University of Illinois at Urbana-Champaign

Big Beam Team

1

PCI

Big Beam Contest

University of Illinois at Urbana-Champaign

Team:

Jonathan Godfrey

Shaoyun Sun

Melissa White

Faculty Advisor:

Professor Daniel Kuchma

June 1, 2003

University of Illinois at Urbana-Champaign

Big Beam Team

2

1.0 Introduction

The University of Illinois at Urbana-Champaign offers a course in experimental

methods in structures and materials to seniors and graduate students in civil engineering.

Three students participating in this course, with the support of our faculty advisor, chose

to combine their diverse backgrounds and skills into a final project and entry into the PCI

Big Beam competition. This year’s Big Beam Team drew upon previous years’ design

models and our own structural design, analysis, and concrete mix design knowledge to

produce a strong, light, and relatively ductile beam.

2.0 Objective

The objective of the project was to work as a team to design, produce, and test an

efficient reinforced concrete beam that would maximize strength-to-weight ratio and

ductility, and to accurately predict its strength properties. The design process focused on

reducing the mass of the cross section while maintaining a high ultimate load capacity. It

was important to maximize the usefulness of each pound of material placed into the beam

because any superfluous weight would essentially count against the result in a

competition. Additionally, the decision to use a high-performance concrete requires extra

care in all aspects of mixture proportioning; including maximum aggregate size, paste

content, water-cement ratio, and any pozzolans or other admixtures that might be used.

Production and testing of the beam also tested the hands-on skills of each participant,

bringing the challenge of creating a nearly 1000 pound steel and concrete beam from

ideas and sketches.

From the formwork construction, to the placing of steel, and even to the mixing,

placement, and curing of the concrete, each step was performed by members of the team

(with the one exception of pre-tensioning the steel strands at the base, which was kindly

performed by Illinois Concrete technicians). Testing the beam required forethought,

planning with others, care, and precision measurements to ensure that the process

proceeded without compromising the results. Finally, accurate calculations of predicted

strength properties of the beam took the strong understanding of structural and material

properties of reinforced concrete, contributed by diverse student backgrounds.

In short, the real objective was to demonstrate that University of Illinois Big

Beam Team could competitively design and produce a very strong and light pre-cast

concrete beam.

3.0 Concrete Mix Design

Based on our knowledge of concrete mix design, this year’s University of Illinois

Big Beam Team elected to develop a high performance concrete for the competition.

Research into this type of material led us to consider a mortar mix, ie: a concrete design

consisting primarily of cement and sand without coarse aggregate, over a more

conventional mix. To further study this option, we produced three mix designs, as shown

in table 3.1. Mix A was based upon the concrete mixture used for last year’s Big Beam

contest, but recalculating the aggregate quantities for a mortar mix. Mixes B and C were

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Big Beam Team

3

similar to each other, varying only by the water-to-cementitious materials ratio and the

use of coarse aggregate.

Tests performed on mixes A, B, and C led to the production of mixes D and E,

which further refined and optimized the strength and workability characteristics of mix

A. An optimal strength mix was found based on concrete cylinders tested in compression

and upon the workability of the each mix. As Table 3.2 shows, the highest strength was

found in mix E, but mix D was chosen for comparable strength and greater workability.

Other materials tested for strength and workability in a concrete mix included

silica fume vs. fly ash and amount of superplasticizer. The ingredients and quantities for

each mix are tabulated in Appendix A.

4.0 Structural Analysis

The big beam was designed as pretensioned beam to be able to withstand a high

cracking load. Increasing pretensioning means increasing the load-to-weight ratio, and

over-pretensioning will produce cracks at the top of the beam just after release. Using

RESPONSE 2002, a reinforced concrete sectional analysis program developed in the

University of Toronto, we optimized the design to find the best performance. The beam,

cast with 12,000 psi concrete, was designed as “Bulb-T”, with two pretensioned strands

for the tensile reinforcement. Figure 4.1 shows the beam and loading set-up.

Figure 4.2 and Table 4.1 give the details of the cross-section. Two 2 ½-in

diameter low relaxation prestressed strands were stressed to provide 60 kips pretension

force. Three #3 reinforcing bars were placed in the top flange as the compressive bars.

Double-leg #2 shear stirrups were distributed along the whole beam at spacing of 6

Mix A B C

5-day Strength (psi) 7267 6100 6551

Mix A D E

2-day Strength (psi) (low) 5536 5644

Table 3.2 Concrete Mix Strengths

Mix A B C D E

Water-Cement Ratio 0.40 0.50 0.38 0.35 0.34

Water-Cementitious

Materials Ratio

0.34 0.34 0.26 0.30 0.29

Aggregate-Cement Ratio 2.25 4.44 4.44 2.25 1.60

Aggregate-Cementitious

Materials Ratio

1.93 3.01 3.02 1.93 1.37

Volume of

Superplasticizer (mL)

5.00 10.00 10.00 18.00 18.00

Use Coarse Aggregate?No No Yes No No

Table 3.1 Concrete Test Mix Parameters

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Big Beam Team

4

inches. To resist the bursting force, three stirrups at 3-inch spacing were fixed within 6

inches from each end.

RESPONSE 2000 was used to determine the load-deformation response. Figure

4.3 shows the moment-curvature curve of section and Figure 4.4 gives the relationship

between load and deflection at the midspan.

Predicted cracking and maximum loads are listed below:

• Cracking moment kipsftM

cr

−

=

39.54

• Cracking load kipsP

cr

54.15=

• Maximum moment kipsftM

−

=

8.71

max

• Maximum load kipsP 51.20

max

=

Figure 4.1- Beam Layout and Loading Set-up

Figure 4.2 – Beam cross-section

ad reinforcement scheme

Gross Trans.

A (in

2

) 58.5 61.3

I (in

4

) 933.5 1003.1

y

t

(in) 5.6 5.7

y

b

(in) 6.4 6.3

S

t

(in

3

) 165.2 177.3

S

b

(in

3

)

147 158.1

f'

c

= 12,000 psi

f

pu

=270.0 ksi

Pretension force before transfer = 60 kips

Pretension force after transfer = 55.85 kips

f

pe

= 182.5 ksi E

pe

= 6.32 x10

-3

Table 4.1. Geometric properties

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Big Beam Team

5

Moment vs. Curvature

0

10

20

30

40

50

60

70

80

-500 0 500 1000 1500 2000

Curvature(rad/10^6in)

Moment(ft-kips)

Load vs. Deflection at midspan

0

2

4

6

8

10

12

14

16

18

20

22

-0.2 0 0.2 0.4 0.6 0.8

Deflection (in)

Load P (kips)

5.0 Construction

The construction of this concrete beam consisted of several stages. The first, of

course, was the construction of the mold. The box mold was build primarily of plywood

and lumber planks, with stiff insulation foam board used to form the details of the I-

shape.

The second stage was the positioning of the steel reinforcement. The prestressed

strands were placed and stressed by an outside contractor. The compressive and shear

reinforcement was placed by hand by our team. See Figures 5.1 and 5.2.

The third stage was the actual placement of the concrete. The concrete was

placed in three batches, with part of each batch being used to form test cylinders and

modulus of rupture bars. Due to the low workablility of our concrete mix design, the

concrete had to be vibrated into placed. The beam and each of the test specimens were

finished using steel trowels.

The next stage of the construction was the assembly of a curing system. Our

curing system consisted of wet burlap placed over the exposed surface of the finished

concrete, heat lamps focused on the beam, humidifiers, and a reflective tarp, wrapped

around the entire system. The produced effect was that of a warm steam room.

The final stage of the construction process involved cutting the prestressing

strands and demolding the beam, see Figure 5.3. Following this procedure, the beam was

returned to the steam-curing environment.

Fi

g

ure 4.3 Moment vs. Curva

t

ure Dia

g

ra

m

Fi

g

ure 4.4 Load vs. Deflection at Mids

p

an

Figure 5.1 – Stretching the prestressed tendon across the formwork

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Big Beam Team

6

6.0 Testing

As specified by the rules for the PCI Big Beam Contest, the following tests were

performed on our material and structural design.

• Three ASTM standard 6-inch by 12-inch concrete cylinders tested in

compression

• Two standard modulus of rupture beams

• One beam (the big beam) tested in flexure.

The prestressed beam was tested after 25 days of curing. The set up for the big

beam test is shown in Figure 6.1.

Fi

g

ure 6.1

–

Testin

g

set u

p

for flexure test of the Bi

g

Bea

m

Figure 5.2 – Reinforcing scheme, including tensile

strands and shear and compression bars

Fi

g

ure 5.3

–

Cuttin

g

the

p

restressin

g

st

r

ands

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Big Beam Team

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7.0 Results

8.0 Conclusions

9.0 Acknowledgements

The University of Illinois Big Beam Team would like to sincerely thank the

following people for their involvement in the project. Their expertise was greatly

appreciated in construction and conducting the test.

PCI member observer…

Unknown at this point

Mike Johnson, Ryan Peacock, and Russ Roy

Illinois Concrete Co., Inc.

Terry Winters

Builders Supply, Champaign

Tim Prunkard and Steve Mathine

Civil Engineering Machine Shop, University of Illinois at Urbana-Champaign

Greg Banas

Structural Engineering Research Laboratory, University of Illinois at Urbana-Champaign

10.0 Appendices

Mix A B C D E

Cement (lb) 3.00 1.60 1.60 3.00 3.25

Silica Fume (lb) 0.50 0.00 0.00 0.50 0.55

Fly Ash (lb) 0.00 0.76 0.75 0.00 0.00

Fine Aggregate (lb) 6.75 7.10 2.48 6.75 5.20

Coarse Aggregate (lb) 0.00 0.00 4.62 0.00 0.00

Water (lb) 1.20 0.80 0.60 1.05 1.10

Superplacticizer (mL) 5.00 10.00 10.00 18.00 18.00

Appendix A: Test Concrete Mix Materials

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Big Beam Team

8

Appendix B. Materials and section properties

Materials

Concrete

Concrete strength

'

c

f

12,000 psi

Modulus of Elasticity

'

57000

cc

fE =

6244 psi

Modulus of rupture

'

5.7

cr

ff =

822 psi

Prestressing strand 0.5 in. dia., 7-wire, low-relax

Area of one strand

P

A

0.153 in

2

Ultimate strength

pu

f

270.0 ksi

Modulus of Elasticity

p

E

28,900ksi

Longitudinal Reinforcing bar #3

Yield strength

y

f

60ksi

Area

s

A

0.11 in

2

Modulus of Elasticity

s

E

29,000ksi

Shear Reinforcing bar #2

Yield strength

yv

f

40 ksi

Area

v

A

0.044 in

2

Modulus of Elasticity

s

E

29,000ksi

Appendix C. Design Calculations

Loss of prestress (ACI 18.6)

Pretension force just before transfer

kipsP

i

60

=

=

偲整敮獩潮瑲o獳s

ksif

p

1.196=

(0.73

pu

f

<0.80

pu

f

, ACI 18.5.1)

At transfer,

psiEpsif

cici

5700,000,10

'

==

Concrete strain at the center of the strands:

3

2

10466.0

−

×=+=

transc

i

transci

i

c

IE

eP

AE

P

ε

Neglect the influence of the self-weight, which is small compared to pretension, then the loss of prestress:

ksiEf

cpp

5.13==Δ

ε

The effective prestress and force after transfer:

ksifff

pppe

5.182=Δ−=

(Effective Prestrain

3

1032.6

−

×=

pe

ε

)

kipsAfP

ppef

85.55==

Stresses in concrete immediately after transfer (ACI 18.4.1)

At the ends:

psifpsi

A

P

S

eP

f

ci

trans

f

transt

f

t

6006759

'

,

=>=−=

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Big Beam Team

9

psifpsi

S

eP

A

P

f

ci

transb

f

trans

f

b

600060.02784

'

,

=<=+=

At the mid-span

Moment of self-weight at mid-span

ftkM

self

−

=

49.1

psifpsi

S

M

A

P

S

eP

f

ci

transt

self

trans

f

transt

f

t

3003658

'

,,

=>=−−=

psifpsi

S

M

S

eP

A

P

f

ci

transb

self

transb

f

trans

f

b

600060.02671

'

,,

=<=−+=

The tensile stresses exceed the limit values, so additional reinforcement shall be provided in the tensile

zone. The tensile stress resultant N

c

at the ends can be obtained from the stress distribution as

kipsN

c

56.8=

. The resistance T provided by 3 #3 reinforcing bars is:

kipsNkipsAksiT

cs

56.89.930 =>=×=

, O.K.

Crack moment M

cr

at mid-span

psif

S

eP

A

P

S

M

f

r

transb

f

trans

f

transb

cr

b

882)(

,,

==+−=

ftkM

cr

−= 5.47

The crack load

kipsP

cr

57.13=

(if consider the effect of self-weight,

kipsP

cr

1.13

=

⤠

=

䙬數畲慬慰慣楴礠⡁䍉‱㠮㜮㈩F

乯Ni湡氠獴牥獳映灲敳瑲p獳敤s獴牡湤猺s

⎪

⎭

⎪

⎬

⎫

⎪

⎩

⎪

⎨

⎧

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−+−= )(1

'

'

1

ωωρ

β

γ

p

c

pu

p

p

pups

d

d

f

f

ff

:

05.0,0,01.0,00927.0,65.0,90.0

''

1

====== ωωρρβγ

pp

,

,17.016.0)(

'

'

<=−+

ωωρ

p

c

pu

p

d

d

f

f

taken as 0.17,

so

ksif

ps

4.206=

21.032.016.0

1

'

=<==

βρω

c

ps

pp

f

f

, Ensuring that the Prestressing steel will yield prior to

concrete crushing.

Flexural capacity

kipsftM

n

−

= 1.56

From RESPONSE 2000, Maximum moment capacity

kipsftM

−

=

8.71

max

and

kipsP 51.20

max

=

Shear design

kipsP 51.20

max

=

, shear force

kipsV

u

25.10

=

=

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Big Beam Team

10

a) Shear strength provided by concrete for prestressed members (ACI 11.4)

i) Flexural-Shear Cracking:

)15.67.1(97.86.0

''

kipsdbfkips

M

MV

dbfV

wc

cri

wcci

=>=+=

ii) Web-shear cracking:

kipsdbffV

wpcccw

14.22)3.05.3(

'

=+=

kipsVVV

cwcic

97.8),min( ==

b) shear strength provided by stirrups

Using two-leg #2 stirrups at 6 in,

kips

s

dfA

V

yvv

s

42.6==

kips

V

kipsVV

u

sc

06.12

85.0

25.10

4.15 ==>=+

φ

, O.K.

Pretensioned Anchorage zones

Force in the strands before release

kipsF

pi

60

=

Ⱐ瑨攠扵牳≥i湧敳楳瑡湣nⰠ

r

P

, should not be less than

4.0% of

pi

F

, so

kipsP

r

4.2=

. (LRFD Art 5.10.10)

2

12.0)20/(4.2/inksifPA

srs

==≥

This amount of vertical reinforcement should be located within the distance h/5 from the end of the beam to

resist bursting stress. Therefore use 3-#2 two-leg stirrups spacing 3.0in ,

22

12.0264.0)044.02(3 ininA

s

>=××=

,O.K.

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Big Beam Team

11

11.0 Lessons Learned

1.

Design vs. construction challenges

2.

Design and development of high performance concrete mix designs.

3.

Concrete mix strength vs. mortar mix strength

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