Box Culvert Design 2

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

= =

12 mm 45 mm 25 N/mm2

γc

=

24 kN/m3

γs

=

20

γw

=

Φ'

=

Soil Cover ,

=

m

( hw , h

=

span/(10 ~15))

Properties of Soil 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)

= =

3 x width < =

Depth limited to

7.2 3

x

m 1.6

4.8

m

7.2

m

=

4.8 m

=

4.8

So

Surcharge on Roof Surcharge Presure (qr) qr

Soil Engineering (Spangler & Handy)

=

96

x

20 kN/m2

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.

Doc. No. Designed Checked Job Code

Ceylon Electricity Board

C E B

Dam Safety Environmental & Civil Structure Maintanance

Reference

Calculation

S.M.P

Date 31.05.2010 Date Page 1 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'

=

K

=

tan φ'

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

1.2

0.406 tan φ' 0.466 0.76

=

1.403

(qr)

=

Cd.γ.Bd2

(qr)

=

101.0

kN/m2

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'

=

0.577

(page-94)

Ka

=

( 1-sin Φ' ) / ( 1+sin Φ' )

=

0.406

(δ = 0 )

q max

= 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

Ceylon Electricity Board

C E B

Dam Safety Environmental & Civil Structure Maintanance

Reference

Calculation

9.1

1.9

S.M.P

Date 31.05.2010 Date Page 1 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)

q ip

= C.h = 9.81 x 1.7 = 16.68 kN/m2

4 - Analysis Reinforced Concrete

Constant K

=

h

Designers

l

{

hs hw

}

Manual (ref-5.1)

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

k8

4.1

Load Case -01 Testing Condition

4.1.1 Hydrostatic Pressure-(Internal) Reinforced

A

B

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

MC =

MD = Ma. K8 k7 = 1.217 kN.m/m

Concrete qip

Designers

2

MA =

Manual C

D

(ref-5.1)

q = qip Pressures

B.M.D

4.1.2 Flexure due to weight of wall Wall weight ( G )

= =

hw.γ.h

q1 = 2.G l.hw

8.2 kN/m

=

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

=

hs.γc

=

4.8

Doc. No. Designed Checked Job Code

Dam Safety Environmental & Civil Structure Maintanance

Reference

Calculation A

B

kN/m2

S.M.P

Date 31.05.2010 Date Page 2 Output

A

B

MA =

MC =

MD

2

= q.l 12.k1 = -0.35

C

D q = q1 Pressures

MB =

B.M.D

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

=

W.L

15 =

10

1.607 kN.m/m

Maximum (-ve) moment (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 4.2

=

0.26 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

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

C E B

C

D

Pressures

B.M.D

Doc. No. Designed Checked Job Code

Dam Safety Environmental & Civil Structure Maintanance

Reference

S.M.P

Calculation 4.2.2 Surcharge on walls,q

MA =

MB =

MC =

A

MD

B

Date 31.05.2010 Date Page 3 Output

A

Reinforced Concrete Designers Manual (ref-5.1)

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

C

D B.M.D

Pressures A

B

C

D B.M.D

Pressures

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

γf

Posotion

qep

q

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

Base midSpan

-1.13

-7.72

2.35

17.29

10.80

1.4

15.12

-0.73

-7.45

6.65

1.4

9.31

Walls middle

*

**

1.43

13.39

Total

U.L.S.

Fixed end mement of the wall due to qep MA

=

MC

W.L

=

15 =

10

1.486 kN.m/m

=

Maximum (-ve) moment

=

(Where x is 0.45L from C)

2.229 kN.m/m W.L 23.3

= 4.2

W.L

-1.0 kN.m/m

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 mid-Span

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

Doc. No. Designed Checked Job Code

Dam Safety Environmental & Civil Structure Maintanance

Reference

Calculation 5 - Check on ground safe bearing pressure 5.1

Load Case -01

Total

(U.L.S.)

S.M.P

Date 31.05.2010 Date Page 4 Output

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

Weight of walls

=

10.20

kN/m2

Weight of Roof + Floor

=

9.60

kN/m2

Surcharge on Roof Hydrostatic Pressure

= =

96.00

kN/m2

16.68

kN/m2

Total Pressure

=

122.28

Total Pressure 5.2

kN/m2 hence ok

150 kN/m2

Load Case -02

Total Pressure 5.3

<

<

kN/m2 hence ok

150 kN/m2

Load Case -03

Total Pressure

<

150 kN/m2

kN/m2 hence ok

6 - U.L.S. of Flexture Maximum Moments kN.m/m Member

Hogging

Roof

-22.70

(L.C-01)

Walls

-24.66

Base

-24.66

Sagging 14.96

(L.C-03)

(L.C-02)

9.31

(L.C-02)

(L.C-02)

16.83

(L.C-03)

i - Slabs Maximum Moment

C E B

=

kN.m/m

Doc. No. Designed Checked Job Code

Dam Safety Environmental & Civil Structure Maintanance

Reference

24.15

Calculation 66.1

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

Analysis was carried out for several load cases of various loading

S.M.P

Date 31.05.2010 Date Page 5 Output

arrangements to find out the maximum effect on the Box culvert Diameter of main reinforcement

=

Diameter of secondary reinforcement

=

Section Thickness

=

Maximum Bending Moment

=

mm mm 200 mm 12 12

24.15

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

Effective depth, d

200

-

45 -

kN.m/m

mm

6

d

= 149

mm

= 149 k

mm 2 M / (bd fcu) =

2

6

2

= (24.15x10 /(1000x149 x25) =

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

Take Z as 0.95d Z = 0.95

d

= 0.95

x

< 0.950 d

149

= 142

mm

6.1.1 Design of main reinforcement As = M / 0.87fyz = 24.15 x106 / 0.87x460x142 = Use

T

As req

2

mm /m 12 @ 250 ( As 426

= mm2/m

426 =

452

mm2/m

As pro

=

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

= 0.30

## 0.13

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

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

Dam Safety Environmental & Civil Structure Maintanance

Reference

Calculation Design shear force, V design

=

65.45 kN/m

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

Effective depth, d

100 As/bd

=

100 x 452

S.M.P

Date 31.05.2010 Date Page 6 Output

= BS 8110

Effective depth

vc

Part 01 table 3.1 Design shear stress

v

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

v

6.3 Bs 8110

1000x149 0.30

0.44 N/mm2

<

vc

Hence o.k

Check in U.L.S. on the ability of the wall to trasmit the axial loads

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

30

600

kN/m

200

1/2( 96.0 x +

=

x

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

=

so Area Percentage of Concrete area

Y

12

@

1131.0 mm2

=

1131.0 x 1000 x

= This is

C E B

>

100 0.4 %

hence o.k.

Doc. No. Designed Checked Job Code

Environmental & Civil Structure Maintanance

Calculation

2 Layers

149

0.759 % >

Minimum of 0.4%

Dam Safety

Reference

200

=

S.M.P

Date 31.05.2010 Date Page 7 Output

C E B

Dam Safety Environmental & Civil Structure Maintanance

Doc. No. Designed Checked Job Code

S.M.P

Date 31.05.2010 Date Page 8