FIRST AND SECOND MOMENT OF AREAS 95
- Determine the second moment of area
and radius of gyration for the trian-
gle shown in Figure 7.20 about (a) axis
DD(b) axisEEand (c) an axis through
the centroid of the triangle parallel to
axisDD ⎡
⎢
⎢
⎣
(a) 729 mm^4 ,3.67mm
(b) 2187 mm^4 ,6.36mm
(c) 243 mm^4 ,2.l2mm
⎤
⎥
⎥
⎦
EE
DD
12.0 cm
9.0 cm
Figure 7.20
- For the circle shown in Figure 7.21,
find the second moment of area and
radius of gyration about (a) axisFFand
(b) axisHH
[
(a) 201 cm^4 , 2.0 cm
(b) 1005 cm^4 ,4.47cm
]
Figure 7.21
- For the semicircle shown in Figure 7.22,
find the second moment of area and
radius of gyration about axisJJ
[3927 mm^4 , 5.0 mm]
Figure 7.22
- For each of the areas shown in
Figure 7.23 determine the second mo-
ment of area and radius of gyration
about axisLL, by using the parallel axis
theorem. ⎡
⎢
⎢
⎣
(a) 335 cm^4 ,4.73cm
(b) 22030 cm^4 , 14.3 cm
(c) 628 cm^4 ,7.07cm
⎤
⎥
⎥
⎦
LL
5.0 cm
3.0 cm
2.0 cm 10 cm
(a) (b) (c)
15 cm 15 cm
18 cm 5.0 cm
Dia = 4.0 cm
Figure 7.23
- Calculate the radius of gyration of a
rectangular 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
centreX,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 ,5.96cm]
- For the sections shown in Figure 7.24,
find the second moment of area and the
radius of gyration about axisXX
[
(a) 12190 mm^4 , 10.9 mm
(b) 549.5 cm^4 ,4.18cm
]
18.0 mm
3.0 mm
12.0 mm
X 4.0 mm X
(a)
6.0 cm
2.5 cm 3.0 cm
2.0 cm
2.0 cm
XX
(b)
Figure 7.24
