Moment of inertia of section
Moment of inertia of section (I= area of section x square of axial length of section)
Moment of inertia of section: moment of inertia of area.
To characterize the ability of an object to resist bending, it is necessary to calculate displacement.
Integral Ix= y^2dF of the quadratic product of the area of each element in the section and the distance of each element from the specified axis of the section.
Moment of inertia of section bar
Polar moment of inertia of section (Ip= area x square of vertical axis).
Moment of inertia Ip: moment of inertia
Polar moment of inertia: polar moment of inertia
The integral I ρ = ρ 2df of the quadratic product of the area of each infinitesimal in the cross section and the distance of each infinitesimal to the specified cross section.
Predict the amount of anti-torsion ability of the object and calculate the angular displacement of the object subjected to torque.
Static torque (x-axis area in plane)
The integral of the product of the area of infinitesimal elements and the distance of each infinitesimal element on the section to the specified axis is called the static moment Sx=∫ydA of the section to the specified axis.
Static bending moment is the area bending moment, which is an important cross-sectional characteristic of members. It is obtained by multiplying the area of a section or part of a section by the distance between the centroid of this area and the centroid axis of the whole section, and is used to calculate stress.
note:
The moment of inertia is multiplied by the second power of distance, and the static moment is multiplied by the first power of distance. There is a difference between moment of inertia and moment of area (static moment).
Extended data:
1, section moment of inertia refers to the integral of the square product of the area of each element in the section and the distance of each element to a specified axis in the section. The moment of inertia of section is a geometric parameter to measure the bending capacity of section. Take the product y of the square of the distance y between the micro-area dA and its matching z-axis in any cross-sectional view? DA is defined as the moment of inertia of the micro-area to the Z-axis, and the integral in the whole graphic range is called the moment of inertia of the section to the Z-axis.
2. The section coefficient is a physical quantity used to describe the influence of the section shape of a part on the force, bending moment and torque of the part. It is the geometric parameter of the section of mechanical parts, which was previously called the section modulus. It is used to calculate the bending strength and torsional strength of parts, or to calculate the maximum stress on the section under the condition of given bending moment or torque, which plays a great role in mechanical calculation. The symbol of general section coefficient is W, and the unit is cubic millimeter. The flexural and torsional strength of the section is directly proportional to the corresponding section coefficient.
References:
Moment of inertia Baidu encyclopedia