Super t beam (l=38 3m)EN Cầu Nguyễn Tri Phương Đà Nẵng

DIMENSION OF MAIN BEAM Height of section of beam edge 800mm Length of section at the beam edge 850mm At the time of completion of tensile Elasticity modulus of concrete when 32,959Mpa Fo

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D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls

II STRENGTH AND ULTIMATE STRESS OF MATERIAL

2.1 Steel:

2.1.1 Prestress reinforcement

Required tensile strength of prestressing steel fpu = 1,860(MPa) (T.5.4.4.1-1)Liquid limit of prestreesing steel fpy = 0.9 fpu = 1,674(MPa) (T.5.4.4.1-1)Before the force transferred to concrete = 0.75 fpu = 1,395(MPa) (T.5.9.3-1)

2.1.2 High-strength steel bar Under standard 22TCN 272-05

2.1.3 Plain reiforcement Under standard TCVN 1651:2008

Liquid limit strength of reinforcement CB400-V fsy = 400(Mpa)

Liquid limit strength of reinforcement CB300-T fsyr = 300(Mpa)

Ultimate stress of concrete

Ultimate compressive stress when force tranfer applied = 0.6 f'ci = 25.5(MPa) (A.5.9.4.1.1)Ultimate tension stress when force tranfer applied =0.58f'ci0.5 = 3.78(MPa) (T5.9.4.1.2)Ultimate compressive stress when losing stress

* Prestressing + long-term load = 0.45 f'c = 22.5(MPa) (T5.9.4.2.1-1)

* Live load +1/2(prestressing+long-term load) = 0.4 f'c = 20(Mpa) (T5.9.4.2.1-1)

* Prestressing + Long-term load + Live load = 0.6 f'c = 30(Mpa) (T5.9.4.2.1-1)Tension stress after losing stress = 0.5 f'c0.5 = 3.54(Mpa) (T5.9.4.2.2-1)

2.2.2 Bridge deck

Theoretical compressive strength of concrete at 28 age days f'cs = 35(MPa) (A.5.4.2.1)Modulus of elasticity Ecs = 0.043 yc1.5 f'cs0 = 29,910(MPa) (A.5.4.2.1)Ultimate compressive stress when losing stress

* Prestressing + long-term load = 0.45f'cs = 15.8(MPa) (T5.9.4.2.1-1)Tension stress after losing stress = 0.5f'cs0.5 = 2.96(Mpa) (T5.9.4.2.2-1)

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2.3 Material conversion factor

Prestressing reinforcement/Concrete of main beam Rpc = Ep / Ec = 5.51

Reinforcement/Concrete of main beam Rsc = Es / Ec = 5.59

Concrete of bridge deck/Concrete of main beam Rdc = Ecs / Ec = 0.84

3 Load and impact

During construction, the following loads shall be considered and calculated

- Self weight of beam

- Tensile force of prestressing strand

- Effect of creep shrinkage during construction

During the using, there are additional loads as follows

- Effect of creep shrinkage during the using

- Weigth of dead load , part 2 (bridge deck, hand rail, wheel guard)

- Live load of vehicle

3.1 Design live load effects on one main beam

3.1.1 Dead load of seft beam

- Lead load of divided wall, DC2= 0.32 kN/m

3.1.2 Weigth of dead load, part 2

- Hand rail, sidewalk, DC5= 2.50 kN/m (Calculation for exteior beam)

Designed live load of vehicle HL-93 consists one combination of

Design truck and load of lane

or two-axled truck and load of lane

3.2.2 Designed truck has total of weight 325 kN

3.2.3 Designed two-axled truck

Two-axled truck consists a pair of axles 110 kN, apart 1.2m Horizontal spacing of wheels

Impact coefficient follows to Clause 3.6.2 - Standard 22TCN272-05

1.20 m

3.2.4 Designed load of lane

Stressing force of designed load of lane does not include impact coefficient

3.2.5 Live load of pedestrian (PL)

Uniform load of pedestrian according to longitudinal of bridge qpl = 6.0kN/m/1side

III DISTRIBUTION COEFFICIENT

1 Calculate the horizontal distribution coefficient due to live load

Look up the table 4.6.2.2.1-1, we have the formula for computation of horizontal distribution coefficient as follows:

The values used for computation :

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+ ts : Thickness of concrete slab of bridge deck = 200 mm

1.1 Distribution coefficient of moment

1 + ((Ld)0.5/6S)tan(θ) = 1.00

3 Computation result of distribution coefficient of load

Position of beam Number of lane gM gV

IV PERIOD OF COMPUTATION

Structure to be analysed through 2 phases as follows:

1 Phase 1

- Computation with load: + Dead live of self section of beam (DC)

+ Dead load of divided wall (DC)+ Acting of Prestressing (PS)R1

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2 Phase 2

- Computation with load: + Dead load of self beam (DC) 18.27 kN/m/1beam

+ Dead load of divided wall (DC) 0.32 kN/m/1beam+ Dead load of self deck (DC) 11.16 kN/m/1beam+ Dead load of remaining formwork 1.00 kN/m/1beam+ Hand rail, sidewalk (DC) 2.50 kN/m/1beam+ Dead load of deck overlays (DW) 3.77 kN/m/1beam+ Wastewater treatment pipe (P) 3.33 kN/m/1beam+ Live load of vehicle (combined compact stress) LL+ IM; human

V LOAD COMBINATION

1 Adjustment coefficient of load

Adjustment coefficient of load : η= ηDηRηΙ (1.3.2)

Flexibility

Load combination at strength limit state I

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Calculated by PhucdhChecked by Dr SongkiatDated 4/21/2010

MORPHOLOGIC FEATURE OF SECTION

I.INTRODUCTION:

Character of reinforcement concrete section shall be calculated in 41 positions of length of beam (0.025Ls for 1 section)

Character of section shall be calculated with two main states

First state : Beam combinate strand before concreting bridge deck

Second state : Beam combinate strand and bridge deck at the time of using

II CHARACTER OF BEAM COMPUTATION SECTION

Height of beginning section of beam : 800(mm)

Width conversion of deck slab : 1,983(mm)

Length of beginning section of beam : 850(mm)

Length of plain section : 1,425(mm)

Length of hollow section : 33,750(mm)

DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT

NGUYỄN TRI PHƯƠNG BRIDGE

STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m

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POSITION OF TENDONS

I DIMENSION OF MAIN BEAM

Height of section of beam edge 800(mm)

Length of section at the beam edge 850(mm)

At the time of completion of tensile

Elasticity modulus of concrete when 32,959Mpa

Force transfer applied

Elasticity modulus of tendon 197,000Mpa

Diameter of wire : 15.2(mm) 140(mm2) 1,589(mm4)

At the time of concreting the bridge deck

concreting the bridge deck

Period of service

force transfer applied

II POSITION OF STRAND

Debonded length (mm)

III CHARACTER OF TENDON SECTION:

Distance to bottom of beam

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Phucdh

Dr Songkiat4/21/2010

COMPUTATION OF INTERNAL FORCE

I DESIGNED INTERNAL FORCE DUE TO DEAD LOAD

ĐAH Moment

ĐAH Shear Table value of influence line for moment

Section x y1 y2 Area (+) Area (+) Area

NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m

Table value of influence line for shear

Calculated byChecked byDated

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MOMENT DUE TO DEAD LOAD

Section Load of

main beam

Divided wall

Remainin

g forwork

Deck overlay Deck slab

Hand rail, sidewalk

Wastewater treatment pipe

Remainin

g forwork

Deck overlay Deck slab

Hand rail, sidewalk

Wastewater treatment pipe

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II DESIGNED INTERNAL FORCE DUE TO LIVE LOAD

MOMENT DUE TO LIVE LOAD

Load of MLL+IM Live load ofSection 145 KN 145 KN 35 KN ΣPiyi 110 KN 110 KN ΣPiyi lane pedestrian(m) yi (m) yi (m) yi (m) (KNm) yi (m) yi (m) (KNm) (KNm) (KNm) (KNm)

SHEAR FORCE DUE TO LIVE LOAD

Load of VLL+IM Live load ofSection 145 KN 145 KN 35 KN ΣPiyi 110 KN 110 KN ΣPiyi lane pedestrian

Notes: Internal force due to live load is already multiplied with impact coefficient

(impact coefficient is only applied for truck, not be applied for load of lane and pedestrian)

III INTERNAL FORCE IN THE MAIN BEAM

Load combination at the state of strength limit I (phase I)

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Exterior beam

State of strength limit I State of using limit

Intermediate

beam

Intermediate beam

State of strength limit I

Shearing force V(KN)

MMaxIntermediate

beam

Intermediate beam

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D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls14.10 114.68 114.68 114.68 545.63 506.18 545.63 344.12 324.21 344.12

IV INTERNAL FORCE IN MAIN BEAM TAKE ACCOUNT OF EFFECT OF PRESTRESSING STRAND

Load combination at the state of strength limit I (phase I)

Mặt cắt

0.94 420.41 -2,422.45 -2,002.04 1,536.34 -2,741.23 -1,204.89 1,009.06 690.16 -2,610.70 -1,601.63 -615.181.88 819.26 -2,426.94 -1,607.69 2,992.44 -2,764.66 227.78 1,965.59 1,344.14 -2,633.01 -667.42 27.642.821,196.55 -2,536.92 -1,340.37 4,368.31 -3,559.11 809.20 2,869.58 1,961.95 -3,389.63 -520.05 267.133.761,552.28 -3,589.60 -2,037.33 5,663.95 -4,753.23 910.72 3,721.04 2,543.57 -4,526.88 -805.85 280.124.701,886.45 -4,082.10 -2,195.66 6,879.35 -5,308.24 1,571.11 4,519.96 3,089.01 -5,055.47 -535.51 561.275.642,199.06 -4,091.74 -1,892.68 8,014.52 -5,369.18 2,645.33 5,266.35 3,598.26 -5,113.51 152.84 1,041.516.582,490.11 -4,827.24 -2,337.14 9,069.45 -6,121.41 2,948.03 5,960.20 4,071.34 -5,829.92 130.28 1,156.387.522,759.60 -4,837.25 -2,077.64 10,044.15 -6,183.92 3,860.22 6,601.52 4,508.24 -5,889.45 712.07 1,563.518.463,007.53 -5,065.90 -2,058.37 10,938.61 -6,447.47 4,491.14 7,190.30 4,908.95 -6,140.45 1,049.86 1,838.739.403,233.91 -5,074.70 -1,840.79 11,752.84 -6,502.45 5,250.38 7,726.55 5,273.49 -6,192.81 1,533.74 2,177.0810.343,438.72 -5,082.66 -1,643.94 12,486.83 -6,552.20 5,934.63 8,210.27 5,601.84 -6,240.19 1,970.07 2,481.7411.283,621.98 -5,089.79 -1,467.81 13,140.59 -6,596.71 6,543.88 8,641.45 5,894.01 -6,282.58 2,358.86 2,752.7212.223,783.67 -5,096.07 -1,312.40 13,714.11 -6,635.98 7,078.13 9,020.09 6,150.00 -6,319.99 2,700.11 2,990.0113.163,923.81 -5,101.52 -1,177.71 14,207.40 -6,670.02 7,537.38 9,346.20 6,369.82 -6,352.40 2,993.80 3,193.6214.104,042.38 -5,106.12 -1,063.74 14,620.46 -6,698.82 7,921.64 9,619.78 6,553.44 -6,379.83 3,239.95 3,363.5315.044,139.40 -5,109.89 -970.49 14,953.28 -6,722.38 8,230.90 9,840.82 6,700.89 -6,402.27 3,438.55 3,499.7615.984,214.86 -5,112.83 -897.97 15,205.87 -6,740.70 8,465.16 10,009.32 6,812.16 -6,419.72 3,589.61 3,602.3016.924,268.76 -5,114.92 -846.16 15,378.22 -6,753.79 8,624.43 10,125.29 6,887.25 -6,432.18 3,693.11 3,671.1617.864,301.10 -5,116.18 -815.08 15,470.34 -6,761.65 8,708.69 10,188.73 6,926.15 -6,439.66 3,749.07 3,706.3218.804,311.88 -5,116.59 -804.72 15,482.22 -6,764.27 8,717.95 10,199.63 6,928.88 -6,442.16 3,757.48 3,707.80

Mphase3 Mphase4

PS Mphase2 Max 1 Max 2 PS

MMax PS Mphase1 MMax

Moment M(KN.m) State of strength limit I

State of strength limit I

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CHART BOUNDARY OF MOMENT

State of service limit (phase2)

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STRESS LOSS

I TOTAL OF STRESS LOSS

I.1 Total of stress loss created by:

Where:

I.2 Stress loss due to elastic shortening

Stress loss due to elastic shortening in each tendon

Where:

and sefl load of section with maximum moment (Mpa)

Section Number of

tendon

Area of tendon P fcgp ΔfpES

I.3 Stress loss due to creep:

Where:

deduct the applied load when carrying out the prestressing

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load at the designed sections

I.4 Stress loss due to shrinkage of concrete:

Where:

H: Surrounded relative humidity = 85 %

I.5 Stress loss due to relaxation of reinforcement:

Where:

+ ΔfpR1 : Loss due to self relaxation of reinforcement when force transfer applied (MPa)

+ ΔfpR2 : Loss due to self relaxation of reinforcement after force transfer (MPa)

I.5.1 Loss due to self relaxation of reinforcement at the time of force transfer Δ f pR1

For the strand with low relaxation :

Where:

+ t : Time from apply of stress to transfer

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D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls6.58 1,287.93 1,674.00 7.00 15.72

7.52 1,290.72 1,674.00 7.00 15.878.46 1,286.88 1,674.00 7.00 15.669.40 1,289.22 1,674.00 7.00 15.7910.34 1,291.33 1,674.00 7.00 15.9111.28 1,293.22 1,674.00 7.00 16.0112.22 1,294.89 1,674.00 7.00 16.1013.16 1,296.34 1,674.00 7.00 16.1814.10 1,297.57 1,674.00 7.00 16.2515.04 1,298.57 1,674.00 7.00 16.3115.98 1,299.35 1,674.00 7.00 16.3516.92 1,299.90 1,674.00 7.00 16.3817.86 1,300.24 1,674.00 7.00 16.4018.80 1,300.35 1,674.00 7.00 16.41

I.5.2 Loss due to self relaxation of reinforcement after force transfer Δ f pR2

I.7 Total of stress loss:

I.7.1 Total of stress loss at the time of force transfer

I.7.2 Total of stress loss after force transfer

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P after all losses P prestress P all losses

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CHECKING THE STRESS IN BEAM

We shall check the stress of top fiber and bottom fiber of beam ( + ) Compressive stress

Stress at top fiber of beam when force transfer applied is to be calculated as follows:

ft1 = Pworking/Agirder - Pworking*estrand1*Yt1/Igirder + Mstg1*Yt1/Igirder

Stress at bottom fiber of beam when force transfer applied is to be calculated as follows:

fb1 = Pworking/Agirder + Pworking*estrand1*Yb1/Igirder - Mstg1*Yb1/Igirder

Ultimate tensile stress when force transfer applied = - 0.58f'ci0.5 = -3.78(MPa)

Ultimate compressive stress when force transfer applied = 0.6f'ci = +25.50(MPa)

SECTION Ptension Pworking Agirder Igirder estrand 1 Mstg1 Yt1 Yb1 ft1 fb1

II STRESS WHEN CONCRETING BRIDGE DECK (deck without load applied)

Stress at top fiber of beam when concreting bridge deck is to be calculated as follows:

ft2 = ft1 + ΔPlosses1/Agirder - ΔPlosses1*estrand1*Yt1/Igirder + Mstg2*Yt1/Igirder

Stress at bottom fiber of beam when concreting bridge deck is to be calculated as follows:

fb2 = fb1 + ΔPlosses1/A girder + ΔPlosses1*estrand1*Yb1/Igirder - Mstg2*Yb1/Igirder

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D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xlsUltimate compressive stress when force transfer applied = 0.45f'ci = +22.50(MPa)

SECTION ΔPlosses1 Agirder Igirder estrand1 Mstg2 Yt1 Yb1 ft2 fb2

III STRESS IN THE PERIOF OF SERVICE

III.1 Stress of beam due to live load +1/2 (Prestressing+Permanent load):

Stress at top fiber of beam in the period of operation is to be calculated by:

ft3 = Plosses/Acomb - Plosses*estrand2*Yt2/Icomb + Mstg3*Yt2/Icomb

Stress at bottom fiber of beam in the period of operation is to be calculated by:

fb3 = Plosses/Acomb + Plosses*estrand2*Yb2/Icomb - Mstg3*Yb2/Icomb

Ultimate compressive stress when force transfer applied = 0.4f'c = +20.00(MPa)

SECTION Plosses Acomb Icomb estrand2 Mstg3 Yt2 Yb2 ft3 fb3

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