Table Of ContentINTERNATIONAL UNION OF THEORETICAL
AND APPLIED MECHANICS
CREEP IN STRUCTURES
COLLOQUIUM
HELD AT STANFORD UNIVERSITY, CALIFORNIA
JULY 11-15, 1960
EDITED BY
NICHOLAS J. HOFF
WITH 156 FIGURES
S PR I N GER -VER LA G
BERLIN / GÖTTIN GEN / HEIDELBERG
1962
ISBN 978-3-642-86016-4 ISBN 978-3-642-86014-0 (eBook)
DOl 10.1007/978-3-642-86014-0
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Foreword
The Colloquium on Creep in Structures was organized as part of the
activities of the International Union on Theoretical and Applied Mecha
nies. It was supported financiaHy by IUTAM, as weH as by the National
Science Foundation, Washington, D. C., U. S. A. The Scientific Commit
tee charged with the work of organization consisted of the foHowing
persons:
NICHOLAS J. HOFF, Stanford University, Stanford, California, Chair
man
FOLKE K. G. ODQVIST, Royal Institute of Technology, Stockholm,
Sweden, Vice-Chairman
R. MAZET, Office National d'Etudes et de Recherehes Aeronautiques,
Chatillon-sous-Bagneux, France
Y. N. RABOTNOV, Academy of Sciences, Novosibirsk, U. S. S. R.
SHUJI TAIRA, Kyoto University, Kyoto, Japan.
The details of the organization of the sessions were entrusted to the
Local Committee consisting of the following persons:
MAX ANLIKER W. H. HORToN
K. BINFORD B. LEMPRIERE
C.C.CHAO L. NICKEL
W. G. FLÜGGE
In order to insure good discussion and, in general, a broad exchange
of ideas among the participants in the meeting, the number of persons
invited to attend was kept to a minimum. Participants not living in the
Stanford area were housed in Donner House of Stern Hall on the Stanford
campus, and were served meals in the dining room of Donner House.
The speakers and observers started to arrive on July 9 and the last ones
left on July 18.
All the scientific sessions were held in the Engineering Building of
Stanford University, where the Colloquium was officially opened at
9.00 A. M. on July 11. The program of the .meeting was as follows:
Monday, July 11
9.00 A. M.: Official Opening 01 Colloquium
Ohairman:
DONALD L. PUTT, Lt. Gen. (ret.) U. S. Air Force; Chairman Advisory
Committee, Industrial Affiliates of Stanford University in Aeronautics
and Astronautics
Speakers:
NICHOLAS J. HOFF, Chairman, Colloquium on Creep in Structures
FREDERICK E. TERMAN, Provost, Stanford University
IV Foreword
JOSEPH M. PETTIT, Dean, School of Engineering, Stanford University
FOLKE K. G. ODQVIST, President, International Union on Theoretical
and Applied Mechanics
9.30 A. M.: Linear Viscoelasticity
Chairman:
OLEG D. SHERBY, Stanford University
E. H. LEE and A. H. CORNELIUSSEN, Brown University, Providence,
Rhode Island, U. S. A.: The influence of viscoelasticity on stress
distribution
H. H. HrLTON, University ofiliinois, Urbana, Illinois, and E. L. W ALSH,
Boeing Aircraft Co., Seattle, Washington, U. S. A.: Torsional Response
of Linear Viscoelastic Plates Subjected to Thermal Stresses
2.00 P. M.: Stress Distribution
Chairman:
HAROLD LIEBOWITZ, Office of Naval Research, U. S. Navy
S. A. PATEL and B. VENKATRAMAN, Polytechnic Institute of Brooklyn,
Brooklyn, New York, U. S. A.: On the creep stress analysis of some
structures
A. PHILLIPS, Yale University, New Haven, Connecticut, U. S. A.:
The shear center 'in creep of beams of thinwalled open cross section
1i.00 P. M.: Reception
in honor of speakers given by Dr. and lVIrs. N. J. HOFF at 782 Esplana
da Way, Stanford, California
Tuesday, July 12
9.00 A. M.: Creep Laws
Chairman:
JAMES J. MURRAY, Office of Ordnance Research
J. MARIN, Pennsylvania State University, University Park, Pennsyl
vania, U; S. A.: Mechanics of creep and combined stresses
S. TAIRA, Kyoto University, Kyoto, Japan: The lifetime of structures
subjected to varying load and temperature
E. T. ONAT and T. T. W ANG, Brown University, Providence, Rhode
Island, U. S. A.: The effect öf incrementalloading on creep behavior
of metals
Wednesday, July 13
9.00 A. M.: Large Deformations
Chairman:
JOHN A. JOHNSON, Lockheed Missiles and Space Division
F. K. G. ODQVIST, Royal Institute of Technology, Stockholm, Sweden:
Applicability of the elastic analogue to creep problems of plates,
membranes and beams
J. HULT, Royal Institute of Technology, Stockholm, Sweden: on
canning problems in creep
12.30 P. M.: Excursion by Chartered Bus
v
Foreword
Thursday, July 14
9.00 A. M.: Disks and Plates
Chairman:
J. N. GOODIER, Stanford University
J. F. BESSELING, Institute of Technology, Delft, Holland: Investiga
tion of transient creep in tubes and disks under radially symmetrie
loading
A. M. WAHL, Westinghouse Electric Corporation, Pittsburgh, Pennsyl
vania, U. S. A.: A comparison of flow criteria applied to elevated
temperature creep of rotating disks with consideration of the transient
condition
T. H. LIN, University of California, Los Angeles, California, U. S. A.:
Bending of a circular plate with non-linear and strain-hardening creep
2.00 P. M.: Cylindrical Shells
Chairman:
WILHELM FLÜGGE, Stanford University
H. PORITSKY, The General Electric Company, Schenectady, New Y ork,
U. S. A.: Creep in cylindrical shells
C. R. CALLADINE, The English Electric Company, Ltd., Whetstone,
Leicestel', England: The creep of a wrinkle
6.00 P. M.: Social Hour at Adobe Creek Lodge, followed by Banquet at 7.00 p. m.
Toastmaster:
NIOHoLAs J. HOFF
Quest Speaker:
RONALD SMELT: "Satellite Environment"
Friday, July 15
9.00 .A. M.: Columns
Chairman:
RALPH H. LONG, National Science Foundation
R. L. CARLSON and W. W. BREINDEL, BatteIle Memorial Institute,
Columbus, Ohio, U. S. A.: On the mechanics of column creep
B. M. LEMPRIERE, Stanford University, Stanford, California, U. S. A. :
Comparison of ranges of applicability of predictions of creep buckling
time
M. ZYOZKOWSKI, Technical University of Krakow, Krakow, Poland:
Geometrically non-linear creep buckling of bars
2.00 P. M.: Assemblies-Torsional Buckling-Damping
Chairman:
F. K. G. ODQVIST, Royal Institute of Technology, Stockholm, Sweden
R. MAZET, Office National d'Etudes et de Recherehes Aeronautiques,
Chatillon-sous-Bagneux (Seine), France: Sur un modele apte a traduire
le fluage sous charge constante des assemblages
A. H. CHILVER, Cambridge University, Cambridge, England: Some
simple models for torsional creep buckling
N. J. HOFF, Stanford University, Stanford, California, U. S. A.: Dam
ping of the vibrations of a coiled spring due to creep
4.45 P. M.: Closure
VI Foreword
A list of the participants and their affiliations folIows:
Professor J. F. BESSELING Institute of Technology, Delft, Holland
Professor R. J. BOLLARD California Institute of Technology
Mr.E.B.BoREK Marquardt Corporation
Dr. J. M. BROWN Hughes Aircraft Company
Dr. C. R. CALLADlNE English Electric Company, Ltd.
Mr. R. L. CARLSON Battelle Memorial Institute
Dr. K. T. CHANG AiResearch Manufacturing Company, Division
of Garrett Corporation
Dr. ROBERT A. CHASE United Technology Corporation
Dr. A. H. CHILVER Cambridge University, Cambridge. England
Monsieur H. DE l'ESTOILE Service Technique Aeronautique, French Air
Force
Monsieur E. FAGE Service Technique Aeronautique, French Air
Force
Dr. ROBERT P. FELGAR Space Technology Laboratories, Inc.
Professor WILHELM FLüGGE Stanford University
Professor Y. C. FuNG California Institute of Technology
Dr. ROBERT GATTS General Electric Company
Professor N ORMAN GOODIER Stanford University
Mr. CHARLES A. HERMACH Ames Research Center NASA
Professor H. H. IIILTON University of Illinois
ProfE'ssor N. J. HOFF Stanford University
Dr. OSCAR HOFFMAN Lockheed Missiles and Space Division
Dr.JANHuLT Royal Institute of Technology, Stockholm,
Sweden
Dr. WILLIAM E. JAHSMAN Stanford University
Mr. JOHN A. JOHNSON Lockheed Missiles and Space Division
Professor MAKOTO KrKUKA WA Osaka University, Osaka, Japan
Mr. BERTRAM KLEIN Convair, Division of General Dynamics Corpo
ration
Professor ALBERT KOBAYASHI Boeing Airplane Company, Aero Space Division
Professor E. H. LEE Brown University
Mr. B. M. LEMPRIERE Stanford University
Dr. HAROLD LIEBOWITZ Office of Naval Research
Professor T. H. LIN University of California at Los Angeles
Professor Hsu Lo Purdue University
Dr. RALPH H. LONG National Science Foundation
Professor J OSEPH MARIN Pennsylvania State University
Mr. H. G. MCCOMB Langley Research Center, NASA
Mr. JAMES J. MURRAY Office of Ordnance Research, U. S. Army
Dr. J. MURZEWSKI Institute of Technology, Krak6w, Poland
Dr. WILLIAM NACHBAR Stanford University " .
Professor F. K. G. ODQVIST Royal Institute of Technology, Stockholm,
Sweden
Professor E. T. ONAT Brown University
Professor S. A. P ATEL Polytechnic Institute of BrooklYll:
Professor ARIS PHILLIPS Yale University
Professor YVES PIRRONEAU University of Nantes, France
Dr. H. PORITSKY General Electric Company
Lt. GEN. D. L. PUTT Stanford University
Professor CEDRIC W. RICHARDS Stanford University
Foreword VII
Dr. CARLO RIPARBELLI General Atomic, Division of General Dynamics
Corporation
Dr. E. E. SECHLER California Institute of Technology
Professor OLEG SHERBY Stanford University
Mr. RONALD SMELT Stanford University
Dr. W. STUIVER IBM Research Laboratory
Professor Y. SUEZAWA Institute of Technology, Tokyo, Japan
Professor S. TAIRA Kyoto University, Kyoto, Japan
Dr. KICHINOSUKE TANAKA Kyoto University, Kyoto, Japan
Provost FREDERICK TERMAN Stanford University
Dr. SITARAMARAO V ALLURI California Institute of Technology
Professor B. VENKATRAMAN Polytechnic Institute of Brooklyn
Dr. A. M. W Am. Westinghouse Electric Corporation
Professor HARRY WILLIAMS Stanford University
Dr. JOHN ZICKEL Aerojet-General Corporation
Dr. M. ZYCZKOWSKI Technical University of Krak6w, Krak6w,
Poland
To provide relief from the scientific·activities, a bus trip was organized
for the afternoon of July 13. The 17 persons who took part in the excur
sion were shown some of the scenic beauties of California and some of
the oldest buildings, dating back to the days of Spanish rule, in Monterey
ld in Carmel.
The banquet was held at Adobe Creek Lodge in a pleasant setting
among the steep foothills of the Coast Range. It was attended by 58 per
sons, including many of the wives of the participants. In the after-dinner
talk, Mr. RONALD SMELT, Chief Scientist of the Lockheed Missiles and
Space Division and a lecturer in the Department of Aeronautical En.
gineering of Stanford University, gave an interesting report on efforts to
investigate the environment in which satellites travel. Although most
informative, the talk was given in a manner understandable to the ladies
present; it was illustrated by an interesting sound film .
.T he.sessions took place in accordance with the prearranged program,
except that the paper written by Professor MAZET was delivered by
Monsieur HUGUES DE L'EsTOILE of the Service Technique Aeronautique
of the French Air Force, and that the titles of some of the papers were
changed slightly.
The meeting clo§led in the afternoon of July 15. N. J. HOFF voiced
the thanks of Stanford University for the work done by the participants,
and FOLKE K. G. ÜDQVIST, President of the International Union for
Theoretical and Applied Mechanics, expressed the appreciation of the
participants for the hospitality shown them by Stanford.
Speakers and discussors enjoyed the possibility offered to them for
the discussion of problems caused by creep in structures. It is hoped that
readers of these proceedings will derive equal benefits from this volume.
Stanford University, California N.J. Hoff
Contents
Page
Foreword ................ . III
Stress Distribution Analysis for Linear Viscoelastic Materials.
By A. H. CORNELIUSSEN and E. H. LEE . . . . . . . . 1
Torsional Response of Linear Viscoelastic Plates Subjected to Thermal Stresses.
By HARRY H. HILTON and EDW.ARD L. WALSH . . . . . . . . . . . 21
On the Creep Stress Analysis of some Structures.
By SHARAD A. PATEL and B. VENKATRAMAN . 43
The ShearCenter in Creep of Beams of Thin-Walled Open Cross Section.
By ARIS PHILLIPS . . . . . . . . . . . . . . . . . . . . . . 65
Mechanics of Creep and Combined Stresses. By J OSEPH MARIN . . . 79
Lifetime of Structures Subjected to Varying Load and Temperature.
By SHUJI TAIRA ................•... 96
The Effect of Incremental Loading on Creep Behavior of Metals.
By E. T. ONAT and T. T. WANG. . . . . . . . . . . . . . 125
Applicability of the Elastic Analogue to Creep Problems of Plates, Membranes
and Beams. By FOLKE K. G. ODQVIST. . . . . . . . . . . . . ... 137
Oil Canning Problems in Creep. By JAN HULT. . . . . . . . . . . .. . 161
Investigation of Transient Creep in Thick-Walled Tubes under Axially Sym-
me~ric Loading. By J. F. BESSELING ................ 174
A Comparison of Flow Criteria Applied to Elevated Temperature Creep of Rota-
ting Discs with Consideration of the Transient Condition. By A. M. WAHL 195
Bending of a Plate with Non-Linear Strain-Hardening Creep. By T. H. LIN 215
Effect of Creep on Stresses in Cylindrical Shells. By H. PORITSKY 229
On the Creep of a Wrinkle. By C. R. CALLADINE. . . . . . . . 245
On the Mechanics of Column Creep. By R. L. C.ARLSON and W. W. BREINDEL 272
Comparison of Ranges of Applicability of Predictions of Creep Buckling Time.
By BRIAN M. LEMPRIERE. . . . . . . . . . . . . . . . . . . . . 291
Geometrically No~-Linear Creep Buckling of Bars. By MICHAL ZYCZKOWSKI 307
Sur un modele apte a traduire le fluage sous charge constante des structures.
Par R. MAZET. . . . . . . . . . . . . . . . . . . . . . . 326
Some Simple Models for Torsional Creep Buckling. By A. H. CHILVER ... 339
Damping of the Vibrations of a Coiled Spring Due to Creep. By N. J. HOFF 355
Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . 374
Stress Distribution Analysis for Linear Viscoelastic
Materials!
By
A. H. Corneliussen and E. H. Lee
Brown University, Providence, Rhode Island, USA
Abstract
The formulation of the differential or integro-differential equations
governing the quasi-static stress analysis problem for linear viscoelastic
bodies is considered, with particular reference to the initial conditions
associated with sudden loading. If classical methods of solving the diffe
rential equations, such as the LAPLACE transform or integrating factor,
are used, the need to evaluate the initial conditions after load applica
tion at t = 0+ presents difficulties. These can be avoided by working
with the lower limit t = 0-, before load application, when the body is still
undisturbed, and, in the case of direct integration of the equations, delta
functions and their derivatives must then be incorporated into the ana
lysis. Examples of both methods of approach are contrasted. The stress
distribution in a spinning hollow circular cylinder with annihilating
inner cavity is evaluated as an example which does not fall within the
scope of the LAPLACE transform method of analysis. The procedures are
justified through the application of the corresponding integral operators.
1. Introduction
In analysing the stress distributions in viscoelastic bodies, a system
of partial differential equations or integro-differential equations con
taining derivatives or integrals with respect to both the space variables
and the time must be solved [1,2]2. It is common to consider applied
surface tractions in the form of the HEAV ISIDE step function in the time
variable:
H(t) = 0, t< 0
(1.1)
= 1, t> 0
1 Sponsored under Department of Defense Contract DA-19-020-0RD-4750,
between the Office of Ordnance Research, US Army, and Brown University.
2 Numbers in square brackets refer to the bibliography at the end of the paper.
1 Hoff, C.reep in Structures
2 A. H. CORNELIUSSEN and E. H. LEE
this being the mathematical idealisation of a rapidly applied load. Many
such problems can be adequately treated on the basis of quasi-static
theory, in which the inertia forces associated with the deformation of the
body can be neglected in comparison with the applied forces. In such an
analysis the effect of the surface tractions, applied suddenly at t,= 0,
is feIt instantaneously throughöut the body. Thus, even though the body
was unstressed for t <0, the dependent variables, the stress and strain
components, may have non-zero initial values after the instantaneous
distribution of the loads. These values will be associated with the time
t = 0+, the situation just before load applieation being assoeiated with
t = 0-. Initial time derivatives of first and higher orders will in general
also be non-zero at t = 0+. Thus the solution of the system of differential
or integro-differential equations must be sought for t >0, with non-zero
initial values at t = 0+. Moreover, these values are not known apriori.
For an isotropie linear viscoelastie body, the stress-strain relations
eontain two pairs of linear operators whieh are analogous to the two
elastie eonstants required to specify linear isotropie elastieity. For eon
venienee, separating the shear and dilatational effeets, the viseoelastie
law s take the form:
(1.2)
(1.3)
where P, Q, P', Q' are linear differential or integral operators; (fij' Cu
the stress and strain tensors respectively, and 8ij andeijtheeorrespond
ing deviators whieh represent shear effeets. The summation eonven
tion for repeated suffixes is utilized, so that (1.3) is the relation between
the average hydrostatic tension, (fiif3, and the dilatation, cw If a rela
tion of type (1.2) or (1.3) between a stress component (f and astrain
component c corresponds to a viscoelastic model with a finite number of
springs and dashpots, it can be represented by differential operators of
finite order, for example:
(1.4)
General linear viseoelastieity ean be represented in terms of the ereep
eomplianee J (t), by the integral relation:
e
Jt
c(t)= J(t-r:)e:dr: (1.5)
- co
and if the material is undisturbed for t< 0, this ean be written in the
form:
e
Jt
e(t)= J(t-r:)~adr:. (1.6)
o cl'!:
