Design-of-prestressed-concrete-bridge-for-barkadahan-bridge-in-brgy.-san-juan-taytay-rizal (1).docx

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

COLLEGE OF ENGINEERING AND ARCHITECTURE Civil Engineering Department

CE 513 Prestressed Concrete Design CE52FA2

DESIGN OF PRESTRESSED CONCRETE BRIDGE FOR BARKADAHAN BRIDGE IN BRGY. SAN JUAN, TAYTAY, RIZAL

Prepared by: Balgemino, John David T. Catalan, Jeannivieve Quenn Anzhel R. Elfa, Cherylle Mae E. Garcia, Mary June B. Mabanta, Michelle N.

Submitted to: Engr. Debbie Lyn Cabacungan Instructor

March 22, 2019

TABLE OF CONTENTS Chapter 1 : PROJECT BACKGROUND......................................................................................................... 1 1.1 Background of the Study ..................................................................................................................... 1 1.2 Project Objectives ................................................................................................................................ 2 1.2.1 General Objective/s ...................................................................................................................... 2 1.2.2 Specific Objective/s ...................................................................................................................... 2 1.3 Project Scope and Limitations ............................................................................................................. 3 1.3.1 Scope of the Project ..................................................................................................................... 3 1.3.2 Limitation of the Project ................................................................................................................ 3 1.4 Project Development ........................................................................................................................... 3 Chapter 2 : LOCATION.................................................................................................................................. 5 2.1 Project Location ................................................................................................................................... 5 Chapter 3 : DESIGN COMPUTATION ........................................................................................................... 8 3.1 Preliminary Data .................................................................................................................................. 8 3.1.1 Input Parameters .......................................................................................................................... 8 3.1.2 Design Loads .............................................................................................................................. 11 3.1.3 Reliability Index........................................................................................................................... 20 3.1.4 Load Combinations ..................................................................................................................... 21 3.2 Material Description ........................................................................................................................... 22 3.3 Material Specifications ....................................................................................................................... 23 3.4 Structural Design of Bridge ................................................................................................................ 24 3.5 Design of Road Cross-Section........................................................................................................... 25 3.6 Prestressed Concrete Beam Bridge Layout ....................................................................................... 25 3.7 Design Flowchart ............................................................................................................................... 27 3.7.1 Prestress Losses ........................................................................................................................ 27 3.7.2 Stress Analysis ........................................................................................................................... 31 3.7.3 Composite Section...................................................................................................................... 36 3.7.4 Tension, Shear, Camber, Deflection ........................................................................................... 40

ii

LIST OF FIGURES Figure 1. 1 Barkadahan Bridge ...................................................................................................................... 1 Figure 1. 2 Bridge Problem ............................................................................................................................ 2 Figure 1. 3 Project Development Plan ........................................................................................................... 4 Figure 2. 1 Map of Rizal with Taytay Highlighted ........................................................................................... 5 Figure 2. 2 Bridge Location ............................................................................................................................ 6 Figure 2. 3 Northbound View of Bridge .......................................................................................................... 6 Figure 2. 4 Southbound View of Bridge ......................................................................................................... 7 Figure 3. 1 Topographic Map of Project Location .......................................................................................... 8 Figure 3. 2 Soil Profile of Project Location ..................................................................................................... 9 Figure 3. 3 Geohazard Map of the Proposed Bridge...................................................................................... 9 Figure 3. 4 Typical Traffic Flow in Barkadahan Bridge ................................................................................. 11 Figure 3. 5 Truck Loading ............................................................................................................................ 13 Figure 3. 6 Design Lane Loading ................................................................................................................. 14 Figure 3. 7 Distance of the Bridge from the Nearest Fault Line ................................................................... 19 Figure 3. 8 Bridge Design Structure ............................................................................................................. 24 Figure 3. 9 Cross-Section of the Road ......................................................................................................... 25 Figure 3. 10 Deformed Shape of the Bridge after application of Loadings ................................................... 26 Figure 3. 11 Moment Diagram of the Bridge ................................................................................................ 26

LIST OF TABLE Table 3. 1 Present Level of Service (LOS) of Bridges by River Crossing .................................................... 10 Table 3. 2 Unit Weight of Materials .............................................................................................................. 12 Table 3. 3 Values of Vo and Zo for Suburban Surface Condition................................................................. 16 Table 3. 4 Base Pressure PB Corresponding to VB = 160 km/h .................................................................. 17 Table 3. 5 Seismic Loading Coefficients ...................................................................................................... 17 Table 3. 6 Values for Coefficient of y and β for service load ........................................................................ 21 Table 3. 7 Values for Coefficients of γ and β for Load Factor Design .......................................................... 22 Table 3. 8 Material Specifications ................................................................................................................ 23

iii

CHAPTER 1 : PROJECT BACKGROUND 1.1 Background of the Study The Proposed Project is a Design of Pre-Tensioned and Post-Tensioned Concrete Beam for the existing cast-in-place bridge known as the Barkadahan Bridge that connects the Laguna Lake Highway (formerly known as C-6 Highway) to Highway 2000 in Taytay, Rizal. Barkadahan Bridge is a 2-lane bridge structure with significant local traffic such as tricycles for commuters and private vehicles coming from different roads in Cainta, Taytay, and Taguig.

Figure 1.1 Barkadahan Bridge Instead of expanding the existing bridge, the proponents decided to build another bridge likely so as to reduce disturbance of traffic along the already congested first bridge. This is the same strategy for the bridge across the Pasig River in Nagpayong/Napindan that will reduce the potential bottleneck for when C-6’s expansion is completed. Unfortunately, the bridges don’t seem to include provisions for exclusive bicycle lanes that are clearly incorporated along much of C-6. DPWH-NCR allocated a total of P114.35 million for the widening and improvement of Barkadahan Bridge which is a combined prestressed concrete girder and concrete flat slab bridge with 11 spans, 3.25 lineal meter east bank approach and 7.8 lineal meter west bank approach. 1

Our Design Project will be focusing on the first and older bridge, with signs of poor construction can be seen throughout the bridge. The existing cast-in-place construction will be replaced with a prestressed concrete beam design. With the improvement of the 245-lineal meter bridge, it is seen to benefit thousands of motorists utilizing Laguna Lake Highway as an alternative route to the congested EDSA and C-5 Road. The Design Process conforms to the standards designated in the National Structural Code of the Philippines – Volume II: Bridges and AASHTO Bridge Design Specifications.

Figure 1.2 Bridge Problem 1.2 Project Objectives The project design team aims to achieve the following objectives: 1.2.1 General Objective/s 

To design a bridge that will provide an improved design of the existing Barkadahan Bridge in Taytay, Rizal.

1.2.2 Specific Objective/s 

To design a bridge conforming to the necessary codes and design standards considering prestress losses, stress analysis, composite section, anchorage, tension, shear, camber and deflection. 2

 

To compute for the initial requirements in designing the prestressed concrete bridge. To provide specifications of structural plans for the design of the prestressed concrete bridge.

1.3 Project Scope and Limitations 1.3.1 Scope of the Project The following are the scopes of the project:  Detailed road plans and specifications of the area subjected to the bridge design  Plans and specification of the design reinforcements  Analysis of the present traffic condition of the area  Only the structure of the bridge will be designed and considered in the structural analysis  The design of the project is based according to the specifications of the bridge design 1.3.2 Limitation of the Project The following are the limitations of the project:   

Cost estimation of materials, equipment and labor for the Project Design Detailed construction management specification of the project Architectural aspects are not included

1.4 Project Development To obtain the optimal prestressed bridge design, the team will follow a series of stages conceptualize by the designers themselves. The steps are distinctly explained and presented in the flow chart at Figure 1.3. To see the scope of the project, the designers will have an actual site visit on the project location vicinity. Data would also be gathered from different researches and studies related to site area. Furthermore, data of Preliminary Investigation and Detailed Site investigation will be requested from Department of Public Works and Highways (DPWH) Central Planning Service. Next, the data gathered will be analyze and study to help the designers decide on the approach that would be used for the design development of the bridge. The designer made sure that the plans for the 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. The detailing for the preferable design will be finalized and will be into the actual project proposal. The conclusion from the project will be based on the knowledge learned and applied by the designers throughout the course of the design.

3

Site Investigation

Data Analysis

Conceptualization of the Project

Evaluation Trade-Off of Design Parameters 2 Trade-offs

Design Scheme & Analysis

Final Bridge Design

Project Conclusion Figure 1.3 Project Development Plan

4

CHAPTER 2 : LOCATION 2.1 Project Location Taytay, officially the Municipality of Taytay, is a 1st class municipality in the province of Rizal, Philippines. According to the 2015 census, it has a population of 319,104 people. It is the third most populous municipality in the country, after Rodriguez and Cainta. It is situated in the province's western portion, bounded by the grids 14° 34’ 24" north latitude and 121° 07’ 48" east longitude. It shares boundaries with Cainta in the Northwest, Antipolo in the North-northeast, Angono in the East-southeast and Taguig in the Southwest. The municipality is sited to East of Pasig and to the North of Laguna Lake. It has an area of 38.80 km2 (14.98 sq mi) representing 3.3% of Rizal Province's land area. The shape of Taytay is rectangular – trapezoidal with gently hilly rolling terrain on its eastern side while relatively flat on its south-western side, including the poblacion. The municipality's highest elevation ranges from 200 to 255 meters which is situated along the inner north-eastern hills of Barangay Dolores, alongside the Antipolo Boundary. Its lowest points are from 5 to 20 meters along the southern portion of Barangay San Juan and Muzon towards Laguna Lake.

Fig 2.1 Map of Rizal with Taytay Highlighted Source: @wikipedia.com

5

Fig 2.2 Bridge Location Source: @googleearth.com

Fig 2.3 Northbound View of Bridge 6

Fig 2.4 Southbound View of Bridge

7

CHAPTER 3 : DESIGN COMPUTATION 3.1 Preliminary Data This section presents the data gathered necessary for the bridge design, specifically the determination of bridge dimensions. Reliable sources of information were utilized by the designers to be able to initialize the project design. Enumerated below are the input parameters desired necessary to the procedure of bridge design. 3.1.1 Input Parameters 3.1.1.1 Topographic Map and Soil Profile The topographic map shown display the surface elevation around the vicinity of project location. Correspondingly, the soil profile projected below the proposed bridge across east and west bank are shown. Elevation of the soil is taken every 20 meters beginning at 0+00 from the East Bank road. The survey data collected from the Department of Public Works and Highways are important to determine the road finished grade.

Figure 3.1 Topographic Map of Project Location Source: en-ph.topographic-map.com

8

18.358 16.622 14.049

Ground Elevation (m)

12.557

12.301

11.339 9.683 9.413 9.154

0

20

40

60

80

100

9

120 140 Stations

9

9.329

160

180

13.105

10.037

200

220

240

260

Figure 3.2 Soil Profile of Project Location Source: DPWH Central Office

Figure 3.3 Geohazard Map of the Proposed Bridge Source: Mines and Geosciences Bureau

9

3.1.1.2 Traffic Flow The Department of Public Works and Highways conducted a traffic count survey on the existing bridge from December 2016 to February 2017. Table 3.1 Present Level of Service (LOS) of Bridges by River Crossing River

No. of Bridges

No. of Lanes

Traffic volume (veh/day)

Traffic Capacity (veh/lane)

Present Level of Service

at LOS E Pasig River

17

70

824,500

618,800 to 681,200

F

Marikina River

9

36

371,600

302,700 to 382,400

E

Manggahan Floodway

4

12

104,400

95,100 to 124,600

E

Total

30

118

1,300,500

1,016,600 to 1,188,200

E

Source: DPWH Central Office The overall capacity of Manggahan floodway is “E” which means that the “operation is at near capacity and unstable level”. Vehicles operate at the minimum spacing from which uniform flow can be maintained. Disruptions cannot be easily dissipated and usually result in the formation of queues and the deterioration of service. On the other hand, the level service in Pasig River is “F”, which means the “forced or breakdown flow and exceeding its capacity”.

10

Figure 3.4 Typical Traffic Flow in Barkadahan Bridge Source: Mines and Geosciences Bureau Figure shows the typical traffic condition in the existing bridge during peak hours, from 4:30 pm to 8:30 pm. It can be inferred that the traffic condition in Barkadahan is worse due to most of the commuters in eastern Rizal are bound to Taguig and Makati and the bridge is only two-lane road, even if the bridge is already widened last 2017.

3.1.2 Design Loads The design loads presented applied primarily to the design of bridge which includes dead loads, live loads, wind loads and seismic loads. In addition, the loads in this section do include those associated with extreme events for the risk assessment of the structure. Design loads will be based on AASHTO LRFD for Highway Bridge Superstructures, NSCP Volume II 2nd Edition (1997) Bridges and DPWH Bridge Design Manual (2015) Volume 5. 3.1.2.1 Dead Loads The dead load consists of the self-weight of the structure and superimposed loads coming from the railing system, sidewalks, signing and the wearing surface. Table shows the unit weight of the materials to be used for the dead loads of the structure.

11

Table 3.2 Unit Weight of Materials Material

Load

a. Concrete Plain Reinforced

23.0 kN/m3

b. Reinforced Concrete

24.0 kN/ m3

c. Structural Steel

77.0 kN/m3

d. Fill Materials

18.0 kN/m3

e. Wearing Surface

1.05 kPa

Source: NSCP Volume 2 ̶ Section 3.3.4 3.1.2.2 Live Loads Live loads are the loads that can change overtime or can move through the surface of the structure. For bridge designs, three types of live load are always considered. The first is the vehicular load, which can be truckload or lane load, whichever governs, the second type is the impact load, which is always present for the live load calculation and the pedestrian load which is applied on sidewalks. The design model used for vehicles is HL-93 based on the DPWH Design Manual. 3.1.2.2.a Vehicular Loads In bridge design, vehicles crossing a bridge come in various shapes, sizes and weights such as motorcycles, cars, buses and trucks. However, the most significantly affect bridge are based on truck loads. Vehicular live loading on the roadway of bridges or incidental structures, designated as HL-93 shall consist of the combination of design truck, design tandem, and design lane load. 3.1.2.2.b Design Truck The weights and spacing of axles and wheels for the design truck shall be specified in the figure. The spacing between the two 145 kN axles shall be varied between 4.3 and 9.1 m to produce extreme force effects.

12

Figure 3.5 Truck Loading Source: DPWH Bridge Manual - Section 10.7.3.1 3.1.2.2.c Design Lane Load According to DPWH Bridge Manual - Section 10.7.3.2, the design tandem shall consist of a pair of 108 kN axles spaced at 1.2 m apart. The transverse spacing of wheels shall be taken as 1.8 m. 3.1.2.2.d Design Tandem The design lane load shall consist of 9.34 kN/m, uniformly distributed in the longitudinal direction. Transversely, the design lane load shall be assumed to be uniformly distributed over a 3.0 m width. The force effect of the design load shall not be subject to a dynamic load allowance. The design loading is shown in the figure below.

13

Figure 3.6 Design Lane Loading Source: DPWH Bridge Manual - Section 10.7.3.3

3.1.2.3 Impact Loads According to NSCP Volume 2 – Section 3.8.2.1, the amount of impact allowance or increment is expressed as a fraction of live load shall be: 𝑰=

𝟏𝟓. 𝟐𝟒 𝑳 + 𝟑𝟖

where L is the span in meters

3.1.2.4 Pedestrian loads According to AASHTO LRFD – Section 3.4.7, pedestrian load is included in the analysis since according to AASHTO LRFD, for bridges designed for both vehicular and pedestrian load and with a sidewalk wider than 600 mm, pedestrian load will be applied in the design.

Pedestrian load ……………………………………………………. 3.6 kPa

14

3.1.2.5 Wind Loads The wind load consists of uniformly distributed loads applied to the exposed area of the structure. It must be noted that the sum of area of all members, with the inclusion of the railing system and floor system, is taken from the exposed area of the structure. Wind load is considered in the design of superstructure for long span bridges. 3.1.2.5.a Horizontal Wind Pressure Wind pressures shall be calculated based on the base design wind velocity (VB) of 160 kph. All girders, decks, attachments, and other structural components which are exposed in elevation are subject to the same uniform wind pressure. For bridges or parts of bridges more than 10m above ground or water level, the design wind velocity VDZ shall be adjusted according to:

𝑽𝟏𝟎 𝒁 𝑽𝑫𝒁 = 𝟐. 𝟓𝑽𝒐 ( ) 𝐥𝐧 ( ) 𝑽𝑩 𝒁𝒐 where: 𝑉𝐷𝑍

=

design wind velocity at design elevation, z (km/h)

𝑉10 = wind velocity above 10 m height or above design water level (km/h) 𝑉𝐵 = 160 km/h 𝑍

base wind velocity (km/h) which has a value of

= height of structure at which wind load are being calculated as measured from ground level or from water level

𝑉𝑂 = friction velocity, specified in Table 2.3 for various upwind surface characteristics 𝑍𝑂 = Table 2.3

friction length of upstream fetch specified in

15

Table 3.3 Values of Vo and Zo for Suburban Surface Condition Parameter

Suburban

Vo (km/hr)

17.6

Zo (mm)

1000

Source: AASHTO LRFD – Section 3.5.1.1

Except for sound barriers, V10 may be established from:    

Basic Wind Map from PAGASA specified in the DCGS. Site-specific wind surveys. In the absence of better criterion, the assumption is V10 = VB = 160 kph

3.1.2.5.b Wind Pressure on Structure A different base design wind velocity may be selected for load combination not involving wind on live load. In the absence of more precise data, design wind pressure, in MPa may be determine as:

𝑽𝑫𝒁 𝟐 𝑽𝑫𝒁 𝟐 𝑷𝑫 = 𝑷𝑩 ( ) = 𝑷𝑩 ( ) 𝑽𝑩 𝟐𝟓𝟔𝟎𝟎 where: 𝑃𝐵

=

base wind pressure specified

The wind force on the structure shall be calculated by multiplying the design wind pressure PD calculated by the exposed area.

16

Table 3.4 Base Pressure PB Corresponding to VB = 160 km/h Structure Component

Windward Load (MPa)

Leeward Load (MPa)

Beams

0.0024

N/A

Source: AASHTO LRFD – Section 3.5.1.2 The total wind loading shall not be taken less than 4.4 kN/m in the plane of a windward chord and not less than 4.4 kN/m on beams and girder spans of the leeward chord.

3.1.2.6 Seismic Load Bridges are designed for seismic loads such that they have low probability of failure due to seismically induced ground shaking. Seismic Loading shall be based on the recommendations of the references mentioned, which is summarized in the table below.

Table 3.5 Seismic Loading Coefficients Importance Classification

I

Essential

1

Zone (Z)

4

Acceleration Coefficient (A)

0.4

Soil Type

II

Site Coefficient (S)

1.2

Source: NSCP Volume 2 ̶ Section 21

17

3.1.2.7 Seismic Hazard The seismic hazard at a bridge site shall be characterized by the acceleration response spectrumfor the site and the site factors for the relevant ground types (site class). For a level 2 earthquake ground motion, the following are the data obtained: Peak Ground Acceleration (PGA) ………………………………………. 0.50 Short-period spectral acceleration coefficient (Ss) at period 0.2 second..1.1 Long-period spectral acceleration coefficient (S1) at period 1 second ….. 0.6

3.1.2.8 Elastic Seismic Response Coefficient and Spectrum The elastic seismic coefficient Cs used to determine the design forces is given by: a. For period less than or equal to T0, the elastic seismic coefficient for the mth mode of vibration, Csm, shall be taken as: 𝑻𝒎 𝑪𝒔𝒎 = 𝑨𝑺 + (𝑺𝑫𝑺 − 𝑨𝑺 ) ( ) 𝑻𝟎 in which: 𝐴𝑆 = 𝐹𝑝𝑔𝑎 𝑃𝐺𝐴 𝑆𝐷𝑆 = 𝐹𝑎 𝑆𝑆 Where: 𝐶𝑠𝑚

=

elastic seismic response coefficient

𝐴𝑆

=

effective peak ground acceleration coefficient

𝐹𝑝𝑔𝑎

=

site coefficient for peak ground acceleration

𝑃𝐺𝐴

=

peak ground acceleration coefficient on rock

18

𝐹𝑎 = coefficient

site coefficient for 0.2-sec period spectral

𝑆𝑆 = horizontal response spectral acceleration coefficient at 0.2-sec period on rock 𝑇𝑚

=

period of vibration of mth mode (s)

𝑇0 0.2 𝑇𝑠

=

reference period used to define spectral shape =

𝑇𝑠 = corner period at which spectrum changes from being independent of period to being inversely proportional to period = 𝑆𝐷1 /𝑆𝐷𝑆 (s)

Figure 3.7 Distance of the Bridge from the Nearest Fault Line

19

3.1.3 Reliability Index The reliability index calculation is based on AASHTO LRFD Bridge Design and Specifications. In the computation of reliability index to determine the reliability assessment of the bridge is given by the following formulas: The safety margin is calculated as: 𝑍 = 𝑅 − (𝐷 + 𝐿) Where: R = resistance D = Dead load L = Live Load (truck loads) S= D+L (total load)

Standard deviation𝜎𝑆 is given by (assuming that D and L are statically independent): 𝜎 2𝑆 = 𝜎 2 𝐷 + 𝜎 2 𝐿

Total load effect mean value is expressed as, 𝜇𝑆 = 𝜇𝐷 + 𝜇𝐿 The total load effect coefficient of variation is given by the equation, 𝑉𝑆 =

𝜎𝑆 𝜇𝑆

Reliability index (β) is given by: 𝜷=

𝐥𝐧(𝝁𝑹 ) − 𝐥𝐧(𝝁𝑺 ) √𝑽𝟐 𝑹 + 𝑽𝟐 𝑺

Note that the target reliability index is 3.5 will be used in the design. Source: AASHTO LRFD Bridge Specifications̶̶ Section 1.2.3

20

3.1.4 Load Combinations The Group Loading combinations for the Service Load Design and Load Factor Design, as recommended by AASHTO and NSCP is taken as:

𝑮𝒓𝒐𝒖𝒑 (𝑵) = 𝜸(𝜷𝑫 𝑫𝑳 + 𝜷𝑳 (𝑳 + 𝑰) + 𝜷𝑪 𝑪𝑭 + 𝜷𝑬 𝑬 + 𝜷𝑩 𝑩 + 𝜷𝑺𝑭 𝑺𝑭 +𝜷𝑾 𝑾 + 𝜷𝑳𝑭 𝑳𝑭 + 𝜷𝑹 (𝑹 + 𝑺 + 𝑻) + 𝜷𝑬𝑸 𝑬𝑸)

Source: NSCP Volume 2 ̶ Section 3.22.1 Where, 𝛾 and 𝛽 are coefficients taken from the tables below which came from AASHTO and NSCP. Other factors and load combination are taken from the same tables.

Table 3.6 Values for Coefficients of 𝜸 and 𝜷 for Service Load Group

𝜷 FACTORS

𝜸

SERVICE LOAD

D

(L+I) (L+I)

CF

E

B

SF

W

WL

LF

R+S+T

EQ

%

I

1

1

1

0

1

𝛽𝐸

1

1

0

0

0

0

0

100

IA

1

1

2

0

0

0

0

0

0

0

0

0

0

150

IB

1

1

0

1

1

𝛽𝐸

1

1

0

0

0

0

0

***

II

1

1

0

0

0

1

1

1

1

0

0

0

0

125

III

1

1

1

0

1

𝛽𝐸

1

1

0.3

1

1

0

0

125

IV

1

1

1

0

1

𝛽𝐸

1

1

0

0

0

1

0

125

V

1

1

0

0

0

1

1

1

1

0

0

1

0

140

VI

1

1

1

0

1

𝛽𝐸

1

1

0.3

1

1

1

0

140

VII

1

1

0

0

0

1

1

1

0

0

0

0

1

133

VIII

1

1

1

0

1

1

1

1

0

0

0

0

0

140

21

IX

1

1

0

0

0

1

1

1

1

0

0

0

0

150

X

1

1

1

0

0

𝛽𝐸

0

0

0

0

0

0

0

100

Table 3.7 Values for Coefficients of 𝜸 and 𝜷 for Load Factor Design 𝜷 FACTORS

𝜸 D

(L+I) (L+I) CF

E

B

SF

W

WL

LF

R+S+T EQ

I

1.3

𝛽𝐷

1.67

0

1

𝛽𝐸

1

1

0

0

0

0

0

IA

1.3

𝛽𝐷

2.20

0

0

0

0

0

0

0

0

0

0

IB

1.3

𝛽𝐷

0

1

1

𝛽𝐸

1

1

0

0

0

0

0

II

1.3

𝛽𝐷

0

0

0

𝛽𝐸

1

1

1

0

0

0

0

III

1.3

𝛽𝐷

1

0

1

𝛽𝐸

1

1

0.3

1

1

0

0

IV

1.3

𝛽𝐷

1

0

1

𝛽𝐸

1

1

0

0

0

1

0

V

1.3

𝛽𝐷

0

0

0

𝛽𝐸

1

1

1

0

0

1

0

VI

1.3

𝛽𝐷

1

0

1

𝛽𝐸

1

1

0.3

1

1

1

0

VII

1.3

𝛽𝐷

0

0

0

𝛽𝐸

1

1

0

0

0

0

1

VIII

1.3

𝛽𝐷

1

1

1

𝛽𝐸

1

1

0

0

0

0

0

IX

1.3

𝛽𝐷

0

0

0

𝛽𝐸

1

1

1

0

0

0

0

X

1.3

1

1.67

0

0

𝛽𝐸

0

0

0

0

0

0

0

%

NOT APPLICABLE

LOAD FACTOR DESIGN

Group

Source: NSCP Volume 2 ̶ Section 3.22, Table 3.22.1A

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. 22

3.3 Material Specifications The following are the material properties of the prestressed concrete bridge based on NSCP Volume 2. Table 3.8 Material Properties of the Prestressed Concrete Bridge

23

3.4 Structural Design of Bridge The design has 3 cells with 21.65 meters total width and a depth of 3.0 meters.

Figure 3.8 Bridge Design Structure

24

3.5 Design of Road Cross-Section The design of road section of the bridge is shown on the figure below. It has a 4-lane with 3.35 meters’ road width and a 3-meter pedestrian side walk at both side.

Figure 3.9 Cross-Section of the Road

3.6 Prestressed Concrete Beam Bridge Layout The design demonstrates the use of the AASHTO LRFD Design Specifications in the design of cast-in-place post-tensioned concrete beam. The bridge is required to cross over a waterway. Figure shows the elevation of the prestressed concrete bridge. A three-span continuous bridge is selected to minimize the depth of the structure. The span lengths are decided to be 84.5-85.5-84.5 m.

25

Figure 3.10 Deformed Shape of the Bridge after application of Loadings

Figure 3.11 Moment Diagram of the Bridge

26

3.7 Design Flowchart 3.7.1 Prestress Losses

START

IDENTIFY Ac, Ic, Sb, St, fpu, fpi, fpy, Eps, f’ci, f’c, L, Aps, W d, Wsd, WL, anchorage seating ∆A, e, RH, V/S, time t, pretensioned or post-tensioned stress-relieved or low relaxation steel

COMPUTE FRICTION LOSS Post-tensioned

COMPUTE ANCHORAGE-SEATING LOSS

27

A A

COMPUTE ELASTIC-SHORTENING LOSS

where 0.90Pi = Pj

Pretensioned

Post-tensioned

COMPUTE CREEP LOSS

Pretensioned

Post-tensioned

B

28

B

COMPUTE SHRINKAGE LOSS

Pretensioned KSH = 1 Alternatively,

COMPUTE RELAXATION OF STEEL LOSS Stress-relieved strands Pretensioned

Post-tensioned

C

29

C

ADD ALL LOSSES Pretensioned

Post-tensioned

Calculate % of each type of loss. Add % of all losses.

END

30

3.7.2 Stress Analysis START

IDENTIFY WSD, W L, span, heigh limit, fpu, f’c, type of concrete, prestressed or post-tensioned.

ASSUME WD then CALCULATE MOMENTS MD, MSD, ML.

COMPUTE FOR fpi, f’ci, fti, ft and fc where: fpi = 0.70 fpu fci = 0.60 f’ci fti = 3√f’ci for midspan section f’c = 0.45 fc ft = 6√f’c to 12√f’c

A

31

A

CALCULATE PRESTRESS LOSSES

FIND MINIMUM REQUIRED SECTION MODULUS OF THE MINIMUM EFFICIENT SECTION For harped or draped tendons, use midspan controlling section:

For straight tendons, use end-support controlling section:

Where

CALCULATE CONCRETE FIBER STRESSES AT TRANSFER CONDITION

B

32

B

CALCULATE CONCRETE FIBER STRESSES AT SERVICE CONDITION

ESTABLISH THE ENVELOPES OF LIMITING ECCENTRICITIES FOR ZERO TENSION Where

AND and . If the tension in the concrete is used in the design, add

and

INVESTIGATE END-BLOCK ANCHORAGE STRESSES. DETERMINE MINIMUM DEVELOPMENT LENGTH

OF WHICH THE TRANSFER LENGTH

C

33

C

DETERMINE COMPOSITE ACTION STRESSES. Revise the section if the concrete fiber stresses exceed maximum allowable concrete fiber stresses both in the precast section and the situ-cast top slab. For Unshored Slab Case Before the top is situ cast

After the top slab is cast and cured, the stresses will be

The fibers stresses of situ cast hardened slab are

Fully shored Slab Case Before shoring and before topping is situ cast

After situ cast is cured

D

34

D

DETERMINE THE STRENGTH OF THE SECTION FOR THE LIMIT STATE AT FAILURE AND FOR SHEAR AND TORSIONAL STRENGTH.

END

35

3.7.3 Composite Section START

IDENTIFY Fpu, f’c, f’ci, W D, W SD, WL, L, straight or draped tendons

COMPUTE MOMENTS MD, MSD, ML, MTOTAL

COMPUTE PERMISSIBLE LINEAR STRESSES At transfer fci = -0.6 f’c fti = 6√𝑓′𝑐𝑖 At service fc = -0.45f’c ft = 12√𝑓′𝑐

A

36

A

YES

IS THE ECCENTRICITY CONSTANT?

YES

NO

YES

L < 30 ft?

Select from rectangular section according to Sb or St controlling.

NO

NO

Select from I section according to Sb or St controlling.

Select from T section according to Sb or St controlling.

INPUT DIMENSIONS

B

37

B

YES

Is the difference between assumed self-weight and calculated self-weight less than or equal to 10%?

NO

Go back to first step

INPUT DIMENSIONS

COMPUTE SECTION PROPERTIES Ac, Ic, Sb, St and r2

COMPUTE RANGE OF INITIAL PRESTRESSING FORCE AND ITS ECCENTRICITY

And

C

38

C

INPUT Pi AND CORRESPONDING dp

COMPUTE ACTUAL FIBER STRESSES At transfer

At service

YES

NO Is the section safe?

Select new dimensions.

END

39

3.7.4 Tension, Shear, Camber, Deflection Shear-web Reinforcement Design

START

IDENTIFY Bw, dp, h, f’c, λ, fy, fpe, fpu, Vu

Ø = 0.75

YES

NO

USE ALTERNATIVE DESIGN METHOD

USE DETAILED DESIGN METHOD

Dp = dp or dp = 0.8h (whichever is larger)

Dp = dp or dp = 0.8h (whichever is larger) Vc is lesser of

40 A

A

A

NO

YES

No web steel

Next section

NO

YES

Use minimum required web steel

NO

YES

Given s ≤ 0.75h ≤ 24 in. COMPUTE

Enlarge section SELECT WEB STEEL

If fpe ≥ 0.4fpu

Or Or

Whichever is smaller.

B

C

41

C B

NO

YES

Next section

Use

For same Av computed above

END

42

Camber and Deflection

START

INPUT Section Properties, load data, material properties, time intervals, prestress loss

CALCULATE FIBER STRESS AT MIDSPAN AND SUPPORT SECTION AT TRANSFER

A

43

A

CALCULATE PRESTRESS CAMBER AND SELF-WEIGHT DEFLECTION

B

44

B

COMPUTE TIME-DEPENDENT FACTORS FOR EACH TIME INTERVAL

NO

TOTAL LONG TERM DEFLECTION FOR COMPOSITE SECTION

YES GO TO STEP 6

YES

IS SECTION NONCOMPOSITE?

COMPUTE TOTAL DEFLECTION AT TIME STEP t FOR NONCOMPOSITE SECTION

IS THERE ANOTHER TIME INTERVAL?

NO

END 45

SECTION PROPERTIES OF SUPERSTRUCTURE

SECTION PROPERTIES OF SUPERSTRUCTURE I. REFERENCE AASHTO Standard Specifications for Highway Bridges, 17th Edition - 2002 II. INPUT A. SUPERSTRUCTURE DATA Effective width of slab

Ws = 5500

mm

ts = 200

mm

Modulus of elasticity (slab f'c = 28 Mpa)

Ecs = 24849

MPa

Modulus of elasticity (girder f'c = 42 Mpa)

Ecg = 30650

MPa

Thickness of slab

Modular ratio (n)

=

𝑐 𝑐

n = 1.233

No. of Girders

N=3

Girder distances from Z-axis

S = 2.1 =0 = 2.1

B. PROPERTIES OF ONE AASHTO GIRDER Type of Girder Area

m m m

Type = III Ag = 0.3613

m2 4

Modulus of Elasticity (z-axis)

Iz = 0.05216

Modulus of Elasticity (y-axis)

Iy = 0.005055 m4

Modulus of Elasticity (x-axis)

Ix = 0.005232 m4

Centroid from bottom

Yb = 0.5146

m

m 46

Centroid from top

Yt = 62.84

cm

Sb = 101436

cm3

St = 82918

cm

W = 0.867

ton/m

Weight Depth of Girder

Dg = 1.143

m

III. SECTION PROPERTIES OF SUPERSTRUCTURE A. DIMENSIONS OF THE TRANSFORMED SECTION Ws_tr = 4.459 =

m

ts_tr = 0.162

m

=

3

B. DISTANCE FROM C.G. OF SECTION TO BOTTOM OF GIRDERS 𝐷 =𝐷 + Dtot = 1.343 m 𝐴

=

𝑐 =

𝐴 +

Atot = 1.98 𝐷 +

𝐴

+

m

𝐴

ycg = 0.843

m

C. MOMENT OF INERTIA ABOUT THE Z-AXIS, Iz =

+

2

2

𝐷

−

− 𝑐

+

m4

Iz = 0.302 D. MOMENT OF INERTIA ABOUT THE Y-AXIS, Iy =

+

𝑔

+𝐴

𝑆𝑖

2

1

Iy = 5.450

m4

47

DESIGN OF INTERIOR DECK SLAB INTERIOR DECK SLAB I. INPUT A. SUPERSTRUCTURE DATA (Considering 1-m strip of deck slab) Thickness of slab ts = 200 Width of slab Effective span length of slab Thickness of future wearing surface

mm

bs = 1000

mm

S = 1694

mm

tfws = 50

mm

Girder width (average)

bg = 482.5

mm

Girder depth (from bottom of slab)

dg = 1143

mm

Typical girder spacing

Sg = 2.93

m

f'c = 28

MPa

fy = 414

MPa

B. MATERIAL DATA AND SPECIFICATIONS Compressive strength of concrete Yield strength of steel Main bar diameter Temperature bar diameter Distribution bar diameter Unit weight of concrete Unit weight of future wearing surface Reduction factor for flexure

db = 16

mm

dt = 12

mm

dd = 16

mm

γconc = 24 γfws = 22

kN/m

kN/m3

φ = 0.9

Clear cover

cc = 40

mm

Area of single main bar

Ab = 201.06

mm2

At = 113.10

mm2

Ad = 201.06

mm2

𝐴 =

2

Area of single temp bar 𝐴 =

2

Area of single dist bar 𝐴 =

3

2

48

II. LOADS AND DESIGN FORCES CALCULATIONS A. DEAD LOAD Weight of slab (including diaphragm) Wslab = 5.04 =

𝛾𝑐

𝑐

.

Weight of wearing surface 𝑓

= 𝑓

𝛾𝑓

+

Wfws = 1.21

kN/m2

WDL = 502.00

kN/m2

MDL = 144.06

kN*m/m

.

Total Weight of DL 𝐷𝐿 =

kN/m2

𝑓

Moment due to DL 𝐷𝐿 𝑆 2

𝐷𝐿 =

B. LIVE LOAD HS 20-444 Truck Loading (wheel load = 144/2)

P = 72

Impact Factor

kN

I = 0.3

Overloading factor (LL inc by 15%) Continuity factor

OP = 1.15 k = 0.8

AASHTO 3.24.3.1 Case A - Main Reinforcement Perpendicular to Traffic Moment due to LL+I 𝐿𝐿 + =

𝑆+

MLL+I = 20.34 𝑓

𝑓

𝑃

+

kN*m/m

𝑃

49

C. DESIGN ULTIMATE MOMENT Ultimate Moment = .

𝐷𝐿 + .

Cracking Moment 𝑐 = .

.

𝑓𝑐

Maximum Steel Requirement 𝛽 =

.

𝑖𝑓 𝑓 𝑐 𝑓𝑐

− .

kN*m/m

Mcr = 26.37

kN*m/m

MU = 231.41

kN*m/m

𝑃

Design Ultimate Moment

.

Mu = 231.41 𝐿𝐿 +

β1 = 0.85 −

𝑖

ρmax = 0.022 = .

.

𝛽

𝑓𝑐 𝑓

+

III. DESIGN OF REINFORCEMENTS A. TOP AND BOTTOM REINFORCEMENTS Effective depth of slab =

d = 152

.

−

k = 0.397

2

𝑓𝑐 .

2

− .

q = 0.634

Required steel ratio =

mm

− 𝑐𝑐 −

=

=

𝑓

ρ = 0.043

𝑓𝑐 𝑓

Minimum steel ratio

ρmin = 0.003

. 𝑖 = 𝑓

Required area of steel

As = 6513.53

mm2

𝐴 =

Spacing of main reinforcement 𝑐𝑖

=

spacing = 30.87

mm

𝐴 𝐴

say

Sb = 200

16 mm @ 200 mm. O.C. reinforcements for top and bottom of slab

mm

50

B. DISTRIBUTION REINFORCEMENT Note: Distribution reinforcement shall be placed transverse to the main steel reinforcement in the bottom of all slabs to provide for the lateral distribution of the concentrated live loads. The area of secondary steel should not exceed 67% of the area for primary reinforcement 𝐴 =

Required area of secondary steel 𝐴

=

𝐴

𝐴 𝑖𝑓 𝐴

%

As_d = 4364.06

mm2

𝐴 𝑖

Spacing of secondary steel 𝑐𝑖

%As = 92.97 𝑆

spacing = 46.07

mm

𝐴 𝐴

=

say

Sd = 300

mm

16 mm @ 300 mm. O.C. distribution reinforcements for bottom of slab C. SHRINKAGE AND TEMPERATURE REINFORCEMENT AASHTO 8.20.1 Minimum area of shrinkage and temperature reinforcement 𝑖 2 As_t = 264.58 𝐴 = 𝑓

mm

2

Maximum spacing of shrinkage and temperature reinforcement 𝑐𝑖

=

𝐴 𝐴

𝑖

spacing = 427.45 say

St = 180

mm mm

12 mm @ 180 mm. O.C. shrinkage and temperature reinforcement for top of slab

51

DETAILED MS EXCEL COMPUTATION OF PRESTRESSED GIRDER PRESTRESSED GIRDER I. REFERENCE AASHTO 2002 II. INPUT A. MATERIAL PROPERTIES Compressive strength of Deck Slab concrete f'c = 20.7

MPa

Compressive strength of Prestressed concrete @ Transfer stage f'ci = 38 MPa Compressive strength of Prestressed concrete @ Service stage f'cs = 42 MPa Modulus of Elasticity of Cast in Place Concrete 𝑐= 𝑓𝑐 E'c = 21520.000 MPa Modulus of Elasticity of Prestressed Concrete @ Transfer Stage 𝑐𝑖 = 𝑓 𝑐𝑖 E'ci = 28972.746 MPa Modulus of Elasticity of Prestressed Concrete @ Service Stage 𝑐 = 𝑓𝑐 E'cs = 30459.481 MPa Unit Weight of Concrete

γconc = 24

kN/m3

γfws = 22

kN/m3

Unit Weight of Wearing Surface Yield Strength of Reinforcing Steel

Fy = 414

MPa

Aps = 98.7

mm2

Tensile Strength of Prestressign Strands fs' = 1860

MPa

Jacking of Prestressing Strands

Fj = 1395

MPa

dv = 12

mm

Nominal Area of Prestressing Strands

𝐹 = .

𝑓 ′

Diameter fo Shear Reinforcement

52

Diameter of Top Reinforcement

dt = 16

mm

db = 25

mm

Es = 200000

MPa

Diameter of Bottom Reinforcement

Modulus of Elasticity of Steel Unit Weight of Steel B. SECTION PROPERTIES Width of Superstructure

γsteel = 77

kN/m3

Ws = 5.5

m

Wearing Surface Thickness

Tfws = 0.05

m

Clear Roadway Width

Wclr = 3.5

m

Area of Parapet

Apar = 0.2

m

Numbr of Lanes

Nl = 1

Girder Type

Gt = 3

Structural Slab Thickness

Ts = 0.2

m

Bearing to Bearing Length

Lb = 18.4

m

Girder Spacing

Sg = 2.1

m

Area of Median Number of Girders Sections to be considered

Amed = 0

m

2

2

Ng = 3 n_sect = 6

Distance where forces are to be considered (from Center to Bearing) Xi = 0 m 2 m 3 m 4 m Lb/4 4.6 m Lb/2 9.2 m 53

Bottom Flange Width

Bfw = 0.559

m

Bottom Flange Width (End Section) 𝑓 = 𝑓 Bfw_end = 0.559

m

Top Flange Width (End Section) 𝐺

= 𝑓

Top Flange Width Height of Girder Web Width

Gtop_end = 0.559

m

Gtop = 0.406

m

Hg = 1.143

m

Wweb = 0.178

m

Area @ Mid-Section

Asg = 0.361

m2

Area @ End Section

Asend = 0.639

m2

0

Asgiri = Asend 0.639

m2

2

Asend

0.639

m2

3

Asg

0.361

m2

4

Asg

0.361

m

4.6

Asg

0.361

m2

9.2

Asg

0.361

m2

𝐴

= 𝑓

Area at Sections Xi

Top Flange Width @ Sections Gtopxi = Xi 0 Gtop_end 0.559 2 Gtop_end 0.559 3 Gtop 0.406 4 Gtop 0.406 4.6 Gtop 0.406 9.2 Gtop 0.406

m m m m m m

Centroid of Girder from Top (Mid-Section) Ytgir = 0.628

m

Centroid of Girder from Top (End Section) Ytgir_end = 0.5715 𝑖 =

m

Centroid of Girder from Bottom (Mid-Section) Ybgir = 0.515

m

2

54

Centroid of Girder from Bottom (End-Section) 𝑖 = 𝑖 Ybgir_end = 0.5715

m

Girder Inertia (Mid-Section)

Ig = 0.052

m

Girder Inertia (End Section)

Ig_end = 0.070

=

4

m4

𝑓

Location of Centroid @ Sections Ytgir_xi = Xi 0 Ytgir_end 0.5715 2 Ytgir_end 0.5715 3 Ytgir 0.628 4 Ytgir 0.628 4.6 Ytgir 0.628 9.2 Ytgir 0.628

m m m m m m

Ybgir_xi = Ybgir_end 0.5715 Ybgir_end 0.5715 Ybgir 0.515 Ybgir 0.515 Ybgir 0.515 Ybgir 0.515

m m m m m m

Xi

0 2 3 4 4.6 9.2

Girder Inertia @ Sections Xi 0

Ig_xi = Ig_end 0.070

m

2

Ig_end

0.070

m4

3

Ig

0.052

m4

4

Ig

0.052

m4

4.6

Ig

0.052

m4

9.2

Ig

0.052

m

0

0.122

m3

2

0.122

m3

3

0.083

m

3

4

0.083

m

3

4.6

0.083

m3

9.2

0.083

m3

4

4

Section Modulus (Top) 𝑆

𝑖

=

𝑖

Xi

Stgir_xi =

55

Section Modulus (Bottom) 𝑆

𝑖

=

𝑖

Sbgir_xi = 0

0.122

m3

2

0.122

m3

3

0.101

m3

4

0.101

m

4.6

0.101

m3

9.2

0.101

m3

Xi

Modular Ration

𝑐 𝑐

=

3

n = 1.415

Height of Composite Section

Hcs = 1.343

m

bfint = 2.1

m

𝑐 =𝑇 +

Flange Width 𝑓𝑖

=

𝑖

+

𝑇

𝑆

𝐿

Effective Width of Flange for Composite Action 𝑓𝑖 B = 1.484 =

m

Centroid From Top of Composite Section 𝑐

=

𝐴

𝑖 𝑖

𝑖

𝐴

Xi

0 2 3 4 4.6 9.2

+𝑇

+ 𝑇

𝑇

𝑖 𝑖 + 𝑇

Ytcs_xi = 0.559 0.559 0.500 0.500 0.500 0.500

m m m m m m

Centroid From Bot of Composite Section 𝑐 = 𝑐 − 𝑐 Ybcg_xi = 0.784 0.784 0.843 0.843 0.843 0.843

m m m m m m

56

Centroid From Top of Composite Section to Centroid from top of Girder 𝑐 = − 𝑐 Ytcg_xi = 0.359 m 0.359 m 0.300 m 0.300 m 0.300 m 0.300 m Inertia @ Neutral Axis of Composite Section =

(

𝑇

)

+

𝑇

𝑐

−

𝑇

2

+

Ina_xi = 0.162 0.140

m4

0.140

m4

0.140

m

0.140

m4

m

𝑇 +

𝑖

−

𝑐

2

4

3

0.452

m3

0.466

m3

0.466

m3

0.466

m

0.466

m3

m

𝑖 𝑖

4

m4

Section Modulus (Bot) of Composite Girder Sbcg_xi = 0.206 𝑆 𝑐 = 𝑐

m

0.162

Section Modulus (Top) of Composite Girder Stcg_xi = 0.452 𝑆𝑐 = 𝑐

+ 𝐴

3

3

0.206

m3

0.165

m3

0.165

m3

0.165

m

0.165

m3

3

Area of Composite Section 𝐴𝑐

=𝐴

𝑖 𝑖 + (𝑇

) Acomp_xi = 0.936

m

2

0.936

m2

0.658

m2

0.658

m2

0.658

m

0.658

m2

2

57

III. LOADS AND FORCES CALCULATION: A. MOMENT DUE TO DEAD LOAD: A-1 MOMENT DUE TO GIRDER ALONE Weight @ End Section =𝐴

𝛾𝑐

Wg_end = 15.334

Weight @ Mid-Section =𝐴

𝛾𝑐

kN/m

𝑐

Wg = 8.666

kN/m

Rg = 93.067

kN

Xmi = 0 30.669 0 0 0 0

m m m m m m

𝑐

Support Reaction 𝑅 =

𝐿

+

−

Moment Equations 𝑖 𝑖=

2

𝑖𝑓

𝑖 𝑖

𝑖−

𝑖=

2

𝑖−

+

𝑖𝑓

𝑖

𝑖

Ymi = 0 0 65.671152 109.340 139.701 476.11869

m m m m m m

Moment due to Girder Weight = 𝑅

𝑖 −

𝑖−

𝑖

58

Mg_xi = 0 155.465 213.530 262.9285 288.40771 380.09822 A-2 MOMENT DUE TO NON-COMPOSITE LOADS Weight of Slab & Diaphragm Wsd = 9.24 = 𝑇

𝛾𝑐

𝑐

𝑅

=

Rsd = 85.008

kN

𝐿 )

Moment @ midspan = 𝑅

Msd_xi = 0 2 151.536 213.444 266.112 293.2776 391.0368

𝑖

𝑖 −

Non-Composite Dead Load Moment 𝐶 = + NCmdl_xi = 0 307.001 426.97402 529.0405 581.68531 771.13502 A-3 MOMENT DUE TO COMPOSITE LOADS Weight of Median =𝐴

𝛾𝑐

Wmed = 0

=𝐴

𝛾𝑐

kN*m kN*m kN*m kN*m kN*m kN*m

kN/m

Wpar = 4.8

kN/m

Wfws = 4.235

kN/m

𝑐

Weight of FWS = 𝑇𝑓

kN*m kN*m kN*m kN*m kN*m kN*m

𝑐

Weight of Parapet

𝑓

kN/m

.

Support Reaction (

kN*m kN*m kN*m kN*m kN*m kN*m

𝑐

𝛾𝑓

.

Total Weight of Composite Loads 𝑐=

+

+

59

𝑓

Wc = 3.0116667 kN/m

Support Reaction 𝑅𝑐 =

Rc = 27.707

kN

𝑐 𝐿

Moment @ Sections

Mc_xi = 0 49.391333 69.5695 86.736 95.590 127.454

kN*m kN*m kN*m kN*m kN*m kN*m

Composite Dead Load Moment Cmdl_xi = 0 = 𝑐 49.391333 69.5695 86.736 95.590 127.454

kN*m kN*m kN*m kN*m kN*m kN*m

𝑐 = 𝑅𝑐

𝑖 −

𝑐

𝑖

2

𝐶

B. MOMENT DUE TO LIVE LOAD (AASHTO 2002) B-1 CONSIDERING AASHTO HS20-44 TRUCK LOAD Distribution Factor DF = 1.250 𝐷𝐹 =

𝑆

Impact Factor 𝐹=

+

IF = 1.3 𝐿

. +

considering 1-wheel line

Pl1 = 36

kN

Pl2 = 144

kN

Pl3 = 144

kN

L1 = 4.27

m

L2 = 4.27

m

Pl1/2 = 18

kN

Pl2/2 = 72

kN

Pl3/2 = 72

kN

Lb = 18.4

m

60

Support Reaction

Rll1 = 93.532 𝐿

𝑅

− .

𝐿

+

=

𝐿

+

+ .

𝐿

Live Load Moment due to Truck Load w/ Impact Factor =

𝑅

𝐿

−

.

( 𝐹 𝐷𝐹)

Mll1 = 898.706

kN*m

B-2 CONSIDERING AASHTO LANE LOAD Concentrated Force @ midspan

Plane = 80

kN

Uniform Lane Load

Wlane = 9.34

kN/m

Support Reaction 𝑅

=

(

Rll2 = 125.928 𝐿 )

+

kN

𝑃

Live Load Moment due to Lane Load w/ Impact Factor 𝐿

2

+

𝐿

𝐹 𝐷𝐹

=

Mll2 = 620.16 Design Live Load Moment 𝑠

Mll_des = 898.706

kN*m kN*m

=

Parabolic Constant (Live Load Moment) =

𝐿

𝑠 2

kll = 10617.985 kg*s -2

Design Live Load Moment @ Sections = ( 𝑖) 2 Mll_xi = 0 42.472 95.562 169.888 224.677 898.706

kN*m kN*m kN*m kN*m kN*m kN*m 61

IV. DESIGN OF GIRDER A. DETERMINATION OF APPROXIMATE AMOUNT OF PRESTRESSING FORCE Assumed Centroid of Cables from Bottom dbot = 0.1 m Parabolic Constant 𝑖

=

kp = 0.005

m-1

−

𝐿

2

Eccentricity from bottom @ Sections =

𝐿

𝑖 −

2

− 𝑖

ebot_xi = 0 0.161 0.226 0.282 0.311 0.415 Service Condition Allowable Tensile Stress 𝑓𝑐 ft = 3.24

𝑓 = .

m m m m m m

MPa

Required Prestressing Force 𝑃𝑖

=

𝑆

+ 𝑖 𝐴

+ 𝑖 𝑖

+

𝑐 + 𝑆 𝑐 𝑆

−𝑓

𝑖

Pireq_xi = -2070.393 -94.628 393.722 635.489 759.375 1540.235 Assumed Total Prestress Loss Prloss_xi = 13.822 14.18 17.1 17.42 17.55 18.55

kN kN kN kN kN kN % % % % % %

62

Effective Prestress Force 𝑃𝑖 𝑓𝑓𝑝

=𝐹

−𝑃

𝐴

Pieff_pr_xi = 118.655 118.163 114.142 113.702 113.523 112.146

kN kN kN kN kN kN

Number of Initial Prestressing Strands 𝑃𝑖 npr_xi = -17.449 = 𝑃𝑖 𝑓𝑓𝑝 -0.801 3.449 5.589 6.689 13.734 Design Number of Prestressing Strands npr_desi = 24 24 24 24 24 24 Jacking Force

Pj_pri = 3304.476 3304.476 3304.476 3304.476 3304.476 3304.476

kN kN kN kN kN kN

kf = 0.001

/m

Friction Curvature Coefficient

μ = 0.2

/rad

Slope due to Friction

ϴ = 0.090

rad

𝑃

=𝐹

𝑝

𝑠

𝐴

B. COMPUTATION OF LOSSES: B-1 LOSS DUE TO FRICTION & ANCHORAGE Friction Wobble Coefficient

=

(

)

𝐿

63

Frictional Loss 𝐹

=

𝑝

Frloss_pr_xi = 1370.067 1367.330 1365.963 1364.598 1363.779 1357.520

𝐹

MPa MPa MPa MPa MPa MPa

Frictional Loss (+3% due to Anchorage) 𝐹 𝐹

𝑝

=

𝑝

−

𝐹

%Frloss_pr_xi = 4.787 4.984 5.082 5.179 5.238 5.687 B-2 LOSS DUE TO ELASTIC SHORTENING Assumed Prestress Loss @ Transfer %pi_xi = 10 10 10 10 10 10

% % % % % %

Number of Identical Prestressing Tendon Nt_pr = 4 Approximate Prestressing force @ Transfer 𝑃

=𝐹

𝑝

𝐴

𝑠

(

−

𝑖 )

Ptrans_pr_xi = 2974.028 2974.028 2974.028 2974.028 2974.028 2974.028 Stress due to Girder Weight 𝑓𝑐

𝑝

=

𝑃

𝑝

𝐴

𝑖 𝑖

+

𝑃

𝑝

kN kN kN kN kN kN

2

fcgp_pr_xi = 4.655 5.400 10.231 11.355 12.033 15.021

−

MPa MPa MPa MPa MPa MPa

64

Stress due to Elastic Shortening 𝑓

𝑝

=

𝑝

−

𝑝

𝑐𝑖

𝑓𝑐

𝑝

Δfpes_pr_xi = 12.049 13.979 26.485 29.394 31.148 38.883

MPa MPa MPa MPa MPa MPa

Percentage loss due to Elastic Shortening 𝑓

𝑝

=

𝑓

𝑝

𝐹

%Δfpes_pr_xi = 0.864 1.002 1.899 2.107 2.233 2.787 B-3 APPROXIMATE ESTIMATE OF TIME-DEPENDENT LOSSES Relative Humidity for Metro Manila RH = 75 Estimation for Relaxation Loss (Low Relaxation Steel) Δfpr = 17

MPa

Correction factor for specified concrete strength at time of prestress transfer to the concrete member γstr = 0.778 𝛾 = +

𝑓 𝑐𝑖

Correction factor for Relative Humidilty of the ambient air 𝛾 = . −( . 𝑅 ) γh = 0.95 Prestressing Steel Stress immediately @ Transfer 𝑓 =𝐹 ( − 𝑖 ) fp_xi = 1255.5 1255.5 1255.5 1255.5 1255.5 1255.5

MPa MPa MPa MPa MPa MPa

65

Stress lost due to Time-dependent factors (Pre-Tensioned) 𝑓

𝑓

=

𝑝

𝐴 𝐴

𝑠

𝛾

𝑖 𝑖

𝛾

Δfplt_pr_xi = 112.720 112.720 139.183 139.183 139.183 139.183

+

𝛾

𝛾

+ 𝑓

MPa MPa MPa MPa MPa MPa

Percent loss due to Time-dependent factors (Pre-Tensioned) 𝑓

𝑝

=

𝑓

𝑝

𝐹

%Δfplt_pr_xi = 8.080 8.080 9.977 9.977 9.977 9.977 SUMMATION OF LOSSES Total Prestress Losses (Pre-Tensioned) 𝑠𝑠

𝑇

𝑖=

𝑓

𝑝

+

𝑓

𝑝

+

𝐹

𝑝

%Pr_lossTotali = 13.731 14.066 16.957 17.264 17.448 18.451

66

C. CHECKING OF STRESSES @ BOTH SERVICE & TRANSFER CONDITION C-1 @ SERVICE CONDITION: Allowable Tensile Stress @ Service Condition 𝑆

𝑖𝑐

𝑖

= −𝑓

Servicetension = -3.24

MPa

Allowable Compressive Stress @ Service Condition 𝑆

𝑖𝑐 𝑐

= .

𝑓𝑐

Servicecomp = 25.2 Prestressing Force @ Service Condition 𝑃𝑓𝑖

𝑝

=𝐹

𝐴

−

𝑠𝑠

𝑠

MPa 𝑇

𝑖

Pfinal_pr_xi = 2850.726 2839.670 2744.125 2733.999 2727.906 2694.756 Bottom Stress @ Service Condition 𝑆

𝑖𝑐

=

𝑃𝑓𝑖

𝑝

𝐴

𝑖 𝑖

+

𝑃𝑓𝑖

𝑝

𝑆

−

𝑖

ServiceBot_xi = 4.462 5.227 8.519 8.415 8.253 4.681

𝑆

+ 𝑖

𝑐 + 𝑆 𝑐

−

MPa MPa MPa MPa MPa MPa

Stress Status (Bottom) @ Service Condition 𝑖𝑐 𝑐

𝑐

𝑖𝑓 𝑆

=

𝑖𝑐 𝑐

𝑆

𝑖𝑐

.

𝑖

𝑆

𝑖𝑐

𝑖

𝑖

servicecheck_bot_xi = ok ok ok ok ok ok Top Stress @ Service Condition 𝑆

𝑖𝑐 𝑇

=

𝑃𝑓𝑖 𝐴

𝑝

𝑖 𝑖

−

𝑃𝑓𝑖

𝑝

𝑆

𝑖

ServiceTop_xi = 4.462 3.420 5.614 5.200 5.028 5.494

+

+ 𝑆 𝑖

MPa MPa MPa MPa MPa MPa

+

𝑐 +

𝑐

67

Stress Status (Top) @ Service Condition 𝑖𝑐 𝑐

𝑐

𝑝

𝑖𝑓 𝑆

=

𝑖𝑐 𝑐

𝑆

𝑖𝑐 𝑇

𝑖

𝑆

𝑖𝑐

𝑖 𝑖

servicecheck_top_xi = ok ok ok ok ok ok C-2 @ TRANSFER CONDITION Allowable Tensile Stress @ Transfer Condition 𝑇

𝑖

=− .

𝑓 𝑐𝑖

Transtension = -1.541

MPa

Allowable Compressive Stress @ Transfer Condition 𝑇

𝑐

= .

𝑓 𝑐𝑖

Transcomp = 22.8 Prestressing Force @ Transfer Condition 𝑃

𝑝

=𝐹

𝑠

𝐴

𝑓

−

MPa +

𝑝

𝐹

𝑝

Ptrans_pr_xi = 3117.738 3106.683 3073.821 3063.695 3057.602 3024.453 Bottom Stress @ Transfer Condition 𝑇

=

𝑃

𝑝

𝐴

𝑖

+

𝑃

𝑝

𝑆

𝑖

TransBot_xi = 4.880 7.688 13.272 14.422 15.006 17.002

−

𝑆

𝑖

MPa MPa MPa MPa MPa MPa 68

Stress Status (Bottom) @ Transfer Condition 𝑇

𝑐

𝑐

𝑖𝑓 𝑇

=

𝑐

𝑇

𝑖

.

𝑇

𝑖

𝑇

𝑖

𝑖

Transcheck_bot_xi = ok ok ok ok ok ok Top Stress @ Transfer Condition 𝑇

𝑇

=

𝑃

𝑝

𝐴

𝑖 𝑖

−

𝑃

𝑝

𝑆 𝑖

+

TransTop_xi = 4.880 2.037 2.705 1.238 0.488 -2.151

𝑆

𝑖

MPa MPa MPa MPa MPa MPa

Stress Status (Top) @ Transfer Condition 𝑇

𝑐

𝑐

𝑝

=

𝑖𝑓 𝑇 𝑃 𝑖

𝑐 𝑇 𝑅 𝑖 𝑓 𝑐

𝑇

𝑖 𝑇

𝑖

TranscheckTop_xi = ok ok ok ok ok Provide Reinforcement @ Top Height of Tensile Region @ Transfer Condition 𝑖=

𝑇

𝑇 𝑇

𝑇 𝑖 + 𝑇

hxi = 0.572 0.239 0.193 0.090 0.036 0.128

m m m m m m

69

Tensile Stress at Top Fiber @ Transfer Condition 𝑇 𝑖=

𝑇

𝑇

𝑖 𝐺

Tvi = 779.435 136.277 106.239 22.720 3.569 56.068

kN kN kN kN kN kN

Steel Area Required 𝐴

𝑖

𝑝

=

𝑇 𝑖 . 𝐹

mm2

Asmin_topi = 3765.4

2

658.3

mm

513.2

mm2

109.8

mm2

17.2

mm2

270.9

mm2

Number of Steel Bars to be used 𝑖𝑓 𝑇 𝑖=

𝑐 𝐴𝑆 𝑖

𝑇 𝑖

𝑇

𝑖

𝑇

𝑖

𝑇

𝑖

𝑖

2

Bartopi = no need no need no need no need no need 1.347 Flexural Reinforcement required during transfer stage 𝐹

=

𝑖𝑓 𝑇

𝑇

𝑖

𝑖

Flextop_chki = Provide Minimum Provide Minimum Provide Minimum Provide Minimum Provide Minimum See Provided Calculation

70

Flexural Reinforcement to be Provided @ top Bartop_desi = 4 4 4 4 4 4 D. CAPACITY OF FLEXURAL REINFORCEMENT Total Dead Load Moment Mdl_xi = 0 = + + 𝑐 356.39247 496.54352 615.7765 677.27561 898.58876 Ultimate Design Moment = .

Mu_xi = 0 555.333 852.557 1168.600 1367.258 3115.362

+

kN*m kN*m kN*m kN*m kN*m kN*m

Capacity Reduction Factor (Flexure) φflex = 1 Stress Block Factor

β1 = 0.754 .

𝛽 =

.

− .

𝑖𝑓 𝑓 𝑐 𝑓𝑐

𝑃

−

𝑖

Factor for type of Prestressing Steel γst = 0.4 Depth from top of composite section to centroid of Prestressing Steel dpri = 1.243 m Width of a web flange member

b'_xi = Bfw_end 0.559 Bfw_end 0.559 Wweb 0.178 Wweb 0.178 Wweb 0.178 Wweb 0.178

m m m m m m

71

Width of Flange of member

b_xi = Bfw_end 0.559 Bfw_end 0.559 Bfw 0.559 Bfw 0.559 Bfw 0.559 Bfw 0.559

m m m m m m

Number of Bottom Reinforcement Barbot_desi = 4 4 4 4 4 4 Area of Bottom Reinforcement 𝐴

=

Asbot_xi = 1963.50

mm2

1963.50

mm2

1963.50

mm

1963.50

mm2

1963.50

mm2

1963.50

mm2

2

𝑠

2

Steel Area required to develop the ultimate compressive strength of the overhanging portion of the flange 𝐴 𝑓 =

.

𝑓𝑐

−

𝑇

𝐹

Asf_xi = 0 0

mm

2

mm2

1950.065 mm2 1950.065 mm2 1950.065 mm2 1950.065 mm2 Steel Area required to develop the compressive strength of the web of a flanged section 𝐴

=

𝑠

𝐴

+

𝐴

𝐹

𝐹

−𝐴 𝑓

Asr_xi = 2951.515 mm2 2951.515 mm2 1001.450 mm2 1001.450 mm2 1001.450 mm2 1001.450 mm2

72

Average stress in Prestressing Steel @ Ultimate Condition 𝑓 = . 𝑓 ′ fsu = 1674 MPa Prestressing Steel Ratio =

𝑠

𝐴

𝑖

ρps_xi = 0.003 0.003 0.003 0.003 0.003 0.003

Effective Depth of Bottom Reinforcement = 𝑐 − dbr = 1.243

m

Depth of Equivalent rectangular stress block 𝐴 𝑓 cxi = 0.248 𝑐 𝑖= . 𝑓𝑐 0.248 0.264 0.264 0.264 0.264

m m m m m m

Nominal Moment Capacity

Mn_xi = 5517.593 5517.593 4967.594 4967.594 4967.594 4967.594

kN*m kN*m kN*m kN*m kN*m kN*m

73

Moment Capacity 𝑐

Mcap_xi = 5517.5933 5517.5933 4967.5937 4967.5937 4967.5937 4967.5937

= 𝑓

kN*m kN*m kN*m kN*m kN*m kN*m

Checking of Design to Actual Moment Capacity 𝑐

𝑖𝑓 . .

=

𝑐 𝑖

Mchk_xi = ok ok ok ok ok ok E. DEFLECTIONS (@ MIDSPAN ONLY) Due to Girder Weight

Due to Non-Composite D.L. =

−

mm

δsd = -12.280

mm

δdc = -1.497

mm

δpf = 42.125

mm

𝐿

𝑐

Due to Composite D.L. 𝑐=

δgir = -12.021

−

𝑐 𝐿 𝑐

Due to Prestressing Force 𝑃𝑓𝑖

𝐿

𝑝

𝑓=

2

𝑐

Computed Total Deflection 𝐷 𝑓 𝑐 𝑖

𝑆

=

𝑖 +

+

𝑐+

𝑓

Deflection_Service = 16.326 Camber

Camber = 15

mm mm

74

F. SHEAR DESIGN Shear Due to Girder Wt 𝑖 𝑖𝑓

𝑖=

𝑖 𝑖

Xgi = 0 30.668976 0 0 0 0 +

𝑖=

𝑖−

𝑖𝑓

𝑖

𝑖

Ygi = 0 0 39.335376 48.001776 53.201616 93.067056 𝑉

=𝑅 −

𝑖−

𝑖

Shear due to Slab & Diaphragm 𝑉

=𝑅

−

𝑖

Shear due to Composite Loads 𝑉𝑐

kN kN kN kN kN kN

𝑖 = 𝑅𝑐 −

𝑐

𝑖

kN kN kN kN kN kN

Vg_xi = 93.067 62.398 53.732 45.065 39.865 0.000

kN kN kN kN kN kN

Vsd_xi = 85.008 66.528 57.288 48.048 42.504 0

kN kN kN kN kN kN

Vcompi = 27.707333 21.684 18.672333 15.660667 13.853667 0

kN kN kN kN kN kN

75

Shear due to Dead Load 𝑉

=𝑉

+𝑉

Vdl_xi = 205.782 𝑖 150.610 129.692 108.774 96.223 0.000

+ 𝑉𝑐

kN kN kN kN kN kN

Shear due to Live Load (Condition 1) 𝑅 𝑉

1

−

=

𝑖𝑓 𝑅

− 𝑅

𝐿

− .

𝑖

𝑖𝑓 𝑖 = 𝑖

Vll_x1i = 93.532 93.532 93.532 93.532 93.532 -50.468

kN kN kN kN kN kN

Shear due to Live Load (Condition 2) 𝑉

2

𝑅 − 𝑅 −

=

𝑖 𝑖𝑓 𝑖 −𝑃

Governing Live Load Design 𝑉

=

𝑉

1

𝑉

𝑖𝑓 𝑖

2

Ultimate Shear 𝑉

= .

𝑉

+

𝑉

𝑖 𝑖𝑓 𝑖 =

Vll_x2i = 125.928 107.248 97.908 88.568 82.964 -40

kN kN kN kN kN kN

Vll_xi = 93.532 93.532 93.532 93.532 93.532 50.468

kN kN kN kN kN kN

Vu_xi = 470.169 398.445 371.251 344.058 327.742 109.348

kN kN kN kN kN kN

76

Max Factored Moment = .

Mmax_xi = 0 555.333 852.557 1168.600 1367.258 3115.362

+

kN*m kN*m kN*m kN*m kN*m kN*m

Moment due to Composite Loads Mdl_comp_xi = 0 𝑚𝑝 = 𝐶 49.391 69.570 86.736 95.590 127.454

kN*m kN*m kN*m kN*m kN*m kN*m

Moment due to Non-composite Mdl_ncomp_xi Loads =0 𝑚𝑝 = 𝐶 307.001 426.974 529.040 581.685 771.135

kN*m kN*m kN*m kN*m kN*m kN*m

Shear due to Unfactored Dead Load @ extreme fiber stress where Tensile stresses is caused by externally applied loads 𝑚𝑝 𝑚𝑝 fd_xi = 0 kPa 𝑓 = + 𝑆 𝑖 𝑆 𝑐 2761.532 kPa 4632.674 kPa 5743.337 kPa 6316.205 kPa 8377.751 kPa Compressive Stress in concrete due to effective prestress forces only 𝑓

=

𝑃𝑓𝑖

𝐴

𝑝

𝑖 𝑖

+

𝑃𝑓𝑖

𝑝

𝑆

𝑖

fpe_xi = 4461.670 8194.545 13728.821 15185.047 15926.710 18490.012

kPa kPa kPa kPa kPa kPa 77

Moment causing flexural cracking @ section A due to externally applied loads 𝑐

=

.

𝑐

𝑓

+𝑓

−𝑓

Mcr_xi = 1589.771 1790.264 2041.446 2098.630 2126.562 2209.592

kN*m kN*m kN*m kN*m kN*m kN*m

Distance of extreme compression fiber to centroid of tension reinforcement 𝑐 = . 𝑐 dcg = 1.0744 m Factored Shear Force occuring simultaneously w/ M max 𝑉𝑖 = 𝑉 Vi_xi = 470.169 kN 398.445 kN 371.251 kN 344.058 kN 327.742 kN 109.348 kN Shear Strength Provided by Concrete 𝑉𝑐𝑖 =

.

𝑓𝑐

𝑐 +𝑉

.

𝑓𝑐

+

𝑉𝑖

𝑐

𝑐 +𝑉

Vci_xi = 400.396 1629.717 1080.622 788.620 667.945 139.526

𝑖𝑓

𝑖𝑓

. =

.

kN kN kN kN kN kN

Resultant Compressive Stress in Concrete (after allowance for all losses) @ centroid of Composite Section due to both prestress and moments resisted by precast member acting alone 𝑓 𝑐

=

𝑃𝑓𝑖

𝐴

𝑝

𝑖 𝑖 +

−

𝑃𝑓𝑖

𝑚𝑝

𝑐

𝑝

𝑐

−

−

𝑖

𝑖

fpc_xi = 4.462 3.987 6.376 6.043 5.874 5.281

MPa MPa MPa MPa MPa MPa

78

Nominal Shear Strength provided by concrete when diagonal cracking results from combined shear & moment 𝑉𝑐

=

.

𝑓𝑐

+ .

𝑓 𝑐

𝑐

Vcw_xi = 1932.647 1847.087 725.238 706.155 696.431 662.387

kN kN kN kN kN kN

Shear Strength provided by concrete 𝑉𝑐 = (𝑉𝑐𝑖 𝑉𝑐 ) Vc_xi = 400.396 1629.717 725.238 706.155 667.945 139.526

kN kN kN kN kN kN

Area of Shear Reinforcement

mm

2

Av = 113.097

2

𝐴 =

Shear Reduction Factor

φv = 0.9

Assumed Spacing @ Section A Spacingi = 75 75 75 150 150 200

mm mm mm mm mm mm

Shear Strength provided by steel

kN kN kN kN kN kN

𝑉 𝑖=

𝐴 𝑆

𝐹 𝑐𝑖

𝑐 𝑖

Vsi = 1341.490 1341.490 1341.490 670.745 670.745 503.059

79

Design Shear Capacity 𝑉𝑐

𝑖=

𝑉𝑐 + 𝑉 𝑖

Shear Check Status 𝑆

=

𝑖𝑓 𝑉𝑐 . .

Vcapi = 1567.697 2674.086 1860.055 1239.210 1204.821 578.326

kN kN kN kN kN kN

Shear_check_i = ok 𝑖 𝑉𝑖 𝑖 ok 𝑖 ok ok ok ok

G. DESIGN SUMMARY Type of AASHTO Girder to be used Gt = 3 Compressive strength of Cast in Place Concrete f'c = 20.7

MPa

Compressive strength of Prestressed concrete @ Transfer Stage f'ci = 38 MPa Compressive strength of Prestressed concrete @ Service Stage f'cs = 42 MPa Number of Prestressing Strands to be used npr_desi = 24 24 24 24 24 24 Total Jacking Force (Pre-Tensioned) Pj_pri = 3304.476 3304.476 3304.476 3304.476 3304.476 3304.476

kN kN kN kN kN kN

80

Allowable Service Compression Servicecomp = 25.2

MPa

Allowable Service Tension Servicetension = -3.24

MPa

Stress @ top during Service Condition ServiceTop_xi = 4.462 3.420 5.614 5.200 5.028 5.494

MPa MPa MPa MPa MPa MPa

Stress @ bottom during Service Condition ServiceBot_xi = 4.462 5.227 8.519 8.415 8.253 4.681 Checking of Stress @ Top and Bottom Servicecheck_top_xi = ok ok ok ok ok ok

MPa MPa MPa MPa MPa MPa

Servicecheck_bot_xi = ok ok ok ok ok ok Allowable Transfer Compression Transcomp = 22.8

MPa

Allowable Transfer Tension Transtension = -1.541

MPa

Stress @ top during Transfer Condition TransTop_xi = 4.880 2.037 2.705 1.238 0.488 -2.151

MPa MPa MPa MPa MPa MPa

81

Stress @ bottom during Transfer Condition TransBot_xi = 4.880 7.688 13.272 14.422 15.006 17.002

MPa MPa MPa MPa MPa MPa

Checking of Stresses @ Top and Bottom Transcheck_top_xi = ok ok ok ok ok Provide Reinforcement @ Top Transcheck_bot_xi = ok ok ok ok ok ok Number of Top ReinforcementBartop_desi = 4 4 4 4 4 4 Diameter of Top Reinforcement of Girder dt = 16

mm

Number of Bottom Reinforcement Barbot_desi = 4 4 4 4 4 4 82

Diameter of Bottom Reinforcement of Girder db = 25 Flexural Moment Capacity

mm

Mchk_xi = ok ok ok ok ok ok

Deflection due to Dead Load @ Midspan only DeflectionService = 16.326

mm

Camber to be used

mm

Camber = 15

Spacing of Shear Reinforcement Spacingi = 75 75 75 150 150 200

mm mm mm mm mm mm

Design of Shear Reinforcement

mm

Shear Check Design

dv = 12

ShearChecki = ok ok ok ok ok ok

83

84

85