Ketter, R. L.

English

Lehigh University: Lehigh Preserve

Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1956
Plastic analysis and design at the undergrduate level,
ASEE Civil Engineering Bulletin 22 (1), p. 7
(December 1956), Reprint No. 114 (56-2)
R. L. Ketter
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Recommended Citation
Ketter, R. L., "Plastic analysis and design at the undergrduate level, ASEE Civil Engineering Bulletin 22 (1), p. 7 (December 1956),
Reprint No. 114 (56-2)" (1956). Fritz Laboratory Reports. Paper 1287.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1287
PLASTIC ANALYSIS AND DESIGN A'l' THE UNDERGRADUATE LEVEL
by
Robert L. Ketter
Since the philosophy of basing design on the maximum
carrying capacity of a structure is rational, since methods for
predicting ultimate strengths are available 9 since these methods
are as simple (if not simpler) than conventional elastic pro-
cedures, and since numerous full scale and model tests have con-
firmed the adequacy of the theory, it is inevitable that such
methods will eventually be taught at the undergraduate level.
As an added incentive, the teaching of the principles will mak.e
it possible to certify the safety of structures designed by
certain approximate procedures currently being used. F0r ex"
ample, if a given tier building is analyzed by both the Portal
and the Cantilever methods variations in caluclated stresses of
as much as 100% may be observed (and some of these may even be
of the opposite sign). It would therefore seem that one or
both of the methods will result in an unsafe structure. But to
be able to justify either by elastic reasoning there would be
required a comparison with the "exact" solution. From a
"plasticity point of view" however, it is noted that both sys-
tems represent possible equilibrium states and are therefore
lower bounds to the true carrying capacity of the structure.
A design based on either of these, procedures is therefore safe.
The justification of the methods of designing certain
details (e.g. riveted or welded connections) according to the
current AISC specification presents another troublesome problem
when approached elastically. When considered plastically how-
ever, they are easilty explained. The influence of foundation
-2
movements, residual stresses, etc .. , are similar problems the
answers to which can be found from plastic analysis ..
At this point it should be emphasized that plastic analysis
is not a II cure-all!! and will not replace elastic design.. Actually,
the types of structures wh.ich fall within the domain of this so-
called IInew ll design procedure are rather limited in number.. On
the other hand, for steel structures they represent a major por-
tion of the tonnage of rolled shapes.. It should also be pointed
out that if deflection rather than strength controls the design,
plastic analysis will not apply ..
HaVing considered the question IIWhy teach plastic analysis?!!,
the ne.xt question for discussion is "What are the limitations of
plastic analysis?1I or IIWhat types of structures can be analyzed by
plastic methods?lI ..
First of all, to be able to use these methods of solution
the material and cross-section must have moment=unit rotation
characteristics such that, as the full plastic moment is approached,
::Large increases in rotation are associated with relatively small
increases in applied moment.. This necessary condition rules out
many engineering materials. Mild structural steel, however, is
ideally suited. Secondly, plastic analysis does not apply where
fatigue :may be a problem (a factor that is fortunately not pre-
send in ordinary building construction) o Local and/or lateral
buckling also must be guarded against.. However, by placing
certain restrictions on the geometry of the cross-section and by
specifing the unsupported length (or a function of it) between
lateral bracing, these conditions will not influence the" design
of the main members.. An additional condition which at first
-3
caused much concern was the problem of variable repeated loadingo
It was known that variations in loads below those predicted on
the basis of simple plastic theory could result in the failure of
the structure. Fortunately, recent analytical and experimental
work has pointed out that for the majority of practical cases en-
countered, this problem is not important. One problem that is
currently receiving attention and for which plastic analysis is
not at present recommended is the design of members subjected to
high axial thrust in addition to bending moments (eogo the columns
in the lower stories of a tier building).
At present then, the types of structures best suited for
plastic analysis are the single and multiple span, one and two
storied, rigid, steel frames o
The neJl:t question is, "How can plastic analysis be included
in an alr(3ady ov~rcrowded undergraduate program of study?". Here
it should be pointed out that it is not at the present time con-
sidered necessary to add a separate course on this subject at the)
undergraduate level. The concepts of and the limitation to plastic
analysis as well as the necessary c~nditions for and the methods
for obtaining a plastic analysis solution can be covered in eJl:ist-
ing courses.
Consider the first course in mechanics, Le. "Statics"o
In this course linkages (i.e. mechanisms) as well as other types
of problems could also be solved for static equilibrium by virtual
displacement methods. This would give the student a good founda-
tion in "work principles" on the most elementary structures and
would prepare him for more advanced consideration of the same
principle that would be covered in later courses o Strength of
Materials and Ind~terminate Analysis could profitably draw upon
this knowl~dge for both elastic and plastic analysis solutions.
205.49 -4
In a course on "Strength of Materi8J.s 11 the inelastic as
well as the elastic/bending behavior of members could be discussed.
Concepts such as the plastification of the cross-section, the re-
distribution of bending moments (for indeterminate structures) as
well as the necessary conditions for a plastic analysis solution
could be covered. In addition several continuous beam pr~blems
that had been analyzed by elastic methods could 'be solved plastic-
ally using the "Equilibrium" method of solution. The emphasis how-
ever should not be on the idea that the same problem is being
solved by two differ.ent methods but rather that two different
problems are being considered; one that describes the behavior of
the structure in the elastic range and the other which gives the
maximum carrying capacity of the structure. The philospphical
question of which is the more desirable criterion of design for a
particular problem should not be considered at this stage.
The laboratory course in Strength of Materials could in-
clude the testing of an indeterminate beam of mild structural
steel to illustrate the phenomenon of redistribution of bending
moments. If time were available, a similar test could be carried
out for a brittle material to point up the basic difference in
their post yield bending behavior.
If an "Advanced Strength of Materials il course is offered,
this could include a more detailed discussion of those concepts
introduced in the first course. There could also be considered
the influence of cross-sectional shape and axial thrust on al ter-
ing the full plastic moment value of the cross-section.. The
various methods for obtaining a plastic analysis solution could
also be introduced.
-5
IIEngineering Materials II could include a discussion of the
properties of materials beyond the elastic limit. The advantages
of a ductile type of bending behavior could be discussed and con-
ditions that limit ductility could be considered.
Since the full advantage of plastic analysis is realized
in the indeterminate structure, it is in such a course that plastic
analysis as such should be taught. If two semesters of this sUb-
ject are offered at the undergraduate level this can easily be ac-
complished. However, if only one is a.vailable it may be difficult
to do justice to both the elastic and the plastic methods. If a
choice between the two is'necessary, it is the opinion of the
author that the elastic methods should receive first preference.
One who knows elastic analysis can easily pick up plastic analysis,
but the converse is not necessarily true. One or two lectures on
plastic analysis would have to suffice for the time being.
The senior steel design course is another place where
plastic analysis could logically be included. For e~ample, a mill
type building that had been designed elastically could be redesigned
plastically in a relatively short amount of time.
The supervised special problem course or thesis at the
undergraduate level is still another place where the student
could introduced to plastic methods. Students of advanced stand-
ing should be encouraged to enroll in such courses.
It is realized that the above outlined coverage of plastic
analysis at the undergraduate level is ambitious to say the least.
Furthermore, it is a program that must develop gradUally and be
altered and adjusted to meet the individual situation. However,
because of the recent interest in this subject as demonstrated
-6
by the increasing number of articles, short courses, etc., it is
considered desirable to acquaint the undergraduate student with
the concepts and limitations of this method of analysis as soon
as possible. This could be accomplished by a series of 3 or 4
lectures and, possibly, a laboratory session in the senior steel
design course. It has been observed that with this much time,
the average student can grasp the basic idea behind plastic an-
alysis and can solve several simple problems.
We have considered several aspects of the "Why" and "How"
of plastic analysis at the undergraduate level. Plastic analysis
will be taught. The only question remaining is WHEN.


Plastic analysis and design at the undergrduate level, ASEE Civil Engineering Bulletin 22 (1), p. 7 (December 1956), Reprint No. 114 (56-2)

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Plastic analysis and design at the undergrduate level, ASEE Civil Engineering Bulletin 22 (1), p. 7 (December 1956), Reprint No. 114 (56-2)

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