Unit 03
Centroid and moment of inertia
Que-1 Fig. Shown an area ABCDEF
Compute the moment of inertia of above area about axis K-K
Ans- as M.I is required to find about axis K-K there is no need to find C.K of area.
Consider above fig. As 2 rectangles as shown below
We know that M.I of section 1 about its C.G and parallel to axis K-K
Distance between CG of section 1 and axis k-k
M.I of section 1 about axis K-K
Similarly
M.I of section 2 about axis K-K
M.I of whole area about axis K-K
Ques 2- Determine the moment of inertia of symmetric I-section about its centroid axis x-x and y-y
Ans- the section is divided into three rectangles 
Total area =A=
=5154.
As section is symmetrical about x-x axis and y-y axis
Centroid will coincide with centroid of rectangle 
w.r.t centroids axis x-x and y-y the centroid of rectangle 
and that of 
for 
about x-x axis
59269202 mm
Similarly
Que-3 Determine moment of inertia of built up section shown in fig. About its centroidal axis x-x and y-y.
Ans- divide given section into rectangle3s and triangles due to symmetrical centroid on axis y-y . a reference axis 1-1is choose as shown on fig
The distance of centroidal axis from 1 – 1
=59.26mm
With reference to centroidal axis x-x and y-y the centroidal of rectangle 
that of 
from 
from 
and that of 
is 
Que-4 Find second moment of shaded portion shown in fig. About its centroidal axis.
Ans – the section B divided into rectangles and triangle and semi- circle
Total area =area of triangle ABC + area of rectangle ACDE – area of semicircle
=3371.68 mm
=95991.77
=132203.6
M.I about centroidal x-x axis= M.I of triangle ABC + M.I of rectangle-M.I of semicircle
Similarly
=1868392 
Que-5 Determine moment of inertia of section shown below about axis possible through centroid and parallel to top most fibre of section also determine moment of inertia about axis of symmetry . Hence find radii of gyration
Ans- give composite section can be divided into two rectangles
Area 
Total area =A=
2900
Due to symmetry centroid lies on symmetric axis y-y
=41.21 mm
The centroid of 
and 
6372442.5 
Similarly
=2824166.7 mm
Hence, M.I of section about an axis passing through centroid and parallel to top most fibre B
Radius of gyoation (k)=
=46.88mm
Similarly
=31.21mm
Que-6 Determine polar moment of inertia about centroidal axis of I section . Also determine radii of gyration with respect to x-x axis and y-y axis
Ans – the section B divided into three parts (rectangles)
Area 
=3696 due to symmetric centroid lies on axis y-y the bottom fibre 1-1 is choose as reference axis to locate centroid
The distance of centroid from 1-1
69.78 mm
With reference with centroidle axis x-x and y-y the centroidal of reactangle 
, 
and 
=12470028mm
1970432mm
Polar moment of inertia =
14440454 mm
