' Area Moment of Inertia' is a property of shape that is used to predict deflection, bending and stress in beams.I x = (1 / 3) (B y b 3 - B 1 h b 3 + b y t 3 - b1 h t 3) (9)Īrea Moment of Inertia vs. I y = (a 3 h / 12) + (b 3 / 12) (H - h) (8b) Nonsymmetrical ShapeĪrea Moment of Inertia for a non symmetrical shaped section can be calculated as I x = (b h / 12) (h 2 cos 2 a + b 2 sin 2 a) (7) Symmetrical ShapeĪrea Moment of Inertia for a symmetrical shaped section can be calculated as Rectangular section and Area of Moment on line through Center of Gravity can be calculated as Rectangular Section - Area Moments on any line through Center of Gravity The diagonal Area Moments of Inertia for a square section can be calculated as I y = π (d o 4 - d i 4) / 64 (5b) Square Section - Diagonal Moments The Area Moment of Inertia for a hollow cylindrical section can be calculated as = π d 4 / 64 (4b) Hollow Cylindrical Cross Section The Area Moment of Inertia for a solid cylindrical section can be calculated as I y = b 3 h / 12 (3b) Solid Circular Cross Section The Area Moment of Ineria for a rectangular section can be calculated as I y = a 4 / 12 (2b) Solid Rectangular Cross Section The Area Moment of Inertia for a solid square section can be calculated as Area Moment of Inertia for typical Cross Sections II.X = the perpendicular distance from axis y to the element dA (m, mm, inches) Area Moment of Inertia for typical Cross Sections I I y = Area Moment of Inertia related to the y axis ( m 4, mm 4, inches 4) The Moment of Inertia for bending around the y axis can be expressed as Y = the perpendicular distance from axis x to the element dA (m, mm, inches )ĭA = an elemental area ( m 2, mm 2, inches 2) I x = Area Moment of Inertia related to the x axis ( m 4, mm 4, inches 4) (9240 cm 4) 10 4 = 9.24 10 7 mm 4 Area Moment of Inertia (Moment of Inertia for an Area or Second Moment of Area)įor bending around the x axis can be expressed as Area Moment of Inertia - Imperial unitsĮxample - Convert between Area Moment of Inertia Unitsĩ240 cm 4 can be converted to mm 4 by multiplying with 10 4 Īlso note that unlike the second moment of area, the product of inertia may take negative values.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. Principal axes Reference Table Area Moments of Inertia

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