Compute the moment of inertia about the x and y axes(KINDLY FOLLOW THE SOLUTION FORMAT PROVIDED) 4 cm6 cm4 cm12 cmActivate Windows 2. Determine the moment of inertia of the T-sectionshown in the figure about its centroidal X, axis.Also, compute the radius of gyration of the areawith respect to the Xo axis.Solution:d₁6"d₂yThe area can be divided into two rectangles. I, for a rectangle is bh³.Solve first for the location of the centroidal axis Xo.PartsArea, in²y, inĪ, in¹Ay, in³84d, indi=21127(6)(2)³ = 4212336d₂=212(2)(6)³ = 36Total2412040120y =24y = 5 inIxo = ΣΙ, + ΣΑd2= 40 +96Ixo = 136 in*Radius of gyration:136Txo√x24Txo = 2.38 in(NN)-XoH-XoAd², in*484896

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Civil Engineering

Compute the moment of inertia about the x and y axes (KINDLY FOLLOW THE SOLUTION FORMAT PROVIDED)

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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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.

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Compute the moment of inertia about the x and y axes (KINDLY FOLLOW THE SOLUTION FORMAT PROVIDED)

2. Determine the moment of inertia of the T-section
shown in the figure about its centroidal X, axis.
Also, compute the radius of gyration of the area
with respect to the Xo axis.
Solution:
d₁
6"
d₂
y
The area can be divided into two rectangles. I, for a rectangle is bh³.
Solve first for the location of the centroidal axis Xo.
Parts
Area, in²
y, in
Ī, in¹
Ay, in³
84
d, in
di=2
1
12
7
(6)(2)³ = 4
2
12
3
36
d₂=2
12(2)(6)³ = 36
Total
24
120
40
120
y =
24
y = 5 in
Ixo = ΣΙ, + ΣΑd2
= 40 +96
Ixo = 136 in*
Radius of gyration:
136
Txo
√x
24
Txo = 2.38 in
(NN)
-Xo
H
-Xo
Ad², in*
48
48
96

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