Find out the moment of inertia of a triangular area, Mechanical Engineering

Find out the Moment of Inertia of a triangular area:

Find out the Moment of Inertia of a triangular area ABC with base b and height d around its base BC. Therefore or otherwise determine the Moment of Inertia around centroidal axis parallel to the base

Solution

Figure illustrates the triangular area ABC with its centroid G, where perpendicular distance from G to BC is = (d/3).

1436_Find out the Moment of Inertia of a triangular area2.jpg

Let a thin strip LM of thickness dy at distance y from the base BC. Letting similar triangles, ALM and ABC,

LM/(d -  y)      =  BC/ d =  b/ d

∴ LM = (b/ d) (d - y)

= b (1 -   (y/d))

∴ Elemental Area dA = b (1 -   (y/d))dy

2447_Find out the Moment of Inertia of a triangular area.png

= bd 3  ((1 /3)-  (1/4 ))=  bd3/12

By using theorem of parallel axes,

1869_Find out the Moment of Inertia of a triangular area1.png

IGX = I BC  -  A  (d/3)2

b d 3  /12 -(bd/2)(d2/9)

Posted Date: 1/29/2013 1:21:42 AM | Location : United States







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