MAE 206
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Engineering Statics -- MAE 206 Course Review
Contents |
Welcome:
I've created a wiki here for you to create an ever-evolving review page. The best way to learn something is to teach it to someone else. Use this space as an opportunity for you as a group to organize what you've learned and keep track of everything you need to review for the final. To edit the page, click on "edit" at the top of the page.
(Fine print: Recall that this page is covered under both privacy laws and copyright laws; the student code of conduct is in effect. Images limited to 640x480. Editing the page is not required, but it will serve you well in learning the material. This is a student production: if something here is incorrect, it's up to you to fix it.)
Points to Remember:
Any object can be treated as a particle as long as size, shape, & orientation don't matter.
Rules for applying equilibrium:
What other topics can you think of?
Trigonometry Review
1. Law of Sines
a. sin(A)/a = sin(B)/b = sin(C)/c
2. Law of Cosines
a. c=sqrt(a^2 + b^2 -2ab*cos(C))
Ways to Express a Force Vector
3 Categories
1. Cartesian: given vector coordinates in 3 dimensional space
a. F = Fxi + Fyj + Fzk
2. Magnitude on a line: given the magnitude of the force and a line, defined by starting and ending coordinates/vectors
a. F = the vector from A=(0,0,0) to B=(x,y,z) with a magnitude of 20N
Converting to Cartesian
a. Find the Position Vector
ex: P = (x,y,z)-(0,0,0) = (x,y,z)
b. Find the Unit Vector
ex: magnitude of P = sqrt(x^2 + y^2 + z^2)
U = P/Pmag = (x,y,z)/sqrt(x^2 + y^2 + z^2)
c. Multiply the Unit Vector by the magnitude of the force
ex: F = Fmag*U =(20)*(x,y,z)/sqrt(x^2 + y^2 + z^2)
F = Fxi + Fyj + Fzk'
3. Magnitude and direction
3a. Projections
3b. Direction Cosines: Given magnitude and angles from the coordinate axes
a. Given: Fmag, Theta(x), Theta(y), Theta(z)
Converting to Cartesian
a. Take the cosine of each angle to find the component of each axis
b. Multiply each cosine by the magnitude of the vector
ex: Fx = Fmag*cos(Theta(x))
Fy = Fmag*cos(Theta(y))
Fz = Fmag*cos(Theta(z))
F = Fxi + Fyj + Fzk
Equilibrium
The state in which the net forces on an object are 0.
The vector components of forces in each direction must add up to 0 in an equilibrium equation.
a. Sum of X components = 0
b. Sum of Y components = 0
c. Sum of Z components = 0
Solving a 3 Dimensional Equilibrium Problem
1. Read the problem. At least twice.
2. Decide where the crucial point in the system is. Draw a Free Body Diagram of that point.
3. List given values.
4. Write each force in it's component form and note the point it acts upon. For forces where the components are not trivially easy to write down, follow these steps:
a. For each force, find the vector which determines the direction the force acts in. In many cases, this is the position vector
between two points.
b. For each force, find the unit vector.
c. Write each force in its component parts as its magnitude time the unit vector.
5. Once each force is in its component parts, the equilibrium equations are the sum of the components in the x, y, and z directions.
6. Solve the system of equilibrium equations for the missing values.
7. Answer the question that was asked.
8. Check your work. Do the answers make sense?
9. Check your units. Incorrect units, or lack of units can cause catastrophes.
Learning Objectives
0. Review vector analysis and trigonometry
1. Branches of Mechanics; how Statics relates to Dynamics & Solids
2. Solving problems using standard steps which can be used every time
3. Differentiating particles, rigid bodies, & systems
4. Specifying a force three basic ways; switching back and forth (in two dimensions and three dimensions)
5. Adding forces; finding a resultant (in two dimensions and three dimensions)
6. Drawing complete FBDs in two dimensions and three dimensions: particles, rigid bodies, systems
7. Calculating internal loads
8. Transitioning from FBDs to equilibrium equations (in two dimensions and three dimensions)
9. Learning to conceptualize three-dimensional objects
10. Defining a moment; learning to manipulate and calculate them using scalar and vector methods
11. Understanding Principle of Transmissibility for forces and Freedom of Moments
12. Understanding two-force members
13. Familiarity with engineering software
14. Difference between a mechanical force and a point force
15. Calculation of a centroid of an area, center of gravity, center of mass by definition and by using composite body methods
16. Area and volume of Bodies of Revolution
17. Calculation of moments of inertia by definition an by using composite body methods
18. Calculation of equivalent loads due to fluid forces
19. Calculation and placement of friction and normal forces; relationship between friction and normal forces
20. Understanding friction for wedges and screws
21. Defining an internal force with correct sign conventions; drawing the FBD of a piece of a beam with internal forces & moments
22. Drawing shear and bending moments by definition and by graphical construction
23. Calculation of internal axial loads in truss systems both by method of joints and the method of sections – application of equilibrium to a joint and to a section
24. Design of a structure – basic design principles
25. Principles of teamwork
26. Dismembering a structure; drawing complete and accurate FBDs of only part of a structure; equal and opposite forces on each member
Links:
- English Wikipedia Article on Statics
- Wikibook (Free Online Textbook) on Statics
- Concept Assessment Tool for Statics
- Free Online Statics Course (Open Learning Initiative)
- Free Online Text "Structural Elements", opening chapter is a summary of Statics
- An Engineering Statics Course from UNL in 2003
- A more recent Statics Course with online notes from University of Kentucky
--Alex R 00:57, 3 August 2008 (EDT)