Final Report for BBC

University Of Central Florida

Big Beam Competition 2012

Design Team 1

Mohamed AlrowaimiNader MehdawiWalid Hamad

Faculty AdvisorDr. Hae-Bum Yun

Sponsoring Producer

Finfrock Industries Inc.

1

TABLE OF CONTENTS

i Cover Page……………………………………………………………….. 1

ii Table of Contents………………………………………………………… 2

iii Acknowledgements………………………………………………………. 3

1 The Beam Configuration ………………………………………………… 4

2 Cross Section Drawings………………………………………………… 5

3 Design Parameters………………………………………………………. 6

4 Beam Predictions………………………………………………………… 7

4.

1

Crack Prediction……………………………………………………. 7

4.

2

Deflection Prediction……………………………………………….. 8

5 Stress in pre-stressing strands…………………………………………… 8

6 Partial Losses…………………………………………………………….. 8

7 Flexural Design and Analysis ………………………………………….... 9

8 Shear Design and Analysis………………………………………………. 10

9 Anchorage Design………………………………………………………... 11

10 Concrete Mix Design Criteria…………………………………………..... 11

11 Cost Estimation…………………………………………………………... 11

12 Conclusion………………………………………………………………. 13

12 Appendix…………………………………………………………………. 14

2

ACKNOWLEDGEMENTS

The Project Team extends his gratitude to Dr. Hae-Bun Yun for introducing us to this contest, guiding and advising us to have a good design.

Next, we would like to thank Joseph Lord, Executive Director of the Florida Pre-stressed Concrete Association (FPCA) for helping us to participate in the big beam contest for the first time.

Also, we would like to thank Mr. Allen R Finfrock, Vice President of FINFROCK Industries Inc., in Orlando, Fla., for their support and sponsoring our prestressed beam.

Last but not least, we thank the Precast/Prestressed Concrete Institute (PCI) for organizing and sponsoring the 2012 PCI Big Beam Contest.

3

1. The Beam Configuration with the shear and the moment diagram

4

2. Cross Section Drawings

Section

Elevation

5

2' 2' 2'2'2'4'2'

#3 Stirrups ,JYP

9.05"

3"

2.95"

6.00"

9.00"

N.A

10.00"

6.00"

1'-3.00"4.00"

6.55"

4.45"

N.A

#3 Stirrups ,JYP

1/2" Ø, 270K Law lax STRANDS

2"2"2"

10.00"

1'-3.00"

2.95"

3"4.00"

3. Design Parameters

f c, =6000 psi

f ci, =0.8 f c

, =4800 psi

f ci=0.6 f c, =2880 psi

f c=0.45 f c, =2700 psi

f ti=3√ f ci, =207.84 psi at the midspan

f ti=6√ f ci, =415.69 psi at the support

f t=12√ f c, =929.52 psi

f y=60,000 psi

M L=10,000∗6∗12=720,000∈−lb Max unfactored moment at midspan

(4) 1/2 270 ksi low lax tendon∅

f pu=270,000 psi

f pi=0.7 f pu=189,000 psi

Section Properties and Parameters

A=114¿2

I=2143.18¿4

c t=6.55∈¿

cb=8.45∈¿

r2=I / A=18.8¿2

6

St=I /c t=327.1¿3

Sb=I /cb=253.7¿3

W D= 11412∗12

∗150=118.7 plf

M D=W Dl2

8=

118.7(16)2

8∗12=45,600∈−lb

Total Losses of the selected T−Section=12.7 %

γ=1−0.127=0.873

4. Beam Predictions

All the beam predictions were computed either manually or by using a Excel spreadsheet. A few

numbers of rectangular and T beam sections were checked on the cracking load. So, the design

was initially dominated by the restriction of that the beam shall not crack under the total applied

service load of 20 kips. Then the selected T-beam section was designed for the flexural load at

transfer and service. A detailed calculation and checks for the flexural bea

m Design and analysis will be presented in Section 7.

4.1. Crack Prediction

It is important to evaluate the first cracking load. Hence, the moment due to the applied live load

(20 kip) and the self-weight of the T-beam were calculated. Then this moment were compared to

the cracking moment to get the exact cracking applied service load.

The predicted design cracking load = 20 kip

7

M cr

M T

=1.01 the beamwill crack at total applied load of 20 kip

As assumed above, the beam will crack at 20 kips or more. The detailed calculations are shown

in appendix.

4.2 Deflection Prediction

The deflection calculation was done based on uncracked prestressed section since the

assumptions of elastic behavior are more applicable than the cracked section. So, the deflection

was calculated at transfer due to the beam’s self-weight and at service due to the total load,

beam’s self-weight and the live load. Also, the camber due to the prestressing force was

calculated and subtracted from the calculated deflections. A summary of the deflections at

transfer and service is shown in the next table.

Loading Stage Deflection (in)

At transfer (midspan) 0.05

At service (midspan) 0.43

The predicted max. deflection = 0.43 in at the Midspan . The detailed deflection calculation is

presented in the appendix.

5. Stress in Prestressing Strands

The initial prestressing stress: f pi=0.7 f pu=189,000 psi

Hence, the initial prestressing force Pi=115688 lb

The effective prestressing stress: f pe=γ f pi=164,997 psi

Hence, the effective prestressing force Pe=100,978.164 lb

6. Partial Losses

The Partial Losses were calculated for the pretension tendon and the results are shown in the

following table:

Stress Level at various Stages Steel Stress (psi) %

8

After tensioning (0.7 Fpu) 189,000 100Elastic shortening loss -10325 -5.5Creep loss -6757.95 -3.6Shrinkage loss -3690 -1.95Relaxation loss -3126.81 -1.65Final Net Stress (FPe) 165100.24 87.3

The percentage of total losses = 12.7 % for this pre-tensioned beam.

7. Flexural Design and Analysis

The following prestressed beam was designed to carry at least total factored load of 32 kips. In

this design, the service load design method was used.

A several section trails were studied with:

Different shapes and dimensions (rectangular and T-Beam)

Different tendon numbers

Different eccentricities

All these sections were checked to choose the best section in weight, cost and strength.

The following spread sheet table shows the most effective Beam. Also, the stresses for the

selected T-Beam were checked on both transfer and service stage as shown in the following

table.

The design was for number of 4 - ½”∅ 270 ksi , low lax straight tendons ,e = 4 “

9

Spreadsheet Calculation of the most effective beamCalculation Sheet

Trial Section # 5

I-Beam

Section Properties Number of Tendons

N# 4

Area (sq in) 114

I (in^4) 2143.184 Prestressing Force

Ct (in) 6.5526 Losses % 12.70

Cb (in) 8.4474 Pi (psi) 115668

r^2 (sq in) 18.79986 Pe (psi) 100978.164

St (cu in) 327.0739

sb (cu in) 253.7093

Eccentricity Support Midspane (in) 4

Transfer LoadFt 399.948 260.5299

Psi

Loading MomentsFb

-2838.26 -2658.53 Psi

Md (in-lb) 45600

Ml (in-lb)720000

Service LoadFt 349.1546 -1991.6

Psi

Mt (in-lb)765600

Fb

-2477.8 179.3647 Psi

10

6.00"

9.00"

N.A

10.00"

6.00"

1'-3.00"4.00"

6.55"

4.45"

8. Shear Design and Analysis

The shear reinforcement was deigned to carry the shear due to the external load. In this

design, it is found that the shear due to the external load Vu is bigger than half of the shear

capacity Vc.

V u .>V c /2

Hence, the shear reinforcement was taken to be the min as Per ACI, (Min Av/S), which came

to 2 # 3 closed tie stirrups, spaced at 2 in center to center.

9. Anchorage Design

The anchorage was reinforced based on the empirical expression by Mattock.

This was found to be 2 #3 closed tie stirrups.

10.Concrete Mix Design Criteria

In our design we will adopt the concrete mix design done by Finfrock Industries Inc. since they

will produce the concrete at their plant.

Self-compacted concrete

Type 3 cement for high early strength

Water cement ratio is 0.38

According to Finfrock the mix will give concrete comprehensive strength of 6000 psi after two

weeks.

11

11.Cost Estimation

The major challenge in the design is how to design a safe member with the least cost and build

an economically competitive structure of suitable strength performance which would satisfy the

requirements. The need for the most efficient cost design solution has led to the need to carry out

accurate cost estimation and a structural cost optimization.

Self-manufacturing costs are proposed to be defined as a sum of:

- The material costs,

- The power consumption costs

- The labor costs.

In our contest will be responsible of just the material costs. So, we have to break down the

material in the beam. Our beam’s materials are:

Concrete volume (yd³) 0.469135

4 strands 0.5 in dia. Length (ft) 64

#3 stirrups length (ft) 8.7

#3 reinforcement weight (lb/ft) 0.376

Using cost price given in the Big Beam contest specifications, we can give a good predicted as

shown:

Material Unit Cost Amount Cost ($)

Concrete $100/cu yd 0.469135 (cu yd) 46.9135

Pre-stressing Strand

$0.30/ft 64 (ft) 19.2

Steel:A615/A706

$0.45/lb 3.2712 (lb) 1.472

Total Cost 67.59

12

12.Conclusion

During the design of the big beam, our team has tried several sections with different shapes,

dimensions, number of tendons and eccentricities to come with the most effective design. The

beam in this report was designed to carry a total factored live load of 32 kips and must not have a

total peak applied load more than 39 kips.

Also, this beam was designed to have the first crack at load equal or bigger than 20 kips (the total

applied service load).

The selected T-section was found to be the most effective section that meets all the requirements

of the contest:

Self-weight =118.7 plf with total weight of 1899.2 lb

Material cost = $ 67.59

4 - ½”∅ 270 ksi lowlax straight tendons

e = 4 “

13

Appendix

Five Trial Sections:-

Trial #1

Calculation Sheet

Trial Section # 1Rectangular 15*10


N# 4

Area (sq in) 150

I (in^4) 2812.5 Prestressing ForceCt (in) 7.5 Losses % 12.70Cb (in) 7.5 Pi (psi) 115668r^2 (sq in) 18.75 Pe (psi) 100978.16St (cu in) 375sb (cu in) 375


Transfer LoadFt 462.672 302.672 Ps

i

Loading Moments Fb -2004.912 -1844.912 Psi

Md (in-lb) 60000

14

Ml (in-lb)720000

Service LoadFt 403.91266 -1676.0873 Ps

i

Mt (in-lb)780000 Fb -1750.288 75.088 Ps

i

Trial #2

Calculation Sheet

Trial Section # 2Rectangular 15*6


N# 4Area (sq in) 90I (in^4) 1687.5 Prestressing ForceCt (in) 7.5 Losses % 12.70Cb (in) 7.5 Pi (psi) 115668r^2 (sq in) 18.75 Pe (psi) 100978.2St (cu in) 225sb (cu in) 225



i

Loading MomentsFb

-3341.52 -3181.52 Psi

Md (in-lb) 36000

Ml (in-lb)720000


i

Mt (in-lb)756000

Fb

-2917.15 18.48 Psi

15

Trial #3

Calculation Sheet

Trial Section # 3I-Beam


N# 4Area (sq in) 150I (in^4) 5312.5 Prestressing ForceCt (in) 7.5 Losses % 12.70Cb (in) 12.5 Pi (psi) 115668r^2 (sq in) 35.41667 Pe (psi) 100978.2St (cu in) 708.3333sb (cu in) 425


Transfer LoadFt -117.936 -202.642 Ps

i

Loading MomentsFb

-1859.76 -1718.58 Psi

Md (in-lb) 60000

Ml (in-lb)720000

Service LoadFt -102.958 -1204.13 Ps

i

Mt (in-lb)780000

Fb

-1623.57 -24.4659 Psi

16

Trial #4

Calculation Sheet



N# 4Area (sq in) 110I (in^4) 2734.924 Prestressing ForceCt (in) 6.5909 Losses % 12.70Cb (in) 8.4091 Pi (psi) 115668r^2 (sq in) 24.86295 Pe (psi) 100978.16St (cu in) 414.9546sb (cu in) 325.2339


Transfer LoadFt 63.46702 -42.5687 Ps

i

Loading MomentsFb

-2474.11 -2338.82 Psi

Md (in-lb) 44000

Ml (in-lb)720000


i

Mt (in-lb)764000

Fb

-2159.9 -125.031 Psi

17

Trial #5

Calculation Sheet



N# 4Area (sq in) 114I (in^4) 2143.184 Prestressing ForceCt (in) 6.5526 Losses % 12.70Cb (in) 8.4474 Pi (psi) 115668r^2 (sq in) 18.79986 Pe (psi) 100978.164St (cu in) 327.0739sb (cu in) 253.7093



i

Loading MomentsFb

-2838.26 -2658.53 Psi

Md (in-lb) 45600

Ml (in-lb)720000


i

Mt (in-lb)765600

Fb

-2477.8 179.3647 Psi

18

Check for stresses for our selected beam section at 32, and 39 kips

For applied 32 kip load, the stresses are:

For applied 39 kip load, the stresses are:

19

Partial Losses of Pre-stressed Beam

1. Elastic Shortening:

∆FPES = n . FCS

Where,

FCS = −PiAc

¿) + Md e

Ic and n =

E s

Eci

e = 4 in and MD = 45600 in-lb

so,

FCS =-1687.1 psi

Modular Ratio n = E s

Eci =

270000004415000

= 6.12

so,

∆FPES = n . FCS

= 6.12 * 1687.1 = 10325 psi

2. Creep Losses:

∆FPCR = Ct

EPS

Ec FCS

Where;

Ct = t 0.6

10+t 0.6 Cu = 140.6

10+140.6 *2 = 0.655

∆FPCR = 0.655 * 270000004415000 * 1687.1 = 6757.95 psi

3. Shrinkage Losses:

20

Time-dependent method

∆FPSH = ϵSH * ES

Where:

ϵSH = t

35+t (ϵSH)u

= 7

35+7 * 820*10-6

= 1.37*10-4

So,

∆FPSH = 1.37*10-4 * 10-6 = 3690 psi

4. Relaxation:

ACI-ASCE method

∆FPR = {kre - J∆(∆FPES + ∆FPCR + ∆FPSH )}C

= {5000 – 0.04(10325+6757.95+3690)}*0.75

= 3126.81 psi

Total Losses

∆FPT = ∆FPES + ∆FPR+ ∆FPCR + ∆FPSH

∆FPT = 10325+6757.95+3690+3126.81

= 23899.76 psi

Stress Level at various Stages Steel Stress (psi) %

After tendioning (0.7 Fpu) 189,000 100Elastic shortening loss -10325 -5.5Creep loss -6757.95 -3.6Shrinkage loss -3690 -1.95Relaxation loss -3126.81 -1.65Final Net Stress (FPe) 165100.24 87.3

The percentage of total losses = 12.7 % for this pre-tensioned beam based on 14 days.

21

Shear Design Calculation

Calculate Vu due to factored loads Pl= 10 kips Pu=16 kips WD=0.118 kips/ft Wu=0.1425 kips/ft

Calculate Vu at 1/2dpFrom shear force diagram Vu= 17.062 Kips

Nominal shear strength Vc :

Req Vn=Vu∅

=17.0620.75

=22.75 kips

ˇ0.4 fpu<fPe108000 psi<160650 psi

Use ACI alternate method

Vc=(0.6 λ√F c '+700vudpMu )Bwdp ≥2 λ√ F c ' bwdp≤ 5 λ√ f c ' bwdp

Caculate Muat dp/2 :Mu=9.37k . ft¿moment daigramvudpMu

=17.062∗13(9.234∗12 )

=2>1 use1

min vc=2 λ√ f c ' bw dp=2∗1∗√6000∗6∗13=12083.70 Ibmax vc=5 λ√ fc ' bw dp=30209.27 Ib

Vc=(0.6 λ√ f c '+ 700∗vudpMu )bwdp=58225.11 Ib>Vc max

useVcmax=30209.27 Ib

22

vc> vu∅

vc2

=30209.272

=15104.6235 k

minAvs

= Apsfpu80 fytdp √ dp

bw

minAvs

=4∗0.193∗2700080∗6000∗13 √ 13

6=0.00389

use ¿3 Av=2∗0.11=0.22Avs

=0.00389

S=56.65∈¿50∈¿

Defection Calculation

Transfer StageDeflection due to Dead load (Self weight)

∆D= 5 w l4

384 Eci I

Eci=3.94 x 106 psi∆ D=0.21∈↓Camber due prestreesing force:

∆C=Pe . e . l2

8 E I∆C=0.161∈↑At service load of uncracked beam

∆D+L=5 w l4

384 E c I+ P.b

24 E I∆D+L=0.19+0.246 ∆D+L=0.43∈¿ The maximum deflection at the midspan

Crack Calculation

Mcr = fr * Sb + Pe ( e + r2/cb )

Mcr = 7.5 (6000)1/2 *253.709 + 100978.2 (4+18.8/8.45)

Mcr = 775965.97 in-lb

23

Mcr/MT = 775965.97/765600

Mcr/MT = 1.01 O.K.

24

Final Report for BBC

Documents

loading moments

beam section

prestressing

steel stress

calculation

effective

prestressed

shear due