Part B: De Design sign Ca Calcul lcul ations
Part B: Design Calculations................................................................................................ Calculations................................................................................................ i Chapter 1: Introduction ................................................................................................. ................................................................................................. 1-1 Chapter 2 Project Statement........................................... .......................................................................................... ............................................... 2-1 2.1 Introduction .............................................. .................................................................................................... ...................................................... ................ 2-2 2.2 Geometric properties ...................................................................................................... 2-3 2.3 Material properties ......................................................................................................... 2-3 2.4 Conclusion ...................................................................................................................... 2-4
Chapter 3 Structural Analysis – Influence Line ................................................................ ................................................................ 3-1
4.3.3 Load Combinations ............................................................................................................. 4-6 4.4 AASHTO LRFD 2012 Design Loads [3] .............................................. ................................................................................ .................................. 4-7
4.4.1 Dead Load Analysis ............................................................................................................. 4-7 4.4.2 Live Load ............................................................................................................................. 4-8 4.4.3 Load Combinations ........................................................................................................... 4-12 4.5 CSA S6-66 Design Loads [4] ..................................................................... ....................... 4-13
4.5.1 Dead Loads ....................................................................................................................... 4-13 4.5.2 Determination of Live Loads ............................................................................................ 4-14 4.5.3 Determination of Total Design Loads ............... ........................ .................. .................. .................. .................. ................... ................... .........4-17 4.6 Summary of Design Loads ...................................................... ........................................ 4-18 4.7 Conclusion .................................................................................................................... 4-18 Reference: .......................................................................................................................... 4-19
Chapter 5 Design of Prestressed Concrete Girder ........................................................... 5-1 5.1 Introduction .............................................. .................................................................................................... ...................................................... ................ 5-3
5.4.7 Design for Shear Reinforcement ................... ............................ .................. .................. .................. .................. .................. .................. ............. .... 5-19 5.4.8 Design for Shrinkage and Temperature Reinforcement ........................ ................................. .................. ................. ........5-21 5.5 CSA S6-66 [4] ............................................. ................................................................................................... ...................................................... .............. 5-22
5.5.1 Prestressing Design .......................................................................................................... 5-22 5.5.2 Choose the Tendon Profile .............................................. ....................................................................................... ......................................... 5-23 5.5.3 Check the Concrete Stresses at Service Load .......... ................... .................. ................... ................... .................. .................. ........... .. 5-24 5.5.4 Check the Flexural Capacity .................. ........................... .................. .................. ................... ................... .................. .................. .................. ........... .. 5-25 5.5.5 Check the Deflections ....................................................................................................... 5-26 5.5.6 Design for Shear Reinforcement ................... ............................ .................. .................. .................. .................. .................. .................. ............. .... 5-26 5.5.7 Design for Shrinkage and Temperature Reinforcement ........................ ................................. .................. ................. ........5-28 5.6 Summary ...................................................................................................................... 5-29 Reference: .......................................................................................................................... 5-30
Chapter 6 Reinforced Concrete Deck Design............................................. ................................................................... ...................... 6-1 6.1 Introduction .............................................. .................................................................................................... ...................................................... ................ 6-2
6.4 CSA S6-66 [3] ............................................. ................................................................................................... ...................................................... .............. 6-13
6.4.1 Design Input ..................................................................................................................... 6-13 6.4.2 Dead Load Effects ............................................................................................................. 6-13 6.4.3 Live Loads ......................................................................................................................... 6-14 6.4.4 Factored Design Moments .................. ............................ ................... .................. .................. .................. .................. .................. .................. ............. ....6-15 6.4.5 Negative Transverse Moment Flexure Design ................. .......................... ................... ................... .................. .................. ........... .. 6-15 6.4.6 Positive Transverse Moment Flexure Design ................... ............................ ................... ................... .................. .................. ........... .. 6-16 6.4.7 Bottom Distribution Reinforcement ................... ............................ .................. .................. .................. ................... ................... ............... ...... 6-17 6.4.8 Top of Slab Shrinkage and Temperature Reinforcement .................. ........................... ................... ................... ............ ... 6-18 6.5 Conclusion .................................................................................................................... 6-19 Reference: .......................................................................................................................... 6-20
Chapter 7 Durability Design ........................................................................................... ........................................................................................... 7-1 7.1 Introduction .............................................. .................................................................................................... ...................................................... ................ 7-2 7.2 Concrete Exposure Condition ................................................ ........................................................................................... ........................................... 7-2
Chapter Cha pter 1: Introducti on Part B of the design report presents a prestressed concrete interior girder as well as the reinforced concrete deck of a 25-meter bridge. Unlike Part A that focuses on the design procedure, detailed calculations with respect to three different design standards were conducted in this part of the design report. Seven chapters are included in this section, and each chapter follows the design procedure described in Part A.
In order to complete the design, the design scope must be defined at first. Thus, this part of the report starts off with a problem statement that includes the detailed information such as the geometry and material properties in Chapter 2. Structural analysis was conducted in Chapter 3 using the concept of influence line to analyze the impact that moving truck loads could bring to the structure. The truck loads are specified differently
Overall, Part B of the project report presents three detailed designs of a 25 meter prestressed concrete bridge with respect to three design standards, and the strength, serviceability and durability designs are all included. The entire design process follows the description in Part A.
Chapter Cha pter 2 Proj Proj ect Statement Statement
Chapter 2 Project Statement........................................... .......................................................................................... ............................................... 2-1 2.1 Introduction .............................................. .................................................................................................... ...................................................... ................ 2-2 2.2 Geometric properties ...................................................................................................... 2-3 2.3 Material properties ......................................................................................................... 2-3 2.4 Conclusion ...................................................................................................................... 2-4
2.1 2. 1 Introducti on In this chapter, it will introduce all the detailed information for this required bridge design such as its geometric properties, material properties as well as the assumption that is being made during the design process. The assigned task for our group is to design a simply supported bridge with four prestressed concrete bridge girder, the specific requirements are in the following sections.
2.2 2. 2 Geometric Geometric p ropert ies In the following figure, it contains the required dimensions for the assigned bridge design[Figure B.1]. All dimensions are in millimeter.
Figure 2.2 Overall Geometry of the Bridge
As the figure above presented, the bridge is a simply supported bridge that have four f our
Ecs
28000 MPa
Ecg
30376 MPa
Table 2.2 Material Properties of Reinforcing Steel Material
Reinforcing steel
fy
400 MPa
Es
200000 MPa
Table 2.3 Material Properties of Prestressed Tendon Material
Prestressed tendon (Seven-wire strand)
fu
1860 MPa
Es
200000 MPa
Chapter 3 Structural Analysis – Influence Line
Chapter 3 Structural Analysis – Influence Line ..................................................................... ..................................................................... 3-1 3.1 Introduction to Influence Line method of analysis ...................................................... ............3-2 3.2 Procedure for Determining Influence Line ............................................... ..............................................................................3-2 ...............................3-2
3.2.1 Tabulate Value Procedure ........................................................................................................ 3-2 3.2.2 Influence-Line Equation ........................................................................................................... 3-2 3.2.3 Qualitative Influence Line ........................................................................................................ 3-3 3.3 Influence Lines for the Design of Bridge .................................................................................3-4 3.4 Code Prescribed Truck Loads for Design ............................................................................ .....3-8 3.5 Shear and Moment Design D esign Envelopes ...................................................................... ............ 3-10 3.6 Conclusion ................................................ ...................................................... .................... 3-12 Reference: ................................................................................. ............................................... 3-13
3.1 3. 1 Introdu Introdu ctio n to Influence Line method method of analysis An influence line is a profile representation of the variation of either the reaction, shear, shear, moment, or deflection at a specific location in a member as an applied concentrated force moves along the member length. Influence lines is a powerful analysis method for the design of bridges, industrial crane rails, conveyors, and other structures where loads move across their span because the influence line enables direct measure of where the moving load should be placed on the structure to create the greatest influence at the specified location. In addition, the magnitude of the associated reaction, shear, moment, or deflection at the specified location can be calculated from the influence-line diagram easily [1]. This section starts with the background information related to the influence line method of analysis with respect to determinate and indeterminate structures, then influence lines specific to the problem statement presented in Ch. 2 are developed for truck loads calculation as specified in the design standards of CSA S6-14, AASHTO
x on the member and then directly calculate the value of reaction, shear and moment as a function of x. The equation of the various line segments can then be determined and plotted. [1]
3.2.3 3.2 .3 Qualit Qualitative ative Infl uence Li ne Influence lines can be determined using both qualitative and quantitative methods. Qualitative influence lines are developed by Heinrich M ̈ uller-Breslau for rapidly constructing the shape of an influence line. The method is referred to as the MüllerBreslau principle, which states that the influence line for a function (reaction, shear, or moment) is to the same scale as the deflected defl ected shape of the beam when the beam is i s acted upon by the function[1]. For statically determinate and indeterminate structures the shape of the influence line is slightly different, which are shown in Figure 3.1 below. For the purpose of this project, determinate influence lines are utilized.
3.3 3. 3 Influ Influence ence Lin es for the Desig Design n of Bri dge In this section, unit load influence lines were developed based on the 25 m, simply supported span that will be designed as part of this project. A quantitative method was employed and the equation of the influence line was determined with respect to a variable, x, the distance of the unit load from the left support. Figure 3.2 and Figure 3.3 shows the unit load influence lines for the reaction at the supports, the shear at 1/4 and 3/4 of the span as well as at the mid-span. Figure 3.4 shows the unit load influence lines for the moment at 1/4 and 3/4 of the span from the left support, sup port, as well as at the mid-span. mid -span. These influence lines were later used to determine the influence associated with the design trucks from CSA S6-14, CSA S6-66 and AASHTO LRFD-12.
Influence Line for Reaction at Left Support 1.2
Influence Line for Shear at 1/4 Span from Left Support 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 0 -0.2 -0.3 -0.4
5
10
15
Influence Line for Shear at Mid-span 0.6 0.5 0.4 0.3
20
25
Figure 3.3 - Unit load influence lines for the shear at the 1/4 and 3/4 span, as well as the mid-span
Influence Line for Moment at 1/4 Span from Left Support 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
5
10
15
20
Influence Line for Moment at 1/2 Span from Left Support
25
Influence Line for Moment at 3/4 Span from Left Support 7 6 5 4 3 2 1 0 0
5
10
15
20
25
Figure 3.4 Unit load influence lines for the moment at the 1/4 and 3/4 span, as well as the mid-span
In addition to the above influence lines, lines , the shear and moment envelope for a moving unit
Maximum Moment Moment Envelope Envelope - Unit Moving Load Load 7 6 5 4 3 2 1 0 0
5
10
15
20
25
Figure 3.5 – Maximum Shear and Moment Envelope for Unit Load Moving along the Bridge
Table 3.2 Tabulated Design Value for Shear and Moment CSA S6-14 Location
from
AASHTO LRFD-14 & CSA S6-66*
Maximum
Maximum
Maximum
Maximum
the left support
Shear [kN]
Moment [kNm]
Shear [kN]
Moment [kNm]
0
404.8
0
283.7
0
6.25
248.55
1853.32
203.3
1292.31
12.5
116.3
2226.25
123.4
1644.25
18.75
248.55
1853.32
203.3
1292.31 1292. 31
25
404.8
0
283.7
0
Shear Design Envelope 450 400 350
Moment Design Envelope 2500
2000
1500 ] m N k [ t 1000 n e m o M
500
0 0
5
10
15
20
Distance from Left Support [m] CSA S6-14
AASHTO LRFD-14 & CSA S6-66*
Figure 3.9 - Shear and Moment Design Envelope
25
Reference: [1] R.C. Hibbeler. Chapter 6: Influence Lines for Statically Determinate Structures, in Structural Analysis, 8th Edition, Pearson Prentice Hall, Upper Saddle River, New Jersey, USA, 2012 [2] M.U. Khaled (N.d.) Influence Lines for Statically Indeterminate Beams [Online]. Available: Available:http://www.sut.ac.th/engineering/civil/courseonline/430332/pdf/02_influencelin e_inde.pdf [3] Canadian Standard Stan dard Association, “Loads,” in Canadian Highway Bridge Design Code, S6-14, Mississauga, ON, Canada: CSA Group, 2014. [4] American Association of State Highway and Transportation Officials, “Loads and Lo ad Factors,” in AASHTO LRFD 2014 Bridge Design Specifications, 6th ed. Washington, DC. [5] Canadian Standards Association, “Loads and Forces,” in S6 -66 Design of Highway Bridges, Ottawa, Canada: CSA, 1966.
Chapter Cha pter 4 Desig Desig n Loads Lo ads
Chapter 4 Design Loads .................................................. ..................................................................................................... ..................................................... 4-1 4.1 Introduction ..........................................................................................................................4-2 4.2 I Girder Specification [1] ........................................................................................................4-2 4.3 CSA S6-14 Design Loads [2] ....................................................................................................4-3
4.3.1 Dead Load Analysis ................................................................................................................... 4-3 4.3.2 Live Load Analysis ..................................................................................................................... 4-4 4.3.3 Load Combinations ................................................................................................................... 4-6 4.4 AASHTO LRFD 2012 Design Loads [3] ......................................................................................4-6
4.4.1 Dead Load Analysis ................................................................................................................... 4-6 4.4.2 Live Load ................................................................................................................................... 4-7
4.1 4. 1 Introducti on In this section, all the design loads are defined based on three difference codes: CSA S614, AASHTO LRFD-14, and CSA S6-66. In this case, only dead loads and live loads are defined calculated, whereas other loads such as snow loads, wind loads and seismic loads are excluded. In this design, the dead loads include the self-weight of prestressed I girders, concrete deck and pavement material. Live loads include truck load and lane load.
4.2 4. 2 I Girder Specifi catio cation n In order to calculate the self-weight of I girder, the cross-section geometry must be determined. Based on Figure 4.1, the span to depth ratio is defined to be:
=18 ℎ
for I
girder section. For the design of a 25-meter span simply supported bridge, the required I girder depth, h, is calculated as follows:
Table 4.1 Basic Geometry Information about the Type IV I-Girder [1] Height Area y (bottom) Moment of Inertia
1.0.530972 0.0.1608528
54789ℎ 24.260,77330ℎ
4.3 CSA S6-1 S6-14 4 Desi Desi gn Loads [2] This section specifically focus on defining any design loads based on CSA S6-14. It consists of dead loads, live loads and corresponding distribution factors, and dynamic impact loads.
4.3.1 4.3 .1 Dea Dead d Load L oad Analy sis The dead loads are calculated based on self-weight of assumed Type IV prestressed Igirder, the 200-mm reinforced concrete deck, and the 3 inch (76.2 mm) bituminous
Once the dead loads are determined, the corresponding moment and shear force are calculated and summarized in Table 4.4.
Table 4.4 Moment and Shear Force due to Dead Loads D istan ce fro m Sup p o rt (m ) M o m en t (kN m ) Shear (kN )
0 .0 0 0 .0 0 37 8 .32
2.5 0 8 5 1.2 1 3 0 2.6 5
5 .00 1 51 3 .2 7 22 6 .99
7.5 0 1 9 86 .1 7 1 5 1.3 3
10 .00 2 26 9 .90 75 .66
1 2.5 0 2 3 64 .4 8 0.0 0
4.3.2 Live Load Analysis The actual live load is determined based the following steps: 1. Determine the moment and shear force caused by CL-W truck loads and CL-W lane loads on a set of points along the along the span. The T he truck loads are calculated based on influence line analysis from Chapter 3, and the results are summarized in Table 4.5. The lane loads are calculated by adding 80% of truck loads with an UDL of 9 kN/m, and the results are summarized in Table 4.6.
3. Determine as the lane modification factor based on §5.6.4.4.
= 0.3.6 3 = 2.83 ℎℎℎ ≤ 1.0 → = 1.0
4. Determine the distribution factors of moment and shear force respectively based on §5.6.4.3.
= + = .×.×.+. ×. =0.5928≥1.05 =0.47 = + = .×.×.+. × =0.7941≥1.05 =0.47
In this case, assume a type A highway and
center to center spacing, equals to 2.7 m. Thus:
Moment:
Shear:
Where
can be found in Table 5.3 and 5.6.
= 25 . Based on Chapter 2, let S,
Using
= 0.5928 (for moment),
= 0.7941 (for shear force),
Dynamic load allowance = 0.25 from §3.8.4.5.3c
S = 1.0
The distributed moment and shear force due to truck loads and lane loads are summarized in Table 4.7 and 4.8 respectively, and the result has shown that the truck loads will govern. Hence, the result calculated from truck loads will be carried on for any further calculations.
Table 4.7 Distributed Moment and Shear Force due to Truck Loads D istance fro m Sup p o rt (m ) M L (kN m ) V L (kN )
0.00 0.00 401.81
2.50 601.69 339.78
5.00 1056.67 283.10
7.50 1551.06 223.64
10.00 1632.72 165.87
12.50 1649.65 115.44
10.00
12.50
Table 4.8 Distributed Moment and Shear Force due to Lane Loads D istance fro m Sup p o rt (m )
0.00
2.50
5.00
7.50
4.4 AASHTO AASHTO LRFD LRFD 2012 2012 Design Lo Loads ads [3] Similar to the previous section, this section specifically specifi cally focus on defining any design loads based on AASHTO LRFD-14. It consists of dead loads, live loads and corresponding distribution factors, and dynamic impact loads.
4.4.1 4.4 .1 Dea Dead d Load L oad Analy sis The dead loads are calculated based on self-weight of assumed Type IV prestressed Igirder, the 200-mm reinforced concrete deck, and the 3 inch (76.2 mm) bituminous pavement. The spacing of interior girders is designed as 2.7 m, which is used as the tributary area calculation. The unit weight of each type of material is listed in Table 4.11.
Table 4.11 Material Unit Weight from AASHTO LRFD-14 Material
AASHTO AA SHTO LRFD-14 (
Bitum inous Wearing Wearing Surface
0.140
)
Unit weight of wearing surf ace: ace:
W = 0.140
Once the unit weight of each structural component is determined, the result of dead loads calculation is presented and summarized in Table 4.12.
Table 4.12 Dead Load Calculations I G ird er D eck P avem ent
0 .5 0 9 0 .5 4 0 .2 0 57 4
4.4.2 4.4 .2 Live L oad The actual live load is determined based the following steps:
1 1 .7 8 1 2 .3 6 4 .5 2
4. Determine the longitudinal stiffness parameters based on §4.6.2.2.1-1:
Where
= = =1.135 =1.135×260,730789×33.2 =1,283,833
5. Determine the live load moment distribution factors for the interior girder based on §4.6.2.2.2b: For two or more design lanes loaded:
=0.075 9.5..12.0×× .
For two or more design lanes loaded:
. . . 8. 8 6 8. 8 6 1, 2 83, 8 33 =0.075 9.5 82 12.0×82×7.87 =0.753→ For one design lane loaded: loaded:
. . . 8. 8 6 8. 8 6 1, 2 83, 8 33 =0.06 14 82 12.0×82×7.87 =0.531 6. Determine live load shear force distribution factors for interior girder based on §4.6.2.2.3a:
For two or more design lanes loaded:
8. Determine the distributed shear force and moment due to live load including impact loading:
= 1 1 100 = ℎ ℎ 1 1 100 The summarized result is shown in Table 4.14.
Table 4.14 Distributed Moment and Shear Force due to Truck load D istan ce fro m Sup po po rt (m ) U nfactore oredM om ent( nt (kN m ) U n facto red Sh ea ear (kN )
0 .0 0 0.00 21 3. 3.6 3
2 .5 0 731. 731.51 18 9. 9.5 3
5 .0 0 1276 1276. .92 1 64 64.61
7 .5 0 1619 1619. .48 1 41 41.34
1 0.00 1844 1844. .64 1 17 17 .24
12 .5 0 1911 1911. .31 92 .9 2
10. The total live load is calculated by adding the land load and truck load with dynamic loading included, and the result is summarized in the Table 4.16.
Table 4.16 Distributed Moment and Shear Force due to Total Live Load (LL+IM) D istance fro m Su p po po rt (m ) U nfactore oredM om ent( nt (kN m ) U n facto red Sh ea ear (kN )
0 .0 0 0.00 31 5. 5.6 4
2.50 929. 929.26 2 71 71.14
5 .0 0 1628 1628. .48 22 5. 5.8 1
7.50 2080 2080. .91 1 82 82.14
1 0 .0 0 2371 2371. .99 13 7. 7.6 4
12 .5 0 2460 2460. .62 92 .9 2
4.4.3 Load Combinations In this design, the following three load combinations were determined based on §3.4.1:
: (
)+
(
) + 1.75(
= 1.25
+
)
Table 4.18 Distributed Moment and Shear Force under Service I Condition D istan ce fro m Su p p or ort (m ) M o m en t (kN m ) Sh ear (kN )
0 .0 0 0 .0 0 6 7 3 .8 9
2 .5 0 1 7 3 5 .3 3 5 5 7 .7 4
5 .0 0 3 0 6 1 .4 8 4 4 0 .7 6
7 .5 0 3 9 6 1 .7 2 3 2 5 .4 4
1 0 .0 0 4 5 2 1 .4 9 2 0 9 .2 9
1 2 .5 0 4 6 9 9 .6 9 9 2 .9 2
Table 4.19 Distributed Moment and Shear Force under Service III Condition D istan ce fro m Su p p or ort (m ) M o m en t (kN m ) Sh ear (kN )
0 .0 0 0 .0 0 6 1 0 .7 6
2 .5 0 1 5 4 9 .4 7 5 0 3 .5 1
5 .0 0 2 7 3 5 .7 8 3 9 5 .6 0
7 .5 0 3 5 4 5 .5 4 2 8 9 .0 1
1 0 .0 0 4 0 4 7 .0 9 1 8 1 .7 7
1 2 .5 0 4 2 0 7 .5 6 7 4 .3 4
4.5 CSA S6-6 S6-66 6 Desi Desi gn Loads [4] This section presents the calculations of the design loads based on the requirements stipulated by the Canadian Bridge Design code CSA S6-66 [M1]. It consists of the calculation of the dead loads, the live loads and their corresponding distribution factors to determine the loads transmitted to the pre-stressed concrete I-girders.
Once the dead loads are determined, the corresponding moment and shear force are calculated and summarized in Table 4.4.2.
Table 4.21 Moment and Shear Force due to Dead Loads Dis tance from Support (m) Moment (kNm)
0.00 0.00
2.50 851.21
5.00 1513.27
7.50 1986.17
10.00 2269.90
12.50 2364.48
Shear (kN)
378.32
302.65
226.99
151.33
75.66
0.00
4.5.2 Determination of Live Loads This section calculates the design live loads to be applied to the bridge and the corresponding distrib distribution ution factors of load transmission to an internal girder based on CSA S6-66. These live loads are imposed onto the bridge as either a truck load or a lane load, whichever one governs. The following procedures are used to determine the live loads.
= 8.86
/ 5.5 = 1.61
This factor is to be applied to the individual wheel loads of the design truck, however, since axle loads were calculated in Ch. 3: Influence lines, the fraction of axle load that is transferred to each girder is determined by dividing the MDF by 2:
= 1.61/2 = 0.805
Therefore, a distribution factor of 0.805 will be applied to the moments produced by the live loads in order to determine the loads per girder.
3. Determination of the Shear Distribution Factor:
According to CSA S6-66 §5.2.1.1 the distribution of shear is determined by the method
5. Determination of Live Loads to be used for design
i)
The live loads due to the HS design truck are determined based on the shear and moment design envelopes calculated in Ch. 3: Influence Lines for various locations along the span of the bridge. These shear or moment values are multiplied by the distribution factor of 0.805 and increased by the impact factor of 24.2%. These loads are shown in the table below.
Table 4.22 Distributed Unfactored Moment and Shear Force Distance from Support (m)
0.00
2.50
5.00
7.50
10.00
12.50
Unfactored Moment (kNm) Unfactored Shear (kN)
0.00 283.70
629.30 251.70
1098.50 218.60
1393.20 187.70
1586.90 155.70
1644.25 123.40
Table 4.23 Distributed Factored Moment and Shear Force
Table 4.25 Distributed Factored Moment and Shear Force Distance from Support (m) Unfactored Moment (kNm) Unfactored Shear (kN)
iii)
0.00 0.00 152.57
2.50 292.01 132.17
5.00 537.04 111.77
7.50 735.09 91.37
10.00 886.16 70.96
12.50 990.25 50.56
Once the truck loads and lane loads were determined, the larger set of values between the two were selected to be used in subsequent calculations. This is based on CSA S6-66 §5.1.8.2 , which states that the loads that produce maximum stress shall be used in the design as the live load component. It was determined that the shear and moment produced by the HS truck governed
Table 4.26 Governing Distributed Moment and Shear Force Dis tance from Support (m)
0.00
2.50
5.00
7.50
10.00
12.50
Unfactored Moment (kNm) Unfactored Shear (kN)
0.00 283.65
629.18 251.65
1098.29 218.56
1392.94 187.66
1586.60 155.67
1643.94 123.38
Table 4.28 Distributed Moment and Shear Force Under ULS Dis tance from Support (m) Moment (k (kNm) Shear (kN)
0.00 0.00
2.50 2849.77
5.00 5015.63
7.50 6461.59
10.00 7371.35
12.50 7656.57
1276.59
1083.11
886.88
696.15
502.67
308.44
4.6 4. 6 Summary Summary of o f Design L oads Table below summarizes the design loads for all three codes, which are subsequently used in the following chapters of this report.
Table 4.29 Summary of Design Moment and Shear Force Distance from CSA S6-14 Support (m) ULS SL S 0.00 0.00 0.00 2203.87 1474.17 2.50 5.00 3892.56 2607.28 7.50 5430.07 3592.04 10.00 5932.16 3960.32 12.50 6079.40 4072.43
Moment (kNm) AASHTO LRFD-14 Strength I Service I 0.00 0.00 2488.34 1634.05 4388.22 2884.70 5674.40 3737.51 6475.68 4266.11 6730.13 4435.08
CSA S6-66 U LS SL S 0.00 0.00 2849.77 1480.39 5015.63 2611.56 6461.59 3379.10 7371.35 3856.50 7656.57 4008.42
CSA S6-14 ULS SLS 1139.61 739.95 942.84 608.45 755.18 481.78 562.79 352.60 373.28 224.94 196.25 103.90
Shear Force (kN) AASHTO LRFD-14 Strength I Service I 1217.57 790.04 1024.39 660.79 828.96 530.26 638.01 402.29 444.82 273.04 251.02 143.44
CSA S6-66 U LS SLS 1276.59 661.96 1083.11 554.31 886.88 445.55 696.15 338.99 502.67 231.33 308.44 123.38
Reference: [1]PCI BRIDGE DESIGN MANUAL (Novermber 2011), Retrieved March 16, 2017 from: https://www.pci.org/uploadedFiles/Siteroot/Design_Resources/Transportation_Engineeri ng_Resources/AASHTO%20I%20Beams.pdf [2] [2] Canadian Standard Association, “Loads,” in Canadian Highway Bridge Design Code, S6-14, Mississauga, ON, Canada. [3] American Association of State Highway a nd Transportation Officials, “Loads and Lo ad Factors,” in AASHTO LRFD 2014 Bridge Design Specifications, 6th ed. Washington, DC. [4]Canadian [4]Canadian Standards Association, “Loads and Forces,” in S6 -66 Design of Highway Bridges, Ottawa, Canada.
Chapter Cha pter 5 Desig Desig n of Prestressed Concr ete Girder
Chapter 5 Design of Prestressed Concrete Girder ................................................................ 5-1 5.1 Introduction ..........................................................................................................................5-3 5.2 Cross-Section Geometry ........................................................................................................5-3 5.3 CSA S6-14 ..............................................................................................................................5-4
5.3.1 Prestressing Design .................................................................................................................. 5-4 5.3.2 Choose the Tendon Profile ....................................................................................................... 5-5 5.3.3 Check the Concrete Stresses at Service Load ............ ..................... .................. .................. .................. .................. ................... .................. ........5-5 5.3.3.1 Initial Condition at Transfer ................... ................................. ............................ ............................ ............................ ............................ ............................ .................... ...... 5-5 5.3.3.2 Conditions at Time of Placing Wet Concrete on G irder ....................................... ..................................................... ........................... ............. 5-6 5.3.3.3 Final Conditions ........................... ......................................... ............................ ............................. ............................. ............................ ............................ ............................ ................ 5-6
5.5.1 Prestressing Design ................................................................................................................ 5-22 5.5.2 Choose the Tendon Profile ..................................................................................................... 5-23 5.5.3 Check the Concrete Stresses at Service Load .......... ................... .................. ................... ................... .................. .................. ................. ........5-24 5.5.3.1 Initial Condition at Transfer ................ .............................. ............................. ............................. ............................ ............................ ............................ .................... ...... 5-24 5.5.3.2 Conditions at Time of Placing Wet Concrete on G irder ....................................... ..................................................... ......................... ........... 5-24 5.5.3.3 Final Conditions ........................... ......................................... ............................ ............................. ............................. ............................ ............................ ........................... ............. 5-24
5.5.4 Check the Flexural Capacity ................................................................................................... 5-25 5.5.5 Check the Deflections ............................................................................................................. 5-26 5.5.6 Design for Shear Reinforcement ............................................................................................ 5-26 5.5.7 Design for Shrinkage and Temperature Reinforcement ........................ ................................. .................. .................. .............. .....5-28 5.6 Summary ............................................................................................................................ 5-29
5.1 5. 1 Introducti on In this chapter, detailed designs of the interior prestressed girder will be performed following three different codes: CSA S6-14, AASHTO LRFD-14 and CSA S6-66. Each design includes the design of the cross-section geometry, tendon profile, check of concrete stress at critical stages, flexural design, shear design, and deflection check.
5.2 5. 2 Cross-Secti Cross-Secti on Geometry As stated in the the previous previous chapter, chapter, AASHTO Type IV girder girder would be used in this design. design. Thus, the span to depth ratio would be around 18 in this case, which is an ideal situation. The detailed geometry is shown in Figure 5.1, and the cross-section property is shown in Table 5.1.
5.3 CSA S6-14 S6-14 [2] [ 2] In this section, the interior girder will be designed using CSA S6-14. In particular, the tendon profile as well as the transverse reinforcement will be determined so that the flexural capacity, shear capacity and deflection will satisfy CSA S6-14.
5.3.1 Prestressing Design Assuming that the centroid of the tendons is located 100 mm above the bottom face of the girder, which means:
= 628 100 = 528 =0.4 ′ = 2.83
At ULS, the maximum maximum tensile tensile stress allowed at the bottom bottom girder is:
The stress in the bottom of the girder is:
5.3.2 5.3 .2 Choos Choos e the Tendon Tendon Profi Profile le In this case, 10 of 24 strands will be draped to the third-points of the span.
Figure 5.2 Tendon Profile CSA S6-14
5.3.3 5.3 .3 Check Check the t he Concrete Stress es at Servi Service ce Load
5.3.3.2 Conditions Conditions at Time of Placing Wet Concrete on Girder At this stage, the concrete concrete in the girder has reached its normal capacity of
= =
prestressing force will be taken as
to be conservative.
5.3.3.3 Final Conditions
= =
Table 5.2 Summary of Flexural Design Calculation
′
, and
5.3.4 5.3 .4 Check Check t he Flexural Capacit y
= 1 1 = 1860 × 1 0.0.2685 × 0.00097× 186050 = 1844 3920 = 0.85 = 0.85 × 50 ××18442336.8 = 72.72.8
Under the ULS loading, the
at mid span is 6079.4 kNm.
The design flexural strength is determined as:
= 2=0.95×3920 ×1844×1283 72.28 =8561.7
5.3.5 5.3 .5 Check Check the t he Reserve Reserve Strengt h after Crack ing
5.3.6 5.3 .6 Check Check the t he Deflect Deflect ion s As shown shown in the the previous previous calculation, calculation, the the girder girder will remain uncracked uncracked under under service service load. Therefore, an elastic and uncracked response is assumed in the deflection calculation. Both short-term and long-term deflection will be determined. a) Immediate deflection due to short-term live loading, • Total live load is determined as:
Thus,
= × × = 0.682682 × 620620 × 1.1.25 = 528. 528.6 528. 6 × 25 = 48 = 48 × 28000 × 0.2463 = 24.24.9 ⁄ 1000
Which is less than the limit of b) Deflections at the Erections,
.
14 10 24 24 46.0 = 8 8 6 = 46.
•
Total deflection at erection is calculated as
1.85 × 1.8 × = 1.8585 × 20.20.9 1.8 ×46.0 =44.1
c) Long-term deflection,
2.4 × 2.2 × 2.3 × 3.0 × = 4.4343 A 20 0 = 200 d
5.3.7 5.3 .7 De Desig sign n for fo r Shear Reinfo Reinfo rcement
Assuming that the #10M rebar is used with provided at the location of
:
, a sample calculation is
5. Determine the value :
0.4 ] [1000 1300 ]=0. 4 = [11500
6. Determine the angle of inclination :
= 297000 0.88 2500 =29
7. Determine the shear resistance resistance contributed by concrete component
= =495.2
:
8. Determine the shear resistance that needs to be provided by shear reinforcement
12. Check if the longitudinal tendons have exceeded the capacity:
= ⁄ 0.5 = 2159 2159..7 kN = = 6777 6777..7
Table 5.3 Summary of Shear Design Calculation Parameter Vf , kN Mf , kNm Vp , kN εx θ β Vc , kN Vs req , kN
1.15
Distance from t he Support, Support, m 2.50 5.00 7.50
10.00
12.50
1049.09
942.84
755.18
562.79
373.28
196.25
1013.78
2203.87
3892.56
5430.07
5932.16
6079.40
35.85
35.85
35.85
35.85
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
29.00
29.00
29.00
33.55
35.03
34.77
0.40
0.40
0.40
0.20
0.17
0.18
495.22
495.22
495.22
250.69
216.14
221.42
518 02
411 76
224 10
276 26
157 14
0 00
requirement for these shrinkage and temperature reinforcement is rebar spacing no more than
•
300
.
For reinforcements parallel to the span:
500 = × 1.1.372 = 686686 = 700700 = 13727 = 196 → 20200
Provide 7 #10M bars with
•
.
For reinforcements perpendicular to the span:
500 /
, with
= 628 100 = 528 At ULS, the maximum maximum tensile tensile stress allowed at the bottom bottom girder is:
= 6 = 511 = 3.52 The stress in the bottom of the girder is:
= 974. 3 1012. 5 3.5252 ≥ 509×10 172.×528 8×10 172.8×10
Figure 5.3 Tendon Profile for ASSHTO LRFD-14
5.4.3 5.4 .3 Check Check the t he Concrete Stress es at Servi Service ce Load
Table 5.5 Stress Limit for ASSHTO LRFD-14 Stress Stress L imi t at Transfer
5.4.3.2 Conditions Conditions at Time of Placing Wet Concrete on Girder At this stage, the concrete concrete in the girder has reached its normal capacity of
= =
prestressing force will be taken as
5.4.3.3 Final Conditions
to be conservative.
=
′
, and
Table 5.6 Summary of Flexural Design Calculation
Pi (kN) eg (mm) Mdg (kNm) ft (MPa) (MPa) fb (MPa) (MPa) Pf (kN) Mds (kNm) Mdg + Mds (kNm) ft (MPa) (MPa) fb (MPa) (MPa) Mda (kNm) Ml (kNm) Mda + Ml (kNm) fts (MPa) ftg (MPa) fbg (Mpa)
Distance from Support dv 0.1L 0.2L 0.3L 0.4L 1150 2500 5000 7500 10000 a) Initi Initi al Conditions at Transfer 4334.4 4334.4 4334.4 4334.4 4334.4 300 336 403 470 470 161.55 331.31 589.00 773.06 883.50 -0.75 -0.85 -0.62 0.10 -0.65 -15.11 -15.03 -15.22 -15.83 -15.19 b) Condition at Time of Placeing Wet Concrete on Girder 3628.8 3628.8 3628.8 3628.8 3628.8 169.50 347.63 618.00 811.13 927.00 331.05 678.94 1207.00 1584.19 1810.50 -1.97 -3.45 -5.39 -6.30 -7.84 -11.51 -10.26 -8.61 -7.83 -6.52 c) Final Conditions 61.99 127.13 226.00 296.63 339.00 383.99 787.50 1400.00 1837.50 2100.00 44 445.97 914.63 1626.00 2134.13 2439.00 -1.17 -2.41 -4.28 -5.61 -6.41 -2.73 -5.00 -8.16 -9.94 -12.00 -11.53 -9.25 -6.10 -4.32 -2.26
0.5L 12500 4334.4 470 920.31 -0.90 -14.98 3628.8 965.63 1885.94 -8.36 -6.08 353.13 2187.50 2540.63 -6.68 -12.68 -1.57
5.4.5 5.4 .5 Check Check the t he Reserve Reserve Strengt h after Crack ing Cracking stress:
=7.5 =7.5√ 7252 = 639 = 4.40
Additional tensile tensile stress stress required required to crack: crack:
= 4.40 1.57 =5.97 Additional caused caused by by this stress: stress:
× 5.9797 = 1543. 1543.5 Therefore the cracking moment is determined as:
Thus,
325. 5 × 25 = 48 = 48 × 28000 × 0.2463 = 15.15.4 ⁄ 1000
Which is less than the limit of
.
e) Deflections at the Erections, •
The elastic deflection due to girder self-weight is
5 5 × 11. 7 8 / × 25 = 384 = 384 × 28000 × 0.1085 =19.72
•
The elastic deflection due to concrete deck is
f) Long-term deflection,
2.4 × 2.2 × 2.3 × 3.0 × = 18.32 A 20 0 = 200 d =max0.9,0.72ℎ=1.15 = (0.6 ) = 41.83
5.4.7 5.4 .7 De Desig sign n for fo r Shear Reinfo Reinfo rcement
Assuming that the #10M rebar is used with provided at the location of
1. Determine
, a sample calculation is
:
as the first critical location that needs to be designed for:
2. Determine the vertical component of the prestressing force
:
=0.0316 316 = 657. 657.5
7. Determine the shear resistance that needs to be provided by shear reinforcement
= =414.0 = = 401 =min0.8 24 = 24 ℎ = 600
8. Determine the required spacing
:
9. Check the maximum spacing
:
Table 5.7 Summary of Shear Design Calculation Parameter
1.15 1113.25 Vf , kN Mf , kNm 1144.64 41.83 Vp , kN εx 0 29 θ 4.8 β υu , MPa 4. 4.85 Vc , kN 657.46 4 13.97 Vs req , kN 41 400.93 s req , mm 600 s max , mm 400 s design , mm Vs design , kN 373.44 Avmin , mm 2 119.10 2925.13 Flt , kN Fp , kN 6115 2
Distance from the Support, 2.5 5 7.5 1024.39 828.96 638.01 2488.34 4388.22 5674.40 41.83 41.83 41.83 0 0.00034 0.00172 29 30.19 35.02 4.8 3.83 2.10 4.45 3.57 2.71 657.46 523.97 287.12 325.10 263.16 309.07 510.52 600.94 0 600 600 600 500 600 600 298.75 237.21 196.94 148.88 178.66 178.66 4112.63 5547.31 6293.97 6115 2 6115 2 6115 2
m 10 444.82 6475.68 0 0.00253 37.86 1.66 2.01 226.82 218.00 0 600 600 177.52 178.66 6778.32 6115 2
12.5 251.02 6730.13 0 0.00257 38.00 1.64 1.13 224.45 26.58 0 600 600 176.61 178.66 6746.49 6115 2
•
For reinforcements parallel to the span:
500 = × 1.1.372 = 686686 = 700700 = 13727 = 196 → 20200
Provide 7 #10M bars with
•
.
For reinforcements perpendicular to the span:
500 = × 1 = 50
= 3 = 255. 255.5 == 1.76 The stress in the bottom of the girder is:
Thus,
= 974. 3 1012. 5 1.7676 ≥ 509×10 172.×528 8×10 172.8×10 377.258.7 4×10 1643 16 43 377. is calculated to be at least 3497 kN.
Assuming that the low-relaxation low-relaxation strand has strength of 1080 MPa ( the long-term losses.
considering all
5.5.3 5.5 .3 Check Check the t he Concrete Stress es at Servi Service ce Load 5.5.3.1 Initial Condition at Transfer Assume the low-relaxation low-relaxation strands strands has an initial strength of 1290 MPa MPa ( Thus,
= 1290 1290 × 3360 3360 = 4334. 4334.4 = =
,
.
5.5.3.2 Conditions Conditions at Time of Placing Wet Concrete on Girder At this stage, the concrete concrete in the girder has reached its normal capacity of
′
, and
Table 5.9 Summary of Flexural Design Calculation Distance from Support dv 0.1L 0.2L 0.3L 0.4L 0.5L 1150 2500 5000 7500 10000 a) Initi Initi al Conditions at Transfer Pi (kN) 4334.4 4334.4 4334.4 4334.4 4334.4 eg (mm) 300 336 403 470 470 Mdg (kNm) 171.02 350.73 623.53 818.38 935.29 ft (MPa) -0.82 -0.98 -0.86 -0.21 -1.01 fb (MPa) -15.05 -14.91 -15.02 -15.57 -14.89 b) Condition at Time of Placeing Wet Concrete on Girder Pf (kN) 3628.8 3628.8 3628.8 3628.8 3628.8 Mds (kNm) 177.73 364.50 648.00 850.50 972.00 Mdg + Mds (kNm) 348.75 715.23 1271.53 1668.88 1907.29 ft (MPa) -2.09 -3.69 -5.83 -6.88 -8.50 fb (MPa) -11.41 -10.05 -8.23 -7.34 -5.96 c) Final Conditions Mda (kNm) 66.30 135.98 241.74 317.29 362.62 Ml (kNm) 288.40 591.47 1051.50 1380.09 1577.25 Mda + Ml (kNm) 354.70 727.45 1293.24 1697.38 1939.87 f ts (MPa) -0.93 -1.91 -3.40 -4.46 -5.10 f tg (MPa) -2.69 -4.93 -8.03 -9.77 -11.81 f bg (Mpa) -11.57 -9.33 -6.23 -4.49 -2.45
12500 4334.4 470 974.26 -1.27 -14.67 3628.8 1012.50 1986.76 -9.05 -5.50 377.73 1642.97 2020.69 -5.31 -12.49 -1.77
5.5.5 5.5 .5 Check Check the t he Defl Deflectio ections ns As shown shown in the the previous previous calculation, calculation, the girder will remain uncracked uncracked under under service load. Therefore, an elastic and uncracked response is assumed in the deflection calculation. Both short-term and long-term deflection will be determined.
=33 . =33830.5 a) Immediate deflection due to short-term live loading, Total live load is determined as:
= × × = = 0.805805 × 320320 × 1.224224 = 315. 315.3 Thus,
= 4 = 4 × √ 7252 7252== 340.40.6 = 2.3535
2. Determine the concrete stress limit
:
3. Determine the shear resistance resistance contributed by concrete component
= ℎ = 2.3535 × 203203 × 1372 1372 = = 654. 654.1
:
4. Determine the shear resistance that needs to be provided by shear reinforcement
= = 1181187.6 654.54.1 = = 533. 533.5 1272 × 400 × 200
5. Determine the required spacing
:
Table 5.10 Summary of Shear Design Calculation
Parameter Vf , kN Vc , kN Vs req , kN s req , mm
s max , mm s design, mm Vs design, kN Avmin, in 2 Avmin, mm 2
1.15 1187.59 654.12 533.47 190.75 638.50 180.00 565.33 0.10 64.20
Distance from the Support, Support, m 2.5 5 7.5 1083.11 886.88 696.15 654.12 654.12 654.12 428.99 23 232.76 42.03 237.21 437.19 2421.21 638.50 638.50 638.50 200.00 400.00 600.00 508.80 254.40 169.60 0.11 0.22 0.33 71.33 14 1 42.67 21 2 14.00
Table 5.11 Summary of Stirrup Design Di s t a n c e 1.15 - 2.6 2.6 - 5 5 74
Sp ac i n g 180 mm 200 mm 400 mm
A m ou nt 8 # 10M 12 # 10M 6 # 10M
10 502.67 654.12 0.00 0.00 638.50 0.00 0.00 0.00 0.00
12.5 308.44 654.12 0.00 0.00 638.50 0.00 0.00 0.00 0.00
5.6 Summary The table below summarizes the prestressing and reinforcing steel design for the prestressed concrete I girder as well as the designed long-term midspan deflection.
Table 5.12 Summary of Prestressed I Girder Summary CSA S6-14
ASSHTO LRFD-14
CSA S6-66
24 x 15 mm Strands:
24 x 15 mm Strands:
24 x 15 mm Strands:
prestressing Tendons
10 Harped; 14 Straight
10 Harped; 14 Straight
10 Harped; 14 Straight
Shear Reinforcement
Total of 52 # 10M Total of 42 # 10M Total of 52 # 10M double-legged double-legged double-legged stirrups stirrups stirrups
Longitudinal (Shrinkage and
Longitudinal: 7 #10M bars
Longitudinal: 14 #10M bars
Longitudinal: 30 #10M bars
Reference: [1]PCI BRIDGE DESIGN MANUAL (Novermber 2011), Retrieved March 16, 2017 from: https://www.pci.org/uploadedFiles/Siteroot/Design_Resources/Transportation_Engineeri ng_Resources/AASHTO%20I%20Beams.pdf [2] [2] Canadian Standard Association, “Loads,” in Canadian Highway Bridge Design Code, S6-14, Mississauga, ON, Canada. [3] [3] American Association of State Highway and Transportation Transportat ion Officials, “Loads and Lo ad Factors,” in AASHTO LRFD 2014 Bridge Design Specifications, 6th ed. Washington, DC. [4]Canadian [4]Canadian Standards Association, “Loads and Forces,” in S6 -66 Design of Highway Bridges, Ottawa, Canada.
Chapter Cha pter 6 Reinf Reinf orc ed Concrete Deck Deck De Desi sign gn
Chapter 6 Reinforced Concrete Deck Design............................................. ........................................................................ ........................... 6-1 6.1 Introduction ..........................................................................................................................6-2 6.2 CSA S6-14 ..............................................................................................................................6-2
6.2.1 Design Input ............................................................................................................................. 6-2 6.2.2 Design Loads ............................................................................................................................. 6-3 6.2.3 Factored Design Moments ....................................................................................................... 6-4 6.2.4 Negative Transverse Moment Flexure Design ................. .......................... ................... ................... .................. .................. .................. ........... 6-5 6.2.5 Positive Transverse Moment Flexure Design ..................... .............................. .................. .................. .................. ................... .................. ........6-6 6.2.6 Bottom Distribution Reinforcement ................... ............................ .................. .................. .................. ................... ................... .................. .............. ..... 6-7 6.2.7 Top of Slab Shrinkage and Temperature Reinforcement .................. ........................... ................... ................... .................. ........... .. 6-8 6.3 ASSHTO LRFD-14 ...................................................................................................................6-8
6.1 6. 1 Introducti on This chapter chapter presents the design and calculation of the bridge’s reinforced concrete deck. Three provisions are used to develop the required deck design, CSA S6-14, ASSHO LRFD-12 and CSA S6-66. The difference and similarity of each of the three designs are summarized and compared at the end of this chapter.
6.2 CSA S6-14 S6-14 [1] [ 1] This section summaries the bridge reinforced concrete deck design based on the provisions of the Canadian Highway Bridge Design Code CSA S6-14. The dead and the live loads are determined and used to calculate the factored design loads. Based on the calculated design loads, the size and spacing of the transverse reinforcement is selected with the consideration of the maximum and minimum spacing requirements and crack control. In addition, top and bottom longitudinal reinforcement layout are also designed based on the code requirement.
6.2.2 6.2 .2 Design Design Loads 6.2.2.1 Dead Loads Unfactored moments due to the dead load of the concrete slab deck and wearing surface per unit width can be approximated using the continuous beam equations:
Deck Load:
− = 11 + = 16
4. 7 0 = 0.200 ×1. ×1 .0 ×23. ×23.5 = − =11 =4.7011×2.7 =3. 115 + = = = 4.70 ×2.7 =2.141
Dynamic load allowance (DLA) for single axle = 0.4 (§3.8.4.5.3)
Transverse live load moment intensity:
= 0.6 10 = 1.7760.106×87.5 ×1.4=29.106 /
For slabs supported over more than 3 supports the transverse live moment intensity may be reduced to 80% of the max bending moment for that determined for a simple span.
=0.8×29.106=23.2848 / = 120. = 1.712076. =90.05% ≥67% =67% =0.67×23.2848=15.60/
Longitudinal live load moment intensity:
+ = 1.2×2. 2×2.141141 1.5×0. 5×0.535535 1.7×23 7×23..2848848 = 42.42.96 / / + = 1.2×2. 2×2.141141 1.5×0. 5×0.535535 1.7×15 7×15..60 = 29.29.89 / /
Positive Longitudinal Factored Moment:
6.2.4 6.2 .4 Negative Negative Transvers e Moment Flexur e Desig Desig n
Assuming 15M-bar 15M-bar Bar area = 200 mm 2 Bar diameter = 16 mm
Effective depth:
=200 162 50 =142 44.49×10 =2.206 = = 1000×142
g = h – h – d d = 200 – 200 – 142 142 = 58 mm A = 2gb/n = 2(58)(1000)/(100 2(58)(1000)/(1000/150)=1 0/150)=17400 7400 mm^2 mm^2 Fs = 0.6 fy = 240 MPa
= = 2407 240733 / / ≤ 2500 250000 / / 6.2.5 6.2 .5 Posit Positive ive Transvers e Moment Moment Flexure Desig Desig n Assuming 15M-bar 15M-bar Bar area = 200 mm 2 Bar diameter = 16 mm
Effective depth:
=200 162 30 = 162
= = 1998 19987.7.3 / / ≤ 2500 250000 / / 6.2. 6. 2.6 6 Bottom Distribu tion Re Reinfor infor cement Amount of bottom slab reinforcement reinforcement as a percentage percentage of the primary reinforcement reinforcement (§8.18.7):
% = 120√ ≤67% % = √ 1202.2.7 =73.0%≤67%
Therefore use 67% of transverse reinforcement
Design transverse reinforcement for positive flexure: 15M at 200 mm spacing with
Use 10M @ 165mm
6.2.7 6.2 .7 Top of Slab Shri nkage and Temperature Reinfor cement Minimum amount of temperature and shrinkage reinforcement (§8.12.6):
Use 5x10M bars with
500 = = ≤ ≤ 300 = 500501000 0 300 = 500/100 =200 ≤ → . Required spacing:
6.3 ASSHTO LRFD-14 [2] This section demonstrates the design of the reinforced concrete deck that sits above the
6.3.2 6.3. 2 Dead Dead Loads L oads Assume that the reinforce reinforced d concrete concrete deck has a similar similar behavior behavior to the the continuous continuous beam. Thus, bending moment generated by the self-weight of concrete deck and wearing surface of a 1 m section are estimated as follow:
− = 11 + = 16
Deck Self-weight:
=4.58 kN/m = 0.20000 ×1. 0 ×22. ×2 2. 9 4. 5 8 ×2. 7 − = 11 = 11 =3.035035 kNkN m + = 16 = 16 = 4.5816×2.7 = 2.087087 kNkN m
6.3.4 6.3 .4 Factor Factored ed Design Mom ent Design for Strength I condition:
− = 1.2525 × 3.3.035 35 1.5050 × 0.729729 1.75×75× 30.30.07 = 57.57.51 // + = 1.2525 × 2.2.087 87 1.5050 × 0.0.501 01 1.75×75× 27.27.53 = 51.51.54 / / :
(
)+
(
) + 1.75(
= 1.25
= 1.50
Negative moment at the support:
Positive moment at the midspan:
6.3.5 6.3 .5 Flexur Flexural al Desig Desig n at Mids pan Assume using #5-bar (15M (15M bar) Bar area = 0.31 in 2 = 200 mm 2 Bar diameter = 0.625 in. = 16 mm
+
)
= 1 0.77.1.871. 3 3 =1.283 = 1 0.7h Where dc = cover + d b/2 = 1 + 0.3 = 1.3 in. = 33 mm h = 7.87 in. = 200 mm
= 0.75 for class 2 condition
= 0.6 fy = 34.8 ksi = 240 MPa
≤ 1.700283××0.34.758 2×1. 2×1.3 = 9.16 in. = 232. 232.6 mm
6.3.6 6.3 .6 Flexural Design at Supp ort Assume using using #5-bar (15M bar) Bar area = 0.31 in 2 = 200 mm 2 Bar diameter = 0.625 in. = 16 mm
6.3. 6. 3.7 7 Botto m Re Reinfo info rcement Perpendicu Perpendicu lar Direction Amount of bottom slab longitudinal longitudinal reinforcement reinforcement as a percentage percentage of the primary reinforcement is calculated (§9.7.3.2):
120√ = √ 1208.8.83 =40.4%≤67%
Therefore use 40.4% of transverse reinforcement.
Transverse reinforcement for positive flexure is designed as: 15M at 200 mm spacing with:
= 1000 1000 / = 0.404404 = 1000000 × 0.0.404 = 404 /
Design longitudinal reinforcement:
Assume using using 10M bars bars
Use 3x10M bars with
= 300300 1000 = 300/100 =333 . Required spacing:
Therefore use 10M @ 330 mm.
6.4 CSA S6-66 S6-66 [3] [ 3] This section outlines the bridge reinforced concrete deck design based on the provisions of the Canadian Design of highway Bridges CSA S6-66 [2]. Similar to the previous two sections, the dead and the live loads are determined and used to calculate the factored design loads. Based on the calculated design loads, the size and spacing of the transverse reinforcement is selected with the consideration consideratio n of the maximum and minimum spacing requirements and crack control. In addition, top and bottom longitudinal reinforcement layout are also designed based on the code requirement.
Deck Load:
Wearing Surface:
+ = 16
4. 7 0 = 0.200 ×1. ×1 .0 ×23. ×23.5 = − =11 =4.7011×2.7 =3. 115 + = 16 = 16 = 4.7016×2.7 =2.141 1. 1 75 = 0.05 ×1. 0 ×23. ×23.5 = − =11 =1.17511×2.7 =0. 779 + = = = 1.175 ×2.7 =0.535
Therefore, S = 1.976 m = 6.5 ft
For slabs supported over three or more supports the transverse live moment intensity shall be reduced to 80% of the max bending moment for both positive and negative moment.
=0.8×18.89=15.11/ 50 = 8.86125 50 0.374 ≥0.3→=0.3 = 125 = 0.3 ×15. ×15.11 = 4.5353 / /
From § 5.1.11.1, the impact formula to determine the impact factor is as follows:
6.4.4 6.4 .4 Factor Factored ed Desig Design n Moments Moment s
= × × 2 = 521. 521.736 1000 1000 = / = 600/200 =334/ =
Assuming 3x15M 3x15M bars with
Crack Control:
= 600
2, the required spacing:
Where dc = cover + d b/2 = 50 + 8 = 58 mm
A = 2gb/n = 2(58)(1000)/(100 2(58)(1000)/(1000/334)=3 0/334)=38744 8744 mm^2 mm^2 Fs = 0.6 fy = 240 MPa
= = 3143 314366 / / ≥ 2500 250000 / /
1000 1000 = / = 600/200 = 333. 333.3 / /
Assuming 3x15M 3x15M bars with with
Crack Control:
Where
= 600
2, the required spacing:
=
dc =g cover db/2 = 30 8 = 38 mm = h – d = 2 0 0 – 162 16 2 = 3 8 m m A = 2gb/n 2gb/n = 238 2Fs381=1000.0006 f0/6 /600 00/2 /200 00 = 2533 25 333 3 mm^2 mm ^2 y = 240 24 0 Mpa Mp a = =23698 ≤25000 →
Required spacing using 10M bars
= 100 ×10000 = 200200 / / 500 ×100
6.4.8 6.4 .8 Top of Slab Shri nkage and Temperature Reinfor cement Minimum amount of temperature and shrinkage reinforcement is limited by minimum area
Use 4x10M bars with
Use
400 = = ≤ ≤ 300 = 400400 1000 = 400/100 =250
10M bars @ 250mm
. Required spacing:
6.5 Conclusion In summary, Table 6.1 summarizes the reinforcement design for the bridge slab. The most conservative transverse reinforcement design was developed based on the AASHTO LRFD-14 design standard, while the S6-66 design was the least conservative due to the use of smaller bars and larger spacing in some cases. For the longitudinal reinforcement, the S6-66 provision results in the most conservative design while the AASHTO LRFD-14 yields yields the least least conservative conservative one.
Table 6.1 Summary of Slab Reinforcement Design Reinfor Reinf orcem cement ent
CSA S6-14 S6-14
AASHTO LRFD-14 LRFD-14
CSA S6-66 S6-66
15M@200 mm
15M@200 mm
15M@330 mm
15M@150 mm
15M@140 mm
15M@165 mm
Transverse: •
Positive moment reinforcement
•
Negative moment
Reference: [1] [1] Canadian Standard Association, “Loads,” in Canadian Highway B ridge Design Code, S6-14, Mississauga, ON, Canada. [2] [2] American Association of State Highway and Transportation Transportat ion Officials, “Loads and Lo ad Factors,” in AASHTO LRFD 2014 Bridge Design Specifications, 6th ed. Washington, DC. [3] Canadian Standards Associatio n, “Loads and Forces,” in S6 -66 Design of Highway Bridges, Ottawa, Canada.
Chapter Cha pter 7 Durabi Durabilit lit y Desig Desig n
Chapter 7 Durability Design ................................................................................................ ................................................................................................ 7-1 7.1 Introduction ..........................................................................................................................7-2 7.2 Concrete Exposure Condition ................................................ .................................................................................................7 .................................................7-2 -2 7.3 Strength ................................................................................................................................7-2 7.4 Water-Cement Ratio ..................................................... .................................................... .....7-3 7.5 Air Content............................................................................................................................7-4 7.6 Slump ...................................................................................................................................7-4 7.7 Water Content ......................................................................................................................7-5 7.8 Cement Content ....................................................................................................................7-6 7.9 Coarse Aggregate Content .....................................................................................................7-7
7.1 7. 1 Introducti on Material’s durability s significantly ignificantly influences the performance of the structure. In order to achieve the strength requirement in the structural design part, concrete mix must be appropriately designed as different mix will result in different chemical and physical properties. In this chapter, concrete mix design will be specified. The general design method is based on Designing and Proportioning Normal Concrete Mixtures in Design and Control of Concrete Mixtures.
7.2 Concrete Exposure Condition According to Table 1 in CSA A23.1-14, A23.1-14, the the bridge bridge deck is classified in C-1 and the girder girder is classified in A-1 [1].
The most common size of aggregate is 25 mm in CSA A23.1-14. Therefore, we will use it as our nominal aggregate size to determine the air content. Entrained air must be used
the average compressive strength [3]. Therefore, in our design, the required average compressive strength for the bridge deck is 49 MPa, and for the girder is 60 MPa.
Table 7.2. Required Average Compressive Strength Specified Compressive Strength (MPa)
Required Average Compressive Strength Stre ngth (MPa)
<21
f’c+7.0
21 to 35
f’c + 8.5
>35
1.1 f’c + 5.0
7.4 Water-Ce Water-Cement ment Ratio Compressive strength is inversely related to the water-cement ratio. The tabulated values
7.5 7. 5 Air Content Cont ent Entrained air must be used in all concrete that will be exposed to freezing and thawing and deicing chemicals and can be used to improve workability even where not required.
For the bridge deck, as it would be exposed to de-ice environment, this will be classified as Severe Exposure.
For the girders, they will be classified as Moderate Exposure. The Maximum Aggregate Size will be 25 mm (1 in). According to Figure 7.1, the air content for the bridge deck is 6% and the air content for the bridge girder is 4.5%. Both of them is in the range of 4-7% which is required in CSA A23.1-14.
concrete to be placed, consolidated and finished. Consistency the ability of freshly mixed concrete to flow. Plasticity determines concrete’s ease of molding.
The slump test is used to measure concrete consistency. For a given proport ion of cement and aggregate without admixtures, the higher the slump, the wetter the mixture. Slump is indicative of workability when assessing similar mixtures. According to Table 7.4, for the bridge deck, the slump should be 75 mm and for the bridge girder, the slump should be 100 mm.
Table 7.4 Recommended Slumps for Various Types of Construction [3]
Table 7.5 Water Content for Specified Air Content and Different Slumps as well as Nominal Maximum Sizes of Aggregate [3]
Table 7.6. Minimum Requirements for Cementing Materials for Concrete [3]
7.9 7. 9 Coarse Coarse Aggregate Content According to Table 7.7, 7.7, 25 mm mm aggregate aggregate and 2.8 fineness fineness moduli moduli should be used used in our case. The corresponding bulk volume is 0.67. A bulk density of 1600 kg/m 3 is assumed. Therefore, the dry mass of coarse aggregate for a cubic meter of concrete is 1600*0.67
7.10 7. 10 Admix tur e Cont Content ent For bridge deck, a 6% air content, 100 ml air entraining per 100 kg of cement material should be used. Therefore, for every cubic meter, 669 kg * 100 ml/100 kg = 669 ml air entraining admixture should be used.
For girder, 4.5% air content should also need 100 ml air entraining per 100 kg of cement. Therefore, for bridge deck, 870 ml air entraining mixture per cubic meter of concrete should be used.
Moreover, the water reducer dosage rate of 3 g per kg of cement results in 3*669 = 2007 g of water reducer per cubic meter of concrete should be used for the bridge deck. 2610 g of water reducer per cubic meter of concrete should be used for the bridge girder.
When using more than one admixture in concrete, the compatibility of intermixing
7.11 Fine Aggregate Content This section presents the calculation to determine the fine aggregate content for the bridge deck and girder.
For the bridge deck, the following calculations are used to determine the estimated mass of fine aggregate:
174 = 0.174174 = 1×1000 669 = 0.223223 = 3000 = 1006 = 0.06 = 1072 = 0 . 4 2680
7.12 Moisture In our case, coarse aggregate moisture content is 2% and fine aggregate moisture content is 6%. Surface moisture contributed by the coarse aggregate is 2% - 0.5% =1.5%, that by the fine aggregate is 6% - 0.7% = 5.3%.
For the bridge deck: Coarse aggregate = 1072*1.02 = 1093.4 kg Fine aggregate = 377.5*1.06 = 400 kg Adjusted water water content: content: 174 - (1072*0.0 (1072*0.015) 15) - (377.5*0.05 (377.5*0.053) 3) = 138 kg kg
For the girder: Coarse aggregate = 1072*1.02 = 1093.4 kg Fine aggregate = 240*1.06 = 254.4 kg
Cement Content
669 kg
Coarse Aggregate Mass
1072 kg
Fine Aggregate Mass
377.5 kg
Admixtures
Slump
669 ml Air Entraining Entraining 2.007 kg Water Reducer Other corrosion inhibitor 75 ± 20 mm
Table 7.9 Concrete Mix Design for Girder Concrete Mix for the Girder per Cubic Meter Class
A-1
Maximum Nominal Aggregate Aggregate Size
25 mm
Water to Cement Ratio
0.2
Reference: [1] Canadian Standards Association, A23.1-14/A23.2-14 Concrete materials and methods of concrete construction/Test methods and standard practices for concrete, Mississauga, Canada: Table 1 . [2] Canadian Standards Association, A23.1-14/A23.2-14 Concrete materials and methods of concrete construction/Test methods and standard practices for concrete, Mississauga, Canada: Table 2. [3] PCA_Manual, Chapter 9 Designing and Proportioning Normal Concrete Mixture, [Online]Available: [Online]Available:http://www.ce.memphis.edu/1112/notes/project_2/PCA_manual/Chap 09.pdf
Ap
d i A: Des Desii
Dr
i
Deck
Bridge Deck
Reinforcement
Bridge Girder
Girder Reinforcement
3D Render -Reinforcing Detail
Bridge Abutment
Finite Element Analysis -Com -Com lete lete Brid Brid e 3D Render -Explored Views
3D Render
Finite Element Analysis
-Project Overview
-Brid -Brid e Gird Girder er
Bridg e Overview Overview Produced By: Bri D&E Design and Engineering Consulting Corp. Copyright by Bri D& E 2017
A
A
A
A
A
A
A
A
A
