Find the moment of inertia about the indicated x and y axes for the shaded area shown.(KINDLY FOLLOW THE FORMAT OF SOLUTION PROVIDED) Y.I15 cm10 cm·X 3. Find the moment of inertia about the indicatedY axis for the shaded area shown.Solutions:The area can be divided into three geometric shapes(triangle, square and a quarter circle). The quartercircle has a negative area since it is not part of theshaded area.PartsArea, in²Triangle1(6)(4) = 12I, in(4)(6)³ = 2436Square117 (4)(4)³ = 21.33-0.055(4)*=-14.08Quarter circle31.251, = ΣΙ, + ΣΑd2lyΣ(4) (4) = 16TL= 31.25 +349.22= 380.47 in*= -12.57d, in4810-(0.424) (4)=8.304Ad², in1921024-866.78349.22

This question is from Engineering Mechanics.

Answered: moment of inertia about the indicated x…

Engineering

Civil Engineering

moment of inertia about the indicated x and y axes

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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Concept explainers

Moments

There are various practical applications of the concept of moments, like a rotation of the crank due to linear motion of the piston, the moment of inertia and its use in designing beams and columns, bending moment concept, torque, twisting moment, etc.

Question

Find the moment of inertia about the indicated x and y axes for the shaded area shown.

(KINDLY FOLLOW THE FORMAT OF SOLUTION PROVIDED)

3. Find the moment of inertia about the indicated
Y axis for the shaded area shown.
Solutions:
The area can be divided into three geometric shapes
(triangle, square and a quarter circle). The quarter
circle has a negative area since it is not part of the
shaded area.
Parts
Area, in²
Triangle
1
(6)(4) = 12
I, in
(4)(6)³ = 24
36
Square
1
17 (4)(4)³ = 21.33
-0.055(4)*=-14.08
Quarter circle
31.25
1, = ΣΙ, + ΣΑd2
ly
Σ
(4) (4) = 16
TL
= 31.25 +349.22
= 380.47 in*
= -12.57
d, in
4
8
10-(0.424) (4)=
8.304
Ad², in
192
1024
-866.78
349.22

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