Why Plastic Design Plastic Design In Structural Steel

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Why Plastic Design Plastic Design In Structural Steel

Transcript Of Why Plastic Design Plastic Design In Structural Steel

Lynn S. Beedle
Prepared for delivery to AISC-USC Conference on
Fritz Engineering Laboratory Department of Civil Engineering
Lehigh University Bethlehem, Pennsylvania
November, 1956
Fritz Laboratory Report No. 205.52

Steel possesses ductility--A unique property that no other structural material exhibits in quite the same way. Through .ductility structural steel is able to absorb large deformations beyond the elastic limit without the dange~ of fracture.
Although there are a few instances where conscious use has been made of this property, by and large the engineer has not been able to fully exploit this ~eature ·of ductility instructural steel. As a result of these ~imitations it turns out that we have been making a considerable sacrifice of economy.
Engineers have k0 ....wn of this ductility for years, and since the 1920's have been attempting to see if some conscious use couldn't be made of this property in design. Plastic design is the realization of that goal. We are now equipped to apply this new design concept to statically loaded frames of structural steel for continuous beam and single story building frames, continuous over one or more spans. This category accounts for a very substantial portion of the total tonnage of fabricated structural steel.produced annually in the United S~ates. Not only are we equipped, . these techniques have already been applied in Europe,' and during this past summer a structure was designed according to the plastic methods and actually erected in Canada.
We have only been able to achieve that goal--namely the producing of .a practical design method--because two important conditions were satisfied. First, the theory concerning the plastic behavior of continuous steel frames has been systematized and reduced to simple design procedures. ,Secondly, every conceivaQle factor that might tend to limit the load-carrying capacity to something less than tQat predicted by the simple plastic theory has been investigated and rules have been formulated to safe-guard against such factors.



It .is our objective in this conference to present to you the available

methods of plastic analysis, the design procedures that have been worked out

using these methods, the experimental verification of these procedures by actual

test results, and .to cover in the time that permits the secondary design consid-

erations that so often are a stumbling block to any new design technique. In

.short, we hope to stimulate your further study of the topic. -If we do not suc-

ceed in demonstrating the simplicity of the plastic method, please remember that

you didn't master all you know about present design methods in a few one-hour


It is the purpose of this particular talk to describe the fundamental concepts involved in plastic design, to justify its application to structural steel frames, and to demonstrate that some ·of the concepts are actually a part of our present design procedures.

To some of you these concepts may be new. Others of you have had some experience in solving problems. It won't hurt any of us, however,to have definitions clearly in mind and these are included in an appendix.



2. S T R U.C TU R A LS T R EN G T H (Functions of Structures)

1. Limits of Usefulness The design of any engineering structure, be ita bridge or building,
is satisfactory if it can be built with the needed economy and if throughout its useful life it carries its intended loads and otqerwise performs its intended function •. As already mentioned, in the process of selecting suitable members for such a structure, it 1s necessary to make a general analysis of structural strength and secondly to examine certain details to assure that local failure does not occur.

The ability to carry the load may be termed "structural strength". Broadly speaking, the structural strength or design load of a steel frame may be determined or controlled by a number of factors, factors that have been called "limits of structural usefulness". These are: first attainment of yield point .stress (conventional design), btittle fracture, fatigue,instability, deflections, and finally the attainment of maximum plastic strength.

2. Plastic Design As An Aspect of Limit Design Strictly speaking, a design based on anyone of the above-mentioned
six factors could be referred to as a "limit design", although the term usually has been applied to the determination of ultimate load as limited by buck-
ling or maximum streng~h, (1) "PLASTIC DESIGN" as an aspect of limit design and
as applied to continuous beams and frames embraces, then, the last of the limits --the attainment of maximum plastic strength.

Plastic design, then, is first a design on the basis of the maximum load the structure will carry as determined from an analysis of strength in the plastic range (that is, a plastic analysis), . Secondly it consists of a



consideration by rules qrformulas of certain factors that ~might otherwise

tend to prevent the structure from attaining the computed maximum load. Some

of these factors may be present in conventional design. Others are associated

only with the plastic behavior of the-structure. But the unique feature of

plastic design is that the ultimate load rather than the yield stress is re-

garded as the design criterion.

It has long been known that whenever members are rigidly connected, the structure has a much greater load-carrying capacity than indicated by the elastic stress concept. . Continuous or "rigid" frames are able to carry increased loads above :"first yield" because -structural steel has the capacity to yield in a ductile manner with no loss in strength; indeed, with frequent increase in resistance. Although the phenomenon will be discribed in complete detail later, in general terms what happens is this: As load is applied to the structure, . the cross-section with the greatest bending moment will eventually reach the y±eld moment. Elsewhere the structure is elastic and the "peak" moment values are less than yield. As load is added a zone of yielding develops at the first critical section; but due to the ductility of steel, the moment at that section remains about constant. The structure therefore calls upon its less-heavily stressed portions to carry the increase in load. .Eventua~ly zones of yielding are formed at other sections until the moment capacity has been used up at all necessary critical sections. After reaching the maximum load value, the structure would simply deform at constant load.

.3. Elastic Versus Plastic Design

We can't repeat too often the distinction between elastic design and

plastic design. In conventional elastic design, a member is selected such that

the maximum allowable stress is equal to 20,000 pounds per square inch at the

working load.














As shown

.in Figure 1 such a beam has a reserve of strength of 1,65 if the yield point



stress is 33,000 pounds per square inch. Due to the ductility of steel there

is a bit more reserve (14% for a wide flange shape). So the total inherent

overload factor of safety is equal to 1.88.

In plastic design, on the other hand; we start .withthe ultimate load . . For if we analyze an indeterminate structure we will find that .we can compute the ultimate load much easier than we can compute the yield load. So we multiply the working load, Pw' by the same load factor (1.88) and then select.a member that will reach this factored load.

If .wetook the trouble to draw the load.-vs- deflect~oncurve:forthe restrained beam we would get the curve shown in Figure 1. It has the same ultimate load as the conventional design of the simple be~and the member is elastic at working load. The important thing to note is that the factor of safety is the same in the plastic design of the indeterminate structure as it is in the conventional design of the simple beam.

While there are other features here, the important thing to get in mind at this stage is that in conventional procedures we find the maximum moment under the working load and select a member such that the maximum stress is not greater than 20 ksi :(the factor of safety inherent in this procedure is 1.88 in.the case of a simple beam); on the other hand in plastic design we
multiply the working load by F = 1.88 and select a memberwhichwill just
support the ultimate load.

Already we have used two new terms: limit design and plastic design. Let's include them in .our list of defini tions (see appendix).




The concept of de.sign based on ultimate load as the criterion is more than 40 years old! The application of plastic analysis to structural design appears to have been initiated by Dr. Gabor Kazinc.zy, a H.ungarian, who published results of his te.sts of clamped girders as early as 1914. (2) He also suggested analytical procedures similiar to thoSE: now current, and designs of apartment-' type buildings were actually carried out.

In his Strength of Materials(3) , Timoshenko refers to early suggestions to utilize ultimate load capacity in the plastic range and states
"such a procedure appears logical in the case .of steel structures submitted to the action of stationary loads, since in such cases a failure owing to the fatigue of metal is excluded and only failure due to the yielding of metals has to be considere.d." Early tests in Germany were made by Maier-Leibnitz(4) who showed that the ultimate
capacity was not affected by settlement of supports of continuous beams. In so doing he corroborated the procedures previously developed by others for the calculation of maximum load capacity. The efforts of Van den Broek(l) in this country and J. F. Baker(5) and his associates in Great Britain to actually utilize the plastic reserve strength as a design cri.terion are well know. (Prof, Van den Broek was teaching about ductility in 1918). ProGress in theory of plastic struct ... ural analysis (particularly that at Brown University) has been sunnnarized by Symonds and Neal(6). A survey of design trends, by Winter(7), discusses briefly many of the factors germain .to plastic design.

For more than ten years the American Institute of Steel Construction, the Welding Research Council, the Navy Department, and the American Iron and Steel Institute have sponsored studies at Lehigh University. These studies have featured not only the verification of this method of analysis through appropriate

tests on large structures, but have given particular attention to the conditions that ,must bernet to satisfy important secondary design requJrements{~),. Much of this will be discussed later in the conference.



4. FUND A ME .N TALC 0 N C ,E P T S With this background of the functions of a structure, let us start with the fundamentals of the simpleplast:ic theory,

1. Mechanical Properties An outstanding property of steel, which (as already mentio~ed) sets
it apart from other struc.tural materials, ·is the amazing ductility whd.chi t possesses, This is characterized by, Figure 2. In F1gure 3 are shown partial tensile stress-strain curves for a number of different steels, Note that when the elastic. limi tis reached, elongations from 8 to 15 times the elastic lim! t take place without any decrease 1n load, Afterwards some increase in strength 1s exhibited as the material strain hardens.

Although the first applicati.on of plastic design is to structures fabricated of structural grade steel, it is no less applicable to steels of higher strength as long as they posess the necessary ductility, Figure 3 attests to the ability ofa wide range of steels to deform plastically with charact~ristics simili.ar to A-7 steeL

It is important to bear in mind that the strains shown in this figure are really very small, As shown in Figure 4, for ordinary structural steel, final failure bY,rupture occurs only after a specimen has stretched some 15 to 25 times the maximum strain that is encountered in plastic design. Even in plastic analysis, at ultimate load tb,e critical strains will not have exceeded aboutL 5% longation. Thus the use of ultimate. strength as the design criterion still leaves available. a major portion of the reserve ductility of steel which can be used as an added margin of safety, Be.ar in mind that this maximum strain of 1,5% is a strain at ultimate load in the structure--not at working load. In most cases under working load the strains will still be below



the elastic limit. We must distinguish also between the term "u1ti.mate 10a.d"

as we u.se it here to mean. t:he maxi.mum load a st.ructu're .will carry, as distinct

from th.e "ultimate strength" exh.ibited by an acceptance te.stcoupon •. So, we will

add that definition to our lis to

2. Maximum Strength of Some Elements On the basis of t.he duct:i.lity of steel (characterized by Figure 4) we
can now quickly calculate the maximum carrying capacity of certain elementary structures .

.As our first example take a tension .member suc,h as an eye bar (Figure

5) . If we compute the ,stress we find t4at

P ·cr. =. A

If we draw th.e load-versus-d~flectionrelationship it will be elastic unti.l

the yield point is reached. As shown in Figure 5 the dq:flection at the elastic

limi t is given by



;Since the stress distribution is uniform across the section, unrestricted

plastic flow ·,will set in when the load reaches the value given by

This is , therefore, the ultimate load. I tis the m.a.x:imum load .the , structure will carry without the onset of unrestricted plastic ftow.
As a second example we will consider the three-bar st.ructureshown in Figure 6. It is selected because it is an indeterminate structure since the state of stress cannot be determined by statics. Consid.er first the elasUc state: .wewill first take equilibrium and obtain:
LoadPlastic DesignStructureStrengthDesign