Advances in Steel Structures - part 11 pps

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L.W. Lu et al.
Figure 4. ATLSS Connector
framed structure, as shown in Figure 4. This type of joint is designed for to be placed by a remote
operator eliminating the need for an ironworker to make the connection (Viscomi, Michalerya and
Lu, 1994). This concept could be used for many secondary bridge connections used for diaphragms
and bracing.
For ease of handling, it is necessary to make the wedge and socket as compact as possible. The
socket is either welded directly to a column flange or to a plate which is then bolted to a column
fange. A high-strength material that is easy to weld and cast is therefore required. Unfortunately,
most of the available high-strength cast steels are not readily weldable. This makes the high-
performance steels the ideal choice for the connector pieces. The ATLSS connectors, made with
HSLA 80 steel, has been found, in laboratory testing, to perform well either as a shear connection or
a part of a full or partial moment connection (Lu, et al 1995). These connectors have been
successfully adopted in the construction of industrial plant structures.
Ultra High-Strength Structural Members
Work is in progress on several investigations on high-strength structural members made of high-
performance steels with good weldability. One of these is a study on concrete filled tubular (CFT)
columns subjected to axial compression or combined axial compression and bending moment
(Varma, et al 1998). The tubes were made of A500 Grade 80 steel (550 MPa yield) and the concrete
had a compressive strength of 110 MPa. The A500 Grade 80 material is similar to the HSLA 80
steel and can be readily cold formed and welded with one-sided welding (within certain plate
thickness). The high-strength CFT members are ideal for use as columns in multi-story building
frames.
Another study is on the local and lateral buckling behavior of flexural members made of HSLA 80
steel, whose stress-strain relationships are different from those of the conventional structural steels
(Ricles, Sause and Green, 1998).
HIGH-PERFORMANCE STRUCTURES UTILIZING INNOVATIVE DESIGN CONCEPTS
Post-Tensioned Connections for Seismic-Resistant Building Structures
The common practice of designing a seismic-resistant steel structure is to utilize its ductility and
High-Performance Steel Structures: Recent Research

81
inelastic energy adsorpbtion capacity. The structure is allowed to yield and deform plastically
under the design level of earthquake excitation. The individual members and connections must be
able to sustain large plastic deformations, while maintaining their resistance. Large plastic
deformations often result in excess damage to the structure, which may affect its function and
safety.
To improve the seismic response of building frames a new type beam-to-column connection has
been developed (Garlock, et al 1998). It is a post-tensioned (PT) connection and is similar to the
unbonded PT connection developed previously for precast concrete construction. The connection
can be easily incorporated into a conventional steel moment-resisting frame. One version of this
connection is shown in Figure 5. It consists of bolted top and seat angles and post-tensioned high-
strength strands running parallel to the beam and anchored outside the connection. The beam
flanges are reinforced with cover plates in order to limit local beam yielding. Also, bearing plates
are placed between the column flange and the beam flanges so that only the beam flanges and the
cover plates are in contract with the column. The deformed configuration of the interior PT
connection subjected to a pair of clockwise bending moments transmitted from the beams is shown
in Figure 6. The moment-rotation (M-er) relationship of the connection is shown in Figure 7(a) and
the load-deflection (P-A) relationship of a beam-column subassemblage containing such a
connection is shown in Figure 7(b).
The behavior of the connection is characterized by a gap opening and closing at the beam-column
interface. The moment to cause this separation is called the decompression moment. The connection
initially behaves as a fully restrained connection; but after decompression it behaves as a partially
restrained connection. The initial stiffness of the connection is the same as that of a fully restrained
connection, where 0r remains equal to zero until the gap opens at decompression. The stiffness of
the connection after decompression is associated with the flexrual stiffness of the tension angles and
Figure 5. Post-tensioned connection
Figure 6. Deformed configuration of
post-tensioned connection
82
M

L.W. Lu e t al.
A
P
D-
A
(a) (b)
Figure 7. Moment-rotation and load-deflection relationships of post-tensioned connection
the axial stiffness of the post-tensioned strands. With continued loading, yielding will develop in the
tension angles, which will cause further softening of the connection. Full yielding and strain
hardening of the tension angles will follow. At a later stage, the compression angles will also yield.
After yielding of the tension and compression angles, the M-0r curve becomes approximately linear
because the connection's stiffness is provided primarily by the axial elastic stiffness of the PT
strands. Upon unloading, the angles will dissipate energy until the gap between the beam flange and
column face is closed (when er is again equal to zero). A complete reversal in moment will result in
a similar behavior occurring in the opposite direction as shown in Figure 7. As long as the strands
remain elastic and no significant yielding occurring in the beams, the post tension force is preserved
and the connection and the subassemblage will remain self-centered upon unloading (Figure 7(b)).
Accordingly, a frame constructed with PT connections will suffer to permanent sway or drift after a
major earthquake event. Studies have shown that the behavior of the connection is controlled by the
level of decompression moment, flexural strength and stiffness of the angles, and the elastic
stiffness of the strands, while the amount of energy dissipation is related to the flexural strength of
the angles. Further work on PT connections is currently in progress at Lehigh University.
Viscoelastic Dampers for Seismic Response Control of Building Structures
A major research was carried out at the ATLSS Center to study the effectiveness of viscoelastic
(VE) dampers in reducing the earthquake response of building structures. The work included
analytical modeling of the VE material and dampers, experimental investigation of the local and
overall behavior of frames with VE dampers under simulated earthquake ground shaking and
development of design methodologies (Kasai, et al 1993, Kasai and Fu, 1995 and Higgins and
Kasai, 1998). The damping material was installed in V-braces of the frame, as shown in Figure 8.
A collaborative program which included shaking table tests three-story, single-bay steel frames with

and without dampers, was conducted at the National Taiwan University of Science and Technology
(Higgins, Chen and Chou, 1996). The test and analytical results demonstrate that a properly
High-Performance Steel Structures: Recent Research
Damper
\
(
yr/
83
Figure 8. Frame with viscoelastic dampers
designed VE damped flame can perform in a damage free manner under major earthquakes
generally considered in design codes. Recent work, however, has shown the undesirable effect of
temperature sensitivity of the high damping VE material, especially when it is used in exposed
structures (Fan, et al 1998). Material, such as natural rubber, whose damping and stiffness
properties are almost unaffected by temperature changes, may be more desirable. Research on
rubber damper is currently in progress at Lehigh University.
Double Hull Ship Structures
Another example of innovative design concept is the double hull structure for ships (Beach, 1990).
Most of the ships in service today are of the conventional hull type, which is basically a single skin
of steel plating stiffened by transverse web frames and longitudinal stiffeners. The double hull is
fundamentally different from the conventional hull in that it has twin skins (or shells) of steel
plating which are separated from each other and stiffened by longitudinal web plates or girders that
span between transverse bulkheads. Other transverse components are eliminated, thus creating a
simple unidirectional, longitudinal structure. Figure 9 compares the conventional hull and the new
double hull.
The simple, unidirectional structure gives rise to several important advantages over the conventional
hull. The redundant hull structure provides greater survivability for the ship when subjected to
collision or grounding forces. The inner hull also serves as an additional barrier against leakages in
case the outer hull is punctured. In the double hull the number of fatigue-critical details is
significantly reduced because the longitudinal girders are not interrupted by stiffeners, brackets, or
transverse frames between bulkheads. The long continuous welds may allow automatic welding and

other advantages in producibility with consequent cost savings. It is envisioned that these ships will
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L.W. Lu et al.
Figure 9. Conventional hull and double hull ship structures
be fabricated from high-performance steels which offer improved weldability, increased strength
and toughness relative to conventional ship steels. The new design and materials should lead to
safer and more affordable ships. Much of the research on double hull ships at Lehigh focused on
hulls made of HSLA 80 steel (Pang, et al 1993, Dexter, et al 1996).
SUMMARY
Brief descriptions of some selected research to develop high-performance structures for civil and
marine construction have been presented. Two approaches are adopted to achieve improvements in
performance and life cycle cost. They are: (1) use of high-performance steels and (2) development
of innovative design concepts. Potential applications of the developed technologies to bridges,
buildings and ships have been discussed.
REFERENCES
Anon (1979). Welding Flaws Close Interstate Tied Arch Bridge, Engineering News Record,
August 16.
Anon (1991). U.S. Navy Reports Welding Procedure Source of Cracks in First Seawolf Submarine,
Welding Journal, 71(9), p. 5.
Beach, J.E. (1990). Advanced Surface Ship Hull Technology - Cluster B, ASNE Symposium on
Destroyer, Cruiser and Frigate, 89-112.
Bolliger, W., Varughese, R., Kaufmann, E., Qin, W.F., Pense, A.W., and Stout, R.D. (1988). The
Effect of Welding and Fabrication Operations on the Toughness of A710 Steel, in "Microalloyed
HSLA Steels," ASM International, p. 277.
High-Performance Steel Structures: Recent Research
85
Dexter, R.J., Ricles, J.M., Lu, L.W., Pang, A.A., and Beach, J.E. (1996). Full-Scale Experiments
and Analyses of Cellular Hull Sections in Compression, Joumal of Offshore Mechanics and Arctic
Engineering, ASME, 118-3,232-237.
Fan, C.P., Lu, L.W., Sause, R., and Ricles, J.M. (1998). Research at Lehigh University on Use of

Viscoelastic Material in Retrofitting Dynamically Load Structures. Proc. Third International
Symposium on Civil Infrastructure Systems Research: Intelligent Renewal, Capri, Italy, 1997,
World Scientific Publishing Co., 137-151.
Fisher, J.W., Pense, A.W., and Hausammann, H. (1982). Fatigue and Fracture Analysis of Defects
in a Tied Arch Bridge, Proc. IABSE Colloquium on Fatigue of Steel and Concrete Structures,
Lausanne, Switzerland.
Fisher, J.W. (1984). Fatigue and Fracture of Steel Bridges, Wiley Interscience, New York.
Garlock, M.M., Ricles, J.M., Sause, R., Peng, S.W., Zhao, C., and Lu, L.W. (1999). Post-
Tensioned Seismically Resistant Connections for Steel Frames. To appear in Proc. 1998 Annual
Technical Session, SSRC, Atlanta, GA.
Graville, B.A. (1976). Cold Cracking in Welds in HSLA Steels, Proc. International Conference on
Welding of HSLA (Microalloyed) Structural Steels, ASM, Rome, Italy.
Gross, J.H., Stout, R.D., and Dawson, H.M. (1998). Copper-Nickel High-Performance 70W/100W
Bridge Steels - Part II, Report No. 98-02, Center for Advanced Technology for Large Structural
Systems, Lehigh University.
Higgins, C., Chen, S.J., and Chou, F.C. (1996). Testing and Analysis of a Steel Frame with
Viscoelastic Dampers, Proc. Eleventh World Conference on Earthquake Engineering, Acapulco,
Mexico, Paper No. 1961.
Higgins, C. and Kasai, K. (1998). Seismic Design, Analysis and Experiment of a Multi-Story
Viscoelastically Damped Steel Frame, Special Issue on Passive Control, ISET Journal of
Earthquake Technology, 35:4.
Kasai, K., Munshi, J.A., Lai, M.L., and Maison, B.F. (1993). Viscoelastic Damper Hysteretic
Model: Theory, Experiment, and Application, Proc. ATC 17-1, Seminar on Seismic Isolation,
Passive Energy Dissipation, and Active Control, Applied Technology Council, San Francisco, CA,
521-532.
Kasai, K. and Fu, Y. (1995). Seismic Analysis and Design Using Viscoelastic Dampers, Proc.
Symposium on a New Direction in Seismic Design, Architectural Institute of Japan, Tokyo, Japan,
113-140.
Lu, L.W., Dexter, R.J., and Fisher, J.W. (1994). High-Performance Steels for Critical Civil
Infrastructure Systems, Proc. Intemational Workshop on Civil Infrastructural Systems, Taipei,

Taiwan, 283-298.
Lu, L.W., Viscomi, B.V., Fleischman, R.B., Lawrence, W.S., Rosa, A.M., and Garlock, R.B.
(1995). Development and Experimental Investigation of New Types of Connections for Framed
Structures Suited for Automated Construction, Proc. First European Conference in Steel Structures,
Athens, Greece, 231-238.
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Pang, A.A., Tiberi, R., Lu, L.W., Ricles, J.M., and Dexter, R.J. (1993). Measured Imperfections and
Their Effects on Strength of Component Plates of a Prototype Double Hull Structure, Journal of
Ship Production, 11-1, 47-52.
Ricles, J.M., Sause, R., and Green, P.S. (1998). High-Strength Steel: Implications of Material and
Geometric Characteristics on Inelastic Flexural Behavior, Engineering Structures 20:4-6, 325-335.
Sause, R. and Fisher, J.W. (1995). Application of High Performance Steel in Highway Bridges,
Proc. ASM International Symposium on High Performance Steels for Structural Applications,
Cleveland, OH.
Varma, A.H., Hull, B.K., Ricles, J.M., Sause, R., and Lu, L.W. (1998). Experimental Studies of
High Strength CFT Beam-Columns, Proc. Fifth Pacific Structural Steel Conference, Seoul, Korea,
893-906.
Viscomi, B.V., Michalerya, W.D., and Lu, L.W. (1994). Automated Construction in the ATLSS
Integrated Building Systems, Automation in Construction 3:1, 35-43.
A UNIFIED PRINCIPLE OF MULTIPLES FOR LATERAL
DEFLECTION, BUCKLING AND VIBRATION
OF MULTI-STOREY, MULTI-BAY, SWAY FRAMES
W.P. Howson and F.W. Williams
Cardiff School of Engineering, Cardiff University, Cardiff CF24 3TB, UK
ABSTRACT
Cheap computing has rightly eliminated tedious hand methods from taught courses. Unfortunately,
this has often unintentionally resulted in the elimination of procedures which give useful structural
behavioural insights into whole families of structures using simplified models which give good
approximate results. Such procedures help designers both to check that computer results are

reasonable and also to gain insight from parametric studies with a manageable number of parameters.
The present paper seeks to rescue one such procedure from relative obscurity and presents almost its
only recent extension. It is the use of substitute one bay (or alternatively Grinter) frames to obtain
results for unbraced and lightly braced multi-storey, multi-bay, sway frames which are exact when
they are unbraced, have inextensible members and obey the Principle of Multiples and otherwise are
good approximations. These results can incorporate cladding and are for : deflections caused by static
lateral (e.g. wind) loading; critical buckling and; natural vibrations. These three types of problem are
unified herein and, because adequate published results exist for the first two types, only (new) natural
frequency results are given. These show that, for unbraced frames, the substitute frame gives
acceptable accuracy for most purposes regardless of how closely the frame obeys the Principle of
Multiples. They also apparently justify a new application, namely to analyse multi-storey, multi-bay
frames with one or more braced bays by using a substitute frame which represents the bracing as
cladding. Exceptionally, when all bays are cross-braced, the Principle of Multiples may be obeyed.
KEYWORDS
Wind load, buckling, vibration, substitute frame, Grinter, Principle of Multiples.
INTRODUCTION
Until the 1960's, the teaching and practice of structural engineering consisted mainly of understanding
the underlying principles, then learning hand methods and practising their use extensively. Because
hand solutions are tedious, engineers thought carefully about their initial design, both before analysing
87
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W.P. Howson and F. IV. Williams
it and as the analysis gave intermediate results which were expected or otherwise. Experienced
designers bought much of their experience by performing such calculations for each design they were
responsible for, often including the analysis of several alternative structures before the design process
was completed. Hence designers and their teachers were keen to develop insights which would enable
them to choose a good design prior to computation commencing and/or to proceed from rejected
designs to acceptable ones via as few analyses of trial designs as possible. The Principle of Multiples
was one useful source of such insights.
The advent of computers and the rapid reduction in computing costs has required a different approach

to the teaching of structures and to how designers obtain experience. The basic principles which need
to be taught and understood have altered little but their implementation in computer programs has led
to new (usually stiffness matrix based) methods being taught. Numerous hand methods are no longer
taught because designers no longer require them and hand calculations are used only to confirm that
students understand the underlying principles and how computer methods work. They are also used
by designers to perform 'spot checks' and simple 'back of the envelope' type calculations to ensure
that computer generated designs and/or analyses are reasonable, both to guard against data errors and
an inappropriate choice of computer program. Therefore methods previously obtained to give insight,
such as the Principle of Multiples, remain valuable instruments in the designer's armoury.
Computing is now so cheap that students and design engineers can build up experience very quickly
by designing and/or analysing a large range of structures. However, it is tempting to overestimate the
extent to which this enables insight and experience to be developed, because a complete structure
usually involves so many design variables that, even if the required large number of computer runs
could be afforded, designers would suffer from information overload unless structural insight can be
used to categorise the results or to reduce their number. Here again, the Principle of Multiples can be
of value.
In the authors' opinion, methods giving insight have often been removed from undergraduate courses,
and hence largely lost to the profession, in the mistaken belief that their value has disappeared.
Therefore, the Principle of Multiples is presented in this paper, starting with the static lateral (wind)
load and critical buckling calculations with which it has historically been principally associated and
then proceeding to examine its value in the vibration context.
THE PRINCIPLE OF MULTIPLES AND SUBSTITUTE FRAMES FOR LATERAL LOAD
AND BUCKLING CALCULATIONS
The Principle of Multiples applies to unbraced, rigidly jointed, multi-bay, multi-storey plane frames
and is exact on the basis of inextensible member theory. Since hand methods of analysis nearly all
assume inextensible members this assumption is acceptable, although most computer programs use
extensible theory both for convenience and to obtain additional accuracy. Numerous authors have
dealt with the use of the Principle of Multiples and associated simple methods for lateral load and
buckling calculations for such frames, e.g. Bolton (1976), Grinter (1936), Home and Merchant (1965),
Home (1975), Lightfoot (1956, 1957, 1958, 1961), Naylor (1950), Williams (1977a, 1977b, 1979),

Williams and Howson (1977), Williams and Butler (1988), Wood (1952,1974), Wood and Roberts
(1975).
Figure 1 applies to lateral load calculations when F r 0, whereas it refers to buckling problems when F
= 0 and W r 0. It is usual to perform the lateral load calculations with W = 0, but non-zero values of
W can be used if the designer wishes to allow for the magnifying effect that vertical loads have on
Unified Principle of Multiples for Lateral Deflection, Buckling and Vibration
W W
k l, k, k2
2F .1~ 3w 3
j-
k3
k4 k 4
2W 2W
2k 2 1 2k 2
ll w wll
4F >~ 2k3 ~_
2 k4
4W 4W
4F~l 4k
1 /
;!
4k2 1112W 12Wl 4k 2
8F ,14' ~
" 4k 3
4 k 4 1.5L
(a)
(b)
(c)
89
,f , .

k3 k 3 2k 3
k4 2k 4 3 2k 4
8W
| 12k 1
8k2 [ 124 w ~f"~,~
8F .IJ,
L
.5L
(d) (e)
Figure 1" Frames (a) - (d) comply with the Principle of Multiples
and (e) is the corresponding Grinter frame
horizontal deflections caused by lateral loading. The Grinter frame of Figure 1 (e) is required later, but
should be ignored for the time being. The Principle of Multiples proves that the frames of Figures
1
(a)-(d) share the same horizontal deflections for lateral loading problems and share the same critical
value of W for buckling problems. The reasons are as follows.
In Figure 1, the k's are values of EI / g for the members, where EI is the flexural rigidity and g is
length. Additionally, values are identical when the subscripts are identical, so that the frame of Figure
1 (a) is symmetrical. Note also that the vertical loading is symmetric. Therefore, considering buckling
first, the frame must buckle with a symmetric or an anti-symmetric mode and it is easily proved that
the anti-symmetric mode gives the lowest possible critical load. Hence any frame which is identical to
frame (a) must have the same critical load Wc and the same deflected shape. Therefore any frame