Structural analysis | Geometry
The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an (for an axis that lies in the plane of the area) or with a (for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension, when working with the International System of Units, is meters to the fourth power, m4, or inches to the fourth power, in4, when working in the Imperial System of Units. In structural engineering, the second moment of area of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam. In order to maximize the second moment of area, a large fraction of the cross-sectional area of an I-beam is located at the maximum possible distance from the centroid of the I-beam's cross-section. The planar second moment of area provides insight into a beam's resistance to bending due to an applied moment, force, or distributed load perpendicular to its neutral axis, as a function of its shape. The polar second moment of area provides insight into a beam's resistance to torsional deflection, due to an applied moment parallel to its cross-section, as a function of its shape. Different disciplines use the term moment of inertia (MOI) to refer to different moments. It may refer to either of the planar second moments of area (often or with respect to some reference plane), or the polar second moment of area . In each case the integral is over all the infinitesimal elements of area, dA, in some two-dimensional cross-section. In physics, moment of inertia is strictly the second moment of mass with respect to distance from an axis: , where r is the distance to some potential rotation axis, and the integral is over all the infinitesimal elements of mass, dm, in a three-dimensional space occupied by an object Q. The MOI, in this sense, is the analog of mass for rotational problems. In engineering (especially mechanical and civil), moment of inertia commonly refers to the second moment of the area. (Wikipedia).
Physics - Mechanics: Torsion (4 of 14) Calculate the "Second Moment of Area"
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the “second moment of area” of a beam of width b and height h. Next video in this series can be found at: https://youtu.be/1xRe5lecQhg
From playlist PHYSICS 16.6 TORSION
Physics - Mechanics: Torsion (3 of 14) What is the "Second Moment of Area"?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain visually what is the “second moment of area Next video in this series can be found at: https://youtu.be/3mD-qioqRWE
From playlist PHYSICS 16.6 TORSION
Mechanical Engineering: Ch 12: Moment of Inertia (6 of 97) What is "Second Moment of Area"?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the “second moment of area”? Next video in this series can be seen at: https://youtu.be/RcpfzaffBcw
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (18 of 97) Second Moment of Area Compared
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what exactly is second moment of area and compare it to moment of inertia. Watch the ending, 7:11, and see what excites physicists. Next video in this series can be seen at: https://youtu.be/
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (13 of 97) Second Moment of Area: Ex. 2
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the second moment of area I(y)=? of a right triangle of negative slope, example 2. Next video in this series can be seen at: https://youtu.be/Nu1TOgCAD-c
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (9 of 97) Summary of 1st & 2nd Moments
Visit http://ilectureonline.com for more math and science lectures! In this video I will summarize what are 1) first moment of area, 2) second moment of area, 3) and moment of inertia. Next video in this series can be seen at: https://youtu.be/YZFovQs5Cx0
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (16 of 97) Second Moment of Area: General: Ex. 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the general formula of the second moment of area J(0)=? (torsional constant) of area of a square, example 3. Next video in this series can be seen at: https://youtu.be/BvYTlP-X4lI
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (17 of 97) Second Moment of Area: General: Ex. 4
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the general formula of the second moment of area J(0)=? (torsional constant) of area of y=ax^2, example 4. Next video in this series can be seen at: https://youtu.be/CNMpzrmWZuY
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (24 of 97) 2nd Moment of Area Rel. to Origin: Ex. 4
Visit http://ilectureonline.com for more math and science lectures! In this video I will find second moment of area I(x)=? of an a-by-a square relative to various distances to the x-axis Next video in this series can be seen at: https://youtu.be/vx82bFqUVfw
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (23 of 97) 2nd Moment of Area Rel. to Origin: Ex. 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will find second moment of area J(final)=? of an up-side-down U relative to the origin. Next video in this series can be seen at: https://youtu.be/CquyNfOJX_Y
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Mechanical Engineering: Ch 12: Moment of Inertia (22 of 97) 2nd Moment of Area Rel. to Origin: Ex. 2
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the second moment of area J(origin)=? of y=kx^2 relative to the origin. Next video in this series can be seen at: https://youtu.be/l4vxqGu2Ig8
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Worldwide Calculus: Centers of Mass and Moments
Lecture on 'Centers of Mass and Moments' from 'Worldwide Integral Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Applications of Integration
Mechanical Engineering: Ch 12: Moment of Inertia (25 of 97) 2nd Moment of Area Rel. to Origin: Ex.5
Visit http://ilectureonline.com for more math and science lectures! In this video I will find second moment of area J(origin)=? of washer and disc relative to the origin. Next video in this series can be seen at: https://youtu.be/V3pHesLWuwY
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA
Physics - Mechanics: Torsion (13 of 14) Calculating the Second Moment or Area: The Circle
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the “second moment of area”=? of the circle. Next video in this series can be found at: https://youtu.be/NnT_Ic8hk_Y
From playlist PHYSICS 16.6 TORSION
Mechanical Engineering: Ch 12: Moment of Inertia (26 of 97) Moment of Inertia=? Rectangle
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the moment of inertia, I(x)=?, I(y)=?, J(origin)=?, of a rectangle. Next video in this series can be seen at: https://youtu.be/oVtiPL3-kd8
From playlist MECHANICAL ENGINEERING 12 MOMENT OF INERTIA / AREA