Structural Engineering Art and Approximation

Prologue

There are textbooks that cover structural analysis, others that tackle design, and some that are comprehensive references for areas of study such as stress analysis. There are few guides that are written from the viewpoint of practising engineers or which are there to train engineers in the art of design; which take structural problems of everyday engineering; to question, for instance: ‘what is useful?’, ‘why do engineers adopt this approach?’ ,‘when is this appropriate?’ or ‘where is this used?’. There are few textbooks that minimise complicated mathematics and design standards, offering an introduction to structural design, which does not intimidate.

This book is intended for undergraduates in their second year onwards through to newly graduated engineers and architects. It gathers together conceptual design methods used by practising engineers for those who seek a clear guide to generic structural problems. In a busy design office, many books and papers are not readily accessible in the sense that puzzling over equations and opaque logic offers little but further obscurity. Materials are reviewed and their appropriateness for particular uses, at the same time, avoiding reference to codes in a manner that aims to bring clarity to the vexed art of structural design.

From the simplest structures, calculation methods are slowly introduced. A qualitative approach with historical references moves into quantitative methods in the later chapters. Units are introduced gradually. The intention is to invite the reader to appreciate that structural design is an art in which the tools of the trade are analytical techniques. It is intended to remove the fear of maths and methodology; to appreciate that even the most breath-taking structures may be conceived with simple principles.

By using simple techniques at the concept stage, a design may be developed with confidence that the characteristics of a particular structure are understood rather than surmised.

In the first part of the new millennium, a dazzling array of materials is available: glulam timber, carbon fibre, aluminium, glass structures, kevlar, nylon, glass fibre, and others. Methods of analysis are undertaken, which would be barely possible without the computer, for example, finite element analysis, time history dynamic analysis, and non- linear plastic analysis of plates.

Design starts at the bottom of a pyramid of choices: selection of materials, method of analysis, structural form, and appropriateness. This all takes place before any detailed design commences. At the top of the pyramid, the final design entails a process of eliminating inappropriate solutions. A contingent part of this procedure will involve sketches and approximate calculations.

Every undergraduate now has their own lap top or personal computer with which they can analyse very complicated structures, increasingly using hand held tablets and even mobile phones with apps. But regardless of technology, a designer must engage in engineering judgement, which is a necessary part of refining and checking these models.

Having been conceived, analysed, checked, and drawn the structure, it still needs to be communicated to clients, architects, contractors, and surveyors. With approximations and sketches to hand, an engineer has to hand a means to communicate the design to those who commission an engineer in the first place.

This book documents a collection of approximate methods which have been collected over a career of over twenty five years in structural engineering design using real examples of built projects. It follows a logical progression of most common types of structure with numerous images and annotated sketches to back up the text.

Fourth Edition (2017)

Chapter 2.4 (continuous beams) has been amended for improved clarity of diagrams. For greater ease of comparison, all bending moments, shears, and reactions have been altered to a percentage of the equivalent simply supported values.

Since the book was originally published, a number of people interested in purchasing the book have asked if foundation engineering is included. In response to this, for completeness, chapter 2.13, regarding foundations, has been added to the book. This is not a comprehensive guide, but it follows the principles of the book, with a description of foundations in their various forms, and outlines some simplified calculation methods to resolve common problems. It is hoped that this will be useful to future readers. that this will be useful to future readers.

Chapter 1.1

1.1 Introduction

Engineering problems are under-defined; there are many solutions, good, bad, and indifferent. The art is to arrive at a good solution. This is a creative activity involving imagination, intuition, and deliberate choice. Ove Arup 20th Century Engineer

Ove Arup, the founder of a global engineering phenomenon, the structural engineering consultancy for the iconic Sydney Opera House, could not have summed up better the art of engineering. It is how one comes up with deliberate choice, which is the essence of the art of structural engineering.

The content is aimed at structural engineering students and newly graduated structural engineers but it may also be of interest to architectural students, practising engineers, architects, and other building professionals.

In the second part of the book, specific examples with accompanying narratives demonstrate common problems and how engineering judgement might be applied to achieve efficiency of form.

The concluding chapters undertake a review of failures, which are instructive and indispensable to educating enthusiastic newcomers to the profession, together with some cautionary advice.

Complex formulae and numbers are avoided. None of the solutions is per se the correct answer. The assiduous designer should always be searching for alternatives and testing the answer for its appropriateness. In a review of structural problems that advance from the simply supported beam to more complex forms such as stadia, it is hoped that this book will assist in providing a solid introduction to the art of structural design.

There are many textbooks available that cover the areas of the theory of structures and others which will instruct in the design of specific materials. What is the need for a book which does not follow structural principles with the rigour of the aforementioned texts?

There are two categorical reasons for the provision of annotated pictorial aids to structural design, both of which involve teaching and education with respect to the subject. The first reason is to advocate and encourage a qualitative appreciation of engineering structural analysis.

The subject matter has been well documented in the work of Dr David Brohn, who has written Understanding Structural Analysis (Brohn 2005, reference 1.) which teaches structural analysis as a qualitative approach, as opposed to a purely quantitative approach. Brohn has published material and has run courses that aim to teach structural behaviour: ‘as a visual language of structural behaviour that can be understood with the minimum of textual comments.’

Brohn has championed the training of young engineers to recognise structural behaviour with the use of diagrams and without reliance on numbers; a qualitative approach. It is reported that the initial tests, which involve some 20 different structural puzzles, have low scores by recently graduated engineers. Over the years, the scores have, if anything, worsened, not improved.

Professor Ian May noted on the website of the Institution of Structural Engineers regarding a study group for the teaching of structural analysis: ‘The need for graduates to have a deep qualitative understanding of the behaviour of structures under load has never been greater, as practical analysis and design are increasingly based on the use of third-party software rather than hand calculations.

The second reason for this publication is to demonstrate that good engineering involves the imaginative use of structural mechanics. The intention is to encourage a visual approach to design. The work of Brohn et al. has exposed a weakness in the education of engineers.

Engineers might not have to be good at producing their own technical drawings, but at the very least, they should be able to interpret drawings and visualisations by others, architects in particular. They should be able to model in their imagination 3-dimensional representations of their design proposals. They should be able to produce hand-drawn sketches so that they may be understood by others.

The skill of conveying solutions in simple diagrammatic forms without having to rely on complex formulae will assist trainees and qualified engineers in building up their own vocabulary and store of answers to problems posed. Real examples are referenced alongside to reinforce the material.

Modern engineering practice in the construction industry likes to emphasise the importance of standards or codes. National procedures set out to ensure that calculations have a unified approach. In the United Kingdom, the profession is moving towards Eurocodes, which are intended to standardise calculation methods across the European community.

Eventually, engineers across Europe will have to master the new vocabulary where, amongst other alterations, dead loads become permanent actions, and live loads might be referred to as variable actions. The unfamiliarity of the terminology and complexity of some of the concepts serve to make intelligibility a tedious and frustrating task. No apology is made for the minimal of reference to national codes within this book.

What is structural engineering? A definition that will suffice is a design process whereby the disposition and size of elements, which constitute a framework, are defined by analysis to have sufficient strength and rigidity. Appropriate geometrical forms and sizes for the elements are chosen, which are most economical for the purpose. The design is communicated by technical drawings, with dimensional form and materials specification, to enable a constructor to build the assembly.

Structural engineering has its place in building construction, sub-sea structures, maritime structures, ships, aeroplanes, and spacecraft, to name but a few. In building construction, structural engineering involves the design of supporting structures which support, for example, floors, walls, storage tanks, mechanical and electrical services; structures that provide rigidity to prevent toppling over in the event of adverse lateral forces – wind, water, earthquake or lack of fit effects.

Why employ an engineer today if there is computer software available that can undertake the structural design? Engineering is the ability to assess design problems, formulate or apply an ingenious or novel solution based on experience and skill, and present this in such a way that the solution can be carried out by others.

Until computers are able to perform this skill, the world will need engineers trained to attain the aptitude and skills needed to make the engineering decisions required of the 3-dimensional computer building models of the future.

Most structural engineers tend to specialise; for instance, some work exclusively on buildings, others on aeronautical structures, and so on. Engineering principles have much in common, but engineering practice is too demanding for engineers to cover all of the fields. This book is mostly concerned with the field of architecture.

How are the budding professionals of tomorrow to be attracted from the talent pool of the schools? A glance at a syllabus for civil/structural engineering is perhaps a defining moment for the school leaver considering the course. Engineering courses offer a virtuous selection of technical subjects. A timetable might include structures, drainage, geotechnical engineering, law, management, fluid mechanics, and hydraulics; enough to wet the palate of the academically or technically inclined, but where’s the joy? Appreciation of the great engineering projects of the past? The art? It is there - it simply needs amplifying, or in today’s jargon, a higher profile.

Aspiring architects have a much more stimulating introduction to the subject. An extract from a website for the UCA (University of Creative Arts) has a succinct introduction: ‘BA (Hons) Architecture is an ARB and RIBA validated course. The course operates as a design laboratory in which you seek radical conceptual approaches to architecture and test them through debate and through application in public space. You consider spatial practice in relation to the human conditions experienced in everyday life as well as in relation to social, political, landform, urban, and virtual environments.’

Two professions that are to form a future relationship diverge in their cultural emphasis from the beginning of their academic study. There are some good courses that bring architecture and engineering together. Bath University is a good example, which runs parallel courses for architectural and engineering undergraduates and actively encourages their collaboration and mutual enlightenment.

It is a challenge to set a curriculum in which all of the compulsory subjects set by the engineering institutions are included in sufficient depth to educate engineering students sufficiently. An engineer needs a certain proficiency in a number of subjects, including materials science, structural mechanics, foundation design, surveying, mathematics, and technical drawing. With a declining trend in applications from the young seeking more lucrative careers, attracted to the world of financiers and accountants, is it not time to address this pressing matter?

Surely, the excitement, the challenges, the intellectual demands on an engineer in the course of a career can be put across more effectively though greater emphasis on teaching both past achievements and fun in design?

Vitruvius, the celebrated Roman architect and engineer, stated that good buildings should demonstrate: ‘Commodity, Firmness and Delight’. The packed syllabus of engineering courses pays high regard to Commodity and Firmness, but engineering students are seldom challenged with Delight. Is it feared that our professional visage might slip from the constraints of impartiality? Why do engineers not appear to be encouraged to delight in the process of fitting the dry mathematical concepts of engineering into the design process? Why not discuss massing, the language of detail, or even its masculinity or femininity?

Many engineering undergraduates may never touch on architecture in their courses, but architectural students are mostly committed to studying structural design. A brief survey is sufficient to confirm that many architects are apprehensive about the study of structures and keep a distance from its practice during their careers. It is common sense to provide guidelines for a professional to whom the planning and conception of a building can only work if it fits within the constraints of the supporting structural skeleton. Often, for simple buildings, a structural engineer is not involved. Architects who spend a career in smaller scale projects generally gain a good intuitive understanding of structures, but it is more difficult for architects involved in larger scale projects.

A selection of design guides for architects, based on simplified structural principles, is available for the teaching of structural design to architectural undergraduates. It is hoped that this book might also provide a reference for architects, giving insight from the viewpoint of a practising engineer in the world of architecture. It may even provide possible structural solutions with which a practising architect may then be able to prompt the project structural engineer to try an alternative approach.

Apprenticeships have been largely replaced today by graduate training after the university education is complete, which entails a good deal of time to connect theory to practice, a frustrating journey that seems to the novice to go backwards before moving forwards. Enthusiastic to enter the real world, the graduate has to learn to apply theory, often forgotten, only to have to satisfy the demands of the building design team, all their own agenda: clients, architects, builders, project managers, and quantity surveyors, to name but a few.

However much an engineer’s education is filled with complex analysis; however strong the emphasis is on codes of practice, the professional engineer, just like the medieval journeyman, has to solve real problems. Those who must conform to the architectural form of buildings that have to be built by contractors grappling with the perplexing task of putting a building together.

Engineers have to work in sympathy with builders, who have to organise the labour, build the temporary support structures and put together large structures safely, which need mechanical lifting devices to raise heavy sub-assemblies.

Engineering is enjoyable. It can also be energy-sapping, puzzling, frustrating, and sometimes tedious in achieving its aims. But it is an engaging and challenging profession. This book provides a link between structural theory and structural design, guiding undergraduates struggling with their project assignments through to graduates employed on real projects.

Nomenclature and units in the book

Dead loads are used to describe the self-weight and service loading combined. Live Loads are used to describe the applied loading of the occupancy.

All units are SI units:

kN – forces;

kNm – moments and torsion;

m – spans and overall dimensions;

mm – deflections

Chapter 2.1

2.1 Efficacy Balance and Grace

If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them. Henry David Thoreau

Efficacy, Balance and Grace

The three pillars of good architecture espoused by the Roman architect Vitruvius are: ‘Commodity, Firmness and Delight’. It is instructive to reinterpret the message to suit engineering. Maybe efficacy, balance and grace also fit the picture.

Efficacy may be defined as the power to produce effects, which is not just efficiency but the ability of a given design to perform its intended function. It is a word which embraces economy in terms of minimising materials used. Well-designed kitchen utensils often seem to be beguilingly simple but with a fitness for purpose, which is a pleasure for the user. Take a knife, for instance, which has a handle fitting snugly in the hand and a blade which has enough width to cut through tough vegetables. It also possesses balance, which makes it easy to hold.

Balance is the means of achieving equilibrium or stability. A bridge with a finely honed weight distribution, such as the historic and well-known Forth Railway Bridge is a beautifully poised structure. In some circumstances, the structural elements are expressed in the external envelope of the building. Part of the art of sculpting the form of a building is to arrange the elements such that they achieve a balanced whole.

Grace is the way in which the sculptural form might transcend its mere function and can become an object of real beauty and delight. Architects are taught to appreciate grace. Engineers should engage in this vitally important component of design. At the least, it should be appreciated that achieving grace of structural form is a skill which takes training and education.

Unlike fine art, architecture and engineering are bound by the necessity of producing buildings and