The Anatomy of Constructing Physiological Relationships with Less Stress
Series on Structures | Episode 2 of 5
Structures: Or Why Things Don’t Fall Down
In this second edition of our Architecture: Structures series, we will open the book and delve into the inner workings of structures of all kinds, with an emphasis on the relationship between humans, animals, plants, and beyond. Over the next several episodes, we will analyze the novel Structures or Why Things Don’t Fall Down, written by the prestigious author, J.E. Gordon. Though written decades previously, in 1978, it is amazing how ahead of the time the book was when first published. Also, the technical aspects ring true as much back then as they do in today’s time. By following along, we will uncover useful tips and tricks that we can take from the world and apply to our own life’s challenges.
“The anatomy within us may define our understanding, but it is the life around us in which we will design.”
What Makes a Good Structure
Materials may jump to the top of the list, but there are several factors in which we need to assess before crowning the best material. The nuances and degree to which different circumstances require different strengths go back millions of years. In our terms, we may reside with elasticity and going with the flow in order to maintain homeostasis. Being able to adapt to any given situation enables humans to evolve in their daily lives and over generations. Different structures tend to utilize favorable materials that are specific to their unique requirements. This foundational truth rings true across nature, including humans. Every individual may have personalized needs, but at the core, we are very similar and would be wise to pay attention to our anatomy and physiology.
Anatomy: The study of the structure and the relationship between body parts
Physiology: The science of how those parts come together to function and keep that body alive.
If you want to get a crash course in these terms before continuing, an overview would beneficial. As we continue our architecture series, we will uncover technical aspects and correlations between structures and our corresponding lives. From ancient times until the early 1800s, little advancement in using mathematics was utilized for building marvelous structures far and wide. That didn’t mean there weren’t fantastic examples of structures far and wide, such as the Parthenon, the postern gate at Tiryns, or the Egyptians’ boats made from papyrus reeds.
“Professor Jacques Heyman has shown conclusively that the cathedral masons, at any rate, did not think or design in a modern way. Although some of the achievements of the medieval craftsmen are impressive, the intellectual basis of their ‘rules’ and ‘mysteries’ was not very different from that of a cookbook. What these people did was to make something very much like what had been made before.”
Formulas for Life
Are you hooked? If not quite yet, then read on because you’re about to be.
Hooke’s Law
As Galileo was exiled for being a trailblazer and person of science, he turned his attention to figuring out the forces around us. He questioned the act of force, but could never quite understand “Why we don’t fall through the floor”.
The credit for the achievement of this fell to Robert Hooke (1635–1702). In the first place, he realized that if a material or a structure is to resist a load, it can only do so by pushing back at it with an equal and opposite force. If your feet push down on the floor, the floor must push up on your feet. This is not only true for floors, but for cathedrals, bridges, airplanes, balloons, furniture, lions, cabbages, and earthworms. In other words, a force cannot just get lost. If this condition is not fulfilled, that is to say if all the forces are not in equilibrium or balance with each other, then either the structure will break or else the whole affair must take off, like a rocket, and end up somewhere in outer space. Hooke noticed in 1676 that not only must solids resist weights or other mechanical loads by pushing back at them, but also that
- Every kind of solid changes its shape — by stretching or contract itself — when a mechanical force is applied to it.
- It is this change of shape which enables the solid to do the pushing back.
Essentially, all materials and structures deflect, to a greatly varying extent, when they are loaded. The science of elasticity is about the interactions between forces and deflections. The stretching and compressing is bending the object on a molecular scale.
Similar to people, when our lives are filled with so many activities and obligations, we feel unable to be our best as we are stretched too thin. In order to combat this, people need to structure their lives in ways that allow themselves to grow, but stay within the means of their physiological boundaries. Expanding one’s comfort zone will in essence allow for a larger and larger zone of comfort, which is self-rewarding and encouraged. Yet, by attempting to do too many things at once, the results as we will see will overwhelm even the best of us. Except for Elon Musk, very few things seem to overwhelm him.
Young’s Modulus (Elasticity)
Young’s Modulus = stresss/train = E
When discussing structures and materials science, another foundational place to build from starts with the invention of stress and strain. Young’s modulus conveys how stiff or floppy a material is. Just as with challenges in your life, you need to break them down into smaller portions. Note, many common soft biological materials do not obey the law, since their elastic behavior follows another type of rule.
Stress = load/area
It expresses how hard (i.e. with how much force) the atoms at a point within a solid are being pulled apart or pushed together by a load.
Strain = extension under load/original length
It expresses how far the atoms at a point within a solid are being dragged apart or pushed together. Stress is not the same thing as strain.
Strength
We can state that the strength of a structure is simply the load (in pounds force or Newtons or kilograms force) that will just break the structure.
Similar but on a more refined scale, the strength of a material is the stress (p.s.i. Or MN/m² or kgf/cm² ) required to break a piece of the material itself.
Examples of goals to aim for are being similar to wood in tensile strength, but closer to the properties of steel in compression strength.
Difference between Stress and Strain
Stress in Your Body and Relationships (Compression and Pushing)
- Pushing on uncomfortable subjects and topics repetitively leads to a build-up in stress and ultimately fracture if not addressed and relieved.
Strain on Your Well-Being (Tension and Pulling)
- Strain (energy) on your mind as you are pulled into several directions and activities will overwhelm a person if they are not prepared to adapt and lighten the load or are resilient enough to deflect the energy for a sustained period of time.
- One of the formulas for life (aim to instill balance)
Evolution has taught us fight or flight (cortisol building up). You may already know this, but may not realize how it takes a toll on your body over time as it accumulates, usually creeping up over weeks and months. This process leads to stress fatigue, which we analyze later in more detail. Similar to structures such as boats, cars, airplanes, and yes bridges and buildings among others, something small may not look like a big issue, until one day the stress fatigue overpowers the work of fracture.
Resilience
The quality of being able to store strain energy and deflect elastically under a load without breaking is called “resilience”.
Resilience may be defined as “the amount of strain energy which can be stored in a structure without causing permanent damage to it”.
One might look to nature and observe how a spider’s web is subject to impact loads arising from flies blundering into it, and the energy of these blows must be absorbed by the resilience in the threads. It turns out that the long radial threads, which form the main load-carrying part of the structure, are three times as stiff as the shorter circumferential threads which have the duty of actually catching the flies.
Naturally, there are many other ways of storing strain energy and getting resilience than by using tension members, such as railway buffers and ships’ fenders. Any shape of structure which is capable of being deflected elastically will have much the same effect. As the path of many inanimate materials is easily identifiable, we shall look below to observe their predetermined destinations.
Griffith Theory
The Griffith theory states that a crack will propagate when the reduction in potential energy that occurs due to crack growth is greater than or equal to the increase in surface energy due to the creation of new free surfaces.
This theory is applicable to elastic materials that fracture in a brittle fashion. One must be aware of any issues in structures and also in personal matters. Once the critical Griffith length is reached, it becomes self-propagating, and therefore very dangerous.
Poisson’s Ratio
Named after the French mathematician and physicist Siméon Poisson, the Poisson effect is the deformation (expansion or contraction) of a material in directions perpendicular to the direction of loading. The value of Poisson’s ratio is the negative of the ratio of transverse strain to axial strain.
For small values of these changes, µ is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson’s ratio values ranging between 0.0 and 0.5. Soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson’s ratio is near 0.5.
As nature has shown, the values for Poisson’s ratio for biological solids are generally higher than metals, stone, and concrete.
Whereas the former and other engineering materials always lie between .25 and .33, biological solids are often around .5.
“Thus, as we are alluding to, the effect of Poisson’s ratio is that, if we pull upon a piece of material, such as a membrane or an artery wall, in one direction it will get longer in that direction, but it will contract, or get shorter, in the direction at right angles. So if two tensions are applied, at right angles to each other, the effects will be additive and the strains will be less than we should expect if either of the stresses were applied separately.”
As we look at the body more, one can see the artery walls do not obey Hooke’s lawn, and the Poisson ratio may be higher than .5.
It should be perhaps be added that, whereas the aorta and the principal arteries expand and contract elastically with each beat of the heart, in the manner we have just been discussing, the state of affairs with the smaller arteries is usually rather different.
The walls of these lesser vessels are provided with muscular tissue which can increase their effective stiffness and so, by restricting the diameter, are able to control the amount of blood which is able to pass to any particular region of the body.
In this way the local distribution of the blood-supply is adjusted. The nature of our body and the living organisms surrounding us encapsulate the beauty that transcends to objects of all kinds.
How Nature Structures Herself
Nature has proven herself of billions of years to be an architect with beauty and function in mind, with an exquisite ability to blend the two through the evolution of every type of environment imaginable.
While we now look at specific examples with living membranes, we will revisit nature’s wonders in subsequent episodes in order to truly appreciate the complexities and strokes of genius that are scattered throughout our lives.
The strains to which present-day living membranes can be extended safely and repeatedly varies a good deal, but may typically lie between 50 and 100 percent.
“The safe strain under working conditions for ordinary engineering materials is generally less than 0.1 percent, and so we might say that biological tissues need to work elastically at strains which are about a thousand times higher than those which ordinary technological solids can put up with.”
Mechanically, the function of living cell membranes are similar to a rather flexible bag. They generally needed to be able to resist tension forces and to be able to stretch very considerably without bursting or tearing. On a human scale, the body takes on different tolls, similar to walls, arches, and dams.
In this excerpt, Gordon elaborates on the explanation and similarities between nature and man-made structures.
“In so far as a backbone behaves like a wall or a masonry column and departure from the ‘middle third rule’ represents some sort of limiting condition, the same kind of rules apply to scaling up an animal as we have seen apply to scaling up a building. Thus if we start with a small animal and progressively increase its size, the necessary thickness of the vertebrae will remain in due proportion. Most of the other bones, however, such as the ribs (fink truss with vertebrae) and the bones of the limbs, are subjected chiefly to bending — rather like the lintels of a temple — and the loads upon them are likely to be proportionate to the mass of the animal. Therefore, such bones have to be made disproportionately thicker.
If we look in a museum at the skeleton of a series of animals in increasing size, such as monkeys, it does appear that, whereas the dimensions of the vertebrae of little monkeys and middle-sized monkeys and gorillas and men are roughly in proportion to the height of the animal, the limb bones and, especially, the ribs become very much thicker and heavier, for the size of the animal, as the scale increases.
In this respect, Nature seems to be cleverer than the Roman architects, who, as they increased the size of their temples, abandoned the rather stocky Doric proportions and built, as a rule, in the florid Imperial Corinthian style, with slender architraves which frequently broke.”
The size of large animals is more likely to be limited by considerations related to the ‘critical Griffith crack length’ in their bones than by the square-cube law.
If there is a rhyme and reason to the way things are created, then one need not look any further than the technical reasoning to explain why things created over millions of years are just the way they have evolved to be.
Covering up Issues Versus Overcoming Challenges
By covering up and patching issues, we feel we are successfully ensuring the safety of the object once more. However, these patches are merely temporary fixes and should be implemented with caution. Real change and real progress requires better design of our lives and structures, including the materials (food we put into our body as well as steel in buildings) to overcome weakness, breakage and ultimately failure.
“In talking of stress concentrations we must note that weakening effects are not exclusively caused by holes and cracks and other deficiencies of material. One can also cause stress concentrations by adding material, if this induces a sudden local increase of stiffness.
Thus if we put a new patch on an old garment or a thick plate of armour on the thin side of a warship, no good will come of it. The reason for this is that the stress trajectories are diverted just as much by an area which strains too little, such as a stiff patch, as they are by an area which strains too much, such as a hole.
Anything which is, so to speak, elastically out of step with the rest of the structure will cause a stress concentration and may therefore be dangerous.
When we seek to ‘strengthen’ something by adding extra material we have to be careful we do not in fact make it weaker.
The inspectors employed by insurance companies and government departments who insist on pressure vessels and other structures being’ strengthened’ by the addition of extra gussets and webs are sometimes responsible, in Gordon’s experience, for the very accidents which they have tried to prevent.”
A Closer Look at Buildings and Center of Gravity
Yoga, meditation, or exercise are closely related to the likes of a feather and airplane in terms of homeostasis and center of gravity/pressure.
As one might use goat yoga or Headspace to meditate throughout the week (if you don’t know what I’m talking about they are both worth looking up). Regardless of your method of de-stressing and finding your zen, the center of gravity can be found in everything around us, as we shall soon explore. But first…goat yoga.
It might perhaps be supposed by the uninitiated that the C.P. (center of pressure) of the lift forces acting on a wing in flight lay at the middle of the wing, half-way between the leading and trailing edges, that is to say, at mid-chord. Actually, it is a well-known fact of aerodynamic life that this is just what does not happen.
The center of pressure of the lift forces on a wing is really not far behind the leading edge, usually near to what is called the ‘quarter-chord’ position: that is to say, 25 percent of the chord behind the leading edge.
It follows that, unless the structure of the wing is designed so that the flexural center is close to the quarter-chord position, the wing must twist. The angle through which the wing will twist will naturally depend upon how stiff the wing is in torsion, but, on the whole, all wing-twisting is a bad and dangerous thing in an airplane and it is the designer’s aim to reduce it as much as possible.
This is why the quill of a bird’s wing feather is usually located around the quarter-chord position.
When there are several forces acting upon a person, practicing mindfulness and exhibiting techniques such as a straight posture with a somewhat puffed out chest, in addition to deep breaths physiologically calms the body down.
In effect, you will boost your confidence and focus your flow better for concentrating on tasks more productively.
Taking time to find your center of gravity and pressure will open up your ability to capitalize on being more of a Doric column in strength.
Work Hard, Stay Strong with Work of Fracture
It is important to take note that the energy required to break a given-cross section of a material defines its ‘toughness’, which is called nowadays ‘work of fracture’ or ‘fracture energy’.
The quantity of energy which is needed to break most kinds of chemical bonds is well known. At least to chemists — and it turns out that, for the most of the structural solids with which we are concerned in technology, the total energy needed to break all the bonds on any one plane or cross-section (known as free surface energy) is very much the same and does not differ widely from 1 Joule per square meter.
Comparable to surface tension in liquids, ‘brittle solids’ are culprits of the same tendencies (not to be confused with tendons which are appropriate strong in tension) and should be avoided if possible in applications where they are in tension. These materials are brittle not, primarily, because they have low tensile strengths — that is to say they need a low force to break them — but rather because it needs only a low energy to break them.
The technical and biological materials which are actually used in tension, and used with comparative safety, all require a great deal more energy in order to produce a new fracture surface.
Stress Fatigue (Reset, Recharge, Go) 335
Again, we look at Structures as it elaborates on the significance of preparing for and observing the concept and reality of stress fatigue.
“One of the most insidious causes of loss of strength in a structure is ‘fatigue’: that is to say, the cumulative effect of fluctuating loads. The dramatic possibilities of fatigue in metals were first exploited in popular literature in 1895 in Kipling’s account of what happened when the propellor of the Grotkau dropped off somewhere in the Bay of Biscay because of a fatigue crack in the tailshaft.
Kipling went out of fashion, but public interest in fatigue was revived in 1948 by Nevil Shute’s No Highway. The success of this story, both as a book and as a film, was no doubt partly due to the character of Mr Honey, the archetypal boffin, but perhaps still more to the three Comet disasters, which occurred not very long afterwards. As Whistler remarked some time ago, Nature keeps creeping up on Art. The circumstances of the Comet accidents were not very different from those imagined in No Highway, except that many more lives were lost and a great deal of damage was done to the British aircraft industry.”
As a matter of fact, engineers’ knowledge of fatigue effects in metals goes back rather over 140 years. Indeed it was not long after the Industrial Revolution that it began to be noticed that the moving parts of machinery would sometimes break at loads and stresses which would have been perfectly safe in a stationary component. This was especially dangerous in railway trains, whose axles would sometimes break off suddenly and for no apparent reason after they had been in service for a time. The effect soon came to be known as ‘fatigue’, and the classical research on the subject was carried out during the middle years of the nineteenth century by a German railway official called Wöhler (1819–1914). From his photograph Herr Wöhler looks exactly what one would expect a German nineteenth-century railway official to look like, but he did a very useful job.
As we have learned, even though there may be a high local stress at the tip of a notch or a crack, the crack will not extend — so long as it is shorter than the ‘critical Griffith length’ — because making it spread requires work to be done against the ‘work of fracture’ of the material.
However, when the stress in the material is a fluctuating one, slow changes take place within the crystalline structure of the metal, and this is particularly likely to happen in the region of a stress concentration.
These changes have the effect of reducing the work of fracture of the metal in such a manner that the crack is able to extend, very slowly, even though it may be much shorter than the ‘critical length’.
In this way a tiny unseen crack may start from any hole or notch or irregularity in a stressed metal and may spread across the material, which is not, as a whole, changed in any obvious way. Sooner or later, such a ‘fatigue crack’ will reach the critical length for an ordinary common or garden crack. When this happens, the crack will immediately speed up and run right across the material, often with very serious consequences. It is usually quite easy to diagnose a fatigue crack after failure because of its characteristic striped or banded appearance.
Before rupture, however, an incipient fatigue failure may be practically impossible to spot, so awareness and periodic evaluation are necessary.
A life lesson here is to constantly be evaluating your situation and assessing how you can adapt in order to prevent fatigue. Whether it’s within your family, friends, work setting, or with your own goals and challenges, establishing a system of purpose and variety in your lifestyle is essential to providing a healthier baseline in activities. By doing so, you stay fresh and able to use the materials you are given to be in the best shape possible, mentally and physically.
Reflecting and Deflecting
In this second edition of Architecture: Structure series, we have discovered how to take a more deflective approach to stresses and challenges in our life. For the sake of a structure that is too rigid, we will be susceptible to acting as a glass mirror, deceivingly unbreakable, yet easily shattered with the right force. There will always be certain stressors that arise, but it is up to the individual to address them properly, rise to the occasion and adapt so the stress does not overwhelm them. One must spread out the load on its shoulder and struts in order to allow for homeostasis in mindset and capabilities. For if we strain and extend ourselves too much in either direction, we will not grow upwards, but yet merely fall down.
By studying nature and adopting many of her fine lessons in anatomy and physiology, we can in turn be better versions of ourselves. We will be able to be elastic when it counts and sturdy for many years as we find our individual center of gravity.
Breaking up your cycle is beneficial every now and then in order to let new positive activities and thoughts into your life. After all, life’s challenges are always changing, so we must not be stagnant and learn to adapt to challenges. By improving each step of the way, we will build and be better structures, bone by bone and brick by brick.
