Compute the coordinates of the centroid (,) of the area shown. Also compute the area moment of intertia about the x' axis that passes through the centroid. лу 2013 Michael Swanbom Cc 10 BY NC SA | d к a *b*c → с x Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 38 mm b 16 mm с 17 mm d 74 mm The y coordinate of the centroid is y = mm. The moment of inertia about the x' axis going through the centroid is I' mm4.

Compute the coordinates of the centroid (,) of the area shown. Also compute the area moment of intertia about the x' axis that passes through the centroid. лу 2013 Michael Swanbom Cc 10 BY NC SA | d к a bc → с x Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 38 mm b 16 mm с 17 mm d 74 mm The y coordinate of the centroid is y = mm. The moment of inertia about the x' axis going through the centroid is I' mm4.

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

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter1: Introduction To Statics

Section: Chapter Questions

Problem 1.12P: A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance...

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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 coordinates of the centroid (x, y) of the area shown. Also compute the area moment of
intertia about the x' axis that passes through the centroid.
2013 Michael Swanbom
cc 040
BY NC SA
a
|
|
d
b
жоже
c *
x
Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.
Variable
Value
a
38 mm
b
16 mm
с
17 mm
d
74 mm
The
У
coordinate of the centroid is y
mm.
The moment of inertia about the x' axis going through the centroid is I'
mm4.

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Step 1: Determine y-coordinate of the centroid, and moment of inertia about x' axis going through centroid

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Step 2: Determine the y-coordinate of the centroid

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Step 3: Determine the moment of inertia about x' axis going through the centroid

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A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).
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