Engineering

"The mortar used for the mix is made (using a mixture) of normal or ic cement and sand in a proportion of 1:1.5 by volume and with a water-cement ratio of 0.55."

"The reinforcement consists of two no. 2 bars along the edges, one of them straight and the other one with the necessary bends to provide the handles to lift and fix the dome to the structure. ...[T]wo layers of galvanized chicken wire, guage 22 with a separation of 13 mm are attached to the bars and directly mounted over the mold, one perpendicular to the other. ...[E]nsure a minimum overlap of 5 cm... and... ensure that these are stretched... to achieve the thinnest section possible."

"The construction of the mold simply consists of making a dome of well compacted earth, covered by a layer of well-finished concrete having a thickness of 8 cm [3.15 inches], with the shape defined by the trusses... used to [shape] the mold."

"The adaption of ferrocement precast roofings in self-help construction projects... permits the use of standard components which are easily erected without sophisticated equipment."

"[I]t was decided to develop a type of roofing based on prefabricated sections. ...With the partial results obtained in this stage, another part of the study could be initiated, i.e. to build this same type of element "in situ"... thus providing solutions for situations in which prefabrication is not appropriate..."

"Ferrocement was chosen as the material for the proposed roofing because of its physical properties (strength in compression and tension, impact, permeability, etc.) and because it is cheap and easy to build."

"[These] low cost, easily built, high quality ferrocement roofings... offer an innovative solution to the serious dwelling problem affecting large numbers of people, especially in the marginal urban areas and rural zones of developing countries..."

"The hull was left untouched for 18 hours after the plaster finishing work had ceased. This allowed the hull to set-up hard enough for the men to drag the steam tent over it. It is not advisable to start steam curing too soon, as the jets of hot water from the steam pipe may wash some of the mortar off the hull while it is still green. Before steam curing began the wooden screeds were removed from around the hull sheer."

"The hulls were steam cured for 24 hours at a temperature of 150°F (66° C). A steam pipe, perforated for its entire length, was placed under the inverted hull and a rubberized canvas steam tent drawn completely over. The temperature was carefully brought up to 150°F (66°C) in a period of four hours. Twenty-four hours were then maintained at this prescribed temperature until, finally, it was allowed to drop slowly to ambient temperature of 85° F (30°C)."

"First a heavy coat was applied all over the hull. Men stationed inside the hull mold began systematically vibrating the mold planking and checking the gaps between the planking for mortar penetration. Once the mortar had all been applied to the satisfaction of the men vibrating and checking, the excess mortar was then scraped back to the mesh. ...A new thin coat was troweled over the hull and allowed to start setting. When it started to set the hull was sponge troweled, the sponge trowel being used in a circular motion to smooth out surface irregularities. As soon as the sponge troweling was finished, the final steel troweling began. This was carried on until the hull surface had set up too hard to be worked on any further, and was as smooth and fair as the plasterers could make it."

"The mortar used for the hulls was a mixture of clean, graded silica sand, ...Portland Cement Type II, and drinking-type water. This silica sand, of the grading and particle shape used in high-strength structures... The sand content used was... one 50-pound (22 Kg) bag of coarse grade, one 100-pound (44 Kg) bag of medium grade and one 50-pound (22 Kg) bag of fine grade. To this graded sand was added two 80-pound (31 Kg) bags of Portland Cement Type II and just sufficient water to make the mortar workable into the hull mesh reinforcing. ...There was one plasterer for roughly every 100 square feet (9 m2) ...Retarders or additives were not used. The sun shelters were moved into place ..."

"The last four layers of mesh were stapled to the hull mold. They were laid in the same way as the first layers. The mesh was fastened... as smoothly and as tightly as possible. It was clipped onto the horizontal rods with 3/4-inch (19 mm) hog rings. ...One-half inch (12.7 mm) hog ring staples which do a neater job could not be located ...All edges of the mesh were stapled down tightly so that no stray ends of mesh would penetrate later through the fresh mortar and thus interfere with the plasterers' work... Mesh over the chain link scuppers was clipped away and the ends fastened down neatly."

"One-inch (25.4 mm) chain links were welded to the hull reinforcing cage where scuppers were to be placed. These links were aligned and welded in at deck level. ...[E]xposed steel pieces such as scuppers or screeds which require welding... should always be cleaned and protectively coated."

"Starter rods for the stem, webs, bulkheads, bilge stringers, and engine beds were welded in place. These starter rods were placed at approximately six-inch (152 mm) centers. They were six inches (152 mm) long where they extended through the hull. Quarter-inch (6.4 mm) holes were drilled for these... The starter rods were lap-welded to either the vertical rods or the horizontals, depending on their position."

"Wooden plugs of the same diameter as each through-hull fitting were cut out and placed on the mold in the exact position where the future through-hull fitting was to be installed later. These were cut from doweling and made one inch (25.4 mm) deep. A hole was drilled in the center of the doweling to ensure that the plug did not split when nailed to the mold. The mesh was cut away under the plug and trimmed neatly at the edges. Some attempt was made to place the doweling in a position clear of the intersecting rods."

"The horizontal rods were welded on. Where a rod terminated on the hull it was lapped for six inches (152.4 mm) with another rod and spotwelded. All the rod joints were treated in this same way. The rods were stapled at approximately three-inch (76 mm) centers. Every second intersection of horizontal with vertical rods was spot welded. As there were two layers of mesh between the vertical and horizontal rods, the mesh was faired smooth in this small area. Care was taken not to burn too large a hole in the plastic sheeting where the rod welding took place."

"Two more layers of mesh were stapled over the mold. Again 1" x 2" (25.4 mm x 51 mm) wide staples were used. The folded mesh was not lapped but just butted."

"The vertical rods were stapled firmly to the hull. An air-powered staple gun was used..."

"The first four layers of mesh were stapled to the mold over the plastic sheeting. Each length of mesh, already folded double, formed two layers. This first layer of mesh strips, 1-1/2 feet (457 mm) wide, was butted together. The second layer of mesh strips was laid out so as to cover the joints where the first layer was butted together, making a total of four layers of mesh."

"Clear plastic 4-millimeter sheathing was hand-stapled to the mold for two reasons: ...To stop the moist mortar from falling through the joints and gaps between the wooden battens planking the mold. ...To form a barrier between the wooden mold and the fresh mortar. If no barrier were placed the wood would draw moisture from the new mortar and reduce its final strength."

"One inch (25 mm), 21 gauge, hexagonal galvanized mesh was used. This mesh was the type manufacturers describe as "reverse twist," galvanized after weaving. Ten layers were applied... Four layers of mesh were stapled to the mold over 4-mil plastic sheathing. Two more layers of mesh were stapled over 1/4-inch (6.4 mm) diameter vertical reinforcing bars which had been stapled on at 6-inch (152 mm) centers. 1/4-inch (6.4 mm) diameter reinforcing bars were then stapled longitudinally over this second layer of mesh. This layer of reinforcing bar was spot-welded to the first layer at approximately every second joint. This second layer of horizontal rods was applied on 3-inch (76 mm) centers. The last four layers of mesh were hogring fastened to the outside of this last layer of rods."

"The construction method chosen was the inverted wooden mold. For hulls up to 50 feet in length, and for utilizing unskilled labor, this method has been shown to be most efficient. ...The shape and fairness of the hull is first established and checked with the quick and easy-to-build wooden mold. ..The use of air-powered staple guns to fasten mesh and rods to the hull mold is a quick and efficient method and can be performed with unskilled labor. ..Lamination of the concrete skin is eliminated as the mortar is applied from one side only and vibrated through the hull shell reinforcing. ...Sagging of large unsupported areas is avoided. The men work from the outside of the hull and downwards."

"[Ferrocement defined:] A thin walled construction, consisting of rich cement mortar with uniformly distributed and closely spaced layers of continuous and relatively small diameter mesh (metallic or other suitable material)."

"RECOMMENDATION 6: Ferrocement in Disaster Relief. After fires, floods, droughts, and earthquakes... [t]ransportation is often disrupted... Supplies of bulky conventional building materials may be stranded outside the disaster area, whereas the basic ingredients of ferrocement may be available on the site or easily transported. The versatility of ferrocement also reduces logistical supply problems: wire mesh, cement, sand, and water can be substituted for the metal used for roofing, woods or plastic for shelters and clinics, asphalt for helipads, steel for bridges, and so on. Moreover, most ferrocement structures, though built for an emergency, will last long after the emergency is over. ...[F]errocement could be used at a disaster site for many purposes: Transport facilities, from simple boats to barges, docks, marinas, helipads, and simple floating bridges or short footbridges as well as road repairs. ...Food-storage facilities, quickly designed to local needs and quickly built, to preserve emergency food supplies. ...Emergency shelters such as, for example, the quonset type of roof, which is easy to erect and highly efficient. ..Public health facilities, such as latrines and clinics, built with ferrocement roofs and stucco-type walls of the same wire mesh and mortar. ...[C]adres of ferrocement workers could be trained in emergency applications and the supervision of local laborers at the disaster site."

"A thin shell is a special kind of vault whose geometry may include many shapes. ...a three-dimensional form made thicker than a membrane, so that it can not only resist tension as membranes do, but also compression. On the other hand, a thin shell is made thinner than a slab, which makes it unable to resist bending, as a slab does. In short, thin shells are structures thicker than membranes, but thinner than slabs. Thin shells are made possible by the use of materials that work well under tension and compression. Masonry has no tensile strength... Only the availability of and made a thin shell possible."

"[W]elded wire reinforcement (WWR) [was] formerly known as welded wire mesh or fabric. Welded steel wire reinforcement is the predominant form... A grid of orthogonal longitudinal and transverse cold-drawn steel wires is welded together at every wire intersection... The size and spacing of the wires can vary... based on the requirements... Welded wire reinforcement can be epoxy coated or zinc coated (galvanized). ...Plain and deformed welded wire reinforcement is covered in... ASTM A1064... Stainless steel wires are specified according to ASTM A1022... Epoxy-coated WWR... in accordance with ASTM A884... Galvanized WWR... with ASTM A1060... Even plain wire used in welded wire reinforcement has both chemical bond and mechanical bond to the concrete. The mechanical bond results from bearing of the welded cross wires against the concrete in the grid of reinforcement."

"Bad ventilation, deep excavation, defective supports, etc., etc., annually bring death to thousands of miners, but this system of operation saves expenses, therefore augments the gains, and gives the mine owners no occasion to be sorry. Neither does the factory-pasha care how many of "his" laborers are torn and rent apart by machinery, poisoned by chemicals, or slowly suffocated by dirt and dust. Profit is the main thing."

"All minerals are limited and especially limited at an affordable rate. Since a techno-industrial civilisation needs minerals, any such civilisation is bound to reach a point where it can’t continue."

"Mining is a uniquely political enterprise. It requires permits and capital, as well as legal and moral defenses strong enough to withstand inevitable litigation."

"Bülfinger... suggests a parabolic relation of the formtension ∝ (distance from the neutral line) m, where the [exponent m] power is a constant to be determined by experiment."

"At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof. Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest."

"In the appendix Mr. Pearson has carefully analysed the conflicting notations of different writers, and proposed a very convenient terminology and notation, which would save great trouble if universally adopted. He has also given an account of experiments carried out by Prof. Kennedy in his mechanical laboratory, which have an important bearing on the limitations of the truth of Hooke's law, or in the language of elasticity, the constancy of the ratio of stress to corresponding strain. The present volume is an indispensable hand-book of reference for the mathematician and the engineer, and in the editing and printing must be considered a very fitting tribute to the wonderful industry and application of its projector, the late Dr. Todhunter."

"A semi-metaphysical hypothesis as to the nature of Elasticity was started by Descartes and extended by John Bernoulli and Euler. It is extremely unsatisfactory, but the attempt to found a valid dynamical theory by did not lead to any more definite results."

"General summary. As the general result of the work... previous to 1800... while a considerable number of particular problems had been solved by means of hypotheses more or less adapted to the individual case, there had as yet been no attempt to form general equations for the motion or equilibrium of an elastic solid. Of these problems the consideration of the elastic lamina by James Bernoulli, of the vibrating rod by Daniel Bernoulli and Euler, and of the equilibrium of springs and columns by Lagrange and Euler are the most important. The problem of a vibrating plate had been attempted, but with results which cannot be considered satisfactory."

"[Girard's] book forms... a most characteristic picture of the state of mathematical knowledge on the subject of elasticity at the time and marks the arrival of an epoch when science was to free itself from the tendency to introduce theologico-metaphysical theory in the place of the physical axiom deduced from the results of organised experience."

"The first section of Girard's treatise is concerned with the resistance of solids according to the hypotheses of Galilei, Leibniz and Mariotte. He notes Bernoulli's objections to the Mariotte-Leibniz theory; but remarks that physicists and geometricians have accepted this theory... [H]e thinks it probable that Galilei's hypothesis of non-extension of the fibres may hold for some bodies—stones and minerals—while the Mariotte-Leibniz theory is true for sinews, wood and all vegetable matters (cf. p. 6). As to Bernoulli's doubt with regard to the position of the neutral surface, Girard accepts Bernoulli's statement that the position of the axis of equilibrium is indifferent, and supposes accordingly that all the fibres extend themselves about the axis AC..."

"The book... introduction is occupied with an historical retrospect of the work already accomplished in the field of elasticity... [and] concludes with an analysis of Girard's own work."

"P. S. Girard. Traite Analytique de la Resistance des solides, et des solides d'e'gale Resistance, Auquel on a joint une suite de nouvelles Experiences sur la force, et Velasticite specifique des Bois de Chine et de Sapin. Paris, 1798. ...This work very fitly closes the labours of the 18th century. It is the first practical treatise on Elasticity; and one of the first attempts to make searching experiments on the elastic properties of beams. It is not only valuable as containing the total knowledge of that day on the subject, but also by reason of an admirable historical introduction... The work appears to have been begun in 1787 and portions of it presented to the Academie in 1792. Its final publication was delayed till the experiments on elastic bodies, the results of which are here tabulated, were concluded at Havre. ...We are... considering the period of the French Revolution."

"Euler... calculate[s] the flexure which may be produced in a column by its own weight. If y be the horizontal displacement of a point on the column at a distance x from its vertex, the equation Ek^2 \cdot \frac{d^2y}{dx^2} + b^2 \int_0^y xdy = 0 is found, where the weight of unit volume of the column is unity and its section a square of side b. ...[I]f a be the altitude of the column and m = Ek^2/b^2, it is found that the least altitude for which the column will bend from its own weight is the least root of the equation,0 = \frac{1 \cdot a^3}{4! m} + \frac{1 \cdot 4 \cdot a^6}{7! m^2} - \frac{1 \cdot 4 \cdot 7 \cdot a^9}{10! m^2} + \frac{1 \cdot 4 \cdot 7 \cdot 10 \cdot a^{12}}{13! m^2} - \mathrm{etc.}Euler finds that this equation has no real root, and thus arrives at the paradoxical result, that however high a column may be it cannot be ruptured by its own weight. <!--(77-78.)p.45"

"Determinatio onerum quae columnae gestare valent. Examen insignis paradoxi in theoria columnarum occurrentis. De altitudine columnarum sub proprio pondere corruentium. [all in] Acta Academiae Petropolitanae [1778, 1780]. The first memoir... points out that vertical columns do not break under vertical pressure by mere crushing, but that flexure of the column will be found to precede rupture. ...[Euler] proposes to deduce a result which is now commonly in use... to find an expression connecting Ek^2 with the dimensions of the transverse section of the column. Euler finds Ek^2 = h \cdot \int x^2 ydx, where x and y... Euler appears however to treat the unaltered fibre or 'neutral line' without remark as the extreme fibre on the concave side of the section of the column made by the central plane of flexure. Thus for a column of rectangular section of dimensions b [with]in, and c perpendicular to the plane of flexure, he finds...Ek^2 = \frac{1}{3} b^3 ch, and the like method is used in the case of a circular section."

"If Q be the total weight of the beam the differential equationEk^2 ad^3 y + Pa (dx)^2 dy + Qx(dx)^2 dy = 0is obtained... This is reduced by a simple transformation to a special case of Riccati's equation, which is then solved on the supposition that \frac{Q}{P} is small. Euler obtains finally for the force P, for which the rod begins to bend, the expressionP = \pi^2 \cdot Ek^2/a^2 - Q \cdot (\pi^2 - 8)/2\pi^2;which shews that the minimum force is slightly reduced by taking the weight of the beam into consideration."

"Euler deduces the equation for the curve assumed by the beam AC fixed but not built in at one end A and acted upon by a force P parallel to its axis. If RM be perpendicular to AC and y=RM, x = AM, he finds\frac{y}{\theta}\cdot \sqrt{\frac{P}{Ek^2}} = sin(x \sqrt{\frac{P}{Ek^2}}),where \theta = \angle RCM. Hence since y = 0, when x = a the length of the beam, a \sqrt{\frac{P}{Ek^2}} must at least = \pi, whence it follows that P must be at least = \pi^2 \cdot \frac{Ek^2}{a^2}. This paradox Euler seems unable to explain."

"If we consider a force F perpendicular to the axis of a beam (or lamina) so as to displace it from the position AC to AD, and \delta be the projection of D parallel to AC on a line through C perpendicular to AC, Euler finds by easy analysis D \delta = \frac{F\cdot a^3}{3\cdot Ek^2}, supposing the displacement to be small. This suggests to him a method of determining the 'moment of stiffness' Ek^2, and he makes various remarks on proposed experimental investigations. He then notes the curious distinction between forces acting parallel and perpendicular to a built-in rod at its free end; the latter, however small, produce a deflection, the former only when they exceed a certain magnitude. It is shewn that the force required to give curvature to a beam acting parallel to its axis would give it an immense deflection if acting perpendicularly."

"1757. Sur la force des colonnes, Mémoires de l'Académie de Berlin, Tom. XIII. 1759... is one of Euler's most important contributions to the theory of elasticity. The problem... is the discovery of the least force which will suffice to give any the least curvature to a column, when applied at one extremity parallel to its axis, the other extremity being fixed. Euler finds that the force must be at least = \pi^2 \cdot \frac{Ek^2}{a^2}, where a is the length of the column and Ek^2 is the 'moment of the spring' or the 'moment of stiffness of the column' (moment du ressort or moment de roideur)."

"Euler devotes his attention to the oscillations of an elastic lamina; the investigation is some what obscure for the science of dynamics had not yet been placed on the firm foundation of : nevertheless the results obtained by Euler will be found in substantial agreement with those in Poisson's Traite de Mecanique, Vol. II."

"Euler takes the case in which forces act at every point of the elastic curve; and he obtains an equation like the first volume of Poisson's Traiti de Mecanique."

"Euler... has hitherto considered the elasticity constant, but he will now suppose that it is variable... S, which is supposed a function of the arc s; \rho is the radius of curvature. He proceeds to find the curve which makes \int S ds/\rho^2 a minimum; and... finds for the differential equation of the required curve\alpha + \beta x -\gamma y = S/\rho where \alpha, \beta, \gamma are constants."

"Euler gives... his investigation of the elastic curve in what he has just called an a priori manner. But this method is far inferior to that of James Bernoulli; for Euler does not attempt to estimate the forces of elasticity, but assumes that the moment of them at any point is inversely proportional to the radius of curvature: thus he... writes... an equation like... Poisson's Traite de Mecanique, Vol. I., without giving any of the reasoning by which Poisson obtains the equation."

"[S]tating that Daniel Bernoulli... had discovered... that the vis potentialis represented by \int ds/R^2 was a minimum for the elastic curve, Euler proceeds to discuss the inverse problem... The curve is to have a given length between two fixed points, to have given tangents at those points, and to render \int ds/R^2 a minimum... No attempt is made to shew why... By the aid of the principles of his book Euler arrives at the following equations where a, \alpha, \beta, \gamma are constants,dy = \frac{(\alpha + \beta x + \gamma x^2)}{\sqrt{a^4 - (\alpha + \beta x + \gamma x^2)^2}}from this we obtainds = \frac{a^2 dx}{\sqrt{a^4 - (\alpha + \beta x + \gamma x^2)^2}}"

"The celebrated work of Euler relating to... the Calculus of Variations appeared in 1744 under the title of Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. ...an appendix called Additamentum I. De Curvis Elasticis ...commences with a statement... shewing the theologico-metaphysical tendency... so characteristic of mathematical investigations in the 17th and 18th centuries. It was assumed that the universe was the most perfect conceivable, and hence arose the conception that its processes involved no waste, its 'action' was always the least required to effect a given purpose. ...Thus we find Maupertuis' extremely eccentric attempt at a principle of Least Action. ...[I]t is... probable that physicists have to thank this theological tendency in great part for the discovery of the modern principles of Least Action, of Least Constraint, and perhaps even of the Conservation of Energy."