Area Moment of Inertia - Typical Cross Sections I
Area Moment of Inertia or Moment of Inertia for an Area - also known as Second Moment of Area - I, is a property of shape that is used to predict deflection, bending and stress in beams.
Area Moment of Inertia - Imperial units
- inches4
Area Moment of Inertia - Metric units
- mm4
- cm4
- m4
Converting between Units
- 1 cm4 = 10-8 m4 = 104 mm4
- 1 in4 = 4.16x105 mm4 = 41.6 cm4
Example - Convert between Area Moment of Inertia Units
9240 cm4 can be converted to mm4 by multiplying with 104
(9240 cm4) 104 = 9.24 107 mm4
Area Moment of Inertia (Moment of Inertia for an Area or Second Moment of Area)
for bending around the x axis can be expressed as
Ix = ∫ y2 dA (1)
where
Ix = Area Moment of Inertia related to the x axis (m4, mm4, inches4)
y = the perpendicular distance from axis x to the element dA (m, mm, inches)
dA = an elemental area (m2, mm2, inches2)
The Moment of Inertia for bending around the y axis can be expressed as
Iy = ∫ x2 dA (2)
where
Iy = Area Moment of Inertia related to the y axis (m4, mm4, inches4)
x = the perpendicular distance from axis y to the element dA (m, mm, inches)
Area Moment of Inertia for typical Cross Sections I
Solid Square Cross Section
The Area Moment of Inertia for a solid square section can be calculated as
Ix = a4 / 12 (2)
where
a = side (mm, m, in..)
Iy = a4 / 12 (2b)
Solid Rectangular Cross Section
The Area Moment of Ineria for a rectangular section can be calculated as
Ix = b h3 / 12 (3)
where
b = width
h = height
Iy = b3 h / 12 (3b)
Solid Circular Cross Section
The Area Moment of Inertia for a solid cylindrical section can be calculated as
Ix = π r4 / 4
= π d4 / 64 (4)
where
r = radius
d = diameter
Iy = π r4 / 4
= π d4 / 64 (4b)
Hollow Cylindrical Cross Section
The Area Moment of Inertia for a hollow cylindrical section can be calculated as
Ix = π (do4 - di4) / 64 (5)
where
do = cylinder outside diameter
di = cylinder inside diameter
Iy = π (do4 - di4) / 64 (5b)
Square Section - Diagonal Moments
The diagonal Area Moments of Inertia for a square section can be calculated as
Ix = Iy = a4 / 12 (6)
Rectangular Section - Area Moments on any line through Center of Gravity
Rectangular section and Area of Moment on line through Center of Gravity can be calculated as
Ix = (b h / 12) (h2 cos2 a + b2 sin2 a) (7)
Symmetrical Shape
Area Moment of Inertia for a symmetrical shaped section can be calculated as
Ix = (a h3 / 12) + (b / 12) (H3 - h3) (8)
Iy = (a3 h / 12) + (b3 / 12) (H - h) (8b)
Nonsymmetrical Shape
Area Moment of Inertia for a non symmetrical shaped section can be calculated as
Ix = (1 / 3) (B yb3 - B1 hb3 + b yt3 - b1 ht3) (9)
Area Moment of Inertia vs. Polar Moment of Inertia vs. Moment of Inertia
- "Area Moment of Inertia" is a property of shape that is used to predict deflection, bending and stress in beams
- "Polar Moment of Inertia" as a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque
- "Moment of Inertia" is a measure of an object's resistance to change in rotation direction.
Section Modulus
- the "Section Modulus" is defined as W = I / y, where I is Area Moment of Inertia and y is the distance from the neutral axis to any given fiber
Related Topics
• Beams and Columns
Deflection and stress, moment of inertia, section modulus and technical information of beams and columns.
• Mechanics
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Related Documents
American Standard Beams - S Beam
American Standard Beams ASTM A6 - Imperial units.
American Standard Steel C Channels.
Dimensions and static parameters of American Standard Steel C Channels
American Wide Flange Beams
American Wide Flange Beams ASTM A6 in metric units.
Area Moment of Inertia - Typical Cross Sections II
Area Moment of Inertia, Moment of Inertia for an Area or Second Moment of Area for typical cross section profiles.
Area Moment of Inertia Converter
Convert between Area Moment of Inertia units.
Beams - Fixed at Both Ends - Continuous and Point Loads
Stress, deflections and supporting loads.
Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads
Supporting loads, moments and deflections.
Beams - Supported at Both Ends - Continuous and Point Loads
Supporting loads, stress and deflections.
British Universal Columns and Beams
Properties of British Universal Steel Columns and Beams.
Cantilever Beams - Moments and Deflections
Maximum reaction forces, deflections and moments - single and uniform loads.
Center Mass
Calculate position of center mass.
Center of Gravity
A body and the center of gravity.
Euler's Column Formula
Calculate buckling of columns.
HE-A Steel Beams
Properties of HE-A profiled steel beams.
HE-B Steel Beams
Properties of HE-B profiled steel beams.
HE-M Steel Beams
Properties of HE-M profile steel beams.
Mass Moment of Inertia
The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration.
Mild Steel - Square Bars Weight
Typical weights of mild steel square bars.
Normal Flange I-Beams
Properties of normal flange I profile steel beams.
Pipe Formulas
Pipe and Tube Equations - moment of inertia, section modulus, traverse metal area, external pipe surface and traverse internal area - imperial units
Radius of Gyration in Structural Engineering
Radius of gyration describes the distribution of cross sectional area in columns around their centroidal axis.
Section Modulus - Unit Converter
Convert between Elastic Section Modulus units.
Steel Angles - Equal Legs
Dimensions and static parameters of steel angles with equal legs - metric units.
Steel Angles - Unequal Legs
Dimensions and static parameters of steel angles with unequal legs - imperial units.
Steel Angles - Unequal Legs
Dimensions and static parameters of steel angles with unequal legs - metric units.
Structural Lumber - Section Sizes
Basic size, area, moments of inertia and section modulus for timber - metric units.
Structural Lumber - Properties
Properties of structural lumber.
Three-Hinged Arches - Continuous and Point Loads
Support reactions and bending moments.
W-Beams - American Wide Flange Beams
Dimensions of American Wide Flange Beams ASTM A6 (or W-Beams) - Imperial units.
Weight of Beams - Stress and Strain
Stress and deformation of vertical beams due to own weight.