In 1712, the Manchu official Tulisen left Beijing for the shores of the lower Volga River, in Russia, to visit a Mongolian khan. It was a distance of over 3,000 miles, and it took him nearly three years to get there and back. The emperor of China had sent him to explore Russian territory and look for an alliance against other Mongolian rivals. He was not invited to see the tsar (the ruler of all Russia), but he wrote a detailed account of the topography, ethnography, and history of all the regions he had crossed.

Seven years later, John Bell, a Scotsman in the service of the Russian tsar, set out from St. Petersburg for Beijing, covering much the same route as Tulisen in the opposite direction. He, too, reported accurately on the region’s geography, politics, and history, gathering scientific knowledge and military intelligence at the same time. Others followed them, like Ivan Unkovski, a Russian officer, who visited the Mongolian khan in Zungharia in 1722, and the French Jesuit Gerbillon, who accompanied the Chinese emperor on his military campaigns in the middle of the century. At the end of the century, the Englishman George Lord Macartney arrived by sea in Beijing in 1793 to negotiate the opening of formal trade relations between Britain and China.

The life of Ana Maria Ribeiro di Garibaldi illustrates for us the changing nature of national identities in the mid nineteenth century. Born into a family of fishermen in 1817 in Morinhos, a small town on the coast of Brazil, she married another village fisherman named Manuel in 1835. It was apparently not a happy marriage. Only four years later, a rebel ship showed up off the shore of Morinhos. The captain caught sight of her and rowed to shore, saying “You will be mine.” She got in the rowboat and went off with him for the rest of her life.

The captain was Giuseppe Garibaldi, a failed revolutionary who had been involved in a revolt in Piedmont (what is now northwestern Italy). Sentenced to death, he fled, arriving in South America in 1836. He became a mercenary for a small state, Rio Grande del Sul, which was trying to secede from Brazil. So it was that he was captaining the Rio Pardo schooner when it stopped off Morinhos in 1839. During the following year, the Brazilian navy closed in on him, and he left the service of the rebel state, which seemed increasingly doomed.

He and Anita then drove a herd of cattle to Montevideo and tried to enter civilian life without much success. They probably married in 1842. She maintained that Manuel had died, but many have cast doubt on this claim. She was in any case accepted as Garibaldi’s wife, and she bore him several children. Three lived.

9.1 Introduction

Vibration is a very common phenomenon in machines. In certain situations, the control of vibration is very essential. To control the vibration, proper understanding of the phenomenon is desired. The essence of vibration is discussed below.

A mechanical system is said to vibrate if it executes a simple harmonic motion or oscillation.

Having struggled to acquire the fundamentals of reading, writing, and arithmetic, Thomas Paine (1737–1809), a collector of excise tax and a Methodist preacher in England, migrated to Britain’s American colonies. In 1774 he arrived in Philadelphia seeking to make his living as an editor and freelance author but already with a radical political agenda. Early on, Paine denounced the slave trade and elaborated a specific plan for its abolition. His popular pamphlet, Common Sense, defended the American cause before public opinion in both Britain and the colonies. It was the first salvo in the career of a man who became the world’s most radical polemicist. During the Valley Forge encampment, a bleak winter for the Revolution, Paine’s popular Crisis rallied Americans, announcing “These are the times that try men’s souls.”

Once the American Revolution had succeeded, Paine returned to England and took up the defense of the French Revolution. In response to the English legislator Edmund Burke’s celebrated polemic against the Revolution, Paine wrote The Rights of Man, one of the most widely read books of all time. Paine’s pamphlets promoted a new republican writing style, a popular political language, accessible to the artisan (skilled manual worker) yet capable of expressing moral outrage and high seriousness. Mocking Burke’s awe of tradition and popular reverence toward the British monarchy, Paine jibed: “A French bastard landing with an armed banditti and establishing himself King of England against the consent of the natives is, in plain terms, a very paltry rascally original. The plain truth is that the antiquity of English monarchy will not bear looking into.” Reading these lines, many ordinary men and women in England, Ireland, Scotland, and Wales never looked at monarchy in quite the same way again.

These two centuries initiated the true unification of the globe. The voyages of European explorers to North and South America began a continuous process of engagement between the Eurasian, African, and New World continents. The exchanges begun by Columbus’ voyage of 1492 included military conquest, migration and settlement, the construction of new empires, the exploitation of tropical lands for valuable commodities, enslavement of much of the African population and extermination of much of the indigenous American population, as well as religious expansion, new trade rivalries, and imperial competition. All of these processes had already worked themselves out in each of the continents independently – the Americas had their empires as well as the Eurasians and Africans – but now they were inexorably tied to each other. The scale of political, commercial, and social exchange widened to include the entire globe.

Equally important, however, were developments in Asia itself. Asia’s riches were the original goal of the European explorers looking for a shortcut to the fabulous East. In Asia, five massive empires expanded dramatically until they ran into each other’s frontiers. The Qing in China, the Mughals in India, the Safavids in Iran, and the Ottomans in the Middle East each conducted vigorous military campaigns, conquering territories on an unprecedented scale. Russia spanned Europe and Asia with its vast territorial reach. Each of them combined techniques of military organization derived from Central Eurasian pastoral nomads with the civil administrative techniques of the settled urbanized regions they ruled. Southeast Asian states also increased their territorial control and administrative integration, like their European counterparts, without uniting into a single empire. The combined effect of European and Asian expansion was to bring a large portion of the earth’s surface under the control of a small number of huge imperial formations. The world shrank in the 1500s because of the interaction of global maritime networks woven by Europeans and the great system of unified empires erected in Asia.

12.1 Introduction

Mechanical member subjected to external moment along the axis is called shaft. The moment is called torque. The state of shaft under torque is called torsion. Due to torsion, the sections of the shaft rotate relative to each other. This relative rotation is called angle of twist. On this basis, the torque is also called twisting moment.

Pure torsion: In general, a mechanical member may be subjected to axial force, shear force, bending moment and twisting moment, simultaneously. If a member is subjected to twisting moment alone, it is said to be in pure torsion as shown in Figure 12.1.

Torsion has wide application in engineering. Electric motors, generators, fans, a few drilling and boring tools are examples of the cases of torsion. The concept is extensively used in mechanical power transmission. A shear stress develops over the sections of the shaft subjected to torque. Estimation of shear stress in the shaft is very necessary for the design of shaft. The stress analysis is presented in section 12.2.

12.2 Analysis of shear stress in a shaft subjected to pure torque

As mentioned, the stress analysis is a statically indeterminate problem. The approach of strength of materials is to make assumptions regarding deformation, analyze strain, apply Hook's law and satisfy boundary conditions.

7.1 Introduction

Kinetics deals with the cause of motion. It is concerned about why the motion varies or how it may be produced. In other words, it looks into the following two aspects:

• Asserting force system required for producing a desired motion of the particle. Suppose a particle is required to move along a circular track, the forces required to perform this task may be estimated.

• Finding the motion of the particle subjected to a given force system. For example, the motion produced due to a sinusoidal variation of force on the particle.

The kinetic analysis of the particle is done with the help of Newton's laws of motion.

Cheap steel of high and uniform quality was the metal of the Second Industrial Revolution. Steel combined the hardness of cast iron with the pliancy of wrought iron and was more enduring than either. It made possible the launching of fleets of ocean liners and the building of skyscrapers in US cities. After a series of inventions, including the Bessemer process, reduced the cost of making low-grade steel, the major remaining obstacle to the production of cheap steel was the availability of suitable iron ore. Until the 1870s steelmaking required iron ore with a low phosphorus content – ores found in some British fields but rarely on the continent.

The solution to this long-standing technical problem was provided by two young amateurs, Sydney Thomas, a London police court clerk who studied chemistry, and his cousin Percy Gilchrist, a Welsh chemist. In 1878 Thomas presented a paper at the British Iron and Steel Institute suggesting that converters lined with limestone could remove phosphorus from ores and enable steelmakers to use the abundant continental deposits of ore in Belgium, France, Germany, and Sweden.

Word of the invention quickly spread to Germany where large industrialists, whose fortunes were based on coal mining and ironmaking, raced one another to England to acquire the license to use the new process. From its beginnings the Second Industrial Revolution would be a transnational process, occurring in many countries simultaneously. The Gilchrist-Thomas process enabled continental industrialists to use their abundant ore to produce cheap steel and by 1910 Germany was the largest European exporter of steel, replacing Britain which had occupied this position for a century.

Truss is a structure made of straight mechanical members to support or transfer the loads to other bodies, e.g., structures used for supporting the power transmission lines, TV towers and the bridges. Structures which support the roof of sheds at railway stations, food grain stores the common examples of the application of truss. The truss is a very common structure in the engineering applications. Figure 4.1 shows a simple truss. AB, BC, AC, etc., are called members of the truss. The members are joined to form a rigid structure. A, B, C, D, etc., are called joints. These members are joined together at the joints by bolts, rivets or welds.

The truss supports the loads at joints and transfers them to the support. In the Figure 4.1, the supports are at A and E. These supports are either pin connected or roller.

The trusses are classified in different ways and in different groups in order to understand the procedure and simplification of analysis.

4.2 Construction of truss

Truss is made of straight members joined at the ends. Members may be joined by rivets or bolts or welded, but they are assumed to be joined by smooth pins. This is the idealization of the joints. It simplifies the analysis of truss.

4.3 Dimensionality of truss

The trusses are classified in two groups on the basis of dimensionality. These are:

(a) Two-dimensional or plane truss

(b) Three-dimensional or space truss

4.3.1 Plane Truss: If the center lines of all the members of the truss lie in a plane, the truss is called plane truss. It is also called two-dimensional truss.

4.3.2 Space Truss: If the center lines of all the members of the truss do not lie in a plane, the truss is called space truss or three-dimensional truss.

4.4 Rigidity of truss

Consider a triangular structure of three members ABC as shown in Figure 4.2a.

Mechanics is the science which describes and predicts the motion of bodies under the application of forces. Engineering mechanics is the branch of engineering which applies the laws of mechanics in design, and is at the core of every machine designed. It is almost impossible to over-emphasize the importance of this subject in engineering. It is apparent that having a sound knowledge of the fundamental principles of engineering mechanics and the techniques of their application are very essential for one to be considered a good engineer.

This book covers course material for the Engineering Mechanics syllabus of most universities in India. This textbook has been designed for undergraduate students pursuing an engineering course. It is expected that the book will also be useful to students preparing for India Engineering Services (IES), GATE and other PSU examinations.

The special features of the book are

• • Discussion on the limitations of the assumptions/idealizations

• • The elastic spring model for finding deflection in the elastic systems

• • Simple integration instead of double and triple integrals for finding moment of inertia

• • Numerous examples to cover all the fundamental principles: the reader is expected to study them carefully

• • Step-by-step problem-solving approach throughout the book

• • Summary in each chapter for quick reference

• • Concept Review Questions and Exercises aimed at strengthening the learnt methods for solving the problems

• • Objective Questions, True/False and Fill in the Blanks questions modeled from the main text to reinforce the understanding of fundamentals.