study of long span prestressed concrete bridge girders

7/21/2019 STUDY OF LONG SPAN PRESTRESSED CONCRETE BRIDGE GIRDERS

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STUDY OF LONG SPAN

PRESTRESSED CONCRETE

BRIDG E GIRDERS

Francis

J

Jacques P.E.

restressed

Concrete of C olorado, Inc.

Denver, Colorado

New safety standards for inter-

state and other high speed highways,

adopted by the AASHO Committee

on Bridges and Structures, recom-

mend that the righthand piers on

undercrossings be eliminated and

that 30 ft. (9m) minimum lateral

clearances on either side of all travel

lanes be provided.

Compliance with these criteria on

a two-way, four-lane undercrossing

requires a girder span of 112 ft.

(34m) for a right angle crossing. The

span increases to 160 ft. (49m) for

a 45 deg. skew crossing.

Following the same criteria on

one-way, two-lane undercrossings

the required girder span becomes

130 ft. (40m) for a right angle cross-

ing and increases to 175 ft. (53m)

for a 45 deg. skew crossing.

The Iargest prestressed girder

presently being built in the Colorado

area is a Type IV AASHO which

will economically span about 105 ft.

(32m). Thus, it became obvious that

if the prestressed industry in the

Colorado area intended to continue

to participate in the bridge girder

business, it had to develop a new

standard girder section or system of

precast girder segments that would

economically span about 150 ft.

46m).

PRESENT STATE OF THE ART

Long span girders

Standard long

span girder sections already being

Table 1. Standard girder sections

Section

Recommended span range, ft.

AASHO Type IV

70 to 105 (21-32m)

AASHO Type V

90 to 120 (27-37m)

AASHO Type VI

110 to 140 (34-43m)

Oregon Section

100 to 140 (30-43m)

Washington 100 Series

100 to 120 (30-37m )

Washington 120 Series

110 to 140 (34-43m)

24

CI Journal



This paper reports on the development of a new Colorado standard

bridge girder section. Computer programs are developed on

final girder designs and final bridge costs.

Nine girder sections are studied in depth, including four proposed

Colorado standard sections. Data are developed for both stone and

lightweight concrete girders with concrete strengths varying from

5000 to 7000 psi 350 to 490 kg/cm2).

used in other parts of the country

are shown in Table 1.

Also, it should be noted that the

maximum recommended spans can

be exceeded by utilizing very close

girder spacings, high strength con-

crete, or lightweight concrete.

Span shortening systems.

Schemes to

reduce effective girder spans were

surveyed.

Fig. la shows an inverted A-frame

center pier used to shorten the main

spans from 130 to 115 ft.

40 to 35m).

Fig. lb shows a 40 ft. 12m) long

cantilevered center girder that al-

lows the use of two 110 ft. 34m)

drop in girders.

Fig. lc shows the end piers ex-

tending into the roadway to shorten

the effective main girder span. This

solution has been used extensively

in Canada.

Other studies

Recently, the Pre-

stressed Concrete Institute commis-

sioned the consulting firm of T. Y.

Lin, Kulka, Yang Associate to

prepare a study

° on long span pre-

Prestressed Concrete for Long Span

Bridges, Prestressed Concrete Institute,

1968,

44 pp.

stressed concrete bridges. The study

emphasized segmental construction

and the necessary joint details. This

system utilizes relatively short girder

sections that are precast at a plant

and hauled to the site where they

are either preassembled and erected

into place, or assembled as they are

being erected. To attain moment

capacity at the joints, the connec-

tions employ cast-in-place concrete

and on-site post-tensioning.

Our past experience with field

splices requiring forming, concreting

and post-tensioning has been less

than satisfactory. Also, we noted

that when construction was over

existing highways, traffic hazards

frequently resulted from the re-

quired shoring. For these and other

reasons we chose to pursue a some-

what different solution to the prob-

lem of providing long span capa-

bilities using precast prestressed

construction.

STUDY CRITERIA

Although considerable informa-

tion was already available on the

various bridge . sections being used

around the country, the question

March April 1971

5



26

f 15

5 f.I5'

15

(a) INVERTED A - FRAME CENTER PIER

260'

<

1

10

110

(b) CANTILEVERED CENTER GIRDER

I60'-O'

30----

00' —

—3

(c) END PIERS EXTENDING INTO ROADWAY

Fig. 1. Span shortening systems

remained: just which section would

prove to be the most econom ical and

the most practical for our use? We

determined that if our solution was

to be lasting and far reaching it

must meet all of the following cri-

teria:

Practicability

Realistic concrete strengths, 6000

psi (420 kg/cm

2

) consistently, per-

haps up to 7000 psi (490 kg /cm2).

Realistic size and weight limits

for precast girders (see Table 2).

Safety

The use of a single unit precast

section appears desirable since it

can span existing roadways with-

out shoring. This eliminates the

inherent shoring hazards.

Esthetics

It appears desirable to eliminate

26

CI Journal



Table 2. Girder size and weight limits

Condition

Size

Weight

Yard handling

No problems

80T 73,000 kg) cranes available

4-40T (36,000 kg) Drott Travel Lifts

Over-road hauling

Have hauled 130 ft.

Allowed 26k (12,000 kg) gross/axle

(40m) lengths—can

5 axles = 95k (43,000 kg) payload

go farther with rear

7 axles = 130k (59,000 kg) payload

steering

Field erection

No problems

140T 127,000 kg) cranes available

the stubby end blocks such as on

the old AASHO sections. Note the

esthetically pleasing appearance

of the end blocks on the Washing-

ton 120 Series girders shown in

Fig. 2.

Also, it seems desirable to elimi-

nate the possibility of texture

blemishes that can result from

field splices.

onomy

The cost of field splicing, in all

cases, appears to be an added cost

Fig. 2. Erecting Washington 120 Series

girders

M arch-Apri l 1971

7



X11-8 r-

4'-6°'

-

,i 2_2 1.

A A SHO Typ e IV

70ft. -

I00ft.

5L3

° °

-'► 2= 4'

I^ -

AASHO Type V

90ft. - I20ft.

IE-3L 6

6'-O°

8

-I 2°-4 1-

AASHO Type VI

1I0ff. - I40ft

4'-O H

T

6 - O

6 ° °

2°-2

k

OREGON SECT.

I00ft - 140ft.

H_2'-O-

4'-1O'1 k-5

-12°O1

WASHINGTON

12(

-^} 2'-4°°It-

6'-W2'

-1

2 °

O,°k

100 S

I

WASH.120 S

)ft.

IIOft. 140ft.

-

^

I 2

-

4

i^ -

5L6

° °

--I 2 '-2 I

C O L O . G 6 6

100 ft. -115 ft.

-^ 2 ' 4°°

IE -

6' 0°°

° °

H 2'-2 k--

COLO. G. 72

105 ft. -

135ft.

^ 21

4°°IF-

6L8 )]

5 ° °

H 2°-2°°H

COLO. G 80

IIOft. - 150ft.

Fig. 3. Girder sections in study

28

CI Journal



that can be justified only if a

single piece section can not be

hauled over-road to the site.

Thus, the author, acting as Chair-

man of the Code and Specifications

Committee of the Colorado Pre-

stressers Association, with the assis-

tance of Mr. Eric Brinkman of

Rocky Mountain Prestress and Mr.

Stan Ruden of Prestressed Concrete

of Colorado, established a more or

less formal goal for the study: To

develop a simple span bridge girder

that will safely and economically

span 150 ft. (46 m) carrying AASHO

HS20-44 loading.

SCOPE OF THE PROGRAM

Girder Sections Nine separate gir-

der sections, shown in Fig. 3, were

selected for detailed study. These

included three AASHO Sections—

Types IV, V and VI; two Washing-

ton State Sections—Series 100 and

120; one Oregon Section; and three

proposed Colorado Sections—G-66,

G-72 and G-80.

Spacing and spans. From the start

we felt it was necessary to make a

cost study that compared final costs

on the basis of total bridge costs

for variable girder spacing and spans,

rather than comparing girder costs

alone. This is due to the fact that

the size of the girder section controls

other factors in the design of the

structure. Generally a relatively deep

girder is capable of carrying a great-

er payload moment when com-

pared to a shallow girder for a given

span and loading. This allows the

deeper girders to be spaced farther

apart than the shallower girders and

results in fewer girders per width of

bridge, but does require a thicker

deck slab with more reinforcement.

Also, the deeper girders require

additional embankment on the road-

way approaches if the minimum

clearance from girders to the road-

way below is to be maintained.

Concrete strengths and type It ap-

peared desirable to provide for vari-

ations in material properties. Two

girder concrete strengths, f^=

6000 and 7000 psi (420 and 490 kg/

cm 2 ), were deemed necessary. Also,

it appeared desirable to use both

lightweight concrete and stone con-

crete in the girders.

At this time it was assumed that

the strength of the cast-in-place deck

concrete would be the same regard-

less of the strength of girder con-

crete, and that only stone concrete

decks would be considered. It was

determined that the thickness of the

cast-in-place deck could be held

constant for a given range of girder

spacings in accordance with the

Colorado Division of Highways

Standards shown in Table 3.

Note that the effective deck thick-

ness is taken as

1/z in. (1 cm) less than

the actual thickness to provide an

integral concrete wearing surface.

Table

3.

Deck thickness vs. girder spacing

Girder Spacing

Deck Thickness, in.

Actual

Effective

6.0 (15cm)

6.5 (17cm)

7.0 (18cm )

7.5 (19cm)

8.0 (20cm )

5.5 (14cm)

6.0 (15cm )

6.5 (17cm )

7.0 (18cm )

7.5 (19cm )

3'-0 to

'-6 (0.9-2.0m)

6'-6 to

' -0 (2.0-2.4m)

8'-0 to

' -0 (2.4-2.7m)

9'-0 to 10'-0 (2.7-3.0m)

10'-0 to 12'-0 (3.0-3.7m)

March April 1971

9



Table 4. Design variable summary

Parameter

Range

Increment

Resulting Numbers

of Variables

Girder sections

9 Sections

9

Girder spacing

3 to 12 ft.

2 ft. (0.6m )

5

(0.9-3.7m)

Spans

90 to 150 f t.

5 ft. (1.5m )

13

(27-46m)

Concrete strengths

6.0 to 7.0 ks i

1.0 ksi 70 kg/cm

2

(420-490 kg/cm2)

Concrete types

Stone or

2

lightweight

Total number of required designs = 9 x 5 x 13 x 2 x 2=

2340

Provision for all of the above vari-

ables resulted in 2340 possible total

number of bridge and girder de-

signs (see Table 4).

Faced with such a large scope of

desired information, we elected to

use electronic computer methods to

develop and analyze the data. Two

computer programs were developed:

1.

A Universal Bridge Girder De-

sign Chart Program

2. A Universal Bridge Costing

Program.

UNIVERSAL BRIDGE GIRDER DESIGN

CHART PROGRAM

A typical design chart is shown

in Fig. 4. Fig. 5 shows the printout

record of input data and tabulation

of end and harping point strand

eccentricities. Fig. 6 shows a tabula-

tion of section properties for both

the non-composite and composite

sections.

Fixed criteria In computing the

composite section properties and in

checking ultimate strength, the ef-

fective width of the deck flange is

limited by the following in accor-

dance with the AASHO specifica-

tions*:

1.

One-fourth of the girder span

length

2.

Center to center distance of

girders

3.

Twelve times the least thick-

ness (effective thickness) of the

slab plus the width of the girder

stem.

Also, the effective deck flange

width is further reduced for section

property calculations by multiplying

the initial effective width by the

ratio of the modulus of elasticity

of the cast-in-place deck concrete

to that of the precast girder. Ra-

tional values for modulus of elastic-

ity are computed by the equation

taken from the ACI Standard Build-

ing Code Requirements for Rein-

forced Concrete:

E 1.5

f

where

w = unit weight of concrete (pcf)

= 28-day compressive strength

psi)

° Standard Specif ications for Highway

Bridges, American Association of State

Highway Officials, Tenth Edition,

1969.

30

CI Journal



e

S

G

F

=

3

0

K

S

I

A

L

F

U

P

S

E

T

=

0

0

I

N

B

2

2

P

S

I

F

C

1

^

Q

w C

N

N

^

r

^

G

^

D

O

C

Q

a

r

t

Z

y

f

p

nS



COLO. SECTION G-80 -SILINE

RECORD 11 INPUT DATA

PRECAST CONCRETE

;IT W11GHT

150.0

PCF

STRLNGTH

6.0 KS1

L

4696.0

K5I

AS/STRAND

0.1531 IN-2

Ft 601 PRESTRESS

23.55

KIPS/STRAND

F S-PR IME

270.0

PSI

N = F CIP)/E PHECAST)

0.707

C-I-P COMPOSITE DECK CUNCRF TE

UNIT WEIGHT

150.0 PCF

STRENGTH

3.0 KSI

L

3320.0 KSI

CREEP FACTOR

1.5

LOAD FACTOR

T.5D+2.5 L+I)

IMPACT FACTOR I

50/ L+125)

TOTAL WEIGHT CURB SIDEWALK K RAILINGS

ETC. = 0.050KLF/GIRDER

PRESTRESSED

STRAND

LOCATION

FINAL

POST,

READ.

RELEPSL

ECCENTRICITY-INCHES

HARPING

POINT

NO.

OF

FORCE

F

STRENGTH

P -------------------

LOCATION FROM

STRANDS

KIPS ENDS

PS I

ENDS

HARPING

pT.

EACH END

12 282.6 1812

32.32

39.13

0.490L

14

329.7

2055

30.82

38.05

0.487L

16

376.8

2298

29.69

37,84

0.485L

18

423.9

2542

28.81

37.68 0.483L

2 0

471.0

2785

28.11

37.55

0.482L

2 2

518.1 3028

27.54

37.44 0.481L

2 4 565.2

3272

27.06

37,35

0.480L

2 6

612.3

3515

26,65

37.28

0.479L

2 8 659,4

3759

26,31

37.21 0,478L

30 706.5 4002

26,00

37.12

0.477L

32

753.6 4245

25,74

36.96

0.477L

34

800,1

4400 24.57

36,83

0,474L

36

847,8

4400 21,99

36.70 0.469L

38

894,9

4400

19.68

36,59

0.464L

4U

942.0

4400

17,60

36,50

0.459L

4 2

989.1

4400

15,72

36.41

0.454L

44

1036.2

4400

14,00

36,27

0.45OL

46

1083.3

4400 12.44

36.13

0.446L

48 1130.4

4400

11.01

35.99

0.442L

Fig. 5. Typical printout of input data and strand eccentricities

Loading

Live load-AASHO HS20-44 (truck

or lane whichever governs)

Dead load-as computed account-

ing for:

1. Girder weight

2. Deck concrete in accordance

with Table 3

3.

Diaphragms at 40 ft. (12 m)

maximum spacing. Diaphragms

are 8 in. (20 cm) thick and

s

gir-

der depth. (Note the slight jump

in the girder spacing curves in

Fig. 4 at 80, 120 and 160 ft. (24, 37

and 49 m) as diaphragms are

added.)

Strand

½-in. dia. (1.3 cm), 270K strand,

harped near midspan. Final prestress

per strand = 23.55k (10,700 kg).

1.

Harping point located by the

program to envelop the moment

diagram.

2.

Minimum strand spacing at the

ends of the girder set at 1

/4

in.

(4.4 cm).

3.

Eccentricity at ends located to

be maximum while meeting the

following criteria:

a.

Limit tension in the con-

crete at the top of the

girder to 3 f

6

b.

Limit bottom compression

to the smaller of 0.4

r

0 6

f

c.

The actual hole spacing

available at the ends.

A tabulation of eccentricities vs.

num bers of strands is in Fig. 5.

PCI Journal



C

COLO. SECTION G-80 -STONE

SECTION PROPERTIES

PRECAST GIRDER

DEPTH WT,/FT.

AREA

Y-TOP

Y-RUT

S-TOP

S-BOT

IN)

KIPS)

IN-2)

IN)

IN)

IN-4)

IN-3)

I

- 3)

90.0

0.737

707.5

40.12

39.88

618675.0

15420.4

15513.6

PRECAS1

GIRDER

WITH

CDNPOSITE

SLAP

GIRDER

SLAB

THICKNESSPIN, SLAP

WIDTH

SPACING ------------------

EFFECTIVE YC-TOP

YC-H T IC

SC-TOP

SC-130T

FT)

TDTAJ

EFFECTIVE IN)

IN)

I`^)

IN-4)

IN-3)

IN-3)

3.0

6.0

5.5

36.0 38.54

46,96

833799,9 21635.3

17755,1

3,5

6,0

5.5

42.0

37.58

47,92

862940.9 22962.7

18008,0

4,0 6.0

5.5 48.0

36.67

48,83

890564.3

24285.0

18238.5

4.5

6.0

5,5

54.0

35.81

49.69

916785.8

25602.3

18449,6

5.0

6.0

5,5

60.0 34,99

50,51

941709,7

26914.5

18643.6

s.5

6.0

5,5

66,0

34,21

51,29

965430.2

28221.7

18822,5

c.0

6.0 5,5

71.0 33.59

51.91

984339.8

29307.2

18961,3

6,5

6.0

5,5

7100

33,59

51,91

984339.8 29307.2

18961.3

6.5 6.5

6.0

77.0

32.50

53,50 1035146.3 31850.0

19348,8

7,0

6.5

6,0 77.0

32.50

53.50

1035146.3

31850.0

19348.8

7.5

6.5

6,0

77.0 32,50

53,50

1035146.3

31850.0

19348,8

N,0

6,5

6.0

77.0 32.50

53,50

1035146.3

31850.0

19348,8

8,0

7,0

6,5

83.0

31,43

55.07 1086152.6

34559.3

19722,7

8.5

7.0

6,5

83.0

31.43

55.07

1086152.6

34559.3

19722,7

9.0

1.0

6.5

83.0 31.43

55,07 1086152.6

34559.3

19722.7

9.0

7.5

7,0

89.0

30.38

56,62 1136975.8 37420.6

20082,1

9,5

7.5

7.0

89.0

30.38

56.62 1136975.8

37420,6

20082,1

10.0

7.5

7,0

89.0

30.38

56.62 1136975.8

37420.6

20082,1

10,0

8.0

7,5

95.0

29.38

58.1,2 1187316.2

40418.9

20427.0

10.5

8,r)

7.5

95.0

29.38

58.12 1187316.2

40418.9

20427,0

11.0 8.0 7,5 95.0

29.38 58,12 1187316,2

40418.9

20427,0

11.5

8.0

7,5

95.0

29.38

58.12 1187316.2

40418.9

20427,0

12.0

8,0

7,5

95.0

29.38

58,12

1187316.2

40418,9

20427.0

Fig. 6. Typical printout of section properties



L

U

WW

U

W

Hc

Q

Wm

U Q

N

3

a

O

<

O

C

0

7

6

N

O

U

Q

C

r

t

m

G

F F F

S

P

R

F

O

C

A

U

P

S

E

T

=

C

O

N

C

R

E

T

E

S

T

R

E

N

G

T

H

S

L B

2

1

2

P

S

I

C 0

u



Girder spacing

Varied from a minimum of 3 ft.

(0.9 m) to a maximum of 12 ft. (3.7

m) in 6 in. (15 cm) increments. This

should insure sufficient range to

meet any desired girder spacing.

Variab le criteria

The following vari-

able criteria are input for each run

of the program:

1.

Concrete strength, type and

weight for both the girder and

deck.

2.

Superimposed load to allow for

the weight of curbs, sidewalks,

railings and asphalt overlay.

3.

Allowable final bottom tension.

4.

Minimum and maximum spans.

Charts. Each bridge girder design

chart consists of overlays of five

families of curves all plotted on axes

of initial camber vs. span.

1.

Camber curves—labeled 121/2,

16

/z, etc.

2.

Release strength curves—la-

beled f = 3000, 3500, etc.

3.

Initial top tension curves—la-

beled ZERO TOP TENSION, etc.

4.

Girder spacing curves—labeled

3'-0 , 4'-0 , etc.

5.

Girder concrete strength

curves—labeled

f

5000, 5500,

etc.

Design concrete strengths for both

the deck slab and the girder are

assigned (see lower left hand corner

of Fig. 4). These values are then

used in computing the ratio of

E0

deck

u

girder; in computing final

ultimate strength capacities; in de-

termining the assigned values to be

used in computing the girder top

tension curves; and in setting the

maximum end eccentricities (han-

dled by the automatic process within

the program).

The charts allow a designer to

pick out a complete girder design

directly from the graphs for any

combination of span and girder

spacing for the assigned material

and design criteria shown at the

bottom of the chart.

EXAMPLES

Some sample problems probably

best explain the use of the charts

(see Fig. 7).

Problem No. 1

Required:

Complete design for a Colorado

G-80, stone concrete girder span-

ning 144 ft. (44 m) with girders

spaced at 6 ft. (1.8 m) centers.

Bridge is to carry AASHO HS20-

44 loading.

Solution:

Number of ½-in. dia. 270K strand

required = 40.

Harping points and eccentricities

as in Fig. 5.

Camber at erection = 2.35 in. ( 6

cm) above level.

Release strength required for

girder,

3500 psi 250 kg/

cm2 ) .

Final concrete strength required

for girder,

f

==

6500 psi (460 kg/

cm2).

Initial top tension in the girder—

no problem.

Deck slab thickness required =

6 in. 15 cm).

Problem No. 2

Required:

For maximum allowable girder

concrete strength, = 7000 psi

(490 kg/cm

2 ) , and given a mini-

mum girder spacing of 6 ft.

(1.8 m) , find maximum allowable

span.

Solution:

Maximum girder span = 150 ft.

(45m).

Problem No. 3

Required:.

Given a span of 116 ft. (35 m) and

a maximum allowable release

March April 1971

5



Table 5. Hauling costs

Weight

Girder Length

Hauling Rate

Equipment Premium

95k 43,200kg) or less

130 ft. 40m ) or less

Standard

None

95k or less

Over 130 ft.

High

Steering trailer

Over 95k

130 ft. or less

Standard

2 extra axles

Over 95k

Over 130 ft.

High

Steering trailer

and 1 extra axle

strength of 5000 psi (350 kg/cm

),

find the maximum permissible

girder spacing.

Solution:

Maximum girder spacing = 11 ft.

(3.4m).

STUDY PROCEDURE

Universal bridge girder design

charts were prepared for the nine

girder sections shown in Fig. 3

for the assigned study criteria. Ma-

terial properties are shown on the

bottom of the chart in Fig. 4.

Next a standard two-span bridge

with a width of 44 ft. 6 in. (13.6 m)

(42 ft. (12.8 m) curb to curb) was

selected as a fairly typical structure.

Six different girder spacings varying

from 4 girders per bridge (11 ft. 6 in.

(3.5 m) girder spacing) to 9 girders

per bridge (5 ft. (1.5 m) girder spac-

ing) were chosen. This permitted

final designs to be tabulated at 5 ft.

(1.5 m) increments of span length

for the six different girder spacings.

Maximum spans are limited to that

span requiring a girder release

strength of 5000 psi (350 kg/cm

) or

a final girder concrete strength of

6000 psi (420 kg/cm

), whichever

governs.

Cost programs. The first cost pro-

gram was developed to estimate ac-

curately the selling cost of the girder

BRIDGE QUA NTITY AND COST SU•14ARY

IT

g

4

QUANTITY

COST

UNIT COST

STRUCTURE EXCAVATION

119.147 CU.YD.® 3.00 357.442

0.035

STRUCTURE BAC (FILL 1

433.434 CU.YD..@ 3.50

1517.02

0.1.5

ST1:a IPILING(10BP42)

120 LIN.F.T:@S6.00

720

0.071

STEELIPILING (129P53)

884.534 LIN.FT.® 7.10

6280.19

0.623

03NCRETE SLOPE PAVING

67 CU.YD.S 46.00

3216

0.319

STEEL IF (ANDRAIL I

530.5 LIN.FT.8 14.04

7448.22

0.738

D V P P R0 0F ING

1306.76 S9.YD.4S0.223

291.407

0.028

PREM. EXPANSION DE V.

126 LiN.FT.® 55.00

6930

0.687

CONC RETE (CLASS A )

162.607 CU.YD. ® 59.00 9593.84

0.951

CON CRETE (CLASS D)

231.018 CU.YD.®569.00

15940.2

1+581

.REINFORCING STEEL

100558. LBS.0 0.13

13072.5

1.296

PREST. CONC.UNIT

18 EACH @ 3198.

57564.

5:71071

T®TAL(ESTIMATED STRUCTURE COST

122931+

AREA OF STRUCTURE (CUB-CURS)

10080 S6.FT.

ESTIMATED STRUCTUR E CO ST PER SOFT.

12.1955

E S T IM A T E D A D D E D E I B A N l9 1 E N T C O S T D U E T O

BEAM DEEPER THAN AASHO TYPE-IV =: 1516.67

Fig. 8. Typical printout of bridge costs

36

PCI Journal



U

o

07

O

1350

R

OTAL BRIDGE COST PER SQ. FT.

13.00 \

1250\\

,̂ -9 (5 -̂0 )

5 -6°)

6 -611 )

4

Grders / \ \̂ ^

Bridge

(1I-6 Spa.)

9.50

.

80 90 100 110

1 2 0 1 2 5

130 140 150

SPAN LENGTH, FEET

Fig. 9. Bridge cos ts fo r a Colo rado G -80 girder

12.00

11.50

11.00

10.50

10.00

6(7-6 )

-- 5(9 -0°)

OPTIMUM GIRDER SPACING

COST CURVE

delivered to the job site and erected

in place.

Yard

selling

cost. No problem since

we already had considerable costing

experience for similar members.

Hauling costs .

Varied according to

a schedule that provided for both

extreme lengths nd extreme

weights in accordance with Table 5.

Erection

costs. Varied according to

weight:

1.

Light girders, 100k 45,500 kg)

or less—standard cost

2.

Heavy girders, over 100k—pre-

mium cost.

Total bridge costs. We next devel-

oped a program that included the

abutment and center pier design for

a typical 90 deg. crossing for each

bridge in accordance with the Colo-

rado Division of Highways Stan-

dards. The program computes all

the necessary quantities, extends the

unit costs and develops a total cost

per square foot. All unit costs, with

the exception of girder costs, are in

accordance with the latest tabula-

tion of yearly cost averages pre-

pared annually by the Colorado Di-

vision of Highways with a provision

to include a suitable escalation mul-

tiplier. See Fig. 8 for a typical print-

out of the costing program.

The effect of added embankment

costs are shown near the bottom of

Fig. 8. The additional embankment

costs are relative to an AASHO Type

IV girder with a depth of 4 ft. 6 in.

(1.4m).

March April 1971

7



TOTAL BRIDGE COST PER : SQ. FT.

/© AASHO

TYPE

OJ

TYPE

Hy?

:-TYPE

12.50

_̂

12.00

f^

GIRDER WT.

-

= 130 K

.50 ̂ _•^

/1

/I

/

0

C OLO. G-80

IRDER WT

NOTE:

13 K̂

//

LL GIRDERS SHOWN HAVE

i

SAME CONCRETE PROPERTIES

J

••

6 Oksi

,i=5.Oksi

10.50

COLO. G

-72y^̂

3.0 ksi

0 •

STONE©i

cslab°

® --

/^

WASHINGTON

10.00 OREGON\̂ -̂ -̂

120

SERIES

G

-72

9.50

80

90 100 110

120 130 140 150 160

SPAN LENGTH, FEET

Fig. 10. Optimum girder spacing cost curves for seven stone concrete girders

TOTAL BRIDGE COST PER SQ.FT.

12.50

COLO.

C OLO. G

8

G 80

LIGHTWEIGHT

COLO

TOSTONE /

1

2.00

STON

LL

11.50

11.00

/̂

1050

-COLO.G-80

o1000

LIGHTWEIGHT

.50

80 90

00 110 120 130 140 150 160 170

SPAN LENGTH, FEET

Fig. 11. Optimum girder spacing cost curves for one girder type with variable

concrete properties

38

CI Journal



COLORADO

G 80

L,__.,

6'-E

COLORADO G 80 A

V 2

OPTIMUM GIRDER SPACING

COST CURVES

Using the data generated from the

two cost programs above, curves

showing total bridge costs vs. span

are plotted for the various girder

spacings studied.

A sample plot for a Colorado G-

80 girder is shown in Fig. 9. When

the end points on each spacing curve

are connected, a smooth curve is

formed that represents costs for op-

timum girder spacing. For example,

if a span of 125 ft. (38m) were re-

quired, we could use a girder spac-

ing of 8 ft. 3 in. (2.5m) most eco-

nomically.

For each type of girder, the best

economy was achieved when opti-

mum girder spacing was used, that

is, when the girder spacing was kept

to a maximum for a given span. This

optimum girder spacing cost curve

was found to be uniquely suitable

for comparing costs on all the vari-

ous girder sections studied.

R SU TS

Optimum girder spacing cost

curves were developed for stone

concrete girders for all nine cross

sections studied for fixed material

criteria of:

irder = 6.0 ksi (420 kg/cm2)

f ,

girder = 5.0 ksi (350 kg/cm2)

slab = 3.0 ksi (210 kg/cm2)

Seven of these curves are plotted

in Fig. 10 for easy comparison.

We also prepared curves for light-

Fig. 12. Comparison of Colorado girder sections

March Apri l 1971

39



I

_

W

n

n

pC

n

C

Q

0

0

0

o

Q

C

o

C

D

.

o

0 C

_

n

o

L

U

WW

C

C

o

w

Q

w

m Q

¢

O

2

3

4

5

6

7

V

S

G

I

R

D

E

R

S

P

R

C

I

N

G

9

P

C

=

F

C

S

L

A

B

=

3

0

K

S

I

A

S

P

H

A

L

T

S

U

R

F

=

2

0

P

S

F

L

O

R

D

I

N

G

R

F

=

6

0

K

S

I

U

P

S

E

T

=

0

0

I

N

B

2

3

2

P

S

I

F

I

B

O



TOTAL BRIDGE COST PER SQ. FT.

12.50

12.00

COLO.

G 80

STONE

i

11.50

6

WS

12

II

ii .

00

;_j//

'

COLO. G-8O

Cr 10.50

NOTE:

a

LL GIRDERS SHOWN H VE

p

0.0

SAME CONC RETE PROPERTIES

f^=6.Oksi

fCi=5.Oksi

fcsIab=3.Oksi

9.50

80

0

00

1 0

20

30

140

50

60

70

SPAN LENGTH, FEET

Fig. 14. Optimum girder spacing cost curves for three stone concrete girders

weight concrete girders (110 pcf)

(1760 kg/m

3

) for the Colorado G-

80 using the same girder and slab

strengths. Next we investigated the

effects of increasing the concrete

strengths in the girder and slab by

1000 psi (70 kg/cm

2

) for both stone

and lightweight girders. These re-

sults are shown in Fig. 11. Curves

7 and 8 are for concrete strengths of:


f ^girder = 5.0 ksi (350 kg/cm2)

f

slab = 3.0 ksi (210 kg/cm2)

Curves 9 and 10 are for concrete

strengths of:


f,

girder = 5.5 ksi (390 kg/cm2)

lab = 4.0 ksi (280 kg/cm

)

Our first surprise came when we

observed that the Washington 120

Series girder (represented by Curve

5, Fig. 10), which is 73

/2

in. (1.87 m)

in total depth, was almost as effi-

cient as our proposed Colorado G-

80 (Curve 7), which was 80 in.

(2.03 m) total depth. We had a 9

percent increase in depth but only

a 2 to 3 percent increase in span

capability.

After a careful study of the de-

sign charts for both the Colorado

G-80 and the Washington 120 Series

girders, we observed that the con-

trolling criteria for maximum span

for the Colorado section was always

the final concrete strength required

for the girder,

f = 6

psi (420

kg/cm

2

)—see design chart, Fig. 4.

The maximum release strength cri-

teria,

5000 psi (350 kg/cm2),

never controlled. In reviewing the

design chart for the Washington 120

Series girder, it was noted that this

section was better balanced . Re-

March April 1971

1



lease strengths controlled the shorter

spans and final girder concrete

strengths controlled the longer

spans. It soon became evident that

the Colorado G-80 was an unbal-

anced section. The bottom flange

contained too much concrete rela-

tive to the top flange. The cross

section of the girder was modified

to arrive at a more balanced sec-

tion—the Colorado G-80A. A com-

parison of the cross-sections of the

two girders is shown in Fig. 12.

The design chart for the G-80A

girder is shown in Fig. 13. Note

that the revision in the shape or

balance of the cross-section (actu-

ally resulting in a slight reduction in

cross-sectional area) yields a span

increase of about 10 ft. (3 m) . Its

optimum cost curve, Curve 11, is

compared to the Colorado G-80 and

the Washington 120 Series girders

in Fig. 14.

SUMMARY

Drawing from the information de-

veloped in this study, the Colorado

Division of Highways has adopted

a new Colorado standard girder sec-

tion, the G-68. This is an intermedi-

ate depth girder capable of span-

ning about 130 ft. (40 m) . Following

general use of this section, a second

standard, the G-80 (actually using

the cross section of the study's G-

80A), will be introduced.

Girder design charts providing for

various combinations of concrete

strengths, external superimposed

loads, and wearing surface systems

have been prepared for the G-68

and are now being used for pre-

liminary designs by the Colorado

Division of Highways.

A new girder section has been

born.

Discussion of this paper is invited. Please forward your discussion to PCI Headquarters

by July 1 to permit publication in the July August 1971 issue of the PCI JOURNAL.

42

CI Journal

study of long span prestressed concrete bridge girders

Documents