390 INTEGRAL CALCULUS
Figure 38.31- Calculate the radius of gyration of a rectan-
gular door 2.0 m high by 1.5 m wide about a
vertical axis through its hinge.
[0.866 m] - A circular door of a boiler is hinged so that
it turns about a tangent. If its diameter is
1.0 m, determine its second moment of area
and radius of gyration about the hinge.
[0.245 m^4 , 0.559 m] - A circular cover, centre 0, has a radius of
12.0 cm. A hole of radius 4.0 cm and centre
X, whereOX= 6 .0 cm, is cut in the cover.
Determine the second moment of area and
the radius of gyration of the remainder about
a diameter through 0 perpendicular toOX.
[14280 cm^4 , 5.96 cm] - For the sections shown in Fig. 38.32, find
the second moment of area and the radius of
gyration about axis[ XX.
(a) 12190 mm^4 ,10.9mm
(b) 549.5cm^4 ,4.18 cm]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=4224 cm^4 ,
IBB=6718 cm^4 ,
Icc=37300 cm^4⎤⎦Figure 38.33- Find the second moment of area and radius
of gyration about the axisXXfor the beam
section shown in Fig. 38.34. [
1350 cm^4 ,
5 .67 cm
]Figure 38.34