1. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
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2. Physical Property Analysis
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Physical Property Analysis
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3. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Physical Properties
A physical property is a property that can be observed or measured without changing the identity of the matter.
Examples of Physical Properties:
Volume Density Color
Surface Area Centroid Moment of Inertia
Mass Odor Temperature
Melting Point Viscosity Electric Charge
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4. Physical Property Analysis
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Physical Property Analysis
The size, volume, surface area, and other properties associated with a solid model are often part of the design constraints or solution criteria.
The following are physical properties presented in typical solid modeling programs:
Volume Density Mass
Surface Area Center of Gravity Moment of Inertia
Product of Inertia Radii of Gyration Principal Axes
Principal Moments Length
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5. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Physical Properties
In this lesson you will investigate the following physical properties:
Volume
Surface Area
Density
Mass
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6. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Volume
Volume is the amount of three-dimensional space occupied by an object or enclosed within a container
Design engineers use volume to determine the amount of material needed to produce a part
Different formulas for different shapes
The teacher may want to supplement student knowledge about the use of formulas and related mathematical properties using variables. 8 4
Rectangular Prism
V = H x W x L
V = 4” x 4” x 8”
V = 128 in.3
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7. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Volume in Cubic Units
Measure volume using cubic units:
Cubic inches (in.3)
Cubic feet (ft3)
Cubic yards (yds3)
Cubic centimeters (cm3)
Cubic meters (m3)
It is imperative to keep your units the same when measuring and calculating volume.
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8. Volume Formulas for Prisms, Cylinders, Pyramids, or Cones
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Volume Formulas for Prisms, Cylinders, Pyramids, or Cones
If B is the area of the base of a prism, cylinder, pyramid, or cone and H is the height of the solid, then the formula for the volume is
V = BH
Note: You will need to calculate the area of the shape for the base of the prism. For example: If the solid is a triangular prism, then you will need to calculate the area of the triangle for the base and then calculate the volume.
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9. Area Formulas for Bases of Prisms, Cylinders, and Pyramids
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Area Formulas for Bases of Prisms, Cylinders, and Pyramids
Rectangular Prism – base is rectangle, therefore A = length * width or A = lw
Cylinder – base is a circle, therefore A = pi * radius of circle squared or A = πr2
Square Pyramid – base is a square, therefore A = length * width or A = lw or side squared since the sides are the same on a square or A = s2
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10. Volume of a Cone A Special Case
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Volume of a Cone A Special Case
A cone is 1/3 of a cylinder
The base of a cylinder is a circle
The area of a circle is A=πr2
Therefore, the formula for the volume of a cone is
V= 1/3Ah
where A=πr2 and h is the height of the cone
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11. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Density
Density is defined as mass per unit volume.
Density is different for every material and can be found in a machinist handbook.
Density is always provided, either by looking in a machinist handbook or from tables provided in 3D modeling software.
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12. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Mass
Mass is the amount of matter in an object or the quantity of the inertia of the object.
Many materials are purchased by weight; to find weight, you need to know the mass.
Polypropylene has a density of .035 lb/in.3
and
Mass = Volume x Density
Explain to students that the units for the inches cubed are cancelled out through division. Since there are inches cubed in the numerator and inches cubed in the denominator, they equal one. One times pounds leaves pounds.
Mass = 128 in.3 x .035 lb/in.3
Mass = 4.48 lb
Using the volume from the previous example: V = 128 in.3
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13. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Surface Area
Surface area is the squared
dimensions of the exterior surface.
Surface area is important when determining coatings and heat transfer of a part.
A= 4in. x 4in. = 16 in.2
B= 4in. x 8in. = 32 in.2
C= 4in. x 8in. = 32 in.2
D= 4in. x 8in. = 32 in.2
E= 4in. x 8in. = 32 in.2
F= 4in. x 4in. = 16 in.2 B C D E F A
A + B+ C + D+ E + F = 160 in.2
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14. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
To start the Mass Property function, right click the solid model name in the Browser.
Pick Properties
Mass Property values will be used for predicting material quantity needed for production, finishing, packaging, and shipping.
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15. Additional Physical Properties
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Additional Physical Properties
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16. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Center of Gravity
A 3D point where the total weight of the body may be considered to be concentrated.
The average location of an object.
If an object rotates when thrown it rotates about its center of gravity.
An object can be balance on a sharp point placed directly beneath its center of gravity
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17. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Centroid
A 3D point defining the
geometric center of a solid.
Do not confuse centroid with the center of gravity.
The two only exist at the same 3D point when the part has uniform geometry and density.
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18. Mass Property Analysis
Principal Axes
Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
The lines of intersection
created from three mutually
perpendicular planes, with the three planes’ point of intersection at the centroid of the part.
The X, Y, and Z axes show the principal axes of the ellipsoid.
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19. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Sources
Brodinski, K. G. (1989). Engineering materials properties and selection. Prentice Hall, Inc.: Englewood Cliffs, NJ.
Budinski, K. G. (1992). Engineering materials (4th Ed.). Prentice Hall, Inc.: Englewood Cliffs, NJ.
Gere, J. M., & Timoshenko, S. P. (1997). Mechanics of materials. PWS Publishing Company: Boston.
Lockhart, S. D., & Johnson, C. M. (1999). Engineering design communication: Conveying design through graphics (Preliminary Ed.). Addison Wesley Longman, Inc.: Reading, MA.
Madsen, D. A., Shumaker, T. M., Turpin, J. L., & Stark, C. (1994). Engineering design and drawing (2nd Ed.). Delmar Publishers Inc.: Albany.
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