[{"data":1,"prerenderedAt":28},["ShallowReactive",2],{"topic-en-strength-of-materials\u002Fbasic-concepts-and-types-of-deformation\u002Fassumptions-and-idealizations":3},{"topic":4,"trail":13,"children":23,"tasks":24,"alternates":25},{"id":5,"name":6,"locale":7,"path":8,"seo_title":6,"seo_description":9,"seo_text":10,"content_html":11,"content_chunks":12},158,"Assumptions and Idealizations in Strength of Materials","en","strength-of-materials\u002Fbasic-concepts-and-types-of-deformation\u002Fassumptions-and-idealizations","Continuum assumption, small deformation, one-dimensional member models, Saint-Venant’s principle, and limits of simplified calculations.","This topic explains why Strength of Materials relies on idealizations and assumptions, including the continuum model, small deformation, beam and bar idealizations, Saint-Venant’s principle, and limits of applicability.","\u003Cp>Strength of Materials uses simplified models that make real structures accessible to engineering equations. Every simplification has a \u003Cstrong>range of applicability\u003C\u002Fstrong>.\u003C\u002Fp>\u003Ch2>Continuum assumption\u003C\u002Fh2>\u003Cp>Material is represented as a continuous medium even though its microscopic structure may be atomic, granular, fibrous, or otherwise heterogeneous. This allows stress and strain to be treated as spatial fields.\u003C\u002Fp>\u003Ch2>Small deformation and displacement\u003C\u002Fh2>\u003Cp>Classical linear problems assume sufficiently small changes in geometry. If displacement substantially changes the equilibrium geometry, a geometrically nonlinear formulation may be required.\u003C\u002Fp>\u003Ch2>Member idealization\u003C\u002Fh2>\u003Cp>When one dimension is much larger than the cross-sectional dimensions, an element can often be modeled as a bar, beam, or shaft. The full three-dimensional geometry is replaced by a longitudinal axis and cross-sectional properties.\u003C\u002Fp>\u003Ch2>Saint-Venant’s principle\u003C\u002Fh2>\u003Cp>At sufficient distance from a load application region, statically equivalent load distributions generally produce similar stress fields. This permits simplification of local load details, but does not remove local stress effects near the point of application.\u003C\u002Fp>\u003Ch2>Idealizations must be justified\u003C\u002Fh2>\u003Cp>Holes, stress concentrations, contact zones, large deformation, anisotropy, and complex geometry may require more detailed models.\u003C\u002Fp>",[],[14,18,22],{"id":15,"name":16,"path":17},45,"Strength of Materials","strength-of-materials",{"id":19,"name":20,"path":21},142,"Basic Concepts and Types of Deformation","strength-of-materials\u002Fbasic-concepts-and-types-of-deformation",{"id":5,"name":6,"path":8},[],[],{"en":26,"uk":27},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Fstrength-of-materials\u002Fbasic-concepts-and-types-of-deformation\u002Fassumptions-and-idealizations","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fopir-materialiv\u002Fosnovni-poniattia-ta-vydy-deformatsii\u002Fhipotezy-ta-idealizatsii",1787712538238]