T Beam Design

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DESIGN OF T-BEAB 10.7 7.500 0.250 1.500 A B C D 0.50 0.50 0.50 0.50 1.125 2.500 2.500 2.500 1.125 9.75

CROSS SECTION OF DECK Required data

Effective Span = 16.000 m

Total length of Deck = 8.700 m

Carriage way width = 7.500 m

Width of Parapet including Kerb = 0.600 m

Width of Footpath = 1.000 m

Thickness of Slab = 0.250 m

No of Longitudinal Girder = 4.000 m Hight of Longitudinal Girder = 1.500 m Spacing of Longitudinal Girder = 2.500 m

Cantiliver Length = 1.125 m

Thickness of Web = 0.250 m

Thickness of Footpath = 0.350 m

Thickness of Kerb = 0.450 m

Thickness of Parapet = 0.200 m

Hight of Parapet above Kerb = 0.900 m

No of Cross Girder = 5.000 m

Spacing of Cross Girder Spacing = 4.000 m Thickness of Cross Girder = 0.300 m

Hight of Cross Girder = 1.500 m

Density of RCC = 25.000 kN/m3

Wearing Coat Thickness = 0.080 m Density of Wearing Coat 22.000 kN/m3

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Haunches and Bulbs of Longitudinal Girder Girder 'A' and 'D'

Bottom Bulb Width = 0.500 m

Bottom Bulb Thickness = 0.250 m

Bottom Haunch 0.125 x 0.125 m

Top Haunch 0.500 x 0.100 m

Girder 'B' and 'C'

Bottom Bulb Width = 0.500 m

Bottom Bulb Thickness = 0.250 m

Bottom Haunch 0.125 x 0.125 m

Top Haunch 0.150 x 0.050 m

DESIGN OF DECK INTERIOR SLAB PANNEL

Dead weight of slab 0.250 x 25.000 = 6.25 kN/m2 Dead weight of wearing coat 0.080 x 22.000 = 1.76 kN/m2

Total weight = 8.01 kN/m2

Considering 70R Tracked vehicle, B = 2.500 m which is placed at the centre of

pannel as shown in fig Conatact ares of vehicle is,

0.84 m in transevers direction 4.57 m in longitudinal direction u = 0.84+2x0.08 1.00 m v = 4.57+2x0.08 4.73 m > 4.000 m hence v = 4.000 m u = 1.00 m u/B = 1/2.5 = 0.4 v/L = 4/4 = 1.00 K = B/L = 2.5/4 = 0.625

Refering to Pigeaud's curves corresponding to 'K'=7' values, the values of moment Co-efficients are,

m1 = 0.085

m2 = 0.034

Impact factor for 70R tracked vehicle = 10% as per IRC-6:2000,Cl:208.3, page No 21,

70R Tracked load for two track = 700.00 kN 70R Tracked load for one track = 350.00 kN Total load per track including impact = 385.00 kN Effective load on span (W) = 385x(4/4.73)

= 325.58 kN 4 .7 3 0 v = L = 4 .0 0 0

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Moment along shorter span ( MB)

MB = W*(m1+1.5*m2)

= 325.581395348837x(0.085+1.5x0.034) = 44.28 Kn-m

Moment along longer span ( ML)

ML = W*(m2+1.5*m1)

= 325.581395348837x(0.034+1.5x0.085) = 52.58 Kn-m

As the slab is continuous, the design bending moments are obtained by applying the continuity factor as,

MB = 0.8x44.2790697674419

= 35.42 Kn-m

ML = 0.8x52.5813953488372

= 42.07 Kn-m

Dead load bending moments are computed using Pigeaud's Curves

Dead Load = 8.01 kN/m2

Ttal DL on pannel = 8.01x4x2.5 = 80.10 kN

(u/B) = (v/L) = 1 as pannel is loaded with UDL K = B/L = 2.500 / 4.000

= 0.625 1/K = 1.6

from Pigeaud's Curves read out the Co-efficients are

m1 = 0.047

m2 = 0.025

Taking the continuity effect, the design moments are, MB = (0.8*W)*(m1+1.5*m2) = 0.8x80.1(0.047+1.5x0.025) = 5.415 kN-m ML = (0.8*W)*(m2+1.5*m1) = 0.8x80.1(0.025+1.5x0.047) = 6.12 kN-m

Hence final design moments in the slabs are obtained as, MB = 35.42 + 5.4148 = 40.838 kN-m

ML = 42.07 + 6.1196 = 48.185 kN-m

Design parameters

Grade of concrete = M-35 = 35 N/mm2

Grade of Steel Fe = Fe-415 = 415 N/mm2 According to IRC-21:2000

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Design Constants: σcbc = 11.67 N/mm2 σst = 200 N/mm2 m = 10 k = m σcbc/( mσcbc + σst) = 10 11.667 10 11.667 200 = 0.37 j = 1-(k/3) = 1 0.37 3 = 0.88 Q = 0.5 x σcbc x j x k = 0.5 11.667 0.88 0.37 = 1.89 dreq = 1E+06 1000 = 159.9 mm dia of rod =16 Overall Depth Provided = 250 mm

Clear Cover = 40 mm Center of reinforcement = 8 mm

Effective depth Provided = 202 mm < dreq Hence O.K. Are of Steel Required =

For Shorter span

Are of Steel Required = 40.84

0.877 200 202 = 1152.4 mm2/m

Minimum reinforcement required = 0.12 % of cross sectional area = 0.12% 1000 250

300 mm2/m Astreq > Astmin

Hence required Ast = 1152.4 mm2/m

Steel Provided = Pro steel/m =

Provide 16mm dia 150 mm c/c 1340.41 Total Steel Provided on Embankment Face = 1340.41 mm2/m

OK and SAFE j x σst x d 1000000 M x 106 48.18 1.89 x x x x x x x x x x x x

x

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

x

x x x x x x x x x x x x x x x x x x + - x x x mm x x

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For Longer span

0.877 200 202 = 1359.7 mm2/m

300 mm2/m Astreq > Astmin

NOT OK DESIGN OF CANTILIVER SLAB

Bellow figure shows the cantiliver portion of the Tee beam and slab bridge deck with dimensional details of cantiliver projection, kerb, hanrails and footpath.

0.20 1.00 0.90 0.35 0.45 0.50 0.50 0.10

CROSS SECTIONAL DETAILS OF CANTILIVER SLAB a). Dead Load Calculation

i) Dech slab = 0.25 1.00 25 6.25 kN/m

ii) Haunch at sopprt = 0.10 25 2.5 kN/m

iii) Foot path = 0.35 1.00 25 8.75 kN/m

iv) Kerb above Footpath = 0.10 0.60 25 1.5 kN/m

v) Parapet = 0.90 0.20 25 4.5 kN/m 2.5 kN/m 4.5 kN/m 1.5 kN/m 6.25 kN/m 8.75 kN/m 0.50 m 0.20 m 0.60 m 1.00 m

LOADING DETAILS OF CANTILIVER SLAB 0.25 0.60 1000000 1.00 x x x x x x x x x x

x

x x x x x x x x x x x x x x x x x x x x x x x x x x x x = = = = =

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Taking Moments at the support

i) Dech slab = 6.25 1.00 0.50 3.13 kN-m

ii) Haunch at sopprt = 0.5 1.25 0.17 0.10 kN-m iii) Foot path = 8.75 1.00 0.50 4.38 kN-m iv) Kerb above Footpath = 1.5 0.60 0.70 0.63 kN-m

v) Parapet = 4.5 0.20 0.90 0.81 kN-m

Total Moment at support 9.04 kN-m

b). Live Load Calculation

Here only footpath live load is considered, becouse footpath is covering the whole cantiliver portion.

According to IRC-6:2010, Cl:209.4(b) Footpath load is taken 5.00kN/m2

5.00 0.40 2 kN/m

0.40 m

Taking Moments at the support = 2 0.40 0.2 0.16 kN-m c). Maximum Bending Moment at Support

i) Dead Load Moment = 9.04 kN-m ii) Live Load Moment = 0.16 kN-m Toatl Moment = 9.20 kN-m Design parameters

Grade of concrete = M- 35 = 35 N/mm2

Grade of Steel Fe = Fe- 415 = 415 N/mm2 According to IRC-21:2000 Design Constants: σcbc = 11.67 N/mm2 σst = 200 N/mm2 m = 10 k = 0.37 j = 0.88 Q = 1.89 dreq = 1E+06 1000 = 69.9 mm dia of rod =10 Overall Depth Provided = 350.00 mm

Clear Cover = 40 mm Center of reinforcement = 5 mm

Effective depth Provided = 305 mm < dreq Hence O.K. Are of Steel Required =

For Shorter span

0.877 200 305 = 172.0 mm2/m 9.20 1.89 M x 106 j x σst x d 1000000 x x = x x x x x x x x = = = = x = = x x x x x x x x x x x x x x

x

_x

x x x x x x x x x x x x x x x x mm

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420 mm2/m Astreq < Astmin

OK and SAFE DESIGN OF LONGITUDINAL GIRDER

Using Courbon's theory, IRC Class 70R Tracked vehicle loads are arranged for maximum eccentricity as shown in bellow figer.

Wheel position of vehicle is taken as per IRC-6:2000. e =1.10

1.62 2.06 C/L of Bridge deck

3.750 3.750

1.25 1.25

TRANSVERSE POSITION OF IRC CLASS 70R TRACKED VEHICLE W = 700 kN

W1 = 350 kN a). Reaction Factors

The reaction factor for outer girder 'A' and 'D' is given by

2W1 neX1

n SX2

Wheare,

W = the eccentric concentrated load n = The number of longitudinal girder

e = the eccentricity of the wheel load from the centre line of the deck X1 = the distance of the girder under consideration from the central

axis of the deck. SX2 ₌

the sum of the distances of longitudinal girders from the centre line of the deck. 2 350 4 1.10 3.750 2 3.750 3.750 1.25 1.25 = 267.4 kN RA = 1 4 RA = 1 + W1 W1 W x x x + x + x x x x

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The reaction factor for inner girder 'B' and 'C' is given by 2W1 neX1 n SX2 here X1 is 0 2 350 4 1.10 0.0 2 3.750 3.750 1.25 1.25 = 175 kN

b). Dead load from slab per girder Dead load of slab is calculated as bellow,

1) Parapet railing 0.20 0.90 25 = 4.5 kN/m 2) Kerb and deck slab 0.70 0.60 25 = 10.5 kN/m

3) Foot path 0.35 1.00 25 = 8.75 kN/m

Total = 23.75 kN/m

Total Dead load of Deck

= 2 23.8 + 7.500 8.01

= 107.6 kN/m

It is assumed that the dead load of deck is shared equally by all the four girders.

There fore Dead load per girder = 107.58 4 = 26.894 kN/m c). Live Load Bending Moment in Girder-'A'

Effective span of girder = 16.00 m Impact factor for 70R tracked vehicle = 0.10 The live load is placed centrally as shown in figer,

4.57 m

700.00 kN

a = 8 m b = 8 m

d). Dead load Bending Moment in girder 'A' and 'D'

0.25 0.25 0.15 0.05 0.50 0.10 1.50 1.50 0.25 0.125 0.125 0.125 0.125 0.250 0.50

Girder 'B' and 'C' C/S Girder 'A' and 'D' C/S

RA = 1 + #### #### 0.50 0.25 0.250 = 1 4 #### x x x + x + x x x x x x x x x x / x x

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Self weight of girder 'A' and 'D' Top haunch 2 0.5 0.50 0.10 16.00 25 20 kN Bottom haunch 2 0.5 0.125 0.125 16.00 25 6.25 kN Web 1 0.25 1.00 16.00 25 100 kN Bottom bulb 1 0.50 0.25 16.00 25 50 kN Total 176.25 kN 11.016 kN/m Self weight of girder 'B' and 'C'

Top haunch 2 0.5 0.15 0.05 16.00 25 3 kN Bottom haunch 2 0.5 0.125 0.125 16.00 25 6.25 kN Web 1 0.25 1.00 16.00 25 100 kN Bottom bulb 1 0.50 0.25 16.00 25 50 kN Total 159.25 kN 9.9531 kN/m Weight of each Cross Girder = 0.30 1.250 25 9.375 kN/m Reaction on Main Girder = 9.375 2.50 23.438 kN Reaction from Dead load on each girder = 26.894 kN/m There fore total Dead load on girder 'A' & 'D' = 26.894 11.016 37.91 kN/m There fore total Dead load on girder 'B' & 'C' = 26.894 9.9531 36.85 kN/m

Maximum Bending Moment for Girder 'A' and 'D' 23.44 kN 23.44 kN 23.44 kN 37.91 kN/m 4 m 4 m 4 m 4 m 16.00 m Mmax = 37.91x16.00x16.00/8+ 1213.1 23.44x16.00/4.00+ = 93.75 = 1400.6 kN-m 23.44x16.00/4.00 93.75

Maximum Bending Moment for Girder 'B' and 'C' 23.44 kN 23.44 kN 23.44 kN 36.85 kN/m 4 m 4 m 4 m 4 m 16.00 m Mmax = 36.85x16.00x16.00/8+ 1179.1 23.44x16.00/4.00+ = 93.75 = 1366.6 kN-m 23.44x16.00/4.00 93.75 x x x x x = x x x x x xx == x x x x xx == x x x x xx == x x x x x = x x x x x xx == x x x x xx == x x x x xx = = x x = x = + = + ==

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e). Design Moment

Design Moments in Girder 'A' and 'D'

Dead Load Moment = 1400.6 kN-m

Live Load Moment = kN-m

Total design Moment = 1400.6 kN-m Design Moments in Girder 'A' and 'D'

Dead Load Moment = 1366.6 kN-m

Live Load Moment = kN-m

Total design Moment = 1366.6 kN-m f). Design of Reinforcement in Girder