Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Two-Dimensional Stress State

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 méthode de l'énergie pour analyser des systèmes isostatiq ...

Description

This lecture covers the concept of two-dimensional stress states, including the principle of superposition, sensor membranes, and the relative variation of volume. It delves into energy density, constraints, and the stiffness matrix. The instructor explains the analysis of stress states for reference axes coinciding with principal axes, as well as for axes different from the main axes. Practical examples, such as a square plate under linear load, are used to illustrate the theoretical concepts. The lecture concludes with the construction of Mohr circles and the calculation of normal and tangential stresses in oblique sections.

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

Instructor

Alain Michel Prenleloup

Official source

Related concepts (32)

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).

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.

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.

Plane stress

In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 (representable as a 2×2 matrix rather than 3×3). A related notion, plane strain, is often applicable to very thick members.

Mohr's circle

Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components.

Related lectures (52)

Principal Stresses and Mohr's Circle

Explores principal stresses, Mohr's Circle, triaxial stress, Hooke's Law, and strain measurements.

Plane Stress Analysis: Equilibrium and Transformation

Explores plane stress analysis, including inclined planes, stress transformation, principal stresses, and shear stresses.

Normal Stresses: Internal Stress and Strain

Introduces internal stress and strain, material properties, and design considerations for axial loads and direct shear.

Shear Center of Cross Sections

Introduces shear center in cross sections, unsymmetric loading, shear stresses, bending effects, and stress analysis at inclined sections.

Geomechanics: Course Introduction