ES220 Statics

1
ES220 Statics

• Exam II Review Notes

2
Equilibrium of Rigid Bodies

• Chapter 4

3
Recall Rigid Body Motion

• Translation
• Caused by Force(s)
• Rotation
• Caused by Moment(s)
• 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.

4
Static Equilibrium of Rigid Bodies

• A body at rest remains at rest
• A body in motion continues to move in a straight
  line at constant velocity
• Conditions for equilibrium
• is a vector pointing from point A to the point
  where acts

5
Moment of a Force about a Point

• Moment Vector
• Magnitude
• Position Vector
• Perpendicular distance d
• Moment vector is perpendicular to both r and F.

6
Forces

• Principal of Transmissibility
• Can slide a force along its line of action
• Very useful in summing moments!

7
Determining Moments in 2D
Determine or - by the right hand rule For the
picture here
8
Determining Moments in 2D

• Right Hand Rule

9
Determining Moments in 3D

• Moment Vector
• Position Vector

10
Calculating a Vector Cross Product
1
2
3
4
5
6
11
Rigid Bodies

• A 2D or 3D bodies with dimensions
• (Contrast with a point, which is infinitely
  small)
• Systems of rigid bodies and supports
• Externally applied forces or moments
• Contact with other things
• Other rigid bodies
• Supports, cables, etc.
• Contact cause reaction forces or moments

12
Rigid Bodies in 2D

• 3 Equilibrium equations
• Therefore, can solve for 3 unknowns
• Examples
• Three support reactions
• Unknown magnitudes of 3 forces, of known
  directions
• Unknown magnitude of 1 force with known
  direction unknown magnitude and direction of 1
  force

13
2D Reactions at Supports and Connections
14
Free Body Diagrams

• Choose body, detach from the ground, supports,
  connections, other bodies
• Draw body and all external forces acting ON body.
• Where body contacts ground, supports,
  connections, or other bodies, draw the
  appropriate reaction forces
• Include weight of body, acting down through the
  center of gravity
• Label the magnitude direction of known forces
• Identify unknown forces/reactions
• Show the line of action, if known
• Include dimensions, which are required in order
  to sum moments, SM 0.

15
Hints for Free Body Diagrams

• Assume unknown forces act in positive direction
• If answer is negative, you assumed the wrong
  direction, and force is in negative direction
• Assume forces in cables and rods are tensile
• If answer is negative, your assumption was wrong,
  and the rod is in compression
• Note that cables can never be in compression!!
• For summing moments
• Resolve forces into x and y components
• Find perpendicular distance from force to the
  point about which you are summing the moment.

16
Example 3 unknowns
17
Example 3 unknowns
18
Example 3 unknowns
19
Two-Force Members

• Pinned at both ends (joints), with no applied
  loads between joints
• Line of action of forces is directed along a line
  drawn between the two joints

20
Three Force Members

• Three forces are either
• Concurrent (all 3 forces pass through a single
  point) (See next slide)
• Parallel

21
Three Force Members Concurrent

• Lines of action of the 3 concurrent forces
  intersect to form a triangle
• Draw known lines of action of 2 forces to
  intersect at a point
• Draw 3rd line of action from point where 3rd
  force acts to intersection point
• Use this triangle to find ?, the direction of the
  3rd force
• Knowing ?, use law of sines to find magnitudes of
  three forces

22
Example
23
Rigid Bodies in 3D

• 6 Equilibrium equations
• Therefore, can solve for up to 6 unknowns
• We often had fewer than 6 unknowns

Break into components
24
3D Reactions at Supports and Connections
25
Example
5 Unknowns
26
Similar for
27
0
Solve for 2 unknowns
Solve for 3 unknowns
28
Centroids and Centers of Gravity

• Chapter 5

29
2D Composite Plates

• Break plate up into common shapes, for which
  centroid coordinates are known
• Determine centroid of composite plate using

30
(No Transcript)
31
Example
32
(No Transcript)
33
2D Composite Wires

• Break wire up into line segments, for which
  centroid coordinates are known
• Determine centroid of composite wire using

34
(No Transcript)
35
3D Composite Bodies

• Break body up into common volumes, for which
  centroid coordinates are known
• Determine centroid of composite body using

36
(No Transcript)
37
Example
38
(No Transcript)
39
(No Transcript)
40
3D Composite Plates/Sheets

• Break plate/sheet up into common shapes, for
  which centroid coordinates are known
• Determine centroid of composite plate/sheet using

41
3D Composite Wires

• Break wire up into line segments, for which
  centroid coordinates are known
• Determine centroid of composite wire using