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A Classic Textbook

A Classic Textbook 288 AIRCRAFT ENGINEERIN G October, 1936 Professo r Timoshenko's "Theory of Elasti c Stability" Reviewed By R . V. Southwell , M.A., F.R.S., F.R.Ae.s.† ITHI N the limits set b y practical con­ survey in a field where change is rapid and Inevitably, as one turn s to detail, personal siderations, stresses in engineering continuous. The publication of this volume is predilections give a bias to one's judgment. materials entail almost exactly pro­ a major event. Thus, as i t seems to me, more frequent appeal portionate strains. But in bodies of elongated I have listened to Timoshenko's lectures, might have been made to considerations of shape, such as rods or thin sheets, displace­ with admiration verging on env y of hi s perfect strain-energy, especially in the later chapters ments are not necessarily proportionate to the technique, and I have witnessed his stimulating which present the difficult theory of thi n plates strains of which they are the integrated result, guidance of research students; but always, in and shells. The energy method which we and hence, for such bodies, Hooke's law may m y mind, his name has stood for learning—for associate (primarily) with the name of Rayleigh hold in respect of some types of displacement is, in Timoshenko's hands, a much-used and tha t encyclopædic knowledge which in this bu t not of others. Applying end thrus t to a very powerful tool; but relatively little is said country we who work on similar problems so long straight rod (or strut), and measuring the often lack. Yet eve n so, in a first reading of about its fundamental basis—it is presented consequent approach of th e ends, we find that this book, his eruditio n is as impressive as his rathe r as a n ingenious device which "works." this increases faster than in proportion to the grasp of th e practical implications of a theo­ Rayleigh is given credit for originating the study thrust ; under a load which would have been retical result. To my shame I have realised of inextensional deformations in rings and shells, quite safe applied as tension, the stru t bows how many names appear in his authors' index and incxtensibility is assumed in the investi­ largely and ceases t o hav e value as a compres­ of which I had not even heard, and in contrast gations of §39, 78 ; but I have not found sion member. mention of Rayleigh's argument, that since I can recall only two important investigations extensional energy is proportional to the of which the book does not tak e cognizance— This is th e simplest example of failure by th e work of W. R. Dean on circular plates in thickness, flexural energy to it s cube, the ex ­ elastic instability, and its essential features were torsion and on corrugate d plating, and that of tensional strains must have the order of the explained by Euler nearly two hundred years A. Robertson on solid struts. If with no other thickness (at least) in order to satisfy the con­ ago : his calculations proved, what Musschcn- purpose, British research workers should read dition of minimum strain-energy. broek's experiments had already shown, that this book in order to acquir e a fitting humility. th e resistance of a slender strut is inversely The notion of th e "reduce d modulus" E. proportional (other things being equal) to the They will gain much besides. In an y investi­ (taken over from the theory of struts which fail square of its length. A sermon might be gation concerned with elastic stability there is a t stresses beyond the elastic limit) is applied preached upon this text to "practical " engi­ (or should be) first, a stage of difficult work b y Timoshenko very boldly to problems of neers who would, if the y had their way, repress done with exhilaration—the analytical treat­ much greater complexity: considering how in our engineering schools all thinking not ment of the problem; secondly, a stage of little we know as ye t about the details of plastic directly related to some problem of immediate hard work done under boredom—the presenta­ distortion, I confess to some feeling of hesitation. importance : for over 100 years engineers dis­ tion of results in curves or numerical tables; I n his treatment of heated bimetallic strips regarded the theor y of Euler and th e experi­ and finally, a stage in which engineering (§45) I suspect that account should have been ments of Musschenbrcck, and b y many even judgment is used t o determin e their application take n of curvature across the width, as well th e work of Bauschinger, Considère and Tet- t o practical design. This third stage is too often as along the length ; the bent strip will, I majer, published in 1889 an d after, was regarded shirked—one suspects for the reason that it think, be par t of a spherical, not a cylindrical as "academic" ; not until the Quebec Bridge calls for th e hardest thinking. No stage is surface. And I wonder whether the problem disaster, early in thi s century, did they recognise omitted in Timoshenko's book: it faces boldly (§47) of the lateral buckling of a narrow tha t these studies might after all b e justified, this question of practica l significance, and makes rectangular cantilever, which (p. 248) is of and even then (despite the evidence of Fair- recommendations which, whether they are importance only when the breadth is very bairn's experiments in connection with the accepted or not, cannot be dismissed on the small in relation to the depth, can really be Britannia and Conway bridges) the elastic plea tha t they are vague. treated safely on th e assumption that the cross- stability of flat plating was left as a harmless section docs not change its shape ; I suspect The result is a mine of information—exactly exercise for mathematicians and the less tha t a different result might be obtaine d using th e kind of information for which designers practically-minded of academic engineers. Aero­ th e theory of flat plates. But these arc my have so long been waiting; they can learn here nautics has altered the picture—no problem in only real difficulties, and probably they can be of everything tha t has been done, and what is its elastic stability could well be harde r than that resolved : one could hardly hope to find none significance for their problems. But, if they of monococque construction; but we d o not in reading 500 closely reasoned pages. desire to understand as well as t o apply, they recognise the true lesson of these historical mus t be prepared to mine. This, as it seems Paper and printing are satisfactory, and th e facts, merely because we now find reason to ad ­ t o me, is a monograph for th e specialist an d diagrams admirably clear, but I must own to mit one more branch of stud y to respectability. th e research worker, rather than a text-book regret that the simplicity of formulas, especially To the aeronautical designer not only struts which can be placed in th e hands of a student those involving integrals, is often impaired by and plates, but tubes, curved shells and com­ after he ha s covered the ground of a n honours unnecessary suffixes and by unwillingness to posite structures, present a possibility of course in Engineering Elasticity. It is too introduce a factor 2. Only with very wide failure by instability . He needs t o hav e avail­ complete, too detailed in its treatment, to make freedom in th e use of founts (which is no t a able all researches in thi s field—and the litera­ attractiv e reading for one who ha s had no feature of this volume) can the integral tur e is large and scattered. Not everyone ca n special contact with its subject. read German easily, very few (in this country) A student, however, may expec t to receive can read Russian a t all ; yet to disregard papers Timoshenko's material through the mediu m of be saved from inelegance : denote (with in those languages is t o lose the greater part of lectures ; it would not be fair to attempt recent work. So for years we have wanted th e criticism from his standpoint (e.g. b y regretting book which now becomes available, in which the th e absence of examples whereby he ma y test Rayleigh, Kelvin and Love) the thickness of a results of theory and experiment are brought his grasp), in view of th e author' s clear state­ plate by 2/i, and all difficulty is removed. The under comprehensive survey. Of the man ment in his preface—"This book proceeds tas k of a compositor is made harder by the from whom we wanted it there has never been directly to particula r problems showing in each necessity of printin g (e.g.) r3 in th e numerator an y question—the name of Timoshenko comes o case under what conditions the question of as a fractional expression when r could quite inevitably into any discussion of clastic stabi­ o stability calls for consideration. " Having said well have been replaced by a. lity ; but we hardly dared to hope that he tha t this is a book for the specialist and for the These are very minor blemishes, and they would undertake, in th e full flood of his own research worker, one is boun d in logic t o judge could very easily be eliminated in a second creative work, this rather thankless task of it from that standpoint—and then, from a edition, which I believe will be wanted soon. broad survey, only one impression can emerge : For this is a book with which no aeronautical *THEORY OF ELASTIC STABILITY. By Professor S. P. Timoshenko. it is th e work of a master, powerful alike in designer, no teacher or research student can [McGraw-Hill. 36s.] conception and in performance. afford to dispense. It will become a classic work. † Professor of Engineering Science in the University of Oxford. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

A Classic Textbook

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Emerald Publishing
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0002-2667
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288 AIRCRAFT ENGINEERIN G October, 1936 Professo r Timoshenko's "Theory of Elasti c Stability" Reviewed By R . V. Southwell , M.A., F.R.S., F.R.Ae.s.† ITHI N the limits set b y practical con­ survey in a field where change is rapid and Inevitably, as one turn s to detail, personal siderations, stresses in engineering continuous. The publication of this volume is predilections give a bias to one's judgment. materials entail almost exactly pro­ a major event. Thus, as i t seems to me, more frequent appeal portionate strains. But in bodies of elongated I have listened to Timoshenko's lectures, might have been made to considerations of shape, such as rods or thin sheets, displace­ with admiration verging on env y of hi s perfect strain-energy, especially in the later chapters ments are not necessarily proportionate to the technique, and I have witnessed his stimulating which present the difficult theory of thi n plates strains of which they are the integrated result, guidance of research students; but always, in and shells. The energy method which we and hence, for such bodies, Hooke's law may m y mind, his name has stood for learning—for associate (primarily) with the name of Rayleigh hold in respect of some types of displacement is, in Timoshenko's hands, a much-used and tha t encyclopædic knowledge which in this bu t not of others. Applying end thrus t to a very powerful tool; but relatively little is said country we who work on similar problems so long straight rod (or strut), and measuring the often lack. Yet eve n so, in a first reading of about its fundamental basis—it is presented consequent approach of th e ends, we find that this book, his eruditio n is as impressive as his rathe r as a n ingenious device which "works." this increases faster than in proportion to the grasp of th e practical implications of a theo­ Rayleigh is given credit for originating the study thrust ; under a load which would have been retical result. To my shame I have realised of inextensional deformations in rings and shells, quite safe applied as tension, the stru t bows how many names appear in his authors' index and incxtensibility is assumed in the investi­ largely and ceases t o hav e value as a compres­ of which I had not even heard, and in contrast gations of §39, 78 ; but I have not found sion member. mention of Rayleigh's argument, that since I can recall only two important investigations extensional energy is proportional to the of which the book does not tak e cognizance— This is th e simplest example of failure by th e work of W. R. Dean on circular plates in thickness, flexural energy to it s cube, the ex ­ elastic instability, and its essential features were torsion and on corrugate d plating, and that of tensional strains must have the order of the explained by Euler nearly two hundred years A. Robertson on solid struts. If with no other thickness (at least) in order to satisfy the con­ ago : his calculations proved, what Musschcn- purpose, British research workers should read dition of minimum strain-energy. broek's experiments had already shown, that this book in order to acquir e a fitting humility. th e resistance of a slender strut is inversely The notion of th e "reduce d modulus" E. proportional (other things being equal) to the They will gain much besides. In an y investi­ (taken over from the theory of struts which fail square of its length. A sermon might be gation concerned with elastic stability there is a t stresses beyond the elastic limit) is applied preached upon this text to "practical " engi­ (or should be) first, a stage of difficult work b y Timoshenko very boldly to problems of neers who would, if the y had their way, repress done with exhilaration—the analytical treat­ much greater complexity: considering how in our engineering schools all thinking not ment of the problem; secondly, a stage of little we know as ye t about the details of plastic directly related to some problem of immediate hard work done under boredom—the presenta­ distortion, I confess to some feeling of hesitation. importance : for over 100 years engineers dis­ tion of results in curves or numerical tables; I n his treatment of heated bimetallic strips regarded the theor y of Euler and th e experi­ and finally, a stage in which engineering (§45) I suspect that account should have been ments of Musschenbrcck, and b y many even judgment is used t o determin e their application take n of curvature across the width, as well th e work of Bauschinger, Considère and Tet- t o practical design. This third stage is too often as along the length ; the bent strip will, I majer, published in 1889 an d after, was regarded shirked—one suspects for the reason that it think, be par t of a spherical, not a cylindrical as "academic" ; not until the Quebec Bridge calls for th e hardest thinking. No stage is surface. And I wonder whether the problem disaster, early in thi s century, did they recognise omitted in Timoshenko's book: it faces boldly (§47) of the lateral buckling of a narrow tha t these studies might after all b e justified, this question of practica l significance, and makes rectangular cantilever, which (p. 248) is of and even then (despite the evidence of Fair- recommendations which, whether they are importance only when the breadth is very bairn's experiments in connection with the accepted or not, cannot be dismissed on the small in relation to the depth, can really be Britannia and Conway bridges) the elastic plea tha t they are vague. treated safely on th e assumption that the cross- stability of flat plating was left as a harmless section docs not change its shape ; I suspect The result is a mine of information—exactly exercise for mathematicians and the less tha t a different result might be obtaine d using th e kind of information for which designers practically-minded of academic engineers. Aero­ th e theory of flat plates. But these arc my have so long been waiting; they can learn here nautics has altered the picture—no problem in only real difficulties, and probably they can be of everything tha t has been done, and what is its elastic stability could well be harde r than that resolved : one could hardly hope to find none significance for their problems. But, if they of monococque construction; but we d o not in reading 500 closely reasoned pages. desire to understand as well as t o apply, they recognise the true lesson of these historical mus t be prepared to mine. This, as it seems Paper and printing are satisfactory, and th e facts, merely because we now find reason to ad ­ t o me, is a monograph for th e specialist an d diagrams admirably clear, but I must own to mit one more branch of stud y to respectability. th e research worker, rather than a text-book regret that the simplicity of formulas, especially To the aeronautical designer not only struts which can be placed in th e hands of a student those involving integrals, is often impaired by and plates, but tubes, curved shells and com­ after he ha s covered the ground of a n honours unnecessary suffixes and by unwillingness to posite structures, present a possibility of course in Engineering Elasticity. It is too introduce a factor 2. Only with very wide failure by instability . He needs t o hav e avail­ complete, too detailed in its treatment, to make freedom in th e use of founts (which is no t a able all researches in thi s field—and the litera­ attractiv e reading for one who ha s had no feature of this volume) can the integral tur e is large and scattered. Not everyone ca n special contact with its subject. read German easily, very few (in this country) A student, however, may expec t to receive can read Russian a t all ; yet to disregard papers Timoshenko's material through the mediu m of be saved from inelegance : denote (with in those languages is t o lose the greater part of lectures ; it would not be fair to attempt recent work. So for years we have wanted th e criticism from his standpoint (e.g. b y regretting book which now becomes available, in which the th e absence of examples whereby he ma y test Rayleigh, Kelvin and Love) the thickness of a results of theory and experiment are brought his grasp), in view of th e author' s clear state­ plate by 2/i, and all difficulty is removed. The under comprehensive survey. Of the man ment in his preface—"This book proceeds tas k of a compositor is made harder by the from whom we wanted it there has never been directly to particula r problems showing in each necessity of printin g (e.g.) r3 in th e numerator an y question—the name of Timoshenko comes o case under what conditions the question of as a fractional expression when r could quite inevitably into any discussion of clastic stabi­ o stability calls for consideration. " Having said well have been replaced by a. lity ; but we hardly dared to hope that he tha t this is a book for the specialist and for the These are very minor blemishes, and they would undertake, in th e full flood of his own research worker, one is boun d in logic t o judge could very easily be eliminated in a second creative work, this rather thankless task of it from that standpoint—and then, from a edition, which I believe will be wanted soon. broad survey, only one impression can emerge : For this is a book with which no aeronautical *THEORY OF ELASTIC STABILITY. By Professor S. P. Timoshenko. it is th e work of a master, powerful alike in designer, no teacher or research student can [McGraw-Hill. 36s.] conception and in performance. afford to dispense. It will become a classic work. † Professor of Engineering Science in the University of Oxford.

Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Oct 1, 1936

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