composite figures

719 Closed Straight Lines | Centroid of Composite Lines

Problem 719
Determine the centroid of the lines that form the boundary of the shaded area in Fig. P-718.
 

Trapezoidal area with isosceles triangle subtracted from the bottom

 

718 Square and Triangles | Centroid of Composite Area

Problem 718
Locate the centroid of the shaded area shown in Fig. P-718.
 

Trapezoidal area with isosceles triangle subtracted from the bottom

 

717 Symmetrical Arcs and a Line | Centroid of Composite Line

Problem 717
Locate the centroid of the bent wire shown in Fig. P-717. The wire is homogeneous and of uniform cross-section.
 

A line and two arcs in vertical symmety

 

716 Semicircular Arc and Lines | Centroid of Composite Figure

Problem 716
A slender homogeneous wire of uniform cross section is bent into the shape shown in Fig. P-716. Determine the coordinates of the centroid.
 

Vertical line, semicircular arc, and 30 deg line

 

715 Semicircle and Triangle | Centroid of Composite Figure

Problem 715
Determine the coordinates of the centroid of the area shown in Fig. P-715 with respect to the given axes.
 

Semicircle surmounted on top of a right triangle

 

714 Inverted T-section | Centroid of Composite Figure

Problem 714
The dimensions of the T-section of a cast-iron beam are shown in Fig. P-714. How far is the centroid of the area above the base?
 

Inverted T-section for centroid problem

 

240 How to locate the centroid of metal plate with circular hole

Problem 240
The shaded area in Fig P-240 represents a steel plate of uniform thickness. A hole of 4-in. diameter has been cut in the plate. Locate the center of gravity the plate. Hint: The weight of the plate is equivalent to the weight of the original plate minus the weight of material cut away. Represent the original plate weight of plate by a downward force acting at the center of the 10 × 14 in. rectangle. Represent the weight of the material cut away by an upward force acting at the center of the circle. Locate the position of the resultant of these two forces with respect to the left edge and bottom of the plate.
 

Rectangular plate with circular hole

 

 
 
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