Reference List

70

Reference List

[1] Shokrieh M. M. and Rahmat M. (2006), “On the reinforcement of concrete

sleepers by composite materials”,Composite Structures, pp. 326-337.

[2] Telford T., Concrete railway sleepers, London.

[3] Taylor H. P. J. (August 1993), “The railway sleeper: 50 years of pretensioned,

prestressed concrete”, The Structural Engineeer, vol. 71.No 16/17, pp. 281-295.

[4] Sadeghi J. M. and Babaee A. (2006), “Structural Optimization of B70 Railway

Prestressed Concrete Sleepers”,Iranian Journal of Science & Technology,

Transaction B, Engineering, Vol. 30, No. B4, Printed in the Islamic Republic of Iran.

[5] Kaewunruen S. and Remennikov A. M. (2008), “Effect of a large asymmetrical

wheel burden on flexural response and failure of railway concrete sleepers in track

systems”, Engineering Failure Analysis.

[6] Standards Australia,Australian Standard AS1085.14 Railway Track Materials,

Part 14: Railway Prestressed Concrete Sleepers, Australia, 2003.

[7] Agro R. (1986) Railway Track Engineering,Delhi,Khanna Publishers.

[8] Gupta B. L. (1982) Text Book of Railway Engineering, Delhi, Standards

Publishers.

[9] De Silva P. (December 2007), Air, Maritime and rail Transportation in Sri

Lanka, Centenary commemoration Publications.

[10] http://www.railwaymuseum.lk/[accessed on 20/05/2012]

[11] Kaewunruen S. and Remennikov A. M. (2008), “Reliability Assessment of

Railway Prestressed Concrete Sleepers”,Australian Structural Engineering

Conference (ASEC), 26-27 June 2008, Melbourne, Australia.

[12] Manalo A., Aravinthan T., Karunasena W. and Ticoalu A. (2010), “A Review of

alternative materials for replacing existing timber sleepers”,composite structures, pp

603-611.

[13] Manual of special rules railways: Part1, Permanent Way, Way and works

Department, 4th ed. State Printing Corporation, 2004.

[14] Mundrey J. S. (2000), Railway trackEngineeering. Tata McGraw-Hill

Publishing Company Limited, New Delhi.

[15] Kaewunruen S. and Remennikov A. M. (2009), “Impact capacity of railway

prestressed concrete sleepers”, Engineering Failure Analysis.

http://www.railwaymuseum.lk/

71

[16] Remennikov A. M., Murray M. H. and Kaewunruen S. (2007), Conversion of

AS 1085.14 for prestressed concrete sleepers to limit states design format, Sydney.

[17] Kaewunruen S. and Remennikov A. (2006), “Rotational capacity of railway

prestressed concrete sleeper under static hogging moment”, The tenth East Asia-

Pacific Conference on Structural Engineering and construction, August 3-5, 2006,

Bankok, Thailand.

[18] Kaewunruen S. and Remennikov A. M. (2006), “Sensitivity analysis of free

vibration characteristics of an in situ railway concrete sleeper to variations of rail pad

parameters”, Journal of Sound and Vibration, pp. 453-461.

[19] www.railway.gov.lk[accessed on 20/05/2012]

http://www.railway.gov.lk/

72

Appendix 1: Prestressed concrete sleeper produced at Ekala with grade 50 N/mm2

concrete

73

Table of Contents

1.0 Notation

2.0 Design Criteria

2.1 Design codes and manuals

2.2 Design loads

2.3 Design velocity

2.4 Design life

2.5 Track details

2.6 Material properties

2.6.1 Concrete

2.6.2 Prestressing steel

3.0 Calculations

3.1 Analysis of the concrete sections

3.1.1 Section at rail seat

3.1.2 Area of the section

3.1.3 Centre of Gravity

3.1.4 Moment of inertia

3.1.5 Section modulus

3.1.6 Section at sleeper centre





3.2 Load calculations

3.2.1 Load calculations according to AS 1085.14 - 2003

3.2.2 Sleeper design bending moments

3.3 Permissible stresses

3.3.1 Stress at transfer

3.3.2 Stress at service

3.4 Adequacy of the section

3.5 Basic equations for rail seat

3.5.1 Positive bending moment

3.5.2 Negative bending moment

3.6 Basic equations for rail centre



3.7 Number of tendons

3.8 Possible tendon arrangement

3.9 Losses

3.9.1 Losses at transfer stage

3.9.2 Losses at service stage

3.9.3 Total prestress loss

74

1.0 Notation

A - Sectional area of sleeper

Aps - Area of tendons

e - Eccentricity (Measured upward from the Neutral Axis)

Es - Modulus of elasticity of steel

Ec - Modulus of elasticity of concrete

fci - Concrete strength at transfer

fpu - Characteristic strength of prestressing tendons

fb - Stress at bottom fibre

ft - Stress at top fibre

I - Second moment of area

Md - Bending moment (BM) due to self weight of sleeper

MR+ - Positive BM (bottom fibres are under tension) at the rail seat

MR- - Negative BM (bottom fibres are under compression) at the rail seat

MC+ - Positive BM (bottom fibres are under tension) at the mid span of the sleeper

MC- - Negative BM (bottom fibres are under compression) at the mid span of the

sleeper

Yb - Distance to the bottom most fibre from neutral axis

Yt - Distance to the top most fibre from neutral axis

Zt - Sectioanl modulus of the top fibre of sleeper

Zb - Sectioanl modulus of the bottom fibre of sleeper

P - Prestressing force in the tendon at the jacking end

yst - Centre of prestressing force

75

2.0 Design Criteria


AS 1085.14-2003 Railway Track Material, Prestressed Concrete

Sleepers

BS 8110 Part 1-1985 : Structural use of concrete, Code of practice

for Design and construction

BS 5896-1980: Specification for High Tensile Steel Wire and

Strand for Prestressing of Concrete

BS 5400-Part 4-1990: Steel, Concrete and Composite Bridges,

Code of Practice for Design of Concrete Bridges

2.2 Design loads

Axle load - 200 kN

Combined vertical design load factor - 2.5 (Clause 4.2.1.3 and

Appendix F of AS 1085.14 - 2003)

2.3 Design velocity

Maximum train velocity - 80 km/h (F4 of AS 2003.14 - 2003)

2.4 Design life

Design life - 50 years

2.5 Track details

Rail type - Rails are assumed heavier than 47 kg/m

Gauge - 1676 mm

Sleeper spacing - 600 mm


2.6.1 Concrete

Compressive strength at 28 days = 50 N/mm2

Compressive strength at load transfer = 25 N/mm2

Density = 24 kN/m3

Modulus of elasticity = 34 kN/mm2

2.6.2 Pre stressing steel

Cold – drawn wire, Relaxation class 2.

Nominal tensile strength = 1670 N/mm2

Tendon diameter = 5 mm

Tendon area = 4

52=19.63 mm2

76

Initial pre stressing force per tendon = 310

75.06.191670

=24.58 kN

Number of tendons per sleeper = 14

Modulus of elasticity = 205 10 kN/mm2

77

Reference Calculations Out put

3.0 Calculations



Figure 1: Dimensions at rail seat

a = 200 mm

b = 250 mm

h = 225 mm


A = 2

)( bah

= 50625 mm2


Yb = )(

)2(

3 ba

bah

= 108.3 mm

Yt = h - Yb = 116.7 mm


I = )(

)4(

36

223

ba

babah

= 212.69 x 106 mm4


Zt = tY

I= 1.822 x 106 mm3

Zb = bY

I= 1.963 x 106 mm3


Figure 2: Dimensions at rail centre

A=50625

mm2

Yb=108.3

mm

Yt=116.7

mm

I=212.69

x106mm4

Zt= 1.822

x106mm3

Zb=1.963

x106mm3

78

4.2.1.4 &

F4 of AS

1085.14

Figure

4.1of AS

1085.14

4.3 of AS

1085.14

Table 4.2

of AS

1085.14

a = 207 mm

b = 250 mm

h = 195 mm


A = 2

)( bah

= 44557 mm2


Yb = )(

)2(

3 ba

bah

= 94.4 mm

Yt = h - Yb = 100.6 mm


I = )(

)4(

36

223

ba

babah

= 140.77 x 106 mm4


Zt = tY

I= 1.399 x 106 mm3

Zb = bY

I= 1.49 x 106 mm3



Combined design load factor = 2.5

Distribution factor, DF = 0.51

Rail seat load, R = 100

DFQj

= 1002

51.02005.2

= 127.5 kN


MR+ = 8

)( gLR =

8

)75.1792.2(5.127 = 16.6 kNm

MR- = 0.67MR+ (>14) = 11.12 (>14) = 14.0 kNm

A=44557

mm2

Yb=94.4

mm

Yt=100.6

mm

I=140.77

x106mm4

Zt= 1.399

x106mm3

Zb=1.49

x106mm3

R=127.5

kN

MR+=16.

6 kNm

MR-=14.0

kNm

79

BS 8110:

Part 1

BS 5896

Table 6

BS 8110:

Part 1

Clause

4.8.5.2

MC+ = 0.05 )( gLR = 0.05 )75.1792.2(5.127

= 6.64 kNm

MC- = 8

)2()(5.0

2LgWgLWgRg

W = )23(

4

gL

R

=

)75.12792.23(

5.1274

= 104.6 kN/m

MC- = 12.91 kNm


fc = 50 N/mm2

fcp = 25 N/mm2


fa,maxt = 0.5 fcp = 25 N/mm2

fa,mint = 0


fa,max = 0.45 f’c = 22.5 N/mm2

fa,min = -0.4 (f’c)0.5 = -2.83 N/mm2


min,max,

,aa

RRbt

ff

MMZZ

)83.2(5.22

10)146.16(,

6

bt ZZ

Zt, Zb > 1.208 x 106 mm3

Zt actual = 1.399 x 106 mm3 > 1.208 x 106 mm3 OK

Zb actual = 1.49 x 106 mm3 > 1.208 x 106 mm3 OK

MC+=6.6

4 kNm

MC-=12.9

kNm

Section

is OK

80



A

Pe t

e

Z

eP .

t

R

Z

M

_ +

+ _

A

Pe b

e

Z

eP .

b

R

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .-

b

R

Z

M fa,min

Rab

b

MfZ

eAZ

Pe min,

/1

Substitute the suitable values;

66

6

106.16)83.2(10963.1

50625/)10963.1(1

e

Pe

ePe

06.9351101 8

(RS PB)

Top Fibre

A

Pe - t

e

Z

eP .+

t

R

Z

M fa,max

Rat

b

MfZ

eAZ

Pe min,

/1


66

6

106.165.2210822.1

50625/)10822.1(1

e

Pe

ePe

09.45.147101 8

(RS PT)

+

81


A

Pe t

e

Z

eP .

t

R

Z

M

_ _

+ +

A

Pe b

e

Z

eP .

b

R

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .+

b

R

Z

M fa,max

Rab

b

MfZ

eAZ

Pe max,

/1


66

6

100.145.2210963.1

50625/)10963.1(1

e

Pe

ePe

31.3128101 8

(RS NB)

Top Fibre

A

Pe - t

e

Z

eP .-

t

R

Z

M fa,min

Rat

t

MfZ

eAZ

Pe min,

/1


66

6

100.14)83.2(10822.1

50625/)10822.1(1

e

Pe

ePe

31.110.407101 8

(RS NT)

+

82



A

Pe t

e

Z

eP .

t

C

Z

M

_ +

+ _

A

Pe b

e

Z

eP .

b

C

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .-

b

C

Z

M fa,min

Cab

b

MfZ

eAZ

Pe min,

/1


66

6

1064.6)83.2(10491.1

44557/)10491.1(1

e

Pe

ePe

57.491659101 8

(RC PB)

Top Fibre

A

Pe - t

e

Z

eP .+

t

C

Z

M fa,max

Cat

b

MfZ

eAZ

Pe max,

/1


66

6

1064.65.2210399.1

44557/)10399.1(1

e

Pe

ePe

21.38.100101 8

(RC PT)

+

83


A

Pe t

e

Z

eP .

t

C

Z

M

_ _

+ +

A

Pe b

e

Z

eP .

b

C

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .+

b

R

Z

M fa,max

Cab

b

MfZ

eAZ

Pe max,

/1


66

6

1091.125.2210491.1

44557/)10491.1(1

e

Pe

ePe

65.33.122101 8

(RC NB)

Top Fibre

A

Pe - t

e

Z

eP .-

t

C

Z

M fa,min

Cat

t

MfZ

eAZ

Pe min,

/1


66

6

1091.12)83.2(10399.1

44557/)10399.1(1

e

Pe

ePe

67.115.366101 8

(RC NT)

Draw combined Magnel diagram using equations. Effective

prestressing force can be calculated using Magnel diagram.

+

84

Figure 3: Combined Magnel diagram for prestressed

concrete sleepers produced at Ekala with grade 50 N/mm2

concrete

According to the combined Magnel diagram;

375101

max

8

eP at e=2.85 mm

267375

101 8

eP

Pe = 267 kN


Diameter of a tendon = 5 mm

Area per prestressing tendon = 4

52= 19.63 mm2


Initial prestressing force per tendon

=310

75.063.191670 = 24.58 kN

Effective prestressing force (15% losses)

= 85.085.24 =20.89 kN

Number of tendonss required =89.20

267= 12.78 Nos.

= 14 Nos.

Because of the symmetry 14 nos. of tendons to be used.

Therefore number of tendons can be reduced to 14 with

grade 50 N/mm2 concrete. It is clear that it can be further

reduced with grade 60 N/mm2 concrete.

e=2.85

mm

Pe=267

kN

Tendons

14 Nos.

0

100

200

300

400

500

600

700

-60 -40 -20 0 20 40 60

1x108/Pe(N)

e(mm)

RS PB RS NB RS PT RS NT

RC PB RC NB RC PT RC NT

85

Limiting range for ‘e’ value

Rail seat; -0.5<e<5.5

Rail centre; -25<e<1.0


Figure 4: Possible tendon arrangement (i) Rail seat, (ii) Rail

centre

Centre of prestressing tendons - yst

From Figure 4;

15521259565414 sty

mmyst 57.103

Centre of tendons are within the limiting range for ‘e’ value.

Figure 5: Centre of prestressing tendons

3.9 Losses


Elastic deformation loss

% load apply to prestress = 75%

Number of bars = 14

Initial prestressing force psyi AfnP

= 310

63.1916701475.0 = 344 kN

Concrete stress, I

eP

A

Pf i

c

icoj

2

yst=103.5

7 mm

86

I = 212695369 mm4

e = 108.33-106.42 = 1.91 mm

Ac = 50625 mm2

212695369

91.110344

50625

10344 233

cojf = 6.795 + 0.006

= 6.801 N/mm2

At the level of steel;

Strain in concrete = strain in steel

s

ps

c

coj

E

f

E

f

)7(

coj

c

sps f

E

Ef

)7(

Es = 195 kN/mm2

Ec(7) = 36 kN/mm2

Loss of prestress = psps Af

= 801.636

195 = 36.83 N/mm2

Percentage loss = %10010344

1463.1983.363

= 2.94%


Shrinkage loss

Shrinkage strain = ɛs = 610100

Loss of prestress = sps EA s

= )10195()1463.19()10100( 36 = 5359 N


53593

= 1.56%

Loss due to relaxation

Maximum relaxation after 1000h = 3.5 %

Relaxation factor = 1.2

Loss due to relaxation = 2.1100

96

100

5.3 iP

= 2.1100

9610344

100

5.3 3 = 13870 N


138703

= 4.03%

Loss due to creep of concrete

Creep coefficient = ϕ = 1.8

Specific creep strain )7(c

ccE

31036

8.1

87

= 5100.5 mm

Loss of stress in steel = pscoj Ef cc

I

eP

A

Pf i

c

icoj

2

= 6.801 N/mm2

= )10195(801.6)100.5( 35 = 66.31 N/mm2

Loss due to creep = 1463.1931.66 = 18223 N


182233

= 5.29%


Total prestress loss = Elastic deformation loss + Loss due to

shrinkage + Loss due to relaxation of steel + Loss due to

creep of concrete = (2.94 + 1.56 + 4.03 + 5.29)% = 13.82 %

= 15.0 % (say)

Total

losses

15%

88


88

Appendix 2: Prestressed concrete sleeper produced at Ekala with grade 60 N/mm2

concrete

89

Table of Contents

1.0 Notation

2.0 Design Criteria


2.2 Design loads

2.3 Design velocity

2.4 Design life

2.5 Track details


2.6.1 Concrete


3.0 Calculations



























3.9 Losses




90

1.0 Notation
















sleeper







91

2.0 Design Criteria



Sleepers







2.2 Design loads

Axle load - 220 kN


Appendix F of AS 1085.14 - 2003)

2.3 Design velocity


2.4 Design life


2.5 Track details


Gauge - 1676 mm



2.6.1 Concrete



Density = 24 kN/m3






92

Tendon area = 4

52=19.63 mm2


75.06.191670 =24.58 kN



93


3.0 Calculations




a = 200 mm

b = 250 mm

h = 225 mm


A = 2

)( bah

= 50625 mm2


Yb = )(

)2(

3 ba

bah

= 108.3 mm

Yt = h - Yb = 116.7 mm


I = )(

)4(

36

223

ba

babah

= 212.69 x 106 mm4


Zt = tY

I= 1.822 x 106 mm3

Zb = bY

I= 1.963 x 106 mm3



A=50625

mm2

Yb=108.3

mm

Yt=116.7

mm

I=212.69

x106mm4

Zt=1.822

x106mm3

Zb=1.963

x106mm3

94

4.2.1.4 &

F4 of AS

1085.14

Figure

4.1of AS

1085.14

4.3 of AS

1085.14

Table 4.2

of AS

1085.14

a = 207 mm

b = 250 mm

h = 195 mm


A = 2

)( bah

= 44557 mm2


Yb = )(

)2(

3 ba

bah

= 94.4 mm

Yt = h - Yb = 100.6 mm


I = )(

)4(

36

223

ba

babah

= 140.77 x 106 mm4


Zt = tY

I= 1.399 x 106 mm3

Zb = bY

I= 1.49 x 106 mm3


3.2.1 Load calculations according to AS 1085.14: 2003




DFQj

= 1002

51.02205.2

= 140.25 kN


MR+ = 8

)( gLR =

8

)75.1792.2(25.140 = 18.32 kNm

MR- = 0.67MR+ (>14) = 11.12 (>14) = 14.0 kNm

A=44557

mm2

Yb=94.4

mm

Yt=100.6

mm

I=140.77

x106mm4

Zt=1.399

x106mm3

Zb=1.49x

106mm3

R=140.3

kN

MR+=18.

3 kNm

MR=14.0

kNm

95

BS 8110:

Part 1

BS 5896

Table 6

BS 8110:

Part 1

Clause

4.8.5.2

MC+ = 0.05 )( gLR = 0.05 )75.1792.2(25.140

= 7.33 kNm

MC- = 8

)2()(5.0

2LgWgLWgRg

W = )23(

4

gL

R

=

)75.12792.23(

25.1404

= 114.84 kN/m

MC- = 14.15 kNm


fc = 60 N/mm2

fcp = 30 N/mm2



fa,mint = 0


fa,max = 0.45 f’c = 27.0 N/mm2

fa,min = -0.4 (f’c)0.5 = -3.1 N/mm2


min,max,

,aa

RRbt

ff

MMZZ

)1.3(0.27

10)143.18(,

6

bt ZZ

Zt, Zb > 1.074 x 106 mm3


Zb actual = 1.49 x 106 mm3 > 1.074 x 106 mm3 OK

MC+=7.3

3 kNm

MC=14.2

kNm

Section

is OK

96



A

Pe t

e

Z

eP .

t

R

Z

M

_ +

+ _

A

Pe b

e

Z

eP .

b

R

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .-

b

R

Z

M fa,min

Rab

b

MfZ

eAZ

Pe min,

/1


66

6

1032.18)1.3(10963.1

50625/)10963.1(1

e

Pe

ePe

18.8317101 8

(RS PB)

Top Fibre

A

Pe - t

e

Z

eP .+

t

R

Z

M fa,max

Rat

b

MfZ

eAZ

Pe min,

/1


66

6

1032.180.2710822.1

50625/)10822.1(1

e

Pe

ePe

24.35.116101 8

(RS PT)

+

97


A

Pe t

e

Z

eP .

t

R

Z

M

_ _

+ +

A

Pe b

e

Z

eP .

b

R

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .+

b

R

Z

M fa,max

Rab

b

MfZ

eAZ

Pe max,

/1


66

6

100.140.2710963.1

50625/)10963.1(1

e

Pe

ePe

56.239.99101 8

(RS NB)

Top Fibre

A

Pe - t

e

Z

eP .-

t

R

Z

M fa,min

Rat

t

MfZ

eAZ

Pe min,

/1


66

6

100.14)1.3(10822.1

50625/)10822.1(1

e

Pe

ePe

97.110.431101 8

(RS NT)

+

98



A

Pe t

e

Z

eP .

t

C

Z

M

_ +

_

+

A

Pe b

e

Z

eP .

b

C

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .-

b

C

Z

M fa,min

Cab

b

MfZ

eAZ

Pe min,

/1


66

6

1033.7)1.3(10491.1

44557/)10491.1(1

e

Pe

ePe

9.361236101 8

(RC PB)

Top Fibre

A

Pe - t

e

Z

eP .+

t

C

Z

M fa,max

Cat

b

MfZ

eAZ

Pe max,

/1


66

6

1033.70.2710399.1

44557/)10399.1(1

e

Pe

ePe

28.31.103101 8

(RC PT)

+

99


A

Pe t

e

Z

eP .

t

C

Z

M

_ _

+ +

A

Pe b

e

Z

eP .

b

C

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .+

b

R

Z

M fa,max

Cab

b

MfZ

eAZ

Pe max,

/1


66

6

1015.140.2710491.1

44557/)10491.1(1

e

Pe

ePe

83.30.128101 8

(RC NB)

Top Fibre

A

Pe - t

e

Z

eP .-

t

C

Z

M fa,min

Cat

t

MfZ

eAZ

Pe min,

/1


66

6

1015.14)1.3(10399.1

44557/)10399.1(1

e

Pe

ePe

19.100.320101 8

(RC NT)



+

100

Figure 3: Combined Magnel diagram for prestressed

concrete sleepers produced at Ekala with grade 60 N/mm2

concrete and axle load of 22 tonnes


361101

max

8

eP at e = +5.5 mm

277361

101 8

eP

Pe = 277 kN




52= 19.63 mm2



=310

75.063.191670 = 24.58 kN


= 85.085.24 =20.89 kN

Number of tendons required =89.20

277= 13.25 Nos.

= 14 Nos.

e=5.5

mm

Pe=277

kN

Tendons

14 Nos.

0

100

200

300

400

500

600

700

-60 -40 -20 0 20 40 60

1x108/pe(N)

e(mm)

RS PB RS NB RS PT RS NT

RC PB RC NB RC PT RC NT

101

Even though the number of tendons are 13.25, 14 nos. to be

provided because of the symmetry of the section. Therefore

axle load can be increased to 22 tonnes for the sleepers

produced at Ekala site with reduced number of tendons and

with grade 60 N/mm2 concrete.


Rail seat; 4<e<7

Rail centre; -24<e<-2.5


Figure 4: Possible tendon arrangement (i) Rail seat, (ii) Rail

centre

Centre of prestressing tendons - yst

From Figure 4;

15521259565414 sty

mmyst 57.103

Centre of prestressing tendons are within the limiting range

for ‘e’ value.


3.9 Losses




Number of bars = 14

yst=103.5

7 mm

102


= 310

63.1916701475.0 = 344 kN

Concrete stress, I

eP

A

Pf i

c

icoj

2

I = 212695369 mm4

e = 4.91 mm

Ac = 50625 mm2

212695369

91.410344

50625

10344 233

cojf = 6.795 + 0.039

= 6.83 N/mm2



s

ps

c

coj

E

f

E

f

)7(

coj

c

sps f

E

Ef

)7(

Es = 195 kN/mm2

Ec(7) = 36 kN/mm2


Loss of stress = 83.636

195 = 36.99 N/mm2


1463.1999.363

= 2.96%


Shrinkage loss



= )10195()1463.19()10100( 36 = 5359 N


53593

= 1.56%





96

100

5.3 iP

= 2.1100

9610344

100

5.3 3 = 13870 N

Percentage loss= %10010344

138703

= 4.03%

103




ccE

31036

8.1

= 5100.5 mm


I

eP

A

Pf i

c

icoj

2

= 6.83 N/mm2

= )10195(83.6)100.5( 35 = 66.59 N/mm2



183003

= 5.32%


Total prestress loss = Elastic deformation loss + Loss due to



= 15.0 % (say)

Total

losses

15%

104


104

Appendix 3: Optimized pre stressed concrete sleeper – Option 1

105

Table of Contents

1.0 Notation

2.0 Design Criteria


2.2 Design loads

2.3 Design velocity

2.4 Design life

2.5 Track details


2.6.1 Concrete


3.0 Calculations



























2.9 Losses




106

1.0 Notation
















sleeper







107

2.0 Design Criteria



Sleepers







2.2 Design loads

Axle load - 200 kN


Appendix F of AS 1085.14-2003)

2.3 Design velocity


2.4 Design life


2.5 Track details


Gauge - 1676 mm



2.6.1 Concrete



Density = 24 kN/m3






108

Tendon area = 4

52=19.63 mm2


75.06.191670

=24.58 kN



109


2.0 3.0 Calculations for Option 1




a = 150 mm

b = 160 mm

c = 240 mm

h1 = 110 mm

h2 = 90 mm


2

)(11

bahA

=17050 mm2

2

)(22

cbhA

=18000 mm2

A = 21 AA = 35050 mm2


ba

bahhY

)2(121 =144.4 mm

)(

)2(

3

22

cb

cbhY

=42 mm

Yb = A

YAYA )2211( = 91.82 mm

Yt = bYhh )21( = 108.18 mm


I1 = )(

)4(

36

1 223

ba

babah

= 17.18 x 106 mm4

I 2= )(

)4(

36

2 223

cb

cbcbh

= 11.99 x 106 mm4

A=35050

mm2

Yb=91.82

mm

Yt=108.2

mm

110

I=22

21 )2(2)1(1)( YYAYYAII bb =121.00 x 106 mm4


Zt = tY

I= 1.12 x 106 mm3

Zb = bY

I= 1.32 x 106 mm3



a = 150 mm

b = 160 mm

c = 220 mm

h1 = 105 mm

h2 = 90 mm


2

)(11

bahA

=16275 mm2

2

)(22

cbhA

=17100 mm2

A = 21 AA = 33375 mm2


ba

bahhY

)2(121 =141.94 mm

)(

)2(

3

22

cb

cbhY

=42.63 mm

Yb = A

YAYA )2211( = 91.06 mm

Yt = bYhh )21( = 103.94 mm

I=121.00

x106 mm4

Zt=1.12x

106 mm3

Zb=1.32x

106 mm3

A =33375

mm2

Yb=91.06

mm

Yt=103.9

4 mm

111

4.2.1.4 &

F4 of AS

1085.14

Figure

4.1of AS

1085.14

4.3 of AS

1085.14

Table 4.2

of AS

1085.14


I1 = )(

)4(

36

1 223

ba

babah

= 14.94 x 106 mm4

I 2= )(

)4(

36

2 223

cb

cbcbh

= 11.44 x 106 mm4

I=22

21 )2(2)1(1)( YYAYYAII bb =108.62 x 106 mm4


Zt = tY

I= 1.045 x 106 mm3

Zb = bY

I= 1.193 x 106 mm3


3.2.1 Load calculations according to AS 1085.14: 2003




DFQj

= 1002

51.02005.2

= 127.5 kN


MR+ = 8

)( gLR =

8

)75.1792.2(5.127 = 16.6 kNm

MR- = 0.67MR+ (>14) = 11.12 (>14) = 14.0 kNm

MC+ = 0.05 )( gLR = 0.05 )75.1792.2(5.127

= 6.64 kNm

MC- = 8

)2()(5.0

2LgWgLWgRg

W = )23(

4

gL

R

=

)75.12792.23(

5.1274

= 104.6 kN/m

MC- = 12.91 kN

I =108.62

x106 mm4

Zt=1.045

x106 mm3

Zb=1.193

x106 mm3

R = 127.5

kN

MR+=16.6

kNm

MR- =14.0

kNm

MC+=6.64

kNm

MC-=12.9

kNm

112

BS 8110:

Part 1

BS 5896

Table 6

BS 8110:

Part 1

Clause

4.8.5.2


fc = 60 N/mm2

fcp = 30 N/mm2



fa,mint = 0


fa,max = 0.45 f’c = 27.0 N/mm2

fa,min = -0.4 (f’c)0.5 = -3.1 N/mm2


min,max,

,aa

RRbt

ff

MMZZ

)1.3(0.27

10)146.16(,

6

bt ZZ

Zt, Zb > 1.018 x 106 mm3


Zb actual = 1.073 x106 mm3 > 1.018 x 106 mm3 OK

Section is

OK

113



A

Pe t

e

Z

eP .

t

R

Z

M

_ +

+ _

A

Pe b

e

Z

eP .

b

R

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .-

b

R

Z

M fa,min

Rab

b

MfZ

eAZ

Pe min,

/1


66

6

106.16)1.3(1032.1

35050/)1032.1(1

e

Pe

ePe

0.8301101 8

(RS PB)

Top Fibre

A

Pe - t

e

Z

eP .+

t

R

Z

M fa,max

Rat

b

MfZ

eAZ

Pe min,

/1


66

6

106.160.271012.1

35050/)1012.1(1

e

Pe

ePe

33.70.234101 8

(RS PT)

+

114


A

Pe t

e

Z

eP .

t

R

Z

M

_ _

+ +

A

Pe b

e

Z

eP .

b

R

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .+

b

R

Z

M fa,max

Rab

b

MfZ

eAZ

Pe max,

/1


66

6

100.140.271032.1

35050/)1032.1(1

e

Pe

ePe

62.4174101 8

(RS NB)

Top Fibre

A

Pe - t

e

Z

eP .-

t

R

Z

M fa,min

Rat

t

MfZ

eAZ

Pe min,

/1


66

6

100.14)1.3(1012.1

35050/)1012.1(1

e

Pe

ePe

5.90.303101 8

(RS NT)

+

115



A

Pe t

e

Z

eP .

t

C

Z

M

_ +

+ _

A

Pe b

e

Z

eP .

b

C

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .-

b

C

Z

M fa,min

Cab

b

MfZ

eAZ

Pe min,

/1


66

6

1064.6)1.3(10193.1

33375/)10193.1(1

e

Pe

ePe

0.341215101 8

(RC PB)

Top Fibre

A

Pe - t

e

Z

eP .+

t

C

Z

M fa,max

Cat

b

MfZ

eAZ

Pe max,

/1


66

6

1064.60.2710045.1

33375/)10045.1(1

e

Pe

ePe

63.40.145101 8

(RC PT)

+

116


A

Pe t

e

Z

eP .

t

C

Z

M

_ _

+ +

A

Pe b

e

Z

eP .

b

C

Z

M

Bottom Fibre

A

Pe + b

e

Z

eP .+

b

R

Z

M fa,max

Cab

b

MfZ

eAZ

Pe max,

/1


66

6

1091.120.2710193.1

33375/)10193.1(1

e

Pe

ePe

18.52.185101 8

(RC NB)

Top Fibre

A

Pe - t

e

Z

eP .-

t

C

Z

M fa,min

Cat

t

MfZ

eAZ

Pe min,

/1


66

6

1091.12)1.3(10045.1

33375/)10045.1(1

e

Pe

ePe

3.100.324101 8

(RC NT)



+

117

Figure 3: Combined Magnel diagram for option 1


314101

max

8

eP at e=0.0 mm

318314

101 8

eP

Pe = 318 kN




52= 19.63 mm2



=310

75.063.191670 = 24.58 kN


= 80.085.24 =20.89 kN

Number of tendons required =88.19

318= 15.99 Nos.

= 16 Nos.

Because of the symmetry 16 nos. of tendons to be used for

option 1.

e=0.0

mm

Pe=318

kN

Tendons

16 Nos.

0

100

200

300

400

500

600

-60 -40 -20 0 20 40 60

1x108/Pe(N

)

e(mm)

RS PB RS NB RS PT RS NTRC PB RC NB RC PT RC NT

118


Rail seat; 0<e<0.5

Rail centre; -27<e<2.0


Figure 4: Possible tendon arrangement(i) Rail seat, (ii) Rail

centre

Centre of prestressing tendons – yst

From Figure 2;

5.1365.1065.765.46416 sty

mmyst 5.91

Centre of prestressing tendons are within the limiting range

for ‘e’ value.


3.9 Losses




Number of bars = 16


= 310

63.1916701675.0 = 393.4 kN

yst=91.5

mm

119

Concrete stress, I

eP

A

Pf i

c

icoj

2

I = 121003519 mm4

e = 91.82-91.5 = 0.32 mm

Ac = 35050 mm2

121003519

32.0104.393

35050

104.393 233

cojf = 11.22 + 0.00033

= 11.22 N/mm2



s

ps

c

coj

E

f

E

f

)7(

coj

c

sps f

E

Ef

)7(

Es = 195 kN/mm2

Ec(7) = 36 kN/mm2


= 22.1136

195 = 60.77 N/mm2

Percentage loss = %100104.393

1663.1977.603

= 4.85%


Shrinkage loss



= )10195()1663.19()10100( 36 = 6124 N


61243

= 1.56%





96

100

5.3 iP

= 2.1100

96104.393

100

5.3 3 = 15862 N

Percentage loss= %100104.393

158623

= 4.03%



120


ccE

31036

8.1

= 5100.5 mm


I

eP

A

Pf i

c

icoj

2

= 11.22 N/mm2

= )10195(22.11)100.5( 35 = 109.4 N/mm2



343603

= 8.73%


Total prestress loss= Elastic deformation loss + Loss due to



= 20.0 % (say)

Total

losses

20%

121


121

Appendix 4: Cost calculation for Option 1

122

Table of Contents

1.0 Introduction - Option 1

2.0 Cost calculation for option 1

2.1 Volume of sleeper

2.2 Cost of concrete per kilometre

2.3 Volume of prestressing wires per sleeper

2.4 Volume of prestressing tendons per sleeper

2.5 Volume of ballast per kilometre

2.6 Cost of ballast per kilometre

2.7 Total cost per one kilometre

123


1.0 Introduction - Option 1

For the comparison purpose three options were selected. The

most economical design was selected and calculations

presented.

2.0 Cost calculation for option 1

2.1 Volume of sleeper

Figure 1: Elevation and sections for option 1

Figure 2: Elevation with prestressing tendons for option 1

Length of the sleeper = 2.792 m

Sleeper spacing = 600 mm

Area of the sleeper at rail seat = 35050 mm2

Area of the sleeper at rail centre = 33375 mm2

Volume of sleeper =

26102

333753505052135050

+ 53033375

=61095.95 mm3

=0.095 m3

Sleeper

volume

0.095m3

124

2.2 Cost of concrete per kilometre

Density of concrete = 2400 kg/m3

Unit weight of sleeper = 095.02400

= 230.3 kg

Number of sleepers per km = 600

101000 3= 1667.67

Total weight of sleepers/km = 67.16663.230

= 383834 kg

Total volume of sleepers/km = 2400

383834= 159.93 m3

Grade of concrete = 60 N/mm2

Concrete cost per m3 = Rs 17,000

Total concrete cost/km = 000,1793.159

= Rs 2,718,825

2.3 Volume of prestressing tendons per sleeper

Figure 3: Possible tendon arrangement for option 1 (i) Rail

seat, (ii) Rail centre

Number of tendons/Sleeper = 16

Diameter of a ten = 5 mm


52= 19.63 mm2

Length of a tendon per sleeper = Length of sleeper

= 2792 mm

Volume per one tendon = 279263.19

= 54820.8mm3

2.4 Cost of prestressing steel per kilometre

Density of steel = 7850 kg/m3

Weight per tendon = 910

8.548207850

125

= 0.43 kg

Total steel weight per sleeper = 1643.0 = 6.88 kg

Total steel weight/km = 67.166688.6

= 11475.8 kg

Cost per one unit of steel = Rs 160,000

Total steel cost/km = 000,1608.11475

= Rs 1,836,128

2.5 Volume of ballast per kilometre

Figure 4: Section through ballast

Where;

G – Gauge

S – Shoulder width

L – Width of the shoulder ballast

d – Depth of the ballast

h – Total depth of the ballast

For broad gauge top width of the ballast is 3350 mm.

Assumption: Top line of the ballast section shall be at the

same level as the top of the sleeper.

Width of the base of the sleeper = 250 mm

Depth of ballast , d = 2

wS =

2

250600

= 175 (mm)

Depth of sleeper at rail seat = 200 mm

h = d + Depth of sleeper at rail seat= 175+200 = 375 mm

Width of the ballast at the base = 23753350

= 4100 mm

Area through section =

910

1375

2

41003350

= 1.396 m2

Volume per one kilometre = 1396.9 m3

Net volume per one km = 1396.9 - 159.93

= 1237 m3

126

2.6 Cost of ballast per kilometre

Cost of ballast per one m3 = Rs 2,500

Total ballast cost/km = 500,21237

= Rs 3,092,500

2.7 Total cost per one kilometre

Total cost per one kilometre =

Cost of concrete/km + Cost of steel/km + Cost of ballast/km

= Rs (2,718,825 + 1,836,128 + 3,092,500)

= Rs 7,647,453

127

Reference Out put

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