1. 7 STATICS ENGINEERS MECHANICS Theorems of Pappus-Guldinus CHAPTER
Lecture Notes:
Professor A. Salam Al-Ammri
Suhad Ibraheem Mohammed
Al-Khwarizmi College of Engineering
University of Baghdad
Theorems of Pappus-Guldinus
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

2. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Contents
Introduction
Theorms of Pappus-Guldinus
Sample Problem 7.3.1
Sample Problem 7.3.2
Sample Problem 7.3.3
Sample Problem 7.3.4
Sample Problem 7.3.5
Sample Problem 7.3.6
Sample Problem 7.3.7
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

3. Introduction
Theorems of Pappus-Guldinus are useful to find a surface area or volume of revolution.
Surface area (As) of revolution
Volume (V) of revolution
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

4. Theorems of Pappus-Guldinus
Surface of revolution is generated by rotating a plane curve about a fixed axis.
Area of a surface of revolution is equal to the length of the generating curve times the distance traveled by the centroid through the rotation.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

5. Theorems of Pappus-Guldinus
Body of revolution is generated by rotating a plane area about a fixed axis.
Volume of a body of revolution is equal to the generating area times the distance traveled by the centroid through the rotation.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

6. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.1
The circular arc is rotated through 360o about the y-axis.Determine the outer surface area of the resulting body, which is a portion of a sphere.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

7. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.2
The body shown in cross section is a complete circular ring formed by revolving the octagonal area about the z-axis. The entire surface is to be covered with a special coating . Determine this surface area.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

8. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.3
The two circular arcs AB and BC are revolved about the vertical axis to obtain the surface of revolution shown. Compute the area A of the outside of this surface.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

9. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.4
The outside diameter of a pulley is 0.8 m, and the cross section of its rim is as shown. Knowing that the pulley is made of steel and that the density of steel is ρ=7.85x103 kg/m3,determine the mass and weight of the rim.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

10. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.5
Calculate the mass m of concrete required to constructthe arched dam shown. Concrete has a density of 2.40 Mg/m3.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

11. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.6
A hand-operated control wheel made of aluminum has the proportions shown in the cross-sectional view. The area of the total section shown is 15,200 mm2, and the wheel has a mass of 10 kg. Calculate the distance to the centroid of the half-section. The aluminum has a density of 2.69 Mg/m3.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad

12. Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad
Sample Problem 7.3.7
A steel die, shown in section ,has the form of a solid generated by revolving the shaded area around the z-axis.Calculate the mass of the die.
2/17/2012
Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad