I am a certified expert in structural engineering (civil engineering), though may not be exactly commonly recognized as such. Therefore, this post may be out of place here in this blog, named as it is, nonexpert. Yet, I will proceed.
I have had a lasting unrequited love affair with buckling of structural elements, beams, columns, beam-columns, plates, shells, you name it. The buckling I am in love with is both elastic and inelastic, and sometimes dynamic too, depending on my lover’s mood. I know when it started – the first course I attended in my post-graduate program at IIT Kanpur, Fall semester 1976.
Prof. Ashwini Kumar - a wonderful teacher whom I have belatedly come to realize as the go-between in this love affair. I had a chance to meet him a little more than two years ago, after 31 years. I was amazed that he actually remembered me; not just me, but every student of that post-graduate class, probably because we were one of his first set of students. At one level, this post is my tribute to him, but I am ambivalent about his reading it. He may fail me now, one thing he did not do when I was formally his student!
While in the undergraduate program, I learned of buckling as early as 1973, at that time it was a simple matter of deriving an equation and applying it. We did not pose that crucial question, why the column does what it does; why does a column buckle? Aeronautical engineers, who study buckling at an order deeper than what the earth-bound civil engineers do, were not too forthcoming with the answer to this question. Even my mentor, batch- and hostel-mate, Sriram Somasundaram, then in the aeronautical engineering stream, was not of much help. But, I do not blame him.
Prof. Kumar had prescribed a book, Principles of Structural Stability Theory (buckling is a manifestation of the structure being unstable) by Alexander Chajes. It is a thin book, easy to read and really comprehend the phenomenon, beyond equations and yet mathematically rigorous.
In the opening pages, the book says something like, “There comes a critical point at which the column does not know whether it should merely compress further or bend itself to relieve the stress under the increasing load. It goes into a tizzy. It buckles not knowing how much to relieve through compression and how much through bending.” This sentiment, taken by the author from another source and duly acknowledged, is the foundation of my understanding of buckling - why the column bifurcates, and why it cannot be determined how it would, where it would snap, so to say.
Note the anthropocentric tone of the statement. Perhaps at that time I had not recognized its impact on my psyche, but now I know that it was huge. It is the reason I fell in love with buckling and I thank Prof. Kumar for that.
When did this realization come about? Much later, when my love had matured into deep admiration for my lover. I have stuck with her for three decades plus, after all, even as she has become more and more complex and complicated, leaving me in her wake.
About teaching scientific phenomenon through an anthropocentric idiom, the first prize goes to the iconic “Double slit” experiment in physics, perhaps the first experiment that tells the experimenter that she will be perpetually short of fully understanding what she set out to understand. It is about whether light is a wave or a particle. I will not go into the details, but as the experiment unfolds layer after layer there would be no experimenter worth his salt who would not ask, “How does the light know which slit to pass through?”
Prof. Feynman tried to put an end to this and asserted that light is a particle. He did not linger on this dual personality as he was not interested in the existential question of what light is, but only on what and how we can know about what light does. There, treating light as a particle helps far more than a wave imagery of it could.
A deeper understanding of this experiment must lead one to conclude that light does not want you to know what it really is, but is willing, ready and able to share some secrets of itself with you. Anthropocentrism.
It is the same with buckling. We have the entire math we need to solve buckling problems, but without ever understanding the why of the process. True, we have developed a model based on a minimization paradigm and we are successful in getting answers. Our structures, designed as per this paradigm have stood the test of time. But, the why of it? We may never know. My lover is way too mysterious.
And, this, in my opinion, is how interest in science can be developed and maintained – anthropomorphize it. It must be recognized that understanding what something is is a never ending process. Never put a full stop, but use all the other punctuation marks – commas, semi-colons, colons and yes, even apostrophes and exclamation marks.
Much as it may be belated, the post is my Teachers Day tribute to Prof. Ashwini Kumar who, through the instrument of Alexander Chajes’s book, opened my eyes to look at engineering mysteries and its mystique.
I have truly buckled.
Raghuram Ekambaram
I have had a lasting unrequited love affair with buckling of structural elements, beams, columns, beam-columns, plates, shells, you name it. The buckling I am in love with is both elastic and inelastic, and sometimes dynamic too, depending on my lover’s mood. I know when it started – the first course I attended in my post-graduate program at IIT Kanpur, Fall semester 1976.
Prof. Ashwini Kumar - a wonderful teacher whom I have belatedly come to realize as the go-between in this love affair. I had a chance to meet him a little more than two years ago, after 31 years. I was amazed that he actually remembered me; not just me, but every student of that post-graduate class, probably because we were one of his first set of students. At one level, this post is my tribute to him, but I am ambivalent about his reading it. He may fail me now, one thing he did not do when I was formally his student!
While in the undergraduate program, I learned of buckling as early as 1973, at that time it was a simple matter of deriving an equation and applying it. We did not pose that crucial question, why the column does what it does; why does a column buckle? Aeronautical engineers, who study buckling at an order deeper than what the earth-bound civil engineers do, were not too forthcoming with the answer to this question. Even my mentor, batch- and hostel-mate, Sriram Somasundaram, then in the aeronautical engineering stream, was not of much help. But, I do not blame him.
Prof. Kumar had prescribed a book, Principles of Structural Stability Theory (buckling is a manifestation of the structure being unstable) by Alexander Chajes. It is a thin book, easy to read and really comprehend the phenomenon, beyond equations and yet mathematically rigorous.
In the opening pages, the book says something like, “There comes a critical point at which the column does not know whether it should merely compress further or bend itself to relieve the stress under the increasing load. It goes into a tizzy. It buckles not knowing how much to relieve through compression and how much through bending.” This sentiment, taken by the author from another source and duly acknowledged, is the foundation of my understanding of buckling - why the column bifurcates, and why it cannot be determined how it would, where it would snap, so to say.
Note the anthropocentric tone of the statement. Perhaps at that time I had not recognized its impact on my psyche, but now I know that it was huge. It is the reason I fell in love with buckling and I thank Prof. Kumar for that.
When did this realization come about? Much later, when my love had matured into deep admiration for my lover. I have stuck with her for three decades plus, after all, even as she has become more and more complex and complicated, leaving me in her wake.
About teaching scientific phenomenon through an anthropocentric idiom, the first prize goes to the iconic “Double slit” experiment in physics, perhaps the first experiment that tells the experimenter that she will be perpetually short of fully understanding what she set out to understand. It is about whether light is a wave or a particle. I will not go into the details, but as the experiment unfolds layer after layer there would be no experimenter worth his salt who would not ask, “How does the light know which slit to pass through?”
Prof. Feynman tried to put an end to this and asserted that light is a particle. He did not linger on this dual personality as he was not interested in the existential question of what light is, but only on what and how we can know about what light does. There, treating light as a particle helps far more than a wave imagery of it could.
A deeper understanding of this experiment must lead one to conclude that light does not want you to know what it really is, but is willing, ready and able to share some secrets of itself with you. Anthropocentrism.
It is the same with buckling. We have the entire math we need to solve buckling problems, but without ever understanding the why of the process. True, we have developed a model based on a minimization paradigm and we are successful in getting answers. Our structures, designed as per this paradigm have stood the test of time. But, the why of it? We may never know. My lover is way too mysterious.
And, this, in my opinion, is how interest in science can be developed and maintained – anthropomorphize it. It must be recognized that understanding what something is is a never ending process. Never put a full stop, but use all the other punctuation marks – commas, semi-colons, colons and yes, even apostrophes and exclamation marks.
Much as it may be belated, the post is my Teachers Day tribute to Prof. Ashwini Kumar who, through the instrument of Alexander Chajes’s book, opened my eyes to look at engineering mysteries and its mystique.
I have truly buckled.
Raghuram Ekambaram
4 comments:
I have always believed in Interpreting reality exclusively in terms of human values and experience.The first lesson of yoga is that the observer,observed and the means of observation are all linked in a whole.Reality itself is the limitation of perception.light is not bothered about Feynman's interpretation.I never realized that mechanical phenomenon are equally subjective.This blog is definitely a great tribute to your teacher.
DS sir, "Interpreting reality exclusively in terms of human values and experience." - Isn't this the meaning of "That thou art" (whatever that may be in Sanskrit) which really means there is no objective reality.
In fact, Feynman was not interested in what light was. he wanted to know what it does. Liewise, I, as a structural engineer, am not interested in what buckling is, only want to know when the structure will get into that state. The parallels, including the anthropomorphism, is are truly parallels. Thanks for taking the effort to read this post, DS sir. I apprecaite it immensely.
Raghuram Ekambaram
Could you please help me with the bending-buckling phenomenon? Read about it long back...
Isn't it essentially the fight between the quadratic and the quartic terms - compression versus curvature, right? Or am I on the wrong track?
Somehow, memory tells me that this is just a type of "phase-transition" or instability. Of course, that is a cottage-industry...understanding complex phase-transitions through simple algebraic expansions. i think it is called Landau theory. Now, that Landau is one helluva guy - at times, I place him above Feynman.
Arjun, you know more about buckling than I do ... no contest ... yes, it is a phase-transition thing, just as you say. But, we don't know why that transition occurs. Of course, we do know the conditions under which it occurs. But, this is always tentative because we never can experience this transition, as ideal conditions never exist (perhaps that is why they are called ideal).
You take the mathematical route of axial and curvature strains. I, as an engineer and a pseudo-mathematician, talk about axial and bending stiffness. We can get an idea whether an object is slender or stoutby looking at it. Whether it would compress or buckle. You, as a real mathematician would do it the other way.
What I was trying to focus on was not the mathematical explanation but in this instance, out of the book by Chajes, I anthropomorphized the stuff and truly it got me interested in the subject more. I have many times asked the structure, "Tell me when you would buckle."
I have lived as a structural enginering psychiatrist for the past 35 years. This was the thrust of my post.
My interest in Feynman is not more than about 25 years, after my learning phase was over. I got interested in him through his lectures which I ahd studiously avoided reading during my physics courses (that is how I survived IIT!). But I have used both the Hamiltonian and Lagrangian methods in my research work, much more of the former though.
I am blissfully unaware of Landau's brilliance though have heard of him many times, always in glowing terms. You just added to the mystique.
Thanks for visiting.
Raghuram Ekambaram
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