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a) Find ū and I Tolm 0,1m %3D 0.3m 0.am' 0Am 0.m

a) Find ū and I Tolm 0,1m %3D 0.3m 0.am' 0Am 0.m

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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## Problem Statement Given the composite shapes in the diagrams below, calculate the centroid \(\bar{y}\) and the moment of inertia \(I\). ### Diagram a) Description: This shape consists of two rectangles arranged vertically. The lower rectangle (1) has a height of 0.3 meters and a width of 0.4 meters. The upper rectangle (2) is aligned with the right side of the lower rectangle, has a height of 0.1 meters, and a width of 0.3 meters. Dimensions: - Lower rectangle (1): - Width: 0.4 m - Height: 0.3 m - Upper rectangle (2): - Width: 0.3 m - Height: 0.1 m - Vertical alignment: The total height is 0.4 meters (0.1 m + 0.3 m). To be found: - Centroid \(\bar{y}\) = ______ - Moment of inertia \(I\) = ______ ### Diagram b) Description: This shape consists of two rectangles arranged vertically but differently than in diagram a). The lower rectangle (1) has a height of 0.8 meters and a width of 0.2 meters. The upper rectangle (2) is aligned with the left side of the lower rectangle, has a height of 0.4 meters, and a width of 0.1 meters. Dimensions: - Lower rectangle (1): - Width: 0.2 m - Height: 0.8 m - Upper rectangle (2): - Width: 0.1 m - Height: 0.4 m - Vertical alignment: The top of the upper rectangle aligns at 1.2 meters from the bottom (0.8 m + 0.4 m). To be found: - Centroid \(\bar{y}\) = ______ - Moment of inertia \(I\) = ______ --- **Instructions:** 1. Divide each composite shape into its basic rectangular parts. 2. Calculate the area of each rectangle. 3. Determine the location of the centroid for each individual rectangle. 4. Use the parallel axis theorem to find the moment of inertia for each individual rectangle about the overall centroidal axis. 5. Sum the individual moments of inertia to find the total moment of inertia for the composite shape.
Transcribed Image Text:## Problem Statement Given the composite shapes in the diagrams below, calculate the centroid \(\bar{y}\) and the moment of inertia \(I\). ### Diagram a) Description: This shape consists of two rectangles arranged vertically. The lower rectangle (1) has a height of 0.3 meters and a width of 0.4 meters. The upper rectangle (2) is aligned with the right side of the lower rectangle, has a height of 0.1 meters, and a width of 0.3 meters. Dimensions: - Lower rectangle (1): - Width: 0.4 m - Height: 0.3 m - Upper rectangle (2): - Width: 0.3 m - Height: 0.1 m - Vertical alignment: The total height is 0.4 meters (0.1 m + 0.3 m). To be found: - Centroid \(\bar{y}\) = ______ - Moment of inertia \(I\) = ______ ### Diagram b) Description: This shape consists of two rectangles arranged vertically but differently than in diagram a). The lower rectangle (1) has a height of 0.8 meters and a width of 0.2 meters. The upper rectangle (2) is aligned with the left side of the lower rectangle, has a height of 0.4 meters, and a width of 0.1 meters. Dimensions: - Lower rectangle (1): - Width: 0.2 m - Height: 0.8 m - Upper rectangle (2): - Width: 0.1 m - Height: 0.4 m - Vertical alignment: The top of the upper rectangle aligns at 1.2 meters from the bottom (0.8 m + 0.4 m). To be found: - Centroid \(\bar{y}\) = ______ - Moment of inertia \(I\) = ______ --- **Instructions:** 1. Divide each composite shape into its basic rectangular parts. 2. Calculate the area of each rectangle. 3. Determine the location of the centroid for each individual rectangle. 4. Use the parallel axis theorem to find the moment of inertia for each individual rectangle about the overall centroidal axis. 5. Sum the individual moments of inertia to find the total moment of inertia for the composite shape.
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