Table 16.1Moment of Inertia of Common ShapesShapeMoment of InertiaRadius of GyrationRectanglebh312bh3I,12hk, =V3hbTrianglebhV18hkz36bh312Circle4J =2SemicircleI, =I,k, - k, -5%3D%3D8.2Ī, = 0.11r= 0.264rQuarter circleI, = I,k, =%3D16Ī, =Ï,=0.055rªk = ky = 0.264r 2. For the shaded area shown, determinea. The location of its centroidb. The moment of inertia and radius of gyration withrespect to its centroidal x - axisc. The moment of inertia and radius of gyration withrespect to its centroidal y - axis160mm| 40 mm200mm40mm1 40 mm120mm

Consider the following figure. (a) Calculate the location of the centroid as follows.…

2. For the shaded area shown, determine a. The location of its centroid b. The moment of inertia and radius of gyration with respect to its centroidal x - axis c. The moment of inertia and radius of gyration with respect to its centroidal y - axis

2. For the shaded area shown, determine a. The location of its centroid b. The moment of inertia and radius of gyration with respect to its centroidal x - axis c. The moment of inertia and radius of gyration with respect to its centroidal y - axis

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Table 16.1
Moment of Inertia of Common Shapes
Shape
Moment of Inertia
Radius of Gyration
Rectangle
bh3
12
bh3
I,
12
h
k, =
V3
h
b
Triangle
bh
V18
h
kz
36
bh3
12
Circle
4
J =
2
Semicircle
I, =I,
k, - k, -5
%3D
%3D
8.
2
Ī, = 0.11r
= 0.264r
Quarter circle
I, = I,
k, =
%3D
16
Ī, =Ï,=0.055rª
k = ky = 0.264r

2. For the shaded area shown, determine
a. The location of its centroid
b. The moment of inertia and radius of gyration with
respect to its centroidal x - axis
c. The moment of inertia and radius of gyration with
respect to its centroidal y - axis
160
mm
| 40 mm
200
mm
40
mm
1 40 mm
120
mm

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