Applied Engineering Mechanics

Statics and Dynamics

C. Poll, G. Boothroyd

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351466127
• Edition: 1
• Topic: Naturwissenschaften
• Subtopic: Mechanik

This is the more practical approach to engineering mechanics that deals mainly withtwo-dimensional problems, since these comprise the great majority of engineering situationsand are the necessary foundation for good design practice. The format developedfor this textbook, moreover, has been devised to benefit from contemporary ideas ofproblem solving as an educational tool. In both areas dealing with statics and dynamics, theory is held apart from applications, so that practical engineering problems, whichmake use of basic theories in various combinations, can be used to reinforce theoryand demonstrate the workings of static and dynamic engineering situations.In essence a traditional approach, this book makes use of two-dimensional engineeringdrawings rather than pictorial representations. Word problems are included in the latterchapters to encourage the student's ability to use verbal and graphic skills interchangeably.SI units are employed throughout the text.This concise and economical presentation of engineering mechanics has been classroomtested and should prove to be a lively and challenging basic textbook for two onesemestercourses for students in mechanical and civil engineering. Applied EngineeringMechanics: Statics and Dynamics is equally suitable for students in the second or thirdyear of four-year engineering technology programs.

1

Some Basic Concepts of Mechanics

1.1 Introduction

Mechanics is a physical science that can be subdivided into statics, which deals with the forces acting on bodies that are at rest (in static equilibrium), and dynamics, which deals with bodies in motion. Dynamics is further subdivided into kinematics, which deals with the motion of bodies without regard to the forces causing the motion, and kinetics, which deals with the relationships between the forces acting on a body and its resulting motion.

In this text no consideration is given to the deformation of a body or the tendency of a body to deform under the action of the forces applied. Such considerations would fall within the subjects of dynamics of fluids and mechanics of deformable bodies or mechanics of materials.

The fundamental quantities used in mechanics are length, time, and mass. All other variables used in analysis can be derived from these. Thus, it is necessary first to define these quantities, then to obtain the derived quantities, and finally to express, in mathematical terms, the basic relationships among the derived quantities. These basic relationships are obtained from fundamental laws commonly known as Newton’s laws of motion. These laws are really deductions based on experiment and physical observations.

1.2 Fundamental Quantities of Length, Time, and Mass

Length is a measure of displacement or relative position. In ancient times, the forearm (cubit) was used as the standard unit of length. However, since forearms differ in size from person to person, obvious difficulties arise in using such a definition. Later, in 1793, the French used the length of a straight line scratched on a bar kept under closely monitored conditions in Paris as the standard unit of length. The length of the line was called a metre and was one ten-millionth of the distance from the equator to the north pole on a line running through Paris. In 1889 the definition of the metre was standardized as the distance (at 0°C) between two fine lines on a platinum-iridium bar preserved at the International Bureau of Weights and Measures in Sevres, France. Today, the metre is defined^∗ as follows: “The metre is the length equal to 1,650,763.73 wavelengths in vacuo of the radiation corresponding to the transition between the levels 2p₁₀ and 5d₅ of the krypton-86 atom.” This standard is believed to be reproducible to about 2 parts in 10⁸. This standard is not used for everyday work. National Standards laboratories will calibrate reference standards up to 1 metre by direct interferometric methods and to an accuracy of about 1 part in 10⁷. These reference standards are used to calibrate the various working standards used in industry.

Mass is a measure of the amount of material in a body. The standard reference mass (and not of weight or of force) of 1 kilogram is held in Paris in the form of a solid platinum-iridium cylindrical block. The reference mass was legalized at the 1st CGPM held in 1889. To compare masses, a balance scale must be used.

Time is a measure of the succession of events. Originally the unit of time, the second, was defined as the fraction 1/86,400 of the mean solar day. The exact definition of “mean solar day” was left to astronomers, but their measurements have shown that, because of irregularities in the rotation of the earth, the use of the mean solar day does not provide the desired accuracy. The difficulty with this early definition was that one could not measure a second by direct comparison with the interval of time defining the second; instead, lengthy astronomical observations were needed. To define the unit of time more precisely, the 11th CGPM (1960) adopted a definition, given by the International Astronomical Union, which was based on the tropical year. Experimental work, however, had already shown that an atomic standard of time interval, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more accurately. Considering that a very precise definition of the unit of time of the International System, the second, is indispensable for the needs of advanced metrology, the 13th CGPM (1967) decided to replace the definition of the second by the following: “The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.”

1.3 Derived Quantities: Velocity and Acceleration

The general study of the relationships between length and time is called kinematics. Figure 1.1a shows an object represented by the point P which is moving along a straight path denoted by the line Os. At a certain time t₁ the object is located a distance s₁ from the stationary reference point O, and at a later time t₂ the object is located a distance s₂ from point O. The time interval under consideration is, therefore, t₂ – t₁ and can be represented by the symbol Δt. Thus, Δt means “the time interval.” Similarly, the displacement of the object is s₂ – s₁, ...