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STEPHEN P. TIMOSHENKO
December 23' 1878-May 29' 1972
BY C. RICHARD SODERBERG
THE MAJOR FACTS of the life of Stephen P. Timoshenko
are by now well known. He was born as Stepen Prokof-
yevich Timoshenko* in the village of Shpotovka in the
Ukraine on December 23, IS78. Stephen's father, born a serf,
had been brought up in the home of a landowner, who later
married Stephen's aunt. His father subsequently received an
education as a land surveyor and practiced this profession
until he himself became a lanclowner of some means.
Timoshenko's early life seems to have been a happy one,
in pleasant rural surroundings. The conclucling decades of
the nineteenth century were a periocI of relative tranquility in
Russia, and the educational ideals of the micldie class were
not much different from, and certainly not inferior to, those
of their counterparts in Western Europe. He concluded his
secondary education with a goicl mecial at the technical
realschule~f in Romny, near Kiev. His father hacl rented an
NOTE: The Academy would like to express its gratitude to Dr. I. P. Den Hartog for
his help in the preparation of this memoir after the death of C. Richard Soderberg
in 1979.
*The spelling of Russian names and terms follows that of E. H. Mansfield and
D. H. Young, "Stephen P. Timoshenko," in: Biographical Memoirs of Fellows of the
Royal Society, vol. 19 (London: The Royal Society, 1973), pp. 679-94.
t Professor Tichvinsky informs me that this designation was already used in Russia
to indicate preparation for entry into technical universities. In most of Western
323
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324
BIOGRAPHICAL MEMOIRS
apartment there in which young Stephen and a friend] lived,
together with Stephen's grandmother. His outstanding sub-
ject appears to have been mathematics. His enjoyment in
helping classmates with their studies anticipated his subse-
quent desire to become a teacher. Timoshenko had already
cieveloped an intuition for goocT teaching, but his early ambi-
tion was to become a railway engineer. His language studies
were less successful, anct his Russian had a strong Ukrainian
accent, but he appears to have been well read in the Russian
classics.
One of the principal objectives of the technical realschule
was to prepare for the entrance examinations to institutions
of higher learning. In IS96 Timoshenko took the exami-
nation to enter the Institute of Engineers of Ways of Com-
munication at St. Petersburg, which he seems to have passed
with honor.* The trip to St. Petersburg, on which he was
accompanied by his mother, opener] his eyes to the outside
worIcl and began his indefatigable habit of traveling and visit-
ing cathedrals, harbors, bridges, and the like, which was to
continue to the enct of his life.
His five years (1896-1901) at the Institute of Ways of
Communication were spent in intensive and single-minded
studies in the sequence of subjects in engineering. But this
period also marked the beginning of the enc! of the years of
political tranquility in Russia, anct soon there were many inci-
dents of student unrest. Timoshenko always took the liberal
view, but one gets the impression that he also regarded these
incidents as obstacles to his own professional clevelopment.
Europe distinction was made between the science-oriented realschule and the
humanities-oriented latinschule. The technical realschule, which came later, was a
"normal" school where science received greater emphasis than in a gymnasium.
* To play safe he also applied to the Institute of Civil Engineers, which gave easier
examinations. The admission rate was twenty to thirty students from among one
thousand who had taken entrance examinations, and only good students dared to
take these exams.
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STEPHEN P. TIMOSHENKO
325
He graduated in 1901; before this he had maple two trips to
Western Europe (luring vacation periods. These trips stimu-
latecI him greatly; they were the beginning of close as-
sociations with outstanding professionals, particularly in
Germany.
His military service, which started in September 1901,
after his second trip abroad, seems to have been a much more
constructive experience than that in corresponding systems
in most European nations at the time. He did not have to
drop his professional contacts completely, and he actually
started his career as a teacher at the Institute during this
period.
Following his military service, in 1902, he married ATex-
andra Archangelskaya, a student in medical school and an
acquaintance from his student days. At that time, he was
serving in the Mechanics Laboratory of the Ways of Commu-
nication Institute, where, in addition to his duties in testing of
materials, he also participated in supplementary lectures in
mathematics given by Professors Stanevich and Bobylev,
among others.
This noncompulsory program of studies seems to have
been important: it brought him into contact with several
young physicists, and he also began to attend the sessions of
the Physical Society. It made him aware of an issue in engi-
neering education that has remained important ever since.
The engineers needed a much more mature background in
science, particularly in mathematics, but the professional
mathematicians of the period pursued very abstract lines of
thought that often failed to attract the interest of the engi-
neering students. The physicist Aleksey N. Krylov appears to
have been one of the first to clarify this situation for
Timoshenko. Later in his life, and at a more advanced stage,
Felix Klein inspires] him the same way. Timoshenko, mean-
while, developed his own utilitarian attitude toward] mathe-
matics.
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326
BIOGRAPHICAL MEMOIRS
In 1903 Timoshenko was made an instructor in the newly
organized St. Petersburg Polytechnic Institute; the following
years at this Institute mark the beginning of his creative
scientific work. He spent the summers in Europe, mostly in
Germany, where he receives] important inspiration from
August Fopp} in Munich, Ludwig Prandt! and Felix Klein at
Gottingen, ant! others. In his autobiography,* Timoshenko
occasionally criticizes] some of the lecture courses at the In-
stitute in St. Petersburg, but he mentions several of the
outstanding teachers, such as Prince Gagarin, the Director of
the Institute, who gave English lessons using results in Love's
Theory of Elasticity as exercises, and Viktor Kirpichev, who
induced him to read G. Lame, Bernhard Riemann, F. Gras-
hof, an(l, perhaps most important, Lord Rayleigh's "Theory
of-Sound." Kirpichev's influence on Timoshenko was very
important; through him he was introcluce(l to the Castigliano
theorem and the Rayleigh-Ritz method. These influences
finally induced Timoshenko to become a teacher rather than
. . .
a practicing engineer.
The school year 190~1905 was much influenced by po-
litical turmoil in Russia- the disastrous Japanese War in-
creased student demonstrations and general unrest. The
Polytechnic Institute in St. Petersburg was closed, and
Timoshenko decided to use the time studying under Prandt}
at Gottingen. PrandtI, already a professor at twenty-nine, had
contributed to Timoshenko's main subject of interest at the
*Stephen P. Timoshenko, As I Remember (New York: Van Nostrand, 1968). The
original of this autobiography was written in Russian after Timoshenko's-trip to
Russia in 1958. It was published in Paris in 1963. The foreword to the Russian
edition was written by Eugene A. Vetchorine, chairman of the Association of
Graduates of St. Petersburg Polytechnic Institute. The translation into English was
by Robert Addis under the guidance of Professors`~. M. Gere and D. H. Young of
Stanford University. The volume contains a complete listing of Timoshenko's publi-
cations as of March 1967. It also contains a list of I~imoshenko's doctoral students
in the United States.
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STEPHEN P. TIMOSHENKO
327
time: the buckling of beams. Here Timoshenko made his first
creative discovery in connection with the buckling of I-beams,
where the torsion of rectangular elements of the section had
to be taken into account. But by this time, Prandt! had left the
fielcI to concentrate on his epoch-making work in connection
with boundary layers in fluicI flow. It is remarkable, and to
some clegree characteristic of Timoshenko's single-minded
devotion to his own studies, that he makes only a passing
reference to this important event.
The stay in Gottingen was important in many other re-
spects. Felix Klein had succeeded in expressing his conviction
of the necessity for strong links between abstract and appliecI
sciences. The School of Philosophy at Gottingen had already
establishect an Institute of AppliecI Mathematics (Car}
Runge), Applier! Mechanics (PrandtI), and Electrical Engi-
neering (Simon). The impressions from these developments
patterned his attitude toward education in technology and
contributed much to his future development as a teacher.
The situation in Russia continued to be characterized by
much political unrest ant] in the summer of 1906 Timo-
shenko resumes! his studies at Gottingen, extending them to
potential theory, thermodynamics, anti other areas, while
continuing his work on elastic stability and buckling. In the
fall of 1906 he was appointed to the Chair of Strength of
Materials at the Polytechnic Institute in Kiev. The return to
his native Ukraine turned out to be an important part of his
career anti also influenced his future personal life. He was
elected clean of the Division of Structural Engineering in
1909; he never ceased to regret the inevitable interference
. , , . , , , . · · . . . ~ . - . - .
with his own work that this position brought. Political unrest
again began to be felt, however, and his icieas of academic
freedom now came uncler scrutiny. In 1911 this conflict led
to his dismissal from the school, together with two other
professors. Ten professors then resigned their positions in
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328
BIOGRAPHICAL MEMOIRS
the spirit of solidarity, so strong were their beliefs in the right
of the cause.
These difficulties notwithstancling, his scientific work
matured, particularly the ideas of strain energy and the
Rayleigh-Ritz method in their application to buckling. In his
own lectures, begun in 1907, he had gradually developed the
technique of beginning a course with the simplest and most
elementary concepts, gradually leading to more complicated
and sophisticated methods of analysis. His first textbook ap-
pearecl in 191 I, a year that marked the beginning of a period
of more than ten years of uncertainty, anxiety, and hardship.
One bright event was his winning the ~ourowski Mecial in
191 l, along with 2,500 gold rubles.*
In the fall of 1911, he went to St. Petersburg and suc-
ceeded in getting part-time teaching work, meanwhile con-
.. . . . . . ~` .
~ , ~
truing nits writing. During the summer of 1912, he and his
wife decided to use the gold rubles from the Jourowski Prize
for a trip abroad. This journey was extended to England,
where Timoshenko attended a mathematical congress in
Cambriclge. He met, for the first time, Lord Rayleigh, A. E.
H. Love, Horace Lamb, and Levi Civita, among others.
One of the lectures at the congress was given by the young
representative from Gottingen, Theoclor von Karman.
Timoshenko found himself hampered by lack of fluency in
English, a lack he determined to remedy as soon as possible.
He did not have a scientific discussion with Lorc! Rayleigh,
chancellor of the University, except as part of the crowd at a
reception in the University museum.
Returning to Russia in the fall of 1912, he resumed part-
time teaching in several schools in St. Petersburg. He was also
invited to teach at the Ways of Communication Institute,
* This illustrates again the courage and solidarity of the Russian men of science,
who awarded their top prize to a man dismissed from his job.
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STEPHEN P. TI MOSHEN KO
329
where he took over some of the work in theoretical mechanics
from Professor Krylov, who tract retired. But events overtook
him before he really got started on this program; he clic] not
resume this work until he had emigrated to the United States.
During this period he also worked on applications of elastic
stability to ship bulkheacls as a consultant to the Naval Minis-
try in St. Petersburg. These activities improved his financial
position, but the living conditions in St. Petersburg were ctif-
f~cult, and his health was impaired. During this period he
happened to meet Paul Ehrenfest, with whom he formed a
lasting friendship. Ehrenfest hacI come from Germany to
Russia in the hope that academic freedom there wouIc! offer
him better opportunities. He was not successful in establish-
ing himself in Russia, but the two met frequently; Ehrenfest
would then enlarge upon the current icleas abroad in
physics- relativity and quantum physics new to Timo-
shenko at the time.
Timoshenko's period of disgrace with the authorities
ended in 1913, when he was confirmed in the position of
professor at the Ways of Communication Institute, an ap-
pointment later extenclec] to inclucle teaching at the Electrical
Engineering Institute of the Polytechnic Institute. In the
autumn of 1913 he was asker to reorganize the teaching of
strength of materials, succeeding Professor Mitinsky. By the
summer of 1914, he considered! this task completecl and went
off with his family on a well-earned vacation at Khapsalw on
the Baltic. There he completed the proofreading of Theory of
Elasticity anti also continued his work on elastic stability
relatecI to ship structures. This work constitutes the fore-
runner of his books Theory of Elasticity, Elastic Stability, and
Plates and Shells, published many years later in English. It was
during this short vacation that WorIc;l War I began, and with
it the beginning of the end of the oIct worIc! order.
During the early war years, Timoshenko continued and
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330
BIOGRAPHICAL MEMOIRS
intensifier] his consulting work, now clirectec! toward aspects
of the war effort shipbuilcling problems for the navy ant]
railroad] transportation- along with service to many military
committees on technical matters. With the gradual clisin-
tegration of the Russian social structure, living conditions
worsened. In the spring of the year of the Revolution ~ 19 17),
he sent his family to the Crimea, later joining them. But even
there the events of the Revolution reached them. Subse-
quently, he left his three children with his family in Kiev
while his wife accompanied him to St. Petersburg. But she
soon returned to Kiev to rejoin her family. During the Christ-
mas holidays of ~ 9 ~ 7, he made a trip to Kiev to visit them; this
turned out to be his final departure from St. Petersburg.
Kiev was held by the Communists for a short while, but in
March 1918 the German army took possession. Things im-
provec! under German discipline, and Timoshenko was
asked to resume his professorship at the Kiev Polytechnic
Institute and to participate in the organization of the
Ukrainian Acaclemy of Sciences. Before long, German
society itself began to disintegrate, anal in 1919 there were
rumors of the White Army advancing from the south. It
arrived in Kiev at the ens! of August, and Timoshenko visited
Rostov to negotiate further on matters of professional educa-
tion with the leadership of the White Army. But it soon
became apparent that this government lacked the necessary
strength, and there was a great deal of mutual suspicion
among Timoshenko's colleagues about the oIcI issue of a
separate Ukrainian state. During this period Timoshenko
was in frequent contact with many of his former students and
colleagues, all despairing about the possibility of a return to
order in Russia. This lect to his decision to leave Russia for
good.
Through his contacts in the Ukraine he was encouraged
to flee to Yugoslavia, where there seemec} to be possibilities
for a position. After many adventures he found himself pro-
OCR for page 331
STEPHEN P. TIMOSHENKO
331
fessor at the newly establisher] School of Engineering in
Zagreb; eventually he also succeeded in bringing his family
there from Kiev. The years in Zagreb he regarded as pleasant
in many ways, even though there were perpetual clifficulties
clue to material shortages of all kinds. The stay in Zagreb
from 1920 to 1922 also included visits to Western Europe and
England, where he renewed his acquaintances with Love,
R. V. Southwell, G. I. Taylor, and others. He also became
acquainted with Piotr Kapitza cluring one of his trips to En-
gland. On his return to Western Europe he visited Weimar to
see his friend Ehrenfest, who now held the Chair of Physics
at Leyden.
Timoshenko's work in Zagreb required that he lecture in
Croatian. His assistants translated his Russian lectures into
Croatian, and he started the series by reacting them in Cro-
atian. In this process the Timoshenko touch was lost. In the
end he clecidect to deliver his lectures in Russian, using as
many Croatian words as possible. Eventually his students
could follow him without difficulty. During this period he
also found it desirable to study more English. He and his
English teacher started the task of translating some of his
papers into English anc! sending them to Processor Love, who
hac] them published in England. Through this process the
name of Timoshenko began to be known to workers in ap-
plied mechanics. To those of us who hearc! him lecture in
English soon after his arrival in the United States, it became
apparent that the Russian-Croatian combination was merely
one example of his utilitarian approach to language.
His career in Zagreb came to a sudden end in 1922, when
he received "a letter from America from a pupil of mine at
the Petersburg Polytechnic, one Zelov," ~ who was then work-
*Viktor Zelov, whose original Russian name was Tselovalnikov, subsequently
became a well-known industrialist in the United States and was founder and presi-
dent of the Viz Manufacturing Company in Germantown, Pennsylvania.
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332
BIOGRAPHICAL MEMOIRS
ing with the Vibration Specialty Company, whose president,
Akimoff, was familiar with Timoshenko's work. Timoshenko
was offered a position with this company and arrived in
Philadelphia alone in June 1922. America depressed and
frightened! him. His work at the Vibration Specialty Com-
pany, although well paid, lacked focus, and his future in the
new world clip not appear bright. After considerable hesita-
tion he cleciclect to stay, however, and in the fall of 1922 he
sent for his wife and youngest child—leaving the other two
children in Germany. He wanted them to get a good educa-
tion, and by this time he knew "that there were no good
engineering schools in America."
From the vantage point in Philadelohiaq
Timoshenko
~ ~ ~ ,
began looking for other jobs, naturally beginning with the
well-known engineering schools. He records that he received
no reply from any one of these. Eventually, one of his letters
reached the engineering group at the Westinghouse Electric
Corporation in East Pittsburgh. He was identified by L. S.
Jacobsen as the author of many interesting papers in applier!
mechanics, and it became this writer's pleasure to make the
first contact with him. Soon after, Timoshenko received a
formal offer to join the Westinghouse Research Laboratory.
The details and background of this introduction of
Timoshenko into American professional life will be clealt with
in the following section.
By 1927 Timoshenko had become well known in the
Unites! States; in that year he joined the faculty at the Uni-
versity of Michigan at Ann Arbor. His position was professor
of graduate mechanics, and he soon had a large following.
The years of his widening influence in applied mechanics
hac! begun. He soon had as many doctoral students as he
couIc! handle.
At Michigan, he also had his first opportunity to realize
his dream of joining applied and abstract sciences. One of his
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STEPHEN P. TIMOSHENKO
339
cireams and with the successors to the old institutions. It is
significant, as observed earlier, that his accounts of his life
following this trip were written in Russian this from the
author of dozens of successful textbooks in English. It is also
worth observing that circumstances prevented him from fully
sharing in the wave of scientific revival that was part of the
World War II scene. The experience of the first epoch of
American superiority in scientific and technological develop-
ments was somehow denied him.
But whatever there was of bitterness was encased within
his innermost being. The principal recollection on the part of
those of us who were privileged to know him during those
first years on the American scene is that of a man of great
wisdom and a keen sense of humor, enhanced by his special
version of the English language. This was usually clevoid of
articles and retained the syntax of Russian, mixed with that
of other languages. When confronted with examples of
American colloquialisms, his favorite expression was a quiz-
zical "What means this?" Some of us who tract the opportunity
to accompany him to international conferences the Con-
gress of Applied Mechanics in Zurich in 1926 is an exam-
ple also were privileged to sense the enormous range of his
acquaintances in the scientific world, acquired cluring his
years of travel. The initial impression was of a remarkable
linguistic versatility on his part, but this impression was tem-
pered when it was discovered that he spoke only one lan-
guage, modif~e<1 in the international circles with French or
German phrases, depending on the makeup of his audience.
His Russian was flawless but always retained the strong
Ukrainian accent.
While Timoshenko was well known in professional circles
all over the world, the number of people admitted to his
innermost sphere of affection was not large. His former
students had a special position; so clic! a small group of his
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340
BIOGRAPHICAL MEMOIRS
early acquaintances in the United States. One has the impres-
sion, however, that real intimacy was reserved for his own
family* and his Russian-speaking friends. Among those who
might be mentioned are G. B. Karelitz, who passed away in
1940, and VIaclimir Zworykin. Professor Leonict M. Tichvin-
sky, in a personal communication, observed that "Timo-
shenko was the last person who knew my parents; he was my
best man when ~ married my first wife, coming from Ann
Arbor to Pittsburgh for this occasion in 1935." In a later
communication Professor Tichvinsky observed that Timo-
shenko, while leading a comfortable life in the United States,
dicl not accumulate any substantial wealth. He left a modest
legacy to be cliviclecl among his chilciren. The royalties from
all his books were assigned to Stanford University.
In the perspective of more than a half century,
Timoshenko's great influence upon applied science and tech-
nology in America resulted less from his original, creative
discoveries than from his ideals of engineering education, his
superb skill as a teacher, and his highly cleveloped pragmatic
skill in using fragments of exact solutions for a variety of
approximate solutions to difficult problems in applied
mechanics. Examples of this are his skillful use of the solu-
tions for beams on elastic foundations to problems such as
railroad rails anti to details of machinery such as highly
stressed dovetail joints. Another example is his frequent use
of the Boussinesq solutions to a variety of intractable prob-
lems in machine structures. He also cIarif~ecl the premises of
the Rayleigh-Ritz iteration method, extending it to a variety
of problems in elasticity and dynamics. Throughout all his
* He was a member of a remarkable family, which contributed much to his world-
wide views and connections. Of his two younger brothers, Serhij (an architect) was
Secretary of Transportation in the Ukrainian government in the early 1920's, while
Vladimir (an economist) was Secretary of Commerce of the Ukraine and later Chief
of Statistics of the AAA under President Franklin D. Roosevelt in Washington and at
Stanford University.
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STEPHEN P. TIMOSHENKO
341
work there is a pragmatic attitude toward mathematics, and
even to theoretical mechanics, which was regarded as one of
his great sources of strength.
This charming pragmatism was new to most of us and
seemed of immense value to the practicing engineers. It is
well to remember that even elementary computer aids, which
we now take for granted, were then many years distant in the
future. Iteration procedures had to be worked out with brute
strength anti untoIcl man-hours. With the development of
modern computers and new methods such as the finite-
element method, many problems once beyonc! our reach
have now become routine. The pragmatic approach may now
seem less essential, but I believe this is only a temporary
phase. In any case, the effectiveness and charm of
Timoshenko's teaching will always be a treasured memory to
his students.
A
A FACTUAL ACCOUNT of the career of Stephen P. Timoshenko has
been condensed from his book As I Remember, aided by tributes and
memoirs by former students and associates, particularly those of
Professor D. H. Young of Stanford University (Donovan H. Young,
"Stephen P. Timoshenko 1878-1972," Applied Mechanics Review,
July 1972. 5 pp.) and Professor Chia-Shun Yih of the University of
Michigan (Chia-Shun Yih, "Stephen P. Timoshenko: A Portrait in
Miniature." A note to the faculty of the College of Engineering,
October 30, 1972.~. These tributes emphasize his years in American
. . .
un~vers~hes.
Since this writer and a few remaining colleagues were part of
the group that first became associated with Timoshenko on his
arrival, in 1923, at the Westinghouse Electric Corporation in East
Pittsburgh, Pennsylvania, we wished to record some of the back-
ground and impressions from his early years there. In the prepara-
tion of this memoir I have been greatly assisted by the members of
the "International Hiking Club" in Wilkinsburg- Professors I. P.
Den Hartog, J. Ormondroyd, and L. S. Jacobsen as well as by
other members of the group, specifically R. E. Peterson, M. Stone,
and Leonid M. Tichvinsky, whose contributions and criticisms I
gratefully acknowledge.
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342
BIOGRAPHICAL MEMOIRS
BIBLIOGRAPHY
1905
Torsional vibrations of shafts. Proc. St. Petersburg Polytech. Inst.,
3:55-106.
Krylov's method for integration of ordinary differential equations.
Proc. St. Petersburg Polytech. Inst., 3:397~06.
Formulas for combined stresses from various strength theories.
Proc. St. Petersburg Polytech. Inst., 3:415-55.
1906
Lateral buckling of I-beams under the influence of forces acting in
the plane of largest rigidity. Proc. St. Petersburg Polytech. Inst.,
4:151-219; 5~1-2):3-34, 262-92.
1907
Stresses in a plate with a circular hole. Proc. Kiev Polytech. Inst.,
9:95-113.
Secondary stresses caused by rigidity of joints. Proc. St. Petersburg
Polytech. Inst., 7: 135~4.
Buckling of a bar on an elastic foundation. Proc. St. Petersburg
Polytech. Inst., 7: 145-57.
Forced vibration of prismatic bars. Proc. Kiev Polytech. Inst. 9:
201-52.
Stability of Plates under Compression. Kiev: Kulzhenko Typography.
60 pp.
1908
On the subject of buckling. Proc. Kiev Polytech. Inst., 8:181-212.
Strength of Materials. Part 1. Kiev: Kiev Polytechnic Institute. 373
PP
Collection of Problems in Strength of Materials. Kiev: Kiev Polytechnic
Institute.
1909
A Course in Elasticity Theory. Part 1. Kiev: Kiev Polytechnic Institute.
Stresses in a circular ring compressed by two opposing forces. Proc.
Kiev Polytech. Inst., 9:21-37.
1910
Application of normal coordinates in analyzing the bending of bars
and plates. Proc. Kiev Polytech. Inst., 10:1-19.
OCR for page 343
STEPHEN P. TIMOSHENKO
343
Stability of elastic systems. Proc. Kiev Polytech. Inst., 10:147-67.
Stability of elastic systems. Proc. Kiev Polytech. Inst., 10:375-560.
Einige Stabilitatsprobleme der Elastizitatstheorie. Z. Math. Phys.,
58:337-85.
19
An Approximate Methodfor Investigating the Stability of Elastic Systems.
Kiev: St. Vladimir University. 25 pp.
A Course in Strength of Materials. Kiev: Kiev Polytechnic Institute.
517 pp.
Erzwungene Schwingungen prismatischer Stabe. Z. Math. Phys.
59: 163-203.
1912
Problems of strength of steam turbines. I. Soc. Technol. St. Peters-
burg, 7: 266-79.
Effect of impact on a beam. Proc. St. Petersburg Polytech. Inst.,
17:407-25.
1913
Bending of bars having a slight curvature. I. Soc. Technol. St.
Petersburg, 13:411-14.
Bending of spherical shells. l. Soc. Technol. St. Petersburg, 17:
549-57.
Plotting the deflection curve. I. Soc. Technol. St. Petersburg, 21:
241-42.
Use of stress functions to study flexure and torsion of prismatic
bars. St. Petersburg. 21 pp. (Reprinted in: Mem. Inst. Ways
Commun., 82:1-21.)
Sur la stabilite des systemes elastiques. Ann. Ponts Chaussees, 1st
part, Memoires et Documents, 9th Ser., 13:496-566; 16:72-132,
373-412.
Zur Frage nach der Wirkung eines Stosses auf einen Balken. Z.
Math. Phys., 62: 198-209.
1914
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RELATED BOOKS
Stephen Timoshenko 60th Anniversary Volume, Contributions to the
Mechanics of Solids Dedicated to Stephen Timoshenko by His
Friends. New York: The Macmillan Co., 1938.
The Collected Papers of Stephen P. Timoshenko. New York: McGraw-
Hill, 1953.
