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Engineering Mechanics I: Statics

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Title: 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
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