Some applications of integration 391
2.0 cm
5.0 cm
3.0 cm
(a) (b) (c)
15 cm
18 cm 10 cm
15 cm
5.0 cm
L L
Dia^5
4.0 cm
Figure 38.31
- Calculate the radius of gyration of a rectan-
gular door 2.0m high by 1.5m wide about a
vertical axis through its hinge.
[0.866m] - A circular door of a boiler is hinged so that
it turns about a tangent. If its diameter is
1.0m, determine its second moment of area
and radius of gyration about the hinge.
[0.245m^4 , 0.559m] - A circular cover, centre 0, has a radius of
12.0cm. A hole of radius 4.0cm and centreX,
whereOX= 6 .0cm, is cut in thecover. Deter-
mine the second moment of area and the radius
of gyration of the remainder about a diameter
through 0 perpendicular toOX.
[14280cm^4 ,5.96cm] - For the sections shown in Fig. 38.32, find
the second moment of area and the radius of
gyration about axis[XX.
(a)12190mm^4 , 10 .9mm
(b) 549 .5cm^4 , 4 .18cm
]
18.0 mm
2.5 cm 3.0 cm
2.0 cm
2.0 cm
6.0 cm
12.0 mm
3.0 mm
XX
XX
4.0 mm
(a) (b)
Figure 38.32
- Determine the second moments of areas about
the given axes for the shapes shown in
Fig. 38.33. (In Fig. 38.33(b), the circular area
is removed.) ⎡
⎣
IAA=4224cm^4 ,
IBB=6718cm^4 ,
ICC=37300cm^4
⎤
⎦
3.0 cm
16.0 cm
9.0 cm
10.0 cm
(a)
(b)
4.0 cm
15.0 cm
9.0 cm
4.5 cm
AA
B
C
B
C
Dia^5
7.0 cm
Figure 38.33
- Find the second moment of area and radius
of gyration about the axisXXfor the beam
section shown in Fig. 38.34. [
1350cm^4 ,
5 .67cm
]
2.0 cm
8.0 cm
2.0 cm
XX
1.0 cm
10.0 cm
6.0 cm
Figure 38.34