Chapter 4 Lewe, 1915; The Dissertation

It all begins with Love, 1892. See page A HISTORY OF SHELL THEORY DEVELOPMENT 1498 to 1906.

What is Lewe saying, and why the secrecy?

The figure showing a Love Wave is a useful illustration of the motion of forces that move and shape the tectonic plates of the earth. Imagine that this motion also occurs at the point of rupture of a beam as it fails, like a tearing motion. The wave motion demonstrated by Love is a result of the interference of many shear waves (S-waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side. 

Notice in the diagram that the Love Waves travel in alternating fashion. This motion occurs at particle scale forming a horizontal {elastic} line perpendicular to the direction of propagation (note alternating motion is of transverse waves). Moving deeper into the material, motion can decrease to a “node” and then alternately increase and decrease as one examines deeper layers of particle.

The figures below from Lewe are showing the same motion in water; at infinitessimal scale it is possible to analyse the forces that hold a molecule of water together, and it is this force that holds all atoms together; the Nuclear Force. At the centre of the molecule lies the Love Wave “node”, or centroid (of bending); here the wave propagation direction is rotational not longitudinal and so the transverse waves are relative to this circular motion. The angle of rotation vector is infinite, ie, it any point selected, at any infinitesimal scale, the tangent angle either side will not be identical – the line is never straight, at any scale. Lewe makes a simplification of this infinite angle change through use of a coefficient table, normalising infinity for calculation purposes. The coefficients can be quantised to the number of integers required to analyse the action of rupture of the elastic line; step changes of angle rather than a continuum, noting that another integer expressing angle change could be inserted in between any two other integers, but that a limit can be applied for calculation purposes. (Of course, at cosmic scale, this normalising of infinity through quantising of vector angle change will create false observations and measurements, so the graphical approach, which Lewe recommends in his Handbuch article, is more appropriate for comprehension of the Universe).

The rotating wave of the forces of tension and bending can be viewed (from the side) as Lewe’s Abb.5. The bending forces create this rotating shape in the tension forces, in this specific load case, showing an offset point of rupture between 2 and 3. Note the wave is divided into 6 sections; ie 5 hinged points are assumed between 7 supports and that, although not stated, this is one of 6 layers of the elastic line (see abb 14.) This figure should be one of six, showing the full cycle of one rotation.

The reference line from 0 to 6 is the z plane rotation about the centre support 3. Lewe shows it as straight, for simplification but, in Reality, the unbalanced rotating force flow is balanced by a bending of this z plane, relative to a horizontal x axis. At both atomic and cosmic scale this bending is the fundamental interaction of two orthogonal forces, Tension is Real, Bending is on the complex plane, and measured as the Fine Structure Constant (not dimensionless, it has units of arcseconds) although the resultant is directly observable in the Universe as the bending of light.

The elastic line in Abb. 14 is shown split into 6 horizontal layers at the interface of the cross-section and all forces are balanced. There were no diagrams in Lewe to illustrate the idea of the fields of force within the elastic line so this is my interpretation of abb. 3 to aid understanding of Abb.14

As the final figure in his theory, Abb. 14, Lewe shows that the motion of the nuclear force that creates the Elastic Tension exists as a balanced clockwise and anticlockwise twist. The blocks represent the load at point of rupture, splitting into 3 sections with motion relative to the gaps, and the waves are the tensile forces responding to this load motion.

Maximum torque in 01,23 or 45.

Maximum support moment X1.

Clockwise rotating moment for support 2.

Counterclockwise rotating moment for support 2.

Maximum supporting moment X2.

Note the load case in Abb.14 is divided only into 5 sections, not 6 as in Abb 5. and that the wave pattern does not repeat. By extending the load case to 6, and also the layers of the elastic line, it can be seen that the pattern repeats each moment, providing that the line does not actually rupture. In plan view the forces can be seen to take the shape of a rotating yin yang.

Load Case F (finish position after one rotation) = Load Case A. The load has been carried across the potential rupture site from left to right. This motion occurs at subatomic scale, within the duration of the energy doing the work, measured by Planck’s Constant, h. This means that all load cases occur at the same time through the cross section of the interface layers (measured relative to the matter that the force has created) so effectively stretching the load across the void and sustaining the atom for another moment. There are cavitations created between the layers, as the split load shifts and rotates, and the effect of all forces creates actions; some ideas are shown of what these may be.

Euler’s interim axis theorem is sketched to the left because the Nuclear Force directly relates to his rigid body axis theorem, in which he proves that an infinitesimal displacement of a rigid body causes one rotation at the centre. Lewe proves however that it is the one rotation of the Nuclear Force that causes an infinitesimal displacement of the rigid body. This displacement manifest as change of vibration m/s2 measured from within, and it is the vibration at the spherical surface that creates a seemingly solid body, measured with a duration in seconds, when experienced from without. The power of the rotation of the Nuclear Force, anticlockwise above, and clockwise below, is generated by the momentum of Earth’s mass, which creates and sustains all matter in the Universe, including itself and the Time in which it exists; and it exists at the centre of the Cosmos and the solar system. (There is an offset of the centroid of rotation of the three bodies of sun, earth and moon. The observed sun orbits about a point between the earth and the moon, the earth and moon rotate around each other about this point. All other observed planetary bodies orbit relative to the sun. Note that the solar system rotates on a flat plane because the linear expansion of the Nuclear Force is the z plane of all Universal rotation)

The intermediate axis theorem shows that the unstable axis is the axis of the smallest mass because it has the greatest mass moment. This moment exists at the centre of the planet, and the unstable axis is Earth’s magnetic poles, hence why magnetic poles switch with a cyclical regularity.

So Lewe proved that the Earth is the centre of the cosmos. That’s useful information I think.

In 1915, after 11 years as a consulting engineer, Lewe presents his method of analysing the motion of a node of the elastic line at particle scale – Matrix Calculus. His companion article in der Handbuch fits the brief for practical application for engineers, but it his Theory that completes the advance in Love’s ‘Natural Philosophy’ to prove the existence of absolute motion at the heart of the Nuclear Force of all substances, and instead of the moment of truth, opens the door for a new discipline, modern science, and a corrupted century of atomic weapons and energy; and with a general population kept in the dark.

The Application of Matrix Calculus to Continuous Beams and Framed Structures

From the Royal Saxon Technical College, Dresden

to obtain a doctoral-engineers approved dissertation

Presented by

Dipl.Ing Dr. sc.nat Viktor Lewe

From Loningen in Oldenburg

Referee: Professor W.Gehler

Co-referee: Gehelmer Hofrat Professor M Forster

Published by Robert Noske Borna-Leipzig.

Dissertation Publishing House, 1915

Notice that Viktor Lewe is using his Natural Science (sc.nat.), 1906 Physics Doctorate title for this paper. It is the only time that he uses it publicly {although how public this document was actually made at the time is not known. Lewe is almost entirely unknown today so it is likely that it had a limited print run, sufficient merely to meet the needs of the doctorate approval process. My copy was formerly in the collection of Prof.Ing Joh. Schlums, from his contemporary collection of academic works, and was in mint, unread condition when received. Although it has been well thumbed since} German Science had arrived at a watershed when ideology began to smother truth so Lewe can be seen as expressing the state of the art in 1915. The information within the dissertation is therefore presented with this provenance, that of Science, where matrix calculus is also being used with application to the theory of relativity – In the previous year, a Johannes Stein (2a), who is listed as the top student for the year under Alexander von Brill on wikidata (like Lewe a year later) , presents his physics doctorate dissertation called Contributions to matrix calculus with application to the Theory of Relativity, another completely unknown work, which is also in the author’s collection {Whatever happened to Johannes Stein?} – so the technique of matrix calculus can be applied to both loadings in beams and to quantum physics.

Contributions to matrix calculation with application to the theory of relativity.

Inaugural dissertation to obtain a doctorate from the Faculty of Natural Sciences at the Eberhard Karls University in Tübingen

presented by Johannes Stein from Glogau (Silesia).

Tübingen

Printed by H. Laupp jr,

1914.

Quantum physics is a description of the complex resultant of forces and effects of the Nuclear Force, bending, m4. Lewe proves that German Physics understood how to build an atomic weapon in 1915, and that, once you know that the Earth is centre of the cosmos and controls time and gravity, the real power of the nuclear force is the corruption of intelligence and control of societal psychopathy.

Introduction to translation

The translation is located in google dropbox: https://docs.google.com/document/d/18bKyKKXoQJ_KHTFJbQpZB1bGnrXZ-woY/edit#heading=h.gjdgxs

Translator’s Notes

14.10.23 – draft only. Translation is via Google and requires much refinement. Engineering terms require detailed understanding before the concepts can be fully understood, consequently many words and phrases have been left unchanged, with just likely syntax corrections shown as strikethrough of original and (suggested) in brackets . Nonetheless , Lewe’s Theory is being brought slowly out into the light. At last.

The dissertation is a Physics paper presented to Engineering. There is no evidence that the information it contains has ever been discredited, and therefore, until proved otherwise, the results demonstrated within should be considered as essentially correct, still current and still in use as a reference for work carried out in both Science and Engineering.

I consider that some information has not been provided, and the manner of the omissions suggests at least in some cases that the original paper may have had the rule run over it by another hand before it was published. For example, from my understanding of Lewe’s theory, there should be six figures, showing the rotation of the rupture point between 2 and 3 as a cycle. The clue is that Abb. 5 is introduced out of sequence and the force relationship shown is not actually referred to in the text. It is used merely to show the arrangement of fixed points j and k, either side of the intermediate supports. Lewe says ‘This possible solution is similar to the well-known graphical method , according to which, for example, when a field (layer) is loaded through an evenly distributed load, all supporting moments except those of the loaded field (layer) are achieved by a simple straight line using the so-called Clayperon. Fixed points J and K can be found according to Fig. 5

There is no need to include this complex diagram (which I believe is one of the six load case diagrams). He is simply illustrating that the fixed points are either side of the support. Has Lewe selected this diagram deliberately to try to slip it through the censor (and succeeded)? In terms of intention, that this diagram remains in his dissertation could be a deliberate attempt to evade censorship by Lewe the hero, or an oversight, by Lewe the villain.

Suspicions about a controlling hand are further confirmed by the 3rd issue of der Handbuch, in 1923. In 1915, Lewe wrote a foreword to his article, but in 1923, these paragraphs have been removed. The link to spending time as Hans Reissner’s assistant is not included, for example. {Reissner is in Brooklyn Illinois in 1942(20) and would be very well placed to pass information to the Portland Cement Association, also based in illinois. From Kurrer(22), it is known that Reissner assisted Lewe to gain habilation to Berlin University in 1920. Removing Lewe’s foreword in the 1923 issue does help to mask this connection, hence my suspicions}

It would appear that this guiding authority, which could even have been Lewe himself, has removed what it considered would lead an inquiring mind towards the world of water, gravity, subatomic force expressed as elastic modulus EI, with a negative Poisson’s ratio, and to Atomic Energy. Also, because Germany was at war, there was a much tighter ring drawn around any secrets that could lead to military advantage. I have attempted to call out the anomalies where I see them and replace or explain them, to aid clarity of understanding, but I may not have seen them all, yet. Notwithstanding these cuts, it is possible to use the information in this paper to begin to construct an atomic explosive device, (not recommended), and therefore it is a very clear indication that German Physics was aware of the Power of Nuclear Energy in 1915, Lewe proves it. That the paper was allowed to be presented and published at all speaks to some possibilities about why;

  • Perhaps the ideas were still in their infancy, and had not been fully grasped. The deliberate misdirections within the dissertation would seem to negate this
  • More interested in practical application of Theory. Move into Engineering to utilise funded opportunities to test his own work in practical fields
  • Lewe personal validation. A second doctorate in Engineering is a rare feat for a physicist. His discovery of absolute motion and the positive moment in the Nuclear Force is a triumph. He may have been allowed this validation for himself as recognition of his genius within his tight circle of peers.
  • Referencing. The document forms the theory that allows the engineering practice to be established in der Handbuch, the Concrete Manual. In the 1915 edition, Lewe hints at an underlying theory, basically claiming that a reference exists, but does not name his dissertation. So the trick the PCA pull in 1942, and which continues today – giving information with no provenance except ‘the theory’ – begins in 1915. For engineering practice to be established there MUST be a published reference. Lewe, 1915, shows the limits of just how oblique a reference can be and still be effective, however illegal. I believe it is this last option that is the most likely reason for publication.

Note that from Love, 1892, we know that the Engineering practice stands on shell theory and elastic planetary motion and provides a solution to Galileo’s problem. In der Handbuch(My refs 4, 5), Lewe provides a graphical method to read off coefficients (and his dissertation provides the table of coefficients on which these graphs are based). The full complexity and power of elastic theory can thus be brought to bear on engineering design practice with much reduced complexity; noting that, because the referencing is so weak, anyone using the design practice could be completely unaware of the link.

From ReynoldsBEng 2008:

I suspect that if the full truth was known at the time, Lewe’s work would not have seen the light of day at all, but we must be grateful that it was. Einstein’s General Relativity can now be seen in a new light, as a deliberate mis-direction. The secrecy begun then, in 1915, still continues today. Exposing the reference damage in the PCA tables and linking them to Lewe will open the door to a new understanding of Quantum and the Cosmos.

The paper was released to Engineering, not to Physics, because it meant that the secrets it contains, about shell theory applied at infinitely small scale, could be centrally controlled. I suspect there are only a handful of physicists today who are actually aware of this document, and it is this select group who have continued to develop the ideas for over a century. By releasing General Relativity in 1915, and then later, at the Solvay Conferences, Heisenberg and Born announcing that Quantum was a closed theory not subject to further modification, German Physics closed the door and laid plans. The Portland Cement Association, Illinois publication in 1942, Circular Concrete Water Tanks without Prestressing is based entirely on Lewe’s matrix calculus work, and yet makes no reference to him at all. This is the second break in the system. Now not just physicists are blind to Lewe’s work but Engineers too who are using it in practice; unless they are curious enough to seek the answer, they have no idea where the information they are using has come from. The seed of secrecy is extended to America in 1942, just in time for the Manhattan Project.

Hiding truth is an incredibly dangerous practice, but in Science, it is against all sense; the result already is catastrophic, with worse to come; atomic energy and reinforced concrete both slow Earth’s momentum because the energy they use is parasitic, literally acting against nature; ‘gravity-defying’ means that gravity is increased for everything else, for as long as the structure stands. At CERN’s behest, and with no evidence-based justification, the metre standard was changed in 1983 from a length of steel to a fraction of the speed of light. The link is then broken, and it is impossible to corroborate whether gravity is increasing or not. If light speed c2 m/s slows (which it is), the metre standard shrinks to accommodate. So now we are all blind, except the self-selecting few.

The Atomic age of glued Eisen und Beton, Iron and Concrete,  is causing a permanent drag on the planets orbital angular momentum. As Earth slows its rate of momentum, gravity increases. Each new reinforced concrete construction, each power plant fuel cell, each atomic explosion, brings us closer to the point of unsustainability. The magnetic pole switch is coming.

Who is more powerful, Nature’s Laws or man’s corruption of these laws?

Time will tell Reynolds BEng Oct 2023

What is Lewe proving?

To put it simply, Lewe proves that when a reinforced concrete shell structure is stable and carrying its own self-weight (plus any designed loading), then there is motion within the atomic structure of the centroids of each span. This applies to loadings in tanks, where the load is on the inside of the radius of the structure, and to arch structures or ceilings, where the load is on the outside. From Reynolds BEng:

Preface Summary – method history

(Lewe translation in bold, {Wikipedia information in square brackets],{Reynolds BEng comments in italics}

Note on references; Number in subscripts are Lewe references, reproduced below the preface text.

Lewe is generally referring mainly to the work of more Engineers not Natural Philosophers so refers to many sources not mentioned by Love, 1892,. Contributors referenced on ‘The History of Shell Theory’ page are denoted [HST] and the wikipedia entry has not been repeated, just the relevant work)

The (theory underlying) continuous beams on simple intermediate supports has been discussed for very many years, and by various authors. The first treatises only gave methods for calculating the column pressures, such as a method by Eytelwein (1808) and later also by Navier (1826) [HST] but these calculations are very complicated. {Lewe does not give a reference for these two works. Navier however is referred to by Love, 1892,  as being a new approach, using his general differential equations of Elasticity. In 1826, referred to by Lewe, Navier established the elastic modulus as a property of materials independent of the second moment of area. (E is the elastic modulus, I is the 2nd moment of Area) }

[Johann Albert Eytelwein (1764 – 1849) was a German engineer who was among the first to examine mechanical problems dealing with friction, pulleys, and hydraulics.  His major publication was the Handbuch der Mechanik fester Körper und Hydraulik (Handbook of Mechanics of Solid Bodies and Hydraulics)[editions in 1801, 1823, 1842] and the Handbuch der Statik fester Körper [1808, 1832]. In these works he examined pulleys and belts and the forces involved, developing on the theory of Euler. The Euler-Eytelwein Formula, also known as the capstan equation was one of the key ideas introduced by him.]

[http://www.engineeringexpert.net/accessed 18.3.24.

The Euler-Eytelwein formula examines friction between belts and pulleys through the relationship of tension between the belts on either side of the pulley. Excellent explanation here

{Lewe states 1808 but it is Eytelwein‘s method for calculating column pressures that Lewe is referring to, the link to pulley friction not being immediately apparent. Perhaps there is another work of Eytelwein that Lewe has access to? We know Eytelwein’s building department published the first German journal of civil engineering, Sammlung nützlicher Aufsätze und Nachrichten, die Baukunst betreffend, so Eytelwein may have contributed an article to this publication in 1808 specifically on column pressures.

Euler is a reference in Love regarding the former’s treatment of the problems of the elastica, and of the vibrations of thin rods. The theory behind the practical method of analysis of belt tension and friction in the Euler-Eytelwein formula assists with the definition of an elastic layer in a Love wave (a result of the interference of many shear waves (S-waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side, where friction is zero and elastic tension is relative to velocity, so here then is a link; the pulley formula is practical application of elastic theory to a specific problem in engineering}

It is immediately clear from this (albeit indirect) connection that Lewe’s theory then is not just specific to frames and beams, but also relates to the motion of the planet as an elastic body}

Bertot(1) {no information found} (Comptes rendus de la Societe des Ingenieurs  (Reports of the Society of Civil Engineers) 1855 p. 278.) published the first analytical relationship for the bending moments of continuous beams on simple intermediate supports at the same height through deriving the Theorem of Three-Moments for field loading.

The first consideration of unequal support heights and the well-known corresponding extension of the Theorem of Three-Moments can be found in the treatise by O. Mohr, Contributions to the Theory of Wood and Iron Construction(2). {Magazine article – Zeitschr. d. Arch.- u. Ing.-Ver. Hannover 1860 S. 323 u. 407 In his treatises on Technical Mechanics (2nd edition)}, O. Mohr, on p. 340, states that these above-mentioned equations are incorrectly attributed to Clapeyron even though they named after this author, since the equation cited by Clapeyron in the Comptes Rendus in December 1857 agrees with Bertot’s. Bertot’s work, however, seems to have remained quite unknown, since Mohr himself only cites Clapeyron as the discoverer of the Three-Moment law in his first relevant treatise in 1860.

{Interesting that Lewe is trying to correct the record on behalf of Bertot, which fact is a possible link to PCA, Illionis in 1942, via HM Westergarrd – see Lewe and the PCA page}

[Christian Otto Mohr (8 October 1835 – 2 October 1918) was a German civil engineer. He is renowned for his contributions to the field of structural engineering, such as Mohr’s circle, and for his study of stress.

In addition to a lone textbook, Mohr published many research papers on the theory of structures and strength of materials. In 1874, Mohr formalised the idea of a statically indeterminate structure. Mohr was an enthusiast for graphical tools {The same technique used by Lewe in his Handbuch article} and developed the method, for visually representing stress in three dimensions. In 1882, he famously developed the graphical method for analysing stress known as Mohr’s circle and used it to propose an early theory of strength based on shear stress. He also developed the Williot-Mohr diagram for truss displacements and the Maxwell-Mohr method for analysing statically indeterminate structures, it can also be used to determine the displacement of truss nodes and forces acting on each member. The Maxwell-Mohr method is also referred to as the virtual force method for redundant trusses. He retired in 1900, yet continued his scientific work in Dresden until his death on 2 October 1918. {Mohr and Lewe are both located in Dresden in 1915}

[Benoît Paul Émile Clapeyron (1799 – 1864) was a French engineer and physicist, one of the founders of thermodynamics. Clapeyron graduated in 1818. He also studied at École des mines {a similar career to H Carpenter}. He supervised the construction of the first railway line connecting Paris to Versailles and Saint-Germain which was financed by Adolphe d’Eichthal, Rothschild, Auguste Thurneyssen, Sanson Davillier and the Péreire brothers.

In 1834, he published a report entitled Mémoire sur la puissance motrice de la chaleur (Memoir on the Motive Power of Heat), in which he developed the work of the physicist Nicolas Léonard Sadi Carnot, deceased two years before. Though Carnot had developed a compelling analysis of a generalised heat engine, he had employed the clumsy and already unfashionable caloric theory. Clapeyron, in his memoire, presented Carnot’s work in a more accessible and analytic graphical form {so O Mohr and Lewe both refer to Clayperon and both use graphical techniques to translate theory to practice}. Clapeyron’s analysis of Carnot was more broadly disseminated in 1843 when Johann Poggendorff {an esteemed physicist} translated it into German.[3]

[[Nicolas Léonard Sadi Carnot (1796 – 1832) was a French mechanical engineer in the French Army, military scientist and physicist, often described as the “father of thermodynamics“. He published only one book, the Reflections on the Motive Power of Fire (Paris, 1824), in which he expressed the first successful theory of the maximum efficiency of heat engines and laid the foundations of the new discipline: thermodynamics. Carnot’s work attracted little attention during his lifetime, but it was later used by Rudolf Clausius and Lord Kelvin to formalize the second law of thermodynamics and define the concept of entropy .It was not until 1834 that Émile Clapeyron published an article in the journal of the École Polytechnique showing how Sadi Carnot’s ideas could be expressed mathematically while emphasizing their explanatory value, and it was not until the reissue of the Réflexions by this same author, supplemented by his comments, that Sadi Carnot began to gradually influence the scientific body.]]

In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot and made a definitive statement of Carnot’s principle, what is now known as the second law of thermodynamics.

These foundations enabled him to make substantive extensions of Clausius’ work, including the formula, now known as the Clausius–Clapeyron relation, which characterises the phase transition between two phases of matter.

Clapeyron also worked on the characterisation of perfect gases, the equilibrium of homogeneous solids, and calculations of the statics of continuous beams, notably the theorem of three moments[5] (

The influence of the design level of the supports {within the beam itself?} was first examined by Köpeke {no information found} in his treatise: On the dimensions of beam layers(3). {Magazine article – Zeitschr. d. Arch.- und Ing.-Ver. Hannover 1856. This is a key reference I think. The whole point of elastic analysis is to split the beam’s elastic line into laminar layers and then analyse at infinitesimal scale} However, this only examines the column pressures of continuous beams and the (but does show that) an assumed reduction of height of the support central columns indicates (there is) a numerical means of reducing the central column pressure {I think this means that Kopeke demonstrates that by allowing a degree of sagging in the design of the beam, by assuming lower central supports, would point to a means of calculating the reduced shear in the beam. So beam dimensions could be reduced within the limits of safety} In the treatise from 1860, however, Mohr warned against relying too much on the advantages of intentionally lowering the supports, in particular after Köpcke, which had been recommended by Scheffler(4){no information found on Scheffler} {perhaps indicating that you could theoretically design a ceiling say which allowed sagging across its width but that without a means to calculate the effect, it would be a fudge, and not recommended. Reference(4) is a Magazine article – Scheffler, Theorie der Gewolbe, Futtermauern and eisernen bracken (Theory of vaults, lining walls and iron bridges), Zeitschr. d. Arch.- und Ing.-Ver. Hannover 1857}

The first graphical treatment {The graphical approach of Clayperon and Mohr is introduced. Note that in Lewe’s 1915 handbuch fur Eiesenbetonbau article, he uses exactly this approach to allow engineers to read off coefficients} of the theory of continuous supports can be found in Culmann, Graph. Statics Zurich 1866 {note Lewe does not assign a reference to this work, see below } , who solved the most important parts of the problem analytically.

Carl Culmann (1821 – 1881) was a German structural engineer. Inspired by the work of Jean-Victor Poncelet, Culmann was a pioneer of graphical methods in engineering (“graphic statics“), publishing his seminal book on the topic, Die graphische Statik in 1865. Culmann had a profound influence on a generation of engineers including Otto Mohr]

{In 2013 M. Schrems & Dr. T. Kotnik published ‘On the extension of graphical statics into the 3rd dimension concerning the relationship between form and force flow and Culman’s work is also referenced by them, indicating that the graphical approach is a powerful tool}

Extract from Abstract of Schrems & Kotnik, 2013; Historically, they (graphic statics) were superseded by analytical methods, due to the relative ease of numerical calculations and the increasing importance of experimentation the developing discipline of engineering with its need for precision. Nowadays, however, with the availability of digital tools and the possibility of visualization of geometry in 3D space there is a re-emerging interest within architecture in graphic statics. It is because of this that a visual dialogue about
force flow based on graphic statics should be fostered because these methods offer a simple yet
precise way to discuss the geometrical dependency of form and forces.}

The basis of all graphic methods is the representation of the elastic line {Bernoulli Brothers and Euler} by O. Mohr(5). {Magazine again – 0. Mohr, Beitrag zur Theorie der Holz-und Eisenkonstruktionen (Contribution to the theory of wood and iron construction), Zeitschrift (magazine) of Arch.- und Ing.-Verein Hannover 1868 S. 19}. W Ritter-Zurich(6)  then applied this familiar (well-established?) drawing process (to his method). {reference 6 (The elastic line and its application to the continuous beam) is extensive and includes several articles by various Engineers. Lewe is referencing all the works associated with graphical analysis under a single reference. They must all make the same point that the process is robust, tried and tested. I think this is all supporting evidence that the graphical method IS the basis of the elastic influence line, so he can move on to his application of it, with matrices instead of graphs}

[Karl Wilhelm Ritter (1847 -1906) was a civil engineer, professor of the Swiss Federal Institute of Technology Zurich, and later rector of the Polytechnic Institute of Zurich (1887–1891).

In 1868, he became a railway engineer in Hungary, and in 1869, an assistant to Carl Culmann. From 1882 to 1905, he held a professorship of engineering in Zurich. Additionally, he would hold the rectorship of the Polytechnic Institute from 1887 to 1891. Ritter worked on the statics of engineering structures and the construction of bridges and railways at the Polytechnic Institute of Zurich. He also continued the teachings of Culmann as a theorist. He regarded statics as an engineering discipline and also developed kinematics. One of his students was Othmar Ammann. Ritter contributed to the theory of calculating reinforced concrete structures, and also wrote a number articles on the state of real structures.

The engineer Vianello(7) {no information found. Vianello, Der Durchgehendre Trager auf elastisch senkbaren Stutzen (The continuous beam on spring supports), Berlin 1904} was the first to graphically treat continuous beams as if on spring supports {ie assume that supports allow sagging in the beam, but construct with fixed supports to control and confine the sagging within the structure of the beam itself, on the elastic line}

[MR18] The English engineers Claxton-Fidler(8) {actually just one person. Claxton-Fidler, A practical treatise on bridge-construktion (sic), London 1. Aufl.1887, 3rd edition 1901.} already have a new general procedure in which both rigid and spring supports can be taken into account in the guidelines, but (their method) only take rigid supports into account {Lewe is saying that Claxton-Fidler missed a trick by not considering spring support as design method for beams with rigid supports, ignoring the elastic line}

[Thomas Claxton Fidler (1841-1917) was a British civil engineer, noteworthy for his 1887 book on bridge construction.]

This process was extended by Professor Ostenfeld(9) {Magazine A Ostenfeld, (Graphic treatment of continuous beams with fixed, spring, pinned and combined spring/pinned supports), Zeitschr. F. Arch. U. ingenieurwesen (Architecture? and Engineering) 1905 after 1903, Issues 1 and 2} in Copenhagen to include spring and pinned supports.

{Here is an interesting deviation in the history of practice post-Lewe. Lewe tells us that in 1903 Ostenfeld is designing using pinned and spring supports, but that on his wikipedia page it specifically states that his 1920 development of method uses ‘rigidly fixed members’. The finite analysis is allowed, but the influence of the elastic line is not revealed}

[Asger Skovgaard Ostenfeld (1866 – 1931) was a Danish civil engineer who specialized in the theory of steel and reinforced concrete structures. He is now considered to be the founding father of the theory of structures in Denmark. Around 1920, Ostenfeld extended Axel Bendixsen’s method of deformations together with the force method creating the dual concept of the method of deformations. His method represented significant progress in that “it enables previously analysed structural elements so to speak, to be built on”. This is achieved through the introduction of rigidly fixed members for the obstruction of joint rotations. It allows the complete frame to be divided into finite elements.]

{No information found on Axel Bedixsen, but several of his works are available here}

{The next section of Lewe’s introduction now moves towards using a table of coefficients instead of a graph. The advantage of the table over the graph from which it is derived is that the finite element is specific, and limits can be defined. Basically the design practice is to read off coefficients from a table and insert into simplified equations. The coefficients in the table are calculated by the designer of the method (in the early case by Winkler) – not by the engineer. This is example of simplification in practice, with complexity underlying; Theory simplified for practical use. This is Lewe’s ‘den mathematische weniger gewandten’  baseline. What does the engineer need to know for the design practice? Less is more}

The table-based treatment of continuous beams can be found first with Winkler .

[Emil Winkler (1835-1888) was a German civil engineer and professor with broad academic interest including engineering mechanics, railway engineering, bridge engineering. Emil Winkler was first to formulate and solve a problem of elastic beam on deformable foundation. The model of a beam on elastic foundation which assumes linear force-deflection relationship is known as Winkler Foundation{link broken on Wikipedia, substituted with this from Science Direct accessed 21.3.24. The method uses the Euler-Bernoulli elastic line}

Professor Winkler published in Prague two books: Lecture on Railway Engineering (1867) and Theory of Elasticity and Strength of Materials (1867). He also studied influence lines and came up with so called Winkler’s unevenness.]

The so-called Winkler numbers directly indicate the maximum and minimum moments and shear forces under field loads for continuous beams with up to five support points and taking equal field widths into account. The author (Lewe) found similar numbers for the same supports, but for line loads(10). {Magazine (supplement no. 22) Lewe, Winklersche Zahlen fur streckenlasten (Winkler’s numbers for continuous loads), Deutsche Bauzeitung 1913. Mitt. No. 22, Lewe referencing his work on Winkler’s numbers. Interesting that Winkler uses 5 way split to analyse, not 6. Lewe uses both in dissertation, but 6 is far superior in terms of understanding the motion of the Elastic Force at ultimate strength}

[Tables that give the lines of influence assuming the same moments of inertia everywhere were created by Lederer and Griot(11). {Published works located for sale but no information found on these engineers. I imagine the lines of influence as contour lines of equal load. Lewe’s later mushroom ceiling work in play here}

Müller-Breslau* states that supporting moments can be calculated linearly from the ordinates of two parabolas {link to Kombolcha Institute of Technology Department of Civil Engineering lecture notes} . The composition is done according to the formula {The lecture notes in the link do not use the notation defined by Lewe. I’m assuming this is the relation between linear velocity and angular velocity of circular motion in opposing directions. w is the rotation rate, u and v are velocity vectors in opposing directions creating M, bending}

{(*15?) No reference is given by Lewe at this point. Reference 15 is detailed but not referred to in the text. This may be error by Lewe? Note Ref 15 is S. Abhandlung von Hertwig in the denkschrift fur  Müller-Breslau (Treatise by Hertwig on the memoire of Muller-Breslau?) (Leipzig, Kroners Verlag) not also in chapter 1, Lewe references vgl. hierzu. Müller-Breslau, Neuere Methoden der Festigkeitslehre (Newer Methods of Strength of Materials) § 21.}

{Note that Muller-Breslau’s Greatest Force is mentioned also in Lewe’s 1915 handbuch article. In that article he also notes an error by Max Meyer (see his picking up on the error with Bertot above)}. Meyer references Muller-Breslau and it is Meyer’s work that Lewe draws on for the handbuch. But note Lewe is not referencing Meyer in this dissertation}

[Heinrich Franz Bernhard Müller (1851 – 1925), (known as Müller-Breslau from around 1875 to distinguish him from other people with similar names) was a German civil engineer who provided significant contributions to the theory of beams and frames in structural analysis. Müller-Breslau was both a practicing engineer and theoretical researcher during his lifetime.[4] He brought the previously separate elements of classical structural analysis together in a unified theory of beams and frames. He systematized the computational methods, in particular the principle of virtual displacements, and applied the energy sets systematically. He also calculated structures of airships. Based on his teaching skills he compiled his first textbook Elementares Handbuch der Festigkeitslehre (Elementary handbook of the strength of materials) in 1875. Two years later he wrote contributions on elasticity and strength as well as structural mechanics for Hütte – Des Ingenieurs Tachenbuch (Hütte’s engineer’s handbook).

Where u and v are constant and for w tables are specified.{u and v are velocities and vectors of twist – angular momentum. Units should be m/s2. Using coefficients is an excellent way of calculating seconds2, the matrix will be 3D 4×4. If you keep the coefficients in subsequent observations, then the s2 will be masked. Everything will be right, but nothing will be explained}

The following work takes a different path in that it starts from the well-known linear equations for statically indeterminate system of n-number (-fach) and takes into account the special characteristics of this system for the so-called Clapeyron’s equations to find a means of specifying a new and simple elimination procedure. Similar attempts to find a simple solution for the system of  linear equations with n-static indeterminates have previously always extended to the general system. Gauss(13){Börsch and Simon, (Treatises on the method of least squares ), Berlin 1887 p. 124; Bauernfeind, Vermessungskund (Surveying) 5th edition Bd. 2 s. 28.} has proposed the solution to the so-called Normal equations in the elimination calculation using the least squares method. He specified an elimination procedure, which is a precursor to determinant-theoretical procedures.

{Gauss is mentioned in Love, 1892 ‘The problem of curved plates or shells was first attacked from the point of view of the general equations of Elasticity by H. Aron. He expressed the geometry of the middle-surface by means of two parameters after the manner of Gauss‘}

[Gauss and Least Squares.  A method that assigns values to unknown quantities in a statistical model, based on the values found by minimizing the sum of squared deviations from the mean. The technique is described as an algebraic procedure for fitting linear equations to data and Legendre demonstrates the new method by analyzing the same data as Laplace for the shape of the Earth.

[Johann Carl Friedrich Gauss (1777 – 1855) was a German mathematician, astronomer, geodesist, and physicist who made contributions to many fields in mathematics and science. Gauss has been referred to as the “Prince of Mathematicians”. In 1809 he published his method of calculating the orbits of celestial bodies. Gauss…..succeeded in connecting the method of least squares with the principles of probability and to the normal distribution. He had managed to complete Laplace’s program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, and define a method of estimation that minimizes the error of estimation. Gauss showed that the arithmetic mean is indeed the best estimate of the location parameter by changing both the probability density and the method of estimation. He then turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter. In this attempt, he invented the normal distribution.]

The author’s intention, as indicated in the title, is to develop a purely computational method that can be used for all cases, the simple rules of which make it possible to quickly find the influence lines of the bending moments, transverse and abutment forces purely schematically. The method developed offers advantages over the known analytical and graphical methods in that it can be used for any design of the connection of the supports (free attachment, rigid connection, differences in the stroke, the moment of inertia and the base of the supports (British Civils terms – cantilever, fixed, trussed, continuous and simply supported beams)), even if the same is (these are) different for the individual sections of the treated support, deviations from the initially suggested schematic treatment of the simple running supports are easily noticeable {Lewe’s design makes assumption of sagging by assuming spring supports, which are not listed here (and not normally used in general construction; here they are a means of transferring theory into practice). The point he is making is that you can use any type of support. In Lewe’s scheme the purpose of the support is merely to prevent the sagging from occurring. Prevention of sagging is key to tapping the additional energy of motion of the Nuclear Force created within the steel at subatomic scale} 

The table attached to the sheet contains all the ordinates (coefficients).{Crucially, just as in the PCA Appendices, the means of deriving the coefficients is not shown}

Pirlet(14) {Der Eisenbau  (The Iron construction). Like a yearbook compilation perhaps?) 1910, 1914, 1915} applied this method to statically indeterminate systems in general and interpreted it as a solution method with a constant number of statically indeterminate solutions. A general approximation method for solving the linear system of equations is given by Hertwig

[Josef Pirlet (1880-1961), not on wikipedia, same age as Lewe. There is a scholarshop award in Acchen University in his name and one reference to a published work; Pirlet, J. (1910): Die Berechnung statisch unbestimmter Systeme (the calculation of statically indeterminate systems. In: Der Eisenbau, v. 1, n. 9 (September 1910), pp. 331-349.]

[August Hertwig (1872 – 1955), not on wikipedia, the son of a factory owner, began studying architecture at Berlin TH in late 1890, but switched to civil engineering in his first year there. He worked as an assistant to, among others, Heinrich Müller-Breslau. Hertwig was appointed professor of structural analysis and steel bridges at Aachen RWTH in 1902 on the recommendation of Müller-Breslau and therefore became the youngest professor in Germany; and he had not yet published anything! He was awarded an honorary doctorate by Darmstadt TH in 1924, whereupon he transferred to Berlin TH {a colleague of Lewe, who was a professor there from 1920 to 1936} to become Müller-Breslau’s successor. He remained at Berlin TH until 1937, where he became a sort of father figure, the head of the many branches of the Berlin school of structural theory]

Influence lines of the cross-sectional forces are directly in the form

where the resulting values of ​​e can be found in the table and the multipliers m can be calculated using the scheme (ie Lewe’s equations derived from his theory).

This simplification, especially in the treatment of continuous calculations with rigidly connected columns or multi-legged frames, will particularly benefit reinforced concrete construction, which will thereby be able to take into account the usual rigid support connection, through which the field moments are reduced . {Lewe is saying that with ‘cast-in’  columns, the additional strength can be included in design factors for the ceiling. Effectively this would mean thinner sections of concrete (shells). Indeed the purpose of Lewe’s design is to access the plastic strength of the reinforcement at the influence line cross sections. If the design of concrete is excessively thick, this reaction cannot occur, because the concrete will carry the load, not the steel} However, this simplification and combination of the treatment of all continuous types of beams can only be achieved by assuming that it is permissible to neglect the resulting elastic longitudinal deflections of the support points in the case of continuous beams with rigidly connected supports. {Elastic longitudinal deflection – What he means is that you can design assuming spring supports, which allow sagging of beam, but you don’t use them in practice. The design will include for fixed supports – in concrete these are likely cast in – see mushroom ceilings. The effect of this is that the deflection occurs internally at the very centre of the steel reinforcement on its particle thin elastic line, extending not in space, m, but into the bending of the Nuclear Force of the atoms of the steel, m4}. The admissibility of this assumption has already been dealt with exhaustively by other authors. Professor Ostenfeld in Copenhagen also introduced this premise in his treatise(16) on multi-stemmed frames. In the chapter “Beam Bridges” of the Handbook for Reinforced Concrete(17)edited by Professor Gehler {Lewe’s referent for this disertation} German reinforced concrete practice was also introduced to these simple formulas. {So, German Standards already allow for construction using the method Lewe is outlining, but now with Science behind the design, rather than perhaps mere engineering experience and intuition}

[ Asger Skovgaard Ostenfeld (1866 – 1931) was a Danish civil engineer who specialized in the theory of steel and reinforced concrete structures. He is now considered to be the founding father of the theory of structures in Denmark. Around 1920, Ostenfeld extended Axel Bendixsen’s method of deformations together with the force method creating the dual concept of the method of deformations. His method represented significant progress in that “it enables previously analysed structural elements so to speak, to be built on”. This is achieved through the introduction of rigidly fixed members for the obstruction of joint rotations. It allows the complete frame to be divided into finite elements.]

[Willy Gehler,(not on Wikipedia) born in 1876 in Leipzig, studied natural sciences and civil engineering. His greatest contribution to German and international civil engineering was the research, experimental testing and application of new materials. As the “father of standardization,” his comments and explanations on the new design specifications and standards for reinforced concrete elements and structures were relevant to other researchers and civil engineers. Unlike most of his colleagues, Gehler acted strongly politically. In the Weimar Republic, during the Nazi era and again in the GDR, he was a member of a political party. He joined the Nazi Party shortly after Hitler’s appointment as chancellor. He was also a supporting member of the SS. It is also known that he had performed numerous experiments for the Organisation Todt and the military on behalf of the SS.] {He also signed the ‘vow of allegiance’ to Hitler and the National Socialist State, along with 900 of his academic colleagues which effectively gave support to the purge to remove academics and civil servants with Jewish ancestry which began earlier in the year with a law passed on 7 April 1933.} {Lewe is not on this list}

  1. Comptes rendus de la Societe des Ingenieurs  (Reports of the Society of Civil Engineers) 1855 p. 278.
  2. Zeitschr. d. Arch.- u. Ing.-Ver. Hannover 1860 S. 323 u. 407.
  3. Zeitschr. d. Arch.- und Ing.-Ver. Hannover 1856
  4. Scheffler, Theorie der Gewolbe, Futtermauern and eisernen bracken (Theory of vaults, lining walls and iron bridges), Zeitschr. d. Arch.- und Ing.-Ver. Hannover 1857
  5. 0. Mohr, Beitrag zur Theorie der Holz-und Eisenkonstruktionen (Contribution to the theory of wood and iron construction), Zeitschrift (magazine) of Arch.- und Ing.-Verein Hannover 1868 S. 19
  6. Ritter, Die Elastische linie u. ihre Anwendung auf den Kontinuierlichen Balken (The elastic line and its application to the continuous beam) 1871, 2nd edition 1883; Die anwendungen der graph. statik (nach Culmann)  (The applications of graphical statics (according to Culmann)) (Part) 3 Tiel: Der konsein bekanntes zeichernerisches Verfahren aufgebaut (The consist was constructed using a well-known drawing practice?) 1900;
    • ferner siehe auch(further see also):
    • Lippich,  Theorie des Kontinuierlichen Tragers konstanten Querschnittes. (theory of the continuous support of constant cross-section). Elementare Darstellung der von Clayperon und Mohr begrundeten analytischen und graphischen Methoden und ihres Zusammenhanges (Elementary presentation of the analytical and graphical methods founded by Clapeyron and Mohr and their connections);
    • Förster’s Bauzeitung (construction newspaper) 1871. Winkler,  Vortage uber Bruckenbau (lectures on bridge construction), Vienna 1875. Bresse, Cours de Mécanique appliqué (Course of Applied Mechanics) 3 Tiel. (part)1865. M. Levy, La Statique Graphique (Graphical Statics) ( IIe (2nd) Partie, Paris 1886.
  7. Vianello, Der Durchgehendre Trager auf elastisch senkbaren Stutzen (The continuous beam on spring supports), Berlin 1904
  8. Claxton-Fidler, A practical treatise on bridge-construktion (sic), London 1. Aufl.1887, 3rd edition 1901.
  9. A Ostenfeld, Graphische behandlung der Kontinuierlichen Trager mit festen, elastisch senkbaren oder drehbaren und elastisch senk-und drehbaren Stutzen (Graphic treatment of continuous beams with fixed, spring, pinned and combined spring/pinned supports), Zeitschr. F. Arch. U. ingenieurwesen (and? Engineering) 1905 after 1903, Issues 1 and 2.
  10. Lewe, Winklersche Zahlen fur streckenlasten (Winkler’s numbers for continuous loads), Deutsche Bauzeitung 1913. Mitt. No. 22.[MR41] 
  11. Dr. {Arthur} Lederer, Analytisches Ermittlung und Anwendung von Einflusslinien (Analytical determination and application of lines of influence){Ernst und Sohn, Berlin 1908}. Griot, {Gustav} Tabellen zum Auftragen der Einsflusslinien (Tables for plotting the influence lines), Zurich 1904. 
  12. Graphische Statik (Graphical Statics) Bd. (Vol) 2 Abt. (Dept) 2.
  13. Börsch and Simon, Abhandlung zur Methode der Kleinsten Quadrate (Treatises on the method of least squares ), Berlin 1887 p. 124; Bauernfeind, Vermessungskund (Surveying) 5th edition Bd. 2 s. 28.
  14. Der Eisenbau 1910, 1914, 1915.
  15. S. Abhandlung von Hertwig in the denkschrift fur  Müller-Breslau (Leipzig, Kroners Verlag)
  16. A. Ostenfeld in Zeischr. Ingenioren 1905 (Kopenhagen) No. 13 s. 83.
  17. Hanbuch fur Eiesenbetonbau, 2nd Aufl (edition) Bd. 6 Kap.1 s. 222.

History summary

Three Moment Theorem

Table based method – Winkler

Graphical method

Least Squares method

Solution method

Approximate method

Computational method – Lewe’s matrix calculus

There should be a return to Graphical Method after computational

Preface Summary

Lewe gives a history of underlying theory for continuous beams on simple intermediate supports.

1855 and the Theorem of Three-Moments (Lewe shows integrity in referencing and points out that the equations should be named after the discoverer, Bertot, not the person they are named after in 1915, which is Clayperon).

1866 Graphical technique

1868 The technique of ‘beam layers’ is discussed, analysing beams as if constructed from laminar layers.

1904 Assume ‘spring supports’ at intermediate columns to allow sagging in the design (the slight difference between theoretical and loaded horizontal profile). Note that if the beam is allowed to sag a little, there is reduced shear overall, due to the increased strength of the reinforcement steel in its plastic range. It is this additional strength that Lewe is utilising, but without allowing sagging.

1904 Table-based treatment (early Coefficient tables) and Lewe states that supporting moments can be calculated linearly from the ordinates of two parabolas.

Lewe then states the basis for the theory in his dissertation and his intention to develop a purely computational method to quickly find the influence lines of the bending moments, transverse and abutment forces. He draws attention to the table of coefficients in the Appendices.

His method allows for the beams to ‘sag’ at the columns, as if the supports were springs. The fact that the columns are actually rigid means that the sagging cannot physically take place, so there is instead a stretching or stressing effect on the reinforcement steel. By designing the steel to stretch, but without physically being able to move, due to being contiguous with the concrete, the stretching force occurs within the atomic structure of the steel instead. It is this stretching force which exposes the motion of the Nuclear Force

The Theory

A beam supported at either end can be subdivided at any point with an assumed support, K. At this point there will be rotational forces acting in either direction

From Lewe, Figure 5. Imagine a loaded concrete beam subject to bending force from its own weight. In each assume the smallest possible point load