Compute the following for the given composite area. a) Locate the centroid with respect to the given axes. b) Determine the centroidal area moments of inertia (Ix, and lyr). y 1.5 ft 1.5 ft 1.5 ft 0.75 ft 6 ft 3 ft 1.5 ft

Compute the following for the given composite area. a) Locate the centroid with respect to the given axes. b) Determine the centroidal area moments of inertia (Ix, and lyr). y 1.5 ft 1.5 ft 1.5 ft 0.75 ft 6 ft 3 ft 1.5 ft

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.132RP: Find the centroid of the truncated parabolic complement by integration.

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Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

Compute the following for the given composite area.
a) Locate the centroid with respect to the given axes.
b) Determine the centroidal area moments of inertia (Ix, and lyr).
y
1.5 ft
1.5 ft
1.5 ft
0.75 ft
6 ft
3 ft
1.5 ft

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Step 1: Given data

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Step 2: Divide given area into different shapes and calculation of x, y coordinates of it's C.G.

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Step 3: Calculation of the centroid with respect to the given axes.

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Step 4: Calculation of the centroidal area moments of inertia

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Step 5: Calculation of the centroidal area moments of inertia

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Step 6: Calculation of the centroidal area moments of inertia

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