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To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Applied Mechanics. Waigwa Solomon. Hannah and M. Hillier , , 1. Application to mechanisms 75 8. IO Inelastic collisions II Collision of partiaIly elastic bodies II Forces on an aircraft in flight Rotodynamic machinery Since my co-author, Mr M.

Hillier, was no longer collaborating on the writing I carried out the revision for the third metric edition myself. The aim, as in the past, has been to retain the original character of the book, with its emphasis on the practical applications of the subject, the implications for design and the importance of the many assumptions that have to be made in engineering analysis.

Key points in the treatment remain: the number of formulae to be memorized is kept to a minimum; each topic is followed by worked examples and a list of problems for practice; purely mathematical derivations such as the moments of inertia are omitted and only results stated; work likely to have been covered in preceding courses is omitted or revised briefly, including centres of gravity, uniform velocity and acceleration; topics such as friction, properties of materials and real fluids, the nature of experimental and graphical work, and dynamics of aircraft are covered in more detail than is usual at this level.

In this edition, the text, worked examples and problems have been thoroughly revised and the diagrams redrawn. In particular, the work on aircraft, rockets and helicopters has been expanded. Although this material is intended only as an introduction to these topics there is an advantage in bringing together in the exercises the principles of statics and dynamics of forces as well as those of thermodynamics, gas dynamics and fluid flows. Some descriptive work on propulsion systems and aerodynamics has been included to support the elementary mechanics.

The coverage of gravitation and satellites in the appendix to Chapter 9 has been increased; to contain the size of the book Chapter 20 Fluid in motion and Chapter 21 Experimental errors and the adjustment of data have been slightly curtailed. The text covers all the requirements of the units of study for the BTEC certificate and diploma courses in Engineering, and some of the aspects of the new work -related advanced GNVQ courses.

It is hoped also that the book will continue to be useful as a supporting text to students on the early stages of higher diploma and degree courses and on comparable courses overseas. My particular thanks are due to my colleague of many years' standing Mr R. Stephens, for his most valuable and ever-ready assistance with this edition. Of the seven fundamental or base units, four will be met with in this book, i.

The sole derived unit for measuring work or energy is the jo u le and that for force is the n e w to n. The SI is a coherent system of units since the product of any two unit quantities in the system is the unit of the resultant quantity. For example, unit velocity metre per second results when unit length metre is divided by unit time second. Normally calculations in the text are carried out by converting all given quantities to these base units, but on occasion it has been found convenient to work in multiple or sub-multiple units.

The kilojoule and kilonewton are particularly convenient. A few non-SI units whose use is accepted have been used where appropriate, for example, the b a r and its multiples as a unit of pressure and the k n o t, a unit of speed, in aerial and marine navigation work. Bell and D. Goldman National Physical Laboratory , published by H. Stationery Office , and to British Standards No. If it were not normal the reaction would tend to resist or assist sliding. In practice it is not possible that there are no frictional forces resisting sliding, but in many cases it may be a fair approximation to reality.

The assumption of smoothness, meaning the complete absence of friction, simplifies the solution to many practical problems. Figure 1. The reaction of the surface must be along the normal to the surface of the roller at the point of contact. This is the case whether or not the roller moves under the load. K n ife - e d g e support The direction of the reaction of a smooth surface to a knife-edge contact is normal to the surface, Fig.

A s im p le s u p p o r t for a beam is one in which the beam rests on a knife-edge. If the joint surfaces are perfectly smooth th e r e is n o r e s is ta n c e to r o ta tio n and the links are free to rotate relative to each other. Each link can then transmit a force o n ly a lo n g its le n g th. Whatever the forces and moments acting on the beam, the reaction at the wall can be represented by its vertical and horizontal components V and H respectively.

There will also be a fix in g - m o m e n t M at the wall see Section 1. The directions can be assumed and the signs finally obtained will indicate the correct directions. An e n c a s tr e or b u ilt- in beam has both ends fixed.

F le x ib le c a b le s a n d b e lts Cables, ropes, cords and belts may be assumed to be weightless unless otherwise indicated. A perfectly flexible cable offers no resistance to bending, compression or shear so that when taut under load it can support only a constant te n s ile force along its length. This tension remains constant even when the cable or belt has its direction changed, e. Where friction is involved, however, as in a belt drive, the tension in the belt changes as it passes over a pulley.

A belt passes over the d r iv in g pulley A then over the d r iv e n pulley B. The friction between belt and pulley alters the tension in the belt, being P on the tight side where it is pulled on to the pulley, and Q on the slack side leaving the pulley. For the driven pulley or fo llo w e r B, the tight side tension in the belt leaving is P , and in the slack side going on it is Q.

The relationship between P and Q can be shown to depend on the angle of contact on the driving pulley and on the coefficient of friction between belt and pulley. C h a p te r 2 Frameworks A framework is an assembly of bars connected by hinged or pinned joints and intended to carry loads at the joints only.

Each hinge joint is assumed to rotate freely without friction, hence all the bars in the frame exert direct forces only and are therefore in tension or compression. A tensile load is taken as positive and a member carrying tension is called a tie. A compressive load is negative and a member in compression is called a s tr u t.

The bars are usually assumed to be light compared with the applied loads. In practice the joints of a framework may be riveted or welded but the direct forces are often calculated assuming pin-joints. This assumption gives values of tension or compression which are on the safe side. Figure 2. In order that the framework shall be s tiff and capable of carrying a load, each portion such as a b c forms a triangle, the whole frame being built up of triangles.

Note that the wall a d forms the third side of the triangle a c d. The forces in the members of a pin-jointed stiff frame can be obtained by the methods of statics, i. The system of forces in such a frame is said to be s ta tic a lly d e te r m in a te. The four bars shown in Fig. This latter arrangement may be converted into a stiff frame by adding a fifth bar b d as shown, Fig. However, if both b d and a c are joined by bars the result, Fig.

The forces in the members cannot then be obtained by the methods of statics alone and the structure is said to be s ta tic a lly in d e te r m in a te or r e d u n d a n t. Another example of an indeterminate structure is a beam built-in at one end and propped at the other end. To find the forces in such a case, information must be available about the d e fle c tio n of the propped end.

Redundant structures are beyond the scope of this book. When studied closely, even the most apparently smooth surfaces consist of 'hills' and 'valleys'. There is a tendency for each surface to shear the tips of the irregularities of the other. Since it is only the projecting 'hills' or high spots which are actually bearing on one another the area of true contact is very much less than the apparent area of contact; this is shown in Fig.

At average loads, the area of true contact is proportional to the load applied and is almost independent of the apparent area of contact.

Hence the friction force, which is determined by the area of true contact, is proportional to the load applied and almost independent of the apparent area of contact: the ratio of friction force to load, , is therefore constant and for a given pair of materials independent of the load. However, for very great loads the area of true contact may not increase in simple proportion to the load but more rapidly.

In practice therefore may increase with the load. Also, as surfaces become worn the value of changes. It would appear that dry friction would be reduced by improving the smoothness of surfaces. For example, surfaces of smooth wood slide more easily on each other than surfaces of emery paper. However, this is only true up to a point, for smooth surfaces will have a greater area of true contact than rough surfaces.

Owing to the attraction between the surface molecules of the materials, there tends to be cohesion or binding together of the surfaces and the greater the area of true contact the greater is this tendency for cohesion. This condition ultimately leads to the surfaces seizing together.

For example, two highly polished dry-metal surfaces will tend to seize together very rapidly under load. Fluid friction viscous friction When there is an excess of lubricant present, two solid surfaces may be separated by a film of fluid so that friction depends wholly upon the lubricant and not on the nature of the surfaces.

The force necessary to produce relative motion is that required to shear the lubricant film. The friction force in fluid friction increases with the velocity of sliding. In contrast to dry friction, the friction force is proportional to the total or apparent area of contact. Fluid friction only exists when there is motion, otherwise the lubricant is squeezed out by the load. In practice all bearings running under design conditions should have fluid-film lubrication.

However, such conditions are not usually met with in engineering practice.


Applied mechanics / J. Hannah, M.J. Hillier.



Applied mechanics by John Hannah and M.J. Hillier.



Applied Mechanics, 3rd Edition




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