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Lecture

Cantilever Beams: Load Examples

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 various examples of cantilever beams with different types of loads, including concentrated loads, distributed loads, and concentrated moments. The instructor demonstrates the analysis of beam deflection and stress distribution for each case.

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.

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Related concepts (23)

Cantilever

A cantilever is a rigid structural element that extends horizontally and is supported at only one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab. When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment. Cantilever construction allows overhanging structures without additional support.

Deflection (engineering)

In structural engineering, deflection is the degree to which a part of a structural element is displaced under a load (because it deforms). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations.

Beam (structure)

A beam is a structural element that primarily resists loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beams, that in turn induce internal stresses, strains and deflections of the beam.

Concentrated solar power

Concentrated solar power (CSP, also known as concentrating solar power, concentrated solar thermal) systems generate solar power by using mirrors or lenses to concentrate a large area of sunlight into a receiver. Electricity is generated when the concentrated light is converted to heat (solar thermal energy), which drives a heat engine (usually a steam turbine) connected to an electrical power generator or powers a thermochemical reaction. As of 2021, global installed capacity of concentrated solar power stood at 6.

Stress–strain analysis

Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.

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Stresses due to Flexure

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

Mechanics of Composite Beams

Explores stresses in composite beams, including normal stresses, longitudinal strains, and moment-curvature relationship.