Box Culvert Design Calculation

Reference

Calculation

Output

Ac

Area of concrete

Acc

Area of concrete in compression

As As min

Area of tension reinforcement 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 Fc

Effective depth of section 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 Hx

Maximum horizontal force Horizontal force in x direction

Hy

Horizontal force in y direction

h

Overall depth

KEL

Knife edge load

L lx

Critical perimeter Dimension of element on x direction

ly

Dimension of element on y direction

lz

Dimension of element on z direction

M Mx

Design ultimate resistance moment 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

 s



 a   fL  f3

D E C

DESIGN UNIT EPC DIVISION

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

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D E C CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Reference Calculation

D E C

DESIGN UNIT

Job Code

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D E EPC DIVISION C CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Reference Calculation

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D DESIGN UNIT E EPC DIVISION C CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Reference Calculation

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D DESIGN UNIT E EPC DIVISION C CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Reference Calculation

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D E C

DESIGN UNIT EPC DIVISION CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

Doc. No. Designed Checked Job Code

Date Date Page

Reference

Calculation

Output

Design of Box Culvert Ground Level

X hs

A

B H

hw

Y

hw

h l

D

C

hs

Figure 01 Dimentional Properties h

=

1.2 m

l

=

1.5 m

H

=

7.2 m

Safe Bearing Pressure

=

150 kN/m2

Section Thickness Main R/F Cover to R/F Grade of Concrete

=

0.2 m

= =

12 mm 45 mm 25 N/mm2 24 kN/m3

Soil Cover ,

=

( hw , h

= span/(10 ~15))

Properties of Soil

γc

=

γs

=

γw

=

Φ'

=

20

kN/m3

9.81 kN/m3 25

o

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)

westbrook)

3 x width

(page-94)

7.2 = 3 x =

m 1.6

4.8 m

3 x width < =

7.2 m

=

4.8 m

=

4.8 x

20

=

96

kN/m2

Depth limited to

So

Surcharge on Roof Surcharge Presure (qr) qr

Soil Engineering (Spangler & Handy)

Casses of conduit installation consider as Ditch Conduit Ditch Conduit 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

C E B

Dam Safety Environmental & Civil Structure Maintanance

Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date 1 Page

Reference

Calculation

Output

Maximum load on ditch condition Depth of cover

=

7.2

m

Surcharge on Roof Surcharge Presure (qr) (qr) = Cd.γ.Bd2 Cd

=

,

1-e-2Kµ'(H/Bd) 2.K.µ'

µ'

= tan φ'

K

=

1-sin φ 1+sin φ

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

=

1-sin φ

Bd =

3.60 m, Consider 1m length of Roof slab

1+sin φ = µ'

= 2.K.µ'.(H/Bd) = Cd

Structural

0.406

= tan φ'

=

0.466 0.76 1.403

(qr)

= Cd.γ.Bd2

(qr)

=

101.0 kN/m2

1.2 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'

=

0.58

(page-94)

Ka

= ( 1-sin Φ' ) / ( 1+sin Φ' )

=

0.41

q max

Ceylon Electricity Board

C E B

Dam Safety Environmental & Civil Structure Maintanance

(δ = 0 )

= γ.Ka.h = 20 x 0.41 x = 73.9 kN/m2

qep

= 20 x 0.41 x = 15.42 kN/m2

q q

= qmax - qep = 58.44 kN/m2

Doc. No. Designed Checked Job Code

9.1

1.9

S.M.P

Date 31.05.2010 Date 1 Page

Reference AASHTO

Calculation

Output

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 = 9.81 x 1.7 = 16.68 kN/m2

4 - Analysis Reinforced Concrete

Constant K

=

h

Designers

l

{ hhs } 3

=

1.21

k1 k3

= =

K+1 K+3

= =

2.21 4.21

k5 k7

=

2K+3

=

5.43

= =

2K+7

=

9.43

3K+8

=

11.64

w

Manual (ref-5.1)

k8

4.1 Load Case -01 Testing Condition 4.1.1 Hydrostatic Pressure-(Internal) Reinforced

A

B

MA =

2 MB = qip.h .K.k7 60.k1.k3 = 0.99 kN.m/m

MC =

MD = Ma. K8 k7 = 1.22 kN.m/m

Concrete qip

Designers Manual

C

D

(ref-5.1)

q = qip Pressures

B.M.D

4.1.2 Flexure due to weight of wall = hw.γ.h

Wall weight ( G )

=

8.2 kN/m

q1 = 2.G l.hw

=

10.20 kN/m2

Reinforced A

Concrete

B

MA =

2 MB = q1.l .K 12.k1.k3 = 0.22 kN.m/m

MC =

MD = Ma. K5 K = -0.97

Designers G

Manual

G

(ref-5.1)

C

D q1 Pressures

B.M.D

kN.m/m

4.1.3 Flexure due to weight of Roof q

C E B

Dam Safety Environmental & Civil Structure Maintanance

= hs.γc

=

4.8

Doc. No. Designed Checked Job Code

kN/m2

S.M.P

Date 31.05.2010 Date 2 Page

Reference

Calculation A

Output

B

MA =

2 = q.l 12.k1 = -0.35

C

D q = q1 Pressures

MB =

B.M.D

MC =

MD

kN.m/m

Addition of moment for Load case 01 Position

Hydrostatic

γf

ulsMb

Walls

Roof

Walls + Roof

γf

ulsMb

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

Roof midSpan

0.99

1.4

1.38

0.22

1.04

1.4

1.45

2.83

Base midSpan

1.22

1.4

1.70

** 1.53

0.82

2.35

1.4

3.29

5.00

Walls middle

* -2.06

1.4

-2.88

-0.38

-0.35

-0.73

1.4

-1.02

-3.90

** 0.82

**

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

=

MC

W.L

=

W.L

=

2.41 kN.m/m

15 =

10

1.61 kN.m/m

Maximum (-ve) moment

=

(Where x is 0.45L from C)

W.L 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 "q"is the rectanguler pressure and "qep" is the triangular pressure 4.2.1 Trianguler Pressure,qep Reinforced Concrete

A

B

MA =

2 MB = qep.h .K.k7 60.k1.k3 = -0.91 kN.m/m

MC =

MD = MA. K8 k7 = -1.13 kN.m/m

Designers Manual (ref-5.1) qep

qep Pressures

C E B

Dam Safety Environmental & Civil Structure Maintanance

C

D B.M.D

Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date 3 Page

Reference

Calculation

Output

4.2.2 Surcharge on walls,q

A

MA =

Reinforced Concrete Designers Manual (ref-5.1)

MB = MC = MD 2 = q.h .K 12.k1 = -7.72 kN.m/m 4.2.3 Surcharge on Roof ,qr MA = MB = MC = MD 2 = q.l 12.k1 = -7.45 kN.m/m Addition of moment for Load Case 2

B

B.M.D A

B.M.D

Walls & Surcharg - Total Roof(LC-1) e (Roof) (Survice)

γf

Total U.L.S.

-16.22

1.4

-22.70

-7.45

-17.62

1.4

-24.66

1.04

17.29

9.70

1.4

13.58

2.35

17.29

10.80

1.4

15.12

-0.73

-7.45

6.65

1.4

9.31

q

A and B

-0.91

-7.72

-0.14

-7.45

C and D

-1.13

-7.72

-1.32

Roof midSpan

-0.91

-7.72

Base midSpan

-1.13

-7.72

*

** 13.39

C

D

qep

1.43

B

Pressures

Posotion

Walls middle

C

D Pressures

Fixed end mement of the wall due to qep MA

=

MC

W.L

=

W.L

=

2.23 kN.m/m

15 =

10

1.49 kN.m/m

Maximum (-ve) moment

=

(Where x is 0.45L from C)

W.L 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

C E B

Posotion

L.C.02 (Service)

Hydrost. (Service)

Total (Service)

L.C.02 (U.L.S.)

Hydrost. (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 midSpan

9.70

0.99

10.69

13.58

1.38

14.96

Base midSpan

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

Dam Safety Environmental & Civil Structure Maintanance

Doc. No. Designed Checked Job Code

Total

(U.L.S.)

S.M.P

Date 31.05.2010 Date 4 Page

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

Weight of walls

=

10.20

kN/m2

Weight of Roof + Floor

=

9.60

kN/m2

Surcharge on Roof Total Pressure

= =

96.00

kN/m2 115.80 kN/m2 hence ok

Weight of walls

=

10.20

kN/m2

Weight of Roof + Floor

=

9.60

kN/m2

Surcharge on Roof Hydrostatic Pressure

= =

96.00

kN/m2

Total Pressure

=

Total Pressure

<

kN/m2 hence ok

150 kN/m2

5.2 Load Case -02

Total Pressure

<

150 kN/m2

5.3 Load Case -03

Total Pressure

<

150 kN/m2

16.68

kN/m2 122.28 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

C E B

Dam Safety Environmental & Civil Structure Maintanance

=

24.15

kN.m/m

Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date 5 Page

Reference

Calculation 6-

Output

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 =

12

=

12

Section Thickness

mm mm = 200 mm

Maximum Bending Moment

=

Diameter of main reinforcement Diameter of secondary reinforcement

24.15

kN.m/m

Assume severe environment condition, for driving rain = 45 mm Cover =

Effective depth, d

200 -

45 -

6

d

= 149

mm

= 149 k

mm 2 = M / (bd fcu)

2

= (24.15x106 /(1000x1492x25) = 0.044 < 0.156 Hence no compression r/f is required M z

= (0.87fy)Asz = (1 - 1.1fyAs/ fcubd) d z z

equation 1 equation 5

from these two equations

= d (0.5+(0.25-k/0.9)1/2 1/2 = d [0.5+(0.25-0.044/0.9) =

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 As = M / 0.87fyz = 24.15 x106 / 0.87x460x142 = 426 mm2/m Use

T

12

@

250

( As

=

As req

=

426 452

2

mm /m

As pro = 452

Minimum area of main rainforcement for slabs 100As / bad = 100x452/(1000x149)

= 0.30

## 0.13

mm2/m mm2/m

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 Therefore shear in the support = =

C E B

Dam Safety Environmental & Civil Structure Maintanance

109.08 x 1.2 /2 65.45 kN/m Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date 6 Page

Reference

Calculation Design shear force, V design

=

Output

65.45 kN/m

=

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

Effective depth, d

100 As/bd = = BS 8110

Effective depth

vc

Part 01 table 3.1 Design shear stress

v

v

100 x 452 1000x149 0.30

= 149 mm 1/3. 1/4 = 0.79x{(100As/bd) (400/d) /1.25 = 0.54 = V/bd = (65.45x103)/(1000x149) = 0.44 N/mm2

<

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

Check h/hw

3.9.3.6.2 3.4.4.1

= =

1.7 / 0.2 8.5 < 12 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)

Ultimate Load /m/Wall

=

0.1 x

=

600

=

30 x

1/2( 96.0 x +

=

200

kN/m 1.7

0.2 x

120 kN/m <

x 1.4 1.7 x 24x1.4 )

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

so Area Percentage of Concrete area

= =

12

@

1131.0 x 1000 x

= This is

C E B

Dam Safety Environmental & Civil Structure Maintanance

> Minimum of 0.4%

200

2 Layers

1131.0 mm2 100 149

0.76 % >

0.4 %

hence o.k.

Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date 7 Page

Reference

C E B

Dam Safety Environmental & Civil Structure Maintanance

Calculation

Output

Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date 8 Page