Note carefully the coordinate system shown. Using this coordinate system determine the location of the Z-centroid and enter your answer in units of ft. 8N9 ft16 ftLightweightConcrete125 lb/ft4 ftVY+3 ft2 ft3 ftSteel493 lb/ft4 ft. A composite solid consists of a rectangular block of lightweight concrete and atriangular wedge of steel with dimensions as shown. The rectangular block has a2 ft radius circular hole drilled through its full depth, perpendicular to the frontand back faces.Assume densities yc = 125 lb/ft³, and ys = 493 lb/ft³.Note carefully the coordinate system shown. Using this coordinate systemdetermine the location of the Z-centroid and enter your answer in units of ft.

Answered: Image /qna-images/answer/44b6951e-d688-430c-a4b7-eb8d4b62cd69.jpg

Answered: Note carefully the coordinate system…

Note carefully the coordinate system shown. Using this coordinate system determine the location of the Z-centroid and enter your answer in units of ft.

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

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.13P: Figure (a) shows the cross section of a column that uses a structural shape known as W867...

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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

Note carefully the coordinate system shown. Using this coordinate system determine the location of the Z-centroid and enter your answer in units of ft.

8
N
9 ft
1
6 ft
Lightweight
Concrete
125 lb/ft
4 ft
V
Y
+
3 ft
2 ft
3 ft
Steel
493 lb/ft
4 ft.

A composite solid consists of a rectangular block of lightweight concrete and a
triangular wedge of steel with dimensions as shown. The rectangular block has a
2 ft radius circular hole drilled through its full depth, perpendicular to the front
and back faces.
Assume densities yc = 125 lb/ft³, and ys = 493 lb/ft³.
Note carefully the coordinate system shown. Using this coordinate system
determine the location of the Z-centroid and enter your answer in units of ft.

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Step 2: Write the z-centroid for each segments.

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Figure (a) shows the cross section of a column that uses a structural shape known as W867 (wide-flange beam, nominally 8 in. deep, weighing 67 lb/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following cross-sectional properties: A=19.7in.2,Ix=272in.4, and Iy=88.6in.4. Determine the dimensions of the rectangle in Fig. (b) that has the same Ix and Iy as a W867 section.
Figure (a) shows the cross-sectional dimensions for the structural steel section known as C1020 (channel with a nominal depth of 10 in., weighing 201b/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following properties for the cross section: A=5.88in.2,Ix=78.9in.4, and Iy=2.81in.4. If two of these channels are welded together as shown in Fig. (b), find Ix and Iy for the resulting cross section.