DESIGN OF T-BEAM DECK SLAB

INPUT DATA

Clear roadway = 7.5 mNo of T beams = 3 m Assuming 3 T-beams at a spacing of = 2.58 m C/CWidth of the bearing = 0 mEffective span of T-beam = 13.4 mAssuming the cross beam at = 3.35 m

= 415

= 25Thickness of the slab = 250 mmThickness of the wearing coat = 50 mmSpan in the transverse direction = 2.58 mEffective span in the transverse direction b = 2.28 mSpan in the longitudinal direction = 13.4 mEffective span in the longitudinal direction l = 13.15 m

Step 11. Maximum bending moment due to dead load:

Weight of the deck slab = 6.25

Weight of the wearing coat = 1.1

Total weight = 7.35

Since the slab is supported on all 4 sides and being continuous, Piegauds curve is usedto get the influence coefficients to compute the moments.Ratio k = Short span/Long span = 0.681/k = 1.47From Piegauds curve

= 0.08

= 0.035

w = Total dead weight = 220.37 KNMoment along short span = (m1+0.15 x m2) x w = 18.79 KN-mMoment along long span = (m2+0.15 x m1) x w = 10.36 KN-m

2. Live load bending moment due to IRC class AA tracked vehicle :size of one panel of deck slab = 2.5 x 3.35 mOne track of tracked vehicle is placed symmetrically in one panel as shownImpact factor fraction = 25 % (as the span is < 5 m)1) Track contact spacing = 0.85 m2)Thickness of the slab = 0.25 m3) Thickness of wearing coat = 0.05 m

Grade of steel fy

Grade of concrete fck

KN/m2

KN/m2

KN/m2

m1

m2

Main beam3.6

2.5 u 2.45

v = 3.35

Figure - 1

3. Class AA track located for the maximum moment on deck slab :

Width of load spreading in the short span

= 0.98 m

v = 3.71 mBut ; v = 3.70844 mRatio k = 0.68 as earlier

u/b = 0.43v/l = 0.28201

= 0.07

= 0.0375

Total load per track including impact = 437.5 KNEffective load on the span = 1598 KNMoment along shorter span = 120.86 KN-mMoment along longer span = 76.71 KN-m

4. Live load B.M due to IRC class AA wheeled vehicle:

a) B.M due to wheel 1:

Tyre contact dimension area: 300 x 150 mmu = 0.472v = 0.354u/b = 0.21v/l = 0.03Using Piegauds curve,

= 0.1965

= 0.175Total load allowing for 25% impact = 78.125 KN

u = 0.85+(2 x 0.05)2 +0.22

m1

m2

m1

m2

0.85 One track

1225 1225

1625

1625

Figure - 2

B.M along short span = 17.40 KN-mB.M along long span = 15.97 KN-m

b) B.M due to wheel 2:

Intensity of loading = 441.085

1225 1225

Figure -3

= 0.0775

= 0.084

Moment along the short span = 35.65 KN-mMoment along the long span = 37.84 KN-m

u/b = 0.66v/l = 0.03

KN/m2

Consider the loaded area of 2.492 x 0.36 m2

m1

m2

Now consider the area of 1.508 x 0.36 m2

150

(2) (1) (3) (5) (4) 1200 (6)

360.5

492.4

300

3.75 t 6.25 t 6.25 t

6.25 t 6.25 t 3.75 t

492 360

1508 2492

6.25 t 6.25 t

= 0.1165

= 0.12Moment along the short span = 32.21 KN-mMoment along the long span = 32.92 KN-m

Net B.M along short span = 1.72 KN-mNet B.M along long span = 2.46 KN-m

c) B.M due to wheel 3:

Figure - 4

Intensity of loading = 264.65

u/b = 0.74v/l = 0.03

= 0.103

= 0.111Moment along the short span = 19.29 KN-mMoment along the long span = 20.38 KN-m

u/b = 0.31v/l = 0.03

= 0.17

= 0.16Moment along the short span = 13.16 KN-mMoment along the long span = 12.36 KN-mNet B.M along short span = 3.06 KN-mNet B.M along long span = 4.01 KN-m

d) B.M due to wheel 4:

m1

m2

KN/m2

Consider the loaded area 1.692 x 0.36 m2

m1

m2

Consider the area of 0.708 x 0.36 m2

m1

m2

492

360

708 1692

3.75 t 3.75 t

2.76 2.040 0.492 0.36

6.25 t

Figure - 5

Intensity of loading = 441.085

u/b = 0.22v/l = 0.21

= 0.11

= 0.047Moment along the short span = 70.11 KN-mMoment along the long span = 38.03 KN-m

u/b = 0.22v/l = 0.16

= 0.135

= 0.0635Moment along the short span = 63.98 KN-mMoment along the long span = 37.08 KN-mNet B.M along short span = 3.06 KN-mNet B.M along long span = 0.48 KN-m

e) B.M due to wheel 5:Net B.M along short span = 3.06 KN-mNet B.M along long span = 0.48 KN-m

f) B.M due to load 6:

Figure - 6

Intensity of loading = 264.65

u/b = 0.22v/l = 0.16

= 0.11

KN/m2

Consider the loaded area 0.492 x 2.76 m2

m1

m2

Consider the loaded area 0.492 x 2.04 m2

m1

m2

KN/m2

Consider the loaded area 2.76 x 0.492 m2

m1

2.76 2.040 0.492 0.36 6.25 t

2.76 2.04

3.75 t

3.75 t

= 0.047Moment along the short span = 42.06 KN-mMoment along the long span = 22.82 KN-m

u/b = 0.22v/l = 0.16

= 0.135

= 0.0635Moment along the short span = 38.39 KN-mMoment along the long span = 22.25 KN-mNet B.M along short span = 1.84 KN-mNet B.M along long span = 0.29 KN-m

g) Total B.M due to all wheels on the spanTotal B.M along short span = 30.15 KN-mTotal B.M along long span = 23.69 KN-m

OUTPUT5. Design B.M

Design B.M along short span = 93.5601 KN-mDesign B.M along long span = 36.5676 KN-m

6. REINFORCEMENTMaximum B.M = 93.5601 KN-mThickness from B.M consideration

=Therefore, d = 164.678 mm

= 170 mmOverall depth = 195 mm

Provide the thickness of slab as = 250 mm

= 300

Reinforcement in short direction:Mx = 93.5601 KN-m

Choose the diameter of the bar = 16 mm

Ast = 200.96Effective depth in short direction, d = 217 mm

=

= 1330.1Spacing = 150 mm Provide 16 mm bars @ a spacing of 150 mm c/c

m2

Consider the loaded area 2.04 x 0.492 m2

m1

m2

Mu (0.138 x fck x b x d2)

Ast(min) mm2

mm2

Ast 0.5 x fck x b x d[1- 1 - 4.6 x Mu/ fck x b xd2]/fy

Ast mm2

Reinforcement in long direction:My = 36.5676 KN-mChoose the diameter of the bar = 12 mm

Ast = 113.04d = 219 mm

= 735Spacing = 150 mmProvide 12mm bars @ a spacing of 150 mm c/c

DESIGN OF CANTILEVER SLAB

Moment due to Dead LoadThe total maximum moment due to dead load/ mtrs width of cantilever slab is computed as follows

Description Load (KN) Lever arm Moment (KN-m)1) Hand rails 1.74 1.03 1.782) Kerb 0 0.9 0.003)Wearing coat 1.00 0.3 0.304)Slab 7.5 0.6 4.50

3.15 0.4 1.26Total 7.84

Moment due to Live LoadDue to the specified minimum clearence,Class AA loading will not operate on the cantilever slab.Hence Class A loading is to be considered. Effective width of dispersion e=(1.2*x)+w

Where, x = 0.2 mw = 0.402 m

Hence e = 0.642 mWhen the wheel load is at the edge of the slab near an abutment,the net effective width of dispersion is given by, = 0.446 mLive load per metre width including impact = 1917 KNMaximum bending moment due to live load = 38.34 KN-m

ReinforcementMain ReinforcementTotal bending moment due to dead load and live load = 46.19 KN-mEffective depth required = 141.71 mmEffective depth provided = 200 mmArea of main reinforcement required = 1051.67Diameter of the bar = 16Number of bars required = 5.23059 6Ast provided = 1206.37Spacing of bars = 166.667

Distribution ReinforcementArea of distribution steel = 240 mm2Diameter of the bar = 8 mmNumber of bars required = 4.78Provide number of bars = 5.00

mm2

Ast mm2

Therefore Ast provided = 251.2 mm2Spacing of the bars = 200 mm

3.35

0.3914731.122388

120.855676.70833

3 2 46 28.26 250 108 50.24 415 15

10 78.5 500 2012 113.04 2516 200.96 3020 314 3522 379.94 4025 490.63 4528 615.44 50

4 46 28.268 50.24

10 78.5012 113.0416 200.9620 314.0022 379.9425 490.6328 615.44

Dia of the bar

mm

Area of steel mm2

2cww nob

1 6 22 9.5 33 12.5 5

10thickness of slab

1 1002 1103 1204 1305 1506 1607 1808 2009 225

10 25011 27512 300