Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 11
11
urban areas of Japan, would be classified as fracture critical in members in the alternate load path did not have sufficient
the United States, but has provided excellent performance. capacity to carry the redistributed loads. It is also true, but
less obvious, that there are determinate structures that can be
Other interesting findings from the scanning tours were shown to meet the definition of redundant by developing new
that the inspection frequency is risk-based in Europe and that alternative load paths--and even a few examples (discussed
the inspectors' qualifications are commensurate with the later) of determinate structures that have demonstrated that
complexity of the bridge. they meet the definition of redundant by surviving a signifi-
cant fracture in service.
REDUNDANCY AND COLLAPSE
OF STEEL BRIDGES As defined in the introduction, FCMs are nonredundant;
however, nonredundant is a broader term because it also
Definition of Redundancy and Contrast includes
to Indeterminacy and FCMs
· Substructures;
The AASHTO LRFD Bridge Design Specifications define
· Members that may be inherently not susceptible to frac-
redundancy as "the quality of a bridge that enables it to per-
ture, such as compression members, but still could lead
form its design function in the damaged state." In NCHRP
to collapse if damaged by overloading, earthquakes, fire,
Report 406 (34), Ghosn and Moses defined superstructure
redundancy as "the capability of a bridge superstructure to terrorism, ship or vehicle collisions; and
continue to carry loads after the damage or the failure of · Members made of materials other than steel.
one of its members," and this definition is also used in the
Substructures such as piers are often nonredundant and
AASHTO Manual for Condition Evaluation and Load and
therefore earthquakes, scour, vehicle collisions (Figure 7),
Resistance Factor Rating (LRFR) of Highway Bridges (3).
Even though it has to do with potential performance in the and ship collisions (Figure 8) have led to most of the major
event of damage, redundancy is a quality of the undamaged collapses of both steel and concrete bridges. For example, an
structure. article published in 2002 just after the collapse of the Inter-
state 40 bridge over the Arkansas River in Oklahoma, listed
Note that these definitions are not clear about what load seven major bridge disasters in the United States up to that
type, magnitude, distribution on the bridge, dynamic ampli- time (35). The two FCBs discussed previously, the Point
fication, and load factors are supposed to be resisted by the Pleasant Bridge and the Mianus River Bridge, were 28% of
damaged structure. Ghosn and Moses attempted to set require- the list. The remaining 72% were the result of substructure
ments for the residual capacity of the damaged superstruc- failure.
ture (34).
· The Arkansas River Bridge, Sunshine Skyway (Florida)
The definitions of redundancy are also not clear regarding (1980), and the Queen Isabella Causeway (2001) bridge
the type and extent of damage. For example, in a bolted or collapses were caused by ship collisions.
riveted built-up member it is likely that a fracture would be · The Schoharie Creek Bridge in New York (1987) and
limited to only one tension element, because it cannot prop- Arroyo Pasajero Bridges in California (1995) collapses
agate directly into neighboring elements. However, a ship were caused by scour.
collision could destroy the entire member.
Ultimately, it is the target level of reliability that designers
and engineers who rate bridges should strive to achieve and
the focus should not exclusively be on redundancy. Redun-
dancy has a major impact on the risk of collapse and this
impact is accounted for appropriately for all types of struc-
tures in both the LRFD Specifications and the LRFR Manual,
as discussed here. Using the LRFD and LRFR procedures, it
is possible to achieve the target level of reliability without
redundancy in a bridge that is more conservatively designed.
Structural redundancy and structural indeterminacy are
often confused and used interchangeably, although they are
really two separate issues. Structural indeterminacy simply
refers to whether or not the forces in a structure can be deter-
mined with statics. A structure that is indeterminate, although FIGURE 7 Example of vehiclebridge collision causing
possibly providing alternate load paths, would not meet the collapse owing to nonredundant substructure. (Courtesy:
definition of redundant if it were to collapse, because the Robert Sweeney.)
OCR for page 12
12
FIGURE 8 Collapse of Queen Isabella Causeway Bridge in Texas in 2001 when pier
was struck by a barge.
In addition to prevention of collapse in the event of frac- in these cases. This is an important point because in these
ture, redundancy of the superstructure is important for sev- cases it reflects on the maximum live load the damaged struc-
eral other reasons. The first is the need to more easily redeck ture is likely to experience in the brief period before closure.
the bridge. Also, as discussed earlier, events other than frac- Periodic inspection may be more helpful in finding fatigue
ture can also damage and completely destroy members of the cracks and fractures because they are often not immediately
superstructure. For example, the fascia girder of the I-610 obvious.) These are compelling reasons for redundancy.
Bridge over the Houston Ship Channel was struck twice by
ships, once in December 2000 and once in May 2001. The These reasons for redundancy (other than fracture) could
highly redundant multigirder bridge withstood each collision, be used to encourage redundancy outright instead of indi-
although both times the bridges had to be closed for repairs. rectly by penalizing FCMs. For example, in the LRFD Spec-
These are compelling reasons to have redundancy. (Note that ifications, redundancy is encouraged in Sections 1.3.2 and
periodic inspection is not really helpful in finding this type of 1.3.4. Load factors are modified based on the level of redun-
damage from collisions or other extreme events because the dancy, and it is stated that multiple-load-path and continuous
damage is usually immediately obvious to the public. A deter- structures should be used unless there are compelling reasons
mination to close and repair the bridge can be made quickly to do otherwise.
OCR for page 13
13
In the LRFR Manual, redundancy is reflected in system nal bolted splice (Figure 11); the bracing system, later-
factors that reduce the capacity of each member in non- als and cross frames within a box member (Figure 12);
redundant systems. The system factors are calibrated so that bolted continuous plates or shapes to give a member
nonredundant systems are rated more conservatively at redundancy (Figures 1315), and single-cell concrete
approximately the same level of reliability associated with boxes with multiple post-tensioning strands. Note that it
new bridges designed using LRFD Specifications, called the must be shown that the damaged member (several pos-
"inventory" level in former rating procedures. Redundant sible cases considered separately with one element frac-
systems are rated at a reduced reliability level corresponding tured or removed) can survive the prescribed loads to be
approximately to the traditional "operating" level. The sys- internally redundant.
tem factor for the most nonredundant bridge types is 0.85. · Structural redundancy is external static indeterminacy
This means that a nonredundant bridge designed for 1.17 (the and can occur in a two or more span continuous girder
inverse of 0.85) times the design load has approximately or truss. Note that only part of an end span between the
equal reliability to a redundant bridge designed for 1.0 times fracture and the pier may be supported by structural
the design load. redundancy and that the part of the end span at the abut-
ment could theoretically collapse. However, internal
According to Ghosn and Moses (34), a redundant super- redundancy of the deck on a composite girder could be
structure has at least one alternate load path and is capable of sufficient to maintain stability of the end span, espe-
safely supporting the specified dead loads and live loads and cially when combined with the structural redundancy,
maintaining temporary serviceability of the deck following as in the Hoan Bridge shown in Figure 9.
failure of a main load-carrying member. They recognized that · Load-path redundancy is internal static indeterminacy
redundancy is related to system behavior rather than individ- arising from having three or more girders or redundant
ual component behavior. The specifications generally ignore truss members. One can argue that the transverse mem-
the interaction between members and structural components bers such as diaphragms between girders can also pro-
(i.e., system behavior) in a bridge, however. vide load-path redundancy (see Figure 12).
Redundancy is often discussed in terms of three types (28, Note that the LRFR Manual (3) and the Bridge Inspector's
29,34): Reference Manual (29) state that "in the interest of conser-
vatism" internal and structural redundancy should be neglected,
· Internal redundancy, also called member redundancy, meaning that load-path redundancy is the only redundancy
exists when a member is comprised of multiple elements that matters. As shown by in-service behavior of fractured
and a fracture that formed in one element cannot propa- FCBs discussed in the next section, neglecting all but load-
gate directly into the adjacent elements. Examples include path redundancy is clearly oversimplifying and possibly
girders with composite deck (the deck remains intact in overconservative.
the event of a girder fracture as in Figure 9); riveted or
bolted built-up girders, tie girders, or tension members Examples of Behavior of FCBs That Experienced
of a truss (Figure 10); split box sections with longitudi- Major Fractures
Two examples of FCB collapses, the Point Pleasant Bridge
(constructed in 1928, Figure 1) and the Mianus River Bridge
(constructed in 1957, Figure 4), have been discussed. These
are the only two examples of collapses of major steel bridges
as a result of fracture in the superstructure. As explained pre-
viously, there were circumstances other than just fatigue and
fracture that were the root cause in both of these failures. On
the other hand, there are numerous examples of bridges with
members that would traditionally have been classified as
FCMs that have fractured, but the bridge did not even par-
tially collapse.
Two-girder FCBs that have experienced either partial or
full-depth fractures but did not collapse include:
· The 1976 full-depth fracture of the US-52 bridge
over the Mississippi River in St. Paul, Minnesota
FIGURE 9 Example of bridge deck acting as catenary with
hinge at fracture location in end span of the approach spans of (called the Lafayette St. Bridge) (see Figure 16) (11,36).
the Hoan Bridge in Wisconsin--two of the three girders had full- (It should be noted that during the course of this syn-
depth fractures in December 2000. thesis, it was mentioned that the bridge remained stable
OCR for page 14
14
(a)
CL SPLICE
5'-3"
3'-0"
6 1/4"
3"
FLANGE SPLICE
CL SPLICE
6 1/4"
6'-8"
PL 1 1/8 PL 1 1/8
3"
PL 1 3/4 2'-9" WEB SPLICE
PL 1 x 7 7/8 (TYP)
(b)
FIGURE 10 Examples of internally redundant members: (a) riveted built-up girder and (b) bolted built-up tie girder proposed
for Blennerhassett Arch Bridge. (Courtesy: Michael Baker Jr., Inc.)
because it leaned on an adjacent bridge). However, · The 1977 full-depth fracture of the I-79 bridge at Neville
interviews with Donald Fleming, former Bridge Engi- Island in Pittsburgh, Pennsylvania (Figure 17) (11,15).
neer of the Minnesota Department of Transportation · The May 2003 fracture of the US-422 Bridge near
(DOT) and John W. Fisher, both of whom were Pottstown, Pennsylvania. The entire bottom flange and
directly involved with the failure investigation, con- approximately 9 in. (230 mm) of the web fractured (37).
firmed that this was not the case. The bridge did sag
6.5 in. (165 mm), but was not supported by the adjacent It is apparent that other elements of these two-girder
bridge. bridges, particularly the deck, along with the floorbeams, cross-
OCR for page 15
15
FIGURE 11 Splitting a box section with a bolted longitudinal splice to give it internal redundancy. (Courtesy: HNTB.)
frames, and stringers, are sometimes able to carry the loads and discussed previously has implications for the loading to
prevent collapse. These alternate load paths were so robust in evaluate the damaged member (residual capacity). A lower
the I-79 and US-422 fractures that there was little or no per- level of residual capacity would be required for members
ceptible deformation of the structure. For example, when a damaged by these other more obvious causes because the
tugboat pilot discovered the I-79 fracture, the bridge was still bridge is likely to be closed within hours after the event.
providing a serviceable roadway. In the case of the Lafayette However, if a fracture goes unnoticed for an extended period,
St. Bridge, displacements of 2.5 in. (63 mm) were noticed the probability of larger permits or illegal loads increases
relative to the adjacent bridge 48 days before the fracture was significantly.
discovered, growing to 6.5 in. (230 mm) as the crack length
increased over that time. As explained in chapter three, some agencies even classify
three-girder bridges as FCBs. The Hoan Bridge fracture, shown
The less obvious nature of the damage in the case of a in Figure 9, is an example of a three-girder bridge end span
fracture as opposed to the other causes such as collisions (which is viewed as most critical owing to inadequate con-
Truss action between
slab and diaphragm
FIGURE 12 Schematic of twin composite tub girder superstructure showing
internal redundancy provided by bracing system and possible alternative load
path provided by slab and diaphragm. (Courtesy: HNTB.)
OCR for page 16
16
tinuity at the joint), with two out of three girders and the web
of the third girder fractured (38).
These fractures in actual bridges are the most valuable
data available to judge the necessity of special provisions for
FCMs. These full-scale tests are much more valuable than
laboratory tests or numerical simulations, because the for-
mer are subject to idealizations and assumptions. Although
not sufficient to prove that two-girder bridges should not be
classified as having FCMs, these incidents do show that
under some circumstances they do not meet the definition of
an FCM.
The survey (see chapter three) revealed several other exam-
ples of FCBs that had experienced major fractures but had
not collapsed. These were usually noticed in an inspection,
but had occurred at an earlier, unknown time. Similar accounts
can be found elsewhere (31,39).
Although not caused by a fracture, a train derailment on a
Redundancy
nonredundant truss bridge, shown in Figure 18, is another
Lower plate
chord example of valuable in-service behavior of a full-scale bridge.
Note that several diagonals, hangers, and upper chord braces
are completely severed, but the truss did not collapse even
FIGURE 13 Redundancy plate bolted to lower chord of SR-33 though a significant portion of the live load remained on the
bridge near Easton, Pennsylvania. (Courtesy: HNTB.) bridge.
FIGURE 14 Tee section bolted to continuous lower flange of box section to provide redundancy. (Courtesy: HNTB.)
OCR for page 17
17
FIGURE 15 Retrofit redundancy plate bolted to web of existing two-girder superstructure
in Poplar Street Bridge complex in East St. Louis. (Courtesy: Wiss, Janney, Elstner
Associates.)
Other interesting field tests have been performed on only deflected 1.2 in. (28 mm). There was no sign of yield-
I-40 bridges over the Rio Grande in Albuquerque, New Mex- ing and no significant change in strains experienced by the
ico (40). The two-girder bridges, which had spans ranging other instrumented members until the bottom flange was
from 131 to 163 ft and were classified as nonredundant completely severed. This suggests that load redistribution did
fracture-critical, were built in 1963. The girders were 10 ft not occur until the bottom flange was completely severed.
deep and spaced at 30 ft on center. A torch cut was used to sim- They also reported that most of the load was redistributed
ulate a fracture of four different lengths to one of the girders in through the damaged girder and stringer deck system to the
the bridge, the last of which was nearly full depth. Idriss et al. interior supports. In general, the load was redistributed from
studied the redistribution of loads, the loading the bridge can the damaged girder to the diagonal bracing, diaphragms,
withstand in the damaged condition, and the potential for col- stringers, deck, floorbeams, and remaining girder.
lapse. The bridges were loaded with a truck that was 95% of
New Mexico legal load and roughly equivalent to HS-18.35. Reliability Studies of Redundancy
Idriss et al. (40) also reported that under dead and live loads A brief summary of selected research studies focusing on
and when the truck was located above the crack, the flange redundancy is presented here. More complete summaries of
OCR for page 18
18
FIGURE 18 Example of train derailment on a fracture-critical
truss bridge that severed several members but did not collapse.
(Courtesy: Robert Sweeney.)
the individual articles and additional articles can be found in
the annotated bibliography in Appendix D.
A large number of studies have attempted to characterize
the reliability of bridge designs with varying redundancy. In
these reliability studies, the degree of redundancy of a system
was examined by reviewing the difference between relia-
FIGURE 16 View of cracked girder in two-girder span of
bility indices. Ghosn and Moses (34) studied redundancy
Lafayette Street Bridge in St. Paul, Minnesota, as an example in highway bridge superstructures by examining the differ-
of a bridge that is sufficiently redundant to avoid collapse ence between the safety indices they defined and those of
despite a fracture of the tension flange and the web of bridges that have been known to perform as desired. Kritzler
one girder. and Mohammadi (41) used the same approach in which they
compared the safety reliability index of a redundant struc-
ture considering all failure paths and the safety index of the
exact same structure with no alternative load path. A reliabil-
ity approach was also used by Moses (42) for the evaluation
of bridge safety and remaining life.
Frangopol and Curley (43) recognized the need for the
development of a better understanding and definition of
redundancy in various types of bridges. They defined the
term R as the redundant factor for a bridge, which is the
reserve strength between component(s) damage and sys-
tem collapse. The redundancy factor was later used in other
studies [e.g., Frangopol and Curley (44), Frangopol and
Nakib (45), Frangopol and Yoshida (46)] to investigate
redundancy of systems.
Ghosn and Moses (34) included both a reliability approach
and a direct system factor approach to evaluate the degree
of redundancy of an existing bridge or when designing a new
bridge. In the reliability approach, relative reliability was
FIGURE 17 View of cracked girder in two-girder span of calculated and a level of redundancy is satisfied if obtained
I-79 Bridge at Neville Island in Pittsburgh as an example of
a two-girder bridge that is sufficiently redundant to avoid
values of the relative reliabilities are greater than or equal to
collapse despite a fracture of the tension flange and the web specified values. In the direct system redundancy approach,
of one girder. adequate load factor ratios (system reserve ratios) are required
OCR for page 19
19
to satisfy a minimum level of redundancy. A bridge is then three-girder system. However, if bracings are considered, the
considered adequate if system reserve ratios are greater than deformation increases by 10% for the two-girder system,
or equal to specified values. whereas almost no increase in the deformation is noticed in
the three-girder system. Heins and Kato (48) also studied the
A drawback of the reliability approach is that it requires effect of bracing on load distribution in a two-girder bridge
measures of statistical variation that are often not available. In system when one of the girders is damaged and found that the
these examples, estimates are made and the results are still deformation of the cracked girder was substantially reduced
insightful, but a great deal of additional data would be required when bracing was used.
to use this approach as a practical tool.
Ghosn and Moses (34) developed recommendations for
It is important to note that it is the reliability of the system the residual capacity of fractured bridges to demonstrate
that is important. As discussed previously, redundancy affects sufficient redundancy. Load factors LF1 and LFd should be
this reliability but not as much as might be assumed. A two- calculated using a three-dimensional finite-element analy-
girder bridge designed for HS-25 for example might have sis. LF1 is the multiple of side-by-side HS-20 trucks that the
greater reliability than a multigirder bridge designed for structure can carry in addition to unfactored dead loads
HS-20 (34). Therefore, one should not place too much empha- (using elastic analysis) before the first member reaches the
sis on redundancy and lose sight of the important goal, sys- resistance predicted by the design specifications. LF1 is typ-
tem reliability. ically on the order of 3.8, depending on the ratio of live load
to dead load
Numerical Simulations of the Residual Capacity LFd is the residual capacity of the damaged structure and
of Fractured Bridges is calculated by performing a nonlinear analysis of the dam-
aged structure (with the FCM removed) under the effect of
Finite-element analysis is increasingly being used to simu-
the unfactored dead load and incrementing the multiple of
late the after-fracture behavior and residual capacity of FCBs.
side-by-side HS-20 truck loads until the system collapses.
These analyses provided insight about the secondary load
Redundancy is considered adequate if the ratio of LFd to LF1
paths in FCB systems after an FCM is severed or otherwise
is greater than 0.5. This means that the damaged structure
removed from the model. In some cases they are used to
should be able to support approximately 1.9 times the side-
get a waiver from FHWA on FCM design requirements for
by-side HS-20 loading. (Figure 19 shows a schematic of the
a new bridge. However, this type of analysis and associated
loading of a damaged girder in terms of multiples of side-by-
waiver of the FCM provisions is presently being done on a
side HS-20 trucks.)
case-by-case basis, and the analysis requirements, loads, and
failure criteria are not always clear. In other cases, they are
Note that this requires a greater residual LFd if the bridge
used to evaluate the residual capacity of existing FCBs.
is originally over-designed, which does not seem logical.
NCHRP Report 406 indicated that bridges that do not meet
Section 6.6.2 of the AASHTO LRFD Bridge Design Spec-
the required load factor ratios could still provide a high level
ifications discusses the fracture limit state. The commentary
of system safety (34).
of this section states that:
The criteria for refined analysis used to demonstrate that part
of a structure is not fracture critical, has not yet been codified.
Therefore, the loading cases to be studied, location of potential
cracks, degree to which the dynamic effects associated with a
fracture are included in the analysis, and fineness of the models
and choice of element type should all be agreed upon by the owner
and the engineer. The ability of a particular software product to
adequately capture the complexity of the problem should also
be considered and the choice of software should be mutually
agreed upon by the owner and the engineer. Relief from full fac-
tored loads associated with the Strength I Load Combinations
of Table 3.4.1-1 should be considered as should the number of
loaded design lanes versus the number of striped traffic lanes (1).
Heins and Hou (47) used an analytical two-girder and
three-girder space frame model to study the effect of bracing
members in bridge structures on the load distribution of two-
girder and multigirder systems after the development of a
crack in one of the girders. Heins and Hou found that when
one crack develops and no bracing is used, the deformation FIGURE 19 Schematic of multiple HS-20 loads on damaged
increases by 40% for the two-girder system and 10% for the superstructure. (Courtesy: HNTB.)
