Second moment of Area (m4) - geometrical constant, dependent on the shape of an object. It is typically denoted with “I” and reflects how its points are distributed in regards to an arbitrary axis. Ix is the moment of inertia around the x axis, and Iy is the moment of inertia around the y axis.
It's different from the first moment of Area, which is part of how resistance to shear deformation a cross-section has is described.
Also know as the area moment of inertia or the second moment of inertia. It can be used in beam theory to predict the resistance of beams to deflection and bending. The deflection of a beam under a given load depends on the geometry of the cross section of the beam. The larger the second moment of area the more resistant to bending the beam is, this is why "I" beams are used in construction, as they have a high second moment of area.
Standard Shapes:
General Formula
For Rectangular Cross-section
Where h= height, b= width
For Circular Cross-section
Where r= radius, d= diameter
For Semi-circular Cross-section
I= 0.11r4
Where r= radius
For Circular Tube
I= ( ro4 – rc4 ) ≈πr3t
Where ro = radius of outer circle, ri =radius of inner circle, t =thickness
For Rectangular Tube
I=
h3 ( 1+ 3 )
Where (h, b >> t ) and h =height, b =width
Quiz to check understanding:
There are five questions, and at the end there will be the results and a brief explanation of the correct answer