Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Beams under Flexure

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 stresses in beams under flexure, including shear forces, bending moments, and design considerations. It explains the relationships among loads, shear forces, and bending moments, as well as the curvature, normal strains, and stresses in beams. The instructor discusses the key geometric properties of cross-sections and the efficiency of structural shapes for beam design.

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

Ontological neighbourhood

Civil engineering

Structural engineering: Topics in structural engineering

Mathematics

Geometry: Differential geometry

Related concepts (32)

Bending moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads.

Bending

In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam.

Shear and moment diagram

Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.

Structural engineering

Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of human-made structures. Structural engineers also must understand and calculate the stability, strength, rigidity and earthquake-susceptibility of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and building services engineer and often supervise the construction of projects by contractors on site.

Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point: The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.

Related lectures (40)

Plastic Hinge Method: Analysis and Design

Explores the plastic hinge method for inelastic deformation estimation and discusses the challenges of force-based design.

Stresses due to Flexure

Covers the calculation of curvature in beams and the design of beams for stress considerations.

Beams under nonuniform bending: Shear stresses and built-up beams

Covers shear stresses in beams and built-up beams, including shear flow calculations and stress superimposition.

Local and Global Ductility

Examines the relationship between different ductilities in seismic engineering, highlighting their significance in structural elements.

Introduction to Structural Mechanics Log in to Mediaspace to watch this video