Big Beam Contest Report 2003 - Dan Kuchma's Website

shootperchΠολεοδομικά Έργα

26 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

49 εμφανίσεις

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
University of Illinois at Urbana-Champaign
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
University of Illinois at Urbana-Champaign
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
University of Illinois at Urbana-Champaign
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
University of Illinois at Urbana-Champaign
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
University of Illinois at Urbana-Champaign
Big Beam Team
7


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
University of Illinois at Urbana-Champaign
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
'
,
=>=−=

University of Illinois at Urbana-Champaign
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
=
=
University of Illinois at Urbana-Champaign
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.

University of Illinois at Urbana-Champaign
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