Concrete Bridge Design Project

8/12/2019 Concrete Bridge Design Project

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University of Toronto

Faculty of Applied Science and Engineering

Department of Civil Engineering

CIV 313Reinforced Concrete

Pedestrian Bridge Design ProjectProject Submission

April 11, 2012

Prepared by:Oscar Kwok 997812728

Shuliang Sun 996007440


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Table of Contents

Page1.0 Introduction. 12.0 Slab / Deck Design..1

2.1 Slab Design....12.1.1 Simply Supported vs. Continuous....1

2.2 Deck Design...32.2.1 Deck Aesthetics / Safety...........3

2.3 Slope of Slab..42.4 Shear Reinforcement Design.4

3.0 T-Beam / Girder Design...53.1 Bending Moment53.1.2 Rebar cut-offs (for Girder)..6

3.1.3 Splicing of Reinforcement..63.1.3.1 Positive Moment Reinforcement..73.1.3.2 Negative Moment Reinforcement..7

3.2 Dimensions.....73.3 Shrinkage / Temperature Reinforcement Design....83.4 Stirrup Design.93.5 Shear Reinforcement of Girder..10

4.0 Column Design.114.1 Slab below Girder...12

4.1.1 Dimensions of Slab....124.1.2 Transverse/Temperature reinforcement ....134.1.3 Design for Shear Reinforcement...13

4.2 Column Design...144.2.1 First Iteration. 15

4.2.1.1 Slenderness Checks...164.2.2 Second Iteration..17

5.0 Cost Estimating..175.1 Slab / Deck Cost Analysis....185.2 Girder Cost Analysis....18

5.3 Column Cost Analysis..195.3.1 Slab below Girder...195.3.2 Columns..19

5.4 Total Cost..196.0 Deflections..207.0 Conclusion...20Appendix


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1.0 Introduction

Our design team has designed a pedestrian bridge for the development of anextensive system of hiking and walking trails within the East Humber River Valley.

Our design presents a balance between minimal construction costs, aesthetics, andsafety. This report will comprise of the decisions we made to come up with thefinal design of the slab, column, girder, and deck.

2.0 Slab / Deck Design

2.1 Slab Design

Concrete slabs are shallow reinforced structural members. The function of the slab

is to span between the beams, girders, and columns. For the design of thepedestrian bridge, the deck will sit on top of the slab

2.1.1 Simply supported vs. Continuous

This design considers different alternatives, which consisted of the simplysupported and continuous beam. To arrive at the final decision of a simplysupported beam, shear and moment diagrams were developed for all cases. Thisincluded the case of a 3 & 4 span pedestrian bridge for the simply supported (seefigure A below) / continuous case (see figure B below).

By developing a chart to compare the 4 different cases, it was easily determinedthat the simply supported beam with 4 spans is the optimal alternative (see chart 1).

Simply Supported

3-span

Simply Supported

4-span

Continuous 3-

span

Continuous 4-

span

Large shear x Small shear Large shear x Large shear x

Large moment x Large moment x Large moment x Small moment

Consistent Consistent Not consistent x Not consistent x

Chart 1: Alternative comparison chart for Simply Supported and Continuous beamcases


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Figure A: Shear and Moment diagrams for Simply Supported beam Cases

Figure B: Shear and Moment diagrams for Continuous Beam cases


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As seen from chart 1 above, the simply supported beam for 4 spans prevails overthe other cases. This is the best case as the shear and moment diagram wasconsistent throughout the entire beam. This is significant because it signifies thatone design will fit all properties and aspects of the bridge designs. If thecontinuous beam was chosen with the inconsistent shear and moment, it wouldimpact the design greatly because different amounts of reinforcements andsupports would have to be provided in different parts of the bridge. This wouldconsiderably increase complication for the workers who provide the labor.Therefore, with a simply supported beam, the same specifications and amounts ofreinforcements can be provided throughout the entire bridge which would increaseefficiency during construction. In addition, the 4-span simply supported beam haslow shear which is the most expensive part of labor in North America.

The slab will be sectioned off into four, 15m clear spans for a total clear distance of

60m. The slab will rest on top of a designed T-beam and column at each of theseclear span sections. This was designed so that the columns will not touch the waterin the centre of the valley.

The slab will be 120mm thick. This was decided as to provide a slab that has highstrength and is relatively light to stand on top of the girders and columns. Otherdimensions used include 40mm cover and reinforcements of #30 bars @150mm.

2.2 Deck Design

The deck must be smooth and safe for pedestrians to walk and travel on. It mustalso account for all types of loads that may be put on it.

For our pedestrian bridge design, the following loads were considered:

Superimposed dead load: 0.5 kN/m 2 Live load: 4.8 kN/m 2 Snow load: 2.4 kN/m 2 Side railings: 0.5 kN/m 2 (included in dead load) Concrete own weight: mkNmmxxmkN /28.114120.0/5.23 3

36.72kN/m2.4)))*(4*(0.5+4))*(4.8*((1.5)+0.5))+0.5)*((4*(((1.25) Wf

2.2.1 Deck Aesthetics / Safety

Wood will be used as a layer on top of the deck. This decision was based on the


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relative light weight of wood, which will not contribute much to the weight of thepedestrian bridge. Therefore the weight of the wood is negligible. Wood is alsoeasy to obtain and install which makes it a good choice in supplementing theconcrete deck.

The use of wood is significant in our design of the pedestrian bridge because it isaesthetically pleasing to the eye. When people walk on the bridge or look at it fromafar, they will see a beautiful wooden bridge instead of a grey slab of concrete.

It also adds safety to our design because it eliminates the rough surface created bythe concrete. Side railings will also be placed on two sides so it will provide safety

buffer for pedestrians traveling on the bridge.

2.3 Slope of slab

The issue of ponding and build-up of rain and snow is an inevitable problem withall bridges. This creates safety and health concerns. Therefore a slope must beincorporated into the structural slab design to drain the excess water thataccumulates on the bridge. A slope of 1-2%is needed on the bridge slab to preventthe buildup of rain and snow during extreme weather.

The slope must be kept at an angle of 1-2% so as to keep the pedestrians fromnoticing while allowing the drainage to flow off the bridge efficiently.

2.4 Shear Reinforcement Design

For the design of the shear reinforcement of the one-way slab, we used the generalmethod because this method allows for shallower crack angles, which permit moreresistance.

Although it is difficult and expensive to reinforce slabs for shear, a check isnecessary to determine whether they are required or not just to be safe.

From: m15ln , mkNwf /72.36 , assuming #10 stirrups and maximum aggregatesize of 20mm

The following can be determined:

kNwfVf 4.2752/(ln))( (at the face of support)


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))12072.0(),659.0(()72.0,9.0max( xxhddv =86.4mm

At a distance of dv from the face of support:kNmkNkNVf 272)0864.0)(/72.36()4.275( (critical section)

Estimate longitudinal strain at mid-depth: 33 100.310554.0 xxx Estimate Crack spacing parameter, Sze: mm

ag

SzSze 4.86

15

35

Determine and factors:33 158.0

Through these calculations, the concrete shear resistance can be determined:

kNdvbcfcVc w 6.48)4.86)(1000)(30)(158.0)(65.0('

kNVV fc 30 and shear reinforcement is not required.

3.0 T-Beam / Girder Design

The T-beam system consists of the slab (which supports the reinforced concretebeams) and girder. The slab and girder framework is then supported by thecolumns.T-beams are included in the design to support the slab and deck.

3.1 Bending Moment

T-beams are useful in resisting compression and shear stresses. In the analysis ofthe design, the concrete slab and t-beam interact as a unit to resist positive bendingmoment. The t-beam has a disadvantage to the I-beam when dealing with tensileforces because it has no bottom flange. This was taken into account and solved by

dv

275.4

272


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setting the t-beams on top of another smaller slab to help balance the negativebending moments.

3.1.2 Rebar cut-offs (for Girder)

The moments on the bridge vary along the length of the member. Therefore, theactual cut-off of the bars must be considered and continued a certain distance so asto develop the strength of the bar. *use the shear criterion in the assessment

ln = 15,000mmWf = 36.72 kN/m + 11.28 kN/m = 48 kN/m

M(max) = kNmwf 75.10328

(ln)2

M(x) =0

2

)( 2

xwfMc

Recall, for the cross-section of the girder was 2 layers of 6 #30 bars 1136.2kNm

Location at which Mf is equal to 1136.2 kNm:M(x) = kNm

xwfMc 2.1136

2

)( 2

=2

)(4875.1032

2x 9.5m, or 5493.5 mm

from support. Therefore, at this point, the reinforcement can be cut back.

Development lengths:

mmdcf

fykkkkl bd 34.1025)30)(

30

400)(8.0)(0.1)(0.1)(3.1(45.0

'45.0 4321

Add dl to actual bar cut-off, 5494 + 1025 = 6519 mm3.1.3 Splicing of Reinforcement

The splicing of reinforcement must be considered when

More than300mm ofconcrete

below bar

uncoated

Normal density

concrete

Slab reinf. Barsare #10 < (#20)


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i) the reinforcement required is in greater length than commercially available ii) when bars are placed short of required length.

In the case of this pedestrian bridge design, we may consider splicing of

reinforcement from the case i. For the design, lap spices would work the best asthey are easy to install and economical. The lap splice would develop more thanthe yield strength of the reinforcement.

3.1.3.1 Positive Moment Reinforcement

)(3

1 As for the simply supported pedestrian bridge. The beam is

constructed monolithically with support and the embedment lengthsatisfies the condition: max(150mm, )cotdv

At simple supports: laVf

Mrld

3.1.3.2 Negative Moment ReinforcementThe negative moment reinforcement is considered by anchoring in the supportingmember with the development length (above).

)(3

1 As provided at the support and extended beyond the point of

inflection

3.2 Dimensions

The dimensions of the t-beam are as follows (see figure 1 below):

hmin =16

000,15

16

ln 940mm

lw=3000mmbw=300mmhf=120mm (slab)

d(eff.) = 940-40-10-30-(2

65 ) =830mm

As= 4200mm 2 (6 #30 bars)bt = 12hf = (12x120) = 1440mmbf = 2bt+bw = 2(1440)+300 = 3180mmCover = 40mm (for exterior slabs)Spacing (min) = 42mm, use 65mm


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Figure 1: Schmatic of T-beam design

Use a case 1 situation because of calculated, Mrf > MfMrf = K kNmxxdbwbfrf 05.415710)810)(3003180)(2.2(10)(

6262

Mf = kNmw 75.10328

)15(72.36

8

ln 22

The As(req) fulfilled the area constraints as As(max) = 6.77x10 4 mm 2 andAs(min) = 772 mm 2 . Therefore, As(max) > As(req) > As(min)

The moment resistance is fulfilled as Mr (=1136.2 kNm) > (=1032.75 kNm)

3.3 Shrinkage / Temperature Reinforcement Design

Reinforcements on the slab is needed to take into account effects of concreteshrinkage and temperature. These effects can cause the slab to crack, thereforeadding reinforcements to the slab wil negate these effects. (See figure 2 below)

As 2)( 240)120)(1000)(002.0(002.0 mmbhreq

hmin

Per 1m spacing


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By using #10 bars, with an Ab = 100 2mm , the spacing could be determined using,

mm

As

Abs 416)1000(

240

100)1000(

smax

=500mm, therefore, use #10bars @ 416 mm on one face

Figure 2: Shrinkage / Temperature Reinforcement design

3.4 Stirrup Design

For the design of the stirrups of the girders, it is best to use #10 stirrups becausethis is the standard that the industry uses. As the design does not have a topcompressive layer of longitudinal reinforcements, there is no need to 90 or135 hooks.

Determine required stirrup spacing (using simplified method):

2200)100(2 mmAv

mmhddv 729)677,729max()72.0,9.0max(

kNbwdvcfcVc 140)729)(300)(30)(18.0)(65.0('

kNVf 275 (from initial shear diagramrefer to figure A)

hmin =

940mm #10

@500mm

6 #30

#30 @ 150mm (from slab desi


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kNVcVf 135 (how much stirrup resistance we need) kNVs 135

Determine spacing:s

sAvfydvVs

cot s= mm

x524

10135

)35)(cot729)(400)(200)(85.0(3

Use s= 500mm

Final Design of Slab & Girder:

3.5 Shear Reinforcement of Girders

The design of the shear reinforcements of the girder will be calculated using thesimplified method because of ease of calculation and proven efficiency.

The procedure used to calculate the shear reinforcements is as follows:

1. Determine parameters:m15ln , mkNmmxxmkNmkNwf /48)120.04/5.23(/72.36 3

2. Calculate 747)72.0,9.0(max( hddv 3. Calculate ,720)15)(48(ln kNwfVf At face of support: kNVf 684

#10 @ 500mm

#30 @ 150mm (from slab desig


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For region 2, using:

4. kNbwdvcfcVc 287' , VcVf and kNVcVfVs 397 5. Determine spacing, s= mm

Vs

sAvfydv182

cot

, mmdS 581)600,7.0min(max ,

mmuse 200@10#

For region 1:6. max528' smms , use s =528mm7. kN

s

sAvfydvVs 181

cot

, with kNVc 287 (as above) kNVfVr 468

8. in region 1, starting about 5242 mm from support, provide #10 @ 400mmFor region 0,

9. 132.01000

230

dv , VfkNbwdvcfcVc 210'

10.in region 0, starting about 10612 mm from support, no stirrups arerequired

4.0 Column Design

7500

1750

mm


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Columns are vertical structural members that transmit axial compression forcesand resist moments.

4.1 Slab below Girder

It was decided that adding a slab below the t-beams to help provide support to thebeams and to increase the aesthetics of it (see figure 3 below) will be beneficial. Ifthe column had been placed directly underneath the t-beams, then the columnswould have had to be significantly large to fit the large clear span of the beams. Itwould also not look good to have the columns underneath the t-beams.

Figure 3: Slab below girder

4.1.1 Dimensions of slab

The slab below the girders was designed to be a bit bigger than the t-beams and fitdirectly underneath it. Therefore, the dimensions were designed as follows:

ml 8.3 mh 9.0 mb 5.0

By considering the super imposed loads, and the own weight of the concrete slaband girders, the weight that the slab would have to support was determined,


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mkNWf /712 and kNmMf 1174

By choosing 2 layers of #30 reinforcements, the depth of the reinforcements was

determined as: mmermmd 845

2

30)(cov40900

With 6, #30 bars, we determined As(req) to be 4200 2mm which fulfills the flexurerequirements since As(min) = 1232 2mm and As(max) = 10979 2mm . Therefore,

(max))((min) AsreqAsAs

In addition, spacing was calculated by s= mmAs

Ab167)1000(

4200

700)1000(

Finally, the moment resistance was concluded to be larger than the factored

moment:kNm

adsfyAsMr 1052)

2

216(845)(400)(85.0)(4200()

2( > kNmMf 915 (refer to

appendix A for more details)

4.1.2 Design of transverse / temperature reinforcement for slab under girders

26 90010)9.0)(5.0)(002.0(002.0)( mmmmbhreqAs

Assuming #10 bars and one-half As(req) on each face:

mmAs

Ab

s 222)1000(

2

900

100

)1000(

, but mmhs 500)500,5min(max

4.1.3 Design for Shear Reinforcement

Similar to the above calculations of shear reinforcement for the original concreteslab, except the calculations for the slab under the beams will use the simplifiedmethod as this slab is considerably smaller than the original slab. But the

simplified method is still able to ensure a safe and more efficient design (see figure6 below).

Calculations for the shear reinforcement are as follows:

kNWfVf 4.14232

ln

mmmmxmmxhddv 5.760)90072.0(),8459.0(()72.0,9.0max(


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mmxdvSz 600)600),7.0max(( kNbwdvcfcVc 146)5.760)(300)(30)(18.0)(65.0(' , VcVf kNVcVfVs 12771464.1423 mm

VssAvfydvs 43

1277

)35tan

1)(5.760)(400)(100)(85.0(

cot

mmxdvS 35.532)600),7.0((max , S < Smax kNVsVcVr 4.14231277146 mmmmcbwdvcfVr 1854)5.760)(500)(30)(65.0)(25.0('25.0(max) , (max)VrVr

4.2 Column Design

The design of the pedestrian bridge consist of 3 columns that separate the bridge

into four, 15m spans (see figure 4 below). As described above, the columns aresituated below the slab which creates an aesthetic appeal.

The design make use of both slender and short columns. Slender columns are usedbecause the moments induced by slenderness effects, weakens the columnappreciably. This is true for the column in the middle (see figure 4).

Figure 4: Overview of popsicle columns

The use of tied rectangular columns will be used because they provide a variable


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cross-sectional shape The ties included in tied columns provide restraint tolongitudinal bars from buckling out through the cover of the column, and hold thereinforcement during construction. They also confine concrete core, providingincreased ductility, as well as serve as shear reinforcement.

The columns will be installed as rigid connections because the use of pins willprovide a more stable connection and will not allow the columns to roll off as whatwould happen if rollers were used. Additionally, as a means to prevent sway; thecolumns will be designed as a braced frame.

4.2.1 First Iteration

Procedure to determine specifications (see appendix A for detailed calculations):

1. Point load on the slab below girder is 554kN (half of point load on the sideof the slab). So to combine the two side loads to calculate the total loadacting on the column, kNPf 11082*554

2. Select 02.0g 3. Calculate

2

1

62738)1('8.0

mmsfyccf

PAg

gg

f

4. Adjust b & h so that they are equal: mmAghb 250 5. Calculate 21255mmAgAst greq 6. Select 4 #25 bars, 22000mmAst 7. Check capacity: 024.0

Ag

Astg

8. Determine kNsfyAstAstAgccf 1169)('8.0maxPr 1 4.2.1.1 Slenderness Checks

The pedestrian bridge design must be checked for slenderness which is significantbecause slender columns carrying axial load and bending moments will havereduced strength due to increased moments arising from transverse deflections.

Slenderness checks procedure (see appendix B for detailed calculations):

1. kNPf 1108 , kNmM 01 , kNmM 1592 (see figure 5 below)


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Figure 5: M2

calculation

2. Assume L-type section3. Using similar triangles, determine heights of columns:

1lu = 7.5m,

2lu =

10m,3

lu = 5m

4. Determine radius of gyration, r=0.3h5. Check slenderness if

)'(

)2/1(1025

cAgf

Pf

MM

r

klu

, k=0.67

6. Find EId

EcIg

1

4.019 , 2

2

)(klu

EIPc

7. Using: 75.0m , 6.0)2

1(4.06.0 M

MCm ,

8. Determine whether Magnified Moment: )03.015()(1

2 hPf

mPc

Pf

CmMMc

9. Determine longitudinal Reinforcement:Ag

Pf,

Agh

Mc

10.Finally, find req from interactive tables in handbook

The above calculations were checks for column specifications of 250mm x 250mm(length x width). The results (refer to appendix B) show that slenderness is not anissue, but we found that these columns are too thin and resemble popsicle


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columns (see figure 7 above). This wouldnt make the pedestrian feel safe when

they are walking on the bridge.

4.2.2 Second Iteration

To give pedestrians a feeling of safety when walking across the bridge and toincrease the aesthetics of it, a specification of 500mm x 500mm for the design ofthe bridge was used. The cost isnt a burden to the project either as the increasedvolume only results in 2606$ increase in cost compared to 250mm x 250mmcolumns.

The above procedure for slenderness checks was repeated and determined that the500mm x 500mm columns are not slender. (refer to appendix C)

This column design does not fail as the (Mr, Pr) is within the failure envelop (seeAppendix E).

5.0 Cost Estimating

For the design of the pedestrian bridge, a concern is with the construction costswhich include the cost of materials and labour.The importance of cost estimating when designing for the pedestrian bridge iscrucial because if our estimates go over the allocated budget, the project will not beable to be implemented.

As can be seen on the design specifications that were initially proposed, the rebar /stirrups & ties are the most material costly and labour intensive aspect of thedesign. Therefore, minimization of these features whenever possible is beneficial.For the calculations of the materials, an application of a safety factor of 1.3 toensure there is enough materials to support all the loads and moments applied onthe bridge is needed. This is necessary since there will always be unexpectedsituations that occur which may add to the bridges loads.

*Note: assume the density of steel to be 80003m

kg


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5.1 Slab / Deck Cost Analysis

The following table summarizes the costs for the slab and deck in one 15m span.Materials Labour

Concrete/m^3

Rebar

/tonne

Formwork

/m^2

Concrete/

m^3

Longitudinal

Rebar

/tonne

stirrups &

ties Formwork

9.4 0.76 83.93 18.7 11.4 0 83.93

Summing the costs for the materials and labour, we get the total costs:

Cost

Materials Labour Total Cost

3175 7416 10592

Therefore the cost for the entire four 15m spans will be 10592 x 4 = $42368.00

5.2 Girder Cost Analysis

The following table summarizes the costs for the girder (t-beams) in one 15m span.

volume (m^3) steel (tons) labor (hrs)

Concrete

/m^3

Formwork

/m^2

Rebar

/tonne Stirrups&ties

Concrete

/ m^3 Formwork

Longitudinal

Rebar

/tonne

stirrups

& ties

9.6 75.7 1.3 0.0036 19.2 75.7 20 0.089


cost $

Materials Labour Total Cost3978 7449 11426

Therefore the cost for the entire four 15m spans will be 11426 x 4 = $45704.00


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5.3 Column Cost Analysis

The cost analysis of the columns will consist of the slab under the girder and eachindividual column.

5.3.1 Slab below Girder

The following table summarizes the costs for one of the three slabs below thegirder.

volume weight of steel labour (hrs)

concrete

(m^3)

formwork

(m^2)

rebar

(tonne)

stirrups and

ties (ton) concrete formwork

longtitudinal

rebar

stirrups

and ties

2.2 15.0 0.17 0.14 4.4 15.0 2.5 3.5


Cost $

material labour total cost

907 1655 2562

Therefore the cost of all 3 of the slabs will be 2565 x 3 = $7695.00

5.3.2 Columns

For the 500 x 500mm columns the following table summarizes the costs for the 3different columns:

volume weight of steel labour (hrs)

concrete

(m^3)

formwork

(m^2)

rebar

(tonne)

stirrups

and ties

(tonne) concrete formwork

longitudinal

rebar

stirrups

and

ties

col1 1.8 14.6 0.12 0.003 3.6 14.6 1.7 0.076

col2 2.63 21.1 0.17 0.004 5.3 21.1 2.53 0.11

col3 1.0 8.1 0.06 0.002 2.0 8.1 0.97 0.042


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Cost $

material labour total costcol1 562 1302 1863

col2 812 1883 2695

col3 311 720 1031

Therefore the cost of the 3 columns are: 1863+2695+1031=$5589.00

5.4 Total Cost

Total Cost = $101,356.00The total cost for the design of the pedestrian bridge is reasonable.

6.0 Deflections

The design of the pedestrian bridge must be checked for deflection to ensure itssafety. To validate the design, the deflections must be less than the maximumallowable.

The following data is given:

mkNmkNmxmkNWd /59.222^/5.0)940.0/5.23( 3 (assuming per 1 mwidth). 22.59kN/m + 0.5 kN/m (side railings) = 23.09 kN/m

h(min)= mm94016

15000

Calculate the immediate dead load deflection and immediate deflection due to deadload using the following formulas:

11

ln2

wMa ,

yt

frIgMcr

12

3bhIg , 23 )()(

3

1kddnAskdbIcr

3

)/)(( MaMcrIcrIgIcrIe

EcsIe

w

384

ln4 (for simply supported)

Our deflection calculation came out to be 6.18mm which is significantly smaller

than the check of mm3.83180

ln

*see appendix D for detailed calculations


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7.0 Conclusion

The development of the extensive system of hiking and walking trails within theEast Humber River Valley has been designed and satisfies all the codes andrequirements of the Concrete CSA handbook.

The use of a simply supported bridge with the dimensions chosen for the slab andgirder worked extremely well. Along with our unique combination of a slab underthe girder, we were able to bring out the aesthetics and increase the efficiency ofour bridge design. Additionally the four 15 m spans that are separated by our threecolumns continues the aesthetic appeal and supports all the loads applied on it.Finally, we have sufficient rebar and reinforcements to support the concrete whichmakes the design extremely strong and safe for the pedestrians to walk on. For thefinal determined cost, it is reasonable and affordable.

Documents

Concrete Bridge Design Project