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1) For the shape shown below, if density is uniform, the center of mass will fall on the centroid. Determine the location of the centroid of the plane shown. y 120 mm 60 mm 40 mm 80 mm 60 mm

1) For the shape shown below, if density is uniform, the center of mass will fall on the centroid. Determine the location of the centroid of the plane shown. y 120 mm 60 mm 40 mm 80 mm 60 mm

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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**Transcription and Explanation:** **1) Problem Statement:** For the shape shown below, if density is uniform, the center of mass will fall on the centroid. Determine the location of the centroid of the plane shown. **Diagram Explanation:** - The plane is a composite shape combining a semicircle, a rectangle, and a circle. - The total width of the figure is 120 mm. - The semicircle has a radius of 60 mm, and it incorporates a circle with a radius of 40 mm. - The height of the larger rectangular section is 80 mm, with an extension of 60 mm beyond the semicircle, making the full vertical span from top to bottom 140 mm (including diameter of the semicircle and the rectangle). **2) Problem Statement:** Determine (a) the location of the centroid and (b) the second moment of mass about x- and y-axes of a parabolic spandrel. Assume uniform density \( \rho_A \). **Diagram Explanation:** - The diagram presents a parabolic spandrel, a two-dimensional shape defined by the parabola \( y = kx^2 \), bounded by vertical and horizontal lines. - The horizontal base of the spandrel has a length \( a \), and the vertical height at the end of the spandrel is \( b \). - The equation of the parabola \( y = kx^2 \) describes the curved portion of the spandrel, with \( k \) being a constant that determines the specific curvature.
Transcribed Image Text:**Transcription and Explanation:** **1) Problem Statement:** For the shape shown below, if density is uniform, the center of mass will fall on the centroid. Determine the location of the centroid of the plane shown. **Diagram Explanation:** - The plane is a composite shape combining a semicircle, a rectangle, and a circle. - The total width of the figure is 120 mm. - The semicircle has a radius of 60 mm, and it incorporates a circle with a radius of 40 mm. - The height of the larger rectangular section is 80 mm, with an extension of 60 mm beyond the semicircle, making the full vertical span from top to bottom 140 mm (including diameter of the semicircle and the rectangle). **2) Problem Statement:** Determine (a) the location of the centroid and (b) the second moment of mass about x- and y-axes of a parabolic spandrel. Assume uniform density \( \rho_A \). **Diagram Explanation:** - The diagram presents a parabolic spandrel, a two-dimensional shape defined by the parabola \( y = kx^2 \), bounded by vertical and horizontal lines. - The horizontal base of the spandrel has a length \( a \), and the vertical height at the end of the spandrel is \( b \). - The equation of the parabola \( y = kx^2 \) describes the curved portion of the spandrel, with \( k \) being a constant that determines the specific curvature.
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