FUNDAMENTAL CONCEPTS—MECHANICS OF DEFORMABLE BODIES

The concepts needed for mechanics of deformable bodies, also referred to as mechanics of materials,are necessary for analyzing and designing various machines and load-bearing structures. These concepts involve the determination of stresses and deformations.

 The analysis of stresses and the corresponding deformations will be developed for structural members subject to axial loading, torsion, and pure bending. This requires the use of basic concepts involving the conditions of equilibrium of forces exerted on the member, the relations existing between stress and deformation in the material, and the conditions imposed by the supports and loading of the member. Subsequent chapters expand on this material, providing a basis for designing both structures that are statically determinant and those that are indeterminant, i.e., structures in which the internal forces cannot be determined from statics alone.

SYSTEMS OF UNITS
The fundamental concepts introduced in the preceding sections are associated with the so-called kinetic units ,i.e., the units of length, time, mass ,and force. These units cannot be chosen independently if Eq.1.1 is to be satisfied. Three of the units may be defined arbitrarily; they are then referred to as basic units. The fourth unit, however, must be chosen in accordance with Eq. (1.1) and is referred to as a derived unit.  Kinetic units selected in this way are said to form a consistent system of units. 

International System of Units (SI Units  †).    In this system, the base units are the units of length, mass, and time, and they are called, respectively, the meter(m), the kilogram(kg), and the second(s). All three are arbitrarily defined. The second, which was originally chosen to represent 1/86 400 of the mean solar day, is now defined as the duration of 9 192 631 770 cycles of the radiation corresponding to the transition between two levels of the fundamental state of the cesium-133 atom.
 

The meter, originally defined as one ten-millionth of the distance from the equator to either pole, is now defined as 1 650 763.73 wavelengths of the orange-red light corresponding to a certain transition in an atom
of krypton-86. The kilogram, which is approximately equal to the mass of 0.001 m 3 of water, is defined as the mass of a platinum-iridium standard kept at the International Bureau of Weights and Measures at Sèvres, near Paris, France. The unit of force is a derived unit. It is called the newton(N) and is defined as the force which gives an acceleration of 1 m/s 2 to a mass of 1 kg ( Fig. 1.2 ). From Eq. (1.1) we write :

1 N5(1 kg)(1 m/s2) 51 kg?m/s 2 (1.5)

 

The SI units are said to form an absolutesystem of units. This means that the three base units chosen are independent of the location where measurements are made. The meter, the kilogram, and the second may be used anywhere on the earth; they may even be used on another planet. They will always have the same significance. 

The  weightof a body, or the force of gravityexerted on that body, should, like any other force, be expressed in newtons. From Eq. it follows that the weight of a body of mass 1 kg ( Above  Fig ) is 

 

Multiples and submultiples of the fundamental SI units may be obtained through the use of the prefixes defined in Table 1.1 . The multiples and submultiples of the units of length, mass, and force most frequently used in engineering are, respectively, the kilometer (km) and the millimeter(mm); the megagram†  (Mg)  and  the  gram (g); and the kilonewton(kN). According to Table 1.1 , we have  :

1  km51000 m      1  mm50.001 m
1  M g51000 kg   1  g50.001 kg
1  kN51000 N

The conversion of these units into meters, kilograms, and newtons, respectively, can be effected by simply moving the decimal point three places to the right or to the left. For example, to convert 3.82 km into meters, one moves the decimal point three places to the right:

47.2  mm50.0472 m
Using scientific notation, one may also write

see table : 

 

The multiples of the unit of time are the minute(min) and the hour(h). Since 1 min 560 s and 1 h 560 min 53600 s, these multiples cannot be converted as readily as the others. 

 By using the appropriate multiple or submultiple of a given unit, one can avoid writing very large or very small numbers. For example, one usually writes 427.2 km rather than 427 200 m, and 2.16 mm rather than 0.002 16 m. †