ECONOMIC AND DESIGN IMPACTS OF CROSS-FRAME … · ... and bridge design since ... steel I-girder...
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ECONOMIC AND
DESIGN IMPACTS
OF CROSS-FRAME
LAYOUT OPTIONS
FOR STEEL I-
GIRDER BRIDGES
WITH SEVERE
SKEWS
DUSTEN OLDS, P.E.
NORMAN L. (NORM)
MCDONALD, P.E.
AHMAD ABU-HAWASH, P.E.
TODD HORTON, P.E.
BIOGRAPHY
Dusten Olds is a Professional
Associate and Bridge Engineer
with HDR Engineering in
Omaha, NE. His background
includes experience in complex
design and modeling as well as
load rating of multiple structure
types. Mr. Olds received his BS
and Masters of Engineering
from Washington University in
St. Louis along with an MBA
from University of Nebraska at
Omaha.
Norman L. (Norm) McDonald is
the State Bridge Engineer for
the Iowa Department of
Transportation. He has worked
for the DOT for 30 years with
the last 15 years as State Bridge
Engineer. Mr. McDonald is a
member of the AASHTO
Subcommittee on Bridges and
Structures and serves as
Chairman of the Technical
Committee for Structural Steel
Design (T-14), Vice-Chair of
the Technical Committee for
Structural Supports for Signs,
Luminaires and Traffic Signals
(T-12), and is a Region III
member on the Technical
Committee for Bridge
Preservation (T-9).
Ahmad Abu-Hawash is the
Chief Structural Engineer with
the Iowa Department of
Transportation and has been
working with the DOT in
highway construction, bridge
rating, and bridge design since
1983. He is responsible for
overseeing the design of major
bridge projects, design policy
review, coordination of bridge
research, and the resolution of
structural fabrication issues.
Ahmad received his BS degree
from the University of Iowa and
his MS degree in Structural
Engineering from Iowa State
University.
Todd Horton is a vice president
and a senior project manager for
HDR Engineering in Omaha,
NE. His background includes
extensive experience in the
design and analysis of tangent
and horizontally-curved steel
plate girder and box girder
bridges using conventional and
finite element methods. Mr.
Horton received his BS and his
MS degrees in Civil
Engineering from the University
of Nebraska.
SUMMARY
Two multi-span severely
skewed steel bridges with
alternate cross-frame layouts
were designed to assess the
economics of a staggered cross-
frame layout versus a
contiguous layout.
For each bridge, the cross-
frames and girders were
designed utilizing consistent
design parameters to assure a
uniform comparison and
produce a practical design.
Factors affecting the economy
of the designs and parameters
influencing the various limit
states for the design of the two
example bridges are presented.
Further, the study evaluates the
recent AASHTO LRFD
specification changes specific to
cross-frames on the bridge
designs. The paper investigates
how the choice of cross-frame
layout influences the design and
cost of the structure, thus
helping the engineer make
educated decisions for future
steel I-girder superstructure
designs.
Page 1 of 11
ECONOMIC AND DESIGN IMPACTS OF CROSS-FRAME
LAYOUT OPTIONS FOR STEEL I-GIRDER BRIDGES
WITH SEVERE SKEWS
Introduction
It has been well documented that steel plate
girder bridges with severe support skews can
develop large cross-frame forces due to relative
girder deflections particularly in the vicinity of
the skewed supports. In recent publications, it
has been suggested that skewed bridges with
staggered cross-frame layouts (staggered) could
be more cost efficient than contiguous cross-
frame layouts which are in-line transverse to the
girders (contiguous). However, there has been
limited data in the form of complete designs to
evaluate the economic impact of cross-frame
layout. It is understood that a staggered cross-
frame layout can result in significantly reduced
cross-frame forces for severely skewed bridges;
however, the trade-off is an increase in girder
bending moment and flange lateral bending
moments.
To evaluate the impact of the cross-frame layout
on a bridge design, two real world bridges, I-80
mainline in Council Bluffs, Iowa and US-75 in
Bellevue, Nebraska were chosen due to their
span lengths, bridge widths, skews and stiffness
to evaluate the effects on girder bending, shear
and fatigue as well as axial forces in the cross-
frame members. Three dimensional finite
element analysis was utilized to account for the
cross-frame stiffness, relative deformations and
flange lateral moments.
Additionally, the influence of recent AASHTO
LRFD specification changes specific to cross-
frames were evaluated on the two bridges noted
above. For example, the 7th Edition of
AASHTO LRFD Design Specification (2014) (§ C4.6.3.3.4)(1) allows the reduction of the axial
rigidity of the cross-frame members to 0.65AE
for single angle members and flange-connected
tee-sections to account for end eccentricity. In
2015, the Interim Revisions (§ C6.6.1.2.1)
changed the fatigue loading for cross-frames to
confine truck placement to one critical
transverse position per each longitudinal
position throughout the length of the bridge. In
the previous code provisions, the truck
positioning included two different transverse
positions and allowed a reduction factor of 0.75
to account for the reduced probability of
adjacent truck positioning over millions of
cycles. These two provision changes were
incorporated into the designs to assess their
effects on each design element and their effects
on the design economy.
Bridge Layout
The purpose of the study was to try to quantify
the design impact and, consequently, the
economic impact of altering the cross-frame
layout on severely skewed bridges. It was
important to select actual bridges that are
representative of current design practice. Studies
have proven that a staggered cross-frame layout
can reduce the cross-frame forces by reducing
the transverse bridge stiffness. The consequence
of reducing the stiffness is an increase in
primary bending moments of the girders and the
more impactful increase in the flange lateral
bending moments due to the cross-frames
staggered (non-contiguous) alignment. It has
been suggested by others that the decrease in the
cross-frame forces would outweigh the increase
in the demand on the girders producing a more
economic design. To evaluate the impact of the
cross-frame layout, the bridges needed to
possess certain physical attributes. The
following attributes were deemed important to
the evaluation of cross-frame layout.
Bridge Attributes Contributing to
High Cross-frame Forces
Skew is the primary reason cross-frames in
bridges with a tangent alignment are designed
for primary force effects. These force effects are
a result of differential deflections between
adjacent girders and are dependent on the skew
and girder spacing. As skew and girder spacing
Page 2 of 11
increases, substantial forces can be induced in
the cross-frames.
As Bridge Width increases, the impact of the
skew is magnified in the negative moment
regions where cross-frames extend from a rigid
point at the support outward to a more flexible
location along adjacent girders.
Span Arrangement: Shorter span lengths or
unbalanced span arrangements are often
susceptible to primary bending fatigue with high
ADTT. Fatigue can have a significant impact on
the cross-frames and the girder flange sizes due
to being subjected to higher fatigue stress
ranges. Bridges which have details governed by
the Fatigue Limit State may be impacted by the
additional flange lateral bending resulting from a
staggered cross-frame pattern.
L/D Ratio is a measure of girder flexibility.
More flexibility increases the demand on cross-
frame members due to the increased relative
deflections between adjacent girders. The span-
to-beam depth (L/D) ratio limit as specified by
AASHTO is merely a guide due to the fact it
does not incorporate the girder stiffness nor the
girder spacing. However, a high L/D ratio
suggests the bridge is a relatively flexible
structure which may increase the demand on the
cross-frames.
Bridge Configurations
Two bridges, each with skews of approximately
45 degrees were designed with alternate
staggered and contiguous cross-frame layouts.
The first structure is the I-80 mainline bridge in
Council Bluffs, Iowa which consists of a 1227
foot, 5 span unit with 44 degree skewed supports
and 270 foot maximum span lengths (Figure 1).
The bridge has
relatively constant
support skews of
approximately 45
degrees at the abutment
and piers, a fairly wide
bridge width of 63 feet,
L/D ratio of 32.7 which is less than the
suggested AASHTO limit (indicating a stiffer
bridge) and the dead load to live load ratio is
such that girder fatigue is not a limiting
criterion. Based on the bridge attributes
discussed above, the I-80 Bridge would be
expected to have high cross-frame forces.
The second bridge is the
US75 Bridge in
Bellevue, Nebraska
which consists of a 462
foot, 3 span bridge with
45 degree skews and 130
to 190 foot spans (Figure
2). The US75 bridge has relatively constant
support skews of approximately 45 degrees at
the abutment and piers, bridge width of 45 feet,
L/D ratio of 40 which is shallower than the
suggested AASHTO limit (indicating a flexible
bridge) and the dead load to live load ratio and
span balance are such that girder fatigue is a
limiting criteria in the positive moment regions
for girder bending. Based on the bridge
attributes discussed above, the US75 Bridge
would be expected to have high cross-frame
forces, also.
Cross-Frame Layout Options
A contiguous pattern and a staggered pattern of
cross-frame layouts were investigated for the
design of the two bridges noted above. The two
cross-frame layouts are shown in Figures 1 & 2
for each of the two bridges.
Staggered cross-frame layouts are typically used
to mitigate the “nuisance stiffness” (2) of the
structure resulting from the transverse stiffness
of the cross-frames at the supports. If the cross-
frames were totally eliminated or the transverse
stiffness significantly lowered, the girder shear
forces would be carried by the girder directly to
the bearings neglecting any slab stiffness.
Increasing the cross-frame stiffness will create
another load path to the pier supports attracting a
percentage of the girder shears. A staggered
cross-frame layout reduces the transverse
stiffness by offsetting the cross-frames rather
than aligning them transversely across the
structure. The offset allows the girder flanges to
deform transversely reducing the stiffness.
Unfortunately, rarely is anything free. The
resulting lateral deformation of the flange plate,
due to the staggered cross-frame alignment,
results in lateral bending moments in the flange
that must be accommodated in the design of the
girders.
Page 3 of 11
Contiguous cross-frame layouts can lead to
excessive cross-frame forces at the skewed
supports. Therefore, there is an advantage to
eliminate select cross-frames near the supports
to reduce the transverse stiffness at these
locations. Cross-frames were removed parallel
to the pier on each side of the pier as shown in
Figures 1 & 2. This pattern is very similar to the
staggered layout except that the stagger is only
located adjacent to the pier and not throughout
the length of the bridge. The advantage of this
layout is the nuisance stiffness near the pier is
reduced while the more effective contiguous
layout is utilized in the positive moment regions.
The contiguous layout significantly reduces the
lateral flange bending moments in the positive
moment regions relative to the lateral flange
bending moments from the staggered layout.
However, the benefit of the smaller lateral
flange bending moments from the contiguous
layout can be offset by the larger cross-frame
forces relative to the staggered layout.
Design Methodology
To effectively evaluate the cross-frame forces
and flange lateral bending moments, a three
dimensional finite element analysis was
performed on both structures utilizing LARSA
4D software. The assemblage of the models
incorporated typical modeling assumptions of
plate elements for the girder webs and deck
while beam elements were utilized for the girder
flanges and cross-frame members. Loading the
structure incorporated direct analysis for the
three dead load stages and influence surfaces
analysis for the loading of all live load effects
Figure 1: I-80 Framing Plan - Stagger & Contiguous Cross-frame Patterns
M
MM
M M
M
M M
M
M
M
M
M
M M
M
M
M
M
M
M
M
M
M M
M
M
M
M
M
M
M
M
M M
M
M M
M
M - Maximum Cross-frame Group
- Typical Cross-frame Group
Staggered
Contiguous
M
130' 193' 139'
22' 24'
3 @ 10.5'
25'
24'25'22'
45°45° 45° 45°
Figure 2: US-75 Framing Plan - Stagger & Contiguous Cross-frame Patterns
Page 4 of 11
conforming to the AASHTO LRFD
Specifications. The design of the girders
utilized STLBRIDGE LRFD software which
incorporated the primary load effects as well as
flange lateral bending moments.
For each of the two bridges, full analysis and
design was performed for the two cross-frame
layout patterns. For each cross-frame layout
pattern, four individual cases with unique code
provision application were analyzed and
designed. The four unique code provision
applications are outlined in Table 1.
For each design, multiple iterations of analyses
were performed to accurately capture the
relative stiffness between the cross-frames
(transverse stiffness) and the girders
(longitudinal stiffness). This involved adjusting
plate sizes and cross-frame member sizes for
each iteration until there was convergence
between the designed size and the size of the
members used in the 3D model.
Girder Design
Although all applicable limit states were
checked in the design of the girders, the primary
controlling limit states were the Strength I Limit
State and Fatigue Limit State. For the Strength I
Limit State, the flange capacities of discretely
braced compression and tension flanges were
checked for the primary strong axis bending
stress (fp) plus 1/3 of the flange lateral bending
stress (fL). The fatigue limit state was checked
for the primary fatigue stress range plus flange
lateral fatigue stress range at the toe of the cross
frame stiffener to flange fillet weld (Figure 3).
The girders were designed by optimizing the
performance ratios to a maximum value of 0.95
for the Strength I Limit State and 0.85 for the
dead load non-composite Strength IV Limit
State. No additional constructability checks
were performed for this study. A Category C’
detail for infinite life was used to determine the
controlling fatigue resistance range of 12ksi for
this study.
Uniform design parameters were applied
consistently for each iteration of design to
Case
Applicable
AASHTO
Version
Description
1 6th EditionOLD CODE - Base case for comparison prior to code provision changes
specific to cross-frames as outlined in Cases 2 & 3.
27th Edition
(2014)
REDUCED CROSS-FRAME STIFFNESS - § C4.6.3.3.4 allow for the
reduction of axial rigidity of the cross-frame members to 0.65AE for single
angle members and flange-connected tee-sections.
37th Edition
(2015)
REVISED CROSS-FRAME FATIGUE LOADING - § C6.6.1.2.1
changed the fatigue loading to confine truck placement to one critical
transverse position per each longitudinal position throughout the length of the
bridge.
47th Edition
(2015)
COMBINED REDUCED CROSS-FRAME STIFFNESS & CROSS-
FRAME FATIGUE LOADING - Application of both the 0.65AE provision
and the cross-frame fatigue loading provision from Cases 2 & 3.
Table 1: Analysis & Design Cases for Each Cross-frame Layout
Figure 3: Fatigue Category Locations
Page 5 of 11
produce comparative results of the total weights
for the two cross-frame layout alternatives.
Final girder plate sizes were based on the worst
case conditions of each girder in the cross
section resulting in one common girder elevation
used for each of the girders comprising the
bridge cross section. This is typical practice for
a tangent girder bridge design.
Cross-Frame Design
Common cross-frame configurations include X-
frame bracing, K-frame bracing and plate
diaphragms. For this study, alternative K-frame
cross-frame configurations were briefly studied.
The I-80 Bridge utilized a K-frame
configuration with the common diagonal node at
mid-length of the top chord and the US75
Bridge utilized a K-frame configuration with the
common node at the bottom chord. The
difference in orientation of the K- frame is
attributed to an inspection access requirement
for the I-80 Bridge design. A comparison of the
cross-frame forces was performed for the I-80
Bridge with the common diagonal node at the
top chord versus the common node at the bottom
chord. The force comparison showed the
diagonal forces remained the same while the top
and bottom chord forces changed depending on
the common node location. The change in
common node location resulted in a similar
percentage decrease in the top chord force
versus the increase in the bottom chord force.
However, the design resulted in a 4% increase in
cross-frame weight with the common node in the
bottom chord of the cross-frame. The bottom
chord demand increase required a larger section
size while the top chord demand decrease did
not allow for a similar decrease in top chord
section size. The top chord section size was
controlled by slenderness, thereby, not allowing
for a proportional decrease in section size
relative to the decrease in design force. The
overall difference in cross-frame weight was
small, thus we decided the orientation of the K-
frame was not a significant factor for this study.
Cross-frames were welded to gusset plates
which were bolted to the cross-frame stiffeners
(Figure 3). Equal leg angles and WT sections
were used for all chords of the cross-frames.
For the higher force members (diagonals and
bottom chords), both angles and WT shapes
were designed. The cross-frame members were
designed with consideration of member end
eccentricities and for a fatigue resistance of 4.5
ksi corresponding to a Category E detail (Figure
3).
Grouping of cross-frames is standard practice
when designing bridges with wide ranges of
cross-frame forces. The process of grouping is
subjective and dependent on the individual
designer’s preference. Two unique cross-frames
were designed for each bridge design iteration;
consisting of a design based on the maximum
cross-frame forces and a design for typical
cross-frame forces. Since it is impractical to
design and detail many different cross-frame
configurations, a common approach in design is
to design two or three different configurations
by grouping the cross-frames. After review of
the cross-frame forces and member designs, it
was evident that two unique designs would
adequately group the cross-frames for each
bridge such that the design could be optimized
without excessive detailing and conservatism.
Iterations of each case allowed for convergence
between the member sizes modelled in the 3D
FEM and the actual design sizes for each cross-
frame member. This resulted in accurate
modeling of transverse stiffness within each 3D
FEM.
Summary of Results
Effect of Reduced Cross-Frame Axial
Stiffness Provision (CASE 2)
In 2014, AASHTO LRFD Specification Section
4.6.3.3.4 recognized the influence of end
connection eccentricities (Figure 4) on the axial
stiffness of cross-frame members consisting of
single angles and flange-connected tee sections.
This code provision was added as a result of
research performed by Wang et al. in 2012 (3).
In lieu of a more accurate analysis, AE of equal
leg single angles, unequal leg single angles
connected to the long leg, and flange-connected
tee-section members may be taken as 0.65AE.
Page 6 of 11
The end welded angle and WT cross-frame
details used on the two bridges qualify for the
reduction in stiffness. To evaluate the impact of
this reduced cross-frame stiffness, the bridges
were redesigned adjusting the cross-frame
member axial stiffness by the 0.65 factor. This
code provision will have an effect on the
resulting forces in the cross-frames and in the
girder lateral flange bending moments due to all
AASHTO limit states. The research related to
this code provision showed that the effect of end
eccentricities is significant and without
consideration of this reduced stiffness in the
analytical bridge model the resulting cross-frame
forces will likely be excessive.
The I-80 and US75 bridge models were
modified to reduce the axial stiffness of the
cross-frame members. The resulting effect was
the reduction in axial forces of all cross-frame
members. The reduction in member forces
resulted in a reduction in member sizing and,
subsequently, a further reduction in stiffness.
The models and member designs were iterated
until the change in member forces extracted
from the model did not affect the designed
section size. The redesign of the cross-frame
members due to the change in stiffness resulted
in minimal or no regrouping of the cross-frame
designs. This change also resulted in changes to
the girder design primarily due to the change in
bottom flange lateral bending moment. Table 2
shows the percent change in cross-frame weight
due to the reduction of the cross-frame stiffness
within each 3D model for both bridges and
cross-frame layout patterns. The reduction in
cross-frame weight ranged from 10%-21% due
to the force reduction in all limit states.
Fatigue Truck Positioning (CASE 3)
In 2015, the Interim Revisions of AASHTO (§ C6.6.1.2.1) changed the fatigue loading
requirements for cross-frames to confine truck
placement to one critical transverse position per
each longitudinal position throughout the length
of the bridge. In the previous code provisions,
the truck positioning included two different
transverse positions and allowed a reduction
factor of 0.75 to account for the reduced
probability of adjacent truck positioning. The
change was based on the extremely low
probability of the truck being located in two
critical transverse positions over millions of
cycles. The new fatigue truck positioning
requirements are illustrated in Figure 5.
The older specification allowed the placement of
the fatigue truck to be placed in different
transverse positions to maximize the negative
and positive response. The resulting force range
was multiplied by 0.75 to account for the
reduced probability of adjacent positioning for
the enveloped response. However, the older
specification also stated that in no case should
the calculated range of fatigue stress be less than
the stress range caused by loading of only one
lane for both the positive and negative response
without utilizing the 0.75 factor.
Comparing the change to the fatigue truck
loading provisions, there can be a substantial
reduction in cross-frame fatigue range
depending on the attributes of the bridge.
I-80 US75
21% 10%
21% 17%Staggered
Table 2: Cross-Frame Weight Savings
Axial Stiffness Provision (Case 2)
BridgeCossframe Layout
Contiguous
Figure 4: End Eccentricity of Angle and WT Cross-frame Members
Page 7 of 11
Structures which are more flexible will
experience a greater reduction of cross-frame
fatigue force ranges. For the bridges analyzed in
this study, the change in the cross-frame fatigue
loading definition affected the I-80 and US75
bridges very differently. Table 3 shows the
reduction in cross-frame weight for the two
bridges for both of the cross-frame layouts.
The I-80 Bridge experienced little change in the
cross-frame fatigue range due to the new fatigue
loading while the US75 Bridge averaged a 15%
reduction in cross-frame weight due to the new
fatigue loading. The weight reduction was
unaffected by the choice of the cross-frame
layout pattern chosen. The difference in the
response to the new fatigue loading is primarily
attributed to the stiffness difference between the
two structures. As mentioned earlier, the L/D
ratio for the bridges indicated that the US75
Bridge was shallower than the suggested
AASHTO limit implying a more flexible
structure. When a truck loading is applied to
each bridge, the I-80 Bridge can be shown to be
approximately two times as stiff as the US75
Bridge in the vertical direction. Also, the
relative deflection of a cross-frame in the
positive moment area of a span is approximately
twice as much for the US75 Bridge relative to
the I-80 Bridge. Since the older code provision
allowed adjacent truck positioning to maximize
the fatigue force range in the cross-frame, a
structure that will experience a greater relative
deflection will be more sensitive to the load
positioning.
Although the fatigue ranges for the I-80 Bridge
were reduced under the new load positioning,
the reduction was less than the US75 Bridge.
Additionally, the Strength I Limit State for
compression typically controlled the design of
the cross-frame members for the I-80 Bridge.
This further limited the impact of the fatigue
loading on the I-80 Bridge.
Comparison between Contiguous and
Staggered Cross-Frame Layouts
(CASE 4)
The primary purpose of the study was to
evaluate the economical impact of selecting a
contiguous or a staggered cross-frame layout.
There are many factors to consider to accurately
determine the most economical solution. As
engineers, our experience is largely design
related as we have direct control over the
analytical procedures and design of the
constituent elements. However, the actual costs
associated with the fabrication and erection are
not easily quantified. Material, fabrication and
erection costs can change dramatically with the
economy, regional cost indexes, fabricator size,
contractor equipment, access to the site, etc.
Therefore, it is well beyond the scope of this
study to accurately determine actual costs and
apply them to the results. This comparison will
focus on the total weight of the cross-frames and
the girder plates. From this we can determine a
least weight solution and apply some basic
material cost data to determine a level of
sensitivity and determine relative cost
I-80 US75
2% 13%
0% 16%
Table 3: Cross-Frame Weight Savings
Due To New Fatigue Loading Provision (Case 3)
Cossframe Layout Bridge
Contiguous
Staggered
(b) One Transverse Position
Figure 5: Fatigue Truck Positioning for Cross-
Frame Forces
(a) Two Transverse Positions
Page 8 of 11
effectiveness of the cross-frame layout options
considered in the study.
The focus of this comparison will be on the two
components that constitute the vast majority of
the superstructure cost. The cross-frame
members and the girder plates will typically
comprise 95% of the cost of the steel
superstructure. Miscellaneous steel components
such as stiffener plates, field splice plates, shear
connectors, bolts and gusset plates typically
comprise about 5% of the steel weight. Only a
small percentage of these steel components will
be impacted by the distribution of material
between the cross-frames and the girder plates.
If we assume a 10% possible change to these
components, the impact to the overall cost of the
steel would be approximately 0.5%. Therefore,
evaluating the weight and estimated cost of the
cross-frames and girder plates should yield
reasonable accuracy when determining the
economic impact of the cross-frame layout.
Additionally, intermediate and crossframe
stiffeners were sized for the two bridges. The
staggered layout resulted in slightly more
stiffeners then the contiguous layout. The
resulting weight difference favored the
contiguous layout, but the difference was
minimal supporting their inclusion with the
miscellaneous steel.
The two subject bridges were designed based on
the 7th Edition of the AASHTO LRFD
Specifications with 2015 Interim provisions
which includes the cross-frame stiffness
reduction and the single lane placement of the
fatigue truck for cross-frame loading. The
designs utilized a contiguous cross-frame layout
modified by removing select high force cross-
frames near supports and a staggered layout as
shown in Figures 1 & 2. The bridges were
designed separately for each case with consistent
design methodology between the contiguous and
staggered cross-frame layout. This included the
use of the same design and analysis software,
modeling assumptions and design parameters.
The analyses and designs were iterated to
account for cross-frames stiffness changes,
girder stiffness changes and regrouping of cross-
frames between the initially assumed member
sizes to those of the final iteration. For each
bridge, the cross-frames were divided into two
groups based on the Strength I Limit State forces
and the Fatigue Limit State force ranges.
Figures 1 and 2 schematically show the locations
of the Maximum Cross-Frame Group and the
Typical Cross-Frame Group for each layout
option of the two bridges. The cross-frame
grouping designs were unique for each bridge
and each layout option. The controlling limit
state for the cross-frame members was
predominately the Fatigue Limit State and the
Strength I Limit State axial compressive
resistance.
Cross-frame Forces & Weight
As expected, the cross-frame forces resulting
from the staggered layout were lower than for
the contiguous layout. Although the average
force reduction varies between the top, diagonal
and bottom chord, the average reduction was
10%-50% for US75 and 10%- 15% for I-80 as
shown in Table 4.
The staggered cross-frame layout for the I-80
Bridge had less of an effect on the cross-frame
forces than the US75 Bridge. Consequently, the
resulting reduction in the total cross-frame
weight was significantly different between the
two bridges. As seen in Table 5, the I-80 Bridge
resulted in a reduction of 5% in cross-frame
weight while the US75 Bridge cross-frame
weight was reduced by 35% when utilizing a
staggered layout. The two bridges considered are
similar in skew, but have differing stiffness,
span arrangement and bridge width attributes.
The two bridges illustrate that the reduced
transverse stiffness resulting from a staggered
cross-frame layout does not necessarily lead to
dramatic force reduction in the cross-frames.
The I-80 Bridge cross-frame weight savings was
not as significant as compared to the cross-frame
weight savings for the US75 Bridge
I-80 US75
15% 10%
14% 50%
10% 25%
Table 4: Average Cross-Frame Force Reduction
With a Staggered Cross-Frame Layout
Cossframe Layout Bridge
Top Chord
Bottom Chord
Diagonal
Page 9 of 11
Girder Weight
The cross-frame layout had a relatively small
effect on the primary moment distribution. The
increased cross-frame stiffness of the contiguous
layout relative to the staggered layout will
change the moment distribution; however, it did
not affect the girder design for these bridges.
The primary impact to the girder design between
the two layout options is the difference in
magnitude of the bottom flange lateral moments.
The impact of the flange lateral bending stress
can be seen in Figure 6. The Strength I flange
lateral bending stress is plotted for the center
girder for span two of each bridge based on the
plate sizes for the contiguous design (prior to
adjusting plate sizes for the staggered design).
The lateral bending stress in the positive
moment region for the contiguous layout was
less than 5 ksi while the lateral stress due to the
staggered layout was near 30 ksi for each bridge.
For the Strength I limit state, one-third of the
lateral bending stress is added to the primary
bending stress to determine the total flange
stress which resulted in an increase of
approximately 10 ksi. Assuming 50ksi is the
factored bending stress allowable strength for
illustration, the reduction in primary bending
resistance due to the flange lateral bending stress
is about 20%.
In addition to the Strength I Limit State, the
Fatigue Limit State must be checked at all cross-
frame stiffener toe locations for the primary plus
flange lateral bending fatigue stress range. The
controlling location in the bottom flange is the
Category C’ fatigue detail at the termination of
the cross-frame stiffener to flange weld (Figure
3) which has an infinite life fatigue resistance of
12 ksi for these bridges. The design assumes a 7
inch wide stiffener, which is the minimum width
to accommodate a bolted gusset plate to stiffener
detail. Note that a wider stiffener would result
in an increase in the lateral bending fatigue
I-80 US75
5% 35%
Table 5: Cross-Frame Weight Savings
With Staggered Layout
Figure 6: Bottom Flange Lateral Bending Stress (Strength I Limit State)
0.0
10.0
20.0
30.0
40.0
50.0
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Stre
ss (
ksi)
Span 2 (Tenth Points)
Lateral Bending Stress - Strength I Limit StateUS75 Stagger US75 Contiguous I-80 Stagger I-80 Contiguous
Figure 7: Bottom Flange Lateral Bending Stress (Fatigue Limit State)
0.0
4.0
8.0
12.0
16.0
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Stre
ss (
ksi)
Span 2 (Tenth Point)
Lateral Bending Stress - Fatigue Limit State
US75 Stagger US75 Contiguous I-80 Stagger I-80 Contiguous
Page 10 of 11
stress which in turn could require additional
flange weight to meet fatigue requirements. As
can be seen in Figure 7, the flange lateral
bending fatigue stress range alone approaches
the fatigue resistance at several locations prior to
adding the primary bending fatigue stress range.
As a result, the US75 and I-80 bridge bottom
flanges were increased in width to accommodate
the increased fatigue demand due to the flange
lateral bending stress induced by the offset
cross-frames in the staggered layout.
In general, the bottom flange lateral bending
stress controlled in the positive moment region
requiring additional flange plate. There was
minimal flange plate increase in the negative
moment region due to the presence of larger
flanges and locations of the lateral bending
stresses relative to the maximum primary
bending stress. The increase in bottom flange
lateral stress in the positive moment region
required a flange width increase while keeping
the thickness at the code prescribed b/t limit of
24. The increase in the girder weight resulting
from the flange lateral bending is shown in
Table 6. The increase in the girder weight was
very similar between the two bridges with a 4%-
6% increase to account for the flange lateral
bending stress.
Total Weight Comparison
Total steel weights were computed for the
various designs of the two bridges. The
contiguous pattern resulted in heavier cross-
frames with a slightly reduced number of cross-
frames compared to the staggered layout. The
total weights of the cross-frames and the girders
for the two layout options are summarized in
Table 7. The total weights consist of the cross-
frame members, girder flanges and web plates.
As indicated in Table 7, the savings of cross-
frame weight by utilizing a staggered cross-
frame layout was offset by the increase in the
girder weight resulting in a total weight increase
of approximately 3 percent for the staggered
layout.
The two bridge designs with different bridge
attributes show a similar weight savings when
the modified contiguous layout is used.
However, the relative cost between the two
cross-frame layout options would be a better
determination of which cross-frame layout
option is optimal with respect to economy. As
discussed previously, a true total cost
comparison is not feasible for this study.
Additionally, a total cost may result in including
too many variables to draw a definitive
conclusion. The difference between the two
layouts is the distribution of weight between the
cross-frame members and the girder plate
material. Therefore, the selection of the cross-
frame framing layout would merely shift steel
weight between the cross-frame members and
girder plates. The labor costs for the fabrication
and the erection of the girders and cross-frames
is essentially fixed since we are not changing the
configuration just increasing material thickness.
Discussions with local fabricators show an
approximate material cost of $0.36/lb. for plate
material and $0.58/lb. for cross-frame members.
Applying a ratio of these costs to the I-80 and
US75 bridge weights, the staggered option
remained 3% heavier for the I-80 bridge and 1%
heavier for the US75 bridge.
The comparison of relative steel weight
difference shows that the staggered cross-frame
layout for the two bridges resulted in a greater
total weight than the contiguous cross-frame
layout. The relative cost of the cross-frame and
girder plate material changes the percentages
slightly, but does not change the conclusion.
Conclusions
To evaluate the impact of the cross-frame layout
on a bridge design, two real world bridges, I-80
I-80 US75
4% 6%
Table 6: Girder Weight Savings With
Contiguous Layout
I-80 US75
2506560 582640
2584170 598880
3% 3%Percent Change
Table 7: Total Weight Summary
Cossframe Layout Bridge
Contiguous
Staggered
Page 11 of 11
mainline in Council Bluffs, Iowa and US-75 in
Bellevue, Nebraska were chosen due to their
span lengths, widths, skews and stiffness to
evaluate the effects of the cross-frame layout on
girder bending, shear and fatigue as well as axial
forces in the cross-frame members. Three
dimensional finite element analyses were
utilized to account for the relative stiffness
differences between cross-frames and girders,
relative deformations and to extract flange
lateral bending moments. For each bridge, the
cross-frames and girders were designed utilizing
consistent design parameters to assure a uniform
comparison and produce practical real world
designs. The following conclusions were made:
The staggered cross-frame layout results
in slightly higher steel weight (cross-
frames plus girder) than the modified
contiguous layout by approximately 3%.
Applying material cost to the weights
based on local fabricator input, the
staggered layout results in 2% higher
costs than the modified contiguous
layout.
For the two bridges studied, the decision
between a staggered or contiguous
layout has a small impact on the overall
economy of the superstructure favoring
a modified contiguous layout by a few
percent.
The 2014 AASHTO 7th Edition
Specification change allowing a
reduction in cross-frame axial stiffness
for single angle and WT shapes
(0.65AE) resulted in a cross-frame
weight reduction in the range of 10%-
21%.
The 2015 Interim Revisions of
AASHTO 7th Edition change that
modified the loading placement of the
fatigue truck for cross-frames fatigue
force ranges resulted in a cross-frame
weight reduction in the range of 2%-
16%. The stiffness of the superstructure
had a significant effect on the magnitude
of the weight savings. The more
flexible bridge resulted in a greater
reduction in cross-frame weight then the
stiffer bridge.
The flange lateral bending moment
resulting from the staggered cross-frame
layout had a significant impact on the
design of the girder bottom flanges.
Increased flange sizes resulted from the
Strength I and Fatigue Limit States. For
bridges controlled by the Fatigue Limit
State for primary bending in the positive
moment region of the girder, the
additional fatigue stress due to lateral
bending at welded transverse stiffeners
can have a substantial impact on the
flexural resistance of the girder.
A three dimensional analysis is highly
recommended for steel plate girder
bridges with extreme skews in which the
cross-frames are staggered or
contiguous. Proper design of the girders
and cross-frames requires the ability to
account for lateral flange bending
moments resulting from the use of a
staggered cross-frame layout.
References
1) American Association of State Highway
Transportation Officials (AASHTO), LRFD
Bridge Design Specifications, 7th Edition,
with Interim Revisions through 2015.
2) Krupicka, G., and Poellot, W.N., “Nuisance
Stiffness,” HDR Bridgeline, Vol. 4, No. 1,
1993 (Omaha).
3) Wang, W., A Study of Stiffness of Steel
Bridge Cross Frames, Dissertation, The
University of Texas at Austin, 2013.