Lecture

Bending Beams: Constraints and Relative Deformation

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In course

MICRO-200: Mechanism Design I

Ce cours introduit les bases de la mécanique des structures : calcul des contraintes et déformations provoquées par les forces extérieures et calcul des déformations. Ces enseignements théoriques sont appliqués à la conception des éléments importants des m ...

Description

This lecture covers the quadratic moment of inertia for beams, relative stresses and strains in bending beams, and the concept of pure flexion. It also explains the position of the neutral axis, the radius of curvature, and the relative strain in different beam sections. The instructor discusses the normal stresses induced by bending, the neutral axis determination, and the link between stress and bending moment in beams.

Instructors (4)

Simon Nessim Henein

Born in 1973 and of Egyptian-Swiss nationality, Simon Henein grew up in Cairo. He obtained an engineering degree at the Ecole Polytechnique Fédérale de Lausanne (EPFL) in 1996 and went on to complete his doctorate at the EPFL in 2000. In 2001, he published the book “Conception des guidages flexibles” which has become a reference in precision engineering. He then joined the Centre Suisse d’Electronique et Microtechnique (CSEM), Neuchatel, Switzerland, where he conceived and developed mechanisms for robotic, aerospace, medical and watchmaking applications. He pursued his research career at the Paul Scherrer Institute, Villigen, Switzerland, where he developed instruments for the Swiss Light Source Synchrotron (SLS). Since November 1st, 2012, he is associate professor in microengineering at the EPFL, holder of the Patek Philippe Chair and director of the Micromechanical and horological design laboratory (Instant-Lab).

Herbert Shea

Expertise soft robotics, wearable haptics, electrostatic actuators, EHD Mission My lab develops flexible polymer-based actuators for a wide range of applications including haptics and soft robotics. More info at https://www.epfl.ch/labs/lmts/ Links from EPFL-LMTS Lab webpage People Research ActivitiesPublications TeachingPublications and Conference papers Link to my lab Education PhD | Physics 1997 – 1997 Harvard University MA | Physics 1993 – 1993 Harvard University

Olivier Chappuis

Danick Briand

Expertise MEMS and MicrosystemsFlexible and Printed ElectronicsEnergy Harvesting and PowerMEMSSmart Sensing SystemsAdvanced Gas Sensing TechnologiesMicrofabrication and Printing technologiesMicrosystems Integration and Packaging Expertise MEMS and MicrosystemsFlexible and Printed ElectronicsEnergy Harvesting and PowerMEMSSmart Sensing SystemsAdvanced Gas Sensing TechnologiesMicrofabrication and Printing technologiesMicrosystems Integration and Packaging Mission Environmentally-friendly technology is a rapid

Official source

Related concepts (24)

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.

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.

I-beam

I-beam is a generic lay term for a variety of structural members with an or -shaped cross-section. Technical terms for similar items include H-beam (for universal column, UC), w-beam (for "wide flange"), universal beam (UB), rolled steel joist (RSJ), or double-T (especially in Polish, Bulgarian, Spanish, Italian and German). I-beams are typically made of structural steel and serve a wide variety of construction uses. The horizontal elements of the are called flanges, and the vertical element is known as the "web".

Radius of curvature

In differential geometry, the radius of curvature (Rc), R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then R is the absolute value of where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature.

Related lectures (64)

Beams under Flexure

Discusses stresses in beams under flexure, including shear forces and bending moments.

Bending Beams: Moment of Inertia and Stress Analysis

Explores moment of inertia in bending beams and stress analysis for beam sections.

Stresses due to Flexure

Explores normal stresses in beams, bending moments, neutral axis, and maximum stresses.

Pure Bending of Beams: Chapter 7b

Explores stresses and strains in beams under pure bending, covering neutral axis, normal stress, moment of inertia, and maximum stress.

Bending of Straight Beams