# Numerical - Moment of inertia on rectangle, given width & depth

Q.  What is the moment of inertia acting on a rectangle of width 15 mm and depth 40 mm about base by using theorem of parallel axes?
- Published on 21 Sep 15

a. 320 x 103 mm4
b. 300 x 103 mm4
c. 240 x 103 mm4
d. 80 x 103 mm4

#### Discussion

• Suhas Pawar   -Posted on 21 Aug 21
Ixx = bd³/12 = 15×40³/12 = 80×10³ mm4
• Mahesh shah   -Posted on 29 Dec 16
Good ans
• Sravanthi   -Posted on 24 Nov 15
According to the theorem of parallel axis,

The moment of inertia about any axis is the algebraic sum of moment of inertia about centroidal axis and the product of area of section and square of distance between centroidal and reference axis.

Iaxis = Ixx + AH2

Given: Width of rectangle = 15 mm, depth of rectangle = 40 mm

Formula: Iaxis = Ixx + AH2

here, A is area of rectangle and H is the vertical distance

H = (depth/2) and Ixx = (bd3) / 12

Solution:

Area of rectangle = bd
Ixx = (bd3) / 12

H = (d/2)2

Substituting the values, we get

Iaxis = Ixx + AH2

Iaxis = [(bd3) / 12] + [bd (d/2)2]

Iaxis = bd3/ 3

Substituting the given values, we get

Iaxis = bd3/ 3

= (15 x 403) / 3 = 320000 mm4

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