Lecture

Beam Deflections: Analysis Methods

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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 analysis of beam deflections, including the double integration method, Macaulay's method, and moment-area method. It discusses the relationship between strength and stiffness in beams, allowable deflection limits, and common assumptions in deflection analysis. The instructor demonstrates the application of these methods through examples and explains the importance of boundary conditions in determining beam deflections and slopes.

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)

Official source

Related concepts (32)

Deflection (engineering)

In structural engineering, deflection is the degree to which a part of a structural element is displaced under a load (because it deforms). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations.

Beam (structure)

A beam is a structural element that primarily resists loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beams, that in turn induce internal stresses, strains and deflections of the beam.

Strength of materials

The field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.

Dirichlet boundary condition

In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.

Neumann boundary condition

In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.

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