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Centroid Practice Problems Identify the X and Y coordinates for the centroid for each of the following shapes. Assume the origin (0,0) is in the lower left corner of the shape. 1)

Centroid Practice Problems Identify the X and Y coordinates for the centroid for each of the following shapes. Assume the origin (0,0) is in the lower left corner of the shape. 1)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Can someone please solve this. Also idk if this is the right subject. I am doing this in principles of engineering

### Structural Analysis of an I-Beam #### I-Beam Diagram The diagram represents an I-shaped beam with labeled dimensions. The beam has two flanges, each 2 inches thick, and a web measuring 7 inches in height. The total width of the flanges varies, with the top flange measuring 8 inches and the bottom flange 10 inches. #### Calculation Table Below the diagram is a table used for calculating the centroid (\( \bar{X} \), \( \bar{Y} \)) of the beam. The table includes columns labeled: - Shape - \( \bar{X}_i \) (X-coordinate of the centroid of each shape component) - \( A_i \) (Area of each shape component) - \( \bar{X}_i A_i \) - \( \bar{Y}_i \) (Y-coordinate of the centroid of each shape component) - \( A_i \) (Repeated from the previous column) - \( \bar{Y}_i A_i \) Three rows are provided for individual calculations, with an additional row for totals. #### Centroid Formulas At the bottom, the formulas for the overall centroid locations are given as: - \( \bar{X} = \frac{\sum \bar{X}_i A_i}{\sum A_i} \) - \( \bar{Y} = \frac{\sum \bar{Y}_i A_i}{\sum A_i} \) These formulas are used to calculate the centroid of the entire beam by summing the individual moments and areas of each shape component. This setup allows for precise and methodical calculation of the I-beam’s centroid, critical for structural stability and design considerations.
Transcribed Image Text:### Structural Analysis of an I-Beam #### I-Beam Diagram The diagram represents an I-shaped beam with labeled dimensions. The beam has two flanges, each 2 inches thick, and a web measuring 7 inches in height. The total width of the flanges varies, with the top flange measuring 8 inches and the bottom flange 10 inches. #### Calculation Table Below the diagram is a table used for calculating the centroid (\( \bar{X} \), \( \bar{Y} \)) of the beam. The table includes columns labeled: - Shape - \( \bar{X}_i \) (X-coordinate of the centroid of each shape component) - \( A_i \) (Area of each shape component) - \( \bar{X}_i A_i \) - \( \bar{Y}_i \) (Y-coordinate of the centroid of each shape component) - \( A_i \) (Repeated from the previous column) - \( \bar{Y}_i A_i \) Three rows are provided for individual calculations, with an additional row for totals. #### Centroid Formulas At the bottom, the formulas for the overall centroid locations are given as: - \( \bar{X} = \frac{\sum \bar{X}_i A_i}{\sum A_i} \) - \( \bar{Y} = \frac{\sum \bar{Y}_i A_i}{\sum A_i} \) These formulas are used to calculate the centroid of the entire beam by summing the individual moments and areas of each shape component. This setup allows for precise and methodical calculation of the I-beam’s centroid, critical for structural stability and design considerations.
**Centroid Practice Problems** Identify the X and Y coordinates for the centroid for each of the following shapes. **Assume the origin (0,0) is in the lower left corner of the shape.** 1. **Right Triangle** - Diagram: A right triangle is shown with dimensions: one leg is 3 units, another leg is 8 units. The vertices are labeled Q, T, and R, with the right angle at T. - Centroid Coordinates: - \(\bar{X} = \) - \(\bar{Y} = \) 2. **Semicircle** - Diagram: A semicircle with a radius of 5 cm is shown. The X and Y axes intersect at the center of its base. - Centroid Coordinates: - \(\bar{X} = \) - \(\bar{Y} = \)
Transcribed Image Text:**Centroid Practice Problems** Identify the X and Y coordinates for the centroid for each of the following shapes. **Assume the origin (0,0) is in the lower left corner of the shape.** 1. **Right Triangle** - Diagram: A right triangle is shown with dimensions: one leg is 3 units, another leg is 8 units. The vertices are labeled Q, T, and R, with the right angle at T. - Centroid Coordinates: - \(\bar{X} = \) - \(\bar{Y} = \) 2. **Semicircle** - Diagram: A semicircle with a radius of 5 cm is shown. The X and Y axes intersect at the center of its base. - Centroid Coordinates: - \(\bar{X} = \) - \(\bar{Y} = \)
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