1. Fundamental Concepts and Principles
Statics
Fundamental Concepts and Principles

2. 1-1 Intro to Mechanics Branch of physical science
Deals state of rest or motion of bodies under action of forces
Divided into three branches
Statics
Concerns the equilibrium of bodies under action of balanced forces
Dynamics
Deals with the motions of bodies under action of unbalanced forces
Strength of materials
Relationships among the external forces applied to the bodies, the resulting stresses and deformation
Study of statics dynamics all bodies are assumed perfectly rigid
Solid in which the distance between any two points in the body remain unchanged

3. 1-2 Nature of Force
Force is defined as effect that may change the state of rest or motion of a body
Applied either direct physical contact between bodies or remote action
Gravitational electrical magnetic are remote
Ball is thrown into air falls to ground
Most other forces are direct
Forces applied to a rope being pulled
Forces between beam and support
Characteristics of a Force
Defined completely by magnitude , direction and point of application
Magnitude of force described by a number
Direction of force indicated by a line
Point of application is the point at which force is exerted
Figure 1-1 page 4

4. 1-3 Scalar and Vector Quantities
Scalar Quantities – described completely by magnitude
Examples – length , area , volume, speed, mass, time etc.
Vector Quantities - characterized by its magnitude, direction, line of action

5. 1-4 Types of Forces Distributed and Concentrated Forces
Exerted on a line, over an area, or throughout an entire volume
Weight of a beam can be treated as a distributed force over its length
Concentrated force is an idealization in which a force is assumed to act at a point
External and Internal Forces
Exerted on the body by another body
Structure if formed by several connected components the forces holding the component parts together are internal forces
Example figure 1-2 page 5

6. 1-5 Types of Force Systems
Forces treated as a group
Forces whose lines of action lie in the same plane are called coplanar forces
Forces whose lines of action act in a three-dimensional space called spatial forces
If line of action of all the forces in a system pass through a common point – concurrent
No common point of intersection forces are nonconcurrent
Examples figure 1-3 page 6

7. 1-6 Newton’s Laws
Newton’s laws now form the foundation of Newtonian mechanics
First Law – A particle remains at rest or continues to move along a straight line with a constant velocity if the force acting on it is zero
Second law – If the force acting on a particle is not zero, the particle accelerates (changes velocity with respect to time) in the direction of the force and the magnitude of the acceleration (the rate of change of velocity per unit time) is proportional to the magnitude of the force
Third Law – the forces of action and reaction between interactive bodies always have the same magnitudes and opposite directions.

8. 1-6 Newton’s Laws F=ma F = force acting on the particel
m = the mass of the particle
a = the acceleration of the particle caused by the force

9. 1=7 Principle of Transmissibility
States that the point of application of a force acting on a rigid body may be placed anywhere along its line of action without altering the conditions of equilibrium or motion of the rigid body.
Example Figure 1-4 page 8
Internal effect of a force on a body is dependent on its point of application
Deformation would be dependent on its point of application
Figure 1-5 page 8

10. 1-8 Systems of Units U.s Customary Units Length = foot (ft)
Force = pound (lb)
Time = second (s)
Slug – unit of mass is derived unit
M=f/a 1 slug = (1lb)/(1ft/s²)=1 lb *s²/ft
Gravitational acceleration = 32.2 ft/s²
Equation 1-2 page 9
1 mile (mi) = 5280 ft
1 inch (in) = 1/12 ft
1 kilo-pound (kip) 1000 lb
1 us ton (ton) = 2000 lb
1 minute (min) = 60s
1 hour (h) = 60 min = 3600s

11. 1-8 Systems of Units SI units Length = meter (m) Mass = kilogram (kg)
Time = seconds (s)
SI units are absolute system
Force = netwon (N)
F-ma
1 N = (1kg) * (m/s²) = 1 kg *m/s²
Gravitational acceleration g=9.81m/s²
Mass of 1kg on the surface of the earth
W=mg
1kg *9.81m/s²
=9.81kg *m/s² = 9.81 N
1 kg = 1000 g
1km = 10³m = 1000 m
1m = 1000mm
1kN =10³N = 1000N
1Mg (metric ton = 10³ kg = 1000 kg

12. 1-9 Unit Conversion Changing units from one system to another
1 ft = .3048m
1 slug = 14.59kg
1lb = N
Example 1-1 page 11
Example 1-2 page 12

13. 1-10 Consistency of Units in an Equation
Example 1-3 page 13
Example 1-4 Page 13
Example 1-5 page 14

14. 1-11 Rules for Numerical Computations
Approximate numbers – usually obtained through some measurement
Significant digits – numbers other then zero’s
Three significant digits
176
0.587
1350
3050
Accuracy and Precision
Accuracy refers to its number of significant digits
Precision refers to the decimal position of the last significant digit
Example 1-6 page 15
Example 1-7 page 16

15. 1-11 rules for Numerical Computation
Rule 1 when approximate numbers are multiplied or divided the result is expressed with the same accuracy as the least accurate number
Rule 2 – when approximate numbers are added or subtracted, the result is expressed with the same precision as the least precise number
Example 1-8 page 16
Example 1-9 page 17
Example 1-10 page 17
When using a calculator retain all digits and round only the final answer

16. 1-12 Review of Mathematics
Right triangles
Side opposite the right angle is called the hypotenuse
Pythagorean theorem
c²=a²+b²
Trigonometry of right triangles
Sin A =opposite side/hypotenuse
Cos A = adjacent side /hypotenuse
Tan A = opposite side/adjacent side
Example 1-11 page 19
Example 1-12 page 19

17. 1-12 Review of Mathematics
Oblique Triangles – none of interior angles is equal to 90
Sum of the interior angles is = 180
The law of sines a/sin A = b/sin B = c/sin C
The law of cosines –see page 20
Example 1-13 page 21
Example 1-14 page 21
Example 1-15 page 22
Example 1-16 page 23