Box Culvert Limit State Xls

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NATIONAL HIGHWAYS AUTHORITY OF INDIA

FOUR LANING OF TIRUPATI-TIRUTHANI -CHENNAI-SECTION OF NH-205

FROM Km 274+800 to Km 341+600 IN THE STATE OF ANDHRA PRADESH

& FROM Km 0+000 TO Km 59+600 IN THE STATE OF TAMIL NADU ON

DESIGN,BUILD,FINANCE,OPERATE AND TRANSFER (DBFOT) TOLL BASIS

Structural Design Report

DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

Note No:39/TTC/CUL-BOX/1X3X3/RO

Concessionaire

TRANSTORY TIRUPATI-TIRUTHANI-CHENNAI TOLLWAYS PVT.LTD.

Document/File No.:

No. of Pages:

22 Designed by:

Venkatesh

Checked by:

Praveen

Approved by:

T R Reddy

R "O"

12/13/2010

Rev

Date

Remarks

DESIGN CONSULTANT

Egis India Consulting Engineers Pvt. Ltd.

9-1-77/3, N0.31, Adjacent ITC Agri Building,

S.D Road, Secunderabad.

(2)

FOUR LANING OF TIRUPATI-TIRUTHANI -CHENNAI-SECTION OF NH-205

FROM Km 274+800 to Km 341+600 IN THE STATE OF ANDHRA PRADESH

& FROM Km 0+000 TO Km 59+600 IN THE STATE OF TAMIL NADU ON

DESIGN,BUILD,FINANCE,OPERATE AND TRANSFER (DBFOT) TOLL BASIS

Structural Design Report

TRANSTORY TIRUPATI-TIRUTHANI-CHENNAI TOLLWAYS PVT.LTD.

22 Praveen

Remarks

Egis India Consulting Engineers Pvt. Ltd.

9-1-77/3, N0.31, Adjacent ITC Agri Building,

S.D Road, Secunderabad.

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Project : Four Laning of Tirupati-Tiruthani-Chennai Section of NH-205 Job Name : Design of Single Cell Box Culvert

Subject : DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

1.0 Design Data

1.1 Dimension Detail

No of cells

=

1 Clear Span

=

3.00 m

Clear Height (at outer edge)

=

3.00 m

Clear Height (at median location)

=

3.000 m

Width of road at top

=

12.00 m

Width of Box

=

12.00 m

Ht of fill (W.C / P.C.C / pavement layers) over the top slab

=

0.065 m

Thickness of top slab

=

600 mm

Thickness of bottom slab

=

600 mm

Thickness of external vertical wall

=

600 mm

Size of haunch

=

150 x

Width of Crash barrier

=

0.500 m

Distance of edge of crash barrier from edge of box

=

0.500 m

Height of surcharge

=

1.20 m

Safe Bearing Capacity of the soil

=

120.00 Permissible Settlement

=

75.00 mm

1.2 Material Properties

Density of concrete

=

25.00 Density of soil

=

20.00 Density of wearing coat

=

22.00 Density of Profile corrective course

=

22.00 Coefficient of active earth pressure

=

0.500 Angle of internal friction (in degree)

=

30.00 deg

1.3 Design Parameters

Grade of Concrete

=

M25

Clear Cover for earth face structural component

=

75 mm

Clear Cover for inside face structural component

=

50 mm

Clear Cover for bottom slab

=

75 mm

=

6.25 =

8.33 =

0.61 =

240 Design Costants:

k

=

0.258 j

=

0.914 R

=

0.981 Base Projection

=

0 mm

KN/m

2

KN/m

3

KN/m

3

KN/m

3

KN/m

3

Permissible direct comp. strength of Concrete (



_cc

)

_N/mm

2

Permissible flexural comp. strength of Concrete (



_cb

)

_N/mm

2

Permissible tensile strength of Concrete (



_ct

)

_N/mm

2

Permissible tensile strength of Steel (



_st

)

_N/mm

2

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DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

NOT OK

OK

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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

2.2.1 Top Slab

Wearing coat thickness = 0.065

Ht of fill (Thickness of W.C / P.C.C / pavement layers) = 1.000m

Load (UDL) on top slab = 0.065*22 = 2.73 KN/m

Wt of Crash barrier per meter = 0KN/m

Total UDL load due to S.I Dead Load = 2.73 KN/m Height of soil on projected portion of base slab = 0.00 m Wt of soil on the projected portion of base slab = 0.00 KN/m

2.3 Earth Pressure

Thickness of top slab = 0.600 m

Height of top haunch = 0.15 m

Clear height between top & bottom slab = 3.00 m

Height of bottom haunch = 0.15 m

Thickness of bottom slab = 0.60 m

Height from top Intensity of Earth pressure (m) 1.300 1.300 0.5 * 20 * 1.3 = 13.00 + 0.300 1.600 0.5 * 20 * 1.6 = 16.00 + 0.150 1.750 0.5 * 20 * 1.75 = 17.50 + 0.900 2.650 0.5 * 20 * 2.65 = 26.50 + 0.900 3.550 0.5 * 20 * 3.55 = 35.50 + 0.900 4.450 0.5 * 20 * 4.45 = 44.50 + 0.150 4.600 0.5 * 20 * 4.6 = 46.00 + 0.300 4.900 0.5 * 20 * 4.9 = 49.00 75 2.4 Live Load Surcharge

Equivalent height = 1.20m

Uniform Intensity of loading = 0.5 * 1.2 * 20 = 12.00

2.5 Braking Load

Carriageway Live Load = 400KN

Width of the box = 12.00 m

Braking Load = 0.2 * 400 / 12 = 6.67 KN

2.6 Additional pressure on edge 1m strip due to eccentricity of Live Load

Live Load = 400.00KN

Width of culvert (parallel to traffic direction) = 4.20 m Width of culvert (perpendicular to traffic direction) = 12.00 m Distance of CG of load from outer edge of box culvert = 3.10m

Transverse Moment = 1162.00 KNm

Section Modulus of box in transverse direction = 100.80 m^3

Upward UDL on edge 1m strip = 11.53KN/m

(KN/m2₎

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Job Name : Design of Single Cell Box Culvert

Subject DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

3.0 Effective width of tyres and load distribution for different vehicular loadings:

Effective span = = 3.60m

Total Width of Box culvert b = = 12.00m

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

Thickness of deck slab = = 0.600m

Width of Crash barrier / Kerb = = 0.50m

Dist. of edge of crash barrier/guard stone from edge of box = 0.50m

Span / Wdith ratio = 12 / 3.6 = 3.33

As per Cl. 305.16.2 of IRC:21, for continous slab

For = 3.33 ;  = 2.6

3.1 Class 70R vehicle: (Refer Appendix 1, IRC : 6-2000 ) 3.1.1 Axle - " l " : 5 t 5 t 5 t 5 t 20 t 20 t 450 1480 450 410 40 410 1070 410 40 410 1220 2790 Transverse Longitudinal Total Load = = 40.00t

Impact factor = (Refer Cl.211.3 of IRC:6-1966) = 1.25

Min. 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 trans direction = 2.38 m

Load on one tyre = 410 = 5.00t

Max. tyre pressure = (Refer Tab 75 = 5.273

Contact width of tyre = (Refer Table of IRC:6-2000) = 360mm

Contact area = 5000 / 5.273 = 948.23

Breadth = 948.23 / 36 360 = 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 = 0.5 + 1.2 + 0.41 / 2 = 1.905 m

c.g of wheel

Effective width = (Refer Cl.305.16.2)

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

= 3.6 / 2 - 1.22 / 2 = 1.190m

= 0.36 + 2 * 0.065 = 0.49 m

Effective width = 2.6 x 1.19 x (1 - 1.19 / 3.6) + 0.49 = 2.56m

(Dispersion width ends with in the deck slab) > 1.48 m (Dispersion width of four wheels overlaps in trans direction)

Effective load in trans direction = 20.00t

Effective width for design = = 4.942m

(In transverse direction)

l_o b / lo b / l_o Kg/cm2 cm2 a (1 - a / lo) + b1 b1

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1.905 2.380

Crash Barrier

0.50 1.20 0.41 0.04 0.41 1.07 0.41 0.04 0.41

Dispersion along span direction = 0.263 + 2 x (0.065 + 0.6) = 1.593 m

(Refer Cl.305.16.3 of IRC:21) > 1.220

Dispersion width for design = (IF(1.593>1.22,(1.593 + 1.22),1.593)

(In longitudinal direction) = 2.813m

Total load = = 40.0t

Dispersion area = 4.942 x 2.813 = 13.90

Load per unit area = 40 / 13.902 = 2.88

Load per unit area with I.F = 2.88 x 1.25 = 3.60

3.1.2 Axle - " m ": (Refer Appendix 1, IRC : 6-2000 )

5 t 5 t 5 t 5 t 20 t 20 t 795 790 795 410 385 410 380 410 385 410 1220 2790 Transverse Longitudinal Total Load = = 40.00t

Distance between the axles in the dir. of traffic = 1.22 m

C/C distance between end wheels in trans direction = 2.38 m

Max. tyre pressure = (Refer Table of IRC:6-2000) = 5.273

Contact area = 5000 / 5.273 = 948.23

Breadth = 948.23 / 36 360 = 26.3 cm

Wheel dimension perp. to span = 0.41 m

Distance from outer edge of kerb to c.g of wheel = 1.905 m

= 3.6 / 2 - 1.22 / 2 = 1.190m

= 0.36 + 2 * 0.065 = 0.49 m

(Dispersion width ends with in the deck slab) > 0.79 m (Dispersion width of four wheels overlaps in trans direction)

m2 t/m2 t/m2 Kg/cm2 cm2 a (1 - a / lo) + b1 b₁

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1.905 2.380

Crash Barrier

0.50 1.20 0.41 0.39 0.41 0.38 0.41 0.39 0.41

(Refer Cl.305.16.3 of IRC:21) > 1.220

Dispersion width for design = (IF(1.593>1.22,(1.593 + 1.22),1.593) = 2.813m (In longitudinal direction)

3.1.3 Axle - " n ": (Refer Appendix 1, IRC : 6-2000 )

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 Transverse Total Load = = 40.00t

c/c distance between end wheels in trans direction = 2.56 m

Max. tyre pressure = (Refer Table of IRC:6-2000) = 5.273

Contact area = 2500 / 5.273 = 474.12

Breadth = 474.12 / 18 180 = 26.3 cm

Wheel dimension perp. to span = 0.23 m

= 3.6 / 2 - 1.22 / 2 = 1.190m

= 0.18 + 2 * 0.065 = 0.31 m

(Dispersion width ends with in the deck slab) > 0.48m (Dispersion width of wheels overlaps in trans direction)

m2 t/m2 t/m2 Kg/cm2 cm2 a (1 - a / lo) + b1 b₁

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1.815 0.280 0.480 0.280 0.480 0.280 0.480 0.280

Crash Barrier

0.50 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.305.16.3 of IRC:21) > 1.220

Dispersion width for design = (IF(1.593>1.22,(1.593 + 1.22),1.593) = 2.813m (In longitudinal direction)

3.2 Class -A vehicle: (Refer IRC : 6-2000,Cl. 207.1 ) 3.2.1 Single Lane Class A

5.7 t 5.7 t 11.4 t 11.4 t 1800 500 1300 500 1200 2300 Transverse Longitudinal Total Load = = 22.80t

Contact width of tyre = = 500mm

Contact breadth of tyre = = 25cm

= 3.6 / 2 - 1.2 / 2 = 1.200m

= 0.5 + 2 * 0.065 = 0.63 m

(Dispersion width crosses the deck slab) > 1.8 m (Dispersion width of two wheels overlaps in trans direction)

0.90 1.800 Crash Barrier 0.50 0.15 0.50 1.30 0.50 m2 t/m2 t/m2 a (1 - a / l_o) + b₁ b₁

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(Refer Cl.305.16.3 of IRC:21) > 1.200

Dispersion width for design = IF(1.58>1.2,(1.58 + 1.2),1.58) = 2.780m (In longitudinal direction)

Load per unit area = 22.8 / 11.273 = 2.03

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 Transverse Longitudinal Total Load = = 45.60t

Min. clear distance from C/B to the edge of the end wheel = 0.15m

Distance between the axles in the direction of traffic = 1.20 m

Contact width of tyre = = 500mm

Contact breadth of tyre = = 25cm

= 3.6 / 2 - 1.2 / 2 = 1.200m

= 0.5 + 2 * 0.065 = 0.63 m

Effective width = 2.6 x 1.2 x (1 - 1.2 / ) + 0.63 = 2.71m

(Dispersion width crosses the deck slab) > 1.8 m (Dispersion width of four wheels overlaps in trans direction)

Effective load in transverse direction = 22.80t

0.90 1.800 1.700 1.800 Crash Barrier 0.50 0.15 0.50 1.30 0.50 1.20 0.50 1.30 0.50 m2 t/m2 t/m2 a (1 - a / lo) + b1 b1

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(Refer Cl.305.16.3 of IRC:21) > 1.200

Dispersion width for design = IF(1.58>1.2,(1.58 + 1.2),1.58) = 2.780m (In longitudinal direction)

Load per unit area = 45.6 / 21.003 = 2.18

3.3 70 R Tracked vehicle

Min. clear distance from C/B to the edge of the end wheel = 1.20m

Length of vehicle in span direction = 4.57m

Contact width of tyre in a direction perpendicular to the span = 0.85m

C/C distance of wheels in a direction perpendicular to span = 2.05m

Distance from outer edge of C/barrier to c.g of wheel = 2.125 m

= 3.6 / 2 = 1.800m

= 0.85 + 2 * 0.065 = 0.98 m

(Dispersion width ends with in the deck slab) > 2.05 m (Dispersion width of wheels overlaps in trans direction)

Effective total load in transvrse direction = 70.00t

2.125 2.050

Crash Barrier

0.50 1.20 0.85 1.20 0.85

(Refer Cl.305.16.3 of IRC:21)

Dispersion width for design = = 5.900 m

(In longitudinal direction)

3.4 Summary of Intensity of Loads: Loading 70R - Axle 'l' 3.600 70R - Axle 'm' 3.598 70R - Axle 'n' 3.598 1 Lane Class A 2.982 2 Lane Class A 3.202 70R-Track 2.763

Design LL intensity for analysis = 3.600

m2 t/m2 t/m2 a a (1 - a / lo) + b1 b1 m2 t/m2 t/m2 Intensity of Load (t/m2₎ t/m2

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4.0 Design of Box Structure: 1 x 3 x 3 without Cushion

Theoretical curtailment point Steel

C/L Bar mark ts1 2526 27 28 29 30 ts2 18 26 27 28 29 ts3 1718 ts4 17 ts5 16 ts6 16 w1 w2 15 w3 w4 15 w6 bs1 14 bs2 14 bs3 1313 bs4 121 2 3 4 5  bs5 1 2 3 4  6 h1 h2 h3 h4 Depth of member (D) = 210 mm

Width of the meber (b) = 1000 mm

Grade of Concrete Used = M30

Grade of steel Fe 500

= 30 N/mm2 Table no:6.5 (IRC:112-2011) = 500 N/mm2 Table no:18.1 (IRC:112-2011)

= 2.5 MPa

= 348 MPa

= 1.5 Basic Page 49: (IRC:112-2011)

= 1.15 Basic Page 30: (IRC:112-2011)

= 0.0035 Up to fck ≤ Table no:6.5 (IRC:112-2011) = 200000 N/mm2 Clause 6.2.2 (IRC:112-2011)

modulus of elasticity of concrete (Ecm) = 31000 MPa

= 6.45

= 0.00417

= 0.67 Cube A2.10 Page : 244 (IRC:112-2011)

= 0.8 0.8 Up to fck ≤ 60Mpa,Eq.A2-33 (IRC:112-2011); 0.8-((fck-60)/500) for 60<fck<110Mpa

= 11.0 Up to fck ≤ 60Mpa,Eq.A2-35 (IRC:112-2011); 1.0-((fck-60)/250) for 60<fck<110Mpa

= 13.400

= 10.720

= 0.400

Effective depth of member (d) = 544.0

= 0.003

= 248.113 mm

Force in compression = Force in Tension from Fig. A2-4 - rectangular Tensile Strength

= = As = M = = = = 0 x = = = = 544x(1-sqrt1-4x0.4x0.003))/(2x0.4) = 1.37320392 mm < 248.113 Safe

Charactristic strength of concrete (f_ck) Charactristic strength of steel (f_y) Tensile strength of concrete (f_ctm)

Design yield strength of shear reinforcement f_ywd = 0.8*f_yk/γ_s Partial material safety factor for concrete (m)

Partial material safety factor for Steel (s)

Ultimate compressive strain in the concrete (є_cu3) modulus of elasticity of reinforcing of steel (E_s) modular ratio α_e(Es/Ecm)

Ultimate tensile strain in the steel (є_s) = [{f_y/(s xEs)}+0.002]

Coefficient to consider the influence of the concret strength () Factor ( ) Factor () fcd =(*fck/m) Factor F_av (f_cd) Factor  = () M/(bd2_{Fav) = k} av

Limiting Neutral axis depth (x lim) = (d*cu3)/(s+cu3)

f_y*A_s fcd *x* b Fav * x*b s s * Fav * x*b f_y f_y*A_{s *}(d-x/2) s f_y*s * Fav * x*b *(d-x) s * fy F_av * x*b_*(d-x) x2_{-dx + M/Fav*b} d-sqrt(d2-4**M/Fav*b)/(2*) d*(1-sqrt(1-4**M/Fav*b*d2_))/(2*_₎ d*(1-sqrt(1-4**kav))/(2*)

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=

= 1.15x10.72x1.373x1000/ 500 = 33.8577158

Provide 2 No's 20

Provided reinfo = 628.32 > 33.86 Safe

Neutral axis dep =

= 471240 1.15x1x30x0.67x0.8x1000 = 25.480 mm < 248.113 Safe Shear design = 0 = = (cotθ+tanθ) = s =

Where K = 1+ √200 <= 2 Where d is depth in mm

√d = = <= = <= 0.02 = 122.66 kN = 261.26 kN = 122.66 kN > 71.0 kN

Hence Shear reinforcement is not required

If required = = = (cotθ+tanθ) = = 0.034 θ = 0.99 = 58.04 <= 2.5 >= 1 = 8 mm 2 legged = s = Spacing, s = Max 484 mm = 11234 mm Min 194 mm

Provide Shear reinforcement vertically 2 legged 8 mm dia @ 11225 mm C/C

= = 0.00078872 Minimum spacing = 127.460827 mm Required reinforcement As s * Fav * x*b fy mm2 mm2 f_y*A_s* m s *fck * * b Longitudinal force (N_Ed) of compression struts (V Rd.max)

α

cw

b

w

zν

1

f

cd

α

cw

b

w

zν

1

f

cd (2/sin2θ) Shear Force by shear

reinforcement (V _Rd.s)

A_swzf_ywdcotθ

Shear resistance of section without shear reinforcement (V_Rd.c) [0.12K(80ρ₁.f_ck)0.33_+0.15σ

cp

]b

w

.d

ν_min _0.031K3/2_fck1/2 σ_cp NEd/Ac 0.2fcd ρ₁ Asl/bw.d shear resistance (ν_Rd.c) V_Rd.c V_NS V _Rd.max

α

_cw

b

_w

zν

_1fcd

α

_cw

b

_w

zν

_1fcd (2/sin2θ) sin2θ V_NS/α_cwb_wzν₁f_cd/2 Cotθ reinforcement

reinforcement (V _Rd.s) A_swzf_ywdcotθ V_NS

A_swzf_ywdcotθ/V_NS

For Beams, minimum shear reinforcement

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4.1 Check for Flexure as per IRC:21: Main Reinforcement

Section Face Xu kav

29 & 30 Top _Bottom ₅₈8 248.11 1.373 544.0 0.0025 33.9 653

248.11 10.019 544.0 0.0183 247.0 653

27&28 Top _Bottom ₆₃6 248.11 1.030 544.0 0.0019 25.4 653

248.11 10.890 544.0 0.0199 268.5 653

16,17 Outside_Inside 87₁₁ 236.71 15.830 519.0 0.0301 390.3 623

236.71 1.980 519.0 0.0038 48.8 623

15 Outside_Inside 34₂₈ 236.71 6.140 519.0 0.0118 151.4 623

236.71 5.052 519.0 0.0097 124.6 623

13&14 Outside_Inside 86₁₆ 236.71 15.646 519.0 0.0298 385.8 623

236.71 2.882 519.0 0.0055 71.1 623

2&3 Top _Bottom 18₆₉ 236.71 3.243 519.0 0.0062 80.0 623

236.71 12.523 519.0 0.0239 308.8 623

4,5&6 Top _Bottom 95₁₄ 236.71 17.306 519.0 0.0329 426.7 623

236.71 2.521 519.0 0.0048 62.2 623

Section Face Bar Mark Diameter Spacing Bar Mark Diameter Spacing

29 & 30 Top ts1 12 120 ts7 0 120 942 Bottom ts3 12 200 ts6 12 200 1131 27&28 Top w1 12 120 ts1 12 120 1885 Bottom ts3 12 200 _ 0 200 565 16,17 Outside_Inside w1_w2 12₁₂ 120₂₀₀ ts1_w5 12₀ ₂₀₀120 1885.0_565.5 15 Outside_Inside w1_w2 12₁₂ 120₂₀₀ _w5_ 0₀ ₂₀₀120 942.5_565.5 13&14 Outside_Inside w1_w2 12₁₂ 120₂₀₀ bs3_- 12₀ ₂₀₀200 1508.0_565.5

2&3 Top bs1 12 200 _ 0 200 565.5

Bottom w1 12 120 bs3 12 120 1885.0

4,5&6 Top bs1 12 200 bs5 12 200 1131.0

Bottom bs3 12 200 b6 0 200 565.5

4.2 Distribution Steel

Section Face Xu kav

Top slab Top _Bottom _15.82.0 248.113_248.113 0.34304_2.70615 544.0_544.0 0.001_0.005 544 533 vertical wall Outside_Inside 21.8_7.0 248.113_248.113 3.92113_1.25938 519.0_519.0 0.008_0.002 519 508

Bottom slab Top 23.8 248.113 4.28289 519.0 0.008 519 508

Bottom 17.3 248.113 3.10791 519.0 0.006

Section Face Bar Mark Diameter Spacing Status

Top slab Top 8 ts2 10 200 393 1.16 OK

Bottom 67 ts4 10 200 393 1.16 OK

vertical wall Outside 97 w3 10 200 393 0.08 OK

Inside 31 w6 10 200 393 0.08 OK

Bottom slab Top 106 bs2 10 200 393 0.08 OK

Bottom 77 bs4 10 200 393 0.08 OK

4.3 Check for Shear as per IRC:21

Section ρ1

top slab 89.0 544 56.0 261.256 Not reqd

Vertical wall 71.0 519 122.7 198.062 Not reqd

Bottom slab 98.0 519 126.3 192.685 Not reqd

Mdes (KN.m) Limiting depth (Xulim) Effective depth provided Ast reqd. (mm2_/m) Min Ast Reqd (mm2/m) Ast provd. (mm2_/m) Mdes (KN.m) Limiting depth (Xulim) Effective depth provided Doverall provd. (m) Deff provd. (m) Ast reqd. (mm2_/m) Ast provd. (mm2_/m)  (% steel) Vdes (KN) Deff provd. (m) Subject to a Minimum shear resistance (νRd.c) Shear Reqd Reinforce ment Provided

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3.00 3.00 Dia Spacing 12 120 10 200 12 200 10 200 10 8 No. 12 200 12 120 12 200 10 200 10 8 No. 10 200 12 200 10 200 12 120 10 200 12 200 10 200 10 200 L1 900 10 200 L2 900 10 10 No. L3 450

Table no:6.5 (IRC:112-2011) Table no:18.1 (IRC:112-2011)

Page 49: (IRC:112-2011) Page 30: (IRC:112-2011)

Table no:6.5 (IRC:112-2011) Clause 6.2.2 (IRC:112-2011)

A2.10 Page : 244 (IRC:112-2011)

0.8 Up to fck ≤ 60Mpa,Eq.A2-33 (IRC:112-2011); 0.8-((fck-60)/500) for 60<fck<110Mpa Cylinder

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Status Status 2.78 6.4 222.7 unsafe OK 3.34 46.4 265.5 unsafe OK 5.57 4.8 445.5 unsafe OK 1.67 50.4 132.7 unsafe Not OK 0.36 69.6 420.2 unsafe OK 0.11 8.8 127.4 unsafe Not OK 0.18 27.2 211.7 unsafe OK 0.11 22.4 127.1 unsafe Not OK 0.29 68.8 336.2 unsafe OK 0.11 12.8 127.3 unsafe Not OK 0.11 14.4 127.3 unsafe Not OK 0.36 55.2 421.2 unsafe OK 0.22 76 251.8 unsafe OK 0.11 11.2 127.4 unsafe Not OK  (% steel) MR with respect to concrete MR with respect to steel

(21)

5.0 Check for Safe Bearing Capacity of Soil

5.1 Summary of Support Reactions

[STAAD III Output]

Support No.

Max Vertical

Reaction

(DL + SIDL +

EP on B/F + B.F +

Surcharge EP +

CWLL)

(KN)

1

43.50

2

39.30

3

35.10

4

33.20

5

31.00

6

26.90

7

22.90

8

20.90

9

13.10

10

11.70

11

7.30

12

3.50

35

0.00

36

0.00 Sum

288.40 Total Load /m

=

Length of Box (along traffic direction)

=

Base Pressure due to vertical loads

=

288.4/(4.200x1)

=

Additional pressure due to eccentricity of CWLL

=

Total Base pressue

=

(22)

288.40 KN

4.200 m

68.67

11.53

80.2 <

120.0 Safe

KN/m

2

KN/m

2

KN/m

2

KN/m

2

(23)

Serviceability Limit State(SLS) Stress Level

= 1000*17.306^3/3+426.7*(544-17.306)^2*(200000/31000) 765389164

Stresses are calculated for Maximum bending moment

= 95*10^6*17.31/765389164

2.15 < 14.4 MPa Safe

= 95*10^6*(544-17.31)/765389164

65.37 < 400 MPa Safe

Crack width Maximum crack width

<= <= 5*(50+12/2) <= 280 mm = = 57346.7*0.0002 = 11.247 mm = = (3.4*50+0.425*0.8*0.5*12))/0.003 = 57347

= 0.8 for Deformed bars = 0.5 for bending = = 426.69/(140*1000) = 0.0030 = = (65.373-0.5*2.5/0.003*(1+6.45*0.003))/200000 = -0.001797 >= 0.000196 0.6*65.373/200000 = 0.000196 Moment of Inertia of cracked section mm4 Maximum compressive stress in concrete Maximum tensile stress

in steel

where spacing of bonded reinforcement with in the

tension zone 5*(C+ф/2)

W_k S_r,max (_sm-_cm)

Maximum crack spacing

S_r,max (3.4c+0.425k₁k₂ф)/ρ_p.eff

Coefficent based on bond propoerties k₁ Coefficent based on distribution of strain k₂

eff As/Ac.eff

(_sm-_cm) _sc- k_t f_ct.eff/__eff_e__.eff))/E_s _>=0.6_

sc / Es

(24)

(25)

Moment of Inertia of cracked section = 1000*0^3/3+1256.68*(544-0)^2*(200000/31000) 2443469285

Stresses are calculated for Maximum bending moment

= 95*10^6*17.31/2443469285

= 5.94 < 14.4 MPa

= 95*10^6*(544-17.31)/2443469285

61.43 < 400 MPa

where spacing of bonded steel with in the tension zone <=

<= 5*(50+16/2)

<= 290 mm

<= 89.98 <= 290

= 0.8 for deformed bars = 0.5 for bending . = = (3.4*50+0.425*0.8*0.5*16)/0.0087 = 19853 mm = = 1256.68/(145*1000) = 0.00867 or No bonded rei > 89.98 > 290 mm = = 638.3409264175 mm = 3.4c+0.17ф = 19929.01932075 mm

= 19852.873563218 mm condition should be check

= 0.5 = = (61.432-0.5*2.5/0.0087*(1+6.45*0.0087))/200000 = -0.000452 >= 0.000184 = 0.000184 = = 19852.9*0.00018 = 3.659 mm < 0.3

modify the section mm4

Max. compressive stress in concrete ( σ_cc)

Maximum tensile stress in steel ( σ_sc)

5*(C+ф/2)

Case 1: Spacing of bonded reinforcement with in the tension zone 5*(C+ф/2) Coefficient based on bond propoerties k1

Coefficient based on distribution of strain k2

Maximum crack spacing S_r,max (3.4c+0.425k₁k₂ф)/ρ_p.eff

Case2 :the spacing of bonded reinforcement

5*(C+ф/2)

Maximum crack spacing S_r,max 1.3 (d-XU)

case 3 : Defermed bar associated with pure bending

Maximum crack spacing S_r,max

ρ_p.eff

Maximum of maximum cracking spacing Srmax

Factor dependent on the duration of the load (kt)

(sm-cm) sc - kt fct.eff/eff e.eff))/Es

>=0.6 σsc / Es

(26)

Safe

condition should be check

0.6*61.432/200000

(27)

Job Name : Design of Single Cell Box Culvert Subject DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

Moment of Inertia of cracked section = 1000*17.306^3/3+426.7*(544-17.306)^2*(200000/31000) 765389164

Stresses are calculated for Maximum bending moment

= 95*10^6*17.31/765389164

2.15 < 14.4 MPa Safe

= 95*10^6*(544-17.31)/765389164

65.37 < 400 MPa Safe

<=

<= 5*(50+0/2)

<= 250 mm

<=

<= 250

= 0.8 for deformed bars = 0.5 for bending . = = (3.4*50+0.425*0.8*0.5*12)/0.0021 = 80952 mm = = 426.69/(202.5*1000) = 0.00211

= (For defferent dia of bars are used)

or No bonded reinforcement with in t >

> 250 mm = = 652.2023921018 mm = 3.4c+0.17ф = 80679.181607256 mm = 80952 mm = 0.5 = = (65.373-0.5*2.5/0.0021*(1+6.45*0.0021))/200000 = -0.002690 >= 0.000196 0.6*65.373/200000 = 0.000196 = = 80952.4*0.0002 = 15.876 mm < 0.2

modify the section mm4

Maximum compressive stress in concrete ( σcc)

Maximum tensile stress in steel ( σ_sc)

where spacing of bonded reinforcement with in the

tension zone 5*(C+ф/2)

Case 1: Spacing of bonded reinforcement with in the tension zone 5*(C+ф/2)

Coefficient based on bond propoerties k1

Coefficient based on distribution of strain k2

Maximum crack spacing Sr,max (3.4c+0.425k1k2ф)/ρp.eff

Equivalent diameter фeq n1ф12 + n2ф22

n1ф1+ n2ф2

Case2 :the spacing of bonded reinforcement

5*(C+ф/2)

Maximum crack spacing Sr,max

1.3 (d-XU)

case 3 : Defermed bar associated with pure bending

Maximum crack spacing Sr,max _ρ p.eff

Maximum of maximum cracking spacing Srmax

Factor dependent on the duration of the load (kt)

(sm-cm) sc - kt fct.eff/eff e.eff))/Es >=0.6 sc / Es

>=0.6 σsc / Es

Wk Sr,max (sm-cm)

very severe and extreme

(28)

Project : Four Laning of Tirupati-Tiruthani-Chennai Section of NH-205

Job Name : Design of Single Cell Box Culvert

Subject :

DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

STAAD PLANE RCC BOX 1 x 3 x 3 without Cushion

*ANALYSIS OF BOX CULVERT WITH SPRING CONSTANT

INPUT WIDTH 79

UNIT METER KN

JOINT COORDINATES

1 0 0 0

2 0.3 0 0

3 0.45 0 0

4 0.836 0 0

5 1.222 0 0

6 1.608 0 0

7 1.993 0 0

8 2.379 0 0

9 2.765 0 0

10 3.15 0 0

11 3.3 0 0

12 3.6 0 0

13 0 0.3 0

14 0 0.45 0

15 0 1.35 0

16 0 2.25 0

17 0 3.15 0

18 0 3.3 0

19 3.6 0.3 0

20 3.6 0.45 0

21 3.6 1.35 0

22 3.6 2.25 0

23 3.6 3.15 0

24 3.6 3.3 0

25 0 3.6 0

26 0.3 3.6 0

27 0.45 3.6 0

28 1 3.6 0

29 1.534 3.6 0

30 2.067 3.6 0

31 2.6 3.6 0

32 3.15 3.6 0

33 3.3 3.6 0

34 3.6 3.6 0

35 3.601 0 0

36 -0.001 0 0

MEMBER INCIDENCES

1 1 2;

2 2 3;

3 3 4;

4 4 5;

5 5 6;

6 6 7;

7 7 8;

8 8 9;

9 9 10;

10 10 11;

(29)

11 11 12;

12 1 13;

13 13 14;

14 14 15;

15 15 16;

16 16 17;

17 17 18;

18 18 25;

19 12 19;

20 19 20;

21 20 21;

22 21 22;

23 22 23;

24 23 24;

25 24 34;

26 25 26;

27 26 27;

28 27 28;

29 28 29;

30 29 30;

31 30 31;

32 31 32;

33 32 33;

34 33 34;

35 36 1

36 12 35

MEMBER PROPERTIES INDIAN

1 11 PRIS YD 0.6 ZD 1

2 10 PRIS YD 0.6 ZD 1

3 TO 9 PRIS YD 0.6 ZD 1

12 TO 18 PRIS YD 0.6 ZD 1

19 TO 25 PRIS YD 0.6 ZD 1

26 TO 36 PRIS YD 0.6 ZD 1

CONSTANTS

E 25000000 ALL

POISSON 0.15 ALL

DENSITY 25 ALL

ALPHA 1.17e-005 ALL

SUPPORTS

1 FIXED BUT FZ MX MY MZ KFY 240.001

12 FIXED BUT FX FZ MX MY MZ KFY 240.001

2 11 FIXED BUT FX FZ MX MY MZ KFY 360

3 10 FIXED BUT FX FZ MX MY MZ KFY 428.572

4 TO 9 FIXED BUT FX FZ MX MY MZ KFY 617.143

35 36 FIXED BUT FX FZ MX MY MZ KFY 0.001

(30)

LOAD 1 SELF WEIGHT

SELFWEIGHT Y -1

LOAD 2 SIDL

MEMBER LOAD

26 TO 34 UNI GY -2.73

LOAD 3 ACTIVE EARTH PR. (BOTH SIDES)

MEMBER LOAD

12 TRAP GX 49 46

13 TRAP GX 46 44.5

14 TRAP GX 44.5 35.5

15 TRAP GX 35.5 26.5

16 TRAP GX 26.5 17.5

17 TRAP GX 17.5 16

18 TRAP GX 16 13

19 TRAP GX -49 -46

20 TRAP GX -46 -44.5

21 TRAP GX -44.5 -35.5

22 TRAP GX -35.5 -26.5

23 TRAP GX -26.5 -17.5

24 TRAP GX -17.5 -16

25 TRAP GX -16 -13

*WEIGHT OF EARTH ON PROEJCTED PORTION OF SLAB

35 36 UNI GY 0

LOAD 4 LIVE LOAD 1(70R TRACKED)

MEMBER LOAD

26 TO 34 UNI GY -27.63

LOAD 5 LIVE LOAD 2 (40T BOGIE )

MEMBER LOAD

26 TO 34 UNI GY -36

LOAD 6 LIVE LOAD 3(CLASS A 2LANE)

MEMBER LOAD

26 TO 34 UNI GY -32.02

LOAD 7 LL SURCHARGE (BOTH SIDES)

MEMBER LOAD

12 TO 18 UNI GX 12

19 TO 25 UNI GX -12

LOAD 8 LL SURCHARGE (LEFT SIDE)

MEMBER LOAD

12 TO 18 UNI GX 12

LOAD 9 LL SURCHARGE (RIGHT SIDE)

MEMBER LOAD

19 TO 25 UNI GX -12

LOAD 10 BRAKING FORCE (LEFT SIDE)

JOINT LOAD

25 FX 6.67

(31)

LOAD 11 BRAKING FORCE (RIGHT SIDE)

JOINT LOAD

34 FX -6.67

LOAD COMBINATION 101

1 1.35 2 1.75 3 1.5

LOAD COMBINATION 102

1 1.35 2 1.75 3 1.5 4 1.5

LOAD COMBINATION 103

1 1.35 2 1.75 3 1.5 4 1.5 7 1.2

LOAD COMBINATION 104

1 1.35 2 1.75 3 1.5 4 1.5 8 1.2 10 1.5

LOAD COMBINATION 105

1 1.35 2 1.75 3 1.5 4 1.5 9 1.2 11 1.5

LOAD COMBINATION 106

1 1.35 2 1.75 3 1.5 5 1.5

LOAD COMBINATION 107

1 1.35 2 1.75 3 1.5 5 1.5 7 1.2

LOAD COMBINATION 108

1 1.35 2 1.75 3 1.5 5 1.5 8 1.2 10 1.5

LOAD COMBINATION 109

1 1.35 2 1.75 3 1.5 5 1.5 9 1.2 11 1.5

LOAD COMBINATION 110

1 1.35 2 1.75 3 1.5 6 1.5

LOAD COMBINATION 111

1 1.35 2 1.75 3 1.5 6 1.5 7 1.2

LOAD COMBINATION 112

1 1.35 2 1.75 3 1.5 6 1.5 8 1.2 10 1.5

LOAD COMBINATION 113

1 1.35 2 1.75 3 1.5 6 1.5 9 1.2 11 1.5

PERFORM ANALYSIS

PRINT SUPPORT REACTION

PRINT MAXFORCE ENVELOPE ALL

FINISH

(32)

1.3 Live load

(a) Single lane of IRC class 70R. (track load) Impact factor =I 25%(For 70 R track and Wheeled load)

0.84

35t 35t 35t 35t

4.57 m

2.06 m Position of live load for maximum Moment

Traffic Direction Track Load

4.57 Approaches Over 3 X= 1.50000001 0.5 0.84 1.22 0.84 1.2 2.12 2.06 ###

Dispersion of single Lane 70 R Track loadover the deck slab Width of live load over the deck of culvert 0.84 m

Now, allowing for the dispersion of load through the deck, Effective width of dispersion (Ref:Cl: 305.16.2 of IRC :21-2000)

Here, a= 1.50000001

= 2.6

Effective width of dispersion B= 2.6 X ### ### 3.00000001) +0.84

= ### m

Therefore net width of dispersion = 1.395 + 2.06 ###

= ### m

Effective length of load at the culvert depth =l' = 4.57 + 2 x ( 0.35 +0.3)

= 5.87 > 3.35

Average intensity of load over the culvert slab= 70 x 1.25

(with impact factor) = 4.57 ###

= ### t/sq.m

(b) Single lane class 70R ,Bogie load (col l) Traffic Direction =b1 = b_ef= a (1-a/l_o) +b₁ f(b/l_o)=  

(33)

0.36 0.36 0.36 0.36

0.45 1.48 0.45

1.22

0.36 0.36 0.36 0.36

0.45 1.48 0.45

Position of live load for maximum Load

1.500000005 1.22 3.00000001 0.5 CL 0.36 0.36 0.36 0.36 Crash Barrier 1.2 0.45 1.48 0.45 1.7 0.81 1.84 0.81

Dispersion of single Lane 70 R Bogie load over the deck slab Now, allowing for the dispersion of load through the deck,

Effective width of dispersion Here, a= 1.675

= 2.6

2.6 X x 1.675 x ( 1- 1.675 3.35)

= 2.5375 m

Therefore net width of dispersion= 1.26875 + 2 x 0.81 + 1.84 1.26875 = 5.9975 m

Width of disperson parallel to span= 0.263 +2 x ( 0.3 +0.35) = 1.563

Eff length of load at the culvert depth =l' =Min.of (1.22+ 1.563) and 3.35 = 2.783

Average intensity of load over the culvert slab= 40 x 1.25

(with impact factor) 2.783 x 5.9975

= ### t/sq.m

(c) Two lane of IRC class A load

Impact factor =I 48%(For IRC class A)

0.5 0.5 0.5 0.5

0.25

1.8 1.7 1.8

bef= a (1-a/lo) +b1

f(b/lo)=

Effective width of dispersion b_ef=

_

(34)

Axil load 2.7 2.7 11.4 11.4 6.8 6.8 6.8 1.1 3.2 1.2 4.3 3 3 CL 0.5 0.5 0.5 0.5 0.5 0.15 1.3 1.2 1.3 0.9 1.8 1.7 1.8

Width of live load over the deck of culvert 0.5 m

Now, allowing for the dispersion of load through the deck, Effective width of dispersion Here, x= 1.675

k= f(b/l)= 2.6

Effective width of dispersion B= 2.6 X x 1.675 x ( 1- 1.675 3.35)

= 2.6775 m

Therefore net width of dispersion 0.9 + 2 x 1.8 + 1.7 + 1.33875 = 7.53875 m

Width of disperson parallel to span= 1.22+ 0.25 +2 (0.3

= 2.77 m

Effective length of load at the culvert depth =l' Min.of 2.77 and 3.35

= = 2.77 m

Average intensity of load over the culvert slab= 11.4 x 4 x x 1.49

(with impact factor) 2.77 x 7.54

= ### t/sq.m

S.No Load Case Avg. Intensity of Load

( a ) Single Lane 70R (Track) 3.950 t/sq.m

( b ) Single Lane 70R (Bogie) 3.000 t/sq.m

( c ) Two lane IRC class A load 2.730 t/sq.m

=bw =

(35)

approaches

0.35

(36)

350

Deck slab 1.26875

(37)

6.8 3 350 m 1.33875 +0.5 0.35)

(38)

PROJECT No.

#REF!

73125

Design of Box Culvert

1000

D/4 < e <

3/2D

Moment

=

34 KNm

150 mm < e <

900 mm

Axial force =

#REF!

KN

Eccectricity =

#REF! m

#REF!

Asc top

8 nos

12 

Ast bottom

5 nos

12 

n

=

113 mm

D

=

600 mm

Clear cover

50 mm

Eff cover

56 mm

d

=

544 mm

dt=dc

=

56 mm

Conc Grade M

25 Ast=

904.32 Asc=

565.2 m

=

11.20 Taking moment of internal and external forces about the centre of tensile steel

We have ;

bxnxc'/2x(d-n/3)+(mc-1)Ascxc'/nx(n-nc)x(d-dc)= Px(e+D/2-dt)

or Stress in concrete c'=

#REF!

Again equating the sum of internal forces to the external forces

We have

or ,Stress in tensile steel t=

#REF!

From these values of c' and t we have from stress diagram

n =

d

(1+t/(mxc'))

or n=

#REF!

mm

Assumed n=

113.00 mm

#REF!

d

t

mm

2

mm

2

N/mm

2

bxnxc'/2+(mc-1)xAscxc'/n(n-dc)-Astxt=

P

N/mm

2

(39)

(40)

DOCUMENT No.

DATE

15-May-17

DESIGNED

CHECKED

PAGE

JM

S.R

e

600 D (Overall depth)

Steel

N assumed

N calculated

Stress in Conc

Stress in Com. Steel

stress in tensile steel

(41)

(42)

Maximum BM = Mreq = 38.6 kN-m (From analysis)

Maximum SF = SFreq = 20 kN

Depth of member (D) = 210 mm

Width of the meber (b) = 1000 mm

Grade of Concrete Used = M30

= 30 N/mm2 Table no:6.5 (IRC:112-2011) = 500 N/mm2 Table no:18.1 (IRC:112-2011) = 1.5 Basic Page 49: (IRC:112-2011) Basic = 1.15 Basic Page 30: (IRC:112-2011) = 0.0035 Up to fck ≤ 60Mpa Table no:6.5 (IRC:112-2011) = 200000 N/mm2 Clause 6.2.2 (IRC:112-2011)

= 0.00417

= 0.67 Cube A2.10 Page : 244 (IRC:112-2Cube

= 0.8 0.8 Up to fck ≤ 60Mpa,Eq.A2-33 (IRC:112-2011); 0.8-((fck-60)/500) for 60<fck<110Mpa = 11.0 Up to fck ≤ 60Mpa,Eq.A2-35 (IRC:112-2011); 1.0-((fck-60)/250) for 60<fck<110Mpa

= 13.400

= 10.720

= 0.400

Effective depth of member (d) = 210 - 40 - 16

= 154

= 0.152

= 70.238 mm

Force in compression = Force in Tension from Fig. A2-4 - rectangular Tensile Strength

= = As = M = = = = 0 x = = = = 154x(1-sqrt1-4x0.4x0.152))/(2x0.4) = 25.005569262 mm < 70.23796 = = 1.15x10.72x25.006x1000/ 500 = 616.53731572 Provide 2 No's 20 Provided reinforcemnt = 628.32 > 616.54

Charactristic strength of concrete (fck)

Charactristic strength of steel (fy)

Partial material safety factor for concrete (m)

Partial material safety factor for Steel (s)

Ultimate compressive strain in the concrete (єcu3)

modulus of elasticity of reinforcing of steel (Es)

Ultimate tensile strain in the steel (єs) = [{fy/(s xEs)}+0.002]

Coefficient to consider the influence of the concret strength () Factor ( ) Factor () fcd =(*fck/m) Factor Fav (fcd) Factor  = () M/(bd2_{Fav) = k} av

fy*As fcd *x* b Fav * x*b s s * Fav * x*b fy fy*As *(d-x/2) s fy*s * Fav * x*b *(d-x) s * fy Fav * x*b *(d-x) x2_{-dx + M/Fav*b} d-sqrt(d2-4**M/Fav*b)/(2*) d*(1-sqrt(1-4**M/Fav*b*d2_))/(2*_₎ d*(1-sqrt(1-4**kav))/(2*) Required reinforcement As s * Fav * x*b fy mm2 mm2

(43)

or

0.8 Up to fck ≤ 60Mpa,Eq.A2-33 (IRC:112-2011); 0.8-((fck-60)/500) for 60<fck<110Mpa 1.0 Up to fck ≤ 60Mpa,Eq.A2-35 (IRC:112-2011); 1.0-((fck-60)/250) for 60<fck<110Mpa

Safe

(44)

Table 6.5 Stress and Deformation Characteristics for Normal Concrete

Strenght classes for Concrete

fck (MPa) fcm(MPa) fctm(MPa) Ecm (GPa) 

M15 15 25 1.6 1.1 2.0 27 1.8 3.5 2.0 3.5 2.0 1.8 3.5 M20 20 30 1.9 1.3 2.5 29 1.9 3.5 2.0 3.5 2.0 1.8 3.5 M25 25 35 2.2 1.5 2.9 30 2.0 3.5 2.0 3.5 2.0 1.8 3.5 M30 30 40 2.5 1.7 3.2 31 2.0 3.5 2.0 3.5 2.0 1.8 3.5 M35 35 45 2.8 1.9 3.6 32 2.1 3.5 2.0 3.5 2.0 1.8 3.5 M40 40 50 3.0 2.1 3.9 33 2.2 3.5 2.0 3.5 2.0 1.8 3.5 M45 45 55 3.3 2.3 4.3 34 2.3 3.5 2.0 3.5 2.0 1.8 3.5 M50 50 60 3.5 2.5 4.6 35 2.3 3.5 2.0 3.5 2.0 1.8 3.5 M55 55 65 3.7 2.6 4.9 36 2.4 3.5 2.0 3.5 2.0 1.8 3.5 M60 60 70 4.0 2.8 5.2 37 2.4 3.5 2.0 3.5 2.0 1.8 3.5 M65 65 75 4.1 2.9 5.4 38 2.5 3.4 2.1 3.3 1.9 1.8 3.3 M70 70 80 4.3 3.0 5.6 38 2.5 3.2 2.2 3.1 1.7 1.8 3.1 M75 75 85 4.4 3.1 5.7 39 2.6 3.0 2.3 2.9 1.6 1.9 2.9 M80 80 90 4.5 3.2 5.9 40 2.6 2.9 2.3 2.8 1.5 1.9 2.8 M85 85 95 4.7 3.3 6.1 40 2.7 2.9 2.4 2.7 1.5 2.0 2.7 M90 90 100 4.8 3.3 6.2 41 2.7 2.8 2.4 2.6 1.4 2.1 2.6

1 Strength designation of concrete,(based on charactristic strength) and corresponding properties to be used in the design are given below. The strains are expressed in per thousand by 0/00 sign. 2 The tabulated values of Ecm are for quartzite/granite aggregate. For other aggregates, they should be multiplied by factors as given below

Lime stone = 0.9 , Sand Sto 0.7 ,basalt = 1.2

Table 6.1 Grades of Reinforced Steel

Fy Grade I Fe 415 415 Fe 415D 415 Fe 500 500 Fe 500D 500 Fe 550 550 Fe 550D 550 Fe 600 600 fctk,0.05(

MPa) fctk,0.95(MPa) cl (0/00) cul (0/00) 2 (0/00) cu2 (0/00) 3 (0/00) cu3 (0/00)

Type of Steel Grade/ Designatio n Mild Steel(MS) High yield strength deformed steel (HYSD Steel)

(45)

(46)

Project : Four Laning of Tirupati-Tiruthani-Chennai Section of NH-205

Job Name : Design of Single Cell Box Culvert

Subject :

DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

STAAD PLANE RCC BOX 1 x 3 x 3 without Cushion

*ANALYSIS OF BOX CULVERT WITH SPRING CONSTANT

INPUT WIDTH 79

UNIT METER KN

JOINT COORDINATES

1 0 0 0

2 0.3 0 0

3 0.45 0 0

4 0.836 0 0

5 1.222 0 0

6 1.608 0 0

7 1.993 0 0

8 2.379 0 0

9 2.765 0 0

10 3.15 0 0

11 3.3 0 0

12 3.6 0 0

13 0 0.3 0

14 0 0.45 0

15 0 1.35 0

16 0 2.25 0

17 0 3.15 0

18 0 3.3 0

19 3.6 0.3 0

20 3.6 0.45 0

21 3.6 1.35 0

22 3.6 2.25 0

23 3.6 3.15 0

24 3.6 3.3 0

25 0 3.6 0

26 0.3 3.6 0

27 0.45 3.6 0

28 1 3.6 0

29 1.534 3.6 0

30 2.067 3.6 0

31 2.6 3.6 0

32 3.15 3.6 0

33 3.3 3.6 0

34 3.6 3.6 0

35 3.601 0 0

36 -0.001 0 0

MEMBER INCIDENCES

1 1 2;

2 2 3;

3 3 4;

4 4 5;

5 5 6;

6 6 7;

7 7 8;

8 8 9;

9 9 10;

10 10 11;

(47)

11 11 12;

12 1 13;

13 13 14;

14 14 15;

15 15 16;

16 16 17;

17 17 18;

18 18 25;

19 12 19;

20 19 20;

21 20 21;

22 21 22;

23 22 23;

24 23 24;

25 24 34;

26 25 26;

27 26 27;

28 27 28;

29 28 29;

30 29 30;

31 30 31;

32 31 32;

33 32 33;

34 33 34;

35 36 1

36 12 35

MEMBER PROPERTIES INDIAN

1 11 PRIS YD 0.6 ZD 1

2 10 PRIS YD 0.6 ZD 1

3 TO 9 PRIS YD 0.6 ZD 1

12 TO 18 PRIS YD 0.6 ZD 1

19 TO 25 PRIS YD 0.6 ZD 1

26 TO 36 PRIS YD 0.6 ZD 1

CONSTANTS

E 25000000 ALL

POISSON 0.15 ALL

DENSITY 25 ALL

ALPHA 1.17e-005 ALL

SUPPORTS

1 FIXED BUT FZ MX MY MZ KFY 240.001

12 FIXED BUT FX FZ MX MY MZ KFY 240.001

2 11 FIXED BUT FX FZ MX MY MZ KFY 360

3 10 FIXED BUT FX FZ MX MY MZ KFY 428.572

4 TO 9 FIXED BUT FX FZ MX MY MZ KFY 617.143

35 36 FIXED BUT FX FZ MX MY MZ KFY 0.001

(48)

LOAD 1 SELF WEIGHT

SELFWEIGHT Y -1

LOAD 2 SIDL

MEMBER LOAD

26 TO 34 UNI GY -2.73

LOAD 3 ACTIVE EARTH PR. (BOTH SIDES)

MEMBER LOAD

12 TRAP GX 49 46

13 TRAP GX 46 44.5

14 TRAP GX 44.5 35.5

15 TRAP GX 35.5 26.5

16 TRAP GX 26.5 17.5

17 TRAP GX 17.5 16

18 TRAP GX 16 13

19 TRAP GX -49 -46

20 TRAP GX -46 -44.5

21 TRAP GX -44.5 -35.5

22 TRAP GX -35.5 -26.5

23 TRAP GX -26.5 -17.5

24 TRAP GX -17.5 -16

25 TRAP GX -16 -13

*WEIGHT OF EARTH ON PROEJCTED PORTION OF SLAB

35 36 UNI GY 0

LOAD 4 LIVE LOAD 1(70R TRACKED)

MEMBER LOAD

26 TO 34 UNI GY -27.63

LOAD 5 LIVE LOAD 2 (40T BOGIE )

MEMBER LOAD

26 TO 34 UNI GY -36

LOAD 6 LIVE LOAD 3(CLASS A 2LANE)

MEMBER LOAD

26 TO 34 UNI GY -32.02

LOAD 7 LL SURCHARGE (BOTH SIDES)

MEMBER LOAD

12 TO 18 UNI GX 12

19 TO 25 UNI GX -12

LOAD 8 LL SURCHARGE (LEFT SIDE)

MEMBER LOAD

12 TO 18 UNI GX 12

LOAD 9 LL SURCHARGE (RIGHT SIDE)

MEMBER LOAD

19 TO 25 UNI GX -12

LOAD 10 BRAKING FORCE (LEFT SIDE)

JOINT LOAD

25 FX 6.67

(49)

LOAD 11 BRAKING FORCE (RIGHT SIDE)

JOINT LOAD

34 FX -6.67

LOAD COMBINATION 101

1 1 2 1 3 1

LOAD COMBINATION 102

1 1 2 1 3 1 4 1

LOAD COMBINATION 103

1 1 2 1 3 1 4 1 7 1

LOAD COMBINATION 104

1 1 2 1 3 14 1 8 1 10 1

LOAD COMBINATION 105

1 1 2 1 3 1 4 1 9 1 11 1

LOAD COMBINATION 106

1 1 2 13 1 5 1

LOAD COMBINATION 107

1 1 2 1 3 1 5 1 7 1

LOAD COMBINATION 108

1 1 2 1 3 1 5 1 8 1 10 1

LOAD COMBINATION 109

1 1 2 1 3 1 5 1 9 1 11 1

LOAD COMBINATION 110

1 1 2 1 3 1 6 1

LOAD COMBINATION 111

1 1 2 1 3 1 6 1 7 1

LOAD COMBINATION 112

1 1 2 1 3 1 6 1 8 1 10 1

LOAD COMBINATION 113

1 1 2 1 3 1 6 1 9 1 11 1

PERFORM ANALYSIS

PRINT SUPPORT REACTION

PRINT MAXFORCE ENVELOPE ALL

FINISH

(50)

4.0 Design of Box Structure: 1 x 3 x 3 without Cushion

Steel 3.00 3.00 Theoretical curtailment point Bar mark Dia Spacing

C/L ts1 12 120 ts2 10 200 2526 27 28 29 30 ts3 12 200 18 26 27 28 29 ts4 10 200 1718 ts5 10 8 No. 17 ts6 12 200 16 w1 12 120 16 w2 12 200 w3 10 200 15 w4 10 8 No. w6 10 200 15 bs1 12 200 bs2 10 200 14 bs3 12 120 14 bs4 10 200 1313 bs5 12 200 121 2 3 4 5  h1 10 200 1 2 3 4  6 h2 10 200 L1 900 h3 10 200 L2 900 h4 10 10 No. L3 450

Maximum BM = Mreq = 38.6 kN-m (From analysis) Maximum SF = SFreq = 20 kN

Depth of member (D) = 210 mm Width of the meber (b) = 1000 mm Grade of Concrete Used = M30

= 30 N/mm2 Table no:6.5 (IRC:112-2011) = 500 N/mm2 Table no:18.1 (IRC:112-2011) = 1.5 Basic Page 49: (IRC:112-2011) = 1.15 Basic Page 30: (IRC:112-2011) = 0.0035 Up to fck ≤ 60 Table no:6.5 (IRC:112-2011) = 200000 N/mm2 Clause 6.2.2 (IRC:112-2011) = 0.00417

= 0.67 Cube A2.10 Page : 244 (IRC:112-2011)

= 0.8 0.8 Up to fck ≤ 60Mpa,Eq.A2-33 (IRC:112-2011); 0.8-((fck-60)/500) for 60<fck<110Mpa Cylinder = 11.0 Up to fck ≤ 60Mpa,Eq.A2-35 (IRC:112-2011); 1.0-((fck-60)/250) for 60<fck<110Mpa = 13.400

= 10.720 = 0.400 Effective depth of member (d) = 544.0

= 0.012 = 248.113 mm Force in compression = Force in Tension from Fig. A2-4 - rectangular Tensile Strength

= = As = M = = = = 0 x = = = = 544x(1-sqrt1-4x0.4x0.012))/(2x0.4) = 6.65155059 mm < 248.113 Safe = = 1.15x10.72x6.652x1000/ 500 = 164.000631 Provide 2 No's 20

Provided reinforcemnt = 628.32 > 164.00 Safe

Neutral axis depth (x) =

= 471240 1.15x1x30x0.67x0.8x1000

= 25.480 mm < 248.113 Safe

Charactristic strength of concrete (fck) Charactristic strength of steel (fy) Partial material safety factor for concrete (m) Partial material safety factor for Steel (s) Ultimate compressive strain in the concrete (єcu3) modulus of elasticity of reinforcing of steel (Es) Ultimate tensile strain in the steel (єs) = [{fy/(s xEs)}+0.002] Coefficient to consider the influence of the concret strength () Factor ( ) Factor () fcd =(*fck/m) Factor Fav (fcd) Factor  = () M/(bd2Fav) = kav

fy*As fcd *x* b Fav * x*b s s * Fav * x*b fy fy*As *(d-x/2) s fy*s * Fav * x*b *(d-x) s * fy Fav * x*b *(d-x) x2 -dx + M/Fav*b d-sqrt(d2-4**M/Fav*b)/(2*) d*(1-sqrt(1-4**M/Fav*b*d2))/(2*) d*(1-sqrt(1-4**kav))/(2*) Required reinforcement As s * Fav * x*b fy mm2 mm2 fy*As* m s *fck * * b

(51)

Job Name : Design of Single Cell Box Culvert Subject : DESIGN OF BOX CULVERT 3M x 3M WITHOUT CUSHION

4.1 Check for Flexure as per IRC:21: Main Reinforcement

Section Face Xu kav Bar Mark Diameter Spacing Bar Mark Diameter Spacing Status

29 & 30 Top _Bottom 10.73₄₄ 248.113 1.842 544.0 0.003382 45 #VALUE! ts1 12 120 ts7 0 120 942 #VALUE! OK

248.113 7.587 544.0 0.013869 187 #VALUE! #VALUE! ts3 12 200 ts6 12 200 1131 #VALUE! #VALUE!

27&28 Top 43.7 248.113 7.535 544.0 0.013775 186 #VALUE! #VALUE! w1 12 120 ts1 12 120 1885 #VALUE! #VALUE!

Bottom 10.00 248.113 1.717 544.0 0.003152 42 #VALUE! #VALUE! ts3 12 200 _ 0 200 565 #VALUE! #VALUE!

16,17 Outside_Inside ₁₂54 236.711 9.780 519.0 0.018701 241 474 623 w1 12 120 ts1 12 120 1885.0 0.36 OK

236.711 2.160 519.0 0.004156 53 105 623 w2 12 200 w5 0 200 565.5 0.11 OK

15 Outside 25.3 236.711 4.563 519.0 0.008762 113 222 623 w1 12 120 _ 0 120 942.5 0.18 OK

Inside 22.3 236.711 4.021 519.0 0.007723 99 196 623 w2 12 200 w5 0 200 565.5 0.11 OK

13&14 Outside_Inside 64.54₁₆ 236.711 11.706_236.711 _2.882 519.0 0.022351_{519.0 0.005541} 289₇₁ 567₁₄₁ ₆₂₃623 _w2w1 ₁₂12 ₂₀₀120 bs3_- 12₀ ₂₀₀200 1508.0_565.5 _0.110.29 OK

OK

2&3 Top _Bottom _59.618 236.711 3.243 519.0 0.006234 80 158 623 bs1 12 200 _ 0 200 565.5 0.11 OK

236.711 10.802 519.0 0.02064 266 523 623 w1 12 120 bs3 12 120 1885.0 0.36 OK 4,5&6 Top 58.89 236.711 10.673 519.0 0.020394 263 517 623 bs1 12 200 bs5 12 200 1131.0 0.22 OK Bottom 14 236.711 2.521 519.0 0.004848 62 123 623 bs3 12 200 b6 0 200 565.5 0.11 OK Mdes (KN.m) Limiting depth (Xulim) Effective depth provided Deff required. (mm) Ast reqd.

(mm2_/m) Min Ast Reqd (mm2/m) A(mmst provd. 2_/m)  (% steel)

(52)

4.2 Distribution Steel

Section Face Xu kav Bar Mark Diameter Spacing Bar Mark Diameter Spacing

Top slab Top _Bottom 10.9_11.0 248.11331 248.113_{248.11331 248.113} _{544.0 0.003467}544.0 0.003444 105.9 544 #VALUE! #VALUE!_#VALUE! ts2_ts4 ₁₀10 200₂₀₀ 0₀ ₂₀₀200 ₃₉₃393 #VALUE!_#VALUE!

vertical wall Outside_Inside 16.1_5.6 248.11331 248.113_{248.11331 248.113} _{519.0 0.001931}519.0 0.005588 128.2 10 508 145₅₀ w3_w6 ₁₀10 200₂₀₀ 0₀ ₂₀₀200 ₃₉₃393 0.08_0.08

Bottom slab Top 14.7 248.11331 248.113 519.0 0.005099 123.2 3 508 132 bs2 10 200 0 200 393 0.08 Bottom 14.9 248.11331 248.113 519.0 0.00516 134 bs4 10 200 0 200 393 0.08

4.3 Check for Shear as per IRC:21

Section Status Vertical wall 71.0 115.0 519 0.1368 0.29 3.352 0.814 OK Bottom slab 98.0 94.0 519 0.1888 0.36 6.80 1.809 OK Mdes (KN.m) Limiting depth (Xulim) Effective depth provided Deff reqd. (m) Doverall provd. (m) Deff provd. (m) Ast reqd. (mm2_/m) Ast provd. (mm2_/m)  (% steel) Vdes (KN)

Axial Compressive Force (KN) Deff provd. (m) Shear Stress vMpa  (% steel)

Multiplying Factor Due to Axial