7+670 (1x10x5.8) R1

Design of RCC BOX Structures
DESIGN OF 1 CELL BOX BRIDGE

1 X 10 X 5.8 m
1.0 DESIGN DATA
1.1 GENERAL INFORMATION
This design is for Box Bridge
1.2 DIMENSION DETAILS

No of cells = 1.00 No.s
Skew Angle = 11.00 deg.
Effective Span = 10.70 m
Effective Span (Skew) = 10.90 m
Clear Span = 10.00 m
Clear Span ( Skew) = 10.19 m
Clear Height (at outer edge) = 5.80 m
Clear Height (at median location) = 5.80 m
Width of road at top = 10.50 m
Width of Box = 15.00 m
Width of Box ( skew) = 15.28 m
Wearing coat thickness = 0.065 m
Ht of fill (W.C / P.C.C / pavement layers) over the top slab = 0.000 m
Thickness of top slab = 0.650 m
Thickness of bottom slab = 0.750 m
Thickness of external vertical wall = 0.700 m
Size of haunch = 0.30 m
x 0.30 m
Width of Parapet Wall/ Crash Barrier = 0.45 m
Width of Footpath = 1.30 m
Distance of edge of parapet wall/Crash Barrier from edge of box = 0.50 m
Height of surcharge = 1.20 m
Safe Bearing Capacity of the soil = 120.00 KN/m2
Permissible Settlement = 10 mm = 10mm
Spring Constant (40*2.5*SBC) 12000 KN/m
Where 2.5 is the factor of safety for soil.
STC Pvt. Ltd. 1

1.3 MATERIAL PROPERTIES

Density of concrete = 25.00 KN/m3
Density of soil = 20.00 KN/m3
Density of Submerged soil = 10.00 KN/m3
Density of wearing coat = 22.00 KN/m3
Angle of internal friction (in degree) = 30.00 deg
Coefficient of earth pressure at rest = 0.500
Coefficient of Active Earth Pressure

sin 2
(   )
Active earth presure Ka = 2
 sin(    ). sin(   i ) 
sin 2
 . sin(    ) 1  
 sin(    ). sin(   i ) 
Backfill Soil Parameter

Φ = 30.00 deg = 0.52 Rad
δ = 20.00 deg = 0.35 Rad
i = 0.00 deg = 0.00 Rad
α = 90.00 deg = 1.57 Rad
Coefficient of horizontal earth pressure Kah for straight = 0.279

face.
Coefficient of active earth pressure = 0.279
1.4 DESIGN PARAMETERS

Grade of Concrete = M 35
Grade of Reinforcement = Fe 500
Clear Cover for earth face structural component = 0.075 m
Clear Cover for inside face/ top slab structural component = 0.040 m
Clear Cover for bottom slab = 0.075 m
STC Pvt. Ltd. 2

Dimensions Detail of RCC Box
wc =0.065 mm
Traffic Direction
0.65
10.00
0.7 0.7
5.80
300
0 0 15.0
300
0.75
11
11.40
STC Pvt. Ltd. 3

2.0 LOAD CALCULATIONS FOR THE BOX STRUCTURE
2.1 DEAD LOAD

Self weight of the structure has been calculated directly in STAAD file by the comment "SELFWEIGHT -1".
2.2 SUPER IMPOSED DEAD LOAD

Wearing coat thickness = 0.065 m
2
Intensity of Loading due to surfacing = 1.430 kN/m
Ht of fill (Thickness of W.C / P.C.C / pavement layers)(Considering Avg. Ht. of fill) = 0m
Load (UDL) on top slab = = 1.43 kN/m
Wt of Parapet Wall/Crash Barrier per meter = 10.00 kN/m
Total UDL load due to S.I Dead Load = 11.43 kN/m
2.3 EARTH PRESSURE

Thickness of top slab = 0.650 m
Height of top haunch = 0.300 m
Clear height between top & bottom slab = 5.80 m
Height of bottom haunch = 0.300 m
Thickness of bottom slab = 0.750 m
Earth Pressure at Rest

Height from top Intensity of Earth pressure
2
(m) (KN/m )
0.390 0.390 0.5 x 20 x 0.390 = 3.900
0.325 0.715 0.5 x 20 x 0.715 = 7.150
0.300 1.015 0.5 x 20 x 1.015 = 10.150
5.200 6.215 0.5 x 20 x 6.215 = 62.150
0.300 6.515 0.5 x 20 x 6.515 = 65.150
0.375 6.890 0.5 x 20 x 6.890 = 68.900
Active Earth Pressure

2
(m) (KN/m )
0.390 0.390 0.279 x 20 x 0.390 = 2.177
0.325 0.715 0.279 x 20 x 0.715 = 3.990
0.300 1.015 0.279 x 20 x 1.015 = 5.664
5.200 6.215 0.279 x 20 x 6.215 = 34.680
0.300 6.515 0.279 x 20 x 6.515 = 36.354
0.375 6.890 0.279 x 20 x 6.890 = 38.447
Submerged Earth Pressure at Rest

(m) (KN/m2)
0.390 0.390 0.5 x 10 x 0.390 = 5.850
0.325 0.715 0.5 x 10 x 0.715 = 10.725
0.300 1.015 0.5 x 10 x 1.015 = 15.225
5.200 6.215 0.5 x 10 x 6.215 = 93.225
0.300 6.515 0.5 x 10 x 6.515 = 97.725
0.375 6.890 0.5 x 10 x 6.890 = 103.350
Submerged Active Earth Pressure

(m) (KN/m2)
0.390 0.390 0.279 x 10 x 0.390 = 4.99
0.325 0.715 0.279 x 10 x 0.715 = 9.15
0.300 1.015 0.279 x 10 x 1.015 = 12.98
5.200 6.215 0.279 x 10 x 6.215 = 79.49
0.300 6.515 0.279 x 10 x 6.515 = 83.33
0.375 6.890 0.279 x 10 x 6.890 = 88.12
STC Pvt. Ltd. 4

2.4 LIVE LOAD SURCHARGE

Equivalent height = 1.20 m
2
Uniform Intensity of loading (Considering coefficient of active earth pressure)= 0.279 x 1.2 x 20 = 6.70 kN/m
2
Uniform Intensity of loading (Considering coefficient of earth pressure at rest)= 0.5 x 1.2 x 20 = 12.00 kN/m
2.5 BRAKING LOAD
Load for one lane 70R 0.2 * 460 = 92 KN

Load for one lane Class A 0.05 * 175 = 8.75 KN
Carriageway Live Load = 100.8 kN
Width of the box = 15.28 m
Braking Load = 1 x 100.75 / 15.28 = 6.59 kN
2.6 CALCULATING BRIDGE TEMPERATURE :

o
Maximum air shade temperature = 40 C
o
Minimum air shade temperature = 4 C
o
Bridge Temperature = 27 C
STC Pvt. Ltd. 5

3.0 Effective width of tyres and load distribution for different vehicular loadings:
Effective span lo = 10.70 m

Total Width of Box culvert b = 15.00 m
Ht of fill (W.C / P.C.C / pavement layers) at edge = 0.065 m

Thickness of deck slab = 0.650 m
Width of Crash barrier / Kerb = 0.45 m

Dist. of edge of crash barrier/guard stone from edge of box = 0.45 m
Span / Wdith ratio b / lo = 15.00 / 10.70 = 1.40
As per Cl. B3.2 of IRC:112-2011(Page-278), for continous slab

For b / lo = 1.40 ; α = 2.80
3.1 Class 70R vehicle (Maximum Bogie Load) (Refer: Clause 204.1.3, Fig.1, IRC : 6-2014 )
3.1.1 Axle - " l " :
5t 5t 5t 5t 20 t 20 t
450 1480 450
410 40 410 1070 410 40 410

1220
2790
Transverse Longitudinal
Total Load = = 40.00 t

Impact factor = (Refer Cl.208.4 of IRC:6-2014) = 1.250
Minimum clear distance from C/B to the edge of the end wheel = 1.20 m
Distance between the axles in the direction of traffic = 1.22 m
C/C distance between end wheels in transverse direction = 2.38 m
410
Load on one tyre = = 5.00 t
Max. tyre pressure = (Refer Annex A of IRC:6-2014) = 5.273 Kg/cm2
Contact width of tyre = (Refer Annex A of IRC:6-2014) = 360 mm
Contact area = 5000 / 5.273 360 = 948.23 cm2

Breadth = 948.23 / 36 = 26.3 cm
Contact area = 360 x 263 mm
Contact width of tyre in a direction perpendicular to the span = 0.36 m

Wheel dimension perpendicular to span = 0.41 m
Dist. from outer edge of kerb to c.g of wheel = 0.45 + 1.2 + 0.41 / 2 = 1.86 m
Effective width, bef = α a (1 - a / lo) + b1 (Refer Cl. B3.2 of IRC:112-2011)
STC Pvt. Ltd. 6

a = the distance of c.g of concentrated load from nearer support

= 10.70 / 2 - 1.22 / 2 = 4.740 m
b1 = 0.36 + 2 x 0.07 = 0.49 m
Effective width = 2.8 x 4.74 x (1 - 4.74 / 10.70) + 0.49 = 7.88 m
(Dispersion width crosses the deck slab) > 1.48 m
(Dispersion width of four wheels overlaps in trans direction)
Effective load in transverse direction = 20.00 t
Effective width for design = 8.177 m

(In transverse direction)
3.155 2.380
Edge of
Box 1.75 1.20 0.41 0.04 0.41 1.07 0.41 0.04 0.41
Dispersion along span direction = 0.263 + 2 x (0.07 + 0.65) = 1.693 m

(Refer Cl. B3.3 of IRC:112-2011) > 1.220 m
Dispersion width for design = (IF(1.69>1.22,(1.69 + 1.22),1.69)

(In longitudinal direction) = 2.913 m
Total load = 40.0 t

Dispersion area = 8.177 x 2.913 = 23.82 m2
Load per unit area = 40 / 23.82 = 1.68 t/m2
Load per unit area with I.F = 1.68 x 1.25 = 2.10 t/m2
3.1.2 Axle - " m ": (Refer: Clause 204.1.3, Fig.1, IRC : 6-2014 )
5t 5t 5t 5t 20 t 20 t
795 790 795
410 385 410 380 410 385 410

1220
2790

Min. clear distance from Crash Barrier to the edge of the end wheel = 1.20 m
C/C distance between end wheels in transverse direction 410 = 2.38 m
Load on one tyre = 5.00 t

Contact width of tyre = (Refer Annex A of IRC:6-2014) 360 = 360 mm
STC Pvt. Ltd. 7

Contact area = 5000 / 5.273 = 948.23 cm2

Breadth = 948.23 / 36 = 26.3 cm

Distance from outer edge of kerb to c.g of wheel = 1.855 m
Effective width = α a (1 - a / lo) + b1 (Refer Cl. B3.2 of IRC:112-2011)

= 10.70 / 2 - 1.22 / 2 = 4.740 m
b1 = 0.36 + 2 x 0.07 = 0.490 m
Effective width = 2.8 x 4.74 x (1 - 4.74 / 1.22) + 0.49

(Dispersion width crosses the deck slab) = 7.88 m
(Dispersion width of four wheels overlaps in trans direction) > 0.79 m

3.155 2.380
Edge of
Box 1.75 1.20 0.41 0.39 0.41 0.38 0.41 0.39 0.41

(Refer Cl. B3.3 of IRC:112-2011) > 1.220

Total load = 40.0 t

3.1.3 Axle - " n ": (Refer: Clause 204.1.3, Fig.1, IRC : 6-2014 )
2.5 t 2.5 t 2.5 t 2.5 t 2.5 t 2.5 t 2.5 t 2.5 t 20 t 20 t

280 480 280 480 280 480 280
230 230 230 230 230 230 230 230

50 250 50 250 50 250 50 1220
2790
STC Pvt. Ltd. 8

Total Load = 40.00 t

Minimum clear distance from Crash Barrier to the edge of the end wheel = 1.20 m
c/c distance between end wheels in transverse direction = 2.56 m
Load on one tyre 230 = 2.50 t

Contact width of tyre = (Refer Annex A of IRC:6-2014) = 180 mm
Contact area = 2500 / 5.273 = 474.12 cm2

Breadth = 474.12 / 18 180 = 26.3 cm


= 10.70 / 2 - 1.22 / 2 = 4.740 m
b1 = 0.18 + 2 x 0.07 = 0.31 m

(Dispersion width of wheels overlaps in trans direction)
Effective load in trans direction = 20.00 t
Effective width for design = = 8.177 m

3.065 0.280 0.480 0.280 0.480 0.280 0.480 0.280

Edge of
Box 1.75 1.20 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23
0.05 0.25 0.05 0.25 0.05 0.25 0.05 0.23

(Refer Cl. B3.3 of IRC:112-2011) > 1.220

Total load = 40.0 t

STC Pvt. Ltd. 9

3.4 Summary of Intensity of Loads:
Loading Intensity of Load (t/m2)

70R - Axle 'l' 2.100
70R - Axle 'm' 2.100
70R - Axle 'n' 2.100
Design LL intensity for analysis = 2.100 t/m2

= 21.00 kN/m2
3.2 Class -A vehicle:
3.2.1 Single Lane Class A (Refer: Clause 204.1.3, Fig.1, IRC : 6-2014 )
5.7 t 5.7 t 11.4 t 11.4 t

1800
500 1300 500

1200
2300

Contact width of tyre = 500 mm

Contact breadth of tyre = 25 cm


= 10.7 / 2 - 1.2 / 2 = 4.750 m
b1 = 0.5 + 2 x 0.065 = 0.63 m
STC Pvt. Ltd. 10


(Dispersion width of two wheels overlaps in trans direction)
0.85 1.800
Edge of
Box 0.45 0.15 0.50 1.30 0.50


(Refer Cl. B3.3 of IRC:112-2011) > 1.200
Dispersion width for design = IF(1.68>1.2,(1.68 + 1.2),1.68) = 2.880 m

(In longitudinal direction)
Total load = 22.8 t

Load per unit area = 22.8 / 19.19 = 1.19 t/m2
STC Pvt. Ltd. 11

3.2.2 Two Lane Class A
5.7 t 5.7 t 5.7 t 5.7 t 22.8 t 22.8 t

1800 1700 1800
500 1300 500 1200 500 1300 500

1200
5300




= 10.7 / 2 - 1.2 / 2 = 4.750 m
b1 = 0.5 + 2 x 0.065 = 0.63 m
Effective width = 2.8 x 4.75 x (1 - 4.75 / ) + 0.63 = 8.03 m

0.85 1.800 1.700 1.800

Edge of
Box 0.45 0.15 0.50 1.30 0.50 1.20 0.50 1.30 0.50


(Refer Cl. B3.3 of IRC:112-2011) > 1.200
STC Pvt. Ltd. 12


Total load = 45.6 t

1 Lane Class A 1.511

2 Lane Class A 1.980
1.1
3.2.3 Three Lane Class A
5.7 t 5.7 t 5.7 t 5.7 t 5.7 t 5.7 t

1800 1700 1800 1700 1800
500 1300 500 1200 500 1300 500 1200 500 1300 500
8800
Transverse
34.2 t 34.2 t
1200
Longitudinal


STC Pvt. Ltd. 13



= 10.7 / 2 - 1.2 / 2 = 4.750 m
b1 = 0.5 + 2 x 0.065 = 0.63 m

0.85 1.800 1.700 1.800

Edge of
Box 0.45 0.15 0.50 1.30 0.50 1.20 0.50 1.30 0.50


(Refer Cl. B3.3 of IRC:112-2011) > 1.200

Total load = 68.4 t

STC Pvt. Ltd. 14

3.3 One lane of 70 R (Bogie) + One Lane Class A
5.0 t 5.0 t 5.0 t 5.0 t 5.7 t 5.7 t

795 790 795 2200 1800
410 385 410 380 410 385 410 1200 500 1300 500
5880
Transverse
31.4 t 31.4 t
1200
Longitudinal




= 10.7 / 2 - 1.2 / 2 = 4.750 m
b1 = 0.5 + 2 x 0.065 = 0.63 m

STC Pvt. Ltd. 15

1.90 1.800 1.700 1.800

Edge of
Box 0.45 1.20 0.50 1.30 0.50 1.20 0.50 1.30 0.50


(Refer Cl. B3.3 of IRC:112-2011) > 1.200

Total load = 62.8 t

3.4 70 R Tracked Vehicle




= 10.7 / 2 - 4.57 / 2 = 3.065 m
b1 = 0.84 + 2 x 0.065 = 0.97 m

STC Pvt. Ltd. 16

2.07 2.040
Edge of
Box 0.45 1.20 0.84 1.20 0.84

Dispersion along span direction = 4.57 + 2 x (0.065 + 0.65) = 6m

(Refer Cl. B3.3 of IRC:112-2011)
Dispersion width for design = IF(6>4.57,(6 + 4.57),6) = 6.000 m

Total load = 70.0 t

Dispersion area = 7.667 x 6 = 46.00 m2
3.5 CLASS AA Tracked Vehicle




= 10.7 / 2 - 3.6 / 2 = 3.550 m
b1 = 0.85 + 2 x 0.065 = 0.98 m

STC Pvt. Ltd. 17

1.63 2.050
Box
0 0.00 1.20 0.85 1.20 0.85


(Refer Cl. B3.3 of IRC:112-2011)

Total load = 70.0 t

3.6 Special Vehicle
2.25 t 2.25 t 2.25 t 2.25 t 2.25 t 2.25 t 2.25 t 2.25 t

244 506 244 806 244 506 244
450 300 450 600 450 300 450
2700
900 900
1800
Transverse
18.0 t 18.0 t
1500
Longitudinal
STC Pvt. Ltd. 18



Contact breadth of tyre = 27.4 cm


= 10.7 / 2 - 1.5 / 2 = 4.600 m
b1 = 1.2 + 2 x 0.065 = 1.33 m



(Refer Cl. B3.3 of IRC:112-2011) > 1.500

Total load = 36.0 t

3.5 Special Vehicle
Loading Intensity of load (t/m2)

70R- Axle 'l' 2.10
70R- Axle 'm' 2.10
70R- Axle 'n' 2.10
1 Lane Class A 1.51
70R-Track 1.68
CLASS-AA Track 1.94
Special Vehicle 1.51
Design LL intensity for Analysis = 2.10 t/m2

= 21.00 KN/m2
STC Pvt. Ltd. 19

Temperature Rise
.1 The top slab is designed for the effects of the distribution of the temperature across the deck depth as given in the sketch below.
Depth of Top Slab = 0.65 m

2
Grade of concrete = 35.00 N/mm
2
Modulus of elasticity = 3.20E+07 KN/m
Coefficient of thermal expansion = 0.000012
17.8 s1
F1
0.15m
4 h/2 s2 x1
0.65m 0.20m F2
N A x2
h/2 x3
0.15m
F3
2.1 s3
.2 Member h h1 h2 h3 T1 T2 T3
o o o
Unit m m m m C C C
Top Slab 0.65 0.15 0.195 0.15 17.8 4 2.1
.3 Member s1 s2 s3 F1 F2 F3 F
Units kN/m2 kN/m2 kN/m2 kN kN kN kN
Top Slab 6835 1536 806 628 150 60 838
.4
CG of
CG of top CG of mid
CG of Section CG of Section bottom
Member block from block from x1 x2 x3 M
from top from bottom block from
top top
bottom
Units m m m m m m m m kNm
Top Slab 0.33 0.33 0.06 0.22 0.05 0.27 0.11 0.28 166.74
STC Pvt. Ltd. 20

Temperature Fall
.1 The top slab is designed for the effects of the distribution of the temperature across the deck depth as given in the sketch below.
Depth of Top Slab = 0.65m

2
Grade of concrete = 35.00 N/mm
2
Modulus of elasticity = 32,000,000 KN/m
Coefficient of thermal expansion = 0.000012
10.6 s1
F1
0.13
h/2
x1
0.7 s2
0.65m N A N F2 A
0.1625 x2
h/2 x3
0.1625 x4
0.8 s3 F3
0.13
F4
6.6 s4
.2 Member h h1 h2 h3 h4 T1 T2 T3 T4
units m m m m m C C C C
Top Slab 0.65m 0.13 0.1625 0.1625 0.13 10.6 0.7 0.8 6.6
.3 Member s1 s2 s3 s4 F1 F2 F3 F4 F
Unit kN/m2 kN/m2 kN/m2 kN/m2 kN kN kN kN kN
Top Slab 4070.40 268.80 307.20 2534.40 282.05 21.84 24.96 184.70 513.55
CG of CG of
CG of
CG of CG of top bottom bottom
Section CG of top mid
Member Section block mid block block x1 x2 x3 x4 M
from block from top
from top from top from from
bottom
bottom bottom
.4
Units m m m m m m m m m m kNm
Top Slab 0.33 0.33 0.05 0.18 0.18 0.05 0.28 0.14 0.14 0.28 27.09
STC Pvt. Ltd. 21

Calculation of Vertical Subgrade Reaction:
The structure as shown is idealised in STAAD. The vertical soil resistance at bottom has been applied in the form of
springs. The value of spring constants has been calculated based on the permissible settlement and bearing capacity.
The bottom slab of structure is idealised as shown in following figure. The equivalent spring is applied at each node
according to subgrade reaction.
10.90
6.500
1 2 3 4 5 6 7 8 9 10
Input Data Coordinate calculation for Bottom Slab

Thickness of top slab 650 mm Node x y z
Thickness of bottom slab 750 mm 1 0.000 0.000 0.000
Thickness of vert wall (SKEW) 700 mm 2 0.350 0.000 0.000
Haunch 300 mm 3 0.650 0.000 0.000
Clear span(SKEW) 10187 mm 4 2.570 0.000 0.000
Clear Height 5800 mm 5 4.490 0.000 0.000
SBC 12.0 t/m2 6 6.410 0.000 0.000
Permissible settlement 10.00 mm 7 8.330 0.000 0.000
8 10.250 0.000 0.000
9 10.550 0.000 0.000
Support No K Value 10 10.900 0.000 0.000
1 & 10 2100.00
2&9 3900.00
3&8 13320.32
4 to 7 23040.64
STC Pvt. Ltd. 22

Creep Coefficent
fck = 35 Mpa
fcm = 45 Mpa
t = 25550 days
to = 90 days
Φ (t, to) = Φo βc ( t , to )
Φo = ΦRH β(fcm) β(to)
ΦRH = Factor to allow for the effect of relative humidity on the notional creep coefficient
= 1+ 1 - RH/100 for fcm ≤ 45 Mpa
0.1 ( ho )1/3
=
1+ 1 - RH/100 for fcm > 45 Mpa
α1 * α2
0.1 ( ho )1/3
RH = Relative humidity of the ambient environment in percent = 80 %

α = coefficient to consider the influence of the concrete strength
α1 = [ 43.75 / fcm ]0.7 α2 = [ 43.75 / fcm ]0.2 α3 = [ 43.75 / fcm ]0.5
β(fcm) = factor to allow for the effect of concrete strength on the notional creep coefficient = 18.78 / √fcm
β(to) = factor to allow for the effect of concrete age at loading on the notional
creep coefficient = 1/ ( 0.1+ to 0.2)
Φo = ΦRH x β(fcm) x β(to)
βc( t , to)= coefficient to describe the development of creep with time after loading
= [ (t - to) / (βH + t - to) ]0.3
βH = coefficient depending on the relative humidity(RH in percent) and the notional member size(ho in mm)
Min 1.5 [ 1+ (0.012 RH)18 ] ho +250 for fcm ≤ 45 Mpa
1500
=
Min 1.5 [ 1+ (0.012 RH)18 + ho +250 α3
for fcm > 45 Mpa
1500* α3
Summary of Creep Coefficent

Element ho (mm) α1 α2 β(fcm) ΦRH β(to) Φo α3 βH βc( t , to) Φ (t, to)
Top Slab 611.01 0.980 0.994 2.800 1.236 0.391 1.352 0.986 1500 0.983 1.329
Side Wall 624.62 0.980 0.994 2.800 1.234 0.391 1.350 0.986 1500 0.983 1.327
Bottom Slab 698.57 0.980 0.994 2.800 1.225 0.391 1.340 0.986 1500 0.983 1.318
Summary of Bending Moment and Shear Force from STAAD File

Distance from
Bending Moment (kN/m) Shear Force (kN)
Member Case Section centreline of
side wall (m) ULS SLS (Rare) SLS (QP) ULS
Mid Span 5.444 500.000 355.000 290.000 13.000
Curtailment 3.406 320.000 300.000 230.000 75.000
Sagging
Face of Haunch 0.650 30.000 30.000 30.000 195.000
Top Slab
deffective 0.950 30.000 30.000 30.000 175.000

Face of Support 0.350 550.000 370.000 245.000 210.000
Face of Haunch 0.650 450.000 295.000 190.000 195.000
Hogging
Curtailment 3.406 55.000 55.000 55.000 92.000
deffective 0.950 380.000 210.000 170.000 180.000
Mid Span 3.250 205.0 205.0 205.0 55.0

Curtailment 2.115 150.0 140.0 160.0 110.0
Sagging
Face of Haunch 0.675 60.0 50.0 50.0 200.0
Side Wall
deffective 1.027 90.0 60.0 60.0 160.0

Face of Support 0.375 630.0 410.0 275.0 385.0
Face of Haunch 0.675 560.0 380.0 260.0 340.0
Hogging
Curtailment 2.115 470.0 330.0 170.0 190.0
deffective 1.027 520.0 400.0 210.0 255.0
Mid Span 5.444 680.000 470.000 380.000 36.000

Curtailment 3.406 590.000 405.000 330.000 100.000
Sagging
Face of Haunch 0.650 80.000 75.000 70.000 320.000
Bottom Slab
deffective 1.050 150.000 90.000 70.000 280.000

Face of Support 0.350 610.000 425.000 335.000 370.000
Face of Haunch 0.650 465.000 325.000 250.000 335.000
Hogging
Curtailment 3.406 85.000 85.000 82.000 180.000
deffective 1.050 370.000 190.000 190.000 260.000
STC Pvt. Ltd. 24

DESIGN OF TOP SLAB

MIDSPAN - SAGGING
Depth of member (D) = 650.00 mm
Width of the member (b) = 1000.00 mm
MATERIAL PROPERTIES :
Grade of concrete, fck = 35 MPa
Mean value of concrete compressive strength, fcm = 45 MPa
Grade of Reinforcement = 500 MPa
fywd 0.8 fyk = 400 MPa
Clear cover of top slab = 40 mm
Modulus of Elasticity steel Es = 200000 MPa
For short Term loading Ecm = 32308 MPa
For long Term loading Ecm' = 13875 MPa
fctm = 2.80 MPa
fcteff = Max of 2.9 Mpa or fctm = 2.90 MPa
fcd = 15.75 MPa
Cross sectional Area, Ac = 6.622 m2
Perimeter in contact with atmosphere u = 21.67 m
Notational size ho = 611.01 mm
Age of concrete at the time of loading = 90 days
t∞ considered = 25550 days
Creep factor Φ= 1.3286
εuk = 0.00450
εud = 0.00405
εcu2 = 0.0035
xumax/d = 0.4636
PERMISSIBLE STRESSES
1) Permissble concrete compressive stresses
Load Combination Permissble Stress
SLS Rare 0.48 fck = 16.8 MPa
SLS QP 0.36 fck = 12.6 MPa
2) Permissble Tensile stress in steel (Rare) 0.6 fy = 300 MPa

0.8 fy = 400 MPa
3) Permissible crack width wk
SLS QP Load combination = 0.3 mm
Maximum Reinforcement
[ Tension Reinf. ] ≤ 0.025AC At section other than Laps
* Tension + Compression + ≤ 0.04AC At any section
Where AC = Gross Cross section Area of Concrete
Minimum Reinforcement :
Ast min = Max [ 0.26 fctm / fyk bt d , 0.0013 bt d ] (Refer IRC:112 clause 16.5.1.1)
bt = Mean width of Tension zone.
STC Pvt. Ltd. 25

A) ULS CAPACITY CHECK (Top Slab Sagging)
Section Mid Span Curtailment point deffective Face of Haunch
Distance from centreline of side wall m 5.444 3.406 0.650 0.950

MED (Sagging) kNm 500.000 320.000 30.000 30.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
Overall depth D mm 650.000 650.000 650.000 650.000
d mm 600.000 600.000 600.000 600.000
Diameter mm 20 16 20 16 20 16 20 16
Area of steel
Spacing mm 200 200 200 200 200 200 200 200
provided 2
Ast, Provided mm 2576.106 2576.106 2576.106 2576.106
Reinforcement (%) 0.429 0.429 0.429 0.429
xmax mm 278.146 278.146 278.146 278.146
xu = 0.87 fyk Ast / 0.362 fck b mm 88.446 88.446 88.446 88.446
Check UR, OK UR, OK UR, OK UR, OK
Ast,cal =M/ 0.87 fyk (d'-0.416 xu) mm2 2040.859 1306.150 122.452 122.452
Ast Max mm2 264866.341 264866.341 264866.341 264866.341
Check Ast Calc. < Ast Provided < Ast Max OK OK OK OK
Ast min mm2 900.000 900.000 900.000 900.000
Check Ast,provided > Ast min OK OK OK OK
∆Fd kN 6.500 37.500 87.500 97.500
z = d- 0.416 xu m 563.207 563.207 563.207 563.207
MED/z +∆Fd kN 894.274 605.675 140.766 150.766
MRd =0.87 fyk Ast (d-0.416 xu) kNm 631.133 631.133 631.133 631.133
MRD/z kNm/m 1120.606 1120.606 1120.606 1120.606
Check MRD/z > MED/z + ∆Fd OK OK OK OK
Distribution steel at bottom of top slab: (Refer IRC:112 clause 16.6.1.1)

Distribution Reinforcement : At Least 20% of the main Reinforcement = 515.22 mm2
Provide 12 @ 125 mm c/c = 904.78 mm2 OK
STC Pvt. Ltd. 26

B) SLS STRESS CHECK

Rare Load combination. Quasi Permanent Load Combination
Ec,eq = Ecm*(MQP+MST) m = Es / Ecm'
MST + (1+ Φ)* MQP
MST = MRARE -MQP
m = Es / Ec,eq
Flexural tensile Strength:
where,
fctm,fl = mean Flexural tensile strength of solid beam

h = total depth of member in mm
Formula used for calculation of stress
dc (depth of neutral axis) = .-m x As + √ ( m2 x AS2 + 2 x m x As x b x d )
b
INA (Transformed) = b x dc3/3 + m x As x (d - dc)2
Compressive stress in concrete σc = MRARE x dc / INA

Tensile stress in steel σs = m x MRARE x (d - dc ) / INA
Stress Check for SLS Load Combinations

SLS (Rare Combination)
Curtailment
Section Mid Span deffective Face of Haunch
point
Distance from centreline of side wall
m 5.444 3.406 0.650 0.950
MED (Sagging) kNm 355.000 300.000 30.000 30.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 600.000 600.000 600.000 600.000
Ast, Provided mm2 2576.106 2576.106 2576.106 2576.106
Checking Section: Cracked or Uncracked
I mm4 1.800E+10 1.800E+10 1.800E+10 1.800E+10
Y = d/2 mm 325.000 325.000 325.000 325.000
σ (Stress) Mpa 6.410 5.417 0.542 0.542
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Cracked Uncracked Uncracked
Finding Stresses considering Cracked Section
Modular ratio 12.909 12.496 14.415 14.415
N.A. depth (dc) mm 169.258 166.969 177.201 177.201
INA mm4 7.786E+09 7.588E+09 8.493E+09 8.493E+09
Compressive stress Mpa 7.717 6.601 0.626 0.626
Max Compressive Stress Mpa 16.800 16.800 16.800 16.800
Check OK OK OK OK
Tensile stress Mpa 253.513 213.936 21.529 21.529
Maximum Tensile Stress Mpa 300.000 300.000 300.000 300.000
Check OK OK OK OK
STC Pvt. Ltd. 27

SLS (Quasi Permanent Combination)

Curtailment
point
m 5.444 3.406 0.650 0.950
MED (Sagging) kNm 290.000 230.000 30.000 30.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 600.000 600.000 600.000 600.000
Ast, Provided mm2 2576.106 2576.106 2576.106 2576.106
I mm4 1.800E+10 1.800E+10 1.800E+10 1.800E+10
Y = d/2 mm 325.000 325.000 325.000 325.000
σ (Stress) Mpa 5.236 4.153 0.542 0.542
fctm,fl Mpa 2.800 2.800 2.800 2.800
Modular ratio 14.415 14.415 14.415 14.415
N.A. depth (dc) mm 177.201 177.201 177.201 177.201
INA mm4 8.493E+09 8.493E+09 8.493E+09 8.493E+09
Check OK OK OK OK
Check OK OK OK OK
C) SLS CRACK WIDTH CHECK (QUASI PERMANENT LOAD COMBINATION)

1) CHECK Ast,min for crack control
Curtailment
point
m 5.444 3.406 0.650 0.950
b mm 1000.000 1000.000 1000.000 1000.000

h mm 650.000 650.000 650.000 650.000
d mm 600.000 600.000 600.000 600.000
Act =bh/2 2
mm 325000 325000 325000 325000
σs = fyk Mpa 500.000 500.000 500.000 500.000
k 1.000 1.000 1.000 1.000
kc 0.400 0.400 0.400 0.400
As,min =kc k fct,eff Act /σs 2
mm 754 754 754 754
As,provided 2
mm 2576.11 2576.11 2576.11 2576.11
Check OK OK OK OK
h 0.00 0.30 0.80 3.00

k 1.00 1.00 0.65 0.65
STC Pvt. Ltd. 28

2) CHECK FOR MAXIMUM SPACING b/w bars.

Curtailment
point
m 5.444 3.406 0.650 0.950
Bar diameter mm 20 20 20 20
Cover mm 40 40 40 40
Provided mm 200 200 200 200
Spacing b/w
bars Calculated mm 250 250 250 250
Check OK OK OK OK
3) CHECK FOR CRACK WIDTH ( IRC 112 / clause 10.3.2 (2) )

Curtailment
point
m 5.444 3.406 0.650 0.950
hc,eff = Min [2.5 (h - d), (h - x)/3 ,
mm 123.95 123.95 123.95 123.95
h/2]
Aceff = hc,eff x b mm2 123951.43 123951.43 123951.43 123951.43
As provided mm2 2576.11 2576.11 2576.11 2576.11
ρpeff = As/Ac,eff 0.0208 0.0208 0.0208 0.0208
Srmax =3.4c + 0.17 Φ /ρPeff mm 299.59 299.59 299.59 299.59
σsc Mpa 208.11 165.05 21.53 21.53
x = neutral axis depth mm 177.20 177.20 177.20 177.20
kt 0.500 0.500 0.500 0.500
αe = Es/Ecm' 14.41 14.41 14.41 14.41
esm - ecm =Max * * σsc - kt fct,eff ( 1+ αe ρP,eff ) /
0.00062 0.00050 0.00006 0.00006
ρP,eff ] /Es , 0.6 σsc/Es ]
wk mm 0.1870 0.1483 0.0193 0.0193
Check OK OK OK OK
D) CHECK FOR SHEAR : ( IRC 112 / clause 10.3.2 (2) )

Check of Shear Reinforcement Requirement
Load combination ULS
Curtailment
point
VED kN 13.00 75.00 175.00 195.00
β 1.0000 1.0000 0.5417 0.7917
βVED kN 13.00 75.00 94.79 154.38
d mm 600.00 600.00 600.00 600.00
bw mm 1000.00 1000.00 1000.00 1000.00
k= Min [ 1 + √200/d , 2 + 1.577 1.577 1.577 1.577
Asl 2 2576.106 2576.106 2576.106 2576.106
mm
ρ1 = Min * Asl/bw d , 0.02 + 0.004 0.004 0.004 0.004
3/2
νmin = 0.031 k fck1/2 0.363 0.363 0.363 0.363
σcp Mpa 0 0 0 0
VRdc =Max * ( 0.12 k (80 ρ1 fck )0.33
+ 0.15 σcp ) bw d , (νmin +0.15σcp ) kN 258.019 258.019 258.019 280.329
bw d ]
No Shear reinf. No Shear reinf. No Shear reinf. No Shear reinf.
Check
Required Required Required Required
STC Pvt. Ltd. 29

DESIGN OF TOP SLAB

SUPPORT - HOGGING
fctm = 2.80 MPa
fcd = 15.75 MPa
εuk = 0.00450
εud = 0.00405
εcu2 = 0.0035
xumax/d = 0.4636

(QP) 0.8 fy = 400 MPa
STC Pvt. Ltd. 30

A) ULS CAPACITY CHECK (Top Slab Hogging)
Section Face of Support Face of Haunch Curtailment point deffective

MED (Hogging) kNm 550.000 450.000 55.000 380.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 600.000 600.000 600.000 600.000
Diameter mm 20 16 20 16 20 0 20 16
Area of steel
Spacing mm 200 200 200 200 200 200 200 200
provided 2
Ast, Provided mm 2576.106 2576.106 1570.796 2576.106
Reinforcement (%) 0.429 0.429 0.429 0.429
xmax mm 278.146 278.146 278.146 278.146
xu = 0.87 fyk Ast / 0.362 fck b mm 88.446 88.446 53.930 88.446
Ast Max mm2 264866.341 264866.341 264866.341 264866.341
Ast min mm2 900.000 900.000 900.000 900.000
∆Fd kN 105.000 97.500 46.000 90.000
z = d- 0.416 xu m 563.207 563.207 577.565 563.207
MED/z +∆Fd kN 1081.551 896.496 141.227 764.708
MRD/z kNm/m 1120.606 1120.606 683.296 1120.606
Distribution steel at top of top slab: (Refer IRC:112 clause 16.6.1.1)

B) SLS STRESS CHECK

MST + (1+ Φ)* MQP
MST = MRARE -MQP
m = Es / Ec,eq
where,

STC Pvt. Ltd. 31


b
INA (Transformed) = bx dc3/3 + m x As x (d - dc)2



m 0.350 0.650 3.406 0.950
MED (Hogging) kNm 370.000 295.000 55.000 210.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 600.000 600.000 600.000 600.000
Ast, Provided mm2 2576.106 2576.106 1570.796 2576.106
I mm4 1.800E+10 1.800E+10 1.800E+10 1.800E+10
Y = d/2 mm 325.000 325.000 325.000 325.000
σ (Stress) Mpa 6.681 5.326 0.993 3.792
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Cracked Uncracked Cracked
Modular ratio 11.636 11.487 14.415 12.848
N.A. depth (dc) mm 162.039 161.161 143.742 168.925
INA mm4 7.168E+09 7.094E+09 5.704E+09 7.757E+09
Check OK OK OK OK
Check OK OK OK OK


m 0.350 0.650 3.406 0.950
MED (Hogging) kNm 245.000 190.000 55.000 170.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 600.000 600.000 600.000 600.000
Ast, Provided mm2 2576.106 2576.106 1570.796 2576.106
I mm4 1.800E+10 1.800E+10 1.800E+10 1.800E+10
Y = d/2 mm 325.000 325.000 325.000 325.000
σ (Stress) Mpa 4.424 3.431 0.993 3.069
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Cracked Uncracked Cracked
STC Pvt. Ltd. 32


Modular ratio 14.415 14.415 14.415 14.415
N.A. depth (dc) mm 177.201 177.201 143.742 177.201
INA mm4 8.493E+09 8.493E+09 5.704E+09 8.493E+09
Check OK OK OK OK
Check OK OK OK OK


m 0.350 0.650 3.406 0.950
b mm 1000.000 1000.000 1000.000 1000.000

h mm 650.000 650.000 650.000 650.000
d mm 600.000 600.000 600.000 600.000
Act =bh/2 mm2 325000 325000 325000 325000
σs = fyk Mpa 500.000 500.000 500.000 500.000
k 1.000 1.000 1.000 1.000
kc 0.400 0.400 0.400 0.400
mm 754 754 754 754
As,provided mm2 2576.11 2576.11 1570.80 2576.11
Check OK OK OK OK
h 0.00 0.30 0.80 3.00

k 1.00 1.00 0.65 0.65


m 0.350 0.650 3.406 0.950
Cover mm 40 40 40 40
Provided mm 200 200 200 200
Spacing b/w
Check OK OK OK OK
STC Pvt. Ltd. 33



m 0.350 0.650 3.406 0.950
hc,eff = Min [2.5 (h - d), (h - x)/3 ,
mm 123.95 123.95 123.95 123.95
h/2]
Aceff = hc,eff x b mm2 123951.43 123951.43 123951.43 123951.43
As provided mm2 2576.11 2576.11 1570.80 2576.11
ρpeff = As/Ac,eff 0.0208 0.0208 0.0127 0.0208
Srmax =3.4c + 0.17 Φ /ρPeff mm 299.59 299.59 404.29 299.59
σsc Mpa 175.82 136.35 63.42 121.99
kt 0.500 0.500 0.500 0.500
αe = Es/Ecm' 14.41 14.41 14.41 14.41
0.00053 0.00041 0.00019 0.00037
wk mm 0.1580 0.1225 0.0769 0.1096
Check OK OK OK OK

VED kN 210.00 195.00 92.00 180.00

β 0.5000 0.5417 1.0000 0.7917
βVED kN 105.00 105.63 92.00 142.50
d mm 600.00 600.00 600.00 600.00
bw mm 1000.00 1000.00 1000.00 1000.00
k= Min [ 1 + √200/d , 2 + 1.577 1.577 1.577 1.577
Asl 2 2576.106 2576.106 1570.796 2576.106
mm
ρ1 = Min * Asl/bw d , 0.02 + 0.004 0.004 0.003 0.004
3/2
νmin = 0.031 k fck1/2 0.363 0.363 0.363 0.363
σcp Mpa 0 0 0 0
VRdc =Max * ( 0.12 k (80 ρ1 fck )0.33

bw d ]
Check
STC Pvt. Ltd. 34

DESIGN OF SIDE WALL

MIDSPAN - SAGGING
fctm = 2.80 MPa
fcd = 15.75 MPa
εuk = 0.00450
εud = 0.00405
εcu2 = 0.0035
xumax/d = 0.4636

(QP) 0.8 fy = 400 MPa
STC Pvt. Ltd. 35

A) ULS CAPACITY CHECK (Side Wall Sagging)

MED (Sagging) kNm 205.000 150.000 60.000 90.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 652.000 652.000 652.000 652.000
Diameter mm 16 0 16 0 16 0 16 0
Area of steel
Spacing mm 150 200 150 200 150 200 150 200
provided 2
Ast, Provided mm 1340.413 1340.413 1340.413 1340.413
Reinforcement (%) 0.206 0.206 0.206 0.206
xmax mm 302.252 302.252 302.252 302.252
xu = 0.87 fyk Ast / 0.362 fck b mm 46.020 46.020 46.020 46.020
Ast Max mm2 162400.000 162400.000 162400.000 162400.000
Ast min mm2 978.000 978.000 978.000 978.000
∆Fd kN 27.500 55.000 100.000 80.000
z = d- 0.416 xu m 632.855 632.855 632.855 632.855
MED/z +∆Fd kN 351.429 292.021 194.808 222.213
MRD/z kNm/m 583.080 583.080 583.080 583.080
Distribution steel at innerside of side wall: (Refer IRC:112 clause 16.6.1.1)

B) SLS STRESS CHECK

MST + (1+ Φ)* MQP
MST = MRARE -MQP
m = Es / Ec,eq
where,

STC Pvt. Ltd. 36


b


Curtailment
point
m 3.250 2.115 0.675 1.027
MED (Sagging) kNm 205.000 140.000 50.000 60.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 652.000 652.000 652.000 652.000
Ast, Provided mm2 1340.413 1340.413 1340.413 1340.413
I mm4 2.310E+10 2.310E+10 2.310E+10 2.310E+10
Y = d/2 mm 350.000 350.000 350.000 350.000
σ (Stress) Mpa 3.106 2.121 0.758 0.909
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Uncracked Uncracked Uncracked
Modular ratio 14.403 15.577 14.403 14.403
N.A. depth (dc) mm 140.532 145.440 140.532 140.532
INA mm4 5.976E+09 6.383E+09 5.976E+09 5.976E+09
Check OK OK OK OK
Check OK OK OK OK

Curtailment
point
m 3.250 2.115 0.675 1.027
MED (Sagging) kNm 205.000 160.000 50.000 60.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 652.000 652.000 652.000 652.000
Ast, Provided mm2 1340.413 1340.413 1340.413 1340.413
I mm4 2.310E+10 2.310E+10 2.310E+10 2.310E+10
Y = d/2 mm 350.000 350.000 350.000 350.000
σ (Stress) Mpa 3.106 2.425 0.758 0.909
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Uncracked Uncracked Uncracked
STC Pvt. Ltd. 37


Modular ratio 14.403 14.403 14.403 14.403
N.A. depth (dc) mm 140.532 140.532 140.532 140.532
INA mm4 5.976E+09 5.976E+09 5.976E+09 5.976E+09
Check OK OK OK OK
Check OK OK OK OK

Curtailment
point
m 3.250 2.115 0.675 1.027
b mm 1000.000 1000.000 1000.000 1000.000

h mm 700.000 700.000 700.000 700.000
d mm 652.000 652.000 652.000 652.000
Act =bh/2 2
mm 350000 350000 350000 350000
σs = fyk Mpa 500.000 500.000 500.000 500.000
k 1.000 1.000 1.000 1.000
kc 0.400 0.400 0.400 0.400
mm 812 812 812 812
As,provided 2
mm 1340.41 1340.41 1340.41 1340.41
Check OK OK OK OK
h 0.00 0.30 0.80 3.00

k 1.00 1.00 0.65 0.65

Curtailment
point
m 3.250 2.115 0.675 1.027
Cover mm 40 40 40 40
Provided mm 150 150 150 150
Spacing b/w
Check OK OK OK OK
STC Pvt. Ltd. 38


Curtailment
point
m 3.250 2.115 0.675 1.027
hc,eff = Min [2.5 (h - d), (h - x)/3 ,
mm 120.00 120.00 120.00 120.00
h/2]
Aceff = hc,eff x b mm2 120000.00 120000.00 120000.00 120000.00
As provided mm2 1340.41 1340.41 1340.41 1340.41
ρpeff = As/Ac,eff 0.0112 0.0112 0.0112 0.0112
Srmax =3.4c + 0.17 Φ /ρPeff mm 379.51 379.51 379.51 379.51
σsc Mpa 252.72 197.25 61.64 73.97
kt 0.500 0.500 0.500 0.500
αe = Es/Ecm' 14.40 14.40 14.40 14.40
0.00076 0.00059 0.00018 0.00022
wk mm 0.2877 0.2246 0.0702 0.0842
Check OK OK OK OK

Curtailment
point
VED kN 55.00 110.00 200.00 160.00
β 1.000 1.000 0.518 0.788
βVED kN 55.00 110.00 103.53 126.01
d mm 652.00 652.00 652.00 652.00
bw mm 1000.00 1000.00 1000.00 1000.00
k= Min [ 1 + √200/d , 2 + 1.554 1.554 1.554 1.554
Asl 2 1340.413 1340.413 1340.413 1340.413
mm
ρ1 = Min * Asl/bw d , 0.02 + 0.002 0.002 0.002 0.002
3/2
νmin = 0.031 k fck1/2 0.355 0.355 0.355 0.355
σcp Mpa 0 0 0 0
VRdc =Max * ( 0.12 k (80 ρ1 fck )0.33
bw d ]
Check
STC Pvt. Ltd. 39

DESIGN OF SIDE WALL

SUPPORT - HOGGING
fctm = 2.80 MPa
fcd = 15.75 MPa
εuk = 0.00450
εud = 0.00405
εcu2 = 0.0035
xumax/d = 0.4636

(QP) 0.8 fy = 400 MPa
STC Pvt. Ltd. 40

A) ULS CAPACITY CHECK (Side Wall Hogging)

MED (Hogging) kNm 630.000 560.000 470.000 520.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 612.500 612.500 612.500 612.500
Diameter mm 25 16 25 16 25 20 25 16
Area of steel
Spacing mm 200 200 200 200 200 200 200 200
provided 2
Ast, Provided mm 3459.679 3459.679 4025.166 3459.679
Reinforcement (%) 0.565 0.565 0.565 0.565
xmax mm 283.940 283.940 283.940 283.940
xu = 0.87 fyk Ast / 0.362 fck b mm 118.781 118.781 138.196 118.781
Ast Max mm2 162400.000 162400.000 162400.000 162400.000
Ast min mm2 918.750 918.750 918.750 918.750
∆Fd kN 192.500 170.000 95.000 127.500
z = d- 0.416 xu m 563.087 563.087 555.010 563.087
MED/z +∆Fd kN 1311.333 1164.518 941.831 1050.981
MRD/z kNm/m 1504.960 1504.960 1750.947 1504.960
Distribution steel at outer side of side wall: (Refer IRC:112 clause 16.6.1.1)
B) SLS STRESS CHECK

MST + (1+ Φ)* MQP
MST = MRARE -MQP
m = Es / Ec,eq
where,

STC Pvt. Ltd. 41


b



m 0.375 0.675 2.115 1.027
MED (Hogging) kNm 410.000 380.000 330.000 400.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 612.500 612.500 612.500 612.500
Ast, Provided mm2 3459.679 3459.679 4025.166 3459.679
I mm4 1.915E+10 1.915E+10 1.915E+10 1.915E+10
Y = d/2 mm 350.000 350.000 350.000 350.000
σ (Stress) Mpa 7.494 6.946 6.032 7.311
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Cracked Cracked Cracked
Modular ratio 11.699 11.810 10.421 10.502
N.A. depth (dc) mm 185.843 186.563 188.585 177.744
INA mm4 9.507E+09 9.577E+09 9.774E+09 8.739E+09
Check OK OK OK OK
Check OK OK OK OK


m 0.375 0.675 2.115 1.027
MED (Hogging) kNm 275.000 260.000 170.000 210.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 612.500 612.500 612.500 612.500
Ast, Provided mm2 3459.679 3459.679 4025.166 3459.679
I mm4 1.915E+10 1.915E+10 1.915E+10 1.915E+10
Y = d/2 mm 350.000 350.000 350.000 350.000
σ (Stress) Mpa 5.026 4.752 3.107 3.838
fctm,fl Mpa 2.800 2.800 2.800 2.800
Cracked/Uncracked Cracked Cracked Cracked Cracked
STC Pvt. Ltd. 42


Modular ratio 14.403 14.403 14.403 14.403
N.A. depth (dc) mm 202.212 202.212 214.753 202.212
INA mm4 1.114E+10 1.114E+10 1.247E+10 1.114E+10
Check OK OK OK OK
Check OK OK OK OK


m 0.375 0.675 2.115 1.027
b mm 1000.000 1000.000 1000.000 1000.000

h mm 700.000 700.000 700.000 700.000
d mm 612.500 612.500 612.500 612.500
Act =bh/2 2
mm 350000 350000 350000 350000
σs = fyk Mpa 500.000 500.000 500.000 500.000
k 1.000 1.000 1.000 1.000
kc 0.400 0.400 0.400 0.400
mm 812 812 812 812
As,provided 2
mm 3459.68 3459.68 4025.17 3459.68
Check OK OK OK OK
h 0.00 0.30 0.80 3.00

k 1.00 1.00 0.65 0.65


m 0.375 0.675 2.115 1.027
Cover mm 75 75 75 75
Provided mm 200 200 200 200
Spacing b/w
bars Calculated mm 437.5 437.5 437.5 437.5
Check OK OK OK OK
STC Pvt. Ltd. 43



m 0.375 0.675 2.115 1.027
hc,eff = Min [2.5 (h - d), (h - x)/3 ,
mm 138.69 138.69 138.69 138.69
h/2]
Aceff = hc,eff x b mm2 138686.53 138686.53 138686.53 138686.53
As provided mm2 3459.68 3459.68 4025.17 3459.68
ρpeff = As/Ac,eff 0.0249 0.0249 0.0290 0.0249
Srmax =3.4c + 0.17 Φ /ρPeff mm 425.37 425.37 401.43 425.37
σsc Mpa 145.82 137.87 78.08 111.36
kt 0.500 0.500 0.500 0.500
αe = Es/Ecm' 14.40 14.40 14.40 14.40
0.00044 0.00041 0.00023 0.00033
wk mm 0.1861 0.1759 0.0940 0.1421
Check OK OK OK OK

VED kN 385.00 340.00 190.00 255.00

β 0.5000 0.5510 1.0000 0.8384
βVED kN 192.50 187.35 190.00 213.78
d mm 612.50 612.50 612.50 612.50
bw mm 1000.00 1000.00 1000.00 1000.00
k= Min [ 1 + √200/d , 2 + 1.571 1.571 1.571 1.571
Asl 2 3459.679 3459.679 4025.166 3459.679
mm
ρ1 = Min * Asl/bw d , 0.02 + 0.006 0.006 0.007 0.006
3/2
νmin = 0.031 k fck1/2 0.361 0.361 0.361 0.361
σcp Mpa 0 0 0 0
VRdc =Max * ( 0.12 k (80 ρ1 fck )0.33
bw d ]
Check
STC Pvt. Ltd. 44

DESIGN OF BOTTOM SLAB

MIDSPAN - SAGGING
fctm = 2.80 MPa
fcd = 15.75 MPa
εuk = 0.00450
εud = 0.00405
εcu2 = 0.0035
xumax/d = 0.4636

(QP) 0.8 fy = 400 MPa
STC Pvt. Ltd. 45

A) ULS CAPACITY CHECK (Bottom Slab Sagging)

MED (Sagging) kNm 680.000 590.000 80.000 150.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 700.000 700.000 700.000 700.000
Diameter mm 20 16 20 16 20 16 20 16
Area of steel
Spacing mm 200 200 200 200 200 200 200 200
provided 2
Ast, Provided mm 2576.106 2576.106 2576.106 2576.106
Reinforcement (%) 0.368 0.368 0.368 0.368
xmax mm 324.503 324.503 324.503 324.503
xu = 0.87 fyk Ast / 0.362 fck b mm 88.446 88.446 88.446 88.446
Ast Max mm2 305615.008 305615.008 305615.008 305615.008
Ast Calc. < Ast Provided < Ast Max OK OK OK OK
Ast min mm2 1050.000 1050.000 1050.000 1050.000
∆Fd kN 18.000 50.000 160.000 140.000
z = d- 0.416 xu m 663.207 663.207 663.207 663.207
MED/z +∆Fd kN 1043.321 939.617 280.626 366.174
MRD/z kNm/m 1120.606 1120.606 1120.606 1120.606
Distribution steel at top of bottom slab: (Refer IRC:112 clause 16.6.1.1)

B) SLS STRESS CHECK

MST + (1+ Φ)* MQP
MST = MRARE -MQP
m = Es / Ec,eq
where,

STC Pvt. Ltd. 46


b
INA (Transformed) = b x dc3/3 + m x As x (d - dc)2


Curtailment
point
m 5.444 3.406 0.650 1.050
MED (Sagging) kNm 470.000 405.000 75.000 90.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 700.000 700.000 700.000 700.000
Ast, Provided mm2 2576.106 2576.106 2576.106 2576.106
I mm4 2.858E+10 2.858E+10 2.858E+10 2.858E+10
Y = d/2 mm 375.000 375.000 375.000 375.000
σ (Stress) Mpa 6.166 5.313 0.984 1.181
fctm,fl Mpa 2.800 2.800 2.800 2.800
Modular ratio 12.784 12.836 13.803 12.534
N.A. depth (dc) mm 184.304 184.618 190.372 182.761
INA mm4 1.085E+10 1.088E+10 1.153E+10 1.067E+10
Check OK OK OK OK
Check OK OK OK OK

Curtailment
point
m 5.444 3.406 0.650 1.050
MED (Sagging) kNm 380.000 330.000 70.000 70.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 700.000 700.000 700.000 700.000
Ast, Provided mm2 2576.106 2576.106 2576.106 2576.106
I mm4 2.858E+10 2.858E+10 2.858E+10 2.858E+10
Y = d/2 mm 375.000 375.000 375.000 375.000
σ (Stress) Mpa 4.985 4.329 0.918 0.918
fctm,fl Mpa 2.800 2.800 2.800 2.800
STC Pvt. Ltd. 47


Modular ratio 14.346 14.346 14.346 14.346
N.A. depth (dc) mm 193.490 193.490 193.490 193.490
INA mm4 1.190E+10 1.190E+10 1.190E+10 1.190E+10
Check OK OK OK OK
Check OK OK OK OK

Curtailment
point
m 5.444 3.406 0.650 1.050
b mm 1000.000 1000.000 1000.000 1000.000

h mm 750.000 750.000 750.000 750.000
d mm 700.000 700.000 700.000 700.000
Act =bh/2 2
mm 375000 375000 375000 375000
σs = fyk Mpa 500.000 500.000 500.000 500.000
k 1.000 1.000 1.000 1.000
kc 0.400 0.400 0.400 0.400
mm 870 870 870 870
As,provided 2
mm 2576.11 2576.11 2576.11 2576.11
Check OK OK OK OK
h 0.00 0.30 0.80 3.00

k 1.00 1.00 0.65 0.65

Curtailment
point
m 5.444 3.406 0.650 1.050
Cover mm 40 40 40 40
Provided mm 200 200 200 200
Spacing b/w
Check OK OK OK OK
STC Pvt. Ltd. 48


Curtailment
point
m 5.444 3.406 0.650 1.050
hc,eff = Min [2.5 (h - d), (h - x)/3 ,
mm 125.00 125.00 125.00 125.00
h/2]
Aceff = hc,eff x b mm2 125000.00 125000.00 125000.00 125000.00
As provided mm2 2576.11 2576.11 2576.11 2576.11
ρpeff = As/Ac,eff 0.0206 0.0206 0.0206 0.0206
Srmax =3.4c + 0.17 Φ /ρPeff mm 300.98 300.98 300.98 300.98
σsc Mpa 232.11 201.57 42.76 42.76
kt 0.500 0.500 0.500 0.500
αe = Es/Ecm' 14.35 14.35 14.35 14.35
0.00070 0.00060 0.00013 0.00013
wk mm 0.2121 0.1820 0.0386 0.0386
Check OK OK OK OK

Curtailment
point
VED kN 36.00 100.00 320.00 280.00
β 1.000 1.000 0.500 0.750
βVED kN 36.00 100.00 160.00 210.00
d mm 700.00 700.00 700.00 700.00
bw mm 1000.00 1000.00 1000.00 1000.00
k= Min [ 1 + √200/d , 2 + 1.535 1.535 1.535 1.535
Asl 2 2576.106 2576.106 2576.106 2576.106
mm
ρ1 = Min * Asl/bw d , 0.02 + 0.004 0.004 0.004 0.004
3/2
νmin = 0.031 k fck1/2 0.349 0.349 0.349 0.349
σcp Mpa 0 0 0 0
VRdc =Max * ( 0.12 k (80 ρ1 fck )0.33
bw d ]
Check
STC Pvt. Ltd. 49

DESIGN OF BOTTOM SLAB

SUPPORT - HOGGING
fctm = 2.80 MPa
fcd = 15.75 MPa
εuk = 0.00450
εud = 0.00405
εcu2 = 0.0035
xumax/d = 0.4636

(QP) 0.8 fy = 400 MPa
STC Pvt. Ltd. 50

A) ULS CAPACITY CHECK (Top Slab Hogging)

MED (Hogging) kNm 610.000 465.000 85.000 370.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 700.000 700.000 700.000 700.000
Diameter mm 20 16 20 16 20 16 20 16
Area of steel
Spacing mm 200 200 200 200 200 200 200 200
provided 2
Ast, Provided mm 2576.106 2576.106 2576.106 2576.106
Reinforcement (%) 0.368 0.368 0.368 0.368
xmax mm 324.503 324.503 324.503 324.503
xu = 0.87 fyk Ast / 0.362 fck b mm 88.446 88.446 88.446 88.446
Ast Max mm2 305615.008 305615.008 305615.008 305615.008
Ast min mm2 1050.000 1050.000 1050.000 1050.000
∆Fd kN 185.000 167.500 90.000 130.000
z = d- 0.416 xu m 663.207 663.207 663.207 663.207
MED/z +∆Fd kN 1104.774 868.639 218.165 687.896
MRD/z kNm/m 1120.606 1120.606 1120.606 1120.606
Distribution steel at bottom of bottom slab: (Refer IRC:112 clause 16.6.1.1)

B) SLS STRESS CHECK

MST + (1+ Φ)* MQP
MST = MRARE -MQP
m = Es / Ec,eq
where,

STC Pvt. Ltd. 51


b



m 0.350 0.650 3.406 1.050
MED (Hogging) kNm 425.000 325.000 85.000 190.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 700.000 700.000 700.000 700.000
Ast, Provided mm2 2576.106 2576.106 2576.106 2576.106
I mm4 2.858E+10 2.858E+10 2.858E+10 2.858E+10
Y = d/2 mm 375.000 375.000 375.000 375.000
σ (Stress) Mpa 5.576 4.264 1.115 2.493
fctm,fl Mpa 2.800 2.800 2.800 2.800
Modular ratio 12.619 12.464 14.058 14.346
N.A. depth (dc) mm 183.288 182.329 191.849 193.490
INA mm4 1.073E+10 1.063E+10 1.171E+10 1.190E+10
Check OK OK OK OK
Check OK OK OK OK


m 0.350 0.650 3.406 1.050
MED (Hogging) kNm 335.000 250.000 82.000 190.000
Width (b) mm 1000.000 1000.000 1000.000 1000.000
d mm 700.000 700.000 700.000 700.000
Ast, Provided mm2 2576.106 2576.106 2576.106 2576.106
I mm4 2.858E+10 2.858E+10 2.858E+10 2.858E+10
Y = d/2 mm 375.000 375.000 375.000 375.000
σ (Stress) Mpa 4.395 3.280 1.076 2.493
fctm,fl Mpa 2.800 2.800 2.800 2.800
STC Pvt. Ltd. 52


Modular ratio 14.346 14.346 14.346 14.346
N.A. depth (dc) mm 193.490 193.490 193.490 193.490
INA mm4 1.190E+10 1.190E+10 1.190E+10 1.190E+10
Check OK OK OK OK
Check OK OK OK OK


m 0.350 0.650 3.406 1.050
b mm 1000.000 1000.000 1000.000 1000.000

h mm 750.000 750.000 750.000 750.000
d mm 700.000 700.000 700.000 700.000
Act =bh/2 2
mm 375000 375000 375000 375000
σs = fyk Mpa 500.000 500.000 500.000 500.000
k 1.000 1.000 1.000 1.000
kc 0.400 0.400 0.400 0.400
mm 870 870 870 870
As,provided 2
mm 2576.11 2576.11 2576.11 2576.11
Check OK OK OK OK
h 0.00 0.30 0.80 3.00

k 1.00 1.00 0.65 0.65


m 0.350 0.650 3.406 1.050
Cover mm 40 40 40 40
Provided mm 200 200 200 200
Spacing b/w
Check OK OK OK OK
STC Pvt. Ltd. 53



m 0.350 0.650 3.406 1.050
hc,eff = Min [2.5 (h - d), (h - x)/3 ,
mm 125.00 125.00 125.00 125.00
h/2]
Aceff = hc,eff x b mm2 125000.00 125000.00 125000.00 125000.00
As provided mm2 2576.11 2576.11 2576.11 2576.11
ρpeff = As/Ac,eff 0.0206 0.0206 0.0206 0.0206
Srmax =3.4c + 0.17 Φ /ρPeff mm 300.98 300.98 300.98 300.98
σsc Mpa 204.63 152.71 50.09 116.06
kt 0.500 0.500 0.500 0.500
αe = Es/Ecm' 14.35 14.35 14.35 14.35
0.00061 0.00046 0.00015 0.00035
wk mm 0.1848 0.1379 0.0452 0.1048
Check OK OK OK OK

VED kN 370.00 335.00 180.00 260.00

β 0.5000 0.5000 1.0000 0.7500
βVED kN 185.00 167.50 180.00 195.00
d mm 700.00 700.00 700.00 700.00
bw mm 1000.00 1000.00 1000.00 1000.00
k= Min [ 1 + √200/d , 2 + 1.535 1.535 1.535 1.535
Asl 2 2576.106 2576.106 2576.106 2576.106
mm
ρ1 = Min * Asl/bw d , 0.02 + 0.004 0.004 0.004 0.004
3/2
νmin = 0.031 k fck1/2 0.349 0.349 0.349 0.349
σcp Mpa 0 0 0 0
VRdc =Max * ( 0.12 k (80 ρ1 fck )0.33
bw d ]
Check
STC Pvt. Ltd. 54

Calculation of Base Pressure
Load Factor for Base Pressure

IRC 6:2014 Table 3.4 Column 2
Permanent Loads (Dead Load, SIDL except Surfacing = 1

Surfacing = 1
Live Load(Leading Load) = 1
Overall Span of Box = 11.613 m

Box Barrel Length Considered = 15.281 m
Unit Weight of Concrete = 25.000 kN/m3
1) Self Weight of Box:

Box cross sectional area = 24.379 m2
Total Box Weight = 9313.128 kN
Factored Total Weight of Box = 9313.128 kN
2) SIDL (Wearing Coat,Crash Barrier, Footpath etc)

Earth Fill/Wearing Coat = 1.430 kN/m2
Crash Barrier = 10.000 kN/m
Width of Crash Barrier = 0.450 m
Total Weight of Wearing Coat over box = 253.769 kN
Total Weight of Crash barrier = 232.267 kN
Total SIDL = 486.037 kN
Factored SIDL Load = 486.037 kN
3) Live Load
(70R Bogie Load) = 400.000 kN
Factored Live Load = 400.000 kN
Maximum Eccentricity of LL from c/l of carriageway = 0.405 m
Eccentric Moment in Transverse Direction = 162 kNm
Inertia of base about Longitudinal axis = 3453.115 m4
Area of Base = 177.46101 m2
Maximum Base Pressure due to Live Load = 400.000 + 162 x 7.6403752

177.461013 3453.115
= 2.61 kN/m2
= 3.27 kN/m2 (Increased by 25%)
Maximum Base Pressure due to DL = 9313.128 = 52.480 kN/m2

177.461013
Maximum Base Pressure due to SIDL = 486.037 = 2.739 kN/m2

177.461013
Total Base Pressure = 58.48 kN/m2 < 120.00 kN/m2

SAFE
STC Pvt. Ltd. 55

7+670 (1x10x5.8) R1

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Design of RCC BOX Structures

DESIGN OF 1 CELL BOX BRIDGE

1.2 DIMENSION DETAILS

STC Pvt. Ltd. 1

1.3 MATERIAL PROPERTIES

Coefficient of Active Earth Pressure

Backfill Soil Parameter

Coefficient of horizontal earth pressure Kah for straight = 0.279

Coefficient of active earth pressure = 0.279

1.4 DESIGN PARAMETERS

STC Pvt. Ltd. 2

Dimensions Detail of RCC Box

STC Pvt. Ltd. 3

2.0 LOAD CALCULATIONS FOR THE BOX STRUCTURE

2.1 DEAD LOAD

2.2 SUPER IMPOSED DEAD LOAD

2.3 EARTH PRESSURE

Earth Pressure at Rest

Active Earth Pressure

Submerged Earth Pressure at Rest

Submerged Active Earth Pressure

STC Pvt. Ltd. 4

2.4 LIVE LOAD SURCHARGE

2.5 BRAKING LOAD

Load for one lane 70R 0.2 * 460 = 92 KN

2.6 CALCULATING BRIDGE TEMPERATURE :

STC Pvt. Ltd. 5

Effective span lo = 10.70 m

Ht of fill (W.C / P.C.C / pavement layers) at edge = 0.065 m

Width of Crash barrier / Kerb = 0.45 m

Span / Wdith ratio b / lo = 15.00 / 10.70 = 1.40

As per Cl. B3.2 of IRC:112-2011(Page-278), for continous slab

410 40 410 1070 410 40 410

Total Load = = 40.00 t

Contact area = 5000 / 5.273 360 = 948.23 cm2

Contact area = 360 x 263 mm

Contact width of tyre in a direction perpendicular to the span = 0.36 m

Effective width, bef = α a (1 - a / lo) + b1 (Refer Cl. B3.2 of IRC:112-2011)

STC Pvt. Ltd. 6

a = the distance of c.g of concentrated load from nearer support

Effective load in transverse direction = 20.00 t

Effective width for design = 8.177 m

Dispersion along span direction = 0.263 + 2 x (0.07 + 0.65) = 1.693 m

Dispersion width for design = (IF(1.69>1.22,(1.69 + 1.22),1.69)

Total load = 40.0 t

410 385 410 380 410 385 410

Total Load = = 40.00 t

Load on one tyre = 5.00 t

STC Pvt. Ltd. 7

Contact area = 5000 / 5.273 = 948.23 cm2

Contact area = 360 x 263 mm

Contact width of tyre in a direction perpendicular to the span = 0.36 m

Effective width = α a (1 - a / lo) + b1 (Refer Cl. B3.2 of IRC:112-2011)

a = the distance of c.g of concentrated load from nearer support

Effective width = 2.8 x 4.74 x (1 - 4.74 / 1.22) + 0.49

Effective load in transverse direction = 20.00 t

Effective width for design = 8.177 m

Dispersion along span direction = 0.263 + 2 x (0.07 + 0.65) = 1.693 m