What are the geometrical characteristics of plane sections?
Geometric characteristics of flat sections?
Area of flat sections.
Sybols and Characteristics
What are the geometrical characteristics of plane sections?
The main geometric characteristics of the section are the area, the static moments of plane sections, the position of the center of gravity, the moments of inertia, the radii of inertia and the moments of resistance.
In calculations of structures for mechanical reliability, it is very often necessary to operate with such characteristics of flat figures as a static moment, axial and polar moments of inertia. Although the calculation of the above geometric characteristics is one of the simplest problems of integral calculus, nevertheless, due to their narrow applied significance, they are practically not considered in the higher mathematics course at the VTU. According to the established tradition, the geometric characteristics of plane figures are studied in the course of strength of materials.
Geometric characteristics
Geometric characteristics - numerical values (parameters) that determine the dimensions, shape, location of the cross section of a deformable structural element that is homogeneous in terms of elastic properties (and, as a result, characterize the resistance of the element to various types of deformation).
Area of flat sections
Sectional area is one of the geometric characteristics used mainly in tension and compression calculations. When calculating torsion, bending, as well as stability, more complex geometric characteristics are used: static moments, moments of inertia, moments of resistance, etc.
Designing structures with optimal shapes and sizes of sections is one of the ways to reduce the weight and cost of machines and structures.
The area bounded by an arbitrary curve is
Area of flat sections
To calculate the geometric characteristics of complex sections consisting of the simplest figures, they are divided into a finite number n of the simplest parts. In this case
