Box Culvert Design Calculation

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Ac Area of concrete

Acc Area of concrete in compression As Area of tension reinforcement As min Minimum area of tension reinforcement

av Length of that part of member traversed by shear failure plane b With (breath) or effective width of section

c Cover to outer diameter d Effective depth of section

Fc Basic force used in defining compressive forces Ft Basic force used in defining tie forces

fcu Characteristic strength of concrete

fs Estimated design service stress in the tension reinforcement fy Characteristic strength of reinforcement

G Shear modulus

H Maximum horizontal force Hx Horizontal force in x direction Hy Horizontal force in y direction h Overall depth

KEL Knife edge load L Critical perimeter

lx Dimension of element on x direction ly Dimension of element on y direction lz Dimension of element on z direction M Design ultimate resistance moment Mx Moment on x axis

My Moment on y axis Mz Moment on z axis q Surcharge load r Internal radius of bend SLS Serviceability limit state T Traction force

t Thickness of the element ULS Ultimate limit state

V Shear force due to design ultimate loads or design ultimate value of a concentrated load

v Design shear stress

vc Design shear stress in concrete x Neutral axis depth

x' Distance from Y axis to the centroid of an element y' Distance from X axis to the centroid of an element

z Lever arm

z' Distance from X - Y plane to point where the considered resultant force acting

Coefficient, variously defined, as appropriate Strain in tension reinforcement

Nominal range of movement Soil friction angle, or diameter Active earth pressure Unit weight of soil Partial load factor Partial load factor

Output Reference Calculation DESIGN UNIT Doc. No. Date Date D E C EPC DIVISION Designed Checked

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s

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a

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fL

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3 f

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D E C DESIGN UNIT Output Date Designed Page D E C Doc. No. Reference Calculation Job Code CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

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Doc. No. D

E

C CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code

Reference Calculation Output

Page Date

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Page

Calculation Output

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

Date Job Code

Date

EPC DIVISION Checked

DESIGN UNIT Reference D E C Designed

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Page

D E

C CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code

Date

DESIGN UNIT Designed

Checked Date

EPC DIVISION

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Date

EPC DIVISION Checked Date

Page Doc. No.

D E C

DESIGN UNIT Designed

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Figure 01 Dimentional Properties

= m

Soil Cover , = m

Safe Bearing Pressure = kN/m2

Section Thickness = m ( hw , h = span/(10 ~15))

Main R/F = mm Cover to R/F = mm Grade of Concrete = N/mm2 Properties of Soil γc = kN/m3 γs = kN/m3 γw = kN/m3 Φ' = o 1 - Permanent Loads Dead Loads

The nominal dead doad consist of the weight of the materials and the part of the structure

Structural Unit Weight of Concrete shall be taken as 24 kN/m3

Engineering Becouse of the arching of soil, check whether the depth above culvert is Design in > 3 x width of culvert ( in which case limit depth to 3 x width )

preactice

(Roger - Depth of cover (H) = m

westbrook) 3 x width = 3 x (page-94) = m 3 x width < = m So Depth limited to = m Surcharge on Roof Surcharge Presure (qr) = x qr = kN/m2 Soil

Engineering Casses of conduit installation consider as Ditch Conduit (Spangler & Ditch Conduit

Handy) A ditch conduit is defined as one which is instaled in a relatively narrow ditch dug in passive or undisturbed soil and wich is then covered with earth backfill. 12 45 25 7.2 20 25 1.1 96 9.81 1.6 4.8 Reference Calculation 7.2 1.2 1.5 0.2 7.2 150 h l 24 Output

Design of Box Culvert

4.8 20

4.8

Date 31.05.2010 Environmental &

Page 1

Ceylon Electricity Board Doc. No.

C E B

Dam Safety Designed S.M.P

H

Checked Date

Civil Structure Maintanance Job Code

Y hs hw Ground Level hs hw A B D C H l h X

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Maximum load on ditch condition Depth of cover = m Surcharge on Roof Surcharge Presure (qr) , (qr) = Cd.γ.Bd 2 1-e-2Kµ'(H/Bd) µ' = tan φ' K =

µ' - coedicient of friction between fill material and side of ditch

K - Active Lateral earth pressure coeficient Bd - Horizontal width of ditch at top of conduit γ - Unit weight (wet density) of filling material H - Height of fill above top of conduite

Cd - Load coeficient for ditch condition

So, K = Bd = m, Consider 1m length of Roof slab

= µ' = tan φ' = 2.K.µ'.(H/Bd) = Cd = (qr) = Cd.γ.Bd 2 (qr) = kN/m2

Structural Horizontal Earth Pressure Engineering

Design in If the backfill properties are known, preactice If wall friction is to be ignored (Roger

-westbrook) K0 = 1-sin Φ' =

(page-94) Ka = ( 1-sin Φ' ) / ( 1+sin Φ' ) =

q max = = x x = kN/m2 qep = x x = kN/m2 q = qmax - qep q = kN/m2 1.403 101.0 Cd 1-sin φ 1+sin φ 1-sin φ 1+sin φ 0.406 7.2 2.K.µ' = 0.466 0.76 3.60 20 0.41 0.58 0.41 15.42 9.1 73.9 20 0.41 1.9 58.44 γ.Ka.h

Civil Structure Maintanance Job Code Page 1

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Designed S.M.P Date

Environmental & Checked Date

C E B

Dam Safety

Ceylon Electricity Board Doc. No.

(δ = 0 ) 1.2

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AASHTO 2 - Vertical Live Loads 3.7.1

For Fill Depths H ≥ 8 feet (2400 mm) and Culvert Clear Span Length, The effect of live load is neglected in design when the depth of fill is more than 8 feet

3 - Hydrostatic Pressure (Internal)

q ip = C.h = x = kN/m2 4 - Analysis Reinforced Concrete Constant K = h hs 3 = Designers l hw Manual k1 = = (ref-5.1) k3 = = k5 = = k7 = = k8 = =

Load Case -01 Testing Condition 4.1.1 Hydrostatic Pressure-(Internal) Reinforced = = qip.h2.K.k7 Concrete Designers = kN.m/m Manual (ref-5.1) = = Ma. K8 = kN.m/m

4.1.2 Flexure due to weight of wall

Wall weight ( G ) = hw.γ.h q1 = 2.G = kN/m2 = kN/m l.hw Reinforced Concrete = = q1.l2.K Designers 12.k1.k3 Manual = kN.m/m (ref-5.1) = = Ma. K5 = kN.m/m

4.1.3 Flexure due to weight of Roof

q = hs.γc = kN/m2

C E B

Dam Safety Designed

9.81 16.68 Date Page 2 S.M.P Date 31.05.2010 Environmental & Doc. No. 1.7 2.21 Output Reference Calculation 3K+8 MA

{

}

1.21 K+1 K+3 2K+3 2K+7 4.1 60.k1.k3 0.99 MC MD K 4.21 5.43 9.43 11.64 MB k7 1.22 8.2 MA MB 10.20 0.22

MC MD -0.97 Checked 4.8 A B D C qip q = qip B.M.D Pressures A B D C q1 G G B.M.D Pressures

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= = =

= q.l2 12.k1

= kN.m/m

Addition of moment for Load case 01

Table - 01 Fixed end mement of the wall for Hydrostatic load

MA = MC =

= kN.m/m = kN.m/m

Maximum (-ve) moment =

(Where x is 0.45L from C)

= kN.m/m

* Calculation of moment at mid span of walls done by aproximatly by adding moment transferred to mid span from FEM to the Maximum negative meoment occurred at 0.45L after moment distribution

** Moment at mid span of the wall is calculated by considering full bending

Calculation of midspan moment due to wall load

Niutral axis depth from A = m

Load Case -02 Culvert empty and trench filled

Lateral soil pressurees giving rise to flexture in the structure "q"is the rectanguler pressure and "qep" is the triangular pressure

4.2.1 Trianguler Pressure,qep Reinforced Concrete = = qep.h2.K.k7 Designers Manual = kN.m/m (ref-5.1) = = MA. K8 = kN.m/m MC MD Job Code -0.91

Civil Structure Maintanance Page 3

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Dam Safety Designed S.M.P 31.05.2010

-2.06 * uls-Mb Total uls -0.35 Roof Date 23.3

Walls + Roof γf MA MB MC MD -0.35 A and B 0.99 1.4 1.38 0.22 Position Hydrost-atic γf uls- Mb Walls -0.14 1.4 -0.19 1.19 C and D 1.22 1.4 1.70 -0.97 -0.35 -1.32 1.4 -1.85 -0.15 Roof mid-Span 0.99 1.4 1.38 0.22 1.04 Base mid-Span 1.22 1.4 1.70 2.35 1.4 ** 0.82 1.53 ** 2.83 3.29 5.00 ** 1.4 1.4 0.82 -1.02 -1.0 1.61 W.L -0.35 -0.73 1.45 W.L 2.41 -2.88 -0.38 -3.90 15 W.L Walls middle 1.4 4.2 0.26 k7 -1.13 MA MB 60.k1.k3 10 A B D C qep qep B.M.D Pressures A B D C q = q1 B.M.D Pressures

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4.2.2 Surcharge on walls,q

= = =

Reinforced = q.h2.K

Concrete 12.k1

Designers = kN.m/m

Manual 4.2.3 Surcharge on Roof ,qr

(ref-5.1) = = =

= q.l2 12.k1

= kN.m/m

Addition of moment for Load Case 2

Fixed end mement of the wall due to qep

MA = MC =

= kN.m/m = kN.m/m

Maximum (-ve) moment =

(Where x is 0.45L from C)

= kN.m/m

Load Case -03

4.2.1 This is load case 02 + Hydrostatic load from Load case 01

1.49 2.23 W.L 23.3 -1.0 1.43 13.39 -7.45 6.65 1.4 9.31 W.L W.L * ** 13.58 -1.13 -7.72 2.35 17.29 10.80 15.12 -0.91 -7.72 1.04 17.29 9.70 1.4 Roof mid-Span Base mid-Span -0.91 -7.72 -0.14 -7.45 -1.13 -7.72 1.4 -22.70 -17.62 1.4 -24.66 -16.22 1.4 Posotion -1.32 -7.45 A and B C and D Posotion L.C.02 (Service) 4.2 1.22 -16.40 -24.66 Hydrost. (Service) Total (Service) L.C.02 (U.L.S.) 1.70 -2.06 C and D -17.62 1.70 0.99 10.69 13.58 9.70 1.38 1.22 12.02 15.12 Base mid-Span 10.80 9.31 6.65 4.59 Walls middle Total (U.L.S.) A and B -16.22 1.38 -21.32 -22.96 0.99 -15.23 -22.70 Hydrost. (U.L.S.) 14.96 Roof mid-Span S.M.P Doc. No. Date 31.05.2010 Environmental & Designed

Civil Structure Maintanance Job Code Page 4

C E B Dam Safety Checked Date Walls middle -0.73 15 10 -2.88 6.43 16.83 Reference Calculation -7.45 qep q Walls & Roof(LC-1) Surcharg -e (Roof) Total (Survice) γf Total U.L.S. Output MA MB MC MD MA MB -7.72 MC MD A B D C B.M.D Pressures Pressures A B D C B.M.D

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5 - Check on ground safe bearing pressure Load Case -01

Hydrostatic Pressure = kN/m2

Weight of walls = kN/m2

Weight of Roof + Floor = kN/m2

Total Pressure = kN/m2

Total Pressure < kN/m2

Load Case -02

Surcharge on Roof = kN/m2

Total Pressure = kN/m2

Total Pressure < kN/m2

Load Case -03

Surcharge on Roof = kN/m2 Hydrostatic Pressure = kN/m2 Total Pressure = kN/m2 Total Pressure < kN/m2 6 - U.L.S. of Flexture Maximum Moments kN.m/m i - Slabs Maximum Moment = kN.m/m 9.60 Page 5 Date 31.05.2010

10.20

C E B

Dam Safety Designed S.M.P

96.00 122.28 Calculation Output Doc. No. 5.1 16.68 9.60 96.00 5.2 Reference 115.80 5.3 10.20 9.60 36.48 hence ok 150 10.20 16.68 hence ok 150 hence ok 150 -22.70 14.96 -24.66 9.31 Sagging Hogging (L.C-03) (L.C-02) -24.66 16.83 24.15 Walls Base Member (L.C-03) (L.C-01) (L.C-02) (L.C-02) Roof

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6 - Design Calculation for Box Culvert U.L.S. of Flexture

Analysis was carried out for several load cases of various loading arrangements to find out the maximum effect on the Box culvert

Diameter of main reinforcement = mm

Diameter of secondary reinforcement = mm

Section Thickness = mm

Maximum Bending Moment = kN.m/m

Assume severe environment condition, for driving rain

Cover = mm Effective depth, d = - 45- 6 d = = k = M / (bd2fcu) 2 = (24.15x106 /(1000x1492x25) = <

Hence no compression r/f is required

M = (0.87fy)Asz equation 1

z = (1 - 1.1fyAs/ fcubd) d equation 5 from these two equations

z = d (0.5+(0.25-k/0.9)1/2 z = d [0.5+(0.25-0.044/0.9)1/2 = < d Take Z as 0.95d Z = d = x = mm

Design of main reinforcement As = M / 0.87fyz

= 24.15 x106 / 0.87x460x142 As req =

= mm2/m mm2/m

Use T @ ( As = mm2/m As pro =

mm2/m Minimum area of main rainforcement for slabs

100As / bad = 100x452/(1000x149) = ## Main r/f

T @

Hence o.k

Design for Shear Reinforcement

Check shear in U.L.S. on roof and floor slabs Take Load case 02

Shear across support = ( - Wt of Base x γf )

= kN/m2

Therefore shear in the support = x 1.2 /2

= kN/m 24.15 6.1 6.2 C E

B Civil Structure Maintanance Job Code Page 6

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Doc. No. 12 12 200 149 mm 149 mm 0.156 0.950 200 0.95 0.95 149 142 141.41 6.1.1 0.30 0.13 0.044 426 12 250 452 426 452 109.08 109.08 65.45 12

Dam Safety Designed S.M.P Date 31.05.2010

250

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Design shear force, V design = kN/m

Effective depth, d = mm

Tension steel across shear plane = Y12 -250 c/c

100 As/bd =

=

BS 8110 Effective depth = mm

Part 01 vc = 0.79x{(100As/bd)1/3.(400/d)1/4/1.25

table 3.1 =

Design shear stress v = V/bd

= (65.45x103)/(1000x149) =

v < vc Hence o.k

Check in U.L.S. on the ability of the wall to trasmit the axial loads Bs 8110 Treat as a column with bending at right angle to wall

3.9.3.6.2 Check h/hw = /

3.4.4.1 = <

hence column is short BS 8110 indicates that the effect of the axial load may be ignored if this force does not exceed 0.1.fcu.(c.s.a.)

hence 0.1.fcu.(C.S.A) = x x

= kN/m

Ultimate Load /m/Wall = x x 1.4

+ x x 24x1.4 )

= kN/m < kN/m

hence o.k.

The above calculation assumes that the wall is cosidered as reignfoced and not mass concrete

vertical R/F provided = Y @ 2 Layers

so Area = mm2

Percentage of Concrete area = x

x

= % > %

> Minimum of 0.4% hence o.k.

100 1000 149 1.7 120 600 12 200 This is 0.4 0.76 12 0.1 30 8.5 0.2 1131.0 1131.0 1.7 0.44 100 x 452 Dam Safety Reference Calculation 200 600 C E B 1.7 Date 149 N/mm2 7 Designed Page 0.2 31.05.2010 Checked Job Code S.M.P Date 0.30 65.45 Output 149 0.54 Doc. No. 1000x149 1/2( 96.0 Environmental &

Civil Structure Maintanance 6.3

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Job Code Page 8 Dam Safety

Environmental &

Civil Structure Maintanance C E B Designed S.M.P Date Reference Output Doc. No. Calculation Checked Date 31.05.2010