CONNECTION DESIGN IN THE 2005 AISC SPECIFICATION

Transcription

CONNECTION DESIGN IN THE 2005 AISC SPECIFICATION
Cynthia J. Duncan, Director of Specifications,
The American Institute of Steel Construction, Inc., Chicago, IL
ABSTRACT
The American Institute of Steel Construction’s Committee on Specifications is
currently developing a new Specification for Structural Steel Buildings,
scheduled to be released in 2005. This document will unify the two design
methods presently used for steel design in the United States, Allowable Stress
Design (ASD) and Load and Resistance Factor Design (LRFD), into one
standard.
In addition to this unification, the entire document is being
reorganized and updated. One area of the specification that continues to
evolve is connection design. The new standard will include several revisions
in the areas of both welded and bolted connection design.
INTRODUCTION
The American Institute Steel Construction (AISC) introduced the first specification for the
design and construction of structural steel buildings in 1923, for the purpose of creating a
standard for the steel industry in the United States. This original document was a mere nine
pages approved by a committee of five, and it has grown to exceed 100 pages, undergoing
numerous revisions based on experience gained over the years and research; both analytical
and test-based. Today, the AISC Committee on Specifications consists of 40 members
currently working on the 2005 Specification for Structural Steel Buildings (1), hereafter
referred to as the 2005 Specification. This new document has a new format unlike any
previous versions, as it will combine both load and resistance factor design (LRFD) and
allowable stress design (ASD) methods into one. More specifically, many of the provisions
have been revised and updated in Chapter J, Design of Connections, since publication of the
most recent AISC specification, the 1999 Load and Resistance Factor Design Specification
for Structural Steel Buildings (2), hereafter referred to as the 1999 Specification. Although
the specification is still in draft form, with two remaining ballots, there are many issues that
can be discussed at this time. Some of the general connection design topics that will be
addressed are compression members with bearing joints, splices in heavy sections, beams
copes and weld access holes, combining bolts and welds, and limitations on bolted and
welded connections. The welding areas that will be revised are effective area and limitations
on effective throat area of groove welds, as well as, effective area, terminations, and strength
of fillet welds. Finally, some of the changes expected for design with bolts and threaded
parts occur in provisions for: the types of fasteners allowed, combined tension and shear
strength, design of slip-critical connections, block shear, and shear lag.
NEW FORMAT AND DESIGN BASIS
Before discussing the new revisions to the connection chapter, it is important to understand
the format of the 2005 Specification. The original 1923 document was based on the
allowable stress design format (ASD), which gives capacities in allowable stresses with the
safety factor incorporated. In 1986, AISC introduced their first load and resistance factor
Connections in Steel Structures V - Amsterdam - June 3-4, 2004
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design (LRFD) specification (3). This design method is consistent with what had been used
world wide, as well as for the design of other materials, for example, cold-formed steel and
concrete. Since 1986, there have been two more versions of the LRFD Specification, in
1993 and 1999, and one revision of the ASD Specification in 1989. For various reasons, the
LRFD method of design has not gained in popularity among steel designers. After careful
consideration of the needs of the design community and observing how other standards
developers have handled the dilemma of incorporating two design philosophies into one
standard, AISC has embarked on the development of a “combined” or single specification,
incorporating both the ASD and LRFD methods. The design capacity will be given in a “sideby-side” format throughout, which consists of a nominal strength for each limit state, followed
by an LRFD resistance factor and an ASD factor of safety. For example, for calculating
tensile yield strength, the new specification will read:
Pn = FyAg
Ωt = 1.67 (ASD)
φt = 0.90 (LRFD)
where the design tensile strength is φtPn and the allowable tensile strength is Pn / Ωt. The
safety factors were determined based on a live load-to-dead load ratio of 3, which results in
1.5 as the target effective load factor for the load combination of 1.2D+1.6L. Therefore, in
most cases, the safety factor is calculated as 1.5/φ and it is given to 3 significant digits. The
required strength or available strength are based on ASCE 7, Minimum Design Loads for
Buildings and Other Structures (4) factored load combinations for either LRFD or ASD,
depending on the method used. This arrangement will result in greater clarity, uniformity and
efficiency when applying AISC specifications. In the final analysis, the only difference
between the LRFD and ASD method of strength design is on the required strength side.
LRFD is based on factored load combinations given in ASCE 7 and ASD is based on service
load combinations in ASCE 7. Chapter J, Design of Connections, begins by stipulating the
design basis, similar to the above followed by more definitive design provisions as discussed
in the following.
GENERAL REQUIREMENTS
Chapter J of the 2005 Specification contains the majority of the connection design provisions
in that document. The first section entitled “General Provisions” contains revisions to such
topics as compression members with bearing joints, splices in heavy sections, beam copes
and weld access holes, bolts in combination with welds, and limitations on bolted and welded
connections.
Compression members with bearing joints
The new provision permits that compression members, other than columns, be proportioned
for the less stringent of: 1. an axial tensile force of 50% of the required compressive strength
of the member or 2. the moment and shear resulting from a transverse load equal to 2
percent of the required compressive strength of the member. The application of this
transverse load should be at the splice location “exclusive of other loads that act on the
member. The member shall be taken as pinned for the determination of the shears and
moments at the splice.” This sub-section begins with a User Note that reminds the designer,
“All compression joints should also be proportioned to resist any tension developed by the
load combinations….” User Notes are a new feature of the 2005 Specification. They are
non-mandatory and are interspersed throughout the document to offer the designer concise
assistance with using the specification.
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This provision is required to account for member out-of-straightness and to resist unexpected
lateral loads that may not have been considered in the design. In the past 40 years of the
AISC Specification, the only requirement that has existed required that splice materials and
connectors have a capacity of at least 50% of the required member strength. In the new
provision 1., the stipulation that these elements be designed for a tensile force provides a
more definitive way to address situations where compression on the connection imposes no
force on the connectors. Although this is a simple way to address this issue, it also can be
very conservative. Therefore, provision 2. was added offering an alternative that more
directly addresses the design intent of these provisions. The application of a lateral load of
2% simulates a kink at the splice, which could be caused by slightly out-of-square finished
ends or other construction conditions.
Splices in heavy sections
The special material toughness requirements for splices of heavy sections connected by
complete-joint-penetration groove welds have previously existed in the 1999 Specification.
The 2005 Specification will include clarification of these requirements. Shrinkage of large
welds between elements that are not free to move causes strains in the material adjacent to
the weld that can exceed the yield point strain. As the Commentary to the 2005 Specification
states, "In thick material the weld shrinkage is restrained in the thickness direction, as well as
in the width and length directions, causing triaxial stresses to develop…." and this can
prevent the steel from deforming in a ductile manner. Thus, special material toughness
requirements, and carefully prepared weld access holes and copes are required for heavy
tension members to prevent brittle fracture.
For both rolled and built-up shapes, special toughness requirements apply to shapes with
flanges or plates exceeding 2 in. (50 mm), when "used as members subject to primary tensile
forces due to tension or flexure and spliced using complete-joint-penetration groove welds
that fuse through the thickness of the member." The latter phrase was added to clarify the
extent of welding required for these provisions to be applicable. The verbiage in the 1999
Specification explaining how the impact test should be performed is replaced with a
reference to ASTM A6/A6M, Supplementary Requirement S30, Charpy V-Notch Impact Test
for Structural Shapes - Alternate Core Location (5). The impact test must meet a minimum
average value of 20 ft-lbs (27 J) absorbed energy at +70°F. The requirements do not apply if
the splices and connections are made by bolting, or if shapes with elements less than 2 in.
thick are welded to a heavy section, or to splices of elements of built-up shapes that are
welded prior to assembling the shape.” On the other hand, the provisions do "apply to builtup cross section consisting of plates exceeding 2 in. that are welded with complete-jointpenetration groove welds to the face of other sections."
Beam copes and weld access holes
When splicing hot rolled shapes with a flange thickness exceeding 2 in. (50 mm) and similar
built-up cross sections, special attention must also be paid to the formation of beam copes
and weld access holes. More detailed rules for the size of an access hole are given;
specifically, the height shall be 1 1/2 times the thickness of the material containing the
access hole, most likely the web thickness, but not less than 1 in. (25 mm) nor greater than 2
in. (50 mm). Room for weld backing must also be provided and no arc of the weld access
hole shall have a radius less than 3/8 in.
For built-up shapes the access hole may
terminate perpendicular to the flange as long as the flange-to-web weld is held back at least
the weld size from the edge. The weld access hole details included in the 2005 Specification
are very similar to those in AWS D1.1, Structural Welding Code-Steel (6).
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Bolts in combinations with welds
The design criteria for bolts in combination with welds in a joint are being completely revised
in 2005. Formerly, only bolts in slip-critical connections were permitted to share load with
welds. In the current draft, the provision reads as follows:
Bolts shall not be considered as sharing the load in combination with welds
except that connections with high-strength bolts installed in standard holes or
short slots transverse to the direction of the load are permitted to be
considered to share the load with longitudinally loaded fillet welds. In such
connections the strength of the bolts shall not be taken as greater than 50% of
the bearing strength of the bolts.
In other words, bolts in standard holes and short slots transverse to the direction of load can
share load with only longitudinally loaded fillet welds, but with a 50% reduction in the bearing
capacity of the bolts. This new provision is based on a recent research paper published in
the AISC Engineering Journal by Kulak and Grondin (7).
Limitations on bolted and welded connections
This section of Chapter J lists under what conditions pretensioned joints, slip-critical joints, or
welds are required. A similar section has existed in the AISC Specification for several
editions. For column splices, the height limitations and the language is being updated and
simplified, such that pretensioned joints, slip-critical joints, or welds are required in column
splices in all multi-story structures over 125 ft (38 m) in height. Formerly, the height limit was
based on the width of the building. The new provision is consistent with the height above
which connections of all beams and girders to columns are required to be pretensioned
joints, slip-critical joints, or welds. The remainder of the list remains unchanged, including
connections where live loads produce impact or reversal of stress and structures carrying
cranes over five-ton capacity.
Minimum strength of connections
A brief section on minimum strength of connections will be deleted. This section, also a
remnant of older versions of the AISC specification, stated a minimum factored load of 10
kips (44 kN) that all connections "providing design strength" should carry (2). The task
committee determined that these minimum loads have no technical basis and had the
potential of giving the designer the false idea that connections with this minimum design load
were adequate for fabrication and construction loads without further analysis.
WELDS
Weld provisions given in AWS D1.1 (6) apply under the 2005 Specification, with the
exception of those modified by the AISC sections listed in the preamble to Section J2. The
intention is for AISC to update their provisions to be consistent with the referenced version of
AWS D1.1. However, due to the different development cycles of the two standards, in some
cases, differences occur.
The most significant revisions to the weld provisions in the 2005 Specification occur in the
following areas: effective area and effective weld sizes for groove welds, and effective area,
terminations, and strength of fillet welds.
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Groove welds
In line with AWS D1.1, as well as more recent research, the tables for effective throat of
partial-joint-penetration groove welds and effective weld sizes of flare groove welds are being
updated. Table J2.1 shown below has expanded to include more combinations of welding
processes and welding positions for partial-joint-penetration groove welds (new portions are
highlighted). The terminology to describe the effective throat thickness has been revised
from "depth of chamfer" to "depth of groove."
Table J2.1 Effective throat of partial-joint-penetration groove welds.
Welding Process
Welding Position
F (flat), H (horiz.),
V (vert.),
OH (overhead)
Shielded Metal Arc
(SMAW)
All
Gas Metal Arc (GMAW)
Flux Cored Arc (FCAW)
All
Groove Type
(AWS D1.1 Figure 3.3)
Effective Throat
J or U Groove
60° V
Depth of Groove
J or U Groove
Submerged Arc (SAW)
F
60° Bevel or V
Shielded Metal Arc
(SMAW)
F, H
45° Bevel
All
45° Bevel
V, OH
45° Bevel
Depth of Groove
Depth of Groove
Minus 1/8-in (3mm)
Depth of Groove
Minus 1/8-in (3mm)
The minimum effective throat thickness of a partial-joint-penetration groove weld is tabulated
in the 2005 Specification with numbers identical to the 1999 LRFD Specification, except the
minimum weld thickness is based on the thickness of the thinner part joined. Previously, it
was determined based on the thicker part joined. The new Specification will read "Minimum
weld size is determined by the thinner of the two parts joined." This is again consistent with
AWS D1.1, where when low hydrogen filler metals or processes are applied, the provisions
are based on the thinner part joined. Due to the prevalence of A992 and other high strength
low alloy steels in construction today, the use of low hydrogen filler metals are required.
Effective weld sizes of flare groove welds are being increased based on a March 2003 report
by Packer and Frater (8) as shown in Table J2.2. This table applies when the flare groove
weld is filled flush to the surface of a round bar, a 90° bend in a formed section, or
rectangular tube. For flare groove welds filled less than flush, the values in Table J2.2 apply
minus the greatest perpendicular dimension measured from a line flush to the base metal
surface to the weld surface. Examples of Flare-V-groove and flare-bevel groove welds are
shown in Figure 1.
Effective throats larger than either Table J2.1 or J2.2 can be qualified by tests.
For flare
groove welds the fabricator must establish by qualification the consistent production of such
larger effective throat thicknesses.
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Table J2.2 Effective weld sizes of flare groove welds.
Welding Process
GMAW and FCAW-G
SMAW and FCAW – S
SAW
Flare Bevel Groove¹
5/8 R
5/16 R
5/16 R
Flare V Groove
3/4 R
5/8 R
1/2 R
General Note: R = radius of joint surface (Can be assumed to be 2t for HSS)
Note 1: For Flare Bevel Groove with R<0.375 use only reinforcing fillet weld on filled flush joint
Figure 1. Examples of Flare V-groove and flare-bevel groove welds.
Fillet welds
The important revisions expected to the fillet weld provisions relate to effective throat, fillet
weld terminations, strength when fillet weld groups are oriented both longitudinally and
transversely to the direction of applied load. Regarding effective throat, historically, an
increase was permitted for submerged arc welding only. This increase has not been found to
be conservative for all process settings. Therefore, the new language allows an increase in
the effective throat using any welding process if consistent penetration beyond the root of the
diagrammatic weld is demonstrated by tests.
In the 1999 Specification, specific criteria for fillet weld terminations were incorporated into
the specification proper. This material has been "tweaked" slightly by revising the language
for terminations where cyclic forces exist. The previous text read, "For connections and
structural elements with cyclic forces, … fillet welds shall be returned around the corner for a
distance not less than the smaller of two times the weld size or the width of the part." This is
now only applicable to "double angle connections and structural elements subject to cyclic
forces." Additionally, the special termination for "fillet welds joining transverse stiffeners to
plate girder webs" now only applies to plate girder webs 3/4 in. (19 mm) thick or less - a less
stringent requirement.
A new provision not yet balloted by the committee at the time of this paper, relates to the
strength of fillet welds when fillet weld groups are concentrically loaded and consist of weld
elements that are oriented both longitudinally and transversely to the direction of applied
load. The combined nominal strength of the fillet weld group shall be determined as the
greater of:
Rwl + Rwt or 0.85 Rwl + 1.5 Rwt
where,
Rwl = the total nominal strength of longitudinally loaded fillet welds
Rwt = the total nominal strength of transversely loaded fillet welds
This new provision follows two existing sub-sections that allow higher design capacities
based on the angle of loading with respect to the weld longitudinal axis. Recent research by
Ng et al. (9, 10) has demonstrated that where fillet welds exist in the same weld group that
are oriented both transverse and longitudinal to the direction of applied load, the existing
provisions are unconservative (2).
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BOLTS AND THREADED PARTS
Similar to design of welds in the AISC Specifications, use of high-strength bolts conforms to
another referenced standard, entitled Specification for Structural Joints Using ASTM A325 or
A490 Bolts, as approved by the Research Council on Structural Connections, hereafter
referred to as the RCSC Specification (11). For instances where the AISC Specification
differs from this referenced document, the AISC Specification controls. The new revisions
that will appear in the 2005 Specification include an expanded list of bolts or threaded rods
permitted, more liberal use of short-slotted holes, and revised procedures for combined
tension and shear in bearing-type connections and design for shear in slip-critical
connections.
High-strength bolts
Sometimes there is a need for larger diameter (greater than 1 ½ in. (38 mm)) or longer than
usual (greater than 12 diameters) high strength bolts, such as anchor rods for fastening
machine bases. Due to the diameter and length limitations of the more commonly accepted
bolts types, such as high-strength bolts, ASTM A325, A490, and F1852 (twist-off type), the
2005 Specification will permit the use of other specified ASTM bolts or threaded rods. Bolts
or threaded rods conforming to the following ASTM specifications are permitted in this case:
ASTM A354 Gr BC, A354 Gr BD, (Quenched and Tempered Alloy Steel Bolts, Studs, and
Other Externally Threaded Fasteners) or A449 (Quenched and Tempered Steel Bolts and
Studs). For slip-critical connections, it is important that the geometry of these special
fasteners, including the head and nut(s) is equal to or (if larger in diameter) proportional to
that provided by ASTM A325 or A490 bolts. Installation must comply with the RCSC
Specification with modifications as necessary to account for the increased diameter and/or
length to provide the design pretension.
Size and use of holes
In addition to permitting other ASTM bolt types, the new specification will relax the
requirements for hole types permitted. Previously, only standard holes were allowed in
member-to-member connections without the approval of the engineer of record (EOR). It is
proposed that additionally short-slotted holes oriented transverse to the direction of load may
also be used routinely without any special approval. This is in response to what is common
practice in the fabrication industry. Short-slotted holes oriented parallel to the load,
oversized holes, or long-slotted holes still require EOR approval.
Combined tension and shear in bearing-type connections
Research has demonstrated that the strength of bearing fasteners subject to combined shear
and tension can be closely represented by an ellipse (12). Previous versions of the AISC
Specification have employed a straight-line representation of the ellipse as shown in Figure
2. In the 2005 Specification, the actual equation for the sloped portion of the approximation
is being given in the provisions, with the more exact elliptical equations given in the
commentary. The provisions read as follows:
The available tensile strength of a bolt subjected to combined tension and
shear shall be determined as φRn or Rn / Ω where φ = 0.75 (LRFD), Ω = 2.00
(ASD), Rn = Fnt′Ab, and Fn t′ = nominal tensile strength per unit area modified
to include the effects of shearing stress, ksi (MPa) defined as
F
Fnt ' = 1.3Fnt − nt fv ≤ Fnt (LRFD)
φFnv
7
Fnt ' = 1.3Fnt −
ΩFnt
fv ≤ Fnt
Fnv
Equation for the sloped line:
⎛ ft
⎜
⎝ φFt
⎞ ⎛ fv ⎞
⎟+⎜
⎟ = 1.3
⎠ ⎝ φFv ⎠
⎛ Ωft ⎞ ⎛ Ωfv ⎞
⎜
⎟+⎜
⎟ = 1.3
⎝ Ft ⎠ ⎝ Fv ⎠
(LRFD)
(ASD)
ft
A
(ASD)
Pt. A = φFt or Ft / Ω
Pt. B = φFv or Fv / Ω
B
fv
Figure 2. Straight-Line Representation of Elliptical Solution.
High-strength bolts in slip-critical connections
One contentious issue in the current draft of the 2005 Specification is how to handle slip
resistance of slip-critical connections. The 1999 Specification gave two procedures for
calculating slip resistance: one method using factored loads and the other based on service
loads. For consistency with the format of the “unified” specification, only one procedure is
being proposed that is purported to give substantially the same results for ASD and LRFD.
This proposed procedure provides “resistance to slip at service loads or resistance to slip at
factored loads with a reliability appropriate for serviceability criteria.” The draft criteria can be
summarized as follows:
The design slip resistance φRn and the allowable slip resistance Rn/Ω shall be determined as:
φ= 1.00
Ω = 1.40
Rn = 1.13µ hscTbNs
where:
µ
hsc
Tb
= mean slip coefficient for Class A (0.35) or B (0.50) surfaces, as applicable, or
as established by tests
= hole factor based on the hole type (standard, oversize, etc.)
= minimum fastener tension, kips (kN)
AFFECTED ELEMENTS OF MEMBERS AND CONNECTING ELEMENTS
This section of Chapter J is applicable to elements of members at connections and
connecting elements, including strength of elements in tension, in shear, and block shear
rupture strength. The latter has gone through numerous revisions in the more recent
versions of the AISC specification and the design procedure is being revised yet another time
in the 2005 Specification, based on the latest research. The new provisions are based on
one equation instead of two as given in the 1999 Specification. The nominal strength,
Rn = 0.6FyAgv + UbsFuAnt
where:
Ubs = 1 when tension stress is uniform; 0.5 when tension stress is nonuniform
Agv = gross area subject to shear, in.2 (mm2)
Ant = net area subject to tension, in.2 (mm2)
8
Anv = net area subject to shear, in.2 (mm2)
and 0.6FyAgv ≤ 0.6FyAnv
For a more detailed discussion of this limit state and its history, see Reference (13).
CONCLUSION
The 2005 Specification will not reach final approval until later in 2004, therefore the material
discussed in this paper is for information only and should not be applied until the final
document is announced. When that happens, the revised provisions in Chapter J for bolted
and welded connection design will be another step forward for the steel design and
fabrication industry in the United States. The AISC Committee on Specifications will
continue to work toward the goals of their mission statement:
Develop the practice-oriented specification for structural steel buildings that provides for
• life safety
• economical building systems
• predictable behavior and response
• efficient use
Based on new information from the areas of research and industry practice, the 2005
Specification for Structural Steel Buildings will allow for continued safe, as well as
economical and efficient steel building designs.
REFERENCES
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
AISC, (2004). Specification for Structural Steel Buildings, Draft dated March 2004,
American Institute of Steel Construction, Chicago, IL.
AISC, (1999). Load and Resistance Factor Design Specification for Structural Steel
Buildings, American Institute of Steel Construction, December 27, Chicago, IL.
Buildings, American Institute of Steel Construction, September 1, Chicago, IL.
ASCE, (2002). Minimum Design Loads for Buildings and Other Structures, ASCE 7,
American Society of Civil Engineers, Reston, Virginia.
ASTM, (2002), Standard Specification for General Requirements for Rolled
Structural Steel Bars, Plates, Shapes, and Sheet Piling, ASTM A6/A6M-02,
American Society of Testing Materials, West Conshohocken, Pennsylvania.
AWS, (2002). Structural Welding Code -Steel, American Welding Society, AWS
D1.1/D1.1M:2002, Miami, Florida.
Kulak, G.L. and Grondin, G.Y. (2003). “Strength of Joints that Combine Bolts and
Welds,” Engineering Journal, AISC, 4th Quarter.
Packer, J.A and Frater, G.S., (2003). "The Effective Throat of Flare Bevel and Flare
V Groove Welds," Final Report to AISC and STI, March.
Ng, A.K.F., Deng, K., Grondin, G.Y., and Driver, R.G., (2004). “Behavior of
Transverse Fillet Welds: Experimental Program,” Engineering Journal, AISC, 2nd
Quarter.
Ng., A.K.F., Driver, R.G., Grondin, G.Y., (2004). “Behavior of Transverse Fillet
Welds: Parametric and Reliability Analyses,” Engineering Journal, AISC, 2nd
Quarter.
9
(11)
(12)
(13)
10
RCSC, (2002). Specification for Structural Joints Using ASTM A325 or A490 Bolts,
Research Council on Structural Connections, Chicago, IL.
Kulak, G.L., Fisher, J.W., and Struik, J.H.A., (1987). Guide to Design Criteria for
Bolted and Riveted Joints, 2nd Edition, John Wiley & Sons, New York, NY.
Geschwindner, L., (2004). “Evolution of Shear Lag and Block Shear Provisions in the
AISC Specification,” Proceedings of the Connections in Steel Structures V
Conference, Amsterdam, The Netherlands.
DEFORMATION CONSIDERATIONS FOR CONNECTION
PERFORMANCE AND DESIGN
Reidar Bjorhovde
The Bjorhovde Group, Tucson, Arizona, U S A
ABSTRACT
A tension test is used to represent the properties of steel, but it has no meaning
for the response of the material in a structure. The uniaxial tension test was
developed as a consensus solution, to have a standard by which similar
materials could be compared to a common base. It does not represent the
actual behavior of the steel in a structure, and was never intended to do so. The
paper addresses the properties of a range of structural steels, how these are
incorporated into design standards and how the standards define deformation
characteristics and demands for bolted and welded connections.
INTRODUCTION
As a construction material, steel has significant advantages over many others: it offers high
strength and stiffness, has adequate deformation capacity and stress redistribution ability for
many applications, it does not crack or otherwise fracture under normal service conditions, and
is available in several strengths and geometric forms. Finally, for most practical purposes it may
also be regarded as isotropic, with resulting benefits.
On the other hand, many structures will experience "non-normal" conditions many times during
fabrication, construction or service. A dynamically loaded structure such as a bridge will
experience fatigue; seismic events impose major deformation demands on structural
components and details; fabrication methods such as welding place very high demands for local
deformation ability of the steel in certain regions of the structure. The state-of-the-art of
computation technology is such that it is possible to incorporate many of these effects explicitly
in the analysis phase, and the quality of fabrication and construction continues to improve as
staff training and equipment are enhanced. However, much of the advanced software is not
suitable for design purposes, and most of this work therefore continues to be strictly researchoriented.
It is a major problem that the material itself is not adequately understood by the professionals
who specify its use for structural purposes. This includes the complexity of its chemical and
metallurgical makeup, as well as the fact that the models that are used by codes to represent its
mechanical response bear little resemblance to what the steel will experience under actual
fabrication and service conditions. For one, it is known that steel is anisotropic, as a result of
production operations as well as other plastic deformation effects. Although the anisotropy
normally is of no particular consequence, it will affect the response of the steel in extreme
loading and deformation demand situations. For another, the behavior of steel is a function of
deformation history, to the effect that an otherwise ductile steel may respond as a high strength,
low ductility material, given the prior occurrence of large displacements.
11
In brief, the complex nature of the response is not generally appreciated. The common
measures, namely, the data obtained from simple uniaxial tension tests, have little bearing on
the in-structure performance. The tension test was developed as a consensus solution, to have
the convenience of a performance standard, by which similar materials could be compared to a
common base. It does not represent the actual behavior of steel in a structure, and was never
intended to.
Many designers tend to consider the requirements of the materials standards as reflecting actual
performance ability. Two- and three-dimensional effects are not recognized, at least in part due
to the inability of design standards to correlate such effects with the elementary material
behavior models that are used. This is done in spite of the fact that multidimensional response
is the key to the behavior of some of the most important regions of the structure. In particular,
experience has shown that this is where problems tend to develop, much more than in any other
areas of the structure (1, 2, 3, 4).
Nevertheless, the focal point for designers continues to be the design codes. For rational
decisions and proper recognition of material abilities, it is essential to appreciate the
relationships between strength and deformation demands, and to assess which one that
governs the end result.
BASIC MATERIAL BEHAVIOR REPRESENTATION
The uniaxial tension test uses engineering stress and strain to define the response of the steel,
for convenience in measurement and because the test results are ultimately intended only for
use in comparison with other steels. With P = applied axial load, A0 = original cross-sectional
area of tension specimen, A = cross-sectional area at load P, l0 = original gage length, l = length
(= instantaneous length) at load P, and ∆l = change in length = (l - l0), the stress and strain are
given by the elementary expressions of Eqs. (1a) and (1b):
σ = P/A0
(1a)
ε = ∆l/l0 = l/l0 - 1
(1b)
and Eq. (1b) can be used to express the instantaneous length as
l = l0 (1 + ε)
(1c)
Although convenient, and suitable as representations of the steel behavior up to and slightly
beyond yielding, these definitions do not recognize that the area changes as the load increases.
Based on the concept of an incompressible material, which is fundamentally correct for steel,
the following holds true
A0l0 = A l
(2)
which can be used to define the true stress, σtr, as
σtr = P/A = Pl/Al = Pl/A0l0 = σ(l/l0) = σ(1 + ε)
(3a)
Similarly. the true strain, εtr, recognizes that the length changes continuously. The strain
increment, dεtr, for an instantaneous length l is given by
dεtr = dl/l
and the total accumulated strain therefore is given by
12
εtr = ∫ (dl/l) = ln (l/l0)
(3b)
For all practical purposes, the engineering and the true strains are equal for small strains, and
the stress-strain curves coincide up to and slightly beyond the yield stress. After this point the
two curves will diverge, to the effect that the true stress will continue to increase until material
rupture.
The most common ductility measure for steel is the elongation at fracture, εu, which is defined in
terms of engineering strain. Somewhat inconveniently, this is a function of the gage length, and
mill test reports must therefore report the magnitude of l0, as either of the commonly used 50 or
200 mm lengths. True strain is clearly a better ductility measure, since it reflects the total
accumulated strain at the point of failure. For equal levels of engineering and true stress, the
true strain is significantly smaller than the engineering strain. Conversely, for equal levels of
engineering and true strain, the true stress is significantly higher than the engineering stress.
UNI- AND MULTI-DIMENSIONAL RESPONSE CHARACTERISTICS
The preceding developments are based on one-dimensional material behavior, with no restraint
offered against deformations in the other orthogonal directions of the steel specimen. Once the
yield stress is reached, plastic deformation takes place, and necking occurs in the area of the
specimen where the failure ultimately will occur. For a more realistic assessment of the
response of the steel under multi-dimensional restraint conditions, it has been shown that the
true stress-true strain relationship is the appropriate representation, unless one proceeds to
utilize yield criteria for multi-dimensional states of strain. However, this is not practical,
especially in view of the need for fairly simple material definitions.
At the same time, the true stress and strain reflect the fact that the steel cannot supply the
amount of deformation indicated by the results of the simple tension test. Even under minor
restraint conditions, fracture takes place at strains that are significantly lower than those
specified by the materials standards.
Complicating the issues further is the fact that the yield ratio has been shown to play a major
role for the deformability of steel. Designating the yield ratio by Y, it is defined as
Yield Stress
Y = ------------------------ = Fy/Fu
Tensile Strength
(4)
where Fy and Fu are the mechanical properties utilized by all common materials standards.
Examining a wide range of structural steels, Kato (5) showed that the deformability decreases
with an increasing value of Y, and the decrease is especially marked for Y-values in excess of
approximately 0.6. As an illustration, Table 1 gives the yield ratios and relevant mechanical
properties for a number of the current American structural steels. The standard numbers are
those of the American Society for Testing and Materials (ASTM); the relevant stress levels are
given in units of MPa (N/mm2). These steels have very similar counterparts within European
and Japanese steelmaking practices, to mention two major areas of steel production. Standards
published by the International Standards Organization (ISO) also reflect these types of
materials.
It is clear that adequate structural performance cannot be guaranteed by basing the material
choice only on the standards' basic properties. In fact, Kato (5) recommended that in order to
assure reasonable and reliable deformation capacity of steel members and connections, as a
13
minimum an upper limit of the yield stress and/or the yield ratio should be specified for each
steel grade.
Based on the above recommendation and substantial research work performed in the aftermath
of the 1994 Northridge earthquake, an enhanced 350 MPa steel grade is now produced by steel
mills in the United States, using a maximum Y-value of 0.85 (6). The specified minimum yield
stress is 350 MPa; the standard also requires a maximum value of Fy of 450 MPa, and the
minimum tensile strength is Fu = 450 MPa. Detailed chemistry requirements are provided, as is
an upper limit on the carbon equivalent, to ensure satisfactory weldability.
Table 1. Yield ratios for common American structural steels.
ASTM Steel Grade
Yield Stress, Fy
Tensile Strength, Fu
Yield Ratio, Y
A36
250
410 - 550
0.62 - 0.45
A572 (50)
350
450
0.77
A588 (50)
350
480
0.71
A852
480
620 - 760
0.78 - 0.64
A913 (65)
450
550
0.81
A992
350
450
0.85 (max)
A514 (t ≤ 63 mm)
700
760 - 900
0.91 - 0.77
ADDITIONAL RESPONSE CONSIDERATIONS
The preceding issues are further complicated by the way tension tests are performed and
reported by steel producers. Specifically, the upper yield point is commonly given as the value
of the representative Fy. Although the use of this property is understandable, from a production
viewpoint, it is not a dependable, realistic value, since it relies heavily on the specifics of the
method of testing. As noted by Lay (7) - "the upper yield stress is not of relevance in design, as
it is lost if small overloads or misalignments occur". Specifically, utilizing dislocation theory as
the basis for yielding or plastic deformation in steel, the upper yield point mobilizes dislocations,
and the lower yield point maintains the "movement" of the dislocations. In essence, yielding is
caused by crystal structure (lattice) defects, in the form of dislocations.
These issues have not been addressed by a number of studies, among them numerous seismic
projects, their reports noting that - "...... 50 percent of the material actually incorporated in a
project will have yield strengths that exceed these mean values. For the design of facilities with
stringent requirements for limiting post-earthquake damage, consideration of more conservative
estimates of the actual yield strength may be warranted" (4). The same reference notes that
"Design professionals should be aware of the variation in actual properties permitted by the
ASTM specifications. This is especially important for yield strength. Yield strengths for ASTM
A36 material have consistently increased over the last 15 years......" (4).
Several other factors also play important roles, such as the steel production methods (e.g.
conventional and thermomechanical control processes (8, 9)). The changes that have taken
place over the past 15 years in North America in going from iron ore and coke-based ingot steel
to scrap-based continuous cast steel have resulted in materials that are significantly different,
but clearly improved in metallurgical and mechanical sense. Steel chemistry and weldability,
and especially the carbon and alloy contents, further emphasize the complex problems facing
the designer and the fabricator in the steel selection process. Some of these issues have now
14
been taken into account, specifically, in the development of the criteria for what is now the most
commonly used structural steel in the United States, the A992 steel (6).
PERFORMANCE INDICATIONS OF CURRENT STRUCTURAL STEELS
Current structural steels in the United States span the range from the mild, carbon-manganese
A36, to the high strength, quenched and tempered A514 and the quenched and self-tempered
A913. The traditional methods have largely given way to continuous casting; for structural
profiles in the US, current (2004) production is based entirely on this technology. As a result,
steel chemistry has changed perceptibly, such that steel now gains its strength less from carbon
and more from a variety of alloying elements. The current steels have significantly lower levels
of carbon than previous production runs. Values of C-content less than 0.10 percent are the
norm; this contrasts with a carbon content of 0.2 percent and higher for earlier steels.
The lower carbon and higher alloying elements contents result in steels with acceptable strength
and ductility characteristics, as defined by the material standards. Further, the lower carbon, in
particular, means that weldability is significantly improved. Fracture toughness is improved as
well, indicating that fatigue performance and resistance to brittle fracture should be enhanced
(9). Nevertheless, localized effects of cold straightening, for example, continue to affect the
performance of the steel, especially in connection regions. On the other hand, the issue of
through-thickness strength and ductility, which used to be regarded as critical for the
performance of seismic connections, for example, has been found to be unimportant (10).
The basic quality and variety of structural steels available to designers and fabricators have
therefore been improved significantly, yet problems persist. As demonstrated earlier in this
paper, this has at least partly been caused by misinterpretation of materials standards and what
they imply for the actual in-structure performance of the steel. Of equal importance are clearly
functions that are controlled directly by the designer and the fabricator: it is unrealistic to expect
the material to provide for all of the stiffness, strength and deformability that are needed by the
structure under all expected service conditions.
An evaluation of the ductility and deformability requirements of the current American structural
steel design specification (11) is provided in the following. It is emphasized that most of these,
where they exist, are implied rather than explicit. This is most likely the result of an engineering
tradition of focusing on stress and strength rather than strain and deformation.
DEFORMATION CRITERIA FOR SOME ELEMENTS AND CONNECTIONS
General observations
Between structural strength, stiffness and deformability, the first two are supplied relatively
easily, although improvements continue to be made through higher strength and improved
production methods. Further, many structures are controlled by the need for stiffness, in the
form of deflection or drift limits or dynamic response characteristics. For these cases the use of
higher strength steel is not advantageous. Framing system, high redundancy, and less reliance
on a limited number of structural elements are keys to successful performance.
Possibly of the greatest significance are the problems and solutions for the variety of connection
types and details that are utilized in structures. These are the regions where the material will be
exposed to the highest degrees of restraint, during shop fabrication and field erection, as well as
during high-demand service conditions. The connections influence local ductility demands and
framing performance, as evidenced by numerous examples from the Northridge earthquake (4).
Many reports of fractured welds and base metal details have been publicized. The basic
15
concept that cyclic loads above yield for low-ductility steel will cause fracture after a few cycles
(and conversely for a high-ductility steel) continues to be correct, but the problem is severely
aggravated under multi-dimensional degrees of restraint.
The following examples examine some of the primary American design criteria for steel
members; it focuses on certain elements only.
Tension members
Chapter D of the AISC Specification (11) details the strength criteria for tension members,
possibly the simplest structural elements, and the ones whose performance is closest to the
uniaxial conditions of the basic tension test. The limit states of gross cross section yielding and
effective net section fracture are well defined, although the reliability of the fracture case is less
than that of the overall yield. The reason for this is the greater variability of the tensile strength
(Fu) of the steel, as well as the influence of the geometry of the net section and the shear lag
associated with the cross-sectional shape and the placement of the end connection.
Ductility is recognized through the reference to strain hardening, stress concentrations, and the
importance of large deformations accompanying the yielding of the gross cross section. These
observations are based on various full- and reduced-scale tension member tests, but no data
are presented on actual deformation demands. However, in view of the relatively simple (other
than within the end connection regions) condition of these members and their satisfactory
behavior over the long term, it is generally accepted that ductility and deformation needs have
been assessed correctly. Deformation data are judged to be roughly comparable to tension
specimen tests, although specific results in support of this finding are not presented. However,
it is understood that the deformations that will occur in full-size tension members will be larger
than those of the material tests, primarily due to residual stress, initial crookedness and
eccentric application of the axial load.
Columns
Chapter E of the AISC Specification (11) gives the design criteria for columns and other
compression members. Since column buckling is primarily a stability phenomenon that is not
related to local or overall deformation demands, the issues of material performance are not
central to the issues at hand.
Beams
Chapter F of the AISC Specification (11) addresses the design criteria for laterally supported
and unsupported beams, and sections of Chapter B details local buckling and other
compactness issues. Chapter I gives the criteria for composite members; these will not be
examined here.
The overall behavior of beams is based on ultimate limit states involving in-plane or out-of-plane
failure. For example, for a laterally supported, compact beam, the ultimate limit state is the
development of a plastic hinge at the location of the maximum moment. The strength in this
case is therefore governed by the fully plastic moment, Mp, of the cross section. As another
example, for a laterally unsupported beam with an unbraced length larger than Lr, the ultimate
limit state is governed by elastic lateral-torsional buckling.
However, in all of these cases there is no clear indication of a required deformation or rotation
capacity. This is implied only through the criteria used to define compactness or the capacity of
the cross section to rotate after reaching the fully plastic moment. Specifically, flange and web
width-to-thickness ratios are established to allow full yielding in the cross section. In addition,
the beam has to be capable of rotating a certain amount beyond what constitutes the theoretical
16
full plastification rotation, θp, before local buckling or strain hardening occurs, at the ultimate
rotation value, θu. The deformation demand is therefore inelastic, and concentrates on the
ability of the compression flange to deform sufficiently longitudinally without buckling locally, and
of the tension flange to deform sufficiently longitudinally before strain hardening or fracture
occurs. The deformation capacity is therefore very much a function of the type of steel, or, in
other words, the level of the yield stress as well as the shape of the stress-strain relationship.
The rotation need also depends on the type of loading, to the effect that structures in seismically
active areas must be capable of supplying significantly larger inelastic rotations. A summary of
some of the key compactness criteria is illustrated in Table 2.
In Table 2 only the requirements for the flange of a W-shape are given, as an example. As an
aside, it is interesting to observe that the current seismic b/t-criterion was used for non-seismic
applications as recently as the 7th edition of the allowable stress design specification of AISC
(1970); the change of the constant from 0.30 to 0.38 was made in the 8th edition (1980).
Table 2. Compactness criteria and associated beam rotation demands.
Non-Seismic
Seismic
0.38 √(E/Fy)
( = 65/√Fy)
0.30 √(E/Fy)
( = 52/√Fy)
≥3
7 to 9
Unbraced length, Lp
1.76ry√(E/Fyf)
-----
Unbraced length, Lpd
-----
0.086ry(E/Fy)
Flange b/t-ratio
Rotation Demand Ratio θu/θp
In the table, the term ry is the y-axis radius of gyration; θu is the rotation developed before local
buckling or strain hardening occurs; and θp is the rotation developed as the fully plastic moment
is reached. The unbraced length criteria pertain to the maximum length that will allow the
development of the fully plastic moment for a laterally unsupported beam. Since plastic design
response characteristics are needed for seismic conditions, the requirements are much more
demanding.
The key data in Table 2 are given in the third line, as the rotation demand ratio, θu/θp. The
original data for the non-seismic ratio are based on numerous beam tests, as reported by Yura
et al. (12). The history of the seismic deformation demand is not as clear; the demand ratio
value of 7 to 9 is primarily based on studies by Popov and others, but specific references for this
work cannot be cited.
For beams in 250 and 350 MPa yield stress steel, the rotation demand ratios are governed by
the occurrence of local buckling or strain hardening in the compression flange. Limited studies
have been made of higher strength steel, but research work at the U. S. Steel Research
Laboratory in the 1960-s and early 70-s showed that for Fy = 700 MPa, tension flange fracture
governed the beam behavior (13). At the time, U. S. Steel was exploring the potential
development of hot-rolled shapes in A514 steel; this was unsuccessful as a result of the limited
rotation capacity.
Studies of beams with yield stress values from 380 to 550 MPa are very limited at this time, and
no definitive conclusions can be reached for such members. However, the practical utilization of
higher strength beams is questionable, especially in seismic areas. This is in part caused by the
"strong column, weak beam" concept, as well as the fact that beam size is frequently governed
by stiffness, rather than strength. Since the modulus of elasticity is independent of the level of
yield stress, using higher strength material beams is unnecessary.
17
Connections
Welds and bolts are addressed in Chapter J of the AISC Specification and connection details
are covered in Chapter K (11). These are the most complex sections of the specification and
the attention given to strength limit states as opposed to deformations is very substantial. This
is done in spite of the fact that the deformation response often controls the actual ultimate limit
state.
In the following only some of the requirements will be examined. However, in view of the severe
deformation demands that are placed on many types of connections, it would seem important to
assess all of these specification criteria in detail, to gain a clear understanding of what is
expected of the material when the connections are designed according to the Specification.
This is especially important for many types of beam-to-column moment connections and some
welded tension member splices, for which localized material deformation demands can be very
high (2, 3).
Welded splices in heavy shapes
The criteria for welded splices in very heavy wide-flange shapes are qualitative, but clear
recognition is given to the fact that the combination of residual stress, localized high deformation
demand due to fabrication operations, high localized hardness, and low fracture toughness in
the core area of hot-rolled shapes have the potential for leading to cracks and propagation of
cracks (2, 3). The event that caused this change in the AISC Specification was the bottom
chord fracture in one of the trusses for the Orange County Civic Center in Orlando, Florida. The
core area problem is much less important now, since continuous cast shapes have smaller and
less pronounced cores. The shapes that cracked in the Florida structure were all ingot-based.
Overlap in fillet welded joints
Single lap welded joints will rotate when subjected to axial forces in the longitudinal direction,
due to the eccentricity of one plate relative to the other. The Specification recognizes the need
for a certain length of overlap between the plates or members in the joint, equal to five times the
thickness of the thinnest part, but not less than 25 mm. If this is satisfied, ". the resulting
rotation will not be excessive....." (11). No specifics are given as regards rotation magnitudes.
Short vs. long bolted joints
Short bolted joints generally deform in such a fashion that localized yielding allows for a
redistribution of the bolt forces, to load each bolt equally. This is not the case with long bolted
joints, for which the non-uniform strain distribution leads to significant differences in the actual
bolt loads. In particular, the outermost bolts will have the higher loads, leading to the potential
for an "unzipping" type of failure. The AISC Specification recognizes this behavior by reducing
the tabulated bolt strength values by 20 percent for connections longer than 1270 mm.
However, the actual deformation demand is only accounted for qualitatively.
Bearing strength at bolt holes
This is one of the few cases where deformation and strength limit states are explicitly
recognized. Research has shown that the hole deformation will increase beyond 6 mm when the
nominal factored bolt load exceeds 2.4dtFu (11). Under many circumstances this will be
unacceptable, due to the contribution of such deformations to overall connection deformations.
If the bolt load increases to 3dtFu, the limit state will be that of hole ovalization or "dishing".
18
Beam-to-column connections
The criteria for the design of the details of beam-to-column connections are given in Chapter K
of the AISC Specification (11). The section provides extensive ultimate limit state criteria for
local flange bending, local web yielding, web crippling, sidesway web buckling, compression
web buckling, panel zone web shear, unframed beam and girder ends, additional stiffeners
requirements for concentrated forces, and additional doubler plate requirements for
concentrated forces. It is only in the treatment of panel zone web shear that strength and
deformation are explicitly recognized. It is formulated qualitatively, to the effect that different
equations are used to determine the nominal strengths if panel zone deformations are
considered in the frame stability analysis.
The Commentary for the Specification gives qualitative observations involving deformation
needs, such as "... that flange must be sufficiently rigid to prevent deformation of the flange ......"
(11). A detailed evaluation is provided for the panel zone behavior and the importance of its
deformation as regards the story and overall drifts of the structure.
SUMMARY
The paper has presented a discussion of issues related to performance demands for steel in
structures, especially under high restraint and high dynamic load conditions. It is shown that the
use of elementary materials standards requirements, which reflect uniaxial tension test
response, is unacceptable as a means to assess the response of the steel in the structure
during actual operating conditions.
Designers and fabricators must fully understand the material behavior. However, it is also clear
that the steel cannot assure satisfactory behavior by itself. Only together, through (1) material
choice, (2) local and overall structural design, and (3) shop and field fabrication techniques and
operations, will overall performance demands be met. In all cases strict adherence to specified
procedures is essential, for what good does a specification do if it is not used? Future
developments may see improved material standards, particularly if upper and lower limits are
placed on the specified yield stress values, and/or yield ratios are defined and required. The
criteria of the A992 standard of ASTM reflect a novel and very significant improvement.
REFERENCES
(1)
(2)
(3)
(4)
(5)
(6)
American Institute of Steel Construction (AISC) (1973), "Commentary on Highly
Restrained Welded Connections", AISC Engineering Journal, Vol. 10, No. 3, Third
Quarter (pp. 61-73).
Fisher, J. W., and Pense, A. W. (1987), "Experience with the Use of Heavy W-Shapes in
Tension", AISC Engineering Journal, Vol. 24, No. 2, Second Quarter (pp. 63-77).
Bjorhovde, Reidar (1988), "Solutions for the Use of Jumbo Shapes", Proceedings, AISC
National Steel Construction Conference, Miami Beach, Florida, June 8-11 (pp. 2-1 to 220).
Federal Emergency Management Agency (FEMA) (2000), "Recommended Seismic
Design Criteria for New Steel Moment-Frame Buildings", Bulletin No. 350, FEMA,
Washington, D.C.
Kato, Ben (1990), "Deformation Capacity of Steel Structures", Journal of Constructional
Steel Research, Vol. 17, No. 1 (pp. 33-94).
American Society for Testing and Materials (ASTM) (2003), "Standard Specification for
Structural Steel Shapes”, Standard No. A992, ASTM, Conshohocken, Pennsylvania.
19
(7)
(8)
(9)
(10)
(11)
(12)
(13)
20
Lay, M. G. (1982), "Structural Steel Fundamentals", Australian Road Research Board,
Vermont South, Victoria, Australia.
Barsom, John M. (1987), "Material Considerations in Structural Steel Design",
Proceedings, AISC National Engineering Conference, New Orleans, Louisiana, April 29May 2 (pp. 1-1 to 1-29)
Barsom, John M. (1996), "High Performance Steels", American Society of Metals
Advanced Materials & Processes, No. 3 (pp. 27-31).
Dexter, R. J. and Melendrez, M. I. (1999), “Through-Thickness Strength and Ductility of
Column Flanges in Moment Connections”, University of Minnesota Research Report to
the SAC Consortium.
American Institute of Steel Construction (AISC) (1999), "Load and Resistance Factor
Design Specification for Structural Steel Buildings", 3rd Ed., AISC, Chicago, Illinois.
Yura, J. A., Galambos, T. V., and Ravindra, M. K. (1978), "The Bending Resistance of
Steel Beams", Journal of the Structural Division, ASCE, Vol. 104, No. ST9, September
(pp. 1355-1370).
Haaijer, G. H. (1989), "Private Communication", Pittsburgh, Pennsylvania.
EVOLUTION OF SHEAR LAG AND BLOCK SHEAR PROVISIONS
IN THE AISC SPECIFICATION
Louis F. Geschwindner, Vice President of Engineering and Research,
The American Institute of Steel Construction
ABSTRACT
The American Institute of Steel Construction (AISC) publishes two standards
for design of steel structures, an allowable stress specification, ASD, and a
limit states specification, LRFD. The AISC Committee on Specifications is in
the process of developing a new standard that will include provisions for
design according to both ASD and LRFD. For connection design, the
specification is evolving as provisions from the previous specifications are
integrated. In particular, the provisions for shear lag and block shear have
seen some evolution. This paper highlights the new provisions and the
changes that have taken place from previous editions of the specifications.
INTRODUCTION
The planned 2005 AISC Specification for Structural Steel Buildings (1) will include provisions
for both allowable strength design (ASD) and load and resistance factor design (LRFD). The
overriding principle guiding the development of these new provisions is that the steel does
not know what method was used in its design. Thus, there should be a single approach for
determining member strength and the modification of that strength to be consistent with the
ASD and LRFD loading provisions of the governing building codes. The AISC Committee on
Specifications and its Task Committees were charged with evaluating the existing ASD and
LRFD provisions and incorporating the best of both standards into the new standard. In
addition, research results that have become available since publication of the previous
standards, ASD in 1989 (2) and LRFD in 1999 (3) should be incorporated. Thus, this new
specification should be a step forward for each design approach.
The original LRFD Specification (4) was calibrated to the then existing ASD Specification (5)
for a live load to dead load ratio, L/D = 3, in order that the new specification produce designs
that were comparable to the existing provisions. The ASD and LRFD design philosophies
are stated in the 2005 Specification (1) draft for ASD as
( D + L ) = Ra ≤
and for LRFD as
Rn
Ω
(1.2 D + 1.6 L ) = Ru ≤ φ Rn
(1)
(2)
where Ra and Ru are the required strengths determined from the ASD and LRFD load
combinations, Rn is the nominal strength, φ is the resistance factor for LRFD, and Ω is the
safety factor for ASD . For the load combination of (1.2D + 1.6L) and L/D = 3, the effective
load factor becomes 1.5. Thus, the relationship between φ and Ω can be determined by
solving Eqs. 1 and 2 for Rn and setting the them equal, thus
21
(1.2 D + 1.6 L ) = 1.5( L + D) = Ω( D + L)
φ
φ
(3)
which yields
Ω=
1.5
φ
(4)
This relationship guides the development of factors of safety for the ASD provisions of the
unified specification, based on the LRFD resistance factors. It will be seen that the resulting
strength provisions for tension members in the 2005 Specification (1) will be the same as
they are in the current ASD (2) and LRFD (3) Specifications. The provisions for shear lag will
be modified slightly to account for some recent research results.
Block shear has seen several changes over the years since it was first introduced into the
specification. However, it will also be seen that the strength provisions for 2005 are
essentially the same as the ASD and LRFD provisions with a slight variation in the
controlling factor.
SHEAR LAG
Shear lag provisions were first introduced in the 1978 AISC ASD Specification (5). This was
to account for the research findings that the net section was not fully effective in providing
fracture strength when all elements of the tension member section were not attached to the
connecting elements The provisions of Section 1.14.2 simply stated that the effective net
area was to be taken as the net area times a reduction factor, thus
Ae = Ct An
(5)
Three cases were identified for determining Ct :
1. W, M, or S shapes with flange widths not less than 2/3 the depth, and structural tees
cut from these shapes, provided the connection is to the flanges and has no fewer
than 3 fasteners per line in the direction of stress. Ct = 0.90.
2. W, M, or S shapes not meeting the requirements of subparagraph 1, structural tees
cut from these shapes, and all other shapes, including built-up cross sections,
provided the connection has not less than 3 fasteners per line in the direction of
stress. Ct = 0.85.
3. All members whose connections have only 2 fasteners per line in the direction of
stress. Ct = 0.75.
The commentary to Section 1.14.2 indicates that these values are reasonable lower bounds
for profile shapes and connection means described in the research of Munse and Chesson
(6). In that research they proposed an equation
Ct ≈ 1 − x l
(6)
that, although not a part of the actual specification provisions, was included in the
commentary.
22
The 1986 LRFD and 1989 ASD Specifications continued the use of these specified reduction
factors, although the symbol was changed to U. In addition, provisions were made for
members connected through welds. For the 1993 LRFD Specification, the equation
developed by Munse and Chesson (6), with an upper limit of 0.9 added, was made a part of
the Specification and the numerical values that had been in use until this time were moved to
the commentary. The background for these changes is reported by Easterling and Girouk
(7). The three previously used cases were made available for designers continued use as
reasonable lower bounds that could be used unless a higher value was determined through
the provided equation. The same provisions were carried over for the 1999 LRFD
Specification (3).
The 2005 Specification (1) needed to consider how the combination of ASD and LRFD
provisions would impact tension member strength and how, if at all, the effective net area
provisions would need to change. Using the relation between φ and Ω presented in Eq. 4,
the design tensile strength, φPn, and the allowable tensile strength, Pn/Ω, for the limit state of
fracture can be taken from
Pn = Fu Ae
φ = 0.75 (LRFD)
(7)
Ω = 2.0 (ASD)
This is the same provision as given in the 1999 LRFD Specification (3) and a comparison
with the 1989 ASD Specification (2) shows that it provides the same allowable strength.
Since effective net area is not a function of design approach, there will be no impact there.
There are two changes being considered for the 2005 shear lag provisions. The first is the
removal of the upper limit on U. There does not appear to be sufficient research results to
warrant retaining this limitation. The work of Munse and Chesson (6) did not include a
recommendation that the shear lag reduction factor have an upper limit, although their
testing program included only a few cases where this might have come into play.
The second change is the addition of a requirement that single angles, double angles, and
WT’s be proportioned so that U is equal to or greater than 0.6. Alternatively, a lesser value of
U is permitted if the tension member is designed for the effect of eccentricity through the use
of the interaction equations. Recent work reported by Epstein and Stamberg (8) suggested
that for WT sections, a lower bound of 0.65 be placed on U.
Since the 2005 Specification (1) will incorporate the previous separate specifications for
single angles and for HSS, the number of shear lag cases has increased. Thus, a table is
being provided to simplify the determination of appropriate U-values.
BLOCK SHEAR
As was the case for shear lag, block shear provisions first appeared in the 1978 ASD
Specification (5). These provisions were the result of the work of Birkemoe and Gilmor (9)
that was directed at the coped beam connection. The provisions, as stated in Section
1.5.1.2.2, indicate that the shear at beam end connections where the top flange is coped,
and in similar situations where failure might occur by shear along a plane through the
fasteners, or by a combination of shear along a plane through the fasteners plus tension
along a perpendicular plane on the area effective in resisting tearing failure, the stress was
to be limited to 0.3Fv This would have resulted in an allowable force equation of
23
Va = 0.3Fu ( Anv + Ant )
(8)
The commentary provided an alternative where the tension and shear areas could be treated
separately as
Va = 0.3Fu Anv + 0.5 Fu Ant
(9)
Obviously this would have provided an increase in allowable strength.
The 1989 ASD Specification (2) brought Eq. 9 from the commentary into the specification
and provided the direction that block shear should also be considered for welded
connections.
Block shear provisions are not as clearly articulated in the 1986 LRFD Specification (4). The
provision for shear fracture is given in the body of the specification but the discussion of
block shear is relegated to the commentary. In the commentary presentation, the possibility
of a combination of yielding on one plane and fracture on the other is introduced and the
following two equations are given
φ Rn = φ [0.6 Fy Agv + Fu Ant ]
(10)
φ Rn = φ [0.6 Fu Anv + Fy Agt ]
(11)
with φ = 0.75 and the largest value of φRn taken as the design strength. It is worth comparing
this first introduction of LRFD block shear provisions with the ASD provisions using the
relationship of φ and Ω presented in Eq.4. Since φ = 0.75, then Ω=2.0. Thus, dividing the
nominal fracture term from Eqs. 10 ands 11 by the safety factor of 2.0 and adding them,
yields Eq. 9.
The 1993 LRFD Specification (10) brought the two block shear equations forward into the
specification but altered the way that the controlling equation was selected. For these
provisions, the controlling factor was fracture. Shear fracture and tension fracture were to be
calculated and the larger fracture term was to be combined with the opposite yield term.
Additional research reported by Ricles and Yura (11) for coped beams and Hardash and
Bjorhovde (12) for gusset plates confirmed that the strength could be determined by the
summation of the shear and tension terms.
The 1999 LRFD Specification (3) continues to use the previously presented block shear
equations but sets an upper limit on the strength that is equal to the sum of the two fracture
terms and can be stated as
φ Rn = φ [0.6 Fu Anv + Fu Ant ]
(12)
which is actually a return to the commentary equation of the 1978 ASD Specification (5),
since Rn from Eq. 12 divided by the factor of safety, 2.0, yields Eq. 9.
For the 2005 Specification (1), the currently proposed block shear provisions have
undergone another slight modification. For shear strength, either fracture or yield, the
relations remain unchanged. For tension strength, two revisions are recommended. The first
is the recognition of the influence of non-uniform tension, as would occur on the block shear
tension face for a coped beam with two rows of bolts, as identified by Ricles and Yura (11).
The second change is the use, for all conditions, of the tension fracture strength, rather than
either tension fracture or yield strength. The resulting provisions are
24
φ Rn = 0.75 ( 0.6 Fy Agv + U bs Fu Ant )
(13)
φ Rn = 0.75 ( 0.6 Fu Anv + U bs Fu Ant )
(14)
but not greater than
When the tension stress is uniform, Ubs = 1.0 and for cases where the tension stress is not
uniform, Ubs = 0.5. This is consistent with the recommendations of Kulak and Grondin (13).
Although the committee considered a more involved approach to the calculation of Ubs, it
was decided to simplify the term so as not to make its determination laborious.
CONCLUSIONS
An evolution of the shear lag and block shear provisions has taken place since their first
introduction in the AISC Specification in 1978 (5). Although the changes have been slight,
they reflect an improving understanding of the behavior that they are attempting to predict.
The intent has always been to provide specification provisions that are sufficiently accurate
so as to provide for safe and economical structures while at the same time providing design
methods that are simple and economical to apply.
The 2005 “unified” Specification (1) is scheduled to receive final approval by the end of
2004. This schedule has been set in order that it may be incorporated into the next revisions
of the NFPA and IBC building codes. Although the provisions presented here for the 2005
Specification are those under consideration at this time. The committee process allows for
changes to be made until the final Specification has received Committee on Specifications
approval. Thus, this description of what might be ahead for the designer should not be relied
upon for design.
NOTATION
Ae
Agt
Agv
An
Ant
Anv
Ct
D
Fu
Fy
L
Pn
Ra
Rn
Ru
Va
x
φ
Ω
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Effective net area
Gross area subjected to tension
Gross area subjected to shear
Net area
Net area subjected to tension
Net area subjected to shear
Shear lag reduction factor from the 1978 ASD Specification
Dead load
Specified minimum tensile strength
Specified minimum yield stress
Live load
Nominal tensile strength
Required strength (ASD)
Nominal strength
Required strength (LRFD)
Allowable shear based on block shear
Distance from shear face to center of gravity of section
Resistance factor
Safety factor
25
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
26
AISC, (2004). Specification for Structural Steel Buildings, Draft dated March 2004,
American Institute of Steel Construction, Chicago, IL.
AISC, (1989). Specification for Structural Steel Buildings – Allowable Stress Design and
Plastic Design, American Institute of Steel Construction, June 1, Chicago, IL.
Buildings, American Institute of Steel Construction, September 1, Chicago, IL.
AISC, (1978). Specification for the Design, Fabrication and Erection of Structural Steel
for Buildings, American Institute of Steel Construction, November 1, Chicago, IL.
Munse, W. H., and Chesson, Jr., E. (1963), “Rivited and Bolted Joints: Net Section
Design,” Journal of the Structural Division, ASCE, Vol. 89, No. ST1, February, pp. 49106.
Easterling, W. S., and Giroux, L. G., (1993), “Shear Lag Effects in Steel Tension
Members,” Engineering Journal, AISC, Vol. 30, No. 3, 3rd Quarter, pp. 77-89.
Epstein, H., I., and Stamberg, H., (2002), “Block Shear and Net Section Capacities of
Structural Tees in Tension: Test Results and Code Implications,” Engineering Journal,
AISC, Vol. 39, No. 4, 4th Quarter, pp. 228-239.
Birkemoe, P. C., and Gilmor, M. I., (1978), “Behavior of Bearing-Critical Double –Angle
Beam Connections,” Engineering Journal, AISC, Vol. 15, No. 4, 4th Quarter, pp. 109115.
Ricles, J. M., and Yura, J. A., (1983), “Strength of Double-Row Bolted Web
Connections,” Journal of the Structural Division, ASCE, Vol. 109, No. ST1, January, pp.
126-142.
Hardash, S. G., and Bjorhovde, R., (1985), “New Design Criteria for Gusset Plates n
Tension,” Engineering Journal, AISC. Vol. 22, No. 2, 2nd Quarter, pp. 77-94.
Kulak, G. L., and Grondin, G. Y., (2002), “Block Shear Failure in Steel Members – A
Review of Design Practice,” Connections in Steel Structures IV, Proceedings of the
Fourth International Workshop, AISC, pp., 329-339.
THE CONSTRUCTABLE STRUCTURE IN STEEL
F. Maatje, ICCS bv, The Netherlands
H.G.A. Evers, ICCS bv, The Netherlands
ABSTRACT
Nowadays engineers still tend to optimize a structure to a minimum of
kilograms, which is the only hard criterion that is available for an engineer
during the design of the structure. In the end this criterion leads to structures
that are expensive and have poor quality.
In this article it is illustrated that selection of a deeper top- and bottom chord
member and the use of 3D-analysis software leads to a reduction of costs of
the total project. Furthermore, it results in improvement of the quality of the
structure as a whole.
THE ISSUE
For most of the structures it applies that they are established in the same way for many
years. An architect makes an architectonic design, a design engineer designs the main
structure and a steel fabricator takes care that the construction will be detailed, fabricated
and erected.
These phases are mostly sequential and do not have much overlap. Consequence is that the
expertise and involvement of the several parties is restricted to his/her own specialty.
Because of this strict separation, but also because of ignorance and incapability, the
engineer often disregards the phases that come next. Most of the times the result is that the
detailing of the structure becomes very complex and that the structure will be difficult to
fabricate.
These things do not have a positive effect on the project financially, constructively,
aesthetical, as well as systematically. By keeping the detailing of the steel into account in an
early stage, a better and more cost effective structure can be designed.
From their own disciplines, ICCS bv and IDCS bv are involved with a lot of steel structures
and they observe that the abovementioned issue frequently occurs. Furthermore, it increases
the last couple of years because the quality of a main design decreases strongly.
STARTING POINTS
Inspired by many examples from the daily practice, the issue will be illustrated by discussion
of a standard truss.
Based on drawings of the architect the design engineer designs a steel structure. This
structure consists of a large amount of trusses that span a large space in two directions.
Therefore, both in longitudinal and transverse direction the main structure is modelled by
trusses that lay on a concrete substructure. For the analysis the centre lines of the profiles
are modelled. Members that come together in a node, thus theoretically intersect at one
point. Result is that there is a simple transfer of forces and no secondary forces or moments
27
arise. In a design phase this is a correct and also convenient choice, as worries about the
detailing and fabrication arise in a later stage.
Figure 1a. Centre lines intersect (actual).
Figure 1b. Centre lines intersect (analysis model).
Figure 2a. Eccentricities e = 100 mm (actual). Figure 2b. Eccentricities (analysis model).
ECCENTRICITIES AND FORCE LEAD-IN
If the structure is made of concrete, the abovementioned approach can be followed. Because
of weight reductions, costs, construction time and erect onsite most of the time the trusses
are made of steel.
But the problem arises when the engineer has realised an “optimum” design on the basis of a
minimum of kilograms. For certain if, as in this outlined situation, high forces are involved. A
small eccentricity, by moving the centre lines, leads to a considerable extra bending moment.
NEN 6772, article 11.6.1 mentions that at determining the joint capacities the eccentricities
may be neglected if:
− 0,55 ≤
e
e
≤ 0,25 or − 0,55 ≤
≤ 0,25
d0
h0
e=0
e=negative
e=positive
Figure 3. Definition of eccentricity.
28
When a section is loaded to its full capacity problems arise. The simple detail that the steel
fabricator had in mind, cannot be realised. The centrelines of the profiles thus have to go
through one point, as the profiles do not have the extra capacity to withstand the extra
moments due to eccentricities.
Moreover, problems are not only caused by shifting the gridlines, but the area of force
application also deserves attention. When the diagonals and bottom- and top chord member
have similar profiling, it is very difficult to realise proper force lead-in without stiffeners.
The maximum allowable normal force in a profile is many times higher than the maximum
allowable shear force. Moreover, this is being reduced considerable when it concerns a web
that is sensitive for local buckling. Proper force lead-in without stiffeners is almost impossible
when the maximum allowable normal force in the diagonal is higher than the shear force
capacity of the bottom- and top chord member.
So not only does the bottom- and top chord member need to have an capacity left in order to
withstand the extra moments due to eccentricities, but, to prevent the need of stiffeners, they
also need to have a shear force capacity that is higher than the normal force capacity of the
diagonal.
The engineer often seems not to be aware of this. In the design he does not, or too little, take
this into account. If he chooses profiles with little reserve capacity in the design stage, it
results in fairly complicated, laborious and therefore expensive details.
Figure 4. Concrete.
Figure 5. Steel, complex details.
THE CONNECTIONS MAKE THE COSTS
The last couple of years the awareness that costs are caused largely by the connections has
sunk in. See former publications (1) regarding costs comparisons in the steel industry.
Additional stiffeners must be prevented because these components are labour-intensive.
Preference is given to simple connections with fin plates, angle cleats or endplates. The
recent price increase of the material is the reason that saving on material becomes an
important item. A good insight in total costs is and stays essential.
In order to come to a structure that is acceptable for all parties, there is a number of
solutions. Every party has its own preference for the ideal structure. An engineer does not
want (m)any eccentricities, a Steel fabricator wants the most simple fabrication possible
without a lot of labour and an architect wants an aesthetical justified structure, especially
when the steel structure remains visible. There is a number of methods to decrease the
amount of labour in the construction afterwards. Below you will find a few possible solutions.
Dealt with is the detail in the bottom chord member, but the same is applicable to
connections at the top chord member.
29
Solution 1: Rotating profiles by 90 degrees
If the starting point remains that the centre lines have to go through one point, the profiles
can be rotated 90 degrees. If necessary, the thickness of profiles must be locally adjusted at
the joint because of the various profile dimensions.
In a truss it only concerns tension or compression members. By detailing the joint with two
plates on the flanges and not bothering the centre lines, no extra forces are introduced and
the connection can be realised with sawing and drilling as main labour. During the
processing stage the tolerance on the clearance between bolts and boltholes have to be
taken into account. This can be done by shortening the tension members or by use of
injection bolts. Furthermore the introduction of holes in the bars means a reduction of the
cross section area. If the tension members are used up till their full capacity, the weakening
due to holes lead to a reduction of the capacity, so that the profile will fail.
The thickening of the profiles, as mentioned above in connection with various profile
dimensions, gives as a side-advantage an increase of the tensile force capacity, so that the
profile complies again. Applying this solution mostly only make sense when the truss in the
nodes is directly loaded by purlins or floor beams.
If a floor or roof rests on the top or bottom chord member and this causes moments, it is
possible that the profiles do not meet the requirements anymore in connection with moments
about the weak axis of the profile.
Figure 6. Rotating 90 degrees.
Solution 2: Strengthen/deepen bottom chord member (and top chord member)
When the diagonals are shifted away from the node simple endplate connections are made
possible and the connection no longer overlap. To enable this, the bottom chord member in
the truss must be deeper than is strictly necessary for transfer of the normal- and shear
forces that appear. This solution cuts both ways: because of the overcapacity of the bottom
chord member it is easy to take up eccentricities. The top flange moves upwards so that the
eccentricities of the diagonals become smaller.
ho
e ≤ ho/4
Figure 7. Deeper beam.
30
Moreover, the web of the deeper profile has a higher capacity, so that use of additional
components in order to lead in the forces properly can be prevented. This will be illustrated
by an example.
Suppose: a truss with a span of 20 meter, completely built up from HE200A profiles both for
the bottom- and top chord member and the diagonals.
.
Figure 8a. Analysis model.
e = 100 mm
Figure 8b. Analysis model due to detailing.
If the diagonals are connected to the bottom- and top chord member via endplates, the
eccentricity, that occurs at the connection of the diagonal on the bottom chord member will
have to be somewhat like100 mm. Suppose: a maximum normal force (Npl HE200A) in the
diagonal of 1200 kN. This gives a vertical force of 1000 kN and thus a moment of 100 kNm.
The maximum moment a HE200A can transfer is 101kNm, without keeping into account the
buckling lengths and moments that are already present as a result of the direct load. So the
“extra” moment cannot be withstood by the bottom chord member. In this realistic situation
the maximal normal force is 600 kN and thus the vertical force is 500 kN. As a result of the
eccentricity this leads to an extra moment of 50 kNm on the beam.
When the Head engineer has totally utilized the bottom- and top chord member, this moment
too cannot be withstood. Not any “extra” moment can be absorbed, so that the steel
fabricator is forced to connect the diagonals in the centre lines, which results in a
complicated and above all laborious connection design.
But what is the maximum normal force that can be absorbed without application of stiffeners
in the bottom and top chord member ? According to article 14 of the NEN6770 the bottom
chord member should be checked for:
= ( c + d )t f
1 w y; d
Yield of the web
F
Local buckling of the web
⎧⎪ t f
⎛t ⎞⎛ c
+ 3⎜ w ⎟ ⎜
Fu;2;d = 0.125 t w2 Ef y;d ⎨
⎜ t f ⎟ ⎜ h − 2t f
⎪⎩ t w
⎝ ⎠⎝
⎞⎫⎪
⎟⎬
⎟⎪
⎠⎭
⎧⎪ t f
⎛t ⎞⎛ c
Fu;2;d = 0.5 t w2 Ef y;d ⎨
+ 3⎜ w ⎟ ⎜
⎜ t f ⎟ ⎜ h − 2t f
⎪⎩ t w
⎝ ⎠⎝
⎞⎫⎪
⎟⎬
⎟⎪
⎠⎭
u ;1; d
31
N c ; s ;d
Global buckling of the web
ω y;buc N c;u;d
≤ 1 with
met bef = h 2 + c 2
In which
tf = the thickness of the flange
fy;d = the value of the yield stress
tw = the thickness of the web
h = the depth of the profile
c = the length over which the force is being exercised E = the value of the elasticity
modulus
From this follows a maximum normal force in the diagonal of 337 kN without the need of
stiffeners in the bottom chord member, whilst the maximum allowable normal force for this
diagonal is 860 kN (HE200A with a buckling length of 3.60m). By strengthening the bottom
chord member to HE240B the normal force in the diagonal becomes 700 kN without
application of the necessary stiffeners in the bottom chord member. A side-advantage is the
increase of the moment capacity of the profile. The moment capacity now becomes 247
kNm. The eccentricity that has become even smaller because of the deeper profile, now
does not give any capacity problems anymore. By only using a deeper profile for the bottom
chord member (and top chord member) the connections are much easier to fabricate.
Table 1. Comparison profile capacities.
Npl [kN]
in diagonal with
buckling length of
3.6 m (HE200A)
Vu;d [kN]
in bottom chord
member without
stiffeners
Maximum
allowable N in
diagonal [kN]
Mpl [kNm]
Bottom chord
member
HE200A
860
280
337
101
HE240B
860
582
700
247
Profile bottom
chord member
Solution 3: Supplementary web plates
If the first two solutions are not possible, web plates can also be chosen. The shear force
capacity of the profile will then increase. The truss built up from HE200A-profiles is taken as
an example again.
Increasing the web thickness of the HE200A into 20 mm (original 6.5 mm), the extra moment
as result of eccentricities can be absorbed without problems, as a result of the eccentricity.
With the available analysis tools it is simple to check if the selected profile complies.
Figure 9. Web plates.
The search for alternative detailing afterwards can be avoided totally, if the engineer in
his/her main design takes account of the fact that he tries to design a simple constructible
structure. In other words: a structure that not only is optimum according to his own criteria,
but is also perfect for the steel fabricator as well as the client. Nobody, not even the client, is
waiting for a design that has an optimum weight, but has complicated details that make the
steel structure unnecessarily expensive.
32
For comparison, a calculation has been made of the truss including detailing, whereby as
starting point the connection with members joined in the centre with complex modelling has
been taken.
Table 2. (-- very complex, - complex, + simple, ++ very simple) (2).
Simplicity
Connection
Erection
Material use
Welding/
Production
Total costs
Starting point: join members in
centre, complex details
--
100 %
100 %
100 %
100 %
Solution 1: Rotate 90 degrees
-
99 %
117 %
51 %
87 %
Solution 2: Deeper bottom
member
++
78 %
128 %
63 %
58 %
Solution 3: Web plate(s) on
bottom chord member
+
84 %
97 %
74 %
72 %
The conclusion is that all three outlined solutions show a considerable reduction of the total
costs in comparison to the original detail. Despite an increase of using material, due to
solutions 1 and 2, the connection has become a lot less complex in comparison with the
original connection design.
DESIGN STAGES
By going through the design stage of a construction once again, there will be indicated how
such problems can be prevented.
The client and the architect set up a list of requirements for the building that has to be
constructed. In the light of this list in combination with the building regulations and the
building code a certain material or a combination of materials to execute the design will be
selected. Every material has its own features. Timber and especially concrete are suitable to
withstand compressive forces, whilst steel is preferably suitable to withstand tensile forces.
The choice of material defines the shape of the main structure it is important that the right
material is used on the right spot.
Points for attention must be:
• Is there taken care of the stability of the structure by means of rigid plates, portals or
bracings
• Are high vertical forces transferred, by trusses with compression-, tension or
compression and tension members
• Is there any concentration of forces, as is the case with structures with large spans.
• How are forces lead in into the structure below.
In daily practice it often seems as if during the main design no account is taken at all of the
fact that the members must be joined.
When the engineer has made the first calculation and thus has an idea about the profiles, he
has to think about how the several profiles must be joined. By choosing for example a deeper
(=stronger) profile a lot of (detailing) sorrow can be prevented. An engineer also can insert
the eccentricities in his calculation and base profiling there-upon. But this is not the usual
procedure for calculations of steel constructions; moreover it gives a considerable increase
of the shear forces and moments in the top chord member and bottom chord member. Also
separating the nodes is a rather laborious for the constructor.
33
See below an example of a truss and the moment- and shear force diagrams.
3
2
Figure 10a. Model without eccentricities.
3
2
3
Figure 10b. Moment diagrams
(Centre lines intersect).
3
excentriciteit is 100 mm
2
Figure 10c. Shear force diagrams
(Centre lines intersect).
2
Figure 11a. Summary of truss with eccentric
connections of the diagonals, eccentricity = 100 mm.
3
2
Figure 11b. Moment diagrams
(Eccentricities).
3
2
Figure 11c. Shear force diagrams
(Eccentricities).
These diagrams show clearly that the maximum moments and especially the shear forces
increase considerably by introducing eccentricities.
A design engineer, who thinks before designing about the way the beams and colums have
to be connected, enables the steel fabricator to construct an efficient and constructible
structure with the use of simple connections. This results in benefit for all parties concerned.
CONCLUSION
Nowadays engineers still tend to optimize a structure to a minimum of kilograms, the only
hard criterion that is available for an engineer during the design of the structure. Finally this
criterion leads to structures that are more expensive and have less quality. Working together
in a design and built-team in which the fabricator also has to assist in the design stage can
prevent these problems.
34
This design and built-team is not always possible, that is why a design engineer has to be
aware that his design also has to be constructed. He has to think whether or not simple
connections are possible with the profiling that is being determined with a calculation
program. He has to start a discussion with the client why sometimes there has to be chosen
for a heavier profile with some overcapacity and why the aim to a minimum weight has to be
left. If, moreover, a 3D finite element program is used, considerable material saving can be
achieved, because of the insight in the spatial distribution of forces.
REFERENCES
(1)
(2)
H.G.A. Evers, F. Maatje, ICCS bv, Cost based engineering and production of steel
constructions, Proceedings of the Fourth International Workshop, Connections in
steel structures IV, Behavior, strength and design, published 2002, Actas do II
Entrocontro Nacional de Construção Metálica e Mista 2, published 1999.
F. Maatje, ECCS bv, Voorcalculeren met behulp van de computer (Cost estimation
with the computer), Bouwen met Staal 1989
35
36
CONTINUING EDUCATION IN STRUCTURAL CONNECTIONS
František Wald, Czech Technical University in Prague, Czech Republic
David Moore, Building Research Establishment, United Kingdom
Milan Veljkovic, Luleå University of Technology, Sweden
Martina Eliášová, Czech Technical University in Prague, Czech Republic
ABSTRACT
The European project Continuing Education in Structural Connections
(CeStruCo) under Leonardo da Vinci initiative No. CZ/00/B/F/PP-134049 was
prepared by partners from seven European countries to disseminate the latest
results in research and standardization during the period of transferring the
European Pre-Standard into the European Standard. The project has started
by a collection of questions from the European practice. The answers to those
questions have been prepared in the form of textbooks in the project partners
national languages. The material is available as an easily accessible
Internet/CD (www.fsv.cvut.cz/cestruco) media, and includes video and audio
files, slides and worked examples.
INTRODUCTION
Education has always been seen as an essential part of the introduction and dissemination
of new methods for the design of steel connections. One of the first educational packages
specialised on connections was produced by Owens and Cheal (1) who prepared
educational material for structural connections. This material has been extended and is now
incorporated into a European educational package called the European Steel Design
Educational Programme, ESDEP (2). This programme is used today by educational
establishments throughout Europe. Other educational packages which build on the work of
ESDEP are available some of which include WIVISS (3) and (4), a set of lectures on CD,
SteelCall (5) and (6), a virtual steel designers office, and SSEDTA which consists of a set of
a)
b)
Figure 1. Screens from collection of questions on project Internet page – a) in partners
languages; b) format of collection.
37
basic lectures on PowerPoint for the design of steel and composite elements, see (7). The
project NFATEC - A New and Flexible Approach to Training for Engineers in Construction
(8), is transferring the successful lessons of SSEDTA into the Internet based lectures and
worked examples (9).
For more than twenty year the European Convention for Constructional Steelwork’s
Technical committee for structural connections (ECCS TC10) has supported the
development and implementation of a common set of design rules for steel connections. It is
therefore not surprising to find that one of this committee’s priorities is to facilitate the
transition of EN1993-1-8 from a European pre-standard; see (10), (11) and (12), to a full
Euro-norm (13). Part of this activity is the development of the necessary educational material
to encourage designers throughout Europe to adopt EN1993-1-8. Consequently, a
programme called “Continuing Education in Structural Connections” (CESTRUCO) was
formed under the European Commission’s Leonardo initiative to collect commonly asked
questions on the background, implementation and use of prEN1993-1-8 and to publish
expert answers to these questions. The CESTRUCTO project was developed from an idea
by Mr. Marc Braham (Astron, Luxembourg), Prof. Jan Stark (TU Delft, The Netherlands) and
Mr. Jouko Kouhi (VTT, Finland) to provide designers with more detailed information on the
background and implementation of the design methods given in prEN1993-1-8.
Figure 2. Project textbooks in project partner’s languages.
38
The project partners were Aristotle University of Thessaloniki, Greece; Bouwen met Staal,
Netherlands; Building Research Establishment Ltd., United Kingdom; Czech Constructional
Steelwork Association Ostrava, Czech Republic; Czech Technical University (contractor),
Czech Republic; EXCON a.s., Prague, Czech Republic; KREKON Design office, Rotterdam,
Netherlands; Luleå University of Technology, Sweden; University of Coimbra, Portugal;
Politechnica University of Timisoara, Romania. The project team consist of the following
people: Prof. C. C. Baniotopoulos (in charge of Chapters on Welding and on Aluminium);
Prof. F. S. K. Bijlaard; Ir. R. Blok (internal review), Mr. J. Brekelmans; Prof. L. S. da Silva
(Chapter on Fire design); Prof. D. Dubina (Chapter on Seismic design); Mrs. M. Eliášová;
Mr. H. G. A. Evers (Chapter on Good and bad detailing); Mr. D. Grecea (Chapters on Hollow
section connections and on Cold-formed connections); Ir. A. M. Gresnigt (Chapter on
Moment connections); Dr. V. Janata (internal review); Prof. B. Johansson; Mr. T. Leino;
Mr. T. Lennon; Mr. T. Měřínský (internal review); Dr. D. B. Moore (editor and Chapter on
Simple connections); Mrs. A. Santiago; Mr. R. L. Schipholt; Dr. Z. Sokol (Chapter on
Structural modelling, Windows help Internet lessons); Ir. C. M. Steenhuis; Dr. M. Veljkovic
(Chapter on Bolts); Prof. F. Wald (project promoter, editor and Chapter on Column bases).
The material was reviewed externally by Prof. D. Beg, Mr. M. Braham, Prof. J. P. Jaspart,
Dr. G. Huber, Mr. J. Kouhi, Prof. F. Mazzolani, Mr. A. J. Rathbone, Prof. J. Studnička,
Dr. F. Turcic, Dr. K. Weynand and Mr. N. F. Yeomans.
PROJECT WORKED PACKAGES
Collection of questions
The collection was based on publications in national journals and on local seminars. The
questions were collected by project internet page, Figure 1, and in paper form as well. The
questions located during the conversion of ENV 1993-1-1 (including Annexes J (11), K (12),
L (10)) into EN 1993-1-8 were taken into account. Together 632 questions were collected
related to the topic.
Answering
All obtained questions were very good. Answers to 101 selected questions were chosen in
the second part of work based on its educative contribution. The agreement between all
partners was not reached for all answers. This is the reason that some nice questions are
missing in final material. The review of answers was prepared in tree steps: locally between
partners, by delegated partners and externally by members of ECCS TC10.
Dissemination
Under the third part of the project, dissemination, were prepared the educational materials
Textbooks and Internet/CD lectures. To facilitate easy of use questions/answers are split into
the following Chapters: Introduction, Bolts, Welding, Structural Modelling, Simple
Connections, Moment Resistance, Connections, Column Bases, Seismic Design, Fire
Design, Hollow Section Joints, Cold-Formed Member Joints, Aluminium Connections, and
Design Cases. Each chapter starts with a brief over-view of the method use in prEN1993-18. This is followed by the commonly asked questions together with their answers. The
materials were localised for use in the partner’s national languages, Figure 2: Czech (300
copies of textbook was printed), Dutch (200 copies), English (1500), Greek (200),
Portuguese (1000), Rumanian (300) and Swedish (200). The translations into Polish and
Spanish are under preparation (written in February 2004). The pilot Seminars of the project
were organised in project partner’s countries to test the material in local environment and to
start to disseminate the material.
39
a)
b)
c)
d)
Figure 3. Example from Textbook Chapter 13 Design cases - a), c) bad solutions of beam to
column joint, b), d) good cases.
2,29°
0,04 rad
a)
b)
Figure 4. Example from Textbook Chapter 13 - Design cases a) bad solution of column
base, b) good design.
40
The pilot Internet Seminar was included in the project. It showed the ability to use in an
efficient way the prepared educational material. The pilot Internet seminar was broadcasted
to seven project partners from Luleå University. Very robust software MARRATECH,
Figure 5 was used to establish an interactive communication between partners. The easy to
use and simple to managed tool consists of windows showing the view of camera from each
partner, a white board and a text messenger. The quality of connection was indicated at each
partner window. By clicking on camera window the particular partner’s picture is enlarged to
allow high quality projection. The white board allows all partners to draw by mouse and to
share with other participants in the session available material such as figures, slides, videos
and files (in MS PowerPoint and Word format). The text message window was very reliable
and helped partners to begin communication. The weak point of the Seminar was audio
quality which was strongly influenced by the internet traffic. This is an important issue since it
is essential part of the lecturing. We all have learned how sensitive is the audio quality,
especially in a case of simultaneous broadcasting to various partners. A communication
between two partners, using so called node to node communication is more robust and
easier to establish. However, our laboratories, well equipped by computers and cameras,
have to be upgraded with adequately equipment for video broadcasting. All the partners were
pleasantly surprised with the performance of the communication tool under routine Internet
connection.
a)
b)
Figure 5. Window of MARRATECH software, a) white board with Microsoft PowerPoint
presentation and text connection; b) from preparation of Internet Seminar.
INTERNET / CD LESSONS
The Internet/CD version, Figure 6, of project materials is based on Microsoft Windows help
format, which is a robust tool for education. The material prepared by RoboHelp tool (14)
allows the easy navigation in partner’s languages and in German and French. The
Internet/CD lessons are equipped with worked examples, Figures 3 and 4, PowerPoint
presentations, slides, videos, worked examples (15) and (16), animations of design cases,
educational software for connection modelling, and design tools available round the Europe.
Partners were so kind to equipped us with their demo version to show how easy may be nice
connection checked by EN1993-1-8. 3000 copies of CD first version were printed at the end
of the project in December 2003. The second version was disseminated in June 2004 based
on evaluation of first ones. Third upgraded version is intended to be published based of
interest of structural steel practice in June 2005.
41
a)
b)
c)
d)
Figure 6. Lesson in Microsoft Windows – a) Title page, b) example of Chapter Bolts,
c) example of Chapter Column bases, d) example of Chapter Aluminium connections.
On the CD may be found the NASCon (Non-linear Analysis of Steel Connections) program
that offers a computer user-friendly tool for the component method. The tool allows modelling
the nonlinear behaviour of different components; see (17) Figure 7. The video film, see
Figure 8, demonstrates the correct design of T-stub connections and bolted splices to avoid
a fatigue failure of bolts. The related to the fire design is equipped with the PowerPoint
lessons including video/audio sequences, see Figure 9.
a)
b)
a) menu of program
b) component behaviour
Figure 7. Program nonlinear analysis of steel connections NASCon (17).
42
b)
a)
Figure 8. The flow of the stresses in the connection in video film Statically Stressed Bolts
in Dynamically Loaded Connections.
a)
b)
Figure 9. a) Front page of PowerPoint lesson ”Connection Design for Fire Safety”,
b) a slide from the lesson “Heating and Cooling of Structure”.
ACKNOWLEDGEMENT
The authors wish to dedicate this work to Mr. Martin Steenhuis, our good friend, who worked
with us in the field of structural connections for many years, launched this project, and who
tragically died in the summer of 2001.
REFERENCES
(1)
(2)
(3)
(4)
Owens G. W., Cheal B. D.: Structural Steelwork Connections, Butterworths, London
1988, ISBN 0-408-01214-5.
ESDEP, European Steel Educational Programme, SCI, London, 1994, www.esdep.org.
Plank R.J.: Wider Vocational Initiative for Structural Steelwork, J. Construct. Steel
Research, 46, (1998), pp 278-279, ISBN 0-08-042997-1.
Chladná M. - Wald F. - Burgess I. W. - Plank R. J.: Contribution of the Structural
Steelwork Educational Programme WIVISS, v Proceedings of the Conference
Eurosteel ´99, Studnička J., Wald F., Macháček J. ed., Vol. 2, Prague,
26 - 29 May 1999, ČVUT Praha, 1999, s. 137 - 140, ISBN 80-01-01963-2.
43
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
44
Roszykiewicz C.,: Breakthrough in Electronic Education for Steel Construction, SCI,
London, 1997.
SteelCal, Electronic Education for Steel Construction, steelcal.steel-sci.org.
SSEDTA, Structural Steelwork Eurocodes: Development of Trans-national Approach,
fp.emberey.plus.com.
NFATEC, A New and Flexible Approach to Training for Engineers in Construction,
http://www.svf.stuba.sk/kat/KDK/NFATEC_E.htm
Muzeau J. P. - Bourrier P., Education for Constructional Steel design: APK - the French
Example, J. Construct. Steel Research, 46, (1998), pp 259-271, ISBN 0-08-042997-1
ENV 1993-1-1: Design of Steel Structures, Eurocode 3, European Pre-Standard, CEN,
Brussels 1992.
ENV 1993-1-1-A2: Design of Steel Structures, Annex J, Joint Design, European PreStandard, CEN, Brussels 1998.
ENV 1993-1-1/A1: Design of Steel Structures, Annex K, Joints in hollow section
structures, European Pre-Standard, CEN, Brussels 1994.
prEN 1993-1-8. Eurocode 3: Design of Steel Structures, Part 1.8: Design of Joints,
European Standard, CEN, Brussels 2003.
RoboHelp office, http://www.ehelp.com.
Jaspart J.P., Renkin S., Guillaume M.L.: European Recommendations for the Design of
Simple Joints in Steel Structures, 1st draft of a forthcoming publication of the Technical
Committee 10 “Joints and Connections” of the European Convention of Constructional
Steelwork (ECCS TC10) prepared at the University of Liège, September 2003.
Wald F. at al: Steel structures 10, Worked examples to Eurocode 3, Czech Technical
University in Prague, Prague 2001, p. 146, ISBN 80-01-02308-7.
Costa Borges L. A.: Probabilistic Evaluation of the Rotation Capacity of Steel Joints
Dissertação apresentada à Faculdade de Ciências e Tecnologia para obtenção do grau
de Mestre em Engenharia Civil, especialidade de Estruturas, Coimbra, 2003.
DOCKING SOLUTION BETWEEN A STEEL TRUSS AND A
CONCRETE TOWER AT THE SKI JUMP IN INNSBRUCK
C. Aste, aste konstruktion, Innsbruck, Austria
A. Glatzl, aste konstruktion, Innsbruck, Austria
G. Huber, aste konstruktion, Innsbruck, Austria
ABSTRACT
The crucial challenge in MBT (Mixed Building Technology) are the connection
elements between the different construction systems. A typical example of an
MBT realisation is the ski jump tower in Innsbruck where a steel cage of hollow
section trusses is cantilevering up to 12,5 m from the central concrete tower in
a height of about 35 m above ground. The transfer of the localised truss forces
into the concrete box section was solved by special pre-stressed docking
devices.
INTRODUCTION
The ski jump in Innsbruck known for the famous annual New Year ”Four-ski-jump-tour“ was
renewed. The original jumping tower (built for the 1976 Olympic winter games) was pulled
down and a new landmark similar to a lighthouse was erected. Zaha Hadid (London) won the
international architectural competition for this significant building. The constructional
realisation was ordered from aste konstruktion and was honoured with the “Austrian State
Award for Consulting 2002”. A speciality of this MBT are the high tension docking devices
between the cantilevering steel cage and the concrete tower.
Figure 1. Panoramic view of “Bergisel” with the new jumping tower.
PROJECT OVERVIEW
“Bergisel” - a glacier hill located to the south of Innsbruck (Figure 1) – has a significant history:
Offering place of the Celts, path marking for the roman-german emperors moving to Rome,
battle field of the Tyrolean war of liberation, centre of the Olympic Winter Games in 1964 and
1976 with the two flame basins and – already since more than 50 years - scene of the
international Four-ski-jump-tour at New Year. In the years 2001 and 2002 these facilities were
fully renewed and extended by new buildings (Figure 2, 3):
45
•
•
•
•
•
•
•
•
•
Concrete tower and cantilevering tower top: described in detail in the following paper
sections.
Approach ramp bridge: sagging fish-bellied steel truss girder with suspension over a
direct span of 69 m, bend with a radius of 100 m, inclination of 35°, overall length
including the take-off building 98 m, approach lane of trapezoidal composite slabs,
erection with a temporary pier within four weeks.
Take-off building and ski-jump platform: concrete abutment looking like the knee of a
ski jumper, length 24 m, fix support of the approach ramp bridge.
Front building: three-storey concrete building with bent roof below the jump platform –
flown-over by the jumpers, technical equipment, power supply, common rooms.
Landing hill: concrete fixing and border bead or retaining wall, transverse ribs, holding
devices for the snow nets and the plastic mats for summer jumping, mat sprinklers.
Reporter cabin tower: four storeys for 31 cabins, steel tube frame.
Coach platform: grate platform close to the take-off building, steel tube frame.
Funicular railway: automatic cabin inclination corresponding to the slope.
Judge tower: redevelopment of the old timber construction.
Figure 2. Project overview.
Office / Company
City / Country
Function
Competence
Bergisel Management Assoc.
Hadid
aste konstruktion
Pichler
IMO-Bau
Vorspann-Technik
Innsbruck / A
London / UK
Innsbruck / A
Bozen / I
Leipzig / D
Oberndorf / A
architect
design office
steel construction
sub-steel constr.
bridge equipment
client
ski jump incl. tower
design calculations and detailing
approach ramp and tower top
erection of ramp and tower top
pre-stressing, ramp suspension
Figure 3. Construction board (tower).
46
CONCRETE TOWER
With 49 m above ground the ridge height of the concrete tower reaches 791 m above sea
level (Figure 4). The foundation was solved with a plate of 20 x 20 x 1,0 m at a level of –11 m
below ground with three basement storeys. The standard cross section of 7 x 7 m and a wall
thickness of 40 cm rises up for about 40 m above the foundation, stabilised with wall
diaphragms to the base plate limits. It contains the two elevators, the stairway and the supply
pit. From 29 m above ground the cross section tapers to 3,7 x 7 m making place for the
jumping access stairway.
Also at this level of cross section change the support girder for the ramp bridge cantilevers
4,5 m with a height of only 1,45 m. This slenderness was necessary to hide this girder in
between the steel truss flanges of the bridge.
The demand of fair-faced concrete in combination with the difficult access and supply
conditions resulted in the choice of a climbing formwork. Concreting started in June 2001.
Figure 4. Concrete tower.
47
STEEL-COMPOSITE TOWER TOP
The tower top is not ordinary - neither in architectural nor in constructional respect. A threelevel steel cap with a rescue level, a restaurant and an observation platform is docked to the
central concrete tower (Figure 5). Being 250 m above the city centre one has a fantastic view
on Innsbruck and the surrounding mountains.
The levels are cantilevering around the concrete core up to 12,5 m. Together with the steel
hollow section frames and the diagonal suspension tubes anchoring back to the concrete
core a steel cage is built (Figure 6). The horizontal stiffening to the core is realised by the
trapezoidal composite slabs. The transparency and elegance of the facade is supported by
the fact that diagonal bars within the front could be avoided and huge glass elements were
placed into the facade.
Figure 5. Tower top – an architectural challenge.
Figure 6. Tower top – sketch of the steelwork construction.
48
DOCKING DEVICES
The crucial challenge in MBT construction are the connection elements between the different
construction systems. Thanks to the common, material-independent design and safety
concept of the constructional Eurocodes the interface problems at the level of design
methods and internal forces lost its deterrent effect and MBT solutions become more and
more usual in daily design practice. The effect is a more economical use of different
materials related to their constructional benefits (strength, stiffness, weight, prefabrication,
strengthening, dismanteling,...) and more innovative architectural solutions.
For the actual case of the Bergisel Ski Jump the considerable docking forces between the
steel cap and the concrete core had been a crucial challenge which was solved by special
pre-stressed steel brackets (Figure 7). These elements of at maximum 550 kg weight were
integrated into the formwork with a tolerance of less than 1 cm.
tension
compression
prestress
Figure 7. Pre-stressed docking devices.
Figure 8. Characteristic docking forces.
The load transfer into the concrete walls was handled with mutual pre-stressing cables
(interior tendons) from one docking point to the opposite one going through the tower.
Additional concentrated rebars in the local load introduction zones were provided to cover
the bursting forces and for crack distribution. The characteristic docking forces can be taken
from Figure 8.
49
Pre-stressing was applied from the opposite side of the fixed anchor after hardening of the
concrete and before connecting the steel sections. Depending on the tension forces either
one or two strands were provided. The conduits were then filled with injection grout against
corrosion.
The resulting necessary welding length led to the geometry of these docking brackets. By the
use of four longitudinal ribs which were welded on site to the slotted push-over hollow
sections the total bracket length could be minimised. The eventual negative influence of the
high welding temperatures on the end anchorage of the pre-stressing strands could be
dispelled by a test specimen. The maximum heat increase was measured to be only 50
degrees.
Attention has to be paid to the fact that the tendon head is no more accessible after
positioning of the steel cage. Therefore this application type is limited to quasi-static loading.
Figure 9. Slotted hollow sections welded to the docking brackets.
Figure 10. Cantilevering steel cage during construction.
CONCLUSIONS
The new building at Bergisel proved to be an excellent combination of architectural shape
and constructional design. Fair-faced concrete, steel and glass together with the harmonious
longitudinal section and the top view are showing the worldwide appreciated style of Zaha
Hadid. Construction and erection were based on modern steel-concrete mixed building
technology: concrete core with climbing formwork, pre-stressed steel docking brackets for
the steel frame cage on the tower top, a pre-stressed very slender concrete cantilever as
upper support of the approach ramp, three-level widely cantilevering steel frame cage on top,
approach ramp in the form of an organic fish-bellied and suspended trough bridge – all in all
“Toccata and Fugue in major F” for a civil engineer and his orchestra.
50
Figure 11. Illuminated structure at night
REFERENCES
(1)
(2)
(3)
(4)
(5)
Aste, C., Glatzl, A., Huber, G. (2002). Ski jump „Bergisel“ – A new landmark of
Innsbruck. 3rd Eurosteel Conference, ISBN 972-98376-3-5, Lisbon.
Aste, C., Glatzl, A., Huber, G. (2002). Schisprungschanze „Bergisel“ – Ein neues
Wahrzeichen von Innsbruck. Stahlbau Heft 3/02, S.171-177, ISSN 0038-9145,
Ernst&Sohn, Berlin.
Aste, C., Glatzl, A., Huber, G. (2003). Steel-concrete mixed building technology at the
ski jump tower of Innsbruck, Austria. International Journal on Steel and Composite
Structures, ISSN 1229-9367, Technopress, Korea.
Aste, C., Glatzl, A., Huber, G. (2003). Innsbruck ski jump: a triumph of mixed building
technology. Concrete Journal, The Concrete Society, Berkshire.
Aste, C., Glatzl, A., Huber, G. (2003). Schisprungschanze „Bergisel“ – Ein neues
Wahrzeichen von Innsbruck. Zement + Beton, www.zement.at, Wien.
51
52

CONNECTION DESIGN IN THE 2005 AISC SPECIFICATION

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