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Civil Engineering
15 cm 10 cm -X

15 cm 10 cm -X

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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Find the moment of inertia about the indicated x and y axes for the shaded area shown. (KINDLY FOLLOW THE SOLUTION IN SAMPLE PROVIDED)

Y. I 15 cm 10 cm ·X
Transcribed Image Text:Y. I 15 cm 10 cm ·X
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
Transcribed Image Text: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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