Lecture

Static Analysis: Simple Beam

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

CIVIL-124: Statics (for GC)

Ce cours a pour but de développer une compréhension des modèles statiques de structures. Il présente l'étude du jeu des forces dans les constructions isostatiques formées de barres, poutres et câbles. ...

Description

This lecture covers the calculation of reaction forces in a simple beam using the method of virtual trips. It includes examples of single cuts to determine support reactions and the application of the theorem of virtual work. Students are guided through the process of calculating Cy, Ay, B, and Ma forces by making simple cuts and analyzing the resulting structure. The lecture also introduces the concept of instantaneous centers of rotation and the relationship between structural deformations and rigid body movements.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

Emmanuel Denarié

Emmanuel Denarié is a civil engineer, with a PhD in Materials Science. He worked for 3 years in a civil engineering company where he was in charge of the design of structures and the maintenance of bridges. He has 30 years’ experience on research and applications in the field of building materials, advanced concretes, and rehabilitation of reinforced concrete structures. He is since 2000 senior scientist and lecturer in the Laboratory for Maintenance and Safety of structures, at Ecole Polytechnique Fédérale de Lausanne (EPFL), in charge of research and development activities on the application of concretes and advanced cementitious materials to the improvement of existing and new structures. In 2013, under the lead of Emmanuel Denarié, in cooperation with CEREMA, Subdivision des Phares et Balises from Lorient, and Lafarge, a turret at sea (Le Cabon, Brittany, France) was reinforced by a cast on site 60 mm thick UHPFRC shell. The strain hardening mix was developed jointly with Lafarge. This successful application in extreme conditions of access and restraint of the substrate (thin ring geometry) opened the way to large-scale industrial applications of UHPFRC for the reinforcement of existing structures.

Katrin Beyer

Since 2017 Associate Professor, School of Architecture, Civil and Environmental Engineering (ENAC), EPFL. Head of the Earthquake Engineering and Structural Dynamics (EESD) Laboratory 2010-2017 Assistant Professor, EPFL. 2008-2010 Post-doctoral researcher, ETH Zürich. 2003-2007 Ph.D., Roseschool / Università di Pavia, Italy. 2001-2003 Ove Arup & Partners, Advanced Technology and Research Group, London. 2001 Diploma, Civil engineering, ETH Zürich.

Official source

Related concepts (28)

Angular velocity

In physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).

Rotation

Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.

Rotation around a fixed axis

Rotation around a fixed axis or axial rotation is a special case of rotational motion around a axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

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.

Rotational energy

Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed: where The mechanical work required for or applied during rotation is the torque times the rotation angle. The instantaneous power of an angularly accelerating body is the torque times the angular velocity.

Related lectures (64)

Rigid body rotation and static equilibrium

Explores rotational motion, moment of inertia, torque, and static equilibrium in rigid bodies.

Instantaneous Center of Rotation

Explains the concept of the instantaneous center of rotation in solid mechanics and how to determine it based on known speeds of points.

Moment of Inertia

Explains the concept of moment of inertia in rigid body rotation and torque.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Polar Decomposition Theorem