Mechanics: Statics and Dynamics


TABLE OF CONTENTS

INTRODUCTION.........................................................1

Chapter
I. General Principles........................................2
I. Systems of Force.........................................4
II. Stress..................................................6
III. Properties of Material.................................7
IV. Bolted and Welded Joints................................10
V. Beams -- A Practical Application.........................13
VI. Beam Design.............................................17
VII. Torsional Loading: Shafts, Couplings, and Keys........19
VIII. Conclusion............................................20

BIBLIOGRAPHY.........................................................21

INTRODUCTION

Mechanics is the physical science concerned with the dynamic behavior of
bodies that are acted on by mechanical disturbances. Since such behavior is
involved in virtually all the situations that confront an engineer, mechanics
lie at the core of much engineering analysis. In fact, no physical science
plays a greater role in engineering than does mechanics, and it is the oldest of
all physical sciences. The writings of Archimedes covering bouyancy and the
lever were recorded before 200 B.C. Our modern knowledge of gravity and motion
was established by Isaac Newton (1642-1727).
Mechanics can be divided into two parts: (1) Statics, which relate to
bodies at rest, and (2) dynamics, which deal with bodies in motion. In this
paper we will explore the static dimension of mechanics and discuss the various
types of force on an object and the different strength of materials.
The term strength of materials refers to the ability of the individual
parts of a machine or structure to resist loads. It also permits the selection
of materials and the determination of dimensions to ensure the sufficient
strength of the various parts.

General Principles

Before we can venture to explain statics, one must have a firm grasp on
classical mechanics. This is the study of Newton\'s laws and their extensions.
Newton\'s three laws were originally stated as follows:

1. Every body continues in its state of rest, or of uniform motion
in a straight line, unless it is compelled to change
that state by forces impressed on it.
2. The change of motion is proportional to the motive force impressed
and is made in the direction in which that force is
impressed.
3. To every action there is always opposed an equal reaction; or the
mutual actions of two bodies on each other are equal and
direct to contrary parts.

Newton\'s law of gravitational attraction pertains to celestrial bodies
or any object onto which gravity is a force and states: “Two particles will be
attracted toward each other along their connecting line with a force whose
magnitude is directly proportional to the product of the masses and inversely
proportional to the distance squared between the particles.
When one of the two objects is the earth and the other object is near
the surface of the earth (where r is about 6400 km) / is essentially
constant, then the attraction law becomes f = mg.
Another essential law to consider is the Parallelogram Law. Stevinius
(1548-1620) was the first to demonstrate that forces could be combined by
representing them by arrows to some suitable scale, and then forming a
parallelogram in which the diagonal represents the sum of the two forces. All
vectors must combine in this manner.
When solving static problems as represented as a triangle of force,
three common theorems are as follows:

1. Pythagorean theorem. In any right triangle, the square of the
hypotenuse is equal to the sum of the squares of the
two legs
2. Law of sines. In any triangle, the sides are to each other as the
sines of the opposite angle
3. Law of cosines. In any triangle, the square of any side is equal
to the sum of the squares of the other two sides minus
twice the product of the sides and the cosine of their
included angle

By possessing an understanding of Newton\'s Laws, following these three
laws of graphical solutions, and understanding vector algebra you can solve most
engineering static problems.

Systems of Force

Systems of force acting on objects in equilibrium can be classified as
either concurrent or nonconcurrent and as either coplanar or noncoplanar. This
gives us four general categories of systems.

The first category, concurrent-coplanar forces occur when the lines of
action of all forces lie in the same plane and pass through a common point.
Figure 1 illustrates a concurrent-coplanar force in such that F1, F2, and W all
lie in the same plane (the paper) and all their lines of action have point O in
common. To determine the resultant of concurrent force systems, you can use the
Pythagorean theorem, the law of sines, or the law of cosines as outlined in the
previous chapter.

Nonconcurrent-coplanar force is when the lines of action of all forces
lie in the same plane but do not pass through a common point as illustrated in
figure 2. The magnitude