64 PCI JOURNAL Journal... · 2018. 11. 1. · 2, and 3 construction is indicated in Fig. 3. Bridge elevation (Example 1). 450 I 2500, 3700 [J 13800 SHOULDERLANE 3000 I 450 LANE SECTION

The Strutted Box WideningMethod for Prestressed ConcreteSegmental Bridges

Kenneth W. Shushkewich,Ph.D., P.E., P.Eng.PresidentKS Bridge EngineersBellevue, Washington

This paper introduces the strutted box widening method (SBWM), a

system that allows a two-lane segmental bridge to be designed and

constructed so that it can be easily widened into a three- or four-lane

bridge at any time in the future. This solution is attractive because

widening only needs to occur if and when traffic volumes warrant it.

Two examples demonstrate how the SBWM can be used to widen a

variable-depth cast-in-place segmental bridge and a constant-depth

precast segmental bridge. Design and construction considerations of

the SBWM are addressed, and the advantages and disadvantages of

the SBWM are outlined. Two particularly appealing potential

applications are described.

Two bridge examples introduce

the strutted box wideningmethod (SBWM). The first ex

ample is a variable-depth cast-in-placesegmental bridge, while the second isa constant-depth precast segmentalbridge. Both are built by the balancedcantilever method of construction. Theconcept can be applied to both precastand cast-in-place segmental bridgesbuilt by a variety of constructionmethods, including the balanced cantilever, span-by-span, incrementallaunch, and heavy lift methods.

Figs. 1 and 2 illustrate the SBWMconcept for a variable-depth bridge

and a constant-depth bridge, respectively. Note that the lane configurations are identical, although the structural system varies somewhat. Let usdefine three stages of construction andarbitrarily assign dates to these stagesof construction. The initial construction of the bridge is two lanes plusshoulders in Year 2003 (Stage 1). Thebridge is widened to three lanes plusshoulders in Year 2020 (Stage 2) andto four lanes plus shoulders in Year2060 (Stage 3). The resulting deckwidths are 13.8 m (45.3 ft) in Stage 1,17.5 m (57.4 ft) in Stage 2, and 21.7 m(71.2 ft) in Stage 3.

What makes the SBWM such an attractive solution is its flexibility.Widening only needs to take placewhen traffic volumes warrant it. If thetraffic volumes do not increase as fastas projected, widening can be delayedas long as necessary. If the traffic volumes increase faster than expected,the bridge can be widened from two tofour lanes directly (i.e., it is not necessary to have an intermediate three-lanebridge). The configuration of thebridge at the end of its service life canbe two, three, or four lanes.

The SBWM concept in essence isquite simple. During Stage 2 construc

64 PCI JOURNAL

tion, exterior compression struts areinstalled and the deck slab is widened.Additional transverse internal prestressing tendons and longitudinal external prestressing tendons are installed and stressed. Widening fromStage 2 to Stage 3 construction is similar. The deck slab is again extended(cantilevered), and additional transverse internal prestressing tendons andlongitudinal external prestressing tendons are installed and stressed.

The structural system varies depending on whether the bridge is variabledepth or constant depth. A variable-depth bridge (Fig. 1) has all compression struts at the same distance fromand the same angle to the deck surface.This means that interior compressionstruts are required to balance the exterior compression struts. This alsomeans that web bending will occur dueto unbalanced live load. A constant-depth bridge (Fig. 2) does not requireinterior compression struts since theforce in the exterior compression strutsis transferred through the bottom slaband taken in torsion. Hence, a constant-depth bridge is structurally moreefficient and easier to design than avariable-depth bridge. However, bothare still very good structural solutions.In order for the compression struts tobe effective, they need to have anangle from the deck surface of at least30 degrees. This means that the sectiondepth may be governed by the compression strut geometry rather than thespan-to-depth ratios.

Although strutted boxes have beenwidely used in the past as solutions forboth segmental bridges and cable-stayed bridges, this represents the firsttime (to the author’s knowledge) thatthe strutted box solution has been usedas the basis for the future widening ofa segmental bridge.

Podolny and Muller1 describe a particularly interesting strutted box segmental bridge. The Kochertal Bridgein Germany is a nine-span constant-depth cast-in-place segmental bridge.The bridge has typical span lengths of138 m (452.8 ft) and a section depth of7.0 m (23.0 ft) (which gives a span-to-depth ratio of 19.7). The bridge is builtin two stages. Stage 1 consists of constructing in balanced cantilever a boxgirder that has a deck width of 13.1 m

EfSH0ULDLR LANE

(43.0 ft) and a soffit width of 8.6 m(28.2 ft). Stage 2 consists of casting8.83 m (29.0 ft) cantilevers on a seriesof precast struts to give a total deckwidth of 30.76 m (100.9 ft) (to accom

modate six lanes of traffic). Althoughthe bridge is built in two stages, thiswas done to facilitate construction,rather than to accommodate futurewidening.

SECTION AT MIDSPAN

STAGE 1 — 2 LANES IN YEAR 2003

17500

450 7500 3700 3700 3700 3000 I 450LANE LANE

324 DIA.STEEL’Z

COMPRESSION STRUT

SECTION AT MIDSPAN SECTION AT PIER


21700

450 I 3000 3700 3700SHOULDER J LANE LANE

3700 3700 3000 I 450LANE LANE SHOULDER

7

SEC11ON AT MIDSPAN

CCC

C

CC

SECTION AT PIER


Fig. 1. Cross section widening for variable-depth bridge (Example 1).

November-December 2003 65

The two bridge examples in thispaper were designed for live load according to the Canadian Code2’3 because they are similar to the NorthSaskatchewan River Bridge in Edmonton, Canada, designed by the author. The live load, lane widths, andshoulder widths are based on theCanadian Code. A comparison withthe live load provisions of theAASHTO Standard Specifications4and the AASHTO LRFD Specifications5 is given in Example 1.

Although the successful low bid byKiewit on the North SaskatchewanRiver Bridge was for the steel alternate, representatives of Kiewit indicated to the author that their bid pricesfor the concrete and steel alternateswere very close. This is especially encouraging because the owner requested that the bids be based solelyon the initial cost, and not the widening costs or the life-cycle costs.Clearly, if the concrete alternate canbe competitive with the steel alternatebased on initial cost, it will have a significant advantage over the steel alternate when widening costs and life-cycle costs are considered.

EXAMPLE 1Consider a three-span variable-

depth cast-in-place segmental bridgebuilt by the balanced cantilevermethod of construction (see Fig. 3).The main span is 160 m (525.0 ft), andthe end spans are each 100 m (328.1ft), giving an overall length of bridgeof 360 m (1181.2 ft). The depth of thesection (see Fig. 1) varies from 9.0 m(29.5 ft) at the pier to 3.6 m (11.8 ft) atmidspan, which gives respective span-

to-depth ratios of 17.8 and 44.4. Thestrut angle is 39 degrees.

The cross section dimensions andcompression strut details are given inFig. 4. The compression struts consistof 0.324 m (12.8 in.) diameter steelpipes with end plates that frame intoconcrete buildouts (blisters) and trans

fer the load directly to the webs fromlongitudinal beams at the deck level.Note that there are two triangular-shaped exterior longitudinal T-beamsand one rectangular-shaped interiorlongitudinal T-beam.

The delineation between Stages 1,2, and 3 construction is indicated in

Fig. 3. Bridge elevation (Example 1).

450 I 2500 , 3700 370013800

[J SHOULDER LANE 3000 I 450LANE SHOULDER

SECTION AT MIOSPAN I SECTION AT PIERSTAGE 1 — 2 LANES IN YEAR 2003

450 I 2500I 17500 I

SHOULDER LANE LANE3700 3700 3700 3000 I 450

LANE SHOULDER f]

324 D STEE ECOMPRESSION STRUT I

SECTION AT MIDSPAN I SECTION AT PIERSTAGE 2 — 3 LANES IN YEAR 2020

I- 21700

-—-

450 I 3000 3700 3700 i 3700 3700 3000 i I 450SHOULDER LANE LANE LANE LANE SHOULDER

SECTION AT MIDSPAN

0

SECTION AT PIER


Fig. 2. Cross section widening for constant-depth bridge (Example 2).

66 PCI JOURNAL

Fig. 4. The top slab thickness forStage 1 varies from 0.250 m (9.8 in.)at the center of the box to 0.500 m(19.7 in.) at the web and 0.225 m (8.9in.) at the end of the cantilever. Thefillet width and thickness dimensionsshown are those required to accommodate the cantilever tendons. The top

slab thickness for Stage 2 is constantat 0.225 m (8.9 in.), while the top slabthickness for Stage 3 varies parabolically from 0.300 to 0.200 m (11.8 to7.9 in.).

The soffit width is 9.0 m (29.5 ft).The bottom slab thickness varies from0.250 m (9.8 in.) at midspan to 0.750

SECTION AT MIDSPAN

Fig. 4. Cross section dimensions (Example 1).

SECTION AT PIER

Fig. 5. Segment layout and strut locations (Example 1).

m (29.5 in.) at the pier. The midspanbottom slab thickness and fillet widthand thickness dimensions are those required to accommodate the bottomspan tendons. The pier bottom slabthickness is that required to resist themaximum compression during balanced cantilever construction (which


LLLLUJJIJLIIiIIIII II

8 x 25—150 I

I I I

I I

Fig. 6. External tendon layout (Example 1).

Fig. 7. Bulkhead details (Example 1).

is greater than the maximum compression due to the Stage 3 service loads).The web thickness of 0.500 m (19.7in.) has been chosen to accommodatethe shear and torsion as well as theweb bending which occurs duringStage 3.

The segment layout and strut locations are shown in Fig. 5. Constrainedby the form traveler lifting capacity onthe one hand and the desire to minimize the total number of segments onthe other, segments of 5.0 m (16.4 ft)length have been chosen. A one-halfsegment unbalance is built into thepier table — 6.0 versus 8.5 m (19.7versus 27.9 ft) — to minimize the unbalanced moment that is transferredinto the pier and foundation. Hence,there are 15 cantilever segments onone side of the cantilever and 14 on

the other. There is a 5.0 m (16.4 ft)abutment segment, two 5.0 m (16.4 ft)segments constructed on falsework,and a 5.0 m (16.4 ft) closure segmentin the end span. Finally, a 3.0 m (9.8ft) closure segment is cast in the mainspan to complete construction of thebridge.

Note that the strut locations fromthe edge of the segment are 1.0 m (3.3ft) on one side of the cantilever and1.5 m (4.9 ft) on the other. This simplifies the form traveler operationssince the strut locations are at thesame location for each form traveler.This also gives the compression strutsa uniform spacing of 5.0 m (16.4 ft)for the length of the bridge, which enhances the appearance of the bridgeand increases the structural efficiencyof the strutted box.

Figs. 6 and 7 show the external tendon layout and bulkhead details. Four25-strand tendons are required eachfor Stage 2 and Stage 3 construction.These straight tendons pass freelywithin the box and are anchored in theabutment diaphragm. Anti-vibrationdevices are required for these simple360 m (1180 ft) long tendons, whichhave no friction losses. Fig. 7 showsthe disposition of all prestressing tendons in the bulkhead.

The strutted box is not overly congested despite the fact that there is asubstantial amount of prestressingsteel. There are 30 cantilever tendonsper web near the pier corresponding tothe 29 segments plus pier table beingcantilevered. There are 16 bottomspan tendons per web near midspan,which are anchored in pairs in anchorblocks at the strut locations. There aresix continuity tendons per web, whichare anchored in pier/abutment diaphragms. The continuity tendons arein a single row near the pier for shearreasons and in two rows near midspanto maximize the eccentricity. The external tendons pass freely within thebox, as can be seen in the section atthe pier and midspan. Finally, there isprovision for future contingency tendons.

An open cellular abutment is recommended to facilitate the anchorage ofthe external tendons as well as the future contingency tendons. It is alsosuggested that interior lighting (whichutilizes a portable generator) be installed inside the box girder duringStage 1 construction to facilitate installation of longitudinal external prestressing tendons for Stages 2 and 3construction, as well as periodic inspection and maintenance for the lifeof the bridge.

The bending moment diagrams for

CANTILEVER TENDONS

SOTEOM SPAN TENDONS


68 PCI JOURNAL

Bending Moment Diagrams for Stage 2 (widening from 2 lanes to 3 lanes)

Ez

a)E0

C)

-30a)

the Stages 2 and 3 widenings areshown in Fig. 8. Individual momentdiagrams due to dead load, superimposed dead load, positive live load,negative live load, and prestressing areplotted. In proportioning the prestressing, a good first step is to load-balancethe dead load moment and allow theaxial compression to offset the superimposed dead load and live load moments Example 2 discusses an alternate method of proportioning the

prestressing so that there is a reserveof compression everywhere.

The stress diagrams for the Stages 2and 3 widenings are shown in Fig. 9.The stresses at the top and bottom ofthe section are shown. Note that thereserve of compression varies fromapproximately 0 to 2.4 MPa (0 to 348psi) for most of the bridge, except nearthe ends, where the reserve reaches 5MPa (725 psi) at the bottom and avery small tension at the top.

Table 1 gives a comparison of thelive load, including the number of traffic lanes and the reduction in live loadintensity as provided by the CanadianCode2’3 and two AASHTO Specifications.4’5 According to the CanadianCode, the bridge has to be designedfor three, four, and six lanes with reduction factors of 0.80, 0.70, and 0.55,respectively. The AASHTO Standardand AASHTO LRFD Specificationsrequire the bridge to be designed for

Ez

Ca)S0

C)C

C6)

60 120 180 240 300

X Distance (m)


90

60

360

SDL

LL+

LL

SDL

LL+

LL

-- —-PT

30

0

-60

-90

60 120 180 240 300 360

X Distance (m)Fig. 8. Bendingmoment diagrams(Example 1).


Stress Diagrams for Stage 2 (widening from 2 lanes to 3 lanes)

three, four, and five lanes; the reduction factors given by the AASHTOStandard Specifications are 0.90, 0.75,and 0.75, while those given by theAASHTO LRFD Specifications are0.85, 0.65, and 0.65.

What is of interest here is the increase in live load (as a percentage)for each code when going from Stage1 to Stage 2 and Stage 3. When widening from two to three lanes (Stage 2),the increase in live load is 16.7 per-

cent according to the Canadian Codeand 11.1 percent according to theAASHTO Standard Specifications toachieve a 50 percent increase in trafficcapacity. When widening from two tofour lanes (Stages 2 and 3 combined),the increase in live load is 37.5 percent according to the Canadian Codeand 38.9 percent according to theAASHTO Standard Specifications toachieve a 100 percent increase in traffic capacity. When the AASHTO

LRFD Specifications are considered,the results are even better at 2.0 and27.5 percent. In all cases, this represents a very good return (in traffic capacity) over investment (in structuralcapacity).

Table 2 gives a load summary comparison when widening from two tothree lanes (Stage 2). The loads, moments, and shears are given for the initial two-lane bridge, the one-lanewidening, and the resulting three-lane

Co0

COCO8)

Cl)

0 60 120 180 240 300

X Distance (m)


360

- -f top

bot

1.0

0.0

-1.0

CO

-2.0Cl)a)

C,)

-3.0

-4.0

-5.0

Fig. 9. Stressdiagrams

(Example 1).

60 120 180 240 300

X Distance (m)

360

70 PCI JOURNAL

bridge. The increase is expressed as apercentage of the one-lane wideningover the two-lane bridge. Note that thedead load of 391.15 kN/m (26.8 k/ft)is the average load per length for thisvariable-depth bridge. Looking at individual components, the dead load increase is 6.8 percent, the superimposed dead load increase is 13.0percent, and the live load increase is16.7 percent. Although the live loadincrease is 16.7 percent, the traffic capacity increase is 50 percent, or threetimes this value. Since the live load isa small fraction of the dead load, therequired increase in superstructuremoment and shear capacity variesfrom 8.6 to 10.0 percent, while thetraffic capacity increase is 50 percent,or five times this value.

Also given in Table 2 are a loadsummary comparison when wideningfrom two to four lanes (Stages 2 and 3combined). Here, the loads, moments,and shears are given for the initial

Table 1. Live load comparison.

two-lane bridge, the two-lane widening, and the resulting four-lane bridge.Again, the increase is expressed as apercentage of the two-lane wideningover the two-lane bridge. Looking atindividual components, the dead loadincrease is 12.7 percent, the superimposed dead load increase is 27.9 per-

cent, and the live load increase is 37.5percent. In this table, the required increase in superstructure moment andshear capacity varies from 17.1 to 20.2percent, while the traffic capacity increase is 100 percent, or five timesthis value.

The SBWM is a very effective solu

Table 2. Load summary comparison for Example 1.

Note; 1 kN/rn = 68.58 lb/fl; 1 MN-rn = 738.1 kip-ft; 1 MN= 225 kips.

Construction Live load Increase

stage (lanes) (percent)

Canadian Code23 -.

______

Stage 1 3 x 0.80=2.40 —

Stage 2 4 x 0.70 = 2.80 0.40/2.40 = 16.7 percent

Stage 3 6x0.55=330 0.90/2.40 = 37.5 percent -

AAS KTO Standard Specifications4

________________

Stagel 3xft90=2.70 _.L z

______

-

4x035=30O O3O/2.7O=II.lpercent

Stage 3 5 x 0.75 = 3.75 1.05/2.70 = 38.9 percent

Stagel

Stage 2

Stage 3

AASHTO LRFD Specifications5

_______

3x0.85=2.55 —

4 x 0.65 = 2.60 0.05/2.55 = 2.0 percent

5 x 0.65 = 3.25 0.70/2.55 = 27.5 percent

Widen from two to three lanes (Stage 2)

Moment,

Pier IL

(MN-rn)

Widen from two to tour lanes (Stages 2 and 3 combined)

Increase

(percent)

6.8 percent

13.0 percent

16.7 percent

Moment,

Pier IR

(MN-rn)

One-lane

widening

26.450

7.326

0.40

—55 .863

—15.473

—18.958

—90.293

—69.084

—19. 34

—25. 3 36

—113.554

2.986

3.597

6.419

23.002

Increase

(percent)

12.7 peicent

27.9 percent

37.5 percent

Three-lane

bridge

4 17.60(1

63.468

4 x 0.70 = 2.80

—8 10. 108

—134.045

—132.704

—1076.857

—998.708

—165.769

—177.354

—1341.831

176. 193

31.160

44.933

252.286

Moment,

Span 2

(MN-rn)

9.2 percent

Two-lane

bridge

39 1.150

56. 142

3 x 0.80 = 2.40

—754.245

—118.5728

—113.746

—986.564

—929.624

— 46.6348

—152.0 18

—1228.277

163.207

27.563

38.514

229.284

—11.345

—1.626

—2.552

—15.523

27.931

3.990

4.097

36.018

DL (kN/m)

Loads SDL (kN/rn)

LL (lanes)

DL

SDL

LL

Total

DL

SDL

LL

Total

DL

SDL

LL

Total

DL

SDL

LL

Total

Shear, DL

Pier IL SDL

(MN)L

LL

Total

Shear, DL

Pier IR SDL

(MN) LL

Total

Two-lane

bridge

39 1.150

56. 142

3 xO.80=2.40

—754.245

—118.573

—113.746

—986.564

—929.624

—146.635

—152.018

—1228.277

163.207

27.563

38.5 14

229.284

—11.345

—1.626

—2.552

—15 .523

18.3 percent

Shear,

Abut I

(MN)

Two-lane

widening

49.508

15.642

0.90

—104.562

—33.036

—42.655

—180.253

—129.308

—40.855

—57.006

—227. 168

24.306

7.680

14.443

46.429[

—1.434

—0.453

—0.957

—2.844

9.2 percent

10.0 percent

Four-lane

bridge

440.658

7 1.784

6 x 0.55 = 3.30

—858.807

—15 1.609

—156.401

—1166.817

—1058.932

—187.489

—209.024

— 1455.445

187.513

35 .243

52.957

275 .7 13

—12.779

—2.079

—3.509

—18.367

3 1.450

5.102

5.634

42.186 17.1 percent

—35.090

—5.740

8.5 percent

—0.766

—0.2 12

—0.425

—1.403

1.880

0.521

0.683

3.084

—12.111

—1.838

—2.977

—16.926

29.811

4.511

4.780

39. 102

9.0 percent

20.2 percent

—31.131

—4.489

—4.690

—40.310

27.931

3.990

4.097

36.0188.6 percent

—2.115

—0.586

—0.782

—3.483

18.3 percent

3.5 19

1.112

1.5 37

6.168

—33.246

—5.075

—5.472

—43.793

—31.131

—4.489

—4.690

—40.3108.6 percent

—3.959

—1.251

—1.759

—6.968

—6.449

—47.279 17.3 percent


Fig. 11. Cross section dimensions (Example 2).

tion in this example, because for anadditional investment of 10 or 20 percent in superstructure moment andshear capacity, the respective return is50 or 100 percent in traffic capacity.

EXAMPLE 2Consider a six-span constant-depth

precast segmental bridge built by thebalanced cantilever method of construction (see Fig. 10). The interiorspans are 60 m (196.9 ft), while theexterior spans are 42 m (137.8 ft), giving an overall length of bridge of 324m (1063.0 ft). The depth of the section(see Fig. 2) is 3.2 m (10.5 ft), whichgives a span-to-depth ratio of 18.8 anda strut angle of 33 degrees. The section depth is governed by the compression strut geometry rather than thespan-to-depth ratio in this example.

The cross section dimensions andcompression strut details are given inFig. 11. The compression struts consist of 0.3 24 m (12.8 in.) diameter

steel pipes with end plates that frameinto concrete buildouts (blisters) andtransfer the load directly to the bottomslab from triangular shaped exteriorlongitudinal T-beams at the decklevel. The top slab thickness for Stage1 varies from 0.250 m (9.8 in.) at thecenter of the box to 0.500 m (19.7 in.)at the web and 0.225 m (8.9 in.) at theend of the cantilever. The top slabthickness for Stage 2 is constant at0.225 m (8.9 in.), while the top slabthickness for Stage 3 varies parabolically from 0.300 to 0.200 m (11.8 to7.9 in.).

The soffit width is 8.0 m (26.2 ft).The bottom slab thickness varies from0.200 m (7,9 in.) at midspan to 0.400m (15.7 in.) at the pier. The midspanbottom slab thickness is a minimumvalue, while the pier bottom slabthickness is that required to accommodate the maximum compression during balanced cantilever construction(which is greater than the maximumcompression due to the Stage 3 service

loads). The web thickness is 0.450 m(17.7 in.).

The segment layout and strut locations are shown in Fig. 12. Each balanced cantilever has a 1.8 m (5.9 ft)pier segment and eight 3.6 m (11.8 ft)typical segments on each side of thecantilever. Closure segments are 0.6 m(2.0 ft). The end spans have a 1.5 m(4.9 ft) abutment segment and three3.6 m (11.8 ft) typical segments whichare assembled on falsework. The construction sequence proceeds from oneend of the bridge to the other, buildingcantilevers P1 to P5 in succession, andpouring closures in the backspan asconstruction proceeds. At the completion of construction, the bridge superstructure sits on fixed bearings at P3and expansion bearings everywhereelse (see Fig. 10). Note that the strutlocations are always 2.1 m (6.9 ft)away from the edge of the segment.This simplifies the casting cell operations since the strut locations are always at the same location in the cast-

Fig. 10. Bridge elevation (Example 2).


72 PCI JOURNAL

42000 60000 60000

10800 8 AT 3600 28800 8 AT 3600 = 28800 8 AT 3600 = 28800 8 AT 3600 = 28800 8 AT 3600 = 28800

_99p 600 900 900 600 900 900 600 900

H.l.I.i.lJ.LLLLLIlI.Ll.I.LlJJI.l.Ll--

STRUT LOCATION (rEP.)

€ ()T 60000 T 60000 T 42000

8 AT 3600 = 28800 8 AT 3600 = 28800 H 8 AT 3600 = 28800 8 AT 3600 = 28800 8 AT 3600 = 28800 II 10800

Fig. 12. Segment layout and strut locations (Example 2).

llIIIIIIIIIIIllI

4 x 9—150 TENDONS 4 x 15—150 TENDONS 4 x 15—150 TENDONS

IIIIlIlIIlIIIIlI

ing cells for the typical segments. Thisalso gives the compression struts auniform spacing of 3.6 m (11.8 ft) forthe length of the bridge.

Figs. 13 and 14 show the externaltendon layout and bulkhead details.Stage 2 and Stage 3 construction eachrequires two 15-strand tendons in theinterior spans and two 9-strand tendons in the exterior spans. Thesedraped tendons are held down at thedeviation diaphragms and anchored atthe pier/abutment diaphragms. Fig. 14

Fig. 13. Externaltendon layout(Example 2).

600 600 600

II.I.l.l.I.lI.i.I.l.I.I.I.l.II.I.l.l.p l.l.lIlLLIILIIILIIIIIIlIIIII[

c1

4 x 15—150 TENDONS 4 x 15—150 TENDONS 4 x 9—150 TENDONS


Fig. 14. Bulkhead details (Example 2).

BOTTOM SPAN TENDONS



Fig. 15. Bending

moment diagrams(Example 2).

z

CIi)

E0

0)C

Ca)

£0

Ez

C8)E0

0)C

-DCa)

£0

X Distance (m)

324

SDL

shows the disposition of all prestressing tendons in the bulkhead. There are14 cantilever tendons per web near thepier and six bottom span tendons perweb near midspan, which are anchored in the anchor blocks. Thedraped external tendons are at the bottom of the section near midspan and atthe top of the section near the pier. Finally, there is provision for future contingency tendons. Again, an open cellular abutment and interior lighting arerecommended.

The bending moment diagrams for

the Stage 2 and 3 widenings are shownin Fig. 15. Individual moment diagrams due to dead load, superimposeddead load, positive live load, negativelive load, and prestressing are plotted.The stress diagrams for the Stage 2and 3 widenings are shown in Fig. 16.The stresses at the top and bottom ofthe section are shown. Note that thereserve of compression varies fromapproximately 0 to 0.6 MPa (0 to 87psi).

The prestressing has been proportioned here by combining the results

of various analyses in a spreadsheet,which is linked to an interactivegraphical plot of the stresses (Fig. 16).The results of the dead load, superimposed dead load, and live load analyses (as well as thermal analyses,6 including positive thermal gradient,negative thermal gradient, temperaturerise, and temperature fall) are imported into the spreadsheet, along withunit load cases of draped prestressingin the exterior spans and the interiorspans. In this way, multipliers for theexterior span prestressing and interior

12

8

4

0

-4

-8

-12

SDL

H--—- LL+H --L—PT I

54 108 162 216 270

X Distance (m)


324

54 108 162 216 270

74 PCI JOURNAL


Co0

Coci)

U,

0.0

CU0

-0.61011)

(1)

-1.2

span prestressing are adjusted to immediately see the effect on thestresses. The optimum amount of prestressing is proportioned to have a reserve of compression everywhere atthe top and bottom of the sectionwhile using the least amount of prestressing.

It is interesting to compare theloads, moments, and shears in Example 2 (Table 3) with those in Example1 (Table 2). When widening from twoto three lanes, the dead load increaseis 13.1 percent in Example 2, whereas

it was only 6.8 percent in Example 1.This makes sense because the overalldead load is smaller for a bridge having shorter spans, meaning that thepercentage increase of the widenedbridge is larger. The superimposeddead load increase and the live loadincrease are the same in both examples at 13.0 and 16.7 percent, respectively. Again, this makes sense because the superimposed dead load andlive load are the same in both examples. The net effect is that the requiredincrease in superstructure moment and

shear capacity varies from 13.6 to 13.9percent in Example 2, whereas itvaries from 8.6 to 10.0 percent in Example 1. When widening from two tofour lanes, the required increase in Superstructure moment and shear capacity varies from 27.1 to 28.1 percent inExample 2, whereas it varies from17.1 to 20.2 percent in Example 1.

To summarize, Examples 1 and 2require an increase in superstructuremoment and shear capacity of 10 and14 percent, respectively, to achieve a50 percent increase in traffic capacity

1.2

0.6-

00

-1.2 -

-1.8

--

flop.

0 54 108 162 216 270 324

X Distance (m)


1.2

0.6 —

_____________

-. -.

-1.8

-2.4

0 54 108 162 216

X Distance (m)

270 324 Fig. 16. Stressdiagrams(Example 2).


Table 3. Load summary comparison for Example 2.

Note: 1 kN/m = 68.58 lb/ft; I MN-rn = 738.1 kip-ft; 1 MN = 225 kips.

(or 20 and 28 percent, respectively, toachieve a 100 percent increase in traffic capacity). The required increase insuperstructure moment and shear capacity is smaller for longer spanbridges than for shorter span bridges.The SBWM solution works very wellin both examples.

CONSTRUCTIONCONSIDERATIONS

One of the fundamental decisionsthat has to be made during a bridgewidening project is whether to allowtraffic on the bridge during construction. This issue also comes into playwhen widening the bridge by theSBWM.

If traffic is allowed on the bridgeduring widening, detours will not berequired, but construction will proceedmore slowly since it will occur adjacent to traffic. Barriers will be required to separate the traffic from the

construction activities. The use ofmoveable knee-braced formwork attached to the web and cantilever willallow the exterior compression strutsto be installed, the concrete deck to beformed and poured, and the transverseprestressing tendons to be installedand stressed.

If traffic is not allowed on thebridge during widening, constructionwill proceed much more rapidly, butthe traffic will have to be detoured.The erection truss shown in Fig. 17can be used to widen the bridge directly from two to four lanes (or fromtwo to three lanes or from three tofour lanes as described previously).The truss facilitates the installation ofthe exterior compression struts. It hassuspended forms at the ends for theStage 2 and Stage 3 concrete deckpours. The ends of the truss havesafety rails as well as extra room forinstalling and stressing the transverseprestressing tendons. The truss bears

over the webs on Hilman rollers,which are locked during the concretepour, and then freed to allow the trussto advance. A staggered pouring sequence is used in the same way as thatfor the deck pour of a composite steelgirder bridge.

DESIGN CONSIDERATIONS

Longitudinal FlexureThe bridge has to be designed for

three stages of construction. By keeping the design for each stage of construction independent as outlinedbelow, the additional design work isnot substantial.

Stage 1 requires the traditional design of a segmental bridge where theconstruction sequence and the time-dependent effects of creep, shrinkage,and relaxation are considered. Prestressing is proportioned to facilitatesegmental construction and to accom

Two-lane

bridge

Widen from two to three lanes (Stage 2)

DL (kN/m) 202.030

LL (lanes)

Moment, DL

Span 2 SDL

One-lane Three-lane Increase

(percent)

13.1 percent

13.0 percent

16.7 percent

Widen from two to four lanes (Stages 2 and 3 combined)

bridge

228.480

63.468

4x0.70=2.80

37.23 1

10.342

12.547

Two-lane

bridge

202.030

56. 142

3x0.80=2.40

32.921

Moment,

Pier 2

(MN-m)

Two-lane

widening

49.508

15.642

0.90

8.067

6

13.8 percent

Moment.

Span 3

(MN-in)

widening

26.450

Loads SDL (kNIm) 56.142 7.326

3 x 0.81) = 2.40 0.40

32921 4310

9.148 . 1.194

10754 1.792

_______

52.823 7.296

—62.672 —8.205

—17416 —2.273

—15.434 —2.572

—95.522 —13.050

29.795 3.90)

• 8.280 1.080

11.369 1.895

49.444 6.876

—59.577 —7.80(1

—16.556 —2.16(1

— 15.6(11) —2.600

—91.733 —12.560

2.97) 0.389

(1.826 0.1(18

0.796 0.133

4.593 0.629

—6.009 —0.787

— 1.670 —(1.218

—1.374 —0.229

—9.053 —1.234

13.7 percent

(MN-rn) LL

Total

DL

SDL

LL

Total

DL

SDL

LL

Total

DL

SDL

LL

Total

DL

S DL

LL

Total

DL

SDL

LL

Total

Moment,

Pier 3

(MN-rn)

13.9 percent

27.2 percent

Shear,

Abut I

(MN)

60.119

—70. 877

—19.688

—18.007

—108.572

33.696

3(1

13.264

56.320

—67.377

—18.7 16

— 18.200

—104.294

3.361

(1.93 3

0.928

5.222

—6.796

—1888

—1.603

—10.287

Four-lane Increase

bridge (percent)

25 1.538 24.5 percent

7 1.784 27.9 percent

x 0.55 = 3.30 37.5 percent

40.988

11.697

14.787

67.472 27.7 percent

—78.030

—22.268

—21.222

—12 1.520

37.097

1(1.587

15.632

63.3)5-

—74177

—21.169

—21.45(1

—116.796

3.701)

1.056

1.094

5.849

—7.482

—2.135

—1.889

—11.5(16

9.148

10.754

52:823

—62.672

—17.4 16

—15.434

—95.522

29.795

8.28))

11.369

—59.577

—16.556

—15.600

—91.733

2.971

0.826

0.796

4.593

-6.009

—1.671)

—1.374

—9.053

2.549

4.033

4j4.649

—15.358

—4.852

—5.788

—25.998

7.301

2.307

4.263

13.872

— 14.6(11)

—4.613

—5.850

—25.062

0.728

(1.230

0.298

—0.465

—(1.5 15

—2.453

13.7 percent

28. I percent

Shear,

Pier 3L

(MN)

13.7 percent

27.3 percent

13.6 percent

27.4 percent

27.1 percent

76 PCI JOURNAL

Fig. 17. Erection truss for bridge widening.

modate the redistribution of stresses.There should be a reserve of compression at the top and bottom of the section at all locations under the effectsof all service loads, both at the initialopening of the bridge and after finallong-term losses have occurred.

Stage 2 requires the design for theincremental loads of Stage 2, and canbe designed elastically because it occurs so far in the future that the time-dependent effects of Stage 1 have littleor no effect. Thus, the Stage 2 incremental loads and the Stage 2 sectionproperties are applied to an elasticanalysis of the completed bridge toallow the prestressing to be proportioned so as to have a reserve of compression at the top and bottom of thesection at all locations.

Stage 3 requires the design for theincremental loads of Stage 3 and canbe designed in a similar manner toStage 2.

Validation of the final design requires analysis for all three stages ofconstruction in a 2D (or even a 3D)time-dependent computer programwith the assumed dates of construction(the assumed dates will need to be replaced by the actual dates in the analysis when widening occurs). Thereshould be a reserve of compression atthe top and bottom of the section at alllocations at any time during the lifetime of the bridge.

It is also necessary to check the ultimate strength design for all threestages of construction. The ultimatestrength at Stage 3 is provided by theinternal tendons of Stage 1 along withthe external tendons of Stage 2 andStage 3.

Longitudinal Shear and Torsion

The webs have to be designed forshear due to dead load, superimposeddead load, and live load, as well as fortorsion due to eccentric live load andoverturning wind. Stage 3 is the controlling case in the design for shearand torsion. It is important that theResal effect be considered in the design. (Note that the Resal effect,which is explained in books on segmental box girder design, relates to thereduction in shear force by the verticalcomponent of the inclined compression flange.) The webs also have to bedesigned for web bending (as discussed in the next section). Of course,the top and bottom slabs also have tobe designed for torsion.

Design for shear and torsion can beperformed by the traditional approachor by the strut-and-tie method. It isalso desirable that the principalstresses be checked to ensure thatcracking of the webs does not occur.

Transverse Design

The transverse analysis for Example1 is facilitated by the creation of twocomputer models:

Finite Element Model — One-halfof the interior span is modeled forStage 3 construction. The model includes plate elements for the top slab,webs, and bottom slab, along with offset beam elements with rigid links forthe longitudinal beams and beam elements for the compression struts. Theappropriate end boundary conditionsare applied. It has been found that a1.0 x 1.0 m (3.3 x 3.3 ft) mesh size isreasonable (although local refinement

to a 0.25 x 0.25 m (0.8 x 0.8 ft) meshsize at the location of concentratedloads is also worthwhile).

Plane Frame Model — A 5.0 m(16.4 ft) unit length of the cross section is modeled for each of the threestages of construction. By having theunit length of the cross section correspond to the spacing of compressionstruts, the model can be run both withand without compression struts tostudy the enveloping cases. A numberof different depths of cross sectionwith different locations of compression struts needs to be considered. Theeffects of concentrated wheel loads aredetermined by using influence surfaces as usual.

The individual elements are designed based on the results of the finiteelement analyses and the plane frameanalyses. These elements include thelongitudinal beams, the compressionstruts, the web reinforcement, and thetop slab transverse prestressing.

Longitudinal Beams — The twotriangular-shaped exterior longitudinalT-beams and one rectangular-shapedinterior longitudinal T-beam take theload from the deck and transfer itthrough the compression struts to theweb. The longitudinal beams thus reduce the deck spans in the transversedirection, which reduces the overallamount of prestressing and reinforcement in the deck. The longitudinalbeams are reinforced with flexural andshear reinforcement.

Compression Struts — The compression struts can consist of either324 mm (12.8 in.) diameter steel pipes(as described previously) having awall thickness of 13 mm (0.5 in.), or


Fig. 18. Transversetendon details.

I —

I —

I —

I —



400 x 400mm (15.7 x 15.7 in.) precastconcrete elements. They are designedfor the axial forces given by the analyses along with the corresponding shearforces and bending moments.

Web Reinforcement — The webreinforcement is designed for longitudinal shear and torsion (as previouslydescribed) in addition to web bending.Web bending is due to the unbalancedlive load being transmitted through thecompression struts to the webs. Themaximum inner face web bending inthe right web occurs when live loadsare placed on both cantilevers,whereas the maximum outer face webbending in the right web occurs whenthe live loads are placed on the rightcantilever as well as between the rect

angular-shaped interior longitudinal Tbeam and the right web. Influencelines have been found to be very useful in positioning live loads so as toproduce the maximum effects.

The finite element analyses haveshown that the maximum web bendingoccurs at the location of the strut, anddies out very quickly at any longitudinal distance away from the strut. It is,thus, recommended that additionalweb bending reinforcement be bandedlocally on either side of the strut in addition to the shear and torsion reinforcement. For this example, thismeans that inner face web bending requires an additional 13 No. 15M reinforcing bars (13 No. 5 bars) at 150mm (5.9 in.) centered about the strut

and bundled with the shear and torsionbars which are also spaced at 150 mm(5.9 in.). The web bending bars arethus placed 900 mm (3.0 ft) on eitherside of the strut. No additional outerface web bending reinforcement is required for this example.

Top Slab Transverse Prestressing— Fig. 18 shows the transverse prestressing tendon layout in plan andsection for the three stages of construction. Each tendon consists of fourstrands in a flat duct. There are twelvetransverse prestressing tendons in eachsegment. Three tendons are stressed inStage 1, three in Stage 2, and six inStage 3. The tendon profile is at thetop of the deck near the web for negative moment, and in the middle of the

C0)

II

_________ ________ ___________________________

IICC

_____

ZL__________(I) (1) U)

C 0 0o SEGMENT PLAN

U) U) U)


78 PCI JOURNAL

deck near midspan for both positiveand negative moment. The stressesand ultimate strength are checked atthe critical locations for all threestages of construction.

Another prestressing scheme to consider is banding the transverse tendonsin plan near the locations of the compression struts. In this way, there willbe more transverse tendons near thecompression struts and fewer transversetendons away from the compressionstruts. This will allow the transverseprestressing to more closely follow theresults of the finite element analyses.

The transverse prestressing ducts forthe Stages 2 and 3 widenings need tobe installed during Stages 1 and 2 construction. These plastic ducts need tobe protected against moisture intrusion,which can lead to freezing and cracking of the deck concrete. One suggestion is to fill the ducts with grease orfoam and cap the ends. The grease orfoam would be flushed out whenwidening occurs. Another suggestion isto place continuous foam backer rod inthe empty ducts for the entire length ofeach tendon and cap the ends. Freezingwater would simply compress thebacker rod and not crack the concrete.The backer rod would be removedwhen widening occurs. At any rate,protection of ducts for the Stages 2 and3 widenings is very important for thedurability of the structure.

Shear Lag

The AASHTO Segmental GuideSpecifications7state that the effectiveflange width may be determined (1)by elastic procedures such as the finiteelement method, (2) by provisionsgiven in the Ontario Highway BridgeDesign Code,8 or (3) by provisionsgiven in the AASHTO SegmentalGuide Specifications.

The overall efficiency of the crosssection predicted by the Ontario Codedrops from a range of 94.9 to 100.0percent in Example 1 to a range of60.5 to 97.1 percent in Example 2.This dramatic drop is expected becauseshear lag is more severe for wideshort-span bridges than for wide long-span bridges. The results validate theuse of the full cross section in the finaldesign for Example 1, and suggest that

Fig. 19. Deck drainage details.

the effective widths need to be reducedin the final design for Example 2. Inclining the compression struts in planas well as in elevation for shorter spanbridges may be a useful method for reducing the amount of shear lag.

Miscellaneous Details

Fig. 19 shows the deck drainage details for the three stages of construction. The Stage I scuppers are locatedto avoid both the longitudinal andtransverse tendon ducts. The deck





drain pipes dump water into an openhopper collector pipe. In wideningfrom Stages 1 to 3, the size of thescuppers and drain pipes increases.since the volume of water to bedrained increases as the deck area increases. The Stages I and 2 scuppersare abandoned in place by removingthe grating and carefully concretingthe remainder of the scupper.

Fig. 19 also shows that the barriercurbs have to be relocated for eachstage of construction. It is suggestedthat stainless steel dowels be used toattach the barrier curbs to the deck.The dowels can be cut flush with thedeck at the time of widening, andthere will not be any corrodable reinforcement near the deck surface.

ADVANTAGES ANDDISADVANTAGES

The SBWM is a valid bridge solution that has a wide range of applications, and it should be considered during the planning stages for any project.Consideration requires the carefulevaluation of both its advantages anddisadvantages, and an evaluation ofthe possible widening needs of thebridge in the future.

The advantages of the SBWM include the following:

1. Flexibility in widening — Thefinal configuration of the bridge at theconclusion of its useful life can betwo, three, or four lanes.

2. Structurally efficient solution —Examples 1 and 2 demonstrate that anincrease in superstructure moment andshear capacity of 10 and 14 percent,respectively, gives a 50 percent increase in traffic capacity (or 20 and 28percent, respectively, gives a 100 percent increase in traffic capacity).

3. Low initial cost — With respectto traditional bid projects, this solutionwill appeal to government agencieswho are under increasing pressure tomake their construction budgets gofurther. This will make sense to taxpayers who will not question why afour-lane bridge has been built whenhardly enough traffic exists for a two-lane bridge. With regard to design-build projects, this especially makes

sense because financing becomes soimportant. Why not pay for easily expanding the capacity of a design-buildbridge when it is required in 20 or 60years rather than today?

4. Reduced incremental cost andschedule — Widening existing bridgesto double the traffic capacity is betterthan building new bridges because theconstruction cost and schedule aregreatly reduced.

5. Reduced prestressing for cantilever construction The amount ofcantilever prestressing required forbalanced cantilever construction is reduced, since a two-lane wide deck iscantilevered rather than a four-lanewide deck. In other words, a 13.5 m(44.3 ft) deck is cantilevered ratherthan a 21.4 m (70.2 ft) deck.

6. Potential to satisfy FHWA performance objectives — When used inconjunction with high performanceconcrete, the SBWM has the potentialto satisfy all ten of the FHWA performance objectives9 for “The Bridge ofthe Future.” It readily satisfies the requirement “easily widened or adaptable to new demands,” and Reference10 discusses how it can be applied tosatisfy other FHWA performance objectives.

Some of the potential disadvantagesof the method include the following:

1. Increased design effort — Thedesigner has to design for three stagesof construction. By keeping the designfor each stage of construction independent, however, the additional amountof design work is not substantial.

2. Greater substructure capacity —The foundations and piers have to bedesigned to support the Stage 3 service loads. Balanced cantilever construction requires increased substructure capacity for unbalanced moments,so there already is adequate load capacity for the Stage 3 service loads(i.e., Examples 1 and 2). Span-by-spanconstruction (and other methods) normally require additional substructurecapacity in Stage 1 to support theStage 3 service loads.

3. Greater shear capacity Theshear reinforcement has to be providedin Stage 1 to support the Stage 3 service loads. For the two examples

given here, the additional shear capacity required in Stage 1 varies from18.3 percent for the variable-depthbridge having 160 m (525.0 ft) spans(Table 2) to 27.4 percent for the constant-depth bridge having 60 m (196.9ft) spans (Table 3). In the best-casescenario, the web thickness requiredfor Stage I and Stage 3 would be thesame, meaning that only additionalshear reinforcement would be required. In the worst-case scenario, alarger web thickness is required forStage 3 than for Stage 1, meaning thatthe additional concrete required for theweb would have to be supported byadditional shear reinforcing and longitudinal prestressing. This additionalconcrete, reinforcement, and prestressing is wasted if widening to Stage 3never occurs. [Note that in Example 2,the vertical component of the prestressing counteracts the demand foran increased web thickness, while inExample 1, an increased web thickness is provided — i.e., 450 versus500 mm (17.7 versus 19.7 in.).]

4. Provision for future prestressing— Although the strands and anchorages for the transverse internal tendons and longitudinal external tendons are installed and stressed inStage 2 and Stage 3 as they are required, provision for this future prestressing has to made in Stage 1. Thismeans that ducts for transverse tendons have to be installed and protected. This also means that blistersfor longitudinal tendon deviation andanchorage (as well as all anchoragezone reinforcement) have to be provided in Stage 1.

5. Possible need to close bridge during widening — If the erection trussdescribed in this paper is used, thebridge will have to be closed duringwidening. If moveable formwork attached to the web and cantilever isused, however, the bridge may notneed to be closed.

TWO POTENTIALAPPLICATIONS

Two potential applications of theSBWM are particularly appealing —namely, for major long-span river

80 PCI JOURNAL

crossings and for long median-basedexpressways.

Suppose that a major long-span rivercrossing needs to be designed and constructed. Present traffic estimates arethat the bridge requires only one lanein each direction (Stage 1). It will takea significant budget and constructioneffort to build this bridge. The ownercan construct this bridge to have thelowest initial cost, or can spendslightly more to allow the bridge to bewidened in the future to have twolanes in each direction (Stage 3).

Long portions of elevated medianbased expressways can be constructedin congested urban environmentswhere right-of-way acquisition is prohibitive. The elevated structure can beconstructed and widened in the future,as discussed in this paper, or it can beconstructed directly to its ultimateconfiguration (three or four lanes).The SBWM allows a very wide elevated superstructure [21.7 m (71.2 ft)]to be constructed while having a rela

REFERENCES

1. Podolny, W. Jr., and Muller, J. M., Construction and Design ofPrestressed Concrete Segmental Bridges, John Wiley & Sons,New York, NY, 1982.

2. CAN/CSA-S-6, “Design of Highway Bridges,” Canadian Standards Association, Toronto, Ontario, Canada, 1988.

3. CAN/CSA-S-6, “Canadian Highway Bridge Design Code,”CSA International, Toronto, Ontario, Canada, 2000.

4. AASHTO, “Standard Specifications for Highway Bridges,”17th Edition, American Association of State Highway andTransportation Officials, Washington, DC, 2002.

5. AASHTO, “AASHTO LRFD Bridge Design Specifications,”Second Edition, American Association of State Highway andTransportation Officials, Washington, DC, 1998.

6. Shushkewich, K. W., “Design of Segmental Bridges for Thermal Gradient,” PCI JOURNAL, V. 43, No. 4, July-August1998, pp. 120-137.

7. AASHTO, “Guide Specifications for Design and Constructionof Segmental Concrete Bridges,” Second Edition, AmericanAssociation of State Highway and Transportation Officials,Washington, DC, 1999.

8. OHBDC, “Ontario Highway Bridge Design Code,” Third Edition, Ontario Ministry of Transportation and Communications,Toronto, Ontario, Canada, 1991.

9. Chase, S. B., “The Bridge of the Future,” HPC Bridge Views,Issue No. 25, January/February 2003, published jointly by theFederal Highway Administration and the National ConcreteBridge Council.

10. Shushkewich, K. W., “Design and Construction of SegmentalBridges to Accommodate Future Widening Using the StruttedBox Widening Method,” Proceedings of the Third PCIIFHWAInternational Symposium on High Performance Concrete, Orlando, FL, October 19-22, 2003.

tively small substructure footprint in ACKNOWLEDGMENTSthe median.

CONCLUDING REMARKSThe strutted box widening method

(SBWM) introduced in this paper allows a two-lane segmental bridge tobe designed and constructed so that itcan be easily widened into a three-laneor four-lane bridge at any time in thefuture. This is an attractive solutionsince widening only needs to be donewhen and if traffic volumes warrant it.

The author believes that the struttedbox widening method should be givenserious consideration by governmentagencies and design-build consortiastarting at the planning stage on anyproject. It is an excellent solution forbuilding an economic and efficientbridge to handle current traffic volumes, while at the same time planningahead to build cost-effective andschedule-effective bridge widenings tohandle future traffic volumes.

The author would like to express hisgratitude to Stantec Consulting andAlberta Transportation for allowinghim to design the three-span concretealternate for the North SaskatchewanRiver Bridge in Edmonton, Canada,using the strutted box wideningmethod, as an independent consultantto Stantec Consulting. The authorwould like to thank Les Hempsey, RegQuinton, Bill van der Meer, and Raymond Yu of Alberta Transportation,along with Carl Clayton of StantecConsulting and Ken Rebel, formerlyof Earth Tech, for their interest andsupport. The author would like tothank his colleague Christophe Deniaud of Stantec Consulting, who did thebulk of the analysis on the NorthSaskatchewan River Bridge.

The author also wishes to expresshis appreciation to the PCI JOURNALreviewers for their valuable and constructive conunents.


Documents

64 PCI JOURNAL Journal... · 2018. 11. 1. · 2, and 3 construction is indicated in Fig. 3. Bridge elevation (Example 1). 450 I 2500, 3700 [J 13800 SHOULDERLANE 3000 I 450 LANE SECTION