Strength of materials - Murdock

In preparing this book the author has had in mind primarily the needs of his own students in strength of materials. He hopes, however, that it will meet a real want in other colleges and technical schools also.

This book has been written with the aim of making intelligible the fundamental principles of the strength of materials without the formal use of the calculus. The works which do not use the ordinary calculus treatment usually omit some important parts such as the deflection of beams, strength of columns, horizontal shear, combined stresses, impact loads, etc. This book is designed to give a fairly complete course in the subject for students who have not had the calculus, or when graphical presentations are preferred. However, a separate chapter giving the derivation of the elastic curve of beams by the calculus method has been included for those who desire such treatment.

Effort has been made to present the derivation of the formulas in a clear and concise manner, in such a way as to enable the student to obtain an adequate comprehension of the principles involved. While the aim is to emphasize the elementary principles and to develop independent reasoning in the student, the ground covered is that usually given in a college course for engineering students. Many illustrative examples and problems are given for the purpose of making clear the application of the theory. Answers to some of the problems are given in order that the student may occasionally check his numerical work. The order of the arrangement is one that has given good satisfaction.

In the deduction of the shear formula it is brought out at the first that the shearing stress is not uniformly distributed over the sectional area of the beam and that the maximum stress is greater than that obtained by dividing the vertical shear by that area. A chapter on graphic integration is included and the graphical method of determining the deflection of beams is utilized. The graphical method appeals to the eye as well as to the reason, and thus supplies an additional avenue of conception. It also shows to advantage the meaning of the constants of integration. The graphical method is also much more readily applicable to beams carrying non uniform distributed loads, and to beams for which the moment of inertia of the cross section is not constant.

When one set of curves is drawn for a given beam carrying a given system of loading, those curves may be used for all similar beams with similar loading. In the chapter on the calculus method an attempt is made to give the physical conception of the constants of integration rather than to treat them simply as mathematical symbols.

As the nature of the behavior of columns under load is very uncertain, the treatment given to columns is largely empirical. Emphasis is laid on the straight line formula, although the Euler and the Rankine formulas are also given.

Although the work has been carefully checked, errors may exist, and for any intimation of these I shall be obliged.

1. INTRODUCTION. Strength of Materials treats of the action of the parts or members of structures or machines in resisting loads and other forces which come upon them. By the use of the principles of mechanics and the properties of materials, it determines the internal forces or stresses which are developed in the simpler forms of construction, as beams and columns, when they are subjected to loads. The properties of the engineering materials are obtained through experimental tests. Many of the formulas derived in strength of materials are based on both theoretical analysis and experimental data, and the subject, therefore, is of a semi-empirical nature.

In architectural and engineering construction, stability, strength, durability, and economy are essential elements. The proper proportioning, spacing, and connection of the parts are important. Too little material in a member would make the structure unsafe, and too much would mean a waste. In general, one member should not be designed in such a way that it will be weaker than others in the structure. Proper design, then, takes into account the properties and qualities of materials and the mechanics of their action in a structure in such a way as to insure safety and economy.

2. MECHANICAL AND PHYSICAL PROPERTIES. The materials of construction possess characteristic properties known as mechanical and physical properties. These properties measure the fitness and ability of the material to sustain external loads or forces under given conditions. Different materials possess these properties in different degrees, and, of course, different grades of the same material differ in their properties. Some of these characteristic properties can be expressed quantitatively between fairly well defined limits which are determined by test, while others may be specified in terms of ability to withstand certain tests and fulfill certain requirements. The mechanical properties include strength, elasticity, stiffness, and resilience. Other physical properties frequently referred to are toughness, ductility, malleability, hardness, fusibility, and weldability.

When a load is applied to a piece or member of a structure the material undergoes a change in size and shape. If on the removal of the load the original size and shape are resumed the material is said to be elastic. Elasticity, then, is the property of a material by which it will regain its original size and shape on the removal of an applied load. A material which will not recover its original dimensions after deformation is termed plastic. If it will only partially recover its original dimensions after deformation it is said to be partially elastic and partially plastic. Most constructional materials are nearly or quite perfectly elastic up to a certain limit of deformation, beyond which they are partly elastic and partly plastic.

The ability to resist change in shape and size when a load is applied is termed stiffness. In elastic materials the amount of change in size and shape is generally proportional to the amount of the load applied.

Materials will differ in their tensile, compressive, and shearing strengths. The strength of a material is ordinarily determined under the application of a static load applied in a slowly increasing amount. The effect of permanent loads, of suddenly applied loads, and of impact loads, and of the repetition of a load many times, requires separate consideration.

A material possesses the property of ductility if the length can be increased and the cross section decreased considerably before rupture occurs. Toughness is that property by which a material will not rupture until it has deformed considerably under loads at or near its maximum strength. This deformation may be produced by stretching, bending, twisting, etc. A tough material gives warning of failure. It will resist impact and will permit rougher treatment in the manipulations which attend fabrication and use. A brittle material will rupture without developing much deformation and without giving warning. Brittle materials are unfitted to resist shock or sudden application of load.


CHAPTER II - DIRECT STRESSES

9. DEFINITIONS. Force is an action of one body upon another which tends to change its shape and to produce a change of motion in the body. In this book the use of the term will generally be restricted to forces which are externally applied to the member.

Stress is an internal action which is set up between the adjacent particles of a body when forces or loads are applied to the body. It is developed whenever the body undergoes a change in shape. Stress may be considered an internal force.

A unit-stress is obtained by dividing the total stress by the area over which it acts if the stress is uniformly distributed. In the case of this uniform distribution the unit-stress is the amount of stress per unit of area of the sectional area. If the stress is not uniformly distributed, the unit-stress, or the intensity of stress, at a point of the sectional area is equal to the amount of stress that would be developed upon a unit of area if the stress were uniform over the area and if its intensity were the same as that at the point.

Deformation is a change in a dimension of a specimen.

Shortening is a decrease in the length of a specimen.

Elongation is an increase in the length of a specimen.

Detrusion is a lateral deformation in which the particles apparently slip past each other. It is caused by a shearing force.

An axial load is one whose line of action coincides with the axis of the member. The axial load may be the resultant of several loads.

An axial stress is one developed by an axial load.

If a plane is passed perpendicular to the axis of a bar, its intersection with the bar is called the cross section, or the section, and its area the sectional area.

10. TENSION. When a load tends to pull the particles of a material directly apart in the direction of the load the material is under tension and the load is a tension load. The internal stresses developed are tensile stresses. The resulting deformation is an elongation. As long as rupture does not occur, the forces acting on all, or on a part of the specimen, are in equilibrium.