Box Culvert Design.xls

Reference Calculation Output

Area of concrete

Area of concrete in compression

Area of tension reinforcementMinimum 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

Ac

Acc

As

As min

av

Fc

Ft

fcu

fs

fy

Hx

Hy

lx

ly

lz

Mx

My

Mz

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β∈sδφσ aγγ fLγ f 3

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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 Designed S.M.P 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

Civil Structure Maintanance Job Code Page 1


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' = 0.577

(page-94) = ( 1-sin Φ' ) / ( 1+sin Φ' ) = 0.406

q max = γ.Ka.h

= 20 x 0.41 x 9.1

= 73.9 kN/m2

= 20 x 0.41 x 1.9

= 15.42 kN/m2

q =

q = 58.44 kN/m2

Ceylon Electricity Board Doc. No.Dam Safety Designed S.M.P 31.05.2010

C E B

Cd.γ.Bd2

1-e-2Kµ'(H/Bd)

2.K.µ'

µ' tan φ'

1-sin φ1+sin φ

µ'

Bd

1-sin φ1+sin φ

µ' tan φ'

Cd.γ.Bd2

K0

Ka

qep

qmax - qep

C E B

Date

Environmental & Checked DateCivil Structure Maintanance Job Code Page 1


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

= 1.217 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

MA MB qip.h2.K.k7

MC MD

MA MB q1.l2.K

MC MD

A B

D C

qip

q = qipB.M.DPressures

A B

D Cq1

G G

B.M.DPressures

Dam Safety Designed S.M.P 31.05.2010



= = =

=

12.k1

= -0.35 kN.m/m

Addition of moment for Load case 01

Position γf Walls Roof γf

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 2.830.82

1.22 1.4 1.70** **

2.35 1.4 3.29 5.001.53 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

= 1.607 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

MA MB MC MD

q.l2

Hydrost-atic

uls- Mb

Walls + Roof

uls-Mb

Total uls

Roof mid-Span

Base mid-Span

Walls middle

MA MC

"q"is the rectanguler pressure and "qep" is the triangular pressure

Trianguler Pressure,qep

MA MB qep.h2.K.k7

MC MD MA. K8

A B

D Cqepqep

B.M.DPressures

A B

D Cq = q1

B.M.DPressures

Doc. No.Dam Safety Designed S.M.P 31.05.2010



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

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

-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 9.311.43 13.39

= W.L = W.L

15 10

= 1.486 kN.m/m = 2.229 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

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

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

MA MB MC MD

q.h2.K

MA MB MC MD

q.l2

qepWalls &

Roof(LC-1)Surcharg -e (Roof)

Total (Survice)

Total U.L.S.

Roof mid-Span

Base mid-Span

Fixed end mement of the wall due to qep

MA MC

L.C.02 (Service)

Hydrost. (Service)

Total (Service)

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

Hydrost. (U.L.S.)

Total (U.L.S.)

Roof mid-Span

Base mid-Span

A B

D C

B.M.DPressures

Pressures

A B

D C

B.M.D




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



5.3 Load Case -03



Surcharge on Roof = 96.00 kN/m2

Hydrostatic Pressure = 16.68 kN/m2



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

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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 < 0.156

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 / (bd2fcu)

(24.15x106 /(1000x1492x25)

(0.87fy)Asz

(1 - 1.1fyAs/ fcubd) d

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

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

As M / 0.87fyz

24.15 x106 / 0.87x460x142 As req

mm2/m mm2/m

mm2/m As pro

mm2/m

100As / bad

Therefore shear in the support = 109.08 x 1.2 /2

= 65.45 kN/m




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

= 0.759 % > 0.4 %

This is > Minimum of 0.4% hence o.k.

C E B

Date

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

(65.45x103)/(1000x149)

N/mm2

not exceed 0.1.fcu.(c.s.a.)




C E B

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Box Culvert Design.xls

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