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.