box culvert design

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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 Ac Acc As As min av Fc Ft fcu fs fy Hx Hy lx ly lz Mx My Mz D Date β s δ φ σ a γ γ fL γ f3

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Page 1: Box Culvert Design

Reference Calculation Output

Area of concreteArea of concrete in compressionArea of tension reinforcementMinimum area of tension reinforcementLength of that part of member traversed by shear failure plane

b With (breath) or effective width of sectionc Cover to outer diameterd Effective depth of section

Basic force used in defining compressive forcesBasic force used in defining tie forcesCharacteristic strength of concreteEstimated design service stress in the tension reinforcementCharacteristic strength of reinforcement

G Shear modulusH Maximum horizontal force

Horizontal force in x directionHorizontal force in y direction

h Overall depthKEL Knife edge loadL Critical perimeter

Dimension of element on x directionDimension of element on y directionDimension of element on z direction

M Design ultimate resistance momentMoment on x axisMoment on y axisMoment on z axis

q Surcharge loadr Internal radius of bendSLS Serviceability limit stateT Traction forcet Thickness of the elementULS Ultimate limit stateV Shear force due to design ultimate loads or design ultimate value of a

concentrated loadv Design shear stressvc Design shear stress in concretex Neutral axis depthx' Distance from Y axis to the centroid of an elementy' Distance from X axis to the centroid of an elementz Lever armz' Distance from X - Y plane to point where the considered resultant

force acting Coefficient, variously defined, as appropriateStrain in tension reinforcementNominal range of movementSoil friction angle, or diameterActive earth pressureUnit weight of soilPartial load factorPartial load factor

Doc. No. DESIGN UNIT Designed

Ac

Acc

As

As min

av

Fc

Ft

fcu

fs

fy

Hx

Hy

lxlylz

Mx

My

Mz

DEC

Date

β∈sδφσ aγγ fLγ f 3

Page 2: Box Culvert Design

EPC DIVISION Checked Date CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code Page

Reference Calculation Output

DEC

Page 3: Box Culvert Design

Doc. No. DESIGN UNIT Designed EPC DIVISION Checked Date CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code Page

Reference Calculation Output

DEC

Date

Page 4: Box Culvert Design

Doc. No. DESIGN UNIT Designed EPC DIVISION Checked Date CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code Page

Reference Calculation Output

DEC

Date

Page 5: Box Culvert Design

Doc. No. DESIGN UNIT Designed EPC DIVISION Checked Date CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code Page

Reference Calculation Output

DEC

Date

Page 6: Box Culvert Design

Doc. No. DESIGN UNIT Designed EPC DIVISION Checked Date CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB) Job Code Page

DEC

Date

Page 7: Box Culvert Design

Reference Calculation Output

Design of Box Culvert

Figure 01Dimentional Properties

h = 1.2 ml = 1.5 m

Soil Cover , H = 7.2 mSafe Bearing Pressure = 150 kN/m2Section Thickness = 0.2 m ( hw , h = span/(10 ~15))

Main R/F = 12 mmCover to R/F = 45 mmGrade of Concrete = 25 N/mm2Properties of Soil

γc = 24 kN/m3γs = 20 kN/m3γw = 9.81 kN/m3Φ' = 25

1 - Permanent Loads1.1 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/m3Engineering 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 mwestbrook) 3 x width = 3 x 1.6(page-94) = 4.8 m

3 x width < = 7.2 m SoDepth limited to = 4.8 m

Surcharge on RoofSurcharge 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 31.05.2010Environmental & Checked Date

o

C E B

Date

Y

hs

hw

Ground Level

hs

hw

A B

D C

H

l

h

X

Page 8: Box Culvert Design

Civil Structure Maintanance Job Code Page 1Reference Calculation Output

Maximum load on ditch condition

Depth of cover = 7.2 m

Surcharge on RoofSurcharge Presure (qr) ,

(qr) =

Cd =

=

K =

- coedicient of friction between fill materialand side of ditch

K - Active Lateral earth pressure coeficient- Horizontal width of ditch at top of conduit

γ - Unit weight (wet density) of filling materialH - 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) = 0.76Cd = 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

Page 9: Box Culvert Design

Environmental & Checked DateCivil Structure Maintanance Job Code Page 1

Reference Calculation Output

AASHTO 2 - Vertical Live Loads3.7.1

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 - AnalysisReinforced Concrete Constant K = h { hs } 3 = 1.21Designers lManual k1 = K+1 = 2.21(ref-5.1) k3 = K+3 = 4.21

k5 = 2K+3 = 5.43k7 = 2K+7 = 9.43k8 = 3K+8 = 11.64

4.1 Load Case -01 Testing Condition4.1.1 Hydrostatic Pressure-(Internal)

Reinforced = =Concrete 60.k1.k3Designers = 0.99 kN.m/mManual(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.k3Manual = 0.22 kN.m/m(ref-5.1)

= = Ma. K5K

= -0.97 kN.m/m

4.1.3 Flexure due to weight of Roofq = 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

Page 10: Box Culvert Design

Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 2

Reference Calculation Output

= = =

=12.k1

= -0.35 kN.m/mAddition 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

-2.06Table - 01

Fixed end mement of the wall for Hydrostatic load

= W.L = W.L15 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 loadNiutral axis depth from A = 0.26 m

4.2 Load Case -02 Culvert empty and trench filledLateral soil pressurees giving rise to flexture in the structure

4.2.1

Reinforced Concrete = =Designers 60.k1.k3Manual = -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

Page 11: Box Culvert Design

Doc. No.Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 3

Reference Calculation Output

4.2.2 Surcharge on walls,q= = =

Reinforced =Concrete 12.k1Designers = -7.72 kN.m/mManual 4.2.3 Surcharge on Roof ,qr(ref-5.1) = = =

=12.k1

= -7.45 kN.m/mAddition 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.L15 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 -034.2.1 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 CB.M.DPressures

Pressures

A B

D C

B.M.D

Page 12: Box Culvert Design

Doc. No.Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 4

Reference Calculation Output

5 - Check on ground safe bearing pressure5.1 Load Case -01

Hydrostatic Pressure = 16.68 kN/m2Weight of walls = 10.20 kN/m2Weight of Roof + Floor = 9.60 kN/m2Total Pressure = 36.48 kN/m2

Total Pressure < 150 kN/m2 hence ok

5.2 Load Case -02

Weight of walls = 10.20 kN/m2Weight of Roof + Floor = 9.60 kN/m2Surcharge on Roof = 96.00 kN/m2Total Pressure = 115.80 kN/m2

Total Pressure < 150 kN/m2 hence ok

5.3 Load Case -03

Weight of walls = 10.20 kN/m2Weight of Roof + Floor = 9.60 kN/m2Surcharge on Roof = 96.00 kN/m2Hydrostatic Pressure = 16.68 kN/m2Total Pressure = 122.28 kN/m2

Total Pressure < 150 kN/m2 hence ok

6 - U.L.S. of FlextureMaximum Moments kN.m/m

Member Hogging SaggingRoof -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 - SlabsMaximum Moment = 24.15 kN.m/m

C E B

Date

Page 13: Box Culvert Design

Doc. No.Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 5

Reference Calculation Output

6 - Design Calculation for Box Culvert

6.1 U.L.S. of FlextureAnalysis 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 mmDiameter of secondary reinforcement = 12 mmSection Thickness = 200 mm

Maximum Bending Moment = 24.15 kN.m/m

Assume severe environment condition, for driving rainCover = 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 1z = equation 5 from these two equations

z =z =

= 141.41 < 0.950 d

Take Z as 0.95dZ = 0.95 d

= 0.95 x 149 = 142 mm

6.1.1 Design of main reinforcement== == 426 426

Use T 12 @ 250 ( As = 452 =

452Minimum area of main rainforcement for slabs

= 100x452/(1000x149) = 0.30 ### 0.13 Main r/fT 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 02Shear 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 / 0.87fyz24.15 x106 / 0.87x460x142 As req

mm2/m mm2/m

mm2/m As pro

mm2/m

100As / bad

Page 14: Box Culvert Design

Therefore shear in the support = 109.08 x 1.2 /2= 65.45 kN/m

Doc. No.Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 6

Reference Calculation Output

Design shear force, V design = 65.45 kN/mEffective depth, d = 149 mmTension steel across shear plane = Y12 -250 c/c

100 As/bd = 100 x 4521000x149

= 0.30

BS 8110 Effective depth = 149 mmPart 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 wall3.9.3.6.2 Check h/hw = 1.7 / 0.23.4.4.1 = 8.5 < 12

hence column is shortBS 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/mhence 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 1001000 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.)

Page 15: Box Culvert Design

Doc. No.Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 7

Reference Calculation Output

C E B

Date

Page 16: Box Culvert Design

Doc. No.Dam Safety Designed S.M.P 31.05.2010Environmental & Checked DateCivil Structure Maintanance Job Code Page 8

C E B

Date