bren166-005

8/12/2019 bren166-005

1/11

Experimental verification of a staycable delta frame model

&1 Parag S. NimsePhD, PEFormer PhD Student, Department of Civil Engineering, University of

Toledo, Toledo, Ohio, USA

&2 Douglas K. NimsPhDAssociate Professor, Department of Civil Engineering, University of

Toledo, Toledo, Ohio, USA

&3 Arthur Helmicki PhDProfessor, School of Electronic and Computing Systems, University ofCincinnati Infrastructure Institute, University of Cincinnati, Cincinnati,Ohio, USA

&4 Victor J. HuntPhDResearch Associate Professor, School of Electronic and ComputingSystems, University of Cincinnati Infrastructure Institute, University ofCincinnati, Cincinnati, Ohio, USA

1 2 3 4

The accuracy of a finite-element model depends on the assumptions made during modelling. A combined

experimental and analytical approach which uses a minimum of expensive instrumentation and construction loading

to verify the modelling assumptions and validate the mathematical model was used to study a delta frame on the

Veterans9Glass City Skyway (VGCS). The VGCS is a twin segmental box girder cable-stayed bridge with three lanes in

each direction located in Toledo, Ohio. The delta frame is a complex and critical element of the bridge that transfers

loads from the box girders to the stay cables. It was instrumented with a sparse array of strain gauges. A small

number of strain gauges were placed in regions of expected high strain. The model was calibrated using the

prestressing loads and was used to investigate potential cracking during construction of the delta frame and was

incorporated in a larger model of the entire bridge. The accuracy of the work was confirmed by inspection for cracking

and strain measurements on the completed bridge.

NotationA cross-sectional area (transformed) of the

bottom chord

Iy, Iz of inertia abouty and z axisMy, Mz moment abouty and z axis

P axial force in the member

Yy, Yz distance fromy and z axis respectively

s normal stress at the gauge location

1. Introduction

The Veterans9 Glass City Skyway (VGCS) (see Figure 1) is a

cable-stayed bridge on the eastern edge of downtown Toledo,

Ohio that spans the Maumee River. It carries six lanes of

interstate I 280. The bridge has a single plane of fanned stays.It has several unique features. It is the first bridge in the USA

to have a stay cable cradle in pylon. At the time it was built, it

had the largest cable stays ever used. It is the only bridge in the

USA with stainless steel stay cable sheathing. It is the first

bridge in the world with glass panels in the pylon internally lit

by programmable light emitting diodes. It also employs delta

frames: a fairly new approach for attaching the single plane ofstays to the roadway box beams.

A research project was developed to study the construction and

service life response of the bridge. The objective was to use

instrumentation and continuous monitoring to collect mea-

surements from a limited number of critical locations on the

structure to understand the overall bridge performance. Delta

frames are critical elements in the structure of the Veterans9

Glass City Skyway (VGCS) cable-stayed bridge. Delta frames

are triangular elements contained within the concrete deck

which carry live and dead loads from the twin box segments

(see Figure 2) to the stay cables. The owner was concerned thatthe lower chords of the delta frames would crack during post-

tensioning, handling and erection. These cracks would close

later when the stays were tensioned. However, it was feared

Bridge Engineering

Volume 166 Issue BE1

Experimental verification of a stay cable

delta frame model

Nimse, Nims, Helmicki and Hunt

Proceedings of the Institution of Civil Engineers

Bridge Engineering 166 March 2013 Issue BE1

Pages 515 http://dx.doi.org/10.1680/bren.10.00023

Paper 1000023

Received 29/06/2010 Accepted 27/07/2011

Published online 22/11/2012

Keywords: bridges/cables & tendons

ice | proceedings ICE Publishing: All rights reserved

5

8/12/2019 bren166-005

2/11

that the hairline cracks would provide a path for water ingress

during the 100 year design life of the bridge. Thus, cracks

during construction could result in future maintenance

problems and shorten the service life of the delta frames.

During design, the delta frames had been modelled with two-

dimensional elements. To confirm there was no cracking, the

present study was performed on one of the first delta frames

cast. Although this study was performed concurrently with the

rest of the bridge instrumentation project, the objectives of the

present study were specific to the delta frames. During this

study a more detailed three-dimensional (3D) model of the

delta frame calibrated by measuring the strains at critical

locations was developed. The calibrated model was then used

to predict surface cracking. The model predictions were

verified by strain measurement and inspection during the

post-tensioning of the delta frame.

The VGCS delta frames are difficult to model because of their

geometry, the boundary conditions associated with various

construction stages and heavy post-tensioning. The slender legsand the massive stay anchor block and tendon anchor blocks

make it difficult accurately to determine the relative stiffnessesof the components. With insight from a priori two-dimensional

(2D) model, a sparse instrument array was designed and a 3D

model calibrated to better estimate the actual state of the

structure. This is less expensive than a full blown instrument

suite while decreasing the uncertainty in the assumptions.

An accurate model is important because the delta frame model

will be used in a larger calibrated model of the entire bridge. A

2D design model is generally conservative and accurate enough

to proceed with the construction of the bridge, but a calibrated

model is necessary to assess the state of the bridge at the end of

construction and to assist with future maintenance.

Delta frames are an innovation that simplify construction of

the main span by supporting the twin box segments with a

single plane of stays (Figures 2 and 3). Delta frames have been

used in the Varina-Enon Bridge over James River and the

Chesapeake and Delaware Canal Bridge (Goni et al., 1999;

Pate, 2000). On the VGCS, there are 42 delta frames, one at

each end of the 20 stay cables, and two delta frames next to the

pylon that have no stays. Each delta frame weighs approxi-

mately 900 kN (100 tons). These delta frames are the largest

and most heavily loaded yet designed. The VGCS Bridge was

constructed using two methods. The backspan (Figure 3) south

of the pylon was built in five spans, using temporary piers. The

main span north of the pylon was built using the cantilever

method to avoid obstructing the navigation channel.

The loading of the delta frame changes completely from

construction to service. The major construction events in the

life of the delta frame are casting, initial post-tensioning,

erecting the delta frame into final position on the bridge, final

post-tensioning and the stressing of the stay. The initial post-

tensioning was done in a storage yard with tendons DF2, DF3

and DF1 being tensioned (Figures 4 and 5). Final post-

tensioning was done with tendon DF4 when the delta frame

was in its final position on the bridge (Figure 6). From theinitial post-tensioning until the stay is tensioned, the bottom

Figure 1. Cantilever construction in progress, VGCS cable-stayed

bridge

Shoulder lane

Southbound lanes

Bottom chordNorthbound lanes

tendon anchor blockMain span cross section

at stay anchorages

(looking upstation)

Shoulder

Girder centre lineTendoncarrying arm

Stay anchor block

Centre line

survey and construction VGCS

Grinder centre line

Delta frame

Anchor keys and

segment keyways

Lane Lane

3.05 m

8.64 m

3.05 m3.66 m 3.66 m 3.66 m

10.87 m

Figure 2. Typical arrangement of a delta frame and segments at

stay anchor locations

Bridge Engineering


Experimental verification of a

stay cable delta frame model


6

8/12/2019 bren166-005

3/11

chord of the delta frame has some regions where the concrete

may experience tensile stresses. When the stay is tensioned, the

entire bottom chord goes into compression, thus eliminating

any tensile stresses. As the entire VGCS is instrumented for

long-term monitoring, the calibrated delta frame model will be

incorporated into the analytical model of the full bridge and

serve the broader purpose of supporting the maintenance of

the bridge throughout its life.

Since both stages of post-tensioning induced tension in regions

of the bottom chord (Figure 2), cracking remained a possibility.

A finite-element model of an individual delta frame was

developed and calibrated against the measured short-term

response for the first stage of post-tensioning, after which the

strain levels at this stage were checked against cracking. This

calibrated model was then used as a component of a more

complex model of the cross-section. Agreement between the

short-term strains calculated using the cross-section model and

the measured strains during the DF4 stressing confirmed the

calibration of the delta frame model. The cross-section model

was then used to check the strain level at potential cracking

locations. At this stage, the long-term strain levels (the combined

strain levels owing to initial post-tensioning, self-weight with

delta frame in its final position and final post-tensioning) were

checked against cracking.

The following sections present descriptions of the instrumen-

tation, data collection and data processing, and discussion of

the observations. The model calibration and strain verifi-

cation process for both stages of post-tensioning is then

discussed.

2. Instrumentation

The instrumentation system was designed to collect strain data

for selected loading conditions in the critical regions of the

delta frames in a form that could be used to validate the

analysis. The critical event that causes significant tension in

the bottom chord of the delta frame was tensioning of the

tendons. Tensioning of the tendons was a relatively slow event

(taking about an hour for three tendons) and the conditions of

interest were the state of strain in the bottom chord before and

after the tensioning of tendons. Therefore, a sampling rate of

15 min was used to capture the effects of interest. To reduce the

instrumentation costs, the delta frame instrumentation was

compatible with the data acquisition systems used for the

instrumentation on the rest of the bridge.

Pier 26 nb and sb

centre line

Pier 29 nb and

sb centre line

Pier 30 nb and

sb centre line

Pier 27 nb and sb

centre line

Stay cable 20b Stay cable 20a

Cantilever span

north of the pylon

Stay 18b anchorage point

location of delta frame 18bTypical stay

anchor point

Stay cable 1b Stay cable 1a

Pier 28 (pylon)

centre line

Back span

south of the

pylon

Figure 3. Main span of Veterans9

Glass City Skyway Bridge

Girder centre lineGirder centre line

Transverse tendons

Tendon DF2

Tendon

DF4Tendon

DF4Tendon

DF3

Tendon DF1

Median

slab

Stay cable

sheath

Inside parapet

Stay anchor

block

Delta frame bottom chord

Delta frame

tendon anchor

block

Delta frame and

segment key ways

looking area

Centre line survey and

construction-VGCS

Tendon DF4

anchor block

Figure 4. Delta frame in final position with tendons shown

Bridge Engineering





7

8/12/2019 bren166-005

4/11

Since it was among the first to be cast, delta frame no.18B (the

delta frame anchoring the eighteenth stay on the back span,

Figure 3) was chosen to be instrumented. A preliminary 2D

model of the delta frame was used to identify regions of

anticipated high tensile strains in the bottom chord. The 2D

model developed simulated the DF2, DF3 and DF1 post-

tensioning. The tensioning of each tendon induces bending in

the bottom chord. The deflected shape corresponding to these

tensioning events can be seen in Figure 7. Since the long-term

goal was to monitor the delta frame through all the important

construction events up to and including the stressing of the stay

cables, the design of the instrumentation took into account the

projected behaviour of delta frame when in its final in-built

position on the bridge and subjected to the tensioning of DF4.

The gauges were located near the regions predicted to have

high tensile stresses and aligned along the length of the bottom

chord of the delta frame. The gauge configuration was sensitive

to both bending and axial deformations and the measured

strains are the sum of bending and axial strains at the gauge

location.

The gauges used were vibrating wire gauges 4200 (embedment)

and model 4911 (sister bar) manufactured by Geokon

(Geokon, 1997). Both gauge types come equipped with built-

in thermistors for temperature monitoring and thermal

correction. The vibrating wire gauge operates on the principle

that the resonant frequency of a stretched wire changes when

the tension in the wire changes. In practice, the gauge contains

a wire stretched between two end blocks. Owing to deforma-

tion of the concrete in which the gauge is embedded, the end

blocks move relative to each other changing the tension in the

wire. Changes in frequency are measured by plucking the wire

and measuring the frequency with an electromagnetic coil. The

embedment gauge has a short gauge length (153 mm) and isanchored by small plates at the end of the gauge. Cracks within

the gauge length or in the region of the end plate could

invalidate the readings. The sister bar has a longer gauge length

(1384 mm) and is anchored by a piece of reinforcing bar which

can span across local cracks. Therefore, cracking will not

invalidate the average strain reading of the sister bar gauges.

The short gauge length allows more accurate capture of peak

strains while the longer gauge length allows meaningful

readings in the event of cracking.

Four embedment and four sister bar gauges were used as

shown in Figure 8. The gauge locations are given in Table 1.The gauge output includes the effects of both axial forces and

moments about the z and y axes. A pair of gauges, consisting

of one gauge of each type, was put at each elevation at each

gauged section. The redundancy of two gauges at the same

vertical location increased the probability that the tensile

strains of interest were captured. However, since both gauges

were at the same elevation, the gauges cannot capture both the

axial and bending force at a section. Therefore, the finite-

element model must be used to find the internal forces and

overall behaviour. Thus, the gauge configuration selected is a

sparse economic array that captures the desired strains, has

sufficient redundancy and can be used to verify the finite-

element model while having a low cost.

3. Data collection

Data were continuously collected at 15 min intervals using a

datalogger beginning the day when the delta frame was cast.

The only time it was interrupted was during the transfer of the

delta frame from the casting bed to the storage yard. The strain

data were collected at 15 min intervals during the initial post-

tensioning and at one-minute intervals during the final post-

tensioning. The collected data were transferred to the laptop

during periodic visits to the casting yard. Delta frame 18B was

cast on 26 September 2003, moved to storage on the 30September 2003; initial post-tensioning was performed on 16

October 2003 and final post-tensioning completed on 9 June

2006.

Projection of DF4 on bottom chord




North bound side South bound side

18BVNTO

18BSNTO

18BSNBI

zaxis

x axis

18BVNBI

18BVNBI

18BBSSBI18BVSTO

18BSSTO

Figure 5. Projected view of delta frame bottom chord with gauge

and tendon locations

Figure 6. Delta frame on the bridge in its final position supported

with temporary beams

Bridge Engineering





8

8/12/2019 bren166-005

5/11

4. Support conditions

The support conditions for initial and final post-tensioning

differ. During initial post-tensioning, the delta frame was

stored in the casting yard in a horizontal position. Figure 9

shows the stored position and supports. For final post-

tensioning (DF4), the delta fame is supported so that it stands

vertically (Figure 6) in its final position on the bridge with

temporary supports. The two keys (Figures 4 and 6) at the

junction of the bottom chord and the tendon-carrying arms on

both ends of the delta frame fit into the keyways in the

segments. At the top, the delta frame is connected to the

segments through the cast-in-place median slab, Figure 4.

Seven transverse tendons run through the top flange of the

segments from the left end of the southbound segment to the

right end of the northbound segment (see Figure 4, transverse

tendons), and they go through the conduits placed inside the

stay anchor block of the delta frame. The delta frame

installation construction sequence begins with the lifting and

supporting of the delta frame into its final position, followed

by the pouring of median slab and area around the keys, then

the stressing of the transverse tendons going through stay

anchor block and ends with the tensioning of DF4.

5. Data processing

5.1 Initial post-tensioning (DF2-DF3-DF1 stressing)

During the initial post-tensioning, tendon DF2 was tensioned,

then tendon DF3 was tensioned and, finally, DF1 was tensioned.

Typical support locations

(symmetric aboutyaxis)

Typical strain gauge location on lower

face of lower chord

y

x

Typical strain gauge location on upper

face of lower chord

Figure 7. Delta frame preliminary deformed shape (from

Chamaria, 2004)

0.38 m0.99 m

Stay anchor block

4.58 m

0.43 m

0.32 m

0.85 m

0.34 m

0.12 m

0.36 m

0.15 m

0.39 m

0.43 m

1.37 m1.37 m

Plan

1.12 m1.02 m

1.32 m

1.52 m

8.22 m

0.32 m

0.61 m

18BSNTO

18BSNTO

18BSNBI

18BSNBIi

18BSSBI

18BSSBI

18BSSTO

18BSSTO

18BVNTO

18BVNTO

18BVNBI

Elevation

18BVNB

18BVSBI

18BVSBI

18BVSTO

18BVSTO

0.26 mTendon anchor block

Figure 8. Delta frame elevation and plan view

Bridge Engineering





9

8/12/2019 bren166-005

6/11

A datum was set corresponding to strain levels at 11:00 am on

the day of initial post-tensioning. During the initial post-

tensioning, tendon DF2 (started at about 1:45 pm and completed

around 2:00 pm) was tensioned first followed by tendon DF3

(completed by 2:30 pm) and finally DF1 (completed by 2:45 pm).

The datum strains were deducted from values at 2:15 pm, 2:30

pm and 2:45 pm. Thus, the strains being studied are the short-term elastic strains solely owing to the initial post-tensioning.

Table 2 shows the final strains (micro strain) at the end of each

15 min time step, starting from 1:45 pm to 2:45 pm. Figure 10

graphically illustrates the change in strains through time for all

the gauges, starting at 11:00 am of October 21, 2003 to 6:00 pm

of the same day. Gauge 18BVNBI failed and its response is not

reported.

5.2 Final post-tensioning (DF4 stressing)

The stressing of DF4 took place when the delta frame was

installed on the bridge. On 9 June 2006 post-tensioning started

at 4:30 pm and ended at 4:45 pm. As for the initial post-tensioning, a datum level was set to a time corresponding to the

start of post-tensioning. Figure 11 illustrates the short-term

change in strain levels corresponding to tensioning. Here the

data collection interval was set to 1 min. Table 3 gives the

change in strain level for each gauge as a result of this activity.

Since the time difference between the datum and the final

reading for both initial and final post-tensioning was very

small, the time-dependent effects such as creep, shrinkage, and

relaxation are negligible.

Gauge

Gauge co-ordinates

inches (25?4 mm )

X Y Z

18BVNTO 2219?31 8?38 6?75

18BSNTO 2223?63 8?75 210?25

18BVNBI 247?00 29?13 211?50

18BSNBI 244?56 28?50 8?00

18BVSTO 230?31 8?50 210?50

18BSSTO 228?06 8?25 7?50

18BVSBI 46?75 29?00 6?00

18BSSBI 44?69 29?00 211?00

Table 1. Gauge locations (see Figure 7 for orientation of the co-

ordinate axes)

Figure 9. Delta frame in storage yard in the horizontal post-

tensioning position

1:45 PMa2:15 PM a 2:30 PM a 2:45PM a

Gauge

DF2

(2:00PM)bDF3

(2:26PM)bDF1

(2:42PM)b

18BVNTO 5?8 20?1 246?6 213?9

18BSNTO 20?1 21?9 42?7 216?8

18BSNBI 2?2 23?0 34?6 91?5

18BVSTO 21?5 273?0 227?5 230?0

18BSSTO 4?9 53?6 24?5 211?5

18BVSBI 20?2 55?8 52?5 74?3

18BSSBI 23?9 225?0 70?2 60?8

All readings in micro strain reported at gauge locationsaTime readings recordedbTime tensioning completedSign convention: (2) compression; (+) tension

Table 2. Strain measurements during the post-tensioning

sequence DF2-DF3-DF1

95VNTO

VSTO VSBI

SNTO SNBI

SSTO

SSBI

75

55

35

15

5

25

45 Time

Hrs: min65

851100 1200 1300 1400 1500 1600

Microstrain

Figure 10. Change in strain owing to DF2-DF3-DF1 post-

tensioning

Bridge Engineering





10

8/12/2019 bren166-005

7/11

6. Discussion

The following observations were made after processing the

data to isolate the responses of each of the post-tensioning

stages (Chamaria, 2004). Figure 5 shows that DF2 lies in the

same vertical plane as gauges 18BSNTO, 18BVSTO and

18BSSBI (average z coordinate 5 210?58 in (2270 mm)) so,

when DF2 is tensioned, these gauges go in compression owing

to the moment about the vertical axis (Myy) whereas the

gauges on the positive z-axis are in tension owing to moment

Myy (see Table 2). Since DF2 is in the arm on the south side

of the delta frame, similar effects can be seen in the north arm,

the difference being that the change in strain is smaller on the

north side. Thus, DF2 tensioning creates an unsymmetric stress

field.

When DF3, which runs through both the north and south arms

and lies on positive side of the z-axis (Figure 5), is tensioned, it

has similar effects. Even after DF3 is tensioned, the delta frame

is still unsymmetrically post-tensioned. Since DF3 goes from

one tendon anchor block to the other, it also pushes the stay

anchor block (Figure 4) down, thus transferring the load

through the V-strut to the central part of the bottom chord

bending it downwards. As a result, the four gauges near the V-

strut show tension, and the gauges at the tendon anchor blocks

show compression (Table 2). The tensioning of DF1 leads to

symmetry in stress field owing to post-tensioning. All four

gauges at the tendon anchor blocks are in compression, and all

four gauges in the centre are in tension. After DF3, DF2 and

DF1 were tensioned, the delta frame remained on its side in the

casting yard for 18 months.

At the end of the storage period, delta frame 18B was shippedto the site and moved into final position where DF4 was

tightened. DF4 (Figure 5) lies on the centreline in the xz plane,

so tensioning of DF4 has an effect similar to tensioning DF3.

DF4 compresses the tendon-carrying arms, moving the stay

anchor block down relative to the tendon anchor blocks,

inducing additional tension in the critical regions of the bottom

chord.

The deformation of delta frame 18B when DF4 is stressed is

constrained by the construction supports. At the deck level, the

stay anchor block is prevented from moving freely because the

median slab is in place and the transverse tendons are stressed(Figures 4 and 6). At the bottom of the delta frame, tendon

anchor blocks are locked into the segments on both sides by

pouring concrete into the gaps in the keyways, making them

part of the segment webs on both sides. Thus, the stiffness of

the entire cross-section comes into play and the movement of

the delta frame is restricted. Despite these constraints, as

expected, the tension in all the gauges increases (Table 3). The

final deflected shaped is as shown in Figure 7.

7. Model

The finite-element model of the delta frame was calibrated

against both the initial and final post-tensioning measurements.The finite-element analysis package Larsa 4D (Larsa, 2006) was

used to simulate the staged post-tensioning DF3-DF2-DF1 as

well as the construction sequence and subsequent final DF4

tensioning. 3D beam elements were used for these models since

Larsa can incorporate tendons only with beam elements. The

structural information, including geometry, section properties,

material properties for both concrete and non-prestressed and

post-tensioning steel, and tendon geometry including eccentri-

cities, was taken from the as-built construction drawings. Larsa

models the tendons as forces with lines of action defined relative

to the centreline of the beam. When the tendon is stressed in

Larsa, a load case of equivalent forces that the tendon wouldexert on the members is generated. Where the tendons curve,

the working points and radius of curvature are input. The

construction event timing came from the post-tensioning logs

30

VNTOVSTOSNTO

SSTOSNBI

SSBIVSBI

25

15

Microstrain

5 Time

hrs: min

0

5

1525 1530 1535 1540 1545 1550

10

20

Figure 11. Change in strain owing to DF4 POST-tensioning only

Gauge Measured strains 4:45 PM Analytical strains

18BVNTO 10?2 3?8

18BSNTO 11?2 6?6

18BSNBI 23?1 27?0

18BVSTO 11?6 10?7

18BSSTO 9?1 8?9

18BVSBI 24?1 26?6

18BSSBI 25?1 27?6

All readings in micro strain reported at gauge locations.

Table 3. Measured against analytic strain immediately after DF4

post-tensioning

Bridge Engineering





11

8/12/2019 bren166-005

8/11

and information provided by the contractor. Table 4 shows the

tendon tensioning log as provided by the contractor.

Since the short-term elastic strains used for calibration reflect

only the change in response of the delta frame for individual

post-tensioning events, only member stiffnesses were involved

in the analysis; member mass and long-term effects had no

influence.

For the initial post-tensioning, analytical constraints were

applied at the field support locations in the storage yard.

Figure 12 shows the model developed for the initial post-

tensioning phase. During initial post-tensioning, the delta

frame was horizontal and separate from the overall structure.The supports were provided at the three locations, two on the

bottom chord beam elements (y,z translation constrained) and

one at the topmost point (xtranslation constrained). Although

the actual delta frame was stored at five degrees to the

horizontal, it was not necessary to simulate this in the model as

all the beam members contributed only stiffness, not weight.

Each of the post-tensioning stages from DF2 to DF3 to DF1

was set as a construction stage in Larsa, and a staged

construction analysis was conducted.

The effects of parameters such as the stiffness of the members

used to simulate the stay anchor block and the tendon anchor

block were observed. These particular elements of the delta

frame are critical to simulating observed response, since the

load from post-tensioning goes to bottom chord through these

elements. The star shape arrangement representing the stay

anchor block shown in Figure 12 was found to be very

sensitive. Some minor adjustments were made to simulate the

loads applied due to stressing of the tendons. The top node in

the arrangement is not the top-most point of the delta frame;

rather it is the point where the tendons DF1 and DF2 cross

each other (Figure 4). The only vertical element in the delta

frame carries this load down to the centre node of the

arrangement. The centre node is connected to the two tendon-

carrying arms with slightly curved elements. Since the tendon

path has to follow the element profile, the elements are curved

such that their radii match exactly that of the radii of tendon

DF3. The other adjustment is that these members are thickerso that they can accommodate the radius of DF4. It was also

found that very stiff beam elements with dimensions summing

up to that of the 3D block geometry (Figure 12) accurately

simulated the measured response.

In its storage position, the delta frame was supported at three

locations (Figure 9); since the points of contact were wooden

blocks, accurately representing the support conditions in the

model was difficult. One of the support locations was the stay

anchor block and other two supports were on the bottom

chord, one about 5?18 m (17 feet) to the left from the centre

line and the other about 5?49 m (18 feet) to the right from the

centre line. As a result, the stay anchor blocks were

cantilevered from the supports. Within reasonable, physical

bounds, the analytical support conditions were varied to

optimise the fit between the analytical and measured response

to determine the final analytical support conditions. It was

found that the model output, although sensitive to support

degrees of freedom, was not sensitive to exact location.

The position and the support conditions for the final post-

tensioning of DF4 are different. For this second model, to

simulate DF4 tensioning, the delta frame was integrated into

the bridge transverse section. The delta frame model becomes

part of a larger model of the entire bridge cross-section

including additional elements, including the northbound and

southbound segments, the median slab and the additional top

Tendon

No. of 0?6 inch

(15?2 mm) strands

Jacking force kips

(4?44 kN)

DF1 19 868

DF2 19 868

DF3 19 868

DF4 27 1266

Table 4. Tendon forces at the end of post-tensioning

Nodes representing

temporary support

locations while stored

in casting yard

Stay anchor

block element

arrangement

Additional location 1 Additional location 2

Figure 12. Delta frame model for initial post-tensioning

Bridge Engineering





12

8/12/2019 bren166-005

9/11

transverse tendons (Figure 4). On site, the delta frame was

raised between the segmentally constructed southbound and

northbound back span (Figure 6), followed by pouring of themedian slab and tensioning of top transverse tendons

(Figure 4) before DF4 was tensioned. All these construction

events were modelled as different stages of construction

occurring on the same day since they happened quickly and

the time dependent effects are negligible. When the delta frame

was positioned such that the anchor keys were placed in the

keyways (Figure 6) and DF4 tensioned, the delta frame

became a part of the entire cross-section in the back span.

The parameters varied in this case were the boundary

conditions. Uncertainty in the support condition stemmed

from the fact that the cross-section model (Figure 13) is a

separate stand-alone model simulating the behaviour of thecross-section when the cross-section will really be part of the

entire bridge model. The elements representing the DF4 anchor

block simulated the stiffness of the physical DF4 anchor block.

8. Model calibration and strain levelverification

The finite-element model was calibrated by varying the

stiffnesses of the anchor and tendon blocks as well as the

support conditions. These parameters were varied to obtain

the best fit between the measured and analytic strains. In

correlating the analytical output from the models with the

recorded data, the following assumptions are made.

(a) The strains are recorded at the gauge location (Table 1)

which is measured at the centre of the gauge. Because the

sister bar and vibrating wire gauges integrate the strain

over their lengths, this assumption is strictly valid only as

long as the bending moment diagram is linear over the

length of the gauge. Acceptable linearity was verified by

the finite-element model.

(b) The contribution of time-dependent effects in concrete

such as creep, shrinkage, and relaxation over the

durations of post-tensioning of DF2-DF3-DF1 and DF4

are negligible.(c) Plane sections remain plane before and after the post-

tensioning.

(d) Concrete is homogeneous

The short-term normal stresses were found by

1. s~ PA

+ MyyzIy

+ MzyyIz

The stresses obtained from the Larsa model were converted to

strains and were compared with the measured data. The initial

and final post-tensioning were considered separately. For

initial post-tensioning, the datum was selected as a strain level

just before the DF2 post-tensioning was started, and the final

reading corresponded to a strain level when DF1 stressing was

completed. Therefore, the isolated strain values capture the

cumulative effect of DF2 to DF1 stressing. Then parametric

changes, such as member stiffness and support conditions,

were made in the model to obtain a better fit between the

actual and analytical strains. Once an acceptable match was

obtained, this model was made a part of the second phase

model with other bridge elements and only the modulus of

elasticity was adjusted for time and the support conditions

varied.

Table 5 shows the correlation between measured strains and

analytical strains from the calibrated model after the initial

post-tensioning. Table 3 shows the correlation after DF4 is

tensioned when the delta frame was installed in the bridge. The

forces at critical sections in the calibrated model were used to

calculate the surface strains for both stages of post-tensioning.

Although there are some differences between the measured and

analytical strains, the calibrated model gave improved insight

into the potential for cracking. The calculated strains based on

the original design models had estimated that the bottom

chord of the delta frame could crack under the proposed post-

tensioning regime. Note that the differences are reduced when

the delta frame model was incorporated into the cross-section

model and results compared as can be seen in Table 3. This

verifies that the calibrated model had captured the critical

behaviour with sufficient accuracy.

Dead load surface strains for both construction events, whenthe delta frame was lying flat in the storage yard and when it

was vertical during DF4 tensioning, were also calculated from

the model. Since total strain levels were required to check

Curved element for

DF4 tendon path

DF4 anchor blocks

Figure 13. Delta frame model for final post-tensioning

Bridge Engineering





13

8/12/2019 bren166-005

10/11

against cracking, corresponding dead load strains were added

to both the end of initial post-tensioning and the final post-

tensioning strains. Samples of concrete were taken while the

delta frame was being cast (Chamaria, 2004). The average

compressive strength was found to be 53?83 MPa (7813 psi)

and modulus of rupture 5?53 MPa (802 psi). The compressive

strength was used to calculate the modulus of elasticity as

34?89 GPa (5061?44 ksi) for the initial post-tensioning. Forfinal post-tensioning, the modulus was calculated based on

CEB-FIP90 (CEB, 1993) code equations. The initial post-

tensioning occurred soon after the 28 day strength test so the

test results could be used directly to calculate the modulus.

This anchors the modulus to a physical measurement. The

DF4 tensioning occurred several months later so an estimate of

the modulus corrected for time is more reasonable. Tables 3

and 5 show the strain level verification for initial and final

post-tensioning events at the gauge locations. Tables 6 and 7

show surface strains from the calibrated model owing to

combined effect of post-tensioning and self-weight. Table 7

also shows surface strains from the calibrated model for twoadditional locations below the centre V shaped struts which

are more critical because they are subjected to higher tensile

strains than locations directly above or below the strain gauges

locations. The theoretical cracking strain values in Tables 6

and 7 are calculated using the modulus of rupture and modulus

of elasticity. The delta frame was also inspected in the field

after the initial post-tensioning and after the second post-

tensioning; no cracks were found.

9. Conclusion

This paper presents an example which demonstrates that a

combined analytical and sparse instrument array approach can

resolve modelling uncertainty at a moderate cost. A sparse

array of instrumentation was used to resolve uncertainties in

the modelling of the delta frame, a complex element, of a cable-

stayed bridge.

The delta frame has massive and thin parts. Estimating the

relative stiffnesses of the parts is difficult and the owner was

very averse to cracking at any stage of the life of the delta

frame. Therefore, a trial delta frame was sparsely instrumentedand calibrated against two different loading and boundary

Gauges

Measured strains Analytical strains

DF2 DF3 DF1 DF2 DF3 DF1

18BVNTO 2?9 245?0 212?2 3?5 260?6 227?4

18BSNTO 21?3 44?1 215?3 24?4 48?2 230?1

18BSNBI 14?1 38?0 95?2 26?2 16?1 58?7

18BVSTO 245?2 226?5 228?8 278?0 233?0 227?8

18BSSTO 23?7 22?4 29?1 37?0 216?6 221?6

18BVSBI 28?0 55?7 77?8 35?8 37?3 61?6

18BSSBI 213?1 73?8 64?7 217?7 65?9 64?5

All readings are in micro strain reported at gauge locations.

Table 5. Comparison of measured to analytical strains for initial

post-tensioning

Gauge

Dead load

strains

Strains owing to

initial post-tensioning Total strains

Theoretical

cracking strain

Required additional strain to

crack bottom chord concrete

18BVNTO 210?6 237?1 247?7 155?0 202?7

18BSNTO 13?5 240?8 227?4 155?0 182?4

18BSNBI 2?4 84?5 86?9 155?0 68?1

18BVSTO 12?7 236?3 223?6 155?0 178?6

18BSSTO 210?0 230?9 241?0 155?0 196?0

18BVSBI 2?5 83?6 86?0 155?0 69?0

18BSSBI 24?4 86?6 82?2 155?0 72?8

Table 6.Combined effect of self-weight and initial post-tensioning

Bridge Engineering





14

8/12/2019 bren166-005

11/11

conditions. This resulted in a verified model with acceptable

accuracy. After calibration, this model was used to check

surface strain levels against cracking at both initial and final

post-tensioning. The prediction of no cracking on the trial

delta frame was visually confirmed when the delta frame was

post-tensioned.

As the entire VGCS is instrumented for long-term monitoring,

the calibrated model of the delta frame was used as a

component of the full bridge model. Thus, the present work

will also contribute to long-term maintenance of the VGCS.

AcknowledgementsThe research was supported by Ohio Department of Trans-

portation (ODOT). The authors gratefully acknowledge the

financial support. The authors would like to thank Jeff Baker,

Mike Meier and David Geckle of ODOT for their support with

project development and the construction monitoring. The

authors would also like to thank Manuel Carballo (FIGG

Bridge Engineers, Inc.) for his technical guidance. The enthu-

siastic support from the contractor, Bilfinger Berger Civil, Inc.,

particularly, Dan Kleinhenz, was deeply appreciated. The

Department of Civil Engineering, The University of Toledo is

also gratefully acknowledged.

REFERENCES

Chamaria BS (2004) Validation of Numerical Analysis with

Experimental Results for a Delta Frame used in Maumee

River Crossing. Masters Thesis, The University of Toledo,USA.

CEB (Comite Euro-International du Beton) (1993) CEB FIP

Model Code 1990. Thomas Telford, London, USA.

Geokon(1997) http://www.geokon.com/. Geokon Inc.,

Lebanon, New Hampshire, USA (accessed 29/03/2012).

Goni JJ, Moreton AJ and Pate WD (1999) Pylon design for

concrete cable-stayed bridges, USA.Structural Engineering

International9(1): 6366.

Larsa (2006) Larsa 4D. Larsa, New York, USA. See http://www.larsa4d.com/products/4D.aspx (accessed 20/03/2012)

Pate DW (2000) Innovative design and construction of

Chesapeake and Delaware canal bridge. Proceedings of

Fifth International Bridge Engineering Conference,

Transportation Research Record, issue number 1696, pp.

4448.

WHAT DO YOU THINK?

To discuss this paper, please email up to 500 words to the

editor at [email protected]. Your contribution will be

forwarded to the author(s) for a reply and, if considered

appropriate by the editorial panel, will be published as

discussion in a future issue of the journal.

Proceedingsjournals rely entirely on contributions sent in

by civil engineering professionals, academics and stu-

dents. Papers should be 20005000 words long (briefing

papers should be 10002000 words long), with adequateillustrations and references. You can submit your paper

online via www.icevirtuallibrary.com/content/journals,

where you will also find detailed author guidelines.

Gauge

Self-weight

strains

Strains owing to

initial +final

post-tensioning

Total strains 5self-weight +

initial+final post-tensioning

Theoretical

cracking strain

Required additional

strain to crack bottom

chord concrete

18BVNTO 5?45 223?56 218?11 155?00 173?11

18BSNTO 7?17 224?80 217?63 155?00 172?63

18BSNBI 7?84 132?63 140?47 155?00 14?53

18BVSTO 5?38 212?77 27?39 155?00 162?39

18BSSTO 4?59 28?77 24?18 155?00 159?18

18BVSBI 12?18 127?91 140?09 155?00 14?91

18BSSBI 11?68 132?14 143?82 155?00 11?18

Location 1 23?10 147?98 144?88 155?00 10?12

Location 2 2

763 156?10 148

?47 155

?00 6

?53

All readings in micro strain reported at the surface of bottom chord.

Table 7. Combined effect of self-weight, initial post-tensioning

and final post-tensioning

Bridge Engineering





15

bren166-005

Documents