Formulas for Mechanical and Structural Shock and Impact

Book Preface

This book is essentially a collection of formulas describing dynamic responses to shock loads. The presentation is inspired by Roark’s classic Formulas for Stress and Strain, which presents equations and explanatory sketches in a compact manner. The theoretical basis is presented in a concise, although somewhat superfi cial manner, as appropriate for a reference work rather than a text intended to teach the subject. Still, this book is a reasonably self-contained tool. Although it is written for engineers in general, experienced dynamicists may also fi nd some new ideas and approaches.

The objective of this book is to provide a meaningful reference in today’s computer oriented environment. Nowadays, due to the development and availability of general purpose structural programs, any large analytical task can be performed by computers. This limits the importance of manual calculations, in general, and of certain analytical methods, in particular, as compared, for example, with the 1960s. Some of the methods in which manual work is and will remain useful in the foreseeable future are

1. Obtaining preliminary fi gures on the anticipated dynamic response of a system that is in an early stage of design and for which a full-scale computation is not practical.

2. The preparatory phase of large-scale calculations where a dynamic model is generated. At this stage, prudent analysts conduct a number of checks to ensure that they neither miss anything important nor incorporate too many unnecessary details, which is wasteful.

3. An indirect verifi cation of computer-generated results by using a simplifi ed model or a calculation method. (This may not only explain some unbelievable results, but may also help to guard against hidden errors, for which there seem to be unlimited opportunities.)

4. Work in preparation for physical testing.

Thus, it is quite clear that the only sensible options for today’s engineers embarking on a hand calculation are the methods and approaches that are concise and relatively easy. Anything more mundane might as well be done by a major fi nite-element (FE) code. This was the major criterion in the selection of problems and methodology. Simplicity is therefore the main purpose and the keynote of this book. Still, not all situations can be explained in an elementary manner. In such cases, it is preferable to provide a set of two or three simple equations, each of them corresponding to some defi nite concept, instead of building a large, complex, single equation. In many instances, the effort to simplify things goes into offering simple approximate equations instead of more complicated, but also more accurate, solutions. (One should note that terms like “manual” or “hand” calculations in a modern setting mean not only the use of a calculator, as they did in the 1970s, but also the use of such simple programs as a spreadsheet or Mathcad.)

There is another advantage in being able to do simplifi ed, although not very accurate, estimates. This is often evident with regard to extreme loads or structures. For example, one can ask: “Is the peak strain to be expected closer to 5% or to 50%?” with one of the answers implying safety and the other indicating danger. To be able to answer such a question early on has a strong impact on the engineering approach to be adopted.

This book is written for engineers and for all others who want to have an insight into how objects and structures respond to sudden, strong impulses that are usually of short duration. Since there is no emphasis on any particular type of structure and the scope is quite broad, those involved in the mechanical aspects of aeronautical, automotive, nuclear, and civil engineering, as well as those in general machine design, may find it equally beneficial.