Browse > Article
http://dx.doi.org/10.12989/scs.2018.28.4.403

Lateral-torsional buckling of functionally graded tapered I-beams considering lateral bracing  

Rezaiee-Pajand, Mohammad (Department of Civil Engineering, Ferdowsi University of Mashhad)
Masoodi, Amir R. (Department of Civil Engineering, Ferdowsi University of Mashhad)
Alepaighambar, Ali (Department of Civil Engineering, Ferdowsi University of Mashhad)
Publication Information
Steel and Composite Structures / v.28, no.4, 2018 , pp. 403-414 More about this Journal
Abstract
In this paper, the lateral-torsional buckling of axially-transversally functionally graded tapered beam is investigated. The structure cross-section is assumed to be symmetric I-section, and it is continuously laterally supported by torsional springs through the length. In addition, the height of cross-section varies linearly throughout the length of structure. The proposed formulation is obtained for the case that the elastic and shear modulus change as a power function along the beam length and section height. This structure carries two concentrated moments at the ends. In this study, the lateral displacement and twisting angle relation of the beam are defined by sinusoidal series. After establishing the eigenvalue equation of unknown constants, the beam critical bending moment is found. To validate the accuracy and correctness of results, several numerical examples are solved.
Keywords
functionally graded material; lateral and torsional buckling; tapered beam; warping; continuous torsional bracing;
Citations & Related Records
Times Cited By KSCI : 7  (Citation Analysis)
연도 인용수 순위
1 Pavlovic, R., Kozic, P., Rajkovic, P. and Pavlovic, I. (2007), "Dynamic stability of a thin-walled beam subjected to axial loads and end moments", J. Sound Vib., 301(3-5), 690-700.   DOI
2 Pi, Y.L. and Bradford, M.A. (2002), "Elastic flexural-torsional buckling of continuously restrained arches", Int. J. Solids Struct., 39(8), 2299-2322.   DOI
3 Rezaiee-Pajand, M. and Masoodi, A.R. (2016), "Exact natural frequencies and buckling load of functionally graded material tapered beam-columns considering semi-rigid connections", J. Vib. Control, 24(9), 1787-1808.
4 Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696.   DOI
5 Schrader, R.K. and Hill, H.N. (1943), "Lateral stability of unsymmetrical I-beams and trusses in bending", Transact. Am. Soc. Civil Engr., 108(1), 261-265.
6 Schurig, M. and Bertram, A. (2011), "The torsional buckling of a cruciform column under compressive load with a vertex plasticity model", Int. J. Solids Struct., 48(1), 1-11.   DOI
7 Shooshtari, A., Heyrani Moghaddam, S. and Masoodi, A. (2015), "Pushover analysis of gabled frames with semi-rigid connections", Steel Compos. Struct., Int. J., 18(6), 1557-1568.   DOI
8 Tsai, H.-C. and Kelly, J.M. (2005), "Buckling of short beams with warping effect included", Int. J. Solids Struct., 42, 239-253.   DOI
9 Valentino, J. and Trahair, N.S. (1998), "Torsional restraint against elastic lateral buckling", J. Struct. Eng. ASCE, 124(10), 1217-1226.   DOI
10 Vieira, R.F., Lisi, D. and Virtuoso, F.B. (2014), "Dynamic analysis of bridge girders submitted to an eccentric moving load", Struct. Eng. Mech., Int. J., 52(1), 173-203.   DOI
11 Yoo, C.H. and Lee, S. (2011), Stability of Structures: Principles and Applications, Elsevier.
12 Vo, T.P., Lee, J., Lee, K. and Ahn, N. (2011), "Vibration analysis of thin-walled composite beams with I-shaped cross-sections", Compos. Struct., 93(2), 812-820.   DOI
13 Winter, G. (1958), "Lateral bracing of columns and beams", J. Struct. Div. ASCE, 84(2), 1561-1583.
14 Ying, J., Lu, C.F. and Chen, W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", J. Compos. Struct., 84(3), 209-219.   DOI
15 Yoon, K. and Lee, P.-S. (2014), "Modeling the warping displacements for discontinuously varying arbitrary crosssection beams", Compos. Struct., 131, 56-69.   DOI
16 Taylor, A.C. and Ojalvo, M. (1966), "Torsional restraint of lateral buckling", J. Struct. Div. ASCE, 92(ST2), 115-129.
17 Banerjee, J.R. and Fisher, S.A. (1992), "Coupled bending-torsional dynamic stiffness matrix for axially loaded beam elements", Int. J. Numer. Methods Eng., 33(4), 739-751.   DOI
18 Andrade, A. and Camotim, D. (2004), "Lateral-torsional buckling of prismatic and tapered thin-walled open beams: assessing the influence of pre-buckling deflections", Steel Compos. Struct., Int. J., 4(4), 281-301.   DOI
19 Attard, M.M. and Kim, M.-Y. (2010), "Lateral buckling of beams with shear deformations-A hyperelastic formulation", Int. J. Solids Struct., 47(20), 2825-2840.   DOI
20 Aydin, R., Gunaydin, A. and Kirac, N. (2015), "On the evaluation of critical lateral buckling loads of prismatic steel beams", Steel Compos. Struct., Int. J., 18(3), 603-621.   DOI
21 Banerjee, J.R. and Williamsm F.W. (1994), "Coupled bendingtorsional dynamic stiffness matrix of an axially loaded timoshenko beam element", Int. J. Solids Struct., 31(6), 749-762.   DOI
22 Barretta, R., Feo, L. and Luciano, R. (2015), "Some closed-form solutions of functionally graded beams undergoing nonuniform torsion", Compos. Struct., 123, 132-136.   DOI
23 Bokaian, A. (1988), "Natural frequencies of beams under compressive axial loads", J. Sound Vib., 126(1), 46-65.
24 Bokaian, A. (1990), "Natural frequencies of beams under tensile axial loads", J. Sound Vib., 142(3), 481-498.   DOI
25 Khelil, A. and Larue, B. (2008), "Simple Solution for the flexuraltorsional buckling of laterally restrained I-beams", Eng. Struct., 30(10), 2923-2934.   DOI
26 Joshi, A. and Suryanarayan, S. (1989), "Unified analytical solution for various boundary conditions for the coupled flexuraltorsional vibration of beams subjected to axial loads and end moments", Int. J. Solids Struct., 20(2), 167-178.   DOI
27 Joshi, A. and Suryanarayan, S. (1991), "Iterative method for coupled flexural-torsional vibration of initially stressed beams", J. Sound Vib., 146(1), 81-92.   DOI
28 Jun, L., Rongying, S., Hongxing, H. and Xianding, J. (2004), "Coupled bending and torsional vibration of axially loaded Bernoulli-Euler beams including warping effects", Appl. Acoust., 65(2), 153-170.   DOI
29 Kim, N.-I. and Lee, J. (2014), "Exact solutions for stability and free vibration of thin-walled Timoshenko laminated beams under variable forces", Arch. Appl. Mech., 84(12), 1785-1809.   DOI
30 El-Mahdy, G.M. and El-Saadawy, M.M. (2015), "Ultimate strength of singly symmetric I-section steel beam with variable flange ratio", Thin-Wall. Struct., 87, 149-157.   DOI
31 Larue, B., Khelil, A. and Gueury, M. (2007), "Elastic flexural-torsional buckling of steel beams with rigid and continuous lateral restraints", J. Constr. Steel Res., 63(5), 692-708.   DOI
32 Kim, N.-I., Jeon, C.-K. and Lee, J. (2013), "Dynamic stability analysis of shear-flexible composite beams", Arch. Appl. Mech., 83(5), 685-707.   DOI
33 Kus, J. (2015), "Lateral-torsional buckling steel beams with simultaneously tapered flanges and web", Steel Compos. Struct., Int. J., 19(4), 897-916.   DOI
34 Lanc, D., Turkalj, G., Vo, T.P. and Brnic, J. (2016), "Nonlinear buckling behaviours of thin-walled functionally graded open section beams", Compos. Struct., 152, 829-839.   DOI
35 Lee, S.-H., Kim, Y.-H. and Choi, S.-M. (2015), "Ultimate strength of long-span buildings with P.E.B (Pre-Engineered Building) system", Steel Compos. Struct., Int. J. 19(6), 1483-1499.   DOI
36 Hashemi, S.M. and Richard, M.J. (2000a), "A Dynamic Finite Element (DFE) method for free vibrations of bending-torsion coupled beams", Aerosp. Sci. Technol., 4(1), 41-55.   DOI
37 Fatmi, R.E. (2007), "Non-uniform Warping Including the Effects of Torsion and Shear Forces. Part I: A General Beam Theory", Int. J. Solids Struct., 44, 5912-5929.   DOI
38 Gellert, M. and Gluck, J. (1972), "The influence of axial load on eigen-frequencies of a vibrating lateral restraint cantilever", Int. J. Mech. Sci., 14(11), 723-728.   DOI
39 Gupta, L.M., Ronghe, G.N. and Naghate, M.K. (2003), "Behaviour and stability of prestressed steel plate girder for torsional buckling", Steel Compos. Struct., Int. J., 3(1), 65-73.   DOI
40 Hashemi, S.M. and Richard, M.J. (2000b), "Free vibrational analysis of axially loaded bending-torsion coupled beams: a dynamic finite element", Comput. Struct., 77(6), 711-724.   DOI
41 Hashemi, S.M., Richard, M.J. and Dhatt, G. (1999), "A new Dynamic Finite Element (DFE) formulation for lateral free vibrations of Euler-Bernoulli spinning beams using trigonometric shape functions", J. Sound Vib., 220(4), 601-624.   DOI
42 Michaltsos, G.T. and Raftoyiannis, I.G. (2012), "The influence of prestressing on the twisting phenomenon of beams", Arch. Appl. Mech., 82(10), 1531-1540.   DOI
43 Leung, A.Y.T. (1991), "Natural shape functions of a compressed Vlasov element", Thin-Wall. Struct., 11(5), 431-438.   DOI
44 Li, S.R. and Batra, R.C. (2013), "Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams", J. Compos. Struct., 95, 5-9.   DOI
45 Masoodi, A.R. and Moghaddam, S.H. (2015), "Nonlinear dynamic analysis and natural frequencies of gabled frame having flexible restraints and connections", KSCE J. Civil Eng., 19(6), 1819-1824.   DOI
46 Joshi, A. and Suryanarayan, S. (1984), "Coupled flexural-torsional vibration of beams in the presence of static axial loads and end moments", J. Sound Vib., 92(4), 583-589.   DOI
47 Huang, Y. and Li, X.F. (2011), "Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity", J. Eng. Mech., 137(1), 73-81.   DOI
48 Ioannidis, G.I. and Avraam, T.P. (2012), "Lateral-torsional buckling of simply supported beams under uniform bending and axial tensile force", Arch. Appl. Mech., 82(10), 1393-1402.   DOI
49 Ioannidis, G., Mahrenholtz, O. and Kounadis, A.N. (1993), "Lateral post-buckling analysis of beams", Arch. Appl. Mech., 63(3), 151-158.   DOI
50 Mohammadi, E., Hosseini, S.S. and Rohanimanesh, M.S. (2016), "Elastic lateral-torsional buckling strength and torsional bracing stiffness requirement for mono-symmetric I-beams", Thin-Wall. Struct., 104, 116-125.   DOI
51 Murthy, M. and Neogy, J. (1969), "Determination of fundamental natural frequencies of axially loaded columns and frames", J. Inst. Engt. (India) Civil Eng. Div., 49, 201-212.
52 Nguyen, C.T., Moon, J., Le, V.N. and Lee, H.-E. (2010), "Lateraltorsional buckling of I-girders with discrete torsional bracings", J. Constr. Steel Res., 66(2), 170-177.   DOI
53 Nguyen, C.T., Joo, H.S., Moon, J. and Lee, H.E. (2012), "Flexural-torsional buckling strength of I-girders with discrete torsional bracing under various load conditions", Eng. Struct., 36, 337-350.   DOI
54 Nguyen, X.-H., Kim, N.-I. and Lee, J. (2015), "Optimum design of thin-walled composite beams for flexural-torsional buckling problem", Compos. Struct., 132, 1065-1074.   DOI
55 Nguyen, H.X., Lee, J., Vo, T.P. and Lanc, D. (2016), "Vibration and lateral buckling optimisation of thin-walled laminated composite channel-section beams", Compos. Struct., 143, 84-92.   DOI
56 Pavlovic, R. and Kozic, P. (2003), "Almost sure stability of the thinwalled beam subjected to end moments", Theor. Appl. Mech., 30(3), 193-207.
57 Nishino, F., Kasemset, C. and Lee, S.L. (1973), "Variational formulation of stability problems for thin-walled members", Ingenieur-Archiv, 43(1), 58-68.   DOI
58 Orloske, K. and Parker, R.G. (2006), "Flexural-torsional buckling of misaligned axially moving beams: II. Vibration and stability analysis", Int. J. Solids Struct., 43(14-15), 4323-4341.   DOI