Buckling Analysis of Steel Fiber Column with Different Cross-Section and Boundary Conditions Using Euler-Bernoulli Beam Theory

Year 2019, Volume: 11 Issue: 1, 330 - 344, 22.05.2019

Mahmut Tunahan Özdemir , Veysel Kobya Mustafa Özgür Yaylı , Ali Mardani Aghabaglou

https://doi.org/10.24107/ijeas.533727

Abstract

Nowadays, with the
help of developing technology, engineering problems which are difficult to
solve have become easily solved in a short time by means of computer software. Certain mathematical algorithms
are used in these analysis methods. The mathematical and numerical solution
methods created provide a significant solution facility for engineering. In
this paper, the buckling analysis of the Euler column model, with elastic
boundaries and containing steel fibers, under pressure effect is performed. In
the column model, three different sections, which have been produced from four
different concrete series, including three different types of fiber reinforced
specimens and one non-fibrous control sample(C) with 0.6% by volume, were
analyzed by using a software. In the study, the
analysis of the critical buckling values depend on length, elastic modulus and
cross-sectional type of the column model has been performed. The results are
shown in graphs and tables. With the results of the analysis, the effect of
slenderness and steel fiber concrete on the critical load in pressure columns have
been investigated.

Keywords

Elastically restrained ends, Euler columns, steel fiber reinforcement, comparison of buckling load

References

• [1] Euler, L., De curvis elasticis. In Methodus inveniendi leneas curva maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattisimo sensu accepti, Lausannae, E65A. O. O. Ser.I., 24, 231-297, 1744.
• [2] Brush, D. O., Almroth, B. O., Buckling of Bars, Plates and Shells, McGraw-Hill Comp., 1975.
• [3] Dinnik, A. N. (1929). Design of columns of varying cross section. Trans ASME, 51(1), 105-14.
• [4] Keller, J. B. (1960). The shape of the strongest column. Archive for Rational Mechanics and Analysis, 5(1), 275-285.
• [5] Tadjbakhsh, I., & Keller, J. B. (1962). Strongest columns and isoperimetric inequalities for eigenvalues. Journal of Applied Mechanics, 29(1), 159-164.
• [6] Taylor, J. E. (1967). The strongest column: an energy approach. Journal of Applied Mechanics, 34(2), 486-487.
• [7] Timoshenko, S. (1970). Theory of elastic stability 2e. Tata McGraw-Hill Education.
• [8] Lee, G.C., Morrell, M.L. and Ketter, R.L., 1972. “Design of Tapered Members” Welding Research Council, Bulletin #173, June 1972.
• [9] Lee, G.C., Chen, Y.C. and Hsu, T.L., 1979. “Allowable Axial Stress of Restrained Multi- Segment, Tapered Roof Girders.” Welding Research Council, Bulletin #248, May 1979.
• [10] Lee, G.C. and Hsu, T.L., 1981. “Tapered Columns with Unequal Flanges.” Welding Research Council, Bulletin #272, November 1981.
• [11] Lee, G.C., Ketter, R.L. and Hsu, T.L., 1981. “Design of Single Story Rigid Frames”, Metal Building Manufacturer’s Association, Cleveland, Ohio.
• [12] Li, Q., Cao, H., & Li, G. (1994). Stability analysis of a bar with multi-segments of varying cross-section. Computers & structures, 53(5), 1085-1089.
• [13] Qiusheng, L., Hong, C., & Guiqing, L. (1995). Stability analysis of bars with varying cross-section. International Journal of Solids and Structures, 32(21), 3217-3228.
• [14] Li, Q., Cao, H., & Li, G. (1996). Static and dynamic analysis of straight bars with variable cross-section. Computers & structures, 59(6), 1185-1191.
• [15] Kim, H. K., Kim, M. S. (2001). Vibration of beams with generally restrained boundary conditions using Fourier series.Journal of Sound Vibration 245(5):771–784. doi: 10.1006/jsvi.2001.3615
• [16] Atay, M. T., & Coşkun, S. B. (2009). Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method. Computers & Mathematics with Applications, 58(11-12), 2528-2534.
• [17] Coşkun, S. B., & Atay, M. T. (2009). Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method. Computers & Mathematics with Applications, 58(11-12), 2260-2266.
• [18] Singh, K. V., & Li, G. (2009). Buckling of functionally graded and elastically restrained non-uniform columns. Composites Part B: Engineering, 40(5), 393-403.
• [19] Yao, F., Meng, W., Zhao, J., She, Z., & Shi, G. (2018). Analytical method comparison on critical force of the stepped column model of telescopic crane. Advances in Mechanical Engineering, 10(10), 1687814018808697.
• [20] Atay, M. T. (2010). Determination of buckling loads of tilted buckled column with varying flexural rigidity using variational iteration method. International Journal of Nonlinear Sciences and Numerical Simulation, 11(2), 97-104.
• [21] Okay, F., Atay, M. T., & Coşkun, S. B. (2010). Determination of buckling loads and mode shapes of a heavy vertical column under its own weight using the variational iteration method. International Journal of Nonlinear Sciences and Numerical Simulation, 11(10), 851-858.
• [22] Al-Kamal, M. K. (2017). Estimating Elastic Buckling Load for an Axially Loaded Column Bolted to a Simply Supported Plate using Energy Method. Alnahrain journal for engineering sciences, 20(5), 1154-1159.
• [23] Yilmaz, Y., Girgin, Z., & Evran, S. (2013). Buckling analyses of axially functionally graded nonuniform columns with elastic restraint using a localized differential quadrature method. Mathematical Problems in Engineering, 2013.
• [24] Ofondu, I. O., Ikwueze, E. U., & Ike, C. C. (2018). Determination of the critical buckling loads of euler columns using stodola-vianello iteration method. Malaysian Journal of Civil Engineering, 30(3).
• [25] Coşkun, S. B. (2009). Determination of critical buckling loads for euler columns of variable flexural stiffness with a continuous elastic restraint using homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation, 10(2), 191-198.
• [26] Başbük, M., Eryılmaz, A., & Atay, M. T. (2014). On Critical Buckling Loads of Columns under End Load Dependent on Direction. International scholarly research notices, 2014.
• [27] Basbuk, M., Eryilmaz, A., Coskun, S. B., & Atay, M. T. (2016). On Critical Buckling Loads of Euler Columns With Elastic End Restraints. Hittite Journal of Science & Engineering, 3(1).
• [28] Pinarbasi, S. (2012). Stability analysis of nonuniform rectangular beams using homotopy perturbation method. Mathematical Problems in Engineering, 2012.
• [29] Robinson, M. T. A., & Adali, S. (2018). Buckling of nonuniform and axially functionally graded nonlocal Timoshenko nanobeams on Winkler-Pasternak foundation. Composite Structures, 206, 95-103.
• [30] Akgöz, B., & Civalek, Ö. (2011). Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Science, 49(11), 1268-1280.
• [31] Huang, Y., Yang, L. E., & Luo, Q. Z. (2013). Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section. Composites Part B: Engineering, 45(1), 1493-1498.
• [32] Huang, Y., & Luo, Q. Z. (2011). A simple method to determine the critical buckling loads for axially inhomogeneous beams with elastic restraint. Computers & Mathematics with Applications, 61(9), 2510-2517.
• [33] Nejad, M. Z., Hadi, A., & Rastgoo, A. (2016). Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory. International Journal of Engineering Science, 103, 1-10.
• [34] Pinarbasi, S. (2012). Buckling analysis of nonuniform columns with elastic end restraints. Journal of Mechanics of Materials and Structures, 7(5), 485-507.
• [35] Şimşek, M. (2016). Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions. Composite Structures, 149, 304-314.
• [36] Gül, U., Aydoğdu, M., & Edirme, E. (2015). Elastik Zemin Üzerinde Oturan Timoshenko Kirişlerinde Dalga Yayınımı.
• [37] Zhang, Y., Zhang, L. W., Liew, K. M., & Yu, J. L. (2016). Buckling analysis of graphene sheets embedded in an elastic medium based on the kp-Ritz method and non-local elasticity theory. Engineering Analysis with Boundary Elements, 70, 31-39.
• [38] Yayli, M. Ö. (2018). Buckling analysis of Euler columns embedded in an elastic medium with general elastic boundary conditions. Mechanics Based Design of Structures and Machines, 46(1), 110-122.
• [39] Timoshenko, S. P., & Gere, J. M. (1961). Theory of elastic stability.
• [40] Wang, C. M., & Wang, C. Y. (2004). Exact solutions for buckling of structural members (Vol. 6). CRC press.