Final-project.docx

Design of Prestressed Concrete Bridge along Tanza and General Trias, Cavite, Connecting Tanza – Trece Martires and General Trias Dr. Roads

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TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES 938 Aurora Boulevard, Cubao, Quezon City

COLLEGE OF ENGINEERING AND ARCHITECTURE Civil Engineering Department

CE 513 Prestressed Concrete Design

DESIGN OF PRESTRESSED CONCRETE BRIDGE ALONG TANZA AND GENERAL TRIAS, CAVITE, CONNECTING TANZA-TRECE MARTIRES AND GENERAL TRIAS DR. ROADS

PREPARED BY: Dalisay, Jayson B. De Guzman, John Alexander Jr. D. Dela Cruz, Beatrice Ann O. Elido, Ruel Uson, Jaela G. CE52FA2

SUBMITTED TO: Engr. Debbie-lyn Cabacungan Instructor

March , 2019

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TABLE OF CONTENTS Chapter 1 : PROJECT BACKGROUND ....................................................................................................... 8 1.1 The Project......................................................................................................................................... 8 1.2 Project Objectives .............................................................................................................................. 9 1.3 Project Scope and Limitations............................................................................................................ 9 1.4 Project Development .......................................................................................................................... 9 Chapter 2 : LOCATION .............................................................................................................................. 10 2.1 Project Location ............................................................................................................................... 10 Chapter 3 : DESIGN COMPUTATION ....................................................................................................... 11 3.1 Description of the Structure.............................................................................................................. 11 3.2 Material Description ......................................................................................................................... 11 3.3 Material Properties ........................................................................................................................... 11 3.3.1 Material Specifications .............................................................................................................. 12 3.3.2 Geometrical and Cross-Sectional Specifications ...................................................................... 13 3.3.3 Design Loads ............................................................................................................................ 14 3.4 I-Beam Description ...................................................................................................................... 15 3.5 Design Methodology ........................................................................................................................ 17 3.6 Geometric Cross-Section of I-Beam ................................................................................................ 18 3.7 Geometric Modeling ......................................................................................................................... 19 3.8 Load Diagrams................................................................................................................................. 19 3.9 Load Combinations .......................................................................................................................... 20 3.9.1 Strength I [1.25DC + 1.50 DW + 1.75(LL + IM)] ........................................................................ 21 3.9.2 Strength IV (1.25DC + 1.50 DW) ............................................................................................... 22 3.9.3 Service I [1.00DC + 1.00 DW + 1.00(LL + IM)].......................................................................... 22 3.9.4 Service III [1.00DC + 1.00DW + 0.80(LL + IM)]......................................................................... 23 3.9.5 Fatigue [0.75(LL + IM)] .............................................................................................................. 23 3.10 Structural Analysis ......................................................................................................................... 24 3.10.1 Strength I Load Combination .................................................................................................. 24 3.10.2 Strength IV Load Combination ................................................................................................ 25 3.10.3 Service I Load Combination .................................................................................................... 26 3.10.4 Service III Load Combination .................................................................................................. 27

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3.10.5 Fatigue Load Combination ...................................................................................................... 28 3.10.6 Maximum Shear and Maximum Moment................................................................................. 29 3.11 Design of Concrete I-Beam ............................................................................................................ 30 3.11.1 Computation of Moment of Inertia ........................................................................................... 30 3.11.2 Stresses at Transfer and Service Load ................................................................................... 33 3.11.3 Fatigue Check ......................................................................................................................... 37 3.11.4 Strength Limit State Check ..................................................................................................... 38 3.11.5 Shear Design .......................................................................................................................... 40 Chapter 4 : FINAL DESIGN ....................................................................................................................... 47 4.1 Beam Schedule................................................................................................................................ 47 4.2 Prestressing and Non-Prestressing Steel Schedule ........................................................................ 48 Chapter 5 : ACTUAL PHOTOS .................................................................................................................. 49 5.1 Existing Cast-in-place Bridge ........................................................................................................... 49 5.2 Proposed Prestressed Concrete Bridge ........................................................................................... 50

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LIST OF FIGURES Figure 1-1. Perspective View of the Superstructure Prestressed Concrete Bridge ...................................... 8 Figure 3-1. Prestressed Concrete Bridge Cross-Sectional View ................................................................ 11 Figure 3-2. HS-20 Truck Loading ............................................................................................................... 15 Figure 3-3. HS-20 Truck Lane Loading ...................................................................................................... 15 Figure 4-1. Final Geometric Cross-Section of the I-Beam.......................................................................... 47

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LIST OF TABLES Table 3-1. Properties of Prestressing Concrete ......................................................................................... 12 Table 3-2. Properties of Prestressing Steel................................................................................................ 12 Table 3-3. Properties of Non-Prestressing Steel ........................................................................................ 13 Table 3-4. Geometrical Properties of the Bridge ........................................................................................ 13 Table 3-5. Geometrical and Cross-Sectional Properties of I-Beam Concrete ............................................ 13 Table 3-6. Design Dead Loads .................................................................................................................. 14 Table 4-1. Prestressing and Non-Prestressing Steel Details ..................................................................... 48

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LIST OF ACRONYMS AASHTO – American Association of State Highway and Transportation Officials NSCP – National Structural Code of the Philippines DPWH – Department of Public Works and Highways LRFD – Load and Resistance Factor Design DC – Dead Load due to Structural Components and Non-Structural Attachments DW – Dead Load due to Wearing Surfaces and Utilities LL – Vehicular Live Load IM – Vehicular Dynamic Load Allowance

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CHAPTER 1 : PROJECT BACKGROUND 1.1 The Project The project is the modification of the cast in place bridge into a pre-stressed concrete bridge located in Cavite connecting the roads of Trece Martires and General Trias. The bridge lets the travelers have another route from Trece Martires to General Trias and vice versa instead of circling around Antero Soriano Highway, making the travel time lesser. It attracts businessman to start their business around the area because the project is located in undeveloped lands, which in turn will boost tourism and economic status of the area. The new superstructure bridge will span about 100 meters with 25 meters in each span of beam used. The bridge will have 4 lanes, with each lane 3 meters in width. The material to be used in the project is prestressed concrete and its specifications conform to the standards in the AASHTO Bridge Design Specifications. The design process conforms to the standards designated in the National Structural Code of the Philippines – Volume II: Bridges.

Figure 1-1. Perspective View of the Superstructure Prestressed Concrete Bridge

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1.2 Project Objectives The following are the objectives of the project: ► To design a bridge using prestressed concrete as the primary material. ► To compute for the initial requirements in designing the prestressed concrete bridge. ► To evaluate the adequacy of the design. 1.3 Project Scope and Limitations The scope of the project includes: ► The design of the prestressed concrete beams to be used in the project. ► The geometric cross-section of the prestressed concrete beam to be used in the project. The limitations of the project include: ► The design of other structural members of the bridge. This includes the following members:  The deck slab of the bridge.  The columns of the bridge in which it is laid.  The concrete barriers of the bridge. ► The construction costs of the bridge. 1.4 Project Development The designer conceptualized the project which needed to comply with the needs of the client. For this, the designer provided the necessary dimensions of the bridge. The designer made sure that the plans for the superstructure bridge conform to the codes and standards provided in the NSCP Volume 2 and AASHTO Bridge Design Specifications, making the design safe, durable and acceptable. Detailing of the plan (ie. Scheduling of the Prestressed Concrete Beam) is also presented here. CONCEPTUALIZATION OF THE PROJECT DESIGN PARAMETERS

DESIGN OF NECESSARY MEMBERS FINAL DESIGN OF THE PROJECT Figure 1-2. Stages of Development of the Project

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CHAPTER 2 : LOCATION 2.1 Project Location

Figure 2-1. Project Location Map

Trece Martires, officially the City of Trece Martires, is a 4 th class city and the de facto capital city of the province of Cavite. According to 2015 census, it has a population of 155, 713 people. The connecting city, General Trias, is a 1st class city in the province of Cavite. It is formerly known as San Francisco de Malabon. It has a population 314, 303 people in the year 2015. The bridge is located in Cavite connecting the roads of Trece Martires and General Trias. The bridge lets the travelers have another route from Trece Martires to General Trias and vice versa instead of circling around Antero Soriano Highway, making the travel time lesser. It attracts businessman to start their business around the area because the project is located in undeveloped lands, which in turn will boost tourism and economic status of the area.

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CHAPTER 3 : DESIGN COMPUTATION 3.1 Description of the Structure The structure is a superstructure prestressed concrete bridge which has a length of 100 meters. It is composed of continuous spans of beam, 25 meters in each span. The span is the one to be designed and not the whole length of the bridge. The design approach for this project is LRFD or Load and Resistance Factor Design and its design processes shall conform to the standards given by NSCP Volume 2. The prestressed concrete beam specifications to be used in the project have geometric crosssections that conform to the standards of AASHTO Bridge Design Specifications.

Figure 3-1. Prestressed Concrete Bridge Cross-Sectional View

Data on the material properties and specifications of prestressed concrete are presented in this chapter. 3.2 Material Description Prestressed concrete is the main material used in the design of the superstructure bridge. For this project, the designer will use precast, prestressed concrete girders as per required by the AASHTO Bridge Design Specifications and NSCP Volume 2. For the prestressing steel, ½ inch diameter-seven wire strand is used. 3.3 Material Properties Listed here are the properties of the materials to be used in the project. They are the following: Concrete, Prestressing Steel, Non-Prestressing Steel. The geometrical and cross-sectional properties of the girders to be used are also listed here.

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3.3.1 Material Specifications Table 3-1. Properties of Prestressing Concrete

PRESTRESSING CONCRETE – NORMAL WEIGHT Property

Formula

Value

Unit

Unit Weight (γconc)

-

23.56

kN / m3

Compressive Strength of Concrete (f’c)

-

34.5

MPa

Initial Compressive Strength at Transfer (f’ci)

0.8f’c

27.6

MPa

Initial Compressive Strength at Service Load (fci)

0.6f’ci

16.56

MPa

Initial Tensile Strength at Service Load (Supports) (fti)

1⁄ √f' 2 ci

2.627

MPa

Initial Tensile Strength at Service Load (Midspan) (fti)

1⁄ √f' 4 ci

1.313

MPa

Compressive Strength at Service Load (fc)

0.45f’c

15.525

MPa

Tensile Strength at Service Load (ft)

√f'c

5.874

MPa

Initial Modulus of Elasticity of Concrete (Eci)

4,700√f'ci

24.692 x 103

MPa

Modulus of Elasticity of Concrete (Ec)

4,700√f'c

27.606 x 103

MPa

Modulus of Rupture (fr)

0.62√f'c

3.642

MPa

Table 3-2. Properties of Prestressing Steel

PRESTRESSING STEEL – ½ INCH DIAMETER-SEVEN WIRE STRAND – STRESS-RELIEVED Property

Formula

Value

Unit

Ultimate Strength (fpu)

-

1,862

MPa

Yield Strength (fpy)

0.85fpu

1,582.7

MPa

Stress due to Jacking Force (fpJ)

0.8fpu

1,489.6

MPa

Initial Stress (fpi)

0.7fpu

1,303.4

MPa

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Service Stress (fpe)

0.8fpy

1,266.16

MPa

Estimated Prestress Losses

-

227.527

MPa

Modulus of Elasticity (Eps)

-

193,000

MPa

Table 3-3. Properties of Non-Prestressing Steel

NON-PRESTRESSING STEEL Property

Formula

Value

Unit

Yield Strength for Main Reinforcement Bar (fy)

-

414

MPa

Yield Strength for Stirrups (fys)

-

275

MPa

Modulus of Elasticity (Es)

-

200,000

MPa

Property

Value

Unit

Height of the Bridge above Ground (z)

35

m

Bridge Width

18

m

Roadway Width

15

m

Lane Width

3

m

Property

Value

Unit

Length (L)

25

m

Spacing of Girders (s)

3

m

Deck Slab Thickness (tdeck)

250

mm

3.3.2 Geometrical and Cross-Sectional Specifications Table 3-4. Geometrical Properties of the Bridge

GEOMETRICAL PROPERTIES OF THE BRIDGE

Table 3-5. Geometrical and Cross-Sectional Properties of I-Beam Concrete

GEOMETRICAL AND CROSS-SECTIONAL PROPERTIES

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Haunch Thickness

200

mm

Haunch Width

2000

mm

Depth (h)

1,828.8

mm

Area of Concrete (Ac)

607,095.56

mm2

Moment of Inertia at Strong Axis (Ix)

279,328,013 ,361.217

mm4

Moment of Inertia at Weak Axis (Iy)

20,950,939, 435.672

mm4

Section Modulus at Top Part of Beam (St)

309,247,021 .888

mm3

Section Modulus at Bottom Part of Beam (Sb)

301,797,459 .635

mm3

Neutal Axis from the Top pf the Beam (yt)

903.252

mm

Neutal Axis from the Bottom pf the Beam (yb)

925.548

mm

3.3.3 Design Loads Listed here are the loads of the structure which will used to determine the parameters needed to design the necessary members. 3.3.3.1 Dead Loads Table 3-6. Design Dead Loads

DC – Dead Load of Components and Attachments Property

Value

Unit

Beam Weight

14.303

kN/m

Deck Slab Weight

17.670

kN/m

Concrete Barrier Weight

1.413

kN/m

Haunch Weight

9.424

kN/m

DW – Dead Load of Wearing Surfaces and Utilities

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Property

Value

Unit

Thickness of Wearing Surface

100

mm

Unit Weight of Wearing Surface

21.582

kN/m3

Wearing Surface Weight

6.475

kN/m

3.3.3.2 Live Loads

36 kN

144 kN 4.27 m

144 kN 4.27 - 9.0 m

Figure 3-2. HS-20 Truck Loading

CONCENTRATED LOAD 80 kN for Moment 116 kN for Shear Uniform Load ; w = 9.4 kN/m per Lane

Figure 3-3. HS-20 Truck Lane Loading

3.4 I-Beam Description The figure below shows a typical cross-section of an I – Beam. An I – Beam is a section that consists of two parts, which are the flange and the web. The web is the vertical plate while the flange is the top and bottom plates. I – Beam are easier to build and cheaper to maintain than other types. This is good for bridges that have short, straight spans. The disadvantage of this is that it doesn’t perform well on bridges that has long spans and is curved because of the torsional forces produced in it which I – Beams are weak at.

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Figure 3-4. Prestressed Concrete I-beam

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3.5 Design Methodology Referring to the codes and standards provided by the AASHTO Bridge Design Specifications, the designers considered a thorough process on how the design of a prestressed concrete beam is done. The flowchart presented is derived and provided by “The Federal Highway Administration”.

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Figure 3-5. Main Flow Chart for the Design of Superstructure Bridges

3.6 Geometric Cross-Section of I-Beam

Figure 3-6. Geometric Cross – Section of I – Beam

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3.7 Geometric Modeling

3.8 Load Diagrams

Figure 3-7. Geometric Modeling

Figure 3-8. Shear Diagram

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Figure 3-10. Moment Diagram

3.9 Load Combinations There are many load combinations that can be applied when designing a bridge. The most common load combinations are the only ones applied for this project. The following are the description of the load combination to be used: 

Strength I – Basic load combination relating to the normal vehicular use of the bridge without wind.



Strength IV – Load combination relating to very high dead load to live load force effect ratios. (Will govern if DL / LL > 7; Span > 185 meters)



Service I – Load combination relating to normal operational use of the bridge with a 90 kph wind and all loads at nominal values. Compression in precast concrete components.



Service III – Load combination relating only to tension in prestressed concrete superstructures with the objective of crack control.



Fatigue – Fatigue and Fracture load combinations relating to repetitive gravitational vehicular live load and dynamic responses under a single design truck.

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The following are the load combinations to be used:  Strength I – 1.25 DC + 1.50 DW + 1.75 (LL + IM)  Strength IV – 1.50 DC + 1.50 DW  Service I – 1.00 DC + 1.00 DW + 1.00 (LL + IM)  Service III – 1.00 DC + 1.00 DW + 0.80 (LL + IM)  Fatigue – 0.75 (LL + IM) where: DC – Dead Load of Structural Components and Non-Structural Attachments (Dead Load) DW – Dead Load of Wearing Surfaces and Utilities (Dead Load) LL – Vehicular Live Load (Live Load) IM – Vehicular Dynamic Load Allowance (Impact Load) (15% – Fatigue, 33% – Others) 3.9.1 Strength I [1.25DC + 1.50 DW + 1.75(LL + IM)]

Figure 3-11. Strength I Load Combination

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3.9.2 Strength IV (1.25DC + 1.50 DW)

Figure 3-12. Strength IV Load Combination

3.9.3 Service I [1.00DC + 1.00 DW + 1.00(LL + IM)]

Figure 3-13. Service I Load Combination

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3.9.4 Service III [1.00DC + 1.00DW + 0.80(LL + IM)]

Figure 3-14. Service III Load Combination

3.9.5 Fatigue [0.75(LL + IM)]

Figure 3-15. Fatigue Load Combination

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3.10 Structural Analysis 3.10.1 Strength I Load Combination

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3.10.2 Strength IV Load Combination

25

3.10.3 Service I Load Combination

26

3.10.4 Service III Load Combination

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3.10.5 Fatigue Load Combination

28

3.10.6 Maximum Shear and Maximum Moment

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3.11 Design of Concrete I-Beam 3.11.1 Computation of Moment of Inertia

30

31

32

3.11.2 Stresses at Transfer and Service Load At Transfer:

Property

Value

Unit

fpi

1,303.4

MPa

Initial % Loss

10%

-

Initial Prestress Loss

130.34

MPa

Total Initial Prestress Loss

1,173.06

MPa

Aps

4,343.217

mm2

33

Pi

5,094,354.275

N

Moment Due to Prestressing – C.G. of Beam – Midspan Moment Due to Self-Weight – C.G. of Beam – Midspan

= =

3,997.6 kN – m 1,163.2 kN – m

Stress Check at Transfer – Midspan

fb

-8.393

MPa

<

-20.7

MPa

OK!

ft

-8.391

MPa

<

1.468

MPa

OK!

Check Total Loss Due to Initial Prestressing

n

6.22

fES

-8.393

MPa

Total Loss

52.24

MPa

<

130.34

MPa

OK!

At Service:

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Prestress Losses at Service Level

Elastic Shortening

-52.24

MPa

fpi

1,303.4

MPa

Aps

4,343.22

mm2

35

Ac

607,095.56

mm2

γk

0.8

-

γst

0.84

-

Δ - fpr

17

MPa

Δ - fpi

135.91

MPa

Total Prestress Force

4,843.8

kN

MPrestressing Strand

3,800.6

kN - m

MDC

3,366.6

kN – m

MDW

1,088.3

kN – m

MLL

3,464.6

kN – m

MLL + IM

7,820.7

kN – m

Stresses at Midspan (Service I)

ft

-7.98

MPa

<

-15.535

MPa

OK!

fb

-7.98

MPa

<

-5.874

MPa

OK!

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3.11.3 Fatigue Check Distribution Factor for 1 Lane Loading

DFS = 1.173 Lane / Beam

Fatigue Checking

ft

-7.98

MPa

fb

0.0024349

MPa

Ration of Compression to Tension Stress

3,276.61

>

2

OK!

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3.11.4 Strength Limit State Check

38

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3.11.5 Shear Design

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Reinforcement Properties Property

Value

Unit

Remarks

Distance to Centroid of Compression Flange, d’

6

mm

-

Distance to Centroid of Bottom Prestressing Tendon, dp,b

84

mm

-

Distance to Centroid of Web Prestressing Tendon, dp,w

76

mm

-

Distance to Centroid of Tension, d

80

mm

-

Top Compression Reinforcement

2 #8 @ 12mm O.C.

Bottom Compression Reinforcement

2 #8 @ 12mm O.C.

Web Compression Reinforcement

2 #8 @ 12mm O.C.

Shear Stirrup Reinforcement

#8 @ 15mm O.C.

Bottom Prestressing Tendons

16 x 36 – ½” Φ Tendons

Web Prestressing Tendons

4 x 36 – ½” Φ Tendons

Shear and Moment Property

Value

Unit

Self-Weight Moment

29,116.96

kN – m

Dead Load Moment

37,500.00

kN – m

Live Load Moment

52,500.00

kN – m

Pi

25,698.10

kPa

Pe

20,558.50

kPa

Vu

6,886.74

kN

Tu

35,868.41

kN – m

The Section is Adequate for the given Loadings!

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Transfer Load Condition Checking Property

Value

Unit

ec

38.18

mm

ft

-0.581

kPa

fb

3.300

kPa

fsi

113.864

kPa

Fsi

189.000

kPa

fsi < Fsi, OK!

f

ti

f

bi

1 e  MG  Pi     St  A St 

0.318

kPa

> - mi [Satisfactory]

1 e  MG  Pi     Sb  A Sb 

3.387

kPa

< Fbi [Satisfactory]

(As')reqd

=

0.000

(ACI 318-11 R18.4.1)

mm2

<

(As')provd

[Satisfactory]

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Serviceability Condition Checking Property

Value

Unit

tdeck

300

mm

B

500.00

mm

Ac

17,529.00

mm2

yt

40.82

mm

yb

59.18

mm

Ic

23,171,159.00

mm4

St

567,642.00

mm3

Sb

391,537.00

mm3

Mmm. TOP FIBER STRESS

MAX. BOT. FIBER STRESS 0.5

me = 0.6fc' = 3.600 kPa, for total loads me, G+D = 0.4fc' = 2.400 kPa, for sustammed loads only me, 0.5(G+D)+L = 0.4fc' = 2.400 kPa, for live + 50% sustammed loads f se

=

155.520 kPa

-Fbe = -(0, 3, or 6)(fc') = -0.465 kPa MAX. ALLOWABLE STRESS Fse = 0.8fy =194.400 kPa, amer all losses

< Fse [Satisfactory]

 1 e  M M M f te  Pe     G D L  S ct  A St 

2.181 kPa

<

me

 1 e  M M f te,G D  Pe     G D  S ct  A St 

1.071 kPa

<

me, G+D [Satisfactory]

 1 e  0.5(M G  M D)  M L  f te,0.5(G D) L  0.5Pe     S ct  A St 

 1 e  M M M f be  Pe     G D L  S cb  A Sb 

1.646 kNis

-0.175 kPa

>

[Satisfactory]

< me, 0.5(G+D)+L [Satisfactory]

-Fbe

[Satisfactory]

43

CHECK ULTIMATE LOAD CONDITION (AASHTO 9.15.1 & 9.17 ACI 318-11 18.7) FACTORED ULTIMATE MOMENT Mu,x = g ( b D MD + b L ML ) = 1.3 [ 1.0 ( M G + MD) + 1.67 ML] (AASHTO Eq. 3-10) = 200579.551 kN-m Mu,y = 41320.410 kN-m 2

2 0.5

Mu = (Mu,x + Mu,y ) = 20791.430 kN-m q=

11.6

deg

COMPRESSION ZONE FACTOR b1 = 0.75 , (ACI 318-11 R10.2.7) TENDON TYPE FACTOR g p = 0.280 , (ACI 318-11 18.7.2) RATIO OF TENSION REmmF. r = 0.001 , RATIO OF COMPR. REmmF. r' = 0.002 , RATIO OF PRESTR. REmmF. rp = 0.006 , mmDEX OF TENSION REmmF. w = 0.013 , mmDEX OF COMPR. REmmF. w' = 0.016 , mmDEX OF PRESTR. REmmF. wp = 0.237 , STRESS mm BONDED TENDONS :





(ACI 318-11 Chapter 2) (ACI 318-11 Chapter 2) (ACI 318-11 Chapter 2) (ACI 318-11 18.7.2) (ACI 318-11 18.7.2) (ACI 318-11 18.7.2)

    f pu d    '  p   , 0.17    f ps  f pu 1     MIN  p '       1 fc dp   

243.940 kPa

44

STRESS mm UNBOUNDED TENDONS :

e s,max = 0.0021 , (ACI 318-11 10.3.4 & 10.3.5) c = 98.2 mm, by pure math method Fc = 32282.5 kPa

  f' f ps  MIN  f se  10  c , f y, f se  60     100 p  

dc =

47.3

mm

f Mn = 2603343 kN-m > Mu [Satisfactory]

'  fc MIN f se 10 , f y, f se 30 f ps   300 p 

 1 e  S  1.2M cr  1.2S b  Pe     7.5 f 'c   M G  cb  1   Sb    Ac S b  

145854

kN-m < f Mn [Satisfactory] (AASHTO 9.18.2 & ACI 318-11 18.8.2)

CHECkN SHEAR CAPACITY (AASHTO 9.20, ACI 318-11 11.1 & 11.4)

d  MAX  0.8h , d p  

 f 'c  MIN 100 , 

84.00 mm

 f 'c

  provd 

77.46 psi

      V ud p   MAX MIN  0.6 f 'c  700MIN 1 , d , 5b wd f 'c  , 2b wd f 'c  , for f se  0.4 f pu b  w     M u    V c      ' 2b wd f c , for f se  0.4 f pu

 Av f yd  , 8b wd f 'c   V s  MIN   S 

3200.40 kPa

MIN  0.75d , 24  , for  4 d f ' V s bw c   S max   MIN  0.375d , 12  , for V s  4b wd f 'c

5441.73

  d   A ps f puS  bw  MAX  50b wS , , for f se  0.4 f pu   f  80 df y y   Av(min)        50b wS , for f se  0.4 f pu   f y

24.00

kPa

1.867 mm2

mm

45

V c  no shear re inf . requd , for case1: V u  2  V  , for case 2: c  V u  V c  Av,requd   Av(min) 2  MAX  Av,cal , Av(min)  , for case 3: V c  V u   V S  V c   unsatisfactory , for case 4:  V S  V c   V u

4.434 mm2 [Satisfactory], Case 3 applicable

CHECkN TORSIONAL CAPACITY (AASHTO 9.21, ACI 318-11 11.1 & 11.5) Acp

=

26880 mm2

Pcp

=

752

fpc

=

0.765 kPa

Aoh

=

25293 mm2

Ph

=

735

At  Tu  S 1.7 Aoh f yv cos 37.5

mm

Tu

>

f pc  Acp2   f 'c   1   5278.243 kN-mPa  P cp  '   4 fc

Thus, Torsional Remmf. Reqd.

mm

0.020 mm2/mm

 Av  2 At 50bw   At   MAX ,   S  S f yv   Total Re qD 

 5 Acp f 'c  f yv   At 25bw   At   f yv  2   MAX 37.5  ,  P h   max  ,     87.77 mm2   cot AL Ph  f yL   S f yv   S   f yL  f yL     

0.595 mm2/mm <

 At  S   ProvD

0.635 mm2/mm

[Satisfactory]

46

CHAPTER 4 : FINAL DESIGN After analyzing the data calculated and considering the specific codes and standards provided by AASHTO, National Structural Code of the Philippines and the Department of Public Works and Highways, the designer have finalized the design of the prestressed concrete beam to be used in the Tanza – Trece – Martires Bridge project. The design is ensured to conform to the standards of various structural codes used as well as the safety of the structure. With this, a detailed geometric cross-section of the girder and the schedule of prestressing and non-prestressing reinforcement to be used are presented in this chapter. 4.1 Beam Schedule

Figure 4-1. Final Geometric Cross-Section of the I-Beam

47

4.2 Prestressing and Non-Prestressing Steel Schedule Table 4-1. Prestressing and Non-Prestressing Steel Details

Prestressing Steel Property

Details

Bottom Prestressing Tendons

16 x 36 – ½” Φ Tendons

Web Prestressing Tendons

4 x 36 – ½” Φ Tendons

Non-Prestressing Steel Property

Details

Top Compression Reinforcement

2 #8 @ 12mm O.C.

Bottom Compression Reinforcement

2 #8 @ 12mm O.C.

Web Compression Reinforcement

2 #8 @ 12mm O.C.

Shear Stirrup Reinforcement

2 legs, #10 @ 8mm O.C.

48

CHAPTER 5 : ACTUAL PHOTOS 5.1 Existing Cast-in-place Bridge

Figure 5-2. Perspective View of the Superstructure Prestressed Concrete Bridge

49

5.2 Proposed Prestressed Concrete Bridge

Figure 5-2. Perspective View of the Superstructure Prestressed Concrete Bridge

50

REFERENCES ► Bridge Design Specifications – LRFD, 6th Edition, 2012, American Association of State Highway and Transportation Officials (AASHTO). Retrieved from: http://utc2.edu.vn/Uploads/File/AASHTO%20LRFD%202012%20BridgeDesignSpecifications%206t h%20Ed%20%28US%29.PDF ► Design Guidelines, Criteria and Standards, DPWH. ► National Structural Code of the Philippines, NSCP Vol. II - Bridges, 2nd Ed., 1997 ► DPWH Department Order No.75, Series of 1992 ► Comprehensive Design Example for Prestresses Concrete (PSC) Girder Superstructure Bridge with Commentary (The Federal Highway Administration) ► American Concrete Institute ► American Society of State Highway and Transportation Officials 2007 ► LRFD Bridge Design – AASHTO Bridge Design Specifications – Loadings and General Information. Retrieved from: http://www.inti.gob.ar/cirsoc/pdf/puentes_hormigon/16-AAC-Load%20HandoutColor.pdf

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