Beams: Distributed Loads

This lecture covers beams with distributed loads, focusing on differential relations between shear force and bending moment. It explains the concepts of sagging and hogging, statically determinate beams, and the method of statics to compute external reactions. The instructor demonstrates examples of beams with concentrated loads and discusses the trapezoidal distributed force. The lecture emphasizes the relationship between bending moment and shear force, as well as the application of the superposition principle. It also addresses the integration of shear force and bending moment diagrams to determine constants and boundary conditions for beams.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (37)

Related concepts (40)

ME-104: Introduction to structural mechanics

The student will acquire the basis for the analysis of static structures and deformation of simple structural elements. The focus is given to problem-solving skills in the context of engineering desig

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.

Robin boundary condition

In mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.

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.

Boundary value problem

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

Cauchy boundary condition

In mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.

Non-Straight Beams in Structural Mechanics

Covers non-straight beams, frames, and matching conditions in structural mechanics.

Introduction to Structural Mechanics

Explores beam bending, stiffness, and curvature in mechanical systems using OCR-extracted slides from EPFL's Spring 2021 session.

Introduction to Structural Mechanics: Matching Conditions

Explores matching conditions in structural mechanics for non-straight beams, frames, and arches, emphasizing differential relations and constant determination.

Beams II: Distributed Loads ME-104: Introduction to structural mechanics

Explores beams with distributed loads and their differential relations between shear force and bending moment.

Finite Difference Grids MATH-351: Advanced numerical analysis

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.