Lecture

Beams II: Distributed Loads

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.

Description

This lecture covers beams with distributed loads, focusing on the differential relations between the shear force and bending moment, as well as the resultant of distributed forces. The instructor explains the relation between bending moment and shear force, along with the matching conditions for different portions of the beam. Various examples are provided to illustrate the concepts discussed.

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

Official source

Related concepts (32)

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.

Statics

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather, is in static equilibrium with its environment. If is the total of the forces acting on the system, is the mass of the system and is the acceleration of the system, Newton's second law states that (the bold font indicates a vector quantity, i.e. one with both magnitude and direction). If , then .

Fictitious force

A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. It is related to Newton's second law of motion, which treats forces for just one object. Passengers in a vehicle accelerating in the forward direction may perceive they are acted upon by a force moving them into the direction of the backrest of their seats for instance.

Related lectures (64)

Shear Stresses in Beams

Explores shear stresses in beams, including their distribution and calculation of shear and moment diagrams.

Diffusion Models

Explores diffusion models, focusing on generating samples from a distribution and the importance of denoising in the process.

Newton's Laws of Motion

Introduces Newton's laws of motion, covering force, mass, frames of reference, and practical examples like friction and springs.

Simple Shear: General Notions and Applications

Explores simple shear, shear stress, strain energy, stress analysis, and torsional shear stress in simple twist.

Magnetostatics: Magnetic Field and Force