Analysis of Sheet Pile Retaining Wall and Tie Back Design for the Abusag Bridge Project

           

ABUSAG BRIDGE PROJECT  STRUCTURAL CALCULATION FOR THE  PROPOSED SHEET PILE     October 17, 2019               

RAYMOND R. ESTO  STRUCTURAL ENGINEER  PRC NO. 0108100 

ITEM:

ABUSAG BRIDGE

Design:

LRP

PART:

DESIGN OF RETAINING WALL WITH TIE BACK

Check:

RRE

Date:

10/17/2019

1.0 Reference: 1.1 AASHTO 1.2 Principles of Geotechnical Engineering

2.0 Input Parameters:

2.1 Retaining Wall Geometry Hforce

=

8.20 m

height of wall considered for calculation

=

0.50 m

twb

=

0.50 m

wall thickness @ bottom

N1

=

2 pcs

number of tie rod 1

H

=

7.20 m

height of wall above the ground

Ht1

=

1.5 m

depth of tie rod 1

D

=

2.00 m

embedment depth

t1

=

28 mm

diameter of rod 1

Dreq =

1.05 m

required embedment depth

T = fyro =

2.0 m

tributary length of pile

twt

wt.

=

Mu =

wall thickness @ top

110.40 kN weight of pile 169.73 kN-m

Tie Rod

moment on pile

2.2 Design Parameters and Material Properties

414 MPa =

1.40 m

N2

=

2 pcs

t2

=

28 mm

Ht3

=

1.40 m

N3

=

2 pcs

t3

=

28 mm

diameter of rod 3

Ht4

=

1.5 m

depth of tie rod 4 number of tie rod 4

=

35.00 MPa

compressive strength of concrete @N4

=

2 pcs

fy

=

414.00 MPa

yield strength of main bars

t4

=

28 mm

λc

=

Фf

24.0 kN/m3 unit weight of concrete

=

0.9

strength reduction factor for flexure

Фv =

0.85

strength reduction factor for shear

q all =

349 kPa

allowable soil bearing pressure

0 deg

backfill slope angle

=

30 deg

angle of internal friction

=

20 deg

angle of friction bet soil and wall

β

=

0 deg

slope of soil face

θ

=

90 deg

wall face batter angle

γ

=

17 kN/m3 unit weight of backfill soil

i

=

Ф δ

Ka

=

0.297

active earth coefficient

Kp

=

6.105

passive earth coefficient

Ko

=

0.500

at rest earth coefficient

I

=

1

μ

=

0.6

importance factor friction factor at the base

nominal tensile strength of tie rod

Ht2

f'c

OK!

number of tie rod 2 diameter of rod 2

Wall h

150 mm

wall thickness

bar

16 mm

diameter of main bars

12 mm

diameter of temperature bars

12 mm

diameter of shear bars

= = temp= v =

OK! Rebar Weld

number of tie rod 3

diameter of rod 4

t OK!

L

= =

8 mm 125 mm

weld thickness required weld length

t1 t2

OK!

= =

3.0 Loadings: 3.1 Case 2: With EQ

8.20 m

Lateral Earth Pressure

1.5 m

1.0 m

Tie Rod 1 1.7 m Tie Rod 2 1.7 m Tie Rod 3 1.7 m Tie Rod 4 1.5 m

2.1 m

Surcharge (Live Load)

Surcharge (Earth)

Wall Inertia

Earthquake

2.1 m 2.1 m

1.0 m 29 kPa

ground surface

4.3 kPa

5.2 kPa

7.8 kPa

#DIV/0!

7.7

3.1.1 Surcharge

91.8 kPa

3.1.1.1 EARTH SURCHARGE LOAD (ES) S

=

8.5

PES(H)

=

4.3 kPa

kPa , Ko S

yes(H) =

4.10

m

yes(H)

=

yes(H) =

4.10

m

yes(H)

=

yes(H)

=

ywall

=

ywall

=

3.1.1.2 LIVE LOAD SURCHARGE (LS) 8.20 m

hwall

=

heq

=

0.61 m

S

=

10.4 kPa

PES(H)

=

5.2 kPa

, Ko S

3.1.2 Earth Pressure 3.1.2.1 EH1 (active)

3.1.4

p

=

29.3 kPa

, Ka γ * (hsoil)

Tload

=

220.9 kN/m

, 0.65Ka γ *H2

EHH

=

29.3 kPa

Wall Intertia + ES Pwall

3.1.5

, EH

=

7.8 kPa

, kh * Wwall

ywall

4.10

=

m

Earthquake a

=

0.40

acceleration coefficient

kh

=

0.38

horizontal seismic coefficient

kv

=

0

θ

=

20.81

vertical seismic coefficient

KAE =

0.70

PAE =

97.7 kPa

, (1-kv)yKae (hsoil)

PAE(H) =

91.8 kPa

, PAE cos δ

PAE(V) =

33.4 kPa

, PAE sin δ

dynamic soil pressure coefficient yAE(H) =

2.73

m

3.2 Load Factors Load Combination

γDC

γEV

γEH

γLSV

γLSH

γEQ

γP

γES

STR Ia

0.9

1.0

2.27

0.0

1.75

0.0

0.45

1.50

STR Ib

1.25

1.35

2.27

1.75

1.75

0.0

0.45

1.50

STR IV

1.5

1.35

2.27

0.0

0.0

0.0

0.45

1.50

EXT Ia

0.9

1.0

0.0

0.5

0.5

1.0

0.45

0.00

EXT Ib

1.25

1.0

0.0

0.5

0.5

1.0

0.45

0.50

SER I

1.0

1.0

1.0

1.0

1.0

0.0

0.45

1.00

ko/ka

3.3 Pressure Loads (Factored) Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

STR Ia

6.4 kPa

9.1 kPa

66.6 kPa

0.0 kPa

0.0 kPa 0.0 kPa

STR Ib

6.4 kPa

9.1 kPa

66.6 kPa

0.0 kPa

STR IV

6.4 kPa

0.0 kPa

66.6 kPa

0.0 kPa

0.0 kPa

EXT Ia

0.0 kPa

2.6 kPa

0.0 kPa

7.8 kPa

91.8 kPa

EXT Ib

2.1 kPa

2.6 kPa

0.0 kPa

7.8 kPa

91.8 kPa

SER I

4.3 kPa

5.2 kPa

29.3 kPa

0.0 kPa

0.0 kPa

8.20 m

Lateral Earth Pressure

1.5 m

1.0 m

Tie Rod 1 1.7 m Tie Rod 2 1.7 m Tie Rod 3 1.7 m Tie Rod 4 1.5 m

2.1 m

Surcharge (Earth)

Surcharge (Live Load)

Wall Inertia

2.03333

2.06667

2.1 m

2.06667

2.1 m

1.53333 1.0 m 29 kPa

ground surface

0.5 4.3 kPa

5.2 kPa

7.8 kPa

3.4.1 Tie Rod1 Force Calculation Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

STR Ia

13.0 kN/m

18.4 kN/m

102.1 kN/m

0.0 kN/m

0.0 kN/m

133.5 kN/m

STR Ib

13.0 kN/m

18.4 kN/m

102.1 kN/m

0.0 kN/m

0.0 kN/m

133.5 kN/m

STR IV

13.0 kN/m

0.0 kN/m

102.1 kN/m

0.0 kN/m

0.0 kN/m

115.0 kN/m

EXT Ia

0.0 kN/m

5.3 kN/m

0.0 kN/m

15.8 kN/m

140.7 kN/m

161.8 kN/m

EXT Ib

4.3 kN/m

5.3 kN/m

0.0 kN/m

15.8 kN/m

140.7 kN/m

166.1 kN/m

SER I

8.6 kN/m

10.5 kN/m

45.0 kN/m

0.0 kN/m

0.0 kN/m

64.1 kN/m

Trod1 = req =

Tie Rod Force

332.29 kN 23.83 mm

3.4.2 Tie Rod2 Force Calculation Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Tie Rod Force

STR Ia

13.2 kN/m

18.7 kN/m

137.6 kN/m

0.0 kN/m

0.0 kN/m

169.5 kN/m

STR Ib

13.2 kN/m

18.7 kN/m

137.6 kN/m

0.0 kN/m

0.0 kN/m

169.5 kN/m

STR IV

13.2 kN/m

0.0 kN/m

137.6 kN/m

0.0 kN/m

0.0 kN/m

150.8 kN/m

EXT Ia

0.0 kN/m

5.4 kN/m

0.0 kN/m

16.1 kN/m

189.7 kN/m

211.1 kN/m

EXT Ib

4.4 kN/m

5.4 kN/m

0.0 kN/m

16.1 kN/m

189.7 kN/m

215.5 kN/m

SER I

8.8 kN/m

10.7 kN/m

60.6 kN/m

0.0 kN/m

0.0 kN/m

80.1 kN/m

Trod = req =

431.01 kN 27.14 mm

3.4.3 Tie Rod3 Force Calculation Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Tie Rod Force

STR Ia

13.2 kN/m

18.7 kN/m

137.6 kN/m

0.0 kN/m

0.0 kN/m

169.5 kN/m

STR Ib

13.2 kN/m

18.7 kN/m

137.6 kN/m

0.0 kN/m

0.0 kN/m

169.5 kN/m

STR IV

13.2 kN/m

0.0 kN/m

137.6 kN/m

0.0 kN/m

0.0 kN/m

150.8 kN/m

EXT Ia

0.0 kN/m

5.4 kN/m

0.0 kN/m

16.1 kN/m

189.7 kN/m

211.1 kN/m

EXT Ib

4.4 kN/m

5.4 kN/m

0.0 kN/m

16.1 kN/m

189.7 kN/m

215.5 kN/m

SER I

8.8 kN/m

10.7 kN/m

60.6 kN/m

0.0 kN/m

0.0 kN/m

80.1 kN/m

Trod = req =

Earthquake

431.01 kN 27.14 mm

91.8 kPa

3.4.4 Tie Rod4 Force Calculation Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Tie Rod Force

STR Ia

9.8 kN/m

13.9 kN/m

85.4 kN/m

0.0 kN/m

0.0 kN/m

109.1 kN/m

STR Ib

9.8 kN/m

0.0 kN/m

85.4 kN/m

0.0 kN/m

0.0 kN/m

95.2 kN/m

STR IV

0.0 kN/m

4.0 kN/m

0.0 kN/m

11.9 kN/m

117.8 kN/m

133.7 kN/m

EXT Ia

3.3 kN/m

4.0 kN/m

0.0 kN/m

11.9 kN/m

117.8 kN/m

136.9 kN/m

EXT Ib

6.5 kN/m

7.9 kN/m

37.6 kN/m

0.0 kN/m

0.0 kN/m

52.1 kN/m

SER I

0.0 kN/m

0.0 kN/m

0.0 kN/m

0.0 kN/m

0.0 kN/m

0.0 kN/m

Trod = req =

273.89 kN 21.63 mm

3.5 Emberment Depth Calculation Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Reaction

STR Ia

3.2 kN/m

4.5 kN/m

8.3 kN/m

0.0 kN/m

0.0 kN/m

16.0 kN/m

STR Ib

3.2 kN/m

4.5 kN/m

8.3 kN/m

0.0 kN/m

0.0 kN/m

16.0 kN/m

STR IV

3.2 kN/m

0.0 kN/m

8.3 kN/m

0.0 kN/m

0.0 kN/m

11.5 kN/m

EXT Ia

0.0 kN/m

1.3 kN/m

0.0 kN/m

3.9 kN/m

11.5 kN/m

16.7 kN/m

EXT Ib

1.1 kN/m

1.3 kN/m

0.0 kN/m

3.9 kN/m

11.5 kN/m

17.7 kN/m

SER I

2.1 kN/m

2.6 kN/m

3.7 kN/m

0.0 kN/m

0.0 kN/m

8.4 kN/m

R = Qpass =

18 kN/m 47 kPa

Dreq =

0.87 m

3.6 Sheet Pile Moment Calculation Lateral Earth Pressure

1.5 m

1.0 m

Tie Rod 1 1.7 m Tie Rod 2 1.7 m Tie Rod 3 1.7 m Tie Rod 4 1.5 m

2.1 m

Surcharge (Earth)

Surcharge (Live Load)

Wall Inertia

Earthquake

1.0 m

8.20 m

0.5

2.1 m 2.1 m

1.0 m 29 kPa

ground surface

4.3 kPa

5.2 kPa

7.8 kPa

3.6.1 Moment above Tie Rod Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Moment

STR Ia

7 kN-m/m

10 kN-m/m

36 kN-m/m

0 kN-m/m

0 kN-m/m

53 kN-m/m

STR Ib

7 kN-m/m

10 kN-m/m

36 kN-m/m

0 kN-m/m

0 kN-m/m

53 kN-m/m

STR IV

7 kN-m/m

0 kN-m/m

36 kN-m/m

0 kN-m/m

0 kN-m/m

43 kN-m/m

EXT Ia

0 kN-m/m

3 kN-m/m

0 kN-m/m

9 kN-m/m

50 kN-m/m

61 kN-m/m

EXT Ib

2 kN-m/m

3 kN-m/m

0 kN-m/m

9 kN-m/m

50 kN-m/m

64 kN-m/m

SER I

5 kN-m/m

6 kN-m/m

16 kN-m/m

0 kN-m/m

0 kN-m/m

26 kN-m/m

3.6.2 Moment on zero shear Find x: (Zero Shear) Assume x <

1.73 m

Load Combination

Tie Rod Force

Pressure

x

STR Ia

43.7 kN/m

82 kPa

0.53 m

STR Ib

43.7 kN/m

82 kPa

0.53 m

STR IV

38.9 kN/m

73 kPa

0.53 m

EXT Ia

54.5 kN/m

102 kPa

0.53 m

EXT Ib

55.6 kN/m

104 kPa

0.53 m

SER I

20.7 kN/m

39 kPa

0.53 m

x

=

0.53 m

91.8 kPa

Assume x >

1.73 m

3.47 m

<

Load Combination

T1+T2

Pressure

x

STR Ia

213 kN/m

82 kN/m

2.60 m

STR Ib

213 kN/m

82 kN/m

2.60 m

STR IV

190 kN/m

73 kN/m

2.60 m

EXT Ia

266 kN/m

102 kN/m

2.60 m

EXT Ib

271 kN/m

104 kN/m

2.60 m

SER I

101 kN/m

39 kN/m

2.60 m

Assume x >

3.47 m

<

T1+T2+T3

Pressure

x

STR Ia

383 kN/m

82 kN/m

4.67 m

STR Ib

383 kN/m

82 kN/m

4.67 m

STR IV

340 kN/m

73 kN/m

4.67 m

EXT Ia

477 kN/m

102 kN/m

4.67 m

EXT Ib

487 kN/m

104 kN/m

4.67 m

SER I

181 kN/m

39 kN/m

4.67 m

5.20 m

<

2.60 m

x

=

4.67 m

6.96 m

6.70 m

Load Combination T2+T3++T4(1/2hn STR Ia

=

5.20 m

Load Combination

Assume x >

x

525 kN/m

Pressure

x

82 kN/m

6.40 m

STR Ib

511 kN/m

82 kN/m

6.23 m

x

=

STR IV

507 kN/m

73 kN/m

6.96 m

x

=

EXT Ia

660 kN/m

102 kN/m

6.46 m

EXT Ib

585 kN/m

104 kN/m

5.61 m

SER I

196 kN/m

39 kN/m

5.04 m

6.7

CASE 1: MOMENT BETWEEN TIE ROD 1 &2

8.20 m

Lateral Earth Pressure

1.5 m

1.0 m

Tie Rod 1 1.7 m Tie Rod 2 1.7 m Tie Rod 3 1.7 m Tie Rod 4 1.5 m

2.1 m

Surcharge (Earth)

Surcharge (Live Load)

Wall Inertia

Earthquake

1.0 m 1.033

2.1 m 2.1 m

1.0 m 29 kPa

ground surface

4.3 kPa

5.2 kPa

7.8 kPa

91.8 kPa

Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Tie Rod1

Moment

STR Ia

13 kN-m/m

19 kN-m/m

81 kN-m/m

0 kN-m/m

0 kN-m/m

-71 kN-m/m

42 kN-m/m 42 kN-m/m

STR Ib

13 kN-m/m

19 kN-m/m

81 kN-m/m

0 kN-m/m

0 kN-m/m

-71 kN-m/m

STR IV

13 kN-m/m

0 kN-m/m

81 kN-m/m

0 kN-m/m

0 kN-m/m

-61 kN-m/m

33 kN-m/m

EXT Ia

0 kN-m/m

5 kN-m/m

0 kN-m/m

16 kN-m/m

112 kN-m/m

-86 kN-m/m

47 kN-m/m

EXT Ib

4 kN-m/m

5 kN-m/m

0 kN-m/m

16 kN-m/m

112 kN-m/m

-89 kN-m/m

49 kN-m/m

SER I

9 kN-m/m

11 kN-m/m

36 kN-m/m

0 kN-m/m

0 kN-m/m

-34 kN-m/m

21 kN-m/m

CASE 2: MOMENT BETWEEN TIE ROD 2 &3

8.20 m

Lateral Earth Pressure

1.5 m

1.0 m

Tie Rod 1 1.7 m Tie Rod 2 1.7 m Tie Rod 3 1.7 m Tie Rod 4 1.5 m

2.1 m

ground surface

Surcharge (Earth)

Surcharge (Live Load)

Wall Inertia

Earthquake

1.0 m

3.100

2.1 m 2.1 m

1.0 m 29 kPa

4.3 kPa

5.2 kPa

7.8 kPa

91.8 kPa

Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Tie Rod1

Tie Rod2

Moment

STR Ia

54 kN-m/m

76 kN-m/m

434 kN-m/m

0 kN-m/m

0 kN-m/m

-347 kN-m/m

-147 kN-m/m

70 kN-m/m

STR Ib

54 kN-m/m

76 kN-m/m

434 kN-m/m

0 kN-m/m

0 kN-m/m

-347 kN-m/m

-147 kN-m/m

70 kN-m/m

STR IV

54 kN-m/m

0 kN-m/m

434 kN-m/m

0 kN-m/m

0 kN-m/m

-299 kN-m/m

-131 kN-m/m

58 kN-m/m 82 kN-m/m

EXT Ia

0 kN-m/m

22 kN-m/m

0 kN-m/m

65 kN-m/m

598 kN-m/m

-421 kN-m/m

-183 kN-m/m

EXT Ib

18 kN-m/m

22 kN-m/m

0 kN-m/m

65 kN-m/m

598 kN-m/m

-432 kN-m/m

-187 kN-m/m

85 kN-m/m

SER I

36 kN-m/m

44 kN-m/m

191 kN-m/m

0 kN-m/m

0 kN-m/m

-167 kN-m/m

-69 kN-m/m

34 kN-m/m

CASE 3: MOMENT BETWEEN TIE ROD 3 & 4

8.20 m

Lateral Earth Pressure

1.5 m

1.0 m

Tie Rod 1 1.7 m Tie Rod 2 1.7 m Tie Rod 3 1.7 m Tie Rod 4 1.5 m

2.1 m

Surcharge (Earth)

Surcharge (Live Load)

Wall Inertia

Earthquake

1.0 m

5.167

2.1 m 2.1 m

1.0 m 29 kPa

ground surface

4.3 kPa

5.2 kPa

7.8 kPa

91.8 kPa

Load Combination

ES

LS

ACTIVE

WALL INER.

EQ

Tie Rod1

Tie Rod2

Tie Rod3

Moment

STR Ia

121 kN-m/m

172 kN-m/m

1072 kN-m/m

0 kN-m/m

0 kN-m/m

-623 kN-m/m

-497 kN-m/m

-203 kN-m/m

42 kN-m/m

STR Ib

121 kN-m/m

172 kN-m/m

1072 kN-m/m

0 kN-m/m

0 kN-m/m

-623 kN-m/m

-497 kN-m/m

-203 kN-m/m

42 kN-m/m

STR IV

121 kN-m/m

0 kN-m/m

1072 kN-m/m

0 kN-m/m

0 kN-m/m

-537 kN-m/m

-442 kN-m/m

-181 kN-m/m

33 kN-m/m 47 kN-m/m

EXT Ia

0 kN-m/m

49 kN-m/m

0 kN-m/m

148 kN-m/m

1477 kN-m/m

-755 kN-m/m

-619 kN-m/m

-253 kN-m/m

EXT Ib

40 kN-m/m

49 kN-m/m

0 kN-m/m

148 kN-m/m

1477 kN-m/m

-775 kN-m/m

-632 kN-m/m

-259 kN-m/m

49 kN-m/m

SER I

81 kN-m/m

99 kN-m/m

472 kN-m/m

0 kN-m/m

0 kN-m/m

-299 kN-m/m

-235 kN-m/m

-96 kN-m/m

21 kN-m/m

Mgovern

=

170 kN-m/m

3.7 Wall Design w

=

104 kN/m



Mu

=

33 kN-m

t

b

=

1600 mm

h

d

=

75.0 mm

v

fc'

=

35.00 MPa

fy

=

414.00 MPa

bar

=

16 mm

∅ 0.85

′

0.85

As N S

1

1 ′

= = =

2 0.85

′

3 8 1291 mm2 6.4192 pcs 150 mm

o.c.

Temp Bars  At N S

= = = =

0.0018 432 mm2 3.8197 pcs 250 mm

o.c.

Shear

= = Vc/2 = Vs = Vbar = N = S = R

83 kN

Vc

91 kN 45 kN 83 kN 25 kN 4 pcs 400 mm

o.c.

Deflection

= = I =  = allow = w

104 kN/m

E

27806 MPa 315000000 mm3 1.016 mm 3.333 mm

= = = =

0.8 12 mm 150.0 mm 12 mm

=

4.12

=

0.01076

=

0.02156

SINGLY

ITEM: PART:

ABUSAG BRIDGE SHEET PILE DESIGN - PRESTRESSED (Hp= 2.1m)

Design:

LRP

Date:

10/17/2019

Check:

RRE

Date:

10/17/2019

1.0 SHEET PILE DESIGN: 1.1 Reference: 1.1.1 Steel Sheet Piling Manual 1.1.2 National Structural Code of the Philippines Volume 2, 2ND Edition, NSCP 1997 1.2 Geometry

Depth of embedment (Trial) Depth of excavation Sheet pile length (trial) Depth of embedment (Design) Sheet pile length (Design)

DP = HP = SPL =

4.00 m 2.10 m

D = SPL =

4.56 m 6.66 m

Depth water level Weight of surcharge

6.10 m

Dw = W sur = HP - Dw =

0.50 m 11.76 kPa 1.6 m

*Addt'l 15% to have 1.5 to 2 factor of safety

1.2.1 Soil properties Soil unit weight Submerged unit weight Angle of friction Active Earth Pressure

γs = γ's =

17.00 kN/m3 12.00 kN/m3 30 deg

φ = KA =

0.33

KP =

3.00

Backfill slope angle

i =

Angle of friction bet. soil and wall

δ =

Wall face batter angle

α =

0 deg 15 deg 57.00 deg

Slope of soil face

β =

33 deg

Coeff. Passive Earth Pressure Coeff.

1.2.2 Other properties γw =

Water unit weight Kh =

At rest Earth Pressure

0.50

z

=

9.81 kN/m3 0.86

Coeff. Acceleration coeff at I=1

0.40

Hor acceleration coeff.

0.20

a = kh = min kh =

0.54

kv =

0.07

Ѳ =

12.14

Seismic earth pressure co KAE =

0.92

Vert acceleration coeff

Note: Importance ( I ) factor use is 1 since culvert is not part of plant operation.

m

ITEM:

ABUSAG BRIDGE

PART: SHEET PILE DESIGN - PRESTRESSED (Hp= 2.1m) 1.3 Wall Pressures Table 1.3.1 Static Pressures at Given Points POINT Surcharge, S (kPa Soil, P (kPa)

Design:

LRP

Date:

10/17/2019

Check:

RRE

Date:

10/17/2019

Water, W (kPa)

S+P

B A0

3.92

0.00

0.00

3.92

3.92

3.92

9.07

0.00

12.99

12.99

A1

3.92

11.07

4.91

14.99

19.89

A2

3.92

27.07

44.15

33.23

75.13

E

3.92

-116.93

4.91

-130.93

-108.11

J

3.92

240.77

4.91

249.44

249.60

S+P+W

Table 1.3.2 Pressures with Seismic Influence at Given Points POINT

Surcharge, S

Soil, P (kPa)

B A0

3.92

0.00

Water, W (kPa) smic Load, EQ (k Net Pressure 0.00

6.27

10.19

3.92

9.07

0.00

1.49

14.48

A1

3.92

11.07

4.91

0.00

19.89

A2

3.92

29.31

49.64

0.00

82.87

E

3.92

-134.85

4.91

0.00

-126.03

J

3.92

245.52

4.91

0.00

254.35

Static Force, PA = Seismic active earth force, PAE = Seismic active earth force, ∆P =

12.29 kN 32.04 kN (Mononobe Okabe Analysis) 19.76 kN

1.4 Stability Static 1.4.1 ∑F=0 13.53 ZP =

+ 8.22 0.86 m

+

190.05

+

178.85Zp

-

366.48

=

56.37

+

159.13

+

44.60

-

488.64

+

+ 8.59 1.12 m

+

234.29

+

190.19Zp

-

476.28

=

+

206.81

+

80.01

-

723.94

+

=

0.80 m 5.01 kN/m

0

1.4.2 ∑MF=0 78.88

+

147.31

=

-2.36

218.24

=

-43.73

Dynamic 1.4.3 ∑F=0 19.74 ZP =

0

1.4.4 ∑MF=0 114.75

+

60.40

Pile width

1.5 STAAD loading

Wall load (PC wall, beam, column, steel fence)+10% allowance 4.55 kN/m Slope Protection = PC column = 0.00 kN/m PC beam = Steel fence = Surcharge

=

3.14

Earth pressure

=

9.52

kN/m

Ground water

=

3.92

kN/m

Earthquake

=

15.05 kN/m

=

0.00 kN/m 0.00 kN/m

kN/m (Note forces are per pile wiidth)

ITEM:

ABUSAG BRIDGE

PART: SHEET PILE DESIGN - PRESTRESSED (Hp= 2.1m) 1.6 Soil springs

Design:

LRP

Date:

10/17/2019

Check:

RRE

Date:

10/17/2019

Using parameters for Zone 1 liquefied state Depth

Reduced soil springs

Reduced soil springs

m

(kPa/m)

kN/m

Pile width

0.80 m

=

0 1

280,000 *B-3/4

331010

2

280,000 *B-3/4

331010

3

280,000 *B-3/4

331010

1.7 Forces (From STAAD Analysis) 1.7.1 Stresses using parameters for liquefied state Service loads Maximum

Case Sustained loads

Compression 50.428

Tension 0

Moment 30.445

Shear 38.328

50.428

0

55.599

56.21

Compression 65.557

Tension 0

Moment 39.578

Shear 49.827

65.557

0

64.733

67.709

Maximum Total loads Ultimate loads

Maximum

Case Sustained loads Maximum Total loads

Load combination: From NSCP volume 2 Service loads

Ultimate loads

Sustained loads = D+Sur+EP+GW

Sustained loads = 1.3D + 1.495(Sur+EP+GW)

Total loads = D+Sur+EP+GW+EQ

Total loads = 1.3D + 1.495(Sur+EP+GW)+1.3EQ

1.8 Required reinforcement for Reinforced concrete sheet pile 1.8.1 Material properties Concrete compressive strength

f'c =

Concrete cover, cc

cc = φf = φv =

Reduction factor for moment Reduction factor for shear fy (MPa)

40.00 MPa 45 mm

β1

=

Ec

=

0.75 ρuser

ρmax

ρmin

414

0.0279

0.0038

12.18

0.0093

Transverse bars 10

275

0.0486

0.0057

7.19

0.0162

Main bars

29725.41 MPa

0.90

25

Deformed bars

0.76

m

Es =

1.8.2 Concrete sheet pile design

Sheet pile area Effective depth

d =

t = w = Asp = 0.40 m

Transverse bars: Concrete shear capacity

Vc =

339.76 kN

Thickness Width

Ties spacing No. of legs Shear reinf. Area Reinf. Shear capacity Shear capacity

S = N = Av = Vs = Vcap =

0.450 m 0.800 m 0.360 m2

Vdesign =

67.71 kNm

75.00 mm 6.00 471.24 mm2 682.51 kN 766.70 kN

>

Vdesign

Okay

200000 MPa

ITEM: PART:

ABUSAG BRIDGE SHEET PILE DESIGN - PRESTRESSED (Hp= 2.1m)

Design:

LRP

Date:

10/17/2019

Check:

RRE

Date:

10/17/2019

1.8.3 Minimum confinement Minimum spacing at ductile region, s

=

hc

=

Ag

=

Ach

=

P Ash1

=

Ash2

=

90.00 mm 700.00 mm 360000.00 mm2 255600.00 mm2

=

1.8.3 For prestressed design. See separate calculation. Using Interaction diagragm

65.56 kN 2 467.87 mm 2 458.19 mm

>

Vs

Okay

>

Vs

Okay

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

LOSSES IN PRESTRESSED SHEET PILE REFERENCES 1. National Structural Code of the Philippines 2010 6th Edition 2. PCI Design Handbook 6th Edition 3. Design of Prestressed Concrete Structures 3rd Edition Si Version by T.Y. Lin and Ned H. Burns RECTANGULAR SHEET PILE GEOMETRY AND SECTIONS pile length, L = m 5.00

800 800 800 800 800

400 400 400 400 400

7 7 7 7 7

56 56 56 56 56

Basic Section Properties cross-sectional area, Ac,bas = distance from bottom surface to NA, ybas = moment of inertial, Ibas =

7 7 7 7 7

344 344 344 344 344

b, mm dp1, 

d2

dp2, 

A B C D E

d1 Prestressing Strand Fp2 Fp1 np1 dp1 np2 dp2

h, 

Table 1A: Section Profile Section Section h b

BASIC SECTION 2 320,000.00 mm mm 200.00 4 4,266,666,667 mm

MATERIAL PROPERTIES Structural Concrete Precast Beam after transfer of prestressing force (at release) compressive strength, f'ci = MPa 27.60 modulus of elasticity, Eci = 27,606.25 MPa during erection (construction stage) compressive strength, f'c1 = 34.50 modulus of elasticity, Ec1 = 27,606.25 at service condition compressive strength, f'c2 = 34.50 modulus of elasticity, Ec2 = 27,606.25 In-situ deck compressive strength, f'c3 = 27.60 modulus of elasticity, Ec3 = 24,691.78 DESIGN PARAMETERS Reinforcing Steel Bar bar dia. main reinforcement, Øm fym bar dia. stirrups, Øs fys bar dia. web reinforcement, Øw fyw

jacking stress, fj =

1,395.00

MPa

MPa MPa

= 25 mm = 414.00 MPa = 10 mm = 276.00 MPa 10 mm = = 276.00 MPa

Strength reduction factor, Φ for tension-controlled, Φt = for compression-controlled, Φc = for shear and torsion, Φs =

0.9 0.65 0.75

24.00 0.894 0.804

Kre J RH % debonded

= = = =

35.00 MPa 0.040 80% (relative humidity) 0%

y

kN/m3 L

C

Designation LE AP M AP RE

E

left end / (start of debonded strand) arbitrary points / (end of debonded strand) midspan arbitrary points / (end of debonded strand) right end / (start of debonded strand)

D

0 1.25 2.5 3.75 5

MPa MPa

B

A B C D E

Prestressing Steel Strands prestressing type: Grade 270 low-relaxation strand ultimate tensile strength, fpu = 1,860.00 MPa yield strength, fpy = 0.9fpu = 1,674.00 MPa modulus of elasticity, Eps = 195,000 MPa mm2 nominal area of strands, Aps = 98.71

MPa MPa

(for pretensioned members) (for pretensioned members) (for pretensioned members) (for normal weight concrete)

Structural Concrete unit weight of concrete, δc = Ec3 / Ec2, nc = β1 = Table 1B: Section location y

Grade 40 or 276.00 MPa Grade 60 or 414.00 MPa 200,000 MPa

A

Prestressing Steel Strand Kes = 1.0 Kcir = 0.9 Ksh = 1.0 Kcr = 2.0

Reinforcing Steel Bar ###### - ###### = ###### - ###### = modulus of elasticity, Es =

LR

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

LOAD CASES Table 2B: Forces and Moments (service loads) Design Moments (Service load condition), kN-m

L/C

Load Combination

SW

selfweight

Hsus

sustained load

0.00

194.00

364.00

15.00

0.00

Hult

ultimate load

0.00

227.00

411.00

19.00

0.00

A

B

C

D

E

0.00

18.00

24.00

18.00

0.00

LOSSES IN PRESTRESS Immediate losses • due to elastic shortening of concrete, ES (immediate loss) initial prestressing force, Po = (n p1 + n p2 ) f j A ps = 1,927,806.30 N location of Pi from bottom, yp = h basic - (n p1 (d p1 - (h - h basic )) + n p2 (dp2 - (h - h basic )))/(n p1 + n p2 ) = 200.00 mm eccentiricity, eb = h basic /2 - y = 0.00 mm Note: (+) if 'e' is below N.A. and (-) if 'e' is above N.A. ES = K es f cir (E ps /E c1 ) 2 fcir = K cir (P i /(bh basic ) + P i e b /I basic ) - M s e /I basic Time-dependent losses • due to shrinkage of concrete, SH (time-dependent loss) V/S = bh/(2(b+h)) = 0.1333 -6 SH = 8.2x10 K sh E ps (1-0.06(V/S))(100-RH) • due to creep of concrete, CR (time-dependent loss) CR = K cr (E ps /E c1 )(f cir - f cds ) location of Pi from bottom, yf = h - (n p1 d p1 + n p2 d p2 )/(n p1 + n p2 ) = 200.00 mm eccentiricity, ef = y tr,bot - y f = 0.00 mm • due to relaxation of tendons, RE (time-dependent loss) fpi = f j = 1,395.00 MPa RE = (K re - J (SH + CR + ES)) C value of C for stress-relieved strand or wire 1 + 9 (f pi /f pu - 0.7) (f pi /f pu ) (f pi /f pu ) C = - 0.55 0.19 0.85 (f pi /f pu )/3.83

for 0.75 ≥ f pi /f pu ≥ 0.70 for 0.70 > f pi /f pu ≥ 0.51

=

for f pi /f pu < 0.51

value of C for low-relaxation strand or wire (f pi /f pu ) (f pi /f pu ) - 0.55 C = 0.9 0.21 (f pi /f pu )/4.25

for f pi /f pu ≥ 0.54

= 1.0119

for f pi /f pu < 0.54

Table 3A: Summary of Losses ##

Section

LE AP M AP RE

A B C D E

Time-dependent losses

Immediate loss fcir, MPa

ES, MPa

∆1f

fcir, MPa

fcds, MPa

SH, MPa

CR, MPa

RE, MPa

∆2f

5.42 4.81 4.61 4.81 5.42

38.30 34.01 32.58 34.01 38.30

38.30 34.01 32.58 34.01 38.30

5.42 4.84 4.67 4.90 5.54

0.00 6.55 12.29 0.51 0.00

31.72 31.72 31.72 31.72 31.72

76.60 160.94 239.55 76.44 78.29

29.48 26.24 23.12 29.66 29.41

176.10 252.91 326.97 171.83 177.73

Table 3B: Initial and Effective Presstress Section

Total Area of strands

A B C D E

1381.94 1381.94 1381.94 1381.94 1381.94

Initial Prestress (after ES)

Effective Prestress

fi, MPa

Pi, N

fe, MPa

Pe , N

1,356.70 1,360.99 1,362.42 1,360.99 1,356.70

1,874,878 1,880,807 1,882,783 1,880,807 1,874,878

1,218.90 1,142.09 1,068.03 1,223.17 1,217.27

1,684,447 1,578,300 1,475,953 1,690,348 1,682,194

% Loss

87% 82% 77% 88% 87%

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

1.8 STRENGTH INTERACTION DIAGRAM SECTION PROPERTIES SECTION DIAGRAM Section Dimension b = 800.00mm h

=

Steel Cover SCb = SCh =

450.00mm

58.00mm 58.00mm

Reinforcing Steel Bar no. of steel bars along 'x' axis =

4

no. of steel bars along 'y' axis = 2 bar diameter, Øb = 16 mm Prestressing Steel Strand

Hoop type

14 12.70 mm

Minor Axis, y

no. of prestressing steel = prestressing strand diameter, Øps = Tied

MATERIAL PROPERTIES Major Axis, x Structural Concrete min. compressive strength @ 28 days, f'c = modulus of elasticity, Ec =

35.00 MPa 27,805.57 MPa

β = 0.8 Reinforcing Steel Bar yield strength = modulus of elasticity, Es

= =

min. yield strength, fy =

276.00 MPa

≤ 12

414.00 MPa ≥ 200,000.00 MPa

16

414.00 MPa

Prestressing Steel Strand min. specified ultimate strength, fpu = min. specified yield strength, fpy =

1,862.00 MPa 1,675.80 MPa

modulus of elasticity, Eps = effective prestressing stress, fpe =

196,507.00 MPa

area of prestressing strand, Aps =

98.71 mm²

1,145.13 MPa

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

Reinforcing Steel Bar Details

Prestressing Steel Strand Details

Rebar distance 'd' from extreme compression fiber Bundled ## 1 d1 = 392.00 N = Ø Bundled ## 2 d2 = 392.00 N = Ø Bundled ## 3 d3 = 392.00 N = Ø Bundled ## 4 d4 = 392.00 N = Ø Bundled ## 5 d5 = 58.00 N = Ø ## ## ##

6 d6 = 58.00 7 d7 = 58.00 8 d8 = 58.00

9 d9 = ## 10 d10 = ## 11 d11 = ##

## 12 d12 = ## 13 d13 = ## 14 d14 = ## 15 d15 = ## 16 d16 = ## 17 d17 = ## 18 d18 = ## 19 d19 = ## 20 d20 = ## 21 d21 = ## 22 d22 = ## 23 d23 = ## 24 d24 =

Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled

Area of reinforcement steel bar, mm² 1 As1 = 201.06 2 As2 = 201.06 3 As3 = 201.06 4 As4 = 201.06 5 As5 = 201.06 6 As6 = 201.06 7 As7 = 201.06 8 As8 = 201.06

= 16 = 16

Prestressing steel distance 'y' from extreme compression fiber Bundled 1 y1 = 392.00 N = Ø = 12.7 Bundled ## 2 y2 = 392.00 N = Ø = 12.7 Bundled ## 3 y3 = 392.00 N = Ø = 12.7 Bundled ## 4 y4 = 392.00 N = Ø = 12.7

= 16

##

= 16 = 16

##

5 y5 = 392.00 6 y6 = 392.00 7 y7 = 392.00

N

=

Ø

= 16

##

N

=

Ø

##

N

=

Ø

= 16 = 16

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

N

=

Ø

=

## 21 y21 = ## 22 y22 = ## 23 y23 =

N

=

Ø

=

## 24 y24 =

8 y8 = 108.00 ## 9 y9 = 108.00 ## 10 y10 = 108.00 ## 11 y11 = 108.00 ##

## 12 y12 = 108.00 ## 13 y13 = 108.00 ## 14 y14 = 108.00 ## 15 y15 = ## 16 y16 = ## 17 y17 = ## 18 y18 = ## 19 y19 = ## 20 y20 =

Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled Bundled

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

12.7

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

N

=

Ø =

Area of prestressing steel strand, mm² Aps1 = 98.71 1 Aps2 = 98.71 2 Aps3 = 98.71 3 4 5 6 7 8

Aps4 = 98.71 Aps5 = 98.71 Aps6 = 98.71 Aps7 = 98.71 Aps8 = 98.71 Aps9 = 98.71

9 As9 =

9

10 As10 = 11 As11 = 12 As12 =

10

13 As13 = 14 As14 = 15 As15 =

13

16 As16 = 17 As17 = 18 As18 =

16

19 As19 = 20 As20 = 21 As21 =

19 21

Aps20 = Aps21 =

22 As22 =

22

Aps22 =

11 12 14 15 17 18 20

Aps10 = 98.71 Aps11 = 98.71 Aps12 = 98.71 Aps13 = 98.71 Aps14 = 98.71 Aps15 = Aps16 = Aps17 = Aps18 = Aps19 =

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

23 As23 = 24 As24 = AsT = 1,608.48 mm²

Aps23 = Aps24 =

23 24

ApsT = 1,381.94 mm²

POINTS ON INTERACTION CURVE • Pure Axial Load Capacity, Po Pn

= 0.85f' c  (A ‐ A psT  ‐ A sT ) ‐ A psT  (f pe  ‐ 0.003E ps ) + A sT f y

Po

= 6,837.43 kN

Φ

=

= 10,519.13 kN Design Axial Load, Pu cap Pcap = S.F. Po

= 5,469.94 kN

• Design Axial Force and Moment at any given value of 'c' 23 c = 397.00 mm a = 317.60 mm Steel Strain when d  c 0.003

c ‐ d

Єs =

c

0.003

d ‐ c c

Prestressing Steel Strain when y  c f pe E ps

Steel strain 1 Єs1 = 0.000038 2 Єs2 = 0.000038 3 Єs3 = 0.000038 4 Єs4 = 5 Єs5 = 6 Єs6 =

0.000038

7 Єs7 = 8 Єs8 = 9 Єs9 =

0.002562

10 Єs10 = 11 Єs11 = 12 Єs12 = 13 Єs13 = 14 Єs14 = 15 Єs15 = 16 Єs16 = 17 Єs17 = 18 Єs18 = 19 Єs19 = 20 Єs20 =

0.002562 0.002562 0.002562

‐

0.003

c ‐ d c

Prestressing strand strain Єps1 = 0.005790 Єps2 = 0.005790 Єps3 = Єps4 =

0.005790

Єps5 = Єps6 =

0.005790

Єps7 = Єps8 =

0.005790

Єps9 = Єps10 =

0.003644

Єps11 = Єps12 =

0.003644

Єps13 = Єps14 =

0.003644

Єps15 = Єps16 = Єps17 = Єps18 = Єps19 = Єps20 =

0.005790 0.005790 0.003644 0.003644 0.003644 0.003644

Єs =

f pe E ps

+

0.003

c ‐ d c

Steel stress fs1 = 7.60 MPa fs2 = 7.60 MPa fs3 = 7.60 MPa fs4 = 7.60 MPa fs5 = 414.00 MPa fs6 = 414.00 MPa fs7 = 414.00 MPa fs8 = 414.00 MPa fs9 = fs10 = fs11 = fs12 = fs13 =

Prestressing strand stress fps1 = 1,137.78 MPa fps2 = 1,137.78 MPa fps3 = 1,137.78 MPa fps4 = 1,137.78 MPa fps5 = 1,137.78 MPa fps6 = 1,137.78 MPa fps7 = 1,137.78 MPa fps8 = 716.07 MPa fps9 = 716.07 MPa fps10 = 716.07 MPa fps11 = 716.07 MPa fps12 = 716.07 MPa

fs14 = fs15 =

fps13 = 716.07 MPa fps14 = 716.07 MPa fps15 =

fs16 = fs17 =

fps16 = fps17 =

fs18 = fs19 =

fps18 = fps19 =

fs20 =

fps20 =

0.65

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

21 Єs21 = 22 Єs22 = 23 Єs23 = 24 Єs24 =

Єps21 = Єps22 =

fs21 = fs22 =

fps21 = fps22 =

Єps23 = Єps24 =

fs23 = fs24 =

fps23 = fps24 =

Nominal Axial Load and Moment Capacity (Pn, Mn) P n = 0.85f' c  (A comp  ‐ A' s  ‐ A' ps ) + A' s f' s  ‐ A' ps f' ps  ‐ A s f s  ‐ A ps f ps = 6,572.51 kN M n = 0.85f' c  (A comp  ‐ A' s  ‐ A' ps ) e 1  + A' s f' s  e 2  ‐ A' ps f' ps  e 3  ‐ A s f s  e 4  ‐ A ps f ps  e 5 = 621.98 kN‐m Ultimate Axial Load and Moment Capacity (Pu, Mu) Єst = ‐0.000038 Φ = 0.65 P u = Φ Pn

M u = Φ Mn

= 4,272.13 kN

= 404.29 kN‐m

13.2.7  Contour Points on Interaction Curve depth of comp.  curve, c (mm)

β

1

1

2

19

3

Unfactored Loads Pn (kN) Mn (kN‐m)

Factored Loads Mu (kN‐m) Pu (kN)

depth of comp.  block, a (mm)

ɸ

0.8

0.80

0.900

‐3206.43

68.27

‐2885.79

61.44

0.8

15.20

0.900

‐2855.72

143.57

‐2570.15

129.21

‐50.27

37

0.8

29.60

0.900

‐2427.09

225.98

‐2184.38

203.38

‐93.11

4

55

0.8

44.00

0.900

‐1763.30

339.24

‐1586.97

305.32

‐192.39

5

73

0.8

58.40

0.900

‐1125.08

437.07

‐1012.57

393.36

‐388.48

6

91

72.80 87.20

‐581.41

517.35

‐523.27

465.62

‐889.83

109

0.8 0.8

0.900

7

0.900

‐101.00

583.70

‐90.90

525.33

‐5779.21

8

127

0.8

101.60

0.900

343.90

639.77

309.51

575.79

1860.33

9

145

0.8

116.00

0.900

747.38

684.97

672.64

616.47

916.49

10

163

0.8

130.40

0.833

1159.28

724.97

965.68

603.90

625.36

11 12

181 199

0.8 0.8

144.80 159.20

0.772 0.722

1565.25 1962.56

757.70 781.47

1208.37 1416.97

584.94 564.22

484.07 398.19

13

217

0.8

173.60

0.680

2380.71

794.16

1618.88

540.03

333.58

14

235

0.8

188.00

0.650

2806.01

799.95

1823.91

519.97

285.09

15

253

0.8

202.40

0.650

3267.63

794.09

2123.96

516.16

243.02

16

271

0.8

216.80

0.650

3713.55

785.41

2413.81

510.52

211.5

17

289

0.8

231.20

0.650

4146.41

773.55

2695.17

502.81

186.56

18

307

0.8

245.60

0.650

4568.83

758.20

2969.74

492.83

165.95

19

325

0.8

260.00

0.650

4982.61

739.08

3238.70

480.40

148.33

20

343

0.8

274.40

0.650

5388.58

716.06

3502.58

465.44

132.88

21

361

0.8

288.80

0.650

5788.40

688.94

3762.46

447.81

119.02

22

379

0.8

303.20

0.650

6182.94

657.61

4018.91

427.45

106.36

23

397

0.8

317.60

0.650

6572.51

621.98

4272.13

404.29

94.63

24

415

0.8

332.00

0.650

6958.22

581.99

4522.84

378.29

83.64

25

433

0.8

346.40

0.650

7340.29

537.51

4771.19

349.38

73.23

26

451

0.8

360.80

0.650

7719.12

488.56

5017.43

317.56

63.29

27

469

0.8

375.20

0.650

8095.47

435.02

5262.06

282.76

53.74

28

487

0.8

389.60

0.650

8469.01

376.89

5504.86

244.98

44.5

eccentricity, e  (mm) ‐21.29

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019 10/17/2019

29

505

0.8

404.00

0.650

8796.02

321.56

5717.41

209.01

36.56

30

523

0.8

418.40

0.650

9165.45

254.13

5957.54

165.18

27.73

31

541

0.8

432.80

0.650

9533.27

182.00

6196.63

118.30

19.09

32

559

0.8

447.20

0.650

9899.33

105.15

6434.56

68.35

10.62

33

577

0.8

461.60

0.650

9987.86

25.17

6492.11

16.36

2.52

34

595

0.8

476.00

0.650

10008.56

‐54.74

6505.56

‐35.58

‐5.47

35

613

0.8

490.40

0.650

10027.93

‐134.47

6518.15

‐87.41

‐13.41

36

631

0.8

504.80

0.650

10046.13

‐214.04

6529.98

‐139.13

‐21.31

37

649

0.8

519.20

0.650

10063.45

‐293.51

6541.24

‐190.78

‐29.17

38

667

0.8

533.60

0.650

10079.75

‐372.80

6551.84

‐242.32

‐36.99

39

685

0.8

548.00

0.650

10095.30

‐452.01

6561.95

‐293.81

‐44.77

40

703

0.8

562.40

0.650

10109.98

‐531.11

6571.49

‐345.22

‐52.53

41

721

0.8

576.80

0.650

10123.93

‐610.13

6580.55

‐396.58

‐60.27

42

739

0.8

591.20

0.650

10137.16

‐689.03

6589.15

‐447.87

‐67.97

43

757

0.8

605.60

0.650

10149.76

‐767.82

6597.34

‐499.08

‐75.65

44

775

0.8

620.00

0.650

10161.95

‐846.58

6605.27

‐550.28

‐83.31

45

793

0.8

634.40

0.650

10173.39

‐925.26

6612.70

‐601.42

‐90.95

46

811

0.8

648.80

0.650

10184.41

‐1003.86

6619.87

‐652.51

‐98.57

47

829

0.8

663.20

0.650

10194.82

‐1082.37

6626.63

‐703.54

‐106.17

48

847

0.8

677.60

0.650

10204.97

‐1160.86

6633.23

‐754.56

‐113.75

49

865

0.8

692.00

0.650

10214.50

‐1239.26

6639.43

‐805.52

‐121.32

50

883

0.8

706.40

0.650

10223.90

‐1317.63

6645.54

‐856.46

‐128.88

51

901

0.8

720.80

0.650

10232.72

‐1395.95

6651.27

‐907.37

‐136.42

ITEM:

ABUSAG BRIDGE

Design:

LRP

Date:

10/17/2019

PART:

DESIGN OF SHEET PILE - PRESTRESSED

Check:

RRE

Date:

10/17/2019

13.2.8  Strength Interaction Curve

STRENGTH INTERACTION DIAGRAM Interaction Curve

Moment and Axial Tension

Axial Compression

Nominal Strength

Moment and Axial Compression

12,000

10,000

8,000

Φ Pn, kN

6,000

5,469.94 kN

4,000

2,000

64.73 kN‐m, 67.71 kN 0 0

100

200

300

400

500

600

700

800

‐2,000

‐4,000

Design Moment and Axial Tension M = Pt =

Φ Mn, kN‐m 

Design Moment and Axial Compression M = 64.73 kN‐m Pc = 67.71 kN

900