Applied Mechanics

1
Applied Mechanics

• Rigid Body Mechanics
• Statics
• Dynamics
• Kinematics
• Kinetics
• Deformable Body Mechamics
• Elasticity
• Plasticity
• Viscoelasticity
• Fluid Mechanmics
• Liquids
• Gases

2
Statics Vs. Deformable Body Mechanics
Statically Indeterminant
Statically Determinant
How is the problem different if the beam is rock?
Wood? Bone? Tooth Enamel?
3
Elasticity
The beam can bend to conform to the constraints
of the supports. (You have done these types of
problems in ENGR 220).
4
Elasticity vs. Plasticity
Elastic You can bend it, but it will come right
back when you remove the external force (like a
spring). Plastic You can bend it, and it will
stay where it left off (like soldering
wire). Some materials tend to behave elastically,
some plastically, but. Almost all materials will
have both behaviors. Small deflection
elastic. Large deflection plastic.
5
Stress-Strain Curve(or Force-Deflection)
6
Elasticity vs. Viscoelasticity
Elastic Force is proportional to deflection
(e.g. a spring). Viscoelastic Force is
proportional deflection AND to rate of deflection
(e.g. silly putty). Viscous Force is
proportional to deflection only (e.g. a shock
absorber or a fluid).
7
Mechanical Analogy
F kx spring (Think of k as Youngs
Modulus) (Circuits q CV or V q/C) F C
dx/dt shock absorber (dashpot) (Circuits ViR,
or V R dq/dt) What about F m d2x/dt2 ? Same
as F ma Newtons law of motion. (Circuits V
L di/dt L d2q/d2t) Mass is inductance
8
If we know something about how circuits behave,
we know something about how mechanical systems
behave.
One major difference Circuits tend to be
discrete. Mechanical systems tend to be
distributed. We must deal with spatial
relationships.
9
Styrofoam Cup

• Is a styrofoam cup elastic, plastic or
  viscoelastic?
• Place your answer here

YES
10
Important Stuff from Chapter 1

• Units must match
• Hierarchy of Mechanical Measures

11
Important Stuff from Chapter 1

• Energy and Torque (Same units, but

Torque is a vector, Energy is a scalar. Torque is
instantaneous, Energy happens over time.
12
Important Stuff from Chapter 1

• Know your greek letters

13
Modeling and Approximation

• In general, it is always best to begin with a
  simple basic model that represents the system.
  Gradually, the model can be expanded on the basis
  of experience
• But
• Do not throw out the baby with the bath water.

14
Generalized Procedure

1. Select the system
2. Postulate characteristics
3. Simplify with approximations
4. Relate body parts to mechanical elements
5. Construct the mechanical model
6. Apply principles of mechanics
7. Solve for unknowns
8. Compare to experiments
9. Repeat from step 3

15
From Chapter 2

• You need to know how to manipulate vectors.
• Vectors are the only way to represent systems in
  space.
• Review Dot product, cross product, how to
  calculate them, and what they mean.
• For distributed systems

16
Vector Arithmetic

• Add Head to tail
• Subtract reverse direction and then add

A
A B
B
A - B