design of free standing walls

ProjectSpreadsheets to BS 8110etc

Client Advisory Group Made by Date Page

Location Grid line 1 rc 30-Oct-2014 101

RETAINING WALL design to BS 8110:1997, BS 8002:1994. BS 8004:1986 etc.Checked Revision Job No

Originated from 'RCC62.xls' v2.3 © 1999-2002 BCA for RCC chg R68

IDEALISED STRUCTURE and FORCE DIAGRAMS DESIGN STATUS: NOT VALID

WARNING :

Passive pressure should

only be considered if it

can be guaranteed that

there will be no future

excavation in front of

the wall.

DIMENSIONS (mm)

H = 4000 B = 3000 Tw = 500

Hw = 1500 BI = 1200 Tb = 1000

Hp = 300 BN = 500 TN = 500

Hn = 1000

MATERIAL PROPERTIES

fcu = 35 N/mm² gm = 1.5 concrete

fy = 460 N/mm² gm = 1.05 steel

cover to tension steel = 50 mm

Max allowable design surface crack width (W) = 0.3 mm

Concrete density = 24 kN/m³

SOIL PROPERTIES Wall Geometry

Design angle of int'l friction of retained mat'l (Ø) = 30 degree

Design cohesion of retained mat'l (C ) = 0 kN/m² (Only granular backfil considered, "C" = zero)

Density of retained mat'l (q ) = 20 kN/m³

Submerged Density of retained mat'l (qs ) = 5.00 kN/m³ [default=2/3*q (only apply when Hw >0) ] =13.33

Design angle of int'l friction of base mat'l (Øb) = 20 degree ASSUMPTIONS

Design cohesion of base material (Cb ) = 10 kN/m² a) Wall friction is zero

Density of base material (qb ) = 10 kN/m³ b) Minimum active earth pressure = 0.25qH

Allowable gross ground bearing pressure (GBP) = 200 kN/m² c) Granular backfill

LOADINGS Surcharge load -- live (SQK) = 10 kN/m² e)Does not include effect of seepage of ground

Surcharge load -- dead (SGK) = 10 water beneath the wall.

Line load -- live (LQK) = 10.3 kN/m f)Does not include deflection check of wall due to

Line load -- dead (LGK) = 43 kN/m lateral earth pressures

Distance of line load from wall (X) = 0 mm h) Design not intended for walls over 3.0 m high

LATERAL FORCES (unfactored) Ka = 0.33 [ default ka = (1-SIN Ø)/(1+SIN Ø) ] =0.33

Kp = 2.04 [ default kp = (1+SIN Øb)/(1-SIN Øb) ] =2.04

Kpc = 2.86 [ default kpc = 2kp0.5

] = 2.86

Kac = 1.15 [ 2ka0.5

]

Force Lever arm Moment about TOE gf Fult Mult

(kN) (m) (kNm) (kN) (kNm)

PE = 47.71 LE = 1.432 68.30 1.40 66.79 95.62

PS(GK) = 13.33 LS = 2.00 26.67 1.40 18.67 37.33

PS(QK) = 13.33 LS = 2.00 26.67 1.60 21.33 42.67

PL(GK) = 0.00 LL = 4.00 0.00 1.40 0.00 0.00

PL(QK) = 0.00 LL = 4.00 0.00 1.60 0.00 0.00

PW = 11.25 LW = 0.50 5.63 1.40 15.75 7.88

Total 85.62 127.26 122.54 183.49

PP = -9.49 (LP-HN) = -0.85 8.11 1.00 -9.49 8.11

i) Does not include check for temp. or shrinkage effects

-

REINFORCED CONCRETE COUNCIL

d)Does not include check of rotational slide/slope failure

(0.2 or 0.3

mm only)

Project Spreadsheets to BS 8110etc




Originated from 'RCC62.xls' v2.3 © 1999-2002 BCA for RCC chg - R68

EXTERNAL STABILITY STABILITY CHECKS : FAILURE

OVERTURNING about TOE F.O.S = 1.50

(using overall factor of safety instead of partial safety factor) LOADING OPTION

Overturning Lateral FORCE (kN) Lever arm (m) Moment (kNm) (select critical load combination)

Moments PE = 47.71 LE = 1.33 63.61 EARTH

PS(GK) = 13.33 LS = 2.00 26.67 Warning:

PS(QK) = 13.33 LS = 2.00 26.67

PL(GK) = 0.00 LL = 4.00 0.00

PL(QK) = 0.00 LL = 4.00 0.00

PW = 11.25 LW = 0.50 5.63

P = 85.62

Pp = -9.49 (LP-HN) = -0.85 8.11

Mo = 130.68

Restoring Vertical FORCE (kN) Lever arm (m) Moment (kNm)

Moments Wall = 33.50 1.45 48.58

Base = 42.00 1.50 63.00 Warning:

Nib = 7.00 0.75 5.25

Earth = 68.25 2.35 160.39

Water = 6.50 2.35 15.28

Surcharge = 26.00 2.35 61.10

Line load = 53.30 1.70 90.61V = 236.55 Mr = 444.20

Factor of Safety, Mr / Mo = 3.40 > 1.50 OK

SLIDING (using overall factor of safety instead of partial safety factor) F.O.S = 1.50

Sum of LATERAL FORCES, P = 85.62 kN

PASSIVE FORCE, Pp x Reduction factor (1) = -9.49 kN Red'n factor for passive force = 1.00BASE FRICTION ( V TANØb + B Cb ) = -116.10 kN

Sum of FORCES RESISTING SLIDING, Pr = -125.58 kN

Factor of Safety, Pr / P = 1.47 < 1.50 FAIL

GROUND BEARING FAILURETaking moments about centre of base (anticlockwise "+") :

Vertical FORCES (kN)Lever arm (m) Moment (kNm)

Wall = 36.00 0.05 1.80

Base = 72.00 0.00 0.00

Nib = 12.00 0.75 9.00

Earth = 68.25 -0.85 -58.01

Water = 6.50 -0.85 -5.53

Surcharge= 26.00 -0.85 -22.10

Line load = 53.30 -0.20 -10.66

V = 274.05 Mv = -85.50

Moment due to LATERAL FORCES, Mo = 130.68 kNm

Resultant Moment, M = Mv + Mo = 45.18 kNm

Eccentricity from base centre, M / V = 0.19 m

Therefore, MAXIMUM Gross Bearing Pressure (GRP) = 109 kN/m² < 200 OK


0

50

100

150

0.00 3.00

BEARING PRESSURE (KN/m²)

PS(QK)

PL(GK)

PL(QK)

PS(GK)

PW

ü

ALLOW BUOYANCY OF BASE






BASE - unloaded side ( per metre length ) BS8110

gf = 1.44 (default = ult mt / non-factored mt. ) =1.44 reference

V ult = 119.77 kN

M ult = 109.13 kNm ( '+' TENSION AT BOTTOM FACE)

BOTTOM REINFORCEMENT : Min. As = 1300 mm2

Table 3.25

f = 16 mm

centres = 150 mm < 766 OK 3.12.11.2.7(b)

Asprov = 1340 mm2 > 1300 OK

MOMENT of RESISTANCE : d = 942 mm

z = 894.90 mm 3.4.4.4

As' = 0 mm2

Mres = 525.51 kNm > 109.13 OK

SHEAR RESISTANCE: 100 As/bd = 0.14%

vc = 0.37 N/mm2

Table 3.8

Vres = 347.70 kN > 119.77 OK 3.5.5.2

CHECK CRACK WIDTH TO BS8110/BS8007 :(Temperature and shrinkage effects not included)

X = 175.85 mm em = -0.00131 BS8007

Acr = 86.81 mm W = -0.31 mm < 0.30 OK App. B.2

NO CRACKING

BASE - loaded side ( per metre length )V ult = 113.83 kN

M ult = -21.98 kNm (TENSION - TOP FACE)

TOP REINFORCEMENT : Min. As = 1300 mm2

Table 3.25

f = 16 mm

centres = 150 mm < 766 OK 3.12.11.2.7(b)

Asprov = 1340 mm2 > 1300 OK

MOMENT RESISTANCE : d = 942 mm

z = 894.90 mm 3.4.4.4

As' = 0 mm2

Mres = 525.51 kNm > -21.98 OK

SHEAR RESISTANCE: 100 As/bd = 0.14%

vc = 0.37 N/mm2

Table 3.8

Vres = 347.70 kN > 113.83 OK 3.5.5.2

CHECK CRACK WIDTH to BS8100/ BS8007 :(Temperature and shrinkage effects not included)

X = 175.85 mm em = -0.00172 BS8007

Acr = 86.81 mm W = -0.41 mm < 0.30 OK App. B.2

REINFORCEMENT SUMMARY for BASE

Type f Centers As Min. As

mm mm mm2

mm2

TOP (DESIGN) T 16 150 1340 1300 OK

BOTTOM (DESIGN) T 16 150 1340 1300 OK

TRANSVERSE T 12 200 565 1300 As < 1300







APPROXIMATE WEIGHT OF REINFORCEMENT

No. Type Dia Length Unit Wt Weight

WALL VERTICAL - External face 7 T 12 3096 0.888 19.24

VERTICAL - Internal face 7 T 20 3160 2.466 54.55

TRANSVERSE (Ext.& Int.) 42 T 12 1000 0.888 37.29

BASE TOP (MAIN) 7 T 16 3128 1.578 34.56

BOTTOM (MAIN) 7 T 16 3128 1.578 34.56

TRANSVERSE ( T & B ) 32 T 12 1000 0.888 28.41

WALL STARTERS (Ext.) 7 T 12 2055 0.888 12.77

WALL STARTERS (Int.) 7 T 20 2375 2.466 41.00

NIB (assume same reinforcement as wall)

INTERNAL FACE (MAIN) 7 T 12 1596 0.888 9.92

EXTERNAL FACE (MAIN) 7 T 20 1660 2.466 28.66

TRANSVERSE (EXT.+ INT.) 14 T 12 1000 0.888 12.43

SUMMARY Approx total reinforcement per metre length of wall (kg) 313.4


Diagrams Project Spreadsheets to BS 8110etc Location Grid line 1 DATA FOR DIAGRAMS I

RETAINING WALL design to BS 8110:1997, BS 8002:1994. BS 8004:1986 etc.sheet 1 of 2 Made by rc Job No R68Originated from 'RCC62.xls' v2.3 © 1999-2002 BCA for RCC Date

DESIGN STATUS: NOT VALID

IF(ABS(ECCY)>B/1000/2,"BEARING FAIL",IF(ABS(ECCY)>(B/1000)/6,(2*VL)/(3*((B/1000)/2-ABS(ECCY))),(VL/(B/1000)*(1+(6*ABS(ECCY))/(B/1000)))))

3

1 88.89

0 108.97 30.3 102.95 30.6 96.92 30.9 90.90 31.2 84.87 31.5 78.85 31.8 72.83 32.1 66.80 32.4 60.78 32.7 54.75 3

3 48.73 33 0.00 0

IF(ECCY<0,B/1000-B/1000/50*B24,B/1000/50*B24)88.89

0 0.00 108.971 0 108.971 0.060 6.538 9.284 0.060 6.538 0.06 6.5381 0.06 107.766 1 107.766 0.060 6.466 8.794 0.060 6.466 0.06 6.4662 0.12 106.561 2 106.561 0.060 6.394 8.312 0.060 6.394 0.06 6.3943 0.18 105.356 3 105.356 0.060 6.321 7.839 0.060 6.321 0.06 6.3214 0.24 104.151 4 104.151 0.060 6.249 7.374 0.060 6.249 0.06 6.2495 0.30 102.947 5 102.947 0.060 6.177 6.918 0.060 6.177 0.06 6.1776 0.36 101.742 6 101.742 0.060 6.105 6.471 0.060 6.105 0.06 6.1057 0.42 100.537 7 100.537 0.060 6.032 6.032 0.060 6.032 0.06 6.0328 0.48 99.332 8 99.332 0.060 5.960 5.602 0.060 5.960 0.06 5.9609 0.54 98.127 9 98.127 0.060 5.888 5.181 0.060 5.888 0.06 5.888

10 0.60 96.922 10 96.922 0.060 5.815 4.769 0.060 5.815 0.06 5.81511 0.66 95.718 11 95.718 0.060 5.743 4.365 0.060 5.743 0.06 5.74312 0.72 94.513 12 94.513 0.060 5.671 3.970 0.060 5.671 0.06 5.67113 0.78 93.308 13 93.308 0.060 5.598 3.583 0.060 5.598 0.06 5.59814 0.84 92.103 14 92.103 0.060 5.526 3.205 0.060 5.526 0.06 5.52615 0.90 90.898 15 90.898 0.060 5.454 2.836 0.060 5.454 0.06 5.45416 0.96 89.693 88.89 16 89.693 0.060 5.382 2.476 0.060 5.382 0.06 5.38217 1.02 88.489 BP 0 108.97 17 88.489 0.060 5.309 2.124 0.060 5.309 0.06 5.30918 1.08 87.284 BPE 1.2 84.874 18 87.284 0.060 5.237 1.781 0.060 5.237 0.06 5.23719 1.14 86.079 BPI 1.7 74.834 19 86.079 0.000 0.000 0.000 0.000 0.000 0.06 5.16520 1.20 84.874 BPZ 3 48.729 20 84.874 0.000 0.000 0.000 0.000 0.000 0.06 5.09221 1.26 83.669 21 83.669 0.000 0.000 0.000 0.000 0.000 0.06 5.02022 1.32 82.464 22 82.464 0.000 0.000 0.000 0.000 0.000 0.06 4.94823 1.38 81.260 23 81.260 0.000 0.000 0.000 0.000 0.000 0.06 4.87624 1.44 80.055 24 80.055 0.000 0.000 0.000 0.000 0.000 0.06 4.80325 1.50 78.850 25 78.850 0.000 0.000 0.000 0.000 0.000 0.06 4.73126 1.56 77.645 26 77.645 0.000 0.000 0.000 0.000 0.000 0.06 4.65927 1.62 76.440 27 76.440 0.000 0.000 0.000 0.000 0.000 0.06 4.58628 1.68 75.236 28 75.236 0.000 0.000 0.000 0.000 0.000 0 0.00029 1.74 74.031 29 74.031 0.000 0.000 0.000 0.000 0.000 0 0.00030 1.80 72.826 30 72.826 0.000 0.000 0.000 0.000 0.000 0 0.00031 1.86 71.621 31 71.621 0.000 0.000 0.000 0.000 0.000 0 0.00032 1.92 70.416 32 70.416 0.000 0.000 0.000 0.000 0.000 0 0.00033 1.98 69.211 33 69.211 0.000 0.000 0.000 0.000 0.000 0 0.00034 2.04 68.007 34 68.007 0.000 0.000 0.000 0.000 0.000 0 0.00035 2.10 66.802 35 66.802 0.000 0.000 0.000 0.000 0.000 0 0.00036 2.16 65.597 36 65.597 0.000 0.000 0.000 0.000 0.000 0 0.00037 2.22 64.392 37 64.392 0.000 0.000 0.000 0.000 0.000 0 0.00038 2.28 63.187 38 63.187 0.000 0.000 0.000 0.000 0.000 0 0.00039 2.34 61.982 39 61.982 0.000 0.000 0.000 0.000 0.000 0 0.00040 2.40 60.778 40 60.778 0.000 0.000 0.000 0.000 0.000 0 0.00041 2.46 59.573 41 59.573 0.000 0.000 0.000 0.000 0.000 0 0.00042 2.52 58.368 42 58.368 0.000 0.000 0.000 0.000 0.000 0 0.00043 2.58 57.163 43 57.163 0.000 0.000 0.000 0.000 0.000 0 0.00044 2.64 55.958 44 55.958 0.000 0.000 0.000 0.000 0.000 0 0.00045 2.70 54.753 45 54.753 0.000 0.000 0.000 0.000 0.000 0 0.00046 2.76 53.549 46 53.549 0.000 0.000 0.000 0.000 0.000 0 0.00047 2.82 52.344 47 52.344 0.000 0.000 0.000 0.000 0.000 0 0.00048 2.88 51.139 48 51.139 0.000 0.000 0.000 0.000 0.000 0 0.00049 2.94 49.934 49 49.934 0.000 0.000 0.000 0.000 0.000 0 0.00050 3.00 48.729 50 48.729 0.000 0.000 0.000 0.000 0.000 0 0.000

###### ###### ###### ######

IF(ECCY>(B/1000)/6,IF(XX>(B/1000/2-ECCY)*3,0,(((B/1000/2-ECCY)*3-XX)/((B/1000/2-ECCY)*3))*BP),((VL/(B/1000)*(1-(6*ECCY)/(B/1000))))+(B/1000-XX)/(B/1000)*(BP-(VL/(B/1000)*(1-

(6*ECCY)/(B/1000)))))

30-Oct-14

0.00

50.00

100.00

150.00

0 5

KN

/M^

2

M

BEARING PRESSURE DIAGRAM

0

50

100

150

0.00 3.00

KN

/M^

2

M

BEARING PRESSURE DIAGRAM

Diagrams

Project Spreadsheets to BS 8110etc Location Grid line 1 DATA FOR DIAGRAMS II

RETAINING WALL design to BS 8110:1997, BS 8002:1994. BS 8004:1986 etc.sheet 1 of 2 Made by rc Job No R68Originated from 'RCC62.xls' v2.3 © 1999-2002 BCA for RCC Date

YY= 3 MTE= 29.37MTLG= 0.00MTLQ= 0.00MTSG= 15MTSQ= 15.00MTW= 0.21

UTM= 86.4286.42

0 0.00 0 0.001 0.06 0.0264 0.062 0.12 0.1056 0.123 0.18 0.2376 0.184 0.24 0.4224 0.245 0.30 0.66 0.306 0.36 0.9504 0.367 0.42 1.2936 0.428 0.48 1.6896 0.489 0.54 2.1384 0.54

10 0.60 2.64 0.6011 0.66 3.1944 0.6612 0.72 3.8016 0.7213 0.78 4.4616 0.7814 0.84 5.1744 0.8415 0.90 5.94 0.9016 0.96 6.7584 0.9617 1.02 7.6296 1.0218 1.08 8.5536 1.0819 1.14 9.5304 1.1420 1.20 10.56 1.2021 1.26 11.642 1.2622 1.32 12.778 1.3223 1.38 13.966 1.3824 1.44 15.206 1.4425 1.50 16.5 1.5026 1.56 18.073 1.5627 1.62 19.735 1.6228 1.68 21.488 1.6829 1.74 23.333 1.7430 1.80 25.272 1.8031 1.86 27.308 1.8632 1.92 29.442 1.9233 1.98 31.677 1.9834 2.04 34.014 2.0435 2.10 36.456 2.1036 2.16 39.004 2.1637 2.22 41.661 2.2238 2.28 44.429 2.2839 2.34 47.309 2.3440 2.40 50.304 2.4041 2.46 53.415 2.4642 2.52 56.644 2.5243 2.58 59.978 2.5844 2.64 63.416 2.6445 2.70 66.96 2.7046 2.76 70.616 2.7647 2.82 74.386 2.8248 2.88 78.274 2.8849 2.94 82.283 2.9450 3.00 86.416 3.00

0 00 1000

1200 10001200 40001700 40001700 10003000 10003000 01000 01000 -1000500 -1000500 00 0

5000 3000

30-Oct-14

0 20 40 60 80 100

0.00

0.60

1.20

1.80

2.40

3.00

ULT. MT (KNM)

WA

LL

(M

)

MOMENT DIAGRAM

-2000

-1000

0

1000

2000

3000

4000

0

1000

2000

3000

4000

WA

LL

(m

m)

BASE ( mm)

WALL GEOMETRY

Project Spreadsheets to BS 8110etc Location Grid line 1 CRACK WIDTH CALCULATIONS

RETAINING WALL design to BS 8110:1997, BS 8002:1994. BS 8004:1986 etc.Made by rc Job No R68Originated from 'RCC62.xls' v2.3 © 1999-2002 BCA for RCC Date

WALL

MR= 15.06 MIN SPACING= 650 ASreq = 484.4 fs = 70.926Asprov%= 0.476As/bd= 0.005 MSBB= 766 ASBBreq =0.01 fs = 0.0023Asprov%= 0.1423

X= 138.01 MSBT= 766 ASBTreq =0.01 fs = 0.0023Asprov%= 0.1423Ic= 3.752E+09

STS= 0.0004ST1= 0.0004ST2= 0.0005179Acr= 86.046864W= -0.02

em= -0.0001

MR= 15.06 MR= 15.06AsBB/bd= 0.0014 AsBB/bd= 0.0014

X= 175.85 X= 175.85Ic= 1.366E+10 Ic= 1.366E+10

STS= 0.0003 STS= -0.0001ST1= 0.0003 ST1= -0.0001ST2= 0.0016535 ST2= 0.0016535Acr= 86.810337 Acr= 86.810337W= -0.31 W= -0.4119

em= -0.0013 em= -0.0017

30-Oct-14

Notes

Disclaimer

Status of spreadsheet

Public release version.

Revision history RCC62 Retaining Wall.xls

Date Version Action Size (kB)

21-Oct-04RCC62 v2.3Names of sides of base on DESIGN sheet changed from

"outside" and " inside" to "unloaded" and "loaded".580

########RCC62 v2.2 Correction when distance X to line load ≤ 0. 565

########RCC62 v2.1 DETR logo replaced by DTI. 563

11-Oct-02RCC62 v2.0 Version 2 enhancements 583

########RCC62 v1.4 Data! Main graphic changed to jpeg 365

########RCC62 v1.3 Crack width calculation to outer base amended 365

15-Apr-01RCC62 v1.2Buoyance option + notes added. Passive pressure reduction

factor rectified398

########RCC62 v1.1Crack width w for top of inner base amended. Notes re crack

widths and cracking added in DATA!398

6-Aug-99RCC62 v1.0First public release.

Includes b version comments 398

All advice or information from the British Cement Association and/or Reinforced Concrete

Council is intended for those who will evaluate the significance and limitations of its contents

and take responsibility for its use and application. No liability (including that for negligence)

for any loss resulting from such advice or information is accepted by the BCA, RCC or their

subcontractors, suppliers or advisors. Users should note that all BCA software and

publications are subject to revision from time to time and should therefore ensure that they

are in possession of the latest version.

This spreadsheet is shareware. It may be distributed freely, but

may not be used for commercial purposes until the user has

registered with the RCC.

Notes

Size (kB)

design of free standing walls

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