recent developments in steel building design

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RECENT DEVELOPMENTS IN STEEL BUILDING DESIGN

by

Lynn S. Beedle

Le-Wu Lu

Erkan Ozer

Department of Civil Engineering

Fritz Engineering Laboratory

Lehigh University

Bethlehem, Pennsylvania

August 1973

Fritz Engineering Laboratory Report No. 237.83

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237.83

TABLE OF CONTENTS

1. INTRODUCTION

Advances

Structural design

2. STRENGTH AND DUCTILITY

Columns

Beam-to-column connections

Frames

3. DESIGN BASED ON PROBABILITY

4. INTERACTION CONSIDERATIONS

Floor systems and shear connectors

Composite beam-to-column action

Integrated structural design

Mixed systems

5. STRUCTURAL SYSTEMS

6. OTHER CONSIDERATIONS

7. SUMMARY

8 • ACKNOWLEDGMENTS

9. ILLUSTRATIONS

10. REFERENCES

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RECENT DEVELOPMENTS IN STEEL BUILDING DESIGN

By Lynn S.Beedle, Le-Wu Lu and Erkan Ozer

I N T ROD U C T ION

Those engaged in the structural research that has been typical of many

steel-indus try-sponsored programs in recent years -- and has been traditional at

the Fritz Engineering Laboratory since its early days -- have the advantage of working

with an advisory committee. Beyond receiving suggestions for needed work this advan-

tage has at least two ramifications: (1) There is always the interest in the engineer-

ing application of a new approach that may arise from the research. (2) The investi-

gators cannot fail to be impressed with the necessary "constraints". Among these con-

straints are time and complexity. A new method that involves more design time or is

more complex in its application, must have a signi.ficanteconomic advantage before it

can become a practical design tool.

It is from this background that recent developments in steel building designI

are discussed in this paper. Which of the developments arising from research have a

potential for improvement in design? Some of these applications are current. Some

are in the future. Some of the source material goes beyond that resulting from the

work of the writers and of their own institution. Not only does it include AISC-

sponsored research, but also that of the American Iron and Steel Institute, Column

Research Council, Research Council on Bolted and Riveted Joints, and the National

Science Foundation.

Lynn S. Beedle is Prof. of Civil Engineering, and Director, Fritz Engineering Laboratory,Lehigh University., Bethlehem, Pa.

Le-Wu Lu is Prof. of Civil Engineering, and Director, Building Systems Division, FritzEngineering Laboratory, Lehigh University, Bethlehem, Pa.

Erkan Ozer is Post-Doctoral Research Associat.e, Fritz Engineering Laboratory, LehighUniversity, Bethlehem,. Pa.

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ADVANCES

These remarks are built upon the thesis that there are four major ways to ad

vance steel building design. Three of these are proven techniques in the United

States. The other (item two) is in an Ilinitial" phase in the United .States but is

incorporated in design practice abroad.

The first is "Strength and ductility": Take advantage of the strength and

ductility of the parts and of the whole. Plastic design is in this field.

Second, one can make design like life. Base it more on probabilities.

Third, one can take advantage of what otherwise are the neglected parts, and

this involves interaction considerations.

Finally one can exploit the arrangements of the material to the fullest •. What

is the best structural system?

STRUCTURAL DESIGN

The overall objectives of structural design are basically three fold: (1)

The structure must meet functional requirements; (2) it must support load and

provide stiffness; and (3) it must satisfy economical requirements. It may be that

in the past the strictly load-carrying aspects have been over-emphasized, and this

comes into focus when one considers the real function of a structure (1).

Now, having made this statement, one still must look at the load limits and

the other major design criteria as a background. These "limits of structural useful

ness" are the plastic limit load, the stability limit, the elastic limit (which is

a hypothetical consideration), the fatigue limit, the fracture limit, and finally

the serviceability criteria of deflection or vibration.

These various limits are used ina number of ways, but their consideration

is eventually a part of particular design procedures, most of which have names. They

are grouped in Fig. 1 in three categories. Whether or not the terms within a given

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group are synonymous is a matter of usage and conjecture. It is to be hoped that in

time this situation can be resolved. (That, in itself, would be a considerable "ad-

vance").

No matter which names are used for a particular design approach they all fi-

nally come down to "Structural Design" -- a process shown in Fig. 2 (which is an adap-

tat ion of an illustration developed by Bruce Johnston). At the top are shown the,

various limits of usefulness. Of course there must be the load study (left) and the

deflection and drift limit evaluation (right). Then through various static or dynamic

analyses, and using either allowable-stress design, plastic design, or load-factor and

limit-states design,one eventually arrives at a "Structural Design".

S T R ENG T HAN D D U C TIL I T Y

The major research areas in which the exploitation of strength and ductility

might be cataloged incorporate: mechanical properties of steel; beams, columns, and

connections; the various failure modes; the behavior of subassemblages and of braced

and unbraced frames; optimum design; and repeated and reversed loading. Comment will

be made only on columns, connections, and frames.

COLUMNS

The stub column test, widely described elsewhere, has a number of useful

functions. It reveals the residual stress effect. It nicely averages cut

the variation in the yield stress across the section. If carried far enough it will

tell us something about local instability. One of the things that the most recent work

is showing is that we can look forward to a relaxation in depth-to-width requirements

for local instability(2). Now, some'shapes such as the Wl4 x 730 of Fig. 3 become so

large that they exceed the capacity of testing machines •. However, the theoretical

work has advanced to the point that it is possible to predict theoretically the in-

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fluences of the internal stresses and their consequent influence on column strength,

and there has been enough experimental work to show that the theory is sound. So

future work will give greater attention to the theoretical side and should require

somewhat less in the way of experimental studies.

The real column is not a stub column, and it is almost never centrally load-

ed. Normally it is loaded biaxially. Usually it is also restrained. Although the

restraint aspect is not yet incorporated, some very recent work should enable us to

tap the unused margin of strength that is available in biaxially loaded columns (3).

Fig. 4 is illustrative. It is presented on a non-dimensional basis, the ordinate being

the moment about the y-axis M divided by the ultimate moment M . similarly with they ~'

abscissa.

There are two groups of curves. The lmverset, identified by "CRC", are for

three L/r-values (0, 40, and 60) and represent application of the current 3-term in-

teraction formula that is the basis for the AISC formula.

at ultimate,

C M C M!:.- + 'mx x my y <1 0p M (I-pIP )+M (I-pIp) •cr ux ex uy ey _,

/In terms of load and mo~ent

(1)

The case chosen is for pIp = 0.30 and using a W8 x 31. (~ike many other things, biy

axial stability is shape-dependent).

The upper curves come from the new theory developed at L~high. These things

should be noted:

(1) The new curves are close together -- which makes it pos-

sible to develop an approximation that is so identified.

(2) The mathematical expression of this approximation has the

appearance, at least, of greater simplicity:

M 1.70 M 1.70( M

X') + (i- ) < 1.0

ux uy(2)

(3) There is a considerable margin of strength available to

~-- us, but not yet tapped for use in design.

The results of this work as well as that from other institutions, is being

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pulled together under the auspices of Task Group 3 of the Column Research Council.

It is expected that this group will be coming up with practical design recommendations

that will enable us to exploit the advantages noted.

Figure 5 shows the contents of the 3rd Edition of the CRC Guide into which

the results of this and other new stability data is being placed (4). Bruce Johnston

is the editor. On the left are shown the chapters that were contained in the second

edition. Evidently the third edition will be much more comprehensive in its coverage

than the second.

BEAM-TO-COLUMN CONNECTIONS

As part of a program designed to exploit more fully the ductile strength of

beam-to-column connections, studies were conducted at Lehigh in which the web panel

was made intentionally weak. The thickness of the web was much less than the present

specifications require. This was done for two reasons. First to follow-up on the

comment that is frequently made (and is true) that the present provisions are too

conservative. Second, is it possible to develop a theoretical prediction of the be-

havior of this web panel under shear loading?

Figure 6 shows one of the test specimens. It was fully welded and horizontal

stiffeners were provided to transmit beam-flange forces into connection panel. It

was found that the increase in shear strength that has always been observed above the

elastic limit is due primarily to the action qf the boundaries, the flanges and stiff-

eners that form the boundary to the connection panel (5).

Figure 7 shows the comparison of the test with the theory. The dotted line

is the theory developed, and the points are the results of the test. To use Prof.

John Baker's expression, "The agreement is almost indecent". In Fig. 7 Vy is the

theoretical load at which yielding should occur in the web panel under the combined

action of the end load V and the axial force P. (The pip ratio for this assemblyy

was about 0.5). V is the load that would correspond to plastic failure of thispc

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assemblage corresponding to the formation of plastic hinges above and below the con-

nection panel. V is the load corresponding to a plast,ic hinge at the beam end (seep

inset in Fig. 7). Of course the web was so thin (about half the specification value)

that the yield value was very low. Even so, the test went on and eventually the con

nection was able to support a load of 216k which is greater than both V and Vpc p.

The presence of the axial force caused early yielding in the web panel, but, because

of the panel boundary action followed by continuous strain hardening, the assembly

was able to sustain a shear stress considerably higher than shear yield stress of the

material. The large inelastic deformation capacity resulted partly from the rotation

of the columns and partly from the shear distortion of the panel zone.

Can one use thinner webs? The answer is yes, but the upper limit may be

somewhat elusive. The limit as far as the web behavior is concerned is probably

the buckling of the web, considerable above V' • Before we can reach this condition,, y

however, the web will have deformed significantly. This will affect the displacement

of the frame and will contribute to some p-~ moment. Thus if these moment increments

are a factor then they will control how thin one can make the web. Methods are

available to predict this ,effect (6).

Next let us look at another case, the one in which the applied moments are

equal and opposite on both sides of the column. As part of the same comprehensive

program, flange-connected, unstiffened joints have been studied. The effect of the

,bending moment can be represented by a couple composed of a compression flange force

and a tension flange force. These forces cause two critical problems: the first is

yielding, usually accompanied by buckling of the column web in the compression zone

'or by fracture in the tension zone, and the second is fracture of welds connecting" ~ ._.....-,... ~... ~':~ ..

the tension flange to the column. The presence of high shear forces may influence,

to some extent, the behavior of the connection as well as its failure mode.

For heavy columns with thick webs and flanges, stiffeners may not be required

to strengthen the connections. Design criteria are available to determine whether or

not stiffeners are necessary for a given situation (7). The criteria are based on the

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results of an earlier investigation on fully welded connections made of A36 steel and

with only small shear forces present. One of the major objectives of the current study

is to evaluate the strength of unstiffened connections made of A572, Grade 55 steel

(yield stress = 55 ksi) and subjected to high shear forces (8). The properties of the

W14 x 176 are such that no stiffeners are needed according to the available design

criteria. An indication of connection geometry and principal variables is shown in

Fig. 8.

First there are flange-welded, web-bolted joints with round holes. Next, the

variable of slotted holes is introduced. Then the web is unconnected. A difference

in beam depth is another variab1e--one that governs how much redistribution we can

get into the flanges. Finally there are tests with bolted web and bolted flange.

Within the latter is a further variable of design based on friction and on bearing

in the flanges and with consideration of both round and oversize holes.

The program was designed to provide answers to the following questions:

(1) If we design the connection to transmit the moment

through the f1anses only and the web for shear only,

will it be possible for these flanges to strain harden

enough to develop the full plastic moment of the beam?

(2) If we ignore the moment altogether when we design for

shear, will we still be able to develop the full p1as-

tic shear capacity?

(3) Will there be sufficient rotation for these conditions?

(4) Will it be too flexible?

(5)· Can .we predict it theoretically?

Figure 9 shows one. of the connections after test. Notice how completely all

of the materi:~l 'has "work~d". For this case (and for this whole program) the con-

nections were proportioned on the basis ·that everything was "critical": .The shear

was adjusted in such a way that the web would be fully yielded when M was reached.. p

Grade 55 material was used; for the bolts, higher stresses were used than are now per-

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mitted, although they are both theoretically and experimentally sound (9). Limiting

values of bit and dlw were chosen for the beam. The same was true of the column di-

mensions. The required distribution was about 70%.

The results of the theoretical approach are shown in Fig. 10 together with

the results of connection C12 (a control test). The agreement is very good and indi-

cates that the theory can take intd account not only the connection web deformation

but also the numerous phases of plastic redistribution and up to the final hinge

condition for the whole assembly. It incorporates the formation of plastic hinges

in the column flanges above and below the beam connections.

Do these hinges really form? Figure 11 gives the answer. The column flange

hinges are evident just above and below the beam-flange connections.

Figure 12 shows the results of the tests with bolted webs. The reference load

used in the figure is the plastic limit load, P. The other three loads are the workp

ing load, P (=P 11.7), the plastic load neglecting the contribution of the beam web,w p

P ,and the plastic load modified to include the effect of shear P Connectionpr ps

C12 was fully welded. C2 used round holes, and C3 used slotted holes. The results

indicate that all the connections carried maximum loads far exceeding the computed

plastic loads P and P (and even P ) and that the load-deflection relationshipspr . ps p

of the connections are very similar. The difference in behavior at loads above the

working load was due to slip of the web plates occurring in the bolted connections.

The high strength bolts eventually went into bearing against the sides of the holes,

and the connections thus "regained" their stiffness. The effect of strain hardening

is again the main reason for the connections to attain the high loads .

.. A detail view of connection C3 given in Fig. 13 shows the remarkable degree

to which plastic action has taken place up to the point of final rupture. In flexure,

in beam shear, in the connection plates, in the bolts, in the web panel, in the columns

throughout one observes complete yieiding and redistribution under the most adverse

possible conditions (10).

The upcoming studies will cover web-connected beam-to-column connections and

_._------- -----::.-g

partial strength connections. These latter are most important because sometimes

the depth of the girder is controlled by drift and not by the carrying capacity.

Mention is made here of an important guide for bolted and riveted joints (11).

It has been developed under the auspices of the Research Council for Riveted and Bolt-

ed Structural Joints. John Fisher and John Struik at Lehigh have been responsible for

its preparation. As of this writing the manuscript is in the hands of John Wiley &

Sons for eventual publication. The chapter headings are as follows:

I-General provisions 10-Alignment of holes

2-Rivets ' II-Surface coatings

3-Bolts l2-Eccentrically loaded joints

FRAMES

4-Symmetric butt splices

5-Truss type connections

6-Shingle joints

7-Lap joints

8-Oversize and slotted holes

9-Filler plates between surfaces

l3-Combination joints

l4-Gusset plates

IS-Beam and Girder Splices

l6-Xension type connections

l7-Beam-to-column.connections

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Since the late 1950's an extensive research program has been carried out to

develop plastic design methods for laterally braced and unbraced multi-story frames.

As part of this program, a study was made to determine the factors that affect the

ultimate strength of these frames. For unbraced frames, the secondary overturning

moment (or. the p...,f'. moment) . is found to be 'one of the most significant factors. The

P-b. moments caused by the gravity loads acting through.the lateral'deflection tend

to reduce the overall strength and stiffness of. the frame and lead to instabili.ty

failure (12).

There are two distinctive types of frame analysis: the first-order analysis

in which the effect of secondary moment is ignored, and the second-order analysis in

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which this effect is included. The significant difference between the load-deflection

curves obtained from the first-and second-order analyses is illustrated in Fig. 14

for a 3-story, 2-bay frame (13). The structure was part of a test series which was

designed to study the general behavior and load-carrying capacity of unbraced multi-

story frames. The substantial reduction in strength for the second-order case shows

the importance of considering the P-6 moment in the analysis and design of such frames.

When the plastic method is used in the design, the effect of secondary moments can

be included in a direct manner in the calculations. In the allowable-stress design,

however, an indirect approach is generally used to account for this effect. This

approach, which will be discussed briefly in the next section, was formulated before

a thorough understanding of the frame instability problem was achieved. For this

reason, there is a strong interest in knowing the real load-carrying capacity of

frames designed by the allowable-stress method in order to assess the true factor of

safety (or load factor).

Strength of Frames Designed by the Allowable-Stress Method

The indirect approach mentioned above is based on the premise that the ef-

fect of frame instability can be taken care of by increasing the column sizes of the

frame being designed. According to the AISC specification, all columns in a planar

frame are to be proportioned to satisfy the following two formulas(14):

f Cmfba 1.0'+ (1 - f )<F Fb·a a

F'e

f fba < 1.00.60F +-

YFb

(3)

(4)

in which fa and f b are, respectively, the computed axial and bending stresses and

F = allowable axial stress if axial force alone existeda

~". Fb allowable compressive bending stress if bending moment alone existed

F' = elastic Euler buckling stress divided by a factor of safety. It is alwayse~.-: .

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computed for the in-plane case of buckling. In equation form it is

given by

F'e (5)

~...

-(~ is the actual length in the plane of bending and r b the corresponding

radius of gyration. K is the effective length factor in the plane of bend-

ing. )

0.6 -M

l > 0.4 for columns inMlC = 0.4M braced frames. - is the ratio of them 2 M2

smaller to larger moments applied at the ends of the member. It is positive

when the member is bent in reverse (double) curvature.

C 0.85 for columns in unbraced frames.m

If the columns in a frame are braced in the perpendicular direction, the in-plane

effective slenderness ratio KLb/rb is to be used in computing-Fa. In the subsequent

discussion, it will be assumed that this condition prevails for all the columns.

The effect of frame instability is recognized in two ways -- the first is the

use of the in-plane K factor in computing F and F', and the second is to assign aa e

C value of 0.85 (instead of a much smaller value as given by the equation C = 0.6 -m M m

10.4M) .

2

(1) Frames Designed Without Considering Frame Instability Effects (Design A)

An extensive study of the load-carrying capacity of unbraced frames designed

by the allowable-stress method has been carried out. A total of seven frames, varying

from 10-story, 3-bay to 40-story, 2-bay ,have been designed by the allowable-stress

method and then-analyzed plastically accoroing to the first- and second~order theory.

Figure 15 shows some of the results obtained for the 10-story, 3-bay frame. The frame

was designed for the bending moment and axial force distributions determined from the

first-order analysis and no consideration was given to the effect of frame instability,Mlthat is, K = 1.0 and C = 0.6 - 0.4-M were used in the design of the columns. All the

m 2beams of the frame are made of A36 steel (yield stress = 36 ksi) and all the columns

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A572 Grade 50 steel (yield stress = 50 ksi) (15).

The load factor (ultimate load/working load) of the frame from the first-order

analysis is 1.51, and that from the second-order analysis is 1.31. Thus the frame in-

stability effect causes a reduction of the ultimate strength of 13%. The load factor

of all the frames studied falls in the range of 1.30 to 1.50.

The results to date indicate that frames designed by the allowable-stress

method but with no consideration being given to the overall instability effect can

achieve a load factor of 1.30 or more (16). This observation raises an important ques-

tion: Is 1.30 adequate? The required load factor in plastic design for braced

frames and for one- and two-story frames is set at 1.30 in the current AISC Speciffca-

tion for the case of combined gravity and wind loads. The same value is also specified

in the specifications of·such countries as Canada, Mexico,and Sweden (in this last case

1.34). Australia, India, South Africa, the United Kingdom, and the USSR use a load

factor of 1.40. Reference 7 contains a summary of the plastic design load factors

used in different countries.

(2) Frames Designed to Include Frame Instability Effect (Designs B, C, and D)

Three different designs were made for the 10-story, 3-bay frame, all including

the effect of overall instability:

Design B: Columns were designed for K = effective length factor determined

for the sidesway mode of in-plane buckling (always greater than

1.0), and using C = 0.85.m

.• Design C: Columns. were designed.for K = 1.0 and C = 0.85.m

"0" "

Both Designs Band C require increases in column sizes only; the beams are essentially

unchanged.

Design D: A second-order design with beams and columns selected according to

the bending moment and axial force distributions given by the

second-order analysis. This design requires increases in both

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beam and column sizes and includes automatically the p-~ moment

at the working load level.

Figure 16a shows the second-order load-deflection curves of Designs Band

C together with that of Design A. The ultimate strength of the frame is increased

13% for Design Band 10% for Design C.

These results indicate that" the use of the effective length factors determined

for the sidesway mode of frame buckling does not significantly improve the strength

of the frame.

A comparison of the ultimate strength of Designs Band D with that of Design A

is shown in Fig.16b. Design D, a more balanced design involving increases in both

the beam and column sizes, achieves a load factor 1.43.

All three designs (B, C, and D) result in increases in the load-carrying ca-

pacity of 10 to 13%, which is approximately equal to the reduction due to frame insta-

bility effect noted in Fig. 15. Among these designs, Design C is the simplest to per-

form.

In summary, if the results of these analyses are typical, a frame designed

by the allowable-stress method according to the AISC specification (14) which

indirectly includes the p-~ effect by assuming the theoretical K-value and

C of 0.85 will actually have a load factor in the vicinity of 1.5 (Design B).m

It also shows that frames designed before 1960 in which the effective

length and p-~ effects are ignored, have a load factor of at least 1.3. The

resulting body of experience would lead one to assume that a load factor of

1.3 is probably satisfactory for the plastic design of unbraced frames.*

... Thus (within the limitations of calculations made) these results point

* The present specifications permit ·p1astic design of braced multi-story frameswith a load factor of 1.70 for gravity load and 1.30 for combined load. Applicationto unbraced frames will be ready shortly, and this experimental evidence for afactor of 1.30 is reassuring (17).

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to significant potential improvements. A separate paper is in preparation

on the subject (16).

There are some important provisos: The frames in the analyses were

two~dimensional planar frames of regular geometry, the L/r-values were in the

practical range, there were no setbacks, and the moment diagram was not an

arbitrary one (such as would be obtained by the cantilever or portal method).

Naturally in plastic design, one would have to take into account the

frame instability effect in a direct way -- for which provisions are available.

(12) •

DES I G N BAS E DON PRO B A B I LIT Y

The second technique for advance given earlier was to make design more

like life -- to base it on probabilities. Load-factor/limit-states design is

";. a method of proportioning structures for multiples of service load. The design

ultimate loads are obtained by applying factors to the service loads and these

are related to the resistance of the structure. This resistance (or "response

function") is itself subject to factors. So the method of "Load-factor and

limit-states design"** involves a consideration of the "Loading Function"

(the dead load, the several kinds of live loads, the various combinations

of these loads, and the load factors that are going to be applied), and of

the "Resistance Function" (according to the applicable limit of usefulness).

These functions are shown in Fig. 17 which also points to the design process. .

as equating the loading function with the resistance function (through the

appropriate analytical techniques). It involves a decision on the load factors

and a conscious attention to the appropriate limit of usefulness (18).

** The other terms shown in the lower porti-on of Fig. 1 would be just asappropriate here.

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Figure 18 affords a partial comparison with allowable-stress design.

As shown in the left, in allowable-stress design one uses the service dead

load and live load and the total must be less than the allowable load P •a

In load-factor design, illustrated here in simplistic terms by plastic design,

we take a factor times the dead load and a factor times the live load and add

selected so that it is greater than the design ultimate load P •t.l

them together to obtain P •u

The plastic limit load of the structure P isp

(To the

right is shown one effect of the use of multiple load factors. With this

technique, one separates out the load factors for live load and dead load

on the assumption that different factors can be used (19). In this case, one

~ould expect that the factor for the dead load will be lower and the factor for

the live· load will be greater. But one can still find that the total loading

function will permit selection of a smaller section. The second design would

be lighter than the first ).

The matter does not stop here. Separating the loading function and

the response function opens the way to consider probability. But at the same

time this is the biggest uncertainty when it comes to future design application.

What are the sources of possible uncertainty that can or should be subjected to

such consideration? The following is a list, expanding on.the one contained in

ASCE Manual 41 (7).

I-Approximations in analysis

2~Approximations in design

3-Stress concentration and residuals

4-Variation in properties

5-Variation in dimensions

6-Workmanship

7-Location

8-Variation in load-type

9-Combinationof loads

lO-Intended use

:....

They enter into what we presently call the factor of safety in allowable-stress

design or into the load factor in plastic design. In load-factor design some

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would enter in the loading function and some in the response function. All

of them are sources of possible uncertainty.

This uncertainty of loading and of response is reflected in Fig. 19,

which is perhaps a more "precise" way of representing the right side of Fig. 18.

Again it is based on a hypothetical load vs. deflection curve of a frame. The

horizontal line at the plastic limit load is not a fixed value but is subject

to variation. The variation would be due to such things as the yield point or

the dimensions of the shape. The statistical variation in the resistance is

suggested by the function fRo Similarly for load -- the load is uncertain,

its actual value can vary considerably, and that is why we have a factor in

the first place. A hypothetical statistical variation in the load is indicated

in Fig. 19 by the function fL. (It reflects a larger spread than that for the

resistance function).

Thus in the actual design, according to the load-factor and limit-states

design concept, the criterion is not that the upper end of the bar "FD" in

Fig. 19 be less than the horizontal line at P , but that the maximum probablep

value of the load F1

L must be less than the minimum carrying capacity FrR.

In equation form this means that:

< F Rr

(6)

I:".I : ...

Is load- and response-factor design a suitable alternative for a11owab1e-

stress design? These are the things we have to think about: the concept of

the multiple load factors; the rational choice of these factors; the possible

combinations to be specified"; and th~ potential economy vs. the complexity. The

American Iron and Steel Institute is sponsoring a major program at Washington

University, St. Louis, under the direction of T.V. Galambos that is examining

-17

many of these factors (20). One needs answers to such quest~ons as these:

What are the statistical'variations? What are the variations of load? What

lire the economies -- Will time and material be saved?

I N T ERA C T ION CON SID ERA T ION S

The third topic, interaction considerations, involves taking advantage

of the otherwise strength-neglected parts of the structure. The discussion

falls into these four categories: (1) Floor systems and shear connectors,

(2) developing composite action at the columns, (3) integrated structural design,

and (4) mixed sys tems •.,

FLOOR SYSTEMS AND SHEAR CONNECTORS

The work on the floor systems and shear connectors has its primary

focus on the behavior of the different types of manufactured floor systems that

are available. When one takes into account composite action in the positive

moment·region, not only is there a strength advantage but the increase in

stiffness is frequently a significant design improvement. In Ref. 21 the

recent developments in this area are described.

COMPOSITEBEAM~TO~COLUMNACTION

Whengrav{ty"ioadsalone are.applied to a frame, positive (or sagging)

bending moments usually develop at the center and negative (or hogging) moments

at the ends of its beams. If shear" connectors are provided between the floor

slab and the beam, it is customary to assume that composite action takes place

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only in the positive moment region of the beam. When lateral loads are subse-

quently applied, the bending moment at the windward end of the beam sometimes

changes its sign -- from negative to positive. Composite action may therefore

take place over more than two-thirds of the span length of the beam. It is

therefore necessary to know the maximum moment that the beam can transmit and

also the behavior of the critical region near the column face. Included in

a current investigation at Lehigh are parameters such as: depth of beam

(relative to a fixed slab thickness), solid slab vs. slab with metal deck, :con-

crete strength, and density of connectors. Complete results of this study will

be presented in a forthcoming report (22). Figure 20 shows one of the

specimens under test.

Figure 21 shows the results of two tests -- one with a solid slab and

the other with its slab cast on a metal deck. The inset in the sketch shows

the loading system diagrammatically. The behavior and the maximum resisting

moment of the two beams are very similar, and they both failed after the con-

crete near the column face was extensively crushed. The plastic moment of the

W12 x 27 shape is 174 kip-ft. and the maximum moment carried by the specimen

having a solid slab is more than 300 kip-ft, an increase of about 80%. In

addition to increasing the strength of the beam, composite action also in-

creases its stiffness, thus reducing the overall frame drift tinder wind. The

effect of.a small gap between the concrete .slab and the column face was also

examined in the study; it is similar to the effect.of slip in a bolted joint:

After coming into· bearing the stiffness becomes that of a member without the

:gap.

-19

INTEGRATED STRUCTURAL DESIGN

The third topic under interaction considerations embraces not only the

two prior topics but also the strength and stiffening effects of floors and

partitions when acting in conjunction with the bare frame.

In the experimental portion of the study at Lehigh, a half-scale test

building, consisting of a steel framework, a composite floor system and light-

gage corrugated partitions, was constructed. A photograph of this "building" is

shown in Fig. 22. The structure was first tested without the floor system

and the partitions. The concrete floor slabs were then connected to the steel

beams by mechanical fasteners and the test repeated. Finally, the ~orrugated

partitions were added to the frame-floor system to study their stiffening effect.

Some sample results from the testing are shown in Figure 23. These

results compare vary favorably with theoretical predictions developed ~n Ref. 23.

It may be concluded for the test building, that the major interaction is between

the frame and the partitions, with the floor system contributing about 5% to the

total stiffness.

MIXED SYSTEMS

The fourth topic under interaction considerations is "mixed systems".

The Japanese have made notable use of this scheme which combines the best

features of both steel and concrete, under the designation "steel-reinforced...

concrete frames"; It· is like building a steel frame and then putting reinforced

concrete around it. Figure 24 is atypical example.

Figure 25 is typical of a number of examples in the United States, this

one by Skidmore, Owings &Merrill. The 8~in. members visible at the top continue

1... ...__ ,__... ... _

-20

at substantially the same size throughout the entire 36-story height of the

building. Does one call this a steel building or"a concrete building? For the

upper floors it looks like a steel building. As the reinforced concrete is

being placed in the lower part is looks like a reinforced concrete building.

No matter what it is called, by combining the best advantages of the two materials,

erection time is reduced, and reported economies of 15% are obtained (24).

S T Rue T U R A L S Y S T EMS

The prior discussion leads directly to the last major topic, which in-

volves the exploitation of the structual system -- optimizing the arrangement

of the material. Figure 26 shows the result of this process which eventually

leads to an indication of the economical number of stories for different

structural systems (25). It is the development of the structural system that

makes economically possible the construction of the so-called "monumental" sky-

scrapers. The same cost per square foot of the floor area becomes applicable to

a 100-story building as is common for 50- or 60-story "conventional" buildings (26).

It is the drift that is the problem. Unless special care is taken, the

extra weight goes into drift control and not into strength. Figure 27 (after Khan)

is illustrative. The "cost index" is plotted against number of stories. The

"ideal" system is the one whose members are selected to support gravity load alone.

As Khan points out, it is as if one imagined a glass dome placed over the building

to protect it from the wind. That is the goal. The development of the tubular

systems, the- framed tube, the tube-in-tube, and the trussed tube are all efforts

in this direction. There is a premium to be paid for height if lateral load is

carried by the conventional system. Instead, one wants every pound of steel re-

quired for gravity load to also participate in the resistance to lateral force.

.. ;; .

-21

The 5-volume, 5200-page PROCEEDINGS of the International Conference on

"Planning and Design of Tall Buildings" is replete with,evidence and references

on the subject of structural systems as well as the other major topics germane

to tall buildings. One of these five volumes, "Structural Design of Tall Steel

Buildings" was prepared under the coord'inating guidance of T. R. Higgins, in

whose honor this paper is presented.

OTHER CON SID ERA T ION S

The prior discussion of four ways to improve structural steel design

has patently emphasized the economical aspect. Two other aspects must be

mentioned.

Increasing cooperation between members of the design team -- the

engineer, the ar~hitect, the planner, the landscape architect -- is essential

not only if economy of the structure is to be attained but also if the

larger functions of the building as part of the community are to be achieved.

Some of this cooperation is coming about automatically, partly as a result of

the size of projects and also because of the increasing importance of the struc-

tural system in the architectural scheme of things ..;~;.""';"';,

The second aspect is the increasing demand for quality -- not only for

structural and architectural quality but for life quality. As noted by

Robertson, "We could start a mile-high building next year -- but do we want to" (27).

Designs must first consider human needs, and this leads to interaction with

another'''team'', the decision-making team· (developers, investors, planning

commissions, government agencies, and organized citizen groups).

In both of these aspects, steel construction is in a crucial position.

On the one hand, it is only possible to build the tallest buildings in steel •

-22

On the other hand, these monumental structures have a very significant influence

on the urban environment. What all of this means is th~t in some respect, at

least, advances in steel building design will depend on the success with which

the design team and the decision-making team meet the real needs of the citizen.

SUMMARY

Four techniques for advancing steel building ~esign are:

(1) To capitalize on the strength and ductility of the

parts and of the whole.

(2) To exploit the potentials of Load-Factor and Limit-States

Design -- which ultimately means ades'ign based on probabi-

1istic considerations.

(3) To take advantage from both a strength and a stiffness

standpoint of the walls, partitions, and floors acting

together with the structural frame.

(4) To exploit the arrangement of the material to the fullest,

developing structural systems that (for example) do not

impose a penalty or premium for height as regards resistance

to wind load.

Among the specific current and potential developments noted are:

(a) The additional available strength in biaxia11y loaded columns

(Fig. 4);

(b). .

The predictability and increased shear-strength capacity of

exterior beam-to-co1umnconnections (Fig. 7);

-" ..

(c) The ability of interior beam-to-co1umn connections to develop

the full plastic beam strength on the basis of designs for

flange connection only (Fig. 12);

...

.,.- ..

-23

(d) The prospect of somewhat simpler allowable-stress design

approaches with regard to frame-stability for planar frames

of regular geometry (Fig. 16);

(e) The significant increases in design strength and stiffness

that are afforded through consideration of walls, partitions,

and floors (Fig. 23);

(f) The overall savings possible through a consideration of

"mixed systems" (Fig. 25);

(g) The wide variety of structural systems emerging out of a

consideration of optimum geometrical configurations (Fig. 26);

(h) The necessity to give increased consideration to human needs

in building design -- needs that require a closer integration

of the various professions in the design team and which

suggest a closer interaction between the designers and the

decision-makers.

A C K NOW LED GEM E N T S

The authors acknowledge the contributions of the following persons

whose work has led to the most recent information presented in this paper:

O. Okten, J. H. Daniels, G. C. Driscoll, Jr. -- the strength of frames

D. P. du Plessis, J. H. Daniels -:- composite assemblages

W. M. El-Dakhakhni, J. H. Daniels -- frame-floor-wall interactions

J •.. S. Huang, D. J. Fielding, W. F.; Chen -- beam-to-column connections

P. Marek, T. V. Galambos -- Load-Factor Design

The sponsors of the various.research projects from which work was

drawn are the American Iron and Steel Institute, the Welding Research Council,

the Pennsylvania Science and Engineering Foundation, and the National Science

Foundation .

~ -.

.' ..

-24

The authors are particularly appreciative of the American Institute

of Steel Construction for the establishment of the "T. R. Higgins Lectureship"

which stimulated the preparation of this paper.

Final acknowledgement is due to "Ted" Higgins himself who has afforded

an inspiration to those who have followed the paths of structural steel research.

REF ERE N C E S

1. Tall, L., Ed.STRUCTURAL STEEL DESIGN, Ronald Press, New York, 1964

(2nd Edition due in 1974).

2. Iyengar, S. N.BEHAVIOR OF THIN PLATES IN THE ELASTIC AND INELASTIC RANGES,

Ph. D.Dissertation, Lehigh University, 1973.

3. Negussie, T., and Chen, W. F.DESIGN CRITERIA FOR STEEL H-COLUMNS UNDER BIAXIAL LOADING,

Fritz Engineering Laboratory Report 389.2, Lehigh University,January 1973.

4. Johnston, B. G., Ed.GUIDE TO DESIGN CRITERIA FOR METAL COMPRESSION MEMBERS, 2nd Edition

John Wiley and Sons, Inc., New York, 1966 (3rd Edition inpreparation).

5. Fielding, D. J., and Huang, J. S .. SHEAR IN STEEL BEAM-TO-COLUMN CONNECTIONS, Welding Journal,

Vol. 50, No.7, July 1971, p. 3l3-s.

6. Fielding, D. J., and Chen, W. F.STEEL FRAME ANALYSIS AND CONNECTION SHEAR DEFORMATION, Journal

of the Structural Evision, ASCE, Vol. 99, STI, January 1973, p. 1.

7. ASCE-WRCPLASTIC DESIGN IN STEEL -- A GUIDE AND COMMENTARY, 2nd Editon,

. ASCE Manual 41, 1971.

8. -Huang, J. S·., Chen,! W. F., and Beedle, L. S.BEHAVIOR AND DESIGN OF STEEL BEAM-TO-COLUMN MOMENT CONNECTIONS, Fritz

Engineering Laboratory Report 333.20, Lehigh University,1973.

9. Fisher, J. W. and Beedle, L. S.CRITERIA FOR DESIGNING BEARING-TYPE BOLTED JOINTS, Journal of

the Structural Division, ASCE, Vol. 91, ST5, October 1965, p. 129.

10. Huang, J. S., and Chen, W. F.STEEL BEAM-TO-COLUMN MOMENT CONNECTIONS, presented at ASCE National

Structural Engineering Meeting held at San Francisco, April 1973 •

".

11.

-25

Struik, J. H.,and Fisher, J. W.DESIGN GUIDE TO MECHANICALLY FASTENED JOINTS, Fritz Engineering

Laboratory Reports 357.1-17, Lehigh University, 1972 (to bepublished).

....

"._" a

12. Driscoll, G. C., Jr. et a1.PLASTIC DESIGN OF MULTI-STORY FRAMES, Lecture Notes and Design

Aids, Fritz Engineering Laboratory Reports 273.20 and 273.24,Lehigh University, 1965.

13. Galambos, T. V., Driscoll, G. C., Jr.,and LU f L. W.RESEARCH ON PLASTIC DESIGN OF MULTI-STORY FRAMES AT LEHIGH

UNIVERSITY, 8th Congress of IABSE, Final Report, September 1968,p. 517.

14. American Institute of Steel ConstructionSPECIFICATION FOR THE DESIGN, FABRICATION AND ERECTION OF STRUC

TURAL STEEL FOR BUILDINGS, AISC, New York, February 1969.

15. Lu, L. W.,and Beedle, L. S.RECENT RESEARCH ON THE STRENGTH, STIFFNESS AND DUCTILITY,

Fritz J;:ngineering Laboratory Report 369.79, Lehigh University,July 1973 (to be published in Proceedings, Australian Confer

ence on the Planning and Design of Tall Buildings).

16. Okten, 0., Morino, S., Daniels, J. H.,and Lu, L. W.STUDIES OF EFFECTIVE COL~rn LENGTH AND FRAME STABILITY, Fritz

Engineering Laboratory Report 375.2, Lehigh University, 1973.

17. Driscoll, G. C., Jr.PLASTIC DESIGN OF UNBRACED MULTI-STORY STEEL FRAMES, American

Iron and Steel Institute (in preparation).

18. Beedle, L. S., Lu~ L. W.,and Lim, L. C.RECENT DEVELOPMENTS IN PLASTIC DESIGN PRACTICE, Journal of

the Structural Division, ASCE, Vol. 95, ST9, September 1969,p. 1911.

19. Marek, P. J.REVIEW OF CZECHOSLOVAK AND FRENCH SPECIFICATIONS, Fritz Engineering

Laboratory Report 37l.2A, Lehigh Unviersity, 1973.

20. Galambos, T. V.LOAD FACTOR DESIGN FOR STEEL BUILDiNGS, Engineering Journal,

AISC, Vol. 9, No.3, July 1972, p. 108.

21.' ...Grant, J. A;,Jr., Fisher, J. W., and Slutter, R. G.HIGH-STRENGTH STEEL COMPOSITE BEAMS WITH FORMED METAL DECK AND LOW

PARTIAL SHEAR CONHECTION, presented at the Second Specialty Conference ori Cold-Formed Steel Structures at the University of

Missouri - Rolla, St. Louis, Missouri, October 1973.

22. du Plessis, D. P.,and Daniels, J. H.STRENGTH OF COMPOSITE BEAH-TO-COL~ CONNECTIONS, Fritz

Engineering Laboratory Report 374.3, Lehigh Universtiy, 1973 •

.. -.

~. e••

--------------------------------""':2:"":6;---------....,

23. E1-Dakhakhni, W. M., and Daniels, J. H. .FRAME-FLOOR-WALL SYSTEM INTERACTIqN IN BUILDINGS, Fritz

Laboratory Report 376.2, Lehigh University, 1973.

24. Fox, A. J., Jr.~ Ed.BUILDING DESIGN REDUCES STEEL WITH CONCRETE-TUBE WIND BRACING,

Engineering News Record, Vol. 186, No. 22, June 3, 1971,p. 18.

25. Iyengar, S. H.PRELIMINARY DESIGN AND OPTIMIZATION OF STEEL BUILDING SYSTEMS,

Proceedings of the International Conference on the Planningand Design of Tall BUildings, Lehigh Universi~y, 1972,Vol. II, p. 185.

26. Khan, F. R.THE FUTURE OF HIGH-RISE STRUCTURES, Progressive Architecture,

October, 1972.

27 •. Fox, A. J., Jr., Ed.HIGH~RISE EXPERTS SCORE PRESENT PLANNING, STRESS IMPACT, SAFETY

Engineering News Record, Vol. 189, No.9, August 31, 1972, p. 12 .

-27

FIGURE TITLES

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Nomenclature for structural design

Structural design

W14 ~. 730 shape

Developed design approximation compared with theory and CRC formula

CRC guide

Exterior beam-to-co1umn connection after testing

Beam load versus beam end rotation at column

Variables

Interior beam-to-co1umn connection after testing

Fig. 10 C12 test results compared with theory

Fig. 11 Interior connection

Fig. 12 Load-deflection curves of three interior connections

Fig. 13 Connection C3 after testing

Fig. 14 Test results compared with first- and second-order theory

Fig. 15 Load-deflection curves of a frame designed by· allowable-stress method

. without consideration of frame instability effect

Fig. 16 Comparison of load-deflection curves of a frame designed by a11owab1e-

stress method with and without consideration of frame instability effect

Fig. 17

Fig. 18

Fig. -19

Fig. 20

Fig. 21

Fig. 22

Fig. 23

Loading function and resistance function as equated in design

Allowable-stress design compared with load-factor and limit-states design. ..

Variation of loading and response functions

Testing of composite beam-to-co1umn connection

Strength of composite beam-to-co1umn connections

Test building with composite floor and partition

Increase in building stiffness due to floor and partition".-.

." ..

Fig. 24 Mixed system (Wakabayashi)

, ....

-28

Fig. 25 Chicago building (Courtesy Engineering News Record)

Fig. 26 Economical number of stories for different structural systems

Fig. 27 Increase in cost due to height (26)

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LYNN S. BEEDLE

j I•• t u ·

1973 T. R. Higgins Lectureship AwardThe 1973 T. R. Higgins Lectureship Award has been presentedto Dr. Lynn S. Beedle, Professor of Civil Engineering andDirector of the Fritz Engineering Laboratory, Lehigh University.

Dr. Beedle joined Lehigh University in 1947 as a ResearchEngineer in the Fritz Engineering Laboratory. His researchactivity at Lehigh has been concerned with studies in plasticdesign of steel structures, studies of influence of residual stresses,research in high-strength bolts, and behavior of welded plategirders. He has served actively in the work of AREA, AWS,CRC, WRC, and is past chairman of the Structural DivisionExecutive Committee of ASCE. Currently Dr. Beedle is servingas a member of the National Science Foundation AdvisoryPanel for Engineering, Director of the Column ResearchCouncil, and Chairman of the ASCE-IABSE Joint Committeeon Planning and Design of Tall Buildings. He is a Member ofthe National Academy of Engineering.

The Award Winning Paper

Published originally in the September 1969 Journal of theStructural Division, ASCE, the paper "Recent Developmentsin Plastic Design Practice" by Lynn S. Beedle, Le-Wu Lu, andLee Chong Lim was selected by the Awards jury as the mostsignificant engineering paper on steel design published fromJanuary 1, 1967 to January 1, 1972. The distinguishedmembers of the jury were: Theodore V. Galambos, WashingtionUniversity (St. Louis); William McGuire, Cornell University;John E. Mueller, Whitehead & Kales Company; Clarkson W.Pinkham, S. B. Barnes Associates; Leslie E. Robertson, SkillingHelle Christiansen & Robertson; Robert S. Sherman,Carolina Steel Corporation.

The T. R. Higgins Lectureship Award

Inaugurated in 1971, the T. R. Higgins Lectureship Awardrecognizes the author of the technical paper judged to be themost significant contribution to the engineering literature onfabricated structural steel published during the period ofeligibility. The annual Award consists of an engraved certificateand a $2,000 honorarium. When there is more than one author,the senior author receives the Award, but the other authors arerecognized by the recording of their names. The winnerpresents an oral review of his paper at the AISC NationalEngineering Conference and at five other locations during theyear.

The Award was established by AISC in honor of Theodore R.Higgins, former AISC Director of Engineering and Research, inrecognition of his substantial contribution to the advancement ofthe structural steel industry through innovative engineering,technical papers, and professional lectures.

Reprinted from AISC Engineering Journal, Fourth Quarter, 1973

Recent Developments in Steel Building DesignLYNN S. BEEDLE, LE-WV LV, AND ERKAN OZER

THOSE ENGAGED in the structural research that has beentypical of many steel-industry-sponsored programs inrecent years-and has been traditional at the FritzEngineering Laboratory since its early days-have theadvantage of working with an advisory committee.Beyond receiving suggestions for needed work thisadvantage has at least two ramifications: (1) There isalways interest in the engineering application of a newapproach that may arise from the research, and (2) theinvestigators cannot fail to be impressed with the necessary "constraints", among which are time and complexity. A new method that involves more design time,or is more complex in its application, must have a significant economic advantage before it can become apractical design tool.

It is from this background that recent developmentsin steel building design are discussed in this paper. Whichof the developments arising from research have a potential for improvement in design? Some of these applications are current. Some are in the future. Some of thesource material goes beyond that resulting from the workof the writers and of their own institution. Not only doesit include AISC-sponsored research, but also that of theAmerican Iron and Steel Institute, Column ResearchCouncil, Research Council on Bolted and RivetedStructural Joints, and the National Science Foundation.

Advances-These remarks are built upon the thesis thatthere are four .major ways to advance steel building design. Three are proven techniques in the United States.The other (item two, below) is in an "initial" phase in

Lynn S. Beedle is Professor of Civil Engineering and Director, FritzEngineering Laboratory, Lehigh University, Bethlehem, Pa.

Le- Wu Lu is Professor of Civil Engineering and Director, BuildingSystems Division, Fritz Engineering Laboratory, Lehigh University,Bethlehem, Pa.

Erkan Ozer is Post-Doctoral Research Associate, Fritz EngineeringLaboratory, Lehigh University, Bethlehem, Pa.

This paper is an updated and expanded version of the T. R. HigginsLectureship Award paper "Recent Developments in Plastic DesignPractice," by Beedle, Lu, and Lim, published in the September 1969Journal of the Structural Division, ASCE. It was presented at theAISC National Engineering Conference in Philadelphia in May 1973.

the U.S., but is incorporated in design practice abroad.The first approach is "strength and ductility": Take

advantage of the strength and ductility of the parts and ofthe whole. Plastic design is in this field.

Second, one can make design like life. Base it more onprobabilities.

Third, one can take advantage of what otherwise arethe neglected parts, and this involves interaction considerations.

Finally, one can exploit the arrangements of thematerial to the fullest. What is the best structural system?

Structural Design-The overall objectives of structuraldesign are basically threefold: (1) The structure mustmeet functional requirements, (2) it must support loadand provide stiffness, and (3) it must satisfy economicalrequirements. It may be that in the past the strictly loadcarrying aspects have been overemphasized, and thiscomes into focus when one considers the real function

of a structure.!Now, having made this statement, one still must look

at the load limits and the other major design criteria as abackground. These "limits of structural usefulness" arethe plastic limit load, the stability limit, the elastic limit(which is a hypothetical consideration), the fatigue limit,the fracture limit, and finally the serviceability criteria ofdeflection or vibration.

These various limits are used in a number of ways,but their consideration is eventually a part of particulardesign procedures, most of which have names. They aregrouped in Fig. 1 in three categories. Whether or not theterms within a given group are synonymous is a matter ofusage and conjecture. It is to be hoped that in time thissituation can be resolved. (That, in itself, would be aconsiderable"advance" .)

No matter which names are used for a .particulardesign approach, they all finally come down to "Structural Design"-a process shown in Fig. 2 (which is anadaptation of an illustration developed by Bruce Johnston). At the top are shown the various limits of usefulness. Of course there must be the load study (left) and thedeflection and drift limit evaluation (right). Then,

98

ENGINEERING JOURNAL/AMERICAN INSTITUTE OF STEEL CONSTRUCTION

ALLOWABLE - STRESS DESIGN

WORKING STRESS DESIGNELASTIC DESIGN

PLASTIC DESIGN

ULTIMATE STRENGTH DE:SIGNLIMIT DESIGN

LOAD-FACTOR DESIGNLIMIT STATES DESIGN

LOAD- AND RESPONSE - FACTOR DESIGNLOAD FACTOR AND LIMIT STATES D£SIGN

Fig. 1 Nomenclature for structural design

through various static or dynamic analyses, and usingeither allowable-stress design, plastic design, or loadfactor and limit-states design, one eventually arrives at a"Structural Design".

Fig. 3. W14X730 shape

ever, the theoretical work has advanced to the point thatit is possible to predict theoretically the influences of theinternal stresses and their consequent influence on column strength, and there has been enough experimentalwork to show that the theory is sound. So future workwill give greater attention to the theoretical side andshould require somewhat less in the way of experimentalstudies.

The real column is not a stub column, and it is almostnever centrally loaded. Normally it is loaded biaxially.Usually it is also restrained. Although the restraint aspectis not yet incorporated, some very recent work shouldenable us to tap the unused margin of strength that isavailable in biaxially loaded columns. 3 Figure 4 is illustrative. It is presented on a non-dimensional basis, theordinate being the moment about the y-axis, Mil dividedby the ultimate moment MUll; similarly with the abscissa.

STRENGTH AND DUCrILITY

The major research areas in which the exploitation ofstrength and ductility might be cataloged incorporate:mechanical properties of steel; beams, columns, andconnections; the various failure modes; the behavior ofsubassemblages and of braced and unbraced frames;optimum design; and repeated and reversed loading.Comment will be made only on columns, connections,and frames.

Columns-The stub column test, widely describedelsewhere, has a number of useful functions. It revealsthe residual stress effect. It nicely averages out thevariation in the yield stress across the section. If carriedfar enough it will tell us something about local instability.One of the things that the most recent work is showingis that we can look forward to a relaxation in depth-towidth requirements for local instability.2 Now, someshapes such as the W14X730 of Fig. 3 become so largethat they exceed the capacity of testing machines. How-

PLASTICDESIGN

STRUCTURALDESIGN

06

04

02

JE,xI~~0301Py

W8x31

Theory

ApproJumat Ion

Fig. 2 Structural design

99

Fig. 4. Developed design approximation compared withtheory and eRe formula

FOURTH QUARTER/l973

Beam-to-Column Connections-As part of a programdesigned to exploit more fully the ductile strength ofbeam-to-column connections, studies were conducted atLehigh in which the web panel was made intentionallyweak. The thickness of the web was much less than thepresent specifications require. This was done for tworeasons. First, to follow-up on the comment that is frequently made (and is true) that the present provisionsare too conservative. Second, is it possible to develop atheoretical prediction of the behavior of this web panelunder shear loading?

Figure 6 shows one of the test specimens. It was fullywelded and horizontal stiffeners were provided to transmitbeam-flange forces into connection panel. It was foundthat the increase in shear strength that has always beenobserved above the elastic limit is due primarily to theaction of the boundaries, the flanges and stiffeners thatform the boundary to the connection panel.s

Figure 7 shows the comparison of the test with thetheory. The dotted line is the theory developed, and thepoints are the results of the test. To use Prof. JohnBaker's expression, "The agreement is almost indecent."

Fig. 6. Exterior beam-to-column connection after testing

(2)

(1)

3'd EDITION (New Chapters)

o STRUCTURAL SAFETY

o DYNAMIC LOAD EFFECTS

o THIN -WALLED METAL CONSTRUCTION

o TUBULAR MEMBERS

o TAPERED STRUCTURAL MEMBERS

o COLUMNS WITH LACING, BATTENSOR PERFORATED COVER PLATES

o MILL BUILDING COLUMNS

o MULTI - STORY FRAMES

o ARCHES

o STIFFENED PLATE CONSTRUCTION

o SHELL AND SHELL LIKE STRUCTURES

o COMPOSITE COLUMNS

GUIDE

(M)1.70 (M )1.70_x + _1/ < 1.0M ux M U1/-

3. There is a considerable margin of strength available to us, but not yet tapped for use in design.

The results of this work, as well as that from otherinstitutions, is being pulled together ~nder the auspicesof Task Group 3 of the Column Research Council. It isexpected that this group will be coming up with practicaldesign recommendations that will enable us to exploitthe advantages noted.

Figure 5 shows the contents of the 3rd Edition of theCRC Guide into which the results of this and other newstability data is being placed.4 Bruce Johnston is theeditor. On the left are shown the chapters that were contained in the second edition. Evidently the third editionwill be much more comprehensive in its coverage thanthe second.

Fig. 5. eRe guide

There are two groups of curves. The lower set, identified by "CRC," are for three LIT-values (0,40, and 60)and represent application of the current 3-term interaction formula that is the basis for the AISC formula. Interms ofload and moment at ultimate,

P + CmxMx Cm1/M1/- + < 1.0PeT M ux(1 - PIP.x) M U1/(1 - PIPtI/) -

The case chosen is for PIP1/ = 0.30 and using a W8X31.(Like many other things, biaxial stability is shapedependent.)

The upper curves come from the new theory developed at Lehigh. These things should be noted:

1. The new curves are close together-which makesit possible to develop an approximation that is soidentified.

2. The mathematical expression of this approximation has the appearance, at least, of greatersimplicity:

• CENTRALLY LOADED COLUMNS

CRC

2 nd EDITION

• PeN'" TRI:l6SMEMBERS WITH ELASTIC

LATERAL RESTRAINTS

• BEAM - COLUMNS

• llElMPIlESSIBN MEMBER BETAIt:SLOCAL BUCKLING OF PLATES

• LATERAL ~L~LATERALLY UNSUPPORTED BEAMS

• PLATE GIRDERS

100


V(kips)

o

Fig. 7. Beam load versus beam end rotation at column

In Fig. 7, V'II is the theoretical load at which yieldingshould occur in the web panel under the combined actionof the end load V and the axial force P. (The PjPII ratiofor this assembly was about 0.5.) The term Vpc is theload that would correspond to plastic failure of thisassemblage corresponding to the formation of plastichinges above and below the connection panel. The termVp is the load corresponding to a plastic hinge at thebeam end (see inset in Fig. 7). Of course the web was sothin (abolit half the specification value) that the yieldvalue was very low. Even so, the test went on and eventually the connection was able to support a load of 216kips, which is greater than both Vpc and Vp • The presenceof the axial force caused early yielding in the web panel,but, because of the panel boundary action followed bycontinuous strain hardening, the assembly was able tosustain a shear stress considerably higher than shear yieldstress of the material. The large inelastic deformationcapacity resulted partly from the rotation of the columnsand partly from the shear distortio~of the panel zone.

Can one use thinner webs? The answer is yes, but theupper limit may be somewhat elusive. The limit as far asthe web behavior is concerned is probably the bucklingof the web, considerably above V'y. Before we can reachthis condition, however, the web will have deformed significantly. This will affect the displacement of the frameand will contribute to some P-f}. moment. Thus, if thesemoment increments are a factor, then they will controlhow thin one can make the web. Methods are availableto predict this effect.6

Next let us look at another case, the one in which theapplied moments are equal and opposite on both sides ofthe column. As part of the same comprehensive program,flange-connected, unstiffened joints have been studied.

101

The effect of the bending moment can be represented bya couple composed of a compression flange force and atension flange force. These forces cause two' criticalproblems: the first is yielding, usually accompanied bybuckling of the column web in the compression zone or byfracture in the tension zone, and the second is fracture ofwelds connecting the tension flange to the column. Thepresence of high shear forces may influence, to someextent, the behavior of the connection as well as itsfailure mode.

For heavy columns with thick webs and flanges,stiffeners may not be required to strengthen the connections. Design criteria are available to determine whetheror not stiffeners are necessary for a given situation.7 Thecriteria are based on the results of an earlier investigationon fully welded connections made of A36 steel and withonly small shear forces present. One of the major objectives of the current study is to evaluate the strength ofunstiffened connections made of A572, Grade 55 steel(yield stress = 55 ksi) and subjected to high shear forces.s

The properties of the W14 X 176 used for the column aresuch that no stiffeners are needed according to the available design criteria. An indication of connection geometry and principal variables is shown in Fig. 8.

First there are flange-welded, web-bolted joints withround holes. Next, the variable of slotted holes is introduced. Then the web is unconnected. A difference inbeam depth is another variable-one that governs howmuch redistribution we can get into the flanges. Finallythere are tests with bolted web and bolted flange. Withinthe latter is a further variable of design based on frictionand on bearing in the flanges and with consideration ofboth round and oversize holes.

The program was designed to provide answers to thefollowing questions:

FLANGE -CONNECTED ~ UNSTIFFENED

FL ANGE - WELDED

WEB- BOLTE.D

ROUND 140LES

SLOTTED 140LES

WE B UNCONNECTED.

BOLT~D FLANGES

Fig. 8. Variables

FOURTH QUARTER/1973

1.0

8

p

,flHH

Test C12 -Pp

0.5

S (in.)

400

o

'200

800

1000 -

P(k)

600

Fig. 77. Interior connection

Fig. 10. C12 test results compared with theory

theoretically and experimentally sound. 9 Limiting valuesof bit and dlw were chosen for the beam. The same wastrue of the column dimensions. The required redistribution was about 70%.

The results of the theoretical approach are shown inFig. 10 together with the results of connection C12 (acontrol test). The agreement is very good and indicatesthat the theory can take into account not only the connection web deformation, but also the numerous phases ofplastic redistribution and up to the final hinge conditionfor the whole assembly. It incorporates the formation ofplastic hinges in the column flanges above and below thebeam connections.

Do these hinges really form? Figure 11 gives theanswer. The column flange hinges are evident just aboveand below the beam-flange connections.

1. If we design the connection to transmit themoment through the flanges only and the web forshear only, will it be possible for these flanges tostrain harden enough to develop the full plasticmoment of the beam?

2. If we ignore the moment altogether when wedesign for shear, will we still be able to developthe full plastic shear capacity?

3. Will there be sufficient rotation for these condi-tions?

4. Will it be too flexible?5. Can we predict it theoretically?

Figure 9 shows one of the connections after test.Notice how completely all of the material has "worked".For this case (and for this whole program) the connections were proportioned on the basis that everything was"critical". The shear was adjusted in such a way that theweb would be fully yielded when M p was reached. Grade55 material was used. For the bolts, higher stresses wereused than are now permitted, although they are both

Fig. 9. Interior beam-to-column connection after testing

102


Figure 12 shows the results of the tests with boltedwebs. The reference load used in the figure is the plasticlimit load, Pp • The other three loads are the workingload Pto (= Pp/1.7), the plastic load neglecting the contribution of the beam web, PPT> and the plastic loadmodified to include the effect of shear, p p •• ConnectionC12 was fully welded. C2 used round holes, and C3 usedslotted holes. The results indicate that all the connectionscarried maximum loads far exceeding the computedplastic loads PPT and p p • (and even Pp ) and that the loaddeflection relationships of the connections are very similar.The difference in behavior at loads above the workingload was due to slip of the web plates occurring in thebolted connections. The high strength bolts eventuallywent into bearing against the sides of the holes, and theconnections thus "regained" their stiffness. The effect ofstrain hardening is again the main reason for the connections to attain the high loads.

A detail view of connection C3, Fig. 13, shows theremarkable degree to which plastic action has taken placeup to the point of final rupture. In flexure, in beam shear,in the connection plates, in the bolts, in the web panel, inthe columns-throughout the entire assembly one observes complete yielding and redistribution under themost adverse possible conditions.1o

The upcoming studies will cover web-connectedbeam-to-column connections and partial strength connections. These latter are most important because sometimes the depth of the girder is controlled by drift andnot by the carrying capacity.

Mention is made here of an important guide forbolted and riveted joints.u It has been developed underthe auspices of the Research Council for Riveted andBolted Structural Joints. John Fisher and John Struik atLehigh have been responsible for its preparation. As of

1.0

p

PP

0.5

o

Fig. 12. Load-deflection curves of three interior connections

103

Fig. 13. Connection C3 after testing

this writing the manuscript is in the hands of John Wiley& Sons for eventual publication. The chapter headingsare as follows:

1-General provisions2-Rivets3-Bolts4-Symmetric butt splices5-Truss type connections6-Shingle joints7-Lapjoints8-0versize and slotted holes9-Filler plates between surfaces

1O-Alignment of holes11-Surface coatings12-Eccentrically loaded joints13-Combinationjoints14-Gusset plates15-Beam and girder splices16-Tension type connections17-Beam-to-column connections

Frames-Since the late 1950's an extensive researchprogram has been carried out to develop plastic designmethods for laterally braced and unbraced multi-story

FOURTH QUARTER/1973

in which fa and fb are, respectively, the computed axialand bending stresses and

Fa allowable axial stress if axial force alone existedF b allowable compressive bending stress if bending

moment alone existedF' e elastic Euler buckling stress divided by a factor

of safety. It is always computed for the in-planecase of buckling. In equation form it is given by

frames. As part of this program, .a study was made todetermine the factors that affect the ultimate strengthof these frames. For unbraced frames, the secondaryoverturning moment (or the P-A moment) is found to beone of .the most significant factors. The P-A momentscaused by the gravity loads acting through the lateraldeflection tend to reduce the overall strength and stiffness of the frame and lead to instability failure. 12

There are two distinctive types of frame analysis:the first-order analysis in which the effect of secondarymoment is ignored, and the second-order analysis inwhich this effect is included. The significant differencebetween the load-deflection curves obtained from thefirst- and second-order analyses is illustrated in Fig. 14for a 3-story, 2-bay frame.13 The structure was part of atest series which was designed to study the generalbehavior and load-carrying capacity of unbraced multistory frames. The substantial reduction in strength forthe second-order case shows the importance of considering the P-A moment in the analysis and design of suchframes. When the plastic method is used in the design,the effect of secondary moments can be included in adirect manner in the calculations. In the allowablestress design, however, an indirect approach is generallyused to account for this effect. This approach, which willbe discussed briefly in the next section, was formulatedbefore a thorough understanding of the frame instabilityproblem was achieved. For this reason, there is a stronginterest in knowing the real load-carrying capacity offrames designed by the allowable-stress method in orderto assess the true factor of safety (or load factor).

Strength of Frames Designed by the Allowable-StressMethod-The indirect approach mentioned above isbased on the premise that the effect of frame instabilitycan be taken care of by increasing the column sizes of theframe being designed. According to the AISC Specification, all columns in a planar frame are to be proportionedto satisfy the following two formulas :14

0.015

Story Heighl=IOft.

8ay Spacing =15 II.

10

Second - Order" , , ,

8

0.010

First - OrderElastic - Plastic

P=24.8 kips

First - Ordern n ,

6

SWAY 6 (in.)

4

Second-OrderElastic-Plastic

2

0.005

First ~ Order, I

ElastiC yl/

/I

II.

o

1.31

1.51

o

2

6

8

H

(kips)

a:o>u<;:a<I

'3

(L b is the actual length in the plane of bendingand rb the corresponding radius of gyration. Kis the effective length factor in the plane ofbending.)

Cm 0.6 - 0.4M 11M 2 2:: 0.4 for columns in bracedframes. MilM 2 is the ratio of the smaller tolarger moments applied at the ends of the member. It is positive when the member is bent inreverse (double) curvature.

Cm = 0.85 for columns in un braced frames.

If the columns in a frame are braced in the perpendiculardirection, the in-plane effective slenderness ratio KLb/rbis to be used in computing Fa. In the subsequent discussion, it will be assumed that this condition prevails forall the columns.

The effect of frame instability is recognized in twoways-the first is the use of the in-plane K factor in computing Fa and F'., and the second is to assign a Cm valueof 0.85 (instead of a much smaller value as given by theequation Cm = 0.6 - 0.4MilM2).

Fig. 74. Test results compared with jirst- and second-order theory

(4)

(3)Cm/b < 1.0(ja/F'e) ]Fb -

~ +fb < 1.00.60Fy Fb -

fa

Fa + [1

(5) Fig. 75. Load-deflection curves of a frame designed by allowable-stressmethod without consideration of frame instability effect

104


Fig. 16. Comparison of load-deflection curves of a frame designed byallowable-stress method with and without consideration of frame

instability effect

(b)(a)

2 2cr:: B B0>-u~0..0..J

* The present specifications permit plastic design of braced multistory frames with a load factor of 1.70 for gravity load and 1.30 forcombined load. Application to unbraced frames will be ready shortly,and this experimental evid.ence for afactor of 1.30 is reassuring .17

Figure 16a shows the second-order load-deflectioncurves of Designs Band C together with that of DesignA. The ultimate strength of the frame is increased 13%for Design Band 10% fo~ Design C.

These results indicate that the use of the effectivelength factors determined for the sidesway mode of framebuckling does not significantly improve the strength ofthe frame.

A comparison of the ultimate strength of Designs Band D with that of Design A is shown in Fig. 16b. DesignD, a more balanced design involving increases in boththe beam and column sizes, achieves a load factor 1.43.

All three designs (B, C, and D) result in increases inthe load-carrying capacity of 10 to 13%, which is approximately equal to the reduction due to frame instability effect noted in Fig. 15. Among these designs,Design C is the simplest to perform.

In summary, if the results of these analyses aretypical, a frame designed by the allowable-stress methodaccording to the AISC Specification l 4, which indirectlyincludes the P-!1 effect by assuming the theoreticalK-value and Cm of 0.85, will actually have a load factorin the vicinity of 1.5 (Design B).

It also shows that frames designed before 1960, inwhich the effective length and P-!1 effects are ignoredhave a load factor of at least 1.3. The resulting body ofexperience would lead one to assume that a load factor of1.3 is probably satisfactory for the plastic design of unbraced frames. *

Thus (within the limitations of calculations made)these results point to significant potential improvements. A separate paper is in preparation on the subject. 16

There are some important provisos: The frames inthe analyses were two-dimensional planar frames ofregular geometry, the L/r-values were in the practicalrange, there were no setbacks, and the moment diagramwas not an arbitary one (such as would be obtained bythe cantilever or portal method).

Frames Designed to Include Frame Instability Effect(Designs B, C, and D, see Fig. 16)-Three different designs were made for the 10-story, 3-bay frame, all including the effect of overall instability:

Design B: Columns were designed for K = effectivelength factor determined for the sidesway mode ofin-plane buckling (always greater than 1.0), andusing Cm = 0.85.

Design C: Columns were designed for K = 1.0 and. Cm = 0.85.

Both Designs Band C require increases in column sizesonly; the beams are essentially unchanged.

Design D: A second-order design with beams andcolumns selected according to the bending momentand axial force distributions given by the secondorder analysis. This design requires increases inboth beam and column sizes and includes auto-.matically the P-!1 moment at working load.

Frames Designed Without Considering Frame Instability Effects(Design A, see Fig. 15)-An extensive study of the loadcarrying capacity of unbraced frames designed by theallowable-stress method has been carried out. A total ofseven' frames, varying from 10-story, 3-bay to 40-story, 2bay, have been designed by the allowable-stress methodand then analyzed plastically according to the first- andsecond-order theory. Figure 15 shows some of the resultsobtained for the 10-story, 3-bay frame. The frame wasdesigned for the bending moment and axial force distributions determined from the first-order analysis andno consideration was given to the effect of frame instability, that is, K = 1.0 and Cm = 0.6 - OAMII M 2 wereused in the design of the columns. All beams of the frameare made of A36 steel (yield stress = 36 ksi) and all columns A572, Grade 50 steel (yield stress = 50 ksi),15

The load factor (ultimate load/working load) of theframe from the first-order analysis is 1.51, and that fromfrom the second-order analysis is 1.31. Thus the frameinstability effect causes a reduction of the ultimatestrength of 13%. The load factor of all the frames studiedfalls in the range of 1.30 to 1.50.

The results to date indicate that frames designed bythe allowable-stress method, but with no considerationbeing given to the overall instability effect, can achievea load factor of 1.30 or more. 16 This obse~vation raises animportant question: Is 1.30 adequate? The required loadfactor in plastic design for braced frames and for oneand two-story frames is set at 1.30 in the current AISCSpecification for the case of combined gravity and windloads. The same value is also specified in the specificationsof such countries as Canada, Mexico, and Sweden (inthis last case 1.34). Australia, India, South Africa, theUnited Kingdom, and the USSR use a load factor oflAO. Reference 7 contains a summary of the plasticdesign load factors used in different countries.

105

FOURTH QUARTER/1973

fDESIGN~I-L-O-AD-I'-NG-' Ir-R-E-SI..!....ST-A-N-CE---"'I

/ ",.."-- F? == ~--P-: y 11 p

I I

I FLI III -- Pc F;L

PPw

L

FDD F,D

l::. l::.

PLASTIC LIMITSTABILITY

LIMITELASTIC L.IMITFATIGUEFRACTUREDEFLECTION(VIBRATION)

DEAD LOAD

LIVE LOAD

Long Term

Short Term

ExtraordinaryCOMBINATIONS

Fig. 77. Loading function and resistance function as equated in design Fig. 78. Allowable-stress design compared with load-factor and limitstates design

Naturally, in plastic design one would have to takeinto account the frame.instability effect in a direct wayfor which provisions are available. 12

DESIGN BASED ON PROBABILITY

The second technique for advance given earlier was tomake design more like life-to base it on probabilities.

Load-factor/limit-states design is a method of proportioning structures for multiples of service load. Thedesign ultimate loads are obtained by applying factorsto the service loads and these are related to the resistanceof the structure. This resistance (or "response function")is itself subject to factors. So the method of "Loadfactor and limit-states design" * involves a considerationof the "Loading Function" (the dead load, the severalkinds of live loads, 'the various combinations of theseloads, and the load factors that are going to be applied),and of the "Resistance Function" (according to theapplicable limit of usefulness). These functions areshown in Fig. 17, which also points to the design processas equating the loading function with the resistancefunction (through the appropriate analytical techniques).It involves a decision on the load factors and a consciousattention to the appropriate li~it of usefulness. IS

Figure 18 affords a partial comparison with allowable-stress design. As shown at the left, in allowablestress design one uses the service dead load and live load,and the total must be less than the allowable load Pa. In.load-factor design, illustrated here in simplistic terms byplastic design, we take a factor tim~s the dead load and afactor times the live load and add them together toobtain Pu . The plastic limit load of the structure, Pp , isselected so that it is greater than the design ultimateload Pu . (To the right is shown one effect of the use ofmultiple load factors. With this technique, one separatesout the load factors for live load and dead load on theassumption that different factors can be used. 19 In thiscase, one would expect that the factor for the dead load

* The other terms shown in the lower portion of Fig. 7 would be just asappropriate here.

will be lower and the factor for the live load will begreater. But one can still find that the total loadingfunction will permit selection of a smaller section. Thesecond design would be lighter than the first.)

The matter does not stop here. Separating the loading function and the response function opens the way toconsider probability. But at the same time this is thebiggest uncertainty when it comes to future design application. What are the sources of possible uncertaintythat can or should be subjected to such consideration?The following is a list, expanding on the one contained inASCE Manual 41. 7

1. Approximations in analysis2. Approximations in design3. Stress concentration and residuals4. Variation in properties5. .variation in dimensions6. Workmanship7. Location8. Variation in load type9. Combination ofloads

10. Intended use

They enter into what we presently call the factor ofsafety in allowable-stress design, or into the load factorin plastic design. In load-factor design some would enterin the loading function and some in the response function. All of them are sources of possible uncertainty. ,

This uncertainty of loading and of response is reflectedin Fig. 19, which is perhaps a more "precise" way ofrepresenting the right side of Fig. 18. Again it is based ona hypothetical load vs. deflection curve of a frame. Thehorizontal line at the plastic limit load is not a fixedvalue, but is subject to variation. The variation would bedue to such things as the yield point or the dimensions ofthe shape. The statistical variation in the resistance issuggested by the functionfR' Similarly for load-the loadis uncertain, its actual value can vary considerably, andthat is why we have a factor in the first place. A hypothetical statistical variation in the load is indicated in

106


Fig. 79. Variation of loading and response fumtions

A

tF,L< F,...R(~5~¢R )

FD

Pp --,,-~-----

p

Fig. 20. Testing of composite beam-to-column connection

Fig. 27. Strength of composite beam-to-column connections

4"j

~W12X27t 1"

"

400

M(kip-ttl

Composite Beam-to-Column Action-When gravityloads alone are applied to a frame, positive (or sagging)bending moments usually develop at the center andnegative (or hogging) moments at the ends of its beams.If shear connectors are provided between the floorslab and the beam it is customary to assume that composite action takes place only in the positive moment region of the beam. When lateral loads are subsequentlyapplied, the bending moment at the windward end of thebeam sometimes changes its sign-from negative topositive. Composite action may therefore take placeover more than two-thirds of the span length of the beam.It is therefore necessary to know the maximum momentthat the beam can transmit and also the behavior of thecritical region near the column face. Included in a current investigation at Lehigh are parameters such as:depth of beam (relative to a fixed slab thickness), solidslab vs. slab with metal deck, concrete strength, anddensity of connectors. Complete results of this study willbe presented in a forthcoming report. 22 Figure 20 showsone of the specimens under test.

(6)

Floor Systems and Shear Connectors-Work on floorsystems and shear connectors has its primary focus on thebehavior of the different available types of manufacturedfloor systems. When one takes into account compositeaction in the positive moment region, not only is therea strength advantage, but the increase in stiffness is oftena significant design improvement. In Ref. 21 recent developments in this area are described.

INTERACTION CONSIDERATIONS

The third topic, interaction considerations, involvestaking advantage of the otherwise strength-neglectedparts of the structure. The discussion falls into these fourcategories: (1) Floor systems and shear connectors, (2)developing composite action at the columns, (3) mtegrated structural design, and (4) mixed systems.

Is load- and response-factor design a suitable alternative for allowable-stress design? In arriving at a decision,these are the things we have to think about: the concept of the multiple load factors; the rational choice ofthese factors; the possible combinations to be specified;and the potential economy vs. the complexity.

The American Iron and Steel Institute is sponsoringa major program at Washington University, St. Louis,under the direction ofT. V. Galambos, that is examiningmany of these factors. 20 One needs answers to such questions as these: What are the statistical variations? Whatare the variations of load? What are the economies-willtime and material be saved?

Fig. 19 by the function fL' (It reflects a larger spreadthan that for the resistance function.)

Thus in the actual design, according to the loadfactor and limit-states design concept, the criterion is notthat the upper end of the bar FD in Fig. 19 be less thanthe horizontal line at Pp , but that the maximum probable value of the load F1L must be less than the minimumcarrying capacity F,R. In equation form this means that:

107

FOURTH QUARTER/1973

6

Integrated Structural Design-The third topic underinteraction considerations embraces not only the twoprior topics, but also the strength and stiffening effectsof floors and partitions when acting in conjunction withthe bare frame.

In the experimental portion of the study at Lehigh, ahalf-scale test building, consisting of a steel framework,a composite floor system, and light-gage corrugatedpartitions, was constructed. A photograph of this "building" is shown in Fig. 22. The structure was first testedwithout the floor system and the partitions. The concretefloor slabs were then connected to the steel beams bymechanical fasteners and the test repeated. Finally, thecorrugated partitions were added to the frame-floorsystem to study their stiffening effect.

Some sample results from the testing are shown inFig. 23. These results compare very favorably withtheoretical predictions developed in Ref. 23. It may beconcluded for the test building that the major interactionis between the frame and the partitions, with the floorsystem contributing about 5% to the total stiffness.

Mixed Systems-The fourth topic under interactionconsiderations is "mixed systems". The Japanese havemade notable use of this scheme which combines the bestfeatures of both steel and concrete, under the designation "steel-reinforced concrete frames". It is like building a steel frame and then putting reinforced concretearound it. Figure 24 is a typical example.

Frome

Composite Floors

~oo

---0-- Experimental

Theoretical

400200 300l> (.IO··in.)

H 4(kip)

Floors and Partitions

~==::::::;:======~ - H

----tr

8

Fig. 22. Test building with composite.floor and partition

Figure 21 shows the results of two tests-one with asolid slab and the other with its slab cast on a metal deck.The inset in the sketch shows the loading system diagrammatically. The behavior and the maximum resisting moment of the two beams are very similar, an.d theyboth failed after the concrete near the column face wasextensively crushed. The plastic moment of the W12X27shape is 174 kip-ft and the maximum moment carried bythe specimen having a solid slab is more than 300 kip-ft,an increase of about 80%. In addition to increasing thestrength of the beam, composite action also increases itsstiffness, thus reducing the overall frame drift underwind. The effect of a small gap between the concreteslab and the column face was also examined in the study;it is similar to the effect of slip in a bolted joint: Aftercoming into bearing, the stiffness becomes that of amember without the gap.

Fig. 23. Increase ill building stiffness due to .floor and partition Fig. 24. Mixed system (Wakabayashi)

108


Fig. 27. Increase in cost due to height (Ref. 26)

I/

,/,/

///

./

"/,," Premium. .. .; for HeightTrodltlonal ~.."""",

............---

5.0

4.0

3.COSTINDEX

2.

I.

Em ~ III [IJ CJ ~ ~.. + +

SEMI· RIGID SHEAR FRAMED FRAMED BUNDLED OIAG.RIGID TRUSS C+I TUBE TUBE TUBE

Fig. 26. Economical number of stories for diiferent structural systems

o

"cost index" is plotted against number of stories. The"ideal" system is the one whose members are selected tosupport gravity load alone. As Khan points out, it is asif one imagined a glass dome placed over the building toprotect it from the wind. That is the goal. The development of the tubular systems, the framed tube, the tubein-tube, and the trussed tube are all efforts in this direction. There is a premium to be paid for height if lateralload is carried by the conventional system. Instead, onewants every pound of steel required for gravity load toalso participate in the resistance to lateral force.

The 5-volume, 5200-page Proceedings of the International Conference on Planning and Design of TallBuildings is replete with evidence and references on thesubject of structural systems as well as the other majortopics germane to tall buildings. One of these fivevolumes, Structural Design of Tall Steel Buildings wasprepared under the coordinating guidance of T. R.Higgins, in whose honor this paper is presented.

Figure 25 is typical of a number of examples in theUnited States, this one by Skidmore, Owings & Merrill.The 8-in. members visible at the top continue at substantially the same size throughout the entire 36-storyheight of the building. Does one call this a steel buildingor a concrete building? For the upper floors it looks like asteel building. As the reinforced concrete is being placedin the lower part it looks like a reinforced concrete building. No matter what it is called, by combining the bestadvantages of the two materials, erection time is reduced,and reported economies of 15% are obtained.24

Fig. 25. Chicago building (Courtesy Engineering News Record)

STRUCTURAL SYSTEMS

The prior discussion leads directly to the last majortopic, which involves the exploitation of the structuralsystem-optimizing the arrangement of the material.Figure 26 shows the result of this process, which eventually leads to an indication of the economical number ofstories for different structural systems.21i It is the development of the structural system that makes economicallypossible the construction of the so-called "monumental"skyscrapers. The same cost per square foot of the floorarea becomes applicable to a 100-story building as iscommon for 50- or 60-story "conventional" buildings.26

It is the drift that is the problem. Unless special care istaken, the extra weight goes in drift control and notinto strength. Figure 27 (after Khan) is illustrative. The

109

FOURTH QUARTER/1973

OTHER CONSIDERATIONS

The prior discussion of four ways to improve structuralsteel design has patently emphasized the economicalaspect. Two other aspects must be mentioned.

Increasing cooperation between members of thedesign team-the engineer, the architect, the planner,the landscape architect-is essential, not only if economyof the structure is to be attained, but also if the largerfunctions of the building as part of the community are tobe achieved. Some of this cooperation is coming aboutautomatically, partly as a result of the size of projectsand also because of the increasing importance of thestructural system in the architectural scheme of things.

The second aspect is the increasing demand forquality-not only for structural and architectural qualitybut for life quality. As noted by Robertson, "We couldstart a mile-high building next year-but do we wantto."27 Designs must first consider human needs, and this

_leads to interaction with another "team", the decisionmaking team (developers, investors, planning commissions, government agencies, and organized citizengroups).

In both of these aspects, steel construction IS In acrucial position. On the one hand, it is only possible tobuild the tallest buildings in steel. On the other hand,these monumental structures have a very significantinfluence on the urban environment. What all of thismeans is that in some respect, at least, advances in steelbuilding design will depend on the success with which thedesign team and the decision-making team meet the realneeds of the citizen.

SUMMARY

Four techniques for advancing steel building design are:

1. To capitalize on the strength and ductility of theparts and of the whole

2. To exploit the potentials of Load-Factor andLimit-States Design:'-which ultimately means adesign based on probabilistic considerations

3. To take advantage from both a strength and astiffness standpoint of the walls, partitions, andfloors acting together with the structural frame

4. To exploit the arrangement of the material to thefullest, developing structural systems that (forexample) do not impose a penalty or premium forheight as regards resistance to wind load

Among the specific current and potential developments noted are:

a. The additional available strength in biaxiallyloaded columns (Fig. 4)

b. The predictability and increased shear-strengthcapacity of exterior beam-to-column connections(Fig. 7)

c. The abillty of interior beam-to-column connections to develop the full -plastic beam strength onthe basis of designs for flange connection only(Fig. 12)

d. The prospect of somewhat simpler allowable~

stress design approaches with regard to framestability for planar frames of regular geometry(Fig. 16)

e. The significant increases iIi design strength andstiffness that are afforded through considerationof walls, partitions, and floors (Fig. 23)

f. The overall savings possible through a consideration of "mixed systems" (Fig. 25)

g. The wide variety of structural systems emergingout of a consideration of optimum geometricalconfigurations (Fig. 26)

h. The necessity to give increased consideration tohuman needs in building design-needs thatrequire a closer integration of the various professions in the design team and which suggest acloser interaction between the designers and thedecision-makers.

ACKNOWLEDGMENTS

The authors acknowledge the contributions of the following persons whose work has led to the most recent information presented in this paper:

O. Okten, J. H. Daniels, G. C. Driscoll, Jr.-thestrength offrames

D. P. du Plessis, J. H. Daniels-composite assemblages

W. M. EI-Dakhakhni, J. H. Daniels-frame-floorwall interactions

J. S. Huang, D. J.Fielding, W. F. Chen-beam-tocolumn connections

P. Marek, T. V. Galambos-Load-Factor Design

The sponsors of the various research projects fromwhich work was drawn are the American Iron and SteelInstitute, the Welding Research Council, the Pennsylvania Science and Engineering Foundation, and theNational Science Foundation.

The authors are particularly appreciative of theAmerican Institute of Steel Construction for the establishment of the T. R. Higgins Lectureship, which stimulatedthe preparation of this paper.

Final acknowledgment is due to "Ted" HigginshiIi-Iself who has afforded an inspiration to those whohave followed the paths of structural steel research.

REFERENCES

1. Tall, L., Ed. Structural Steel Design Ronald Press, New York,1964, (2nd Edition due in 1974).

2. Iyengar, S. N. Behavior of Thin Plates in the Elastic andInelastic Ranges Ph.D. Dissertation, Lehigh University, 1973.

110


3. Negussie, T., and Chen, W. F. Design Criteria for Steel HColumns under Biaxial Loading Fritz Engineering LaboratoryReport 389.2, Lehigh University, January 1973.

4. Johnston, B. G., Ed. Guide to Design Criteria for MetalCompression Members 2nd Edition John Wiley & Sons,Inc., New York, 1966 (3rd Edition in preparation).

5. Fielding, D. J. and Huang, J. S. Shear in Steel Beam-toColumn Connections Welding Journal, Vol. 50, No.7,July 1971,p. 313-s.

6. Fielding, D. J., and Chen, W. F. Steel Frame Analysis andConnection Shear Deformation Journal of the StructuralDivision, ASCE, Vol. 99, STI, January 1973,p. ,.

7. ASCE-WRC Plastic Design in Steel-A Guide and Commentary 2nd Edition, ASCE Manual 41, 1971.

8. Huang, J. S., W. F. Chen and L. S. Beedle Behavior andDesign of Steel Beam-to-Column Moment ConnectionsFritz Engineering Laboratory Report 333.20, Lehigh University,1973.

9. Fisher, J. W. and Beedle, L. S. Criteria for Designing Bearing-Type Bolted Joints Journal of the Structural Division,ASCE, Vol. 91, ST5, October 1965, p. 129.

10. Huang, J. S., and Chen, W. F. Steel Beam-to-Column Moment Connections presented at ASCE National Structural Engineering Meeting held at San Francisco, April 1973, ASCE Preprint No. 1920.

11. Struik, J. H., and Fisher, J. W. Design Guide to Mechanically Fastened Joints Fritz Engineering Laboratory Reports357.1-17, Lehigh University, 7972 (to be published). .

12. Driscoll, G. C., Jr. et al. Plastic Design of Multi-Story'Frames Lecture Notes and Design Aids, Fritz Engineering Laboratory Reports 273.20 and 273.24, Lehigh University, 1965.

13. Galambos, T. v., G: C. Driscoll, Jr., and L. W. Lu Researchon Plastic Design of Multi-Story Frames at Lehigh University 8th Congress of IABSE, Final Report, September 1968,p.517.

14. American Institute of Steel Construction Specification for theDesign, Fabrication and Erection of Structural Steel forBuildings AISC, New York, February 1969.

15. Lu, L. W., and Beedle, L. S. Recent Research on the Strength,Stiffness and Ductility of Steel Buildings Fritz EngineeringLaboratory Report 369.79, Lehigh University, July 1973 (to be

111

published in Proceedings, Australian Conference on the Planningand Design of Tall Buildings).

16. Okten, 0., S. Morino, J. H. Daniels, and L. W. Lu Studies ofEffective Column Length and Frame Stability Fritz Engineering Laboratory Report 375.2 Lehigh University, 7973.

17. Driscoll, G. C., Jr. Plastic Design of U nbraced MultiStory Steel Frames American Iron and Steel Institute (inpreparation) .

18. Beedle, L. S., L. W. Lu, and L. C. Lim Recent Developmentsin Plastic Design Practice Journal of the Structural Division,ASCE, Vol. 95, ST9, September 1969, p. 1911.

19. Marek, P. J. Review of Czechoslovak and French Specifications Fritz Engineering Laboratory Report 377 .2A, LehighUniversi,)', 1973.

20. Galambos, T. V. Load Factor Design for Steel BuildingsEngineering Journal, AISC, Vol. 9, No.3, July 1972, p. 108.

21. Grant, J. A., Jr., J. W. Fisher, and R. G. Slutter, HighStrength Steel Composite Beams with Formed MetalDeck and Low Partial Shear Connection presented at theSecond Specialty Conference on Cold-Formed Steel Structures at theUniversity of Missouri-Rolla, St. Louis, Missouri, October1973.

22. du Plessis, D. P., and Daniels, J. H. Strength of CompositeBeamcto-Column Connections Fritz Engineering LaboratoryReport 374.3 Lehigh University, 1973.

23. El-Dakhakhni, W. M., and Daniels, J. H. Frame-Floor-WallSystem Interaction in Buildings Fritz Laboratory Report376.2, Lehigh University, 1973.

24. Fox, A. J., Jr., Ed. Building Design Reduces Steel withConcrete-Tube Wind Bracing Engineering News Record,Vol. 186, No. 22, June 3, 1977, p. 18.

25. Iyengar, S. H. Preliminary Design and Optimization ofSteel Building Systems Proceedings of the International Conference on the Planning and Design of Tall Buildings, LehighUniversity, 1972, Vol. 11,p. 185.

26. Khan, F. R. The Future of High-Rise Structures ProgressiveArchitecture, October, 1972,

27. Fox, A. J., Jr., Ed. High-Rise Experts Score Present Planning, Stress Impact, Safety Engineering News Record, Vol.189, No.9, August 31,1972, p. 12.

FOURTH QUARTER/1973

recent developments in steel building design

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