Box Culvert Design

(1)

Reference

Calculation

Output

Area of concrete

Area of concrete in compression Area of tension reinforcement

Minimum area of tension reinforcement

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

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

Characteristic strength of concrete

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

G Shear modulus

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

KEL Knife edge load L Critical perimeter

Dimension of element on x direction Dimension of element on y direction Dimension of element on z direction M Design ultimate resistance moment

Moment on x axis Moment on y axis 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

Doc. No.

DESIGN UNIT

Designed

A_c A_cc A_s A_{s min} a_v F_c F_t f_cu f_s f_y H_x H_y l_x l_y l_z M_x M_y M_z

D

E

C

Date

β

¿

_s

δ

φ

σ

_a

γ

_fL

γ

_f3

(2)

EPC DIVISION

Checked

Date

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

Job Code

Page

Reference

Calculation

Output

D

E

C

(3)

Doc. No.

DESIGN UNIT

Designed

EPC DIVISION

Checked

Date

Job Code

Page

Reference

Calculation

Output

D

E

C

(4)

Doc. No.

DESIGN UNIT

Designed

EPC DIVISION

Checked

Date

Job Code

Page

Reference

Calculation

Output

D

E

C

(5)

Doc. No.

DESIGN UNIT

Designed

EPC DIVISION

Checked

Date

Job Code

Page

Reference

Calculation

Output

D

E

C

(6)

Doc. No.

DESIGN UNIT

Designed

EPC DIVISION

Checked

Date

Job Code

Page

D

E

C

(7)

Reference

Calculation

Output

Design of Box Culvert

Figure 01 Dimentional Properties

h = 1.2 m

l = 1.5 m

Soil Cover , H = 7.2 m

Safe Bearing Pressure = 150 kN/m2

Section Thickness

= 0.2 m ( hw , h = span/(10 ~15))

Main R/F

=

12

mm

Cover to R/F

=

45

mm

Grade of Concrete

=

25

N/mm2 Properties of Soil

γc

=

24

kN/m3 γs = 20 kN/m3

γw

=

9.81

kN/m3 Φ' = 25 1 - Permanent Loads 1.1 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) = 7.2

m

westbrook) 3 x width = 3 x

1.6

(page-94) = 4.8 m 3 x width

<

= 7.2 m So

Depth limited to

=

4.8 m

Surcharge on Roof

Surcharge Presure (qr) = 4.8 x 20 qr = 96 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.

Ceylon Electricity Board

Doc. No.

Dam Safety

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31.05.2010

Environmental &

Checked

Date

o

C

E

B

Date

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

(8)

Civil Structure Maintanance

Job Code

Page

1 Reference

Calculation

Output

Maximum load on ditch condition

Depth of cover = 7.2 m

Surcharge on Roof

Surcharge Presure (qr) , (qr) = Cd = =

K

=

-

coedicient of friction between fill material

and side of ditch

K

-

Active Lateral earth pressure coeficient -

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 = 3.60 m, Consider 1m length of Roof slab

= 0.406 = = 0.466 2.K.µ'.(H/Bd) = 0.76 Cd = 1.403 (qr) = (qr) =

101.0

kN/m2

Structural 1.2 Horizontal Earth Pressure Engineering

Design in If the backfill properties are known, preactice If wall friction is to be ignored (δ = 0 ) (Roger

-westbrook) = 1-sin Φ' = 0.58

(page-94) = ( 1-sin Φ' ) / ( 1+sin Φ' ) = 0.41

q max

=

γ.Ka.h

=

20 x

0.41 x

9.1 = 73.87 kN/m2

=

20 x

0.41 x

1.9 = 15.42

kN/m2

q

=

q

=

58.44 kN/m2

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Dam Safety

Designed

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31.05.2010

C

E

B

C_d.γ.B_d2

1-e

-2Kµ

_'

(H/Bd) 2.K.µ' µ' tan φ'

1-sin φ

1+sin φ µ' B_d

1-sin φ

1+sin φ µ' tan φ' C_d.γ.B_d2 K₀ K_a

q

ep

q

max

- q

ep

C

E

B

Date

(9)

Environmental &

Checked

Date

Job Code

Page

1 Reference

Calculation

Output

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)

= C.h

=

9.81 x

1.7 = 16.68

kN/m2

4 - Analysis Reinforced Concrete Constant K = h

{

hs

_}

3 = 1.21 Designers l Manual k1 = K+1 = 2.21 (ref-5.1) k3 = K+3 = 4.21 k5 = 2K+3 = 5.43 k7 = 2K+7 = 9.43 k8 = 3K+8 = 11.64

4.1 Load Case -01 Testing Condition

4.1.1

Hydrostatic Pressure-(Internal)

Reinforced

=

Concrete

60.k1.k3

Designers

=

0.99 kN.m/m

Manual (ref-5.1)

=

= Ma. K8

k7

= 1.22

kN.m/m

4.1.2

Flexure due to weight of wall

Wall weight ( G ) = hw.γ.h

q1 = 2.G

= 10.20

kN/m2

= 8.2 kN/m

l.hw

Reinforced Concrete

=

Designers

12.k1.k3

Manual

=

0.22 kN.m/m

(ref-5.1)

=

= Ma. K5

K

=

-0.97 kN.m/m

4.1.3

Flexure due to weight of Roof

q = hs.γc = 4.8

kN/m2

Doc. No.

C

E

B

q

ip hw

M

A

M

B

q

ip

.h

2

_.K.k7

M

C

M

D

M

A

M

B

q1.l

2

_.K

M

C

M

D A B D C qip q = qip B.M.D Pressures A B D C q1 G G B.M.D Pressures

(10)

Dam Safety

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Environmental &

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Date

Job Code

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2 Reference

Calculation

Output

=

12.k1

=

-0.35 kN.m/m

Addition of moment for Load case 01

Position

γf

Walls

Roof

γf

Total uls

A and B

0.99

1.4

1.38

0.22

-0.35 -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

0.99

1.4

1.38

0.22 **

1.04 1.4 1.45 2.83 0.82

1.22

1.4

1.70 **

**

2.35 1.4 3.29 5.00

1.53

0.82

*

1.4 -2.88

-0.38

-0.35 -0.73 1.4 -1.02 -3.90

-2.06

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

= W.L = W.L

15 10

= 1.61 kN.m/m = 2.41 kN.m/m

Maximum (-ve) moment = W.L

(Where x is 0.45L from C) 23.3

= -1.0 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 = 0.26 m

4.2 Load Case -02 Culvert empty and trench filled

Lateral soil pressurees giving rise to flexture in the structure

4.2.1 Reinforced Concrete

=

Designers

60.k1.k3

Manual

= -0.91 kN.m/m

(ref-5.1)

=

k7

= -1.13

kN.m/m

C

E

B

Date

M

A

M

B

M

C

M

D

q.l

2

Hydrost-atic

uls-

Mb

Walls + Roof

uls-

_Mb

Roof mid-Span Base mid-Span Walls middle MA MC

"q"is the rectanguler pressure and "q

ep"

is the triangular pressure

Trianguler Pressure,q

ep

M

A

M

B

q

ep

.h

2

_.K.k7

M

C

M

D

M

A

. K8

A B D C qep qep B.M.D Pressures A B D C q = q1 B.M.D Pressures

(11)

Doc. No.

Dam Safety

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31.05.2010

Environmental &

Checked

Date

Job Code

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3 Reference

Calculation

Output

4.2.2

Surcharge on walls,q

=

Reinforced

=

Concrete

12.k1

Designers

= -7.72 kN.m/m

Manual 4.2.3

Surcharge on Roof ,qr

(ref-5.1)

=

12.k1

=

-7.45 kN.m/m

Addition of moment for Load Case 2

Posotion q γf Total U.L.S.

A and B -0.91 -7.72 -0.14 -7.45 -16.22 1.4 -22.70 C and D -1.13 -7.72 -1.32 -7.45 -17.62 1.4 -24.66 Roof mid-Span -0.91 -7.72 1.04 17.29 9.70 1.4 13.58 -1.13 -7.72 2.35 17.29 10.80 1.4 15.12 Walls middle

*

**

-0.73 -7.45 6.65 1.4 9.31 1.43 13.39 = W.L = W.L 15 10 = 1.49 kN.m/m = 2.23 kN.m/m

Maximum (-ve) moment = W.L

(Where x is 0.45L from C) 23.3

= -1.0 kN.m/m

4.2 Load Case -03

4.2.1

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

Posotion Total (U.L.S.)

A and B -16.22 0.99 -15.23 -22.70 1.38 -21.32 C and D -17.62 1.22 -16.40 -24.66 1.70 -22.96 Roof mid-Span 9.70 0.99 10.69 13.58 1.38 14.96 10.80 1.22 12.02 15.12 1.70 16.83 Walls middle 6.65 -2.06 4.59 9.31 -2.88 6.43

C

E

B

Date

M

A

M

B

M

C

M

D

q.h

2

_.K

M

A

M

B

M

C

M

D

q.l

2

q

ep _Roof(Walls & _LC-1) Surcharg _{-e (Roof)} _(Survice)Total

Base mid-Span

Fixed end mement of the wall due to qep

MA MC

L.C.02

(Service) (Service)Hydrost. (Service)Total (U.L.S.)L.C.02 Hydrost. (U.L.S.)

Base mid-Span A B D C B.M.D Pressures Pressures A B D C B.M.D

(12)

Doc. No.

Dam Safety

Designed

S.M.P

31.05.2010

Environmental &

Checked

Date

Job Code

Page

4 Reference

Calculation

Output

5 - Check on ground safe bearing pressure

5.1 Load Case -01

Hydrostatic Pressure = 16.68 kN/m2

Weight of walls = 10.20 kN/m2

Weight of Roof + Floor = 9.60 kN/m2

Total Pressure = 36.48 kN/m2

Total Pressure < 150

kN/m2

hence ok

5.2 Load Case -02

Surcharge on Roof = 96.00 kN/m2

kN/m2

hence ok

5.3 Load Case -03

Surcharge on Roof = 96.00 kN/m2

Hydrostatic Pressure = 16.68 kN/m2

kN/m2

hence ok

6 - U.L.S. of Flexture

Maximum Moments kN.m/m

Member Hogging Sagging

Roof -22.70 (L.C-01) 14.96 (L.C-03) Walls -24.66 (L.C-02) 9.31 (L.C-02) Base -24.66 (L.C-02) 16.83 (L.C-03) i - Slabs Maximum Moment = 24.15 kN.m/m

C

E

B

Date

(13)

Doc. No.

Dam Safety

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31.05.2010

Environmental &

Checked

Date

Job Code

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5 Reference

Calculation

Output

6 -

Design Calculation for Box Culvert

6.1 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 = 12

mm

Diameter of secondary reinforcement = 12

mm

Section Thickness

= 200 mm

Maximum Bending Moment

=

24.15 kN.m/m

Assume severe environment condition, for driving rain

Cover = 45

mm

Effective depth, d = 200 - 45- 6 d = 149 mm

=

149 mm k = 2 = =

0.044

< 0.16 Hence no compression r/f is required

M = equation 1

z = equation 5 from these two equations z = z = = 141.41 < 0.950 d Take Z as 0.95d Z = 0.95 d = 0.95 x 149 = 142

mm

6.1.1 Design of main reinforcement =

= =

= 426 426

Use T 12 @

250

( As = 452 =

452

Minimum area of main rainforcement for slabs

= 100x452/(1000x149) = 0.30 ###0.13 Main r/f

T 12 @ 250

Hence o.k

6.2 Design for Shear Reinforcement

Check shear in U.L.S. on roof and floor slabs

Take Load case 02

Shear across support

=

( 115.80 - Wt of Base x γf )

=

109.08 kN/m2

C

E

B

Date

M / (bd2_f cu) (24.15x106_/(1000x1492_x25) (0.87f_y)A_sz (1 - 1.1f_yA_s/ f_cubd) d d (0.5+(0.25-k/0.9)1/2 d [0.5+(0.25-0.044/0.9)1/2 A_s M / 0.87f_yz 24.15 x106_{/ 0.87x460x142} _A s req

mm

2

_/m

_mm2_/m

mm

2

_/m

_A

s pro mm2_/m 100A_s / b_ad

(14)

Therefore shear in the support =

109.08 x 1.2 /2

=

65.45 kN/m

Doc. No.

Dam Safety

Designed

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Environmental &

Checked

Date

Job Code

Page

6 Reference

Calculation

Output

Design shear force, V design = 65.45 kN/m Effective depth, d = 149

mm

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

100 As/bd =

100 x 452

1000x149

=

0.30

BS 8110 Effective depth

=

149 mm

Part 01

=

table 3.1

=

0.54

Design shear stress v = V/bd = = 0.44

v

<

vc

Hence o.k

6.3 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

=

1.7 /

0.2

3.4.4.1

=

8.5 <

12 hence column is short

BS 8110 indicates that the effect of the axial load may be ignored if this force does

hence

0.1.fcu.(C.S.A)

=

0.1 x

30 x

200

= 600 kN/m

Ultimate Load /m/Wall = 1/2( 96.0 x 1.7 x 1.4 + 0.2 x 1.7 x 24x1.4 ) = 120 kN/m < 600 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 12 @ 200 2 Layers

so Area = 1131.0 mm2

Percentage of Concrete area = 1131.0 x 100 1000 x 149 = 0.76 % > 0.4 % This is > Minimum of 0.4% hence o.k.

C

E

B

Date

v

c

0.79x{(100As/bd)

1/3.

_(400/d)

1/4

_/1.25

(65.45x103_)/(1000x149) N/mm2

(15)

Doc. No.

Dam Safety

Designed

S.M.P

31.05.2010

Environmental &

Checked

Date

Job Code

Page

7 Reference

Calculation

Output

C

E

B

(16)

Doc. No.

Dam Safety

Designed

S.M.P

31.05.2010

Environmental &