Table Of ContentA TREATISE
ON
THE STRENGTH OF MATERIALS.
WITH RULES FOR APPLICATION IN ARCHITECTURE,
THE CONSTRUCTION OF SUSPENSION BRIDGES, RAILWAYS, ETC.;
AND AN APPENDIX ON THE POWER OF LOCOMOTIVE ENGINES,
AND THE EFFECT OF INCLINED PLANES AND GRADIENTS.
BY PETEE BAELOW, F.E.S.,
MEM. INST. OF FRANCE J OF THE IMP. AND ROYAL ACADEMIES OF PETERSBURG!! AND BRUSSELS ;
OF THE AMER. SOC. ARTS J AND HON. MEM. INST. CIVIL ENGINEERS.
A NEW EDITION.
REVISED BY HIS SONS,
P. W. BAELOW, F.E.S., AND W. H. BAELOW, F.E.S.,
MEM. INST. C.E., MEM. 0£ COUNCIL INST. C.E.
TO WHICH ARE ADDED A SUMMARY OF EXPERIMENTS BY
EATOJST HODGKINSON, F.E.S.,
WILLIAM FAIEBAIEN, F.E.S.,
AND
DAVID KIEKALDY;
AN ESSAY (WITH ILLUSTRATIONS) ON THE EFFECT PRODUCED BY PASSING
WEIGHTS OVER ELASTIC BARS.
BY THE EEV. EOBEET WILLIS, M.A., F.E.S.
AND FORMULAE FOE- CALCULATING GIRDERS, ETC.
THE WHOLE ARRANGED AND EDITED
BY WILLIAM HUMBEE,
ASSOC. INST. C.E., AND MEM. INST. M.E.
WITH PLATES AND NUMEROUS WOODCUTS.
LONDON :
LOCKWOOD & CO., 7, STATIONERS' HALL COURT.
1867.
Published by ICE Publishing, 40 Marsh Wall, London E14 9TP.
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ISBN: 978-0-7277-5057-0
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this respect by the author or publishers.
LONDON :
BRADBURY, EVANS, AND CO., PRINTERS, WHITEFRIARS.
PKEFACE TO THE PEESENT EDITION.
A FIFTH edition of Professor Barlow's very valuable work
appeared in 1851. This, the Sixth edition, has been carefully
corrected ; and, although it is not increased in external dimen
sions, owing to the economy of space in printing, it has been
greatly enlarged, and will be found to contain much additional
interesting matter.
There have been no alterations of consequence in the first part
of the treatise—on the Strength of Timber. The following
important and valuable additions, however, have been made to
that part treating of Cast Iron : (1) Experiments by Eaton
Hodgkinson, Esq., on the Strength of Cast Iron of various denomi
nations ; (2) An extract from papers on the Transverse Strength
of Beams, by W. H. Barlow, Esq., F.R.S., with an appendix by
the late Professor Barlow; and (3) a short article on the Strength
of Cast Iron Columns. From the next division of the Treatise, the
description of the Proving Machine in Woolwich Dockyard, and
the article on the Comparative Strength of Parallel Rails of various
sections, have been omitted. There have been introduced experi
ments by W. Fairbairn, Esq., on Iron and Steel Plates, on the
behaviour of Girders subjected to the Vibrations of a Changing
Load, and on various cast and wrought iron beams ; also numerous
experiments by D. Kirkaldy, Esq., on wrought iron and steel bars.
At the end of the volume will be found a short Appendix of
formulae for ready application in calculating bridges and girders.
An explanation is necessary for the apparent want of order in
the distribution of some of the new matter that has been intro
duced ; more especially for that of placing experiments on Cast
Iron beams in the portion of the work devoted to Malleable Iron.
a 2
iv PREFACE.
It was thought advisable, however, to disregard strict classification
of material, in order that JVtr. Fairbairn's experiments might
appear together.
The entire work has been revised by Professor Barlow's sons,
Peter William Barlow, Esq., F.R.S., and William Henry Barlow,
Esq., F.R.S., to whom I beg to tender my sincere thanks, as also to
William Fairbairn, Esq., LL.D., F.R.S., and David Kirkaldy, Esq.,
for their valuable assistance.
As a small tribute of respect and esteem for the late Professor,
I have inserted a short memoir of his life, feeling confident that
it will be received with pleasure by the members of a Profession
for which he has done so much.
W. H.
ABINGDON STREET, WESTMINSTER,
August, 1867.
EXTRACT FROM AUTHOR'S PREFACE TO THE
FOURTH EDITION.
THE first edition of my " Essay on the Strength and Stress of
Timber " was published in 1817, since which it has gone through
three editions : another edition having been called for, I have
thought it right to remodel the whole, and to introduce into it a
great variety of matter not found in the original work. At the
time of the first publication, the construction of suspension
bridges was in its infancy; and the application of malleable iron
for the purposes of railways, unknown. These, and various novel
applications of timber, iron, and other materials, to different
mechanical works, have rendered it necessary to investigate ex
perimentally and theoretically, many subjects which were not
known when the first edition of this work was published, and
which it was difficult to introduce without remodelling the whole.
This has been accordingly done, and it is hoped that the utility
of the work has been thereby greatly increased.
MEMOIE OF PETEE BAELOW,*
HON. M. INST. C.E.
•
MR. PETER BARLOW was born in Norwich, in October, 1776, and was
sent at an early age to a foundation school, where he acquired a good
English education. He was then placed in a mercantile establishment in
Norwich, and while in that position and still at an early age, he, together
with some young friends of a similar turn of mind, formed a juvenile
scientific society, where they discussed questions in mathematics and the
physical sciences, for which young Barlow had a natural predilection, and
eventually, by his industry and perseverance, he acquired considerable
scientific knowledge.
The political excitement of the times broke up this little society, and the
members of it became dispersed, some entering the Army and others the
Navy, whilst Mr. Barlow, turning his attention to tuition, for which he had
partially qualified himself by careful study, although without enjoying the
advantage of good masters, obtained the mastership of a school. He soon
became a regular correspondent of "The Ladies' Diary," then under the
management of Dr. Hutton, Professor of Mathematics at Woolwich, under
whose advice Mr. Barlow was induced, in 1801, to become a candidate for
the post of additional Mathematical Master at the Royal Military Academy,
a position which was only obtained after a severe competitive examination.
There he became acquainted with Mr. Bonnycastle, to whose judicious
advice and assistance he always acknowledged himself to have been much
indebted. Under the same advice he, in 1808, commenced writing for the
" Encyclopaedia" conducted by Dr. Rees, and from the letter H to the end,
he contributed the majority of the mathematical articles of that work. In
1811 he published his first work on the " Theory of Numbers," and in
1814 appeared his " Mathematical Dictionary," and immediately after
wards his " Mathematical Tables," a work which has since been reproduced
by the Society for the Diffusion of Useful Knowledge. In 1817 he pub
lished the first edition of an "Essay on the Strength of Timber and other
* Excerpt Annual Report of the Institution of Civil Engineers, 1862-3.
vi MEMOIR.
Materials," founded on experiments made in the Dockyard and the Arsenal
at Woolwich, by permission of the Admiralty and of the Board of Ordnance.
While thus engaged he became acquainted with the late Thomas Telford,
and assisted him in experiments and calculations for his then proposed
structure of the Menai Suspension Bridge, and also conducted for him a
series of experiments on the tides in the Thames, in reference to the then
projected erection of the new London Bridge. In the report upon the latter
subject, the effects which the removal of the old London Bridge have since
manifested upon the bridges of Westminster and Blackfriars were fully
considered. About this time he also contributed many articles to the
" Encyclopaedia Metropolitana." In 1819 his attention was directed to the
variation of the compass needle and the local attraction of ships, and he was
induced to undertake a series of experiments, with a view to discover the
laws of the reciprocal action subsisting between magnets and simple iron
bodies, and to devise some means of correcting the errors of compasses on
shipboard. The Government liberally allowed him the facilities which the
Dockyard and the Arsenal at Woolwich presented for prosecuting these
experiments, and the laws of terrestrial magnetism which he, after much
labour, discovered, were subsequently confirmed by Captain Basil Hall,
Captain Mudge, and other officers. These laws and their proposed applica
tion for correcting the local attractions of ships formed the subject of his
Ci Essay on Magnetic Attractions," published in 1820. In a second edition
of this work, in 1823, it was shown that all the laws which had, up to that
time, rested on experimental deductions, were consistent with a certain
hypothesis of magnetic action, which theory was subsequently elaborated
and confirmed in a more general investigation of the subject by M. Poisson,
in a memoir read to the Institute of France in 1824. All doubt on the
subject being now removed, Mr. Barlow received numerous gratifying marks
of approbation. He was elected on the Council of the Royal Society, and
received the Copley medal. He also received the reward for useful dis
coveries, provided by Parliament, in connexion with the then existing
Board of Longitude. He further received a handsome personal present
from the Emperor of Russia, and was elected a member of the Imperial
Academy of Brussels, a corresponding member of the Institute of France,
and received many other similar distinctions.
On the 31st of January, 1825, he presented to the Institution of Civil
Engineers a communication " On the Force exerted by Hydraulic Pressure
in a Bramah Press ; the resisting power of the cylinder, and rules for com
puting the thickness of metal for presses of various powers and dimensions."*
Mr. Barlow next turned his attention to electro-magnetism, and was the
author of a work on that subject. While engaged in the experiments he
* Vide Trans. Inst. C. E., vol. i. p. 133.
MEMOIR. vii
conceived the idea of making electro signals by deflecting a magnetic needle
with a current of electricity, generated by a galvanic battery, and passed
along a conducting wire. With this object he caused an experiment to
be made upon a mile of copper wire, arranged upon posts in his garden,
at Rushgrove Cottage, Woolwich. The battery employed consisted of
about twenty pairs of plates 15 inches square. No insulation was given
to the wires, and no coil was employed to multiply the action upon the
needle. In this experiment, which contained the germ of an invention
destined afterwards to become of such important public utility, although
a certain amount of deflection was obtained, yet from imperfect insulation
increased length of wire was found to produce great loss of power, and as
other subjects of great interest occupied his mind at this time, he discon
tinued his experiments upon the electric telegraph.
Although engaged at this time in contributing articles to several
scientific works, he applied himself to the improvement of achromatic
object-glasses, on which subject he communicated a paper to the Royal
Society.* Pursuing this subject, he was led to try the effect of substituting
a fluid contained between two sheets of plate, or crown glass, instead of
using the concave flint glass lens, generally employed, and he constructed
two telescopes on this principle. Subsequently the Council of the Royal
Society engaged Mr. Dollond to construct a fluid lens telescope under his
superintendence, the result of which was satisfactorily reported upon by
Sir J. Herschel, Professor Airy, and Admiral Smyth.
Between the years 1833 and 1835 he was engaged in the prosecution of an
extensive series of mechanical and other experiments, and in the production
of a volume containing a description of '' The Manufactures and Machinery
of Great Britain."
The railway system was at this time in its infancy, and before Engineers
had established practical data, Mr, Barlow was much occupied in experi
ments, and in testing the strength and best form of section of railway bars,
the effect of gradients and curves, and in determining other questions.
In 1836 he was appointed one of the Royal Commissioners for determining
the best system of railways for Ireland, the report on this subject being
presented to Parliament in 1838.
In 1839 he was appointed on a similar commission for determining the
best route to Scotland and Wales, and the most convenient port for steam
communication with Ireland.
On the 5th of March, 1839, a Paper of his was read at the Institution of
Civil Engineers, entitled " An Investigation into the Power of Locomotive
Engines, and the effect produced by that power at different Velocities." j"
* Vide Phil. Trans., 1827, p. 231.
f Vide Minutes of Proceedings, Inst. C.E., vol. i. (1839), p. 46, and Trans. Inst. C.E.,
vol. iii. p. 183.
MEMOIR.
In 1842 he was similarly employed upon an inquiry into the general
merits of the atmospheric system, and in 1845 he was appointed one of the
Gauge Commissioners, in which he was associated with Sir Frederick Smith
and Professor Airy.
In 1847, being then seventy-one years of age, he retired from his duties
at the Royal Military Academy, and in consideration of his eminent public
services, the Government awarded him his full pay on his retirement.
From this time, although he ceased to engage in active professional duties,
he continued to take a lively interest in all the leading scientific questions
of the day.
So late as the year 1857, although he was eighty-one years of age, he
wrote a postscript to a Paper communicated to the Royal Society by his son,
Mr. W. H. Barlow, M. Inst. C.E., on the " Resistance of Flexure," which
postscript contained a mathematical investigation of considerable difficulty.
Mr. Barlow was elected a Fellow of the Royal Society in May, 1823, and
he was a member of most of the other scientific societies of this and other
countries. He joined the Institution of Civil Engineers as an Honorary
Member in 1820, and always took much interest in the proceedings. Of a
kindly and cheerful disposition, he retained his full powers of mind until his
death, which took place on the 1st of March, 1862, deeply regretted by his
numerous friends, and especially by those Officers, his former pupils, who,
whilst under his guidance at the Royal Military Academy, had ever found
him as valued a friend as a conscientious and talented tutor.
CONTENTS.
ART. PAGE
iii
Extract from Preface to the Fourth Edition . . .. iv
Memoir of Peter Barlow v
ON THE STRENGTH OF TIMBER.
Experiments on direct cohesion, by Musschenbroeck 2 . 2
the effect of seasoning 5 . 5
direct cohesion, at the Royal Military Academy 9 . . 10
lateral adhesion 13 . . 14
Mechanism of the transyerse strain 17 . . 16
Resulting formulae 28 . . 25
Mechanical action of the fibres to resist fracture . . . 30 . . 29
Resulting formulae 41 . . 34
On the deflection of beams 44 . . 36
Investigation relating to the elastic curve . . .. 47 . . 37
Another mode of investigating the amount of deflection . . 48 . 39
Deflection of beams supported at each end, and loaded with a
central weight 51 . . 43
The same, when uniformly loaded 52 . . 44
Deflection of beams as depending on their breadth and depth. 53 . . 46
Experiments on deflection . . . . . . .. 54 . . ib.
Dupin's experiments and deductions 60 . . 51
General practical deductions 63 . . 52
Experiments on the transverse strength of timber . 64 . . 53
by Buffon 65 . 55
by Beaufoy 67 . . 58
= by Peake and Barrallier 69 . . 59
by Couch 72 . . 63
on woods of different kinds, made at the Royal
Military Academy 77 . . 66
Determination of practical data . 99 . . 79
Table of Data 101 . . 82
