Elementary Statics Research Articles

Helicopter blade droop as an application of simple beam theory

It is a commonly observed fact that the blades of a helicopter droop under their own weight when the aircraft is static but become almost straight when they start spinning. This phenomenon is commonly attributed to ‘rotational stiffness’. In this short article we present a simple calculation for the shape of the blades of a helicopter in static and rotating condition. We show that the deflection or droop of the tip of the blade reduces by a factor of about 30 when it changes from static to full-speed rotation. This calculation is at the undergraduate level and can complement a course in differential equations, elementary statics or elasticity theory.

On the Treatment of Statical Indeterminacy in the Elementary Statics of Particles and Rigid Bodies

The inability to determine reactions beyond a maximum of six for a three-dimensional rigid body (or three for a planar rigid body) is termed statical indeterminacy and represents a flaw in the elementary statics of particles and rigid bodies because the indeterminate reactions cannot be obtained by methods developed from within the subject. As noted in virtually every modern textbook on statics, statical indeterminacy may be resolved by relaxing the assumption of structural rigidity. This theory forms the content of the mechanics of deformable solids, which considers the stretching, twisting and bending of elastic bars. The indeterminacy may also be resolved by maintaining structural rigidity but relaxing the assumption of support rigidity. Because deformable supports may be modeled by lumped linear and torsional springs (which are traditionally part of the statics of particles and rigid bodies), analysis of statically indeterminate reactions in such systems utilizes no new concepts except that of rigid body translation and rotation. The purpose of this paper is to demonstrate, by means of example, that this class of statically indeterminate problem is amenable to simple solution and therefore should be treated in standard presentations of the subject.

Applying elementary statics to a historical anemometer

A simple analysis of the basic plate anemometer shows how its sensitivity depends on the wind speed and the mass of the plate.

System Theory in a Unified Curriculum

The incessant search for unifying concepts in engineering education has, in recent times, stepped up its pace to match the tempo of our scientific and technological progress. Although a single unified curriculum for all engineering problems would indeed be a utopia, there is hope, nevertheless, that certain apparently diverse areas of engineering can be regrouped with emphasis on the basic disciplines underlying them. System theory, which is briefly exposed here, is one such fundamental discipline with its mainsprings in the mathematical model of linear-graph theory. The chief assertion of this paper is that system theory could very well serve as a basis for unifying the areas of 1) circuit theory, 2) circuit aspects of electronics, 3) rotating machinery, 4) elementary statics and dynamics, and 5) system analysis. The ideas presented here are sufficiently supported by the authors' classroom experiences. In the light of the curriculum proposed, certain of the inevitable implications for Canadian electrical engineering are discussed.

Elementary Statics for Students of Social Science and Business. R. Clay Sprowls

Previous articleNext article No AccessBook ReviewsElementary Statics for Students of Social Science and Business. R. Clay Sprowls David L. WallaceDavid L. Wallace Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Social Service Review Volume 31, Number 1Mar., 1957 Article DOIhttps://doi.org/10.1086/640207 Views: 1Total views on this site Copyright 1957 The University of ChicagoPDF download Crossref reports no articles citing this article.

Problem of the Stillson Wrench

There seems to be some difficulty in understanding the basic principles underlying the working of the Stillson type of wrench, and the object of the present article is to elucidate these from considerations of elementary statics. It is found that such considerations suffice to give an explanation of the way in which the wrench works, and an attempt is made to give a measure of the efficiency of the wrench by deriving the “torque magnification factor.”

Cours de mecanique

IN order to avoid the current delays of printing, M. H. Beghin's book has been manifolded from typescript, a process which does not make for elegance; but the merits of the work are not thereby obscured. Based on lectures given at the Ècole Polytechnique, the first volume deals with kinematics, with elementary statics, and with dynamics of a particle and of simple rigid bodies, going as far as Lagrange's, Appell's and Hamilton's equations. Vector methods are used when appropriate, but are not overdone.

Elementary Statics: a Text-Book for Engineers. By M. Appleby. Pp. viii, 164. 7s. 6d. 1939. (Cambridge)

Elementary Statics: a Text-Book for Engineers. By M. Appleby. Pp. viii, 164. 7s. 6d. 1939. (Cambridge)

Examples in Elementary Statics and Dynamics. By R. C. Fawdry. With Answers. Pp. vii, 145, xviii. 3s. 6d. 1934. (Bell)

Examples in Elementary Statics and Dynamics. By R. C. Fawdry. With Answers. Pp. vii, 145, xviii. 3s. 6d. 1934. (Bell)

Elementary Statics of Two and Three Dimensions. By R. J. A. Barnard. Pp. 254. 7s. 6d. 1921. (Macmillan.)

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(1) Elementary Statics of Two and Three Dimensions (2) Theoretical Mechanics: An Introductory Treatise on the Principles of Dynamics, with Applications and Numerous Examples (3) and (4) Idromeccanica Piana

(1) PROF. BARNARD'S new book makes an ex-cellent text-book for the higher years in pass degree courses and for the first part of honours courses in applied mathematics. The scope is that generally expected, a chapter on forces in three dimensions being included. In treatment the book is orthodox and safe, so orthodox in fact that centres of gravity are left to quite a late chapter, as if the finding of centres of gravity were an aim in itself. The proof of the vector property of couples is very effective. (1) Elementary Statics of Two and Three Dimensions. By R. J. A. Barnard. Pp. vii + 254. (London: Macmillan and Co., Ltd., 1921.) 7s. 6d. (2) Theoretical Mechanics: An Introductory Treatise on the Principles of Dynamics, with Applications and Numerous Examples. By Prof. A. E. H. Love. Third Edition. Pp. xv + 310. (Cambridge: At the University Press, 1921.) 30s. net. (3) and (4) Idromeccanica Piana. By Prof. Umberto Cisotti. Parte Prima. Pp. xii + 152. Parte Seconda. Pp. viii + 155–373. (Milano: Libreria Editrice Politecnica, 1921.) Lire 24 and 32 respectively.

The Elementary Theory of Statical Stability

There are some problems in elementary mathematics that the average student is apt to consider as matter for memorising without any great effort being either useful or advisable at understanding them. Experience in teaching elementary statics shows that the theory of stability is an example of such a problem. The average student often does not appreciate the principle of the method generally adopted to investigate the stability of the equilibrium of one body resting on another. He is not generally in a position to grasp the significance of an “infinitesimal displacement,” or the meaning of “proceeding to the second order of small quantities” when the equilibrium is “neutral” to the first order. He is further puzzled by the fact that what appears to be neutral equilibrium becomes, when higher orders of small quantities are taken into account, stable in one case, unstable in another, whilst remaining neutral in a third. These difficulties can be overcome if we adopt a slight modification of the treatment given in the text-books. The object of this article is to explain the method used by the author for lecturing purposes, and not to obtain new results.

(1) A Textbook of Elementary Statics (2) A Shorter Algebra (3) Key to “A New Algebra” (4) Practical Surveying and Elementary Geodesy (5) Practical Science for Engineering Students (6) Bell's Outdoor and Indoor Experimental Arithmetics

(1) THIS is a delightful book that will rejoice the heart of the students of Birmingham and of many another university. No longer have we the problem of the elephant balancing upon a ball, the ball a foot in diameter and the elephant of negligible mass. In place of the old artificial kind we have, all the way through the book, entrancing problems from everyday life. In method of treatment also Dr. Heath's sympathies are of the widest. We find the link-polygon freely used, and that useful lettering device of Bow's not despised. We find graphical methods given their due place; we find bending moments duly treated; we find so many good thing that the book, though apparently designed for the pure mathematician, ought to be adopted by the engineer also.

(1) Easy Exercises in Algebra for Beginners (2) Plane Geometry for Secondary Schools (3) Cartesian Plane Geometry Part i (4) A Sequel to Elementary Geometry (5)Text-book of Mechanics Vol ii (6) Elementary Statics (7) Elementary Trigonometry With Answers

(1) Easy Exercises in Algebra for Beginners (2) Plane Geometry for Secondary Schools (3) Cartesian Plane Geometry Part i (4) A Sequel to Elementary Geometry (5)Text-book of Mechanics Vol ii (6) Elementary Statics (7) Elementary Trigonometry With Answers

An Introduction to Elementary Statics (Treated Graphically)

An Introduction to Elementary Statics (Treated Graphically)

An Introduction to Elementary Statics (Treated Graphically)

An Introduction to Elementary Statics (Treated Graphically)

An Introduction to Elementary Statics (treated graphically). By R. Nettell, M.A. 2s. (London, Edward Arnold.)

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A Treatise on Elementary Statics for the Use of Schools and Colleges. By W. J. Dobbs, M. A. London, A. & C. Black, 1901. (Pp. xi, 311.)

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A Treatise on Elementary Statics for the Use of Schools and Colleges

A Treatise on Elementary Statics for the Use of Schools and Colleges

University and Educational Intelligence

CAMBRIDGE.—Sir David Salomons, who founded in 1895 at Gonville and Caius College a scholarship to be called the Salomons Engineering Scholarship, has, on the occasion of the celebration of the 550th anniversary of the foundation of the college, increased the annual value of the scholarship from 40/. to about 70/. The scholarship is open to persons not yet in residence, and is tenable for three years. The person elected is to make a. declaration that he bona fide intends to enter the engineering profession as a civil and electrical engineer, and will, if required by the governing body of the college, become a candidate for the Mechanical Sciences Tripos. The next examination will be held on Tuesday, November 1, 1898. Candidates must not be more than nineteen years of age on October 1, 1898. The successful candidate will be required to commence residence in October 1899. The subjects of examination will be Euclid, Algebra, Plane Trigonometry, Geometrical and Analytical Conic Sections, Elementary Statics and Dynamics, and Differential Calculus Physics, including Dynamics and Hydrostatics, with practical work. Candidates must send their names, with testimonials of good conduct and certificate of birth, on or before Tuesday, October 25, to one of the tutors, the Rev. E. S. Roberts or Dr. J. S. Reid.