Essay/Term paper: Mechanics: statics and dynamics

Essay, term paper, research paper:  Science

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 and direction of the resultant force can be determined
by the rectangular component method using the first two equations in figure 2,
and the perpendicular distance of the line of action of R from the axis of
rotation of the body can be found using the third equation in figure 2.

Concurrent-noncoplanar forces are when Application the lines of action
of all forces pass through a common point and are not in the same plane. To
find the resultant of these forces it is best to resolve each force into
components along three axes that make angles of 90 degrees with each other.

Nonconcurrent-noncoplanar forces are when the lines of action of all
forces do not pass through a common point and the forces do not all lie in the
same plane.

Stress

When a restrained body is subject to external forces, there is a
tendency for the shape of the body that is subject to the external force to be
deformed or changed. Since materials are not perfectly rigid, the applied
forces will cause the body to deform. The internal resistance to deformation of
the fibers of a body is called stress. Stress can be classified as either
simple stress, sometimes referred to as direct stress, or indirect stress.

The various types of direct stress are tension, compression, shear, and
bearing. The various types of indirect stress are bending and torsion. A third
variety of stress is categorized as any combination of direct and indirect
stress.

Simple stress is developed under direct loading conditions. That is,
simple tension and simple compression occur when the applied force is in line
with the axis of the member and simple shear occurs when equal, parallel, and
opposite forces tend to cause a surface to slide relative to the adjacent
surface. When any type of simple stress develops we can calculate the magnitude
of the stress by the formula, where:

· s = average unit stress;
· F = external force causing stress to develop;
· A = area over which stress develops.

Indirect stress, or stress due to bending should be properly classified
under statics of rigid bodies and not under strength of materials. The bending
moment in a beam depends only on the loads on the beam and on its consequent
support reactions. Torsion is when a shaft is acted upon by two equal and
opposite twisting moments in parallel planes. Torsion can be either stationary
or rotating uniformly. Indirect stress will be discussed in detail in later
sections.

Properties of Material

In order for the engineer to effectively design any item, whether it is
a frame which holds an object or a complicated piece of automated machinery, it
is very important to have a strong knowledge of the mechanical and physical
properties of metals, wood, concrete, plastics and composites, and any other
material an engineer is considering using to construct an object. The rest of
this paper will deal with strength of materials and how to best choose a
material and construction technique to effectively accomplish what was set out
without "over-engineering."

Strength of materials deals with the relationship between the external
forces applied to elastic bodies and the resulting deformations and stresses.
In the design of structures and machines, the application of the principles of
strength of materials is necessary if satisfactory materials are to be utilized
and adequate proportions obtained to resist functional forces.

In today's global economy is crucial for success to be able to build the
"biggest and best" while spending the least. To do that successfully it is
imperative to have a firm understanding of different materials and their correct
uses. The load per unit area, called stress, and the deformation per unit
length, called strain, must be understood. The formula for stress is:


The formula for strain is:


The amount of stress and strain a material can endure before deformation
occurs is known as the proportional limit. Up to this point, any stress or
strain induced into the material will allow the material to return to its
original shape. When stress and strain exceed the proportional limit of the
material and a permanent deformation, or set, occurs the object is said to have
reached its elastic limit. Modulus of elasticity, also called Young's modulus,
is the ratio of unit stress to unit strain within the proportional limit of a
material in tension or compression. Some representatives values of Young's
modulus (in 10^6 psi) are as follows:

· Aluminum, cast, pure...................................9
· Aluminum, wrought, 2014-T6............................10.6
· Beryllium copper......................................19
· Brass, naval..........................................15
· Titanium, alloy, 5 Al, 2.5 Sn.........................17
· Steel for buildings and bridges, ASTM A7-61T...29

Once the elastic limit of a material is reached, the material will
elongate rather easily without a significant increase in the load. This is
known as the yield point of the material. Not all materials have a yield point.
Some repre