent welds. The welding procedure took around an hour and the preload was manually adjusted to mitigate the thermal expansion and oil leakage from the loading cylinder. 4. The column cooled for about an hour and then was loaded to failure. The preload ratios (ratio of preload and load resistance of the base section) were selected from 0.46 to 0.93. Fig. 1. Cross-sections of specimens (base section is hatched) with positions of strain gauges (SG) and draw-wire sensors (W) on the cross-section at mid-height; strengthening pattern O on the left, pattern H on the right. 2.2. Numerical research Numerical analysis was conducted using ANSYS® Academic Research, Release 16.2 software. Description of models and their validation are described in detail in [17]. For the parametric study, four node SHELL 181 element type and the bilinear isotropic material model with Young’s modulus of elasticity E = 210 GPa, yield strength fy = 235 MPa and nominal yielding plateau slope 21 MPa were used in all cases. Note that the strengthening flanges had the same width as the base section column flange in the parametric study (see Fig. 2). Variable parameters were summarised in Table 1. Not all parameters were combined with each other but regardless the study contains 574 numerical models. The range of relative slenderness ߣҧ was 0.523–2.061 and 0.439–1.992 for base section and strengthened section, respectively. z SGs2 SGs1 SG01 SG02 SG03 SGs3 SG04 SGs4 12 15 y z SGs1 SG01 SGs2 SG02 SG03 SGs3 SG04 SGs4 15 5 y W1 W2 W1 W2 W3 W4 W3 W4 5 5 10 100 10 12 96 12 120 120 100 10 10 880 810 96 120 116 10 121 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 Table 1. Variable parameters in numerical parametric study. Column length 2, 3, 4, 5 m Strengthening pattern O, H Pinned axis strong axis, weak axis Preload magnitude (pattern H, pinned perpendicular to the strong axis) 30 kN steps for 5 m length, 50 kN steps otherwise Preload ratios (pattern H, pinned perpendicular to the weak axis) 0.2, 0.4, 0.6, 0.8 Preload ratios (pattern O) 0.25, 0.5, 0.75 Equivalent initial bow imperfection L/200, L/300, L/600 Thickness of strengthening plates 4, 8, 10, 12 mm Fig. 2. Mapped mesh, boundary conditions and the first eigenvalue shape of the column strengthened with pattern H used in parametric study. 2.3. Analytical solution The simple analytical solution is based on the formula used in Czech technical recommendations [7] extended by a coefficient k, which diminishes the effect of preload on the load resistance of the member strengthened under preload: 1 1, 00 1 ,, 1, ,0, 1 d         yzz Rs yRkzb Rs Rkb fA NkN fA Nk N NkN N Nk FF (1) From Equation (1) a coefficient k can be determined: 00 1 00, 1 ,0, AA N AN N AN k zz RszzRkb     FF FF (2) Coefficient k equal to 1 leads to elastic design; k equal to 0 leads to complete neglect of the effect of preload. Equation (2) serves to obtain k from numerical analyses and then, after statistical evaluation, a characteristic coefficient k can be used to evaluate the resistance of the member strengthened under load Ns,R using Equation (3). ¸ ¸ ¹ · ¨ ¨ © § 1 ,0, ,, 1,,, Rkb Rkzb RkzbRs N N NkNN (3) 122 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 3. Results and discussions 3.1. Experimental research Using the thermochalk, the area of the base cross-section affected by a temperature higher than 320°C near one weld was only 1 cm2 (5 % of the base cross-section). Use of symmetrical intermittent welds and thin wire electrode contributed to this low impact of welding on column deflection and elongation during welding and hence the material degradation could be neglected. On the other hand, the weld cooled very fast which can lead to occurrence of brittle martensite [18]. The welding process is captured in Fig. 3. Welds did not fail in any case even at large deflections after the collapse. Table 2. Overview of specimens used in experimental research, their load resistances and comparison with finite element models and suggested analytical method. Column Preload [kN] Preload ratio Load resistance [kN] Reduction ratio FEM Load resistance [kN] Ns,R (k = 0.5) [kN] O1 0 0 1084 960 877 O2 0 0 1076 960 877 O3 200 0.93 907 0.84 790 570 O4 170 0.79 983 0.91 892 616 O5 140 0.65 880 0.81 855 662 O6 110 0.51 1027 0.95 919 708 H1 0 0 994 1046 1020 H2 0 0 1083 1046 1020 H3 200 0.46 982 0.95 999 884 H4 300 0.69 930 0.90 951 816 H5 200 0.46 962 0.93 999 984 H6 300 0.69 967 0.93 951 816 Fig. 3. Gas metal arc welding of intermittent welds captured by a camera and a thermal imager; buckled column H2. 0.7 0.8 0.9 1.0 0100 200 300 400 Reduction ratio Preload [kN] Exp_O Exp_H FEM_O FEM_H 123 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 Fig. 4. Load–deflection curves of columns in experimental research; columns strengthened without preload are marked with dashed lines. The analytically determined buckling resistances according to EN 1993-1-1 [19] using the yield strength determined from tensile coupon tests are for the strengthening pattern O Nb,0,Rk = 215 kN and Nb,z,Rk = 877 kN and for the strengthening pattern H Nb,0,Rk = 432 kN and Nb,z,Rk = 1020 kN. Experimental load resistance which is lower than the analytical buckling resistance is highlighted in red colour in Table 2. Note that the resistance of the base section was determined using standard procedure by EN 3 [19]. The experimental resistance would probably be slightly higher and thus the preload ratios lower. The reduction ratio is the ratio of the load resistance of column strengthened under load to the load resistance of column welded without preload. The load–deflection curves are in Fig. 4. The load resistance of columns strengthened under preload was in all cases smaller than the load resistance of columns welded without preload. All columns failed via flexural buckling as expected with one exception of column H6 which buckled around axis y despite the orientation of knife-edge bearings. This case shows that knife-edge bearings cannot ensure fixed boundary condition. To equalise critical loads perpendicular to both axes, the buckling length for the direction around the “fixed” axis should be equal to 1924 mm (3000/1.56). In the case of the column O3 (preload ratio 0.93), the base section deflected by nearly 5 mm (L/600), which is a significant deflection and strengthening under such high preload ratios cannot be recommended. 3.2. Numerical research and analytical solution Using results of numerical models and Equation (2), coefficient k can be determined for each column strengthened under load. The distribution of coefficient k is shown in Fig. 5 and Fig. 6. Coefficient k Average 0.230 Median 0.216 Minimum -0.075 Maximum 0.716 95% quantile 0.488 Number of samples 382 Fig. 5. Distribution of coefficient k depicted in a histogram. 0 200 400 600 800 1000 1200 -5 0 5 10 15 20 25 Axial force N[kN] Deflection wy[mm] O1 O2 O3 O4 O5 O6 0 200 400 600 800 1000 1200 -5 0 5 10 15 20 Axial force N[kN] Deflection wy[mm] H1 H2 H3 H4 H5 H6 0 20 40 60 80 100 120 Frequency coefficient k 124 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 Fig. 6. Coefficient k in dependence on relative slenderness of the strengthened section; preload ratios are marked with distinctive colour. The buckling curves in EN 1993-1-1 are designed so that the biggest impact of initial imperfections is at relative column slenderness ߣҧ = 1. Kala and Kala [20] used sensitivity study on various initial imperfections and concluded that for hot-rolled I shaped column IPE 220 residual stress is the most important factor at ߣҧ = 0.68 and initial crookedness at ߣҧ = 0.97. It seems that the coefficient k is the highest at higher relative slenderness, from 1 to 2 (see examples in Fig. 6). That means the preload affects the reduction ratio the most at this relative slenderness from 1 to 2. Authors presume that the stress locked in by the strengthening under load has a greater effect at low relative slenderness and with increasing slenderness the effect of increased initial deflection is becoming more significant. The correlation of coefficient k on base section or strengthened section slenderness or thickness of strengthening plates is not completely clear yet. Therefore, authors suggest a use of k = 0.5, which is slightly safer value than 95% quantile (see Fig. 5). Comparison of numerical analyses with two analytical methods – (k) suggested method with coefficient k = 0.5; (TP) method according to [7] – is shown on the example of base section HEA 100 strengthened via plates thickness 10 mm with pattern H, pinned around axis z and initial imperfection L/300 in Fig. 7. Fig. 7. Comparison of numerical models with analytical methods of strengthening under load. 0.0 0.2 0.4 0.6 0.8 0.5 0.7 0.9 1.1 1.3 1.5 Coefficient k Relative slenderness of strengthened section O - y-y pinned 0.25 0.5 0.75 0.0 0.2 0.4 0.6 0.8 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 Relative slenderness of strengthened section H - y-y pinned 0.2 0.4 0.6 0.8 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Reduction ratio Preload ratio FEM L=2m FEM L=3m FEM L=4m FEM L=5m k L=2m k L=3m k L=4m k L=5m TP L=2m TP L=3m TP L=4m TP L=5m 125 Martin Vild and Miroslav Bajer / Procedia Engineering 190 ( 2017 ) 118 – 125 4. Conclusions Strengthening under load using welded plates is a feasible method. Use of thin electrode wire is recommended for strengthening under load to keep the heat affected zone small and to limit the elongation of the steel member during a welding process and shrinkage after cooling. The simple analytical solution with a coefficient k was introduced. Based on the comprehensive numerical parametric study validated by experimental research, the value of coefficient k is suggested equal to 0.5. This method yields safe results and allows material savings compared to the commonly used method in the Czech Republic. Completely neglecting the effect of preload as suggested by some researchers seems hazardous. Strengthening under preload ratios higher than 0.8 is in some cases feasible but not recommended, because the deflection caused by preload and welding can lead to significant deflections which could affect serviceability. Nevertheless, the reduction of load resistance in the experiment was only 19 % for preload ratio 0.93. Acknowledgements The financial support of projects No FAST-J-16-3560, FAST-S-16-2994 and GA14-25320S are gratefully acknowledged. References [1] R.L. Brockenbrough, AISC Rehabilitation and Retrofit Guide, 2003, Pittsbourg. 334 p. [2] T.P. O’Sullivan, Strengthening of Steel Structures under Load, ICE Proceedings. 2 (1953) 76–95. [3] NR. Nagaraja Rao, L.Tall, Columns reinforced under load, Welding Journal. 42 (April 1963) 54 p. [4] R.H.R.Tide, Reinforcing Steel Members and the Effect of Welding, AISC Engineering Journal, 1990, 129-131. [5] Z. Wu, G.Y. Grondin, Behaviour of Steel Columns Reinforced with Welded Steel Plates. Edmonton, 2002. Structural Engineering Report. University of Alberta. [6] L. Spal, Retrofit of Steel Structures (Rekonstrukce ocelových konstrukcí). Praha: Státní nakladatelství technické literatury, 1968, 183 p. [7] Pontex, s.r.o., TP 42 – Repair, Renovation and Redevelopment of Steel Load-Bearing Structures of Bridges (Opravy, obnovy a přestavby ocelových nosných konstrukcí mostů). Praha: Ministerstvo dopravy, 2014, 64 p. [8] M. Vašek, Collapse, Failure and Retrofit: Timber and Steel Structures (Havárie, poruchy a rekonstrukce: dřevěné a ocelové konstrukce). Praha: Grada, 2011. Stavitel. ISBN 978-80-247-3526-9. [9] J.H. Brown, Reinforcing Loaded Steel Compression Members. AISC Engineering Journal, 1988, 161-168. [10] T.D. Ricker, Field welding to existing steel structures. AISC Engineering Journal, 1988. 16 p. [11] V.M. Kolesnikov, O normach po rasčotu stalnych konstrukcij, usiljennych pod nagruzkoj, Promyšlennoje strojitělstvo. 1962, 10: 46-50. cit. in: L. Spal, Rekonstrukce ocelových konstrukcí. Praha: Státní nakladatelství technické literatury, 1968, 183 p. [12] H. Marzouk, S. Mohan, Strengthening of wide-flange columns under load, Canadian Journal of Civil Engineering. 17 (1990) 835-843. ISSN 0315-1468. DOI: 10.1139/l90-094. [13] M. Vild, M. Bajer, Strengthening under Load: Experimental and Numerical Research. IOP Conference Series: Materials Science and Engineering, 96 (2015) 1-10. ISSN 1757-8981, DOI: 10.1088/1757-899X/96/1/012062. [14] M. Vild, M. Bajer, Strengthening of Steel Columns under Load: Torsional-Flexural Buckling, Advances in Materials Science and Engineering, 2016, ISSN: 1687-8434. DOI: 10.1155/2016/2765821. [15] H. Unterweger, Ultimate Load Capacity of Columns Strengthened under Preload. Advances in Steel Structures, 1999, 117-124. [16] G. Huenersen, H. Haensch, J. Augustyn, Repair welding under load. Welding in the World. 28 (1990) 174-182. [17] M. Vild, M. Bajer, Strengthening under Load: The Effect of Preload Magnitudes, Procedia Engineering, 161 (2016) 343-348. ISSN: 18777058. DOI: 10.1016/j.proeng.2016.08.570 [18] K. Masubuchi, Analysis of Welded Structures: Residual Stresses, Distortion, and Their Consequences, Pergamon Press, 1980. 642 p, ISBN13: 978-1483172620. [19] CEN, EN 1993-1-1:2005 Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings, 2009. [20] Z. Kala, J. Kala, Sensitivity analysis of stability problems of steel structures using shell finite elements and nonlinear computation methods, AIP Conference Proceedings. 1389 (2011) 1865-1868. ISSN: 0094243X, DOI: 10.1063/1.3636974.