Culvert 1

Project Job ref.Qatar Primary Routes Dukhan Highway Central Contract 5090882

Part of Structure Calc sheet no. rev.

Drawing ref. Calc. by Date Check by Date

Uday JAN-11

Ref. Calculations Output

INDEX

Sr No Content Page No

1.0 A1

2.0

2.1 Box Culvert Load calculations B1 to B8

2.2 Box Culvert Robot output C1 to C38

2.3 Top slab -SAM Results D1 to D20

2.4 Vertical wall -SAM Results E1 to E20

2.5 Base slab -SAM Results F1 to F20

3.0

3.1 Calucation of Forces & Moments G1 to G6

3.2 SAM Results H1 to H30

4.0

4.1 Calucation of Forces & Moments I1 to I6

4.2 SAM Results J to J20

APPENDIX A List of Drawings

Drg No Title

i ERC 0638/D2/CC/QP/4651 A Highway plan for Culverts Ch 16+200 to 16+800

ii ERC 0638/D2/CC/QP/4651 A GA & Reinforcement details ( Single Cell )

ii ERC 0638/D2/CC/QP/4652 A Details Of Wing wall ( Single Cell )

WS Atkins & Partners Overseas P O Box 7562 Abu

Dhabi United Arab Emirates

Proposed additional Q.P 14 Ethylene pipe culvert box-Single Cell

Introduction & design data

Box Culvert Design- Single Cell

Wing wall 4.0m Height.

Wing wall 2.50 Height.

Introduction & Design data.

Introduction & Design data.

Box Culvert DesignSingle Cell

Design Of Wing Wall 4.0m Height

Design Of Wing Wall 2.5m Height

APPENDIX AList Of Drawings.

APPENDIX AList Of Drawings.

file:///var/www/apps/conversion/tmp/scratch_5/312718648.xlsx 312718648.xlsx




Drawing ref. Calc. by Date Check by

Uday Jan 11


1.0 Introduction

1.1 Design codes

BS 8007 Water retaining structure.

BS 8110 Code of practice for design and construction.

BD 31 / 01 The design of Buried Concrete Box and Frame Structures.

Volume 2 , Section 2 , Part 12

BD 28 / 87 Early Thermal Cracking of Concrete.

1.2 Design data

1.2.1 Material

Structural concrete for roof, wall and bases

Mass concrete Class C

Reinforced concrete Class B C40

Reinforcing steel Grade 420

1.2.2 Material unit weight.

Concrete Reinforced & Mass 25.0

Finishes and waterproofing 23.0

Earth 20.0

1.2.3 Live load

Live load 1.50

1.2.4 Earth pressure coefficient

Coefficient of active pressure Ka min 0.20

Coefficient of active pressure Ka 0.33

Coefficient of passive pressure Kp 3.00

Coefficient of earth pressure at rest Ko 0.60

1.2.5 Cover

Clear concrete cover to steel reinforcement as per following

Base slab Bottom face 100 mm

Top face 75 mm

Top slab Backfill face 75 mm

Inner face 50 mm

Walls Earth face 75 mm

Internal faces Inner face 50 mm

1.2.6 Crack width

Tensile faces of elements ate checked for crack width 0.200 mm

1.2.7 Bearing capacity



Following pages furnish the design calculation for box culvert.Culvert is underground rectangular in shape,Vertical walls are supported by base slab.It is designed for earth pressure & other forces as applicable.

kN/m3

kN/m3

kN/m3

kN/m2






Uday Jan 11




Safe bearing capacity 200 kN/m2






Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11









Uday Jan 11




Reinforcement calculation:

Component Thk-mm Main c/c Wt-kg/m Wt SayI] Vertical wall Outer face 500 16 100 1.578 15.78

Reservoir Inner face 16 100 1.578 15.78

Mini rein @ 0.30 % 11.78

Total 43.34 87 126 150

2] Roof slab Main bottom 400 16 100 1.578 15.78

Reservoir Main top 16 100 1.578 15.78

Main bottom 16 100 1.578 15.78

Main top 16 100 1.578 15.78

Total 63.13 158 229 250

3] Base slab Main bottom 1500 16 100 1.578 15.78


Main bottom 16 100 1.578 15.78

Main top 16 100 1.578 15.78

Total 63.13 42 61 100

4] Column Main bottom 202.5 16 4 1.578 6.31

Reservoir Links 12 7 0.888 11.19

Total 17.50 86 125 150

5] Pump station Main E face 425 25 100 3.853 38.53

Vertical wall Op face 12 100 0.888 8.88

Minimum 12 150 0.888 5.92

Minimum 12 150 0.888 5.92

Total 59.25 139 202 225

6] Pump station Main bottom 200 12 150 0.888 5.92

Planks Op face 12 200 0.888 4.44

Minimum 12 200 0.888 4.44

Minimum 12 200 0.888 4.44

Total 19.24 96 139 150


Beam U Op face 25 4 3.853 15.41

Links 16 6 1.578 56.82

Side bars 16 25 1.578 39.46

Total 136.95 124 180 200

kg/m3

kg/m3

kg/m3

kg/m3

kg/m3

kg/m3

kg/m3






Uday Jan 11









Uday Jan 11







Uday Jan 11


2.0 Introduction

2.1 Loads on box culvert

i Dead load Top slab , base slab , Walls

ii Vertical earth load

iii Vertical vehicular live load HA or HB loads

iv Horizontal earth pressure

v Horizontal live load surcharge

vi Horizontal force due to Traction HA or HB loads

General arrangement

C Line of Dukhan highway

Plan ( Indicative only )

Proposed Finished

Road level 29.839

H= 1.025 1.325

6.600

0.600

7.475

0.800 3.500 1.500 0.800 6.625

EGL

5.000 6.150

0.850




Following pages furnish the design calculation for Single cell Box culvert.It is below ground & rectangular in plan,It is designed for earth pressure & vehicular live load forces as applicable.

LL=

A

B




Uday Jan 11





Section

3.0 Load calculation

3.1 Dead load

i Load due to top slab 0.600 25 V1 = 15.00

ii Load due earth fill 1.025 20 V2 = 20.5

iii Horizontal earth pressure at A 0.60 7.475 20 H1 = 89.7

iv Horizontal earth pressure at B 0.60 1.325 20 H1 = 15.9

3.2 Highway loading

3.2.1 HA load

Notional lane width bl = 3.60 meter

Loaded length L = 5.00 meter

BS5400-2-2206 For loaded length up to & including 50 m UDL in KN/m of notional length by follwing equation

6.2.1 HA UDL 336 1 5.00 0.67 W = 114.30 kN/m

KEL = 120.00 kN

Wheel load = 100.00 kN

Part 12 BD/01 As depth of fill >0.6 m HA load shall be replaced by 30 Units of HB loading.

3.2.1 (ii)

3.2.2 HB-load

The HB vehicle defined in the Standard represents four axles with four wheels per axle

Load per axle with four wheels = 10.00 kN

Load per wheel 10.00 4 = 2.50 kN

Part 12 BD/01 HB load-30 units

3.2.1 b (ii) Minimum of 30 units of HB loading shall be applied to structure

Load for 30 unit containg one axle 30.0 10.00 = 300.00 kN

Load per wheel 300.00 4 = 75.00 kN

3.2.1 c (ii) Considering dispersion of wheel load through the fill longitudinaly & Transversly at 2 vertically to1 horizontally

Effective presure under wheel = 1.10

Contact area under wheel 75.00 1100 = 0.0682

size of square shape area = 0.2611 m2

say = 0.250 meter

Dispersion of wheel load

BL 1.28

1.00

Bw

4.28 1.00

1.00

kN/m2

kN/m2

kN/m2

kN/m2

For the purpose of calculating the loads to be applied to the top slab one carriageway notational lanes is considered

W = 336 [ 1/L] 0.67

N/mm2

m2

x

x

x

x

x

x

x x




Uday Jan 11





1.80 spacing 6-11-16-21-26 1.80

1.80 1.00 1.00 1.00

fill depth fill depth

2:1 1.025 2:1 1.025

1.275 1.275 4.275

Dispersion in longitudinal direction Dispersion in transverse direction

Despersion width in transverse direction Bw = 4.275 meter

Despersion length in longitudinal direction = 1.28 meter

Intensity of load 75.00 4.00 1.28 4.28 = 55.04

For 30 Units say = 55.04

Udl load per meter 300 4.28 = 70.18 kN/m

say = 72.00 kN/m

On concervative side considering as point load 72.00 1.275 = 91.80 kN

For 45Units

On concervative side considering as point load 91.80 1.500 = 137.70 kN

3.2.3 HB traction

30 units

HB longitudinal load = 25 % of nominal HB load 25 1200 100 = 300 kN

Force per wheel 300 8 = 37.50 kN

Traction force for 30 Units per notional lane 300 3.25 = 92.31 kN

Traction force for 45 Units per notional lane 92 1.5 = 138.46 kN

Part 12 BD/01

Traction force is modified by applying factor Kt

3.2.7 e Factor

= 6.60 meter

H = 1.03 meter

Kt = 0.93

Traction force for 30 Units per notional lane 92.31 0.93 = 85.77 kN

Traction force for 45 Units per notional lane 138.46 0.93 = 128.65 kN

3.2.4 Horizontal Live load

Part 12 BD/01 Vertical live load

3.2.6 (a) 30 units of HB = 12.0

45 units of HB = 20.0

4.0 Load & Load combinations

4.1 Loads Comb 1 Comb 4

SLS ULS SLS ULS

1 Self wt DL V1 1.0 1.20 1.0 1.20

2 Earth fill load SDL V2 1.0 1.20 1.0 1.20

3 Vertical live load LL V3 1.1 1.30

4 Earth pressure EP H1 1.0 1.50 1.0 1.50

5 Live load Surcharge LLS H2 1.0 1.50 1.0 1.50

6 Traction TR H3 1.0 1.0 1.10

BL

kN/m2

kN/m2

Kt = [ LL - H ) / [ L

L - 0.6 ] but 1 > Kt > 0

LL

psc

= K.vsc

vsc

kN/m2

kN/m2

x

x

x

x

x

x

x

x




Uday Jan 11





4.2 Load cases & Load factors Following load cases are analysed

i A/1 Max Vertical load with Max Horizontal load v A/5 Traction with Min Vertical load

Part 12 BD/01 ii A/2 Min Vertical load with Max Horizontal load vi A/6 Sliding

Appendix-A iii A/3 Max Vertical load with Min Horizontal load vii A/7 Bearing pressure

iv A/4 Traction with Max Vertical load

4.2.1 Live load 3-LL= 2.15

2-SDL= 1.40 1.325

ULS 19.80 27.03 H= 1.025 30.80 27.03 19.80

SLS 7.20 15.90 20.5 22.00 15.90 7.20

1-DL= 1.40

7.475

6.150

SLS 7.20 89.70 Box structures 89.70 7.20

ULS 19.8 152.49 152.49 19.80

5-LLSC 4-Earth Load 4-Earth 5-LLSC

0.60 0.60 K 0.60 0.60

20.00 20.00 20.00 20.00

2.75 1.70 1.70 2.75

Combination 1-DL 2-SDL 3-LL 4-Earth 5-LLSC

7-101 1.00 1.00 1.10 1.00 1.00

1.20 1.20 1.30 1.50 1.50

1.10 1.10 1.10 1.10 1.10

1.32 1.32 2.15 1.65 2.75

8-201 1.40 1.40 2.15 1.70 2.75

Digram A/1a Maximum Vertical load with Maximum Horizontal load

4.2.2 No live load 0.00

2-SDL= 1.00 1.325

ULS 19.80 27.03 H= 1.025 22.00 27.03 19.80

SLS 7.20 15.9 22.00 15.9 7.20

1-DL= 1.00

7.475

6.150

SLS 7.20 89.7 Box structures 89.7 7.20

ULS 19.80 152.49 152.49 19.80

5-LLSC 4-Earth Load 4-Earth 5-LLSC

0.60 0.60 K 0.60 0.60

20.00 20.00 20.00 20.00

2.75 1.70 1.70 2.75

KN/m2

KN/m2

KN/m2

kN/m3

fL.

f3

SLS- fL

fL

.f3

ULS-fL.

f3

ULS-fL.

f3

KN/m2

KN/m2

KN/m2

kN/m3

fL.f3




Uday Jan 11





Combination 1-DL 2-SDL 3-LL 4-Earth 5-LLSC 4-Earth 5-LLSC

9-102 1.00 1.00 0.00 1.00 1.00 1.00 1.00

1.00 1.00 0.00 1.50 1.50 1.50 1.50

1.00 1.00 0.00 1.10 1.10 1.10 1.10

1.00 1.00 0.00 1.65 2.75 1.65 2.75

10-202 1.00 1.00 0.00 1.70 2.75 1.70 2.75

Digram A/2a Minimum Vertical load with Maximum Horizontal load

4.2.3 Live load 3-LL= 2.15

2-SDL= 1.40

ULS 5.30 H= 1.025 30.80 5.30 1.325

SLS 5.30 22.00 5.30

1-DL= 1.40

7.475

6.150

SLS 29.90 Box structures 29.90

ULS 29.90 29.90

4-Earth Load 4-Earth

0.20 K 0.20

20.00 20.00

1.00 1.00

Combination 1-DL 2-SDL 3-LL 11-Earth 11-Earth

12-103 1.00 1.00 1.10 1.00 1.00

1.20 1.20 1.30 1.00 1.00

1.10 1.10 1.10 1.00 1.00

1.32 1.32 2.15 1.00 1.00

13-203 1.40 1.40 2.15 1.00 1.00

Digram A/3a Maximum Vertical load with Minimum Horizontal load

4.2.4 Live load 3-LL= 2.15

Traction 1.82 2-SDL= 1.40

ULS 156.1 14.87 H= 1.025 30.80 15.90 1.325

SLS 85.77 8.75 22.00 15.90

1-DL= 1.40

7.475

6.150

SLS 3.96 49.335 Box structures 89.70

ULS 10.89 83.87 89.70

5-LLSC 3-Earth Load 3-Earth

0.33 0.33 K 0.60

12.00 20.00 20.00

SLS- fL

fL

.f3

ULS-fL.

f3

ULS-fL.

f3

KN/m2

KN/m2

kN/m3

fL.

f3

SLS- fL

fL

.f3

ULS-fL.

f3

ULS-fL.

f3

KN/m2

KN/m2

kN/m3

1111

15 14 16




Uday Jan 11





2.75 1.70 20.00

1.00


17-104 1.00 1.00 1.10 1.00 1.00 1.00 1.00

1.20 1.20 1.30 1.50 1.50 1.10 1.00

1.10 1.10 1.10 1.10 1.10 1.10 1.00

1.32 1.32 2.15 1.65 2.75 1.82 1.00

18-204 1.40 1.40 2.15 1.70 2.75 1.82 1.00

Digram A/4a Traction With Maximum Vertical load

4.2.5 Live load 3-LL= 1.50


ULS 156.10 14.87 H= 1.025 22.00 15.90 1.325

SLS 85.77 8.75 22.00 15.90

1-DL= 1.00

7.475

6.150


ULS 10.89 83.87 89.70

5-LLSC 3-Earth Load 3-Earth

0.33 0.33 K 0.60

12.00 20.00 20.00

2.75 1.70 1.00


19-105 1.00 1.00 1.10 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.50 1.50 1.10 1.00

1.00 1.00 1.00 1.10 1.10 1.10 1.00

1.00 1.00 1.50 1.65 2.75 1.82 1.00

20-205 1.00 1.00 1.50 1.70 2.75 1.82 1.00

Digram A/5a Traction With Minimum Vertical load

4.2.6 Live load 3-LL= 1.50


ULS 156.10 14.87 H= 1.025 22.00 15.90 1.325

SLS 85.77 F3 8.745 22.00 15.90

1-DL= 1.00

7.475

F2 F1 6.150 F4


ULS 10.89 83.87 Box structures 89.70

fL.

f3

15-LLSC 6-Traction

SLS- fL

fL

.f3

ULS-fL.

f3

ULS-fL.

f3

KN/m2

KN/m2

KN/m2

kN/m3

fL.

f3

15-LLSC 6-Traction

SLS- fL

fL

.f3

ULS-fL.

f3

ULS-fL.

f3

KN/m2

KN/m2

KN/m2

15 14 16

15 14 21




Uday Jan 11





LLSC Earth Load Earth

0.33 0.33 K 0.60

20.00 20.00

2.75 1.70 1.00


22-106 1.00 1.00 1.10 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.50 1.50 1.10 1.00

1.00 1.00 1.00 1.10 1.10 1.10 1.00

1.00 1.00 1.50 1.65 2.75 1.82 1.00

23-206 1.00 1.00 1.50 1.70 2.75 1.82 1.00

Digram A/6a Sliding

Sliding check as per A/6 a

Part 12 BD/01

4.4.2 ( c )

= design angle of base friction = =

Considering design angle of shearing resistance = = 30 degrees

= 0.75 tan 30 = 0.43

form results tabulated ref 5.1 = 683.00 kN

683.0 0.43 = 295.75 kN

F1 due to earth pressure

At base 0.33 20.00 7.48 1.70 = 83.87

At top 0.33 20.00 1.33 1.70 = 14.87

F1 83.87 14.87 0.50 6.150 = 303.61 kN

F2 due to surcharge pressure 0.33 12.00 6.15 2.75 = 66.97 kN

F3 due to Traction 85.77 1.10 1.10 1.50 = 155.67 kN

F4 Relieving Earth Pressure

At base 0.60 20.00 7.48 1.00 = 89.70

At top 0.60 20.00 1.33 1.00 = 15.90

F4 89.70 15.90 0.50 6.150 = 324.72 kN

Following relationship to be satisfied for the structure as a whole

[ Relieving Earth Pressure + FR ]

303.61 66.97 155.67 = 526.26 kN

[ Relieving Earth Pressure + FR ] 324.72 295.75 = 620.47 kN

OK

4.2.7 Live load 3-LL= 1.10

2-SDL= 1.00

H= 1.025 22.00 1.325

15.9 22.00 15.9

1-DL= 1.00

7.475

kN/m3

fL.

f3

15-LLSC 6-Traction

SLS- fL

fL

.f3

ULS-fL.

f3

ULS-fL.

f3

Friction force (FR) developed at the base is given by

FR = V

tot.tan

b

b

tan b 0.75 x tan'

'

tan b

b

Vtot

.

FR = V

tot.tan

b

kN/m2

kN/m2

kN/m2

kN/m2

[ Traction + Distrubing Earth Pressure ) fL.

f3 <

[Traction+Distrubing Earth Pressure) fL.

f3 =F1+F2+F3

KN/m2

x

x

x x

x x

+ xx

x x

x x

x x

x x

+ xx

+ +

+

x




Uday Jan 11





6.150

7.20 89.7 Box structures 89.7

Load LLSC Earth Earth

K 0.60 0.60 0.60

20.00 20.00

Combination 1-DL 2-SDL 3-LL 4-Earth 5-LLSC 4-Earth

24-107 1.00 1.00 1.10 1.00 1.00 1.0

Digram A/7a Bearing pressure

5.0 Structure is analysed for above load caes using ROBOT Millenuim & sectiona are designed.

Results are tabulated below [ Ref output sheets attached ]

Load case A/1a A/2a A/3a A/4a A/5a A/6a A/7a

1.0 Top slab

1.1 SLS+BM kN.m 139 29 174 152 152 152 143

-BM kN.m -156 -87 -121 -202 -202 -202 -186

1.2 ULS

+BM kN.m 234 11 310 283 187 187

-BM kN.m -278 -128 -203 -510 -454 -454

-Vu-kN -410 92 -410 -520 -398 -398

+Vu-kN 129 0 129 239 200 200

2.0 Vertical wall

2.1 SLS+BM kN.m 110 (i) 122 74 74 74 74 100

-BM kN.m -165 (o) -121 -158 -210 -210 -210 -220

2.2 ULS

+BM kN.m 231 283 161 77 100 100

-BM kN.m -285 -158 -267 -615 -558 -558

-Vu-kN -361 -360 -62 -570 -578 -578

+Vu-kN 32 11 22 156 150 150

3.0 Base slab

3.1 SLS-BM kN.m -79 -221 -185 -185 -185 -171

+BM kN.m 158 86 177 177 177 215

3.2 ULS

-BM kN.m -241 -12 -366 -485 -396 -396

+BM kN.m 305 259 115 554 535 535

-Vu-kN -485 -48 -457 -416 -292 -292

+Vu-kN 160 201 410 495 362 362

5.1 Summary of design

Item Depth Reinforcement [ Ref SAM analysis results sheets attached ]

i Top slab 600 20-100 Top Main Reinforcement

20-100 Bottom Main Reinforcement

16-100 Minimum reinforcement top & Bottom

ii Vertical walls 800 25-100 Main vertical reinforcement near earth face

KN/m2

kN/m3

SLS- fL

-163 (T)

174 (B)




Uday Jan 11





20-100 Main vertical reinforcement far from earth face

16-100 Minimum horizontal reinforcement on both faces.

iii Base slab 800 20-100 Top Main Reinforcement

25-100 Bottom Main Reinforcement

16-100 Minimum reinforcement top & Bottom

5.2 Bearing pressure check

Maximum vertical load from structure at base V = 744 kN

Mement acting at base M = 7.27 kN.m

Width of base B = 1.00 meter

Length of base L = 6.60 meter

Bearing pressure at base P/A 744.0 1.00 6.60 p = 112.73

Bearing pressure at base M/Zxx 7.27 6.0 1.00 6.60 6.60 p = 1.00

Maximum pressure 112.73 1.00 p = 113.73

END

kN/m2

kN/m2

kN/m2

<200 kN/m2 ok

x

xx x

+ x




Uday Jan 11





Bearing pressure

Live load 25.00

H= 0.000 50.00 1.325

0.00 0 0 0.00

7.475

0.000

0.80

1.70 0.6 1.70

4.00

173.54 136.24

Net pr 24.037 116.24

BM 167.96 kN.m

VU= 174.36 kN

Wt LA BM

Earth wt 1.70 7.475 20 254.15 1.15 292.27

KN/m2

KN/m2

KN/m2




Uday Jan 11





SLL 1.70 1.000 12 20.4 1.15 23.46

Force from BM from analysis 345 0 -266

Toptal 619.55 49.733

PA 154.89

M/Z 18.65

Pmax 173.54

Pmin 136.24

4.2 Design of vertical wall

Depth of section h 150 mm

Width of section 1000 mm

Total design moment SLS BM #REF! kN-m

Total design moment ULS BM kN-m

BS8007 Grade of concrete or cube strength fc 40

Table 3.1 Stress in reinforcement fy 420

Modulus of Elasticity of concrete E28 31000

Modulus of Elasticity of reinforcement steel Es 200000

Nominal cover to reinforcement Cnom 35 mm

Area of reinforcement 12 dia 100 mm c/c + 0 dia 0 Nos 1131

Actual Cover to reinforcement 75 mm

Modular ratio = Es / Ec 200000 31000 m 6.45

Effective depth 150 75 6 69 mm

Ultimate check:

Mu b deff Ast k Z 0.95d Z Mu

kN/m mm mm mm mm mm kN.m

1000 69 1131 #VALUE! #VALUE! 66 ### #VALUE! ###

1000 2 = 6.45 1130.97 69 -1

1.00 14.593 = 1006.9 25.26 mm

[d-x] 43.74 mm

NA to crack surface 84.736

4 Second moment if inertia of cracked section in concrete units I=

1000 25.26 3.0 6.45 1131.0 44 5374873 13957425 19332298

5 Elastic section modulus :

Concrete Zc = I/dc 19332298 25.26 765221

Steel Zs = 19332298 43.74 442019.234

6 Stress in concrete BM / Zc #REF! 1000000 765221.19 # #REF!

Stress in steel #REF! 1000000 6.45 442019.23 #REF!

7 Strain in conc & Steel

Strain in Concrete Stress / Ece #REF! 31000 #REF!

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

mm2

Neutral axis equation bn2/2 = m. Ast . [d-n]

b.dc3 / 3 + m .As [ d-dc]2

mm4

mm3

mm3

N/mm2

N/mm2

c

+

n2

2n

n2

2n+ n

3+

2




Uday Jan 11





Strain in Steel = Stress / Es 200000

Strain at the level where crack is being checked. #VALUE!

Bar dia spacing Cnom d h bt a' As x

12 100 35 69 150.00 1000 110.00 1131 25.26

BM=DL+LL h-x a'-x d-x

#REF! #VALUE! 58.66 124.74 84.74 43.74 0.000356

BS8007:1987 stiffening effect of concrete for crack width of 0.2 mm

B.4 (3)

= #VALUE! 1000 125 85 3 200000 1131 43.74

#VALUE! 0.0003561 1.000 stiffening effrct considered #VALUE!

3.00 58.66 #VALUE! #VALUE! ### mm

1 2 58.66 35.00 1 2 0.19

150.00 25.26

Depth D = 150 mm

Effective depth deff = 69 mm

Width of section b = 1000 mm

Shear force = Vu = #REF! kN

Shear stress v /bd #REF! 1000 1000 69 V = #REF!

BS 8110 P % of steel = 1131 100 1000 69 = 1.64 P %

Table3.8 400/d 400 69 = 5.80

fcu = 40.0 = 1.17

Table3.8 Design concrete shear stress vc. = = 1.35

Check for Early thermal cracking

R w

40 460 250000 1.59 863 0.67 16 0.20 0.200 0.0001 0.0002

sp -req Pro-sp As-pro Remark

1.2E-05 35 20 0.000528 172 863 16 233 100 2011 OK

Provide 12 ida 100 mm c/c at centre of wall in one layer in both direction

5 Bearing pressure calculation

5.1 Weight calculation

i] Top screed 1.500 0.750 0.100 1.000 23 = 2.59 kN

ii] Slab portion 1.500 0.750 0.200 1.000 25 = 5.63 kN

iii] Long walls 1.500 0.150 #REF! 2.000 25 = kN

iv] Short walls 0.450 0.150 #REF! 2.000 25 = kN

v] Base slab 1.500 0.750 0.150 1.000 25 = 4.22 kN

Total weight = #VALUE! kN

5.2 Bearing pressure :

a] Net wt of of structure = #VALUE! kN

b] Live load 1.500 0.750 1.000 1.000 1.5 = 1.69 kN

d] Other load 0.000 0.000 0.000 0.000 0 = 0 kN

Total weight for bearing pressure = #VALUE! kN

s

1

s

acr

2

2 =1.b

t. [ h-x ]. [ a' - x ] / [ 3.Es.As. [ d-n ]

m

w= 3.acr.m / [ 1 + 2 [ a

cr - C

min ] / [h-x]

N/mm2

(fcu/25)1/3 N/mm2

0.79.P1/3 .[ 400/d ]1/4 / m N/mm2

fcu-

mpa fy-mpa Ac-mm2 f

ct* A

st-mm2 f

ct*/f

b

sh

ult

T1

T2

th

0.8(T1+T

2) A

stA

st (reqd.)

+ +




Uday Jan 11





Bearing pressure : ### 1.50 0.75 = #VALUE!

3.4 Design of Base slab:

self wt of base slab 0.150 -25 = -3.75

Net Design pressure = #VALUE!

Considering design pressure for base slab = 23.00

Base slab is supported by vertical wall at all edges.

Length of short span Lx 0.45 meter

Length of long span Ly 0.45 meter

r = Ly/Lx r 1.00

0.50

Load taken by short span 23.00 0.500 Wx 11.50 kN/m

Load taken by long span 23.00 11.50 Wy 11.50 kN/m

Multiplying factor for Span moment Mx = 0.86

Multiplying factor for Span moment My = 0.86

0.08 kN.m

0.08 kN.m

0.19 kN.m

0.19 kN.m

Shear force short span Vx=1.5 . W.Lx / 3 5.18 kN

Shear force Long span Vy= 1.5\.W.Lx[ r / (2+r ) ] 5.18 kN

3.4.1 Design of Base slab For -BM on Top face due to upward load

Depth of section h 150 mm

Width of section b 1000 mm

Total design moment SLS BM 0.19 kN-m

Total design moment ULS BM 0.29 kN-m

BS8007 Grade of concrete or cube strength fc 40

Table 3.1 Stress in reinforcement fy 420

Modulus of Elasticity of concrete E28 31000

Modulus of Elasticity of reinforcement steel Es 200000

Nominal cover to reinforcement Cnom 35 mm

Area of reinforcement 12 dia 100 mm c/c + 0 dia 0 Nos 1131

Actual Cover to reinforcement 75 mm

Modular ratio = Es / Ec 200000 31000 m 6.45

Effective depth 150 75 6 69 mm

Ultimate check:

Mu b deff Ast k Z 0.95d Z Mu

kN/m mm mm mm mm mm kN.m

0.29 1000 69 1131 0.00152853 69 66 66 32 OK

1000 2 = 6.45 1130.97 69 -1

1.00 14.593 = 1006.9 25.26 mm

[d-x] 43.74 mm

kN/m2

kN/m2

kN/m2

kN/m2

Load coefficient Wx / W = r4/[ 1+r4 ]

1-5/18 [ r2/(1+r4)]

1-5/18 [ r2/(1+r4)]

Mid span moment + ve , Mx = Wx Lx2 .MF / 24

Mid span moment + ve , My = Wy Ly2 .MF / 24

Support moment -ve , Mx = Wx Lx2 / 12

Support moment -ve , My = Wx Lx2 / 12

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

mm2

Neutral axis equation bn2/2 = m. Ast . [d-n]

n2

2n

n2

2n+ n




Uday Jan 11





NA to crack surface 84.736

4 Second moment if inertia of cracked section in concrete units I=

1000 25.26 3.0 6.45 1131.0 44 5374873 13957425 19332298

5 Elastic section modulus :

Concrete Zc = I/dc 19332298 25.26 765221

Steel Zs = 19332298 43.74 442019.234

6 Stress in concrete BM / Zc 0.19 1000000 765221.19 OK 0.25 20.0

Stress in steel 0 1000000 6.45 442019.23 OK 2.83 100.0

7 Strain in conc & Steel

Strain in Concrete Stress / Ece 0.25 31000 0.000008

Strain in Steel = Stress / Es 2.8 200000 0.000014

Strain at the level where crack is being checked. 0.000027

Bar dia spacing Cnom d h bt a' As x

12 100 35 69 150.00 1000 110.00 1131 25.26

BM=DL+LL h-x a'-x d-x

0.2 0.000027 0.000014 58.66 124.74 84.74 43.74 0.000356

BS8007:1987 stiffening effect of concrete for crack width of 0.2 mm

B.4 (3)

= 0.000027 1000 125 85 3 200000 1131 43.74

0.000027 0.0003561 1.000 stiffening effrct considered -0.00033

3.00 58.66 -0.00033 -0.058 -0.042 mm

1 2 58.66 35.00 1 2 0.19

150.00 25.26

3.4.2 Check for Early thermal cracking

R w

40 460 75000 1.59 259 0.67 12 0.20 0.200 0.0001 0.0002

sp -req Pro-sp As-pro Remark

1.2E-05 35 20 0.000528 39 259 12 437 100 1131 OK

Provide 10 dia 100 c/c in 1 layer in both direction.

3.4.3 Check for shear

Depth D = 150 mm

Effective depth deff = 69 mm

Width of section b = 1000 mm

Shear force = Vu = 5.18 kN

Shear stress v /bd 5.18 1000 1000 69 V = 0.08

BS 8110 P % of steel = 1131 100 1000 69 = 1.64 P %

Table3.8 400/d 400 69 = 5.80

fcu = 40.0 = 1.17

Table3.8 Design concrete shear stress vc. = = 1.35

No shear reinforcement is required

T12-100 c/c

b.dc3 / 3 + m .As [ d-dc]2

mm4

mm3

mm3

N/mm2 N/mm2

N/mm2 N/mm2

c

s

1

s

acr

2

2 =1.0 b

t. [ h-x ]. [ a' - x ] / [ 3.Es.As. [ d-n ]

m

w= 3.acr.m / [ 1 + 2 [ a

cr - C

min ] / [h-x]

fcu-

mpa fy-mpa Ac-mm2 f

ct* A

st-mm2 f

ct*/f

b

sh

ult

T1

T2

th

0.8(T1+T

2) A

stA

st (reqd.)

N/mm2

(fcu/25)1/3 N/mm2

0.79.P1/3 .[ 400/d ]1/4 / m N/mm2

+

+ +

3+

2




Uday Jan 11





T12-100 c/c

T12-100 c/c

T12-100 c/c

T12-100 c/c T12-100 c/c

END

For Bearing presure




Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11








Uday Jan 11





Reinforcement calculation:

Component Thk-mm Main c/c Wt-kg/m Wt SayI] Vertical wall Outer face 500 16 100 1.578 15.78

Reservoir Inner face 16 100 1.578 15.78

Mini rein @ 0.30 % 11.78

Total 43.34 87 126 150

2] Roof slab Main bottom 400 16 100 1.578 15.78


Main bottom 16 100 1.578 15.78

Main top 16 100 1.578 15.78

Total 63.13 158 229 250

3] Base slab Main bottom 1500 16 100 1.578 15.78


Main bottom 16 100 1.578 15.78

Main top 16 100 1.578 15.78

Total 63.13 42 61 100

4] Column Main bottom 202.5 16 4 1.578 6.31

Reservoir Links 12 7 0.888 11.19

Total 17.50 86 125 150

5] Pump station Main E face 425 25 100 3.853 38.53

Vertical wall Op face 12 100 0.888 8.88

Minimum 12 150 0.888 5.92

Minimum 12 150 0.888 5.92

Total 59.25 139 202 225


Planks Op face 12 200 0.888 4.44

Minimum 12 200 0.888 4.44

Minimum 12 200 0.888 4.44

Total 19.24 96 139 150

kg/m3

kg/m3

kg/m3

kg/m3

kg/m3

kg/m3




Uday Jan 11






Beam U Op face 25 4 3.853 15.41

Links 16 6 1.578 56.82

Side bars 16 25 1.578 39.46

Total 136.95 124 180 200kg/m3




Uday Jan 11





312718648.xlsx - W1_h=4.00m

ProjectDOHA WEST

Part of Structure Head Wall for pipe culvert

WS Atkins & Partners Overseas Head wall design- 1,65m Height

Drawing Ref Calc by Date

DW077-P00-ATK-SW-7065 AN 07 Oct 2015

Design Data for the Retaining wall considered

Wall height above footing H = 2000 mm

Top of wall thickness 400 mm

Bottom of wall thickness 400 mm

Heel length (Backfill side) 1750 mm

Toe length 1200 mm

Thickness of base slab D = 600 mm

Total base slab length B = 3350 mm

Toe backfill above footing H3 = 0 mm Backfill above toe is ignored

Horizontal distance from edge of top wall to slope of soil Ds = 500 mm

Density of soil 20

Angle of repose, backfill ø = 34 Degree Degree = 0.593 Rad

Angle of repose, bearing 11.5 Degree Degree = 0.201 Rad

Backfill slope angle ß = 11.3 Degree Degree = 0.197 Rad

Density of concrete 25

Concrete grade fcu = 40 N/mm²

Reinforcement grade fy = 500 N/mm²

Live Load Surcharge Udl = 20 kN/m²

Allowable soil pressure Qall = 250 kN/m²

Load factor for Ultimate check LF = 1.65

Coefficent of friction 0.20 0.20

FOS against overturning FOS o = 1.50 1.50

FOS against sliding FOS s = 1.20

cosß - Sqrt{(cosß)² - (cosø)²}

Active earth pressure coefficient, Ka = cosß ---------------------------------------------

cosß + Sqrt{(cosß)² - (cosø)²}

Therefore Ka = 0.298

Pressure at rest coefficient, Ko (minimum 0.5) Ko = (1 - sinø) (1 + sinß) = 0.527

Selected Pressure at rest coefficient, Ko Ko = 0.527

Passive earth pressure coefficient, Kp Kp = 1 + sinø = 1.50

PO Box 7562 Abu Dhabi United Arab Emirates

t1 =

t2 =

L1 =

L2 =

s = kN/m3

ø1 =

c = kN/m3

=

312718648.xlsx - W1_h=4.00m

1 - sinø

USING ACTIVE EARTH PRESSURE Ka FOR STABILITY CHECK

Height of surcharge H1 = 1.25 x tan ß = 0.25 m

Total height of soil, Hs = H + D + H1 = 2.85 m

H2 = H + H1 = 2.25 m

312718648.xlsx - W1_h=4.00m

ProjectDOHA WEST




DW077-P00-ATK-SW-7065 AN 07 Oct 2015

The relevant calculations are shown in the following table:

Magnitude Dist. Moment

Load due to of load from (a) about (a)

W (KN) (m) (kN.m)

Stem (W1)

0.40 x 2.00 x 25.00 20.00 1.40 28.0

0.00 x 1.00 x 25.00 0.00 1.20 0.0

Wt. of earth (W2)_above heel

1.75 x 2.00 x 20.00 70.00 2.48 173.3

0.12 x 1.25 x 20.00 3.12 2.93 9.2

Base slab (W3)

3.35 x 0.60 x 25.00 50.25 1.68 84.2

Toe backfill (W4)

0.00 x 1.20 x 20.00 0.00 0.60 0.0

0.298 x 20.00 2.85

x 0.204.74 3.35 15.9

2 Stabilizing moment <== 310.5

0.298 x 20.00 2.85

x 0.98 6 -22.5

Minus moment of surcharge, M = (Udl x Ka x Hs² /2 ) * cos(ß)

0.298 x 20.00 2.85

x 0.98-23.7

2 Overturning moment <== -46.2

Total 148.11 264.21

Therefore (eccentrity relative to point (a) z = 264 / 148 = 1.784 m

Eccentricity e (relative to C.G.) = B/2 - z = -0.109 m < B/6, So O.K.

Maximum and minimum pressures at the base are given by

p = W ( 1 ± 6e ) kN/m², W = 148.1114 kN

B B

= 44.21 ± -8.62

p toe = 35.59 kN/m² less than 250.0 kN/m², So O.K.p heel = 52.83 kN/m², So O.K. (No tension)

Pressure at junction of stem with toe

= 35.594062 - 35.59406 - 52.83 x 1200 = 41.76836 kN/m²

3350

Pressure at junction of stem with heel

= 52.830645 + 35.59406 - 52.83 x 1750 = 43.82646 kN/m²

3350

CHECK FOR OVERTURNING AND SLIDING

Factor of safety against overturning

= Stabilizing moment = 310.5 = 6.71 > 1.5 ==> So O.K.

Overturning moment 46.2

Total earth pressure + surcharge =


Vertical soil pressure, Pv =(Ka gs Hs2 /2) sin(ß)

Minus moment of soil pressure, M = {Kags*Hs3/6}*cos(ß)

P = Ka x s x Hs x Hs/2 + Udl x Ka x Hs

312718648.xlsx - W1_h=4.00m

= 24.2 + 16.97 = 41.2 kN

Therefore horizontal earth pressure = P * cos ß = 40.36 kN

Maximum available friction without surcharge weight

0.203 x 148.11 = 30.1336 kN

Factor of safety against sliding = = 0.747 < 1.2 ==> So Not O.K.

P * cosß

= W =

* W

312718648.xlsx - W1_h=4.00m

ProjectDOHA WEST




DW077-P00-ATK-SW-7065 AN 07 Oct 2015

A key is to be provided or consider passive pressure to increase resistance against sliding

Provide a key of 850 mm deep and 400 mm wide under the stem to increase factor of

safety against sliding. Sliding will take place along the surface at the bottom of key.

Total active pressure

where Hk = Hs + Depth of key

= 40.8 + 22.04 kN = 3.70 m

= 62.803 kN

Total weight at the bottom level of the key = W + Wt. of key + Wt. of soil

Wt = 151.360 + 8.5 + 50.15 = 210.0101 kN

Total passive pressure

= 31.496 kN

42.73 + 31.496 = 74.22

Factor of Safety for Sliding = Fr = 1.205 > 1.20 ==> So O.K.

Pa x cosß

REINFORCEMENT DESIGN FOR STEM (USE Ko IF Ka < Ko FOR REINFORCEMENT DESIGN)

Maximum bending moment at the bottom of the stem due to earth pressure and surcharge

M = 0.516962 x 20 x 2.00 ^3 + 20.68 x 1

6.00

= 13.8 + 20.7 = 34.5 kNm

Concrete cover = 75 mm Hence for 12 mm main bars,

effective d = 319 mm

Mu = 1.65 x 34.5 = 0.558817

1000 x 319 ^2

lever arm, z = 303.05 mm 0.0140

As req. = 431 mm²

As min. = 600 mm²

Therefore provide T 12 150 mm c/c As, prov. = 753.984 mm² > As req. So O.K.

100As,prov./bd = 0.236359

Main Vertical Reinforcement For Exposed Wall

Provide minimum shrinkage and temperature steel = 0.12%bh = 480 mm²

Therefore provide T 12 200 mm c/c A's, prov. = 565.488 mm² > As req. So O.K.

100A's,prov./bd = 0.177

Distribution steel

Provide minimum steel = 0.13%bh = 520 mm²

Therefore provide T 12 200 mm c/c As = 565.488 mm² > As req. So O.K.

DEFLECTION CHECK - TOP OF CANTILEVER

Slenderness ratio = 2000 / 319 = 6.27

Therefore allowable = 7.00 x modification factors = 17.13 ==> So OK !


= Pa = Ka x s x Hk x Hk/2 + Udl x Ka x Hk

= Pp = Kp x s x (Depth of base slab + Depth of key)2/2

Total horizontal resisting force, Fr = x Wt + Pp

x 106

bd2

K = Mu / bd2 fcu =

312718648.xlsx - W1_h=4.00m

1.85

where fs = 248.679 < 0.8fy So OK !

Compression reinforcement modification factor = 1+ 100A's,prov/bd/(3+ 100A's,prov/bd) = 1.06

Modification factor for triangular load = 1.25

Tension reinforcement modification factor = 0.55 + ( 477 - fs )/{120(0.9 + M/bd2)} =

312718648.xlsx - W1_h=4.00m

ProjectDOHA WEST




DW077-P00-ATK-SW-7065 AN 07 Oct 2015

CURTAILMENT OF STEM REINFORCEMENT

At depth 'h' metres from top, let As be the steel required.

Effective depth = ( 319 + 0 x h )

2

Bending Moment = x Ko * cosß + Udl x Ko * cosß x h x h / 2

6

Mu = 1.723207 1.65 + 5.16962 1.65

= 2.84 8.529872

As = 2.843291 8.529872

0.87 fy z

At depth 'h' Ult. Bending Effective Area

metres from Moment Depth Req.

top ( kN-m ) d (mm) (mm²)

0.00 0.0 319.00 600

0.20 0.4 319.00 600

0.40 1.5 319.00 600

0.60 3.7 319.00 600

0.80 6.9 319.00 600

1.00 11.4 319.00 600

1.20 17.2 319.00 600

1.40 24.5 319.00 600

1.60 33.5 319.00 600

1.80 44.2 319.00 600

2.00 56.9 319.00 600

CHECK ULTIMATE SHEAR STRESS AT BASE OF STEM (USE Ko IF Ka < Ko)

Total shear at base of stem =

= 20.68 + 20.68 = 41.36 kN

Ultimate shear stress v = 1.65 x 41357 = 0.214 N/mm²

1000 x 319

Allowable shear stress, vc = 0.484 N/mm² > v, So O.K.

DESIGN OF TOE SLAB (PRESSURE USE Ko IF Ka < Ko) _ BOTTOM STEEL

Self load of the base per metre run = 0.6 x 25 = 15 kN/m

The force acting on toe are pressure from soil acting upwards and self-weight acting downwards.

If Ka < Ko, then Ko will be used for pressure calculation to get the worst bending moment and shear.

W = 151.8 kN

Moment about a = 228.59 kNm

Therefore z = 228.5886 / 151.7613 = 1.506238 m

Eccentricity e = B/2 - z = 0.17 m < B/6, so O.K. !

Therefore Maximum and minimum pressures at the base are given by

p = W ( 1 ± 6 e ) = 45.302 ± 13.693 kN/m²

B B

p toe = 58.99 kN/m²


s x h3

h3 x h2 x

h3 + h2

h3 + h2

P = Ko * cosß x s x H x H/2 + Udl x Ko * cosß x H

312718648.xlsx - W1_h=4.00m

p heel = 31.61 kN/m²


= 58.994889 - 58.99489 - 31.61 x 1200 = 49.18498 kN/m²

3350


= 31.608892 + 58.99489 - 31.61 x 1750 = 45.92 kN/m²

3350

312718648.xlsx - W1_h=4.00m

ProjectDOHA WEST




DW077-P00-ATK-SW-7065 AN 07 Oct 2015

Therefore Maximum Bending Moment

= 49.18498 - 15 ) x 1.2 +

2.00

2 1.2

43.994889 - 34.2 ) x x 1.2 x

3 2.0

= 29.3 kNm



Mu = 1.65 x 29.3 = 0.181007

1000 x 517

lever arm, z = 491.15 mm 0.0045

As req. = 226 mm²

As min. = 900 mm²


100As,prov./bd = 0.194451

CHECK FOR SHEAR

Maximum shear force = 43.99489 + 34.18 x 1.2 = 46.90792 kN

2


1000 x 517


DESIGN OF THE HEEL SLAB _ TOP STEEL

The forces acting on the heel are pressure of soil acting upwards and weight of earth retained and self-weight acting downwards.



Load due to of load fr. c about c

W (kN) (m) (kNm)

Wt. of earth (W2)

1.75 x 2.00 x 20.00 70.00 0.88 61.3

0.12 x 1.25 x 20.00 3.12 1.33 4.2

Wt. of heel slab (W3a)

1.75 x 0.60 x 25.00 26.25 0.88 23.0

Vertical soil pressure Pv

72.9 x 0.1959461 14.28 1.75 25.0

Deduct for upward pressure

31.6 x 1.75 55.32 0.88 -48

14.31 x 0.88 12.52 0.58 -7.3

Total 45.82 57.66

Therefore maximum bending moment for heel slab = 57.7 kN-m

And maximum shear force for heel slab = 45.8 kN

Concrete cover = 75 mm

Hence for 16 mm main bars, effective d = 517 mm


x 106

bd2

K = Mu/bd2fcu =

312718648.xlsx - W1_h=4.00m

Mu = 1.65 x 57.7 = 0.355958

1000 x 517 ^2

lever arm, z = 491.2 mm 0.0089

As req. = 445 mm²

As min. = 900 mm²

100As,prov./ bd = 0.194451

Therefore provide T 16 200 mm c/c As, prov. = 1005.312 mm²

> As req. So O.K.

x 106

bd2

K = Mu / bd2 fcu =

312718648.xlsx - W1_h=4.00m

ProjectDOHA WEST




DW077-P00-ATK-SW-7065 AN 07 Oct 2015

Distribution steel

Provide minimum steel = 0.13%bh

= 780 mm²

Therefore provide T 16 200 mm c/c As = 1005.312 mm²

> As req. So O.K.

CHECK FOR SHEAR

Maximum shear force = 45.8 kN


1000 x 517



312718648.xlsx - W1_h=4.00m

312718648.xlsx - W1_h=4.00m

Job ref

5099998

Calc sheet no. rev

2Check by Date

Backfill above toe is ignored

mm

mm

mm

312718648.xlsx - W1_h=4.00m

312718648.xlsx - W1_h=4.00m

Job ref

5099998

Calc sheet no. rev

Check by Date

Moment

about (a)

(kN.m)

28.0

0.0

173.3

9.2

84.2

0.0

15.9

310.5

-22.5

-23.7

-46.2

264.21

312718648.xlsx - W1_h=4.00m

312718648.xlsx - W1_h=4.00m

Job ref

5090882

Calc sheet no. rev

Check by Date

kN

> As req. So O.K.

> As req. So O.K.

> As req. So O.K.

312718648.xlsx - W1_h=4.00m

312718648.xlsx - W1_h=4.00m

Job ref

5099998

Calc sheet no. rev

Check by Date

312718648.xlsx - W1_h=4.00m

312718648.xlsx - W1_h=4.00m

Job ref

5090882

Calc sheet no. rev

Check by Date

> As req. So O.K.


312718648.xlsx - W1_h=4.00m

312718648.xlsx - W1_h=4.00m

Job ref

5099998

Calc sheet no. rev

Check by Date

312718648.xlsx - W1_h=4.00m

312718648.xlsx - W2_h=2.50m

ProjectQP Culverts

Part of Structure Box Culvert

WS Atkins & Partners Overseas Wing walls design- 2.5 m Height


Uday 23 Jan 2011

Design Data for the Retaining wall considered

Wall height above footing H = 2500 mm

Top of wall thickness 500 mm

Bottom of wall thickness 500 mm

Heel length (Backfill side) 1400 mm

Toe length 500 mm

Thickness of base slab D = 500 mm

Total base slab length B = 2400 mm

Toe backfill above footing H3 = 0 mm Backfill above toe is ignored

Horizontal distance from edge of top wall to slope of soil Ds = 0 mm

Density of soil 17

Angle of repose, backfill ø = 34 Degree Degree = 0.593 Rad

Angle of repose, bearing 27.2 Degree Degree = 0.475 Rad

Backfill slope angle ß = 0.0 Degree Degree = 0.000 Rad

Density of concrete 25

Concrete grade fcu = 40 N/mm²

Reinforcement grade fy = 420 N/mm²

Soil surcharge_Live Load Surcharge Udl = 0 kN/m²

Allowable soil pressure Qall = 200 kN/m²

Load factor for Ultimate check LF = 1.65

Coefficent of friction 0.514 0.514

FOS against overturning FOS o = 1.50 1.50

FOS against sliding FOS s = 2.00

cosß - Sqrt{(cosß)² - (cosø)²}

Active earth pressure coefficient, Ka = cosß ---------------------------------------------

cosß + Sqrt{(cosß)² - (cosø)²}

Therefore Ka = 0.283

Pressure at rest coefficient, Ko (minimum 0.5) Ko = (1 - sinø) (1 + sinß) = 0.500

Selected Pressure at rest coefficient, Ko Ko = 0.500

Passive earth pressure coefficient, Kp Kp = 1 + sinø = 2.68


t1 =

t2 =

L1 =

L2 =

s = kN/m3

ø1 =

c = kN/m3

=

312718648.xlsx - W2_h=2.50m

1 - sinø

USING ACTIVE EARTH PRESSURE Ka FOR STABILITY CHECK

Height of surcharge H1 = 1.40 x tan ß = 0.00 m

Total height of soil, Hs = H + D + H1 = 3.00 m

H2 = H + H1 = 2.50 m

312718648.xlsx - W2_h=2.50m

ProjectQP Culverts




Uday 23 Jan 2011



Load due to of load from (a) about (a)

W (KN) (m) (kN.m)

Stem (W1)

0.50 x 2.50 x 25.00 31.25 0.75 23.4

0.00 x 1.25 x 25.00 0.00 0.50 0.0

Wt. of earth (W2)_above heel

1.40 x 2.50 x 17.00 59.50 1.70 101.2

0.00 x 1.40 x 17.00 0.00 1.93 0.0

Base slab (W3)

2.40 x 0.50 x 25.00 30.00 1.20 36.0

Toe backfill (W4)

0.00 x 0.50 x 17.00 0.00 0.25 0.0

0.283 x 17.00 3.00

x 0.000.00 2.40 0.0

2 Stabilizing moment <== 160.6

0.283 x 17.00 3.00

x 1.00 6 -21.6

Minus moment of surcharge, M = (Udl x Ka x Hs² /2 ) * cos(ß)

0.283 x 0.00 3.00

x 1.000.0

2 Overturning moment <== -21.6

Total 120.75 138.96

Therefore (eccentrity relative to point (a) z = 139 / 121 = 1.151 m

Eccentricity e (relative to C.G.) = B/2 - z = 0.049 m < B/6, So O.K.

Maximum and minimum pressures at the base are given by

p = W ( 1 ± 6e ) kN/m², W = 120.75 kN

B B

= 50.31 ± 6.19

p toe = 56.50 kN/m² less than 200.0 kN/m², So O.K.p heel = 44.12 kN/m², So O.K. (No tension)


= 56.500199 - 56.5002 - 44.12 x 500 = 53.92199 kN/m²

2400


= 44.124801 + 56.5002 - 44.12 x 1400 = 51.34378 kN/m²

2400

CHECK FOR OVERTURNING AND SLIDING

Factor of safety against overturning

= Stabilizing moment = 160.6 = 7.43 > 1.5 ==> So O.K.

Overturning moment 21.6

Total earth pressure + surcharge =


Vertical soil pressure, Pv =(Ka gs Hs2 /2) sin(ß)

Minus moment of soil pressure, M = {Kags*Hs3/6}*cos(ß)

P = Ka x s x Hs x Hs/2 + Udl x Ka x Hs

312718648.xlsx - W2_h=2.50m

= 21.6 + 0.00 = 21.6 kN

Therefore horizontal earth pressure = P * cos ß = 21.63 kN

Maximum available friction without surcharge weight

0.514 x 120.75 = 62.05707 kN

Factor of safety against sliding = = 2.869 > 2.0 ==> So O.K.P * cosß

= W =

* W

312718648.xlsx - W2_h=2.50m

ProjectQP Culverts




Uday 23 Jan 2011

Provide a key of 0 mm deep and 0 mm wide under the stem to increase factor of

safety against sliding. Sliding will take place along the surface at the bottom of key.

Total active pressure

where Hk = Hs + Depth of key

= 21.6 + 0.00 kN = 3.00 m

= 21.628 kN

Total weight at the bottom level of the key = W + Wt. of key + Wt. of soil

Wt = 120.750 + 0 + 0 = 120.75 kN

Total passive pressure

= 5.703299 kN

62.06 + 5.703299 = 67.76

Factor of Safety for Sliding = Fr = 3.133 > 2.00 ==> So O.K.

Pa x cosß

REINFORCEMENT DESIGN FOR STEM (USE Ko IF Ka < Ko FOR REINFORCEMENT DESIGN)

Maximum bending moment at the bottom of the stem due to earth pressure and surcharge

M = 0.5 x 17 x 2.50 ^3 + 0.00 x 1.25

6.00

= 22.1 + 0.0 = 22.1 kNm



Mu = 1.65 x 22.1 = 0.210039

1000 x 417 ^2

lever arm, z = 396.15 mm 0.0053

As req. = 252 mm²

As min. = 750 mm²


100As,prov./bd = 0.385731

Main Vertical Reinforcement For Exposed Wall

Provide minimum shrinkage and temperature steel = 0.12%bh = 600 mm²

Therefore provide T 16 125 mm c/c A's, prov. = 1608.499 mm² > As req. So O.K.

100A's,prov./bd = 0.386

Distribution steel

Provide minimum steel = 0.13%bh = 650 mm²

Therefore provide T 16 125 mm c/c As = 1608.499 mm² > As req. So O.K.

DEFLECTION CHECK - TOP OF CANTILEVER

Slenderness ratio = 2500 / 417 = 6.00

Therefore allowable = 7.00 x modification factors = 19.49 ==> So OK !


= Pa = Ka x s x Hk x Hk/2 + Udl x Ka x Hk

= Pp = Kp x s x (Depth of base slab + Depth of key)2/2

Total horizontal resisting force, Fr = x Wt + Pp

x 106

bd2

K = Mu / bd2 fcu =

312718648.xlsx - W2_h=2.50m

2.00

where fs = 122.3967 < 0.8fy So OK !

Compression reinforcement modification factor = 1+ 100A's,prov/bd/(3+ 100A's,prov/bd) = 1.11

Modification factor for triangular load = 1.25

Tension reinforcement modification factor = 0.55 + ( 477 - fs )/{120(0.9 + M/bd2)} =

312718648.xlsx - W2_h=2.50m

ProjectQP Culverts




Uday 23 Jan 2011

CURTAILMENT OF STEM REINFORCEMENT

At depth 'h' metres from top, let As be the steel required.

Effective depth = ( 417 + 0 x h )

2.5

Bending Moment = x Ko * cosß + Udl x Ko * cosß x h x h / 2

6

Mu = 1.416667 1.65 + 0 1.65

= 2.34 0

As = 2.3375 0

0.87 fy z

At depth 'h' Ult. Bending Effective Area

metres from Moment Depth Req.

top ( kN-m ) d (mm) (mm²)

0.00 0.0 417.00 750

0.25 0.0 417.00 750

0.50 0.3 417.00 750

0.75 1.0 417.00 750

1.00 2.3 417.00 750

1.25 4.6 417.00 750

1.50 7.9 417.00 750

1.75 12.5 417.00 750

2.00 18.7 417.00 750

2.25 26.6 417.00 750

2.50 36.5 417.00 750

CHECK ULTIMATE SHEAR STRESS AT BASE OF STEM (USE Ko IF Ka < Ko)

Total shear at base of stem =

= 26.56 + 0.00 = 26.56 kN


1000 x 417


DESIGN OF TOE SLAB (PRESSURE USE Ko IF Ka < Ko) _ BOTTOM STEEL

Self load of the base per metre run = 0.5 x 25 = 12.5 kN/m

The force acting on toe are pressure from soil acting upwards and self-weight acting downwards.

If Ka < Ko, then Ko will be used for pressure calculation to get the worst bending moment and shear.

W = 120.8 kN

Moment about a = 122.34 kNm

Therefore z = 122.3375 / 120.75 = 1.013147 m

Eccentricity e = B/2 - z = 0.19 m < B/6, so O.K. !

Therefore Maximum and minimum pressures at the base are given by

p = W ( 1 ± 6 e ) = 50.313 ± 23.5026 kN/m²

B B

p toe = 73.82 kN/m²


s x h3

h3 x h2 x

h3 + h2

h3 + h2

P = Ko * cosß x s x H x H/2 + Udl x Ko * cosß x H

312718648.xlsx - W2_h=2.50m

p heel = 26.81 kN/m²


= 73.815104 - 73.8151 - 26.81 x 500 = 64.02235 kN/m²

2400


= 26.809896 + 73.8151 - 26.81 x 1400 = 54.23 kN/m²

2400

312718648.xlsx - W2_h=2.50m

ProjectQP Culverts




Uday 23 Jan 2011

Therefore Maximum Bending Moment

= 64.022352 - 12.5 ) x 0.5 +

2.00

2 0.5

61.315104 - 51.5 ) x x 0.5 x

3 2.0

= 7.3 kNm



Mu = 1.65 x 7.3 = 0.077917

1000 x 392

lever arm, z = 372.4 mm 0.0019

As req. = 88 mm²

As min. = 750 mm²


100As,prov./bd = 0.341943

CHECK FOR SHEAR

Maximum shear force = 61.3151 + 51.52 x 0.5 = 28.20936 kN

2


1000 x 392


DESIGN OF THE HEEL SLAB _ TOP STEEL




Load due to of load fr. c about c

W (kN) (m) (kNm)

Wt. of earth (W2)

1.40 x 2.50 x 17.00 59.50 0.70 41.7

0.00 x 1.40 x 17.00 0.00 0.93 0.0

Wt. of heel slab (W3a)

1.40 x 0.50 x 25.00 17.50 0.70 12.3

Vertical soil pressure Pv

38.3 x 0 0.00 1.40 0.0

Deduct for upward pressure

26.8 x 1.40 37.53 0.70 -26

27.42 x 0.70 19.19 0.47 -9.0

Total 20.27 18.67

Therefore maximum bending moment for heel slab = 18.7 kN-m

And maximum shear force for heel slab = 20.3 kN

Concrete cover = 100 mm

Hence for 16 mm main bars, effective d = 392 mm


x 106

bd2

K = Mu/bd2fcu =

312718648.xlsx - W2_h=2.50m

Mu = 1.65 x 18.7 = 0.200465

1000 x 392 ^2

lever arm, z = 372.4 mm 0.0050

As req. = 226 mm²

As min. = 750 mm²

100As,prov./ bd = 0.341943

Therefore provide T 16 150 mm c/c As, prov. = 1340.416 mm²

> As req. So O.K.

x 106

bd2

K = Mu / bd2 fcu =

312718648.xlsx - W2_h=2.50m

ProjectQP Culverts




Uday 23 Jan 2011

Distribution steel

Provide minimum steel = 0.13%bh

= 650 mm²

Therefore provide T 16 150 mm c/c As = 1340.416 mm²

> As req. So O.K.

CHECK FOR SHEAR

Maximum shear force = 20.3 kN


1000 x 392



312718648.xlsx - W2_h=2.50m

312718648.xlsx - W2_h=2.50m

Job ref

5090882

Calc sheet no. rev

Check by Date

Backfill above toe is ignored

mm

mm

mm

Bowles P.712

312718648.xlsx - W2_h=2.50m

312718648.xlsx - W2_h=2.50m

Job ref

5090882

Calc sheet no. rev

Check by Date

Moment

about (a)

(kN.m)

23.4

0.0

101.2

0.0

36.0

0.0

0.0

160.6

-21.6

0.0

-21.6

138.96

312718648.xlsx - W2_h=2.50m

312718648.xlsx - W2_h=2.50m

Job ref

5090882

Calc sheet no. rev

Check by Date

kN

> As req. So O.K.

> As req. So O.K.

> As req. So O.K.

312718648.xlsx - W2_h=2.50m

312718648.xlsx - W2_h=2.50m

Job ref

5090882

Calc sheet no. rev

Check by Date

312718648.xlsx - W2_h=2.50m

312718648.xlsx - W2_h=2.50m

Job ref

5090882

Calc sheet no. rev

Check by Date

> As req. So O.K.


312718648.xlsx - W2_h=2.50m

312718648.xlsx - W2_h=2.50m

Job ref

5090882

Calc sheet no. rev

Check by Date

312718648.xlsx - W2_h=2.50m

Documents

Culvert 1