Ban tinh dam super t khue dong

Structure DateĐẶC TRƯNG MẶT CẮT - MORPHOLOGIC FEATURE OF SECTION I.INTRODUCTION: Character of reinforcement concrete section shall be calculated in 41 positions of length of beam 0.025Ls

Package :A23 + A24 + B27

tiểu hợp phần c12: cầu khuê đông Subcomponent c12: khue dong bridge

Bảng tính Dầm super-T Super-T girder calculation

(Shop drawing design stage)

(Version 1)

Ha noi: 10 2011

Package :A23 + A24 + B27

tiểu hợp phần c12: cầu khuê đông Subcomponent c12: khue dong bridge

Bảng tính dầm super-T Super-T girder calculation

(Shop drawing design stage)

(Version 1)

NHà thầu Contractor

T− vấn giám sát Consultant

Chủ đầu t−

Employer

Ha noi: 10 2011

-SUPER-T GIRDER SPAN 37.5M

Structure Date

I KÍCH THƯỚC HÌNH HỌC - STRUCTURAL PARAMETER:

II CƯỜNG ĐỘ VÀ ỨNG SUẤT GIỚI HẠN CỦA VẬT LIỆU - STRENGTH AND ULTIMATE STRESS OF MATERIAL

2.1 Thép - Steel:

2.1.1 Cốt thép ứng suất trước - Prestress reinforcement

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge Duong Van Chien

Super-T beam L=37.5m

InputData-1/5

(Pre-tensioning)

2.1.2 Thanh cường độ cao - High-strength steel bar (Standard 22TCN 272-05)

2.1.3 Cốt thép thường - Plain reiforcement (Standard TCVN 1651:2008)

2.2 Bê tông - Concrete

InputData-1/5

2.2.1 Dầm chủ - Main beam

1.5

f'c 0.5

0.5

Ultimate stress of concrete

Ultimate tension stress when force tranfer applied =0.58f'ci

0.5

Ultimate compressive stress when losing stress

0.5

2.2.2 Mặt cầu - Bridge deck

1.5

f'cs 0.5

Ultimate compressive stress when losing stress

0.5

2.3 Material conversion factor

3 Tải trọng - Load and impact

During construction, the following loads shall be considered and calculated

- Self weight of beam

InputData-2/5

- 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

3.1.2 Weigth of dead load, part 2

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

InputData-2/5

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

9.3 kN/m

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

3.2.5 Live load of pedestrian (PL)

III HỆ SỐ PHÂN BỐ - 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 :

1.1 Distribution coefficient of moment

InputData-3/5

1.2 Distribution coefficient of shear force

1 + ((Ld)0.5/6S)tan(θ) = 1.00

3 Computation result of distribution coefficient of load

IV GIAI ĐOẠN TÍNH TOÁN - PERIOD OF COMPUTATION

Structure to be analysed through 2 phases as follows:

1 Giai đoạn 1 - Phase 1

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

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

2 Giai đoạn 2 - Phase 2

+ Live load of vehicle (combined compact stress) LL+ IM; human

InputData-4/5

V TỔ HỢP TẢI TRỌNG - LOAD COMBINATION

1 Hệ số điều chỉnh tải trọng - Adjustment coefficient of load

Adjustment coefficient of load : η= ηDηRηΙ (1.3.2)

Flexibility

2 Trạng thái giới hạn và tổ hợp tải trọng - Strength limit states and load combination coefficient: (3.4)

Load combination at strength limit state I

Structure Date

ĐẶC TRƯNG MẶT CẮT - 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 ĐẶC TRƯNG CÁC MẶT CẮT TÍNH TOÁN - CHARACTER OF BEAM COMPUTATION SECTION

f sup A conc I conc. e conc. A strand I strand e strand A*e A combI I combI e combI

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge Duong Van Chien

Section Stage I (at the time of concreting the bridge deck)

f sup A conc. I conc. e conc. A strand I strand e strand A*e A combI I combI e combI

f sup A combI I combI e combI A slab I slab e slab A*e A combI I combI e combI

Section Trạng thái II ( lúc khai thác) Stage II (At service)

f sup A compI I compI e compI A strand I strand e strand A*e A compI I compI e compI

At the time of completion of tensile

Elasticity modulus of concrete when 32959 Mpa

Force transfer applied

At the time of concreting the bridge deck

Elasticity modulus of concrete when 35750 Mpa

concreting the bridge deck

Period of service

Elasticity modulus of concrete when 35750 Mpa

force transfer applied

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge Duong Van Chien

Super-T beam L=37.5m

Super-T 37,5m-Tendon-1/3

force transfer applied

III ĐẶC TRƯNG MẶT CẮT CÁP DƯL - CHARACTER OF TENDON SECTION:

Section Position Row A Row B Row C Row D Row E Total A conversion

Distance to bottom of beam

Section Position Row A Row B Row C Row D Row E Total A conversion

Distance to bottom of beam

Structure Date

TÍNH NỘI LỰC - COMPUTATION OF INTERNAL FORCE

I NỘI LỰC THIẾT KẾ DO TĨNH TẢI - DESIGNED INTERNAL FORCE DUE TO DEAD LOAD

ĐAH Moment

ĐAH Shear

Table value of influence line for moment

(Shop drawing design stage)

Da Nang priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super-T beam L=37.5m

Bridge joint stock

Section Load of

main beam

Divided wall

Remaining forwork

Deck overlay Deck slab

Hand rail, sidewalk

Wastewater treatment pipe

Remaining forwork

Deck overlay Deck slab

Hand rail, sidewalk

Wastewater treatment pipe

MÔ MEN DO HOẠT TẢI - MOMENT DUE TO LIVE LOAD

Load of MLL+IM Live load of

LỰC CẮT DO HOẠT TẢI - SHEAR FORCE DUE TO LIVE LOAD

Load of VLL+IM Live load of

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)

Standard truck Designed two-axle vehicle

Super-T 37,5m-Loading-3/6

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

Intermediate beam MMax

Exterior

beam

Intermediate beam MMax Exterior

beam

Intermediate beam MMax

State of strength limit I State of strength limit I State of using limit

Exterior

beam

Intermediate beam VMax

Exterior beam

Intermediate beam VMax

Exterior beam

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

Mặt cắt

0.92 403.77 -3,056.52 -2,652.75 1,528.19 -3,400.94 -1,872.75 1,004.24 685.15 -3,238.99 -2,234.75 -934.341.84 786.83 -3,062.19 -2,275.35 2,976.53 -3,430.75 -454.22 1,956.17 1,334.36 -3,267.38 -1,311.21 -299.332.76 1,149.19 -3,289.35 -2,140.15 4,345.01 -4,432.77 -87.75 2,855.79 1,947.62 -4,221.68 -1,365.89 -163.223.68 1,490.84 -3,822.24 -2,331.39 5,633.64 -5,027.54 606.10 3,703.11 2,524.94 -4,788.13 -1,085.03 130.874.60 1,811.79 -4,307.61 -2,495.82 6,842.41 -5,565.42 1,277.00 4,498.11 3,066.31 -5,300.40 -802.28 416.115.52 2,112.03 -4,317.43 -2,205.40 7,971.33 -5,629.23 2,342.10 5,240.81 3,571.73 -5,361.17 -120.36 891.156.44 2,391.56 -5,041.94 -2,650.38 9,020.39 -6,353.03 2,667.36 5,931.20 4,041.21 -6,050.50 -119.30 1,015.967.36 2,650.39 -5,052.01 -2,401.62 9,989.60 -6,417.77 3,571.83 6,569.28 4,474.75 -6,112.16 457.12 1,418.678.28 2,888.51 -5,061.27 -2,172.76 10,878.95 -6,477.33 4,401.62 7,155.05 4,872.34 -6,168.88 986.17 1,787.909.20 3,105.93 -5,069.73 -1,963.80 11,688.44 -6,531.71 5,156.73 7,688.51 5,233.99 -6,220.67 1,467.84 2,123.6510.12 3,302.63 -5,077.37 -1,774.74 12,418.08 -6,580.90 5,837.17 8,169.67 5,559.69 -6,267.53 1,902.14 2,425.9311.04 3,478.64 -5,084.22 -1,605.58 13,067.86 -6,624.92 6,442.94 8,598.51 5,849.45 -6,309.45 2,289.06 2,694.72

MMax 1 MMax 2 PS Mphase3 Mphase4

MMax PS Mphase1 MMax PS Mphase2

Moment M(KN.m) Phase I

State of strength limit I State of strength limit I

Super-T 37,5m-Loading-6/6

11.96 3,633.93 -5,090.25 -1,456.32 13,637.79 -6,663.76 6,974.03 8,975.05 6,103.26 -6,346.44 2,628.61 2,930.0412.88 3,768.52 -5,095.48 -1,326.96 14,127.86 -6,697.42 7,430.44 9,299.28 6,321.12 -6,378.49 2,920.79 3,131.8813.80 3,882.41 -5,099.91 -1,217.50 14,538.08 -6,725.90 7,812.18 9,571.20 6,503.04 -6,405.62 3,165.58 3,300.2414.72 3,975.58 -5,103.53 -1,127.94 14,868.44 -6,749.20 8,119.24 9,790.81 6,649.02 -6,427.81 3,363.00 3,435.1215.64 4,048.06 -5,106.35 -1,058.29 15,118.94 -6,767.32 8,351.62 9,958.12 6,759.05 -6,445.07 3,513.05 3,536.5216.56 4,099.82 -5,108.36 -1,008.53 15,289.59 -6,780.27 8,509.33 10,073.11 6,833.14 -6,457.40 3,615.71 3,604.4417.48 4,130.88 -5,109.56 -978.68 15,380.39 -6,788.03 8,592.35 10,135.80 6,871.28 -6,464.80 3,671.00 3,638.8818.40 4,141.23 -5,109.97 -968.73 15,413.38 -6,790.62 8,622.76 10,158.18 6,885.48 -6,467.26 3,690.92 3,651.85

Structure Date

MẤT MÁT ỨNG SUẤT - LOSS STRESS

I TỔNG MẤT MÁT ỨNG SUẤT -TOTAL OF LOSS STRESS

I.1 Total of loss stress created by:

∆fpT = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR (A.5.9.5.1-2)

Where:

∆fpT : Total of stress loss (Mpa)

∆fpES : Stress loss due to elastic shortening (Mpa)

∆fpSR : Stress loss due to shrinkage (Mpa)

∆fpCR : Stress loss due to creep (Mpa)

∆fpR : Stress loss due to relaxation of reinforcement (Mpa)

I.2 Stress loss due to elastic shortening

Stress loss due to elastic shortening in each tendon

Where:

fcgp = Stress in concrete at the center of tendon when force tranfer applied

and sefl load of section with maximum moment (Mpa)

fcgp = (P/Ag) + (Pi*e2/Ig) - (Mg*e/Ig)

Ep = 197,000 (MPa) Elasticity modulus of tendon

Eci = 32,959 (MPa) Elasticity modulus of concrete when force transfer applied

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge Duong Van Chien

I.3 Stress loss due to creep:

∆fpCR = 12*fcgp - 7*∆fcdp (A.5.9.5.4.3)

Where:

fcgp: Stress of concrete at the center of tendon when force tranfer applied (MPa)

∆fcdp: Change of concrete stress at the center of tendon due to permanent load of each section

deduct the applied load when carrying out the prestressing

∆fcdp = - M*e/Ig

M = (kN.m) Moment due to formwork, bridge deck, hand rail and permanent

load at the designed sections

Ig = (m4) inertia moment of cross-section

e = (m) Distance from neutral axis to the center of tendon

H: Surrounded relative humidity = 85 %

I.5 Stress loss due to relaxation of reinforcement:

∆fpR = ∆fpR1 + ∆fpR2Where:

+ ∆fpR1 : Loss due to self relaxation of reinforcement when force transfer applied (MPa)

+ ∆fpR2 : Loss due to self relaxation of reinforcement after force transfer (MPa)

For the strand with low relaxation :

∆fpR1 = [log(24t)/40][fpj/fpy - 0,55]fpj

Where:

+ t : Time from apply of stress to transfer

+ fpj : Initial stress in tendon at the end of tension time

fpj = Pj/Aps - ∆fpES+ fpy : Yield strength of tendon (MPa)

Super-T 37,5m-LossStress-2/4

∆fpES = Loss due to elastic shortening after transfer (MPa)

∆fpSR = Loss due to shrinkage after transfer (MPa)

I.6 Total of stress loss:

I.6.1 Total of stress loss at the time of force transfer

∆fpT1 = ∆fpES + ∆fpR1

I.6.2 Total of stress loss after force transfer

∆fpT2 = ∆fpES + ∆fpSR + ∆fpCR + ∆fpR1 + ∆fpR2

Section Jacking

force ∆∆f pES ∆∆f pCR ∆∆f pSR ∆f∆pR1 ∆∆f pR2 ∆∆f pT1 ∆f∆pT2 P All loss P after all loss

Distance from support (m)

Prestress force before and after all losses

P after all losses P prestress P all losses

Super-T 37,5m-LossStress-4/4

Structure Date

KIỂM TRA ỨNG SUẤT DẦM CHỦ - CHECKING THE STRESS IN BEAM

I THỜI ĐIỀM CHUYỀN LỰC SANG BÊ TÔNG - STRESS AT THE TIME OF FORCE TRANSFER

We shall check the stress of top fiber and bottom fiber of beam

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'ci

0.5

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

Da Nang priority Infrastructure Investment Project Checked by

Sub_component C12 - Khue Dong bridge Duong Van Chien Super-T beam L=37.5m

Bridge joint stock

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 + ∆Plosses1/Agirder - ∆Plosses1*estrand1*Yt1/Igirder + Mstg2*Yt1/Igirder

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

fb2 = fb1 + ∆Plosses1/A girder + ∆Plosses1*estrand1*Yb1/Igirder - Mstg2*Yb1/Igirder

Ultimate tensile stress when force transfer applied = - 0.5f'ci

0.5

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 + Mstg3*Yt2/Icomb

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

fb3 = Plosses/Acomb - Mstg3*Yb2/I comb

Ultimate tensile stress when force transfer applied = - 0.5f'ci

0.5

III.2 Stress of beam due to live load + Prestressing + Permanent load :

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

ft4 = Plosses/Acomb + Mstg4*Yt2/Icomb

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

fb4 = Plosses/Acomb - Mstg4*Yb2/I comb

Ultimate tensile stress when force transfer applied = - 0.5f'ci

0.5

Structure Date

KIỂM TRA TRẠNG THÁI GIỚI HẠN - CHECKING THE STATE OF STRENGTH LIMIT IN BEAM

I KIỂM TRA GIỚI HẠN VỀ CỐT THÉP - CHECKING THE REINFORCEMENT LIMITS

I.1 Hàm lượng cốt thép tối đa - Maximum reiforcement limit

Percentage of reinforcement shall be limited so that:

Where:

+ c : Height of compression region

+ de : Distance from extreme compression fiber to the center of tension reinforcement

(5.7.3.1-2)

+ β1 : Stressing cubic coefficient

+ b : Width of compressive flange

+ bw : Width of web

+ h : Height of compressive flange

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge Duong Van Chien

Super-T beam L=37.5m

65,005,0.728'f85,

y s ps ps

s y s p ps ps e

fAfA

dfAdfAd

f w c 1 pu

ps

d

fkAbβf0,85

)hb(bfβ0,85fAc

+ hf : Height of compressive flange

+ fps : average stress in prestressing tendon

(5.7.3.1.1-1)

+ dp (ds): Distance from extreme compression fiber to the center of tendon (plain tensile iron)

+ k : Coefficient depend on nature of reinforcement

y s ps ps

s y s p ps ps e

fAfA

dfAdfAd

f w c 1 pu

ps

d

fkAbβf0,85

)hb(bfβ0,85fAc

ck(1ff

p pu

ps = −

)f

f2(1,04k

pu py

−

=

Super-T 37,5m-LimitStateChk-1/6

16.56 0.69 240 0.280 Cantilever 182 1,740 0.10 OK

1.2 Hàm lượng cốt thép tối thiểu - Minimum reinforcement limit (5.7.3.3.2)

Volume of prestressing tendon and plain reiforcement shall be sufficient to develop bending resistance Mr, take less-than value of :

Z

If

II KIỂM TRA KHÁNG UỐN - CHECK MOMENT RESISTANCE

The factored moment resistance Mr , shall be taken as:

Where:

ϕ = 1.00 : Resistance factored as specified in Article 5.5.4.2

Mn = Aps*fps * + 0.85*f'c*(b-bw)*β1*hf* (5.7.3.2.2-1)

+ Mu : Flexural moment in beam due to applied load

+ Mr : Factored flexural moment of beam

+ Mn : Nominal flexural resistance moment of beam

+ dp : Distance from extreme compression fiber to the center of tendon

+ fps : Avarage stress in tendon ≤ fpy

+ a = c.β1 : Thickness of equivalent stress block

t

comb r cr

Z

If

Super-T 37,5m-LimitStateChk-2/6

III KIỂM TRA KHÁNG CẮT - CHECK SHEAR RESISTANCE

III.1 Nominal shear resistance

Nominal shear resistance Vn shall take less-than value of :

=

y v ' c vmin

fsbf0.83

+ bv : Width of minimum web of beam (mm)

+ dv : Effective shear height (mm), dv = max(0,9de ; 0,72h)

+ s : Distance of hoop reinforcement (mm)

+ β : Capability coefficient of crossed crack concrete

+ θ : Inclination angle of crossed compressive stress (Độ)

+ α : Inclination angle of cross reinforcement on longitudinal center line (degree)

+ Av : Area of shear reinforcement in distance of s (include area of plain reiforcement + prestressing reiforcement) (mm2)

+ Vp : Component of effective prestress towards active shearing force,

is positive (+) if in opposing direction of shearing force

+ αi : Inclination angle of strand compared with horizontal direction

Proposed arrangement of hoop reinforcement ia as follows:

=

y v ' c vmin

fsbf0.83

Super-T 37,5m-LimitStateChk-3/6

III.2 Determination of ββββ and θθθθ

β and θ taken from the table 5.8.3.4.2-1 depend on the ratio v/f'c and improvise in reinforcement of flexure side

Shear stress in concrete v :

p ud b

V V v ϕ

ϕ

−

=

002,0A

EAE

fAcotV5,0N5,0dM

ps p s s

po ps u

u v

u

+

−θ+

+

=ε

ps p s s c c

ps p s s ε

AEAEAE

AEAEF

++

+ fpo : Stress in tendon when stress in concrete around it is zero

fpo = fpe + fpc.Ep/Ec

+ fpe : Effective stress in tendon after deduct the loss

+ fpc : Compressive stress at section's center fpc = F/A

+ Nps = Σfps.Aps.cosαi :Axial force effects on beam due to prestress Nps

Determination of parameter ββββ and θθθθ

p ud b

V V v ϕ

ϕ

−

=

002,0A

EAE

fAcotV5,0N5,0dM

ps p s s

po ps u

u v

u

+

−θ+

+

=ε

ps p s s c c

ps p s s ε

AEAEAE

AEAEF

++

+

=

Super-T 37,5m-LimitStateChk-4/6

IV CHECK SHEAR RESISTANCE AT INTERFACE PLANE

At Strength-I: Calculation shear Vu = 1,704.48 (KN)

The horizontal shear per unit length Vh , shall be taken as:

Vh = Vu/de (KN/m)

de = 1.673 (m) The distance between the centroid of steel in tension side of the beam to the centre

of the compression block in the deck

Acv = 1.35 (m2) Area of concrete in shear transfer plane

Avf = 6,434 (mm2) Area of shear reinforcement crossing the shear plane

fy = 400 (MPa) yield strength of reinforcement

c = 0.52 (MPa) Cohesion factor specified in 5.8.4.2

Super-T 37,5m-LimitStateChk-5/6

Pc = 0.00 (KN) Permanent net compressive force normal to the shear plane; if force is tensile; Pc=0f'c = 35 (MPa) Specified 28 day copressive strength of the weaker concrete

At Strength-I: Calculation shear Vu = 1,474.65 (KN)

The nominal shear resistance of the interface plane Vn , shall be taken as:

Acv = 1.12 (m2) Area of concrete in shear transfer plane

Avf = 1,583 (mm2) Area of shear reinforcement crossing the shear plane

Avf hor = = 1583 (mm2) area of horizontal-bar reinforcement crossing the shear plane

fy = 400 (MPa) yield strength of reinforcement

c = 0.52 (MPa) Cohesion factor specified in 5.8.4.2

Pc = 3,727 (KN) Permanent net compressive force normal to the shear plane; if force is tensile; Pc=0f'c = 35 (MPa) Specified 28 day copressive strength of the weaker concrete

V CHECK PRETENSION ANCHORAGE ZONES (5.10.10)

At Strength-I: Calculation axial force Nu = 4,114 KN

The bursting resistance of pretension anchorage zone Pr , shall be taken as:

Pn = fs*As

Where:

fs = 140 (MPa) Stress in steel not exceeding 140 Mpa

As = 3,267 (mm2) Total area of vertical reinforcement located within the distance h/5 from the ending

Super-T 37,5m-LimitStateChk-6/6

Structure Date

I HALVING JOINT DESIGN

350Arrange the reinforcement according to strut-and-tie model (A.5.6.3)

Height of section of other beam 800 (mm)

Length of section of other beam 850 (mm)

Distance from bearing center to the be 350 (mm) 100

643

136

Checking the internal force produced in halving joint:

Maximum counter force calculated for strength combination 1

Vu = 1,704.48 (KN)

α = 43 (degree) Inclination angle compared to the vertical diretion of the bar C1

Compressive force in bar C1

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge Duong Van Chien

Super-T beam L=37.5m

Strut-and-tie model for halving joint design

C1 T2

T1Section A

I.1 Checking the cross bracing T 1

Nominate resistance of tension bracing bar shall be taken as:

Pn=fyAst+Apsfpe= 2573.5927 KN

Where:

n = 8 (bar) : Number of tension high-strength steel bar

D = 32 (mm) : Diameter of tension high-strength steel bar in the beam

Ast= 6,433.98 (mm2) : Total of tension high-strength reinforcement

fy= 400 (Mpa) : Liquid limit of high-strength steel bar

Aps= 0.00 (mm2) : Total area of tension prestressing steel

III KIỂM TRA THANH NÉN C 1

Sức kháng danh định của thanh chịu nén phải lấy bằng:

Trong đó:

lb sinα+hacosα = 520 (mm) : Kích thước thanh chịu nén

lb= 450 (mm) : Kích thước ngang của gối cao su kt(450x600)mm

Acs= 199,855 (mm2) : Diện tích mặt cắt ngang hữu hiệu của thanh chịu nén

fcu=min(f'c/(0.8+170ε1),0.85f'c)= 42.50 Mpa: Ứng suất chịu nén giới hạn

Nominate resistance of compressive bar shall be taken as:

Where:

la sinα = 284 (mm) : Dimension of compressive bar

Acs= 108,945 (mm2) : Area of effective section of compressive bar

fcu=min(f'c/(0.8+170ε1),0.85f'c)= 42.50 Mpa: ultimate compressive stress+F40

Calculation axial force Nu = 360.86 (KN)

II.1 Design for flexure and horizontal

The area of primary tension reinforcement, As ,shall satisfy the requirements :

As ≥ 0.667Avf required + An(A.5.13.2.4)

Vu

Grillage b ar

Horizontal bar

Punching crack

Nu

Nuc

Section centroid

d1

d2

Super-T 37,5m-HalvingJoint -2/3

As ≥ 0.667Avf required + An(A.5.13.2.4)

Area of tie within a distance equal to 2/3 height of halving section from primary reinforcement

Ah ≥ 0.5 (As - An)

Where

Avf required = [(1.1Vu + cAcv)/µ - Pc ] /fy

Avf required = 10743 (mm2)

Avf grillage = 6434 (mm2) Area of grillage-bar reinforcement crossing the shear plane

Avf hor. = 4909 (mm2) Area of horizontal-bar reinforcement crossing the shear plane

Avftotal = 11343 (mm2) Total area of reinforcement crossing the shear plane

Ah hor. = 7213 (mm2) area of horizontal-bar reinforcement within 2/3 height of section

⇒ A h min = 3583 (mm2) < A h = 7213 (mm 2 ) => OK

II.2 Design for punching shear

The nominal punching shear resistance Vn , shall be taken as:

Super-T 37,5m-HalvingJoint -2/3

Vn = 0.328 f'c (W+L+de)de (5.13.2.5.4)

where

Super-T 37,5m-HalvingJoint -3/3

Structure Date

DEFLECTION AND CAMBER OF BEAM

I INTRODUCTION:

Deflection of beam shall be calculated in 3 main states:

Phase II : Deflection when force transfer applied until concreting the bridge deck

Operation phase : Deflection of service phase

II DEFLECTION WHEN FORCE TRANSFER APPLIED

II.1 Deflection due to sefl weight of main beam (phase I)

Where:

+ DCI : Load due to beam self weight in phase I

+ Li : Factored span length

+ Eci : Elasticity modulus of concrete in phase I, Eci = 32,959 (MPa)

+ II : Moment of inertia of beam in phase I

II.2 Camber of beam due to prestress

Camber due to prestress is calculated according to the following formula:

Bui Van Duan

Checked by

Duong Van Chien

(Shop drawing design stage)

Bridge joint stock

company no.12

Sub_component C12 - Khue Dong bridge

Super-T beam L=37.5m

I ci

i I DCI

I E L DC

384

.

= δ

Super-T 37,5m-Def&Camb-1/4

Where:

+ Mp : Moment created by prestress on beam center

+ Li : Factored span length

+ Eci : Elasticity modulus of concrete in phase I

+ II : Moment of inertia of beam in phase I

Length of design span (m)

Deflection of girder at transfer

I ci

i P P

I ci

i P P

I E

L e P I E

L M

8 8

2 2

=

= δ

Super-T 37,5m-Def&Camb-1/4

16.56 31.12 -74.65 -43.53 Camber

III DEFLECTION WHEN FORCE TRANSFER APPLIED UNTIL CONCRETING THE BRIDGE DECK

III.1 Deflection of main beam due to dead load (phase II)

Trong đó :

+ DCII : Load due to beam self weight + bridge deck phase II

+ Li : Factored span length

+ Eci : Elasticity modulus of concrete in phase II, Eci = 32,959 (MPa)

+ III : Moment of inertia of beam in phase II

III.2 Camber of beam due to prestress

Camber due to prestress is calculated according to the following formula:

Where:

+ Mp : Moment created by prestress on beam center

+ Li : Factored span length

+ Eci : Elasticity modulus of concrete in phase II

+ III : Moment of inertia of beam in phase II

II ci i II DCII

I E L DC

384

.

= δ

II ci

i P P

II ci

i P P

I E

L e P I E

L M

8 8

2 2

=

= δ

Length of design span (m)

Deflection of girder at topping

Super-T 37,5m-Def&Camb-2/4

IV DEFLECTION OF OPERATION PHASE

IV.1 Deflection of main beam due to dead load (service phase)

Where:

+ DCKT : Load due to total of dead load

+ Li : Factored span length

+ Ec : Elasticity modulus of concrete in service phase, Ec = 35,750 (MPa)

+ IKT : Moment of inertia of beam in service phase

IV.2 Camber of beam due to prestress

Camber due to prestress is calculated according to the following formula:

Where:

+ Mp : Moment created by prestress on beam center

+ Li : Factored span length

+ Ec : Elasticity modulus of concrete in service phase,

+ IKT : Moment of inertia of beam in service phase

IV.3 Deflection due to live load

According to 3.6.1.3.2, live load of deflection taken from higher value of :

+ Deflection due to vehicle load

+ Deflection due to 25% vehicle load + lane load

Deflection due to lane load:

KT c i KT DCKT

I E L DC

384

= δ

KT c

i P P

KT c

i P P

I E

L e P I E

L M

8 8

2 2

=

=

δ

i W P

I E

L M

8

2

= δ

Super-T 37,5m-Def&Camb-3/4

Deflection due to vehicle load:

Where:

+ Pi : Axle load number ith

+ ci : Distance from position of axle load apply to the bearing

I E

8

KT c

i LL P

I E

L M

8

2

= δ

Super-T 37,5m-Def&Camb-3/4