Question

Determine the mass moment of inenta
about the centroidal axis of the section the
upper web and lower webs are 20mm x 25mm and Mange is 25mm x 150mm,​

Answer 1

Answer:

Given,

Inertia at center is 20kg−m

2

Let,

Mass of square plate, =m

Side of square, =a

Inertia about perpendicular axis at center of square, I

z

=

6

ma

2

=20kg−m

2

Apply perpendicular axis theorem

I

z

=I

x

+I

y

=2I

x

(square has same side)

I

x

=

2

I

z

=

12

ma

2

Edge of square is at distance,

2

a

from center.

Apply parallel axis theorem I

edge

=I

x

+m(

2

a

)

2

I

edge

=

12

ma

2

+m(

2

a

)

2

I

edge

=

3

ma

2

=2×

6

ma

2

=2I

Z

I

edge

=2×20=40kg−m

2

I

edge

=40kg−m

2