ENGINEERING MECHANICS (Part II)

N 1

RIGID BODY MOTION (I)

The study of the motion of rigid bodies is an important topic in engineering mechanics. This chapter, and most of those which follow, are devoted to the development of analytical techniques for two-and three-dimensional rigid body motion and equilibrium problems. A rigid body is an idealization of a real, solid body. It is assumed to possess the property that the relative positions of points within the body cannot change. That is, distances bet­ween any pairs of points remain constant. A rigid body can have rather complicated motion, particularly in three dimensions, in spite of the fact that the relative positions of points within it remain unchanged. Perhaps it is better to say that describing rigid body motion is much more complicated than describing the motion of a single particle.

There are three types of plane rigid body motion: (a) trans­lation, (b) fixed axis rotation, and (c) general plane motion.

A body in translation, moves in such a way that the orien­tations of lines in the body at all subsequent positions are parallel to the corresponding initial orientations of the lines. That is, horizontal lines remain horizontal; vertical lines re­main vertical, etc. In translation, all points in the body undergo equal displacements in equal intervals of time. Hence, all particles have equal velocities and equal accelerations at any instant. Fоr a rigid body in translation it is possible to speak of the velocity and the acceleration of the body as a whole at a particular instant.

Notes:

rigid body - твердое тело, жесткое тело

the relative positions of points - относительные положения точек

rather - довольно

translational motion - переносное движение

fixed axis rotation - вращение вокруг неподвижной оси general plane motion - общее плоскостное движение

displacement - перемещение

translation - перенос

in spite of - несмотря на

N 2

RIGID BODY MOTION (II)

In fixed axis rotation, where the axis is perpendicular to the plane of motion, each particle of the body moves in a cir­cular path whose radius is the distance of the particle in ques­tion from the fixed axis. All the equations developed for cir­cular motion can be applied in describing this kind of motion. Since the body is rigid, any line drawn radially outward from the axis of rotation remains straight and has the same angular velocity as any other such line. In fact all lines on the body, whether radial or not, have the same angular velocity. Thus, the angular velocity of any line can be assigned to the body as a whole.

For the case of general plane motion, no line continues to have any particular orientation with respect to a fixed line, nor does any one point remain stationary, as in fixed axis ro­tation. General plane motion can be thought of as a combination of translation and rotation. The description of general plane motion involves the simultaneous specification of the motion of some reference point and the rotation about an axis through this point perpendicular to the plane of the figure.

Notes:

fixed axis rotation - вращение вокруг неподвижной оси

the particle in question - рассматриваемая частица

circular - круговой

angular - угловой

radial - радиальный

general plane motion - общее плоскостное движение

with respect to - по отношению к

reference point - исходная (опорная) точка; точка сравнения

N3

MECHANICAL SYSTEMS (I)

A mechanical system is defined as anything that is composed of matter. The first step in an analysis of a mechanical system should be a precise and definitive description of the system un­der consideration. Since the modern theories of the constitution of matter will not be considered, the particles that compose a mechanical system are regarded as mathematical abstractions; they are more properly called "material points". The simultane­ous positions of all the material points of a mechanical system are called the "configuration of the system". For example, the dis­placement vector field of a deformable body defines a configura­tion of the body. To define the configuration of a mechanical system, we require a coordinate system that is attached to some rigid system, known as a "reference frame". In the theory of kinematics the reference frame is arbitrary.

A general problem of statics is to determine the equilibrium configurations of mechanical systems under prescribed types of loadings and to ascertain which among them are stable. An impor­tant general problem of dynamics is to express the configuration of a given mechanical system as a function of time.

A mechanical system is said to experience a displacement if any of its material points are displaced. In other words, any change of the configuration of a mechanical system is a dis­placement.

N о t e s :

under consideration - рассматриваемый

material point - материальная точка

displacement vector field - поле вектора перемещения

reference frame - рамка отсчета

arbitrary - произвольный

prescribed - зд. : заранее данный

loading - нагрузка

N 4

STATIC STRESS-STRAIN PROPERTIES IN

TENSION AND COMPRESSION

(I)

Most engineers are primarily concerned with the development and design of machines, structures and products of various kinds. Since these constructions are usually subjected to internal for­ces and deformations called stresses and strains, the properties of materials under the action of these stresses and strains for various environments become an important engineering considera­tion. The macroscopic properties of materials when subjected to these stresses and strains are called the mechanical properties. The study of the macroscopic stress-strain properties of materi­als may be referred to as solid state mechanics in the same way as solid state physics refers to the atomic and molecular beha­viour of materials on the submicroscopic level. An understanding of the stress-strain properties of materials are important, since high values of stress and strain may result in the failure of a construction. Failures may lead to loss of life and costly damage when airliners or trains are wrecked or a bridge collapses. Sometimes failures do not lead to loss of life but involve need­less costly repairs, delays in operation, or replacement of parts.

Notes:

are subjected - подвержены

stress - напряжение

strain - деформация

refer to - ссылаться на

stress-strain properties - соотношение между напряжение и дефор­мацией, уравнение механического состояния

solid state mechanics - механика твердого тела

failure - разрыв, повреждение

value - значение, величина

result in - приводить к

N 5

STATIC STRESS-STRAIN PROPERTIES

IN ТENSION AND COMPRESSION

(II)

A thorough knowledge of material stress-strain behavior is required by the engineer so that failures can be avoided. Such knowledge is also necessary in order to utilize materials most economically. Fоr example, if the stresses or strains in a component of a machine or structure are too low, the size of the part is larger than necessary and the material is not being used economically. The need for a careful consideration of material properties has also been made necessary in recent years by the increased scarcity of certain materials and the need for the use of substitute materials. Many new developments in the transpor­tation, power and other industries, for both domestic and milita­ry applications, have led to the development of new materials with improved properties. Materials with high resistance to ele­vated temperatures are needed for many modern constructions such as jet engines, rockets, missiles, high-speed aircraft, and nuclear reactors. Sometimes these applications require considera­tion of corrosion, impact and fatigue properties in addition to temperature properties.

Notes

material stress-strain behaviour - поведение материалов при деформации

failure - разрыв, повреждение

jet engine - реактивный двигатель

Impact properties - ударные свойства

scarcity - нехватка

both...and - как ..., так и …

N 6

STATIC STRESS-STRAIN PROPERTIES IN TENSION AND COMPRESSION

(III)

Many kinds of engineers and scientists contribute to the de­velopment of the materials required in our modern civilization. Geologists explore and detect the sources of our raw materials, and the mining engineer aids in obtaining these materials from the earth's surface. The refinement of these raw materials and the development of new types of materials is the concern of the metallurgist and chemist. After materials are refined they are processed and fabricated into final shapes and forms used for various constructions and products. The processing and fabri­cation of materials is one of the main responsibilities of the industrial engineer. The selection of a particular material, fabricated in a specific way, then becomes the function of many types of engineers. The civil, mechanical or aeronautical engi­neers in their capacities as machine or structural designers may have the responsibility of selecting a material and speci­fic size of members for the components of a machine or structure. In making these designs, the services of a stress analyst, vib­ration analyst, and materials engineer are often used.

In addition to the mechanical or stress-strain properties, the designer must consider all physical and chemical properties in the selection of a material and the size of a member. Physi­cal properties of materials include, in addition to the mechani­cal properties, the thermal, electrical and acoustical proper­ties. Important chemical properties of materials include the re­sistance of materials to various types of corrosive environ­ments.

N о t e s :

the processing and fabrication of materials - обработка и отделка материалов

refinement - переработка

member - зд.: деталь

aeronautical engineer - инженер-аэронавт

N 7

STATIC STRESS-STRAIN PROPERTIES IN TENSION AND COMPRESSION

(IV)

Other factors that designers must consider in selecting ma­terials are durability, appearanсe and cost. Appearance is an important consideration in constructions of various kinds that are not hidden from view as, for example, bridges, buildings, aircraft, trains, and domestic equipment. The cost of a mate­rial may often be a deciding factor in its selection. In consi­dering cost, it is not only the initial cost that is referred to but also the maintenance and replacement costs of the part. By durability of a material is meant its resistance to internal or external destructive conditions. These destructive conditions may be chemical, electrical, thermal and mechanical in nature or combinations of these conditions. Sometimes heat or light is de­structive. Variations of temperatures, as in the alternating processes of thawing and freezing, will produce damage as, for example, in the weathering of concrete. Corrosion of metal struc­tures by air, water and various chemicals represents an important destructive condition. In machinery, the wearing of rotat­ing parts by friction is another common type of destructive con­dition. The foregoing discussion indicates that there are many and varied factors that the designer must consider in selecting the best material for a given application.

Notes:

appearance - внешний вид

maintenance - ремонт, техническое обслуживание

durability - прочность, продолжительность службы

wearing - износ

friction - трение

N 8

STATIC STRESS-STRAIN PROPERTIES IN TENSION AND COMPRESSION

(V)

Tension and compression are the most common macroscopic me­chanical tests since they are usually the simplest static tests. Although the quantitative values of the material properties based on these tests may differ considerably from the property values of the actual structural or machine member, the results obtained provide qualitative values of the properties for va­rious possible materials. Tension tests are most commonly made for both ferrous and nonferrous metals where the stresses pro­duced include tension, while compression tests are performed on many nonmetallic materials such as concrete, timber, and brick, where the material is most commonly used in compression. Tension and compression tests are made not only to determine the properties of materials, based on samples of the materials, but they are also used as tests of the fabricated member or pro­duct Fоr example, tension test are conducted to determine the strength of wire, rods, tubing, reinforcing rods, fabrics, anchor chains, crane hooks, and eyebars. In the same way, com­pression tests are performed on tile, masonry blocks, building blocks, cast iron and concrete pipe, and concrete columns.

Notes:

test - испытание