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

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

Structural Analysis
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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Compute the moment of inertia about the x and y axes (KINDLY FOLLOW THE SOLUTION FORMAT PROVIDED)
4 cm 6 cm 4 cm 12 cm Activate Windows
Transcribed Image Text:4 cm 6 cm 4 cm 12 cm Activate Windows
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
Transcribed Image Text: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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