BANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANH

BANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANH

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【I.General】

SHEET NO : 1 / 1

1 GENERAL

1.1 Design standard

Specification for Bridge Design: 22TCN-272-05

1.2 Material strength and stress limits

1.2.1 Prestressing Steel:

Type of low relaxation strand complies with : ASTM A416, Grade 270

Diameter of tendon = 15.2 mm

Area of tendon = 140mm2

Tensile Strength fpu = 1860 MPa

Yield Strength fpy = 1674 MPa

Modulus of elasticity of strand Ep = 197000Modulus Ratio np = Ep/Ec = 6.00

Stress in the prestressing steel at jacking = 1395 MPa <=> Jacking Force = 195.30 kN 1.2.2 Reinforcing Steel:

Reinf Standart ASTM or TCVN 1651-2008

Yield strength fs = 400MPa

Modulus of elasticity Es = 200000MPa

1.2.3 Concrete:

1.2.3.1 Main Girder:

Specified compressive strength at 28 days f'c = 50MPa

Compressive strength at time of initial prestress f'ci = 42.50 MPa

Modulus of elastic of concrete at release time Eci = 35041 MPa (5.4.2.4-1)

1.2.3.2 Deck Slab:

Specified compressive strength at 28 days f'c = 35MPa

1.3 Design loads and load combination

1.3.1 Dead Loads:

+ Unit weight of reinforcement Concrete = 7850 Kg/m3

+ Unit weight of asphant concrete = 2300 Kg/m3

1.3.2 Live Loads:

+ Live Loads HL93

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】

SHEET NO : 1 / 4

2 GEOMETRIC PROPERTIES

2.1 Dimension profiles

Distance from bearing to end of girder L1 = 550mm

Distance from bearing to girder notch L2 = 450mm

Length of full section (not inlcude notch) L3 = 1200 mm

Items Notation Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Sec 6 Sec 7

Effective width of concrete slab B 2350.0 2350 2350 2350 2350 2350 2350

b11 b9

SECTION C-C SECTION A-A

b8

b3 b1

11

4

6 7 8

5 b10

BB

b3 b1

1 3

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2.2 Section properties in each stage

2.2.1 Stage I&II: Non-composite section

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-05 Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】

-Static moment of inertia of

component about bottom s1 (mm3

) 83484375 8.3E+07 8.3E+07 8.3E+07 8.3E+07 8.3E+07 3.7E+07

) 4.13E+08 4.1E+08 4.1E+08 4.1E+08 4.1E+08 -

-s5 (mm3) 10587500 1.1E+07 1.1E+07 1.1E+07 1.1E+07 3.3E+08 2.3E+07

-2.2.1.3 Centroid

of component to neutral axis e2 (mm) -877 -877 -877 -874 -869 896 384

) 22309028 2.2E+07 2.2E+07 2.2E+07 2.2E+07 -

-I10 (mm4) 22851563 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2E+07

D = 15.2 mm I12 (mm4) 691748.4 691748 691748 628862 518811 518811 0E+00

Sum (a) 1.21E+11 1.2E+11 1.2E+11 1.2E+11 1.2E+11 3.2E+11 3.1E+10

Distance from neutral axis

to top fiber of girder

to bottom fiber of girder

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SHEET NO : 4 / 4

b Moment of inertia of components about centroid of section

I1 (mm4

) 3.86E+10 3.9E+10 3.9E+10 3.8E+10 3.8E+10 3.2E+10 7E+09

I2 (mm4) 4.32E+08 4.3E+08 4.3E+08 4.3E+08 4.2E+08 -

-I3 (mm4) 5.13E+09 5.1E+09 5.1E+09 5.1E+09 5E+09 4.3E+09 7.5E+08

I4 (mm4) 1.27E+09 1.3E+09 1.3E+09 1.2E+09 9.2E+08 -

-I5 (mm4) 6.02E+09 6E+09 6E+09 6.1E+09 6.2E+09 1.4E+10 4.6E+08

I12 (mm4) 1.23E+10 1.2E+10 1.2E+10 1.1E+10 8.2E+09 8.2E+09

-Sum (b) 1.61E+11 1.6E+11 1.6E+11 1.6E+11 1.6E+11 1.5E+11 2.7E+10Moment of inertia stage I&II II&II (mm4

) 2.82E+11 2.8E+11 2.8E+11 2.8E+11 2.8E+11 4.7E+11 5.7E+10

2.2.2 Stage III: Composite section

-rectangle h (mm) 195 195 195 195 195 -

-A9 (mm2

) 458250 458250 458250 458250 458250 - Total section area ΣA III (mm2) 1220663 1220663 1220663 1217863 1212963 1668275 897875

Moment of inertia stage I&II II&II (mm4

) 2.82E+11 2.8E+11 2.8E+11 2.8E+11 2.8E+11 4.7E+11 5.7E+10

e(mm) -385 -385 -385 -385 -384 - -

(mm4) 1.13E+11 1.1E+11 1.1E+11 1.1E+11 1.1E+11

-Moment of inertia of K9 I9 (mm4) 1.45E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09 - -

Distance from K9 to bottom

fiber of girder

Static moment of K9 about

bottom fiber of girder

to top fiber of girder

to bottom fiber of girder

to top fiber of slab

to center of tendons

of stage I to stage II

Moment of inertia about

centroid of section at stage

II

Distance from center of K9

to neutral axis of composite

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】

SHEET NO : 1 / 4

3 TENDON ARRANGEMENT

3.1 Input date

Using straight tendons with diameter 15.2 mm <=> A_ten 140.0 mm2

To reduce tensile stress at bearing locations, unbonded tendons are created by using PE tube

Effective length of tendons

+3000+3000

3000 +

70005000

++

+

300030003000+

70005000

++++

50005000

2 4 6 8 10 12

3 5 7 9 11

ROW A - HÀNG A ROW C - HÀNG C ROW D - HÀNG D

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SHEET NO : 2 / 4

3.2 Sum of tendons at sections

Section Distance from center of tendons to bottom fiber of girder Distance from center of all tendons ΣA ps (mm 2 )

3.3 Force transfering length & developing length of tendons

Developing length of normal tendon (mm) ld = [0.15fps-0.097fpe]dp = 2535 (5.11.4.2-272-05)Developing length of covered tendon (mm) ld = 2[0.15fps-0.097fpe]dp = 5071 (5.11.4.3-272-05)Group 1: 25 tendons with bond length taken from girder edge 0 mm

Group 2: 2 tendons with bond length taken from girder edge 1000 mm

Prestress of tendons at tension stage - prestress loss due to shrinkage = 1304 MPa

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SHEET NO : 3 / 4

3.4 Internal forces due to prestressed tendons at sections

PRESTRESSING FORCE FOR TENDONS

Group number Distance from section to girder notch (mm)

Prestressing moment at tension stage (kN-m)

677.77 677.77 677.77 680.23 685.59 750.67 0.00-866.83 -866.83 -866.83 -864.37 -859.01 -793.93 0.00693.17 693.17 693.17 695.63 700.99 896.07 0.00661.74 661.74 661.74 664.20 830.99 896.07 0.00665.67 665.67 665.67 825.63 830.99 896.07 0.00

Sum of moment (kN-m) -4867.15 -4867.15 -4867.15 -4399.04 -3151.67 -3362.00 0.00 Prestressing moment after all stress losses (kN-m)

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Lực nén trước và sau các mất mát ứng suất Compression forces before and after all prestress loss

P cang cap - P at tension stage

P sau mat mat us - P after all prestress loss

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【IV.Distribution】

SHEET NO : 1 / 2

4 LIVE LOAD DISTRIBUTION FACTOR

4.1 Superstructure profiles

Multiple presence factor (lane factor) m = 0.85 Section 3.6.1.1.2 - 22TCN-272-05)

Width of loaded lane within cantilever slab de = 800mm

Width between top flanges of girder b = 1050 mm

Design for exterior/interior girder ( E/I ) E

4.2 Effective width of girder flange According to Section 4.6.2.6 in 22TCN-272-05)

1/4 Le = 9275 mm bei/2 + 1/8 Le = 5813 mm

12ts + b/2 = 2865 mm bei/2 + 6ts + b/4 = 2607.5 mm

S = 2350 mm bei/2 + wo = 2325 mm

=> bei = 2350 mm => bee = 2325 mm

4.3 Live load distribution factor According to Section 4.6.2.2.2 - 22TCN-272-05)

Applied section according to Table 4.6.2.2.1.1 is typical section c

Moment distribution for interior girders

Shear distribution for interior girder

For >2 loaded lanes:

Shear distribution for exterior girder

For >2 loaded lanes:

gs,E = (0.8 + de/3050)gs,I = 0.808 Table 4.6.2.2.3b-1-22TCN-272-05)

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【IV.Distribution】

SHEET NO : 2 / 2

Reduction of load distribution factor for moment in longitudinal beams

Moment distribution for exterior girder = 0.555

Shear distribution for exterior girder = 0.979

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【V.Loads】

SHEET NO : 1 / 2

5 LOADS AND LOAD COMBINATIONS

5.1 Superstructure profiles

Width of pedestrian path (1 side) 0.000 m

Wearing surface thickness tw = 0.050 m

Multiple presence factor (lane factor) m = 0.850

Weight of precast concrete plate 0.635 kN/m

Asphalt concrete density γw = 22.563 kN/m3

5.2 Dead load on each girder

Stage 1

Dead load of girder 18.698 kN/m = Cross section area x γc

Stage 2

Dead load of concrete slab 11.191 kN/m = W * ts * γc / Nb

Dead load of precast plate 0.635 kN/m

Stage 3

Dead load of parapet 3.850 kN/m

DL of Technical Box 0.000 kN/m

DL of wearing surface 2.143 kN/m = Wl * tw * γw / Nb

LOADS APPLIED ON GIRDERS

P3

P2

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【V.Loads】

SHEET NO : 2 / 2 Self weight, lane load,

dead load of concrete slab, wearing surface, parapet

Load distribution

5.3 Live loads

Loads induce bending moment

IF = 1+ IM Dist factor (Load x factor) (P x DF x IM)

Loads induce shear

IF = 1+ IM Dist factor

(Load x factor) (P x DF x IM)

Maximum load factor

LC Dead load Live load Lane load Shrink.

STRENGTH-1 1.25 1.25 1.25&1.50 1.75 1.75 0.5

Le

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【VI.Stress Losses】

∆ fpT : Total stress losses (Mpa)

∆ fpES : Loss due to elastic shortening (Mpa)

∆ fpSR : Loss due to shrinkage (Mpa)

∆ fpCR : Loss due to creep of concrete (Mpa)

∆ fpR2 : Loss due to relaxation of steel after transfer (Mpa)

6.1 Loss due to elastic shortening

Loss due to elastic shortening of each prestressing tendons

∆ fpES = E = Epfcgp/Eci Section 5.9.5.2.3a-1 - 22TCN-272-05) Where:

fcgp

and the selfweight of the member at the sections of maximum moment (Mpa)

Ep = 197000 (MPa) Elastic modulus of prestressing tendon

Eci = 35041 (MPa) Elastic modulus of concrete at transfer

Area of Tensile strength Prestress Totaltendon of tendon at transfer Prestress(m2) (MPa) (MPa) (kN) Sec 1 18.55 44 0.006160 1860 1395 8593

P = (kN) Axial force in tendon at midspan

Mg = (kN.m) Bending moment due to selfweight at midspan

Ag = (m2) Cross section area of girder at midspan

Ig = (m4) Moment of inertia of girder at midspan

y = (m) Distance from neutral axis to bottom fiber of girder

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

(m) (m) (kN.m) (m2) (m4) (MPa) (MPa) Sec 1 0.823 0.632 3217 0.7624 0.2822 16.222 91.20

Section Length No strands

= Sum of concrete stresses at the center of prestressing tendons due to prestressing force at transfer

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【VI.Stress Losses】

SHEET NO : 2 / 2

6.2 Loss due to creep of concrete

∆ fpCR=12*fcgp-7* ∆ fcdp > 0 Section 5.9.5.4.3-1 - 22TCN-272-05) Where:

fcgp: Stress in concrete at center of tendon at transfer (Mpa)

∆ fcdp: Change of stress in concrete at center of tendon due to permanent loads at each section

taken as ∆ fcdp.

∆ fcdp = Mp-Iie-II/Ig-II+Mp-IIIe-III/Ig-IIIWhere:

Mp: bending moment which changes prestressing stress at center of tendon

due to permanent loads Section e-II e-III Mp-II Mp-III Ig-II Ig-III ∆ fcdp ∆ fpCR

(m) (m) (kN.m) (kN.m) (m4) (m4) (MPa) (MPa) Sec 1 0.632 1.016 2034.69 1031.19 0.2822 0.5839 6.350 150.21

H = 85% Everage annual ambient relative humidity

6.4 Loss due to relaxation and total prestress loss

∆ fpR2 = 30%[138-0.4 ∆ fpES-0.2( ∆ fpSR+ ∆ fpCR)] (MPa) Section 5.9.5.4.4c-1-22TCN-272-05)

30% is reduction factor for relaxation rate (According to ASTM A 416M)

∆ fpT = ∆ fpES + ∆ fpES + ∆ fpCR + ∆ fpCR2

Section ∆ fpES ∆ fpSR ∆ fpCR ∆ fpR2 ∆ fpT fpe check fpe

(MPa) (MPa) (MPa) (MPa) (MPa) (MPa) Sec 1 91.20 29.45 150.21 19.68 290.53 1104.47 OK

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】

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Area of influence line (+) Ω7 = 8.246

7.2 Influence lines for shear force

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Area of influence line (+) Ω7 = 18.103 (-) Ω7 = -0.003

7.3 Internal forces due to dead loads

Summary table of influence areas

Span length Area of influence line

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7.4 Internal forces due to live loads

Applied live loads on girders

P3

P2

P1

P4

P5

A2=4.3

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Suddent prestres

s loss

Total pre

force at transfer

Total prestress loss

Total pre

force after all loss

Bending moment due to prestress

at transfer

Bending moment due to prestress after all loss

(m2) (MPa) (MPa) (kN) (MPa) (kN) (kN.m) (kN.m)

Internal forces due to wheel axles x DF x IM

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SHEET NO : 6 / 8

7.4.4 Load Combinations:

Load combination for Service State

1 Girder selfweight 3217.04 3082.04 2677.04 1848.24 1196.80 546.85 154.192

Stage 2

3 Selfweight of concrete slab 1925.38 1844.59 1602.19 1106.16 716.28 327.29 92.28

4 Selfweight of precast concrete plate 109.31 104.72 90.96 62.80 40.66 18.58 5.24

Stage 3

5 Wearing surface dead load 368.79 353.31 306.89 211.88 137.20 62.69 17.68

6 D.L of parapet & Technical Box 662.40 634.60 551.21 380.56 246.42 112.60 31.75

8 Pedestrian

Sum of all stages 1+2+3 8995.39 8640.27 7519.59 5210.77 3379.80 1546.21 301.13

2

Stage 2

3 Selfweight of concrete slab 0.00 42.52 85.05 135.41 164.50 189.12 202.55

4 Selfweight of precast concrete plate 0.00 2.41 4.83 7.69 9.34 10.74 11.50

Stage 3

6 D.L of parapet & Technical Box 0.00 14.63 29.26 46.59 56.60 65.07 69.69

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SHEET NO : 7 / 8

Load combination for Strength-I Limit State

1 Girder selfweight 1.25 4021.30 3852.55 3346.30 2310.30 1496.00 683.56 192.742

Sum of all stages 1+2+3 12699.41 12208.47 10638.89 7395.73 4811.05 2236.71 395.50

1 Girder selfweight 1.25 0.00 88.82 177.63 282.81 343.58 395.00 423.052

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SHEET NO : 8 / 8

Load combination for Fatigue Limit State

Sum of all stages 1+2+3 2034.36 1965.75 1718.48 1200.85 781.83 358.65 0.00

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05 Calculation Super T Girder L=38.2m_Skew 20.xls【VIII.Resistance】

SHEET NO : 1 / 5

8.1 Bending moment resistance

Average stress in prestressing tendons fps = fpu*(1 - k*c/dp) (Section 5.7.3.1.1-1-22TCN-272-05)

(Section 5.7.3.1.1-2-22TCN-272-05)Distance from C.L to compression part c = Aps*fpu + As*fy - A's*f'y - 0.85*β1*f'c*(b-bw)*hf

0.85*b1*f'c*bw + k*Aps*fpu/dp

(Section 5.7.3.1.1-3 - 22TCN-272-05 - Assume equivalent section as T-section)

Ultimate tensile strength of prestressing tendon fpu = 1860 MPa

Yield strength of tensile reinforcing bar fy = 400 MPa

Yield strength of compressive reinforcing bar f'y = 400 MPa

Distance from extreme compression fiber to center of all tendons dp = mm

Bending moment resistance Mr = ϕ*Mn (Section 5.7.3.2.1-1 - 22TCN-272-05)Where:

Resistant factor for bending and tension of prestressed concrete ϕ = 1

Mn = Aps*fps*(dp - a/2) + As*fî*(ds - a/2) - A's*f'y*(d's - a/2) (Section 5.7.3.2.2-1 - 22TCN-272-05)

Distance from extreme compression fiber to center of compression reinforcing barsd's = mm

Distance from extreme compression fiber to center of tensile reinforcing barsds = mm

Bending moment at Strength-I kNm 12699 12208 10639 7396 4811 2237 395

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