Lecture

Axially Loaded Columns: Buckling and Stability

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In course

CIVIL-238: Structural mechanics (for GC)

The course discusses the basic principles of structural mechanics, analyzing the performance of materials and structures against loading and focuses on the stress strain relationships and the effect of axial, bending, shear and torsional loadings on engin ...

Description

This lecture covers the behavior of axially loaded columns, focusing on buckling phenomena and critical loads. Topics include Euler buckling, differential equations for column buckling, and practical examples of calculating buckling loads for steel columns.

Instructors (2)

Anastasios Vassilopoulos

PERSONAL INFORMATION Name : Anastasios P. Vassilopoulos email : anastasios.vassilopoulos@epfl.ch Tel: 41 21 6936393 Fax: 41 21 6936240 SUMMARY OF QUALIFICATIONS 1995: Dipl. Mechanical Engineer, University of Patras, Greece 2001: Dr Mechanical Engineer, Doctoral thesis in fatigue of composite materials from the Dept. Mechanical Engineering and Aeronautics, University of Patras, Greece CURRENT POSITION Senior Scientist (MER), Composite Construction Laboaratory (CCLab), EPFL PREVIOUS POSITIONS 2006-2012 Research and Teaching Associate, Composite Construction Laboaratory (CCLab), EPFL 2002-2006 Assisstant Professor, Technological Educational Institute (TEI) of Patras, Greece 2001-2003 Post-doctoral Research associate, (Part-time) Dept. Mechanical Engineering and Aeronautics of the University of Patras, Greece. EDUCATION 1990 - 1995 Graduate student, Dept. Mechanical Engineering and Aeronautics, University of Patras, Greece October 1994-January 1995 Dept. Mechanical Engineering, University of Bristol, U.K. (In the frame of Erasmus project for the final year thesis, under the supervision of Prof. R. D. Adams) 1995 - 2000 Research assistant, Dept. Mechanical Engineering and Aeronautics, University of Patras. LANGUAGES English, Greek, French COMMUNITY ACTIVITIES (Member of) Council of the European Society of Composite Materials (ESCM) Council of the European Society of Experimental Mechanics (EuraSEM) The European Structural Integrity Society (ESIS) The European Energy Research Alliance (EERA, JP WIND) The Technical Chamber of Greece (TCG) The Hellenic Association of Mechanical & Electrical Engineers SCIENTIFIC-RESEARCH INTERESTS Experimental methods for the study of the behavior of composite materials under static and fatigue loading Development of analytical methods for the study of the behavior of FRP composite materials under variable amplitude complex stress states Development of fatigue life prediction methodologies for composite materials and structures Design of constructions with composite materials

Dimitrios Lignos

Prof. Lignos joined the École Polytechnique Féderale de Lausanne (EPFL) in 2016 from McGill University in Canada where he was a tenured Associate Professor and a William Dawson Scholar for Infrastructure Resilience. He holds a diploma (National Technical University of Athens, NTUA, 2003), M.S. (Stanford University, 2004) and Ph.D. (Stanford University, 2008). In addition, he was a post-doctoral scientist at Stanford University (2009) and in Kyoto University (2010). Prof. Lignos teaches graduate and undergraduate courses in seismic design, nonlinear behaviour of steel and composite structures as well as supplemental damping systems, Structural Stability, Nonlinear Analysis and Performance-based Earthquake Engineering. His awards for teaching, research and service in Civil Engineering include the 2011 Outstanding Teaching Award (Faculty of Engineering, McGill University), as well as the Outstanding reviewer (2012, 2013) award from ASCE, the 2013 State-of-the-Art in Civil Engineering Award by ASCE and the 2014 Christophe Pierre Award for Research Excellence - Early Career. Just recently, he received the 2019 Walter L. Huber Civil Engineering Research Prize from ASCE for significant contributions in developing state of the art methods to simulate extreme limit states in steel structures.Prof. Lignos is a member of ASCE and the Earthquake Engineering Research Institute. He acts as an Associate Editor for Metal Structures and Seismic Effects of the ASCE Journal of Structural Engineering. He joined the Editorial Board of Earthquake Spectra and Earthquake Engineering and Structural Dynamics International journals. He serves as an acting member of the CEN/TC 250/SC 8/WG 2 and has been selected as a member of the Project Team (PT2) for the Eurocode 8-Part 1 Current Revisions for Steel and Composite Structures. He is also a member of the Canadian Standards Association (CSA) S16 technical committee for Steel Structures. Prof. Lignos is involved as a NEHRP consultant in numerous research-to-practice projects related to the behaviour and nonlinear modelling and analysis of structures applicable to the engineering practice through the Applied Technology Council (ATC). Detailed Curriculum Vitae (last update September 2018)

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Related concepts (27)

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Structural analysis

Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships.

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Homogeneous differential equation

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.

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