Was ist das Flächenmoment und Widerstandsmoment? | Einführung in die Spannungstheorie | Mechanik

Required: a) the axial moment of area Ix = Iy, b) the axial section modulus Wx = Wy. Böge 770 Exercise and image quote from Exercise Collection: Engineering Mechanics 23rd, revised and expanded edition Springer Vieweg © Springer Fachmedien Wiesbaden 2017 Alfred Böge, Gert Böge, Wolfgang Böge Illustrations: Graphics & Text Studio Dr. Wolfgang Zettlmeier, Barbing Klementz Publishing Services, Freiburg lernflix.at offers individual online tutoring in mechanics and statics. For more information, visit https://lernflix.at The area moment of inertia, also known as the second-order moment of area, is a geometric quantity used in strength of materials. It is derived from the cross-section of a beam and was introduced to calculate its deformation and stress under bending and torsional loading. The formulas used include the area moment of inertia along with other quantities, such as those for the load and the properties of the material used. The area moment of inertia is also used to calculate loads whose exceedance leads to the buckling of bars or the buckling of shells. The area moment of inertia should not be confused with the (mass) moment of inertia, which characterizes the inertia of a rotating body with respect to angular acceleration. The axial area moment of inertia Ia summarizes the cross-sectional dependence of the bending of a beam under load. The larger the axial area moment of inertia, the smaller the bending and the internal stresses arising in the cross-section. The most important dimension in the cross-section is the extension in the direction of the applied force. All area moments of inertia mentioned here are referenced to a specific point, namely the centroid of the area. For all other points, the area moments of inertia can be calculated using Steiner's theorem. The section modulus W can be used in linear elasticity theory to determine the maximum stress (stress) occurring at the cross-sectional edge. It is the quotient of the area moment of inertia and the distance amax of the edge from the neutral axis. In engineering mechanics, the section modulus W is a quantity derived solely from the geometry (shape and dimensions) of a beam's cross-section. It is a measure of the resistance a beam offers to the development of internal stresses when subjected to a load. For bending, the section modulus W is referred to as the axial or bending section modulus W, while for twisting (torsion), the section modulus Wp is referred to as the polar section modulus Wt. The section modulus of a cross-section has a simple geometric relationship to the area moment of inertia, which is used in cross-sectional design to calculate the deformation of a beam under load (see also stiffness). Section modulus and area moment of inertia are included in general technical manuals, often in common tables, depending on the typical dimensions of geometrically simple surfaces and standardized material profiles (e.g., steel profiles). Mechanics tutoring in Villach