**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Elastic Strain Energy: Castigliano's Theorem

Description

This lecture covers the concept of elastic strain energy, focusing on Castigliano's theorem to determine vertical displacements in embedded beams. It also discusses Clapeyron's formulas, Betti-Rayleigh reciprocity theorem, and applications in calculating deflections and stored energy in coil springs.

Official source

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.

In course

ME-232: Mechanics of structures (For GM)

L'étudiant acquiert les bases de l'analyse des contraintes et déformation des poutres élastiques linéaires soumises à la traction, cisaillement, torsion, flexion; les coefficients d'influence et la m

Instructor

Related concepts (31)

Stress (mechanics)

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).

Shear modulus

In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: where = shear stress is the force which acts is the area on which the force acts = shear strain. In engineering , elsewhere is the transverse displacement is the initial length of the area. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi).

Stress–strain curve

In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves.

Shear strength

In engineering, shear strength is the strength of a material or component against the type of yield or structural failure when the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a paper is cut with scissors, the paper fails in shear. In structural and mechanical engineering, the shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component (e.

Cauchy stress tensor

In continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e: or, The SI units of both stress tensor and traction vector are N/m2, corresponding to the stress scalar.

Related lectures (34)

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Introduction to Structural Mechanics: Stress and Strain

Covers stress equilibrium, strain, and constitutive equations in 2D and 3D.

Linear Elasticity in 3D: Beam Bending

Covers linear elasticity in 3D, focusing on beam bending and stress-strain behavior of materials.

Introduction to Structural Mechanics

Covers the fundamentals of structural mechanics, focusing on beams, sign conventions, types of beams, and methods to calculate stress resultants.

Mechanics of Slender Structures: Elasticity & BucklingME-411: Mechanics of slender structures

Explores 3D elasticity, beam bending, and buckling phenomena in slender structures.