Strength of Materials: Problems and Methods

All solids possess to some extent the properties of strength and stiffness, i.e., they are capable of sustaining within certain limits the action of external forces without fracture or any appreciable change in their geometrical dimensions.

Strength of materials is the science of resistance and stiffness of engineering structures. The methods of this science are used in design practice to determine necessity, reliable dimensions of machines parts and various structural members.

The fundamental principles of strength of materials are based on the laws of statics without the knowledge of which study of strength of materials is inconceivable.

In contrast to theoretical mechanics, strength of materials deals with problems in which emphasis is placed on the properties of deformable bodies, while the laws of motion of a body as a whole are not only relegated to the background but in some cases are altogether irrelevant. At the same time, due to the generality of its fundamental principles strength of materials maybe regarded as a section of mechanics which is called mechanics of deformable solids.

Mechanics of deformable solids includes also other branches, such as the mathematical theory of elasticity which treats essentially the same problems as strength of materials. The difference between strength of materials and the mathematical theory of elasticity lies in the approach to the solution of problems.

In the mathematical theory of elasticity which also studies the behavior of deformable solids the problems are stated more rigorously. Hence the solution of problems in many cases calls for a complex mathematical apparatus and frequently involves cumbersome computational operations.

In consequence the possibilities for practical applications of the methods of the theory of elasticity are limited. On the other hand, a more comprehensive analysis of the various phenomena is attained.

The mathematical theory of elasticity is to develop simple practicable procedures for designing typical, most common structural elements. Extensive use is made of various approximate methods. In strength of materials, the necessity of bringing the solution of each practical problem to a numerical result often calls for simplifying hypotheses, i.e. assumption which are subsequently supported by comparing calculations with experiment. In developing approximate methods of design strength of materials often uses the results of exact analysis by methods of the mathematical theory of elasticity.

In view of its applied character strength of materials pursues wider aims than the mathematical theory of elasticity.

The objective of strength of materials is not only to reveal the inherent features of phenomena but also to provide background for the correct interpretation of the laws so obtained in the assessment of efficiency and servicability of the structure under considerations. This question is not touched upon in the mathematical theory of elasticity.

 

Among the sciences dealing with deformable bodies now sections of mechanics on the boderline between strength of materials and t theory of elasticity, such as applied elasticity, have sprung up, and developed during the last decades: related branches have originated, such as the theory of plasticity, the theory of creep, etc. New sections of the science of strength having a specific practical applicability have been developed on the basis of the general principles of strength of materials. These compose structural engineering, structural mechanics of aircraft, the theory of strength of welded structures and many others. The methods of strength of materials do not remain unaltered. They undergo changes as new goals are set and new practical requirements emerge. In engineering design the methods of strength of materials should be applied imaginatively and it should be remembered that the success of practical design far from resting upon the application of a complex mathematical apparatus, rather depends upon the ability to gain a clear insight into the phenomenon under study, to find the optium simplifying assumptions and to bring the calculation to simple numerical result.

Part 3. Speaking practice