Engineering Mechanics I: Statics

1
Engineering Mechanics I Statics

• Chapter 1 Introduction to Statics

2
Mechanics

• Concerned with the state of rest or motion of
  bodies subjected to the action of forces

Statics
Rigid-Body Mechanics

• Equilibrium of bodies

Dynamics
Deformable-Body Mechanics
Mechanics
- Accelerated motion
Fluid Mechanics
3
Fundamental Concepts

• Basic Quantities
• Length locate position and describe size
• Time succession of events
• Mass measure of inertia of a body
• resistance to a change in velocity)
• Force push or pull exerted by one body
• on another
• Direct contact
• Remote action (gravitational, electrical,
  magnetric forces)

4
Fundamental Concepts

• Idealizations
• Particle consider mass but neglect size
• Rigid body
• combination of large number of particles
• neglect material properties
• no deformation
• Concentrated force
• loading area is small compared to overall
  size
• assumed to act at a point on a body

5
Scalars and Vectors

• Scalar quantities with only magnitude
• Vector magnitude direction
• Free vector
• Sliding vector
• Fixed vector

6
Vectors

• A vector quantity V, is represented by a
  line segment
• Line direction (measured by q)
• Arrowhead sense
• Length magnitude
• -V same magnitude as V, opposite direction

7
Vector operations

• Vector sum (triangle law or parallelogram)
• V V1 V2
• Vector subtraction
• V V1 - V2

8
Vector operations

• A generic triangle of forces, the sine and cosine
  rules can be used to determine the magnitude
• Cosine rule
• Sine rule

9
Vector operations

• Vector components
• mutually perpendicular Rectangular components
• Unit Vector ( )

Direction (dimensionless)
Magnitude
10
Vector operations

• Dot product or scalar product

11
Vector operations

• Cross product or vector product
• direction is specified by the right-hand rule

12
Fundamental Concepts

• Newtons Three Laws of Motion
• First Law A particle originally at rest, or
  moving in a straight line with constant velocity
  , will remain in this state provided the particle
  is not subjected to an unbalanced force.

13
Fundamental Concepts

• Newtons Three Laws of Motion
• Second Law A particle acted upon by an
  unbalanced force F experiences an acceleration a
  that has the same direction as the force and a
  magnitude that is directly proportional to the
  force

F ma
14
Fundamental Concepts

• Newtons Three Laws of Motion
• Third Law The mutual forces of action and
  reaction between two particles are equal and,
  opposite and collinear

15
Fundamental Concepts

• Newtons Law of Gravitational Attraction
• F force of gravitation between two
  particles
• G constant of gravitation
• 6.673x10-11 m3/(kg.s2)
• m1,m2 mass of each of the two
  particles
• r distance between the two particles
• Weight
• , letting yields

g 9.81 m/s2 (see Table D/2 in appendix D)
16
Units

• SI units Système International dUnités
• SI system specifies length in meters (m), time in
  seconds (s) and mass in kilograms (kg)
• Unit of force, called Newton (N) is derived from
  F ma
• N kg.m/s2
• Therefore, 1 Newton is the force required to give
  a mass of 1 kg an acceleration of 1 m/s2

17
Prefixes
Exponential Form Prefix SI Symbol
Multiple
1 000 000 000 109 Giga G
1 000 000 106 Mega M
1 000 103 Kilo k
Sub-Multiple
0.001 10-3 Milli m
0.000 001 10-6 Micro µ
0.000 000 001 10-9 nano n
Most efficient way of learning is to solve
problems!!!