Box Culvert Design

 

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

W iitth ((b breath) or e efffective w wiidth o off 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

f cu cu

Characteristic strength of concrete

f s

Estimated design service stress in the tension reinforcement

f y

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

l

Dimension of element on y direction

lz

Dimension of element on z direction

M

Design ultimate resistance moment

y

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 lilimit s sttate

T

Traction force

t

Thickness of the element

ULS

Ultimate limit state

V

Shea Shearr ffor orce ce du due e tto o des desig ign n ult ultim imat ate e loa loads ds or de desi sign gn ul ulti tima mate te va valu lue eo off a concentrated load

v vc

Design shear stress Design shear stress in concrete

x

Neutral axis depth

x'

Dist istance ffrrom Y axis to tth he ce centroid of of a an ne ele leme men nt

y' 

Distance from X axis to the centroid of an element

z

Lever arm

z'

Dist Distan ance ce fr from om X - Y plan plane e tto o poi point nt wher where e tthe he co cons nsid ider ered ed re resu sult ltan antt force acting

  

Strain in tension reinforcement

 

Nominal range of movement

 

Soil friction angle, or diameter 

 s

  a

D E C

Coefficient, variously defined, as appropriate



 Active earth pressure

 

Unit weight of soil

    fL     f  3

Partial load factor  Partial load factor 

 DESIGN UNIT  EPC DIVISION  CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

Doc. No. Designed Checked Job Code

Date Date Page

 

Reference

D E C

Calculation

 DESIGN UNIT EPC DIVISION  CENTRAL ENGINEERING ENGIN EERING CONSULTANCY CONSU LTANCY BUREAU (CECB) (CEC B)

Output

Doc. No. Designed Checked Job Code

Date Date Page

 

Reference

D E C

Calculation

DESIGN UNIT  EPC DIVISION CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

Output

Doc. No. Designed Checked Job Code

Date Date Page

 

Reference

D E C

Calculation

DESIGN UNIT  EPC DIVISION  CENTRAL ENGINEERING ENGIN EERING CONSULTANCY CONSU LTANCY BUREAU (CECB) (CEC B)

Output

Doc. No. Designed Checked Job Code

Date Date Page

 

Reference

D E C

Calculation

 DESIGN UNIT EPC DIVISION CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

Output

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

hs

 

C

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

=

mm

=

12 45 25

γs

γc

= =

24 20

kN/m3 kN/m3

γw

=

Φ'

=

Soil Cover ,

=

( hw , h

=

span/(10 ~15))

mm N/mm2

Properties of Soil

9.81 kN/m3 25

o

1 - Perm Permanent anent Loads 1.1

Dead Loads The nominal dead load consist of the weight of the materials and the part of the structure

Structural Engineering Design in

Unit Weight of Concrete shall be taken as 24 kN/m3 Because of the arching of soil, check whether the depth above culvert is > 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

Depth limited to

=

4.8 m

=

4.8

So

Surcharge on Roof  Surcharge Presure ((q qr) qr

Soil Engineering (Spangler & Hand Handy) y)

=

96

x

20 kN/m2

Casses of conduit installation consider as Ditch Conduit Ditch Conduit Ad dit itch ch cond condui uitt iis sd def efin ined ed as on one e whi which ch is in inst stal aled ed in a rrel elat ativ ivel ely y nar narro row w ditch dug in passive or undisturb undisturbed ed soil and which is then covered with ea earth rth 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

=

m

7.2

Surcharge on Roof  Surcha rcharg rge e Presu resure re (qr (qr) (qr)

=

-

Cd

=

µ'

=

K

=

,

2 Cd.γ.Bd

1-e

µ

'

2.K.µ' tan φ'

1-sin φ 1+sin φ

µ'

-

K

coedicient of friction between fill material and side of ditch

-  Active Lateral earth pressure ccoeficient oeficient Horizontal width of ditch at top of conduit

Bd

-

γ

-

Unit weight (wet density) density) of filling material

H

-

Height Height of fill fill abo above ve top top o off condu conduite ite

Cd

-

Load Load co coe efici ficie ent for ditc ditch h cond condit itio ion n

So, K

µ'

=

1-sin φ

=

1+sin φ 0.406

= =

2.K 2.K.µ .µ'.( '.(H/ H/Bd) Bd) = Cd

Structural

1.2

Bd =

Consider 1m length of Roof slab 3.60 m, Co

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'

=

0.58

(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 Vertical Live Live Loa Loads ds

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 Hydrostatic Pressure Pressure (Int (Internal) ernal)

q ip

4-

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

Ana Analy lysis sis

Reinforced Concrete

Constant K

=

h

Designers

l

{ hhs }

3

=

1.21

k1 k3

= =

K+1 K+3

= =

2.21 4.21

k5

=

2K+3

=

5.43

= =

2K+7

=

9.43

3K+8

=

11.64

w

Manual (ref-5.1)

k7 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 = 1.22 kN.m/m

Concrete qip

Designers

2

M A =

Manual D

(ref-5.1)

q = qip Pressures

C B.M.D

4.1.2 Flexure due to weight of wall W all weight ( G )

= =

hw.γ.h

q1 = 2.G l.hw

8.2 kN/m

=

10.20 kN/m2

Reinforced A

Concrete

B

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)

D q1 Pressures

2

M A =

C B.M.D

kN.m/m

4.1.3 Flexure due to weight of Roof  q

C E B

Dam Safety Environmental & Civil Structure Maintananc Maintanance e

=

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

M A = D

MC =

MD

2

= q.l 12.k1 = -0.35

C

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 M A

=

MC

W.L

=

W.L 10

15 =

1.61 kN.m/m

Maximum (-ve) moment

=

2.41 kN.m/m

=

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 ** Momen Momentt at mid span of the wall is cal calculate culated d by considering considering ful fulll 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 "q ep" is the triangular pressure 4.2.1 Trianguler Pressure,qep Reinforced Concrete

A

B

2

M A =

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

MC =

MD = M A. K8 k7

Designers Manual (ref-5.1) qep

qep Pressures

D

  B.M.D

C

=

C E B

Dam Safety Environmental & Civil Structure M aintanance aintanance

Doc. No. Designed Checked Job Code

-1.13 kN.m/m

S.M.P 

Date 31.05.2010 Date 3 Page

 

Reference

Output

Calculation 4.2.2 Surcharge on walls,q

A

M A =

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  M A = MB = MC = MD 2 = q.l

B

D

C B.M.D

Pressures A

B

12.k1 D

= -7.45 kN.m/m  Addition of moment for Load Load Case 2

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

Posotion

qep

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

Walls middle

*

**

1.43

13.39

C

Pressures

Fixed end mement of the wall due to q ep M A

MC

=

W .L

=

1.49 kN.m/m

=

W .L

=

2.23 kN.m/m

15

10

Maximum (-ve) moment

= =

4.2

W.L 23.3

(Where x is 0.45L from C)

-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 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

 

Calculation

Reference

Output

5 - Check on gr ground ound safe bea bearing ring pressure pressure 5.1

Load Case -01 =

16.68

kN/m2

W eight of walls

=

10.20

kN/m2

W eight of Roof + Floor

=

9.60

kN/m2

=

36.48

W eight of walls

=

10.20

kN/m2

W eight of Roof + Floor

=

9.60

kN/m2

Surcharge on Roof

=

96.00

Total Pressure

=

Hydrostatic Pressure

Total Pressure Total Pressure 5.2

Load Case -02

Total Pressure 5.3

<

kN/m2 hence ok

150 kN/m2

<

150 kN/m2

kN/m2 115.80 kN/m2 hence ok

Load Case -03

W eight of walls

=

10.20

kN/m2

W eight of Roof + Floor

=

9.60

kN/m2

Surcharge on Roof

=

96.00

kN/m2

Hydrostatic Pressure

=

Total Pressure

=

Total Pressure

<

16.68 kN/m2 122.28 kN/m2

150 kN/m2

hence ok

6 - U.L.S U.L.S.. of Flextur Flexture e 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 Maintananc Maintanance e

=

24.15

kN.m/m

Doc. No. Designed Checked Job Code

S.M.P 

Date 31.05.2010 Date Page 5

 

Reference

Calculation 6-

Output

Design Calculation for Box Culvert

6.1

U.L.S. of Flexture

 Analysis was was carried out ffor or several load cases of various loading 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 12 mm 200 mm 12

24.15

kN.m/m

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

Effective depth, d

200 -

45 -

6

d

= 149

mm

= 149 k

mm (bd d f cu) = M / (b

2

6

2

= (24.15x10  /(1000x149 x25) =

0.044

< 0.156

Hence no compression r/f is required M z

= (0.87f y)Asz = (1 - 1.1f y As/ f cubd) d z z

equation 1 equation 5

from tth hese ttw wo eq equations

1/2 = d (0.5+(0.25-k/0 (0.5+(0.25-k/0.9) .9) 1/2 [0.5+(0.25-0.044/0.9) 044/0.9) = d [0.5+(0.25-0.

=

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 / 0.87f yz = 24.15 x106 / 0.87x460x142 = Use

T

426

 As req

2

mm /m ( As 12 @ 250

=

426 =

452

2

mm /m

2

mm /m

 As pro = 2

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

452 = 0.30

## 0.13

mm /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

Output

Calculation Design shear force, V design

=

65.45 kN/m

Effective depth, d

=

149 mm

Tensio Ten sion n steel steel acro across ss shea shearr plane plane = Y1 Y12 2 -250 -250 c/c c/c 100 As/bd

=

100 x 452 1000x149 0.30

= BS 8110

Effective depth

vc

Part 01 table 3.1

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

= Design shear stress

v

= V/bd = (65.45x10 3)/(1000x149) =

v

6.3 Bs 81 8110

0.44 N/mm

<

2

vc

Hence o.k

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

Tre Treat as a c col olu umn with ith ben bend din ing g at at rig right ht an angl gle e tto o wal walll

Check h/hw

3.9.3.6.2 3.4.4.1

0.2

=

1.7 /

=

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.f ccu.( u.(c.s.a.)

hence

0.1.fcu.(C.S.A)

Ultimate Load /m/Wall

=

0.1 x

30

=

600

kN/m

x

=

1/2( 96.0 x

=

120 kN/m <

+

200 x 1.4

1.7 x

0.2

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

 

Dam Safety Environmental & Civil Structure Maintanance

>

200

Min inim imum um of 0. 0.4% 4%

2 Layers

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