Unit load distribution coefficient.q ###

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

0 ### ### ### ### ### ### ### ### ### ###b/4 ### ### ### ### ### ### ### ### ### ###b/2 ### ### ### ### ### ### ### ### ### ###3b/4 ### ### ### ### ### ### ### ### ### ###

b ### ### ### ### ### ### ### ### ### ###

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

0 ### ### ### ### ### ### ### ### ### ###b/4 ### ### ### ### ### ### ### ### ### ###b/2 ### ### ### ### ### ### ### ### ### ###3b/4 ### ### ### ### ### ### ### ### ### ###

b ### ### ### ### ### ### ### ### ### ###

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b ### ### ### ### ### ### ### ### ### ###

-3b/4 ### ### ### ### ### ### ### ### ### ###

-b/2 ### ### ### ### ### ### ### ### ### ###

-b/4 ### ### ### ### ### ### ### ### ### ###0 ### ### ### ### ### ### ### ### ### ###

b/4 ### ### ### ### ### ### ### ### ### ###b/2 ### ### ### ### ### ### ### ### ### ###3b/4 ### ### ### ### ### ### ### ### ### ###

b ### ### ### ### ### ### ### ### ### ###

For no torsion grillage a = 0 K0

Row integral

Ref. Pt Load at

For full torsion grillage a = 1 K1

Row integral

Ref. Pt Load at

Ka= K0+(K1-K0)x(a)0.5

Row integral

Ref. Pt Load at

Distribution coefficient K' for SIDL

0.5 t/m 0.5 t/m

#REF! #REF! #REF! #REF! #REF!

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 0.50 ### ### ### ### ### ### ### ### ###-3b/4 0.00 ### ### ### ### ### ### ### ### ###-b/2 0.00 ### ### ### ### ### ### ### ### ###-b/4 0.00 ### ### ### ### ### ### ### ### ###

0 0.00 ### ### ### ### ### ### ### ### ###b/4 0.00 ### ### ### ### ### ### ### ### ###b/2 0.00 ### ### ### ### ### ### ### ### ###3b/4 0.00 ### ### ### ### ### ### ### ### ###

b 0.50 ### ### ### ### ### ### ### ### ###1.00

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

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

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' ### ### ### ###

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Distribution coefficient K' for live load (1 lane class A)

#REF! #REF! #REF! #REF! #REF!

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 2.12 ### ### ### ### ### ### ### ### ###-3b/4 4.62 ### ### ### ### ### ### ### ### ###-b/2 4.66 ### ### ### ### ### ### ### ### ###-b/4 0.00 ### ### ### ### ### ### ### ### ###

0 0.00 ### ### ### ### ### ### ### ### ###b/4 0.00 ### ### ### ### ### ### ### ### ###b/2 0.00 ### ### ### ### ### ### ### ### ###3b/4 0.00 ### ### ### ### ### ### ### ### ###

b 0.00 ### ### ### ### ### ### ### ### ###11.40

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

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

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' ### ### ### ###

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

Class A 1.8m 0.95

m

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Distribution coefficient K' for live load (2 lane class A)

#REF! #REF! #REF! #REF! #REF!

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 2.12 ### ### ### ### ### ### ### ### ###-3b/4 4.62 ### ### ### ### ### ### ### ### ###-b/2 4.99 ### ### ### ### ### ### ### ### ###-b/4 5.37 ### ### ### ### ### ### ### ### ###

0 4.95 ### ### ### ### ### ### ### ### ###b/4 0.75 ### ### ### ### ### ### ### ### ###b/2 0.00 ### ### ### ### ### ### ### ### ###3b/4 0.00 ### ### ### ### ### ### ### ### ###

b 0.00 ### ### ### ### ### ### ### ### ###22.80

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

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

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' ### ### ### ###

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Class A 1.8m 0.95m

Class A 1.8m 1.7m

Distribution coefficient K' for live load (3 lane class A)

#REF! #REF! #REF! #REF! #REF!

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 2.12 ### ### ### ### ### ### ### ### ###-3b/4 4.62 ### ### ### ### ### ### ### ### ###-b/2 4.99 ### ### ### ### ### ### ### ### ###-b/4 5.37 ### ### ### ### ### ### ### ### ###

0 4.95 ### ### ### ### ### ### ### ### ###b/4 4.99 ### ### ### ### ### ### ### ### ###b/2 4.62 ### ### ### ### ### ### ### ### ###3b/4 2.54 ### ### ### ### ### ### ### ### ###

b 0.00 ### ### ### ### ### ### ### ### ###34.20

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

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

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' ### ### ### ###

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Class A 1.8m 0.95m

Class A 1.8m 1.7m

Class A 1.8m 1.7m

Distribution coefficient K' for live load (70 - R)

#REF! #REF! #REF! #REF! #REF!

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 0.00 ### ### ### ### ### ### ### ### ###-3b/4 4.75 ### ### ### ### ### ### ### ### ###-b/2 6.15 ### ### ### ### ### ### ### ### ###-b/4 6.10 ### ### ### ### ### ### ### ### ###

0 0.00 ### ### ### ### ### ### ### ### ###b/4 0.00 ### ### ### ### ### ### ### ### ###b/2 0.00 ### ### ### ### ### ### ### ### ###3b/4 0.00 ### ### ### ### ### ### ### ### ###

b 0.00 ### ### ### ### ### ### ### ### ###17.00

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

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

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' ### ### ### ###

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

70 - R

1.93m

2.18m

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Distribution coefficient K' for live load (1lane class A + 70 - R)

#REF! #REF! #REF! #REF! #REF!

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 0.00 ### ### ### ### ### ### ### ### ###-3b/4 4.75 ### ### ### ### ### ### ### ### ###-b/2 6.15 ### ### ### ### ### ### ### ### ###-b/4 6.33 ### ### ### ### ### ### ### ### ###

0 5.47 ### ### ### ### ### ### ### ### ###b/4 4.84 ### ### ### ### ### ### ### ### ###b/2 0.86 ### ### ### ### ### ### ### ### ###3b/4 0.00 ### ### ### ### ### ### ### ### ###

b 0.00 ### ### ### ### ### ### ### ### ###28.40

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

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

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' ### ### ### ###

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

70 - R

1.93m

2.18m

Class A 1.8m

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

End cross girder

Total 74.00 t 64.00 t 64.00 t 74.00 t

3.100 3.100 3.100

0.75 1.600 0.75 0.75 1.650 0.7 0.75 1.600 0.75

A B C D E F

DF 1.00 0.48 0.52 0.52 0.48 0.47 0.53 0.52 0.48 1.00

FEM 55.50 0.00 0.00 -12.00 12.00 0.00 0.00 -11.20 12.00 0.00 0.00 -55.5

Balance -55.50 5.81 6.19 -6.29 -5.71 5.24 5.96 -6.30 -5.70 55.50

C O -27.75 -3.14 3.10 2.62 -2.86 -3.15 2.98 27.75

Balance 14.95 15.94 -2.99 -2.72 2.81 3.20 -16.12 -14.61

C O 0.00 -1.50 7.97 1.40 -1.36 -8.06 1.60 0.00

Balance 0.72 0.77 -4.91 -4.47 4.41 5.01 -0.84 -0.76

C O 0.00 -2.46 0.39 2.20 -2.23 -0.42 2.51 0.00

Balance 1.19 1.27 -1.36 -1.23 1.24 1.41 -1.32 -1.19

C O 0.00 -0.68 0.63 0.62 -0.62 -0.66 0.71 0.00

Balance 0.33 0.35 -0.66 -0.60 0.60 0.68 -0.37 -0.34

C O 0.00 -0.33 0.18 0.30 -0.30 -0.19 0.34 0.00

Balance 0.16 0.17 -0.25 -0.23 0.23 0.26 -0.18 -0.16

C O 0.00 -0.12 0.08 0.11 -0.11 -0.09 0.13 0.00

Balance 0.06 0.06 -0.10 -0.09 0.09 0.11 -0.07 -0.06

Total M 55.50 -55.50 -4.54 4.54 7.79 -7.79 7.13 -7.13 -4.93 4.93 55.50 -55.50

Max support moment (DL+SIDL) = 55.5 t-m

Max span moment (DL+SIDL) = 17.8 t-m

Width of cross girder 0.3

Designed of deep beam [ As per clause 28.2, IS 456-2000 ]

For span AB L = 3.1 D = 2.06

L/D = 1.505 >= 1 for continuous beam

Lever arm Z = 0.2*(3.100+1.5*2.06) = 1.238 m

For span CD L = 1.5 D = 2.06

L/D = 0.728 < 1 for continuous beam

The end cross girder is designed as a continuous deep beam for bearing replacement condition, continuous over knife supports at the jack locations. The center line of jacks are taken to be 750 mm from the center line of main girders.

Lever arm Z = 0.5*1.500 = 0.750 m

Required Ast for span moment =17.836/0.750*24000 = 9.91

Minimum Ast at bottom =0.2%bd =0.002*40*206 = 12

Provide 3 nos 20 f + 2 nos 20 f

at bottom within a depth of (0.25D - 0.05L) = 0.440 m

from bottom face with a development length of (0.8*35*dia of bar) = 560 mm

Provided Ast = 15.7

Required Ast for max support M =55.500/1.238*24000 = 18.68

Required in the top 0.2D = 9.4

Provide 3 nos 20 f + 2 nos 16 f

Provided Ast = 13.4

0.3 D on either side of mid depth Steel required = 9.3

Provide 7 nos 16 f

Provided Ast = 14.1

Hanging reinforcement [ As per clause 28.3.3, IS 456-2000 ]

Total shear = 74.0 t

Required Ast as hanging reinf. =74.0*10000/20000 = 37.0

Distribution length = 1.99 m

Required Ast per m length =37.0/1.988 = 18.6

Provide 2 L 16 f @ 180 c/c as vertical reinforcement

Provided Ast = 22.3

Side face reinforcement [As per clause 31.4 IS-456, 2000]

0.12 % of web area on either face with spacing not more then 450 mm.

Required Ast =0.001 *118*30 = 4.25

Provide 7 nos 16 f on either face of cross girder.

Provided Ast = 14.1

=M/sst*Z cm2

cm2

cm2

=M/sst*Z cm2

cm2

cm2

cm2

cm2

cm2

cm2/m

cm2/m

cm2

cm2

DESIGN OF LONGITUDINAL CANTILEVER

#REF! Longitudinal overhang 1.1

0.5

1.5 3 3 3 1.5

SECTION A - A

Design of Extended Top Flange(outer girder)

Calculation of Dead Load, SIDL and LLS.No. Load Description Load Eccentricity Moment

(t) (m) (t-m)

1 Dead Load from slab =0.5*1.1*2.4 1.32 0.550 0.735 Wt. of wearing coat 0.19 0.550 0.11

For most eccentric position of live load

Class 70R wheel 8.5t

Position of w1 and w2 load from face of diaphragm= 0.9685

Dispersion widthw1 and w2 = 2.0222 t Sine the distance between wheel is 1.93m hence overlap

Total width of dispersion = 3.9522

Total Liveload = 17

The longitudinal cantilever is the portion of the cast in situ deck slab beyond the bearing and it extends upto expansion gap. Deck slab in this portion is therefore designed as "slab supported at edges", supporting conditions being as applicable. The deck slab is assumed as cantilever supported at face of diaphragm.

Moment (liveload) = 4.1659076 tm

Total Moment = 5.00

k 10/(10+15.004) 0.400j 1-0.3999/3 0.867Q 0.5*1333*0.400*0.867 231.0Effective depth reqd

= SQRT(5.00/(231.0*))= 0.147 m

Effective depth provided= 0.5+-0.04-(12/2000)= 0.454 m OK

Ast reqd. at top= M / ( ft * j * d)

= 6.4

Ast provided at top

10nos. 12f = 11.3

cm2

cm2

Reinforcement of cross girder at the pin bearing

Horizontal seismic force coming on the cross girder 155 t

span of cross girder 2.335 m

Max moment 45.24063

Ast reqd 55.44194

64.3072