DETERMINATION OF THE CRITICAL BUCKLING LOADS OF EULER COLUMNS USING STODOLA-VIANELLO ITERATION METHOD

Ofondu I.O., Ikwueze E.U., Ike C.C.

Abstract


The Stodola-Vianello iteration method was implemented in this work to determine the critical buckling load of an Euler column of length l with fixed end (x = 0) and pinned end (x = l), where the longitudinal axis is the x-direction.The critical buckling loads were found to be variable, depending on the x-coordinate. Integration and the Rayleigh quotients were used to find average buckling coefficients. First iteration gave relative errors of 4% using integration and 2.5% using Rayleigh quotient.Second iteration gave average relative errorsless than 1% for both the integration and the Rayleigh quotients. Better estimates of the critical buckling loads were obtained using the Rayleigh quotient in the Stodola-Vianello’s iteration.

Keywords


Stodola –Vianello’s iteration method Euler column, critical buckling load, flexural buckling.

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References


Arbabi F. and Li F. (1991). Buckling of variable cross-section columns – integral equation approach. Journal of Structural Engineering ASCE Vol 117 No 8 pp 2426 – 2441. Doi.10.1061/(ASCE) 0733-9445 (1991) 117: 8 (2426).

Atay M.T. (2009). Determination of critical buckling loads for variable stiffness Euler columns using homotopy perturbation method. Int. Journal Nonlinear Sci and Numer. Simulation Vol 10 Issue 2 pp 199 – 206.

Coskun S.B. (2010). Analysis of Tilt – Buckling of Euler Columns with Varying Flexural Stiffness using Homotopy Pertubation Method. Mathematical Modelling and Analysis Volume 18 Number 3 pp 275 – 286. Doi:10.3846/1392-6292.2010.15.275-286.

Coskun S.B. and Atay M.T. (2009). Determination of critical buckling loads for elastic columns of constant and variable cross-sections using variational iteration method. Computers and Mathematics with Applications Vol 58 Issues 11 – 12 pp 2260 – 2266. https//doi.org/10.1016/j.camwa 2009.03.072

Homepages. engineering. auckland. ac.nz/./07 Elasticity_ Applications _05_Buckling pdf. Accessed in Feb. 2017.

Huang Yong and Luo Qi – Zhi (2011). A simple method to determine the critical buckling loads for axially inhomogeneous beams with elatic restraint. Computers and Mathematics with Applications Vol 61, pp 2510 – 2517. http:/doi.org/10.1016/j.camwa.2011.02.037.

Jayaram M.A (2007): Mechanism of Materials with Programs in C,Prentice Hall of India Private Ltd New Delhi.

Lagace P.A (2009): Unit M.4.7.The Column and Buckling, 16.003/004, Unified Engineering, Department of Aeronautics and Astronautics, Massachusette Institute of Technology web mit.edu/16/unified/www. SPRING/materials/Lectures/M.4.7 _ Unified 09. pdf. Accessed in Feb. 2017.

Lowe P.G (1971): Classical theory of Structures Based on the Differential Equation, Cambridge University Press, Cambridge.

Megson T.H. G (2005): Structural and Stress Analysis, Second Edition, Elsevier, Butterworth Heinemann, Amsterdam.

Punmia B.C, Jain A.K., Jain A.K. (2002): Mechanics of Materials, Laxmi Publications (P) Ltd New Delhi. http//books. google. com/books? isbn= 8170082153

Rao, P.V. Unit IV, Theory of Columns, http//www.svce.ac.in/--/Unit%/20111%20(a)%20-%20Theory%20 of % Columns %20__Rao. pdf Accessed in Feb. 2017.

Riley C.E. (2003). Elastic Buckling Loads of Slender Columns with Variable Cross-section by the Newmark Method. MSc Thesis Department of Civil Engineering, Colorado State University, Fort Collins Colorado pp 147.

Yayli M.O. (2018). Buckling analysis of Euler columns embedded in an elastic medium with general elastic boundary conditions. Mechanics Based Design of Structures and Machines Vol 46 Issue 1 pp 110 – 122. https://doi.org/10.1080/15397734.2017.1292142.




DOI: https://doi.org/10.11113/mjce.v30n3.514

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