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Lecture

Simple Shear: General Notions and Applications

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 general notions and applications of simple shear, including the introduction of shifting constraints, energy of normal stresses, analysis of deformation, and expression of forces. It also delves into the evaluation of stresses, equilibrium equations, and strain energy in simple shear. The lecture further explores the concept of shear stress, the use of Mohr circles for stress analysis, and the relationship between Young modulus and slip modulus. Additionally, it discusses the torsional shear stress in simple twist, equilibrium equations in torsion, and the calculation of stresses and strains. The lecture concludes with an explanation of the moment of inertia in flat areas and the integral form of static moment and moment of inertia.

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Instructor

Alain Michel Prenleloup

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

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).

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.

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).

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.

Shear stress

Shear stress (often denoted by τ (Greek: tau)) is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. The formula to calculate average shear stress is force per unit area.: where: τ = the shear stress; F = the force applied; A = the cross-sectional area of material with area parallel to the applied force vector.

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