Strength of materials a text-book for manual training schools

In the following pages the attempt is made to give a presentation of the subject of the strength of materials, beams, columns, and shafts, which may be understood by those not acquainted with the calculus. The degree of mathematical preparation required is merely that now given in high schools, and includes only arithmetic, algebra, geometry, and such a course in mechanics as is found in elementary works on physics. In particular the author has had in mind the students in the higher classes of manual training schools, and it has been his aim to present the subject in such an elementary manner that it may be readily comprehended by them and at the same time cover all the essential principles and methods.

As the title implies the book deals mainly with questions of strength, the subject of elastic deformations occupying a subordinate place. As the deductions of the deflections of beams are best made by the calculus they are not here attempted, but the results are stated so that the student may learn their uses; later, if he continues the study of engineering, his appreciation of the proofs that he will then redd will be accompanied with true scientific interest.

All the rules for the investigation and design of common beams, including the subject of moment of inertia, are here presented by simple algebraic and geometric methods. No Greek letters are used, and algebraic operations are made as simple as possible. As the mechanical ideas involved are by far the most difficult part of the subject, a special effort has been made to clearly present them, and to illustrate them by numerous practical numerical examples.

A chapter on the manufacture and general properties of materials is given, as also one on resilience and impact. Problems for students to solve are presented, and it should be strongly insisted upon that these should be thoroughly and completely worked out. It is indeed only by the solution of many numerical exercises that a good knowledge of the theory of the subject can be acquired.


NOTE TO THE FIFTH EDITION.

To this edition a new chapter has been added which deals with reinforced concrete, especially with columns and beams; in this the attempt has been made to clearly set forth the laws of distribution of the stresses between the concrete and the steel and to explain the fundamental principles for investigation and design. Minor changes have been made in other chapters, and many new problems for students have been added. Compared with the fourth edition, the number of problems has been increased from 84 to 140, and the number of pages from 128 to 156.

A bar under compression whose length is greater than about ten times its thickness is called a column or a strut. For shorter lengths the case is one of direct compression where the rules of Art. 5 apply. For the short specimen failure occurs by the shearing or splintering of the material. For the strut or column, however, failure generally occurs by a sidewise bending; this induces bending stresses, so that the phenomena of stress are more complex than in a beam.

Wooden and cast-iron columns are usually square or round, and are sometimes built hollow. Wrought-iron columns are made by riveting together channels, plates, and angle-irons. It is clear that a square or round section is preferable to a rectangular one, since then the tendency to bend is the same in all directions. For a rectangular section the bending will evidently occur in a plane parallel to the shorter side of the rectangle; thus in investigating such a column the depth d is this shorter side instead of the longer one, as in beams. When a single I beam is used as a column it tends to bend in a plane parallel to the flanges, and hence the moment of inertia to be used in its discussion is l', which is given in the last column of the table in Art. 30, the axis for this coinciding with the middle line of the web.

If a short prism whose section area is A be loaded with the weight P, the unit-stress is P/A, and this is uniformly distributed over the area A. For a column, however, this is not the case; while the mean unit-stress is still P/A the unit-stress on the concave side, if bending occurs, may be very much greater than P/A. The longer the column the greater is this unit-stress on the concave side liable to become, and hence a long column cannot carry so large a load as a short one.

There are three ways of arranging the ends of columns. Class (a) includes those with 'round ends' or those having their ends hinged on pins. Class (b) includes those with one end round and the other fixed; the piston-rod of a steam-engine is of this type. Class (c) includes those having fixed ends; these are used in bridge and building constructions. The figure here given is a symbolical representation, and is not intended to imply that the ends of the columns are necessarily enlarged in practice. It is found by experiment that class (c) is stronger than {b), and that [b) is stronger than (a).


Art. 34. Formula for Columns.

Columns and struts generally fail under the stresses produced by combined compression and bending. The phenomena are so complex that no purely theoretical formula will fully represent all cases. The formula of Rankine is that which has the best rational basis, but this cannot here be fully developed, as the laws of deflection have not yet been discussed.