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Fundamental Concepts and Principles

• 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

• 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

• Scalar Quantities – described completely by magnitude

• Examples – length , area , volume, speed, mass, time etc.

• Vector Quantities - characterized by its magnitude, direction, line of action

• 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

• 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

• 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.

• F=ma

• F = force acting on the particel

• m = the mass of the particle

• a = the acceleration of the particle caused by the force

• 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

• 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

• 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

• Changing units from one system to another

• 1 ft = .3048m

• 1 slug = 14.59kg

• 1lb = 4.448 N

• Example 1-1 page 11

• Example 1-2 page 12

• Example 1-3 page 13

• Example 1-4 Page 13

• Example 1-5 page 14

• Approximate numbers – usually obtained through some measurement

• Significant digits – numbers other then zero’s

• Three significant digits

• 176

• 0.587

• 1350

• 3050

• 0.00408

• 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

• 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

• 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

• 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