[{"data":1,"prerenderedAt":29},["ShallowReactive",2],{"topic-en-strength-of-materials\u002Fbasic-concepts-and-types-of-deformation\u002Fstress-and-strain-at-a-point":3},{"topic":4,"trail":14,"children":24,"tasks":25,"alternates":26},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},166,"Stress and Strain at a Point","en","strength-of-materials\u002Fbasic-concepts-and-types-of-deformation\u002Fstress-and-strain-at-a-point","Stress and Strain at a Point: σ, τ, ε and γ","Introduction to normal and shear stresses and normal and shear strains as local measures of the mechanical state of a material.","This topic introduces local measures of stress and strain: normal stress, shear stress, normal strain, and shear strain, and distinguishes cross-sectional internal resultants from stress at a material point.","\u003Cp>Internal force resultants describe the total interaction between portions of a body across a section. To describe this interaction \u003Cstrong>locally\u003C\u002Fstrong> at a material point, stress is introduced. Local changes in geometry are described by strain.\u003C\u002Fp>\u003Ch2>Stress\u003C\u002Fh2>\u003Cp>The internal interaction acting on a small oriented area can be resolved into a component normal to the area and a component lying in its plane. These define \u003Cstrong>normal stress $\\sigma$\u003C\u002Fstrong> and \u003Cstrong>shear stress $\\tau$\u003C\u002Fstrong>.\u003C\u002Fp>\u003Cp>Stress is not a force. A force or internal resultant is an integrated quantity, while stress describes the intensity of distributed internal interaction. Its dimension is force per unit area.\u003C\u002Fp>\u003Ch2>Normal strain\u003C\u002Fh2>\u003Cp>\u003Cstrong>Normal strain $\\varepsilon$\u003C\u002Fstrong> describes the relative change in length of a material line element. For a one-dimensional small elongation, its average value is $\\varepsilon=\\Delta l\u002Fl$.\u003C\u002Fp>\u003Ch2>Shear strain\u003C\u002Fh2>\u003Cp>\u003Cstrong>Shear strain $\\gamma$\u003C\u002Fstrong> describes the change of an initially right angle between material directions. It is particularly important in shear and torsion.\u003C\u002Fp>\u003Ch2>State at a point\u003C\u002Fh2>\u003Cp>The values of $\\sigma$, $\\tau$, $\\varepsilon$, and $\\gamma$ depend on position and on the orientation of the plane or direction considered. A complete stress and strain state is multicomponent and is developed later in dedicated topics. At this introductory stage, the key distinction is between global internal resultants and local material measures.\u003C\u002Fp>",[],[15,19,23],{"id":16,"name":17,"path":18},45,"Strength of Materials","strength-of-materials",{"id":20,"name":21,"path":22},142,"Basic Concepts and Types of Deformation","strength-of-materials\u002Fbasic-concepts-and-types-of-deformation",{"id":5,"name":6,"path":8},[],[],{"en":27,"uk":28},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Fstrength-of-materials\u002Fbasic-concepts-and-types-of-deformation\u002Fstress-and-strain-at-a-point","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fopir-materialiv\u002Fosnovni-poniattia-ta-vydy-deformatsii\u002Fnapruzhennia-ta-deformatsii-v-tochtsi",1787778344607]