Is It Strong Enough?: Simple Strength Assessments

Is it

STRONG

Enough?

SIMPLE STRENGTH ASSESSMENTS

Dieter Wieneke, BSc, CEng, MIMechE

(retired Chief Stressman of Marconi Underwater Systems)

Copyright © 2016 Dieter Wieneke, BSc, CEng, MIMechE.

All rights reserved. No part of this book may be reproduced, stored, or transmitted by any means—whether auditory, graphic, mechanical, or electronic—without written permission of both publisher and author, except in the case of brief excerpts used in critical articles and reviews. Unauthorized reproduction of any part of this work is illegal and is punishable by law.

ISBN: 978-1-4834-4777-3 (sc)

ISBN: 978-1-4834-4780-3 (hc)

ISBN: 978-1-4834-4779-7 (e)

Library of Congress Control Number: 2016903953

Because of the dynamic nature of the Internet, any web addresses or links contained in this book may have changed since publication and may no longer be valid. The views expressed in this work are solely those of the author and do not necessarily reflect the views of the publisher, and the publisher hereby disclaims any responsibility for them.

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CONTENTS

Introduction

Step One

Chapter 1 Load cases

Section (a) Listing load cases

Section (b) Sources of load cases

Section (c) Load types

1. Mass

2. Rotation

3. Pressure

4. Temperature

5. Deflections

6. Vibration

6 a) Long-term regular dynamic forces

6 b) Long-term irregular dynamic forces

6 c) Short-term shock and impact loads

7. Moving loads

8. Magnetic and electrical effects

9. Manufacturing processes

10. Failure cases

11. Misuse

Section (d) Summary

Step Two

Chapter 2 Safety Factors

Section (a) Load levels

Section (b) Calculation accuracy

Section (c) Material strength

Section (d) Manufacturing variability

Section (e) Service practice

Section (f) Safety factor types

Section (g) Suggested values of safety factor

Section (h) Summary

Step Three

Stress and deflection predictions

Chapter 3 Structural data

Chapter 4 Classification of the structure by component type

Chapter 5 Support reactions

Section (a) Newton and physics

Section (b) Components of a load

Section (c) Determinate and indeterminate structures

Section (d) Constraints

Section (e) Finding the reactions

Section (f) Summary

Chapter 6 Loads and the manner of their application

Section (a) Point loads and moments

Section (b) Line loads

Section (c) Torque and Couples

Section (d) Pressure

Section (e) Body forces

Section (f) Slope-induced components

Section (g) Pre-tension

Section (h) Temperature-induced forces

Section (i) Magnetic and electrical forces

Section (j) Summary

Chapter 7 Calculations

Section (a) Mathematics, physics, and useful techniques

1. Newton’s Laws

2. Linearity

3. Slow load application

4. Stationary conditions

5. Load components

6. Load circuit

7. Partial structures

8. Visualizing deflections

9. Properties of plane areas or things you must know about your components

10. Stiffness

11. Mathematics

12. Errors

13. Significant figures

14. Manipulation of equations

15. Summary

16. Addendum – how to calculate the I of a composite section

Section (b) Units

Section (c) Stress and strain

1. Pure Tension and compression

Bars and beams

Plates in tension

Plates in compression

2. Bending theory

Beams

Plates

Frameworks

3. Shear

4. Torsion

5. Addition of stresses

6. Joints

Nuts and Bolts

Rivets

Blind fasteners

Welds

Bonding

Trapping

Friction

Lugs

7. Stress concentrations

8. Poisson’s ratio, ν

Section (d) Finite Elements

Section (e) Dynamics

Beam

Membranes

Plates

Section (f) Summary

Step Four

Chapter 8 Stress and strength comparison

Section (a) Materials

1. Metals

2. Reinforced Plastics or composite material

3. Unreinforced plastics

4. Ceramics

5. Timber

6. Magiconium

Section (b) Allowable stresses

1. Ultimate

2. Yield or proof strength

3. Buckling strength

4. Fatigue strength

Mean and alternating stresses

SCF

Surface conditions

Stress corrosion

Multiaxial stress

Temperature

5. Creep strength

6. Stress corrosion cracking strength

7. Limiting Deflections

8. Vibrations

9. Common materials’ strength

10. Bolt allowable stresses

Section (c) Reserve Factor

Chapter 9 Chapter 9: Examples

1. A chair

2. The fan

3. The joist

4. The wheelie bin

5. The spoked wheel

Glossary

Bibliography

INTRODUCTION

Stress and structural analysis: the art and science of strength estimation

(or how to make sure things do not break)

It is not necessary for any structure to break. Structures means anything manufactured or built by anyone to some design or specification. It could be large or small, made of any material, or a single piece or a large collection of individual pieces joined together by any method. It could operate or be used in the widest possible selection of environments, hot or cold, wet or dry, stationary or moving.

Modern structural analysis – that is, finding the various strengths of the structure by calculation – is good enough to avoid all failures. Obviously, the structures must not be misused, but if they are properly made, maintained, and used, they should never break within their recognised and acknowledged life, if such a life has been established. The analysis may need the use of computers and elaborate programs run by experts, but nothing should ever break.

In the distant past, this was not so. It can be imagined how the ancients, in whichever civilization in the world, cursed when a large stone lintel over a doorway broke. It was all right last time, they may have thought, before realizing that the stone was a bit thinner this time or there had not been another storey over the earlier lintel. When they used a thicker stone, all was well, and they would have noted the necessary dimensions for success. Nowadays the necessary size can be calculated to a high degree of accuracy. Repeated trial and error to establish sufficient strength for a structure is unnecessary.

But still things break prematurely. This is irritating to a stressman, or structural analyst, or, the latest term, a structural integrity engineer like me. Stressmen are engineers whose job it is to make sure that things do not break. They can achieve this by a combination of calculation and test, a process to be described in this book. Such failures are irritating because they are unnecessary. Sorry to repeat myself, but in our times, nothing should break. Tests may have to be done as a final check on the design, strength calculations, and manufacture of the artefact, but only in important circumstances such as when safety or lots of money is at stake.

It is quite clear that often makers do not consider the strength of their product sufficiently. If they did a detailed assessment, including the effects of time and the environment, there would be much less to grumble about. Usually, however, they only call on the services of stress engineers when things have gone wrong. They have taken a chance that all will be well, that nothing breaks. If they are lucky, and they often are, especially if they have done nothing out of the ordinary, then they save time, money, and trouble; profit improves. If they are not lucky, it usually costs more to put right the failure than it does to do the job properly in the first place. It has been estimated that structural failures cost several per cent of the GDP per annum, some tens of billions of pounds sterling. This is a huge cost, especially since it is largely unnecessary.

It must be admitted, of course, that some things are well known to be fragile, and it has always been recognised that care must be taken with them. China cups are an example; there is no point in doing any analyses or tests on them. But some things are expected to be strong enough for their purpose, and it should be remembered that nowadays everyone has a duty of care for almost everyone else. In this litigious age, someone may insist on having this duty fulfilled. There are laws and regulations about many types of structures which have to be satisfied, and even where there are not, it may one day be necessary to show that attention has been paid to the strength of the item.

For regulatory purposes – say, satisfying the Building Regulations – it may be necessary to pay an expert in the field to produce a report, as the authorities concerned would not know whether to trust a nonprofessional’s figures. However, if attention has been paid to the strength of the structure, this should not reveal any faults.

Costs are not just measured in money and time, interdependent quantities. Safety of life and limb may be involved; in that case, analysis and/or test is paramount. Whatever needs to be done will have to be done, and it must be done early. In established industries, the relevant authorities have usually imposed regulations to ensure safety and often environmental conditions nowadays.

There is a further cost which people do not seem always to realise, and that is to their reputations. When they appear to have failed in some respect, their critics, who will not necessarily be detractors, will think less of them. Such loss of faith may even be fatal to the careers of individuals and the business of companies. By contrast, those who correct the fault may make their reputations.

By the way, failure means that the structure no longer does its work sufficiently well. It is not necessary for there to be a fracture or an obviously bent piece of material. It may be that the structure remains apparently unaffected but merely that the safety margin has been encroached. More about safety margins later.

Purpose of this book

Many people have responsibility for the integrity of an artefact but are not structural experts, nor do they want to be. The purpose of this book is to help them understand their structures and then carry out simple calculations to discover their strengths and weaknesses. I am thinking of entrepreneurs, designers with many duties other than just the strength of their structures, inventors, students and their projects, and even managers who are trying to monitor the progress of people working for them. We will consider a structure of interest to you. Either it exists and you must find out what its strength is or it has yet to be designed and made.

Like managers and designers, stressmen need to know all about a structure from its birth to its death, every aspect. There may be a critical situation at any time that has to be dealt with. The strength analysis process can therefore be used as a checklist of important points in the scheme. If something is important structurally, it may be important in other respects. This could be useful to a manager.

This is all about physical structures made of wood, metal, ceramics, concrete, or plastic (reinforced or not). They are never made for their own sake. They always support or contain something to serve some other primary purpose. A teapot is a structure intended to contain tea; if it survives to become an antique and it is revered, it may be considered a work of art. So then the structure exists so that people may remember its creator or admire his workmanship. The pot now has a different role; it supports memory or admiration but not tea any longer. That would be too risky. Such a secondary role for structures, however, does not mean it’s unimportant, and one of the most important characteristics of any structure is its strength.

All physical structures of any scale, from bridges and skyscrapers to watch springs and cotton threads, aeroplanes to roller blades, elephants to fleas, whether synthetic or natural, can have their strengths calculated. An approximate first estimate can be made with a calculator and only a little mathematical knowledge, merely arithmetical. If you can do numbers sufficiently well to control your budget, you can do this. You just have to get used to it. Persevere; do not let it beat you. You will be rewarded with useful knowledge. Designers will not design things that break; users will be able to estimate how far they can stretch the use of existing artefacts. If, however, even simple mathematics daunts you, then the first two chapters will enable you to describe your project to a stressman.

Readership

As mentioned before, this book is aimed at those people whose principal purpose is not structural analysis or stressing but whose work involves designing structures which must not fail, whether for safety or economic reasons. By following a simple procedure, most people should be able to check a preliminary design so that it is safe and fulfils its purpose. This should apply to almost all types of goods, to use the economics term – any material, any size, any shape, any purpose, any structure or part or component of an artefact or product. Even designers in a highly technical and regulated sphere producing bridges, cranes, nuclear reactors, and aeroplanes may benefit from a quick initial strength estimate.

However, designers and others must have a sufficient understanding of how structures behave and work in order to be able to make quick but not misleading estimates of their strengths, so one other aim is to give the reader some help in gaining this feel for structures. This could be described as the art bit. When you have had some practice, you will get a sense of how structures work. In particular, once you have investigated your structure, you will understand it and its limitations and possibilities. This sense will have to have two aspects. The first concerns static (and so-called quasi- static) analysis, where nothing moves, the loads being successfully supported by the structure. The second involves a trickier consideration, that of dynamic or vibrations analysis. This is often not investigated until after the first items have been produced or even sold or unwanted wobbles ruin performance or induce fatigue failure. An expert may have to be consulted.

The idea, therefore, is to give anybody the ability to estimate the strength of any structure in a safe, conservative, and simple way.

Mathematics

It is intended to describe a process – a series of steps always undertaken – to prove a structure’s strength in a given set of circumstances. The process is not particularly onerous mathematically. Only simple equations will be used, no simultaneous or differential equations – only easy algebra. All the difficult stuff can be left to the mathematicians. It will be mostly a matter of substituting values into formulae.

The mathematical stuff is well documented and widely available. Every professor in every structures department in every university in the world has written papers and books giving the basic physics and maths of the subject. Their collected wisdom, in the form of equations giving stresses in particular situations, has been turned into compendia. Roark’s Formulas for Stress and Strain (now by Young et al.) is only the best known. For a deeper understanding, I recommend the books by Stephen Timoshenko. Robert D. Blevins wrote a vibration compendium called Formulas for Natural Frequency and Mode Shapes. Computer programs that do the arithmetic in these books for you are available, which makes the process easy. The use of these in an intelligent way will enable anyone to ensure the strength of his or her structure, albeit leaving it somewhat heavy.

However, all these formulae which have been discovered over the past couple of centuries are based on simplified structures: beams of constant section, plates of unvarying thickness and simple shapes (square, rectangular, circular), a restricted set of edge conditions (which describe how a structure is supported), idealised or simplified loading. The result of applying these conditions to real structures which rarely display them is that the calculated stresses are approximate. This requires that the calculations must be conservative – that is, for safety’s sake, they must overestimate the stress rather than underestimate it. This necessarily means the structure will be heavier than it could be if more accurate calculations were made. When more accurate results are required or the structure is too difficult to idealise by the use of simple formulae, another technique called Finite Element analysis has to be used. This needs computers, complex programs, and expert practitioners.

A word about the concept of stress; we do not refer here to the woolly, psychological state suffered by overworked people. Mechanical stress is precisely defined and takes into account two parameters: the load, including its method of application, and the shape, especially the cross-sectional shape in relation to the other dimensions, of the structure carrying the load. It is the result of small distortions in the structure which necessarily occur when a structure is loaded. There are standard equations which give the stress at any point in a structure. All you have to do is substitute the numbers for the letters in the equation, having chosen it, and do the arithmetic.

Resort to specialists or experts

This is intended to indicate when experts ought to be consulted. Obviously, the time and circumstances will vary. It will depend on the knowledge and expertise of the designer and on the consequences of breakages.

Refinements to a structure which remove significant quantities of material, or introduce a substantial change, on a subsequent design pass may need the attention of a specialist. The reasons for the specialist’s involvement may be that the weight of the structure needs to be reduced or even minimised or that fatigue or creep (both time-dependent quantities) is involved, or an accurate figure for deflection is needed or a cheap material of lesser quality is being used, or just that the change needs formal stressing for regulatory purposes.

If, however, the component is not high-tech, or not completely new, a simple analysis, such as will be developed here, should be enough to guarantee its integrity. The phrase completely new implies structural novelty – any material or manufacturing method or shape that is unconventional in the relevant situation and therefore not proved.

Choose your expert carefully; he will only be a true expert if he has done similar work before. You need to question him as closely as you can to find out exactly what he has done. Also obtain the results of his work. If he is any good, he will be honest with you and, if necessary, suggest he works in stages or gets help. Many consultancies advertise in the specialist press. Also try to get practical, measured cross-checks. If possible, real results should always support theory.

Value

As has been said, the point of assessing structural strength is to avoid failure, which has costs in terms of safety, money, time, and reputation. Despite the existence of modern analytical and experimental techniques, there are still many design failures. The cause is likely to be insufficient attention to strength early on in the design process. It is cheaper to do some work on strength at this time. There are, of course, many other causes of structural failure.

Industrial application

Each established industry has its own methods of working; in fact, each company may have its own processes to ensure safe and sound structures. They will also have official regulations to meet if there are any public safety concerns. This applies to the petrochemical industry and the civil, nuclear, and aeronautical industries as well as to anyone who makes bridges, cranes, ships, cars, and so forth. Each uses particular materials such as steel or aluminium and whatever experience has shown to be suitable from time to time. Each develops manufacturing methods and techniques. Each uses particular types of structure, be it beams, tubes, or plates. It is a major matter for them to change any of these things.

But there are many products that are not regulated and in which some self-imposed good practices would be beneficial. It cannot be emphasised too much that early on in each project is the time to think about the required strength of the components, not when it is realised that failures will occur. It will cost much more in time, trouble, and money to put right than to incorporate sufficient strength in the first place.

Four steps

In principle, there are four tasks to consider in the strength estimation process, and it is necessary to pursue each fully to its completion; otherwise, critical situations can be missed. They are as follows:

1. The discovery of load cases

2. The setting of safety factors

3. Stress and deflection predictions

4. Comparison of stresses and deflections with allowable values

Load cases describe the life of the artefact, from deciding on the raw material with which to manufacture it to scrapping it. Anything that happens throughout its life will impose some sort of stress, and although in many circumstances this will be negligible, it cannot be assumed so. Some thought must be given to every phase of the artefact’s entire existence.

Safety factors, also known as design factors, acknowledge the fact that none of the information or the calculation method is entirely accurate. Clearly this affects the quality of the calculation, and safety factors provide a margin between real stress and a calculated theoretical value which must be higher. Authorities such as the Civil Aviation Board or some parliamentary quango or working committees usually set the actual size of the factors. Their derivation can be quite complex so-called partial factors based on statistics. This sort of thing ought to be left to experts. The present work will give some simple suggestions.

Most people will consider stress and deflection predictions the hard bit. At the level proposed here, it ought to be manageable by anyone with some experience at handling numbers. The great thing is never to believe the first result; always assume that a mistake has been made and cross-check somehow.

Allowable values of stress and possibly deflections have to be taken from authoritative sources. It is lengthy and expensive and the job of experts to establish the strength of particular materials. Materials must also have a good provenance.

These tasks will be considered in more detail in the following chapters.

Summary

My intent is to help non-specialists design or use their structures so that they do not break. This can be achieved by using knowledge about their shape and situation and substituting numbers into easy equations. This process is known as doing simple hand calculations. I believe people need not be at all fearful of these equations, as they are only arithmetical.

While emphasising the value of early consideration of structural strength, I also point out that each type of artefact in each industry will settle down to a near optimum design and manufacturing technique. Change from this may be risky and expensive.

I have classified the task into four parts: discovering the load cases, setting the safety factors, performing the arithmetic, and comparing the stresses with the permissible values.

Throughout this book, I have mentioned the effect of official regulations and have tried to indicate when experts ought to be consulted.

Overall, the general idea behind the book is to determine whether any part of the structure under consideration has high stresses relative to allowable ones. If it does, experts ought to be consulted. If not, there is no need to worry.

STEP ONE

CHAPTER 1

Load cases

First an explanation of the term load case: a load, of course, is something physically forceful – a weight, pressure, an electrical or magnetic field, temperature, a twist or moment, a poke with a stick – anything that produces force. A load case describes a period in time, long or short, in which a load or set of loads is applied to a structure or part of it. A load case should describe a particular limited set of circumstances, a single event. It is better to have two or more cases which can be combined than to have a complex case which straddles two situations. This only causes muddle.

Section (a) Listing load cases

As indicated in the Introduction the first job is to compile a list of load cases. This should be comprehensive, from birth to death of the artefact. There are at least four reasons for making a list. First, it helps ensure that