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The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment of inertia of the section about its base a-a. Assume b = 15 in., h = 6 in., r = 4 in, R = 6 in. a Answer: la-a = i b R in.4 h ---α

The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment of inertia of the section about its base a-a. Assume b = 15 in., h = 6 in., r = 4 in, R = 6 in. a Answer: la-a = i b R in.4 h ---α

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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## Moment of Inertia Calculation for Cross Section of Bearing Block ### Problem Statement: The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment of inertia of the section about its base \(a \text{-} a\). ### Given: - \( b = 15 \text{ in.} \) - \( h = 6 \text{ in.} \) - \( r = 4 \text{ in.} \) - \( R = 6 \text{ in.} \) ### Diagram Explanation: The diagram consists of a semi-circular area on top of a rectangular area. The rectangle has: - A base \( b \) which is 15 inches long. - A height \( h \) which is 6 inches. The semicircle on top of the rectangle has: - An outer radius \( R \) which is 6 inches. - An inner cut-out semicircle with a radius \( r \) which is 4 inches. Together, these shapes form the full cross-sectional area of the bearing block referred to as the shaded region. ### Calculation: To find the moment of inertia \( I_{a \text{-} a} \) about the base \( a \text{-} a \), appropriate formulas and geometric considerations will be applied. Answer: \( I_{a \text{-} a} = \boxed{\text{ }} \text{in.}^4 \) Note: The actual numerical answer will involve computation based on the standard formulas for the moment of inertia of composite areas.
Transcribed Image Text:## Moment of Inertia Calculation for Cross Section of Bearing Block ### Problem Statement: The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment of inertia of the section about its base \(a \text{-} a\). ### Given: - \( b = 15 \text{ in.} \) - \( h = 6 \text{ in.} \) - \( r = 4 \text{ in.} \) - \( R = 6 \text{ in.} \) ### Diagram Explanation: The diagram consists of a semi-circular area on top of a rectangular area. The rectangle has: - A base \( b \) which is 15 inches long. - A height \( h \) which is 6 inches. The semicircle on top of the rectangle has: - An outer radius \( R \) which is 6 inches. - An inner cut-out semicircle with a radius \( r \) which is 4 inches. Together, these shapes form the full cross-sectional area of the bearing block referred to as the shaded region. ### Calculation: To find the moment of inertia \( I_{a \text{-} a} \) about the base \( a \text{-} a \), appropriate formulas and geometric considerations will be applied. Answer: \( I_{a \text{-} a} = \boxed{\text{ }} \text{in.}^4 \) Note: The actual numerical answer will involve computation based on the standard formulas for the moment of inertia of composite areas.
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