ES220 Statics

1
ES220 Statics

• Exam I Review Notes

2
Statics of Particles

• Chapter 2

3
Particle Motion

• Translation
• Caused by a Force
• Several applied Forces
• Determine magnitude and direction of single
  resultant force, which determines direction of
  impending translation.
• Statics Interested in balancing applied forces
  to prevent translation (called Equilibrium)

4
Force is a Vector

• A Force consists of
• Magnitude
• Direction
• Line of Action
• Sense
• Point of application
• For a particle, all forces act at the same point
  of application
• (contrast with a scalar, which has only a
  magnitude)

5
Forces (Vectors) Add by the Parallelogram Law

• Can solve
• Graphically
• Using trigonometry
• Resolve into x and y components
• R is the resultant force acting on particle A

6
Simple Example
7
Solve using Trigonometry
Law of sines
Law of cosines
8
Resolving Vectors intox and y Components
Unit vectors
f
?
9
Resultant Force Actingon a Particle
Magnitude
Direction
10
Example
11
Forces in 3D
12
Magnitude Direction in 3D
Magnitude Direction
13
Determining Forces from Unit Vectors
dy
dz
dx
14
Equilibrium

• Using Components
• Graphically

15
Equilibrium Problems

• In 2D, have 2 equations, so can solve for 2
  unknowns
• Find magnitudes of two forces with known
  directions
• Find magnitude and direction of one force,
  knowing magnitude and direction of other force(s)
• In 3D have 3 equations, so can solve for 3
  unknowns

16
Rigid Bodies Equivalent Systems of Forces

• Chapter 3

17
Rigid Body Motion

• Translation
• Caused by a Force
• Rotation
• Caused by a Moment
• A Force acting at a distance from a Point
• Several applied Moments
• Determine magnitude and direction of single
  resultant moment, which determines direction of
  impending rotation.

18
Forces

• Principal of Transmissibility
• Can slide a force along its line of action

19
Moment of a Force about a Point

• Moment Vector
• Magnitude
• Position Vector
• Perpendicular distance d

20
Determining Moments in 2D
Determine or - by the right hand rule For the
picture here
21
Determining Moments in 2D

• Right Hand Rule

22
Determining Moments in 3D

• Moment Vector
• Position Vector

23
Calculating a Vector Cross Product
1
2
3
4
5
6
24
Scalar Product

• Find the angle between two vectors, knowing the
  components
• Find the projection of a vector onto the line of
  action of another vector

25
Moment of a Force, F,About a Line, OL
MOL measures the tendency for the force, F,
applied at A to cause the rigid body to rotate
about line OL
Called a mixed triple product
26
Moment of a Couple

• A Couple consists of two forces
• Same magnitude
• Parallel lines of action (but not co-linear)
• Opposite sense
• Moment caused by the couple

d
Direction determined by right hand rule
27
Moments Caused by Couples

• Moment vector caused by a couple is sometimes
  called a couple vector
• Has components
• Moment caused by a couple is a free vector you
  can place it at any point

28
Moments Caused by Couples

• Can add moments caused by two or more couples
• In 2D

Determine or - by the right hand rule
29
Equivalent Couples

• Two couples are equivalent if they cause the same
  moment

30
Force-Couple System

• A force, F, acting at point A can be replaced by
  the force, F, and a moment, MO, acting at point O.

31
Create a Force-Couple System at a Chosen Point
F
F
F
F
A
B
A
B
A
B


MA
d
F
MA d F
32
Replace a Force-Couple System with Just Forces
F
F
A
A
F2

d2
MA
F2
C
C
d2 F2 MA
33
Reducing a System of Forces to a Resultant
Force-Couple System (at a Chosen Point)
F1
R
r1
r2
F2
A

r3
MA
F3
34
Reduce a System of Forces to a Single Resultant
Force
F1
R
R
R
r1
r2
B
F2
A


r3
MA
MA
R
R
F3
B
Using method from prior slide

35
R
R
Ry
B
B
A
Rx
Rx
A
Ry
MA
R
R
dx
dx R MA