Mechanics of materials - Merriman

Since 1885, when the first edition of this work was published, many advances have been made in the subject of Mechanics of Materials. Some of these have been noted in the additions to subsequent editions, but to record and correlate them properly it has now become necessary to rewrite and reset the book. In doing so the author has endeavored to keep the facts of experiment and practice constantly in view, for the theory of the subject is merely the formal expression and generalization of observed phenomena. The subject, indeed, no longer consists of a series of academic exercises in algebra and rational mechanics, but it is indispensably necessary that the phenomena of stress should be clearly understood by the student. While laboratory work is a valuable aid to this end, it is important, in the opinion of the author, that no recitation or lecture should be held without having test specimens at hand with which to illustrate the physical phenomena.

The same general plan of treatment has been followed as before, but the subdivisions are somewhat different, and the fifteen chapters of the last edition have been increased to nineteen. The statement of average values of the principal materials of engineering has proved so advantageous to students that it is here also followed. Numerous numerical examples are given in the text to exemplify the formulas and methods, these generally relating to cases that arise in practice. To encourage students to think for themselves, one or more problems are given at the end of each article; for the experience of the author has indicated that the solution of many numerical exercises is required in order that students may become well grounded in theory.

Most of the topics of the last edition have been treated in a fuller manner than before. The subjects of impact on bars and beams, resilience and work, and apparent and true stresses have been much changed with the intention of rendering the presentation more clear and accurate. Among many new topics introduced are those of economic sections for beams, moving loads on beams, constrained beams with supports on different levels, the torsion of rectangular bars, compound columns and beams, reinforced-concrete beams, plates under concentrated loads, internal friction, rules for testing materials, and elastic electric analogies. A few changes in algebraic notation have been made in order that similar quantities may always be designated by letters of the same type; Greek letters are used only for angles and abstract numbers.

Compared with the ninth edition, the number of articles has been increased from 151 to 188, the number of tables from 8 to 20, the number of cuts from 85 to 250, and the number of problems from 222 to 305. Although the length of each page has been increased eight percent and smaller type has been used for formulas and problems, the number of pages has been increased from 378 to 518. While the main purpose in rewriting and enlarging the book has been to keep it abreast with modern progress, the attempt has also been made to present the subject more clearly and logically than before, in order both to advance the interests of sound engineering education and to promote sound engineering practice.

When a prism has a length longer than about eight or ten times the least side of its cross-section, it is called a column or strut. When the length of the prism is only four or six times as long as the least side of its cross-section, the case is one of simple compression the constants for which are given in Art. 5. Under simple compression the failure occurs for brittle materials by oblique shearing and for plastic materials by enlargement and cracking (Art. 18). In the case of a column, however, failure is apt to occur by a sidewise bending which causes flexural stresses. The longer the column the greater is the liability to lateral flexure.

Wooden columns are usually square or round, and when of large size they may be built hollow. Cast-iron columns are usually round and hollow. Wrought-iron columns were built prior to 1900 of a great variety of forms, but structural steel has since been almost entirely used. Rolled I beams may be used, but most steel columns are formed by riveting together channels, angles, and plates (Art. 44). Columns are extensively used in buildings and bridges. A piston-rod of a steam-engine, or the parallel rod of a locomotive, is a column when it is under compression. It is clear that a square or round section is preferable to an unsymmetrical one, since then the liability of the column to bend is the same in all directions. For a rectangular section, the plane of flexure will evidently be perpendicular to the longer side of the cross-section, and in general the plane of flexure will be perpendicular to that axis of the cross-section for which the moment of inertia is the least; for Art. 56 shows that the deflection of a beam varies inversely as I, In designing a column it is hence advisable that the cross section should be so arranged that the moments of inertia about the two principal rectangular axes should be closely equal.
 

ART. 77. DEFINITIONS AND PRINCIPLES

When a short prism of section area a is under compression in the direction of its length and the resultant force P acts through the centers of gravity of the end sections, the internal stress is uniformly distributed over the section, and hence the compressive unit-stress S is P/a. For a long prism, or column, this is not always the case, for any sidewise deflection will cause flexural stress which will render the unit-stress on the concave side of the column, greater than P/a and that on the convex side less than P/a. Hence for any given section, the load P should be taken smaller for a long column than for a short one, since evidently the liability to bending increases with the length.

The Axis of a column is the line passing through the centers of gravity of the cross-sections. When the column is straight, the axis is a straight line; if it bends laterally, the axis is the elastic curve. An 'axial load' is one having its line of action coinciding with the centers of gravity of the two end sections; the term concentric load is used by some writers for this case The load P is regarded as axial in the greater part of this chapter this being the most common case in practice.