General Principles of Structural Analysis

The purpose of the analysis is to decide whether or not the structure meets the requirements of reliability. It is necessary first of all to formulate the basic principles for assessing the conditions of reliability. Otherwise the analysis of a specific structure will serve no purpose. Thus, if it is stresses that are determined in a structure, one should clearly visualize why this is done and what is to be done with the stresses so obtained. Similarly, if the shape of a deformed body is determined, it is necessary first to think of ways to use the result obtained in the assessment of the reliability of the structure. All these questions find their solution in the choice of the general method of analysis.

The most commonly used method of analysis of machine parts and structural elements is the analysis based on stresses. At the basis of this method lies the assumption that the criterion of reliability of a structure is the stress or, rather, the state of stress at a point. The procedure of an analysis is as follows.

As a result of the analysis of a structure, the point is located in the body where the maximum stress occurs. The value of the stress thus found is compared with the limiting value for the material, as determined prior laboratory tests. By comparing the calculated design stresses with the limiting stresses the strength of the structure is assessed.

This method is used in the solution of most practical problems. It does not follow, however, that this approach is the only possible one. In some cases other methods are found to be more effectual. Sometimes analysis based on stresses is totally unacceptable, for example, in the varification of certain structures to high temperature gradients (rocket castings, etc.).

In a number of cases the basic conception of the foregoing method that stresses at a single point may be regarded as the controlling factor in the assessment of the reliability of the whole structure is not always justifiable.

As the simplest illustrative example the notched bar. When this bar is stretched the stresses at the point A collated at the root of the notch are appreciably greater than for a smooth bar stretched by the same forces. If we proceed the method of stresses, we must conclude that the notched bar is not so strong as the other one, i.e., that the un notched bar can withstand a larger load. This is not, however, always the case. For some materials, such as high-carbon steel, glass, stone and the like, a notched bar is, in fact, less strong than a smooth bar. If, however, both bars are made of low-carbon steel, copper, bronze or aluminium, the notched bar can withstand a larger load. Thus the stress at a point do not always or fully characterize the condition of failure of a structure.

 

In view of the above consideration, in some cases use is made of the method of analysis based on failure loads. This method determines analytically not stresses but the limiting load that a structure may carry without fracturing or substantially changing its shape. The limiting (failure) load is compared with the working load, and thus the service strength of the structure is ascertained. The disadvantage of this method is that the determination of the limiting load by calculation is feasible only for the simplest structural schemes.

The choice of methods of analysis is governed by the conditions of service of a structure and the requirements that it is to meet. If we are to minimize the changes in the shape of a structure, as, for example, in the design of the reflector of a projector or the mirror system of an astronomic instrument, the analysis is made on the basis of allowable displacements and is commonly referred to as stiffness analysis. This does not obviously, exclude a simultaneous check on the strength of system on the basis of stresses.

In addition to the foregoing methods of analysis there are many other methods associated with qualitatively different phenomena, such as stability, effects of repeated loads, dynamic effects, etc.

The course in strength of materials does not presume to specify where and when one or another of the foregoing methods of analysis should be used for particular structures. This science is primarily concerned with practicable of solving problems associated with the determination of stresses, strains, displacements limiting loads etc., in typical structural elements. The reliability of a structure in specific conditions is mainly studied in such courses as machine parts, aircraft strength, ship strength, etc.

Nevertheless, when studying strength of materials one should remember that the determination of stresses and displacements is not an end in itself and that the inevitable question is whether the results obtained can be used in the assessment of the structure reliability.

Part 3. Speaking practice

1. Make sure you know the following words and word combinations:

Visualize, to collate, to fracture, substantially, to presume, to occur, ascertain, strain to regard as, to meet the requirements, to obtain the result, to assess the conditions, justifiable, solution to the problem, presume.

2. Find the synonyms to:

To obtain, similarly, to determine, solution, to locate, to occur, to conclude, to withstand, to ascertain, calculation, to assess.

The antonyms to:

To meet, strong, smooth, disadvantage, simplest, to minimize, displacement, to exclude.