Package EX-10 Bridge Name Lach Tray Brid Abutment Calsulation

8/15/2019 Package EX-10 Bridge Name Lach Tray Brid Abutment Calsulation

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Package: EX-10

Bridge name: Lach Tray Bridge

Abutment Name: A1, A2

1. MATERIALS

1.1. Material Unit Weights

• Unit Weight of Concrete 2500= kg/m3 → γc 24.5= kN/m

3

• Unit Weight of Soil 1800= kg/m3 → γs 17.7= kN/m3

• Unit Weight of Saturated Soil 1100= kg/m4 → γsw 11.0= kN/m4

1.2. Concrete

Compressive Strength of concrete at 28 days f'c 35= MPa

Modulus of Elasticity Ec 31799= MPa

Stress Block Factor β1 0.80=

Modulus of Rupture f r =0.63√f'c 3.73= MPa

1.3. Reinforcement Reinf . Standart: 1

Yield strength f y 420= MPa

Modulus of elasticity Es 200000= MPa

Reinforcing bar Area

Diameter 10 13 16 19 22 25 29 32 36

(mm2) 71 129 199 284 387 510 645 819 1006

2. LOADS FROM SUPERSTRUCTURE

2.1. Dead load Number of Girders ng 8= girders

Width of Bridge W 16.50= m

Volume Gravity Reaction

(m3) (kN/m3) (kN) 1 - Main Girder 220.00 24.5 2697.8

2 - Deck Slab 126.39 24.5 1549.9

3 - Diaphargms 15.00 24.5 183.9

4 - Precast plank 11.40 24.5 139.8

5 - Curbs 28.73 24.5 352.2

6 - Railing and other 10.0

7 - Surface wearing 48.10 22.6 542.7

DC 4923.6

DW 552.7

2.2. Live load

Vehicular live loading name HL-93

Number of lanes 4=

Mutiple Presence Factors of Live Load 0.650=

0.004448

0.3048 P1 35 kN V1 4.3 m

P2 145 kN V2 4.3 m

P3 145 kN

P4 110 kN V3 1.2 m

P5 110 kN

Wl 9.3 kN/m

ABUTMENT CALCULATION

Design Truck

Design Tandem

Design Lane Load

Total

Forces Wheel Spacing

Reaction due to dead load of super-T girder Span

Members

Live load

Ha no i - Hai Phong Exp resswa y Projec t

V1 = 4.3m V2 = 4.3m - 9.0m

Design Truck

35kN 145kN 145kN

Design Tandem

1.200m

Abutment-A1A2(OK).xls - SuperLoad Date: 9/26/2011 Page: 1 of 3


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Dynamic Load Allowance

Component IM

Deck Joint - All Limit States 75%

All Other Components

Fatigue and Fracture Limit State 15%All Other Limit States 25%

Total span length Lst 38.300= m

Calculation span leng Ls 37.600= m

Pedestrian load 0.0= kN/m2

Width of 1 sidewalk Wsw 0.000= m

Number of sidewalk nsw 0.000=

Pedestrian load Wp 0.0= kN/m

Pedestrian Live

P1 P2 P3 Total P4 P5 Total Load LoadReaction 70.2 333.9 377.0 781.1 365.0 286.0 651.0 454.6 0 1430.9

Notes: Reaction due to live load HL- 93 = max (Rtruck, Rtandem) + Rlane

Combine live load HL-93 and pedestrian for disadvantage

2.3. Braking force BR 211.3= KN

2.4. Temprature Load

Uniform temperature change ΔT = +/-20.0 oCCoefficient of thermal expansion 1.08E-5= /

oC

Movement Δu 0.0081= m

Shear Modulus of Elastomer G 1000= KPa

Area of bearing Ab 0.158= m2

Height of bearing hrt 0.078= m

Horizontal Force due to ΔT H = G.A.Δu/hrt 131.2= KN

2.5. Creep and Shrinkage Load

Convert to Uniform temperature change ΔT = 20.2= - oCMovement Δu 0.0082= m

Horizontal Force due to ΔT H = G.A.Δu/hrt 132.6= KN

2.4. Wind Load

The design wind velocity, V, shall be determined from: V = S.VB

where: VB: Basic 3 second gust wind velocity with 100 years return period appropriate to the Wind Zone

in which the bridge is located, as specified in table.

VB

(m/s)

I 38 Wind zone: IVII 45 VB 59.0= m/s

III 53

IV 59

S: Correction factor for up wind terrain and deck height S 1.140=

V 67.3= m/s

Wind zone according to

TCVN 2737-1995

Design Truck Design Tandem Lane

Load

Design Truck

Design Lane Load

R

WL

Ls

LIVE LOAD APPLYING ON SUPERSTRUCTURE

P1 P3P2

R

Design Tandem

R

P4 P5

Design Lane load9.3 kN/m

Design Tandem

1.200m

110kN 110kN



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2.5.1. Wind load on structures

Transverse wind load on structure

Overall width of the bridge between outer faces of parapets b 15.700= m

Depth of superstructure, including solid parapets d 3.060= m

Ratio b/d 5.131=

Dag coefficient Cd = f(b/d) 1.4= Area of the structures for calculation of transverse wind load At 58.599= m2

Transverse wind load PD = max(0.0006V2.Cd. At,1.8At) = 222.7= KN

Longitudinal wind load FWSL = 0.25PD = 111.3= KN

2.5.2. Wind load on vehicles (WL)

Transverse wind load on vehicle 28.7= KN

Longitudinal wind load on vehicles 28.7= KN

Vertical wind load

Area Av 315.975= m2

Vertical wind load Pv = 0.00045V2.Av 643.2= KN

2.6. Earthquke effects (EQ)

Acceleration coefficient A 0.1168=

Seismic Performance Zones 2

Soil profile type IV

Site Coefficients S 2=

Response Modification Factor

For Stem wall R 1.5=

For Foundation R 1.0=

Elastic seismic response coefficient Csm 0.292=

Longitudinal Force due to Earthquake EQ 3198.1= KN



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3.2. Internal Forces at Bottom Footing

Loading Data:

Ht 10.000= m

KA 0.297=

kh 0.175=

kv 0.070=

θ 0.19= rad

δs 0.35= rad

KAE 0.442=

ABUTMENT LOADS

Area Length Force X1 Arm 1 Arm 2

Moment

MLong

Moment

MTrans

(m2) (m) (kN) (m) (m) (m) (kN•m) (kN•m)

Selfweight

Section A 6.25 16.500 2529.1 1.250 2.500 - 6322.9 -

Section A1 3.75 16.500 1517.5 3.250 0.500 - 758.7 -

Section B 7.95 16.500 3217.1 3.250 0.500 - 1608.5 -

Section C 8.75 16.500 3540.8 5.750 -2.000 - -7081.6 -

Section D - - - - - - - -

Section E 1.10 16.500 445.1 3.750 - - - -

Section F 15.93 1.600 624.9 5.750 -2.000 - -1249.8 -

Section G - - - - - - - -

Section H 10.33 1.600 405.2 5.750 -2.000 - -810.3 -

Section I 0.14 14.900 49.3 4.133 -0.383 - -18.9 -

Section J 5.00 1.600 196.2 8.367 -4.617 - -905.8 -

Bearing Seat 0.04 4.800 4.7 3.100 0.650 - 3.1 -

Concrete Block 0.61 3.360 50.2 3.100 0.650 - 32.6 -

Shield Wall 1.50 0.400 14.7 3.000 0.750 - 11.0 -

Curb 0.75 6.000 110.4 6.500 -2.750 - -303.5 -

Railing - - 6.0 6.500 -2.750 - -16.5 -Total (DC) 12525.2 -1649.5

Buoyancy effect on Abutment

Section A - - - - - - - -

Section A1 - - - - - - - -

Section B - - - - - - - -

Section C - - - - - - - -

Section D - - - - - - - -

Section F - - - - - - - -

Section G - - - - - - - -

Section H - - - - - - - -

Section J - - - - - - - -

Total (WA) - - -Soil weight

Section F 15.93 14.900 4189.9 5.750 -2.000 - -8379.9 -

Section G - - - - - - - -

Section H 10.33 14.900 2716.6 5.750 -2.000 - -5433.1 -

Section K 1.25 16.500 364.2 1.250 2.500 - 910.5 -

Description

V E R T I C A L L O A D S

Live Load

Surcharge

+M

+H

+V

Sign Convention

EJ

Ht

(K A, KEA)γsHt

Vertical

Reaction

EQ, BR

F

H

B

D

G

A C

Live Load

Surcharge

X

A1

Ht/3

0.5HKP1

δ

PH1

PV1

P2δ

PH2

PV2

I

Abutment-A1A2(OK).xls - Analysis Date: 9/26/2011 Page: 2 of 13


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Horizoltal Wind Load on Structure - - 222.7 - - 7.850 - 1748.0

Horizontal Wind Load on Vehicle - - 28.7 - - 7.800 - 224.1

EQ form Superstructure - - 479.7 - - 7.800 - 3741.8

EQ from Abutment

Section A 6.25 16.500 221.6 - - 1.250 - 276.9

Section A1 3.75 16.500 132.9 - - 1.250 - 166.2

Section B 7.95 16.500 281.8 - - 5.150 - 1451.3

Section C 8.75 16.500 310.2 - - 1.250 - 387.7

Section D - - - - - - - -

Section E 1.10 16.500 39.0 - - 8.900 - 347.0

Section F 15.93 1.600 54.7 - - 4.775 - 261.4

Section G - 1.600 - - - 7.050 - -

Section H 10.33 1.600 35.5 - - 8.525 - 302.6

Section I 0.14 14.900 4.3 - - 9.250 - 40.0

Section J 5.00 1.600 17.2 - - 9.060 - 155.7

Bearing Seat 0.04 4.800 0.4 - - 7.850 - 3.2

Concrete Block 0.61 3.360 4.4 - - 0.870 - 3.8

Shield Wall 1.50 0.400 1.3 - - 8.550 - 11.0

Curb 0.75 6.000 9.7 - - 10.600 - 102.5

Railing - - 0.5 - - 11.400 - 6.0

Total 1113.5 - 3515.4

Notes: 1. Distance 'X' is measured horizontally from Toe of Abutment to C.G. of Section

2. Moment 'Arm' is measured from Pile C.G. Horizontally and from Underside of Footing Vertically

SUMMARY LOADING AT FOOTING CENTER

Vertical

V Hx My Hy Mx

(kN) (kN) (kN•m) (kN) (kN•m)

Seflweight of Abutment DC 12525 - -1650 - -

DC of Superstructure DC 4924 - 3200 - -

DW of Superstructure DW 553 - 359 - -

Soil cover at toe EV 7271 - -12902 - -

Earth Pressure EH 1481 4070 8012 - -

Vertical pressure due to LL surcharge ESV 562 - -1123 - -

Horizontal pressure due to LL surcharge ESL 181 448 1564

Live Load from Superstructure LL 1431 - 930 - -

Braking Force BR - 106 829 - -

Longitudinal Wind Load on Superstructure WSL - 56 437 - -

Longitudinal Wind Load on Vehicle WLL - 14 113 - -

Horizontal Wind Load on Superstructure WST - - - 223 1748

Horizontal Wind Load on Vehicle WLT - - - 29 224

Vertical Wind LoadWS

V 643 - 418 - -Temperature Load TU - 66 515 - -

Earth pressure due to EQ EH-EQ 2205 6057 11924 - -

EQ from Abutment EQ - 3712 11718 1113 3515

EQ from Superstructure EQ - 1599 12553 480 3742

Buoyancy effect on Abutment WA - - - - -

Buoyancy effect on Soil WA - - - - -

Transverce

Symbol

Longitudinal

H O R I Z O N T A L L O A D S

Description



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LOAD FACTOR

Service

STR-IA STR-IB STR-IIIA STR-IIIB SER-I EXT-IA EXT-IB

Seflweight of Abutment DC 1.25 0.90 1.25 0.90 1.00 1.25 0.90

DC of Superstructure DC 1.25 0.90 1.25 0.90 1.00 1.25 0.90

DW of Superstructure DW 1.50 0.65 1.50 0.65 1.00 1.50 0.65

Soil cover at toe EV 1.35 0.90 1.35 0.90 1.00 1.35 0.90

Earth Pressure EH 1.50 0.90 1.50 0.90 1.00 - -

Vertical pressure due to LL surcharge ESV 1.75 1.75 1.35 1.35 1.00 0.50 0.50

Horizontal pressure due to LL surcharge ESL 1.50 0.75 1.50 0.75 1.00 0.50 0.50

Live Load from Superstructure LL 1.75 1.75 1.35 1.00 1.00 0.50 0.50

Braking Force BR 1.75 1.75 1.35 1.00 1.00 0.50 0.50

Longitudinal Wind Load on Superstructure WSL - - 0.40 0.40 0.30 - -

Longitudinal Wind Load on Vehicle WLL - - 1.00 1.00 1.00 - -

Horizontal Wind Load on Superstructure WST - - - - - - -

Horizontal Wind Load on Vehicle WLT - - - - - - -

Vertical Wind Load WSV - - - - - - -

Temperature Load TU 0.50 0.50 0.50 0.50 0.50 - -

Earth pressure due to EQ EH-EQ - - - - - 1.00 1.00

EQ from Abutment EQ - - - - - 1.00 1.00

EQ from Superstructure EQ - - - - - 1.00 1.00

Buoyancy effect on Abutment WA 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Buoyancy effect on Soil WA 1.00 1.00 1.00 1.00 1.00 1.00 1.00

LOAD COMBINATIONS

Longitudinal Transverce

N Hx My Hy Mx

(kN) (kN) (kN.m) (kN) (kN.m)

Description Symbol

Strength IA STR-IA 38436 6995 793 0 0

Strength IB STR-IB 27563 4217 -229 0 0

Strength IIIA STR-IIIA 37639 6990 826 0 0

Strength IIIB STR-IIIB 26265 4174 -812 0 0

Service I SER-I 28927 4688 -279 0 0

Extreme IA EXT-IA 35747 11645 22353 1593 7257

Extreme IB EXT-IB 25898 11645 27311 1593 7257

Internal Force at Head Pile

Com. P1 P2 P3 P4 M1 M2 M3 M4

(kN) (kN) (kN) (kN) (kN.m) (kN.m) (kN.m) (kN.m)

1 STR-IA -23660 - - -14775 -9599 - - -9599

2 STR-IB -16335 - - -11228 -5860 - - -5860

3 STR-IIIA -23264 - - -14375 -9587 - - -9587

4 STR-IIIB -15557 - - -10708 -5861 - - -5861

5 SER-I -17298 - - -11629 -6517 - - -6517

6 EXT-IA -28971 - - -6775 -13794 - - -137947 EXT-IB -24920 - - -978 -13279 - - -13279

Note: the above pile internal forces are taken from a 3D pile analysis software

SymbolDescription ExtremeStrength

No.

Load combinations

M

V

P1, M1

H

Back fill sideFront side

+M

+H

+V

Quy − íc P2, M2 P3, M3 P4, M4



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3.3. Section analysis

Internal Force at Section A-A

Area Length Force X1 Arm Moment

(m2) (m) (kN) (m) (m) (kN•m)

Selfweight of Abutment

Section I 0.14 14.900 49.3 4.133 -0.383 -18.9

Section E 1.10 16.500 445.1 3.750 - -

Curb 0.75 1.000 18.4 3.750 - -

Total (DC) 494.5 -18.9

Earth Pressure (EH) - 16.500 197.0 - 0.880 173.4

Horizontal Pressure due to Surcharge - 16.500 109.2 - 1.100 120.2

Earth Pressure due to EQ - 16.500 293.2 - 0.880 258.0

EQ from Abutment

Section I 0.14 14.900 14.4 - 0.750 10.8

Section E 1.10 16.500 130.0 - 1.100 143.0

Curb 0.75 1.000 5.4 - 2.800 15.0

Total 144.4 153.8



Summary Load Combinatons at Section a-a

Longitudinal

N Hx My(kN) (kN) (kN)

Description Symbol

Service SER 494 306 275

Strength IA STR-IA 618 487 447

Extreme IA EXT-IA 618 492 448

Description

Load Combinations

A

X

B

C

D

(K A, KEA)γsHtLive Load

surcharge

Vertical

Reaction

EQ, BR

Live Load

surcharge

Ht

Ht/3

0.5H P1

δ

PH1

PV1

P2δ

PH2

PV2

P1, M1 P2, M2 P3, M3 P4, M4



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Horizoltal Wind Load on Structure - - 222.7 - - 5.350 - 1191.3

Horizontal Wind Load on Vehicle - - 28.7 - - 5.350 - 153.7

EQ form Superstructure - - 479.7 - - 5.350 - 2566.5

EQ from Abutment

Section B 7.95 16.500 281.8 - - 2.650 - 746.8

Section D - - - - - - - -

Section E 1.10 16.500 39.0 - - 6.400 - 249.6

Section F 15.93 1.600 54.7 - - 2.275 - 124.5

Section G - 1.600 - - - - - -

Section H 10.33 1.600 35.5 - - 6.025 - 213.8

Section I 0.14 14.900 4.3 - - 6.750 - 29.2

Section J 5.00 1.600 17.2 - - 6.560 - 112.7

Bearing Seat 0.04 4.800 0.4 - - 5.350 - 2.2

Concrete Block 0.61 14.900 19.5 - - -1.630 - -31.8

Shield Wall 1.50 0.400 1.3 - - 6.050 - 7.8

Curb 0.75 6.000 9.7 - - 8.100 - 78.3

Railing - - - - 8.900 - -

Total 463.4 - 1533.2



SUMMARY LOADING AT SECTION B-B

Vertical

V Hx My Hy Mx

(kN) (kN) (kN•m) (kN) (kN•m)

Selfweight of Abutment DC 3842 - -254 - -

DC of Superstructure DC 4924 - 739 - -

DW of Superstructure DW 553 - 83 - -

Earth Pressure EH - 2289 6868 - -

Horizontal pressure due to LL surcharge ESH - 372 1397 - -

Live Load from Superstructure LL 1431 - 215 - -

Braking Force BR - 106 565 - -

Longitudinal Wind Load on Superstructure WSL - 56 298 - -

Longitudinal Wind Load on Vehicle WLL - 14 77 - -

Horizontal Wind Load on Superstructure WST - - - 223 1191

Horizontal Wind Load on Vehicle WLT - - - 29 154

Vertical Wind Load WSV 643 - 96 - -

Temperature Load TU - 66 351 - -

Earth pressure due to EQ EH-EQ - 3407 10222 - -

EQ from Abutment EQ - 1496 5208 463 1533

EQ from Superstructure EQ - 1599 8555 480 2567

Buoyancy effect on Abutment WA - - - - -

Longitudinal Transverse

Description Symbol

H O R I Z O N T A L L O A D

S



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LOAD FACTOR

Service

STR-IA STR-IB STR-IIIA STR-IIIB SER-I EXT-IA EXT-IB

Selfweight of Abutment DC 1.25 0.90 1.25 0.90 1.00 1.25 0.90

DC of Superstructure DC 1.25 0.90 1.25 0.90 1.00 1.25 0.90

DW of Superstructure DW 1.50 0.65 1.50 0.65 1.00 1.50 0.65

Earth Pressure EH 1.50 0.90 1.50 0.90 1.00 - -

Horizontal pressure due to LL surcharge LLSl 1.50 0.75 1.50 0.75 1.00 0.50 0.50

Live Load from Superstructure LL 1.75 1.75 1.35 1.35 1.00 0.50 0.50

Braking Force BR 1.75 1.75 1.35 1.35 1.00 0.50 0.50

Longitudinal Wind Load on Superstructure WSL - - 0.40 0.40 0.30 0.50 0.50

Longitudinal Wind Load on Vehicle WLL - - 1.00 1.00 1.00 - -

Horizontal Wind Load on Superstructure WST - - - - - - -

Horizontal Wind Load on Vehicle WLT - - - - - - -

Vertical Wind Load WSV - - - - - - -

Temperature Load UT 0.50 0.50 0.50 0.50 0.50 - -

Earth pressure due to EQ EQW - - - - - 1.00 1.00

EQ from Abutment EQL - - - - - 1.00 1.00

EQ from Superstructure EQ - - - - - 1.00 1.00

Buoyancy effect on Abutment WA 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Summary Load Combinatons at Section B-b

Longitudinal Transverse

N Hx My Hy Mx

(kN) (kN) (kN) (kN) (kN.m)

Description Symbol

Strength IA STR-IA 14291 4210 14667 0 0

Strength IB STR-IB 10753 2557 9259 0 0

Strength IIIA STR-IIIA 13718 4205 14551 0 0

Strength IIIB STR-IIIB 10180 2552 9143 0 0

Service I SER-I 10750 2831 9953 0 0

Extreme IA EXT-IA 12502 6769 25952 943 4100

Extreme IB EXT-IB 8964 6769 25712 943 4100

Internal Force at Section C-C

Load Internal Force at head pile Sefl Shear Moment

Comb. P1 P2 M1 M2 weight (kN/m) (kN•m)

STR-IA -23660 N/A -9599 N/A 3161 -20499 -29307

STR-IB -16335 N/A -5860 N/A 2276 -14059 -19350

STR-IIIA -23264 N/A -9587 N/A 3161 -20103 -28900

STR-IIIB -15557 N/A -5861 N/A 2276 -13280 -18572SER-I -17298 N/A -6517 N/A 2529 -14769 -20653

EXT-IA -28971 N/A -13794 N/A 3161 -25810 -38814

EXT-IB -24920 N/A -13279 N/A 2276 -22644 -35354

Note: • Self weight is included and

• Soil weight above pile cap is ignored

Extreme

Load Combinations

Symbol StrengthDescription



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Internal Force at Section D-D

Area Length Force X1 Arm Moment

(m2) (m) (kN) (m) (m) (kN•m)

Self weight

Section C 8.75 16.500 3540.8 5.750 -1.750 -6196.4

Section F 15.93 1.600 624.9 5.750 -1.750 -1093.6

Section G - - - - - -

Section H 10.33 1.600 405.2 5.750 -1.750 -709.0

Section I 0.14 14.900 49.3 4.133 -0.133 -6.6

Section J 5.00 1.600 196.2 8.367 -4.367 -856.7

Curb 0.75 6.000 110.4 6.500 -2.500 -275.9

Railing - - 6.0 6.500 -2.500 -15.0

Total 4932.7 -9153.2

Soil

Section F 15.93 14.900 4189.9 5.750 -1.750 -7332.4

Section G - - - - - -

Section H 10.33 14.900 2716.6 5.750 -1.750 -4754.0

Total 6906.5 -12086.3

ESv heq = 610 mm - 14.900 561.7 5.750 -1.750 -983.0



3. Buoyancy is ignored

Summary Internal Force at Section d-d

Comb. Shear Moment

P4 P3 P2 M4 M3 M2 N M (kN/m) (kN•m)

STR-IA -14775 N/A N/A -9599 N/A N/A 16473 -29478 1697 -9526

STR-IB -11228 N/A N/A -5860 N/A N/A 11638 -20836 410 -4240

STR-IIIA -14375 N/A N/A -9587 N/A N/A 16473 -29478 2098 -10316

STR-IIIB -10708 N/A N/A -5861 N/A N/A 11638 -20836 931 -5281

SER-I -11629 N/A N/A -6517 N/A N/A 12822 -22960 1193 -6219

Wing Wall Calculation

Wing Wall is modeled and Calculated by ACES5.5 program:

d4 1.5000= m tgφ 5.250=

h1 3.5000= m Earth Pressure due to LL Surcharge 3.202= KN/m

h2 4.0000= m

b2 3.5000= m

b3 3.5000= m

b4 2.0000= m

Internal Force at Head Pile

V E R T I C A L L O A D S

Description

F

E

h1

h2

b4b3

b2

Ht

K AγsHtLL Surcharge

LL Surcharge

0.4Ht

0.5H

d4



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SERVICE – Element Moment X:

SERVICE – Element Moment Y:



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STRENGTH – Element Shear X:

STRENGTH – Element Shear Y:



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Factored Shear Vu 487= KN

Factored Moment Mu 487= KNm

Factored Axial Force Nu 618= KN

Service Moment Ms 275= KNm

h 500= mm

b 16500= mm

d1 70= mm

d2 0= mm

d3 362= mm

d's 68= mm

de = ds 430= mm

Tension Reinforcement Compresion Reinf. Transverse Reinf.

Number (bars) ns 132= n's 66= nv 68=

Diameter (mm) Ds 16= D's 16= Dv 16=

Area (mm2) As 26268= A's 13134= Av 13532=

Spacing (mm) s 125= d 250= sv 500=

Resistance factor for Flexure: ϕ 0.90=

Resistance factor for Shear: ϕv 0.90=

Flexural Resistance

Distance from extreme compression fiber to the neutral axis: c 28= mm

Depth of the equivalent stress block: a 22= mm < 2d's

Factored Flexural Resistance Mr 4158= kN•m > 487 kN•m O.K.

Maximum Reinf. c / d e 0.065 = < 0.42 O.K.

1.2 times the cracking moment 1.2Mcr 2562= kNm

1.33 times the factored moment 1.33Mu 647= kNm

Minimum Reinf. Min (1.2*Mcr or 1.33*Mu) 647= kN•m < 4158 kN•m O.K.

Control of cracking by distribution of reinforcement

Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state

does not exceed f sa, determined as:

n = Es/Ec 6.290= dc 84= mm

A 21000= mm

0.023= Z 30000= N/mm

f sa 248= Mpa

0.194= 0.6f y 252= Mpa

j = (1-k/3) 0.935=

26= Mpa Check: OK

REINFORCEMENT

SECTION DIMENSIONS

SECTION A-A CHECK

0.85•f'c•a•b

As•f y

a A's•f y

b

h ds

d2

d's

d3

d1

nv,Dv

ns, Ds

n's, D's


y3/1c

sa f 6.0) Ad(

Zf ≤=

s

s

bd

nAm =

m2mmk 2 ++−=

ss

ss

jd A

Mf =

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SECTION A-A CHECK


Shear Resistance

Effective Shear Depth dv 419= mm

Effective Shear Width bv 16500= mm

Regions requiring transverse reinforcement: Vu > 0.5 ϕVcVu 487= < 4937= KN No need

The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv)

for which:

Determination of and θ

Angle of inclination of transverse Reinf. to longitudinal axis α 90= 0

Angle of inclination of diagonal compressive stresses θ 24.3= 0 (Supposition)

Shear stress on the concrete vu = Vu/(ϕbvdv) 78= KN/m2

Strain in the reinforcement on the flexural tension side of the member

0.00013= ≤ 0.001 OK

1000*εx 0.128=

Ratio vu/f'c 0.002=

Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) 3.2= [ β = F(v/f'c, 1000*εx)]

Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) 24.3= 0

Vc 10972= kN

Vs 10519= kN

Vn1 21492= kN

Vn2 60459= kN

Norminal Shear Resistance Vn 21492= kN

Factored Shear Resistance Vr 19342= kN > 487 kN O.K.

Minimum transverse reinforcement 9645= mm2

O.K.

Maximum spacing of transverse reinforcement

If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm

If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm

vu 0.08= Mpa < 0.125f'c 4.38= Mpa

sv < smax 335= mm O.K.

vvcc db'f 083.0V β=

s

sin)gcotg(cotdf AV

vyv

s

α+θ=

ss

uuv

u

x AE2

gcotV5.0N5.0d

M

θ++=ε

y

vcminv

f

sb'f 083.0 A =

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h 1500= mm

b 16500= mm

d1 75= mm

d2 0= mm

d3 1355= mm

d's 70= mm

de = ds 1425= mm




Area (mm2) As 67320= A's 18744= Av 13532=

Spacing (mm) s 125= d 250= sv 500=



Flexural Resistance




Maximum Reinf. c / d e 0.051= < 0.42 O.K.







n = Es/Ec 6.290= dc 89= mm

A 22125= mm

0.018= Z 30000= N/mm

f sa 240= Mpa

0.173= 0.6f y 252= Mpa

j = (1-k/3) 0.942=

110= Mpa Check: OK

REINFORCEMENT

SECTION DIMENSIONS

SECTION B-B CHECK

0.85•f'c•a•b

As•f y

a A's•f y

b

h ds

d2

d's

d3

d1

nv,Dv

ns, Ds

n's, D's


y3/1c

sa f 6.0) Ad(

Zf ≤=

s

s

bd

nAm =

m2mmk 2 ++−=

ss

ss

jd A

Mf =

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SECTION B-B CHECK


Shear Resistance





for which:






0.00061= ≤ 0.001 OK

1000*εx 0.611=

Ratio vu/f'c 0.006=



Vc 28244= kN

Vs 25477= kN

Vn1 53721= kN

Vn2 201576= kN




O.K.




vu 0.20= Mpa < 0.125f'c 4.38= Mpa



s

sin)gcotg(cotdf AV

vyv

s

α+θ=

ss

uuv

u

x AE2

gcotV5.0N5.0d

M

θ++=ε

y

vcminv

f

sb'f 083.0 A =

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h 2500= mm

b 16500= mm

d1 120= mm

d2 0= mm

d3 2260= mm

d's 120= mm

de = ds 2380= mm




Area (mm2) As 67320= A's 51084= Av 13532=

Spacing (mm) s 125= d 125= sv 500=



Flexural Resistance











n = Es/Ec 6.290= dc 129= mm

A 32125= mm

0.011= Z 30000= N/mm

f sa 187= Mpa

0.136= 0.6f y 252= Mpa

j = (1-k/3) 0.955=

135= Mpa Check: OK

REINFORCEMENT

SECTION DIMENSIONS

SECTION C-C CHECK

0.85•f'c•a•b

As•f y

a A's•f y

b

h ds

d2

d's

d3

d1

nv,Dv

ns, Ds

n's, D's


y3/1c

sa f 6.0) Ad(

Zf ≤=

s

s

bd

nAm =

m2mmk 2 ++−=

ss

ss

jd A

Mf =

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SECTION C-C CHECK


Shear Resistance





for which:






0.00061= ≤ 0.001 OK

1000*εx 0.611=

Ratio vu/f'c 0.017=



Vc 47565= kN

Vs 42905= kN

Vn1 90470= kN

Vn2 339455= kN




O.K.




vu 0.59= Mpa < 0.125f'c 4.38= Mpa



s

sin)gcotg(cotdf AV

vyv

s

α+θ=

ss

uuv

u

x AE2

gcotV5.0N5.0d

M

θ++=ε

y

vcminv

f

sb'f 083.0 A =

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h 2500= mm

b 16500= mm

d1 166= mm

d2 0= mm

d3 2234= mm

d's 100= mm

de = ds 2334= mm




Area (mm2) As 51084= A's 67320= Av 13532=

Spacing (mm) s 125= d 125= sv 500=



Flexural Resistance




Maximum Reinf. c / d e 0.023= < 0.42 O.K.







n = Es/Ec 6.290= dc 77= mm

A 19250= mm

0.008= Z 30000= N/mm

f sa 263= Mpa

0.121= 0.6f y 252= Mpa

j = (1-k/3) 0.960=

54= Mpa Check: not.OK

REINFORCEMENT

SECTION DIMENSIONS

SECTION D-D CHECK

0.85•f'c•a•b

As•f y

a A's•f y

b

h ds

d2

d's

d3

d1

nv,Dv

ns, Ds

n's, D's


y3/1c

sa f 6.0) Ad(

Zf ≤=

s

s

bd

nAm =

m2mmk 2 ++−=

ss

ss

jd A

Mf =

Abutment-A1A2(OK).xls - D-D Date: 9/26/2011 Page: 1 of 2


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SECTION D-D CHECK


Shear Resistance





for which:






0.00013= ≤ 0.001 OK

1000*εx 0.127=

Ratio vu/f'c 0.001=



Vc 60620= kN

Vs 58124= kN

Vn1 118744= kN

Vn2 333816= kN




O.K.




vu 0.05= Mpa < 0.125f'c 4.38= Mpa



s

sin)gcotg(cotdf AV

vyv

s

α+θ=

ss

uuv

u

x AE2

gcotV5.0N5.0d

M

θ++=ε

y

vcminv

f

sb'f 083.0 A =

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25/30





h 800= mm

b 1000= mm

d1 71= mm

d2 0= mm

d3 659= mm

d's 70= mm

de = ds 729= mm




Area (mm2) As 3096= A's 1136= Av 796=

Spacing (mm) s 125= d 250= sv 500=



Flexural Resistance











n = Es/Ec 6.290= dc 87= mm

A 21750= mm

0.027= Z 30000= N/mm

f sa 243= Mpa

0.206= 0.6f y 252= Mpa

j = (1-k/3) 0.931=

55= Mpa Check: OK

REINFORCEMENT

SECTION DIMENSIONS

SECTION E-E CHECK

0.85•f'c•a•b

As•f y

a A's•f y

b

h ds

d2

d's

d3

d1

nv,Dv

ns, Ds

n's, D's


y3/1c

sa f 6.0) Ad(

Zf ≤=

s

s

bd

nAm =

m2mmk 2 ++−=

ss

ss

jd A

Mf =

Abutment-A1A2(OK).xls - E-E Date: 9/26/2011 Page: 1 of 2


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SECTION E-E CHECK


Shear Resistance





for which:






0.00022= ≤ 0.001 OK

1000*εx 0.223=

Ratio vu/f'c 0.005=



Vc 1044= kN

Vs 965= kN

Vn1 2009= kN

Vn2 6188= kN




O.K.




vu 0.19= Mpa < 0.125f'c 4.38= Mpa



s

sin)gcotg(cotdf AV

vyv

s

α+θ=

ss

uuv

u

x AE2

gcotV5.0N5.0d

M

θ++=ε

y

vcminv

f

sb'f 083.0 A =

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28/30

SECTION F-F CHECK


Shear Resistance





for which:






0.00033= ≤ 0.001 OK

1000*εx 0.333=

Ratio vu/f'c 0.012=



Vc 982= kN

Vs 895= kN

Vn1 1877= kN

Vn2 6196= kN




O.K.




vu 0.41= Mpa < 0.125f'c 4.38= Mpa



s

sin)gcotg(cotdf AV

vyv

s

α+θ=

ss

uuv

u

x AE2

gcotV5.0N5.0d

M

θ++=ε

y

vcminv

f

sb'f 083.0 A =

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CREEP AND SHRINKAGE

General input

Length of girder L 38.3= m

Number of Strands ntr 42= strandsJacking Force P j 195 KN

Elastic Shortening L = 14.1 mm

Average ambient relative humidity H 85= %

Specified compressive strength of concrete of girder at 28 days f'c 50= Mpa

Compressive strength of concrete of girder at time of initial prestress f'ci 42.5= Mpa

Modulus of elasticity Ec 38007 Mpa

Eci 35041 Mpa

Coefficient of thermal expansion for normal concrete ε 1.08E-5=Creep coefficient

The creep coefficient may be estimated as:

Where:

kf = 62/(42+f'c) : Factor for the effect of concrete strength

t : Maturity of concrete (day)

ti : Age of concrete when load is initially applied (day) ti 3= days

kc : Factor for the effect of the volume-to-surface ratio of the component specified

Figure 5.4.2.3.2-1 of AASHTO LRFD 2004 or taken as:

10 150 10950

Area of Section, A (m2) 0.635 0.635 0.993

Perimeter of Section, P (m) 10.248 10.248 12.434

Volume to Surface ratio, A/P (mm) 62 62 80

kc 0.665 0.806 0.818

kf 0.674 0.674 0.674

Creep coefficient, ψ(t,ti) 0.292 0.969 1.424Strain due to shrinkage

The strain due to shrinkage, esh, at time, t, mat be taken as:

Where:

t : Drying time (day)

kh : Humidity Factor

kh = (140-H ) / 70 for H < 80%

kh = 3(100-H )/ 70 for H ≥ 80% kh 0.643=ks : Size factor specified Figure 5.4.2.3.3-2 of AASHTO LRFD 2004 or taken as:

10 150 10950

Area of Section, A (m2) 0.635 0.635 0.993

Perimeter of Section, P (m) 10.248 10.248 12.434

Volume to Surface ratio, A/P (mm) 62 62 80kh 0.643 0.643 0.643

ks 0.684 0.829 0.830

Strain due to shrinkage, εsh -0.00005 -0.00022 -0.00027

Item

Item

Maturity of concrete (day)



( ) ( )

( )6.0

i

6.0

i118.0

if ci

tt0.10

ttt

120

H58.1kk5.3t,t

−+

−⎟ ⎠

⎞⎜⎝

⎛ −=ψ −

3

hssh 1051.0t0.35

tkk −×⎟

⎠

⎞⎜⎝

⎛ +

−=ε

⎥⎦

⎤⎢⎣

⎡ −

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+

+=923

)P/ A(70.31064

t45

tte26

t

k)P/ A(0142.0

s

⎥⎦

⎤⎢⎣

⎡ +

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+

+=−

587.2

e77.180.1

t45

tte26

t

k)P/ A(0213.0)P/ A(0142.0

c

Abutment-A1A2(OK).xls - CR&SH Date: 9/26/2011 Page: 1 of 2


30/30


Movement due to Creep

10 150 10950

Shortening (mm) 4.1 13.7 20.1

Movement due to Shrinkage

10 150 10000

Shortening (mm) 1.9 8.4 10.4

Movement due to Creep and Shrinkage L 8.4= mm

Convert to Uniform Temperature Change T -20= 0C

Item

Item



Package EX-10 Bridge Name Lach Tray Brid Abutment Calsulation

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Transcript of Package EX-10 Bridge Name Lach Tray Brid Abutment Calsulation