Psc Girder Design 1d5y1r

PROPERTIES FOR GRILLAGE ANALYSIS SPAN 18.571 OR say 19 m

Length of each segment =

Transverse End Crossgirder

1.1875

0.794 0.240

slab diaph

A

Yt

Ayt

Ayt2

Iself

0.1905 0.6000

0.1200 0.9900

0.0229 0.5940

0.0027 0.5881

0.0009 0.1125

0.6169

0.5908

0.1134

0.7905

1.500

0.400 Yt

=

Iz

= = = =

Ix

0.6169 = 0.7905 0.1134 + 4 0.2229 m 0.002 slab + 4 0.0284 m

0.7803 m 0.5908

-

0.6169

x

0.7803

0.027 diaph = (half for slab & full for diaph)

Intermediate Crossgirder

1.188 0.240

slab diaph

A

Yt

Ayt

Ayt2

Iself

0.2850 0.4500

0.1200 0.9900

0.0342 0.4455

0.0041 0.4410

0.0014 0.0844

0.4797

0.4451

0.0857

0.7350

1.500

0.300 Yt

=

Iz

= = = =

Ix

0.4797 = 0.7350 0.0857 + 4 0.2178 m 0.002 slab + 4 0.0140 m

0.6527 m 0.4451

-

0.4797

x

0.6527

0.012 diaph = (half for slab & full for diaph)

Slab Transverse 1.188 A Iz

= =

Ix

=

2 0.285 m 1.188 x 12 4 0.00237 m

0.240 0.240 (Half )

3

=

4 0.00137 m

Effects of Curvature Torsion due to the effects of curvature has been calculated as per the formulae in Raina. t = applied torque per unit length = w X e R = Radius of element at CL of section t' = any locally applied torque (udl or distributed over a dispersion width) T = Torsional moment as a result of M, w and t' M = Moment externally applied (including parasitic moment) W = shear w = UDL weight (self wt+SDL etc) e = r.Iyy / (R.w) ecc of the CG of the uniformly distributed self wt measured from the CL of the section r = density of the material Iyy = MI about vertical axis through CG of section. a = distance from CL of torque span to point under consideration torque span = Length of structure between points of torsional restraint.

w = Iyy = length = depth = web = width = CG bot = r = e = R = V = camber = Centrifugal force = Ecc of CF =

DL (deck slab only) SIDL 75.6 + 57.5 40.3 m4 20.5 m 1.7 m 0.3 m midspan 0.6 12.6 m 1.19 m 25.0 kN/cum 0.084 m (outward) 90 m 25 kmph 3.1% 0.055 x 1000 1.200 m (LL) + 0.5

1--1 Distance 0 Effects of Curvature Torsion due to DL & SIDL ecc due to curvature = Shear due to DL + SIDL 1364.3 Torsion = total shear x ecc 114.6 (ecc due to curvature x shear force) Torsion due to centrifugal force Coeff of centrifugal force = V.V/(127R) Distance betn CG of girder & CG of LL = torsion due to centrifugal force = (LL shear x coeff of centrifugal force x ecc)

0.055 1.7 47.8

Torsion due to Bending Moment effect = M/R

Total =

133.1 kN

m at supp

kN / m (cg top)=

2--2 0.9D 1.35

20.5 m = 1.7 m

3--3 L/8 2.321375

0.084 m 1184.6 1055.3 99.5 88.7

m 41.5

37.0

2.67 kN/m

4--4 L/4 4.64275

5--5 3L/8 6.964125

6--6 L/2 9.2855

746.3 62.7

437.3 36.7

128.4 10.8

26.1

15.3

4.5

Radius of Curvature = infinity for the straight girders

Total Additional torsion in superstr due to curvature of the deckslab Torsion in the total superstr. 162.4 141.0 Torsion per girder 5 girders = 32.48 28.20

125.6 25.12

88.8 17.77

52.1 10.41

15.3 3.06

Additional Moment due to torsion (kNm) Eq. Moment =T/1.7*(1+d/b)

100.5

71.1

41.6

12.2

74.5

64.7

Design of Post Tensioned Beam Outer Girders ALL DISTANCES ARE IN M, STRESSES IN MPA, FORCES IN KN AND MOMENTS IN KNM Tension (-) Compression (+), anti-CW (+), CW (-) 1.00 0.18 0.10 Girder Length Span of girder c/c of bearing L/D Girder overhang on bearing

19.2 m 18.571 m 10.67 0.314 m

0.300 0.20 0.24

SECTION PROPERTIES Area x from bottom distance from cg Moment Total Moment Moment I yy Total Moment Iyy PRE-CAST GIRDER Area Area * x cg. Of girder Mom of inertia Top cg Ztop Zbot

Mid span 1.000 1.000 0.600 0.600 0.180 0.180 0.240 0.000 0.300 0.600 0.280 0.237 0.440 0.000 1.500 1.500 0.240 0.240 2.650 2.650 2.650 2.325 Mid span web top flange 0.450 0.126 0.750 1.410 0.061 0.599 0.084 0.000 0.182 0.003 0.002 0.049 mid span 0.713 0.983 0.578 0.791 0.811 0.805 0.182 0.201 0.689 0.695 0.264 0.289 0.224 0.250

Composite girder Area Area * x cg. Of girder Mom of inertia Top cg Ztop Zbot Ztop girder

mid span 1.349 1.619 1.608 1.822 m2 1.192 1.125 m 0.402 0.458 m4 0.548 0.615 m 0.734 0.744 m3 0.337 0.407 m3 1.307 1.220 m3

Width of top flange(PSC) Width of bot flange(PSC) Thk of top flange Thk of bot flange Web thickness Thk of top fl at web Thk of bot fl at web Depth of girder Thickness of top slab Beff of top slab Spacing of girders Actual width of slab

(Ay)p (Ay)c

Density Concrete (kn/cu.m)

0.045 0.317

0.065 0.380

25 Girder slab

m. m. m. m. m. m. m. m. m. m.

0.60 Midspan

0.60 End(s)

1.8

1.5 Web Taper profile =MIN(spacing,12*web thk))*Eslab/Egird

Outer Girder slab

0.035 1.287 0.476 0.000

bot flange 0.072 0.120 0.691 0.000

0.039 0.000191

m2 m m4 m m3 m3

s web top flange 0.030 0.900 0.072 0.011 0.307 0.750 1.410 1.301 0.504 0.055 0.605 0.496 0.000 0.169 0.000 0.000 0.201 0.00459 0.027 0.00031 0.007 0.034 Torsional Property mid end slab 0.010 0.010 web 0.008 0.071 top fl 0.002 0.002 bot fl 0.002 0.000 Ixx = 0.022 0.083

m3 m3

fck fck

40 Mpa 40 Mpa

Ec Ec

31622.8 Mpa 31622.8 Mpa

bot flange 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0

Slab 0.636 1.620 0.428 0.003

0

(for use in staad)

Sectional Properties Section No. Section at Distance (x) Area of Girder m

1--1 2--2 0.9D 0.000 1.350

2 4

Moment of Inertia m CG of Section (bot) m

3--3 L/8 2.321

4--4 L/4 4.643

5--5 3L/8 6.964

6--6 L/2 9.286

0.983

0.983

0.889

0.713

0.713

0.713

0.201 0.805

0.201 0.805

0.194 0.807

0.182 0.811

0.182 0.811

0.182 0.811

Z bot of section m

4

0.250

0.250

0.241

0.224

0.224

0.224

Z top of section m Width of Web m

4

0.289 0.600

0.289 0.600

0.280 0.496

0.264 0.300

0.264 0.300

0.264 0.300

1.619

1.619

1.525

1.349

1.349

1.349

0.458 1.125

0.458 1.125

0.438 1.148

0.402 1.192

0.402 1.192

0.402 1.192

0.407

0.407

0.382

0.337

0.337

0.337

1.220

1.220

1.246

1.307

1.307

1.307

0.744

0.744

0.741

0.734

0.734

0.734

Area of CompositeGirder m

2

4

Moment of Inertia m CG of Section (bot) m Z bot of section m Z top of girder. m

4

4

Z top of Composite m

4

Calculation of Bending Moments due to the following at Various X n Dead Load of the PSC Girder only C/S Area of Girder .

.

. U.D.L due to Dead Load

Additional Area at End Section .

.

. U.D.L due to Dead Load

2

=

0.7

m

= =

0.7 17.8

x kN/m

=

0.983

-

25 0.713

= 0.270 x = 6.8 kN/m 24.6 kN/m

m

2

25

17.8 kN/m 0.3145

1.8

1.5

reaction of girder only = 2.1145 x + 17.8 x = 190.486 KN Section No. 1--1 2--2 3--3 Section at 0.9D L/8 Distance (x) 0 1.35 2.32 Shear (kN) 182.8 149.6 131.5 Moment(kNm) -1.2 233.5 435.2

Dead Load of the Deck Slab UDL due to Deck slab = Reaction at Section No. Section at Distance (x) Shear (kN) Moment(kNm)

2.325 m x 13.950 KN/m x

5.9855

24.6 + 5.9855 4--4 L/4 4.64 82.8 633.6

0.240 m x 9.6 m =

1.5 x

5--5 3L/8 6.96 41.4 795.7

Centreline 21.21

6--6 L/2 9.29 0.0 861.6

25 T/cum = 133.92 KN

13.95 KN/m

1--1 2--2 3--3 4--4 5--5 6--6 0.9D L/8 L/4 3L/8 L/2 0 1.35 2.32138 4.64275 6.96413 9.2855 133.9 115.1 101.5 69.2 36.8 4.4 0.0 162.2 263.1 451.0 563.8 601.4

Weight of Interm. Diaphragm = Number of intermediate diaphragms = Section No. 1--1 Shear (kN) 11.1 Moment(kNm) 0.0

1.260 X 1 2--2 11.1 15.0

3--3 11.1 25.8

0.3 => 4--4 11.1 51.6

x 2.350 x 25 = reaction = 11.1038 KN 5--5 6--6 11.1 0.0 77.3 103.1

22.21 KN

Dead Load of the Deck Slab+Diaphragms only Section No. 1--1 2--2 Section at 0.9D Distance (x) 0 1.35 Shear (kN) 145.0 126.2 Moment(kNm) 0.0 177.1 Torsion(kNm) 0.0 0.0 Super Imposed Dead Load : Section No. 1--1 2--2 Section at 0.9D Shear (kN) 280.5 232.1 Moment(kNm) 322.1 618.8 Torsion(kNm) 99.4 73.5

3--3 L/8 2.32 112.6 288.9 0.0

4--4 L/4 4.64 80.3 502.6 0.0

5--5 3L/8 6.96 47.9 641.1 0.0

6--6 L/2 9.29 4.4 704.5 0.0

(Shear & moment from staad) 3--3 4--4 5--5 L/8 L/4 3L/8 184.0 133.2 32.5 850.4 1016.1 1145.1 48.6 30.4 16.0

6--6 L/2 81.9 1108.1 37.0

Due to Curvature Effect Section No. 1--1 2--2 3--3 4--4 Section at 0.9D L/8 L/4 Shear (kN) 0.0 0.0 0.0 0.0 Moment(kNm) 74.5 64.7 100.5 71.1 Torsion(kNm) 0.0 0.0 0.0 0.0 The Effect of Live Load is taken from STAAD Results. Governing Loads due to LL with impact (From STAAD Summary) Section No. 1--1 2--2 3--3 4--4 Section at 0.9D L/8 L/4 Shear (kN) 135.6 134.0 131.7 129.7 Moment(kNm) 195.6 373.2 545.9 715.1 Torsion (kNm) 30.6 24.9 19.4 14.5

5--5 3L/8 0.0 41.6 0.0

6--6 L/2 0.0 12.2 0.0

5--5 3L/8 127.7 1212.8 12.5

6--6 L/2 126.5 1378.8 16.5

Summary of Shear & Moments at Various X ns Moment / Shear due to . 1--1 1) Dead Load of PSC Girder M -1.2 S 182.8 T 0.0

2--2 0.9d 233.5 149.6 0.0

3--3 L/8 435.2 131.5 0.0

4--4 L/4 633.6 82.8 0.0

5--5 3L/8 795.7 41.4 0.0

6--6 L/2 861.6 0.0 0.0

2) Dead Load of Deckslab

M S T

0.0 145.0 0.0

177.1 126.2 0.0

288.9 112.6 0.0

502.6 80.3 0.0

641.1 47.9 0.0

704.5 4.4 0.0

3) S.I.D.Load

M S T

322.1 280.5 99.4

618.8 232.1 73.5

850.4 184.0 48.6

1016.1 133.2 30.4

1145.1 32.5 16.0

1108.1 81.9 37.0

270.1 437.9 135.6 134.0 30.6 24.9 Moment in kNm

646.4 131.7 19.4 S

4)Vehicular Live Load +Curvature Effects

M S T M

786.2 1254.5 129.7 127.7 14.5 12.5 Shear in kN

CHECK FOR PRESTRESSING AND STRESSES Check for stresses (Stage I- stressing all cables to full design force) Horizontal Component of Cable forces at various X n .(from prestress calculations) Cable 1--1 2--2 3--3 4--4 5--5 Nos 0.9D L/8 L/4 3L/8 1 2169.2 2181.1 2195.6 2228.4 2258.4 2 1602.9 1610.4 1618.7 1637.7 1655.6 3 2217.6 2225.9 2233.9 2252.6 2270.7 Σ Force 5989.7 6017.5 6048.3 6118.7 6184.7 Vertical Component of Cable forces at various X n . Cable 1--1 2--2 Nos 0.9D 1 283.0 266.8 2 147.2 138.1 3 109.4 102.1 Σ Force 539.6 507.0

3--3 L/8 234.9 120.3 87.9 443.1

4--4 L/4 157.2 77.1 53.4 287.7

5--5 3L/8 77.4 32.9 18.3 128.7

6--6 L/2 2223.6 1600.7 2192.6 6016.9

6--6 L/2 0.0 0.0 0.0 0.0

1391.0 126.5 16.5 T Torsion in kNm

Effect of Prestressing :-

(Stage I)

Sections Force, F( KN ) Area, A(m 2 ) F/A (KN/m 2 ) Yb (m) Cable y (m) e = Yb-y (m) Zt (m 3 ) Zb (m 3 ) F x e / Zt Fxe / Zb F/A -(Fxe / Zt) F/A +(Fxe / Zt)

1--1 5989.7 0.98 6090.66 0.80 0.75 0.06 0.29 0.25 1201.77 1390.94 4.89 7.48

2--2 6017.5 0.98 6118.9 0.80 0.61 0.19 0.29 0.25 4002.93 4633.05 2.12 10.75

3--3 6048.3 0.89 6800.15 0.81 0.54 0.27 0.28 0.24 5829.89 6785.33 0.97 13.59

4--4 6118.7 0.71 8581.66 0.81 0.40 0.41 0.26 0.22 9566.49 11251.5 -0.98 19.83

5--5 6184.7 0.71 8674.18 0.81 0.32 0.49 0.26 0.22 11503 13529.1 -2.83 22.20

6--6 6016.9 0.71 8438.79 0.81 0.30 0.51 0.26 0.22 11619.4 13666 -3.18 22.10

Check for

0% loss in force

kN/m2 kN/m2 Mpa Mpa

Time Dependent Losses consisting of the following ;Losses 1 Elastic Shortening of Wires: (Vide Cl:11.1 of I.R.C:-18-2000) 0.5 x m x Stress at C.G of the Cables at that X n . Loss = It is proposed to stress the cables after 28 Days when the concrete attains 40.0 MPa. The effect of Prestress & Dead Load acts together. Descriptions Prestress Stage I Dead Load Resultant

1--1 4.89 7.48 0.00 0.00 4.88 7.49 1--1

σt σb σt σb σt σb

Sections

Stress at

2--2 2.12 10.75 0.81 -0.94 2.92 9.82 2--2

3--3 0.97 13.59 1.55 -1.81 2.52 11.78 3--3

4--4 -0.98 19.83 2.40 -2.82 1.42 17.01 4--4

5--5 -2.83 22.20 3.01 -3.55 0.19 18.66 5--5

6--6 -3.18 22.10 3.26 -3.84 0.08 18.27 6--6

4.88

2.92

2.52

1.42

0.19

0.08

0.8

0.9

1.0

1.1

1.2

1.2

the C.G of the Cables

6.19

Average stress at C.G of the X n . ∴ Loss for stage I cables Initial Stress in cables =

7.00

8.47

12.87

0.75

0.61

0.54

0.40

7.49

9.82

11.78

17.01

= = =

0.5 x 2 56.87 N/mm 2 1191.49 N/mm

10.0

x =

Losses 2 Losses from Stage I prestress to addition of Deckslab I.e., 28 days to Creep of Concrete:(Vide Cl:11.1 of I.R.C:-18-2000) 1--1 2--2 3--3 4--4 Prestress Stage I σt 4.66 2.01 0.92 -0.94 σb 7.12 10.24 12.94 18.89 Dead Load σt 0.00 0.81 1.55 2.40 σb 0.00 -0.94 -1.81 -2.82 Resultant σt 4.7 2.8 2.5 1.5 σb 7.1 9.3 11.1 16.1 Sections

1--1

Stress at the C.G of the Cables

Average stress at C.G of the X n . Concrete maturity at Concrete maturity at Creep strain during this period

14.72

14.62

0.32

0.30

18.66

18.27

2 11.37 N/mm 11.4 4.77 %

42 days 5--5 -2.69 21.14 3.01 -3.55 0.3 17.6

6--6 -3.03 21.05 3.26 -3.84 0.2 17.2

2--2

3--3

4--4

5--5

6--6

4.65

2.82

2.48

1.46

0.32

0.24

0.75

0.89

0.96

1.10

1.18

1.20

5.90

6.66

8.03

12.19

0.75

0.61

0.54

0.40

7.13

9.30

11.13

16.06

13.92

40.0 / 40 42.3 / 40 = 0.00002 /

13.81

0.32

0.30

17.60

17.21

10.08 MPa.

= 28 days = 42 days =

Loss 3

= = 10

100 % 106 % MPa.

coeff coeff

= =

0.0004 0.0004

Es

= =

195000 0.00002

x

10.08 10

(Vide Cl:11.1 of I.R.C:-18-2000) 28 days = 0.00019 42 days = 0.00018 = 0.00001 ∴ Loss = 0.00001

x

195000

∴ Loss Shrinkage of Concrete:Shrinkage coeff at age Shrinkage coeff at age Shrinkage Strain during this period

x

1.8 MPa.

=

Relaxation of H.T.Steel (Vide Cl:11.1 of I.R.C:-18-2000) Average stress in HTS = 0.6399 x UTS when stressed (after friction and slip) for stage 2 Relaxation loss for HTS for this stress = 1.7487 % Relaxation loss for HTS on 28 days means 0 hrs after stressing Relaxation loss for HTS for this period = 0.000 % of initial stress Relaxation loss for HTS on 42 days means 336 hrs after stressing Relaxation loss for HTS for this period = 1.295 % of initial stress Relaxation loss from 28 days to 42 days for stage I =( 1.295 0.000 ) x 1191 = Total Time dependent Losses 4 = for stage I cables = 4.65 + 1.8 + 15.43 = 21.85 MPa. % loss (of initial stress) = 21.85 / 1191.49 = 1.834 % Loss 2 stage I

Losses 3 Losses from addition of Deckslab till addition of SIDL I.e., 42 days to Creep of Concrete:(Vide Cl:11.1 of I.R.C:-18-2000) 1--1 2--2 3--3 4--4 Prestress Stage I σt 4.57 1.98 0.91 -0.92 σb 6.99 10.04 12.69 18.52 Dead Load σt 0.00 0.81 1.55 2.40 σb 0.00 -0.94 -1.81 -2.82 Deck Slab + Diaphragm σt 0.00 0.61 1.03 1.90 σb 0.00 -0.71 -1.20 -2.24 Resultant σt 4.6 3.4 3.5 3.4 σb 7.0 8.4 9.7 13.5 Sections

1--1

Stress at the C.G of the Cables

Average stress at C.G of the X n . Concrete maturity at Concrete maturity at Creep strain during this period

6--6 -2.97 20.64 3.26 -3.84 2.67 -3.14 3.0 13.7

3--3

4--4

5--5

6--6

3.40

3.49

3.38

2.80

2.96

0.75

0.89

0.96

1.10

1.18

1.20

6.35

7.47

10.79

0.61

0.54

0.40

6.99

8.40

9.68

13.46

11.88

42 days = 60 days = Es

42 / 40 43.89 / 40 = 0.00002 / = 195000 = 0.00002 x

(Vide Cl:11.1 of I.R.C:-18-2000) 42 days = 0.00018 60 days = 0.00017 = 0.00001 ∴ Loss = 0.00001

x

11.52

0.32

0.30

14.33

13.67

8.96 MPa.

=

∴ Loss Shrinkage of Concrete:Shrinkage coeff at age Shrinkage coeff at age Shrinkage Strain during this period

5--5 -2.64 20.74 3.01 -3.55 2.43 -2.86 2.8 14.3

2--2

5.78

15.43 MPa.

60 days

4.56

0.75

4.65 MPa.

=

195000

= = 10 8.96 10

195000

106 % 109.7 % MPa. x

coeff coeff

195000

=

= =

=

0.0004 0.0004

2.73 MPa.

2 MPa.

Relaxation of H.T.Steel (Vide Cl:11.1 of I.R.C:-18-2000) Average stress in HTS = 0.6399 x UTS when stressed (after friction and slip) for stage 1 Relaxation loss for HTS for this stress = 1.7487 % Relaxation loss for HTS on 42 days means 336 hrs stressing I Relaxation loss for HTS for this period = 1.295 % of initial stress Relaxation loss for HTS on 60 days means 768 hrs after stressing Relaxation loss for HTS for this period = 1.627 % of initial stress Relaxation loss from 42 days to 60 days for stage I =( 1.627 1.295 ) x 1191 = Total Time dependent Losses 5 =

3.95 MPa.

for stage I cables % loss (of initial stress) =

= 8.94

2.7 + / 1191.49 =

2.3

+ 0.751 %

3.95 = 8.94 MPa. Loss 3 stage I

Losses 4 Losses in prestressing from addition of SIDL to infinity 60 days to Creep of Concrete:(Vide Cl:11.1 of I.R.C:-18-2000) 1--1 2--2 3--3 4--4 5--5 Prestress Stage I σt 4.53 1.96 0.90 -0.91 -2.62 σb 6.93 9.96 12.59 18.37 20.57 Dead Load σt 0.00 0.81 1.55 2.40 3.01 σb 0.00 -0.94 -1.81 -2.82 -3.55 Deckslab+diaphragm σt 0.00 0.61 1.03 1.90 2.43 σb 0.00 -0.71 -1.20 -2.24 -2.86 SIDL σt 0.26 0.51 0.68 0.78 0.88 σb -0.79 -1.52 -2.23 -3.01 -3.40 Resultant σt 4.79 3.89 4.16 4.17 3.70 σb 6.14 6.79 7.35 10.30 10.77 Sections

1--1

Stress at the C.G of the Cables

2--2

3--3

4--4

5--5

6--6

3.89

4.16

4.17

3.70

3.83

0.75

0.89

0.96

1.10

1.18

1.20

Shrinkage of Concrete:Shrinkage coeff at age Shrinkage Strain till infinity

5.61

6.21

8.67

9.27

8.94

0.75

0.61

0.54

0.40

0.32

0.30

6.14

6.79

7.35

10.30

10.77

10.22

60 days =

∴ Loss

6--6 -2.95 20.48 3.26 -3.84 2.67 -3.14 0.85 -3.29 3.83 10.22

4.79

5.47

Average stress at C.G of the X n . Concrete maturity at Creep strain till infinity Es

infinity

= = =

= 43.89 / 0.00036 / 195000 0.00036

7.36 MPa. 40.00 = 10 MPa. x

(Vide Cl:11.1 of I.R.C:-18-2000) 60 days = 0.00018 = 0.00015 ∴ Loss = 0.00018

7.36

x 10

x

195000

109.7 %

195000

Relaxation of H.T.Steel (Vide Cl:11.1 of I.R.C:-18-2000) Relaxation loss for HTS on 60 days means 768 hrs after stressing Relaxation loss for HTS for this period = 1.627 % of initial stress Relaxation loss for HTS for 500000 hrs 5.246 % of initial stress Relaxation loss from 60 days to 500000 hrs after stressing Stage I cables =( 5.246 1.627 ) x 1191 Total Time dependent Losses 4 (I)= % loss (of initial stress) for stage I= Summary of Losses at mid span Values in % of initial stress Stage I Instantaneous Losses cables Friction Loss 3.36 Slip Loss 5.21 Elastic Shortening 4.77 13.34 Time Dependent Loss Steel relaxation 5.25 Shrinkage 3.30 Creep 3.58 Total Losses 12.13 20% extra time dep losses 2.4 Total Losses 14.6

51.82 + 130.23

/

35.3 1191 =

+

43.12 = 10.930 %

=

=

coeff

=

=

51.8 MPa.

35.3 MPa.

43.1 MPa. 130.2 MPa. Loss 4

0.0004

Recapitulation of Stresses at Various X n . 1--1 Prestress Stage I σt 3.88 σb 5.93

2--2 1.68 8.52

3--3 0.77 10.77

4--4 -0.78 15.73

5--5 -2.24 17.60

6--6 -2.52 17.53

Dead Load

σt σb

0.00 0.00

0.81 -0.94

1.55 -1.81

2.40 -2.82

3.01 -3.55

3.26 -3.84

Deck slab + Diaphragm

σt σb

0.00 0.00

0.61 -0.71

1.03 -1.20

1.90 -2.24

2.43 -2.86

2.67 -3.14

SIDL Load

σt σb

0.26 -0.79

0.51 -1.52

0.68 -2.23

0.78 -3.01

0.88 -3.40

0.85 -3.29

Resultant

σt σb

4.14 5.15

3.61 5.36

4.04 5.54

4.30 7.65

4.08 7.81

4.26 7.26

Live Load

σt σb

0.22 -0.66

0.36 -1.08

0.52 -1.69

0.60 -2.33

0.96 -3.72

1.06 -4.12

Final stress

σt σb

4.36 4.48

3.97 4.28

4.55 3.84

4.90 5.32

5.04 4.09

5.32 3.14

Final stress (with 50% LL) σt 4.25 3.79 4.29 4.60 4.56 4.79 (for temperature check) σb 4.81 4.82 4.69 6.48 5.95 5.20 Remarks about Stresses at various Conditions. (Vide Cl: 7.1 to 7.1.4 of IRC:-18-2000 ) Permissible Stress in Concrete at Stage I Prestress Maximum Compressive Stress immediately after Prestressing shall not exceed minimum of the following 20 N/mm 2 or 0.5 Fcj Fcj = Expected Concrete Strength at the time of Prestressing. 2 = 0.5 x 40 = 20 N/mm 2 Max Compressive Stress developed = 17.60 N/mm Hence O.K Temporary Tensile Stress in the extreme fibre immediately after Prestressingshall not exceed, = 1 of Maximum Compressive Stress immediately after Prestressing 10 2 = -1 x 17.60 = -1.76 N/mm 10 x x 2 Minimum Stress developed = 0.08 N/mm Hence O.K Permissible Stress in Concrete at Service Condition Maximum Compressive Stress allowed during Service Condition = 0.33 Fck 2 = 0.33 x 40 = 13 N/mm Maximum Compressive Stress attained at Service 2 = 5.3 N/mm Hence O.K Minimum Stress attained at Service 2 = 3.139 N/mm No Tension is developed .The Stresses are Compressive only.Hence O.K Check for Stress in top slab DL σ t(slab) midspan 0 σ t(slab) 0 Check for Deflection at Midspan. Downward deflection is given by δ

PS I 0 0

= M L E I

= = = =

SL+diaph 1.0 0.0

PS II 0.0 0.0

SIDL 1.5 0.4

5 x M x L2 48 ExI Moment Span Modulus of Elasticity of Concrete Moment of Inertia ∴δ1 = 5 x 48 x = 0.01148 m = 11.48 mm

LL 1.9 0.4

Total 4.4 0.8

= 4065 kNm = 18.571 m = 31622.8 Mpa 4 = 0.402 m 4.06523 x 31622.8 x

allowable 13.33 Safe 13.33 Safe

18.57 0.402

2

Upward deflection due to prestress = P x e x L2 8xExI = Prestressing Force at Mid Span = eccentricity ∴δ 2 = 6.0E+00 8 = 0.010 = 10.40 ∴ Net δ = 11.48 = 1.09 = L 800

P e

Permissible Deflection

= = x x m mm =

6017 KN 0.51 m 0.50978 x 31622.8 x

10.40 Downward 18571 800

18.57 0.402

=

2

23.2 mm

HenceO.K

Minimum reinforcement IRC 18-2000: cl.15.1 atleast 10 mm dia bar at not greater than 200 mm. IRC 18-2000: cl.15.2 Vertical dirn. 0.18% of web area IRC 18-2000: cl.15.3 Longit. Min. 0.15% of c/s area for Upto M45; beyond M45, 0.18%. min Longit. Steel reqd 1069.5 mm2 10 dia 14 Nos in web+top+bot flange min Web vertical steel 540 mm2/m 10 dia 2 lg 200 mm spacing (Note: the values given here are only as a check for min. steel. Actual steel provided is checked in the following sections) Ultimate load Capacity (IRC 18:2000 cl 12 & 13) Check for Ultimate Strength at Various X n . Failure by yield of steel ( Under Reinforced section ) M ult ( Steel )

=

0.9 d b A s f p

As

=

Area of High Tensile Steel

fp

=

The Ultimate Tensile Strength of Steel .

db

=

The Depth opf the beam from the maximum compression edge to C.G of Tendons.

+

0.87 d b A st f y

(Ast and fy are for non-prestressed steel) (This is neglected)

Failure by crushing of concrete ( over reinforced section ) M ult ( Con :) b Bf t Sections 2

A s (m ) f

p

(kN/m 2 )

d b (m)

= = = = X n 1-1 0.005 1862000

0.993

0.176 b d b 2 f ck + (2/3) x 0.8( B f - b )(d b - t / 2)x t x fck width of the Web. Overall width of the top flange of PSC Girder.or Slab Eff width Average thickness of flange. X n 2-2 0.005

X n 3-3 0.005

X n 4-4 0.005

X n 5-5 0.005

X n 6-6 0.005

1862000

1862000

1862000

1862000

1862000

1.127

1.203

1.342

1.420

1.439

M ult(HT Steel ) (kNm)

8543

9697

10350

11543

12216

12377

M ult(Tot Steel ) (kNm) b (m) B f (m) t (m)

8543 0.600 2.650 0.240

9697 0.60 2.650 0.240

10350 0.40 2.650 0.240

11543 0.30 2.650 0.240

12216 0.30 2.650 0.240

12377 0.300 2.650 0.240

M ult( Conc ) (kNm)

13332

15943

16577

18507

19905

20245

M ult (section) 1.5*DL+2*SIDL+2.5*LL (kNm)

8543 1383

9697 3096

10350 4623

11543 5987

12216 7961

12377 8445

Remarks

Safe

Safe

Safe

Safe

Safe

Safe

Check for Ultimate Shear Strength at Various X n . (Vide Cl:14.1 of I.R.C:-18-2000) Sections Uncracked in flexure V co = 0.67bd (f t +0.8 f * f t ) Ultimate Shear Resistance of the X n . V co = = b Width of Webs - (2/3 x Duct Diametre) if the Cables are grouted. = d Overall depth = ft Max principal stress 0.24 fck = f Stress at c.g at the section due to prestress after inst: loss is ed.

Sections Cracked in flexure V cr

=

db

0.037bd b f ck + (M t xV/M) = Distance of extreme comp.fibre from centroid of tendons.

Mt = (0.37 f ck + 0.8 f pt ) I/y V and M = Ultimate Shear & corresponding moment at the section V cr (min) = 0.1bd f ck Acc.to IRC :18 - 2000 Cl. No. 14.1.5 &Table 6. V Capacity db

P Sin( θ ) if the X n is Uncracked. =( 4700 x b x db )+ = 0.8 x Overall Depth or Dist: from comp: face to C.G of Tendons,which ever is more.

Shear Design(IRC 18:2000 cl 14.1) Section Vult (5%extra) f pt due to prestress (bottom fibre)

ft = 1--1 1461 4.89

1.52 Mpa 2--2 3--3 1274 1117 2.12 0.97

4--4 835 -0.98

5--5 544 -2.83

6--6 511 (1.5*DL+2*SIDL+2.5*LL) -3.18

f pc due to prestress(top fibre) Total Prestress force Area of precast section I p of precast section cg of cables in precast section cg of precast section cg of composite section f (stress at composite cg )

7.48 5989.7 1.0 0.2 0.7 0.8 1.1 5.5

10.75 6017.5 1.0 0.2 0.6 0.8 1.1 4.3

13.59 6048.3 0.9 0.2 0.5 0.8 1.1 3.9

19.83 6118.7 0.7 0.2 0.4 0.8 1.2 3.3

22.20 6184.7 0.7 0.2 0.3 0.8 1.2 2.3

22.10 6016.9 0.7 0.2 0.3 0.8 1.2 2.0

Section M pc =1.5*DL moment of girder

1--1 -2

2--2 350

3--3 653

4--4 950

5--5 1193

6--6 1292

f cm (stress at comp. Cg due to Mpc)

0.0

-0.6

-1.1

-2.0

-2.5

-2.7

f' = 0.8*f' +f cm

4.4

2.9

2.0

0.6

-0.7

-1.1 0.0

V c1 =1.5*DL shear of girder

274.1

224.3

197.2

124.1

62.1

I c of composite section

0.5

0.5

0.4

0.4

0.4

0.4

f s =V c1 *(A y ) p /(I p *b)

0.1

0.1

0.1

0.1

0.1

0.0

check if f s < f t

Safe

Safe

Safe

Safe

Safe

Safe

V c2 =(I c *b)/(A yc )*[(f t 2 +f *f t ) 1/2 -f s ] V co = V c1 +V c2

2260 2534

2057 2282

1769 1966

1651 1775

1499 1561

V co = 0.67bd(ft 2 +0.8f f t ) 1/2

1466

1335

649

612

551

1470 1470 IRC 18:2000 cl 14.1.2.2 (for precast girders+slab) 531 IRC 18:2000 cl 14.1.2.1 (superstr is cast at once) 4494

M t =(0.37*sqrt(f ck )+.8*f pt )*Z b

2078

2731

2965

4086

4512

V cr =0.037*b*db*(f ck ) 1/2 +(M t /M)V V cr (min) = 0.1bd(fck)^0.5 Section is V (Psin a ) due to Cables V co (uncracked section incl Psin α )

2301 660

1248 660

784 330

647 330

391 330

356 330

uncracked uncracked uncracked uncracked uncracked uncracked

540 3074

507 2789

443 2409

288 2063

129 1690

0 (for uncracked only) 1470

V cr (Cracked section)

2301

1248

784

647

391

356

V c (section)

2301

1248

784

647

391

356

4072 1 Safe No Min.reqd 200 133 0 145 12 4 452 278 Safe

4040 1 Safe No Reqd 200 133 8 138 12 4 452 271 Safe

3294 1 Safe No Reqd 200 66 109 23 12 4 452 132 Safe

1858 1 Safe No Reqd 200 66 62 34 12 2 226 100 Safe

1731 1 Safe No Reqd 200 66 50 22 12 2 226 88 Safe

1623 1 Safe No Reqd 200 66 51 40 12 2 226 106 Safe

V c (section capacity) web width to be reduced by (2/3 of Is V ult <= V capacity Is V ult <= 0.5*V c section Shear Reinft required or not Assume Spacing Min Asv Required Asv required Asv reqd for torsion dia of shear reinft No. of legs Asv provided Total Asv reqd.

IRC 18:2000 cl 14.1.5 cable/s IRC 18:2000 cl 14.1.5 IRC 18:2000 cl 14.1.4 IRC 18:2000 cl 14.1.4 IRC 18:2000 cl 14.1.4 (See Torsion Calculations below)

Torsion Design(IRC 18:2000 cl 14.2) Vt= Section 1--1 Tult (KNm) 275 sum of bd3/3 0.11 T in slab KNm 31.7 T in top flange KNm 7.8 T in web KNm 235.8 T in bottom flange KNm 0.0 Shear Stress in Slab(Mpa) due to torsion 0.43 Shear Stress in Top fl (Mpa) due to torsion 0.39 Shear Stress in Web (Mpa) due to torsion 1.17 Shear Stress in Bot fl (Mpa) due to torsion 0.00 ult Shear Stress V/bd (Mpa.) 1.40 ult Torsion shear stress (Mpa) 1.17 Total shear stress 2.57 Vtc (allowable) for torsion 0.42 Vtu (allowable) 4.70 Provide Torsional shear reinft Reqd. Is ultimate shear safe Safe Torsion reinft. Asv in top slab mm2 / m 172 Asv in top flange mm2 / m 151 Asv in web mm2 / m 726 Asv in bot flange mm2 / m 0 Asl in top slab mm2 498 Asl in top flange mm2 178 Asl in web mm2 1448 Asl in bot flange mm2 0

Design of Shear Connectors (with slab) Section 1--1 2--2 A*y (first moment of top slab) 0.315 0.315 VL=V(sidl+ll)*A*y/I KN/m 769 680 shear stress Mpa. 0.77 0.68 Qu of vert. Strps(KN) 176 176 spacing reqd (mm) 458 517 stirrup spacing ok/not 1 1 min shear (12 dia 2 lg) at 200 mm spacing Q (of slab at critical pl.) Shear flow KN/m 0.4*L*(fck)^.5 (slab) 0.7*As*fy+.08*L*(fck)^.5 (based on slab reinft of .9%)

Ast/m (in slab) min Ast prov. In slab (16@150) Min Ast reqd in Top flange Min Ast reqd in Bot flange Provide 16@ Ast provided = Longitudinal steel in top flange Longitudinal steel in web (mid) Extra Longl. steel in web (end) Longitudinal steel in bot flange

0.17 0 1214 749 1 1157 2680 1 1131 1131 200 1005 6 12 12 6

0.17 11 1214 749 1 1157 2680 1 1131 1131 200 1005 Nos Nos Nos Nos

4.70 2--2 209 0.11 24.1 6.0 179.2 0.0 0.33 0.29 0.89 0.00 1.22 0.89 2.11

Mpa 3--3 146 0.07 25.9 8.6 14.9 16.7 0.35 0.35 0.10 0.59 1.29 0.10 1.40

Vc = 4--4 97 0.03 38.1 12.6 21.9 24.5 0.51 0.52 0.40 0.87 1.60 0.40 2.00

0.42 5--5 63 0.03 24.8 8.2 14.2 15.9 0.33 0.34 0.26 0.57 1.04 0.26 1.30

Mpa 6--6 115 0.03 45.2 15.0 26.0 29.1 0.61 0.61 0.47 1.03 0.98 0.47 1.45

Reqd. Safe

No Safe

No Safe

No Safe

Reqd. Safe

131 115 689 0 379 135 1448 0

141 166 115 401 408 195 206 337

207 243 168 589 599 287 303 470

135 158 109 383 389 187 197 322

246 289 200 699 711 340 360 587

3--3 0.300 593 0.59 176 594 1

4--4 0.272 481 0.48 88 366 1

5--5 0.272 308 0.31 88 571 1

0.17 140 1214 749 1 1157 2680 1 1131 1131 200 1005

0.17 79 1214 749 1 1157 2680 1 565 589 200 1005

0.17 64 1214 749 1 1157 2680 1 565 565 200 1005

0.17 65 1214 749 1 1157 2680 1 565 699 200 1005

679 942 942 679

mm2 mm2 mm2 mm2

12 10 10 12

Refer Temperature design stress in the following section.

dia dia dia dia

6--6 0.272 329 IRC 22:cl 611.4.2.5 0.33 0.77 < 2.1 88 safe 535 1 Safe

IRC 22:cl 611.5.1 IRC 22:cl 611.5.1 Safe IRC 22:cl 611.5.2.3 Safe mm2/ m 50% of web mm2/ m 50% of web mm mm2/ m Reqd is Reqd is Reqd is Reqd is

340 360 1448 587

OK OK OK OK

STAGE I PRESTRESSING CABLES DATA Input particulars Effective span c to c of bearings Modulus of elasticity of steel UTS of Ht strands(Class2) UTS of Ht strands(Class2) Type of strands used T Maximum jack pressure = Grade of concrete Ec

L Es Fy Fy 13 As 0.9 X

18.571 195000 19000 1862 98.7 0.85 40 31622.78

=

m 2 N/mm 2 Kg/cm N/mm 2 2 MM =

initital stress 2 13300 Kg/cm 1303.4 N/mm 2 0.765 of UTF

N/mm2

Details of different strands Cable No of capacity strands stressed Types of cables Cable 1 Cable 2 Cable 3

Sheathin Jack g Int dia type Dia

19 19 19

19 T 14 T 19 T

No. 13 13 13

1 1 1

Coefficient fo friction

k u Slip ed s Each cable is to be stressed from both ends simultaneously.

Area 1875.3 1381.8 1875.3 5132.4 0.002 0.17 0.006

UTF (kN) 3491 2572 3491 9554 Per m per rad. m

85 K-350 85 K-350 85 K-350

CABLE PROFILES (TYPICAL)

L4

Y4 Horizontal Splay of Cables Bearing CL -X3

+X3 Y3 L/2

Y2 Y1 Xa 314.5

X2

X3

X1

Elevation of a typical Cable Typical cases of slip loss Po

P1

X4 P4 P2

Po'

P3

P1' L1

is permissible

L2 L3

Case 1 (X4 case)

Jack piston area 490 490 490

Length Stress of cable upto (of for jack UTS) 0 0 0

0.7 0.7 0.7

Po P1

P2

X5 P4

Po'

P3

Case 2 (X5 case)

P2'

P1' L1 L2

Po

L3

P1

P3 Case 3 (Y5 case) Y5

P2

P1'

P0'

P2'

P3'

L1 L2 L3

CABLE PROFILE(Stressing from both ends) Cable nos 1 2 No. of cables 1 1 Total force 3491 2572 Check for length 9.450 9.450 9.450 Xa 0 0 X1 0.120 0.620 Y1 0.480 0.300 Y1+Y2+Y3 1.5 0.350 1.150 0.750 X3 1.000 1.000 Y4a (hor splay 1) 0.000 0.000 L4a 1.000 1.500 Y4a (hor splay 2) 0.000 L4b 1.000 X2 8.330 7.830 c=(Y2+Y3)/X2(X2+2*X3) 0.008 0.006 a1 Atan(2*c*X2)(Rad) 0.129 0.091 (degree) 7.388 5.229 Y2 = 0.540 0.358 L1 = X3/cosa1 1.008 1.004 L2 = L1+X2+2y2^2/3*X2 9.362 8.845 L3 = L2+X1 9.482 9.465 a2 =2*Atan(2*Y4/X4) 0.000 0.000 Stress before slip (UTS) P0 0.700 0.700 P1 =Po/Exp(kL1) 0.699 0.699 P2 =Po/Exp(u(a1+a2)+kL2) 0.672 0.677 P3 =Po/Exp(u(a1+a2)+kl3) 0.672 0.676 Elongation (mm) 62.2 62.2 (Xa*Po+(Po+P1)L1+(P1+P2)* (L2-L1)+(P2+P3)(L3-L2))Fy/2Es Fav =((Po+P1)L1+(P1+P2)* 0.687 0.688 (L2-L1)+(P2+P3)(L3-L2))/(2xL3) Stress after slip (UTS) Po' 0.626 0.626 P1' 0.628 0.627 P2' 0.654 0.648 P3' 0.637 0.622 P4 0.637 0.622 Fav 0.640 0.636 X4 X5 Y5 0.018 0.027 Selected Case Y5 Y5 Y5

3 1 3491 9.450 0 1.120 0.120 0.350 1.000 0.000 1.500 0.000 1.000 7.330 0.003 0.049 2.821 0.181 1.001 8.334 9.454 0.000 0.700 0.699 0.683 0.681 62.3

0.691

0.636 0.637 0.653 0.628 0.628 0.644

0.027

base len gir len diff 19.96 19.2 0.76

Total length - 150 mm for setting 0 mm extra length of cable)

Slip travels upto

9.450

9.450

9.450

CABLE COORDINATES CABLE NO At 9.2855 At 0.9D from 7.94 L/8 6.96 L/4 4.64 3L/8 2.32 L/2 0

1

2

3

1.150 0.956 0.845 0.639 0.518 0.48

0.750 0.613 0.535 0.395 0.317 0.3

0.350 0.276 0.235 0.162 0.125 0.12

CABLE FORCES AND MOMENTS Cable number 1 2 3 P (average) 2232.93 1636.79 2247.065 At midspan Distance from cg to bottom fibre=Yb 0.811 0.811 0.811 Distance from bottom fibre to cable cg=Yc 0.480 0.300 0.120 a radian 0.000 0.000 0.000 Eccentricitye=Yb-Yc 0.331 0.511 0.691 Pi 2223.6 1600.7 2192.6 Pi cosa 2223.6 1600.7 2192.6 Pisina 0.0 0.0 0.0 Picosa*e 735.4 817.5 1514.4 At 3l/8 Yb Yc a radian e=Yb-Yc Pi Picosa Pisina Picosa*e

0.50978 m

avg ecc

0.49098 m

avg ecc

0.41272 m

avg ecc

0.27014 m

avg ecc

0.19215 m

2.32138 0.811 0.518 0.034 0.293 2259.7 2258.4 77.4 661.6

0.811 0.317 0.020 0.494 1655.9 1655.6 32.9 817.5

0.811 0.125 0.008 0.686 2270.8 2270.7 18.3 1557.4

At quarter span4.64275 Yb Yc a radian e=Yb-Yc Pi Picosa Pisina Picosa*e

0.811 0.639 0.070 0.171 2233.9 2228.4 157.2 382.0

0.811 0.395 0.047 0.416 1639.5 1637.7 77.1 681.5

0.811 0.162 0.024 0.649 2253.2 2252.6 53.4 1461.9

At 1/8 span Yb Yc a radian e=Yb-Yc Pi Picosa Pisina Picosa*e

0.807 0.845 0.107 -0.038 2208.2 2195.6 234.9 -83.3

0.807 0.535 0.074 0.271 1623.2 1618.7 120.3 439.5

0.807 0.235 0.039 0.572 2235.6 2233.9 87.9 1277.7

0.805 0.956 0.122 -0.151 2197.4 2181.1 266.8 -329.1

0.805 0.613 0.086 0.192 1616.3 1610.4 138.1 308.9

0.805 0.276 0.046 0.529 2228.3 2225.9 102.1 1176.4

At 0.9D Yb Yc a radian e=Yb-Yc Pi Picosa Pisina Picosa*e

avg ecc

6.96413

7.9355

At Yb Yc a radian e=Yb-Yc Pi Picosa Pisina Picosa*e

9.2855 0.805 1.150 0.130 -0.345 2187.6 2169.2 283.0 -749.0

0.805 0.750 0.092 0.055 1609.7 1602.9 147.2 87.7

0.805 0.350 0.049 0.455 2220.3 2217.6 109.4 1008.4

avg ecc

0.05796 m

Average stress in steel 0.64023 times UTS Cable Cordinates Of all the Cables CABLE 1 CABLE 2 CABLE 3 X (m)

Y (mm)

Y (mm)

Y (mm)

0

480

300

120

1

486

301

120

2

508

311

123

3

545

333

132

4

597

367

148

5

665

412

171

6

749

469

200

7

849

538

236

8

963

618

279

8.450

1020

658

301

9.286

1129

735

342

9.450 1150 Curve Starts 0.120 at

750 0.620

350 1.120

Curve Ends 8.450 at

8.450

8.450

Type

No of Force in Duct dia Jack Type Cable strands Cable (mm) (or eqv) Length stressed (jack) (mm) (kN)

Elongati angle at Stressin on (each anchora g Stage end) ge (deg) (mm)

Cable No. 1 19-T-13 2 19-T-13 3 19-T-13 Note cable length includes

19 14 19

2443.7 85 K-350 1800.4 85 K-350 2443.7 85 K-350 0 mm extra for jacking.

18963 18930 18908

62.2 62.2 62.3

7.388 5.229 2.821

1 1 1

9482 9465 9454

DESIGN OF END BLOCK Refer Clause 17.2 of IRC:18-2000 0.35 1 0.40 2 0.40

Anchorage plate size assumed 270 mm

3 270 Min. concrete beyond anchorage edge = 0.165 = 0.165 > 0.05 Safe Moment from Moment from bottom Rt. Edge 2262.8 590.3 1085.9 434.4 699.0 599.1 4047.72 1623.80 are taken as horizontal only

0.35 0.27 0.60 STAGE 1 CABLES Jacking/Stressing forces Force in Cable 1 Force in Cable 2 Force in Cable 3

in cables (after slip& friction) 1967.7 KN Cable type 1447.9 KN Cable type 1997.1 KN Cable type

Check for bursting forces, case 1

0.165

19 T 13 19 T 13 19 T 13

(Note: here all forces vertical is neglected)

Max force = 1997.1 KN size of eff sq. = 0.350 m from bottom Hence, 2Yo = 0.70 m. Size of each anchorage is 270 mm square Along Vertical line of action, anchorage size 2Ypo= 1 x 0.27 = 0.27 m Ypo/Yo = 0.27 / 0.70 = 0.386 For this ratio of Ypo/Yo, from Table 11 of above code, Fbst/Pk = 0.20 Now Pk = 1997.1129 kN Hence, Fbst = 407.98 kN For external anchorage the design force has to be increased by 10%. Hence, revised Fbst = 448.78 kN This max stress occurs at 0.5*Yo = 0.5 x 0.350 = 0.175 m with 0.87Fy permissible stress Providing 12 φ mesh reinforcement , For Fy = 415 Mpa, Area of steel reqd. = 448.78 x 1000 = 1242.99 mm2 0.87 x 415 Number of bars reqd. = 1242.99 = 11 Nos 113.10 (note vertical check gives more steel than the horizontal check hence only vertical check has been done) Bearing Stress As the anchorages are set out as per the manufacturer's specifications for embedded anchorages, bearing stress checks are not carried out. Refer Note ii under clause 7.3 of IRC:18-2000.

Design temperatrure differences Idealised section 2.650

2.650

0.332

0.325

1.018

0.97 0.300

0.600

0.390

0.44 0.600

1.740

0.6

Mid Section

Temperature Rise case 17.8'C

1.740

End Section

Temperature Fall case 10.6'C 0.25

h1

0.15

h1

4'C h2

0.7'C 0.25

h2 0.2 h

0.2 h3 h3

0.15 0.8'C

h4

0.25 2.1'C 6.6'C h1=0.3h (Max 0.15m) h1=h4=0.2h<=0.25m h2=0.3h>=0.1m<=0.25m h2=h3=0.25h <=0.20m h3=0.3h <=0.15m h1 0.25 h1 0.15 h2 0.2 h2 0.25 h3 0.2 h3 0.15 h4 0.25 CALCULATION OF THERMAL STRESSES AT MID SECTION TEMPERATURE RISE CASE Section

Depth m

Width m

Area (m^2)

Y from top (m)

Ay (m^3)

I (m^4)

t (C)

At (m^2.C)

It (m^3.C)

1 2 3 4 5 6

0.15 0.15 0.10 1.02 0.17 0.15

2.750 2.750 0.300 0.300 0.600 0.600

0.413 0.407 0.031 0.305 0.104 0.090

0.075 0.224 0.349 0.909 1.504 1.665

0.031 0.091 0.011 0.277 0.156 0.150

0.002 0.020 0.004 0.252 0.234 0.250

10.900 2.815 0.815 0.000 0.000 1.050

4.496 1.147 0.025 0.000 0.000 0.095

0.025 0.058 0.003 0.000 0.000 0.262

Sum

1.74

0.716

0.762

5.762

0.348

1.349

Coefficient of thermal expansion α = εo*ΣA εo∗ΣA*Y

-

0.0000117

θ*ΣA*Y θ*ΣA*Y2 θ εo

= = 0.000083 0.000094

α*A*T α*A*T*Y

Ec

31623

N/mm2

ε o-yθ θ -α αt Point

Y from top (m)

1 2 3 4 5 6 7

0 0.15 0.30 0.40 1.42 1.59 1.74

y*theta

0.00E+00 1.24E-05 2.47E-05 3.32E-05 1.18E-04 1.32E-04 1.44E-04

t 'C 17.80 4.00 1.63 0.00 0.00 0.00 2.10

alfa*t

2.08E-04 4.68E-05 1.91E-05 0.00E+00 0.00E+00 0.00E+00 2.46E-05

Comp / Fci=Ec(ε (εo(ε Ten yθ θ -α αt) MPA

-1.14E-04 3.47E-05 5.02E-05 6.08E-05 -2.36E-05 -3.79E-05 -7.49E-05

-3.615 1.098 1.586 1.922 -0.745 -1.197 -2.367

Compression Tension Tension Tension Compression Compression Compression

Temperature Fall in Mid section Section

Depth m

Width m

Area (m^2)

y from top (m)

Ay (m^3)

I (m^4)

t (C)

At (m^2.C)

It (m^3.C)

1 2 3 4 5 6 7

0.250 0.048 0.152 0.840 0.128 0.073 0.250

2.750 2.750 0.300 0.300 0.300 0.600 0.600

0.688 0.132 0.046 0.252 0.038 0.044 0.150

0.125 0.274 0.374 0.870 1.354 1.454 1.615

0.086 0.036 0.017 0.219 0.052 0.063 0.242

0.011 0.010 0.006 0.191 0.070 0.092 0.391

5.650 0.616 0.266 0.000 0.255 0.655 3.700

3.884 0.081 0.012 0.000 0.010 0.028 0.555

0.061 0.006 0.002 0.000 0.018 0.060 1.448

Sum

1.740

0.716

0.771

4.571

1.594

1.349

Coefficient of thermal expansion α = εo*ΣA εo∗ΣA*Y

-

0.0000117

θ*ΣA*Y θ*ΣA*Y2 θ εo

= = 0.000025 0.000053

α*A*T α*A*T*Y

Ec

31623

N/mm2 ε o-yθ θ -α αt

Comp / Fci=Ec(ε (εo(ε Ten yθ θ -α αt) MPA

Point

Y from top (m)

y*theta

t 'C

alfa*t

1 2 3 4 5 6 7 8

0 0.250 0.298 0.450 1.290 1.418 1.490 1.740

0.00E+00 6.21E-06 7.41E-06 1.12E-05 3.21E-05 3.52E-05 3.70E-05 4.32E-05

10.6 0.700 0.532 0.000 0.000 0.446 0.800 6.600

1.24E-04 8.19E-06 6.22E-06 0.00E+00 0.00E+00 5.22E-06 9.36E-06 7.72E-05

-7.12E-05 3.84E-05 3.92E-05 4.16E-05 2.08E-05 1.24E-05 6.45E-06 -6.76E-05

-2.251 1.215 1.240 1.317 0.657 0.392 0.204 -2.139

Section

Depth m

Width m

Area (m^2)

Y from top (m)

Ay (m^3)

I (m^4)

t (C)

At (m^2.C)

It (m^3.C)

1 2 3 4 5 6

0.15 0.129 0.121 0.970 0.22 0.15

2.750 2.750 0.6 0.6 0.6 0.6

0.413 0.356 0.072 0.582 0.132 0.090

0.075 0.215 0.340 0.885 1.480 1.665

0.031 0.076 0.025 0.515 0.195 0.150

0.0023 0.0164 0.0084 0.4558 0.2891 0.2495

10.900 2.966 0.966 0.000 0.000 1.050

4.496 1.054 0.070 0.000 0.000 0.095

0.025 0.049 0.008 0.000 0.000 0.262

Sum

1.740

0.992

1.022

5.715

0.344

Tension Compression Compression Compression Compression Compression Compression Tension

END SECTION Temperature Rise

1.644

Coefficient of thermal expansion α = εo*ΣA εo∗ΣA*Y

-

0.0000117

θ*ΣA*Y θ*ΣA*Y2 θ εo

= = 0.000086 0.000092

α*A*T α*A*T*Y

Ec

31623

N/mm2

ε o-yθ θ -α αt

Comp / Fci=Ec(ε (εo(ε Ten yθ θ -α αt) MPA

Point

Y from top (m)

y*theta

t 'C

alfa*t

1 2 3 4 5 6 7

0 0.150 0.279 0.400 1.370 1.590 1.740

0.00E+00 1.29E-05 2.40E-05 3.43E-05 1.18E-04 1.37E-04 1.49E-04

10.6 0.700 0.423 0.000 0.000 0.770 0.800

1.24E-04 8.19E-06 4.94E-06 0.00E+00 0.00E+00 9.01E-06 9.36E-06

-3.16E-05 7.14E-05 6.35E-05 5.81E-05 -2.52E-05 -5.31E-05 -6.63E-05

-0.998 2.258 2.009 1.838 -0.796 -1.678 -2.097

Section

Depth m

Width m

Area (m^2)

y from top (m)

Ay (m^3)

I (m^4)

t (C)

At (m^2.C)

It (m^3.C)

1 2 3 4 5 6 7

0.250 0.029 0.171 0.840 0.080 0.120 0.250

2.750 2.750 0.600 0.600 0.600 0.600 0.600

0.688 0.080 0.102 0.504 0.048 0.072 0.150

0.125 0.265 0.365 0.870 1.330 1.430 1.615

0.086 0.021 0.037 0.438 0.064 0.103 0.242

0.011 0.006 0.014 0.381 0.085 0.147 0.391

5.650 0.649 0.299 0.000 0.160 0.560 3.700

3.884 0.052 0.031 0.000 0.008 0.040 0.555

0.061 0.004 0.004 0.000 0.014 0.082 1.448

Sum

1.740

0.992

1.035

4.570

1.612

Compression Tension Tension Tension Compression Compression Compression

Temperature Fall

1.644

Coefficient of thermal expansion α = εo*ΣA εo∗ΣA*Y

-

0.0000117

θ*ΣA*Y θ*ΣA*Y2 θ εo

= = 0.000031 0.000051

α*A*T α*A*T*Y

Ec

31623

N/mm2 ε o-yθ θ -α αt

Point

Y from top (m)

y*theta

t 'C

alfa*t

1 2 3 4 5 6 7 8

0 0.250 0.279 0.450 1.290 1.370 1.490 1.740

0.00E+00 7.68E-06 8.58E-06 1.38E-05 3.96E-05 4.21E-05 4.58E-05 5.34E-05

10.6 0.700 0.598 0.000 0.000 0.280 0.800 6.600

1.24E-04 8.19E-06 6.99E-06 0.00E+00 0.00E+00 3.28E-06 9.36E-06 7.72E-05

Comp / Fci=Ec(ε (εo(ε Ten yθ θ -α αt) MPA

-7.30E-05 3.52E-05 3.55E-05 3.72E-05 1.14E-05 5.69E-06 -4.08E-06 -7.96E-05

-2.308 1.112 1.122 1.177 0.361 0.180 -0.129 -2.518

stress with 50% LL Mpa 4.36 4.79

Net stress Mpa 2.11 3.69

Tension Compression Compression Compression Compression Compression Tension Tension

0.16868

SUMMARY (Check with 50% LL)

Mid section Top Slab Top Flange Web Bottom fl

Temp rise Temp Fall Stress(MPA) Mpa 3.61 -2.25 -1.10 1.22 -0.59 0.99 2.37 -2.14

Max Tension Mpa -2.25 -1.10 -0.59 -2.14

End section Top Slab Top flange Web Bottom fl

Temp rise Temp Fall Stress(MPA) Mpa 1.00 -2.31 -2.26 1.11 -0.52 0.77 2.10 -2.52

Max Tension Mpa -2.31 -2.26 -0.52 -2.52

At the end spans, tensile force = Provided extra

126.60 10

KN mm dia at

240

5.20 stress with 50% LL Mpa 0.81 4.25

3.06 Net stress Mpa -1.50 1.99

4.81

2.30

mm c/c at top and bottom in slab is sufficient for this

Design Of End Diaphragm Diaphragm is designed for two Loading Condition 1 ) Selfweight Of Diaphragm + Reaction From Superstructure ( Girders ) ( Service Condition ) 2 ) Replacement Of Bearing / Superstructure ed on Jacks - ( No Live Load ) Diaphragm is spanning between 4 girders . It act as continuous beam Diaphragm is designed for Jacking end Force During Bearing Replacement Jacks are kept at distance mentioned below away from the face of the girder as shown in figure. Hence It acts as a continuous beam between 6 Jacks. Jack Positions are as shown in figure & indicated by T To Y

During Bearing Replacement there will be no Live Load Hence Only Dead Loads and SIDL are considered (in KNs) G2 G4 G1 G3 Reactions due to 1) Selfweight 2) S.I.D.L.

335.51 366.57 702.08

335.51 19.1 354.61

335.51 19.91 355.42

335.51 365.53 701.04

Girder & Jack Positions G1 702

G2 355

G3 355

Diaphragm

G4 701

2750 1500 500

1750 T 200

1000 1750 U V 200 200

1000 1750 W X 200 200

350

600 mm

Thickness of base of girder 8713.56 / 4.125 m

CG of girder loads CG of Jacks

500.00 Y 200 Jack distances.

2113.15 =

4.123 m

from G1

T To Y are Jack positions at the time Of Bearing replacement Note: all the jacks will have the same force as they are connected to the same hydraulic pump. Note: the self weight of diaphragm has been considered in the reactions of girders and hence, not taken again. Force in the jacks =

M (T) = M(U) = M(G2)= M(V)=

702 351 702 963 702 962.193 702 355 1031.96

6 xP= P= x KNM x KNM x KNM x x KNM

0.5 =

2113.15 KN 352.192 KN 351.04 KNm

2.25 -

352.192 x

1.75 =

963.344 KNm

2.75 -

352.192 x

2.25 -

352.192 x

3.25 0.2

352.192 x

2.75 -

352.192 x

1 +

0.5

M(W) =

702 x 355 x 1032.16 KNM

5 1.95 -

352.192 x 352.192 x

4.5 1.75

352.192 x

2.75 +

M(G3)=

702 x 355 x 1032.22 KNM

5.5 2.45 -

352.192 x 352.192 x

5 2.25

352.192 x

3.25 +

Design Moment is

1032 kNm

Shear is taken on right side. S(G1) = 702 S(T) = 350 S(U) = -2 S(G2)= 352 S(V)= 0 S(W) = -352 S(G3)= 3 S(x)= -349 S(Y)= -701 Max Design Shear is

702 kN

(Note: this is at the jack face or the CL of the girder. Actual shear will be little less)

Check For Moment Of Resistant Grade Of Concrete L/D min = M 40 Grade Of Steel Fe 415 Acc.to IRC : 21 -2000 Cl. No. 303.1 σ cbc = Permissible Bending Stress in Concrete Permissible Bending Stress in bending for H.Y.S.D. bars Modular Ratio = 10

K

1750 /

13.3

σ st

Lever Arm for Deep beam=

0.2*(l+1.5D) for 1
m x σ cbc = m x σ cbc +

133.3333333 133.333 + 200

=

σ st

J = 1 - K/3 Q = 1 / 2 * σ cbc * j * k Moment Of Resistant = =

= =

0.867 1.42 2 Q. B.D 1120 kN - mtr

Clear Cover Bar Dia deff provided Steel Required

=

1500 =

Mpa =

=

Using

Mpa

0.40 =

But here J =

800 /

> Max Moment ∴ Hence Safe

=

1500 =

0.53333

1031.96 kN - mtr

50 mm 32 mm =

1500

-

50

-

= 1354.0

96

M

=

1031963075.27 200 x 0.533 x 1354.0 2 7145.24 mm

32

mm dia bar

∴ No of Bars =

Side face reinft Side face reinft reqd as per IS 456:2000 is Provide

<

800 mm

σ st x j x d =

200

1.167 Deep Beam

16 dia

12

-Ast

0.2D = 300 Ast1 (0.5(L/D-.5)=

Mid ht

0.3D = Ast2 =

+Ast

0.25D-0.05L = Ast =

3 bars

450 6 bars

9

0.002 X 2 = 1050 mm Nos. on each face

350 x 2 4825.49 mm

288 mm 9 bars

1500

2.5

a) Check for Max Shear Total Shear Shear stress ,

702.08 kN V Bxd = The design shear across the section = Effective depth of the section = Breadth of slab

V d B

.

.

= =

τ

=

.τ

Maximum Permissible Shear Stress :b = 350 mm d revised = 1354 mm p = 1.53 % 2 f ck = 40.00 N/mm

τc τ max

Vsteel Spacing

0.49 2.5 V / bd

=

V −τ c*b*d σ sc X A SV X d

=

Assuming A SV

N/mm 2 2 N/mm = =

= = =

Vst legged 226.08

2 =

σ sc

= Spacing of stirrups Provide 2

200 legged

702.1 x 1000 350 x 1354.00 ( Vide cl - 304.7.2 of I.R.C:-21-2000 )

1.481 1.481 46.987

12 mm 2

( Vide cl - 304.7.1.1 of I.R.C:-21-1987 )

=

1.48

2

N/mm 0.49 N/mm 2 2.5 Shear reinft. Reqd.

> < T

N/mm

2

Shear reinft. reqd SAFE

dia stirrups

N/mm 2 = 12

130.3 mm dia stirrups at

125.0

DESIGN LOADS During Service (KN, KNm) SHEAR DL SIDL LIVE LOAD Total End Diaph77.12 104.3 181.467 Mid Diaph 211.74 236.0 447.725 TORSION DL End DiaphMid Diaph -

SIDL LIVE LOAD 15.78 25.2 0 5.5

Total

MOMENTSDL End DiaphMid Diaph -

SIDL LIVE LOAD 189.07 55.6 -757.62 610.7

Total 244.69 757.62

c/c

Shear with Torsion 368.9 476.9

41.0 5.5 Moment with Torsion 274.4 760.8

Check For Moment Of Resistant for Intermediate Diaphragm Grade Of Concrete L/D min = M 40 Grade Of Steel Fe 415 Acc.to IRC : 21 -2000 Cl. No. 303.1 σ cbc = Permissible Bending Stress in Concrete Permissible Bending Stress in bending for H.Y.S.D. bars Modular Ratio = 10

K

2750 /

13.3

σ st

Lever Arm for Deep beam=

0.2*(l+1.5D) for 1
m x σ cbc = m x σ cbc +

133.3333333 133.333 + 200

J = 1 - K/3 Q = 1 / 2 * σ cbc * j * k Moment Of Resistant = =

Clear Cover Bar Dia deff provided

σ st = =

=

0.867 1.78 Q . B . D2 1400 kN - mtr

1500 =

Mpa =

200

=

1.833 Deep Beam

<

Mpa

1000 mm

0.40 =

But here J =

> Max Moment ∴ Hence Safe

1000 /

=

1500 =

0.66667

760.84 kN - mtr

50 mm 32 mm =

1500

-

50

-

96

= 1354.0

2.5

Steel Required

M

=

σ st x j x d

=

760835523.24 200 x 0.667 x 1354.0 2 4214.38 mm

32

mm dia bar

=

Using

∴ No of Bars =

(Note: MOST standard drawings have same reinf at top and bottom) Side face reinft Side face reinft reqd as per IS 456:2000 is Provide

10 dia

a) Check for Max Shear Total Shear Shear stress ,

Mid ht

0.3D = Ast2 =

+Ast

0.25D-0.05L = Ast =

0.002 X 2 = 1050 mm Nos. on each face

.

= =

τ

=

.τ

Maximum Permissible Shear Stress :b = 350 mm d revised = 1354 mm p = 1.02 % 2 f ck = 40.00 N/mm

τc τ max

Vsteel Spacing Assuming A SV

N/mm 2 N/mm 2 = =

= = =

0.42 2.5 V / bd

=

V −τ c*b*d σ sc X A SV X d

= 2 =

σ sc = Spacing of stirrups Provide 2

Vst legged 226.08 200 legged

12 2 mm N/mm = 12

4 bars

450 2 bars

6

476.87 kN V Bxd = The design shear across the section = Effective depth of the section = Breadth of slab

V d B

.

11

0.2D = 300 Ast1 (0.5(L/D-.5)=

-Ast

1500 x 2 1608.5 mm

> < T

350

( Vide cl - 304.7.1.1 of I.R.C:-21-1987 )

476.9 x 1000 350 x 1354.00 ( Vide cl - 304.7.2 of I.R.C:-21-2000 )

1.006 1.006 27.784

238 mm 6 bars

=

N/mm 2 0.42 N/mm 2 2.5 Shear reinft. Reqd.

1.01

2

200.0

2

Shear reinft. reqd SAFE

dia stirrups

220.4 mm dia stirrups at

N/mm

c/c

All these loads are less than or equal to the loads experienced during the jacking operations.