3.3.1 Retaining Wall

RW ID : RWR1 0.50

Concrete Strength, f'c = 21 MPa

Steel Yield Strength, fy = 414 MPa

250

18.50

23.6

40 3.90

10 4.50

0.175

0.985

0.450

Pa = 111.7 kN/m0.60

19.50 kN/m

110.0 kN/m C 0.70 0.70

Factor of Safety Against Overturning (consider 1-m strip)

Weight/unit Moment arm

Section Area length from point C Moment

No. (kN/m) (m) (kN-m)

3.90 x 0.50 = 1.95 23.60 x 1.95 = 46.02 1.15 52.92

x 0.20 x 4.50 = 0.45 23.60 x 0.45 = 10.62 0.83 8.85

1.80 x 0.60 = 1.08 23.60 x 1.08 = 25.49 1.60 40.78

3.90 x 1.80 = 7.02 18.50 x 7.02 = 129.87 2.30 298.70

x 1.80 x 0.681 = 0.613 18.50 x 0.613 = 11.3333 2.60 29.47

= 19.50 3.20 62.40

242.83 493.12

Ph = 190.0

h/3

= 2.59 > 2, safe against overturning

Allow. Soil Bearing Capacity, qa = kN/m2

Soil Unit Weight, s = kN/m3 W1

Concrete Unit Weight, c = kN/m3

Angle of Internal Friction, =

Inclination of ground surface, =sin = W2

cos = W3

Backfill Pressure Hor. Coeff., kh =

Pv = Pa sin =

Ph = Pa cos =

-Tabulation to determine Righting Moment, MR

(m2)

W1

W21/2

W3

W4

W51/2

Pv

R = MR =

-Overturning Moment, MO

MO = Ph (h/3)

FSoverturning =MR

MO

-Soil Pressure

BCL

Rx =

x e R e =

= 1.248 m =

< B/6 =

= R/B(1 ± 6e/B)

= 179.16 < 250

= 15.11

-Design of Wall (consider 1-m strip)

0.217

66.46 kN-m

625 mm

P 0.0005

z 0.0034

2114

3.90 using 20

314.2

spacing = 0.149 m

-Design of Heel

25.49 kN

129.87 kN

11.333 kN

= 179.16

= 15.11

q'q' = 61.0405 using

spacing =

= 41.34 kN

= 27.19 kN

MR - MO

qmax qmin qmax

qmin

qmax kN/m2

qminkN/m2

Coeff. of Active Pressure, kh =

Moment, MU =

deff =

reqd =

min =As = mm2

mm barA1bar = mm2

W3 = Moment, MU =

W4 = deff =

W5 = reqd =qmax kN/m2 min =

qminkN/m2 As =

qmin

kN/m2

A1bar =

R2

R1

R1

R2

RW ID : RWR2

0.681 Concrete Strength, f'c = 21 MPa


150

18.50

Pa 23.6

40

Ph 10

0.175

0.985

0.450

Pa = 111.0 kN/m

19.37 kN/m

1.80 109.3 kN/m


Weight/unit

Moment Section Area length

(kN-m) No. (kN/m)

52.92 3.80 x 0.50 = 1.90 23.60 x

8.85 x 0.30 x 4.50 = 0.68 23.60 x

40.78 1.90 x 0.70 = 1.33 23.60 x

298.70 3.80 x 1.90 = 7.22 18.50 x

29.47 x 1.90 x 0.663 = 0.630 18.50 x

62.40

493.12

kN-m


W5


W4 Pv Soil Unit Weight, s = kN/m3



Inclination of ground surface, =sin =

cos =Backfill Pressure Hor. Coeff., kh =

Pv = Pa sin =

Ph = Pa cos =


(m2)

W1

W21/2

W3

W4

W51/2

Pv


Ph (h/3)

FSoverturning =MR

MO

-Soil Pressure

BCL

R

B/2 - x x e

0.35 m

0.42 m

SAFE


P

z

3.80

-Design of Heel

164.4 kN-m 31.39 kN

525 mm 133.57

0.0016 11.656 kN

0.0034

1775

20 q'

314.2

0.177 m

= 29.76 kN

= 80.22 kN

qmax qmin

kN/m2


W3 =

W4 =

W5 =

mm2

mm barqminmm2

R2

R1

R1

R2

0.50 RW ID :

0.663

Pa

3.80

4.50 Ph

0.70

C 0.80 0.80 1.90

Factor of Safety Against Overturning (consider 1-m strip) Factor of Safety Against Overturning (consider 1-m strip)


length from point C Moment Section

(kN/m) (m) (kN-m) No.

1.90 = 44.84 1.35 60.530.68 = 15.93 1.00 15.931.33 = 31.39 1.75 54.937.22 = 133.57 2.55 340.60

0.630 = 11.6562 2.87 33.41

= 19.37 3.50 67.79

256.75 573.20

Ph = 188.1 kN-m

h/3

> 2, safe against overturning

W5

Allow. Soil Bearing Capacity, qa =

W1 W4 Pv


Inclination of ground surface, =W2

W3



W1

W2

W3

W4

W5

Pv

R = MR =


MO = Ph (h/3)

FSoverturning =

-Soil Pressure

x =R e = B/2 - x

= 1.500 m = 0.25 m

< B/6 = 0.45 m

= R/B(1 ± 6e/B)

= 147.96 < 150 SAFE

= 42.22


0.217

61.48 kN-m

725 mm

0.0003

0.0034 z

2452

using 20 3.80

314.2

spacing = 0.128 m

-Design of Heel

kN 114.7 kN-m

kN 625 mm

kN 0.0008

= 147.96 0.0034

= 42.22 2114

q' = 73.5536 using 20

314.2

spacing = 0.149 m

MR - MO

qmax

qmin

qmax kN/m2 kN/m2

qminkN/m2


Moment, MU =

deff =

reqd =

min =As = mm2

mm barA1bar = mm2

Moment, MU =

deff =

reqd =qmax kN/m2 min =

qminkN/m2 As = mm2

kN/m2 mm barA1bar = mm2

RWR3 0.50

Concrete Strength, f'c = 21 MPa


150

18.00

23.6

40 3.80

10 4.50

0.175

0.985

0.450

Pa = 108.0 kN/m0.70

18.84 kN/m

106.3 kN/m C 0.80 0.80 1.90



Area length from point C Moment

(kN/m) (m) (kN-m)

3.80 x 0.50 = 1.90 23.60 x 1.90 = 44.84 1.35 60.53

x 0.30 x 4.50 = 0.68 23.60 x 0.68 = 15.93 1.00 15.93

1.90 x 0.70 = 1.33 23.60 x 1.33 = 31.39 1.75 54.93

3.80 x 1.90 = 7.22 18.00 x 7.22 = 129.96 2.55 331.40

x 1.90 x 0.663 = 0.630 18.00 x 0.630 = 11.3412 2.87 32.51

= 18.84 3.50 65.95

252.30 561.26

Ph = 183.0 kN-m

h/3


W5


Soil Unit Weight, s = kN/m3 W1 W4




cos = W3


Pv = Pa sin =

Ph = Pa cos =


(m2)

1/2

1/2

R = MR =


MO = Ph (h/3)

FSoverturning =MR

MO

-Soil Pressure

BCL

Rx =

x e R e = B/2 - x

= 1.499 m = 0.25 m

< B/6 = 0.45 m

= R/B(1 ± 6e/B)

= 145.55 < 150

= 41.34


0.283

78.01 kN-m

725 mm

P 0.0004

0.0034

2452

using 20

314.2

spacing = 0.128 m

-Design of Heel

31.39 kN 111.5 kN-m

129.96 kN 625 mm

11.341 kN 0.0008

= 145.55 0.0034

= 41.34 2114

q'q' = 72.2173 using 20

314.2

spacing = 0.149 m

= 29.33 kN

= 78.55 kN

MR - MO

qmax qmin qmax

qmin

qmax kN/m2 kN/m2

qminkN/m2


Moment, MU =

deff =

reqd =

min =As = mm2

mm barA1bar = mm2

W3 = Moment, MU =

W4 = deff =


qminkN/m2 As = mm2

qmin


R2

R1

R1

R2

RW ID : RWL1

0.663 Concrete Strength, f'c = 21 MPa


150

18.50

Pa 23.6

40

Ph 10 4.50

0.175

0.985

0.450

Pa = 111.0 kN/m

19.37 kN/m

109.3 kN/m


Weight/unit

Section Area length

No. (kN/m)

3.80 x 0.50 = 1.90 23.60 x 1.90 = 44.84

x 0.30 x 4.50 = 0.68 23.60 x 0.68 = 15.93

1.90 x 0.70 = 1.33 23.60 x 1.33 = 31.39

3.80 x 1.90 = 7.22 18.50 x 7.22 = 133.57

x 1.90 x 0.663 = 0.630 18.50 x 0.630 = 11.6562

= 19.37

256.75

Ph

h/3



Pv Soil Unit Weight, s = kN/m3



Inclination of ground surface, =sin =

cos =Backfill Pressure Hor. Coeff., kh =

Pv = Pa sin =

Ph = Pa cos =


(m2)

W1

W21/2

W3

W4

W51/2

Pv

R =


FSoverturning =MR

MO

-Soil Pressure

BCL

Rx =

x e R

= 1.500

= R/B(1 ± 6e/B)

SAFE = 147.96

= 42.22


P

z

3.80

spacing =

-Design of Heel

31.39 kN

133.57 kN

11.656 kN

= 147.96

= 42.22

q'q' = 73.5536

= 29.76 kN

= 80.22 kN

MR - MO

qmax qmin qmax

qmin

qmax

qmin


Moment, MU =

W3 =

W4 =

W5 =

qmax

qmin

mm barqmin

R2

R1

R1

R2

0.50 RW ID : RWL2

0.663 Concrete Strength, f'c =

Steel Yield Strength, fy =

Pa

3.80

Ph

0.70

C 0.80 0.80 1.90


Moment arm

from point C Moment Section Area

(m) (kN-m) No.

1.35 60.53 3.80 x

1.00 15.93 x 0.30 x

1.75 54.93 1.90 x

2.55 340.60 3.80 x

2.87 33.41 x 1.90 x

3.50 67.79

573.20

= 188.1 kN-m

> 2, safe against overturning

W5

Allow. Soil Bearing Capacity, qa =

W1 W4 Pv Soil Unit Weight, s =

Concrete Unit Weight, c =


Inclination of ground surface, =W2

W3


Pv = Pa sin =

Ph = Pa cos =


(m2)

W1

W21/2

W3

W4

W51/2

Pv

MR =


MO = Ph (h/3)

FSoverturning =MR

MO

-Soil Pressure

B

R

e = B/2 - x x e

m = 0.25 m

< B/6 = 0.45 m

R/B(1 ± 6e/B)

< 150 SAFE


0.238

67.43 kN-m

725 mm

0.0003

0.0034 z

2452

using 20 3.80

314.2

spacing = 0.128 m

-Design of Heel

114.7 kN-m

625 mm

0.0008

0.0034

2114

using 20 q'

314.2

spacing = 0.149 m

=

=

qmax

kN/m2 kN/m2

kN/m2


Moment, MU =

deff =

reqd =

min =As = mm2

mm barA1bar = mm2

Moment, MU =

deff =

reqd =

kN/m2 min =

kN/m2 As = mm2


R1

R2

0.50

Concrete Strength, f'c = 21 MPa 0.663


150

18.50

23.6 Pa

40 3.80

10 4.50 Ph

0.175

0.985

0.450

Pa = 111.0 kN/m0.70

19.37 kN/m

109.3 kN/m C 0.80 0.80 1.90



Area length from point C Moment

(kN/m) (m) (kN-m)

0.50 = 1.90 23.60 x 1.90 = 44.84 1.35 60.53

4.50 = 0.68 23.60 x 0.68 = 15.93 1.00 15.93

0.70 = 1.33 23.60 x 1.33 = 31.39 1.75 54.93

1.90 = 7.22 18.50 x 7.22 = 133.57 2.55 340.60

0.663 = 0.630 18.50 x 0.630 = 11.6562 2.87 33.41

= 19.37 3.50 67.79

256.75 573.20

Ph = 188.1 kN-m

h/3


W5


Soil Unit Weight, s = kN/m3 W1 W4 Pv




cos = W3


Pv = Pa sin =

Ph = Pa cos =


(m2)

R = MR =

MO = Ph (h/3)

MR

MO

BCL

x = e R e = B/2 - x

= 1.500 m = 0.25 m

< B/6 = 0.45 m

= R/B(1 ± 6e/B)

= 147.96 < 150 SAFE

= 42.22


0.238

67.43 kN-m

725 mm

P 0.0003

0.0034

2452

using 20

314.2

spacing = 0.128 m

31.39 kN 114.7 kN-m

133.57 kN 625 mm

11.656 kN 0.0008

= 147.96 0.0034

= 42.22 2114

q' = 73.5536 using 20

314.2

spacing = 0.149 m

29.76 kN

80.22 kN

MR - MO

qmin qmax

qmin

qmax kN/m2 kN/m2

qminkN/m2


Moment, MU =

deff =

reqd =

min =As = mm2

mm barA1bar = mm2

W3 = Moment, MU =

W4 = deff =


qminkN/m2 As = mm2

qmin


R2

R1

DESIGN OF RETAINING WALL

INPUT DATA:Concrete Strength, f'c = 41.4 MPaSteel Yield Strength, fy = 414 MPaRetaining Wall height, h = 3.00 m = 9.84 ft.Dia. of main bar, = 16 mmThickness, t = 300 mmEffective thickness, = 272.00 mm

LATERAL LOADS:Soil: = 0.000 ksf = 0.00 kPa

= 0.00 kN @ 1.00 m

Surcharge: Psc = 0 ksfWu = 0.000 ksf = 0 kPa

Water: Pw = 0.614 ksf = 29.467 kPa= 61.88 kN @ 1.00 m

3.00

1.00 m

SURCHARGE WATER + SOIL

MOMENTS:-Mu = 34.38 kN-m

0.00130.0034

As = 919.81PROVIDE 16 218.6 m. O.C.

+Mu = 18.33 kN-m0.00070.0034

As = 919.81PROVIDE 16 218.6 m. O.C.

d1

deff

Ps = khFPsu

FPwu

FPu =

reqd =min =

-mm @

reqd =min =

-mm @


61.9 kN


INPUT DATA:Concrete Strength, f'c = 28 MPa

Steel Yield Strength, fy = 414 MPaRetaining Wall height, h = 1.70 m = 5.58 ft.

Dia. of main bar, = 16 mmThickness, t = L/25 = 68 mm

Use t = 200 mmEffective thickness, = 117 mm

1.70

h/2

h/3

Assume surcharge = 200 psf= 9.58 kPa

=surcharge

= 0.599 m

Ca = = 0.33

= 9.14 kN

= 7.95 kN


0.01310.0034

As = 1529.61PROVIDE 16 0.13144654 m. O.C.

+Mu = 31.60 kN-m0.00660.0034

As = 768.81PROVIDE 16 0.2615 m. O.C.

d1

deff

P1

P2

Cash1 CawH

h1 s

1 - sin 1 + sin

P1 = Cash1

P2 = CawH2/2

reqd =min =

- mm @

reqd =min =

- mm @


Subject : Design of Retaining WallDate : 20-Aug-02Designer : BoyceMark : RW-1

Minimum t = L/25 = 54 say 200 mm

d = 154 mm

H = 1.35

8.10 kPaDESIGN CRITERIA :

f'c = 28 mPafy = 276 mPa

surcharge = 0.1 kPa

= 18.00 kN/m3 = 30 degrees

= 0.1 kN/m3

Ca =

= 0.333

== 0.006 m

Considering 1-m strip of wall :

-Mu = 3.49 kN-m

Check for Shear :

Vu = 7.72 kN= 115.44 kN Safe

Vertical Reinforcements :dia bar = 12 mm

= 113.10

Ca

sH =

s

w

1-sin1+sin

h1

surcharges

Vn

As1 mm2

-Mu = 3.49 kN-mRn = 0.16

= 0.00059 0.0025

As = 385.00s = 293.76 mm say 300 mm

Horizontal Reinforcements :dia bar = 12 mm

= 113.10

As = 200

s = 565.49 say 300 mm

min

mm2

As1 mm2

mm2

mm2

0.03 kPa 0.135 kPa

h1

Ca

sh

1 =

wH =

PROPOSED EDITHA MANSIONDESIGN OF RETAINING WALL

INPUT DATA:Concrete Strength, f'c = 28 MPaSteel Yield Strength, fy = 414 MPaRetaining Wall height, h = 2.70 m = 8.856 ft.Dia. of main bar, = 16 mmThickness, t = 250 mmEffective thickness, = 222.00 mm

LATERAL LOADS:Soil: = 0.292 ksf = 14.02 kPa

= 32.19 kN @ 0.90 m

Surcharge: Psc = 0.165 ksfWu = 0.281 ksf = 13.461 kPa

Water: Pw = 0.553 ksf = 26.52 kPa= 50.12 kN @ 0.90 m

2.70

0.90 m

SURCHARGE WATER + SOIL


0.00300.0034

As = 750.72PROVIDE 16 267.8 m. O.C.

+Mu = 28.85 kN-m0.00160.0034

As = 750.72PROVIDE 16 267.8 m. O.C.

d1

deff

Ps = khFPsu

FPwu

FPu =

reqd =min =

-mm @

reqd =min =

-mm @

PROPOSED EDITHA MANSIONDESIGN OF RETAINING WALL

82.31 kN

Documents

3.3.1 Retaining Wall