NUMERICAL SIMULATION FOR CRITICAL ELASTIC MOMENT OF STEEL BEAMS WITH DIFFERENT CROSS SECTIONS

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 6, June 2018, pp , Article ID: IJCIET_09_06_080 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed NUMERICAL SIMULATION FOR CRITICAL ELASTIC MOMENT OF STEEL BEAMS WITH DIFFERENT CROSS SECTIONS Juned Raheem Civil Engineering Department, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, India Dr. S.K Dubey Civil Engineering Department, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, India Dr. Nitin Dindorkar Civil Engineering Department, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, India ABSTRACT Lateral Torsion Buckling (LTB) may be a failure criterion for beams in flexure. The AISC defines Lateral Torsion Buckling because the buckling mode of a flexural member involving deflection traditional to the plane of bending occurring at the same time with twist regarding the shear center of the cross-sectional. LTB happens once the compression portion of a beam isn't any longer comfortable in strength and instead the beam is restrained by the strain portion of the beam that causes deflection or twisting to occur. The styles bending resistance moment of laterally unsupported beams area unit calculated as per Section of Indian customary Code for General Construction in Steel-Code of follow, IS 800:2007. Elastic crucial moment Mcr is a very important parameter to require account of LTB. ANNEX E (CL ,IS 800:2007) of the code offers the tactic of calculative Mcr,, thus the elastic lateral torsional buckling moment for various beam sections, considering loading and support condition is obtained and results area unit valid victimisation FEM modeling techniques. the consequences of assorted parameters effecting lateral torsional buckling was studied and analyzed totally. The results obtained within the study are corroboratory the present ISCODE technique for calculation of Mcr for doubly symmetrical I section. however the results of elastic symmetrical moment obtained for Channel section aren't in complete agreement with FEM modeling technique. thus it needs additional modification for channel section. The package tool ANSYS is employed for FEM modeling technique. Key words: Lateral torsion buckling, Elastic Critical Moment, I Beam, Channel Beam, FEM, Stiffness editor@iaeme.com

2 Numerical Simulation for Critical Elastic Moment of Steel Beams with different Cross Sections Cite this Article: Juned Raheem, Dr. S.K Dubey and Dr. Nitin Dindorkar, Numerical Simulation for Critical Elastic Moment of Steel Beams with different Cross Sections, International Journal of Civil Engineering and Technology, 9(6), 2018, pp INTRODUCTION One of the problems engineers confront, when they design beam with an open cross area is Lateral Torsional buckling, regularly referred as LT-buckling. LT-Buckling will take place in major Axis bending of beam while the stiffness approximately the primary axis is comparatively larger to the stiffness of the same about the minor axis.[1] In this phenomenon compression flange will buckle in the course transverse to the load earlier than the steel yields results in pulling beam sideways, whereas the flange because of being in tension will preserve the beam in vicinity. This phenomenon is known as lateral-torsional buckling and metallic beam for its particular purpose.[2] When designing with attention of LT-buckling in step with the IS 800:2007 design code, Herein after called ISCODE, one Major parameter to be considered could be the slenderness of beam. For its strength two parameters are used; the plastic moment capability of the section, Mpl, and the elastic critical moment, Mcr.[15] The lesser the Mcr, the higher can be the relative slenderness. A better relative slenderness will bring about a low value of reduction factor, thereby reducing the design moment capability of the beam.various methods have been developed for the solution of singly symmetric I section subjected to eccentric loading.[3] Further method is also developed for singly symmetric section subjected to linearly varying moments.[4],[5] There are various factors which influence the M cr such as stiffness about the minor axis, torsional stiffness, warping stiffness, span length, support conditions, Type and application of the weight, material properties and symmetry about the foremost and minor axis.[17][18] However lateral torsional buckling in short beams is because of distortion of web and consequently lateral torsion buckling answer predicts an overestimated criticall load.[8] Indian standard code does now not offer any answer for elastic critical moment of channel section.[15] However it gives the elastic critical moment for doubly symmetric and mono symmetric I segment beams. Channel section has been analysed for Mcr, the usage of three component components of Eurocode-3 and demonstrated with special softwares consisting of ADINA, COLBEAM, LTBEAM, SAP2000 and STAAD pro however did not set up any conclusion. [11] In present situation, maximum of the commercial Structural engineering software program will bear in mind lateral torsional buckling at some stage in the evaluation of capability of steel beams. ANSYS software program as a present day method based totally on FEM simulation and modeling is used for advanced engineering simulation purpose. The process has three stages preprocessing, solution and post processing. [21] 2. PRESENT EVALUATION In Various technical papers it is seen that work has been done on the analysis of lateral torsional buckling in number of ways such as analytical and parametric analysis by using software such as ADINA, COLBEAM, SAP2000 etc[10] and also Experiments has been done to evaluate the same[13]. So, referring from all those papers some steps have been taken to analyze lateral torsional buckling of steel beam by using Indian Standard codes IS 800 :2007, in which ANNEX E and Clause eight.2.2 gives the formulae for the calculation of elastic critical moment which is beneficial to calculate the effect of lateral torsional buckling in phrases of moment. Considering this, one problem of simply supported beam of 4m span with concentrated load of 1KN applied at mid span has been selected to evaluate the elastic critical moment. The calculation is performed manually by way of the use of process said in editor@iaeme.com

3 Juned Raheem, Dr. S.K Dubey and Dr. Nitin Dindorkar ISCODE. After that Analyzing the beam through the use of ANSYS SOFTWARE by modeling the same section as stipulated in IS: SP: 1:6 :1984. The critical moment values are in comparison with the guide calculation. 3. LATERAL TORSIONAL BUCKLING AS STIPULATED IN IS: 800: 2007[15] 3.1. For Doubly Symmetric Prismatic Beams The elastic critical moment corresponding to lateral torsional buckling of a doubly symmetric prismatic beam subjected to uniform moment in the unsupported length and torsionally restraining lateral supports is given by: [ ( ) ] Where I t = Torsional constant (Section 3.1.7) I w = warping constant (section ) G = Modulus of rigidity L LT = Effective length against lateral torsional buckling (Section 3.1.9) 3.2. Simplified equation for prismatic members made of standard rolled I- sections and welded doubly symmetric I-sections I t = Torsional constant (Section 2.1.7) I w = Warping constant (section ) I y = Moment of inertia, r y = Radius of gyration about the weak axis ( ) [ { }] L LT = Effective length for lateral torsional buckling (Section 2.1.9) h f = Center to center distance between flanges t f = Thickness of the flange 3.3. For Sections Symmetric about Minor Axis In case of a beam which is symmetrical only about the minor axis, and bending about major x-axis, the elastic critical moment for lateral torsional buckling is given by the general equation. {[( ) ( ) ( )] ( )} Where: c 1, c 2, c 3 = factors depending upon the loading and end restraint conditions (Table 5, 6) editor@iaeme.com

4 Numerical Simulation for Critical Elastic Moment of Steel Beams with different Cross Sections K, K w = effective length factors of the unsupported length accounting for boundary conditions at the end lateral supports. K = 0.5 (For complete restraint against rotation about weak axis = 01 (For free rotation about weak axis) = 0.7 (For one end fixed and other end free) = Factor for warping restraint. K w Unless special provisions to restrain warping of the section at the end lateral supports are made, K w should be taken as 1.0. y g =distance between the point of application of the load and the shear centre of the cross section in y- direction and is positive when the load is acting towards the shear centre from the point of application. y j ( ) y s = coordinate of the shear centre with respect to centroid and is positive when the shear centre is on the compression side of the centroid. y, z = coordinates of the elemental area with respect to centroid of the section The y j can be calculated by using the following approximation For Plain flanges y j = 0.8 ( 2β f 1) h y /2.0 (when β f > 0.5) y j = 1.0 ( 2β f 1) h y /2.0 (when β f 0.5 ) Lipped flanges y j = 0.8 ( 2β f 1) (1+ h l /h h y /2 (when β f > 0.5) y j = ( 2β f 1) (1+ h l /h)h y /2 (when β f 0.5) Where; h l = height of the lip h = overall height of the section 4. FINITE ELEMENT METHOD SIMULATION TECHNIQUE ANSYS was started in It was started to develop finite element analysis software for structural physics that could simulate static, thermal and dynamic problems. It is a finite element analysis tool used for structural analysis, including linear and nonlinear studies. This computer simulation product provides finite elements to model behavior, and supports material models and equation solvers for a wide range of mechanical design problems editor@iaeme.com

5 Elastic critical moment Mcr (knm) 5. RESULTS & DISCUSSION Juned Raheem, Dr. S.K Dubey and Dr. Nitin Dindorkar Figure 1 ANSYS user interface showing model of I-Beam 5.1. For Doubly Symmetric I-Section Table 1 Comparison of M cr obtained for an I-Section subjected to concentrated load at mid span M cr for I-Section Section M cr ANSYS (knm) M cr theoretical (knm) Percentage Error ISMB ISMB ISMB ISMB ISMB ISMB ISMB Percentage Error = ( ) ( ) ( ) Comparison for I-Section Mcr, ANSYS Mcr,Theor ISMB175 ISMB200 ISMB250 ISMB300 ISMB350 ISMB400 ISMB500 Figure 1 Comparison of M cr Value obtained from Section editor@iaeme.com

6 Numerical Simulation for Critical Elastic Moment of Steel Beams with different Cross Sections 5.2. For Mono Symmetric Channel Section Table 2 Comparison of Mcr values for Channel section subjected to concentrated load at mid span M cr for Channel Section Section M cr ANSYS (knm) M cr theoretical Percentage Error (knm) ISMC ISMC ISMC ISMC ISMC COMPARISION FOR CHANNEL SECTION Mcr ANSYS (knm) Mcr theoretical (knm) ISMC175 ISMC200 ISMC250 ISMC300 ISMC400 Figure 2 Comparison of Mcr Value obtained from Section % VARIATION FOR I- SECTION % VARIATION FOR CHANNEL SECTION Figure 3 Comparison for % variation for I-section and Channel section 6. CONCLUSIONS In the current study various factors which will affect the lateral torsional buckling have been analyzed. After analyzing the factors, the elastic critical moment, M cr, have been evaluated for the various hot rolled steel section given in IS:SP using theoretical method given in editor@iaeme.com

7 Juned Raheem, Dr. S.K Dubey and Dr. Nitin Dindorkar IS: 800: 2007 in Clause and validation of these results is done using ANSYS software which works on FEM technique. The conclusion that can be made for I-section will be: The results obtained for critical moment from the ISCODE provision agrees completely with the FEM technique generating a authenticated and safe approach for the beams. The typical variation in the values of critical moment from the two methods is approximately under 1%. For a given span, the variation of the values converges to approx 0.5% variation only as we move to the section with more stiffness i.e., having more warping and torsional resistance. Hence it can be concluded that the results from the two methods will be more authentic with section having larger stiffness. Beam of Channel section of various section which are stipulated in IS Steel table are modeled in ANSYS. The beam is subjected to a point load on the upper flange of the section for calculation of critical buckling moment. The critical buckling moment was obtained from ISCODE stipulated formulas.. Although Eurocode generally follows 3-factor formula for unsymmetrical section. The conclusions that can be drawn from the results are: The results obtained for critical buckling moment from manual calculation using general equation are not in conformation with the FEM technique software ANSYS. The variation in the results by the two methods was of order of about approx 5-15%. The variation is seems to be converging as we move to more stiffed section. The results obtained from ISCODE stipulation are on the safer side for the design purpose but this may lead to economical loss. 7. DISCUSSION The results from methods for I-Section are in complete agreement with every other, then again for a Channel segment the end result version is of order approx 15%. As the ISCODE doesn t provide any formulation to calculate the lateral torsional buckling moment for non symmetrical section therefore the method used for calculating the critical buckling moment won't incorporate all the elements efficiently. Further study is needed to generate a end result for calculation of critical moment for non- symmetrical section. One of the motives for this variation in outcomes for Channel section is because of the utility of the load on the flange producing torsion stresses within the flange because the eccentricity of load consequences in moment distribution over the web element. REFERENCES [1] Clark, J. W. and Hill, H. N. [1960], Lateral Buckling of Beams, J. of the Structural Division, Vol. 86, No. ST7, July 1960, ASCE, pp [2] Peköz, T. [1969] (with a contribution by N. Celebi), Torsional-Flexural Buckling of Thin-Walled Sections Under Eccentric Load, Cornell Engineering Research Bulletin 69-1, Cornell University. [3] Peköz, T. and Winter, G., [1969] Torsional-Flexural Buckling of Thin-Walled Sections Under Eccentric Load, J. of the Structural Division, Vol. 95, No. ST5, May, 1969, ASCE, pp editor@iaeme.com

8 Numerical Simulation for Critical Elastic Moment of Steel Beams with different Cross Sections [4] Kitipornchai, S., wang, C. M. and Trahair, N. S. [1986], Buckling of Monosymmetric I- Beams Under Moment Gradient, J. of the Structural Division, Vol. 112, No. ST4, Apr., 1986, ASCE, pp [5] Peköz, T, Lateral Buckling Of Singly Symmetric Beams Eleventh International Specialty Conference on Cold-Formed Steel Structures St. Louis, Missouri, U.S.A., October (1992) [6] Salmon, C.G., and J.E. Jhonson[1996], Steel Structures, Design and Behavior, 4 th edn, Harper Collins, NY, 1996, P [7] F. Mohri, A. Brouki, J.C. Roth, Theoretical and numerical stability analyses of unrestrained, mono-symmetric thin-walled beams Journal of Constructional Steel Research, Vol. 59 (2003), pp [8] Avik Samanta, Ashwini Kumar, Distortional buckling in monosymmetric I-beams Thin-Walled Structures 44 (2006), pp [9] H.H. (Bert) Snijder, J.C.D. (Hans) Hoenderkamp, M.C.M (Monique) Bakker H.M.G.M.(henri) Steenbergen C.H.M.(Karini) de Louw Design rules for lateral torsional buckling of channel sections subjected to web loading Stahlbau 77 (2008), pp [10] Martin Ahnlén, Jonas Westlund Lateral Torsional Buckling of I-beams Division of Structural Engineering Steel and Timber Structures Chalmers University Of Technology Göteborg, Sweden Master s Thesis 2013:59 (2013) [11] Hermann Þór Hauksson, Jón Björn Vilhjálmsson Lateral-Torsional Buckling of Steel Beams with Open Cross Section Division of Structural Engineering Steel and Timber Structures Chalmers University Of Technology Göteborg, Sweden 2014 Master s Thesis 2014:28 (2014) [12] L. Dahmani, S. Drizi, M. Djemai, A. Boudjemia, M. O. Mechiche Lateral Torsional Buckling of an Eccentrically Loaded Channel Section Beam World Academy of Science, Engineering and Technology, International Journal of Civil and Environmental Engineering, Vol:9, No:6, pp (2015) [13] Jan Barnata, Miroslav Bajera, Martin Vilda, Jindřich Melchera, Marcela Karmazínováa, Jiří Pijáka Experimental Analysis of Lateral Torsional Buckling of Beams with Selected Cross-Section Types Procedia Engineering, 195 (2017), pp [14] Carl-Marcus Ekström, David Wesley, Lateral-torsional Buckling of Steel Channel Beams Division of Structural Engineering Chalmers University Of Technology Gothenburg, Sweden 2017 Master s Thesis 2017:52 (2017) [15] IS 800 : 2007 General construction in steel code of practice (third edition) [16] Dimensions for Hot rolled steel beam, column, channel and angle sections ( Third Revision ) IS [17] Subramanian, Design Of steel Structures, Textbook [18] Ramchandra, Design Of steel Structures, Textbook [19] Trahair N.S. (1993): Flexural-Torsional Buckling of Structures, CRC Press, Boca Raton, [20] Timoshenko S.P. and Gere J. (1961): Theory of Elastic Stability (2nd ed.), McGraw-Hill, New York, 1961 [21] ANSYS Softwarehttp:// editor@iaeme.com